Applied Science, Faculty of
Biomedical Engineering, School of
DSpace
UBCV
Maclean, Luke Jeffrey
Doctor of Philosophy - PhD
University of British Columbia
Spinal surgery, particularly pedicle screw placement, demands exceptional precision to avoid severe complications such as neurological injury, vascular damage, and mechanical instability. Current navigation techniquesâincluding freehand methods, fluoroscopy, computed tomography (CT)-based navigation, and robotic systemsâoffer varying degrees of accuracy but are constrained by challenges such as high costs, radiation exposure, and workflow disruptions. To address these limitations, this thesis proposes and evaluates an innovative, ultrasound-augmented, self-localizing drill guide that integrates polymer-based capacitive micromachined ultrasonic transducers (poly-CMUTs) for real-time surgical navigation. The research methodology comprised computational simulations, experimental evaluations, and machine learning-based optimizations. Initial benchmarking of existing technologies (Chapter 2) highlighted persistent challenges in achieving a balance between accuracy, cost, and safety in pedicle screw navigation. Computational modeling (Chapter 3) then demonstrated that strategically placed ultrasound transducers could achieve sub-millimetric localization accuracy, providing a foundation for the tool's design. Experimental studies (Chapter 4) validated the accuracy of poly-CMUT transducers in measuring bone surfaces, while machine learning techniques (Chapter 5) significantly improved bone segmentation and registration accuracy. Finally, prototype emulation studies (Chapter 6) confirmed the clinical feasibility of the ultrasound-augmented drill guide, demonstrating its potential to match or exceed the performance of existing systems without the need for ionizing radiation. The findings underscore the clinical and practical implications of integrating ultrasound into surgical tools. The proposed approach offers a radiation-free, cost-effective, and highly accurate alternative to CT-based navigation systems, with broad applicability in spinal surgery and potential extensions to other surgical domains. Future work will focus on translating these promising experimental results into clinical practice, exploring regulatory pathways, and refining the system for real-world applications. The thesis advances the field of spinal navigation by presenting a novel approach that prioritizes patient safety, surgeon convenience, and healthcare accessibility.
The Design and Validation of Ultrasound-Augmented Self-Localizing Tools for Dynamic and Adjustable Registration and Navigation in Spinal Surgery by Luke Jeffrey MacLean B.Eng., McGill University, 2016 M.H.Sc., University of Toronto, 2018 M.D., University of British Columbia, 2025 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate and Postdoctoral Studies (Biomedical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2025 © Luke Jeffrey MacLean, 2025ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: The Design and Validation of Ultrasound-Augmented Self-Localizing Tools for Dynamic and Adjustable Registration and Navigation in Spinal Surgery submitted by Luke Jeffrey MacLean in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biomedical Engineering Examining Committee: Antony Hodgson, Professor, Biomedical Engineering and Mechanical Engineering, UBC Supervisor John Street, Assistant Professor, Orthopaedics, UBC Co-supervisor Christopher R. Honey, Professor and Division Head, Neurosurgery, UBC University Examiner Roger C. Tam, Associate Professor, Biomedical Engineering and Radiology, UBC University Examiner Edmond H. M. Lou, Professor, Electrical & Computer Engineering; Adjunct Professor, Biomedical Engineering, Surgery and Radiology, University of Alberta External Examiner Additional Supervisory Committee Members: Robert Rohling, Professor, Biomedical Engineering and Electrical & Computer Engineering, UBC Supervisory Committee Member Edmond Cretu, Associate Professor, Electrical & Computer Engineering, UBC Supervisory Committee Member Andrei Krassioukov, Professor, Physical Medicine & Rehabilitation, UBC Supervisory Committee Member iii Abstract Spinal surgery, particularly pedicle screw placement, demands exceptional precision to avoid severe complications such as neurological injury, vascular damage, and mechanical instability. Current navigation techniquesâincluding freehand methods, fluoroscopy, computed tomography (CT)-based navigation, and robotic systemsâoffer varying degrees of accuracy but are constrained by challenges such as high costs, radiation exposure, and workflow disruptions. To address these limitations, this thesis proposes and evaluates an innovative, ultrasound-augmented, self-localizing drill guide that integrates polymer-based capacitive micromachined ultrasonic transducers (poly-CMUTs) for real-time surgical navigation. The research methodology comprised computational simulations, experimental evaluations, and machine learning-based optimizations. Initial benchmarking of existing technologies (Chapter 2) highlighted persistent challenges in achieving a balance between accuracy, cost, and safety in pedicle screw navigation. Computational modeling (Chapter 3) then demonstrated that strategically placed ultrasound transducers could achieve sub-millimetric localization accuracy, providing a foundation for the tool's design. Experimental studies (Chapter 4) validated the accuracy of poly-CMUT transducers in measuring bone surfaces, while machine learning techniques (Chapter 5) significantly improved bone segmentation and registration accuracy. Finally, prototype emulation studies (Chapter 6) confirmed the clinical feasibility of the ultrasound-augmented drill guide, demonstrating its potential to match or exceed the performance of existing systems without the need for ionizing radiation. The findings underscore the clinical and practical implications of integrating ultrasound into surgical tools. The proposed approach offers a radiation-free, cost-effective, and highly accurate alternative to CT-based navigation systems, with broad applicability in spinal surgery and potential extensions to other surgical domains. Future work will focus on translating these promising experimental results into clinical practice, exploring regulatory pathways, and refining the system for real-world applications. The thesis advances the field of spinal navigation by presenting a novel approach that prioritizes patient safety, surgeon convenience, and healthcare accessibility. iv Lay Summary Spinal surgery is a complex and delicate process that involves placing screws into the spine to stabilize it during procedures like spinal fusions. While current technologies like X-rays and robotic systems help improve accuracy, they often expose patients to radiation and require expensive equipment, making them less accessible. My research focuses on creating a safer and more affordable alternative using ultrasound technology integrated directly into a surgical tool. This new approach aims to guide surgeons more accurately without the need for radiation or complex imaging equipment, potentially improving patient safety and reducing costs in healthcare settings. v Preface In this thesis, all chapters were written by me. The work presented in this thesis has resulted in conference [C]. journal [J] publications and associated intellectual property [IP], which are described in following. Chapter 2 The work presented in chapter 2 was published as a peer reviewed journal article in the Journal of Neurosurgery: Spine along with my colleagues from the Johns Hopkins Neurosurgery program as: [J1] MacLean L, Hersh AM, Bhimreddy M, Jiang K, Davidar AD, Weber-Levine C, Alomari S, Judy BF, Lubelski D, Theodore N. Comparison of accuracy, revision, and perioperative outcomes in robot-assisted spine surgeries: systematic review and meta-analysis. J Neurosurg Spine. 2024 Jul 5;41(4):519â531. doi: 10.3171/2024.4.SPINE23917. PMID: 38968628. I was responsible for developing the research question, designing the evaluation framework, conducting the statistical and technical analyses, and writing the manuscript. The other listed authors contributed to data collection, clinical interpretation, and revision of the manuscript. This work systematically evaluated clinical outcomes across multiple robotic spine platforms, identifying key trade-offs in operative duration, radiation exposure, and blood loss. These findings helped define the performance limitations of existing navigation approaches and motivated the subsequent exploration of an ultrasound-based alternative presented in later chapters. vi Chapter 3 The work presented in chapter 3 was presented at two conferences, published in a peer reviewed journal article in IJMCAS, and resulted in a preliminary patent approval and ongoing patent application. The summary of this material is presented in following: [J2] MacLean LJ, Street J and Hodgson AJ. Design of an ultrasound emitting drill guide for freehand pedicle screw navigation. Intl J Med Robot & Comp Asst Surg. Aug 2023. [C1] MacLean LJ, Hodgson AJ. Design of an Ultrasound-Augmented Drill Guide for Freehand Pedicle Screw Navigation. CITAC 2022. [C2] MacLean LJ, Hodgson AJ. Design of an Ultrasound-Augmented Drill Guide for Pedicle Screw Navigation. CAOS 2022. [IP1] MacLean LJ, Hodson AJ. Self-Localizing Ultrasound Augmented Surgical Drill. Methods and Apparatus for Localization and Navigation of Surgical Tools. US Patent No. 63/349,635. June 2023. I was primarily responsible for formulating the research question, programming the simulation and registration, designing and optimizing the device and algorithmic parameters, analyzing the data, and writing the manuscript. Co-authors contributed through critical feedback, clinical insight, and review of the manuscript. This computational study established the technical feasibility and optimal design of an ultrasound-augmented drill guide for pedicle screw localization, laying the foundation for experimental validation in subsequent chapters. Chapter 4 Preliminary aspects of the work presented in Chapter 4 were presented at the IEEE International Ultrasonics Symposium (IUS) in September 2021. Subsequently, these results were published in the peer reviewed proceedings of the same meeting. These are summarized in following: [J3] MacLean LJ, Hodgson AJ. Accuracy of Position and Pose Estimates of Ultrasound Probe Relative to Bony Anatomy. IEEE IUS Proc. Sept 2021. [C3] MacLean LJ and Hodgson AJ. Accuracy of Position and Pose Estimates of Ultrasound Probe Relative to Bony Anatomy. IEEE IUS 2021. I was responsible for the research design, development and execution of simulation and experimental protocols, data analysis, and manuscript preparation. Co-authors contributed to transducer fabrication, system integration support, and manuscript review. This chapter synthesized k-Wave-based simulations, phantom testing, and poly-CMUT transducer experiments to validate the key technical components needed for ultrasound-based spinal navigation, directly informing the prototype system evaluated in later chapters. vii Chapter 5 The work presented in Chapter 5 has been accepted for publication in Medical Imaging Analysis (2025). Preliminary components were presented at AAPM 2022 and CAOS 2022. Related methods and supporting techniques were publishes as two chapters in The Abundant Promise of Ultrasound in Neurosurgery (2022) and then presented at the Hamlyn Surgical Robotics Symposium (2022) with a supporting conference article. Supporting details are featured in the appendices. This work is summarized in following: [J4] China D, MacLean LJ, Wei J, Theodore N, Johnson N, Crawford N, Ding K, Uneri A. Automated Ultrasound Image Labeling and Vertebra Segmentation for Intraoperative Guidance of Spine Surgery. Medical Physics. 2025. [C4] MacLean LJ, China D, Siewerdsen J, Uneri A. Ultrasound Image Quality for Segmentation of Spinal Bone Surfaces. American Assoc of Physicists in Med. 2022. [C5/J5] LJ MacLean and N Theodore. Design and Characterization of Robotically-Guided Ultrasonic Bone Cutting for Laminectomies and Facetectomies. The Hamlyn Symposium on Medical Robotics: "MedTech Reimagined". June 2022. [C6] China D, MacLean LJ, Uneri A. Intraoperative Ultrasound Imaging for Vertebral Tracking in Spine Surgery. CAOS 2022. [IP2] MacLean LJ. BoneâUltrasound Interactions in Neurosurgery. The Abundant Promise of Ultrasound in Neurosurgery. Ch. 8. Dec 2022. [IP3] MacLean LJ. Other Emerging Novel Applications of Ultrasound in Neurosurgery. The Abundant Promise of Ultrasound in Neurosurgery. Ch. 9. Dec 2022. I was responsible for developing the image quality optimization for training the machine-learning segmentation model, setting up the automated data collection pipeline for automated labelling of the training set and preliminary evaluation of the segmentation network. Network design and training lead by my colleague Dr. China. This work contributed a validated segmentation approach, image quality analysis and dataset curation pipeline that improved the viability of ultrasound-based spinal localization. viii Chapter 6 This chapter has been accepted for a podium presentation at CAOS 2025 and has been drafted as a pending journal submission. These are summarized in following: [C7] MacLean LJ, Cretu E, Street J & Hodgson AJ. Evaluating Ultrasound-Integrated Tools through Self-Localization of Tracked Ultrasound Probes. Computer Assisted Orthopaedic Surgery. Davos, Switzerland. June 2025. [J6] MacLean LJ, Cretu E, Street J & Hodgson AJ. Evaluating Ultrasound-Integrated Tools through Self-Localization of Tracked Ultrasound Probes. 2025. (Pending) I was responsible for designing and executing the experimental protocols, developing the data analysis and localization algorithms, conducting all technical evaluations, and preparing the manuscript. Co-authors contributed technical insights into the experimental design, clinical application considerations and preparing the manuscript. This chapter provides the first 3D validation of the proposes methodology for registering multi-planar ultrasound to a priori 3D scans of spinal anatomy. Therefore, this work demonstrates how appropriate ultrasound configuration enables the feasibility of the proposed radiation-free, self-localizing navigation tool. Declaration on Generative AI Generative AI (ChatGPT-4) was used to review grammar and writing clarity. It further improved programming efficiency for custom MATLAB functions used in the analysis. All research design, data interpretation, and writing decisions were independently developed and authored by me. ix Table of Contents Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface ............................................................................................................................................ v Table of Contents ........................................................................................................................ ix List of Tables .............................................................................................................................. xv List of Figures ............................................................................................................................ xvi List of Abbreviations ............................................................................................................ xxviii Acknowledgements ................................................................................................................. xxxi Dedication ................................................................................................................................ xxxii Chapter 1 Background to the Problem and the Proposed Solution ......................................... 1 1 Concerns Related to Pedicle Screw Placement ........................................................................ 1 2 Existing Surgical Methods: Progress and Persistent Gaps ...................................................... 4 2.1 Freehand Placement ........................................................................................................... 5 2.2 Fluoroscopic Guidance ...................................................................................................... 6 2.3 CT-Based Surgical Navigation .......................................................................................... 7 2.4 Robotic Systems ................................................................................................................ 8 2.5 Balancing Cost and Accuracy ............................................................................................ 8 3 Concept of Ultrasound-Augmented Self-Localizing Drill Guides .......................................... 9 4 Research Objective ................................................................................................................ 12 5 Related Literature ................................................................................................................... 12 5.1 US Transducer Technologies ........................................................................................... 12 5.2 Use of US in Spine Surgery ............................................................................................. 14 5.3 US-Only Sensing and Navigation .................................................................................... 15 5.4 State Estimation Techniques ........................................................................................... 15 5.5 Accuracy Requirements for Screw Placement ................................................................ 16 5.6 Summary .......................................................................................................................... 16 6 Knowledge Gaps and Research Questions ............................................................................ 17 6.1 Establishing Accuracy Objectives and Related Performance Metrics ............................ 18 6.2 Determining Most Promising Design Configurations for Ultrasound-Augmented Drill Guides .................................................................................................................................... 19 x 6.3 Validating performance of key components in the proposed design under more realistic use (application) conditions ................................................................................................... 20 6.4 Validating that bone surfaces visible in US images produced by poly-CMUT arrays can be identified with sufficient accuracy for the intended application ....................................... 21 6.5 Demonstrating that an integrated emulation of the proposed ultrasound-augmented, self-localizing drill guide concept can produce sufficiently accurate localization estimates in anatomically realistic, simplified surgical scenarios ............................................................. 22 7 Specific Research Questions and Thesis Organization .......................................................... 23 Chapter 2 Benchmarking Navigation in Spine Surgery: A Systematic Evaluation of Emerging Clinical Technologies ................................................................................................ 25 1 Introduction1 .......................................................................................................................... 25 2 Methods.................................................................................................................................. 26 2.1 Literature Search .............................................................................................................. 26 2.2 Data Collection ................................................................................................................ 27 2.3 Statistical Analysis .......................................................................................................... 28 3 Results .................................................................................................................................... 30 3.1 Study Characteristics ....................................................................................................... 32 3.2 Accuracy .......................................................................................................................... 33 3.3 Intraoperative Revision and Reoperation Rate ................................................................ 34 3.4 Operative Time ................................................................................................................ 35 3.5 Blood Loss and Radiation Dose ...................................................................................... 36 3.6 Publication Bias ............................................................................................................... 37 4 Discussion .............................................................................................................................. 38 4.1 Comparing Performance Metrics ..................................................................................... 38 4.2 Publication Bias ............................................................................................................... 39 4.3 Implications for Navigation Technologies ...................................................................... 39 4.4 Limitations ....................................................................................................................... 40 5 Conclusion ............................................................................................................................. 40 Chapter 3 Tool Design through High-Powered Computing ....................................................42 1 Introduction and Motivation1 ................................................................................................. 42 2 System Requirements ............................................................................................................. 43 2.1 Position Estimation Accuracy ......................................................................................... 44 2.2 Localization and Capture Ranges .................................................................................... 45 2.3 Cannula Radius ................................................................................................................ 45 xi 3 Design Space .......................................................................................................................... 45 3.1 Design Parameters ........................................................................................................... 46 3.2 Objective Function for Optimization Localization .......................................................... 47 4 Methodology and Design Process .......................................................................................... 49 4.1 Phase 1: Establish General Feasibility ............................................................................. 51 4.2 Phase 2: Determine the Initial Design Parameters .......................................................... 52 4.3 Phase 3: Assess the Sensitivity to Measurement Uncertainty ......................................... 52 4.4 Phase 4: Investigate Failed Localizations ........................................................................ 53 4.5 Phase 5: Compare Different Optimization Techniques ................................................... 53 4.6 Phase 6: Select the Array Configuration ......................................................................... 54 4.7 Phase 7: Validate Final Design ........................................................................................ 55 5 Simulation Results ................................................................................................................. 56 5.1 Establish General Feasibility ........................................................................................... 56 5.2 Determine Initial Design Parameters ............................................................................... 57 5.3 Assess Sensitivity to Measurement Uncertainty ............................................................. 58 5.4 Investigate Failed Localizations ...................................................................................... 59 5.5 Compare Optimization Techniques ................................................................................. 61 5.6 Select the Array Configuration ........................................................................................ 63 5.7 Validation of the Final Design ......................................................................................... 64 6 Discussion .............................................................................................................................. 66 6.1 Key Results ...................................................................................................................... 66 6.2 Strengths and Limitations of the Computer Simulation .................................................. 69 6.3 Relationship to Prior Literature ....................................................................................... 70 6.4 Overview and Prototyping Recommendations ................................................................ 70 7 Concluding Remarks .............................................................................................................. 71 Chapter 4 Experimental Evaluation of Key System Elements ............................................... 72 1 Introduction and Rationale for Key System Elements ........................................................... 72 1.1 Overview of Studies ........................................................................................................ 72 2 Study 1 - Simulation of Ultrasound-Bone Interaction and Signal Processing ...................... 73 2.1 Methods: Modeling Ultrasound-Bone Interactions ........................................................ 74 2.2 Results: Accuracy of Bone Surface Detection ................................................................ 82 2.3 Discussion: Implications and Limitations ....................................................................... 90 xii 2.4 Conclusion: Measurement Feasibility and Method Selection ........................................ 93 3 Study 2 - 2D Localization of 3D Printed Phantoms with a Linear Probe ............................. 93 3.1 Research Aims of 2D Localization .................................................................................. 94 3.2 Experimental Setup and Methods .................................................................................... 94 3.3 Results ............................................................................................................................. 97 3.4 Discussion ........................................................................................................................ 98 3.5 Summary ........................................................................................................................ 100 4 Study 3 - Rangefinding using a Linear Poly-CMUT Array ................................................ 101 4.1 Methods and Experimental Design ................................................................................ 101 4.2 Experimental Rangefinding Results .............................................................................. 107 4.3 Discussion of poly-CMUT Rangefinding Experiments ................................................ 112 5 Summary of Basic Component Testing ............................................................................... 114 Chapter 5 Image Quality Optimization and Automated Labelling for Machine Learning Vertebral Segmentation ............................................................................................................ 115 1 Research Objectives ............................................................................................................. 116 2 Methods................................................................................................................................ 117 2.1 Optimizing Image Quality ............................................................................................. 117 2.2 Dataset Creation for ML Training ................................................................................. 123 2.3 Convolutional Neural Network for Segmentation ......................................................... 126 3 Results .................................................................................................................................. 130 3.1 Image Quality Optimization .......................................................................................... 130 3.2 CNN Segmentation Performance .................................................................................. 137 4 Discussion ............................................................................................................................ 143 4.1 Key Findings ................................................................................................................. 144 4.2 Relevance to Pre-existing Literature ............................................................................. 145 4.3 Limitations ..................................................................................................................... 146 4.4 Future Work ................................................................................................................... 146 5 Experimental Conclusions ................................................................................................... 147 6 Summary .............................................................................................................................. 148 Chapter 6 Evaluating Anticipated Performance of Self-Localized Drill Guides by Emulating Proposed Designs ................................................................................................... 150 1 Research Questions .............................................................................................................. 150 2 Methods................................................................................................................................ 151 xiii 2.1 Experimental Setup ........................................................................................................ 152 2.2 Experimental Procedures ............................................................................................... 155 2.3 Tool Localization ........................................................................................................... 158 2.4 Data Processing ............................................................................................................. 159 3 Results .................................................................................................................................. 160 3.1 US Probe Calibration Accuracy .................................................................................... 160 3.2 Typical Scans by Model and Probe ............................................................................... 161 3.3 Point Cloud Consistency with Models .......................................................................... 162 3.4 Localization Accuracy Across Designs ......................................................................... 163 3.5 Measurement Accuracy Across the Image .................................................................... 165 3.6 Accuracy Against the Number of Measurements .......................................................... 166 4 Discussion ............................................................................................................................ 167 4.1 Relation to Existing Literature ...................................................................................... 167 4.2 Strengths and Limitations .............................................................................................. 169 4.3 Clinical Relevance ......................................................................................................... 170 4.4 Future Directions ........................................................................................................... 170 5 Conclusion ........................................................................................................................... 171 Chapter 7 Concluding Remarks .............................................................................................. 172 1 Key Findings and Contributions .......................................................................................... 172 1.1 Benchmarking of Current Pedicle Screw Navigation Technology ............................... 173 1.2 Tool Design Validated in Simulation ............................................................................ 174 1.3 Experimental Verification of Ultrasound-Based Localization ...................................... 176 1.4 Machine Learning Optimization for Bone Localization ................................................ 178 1.5 Prototype Emulation Confirms Feasibility of Ultrasound-Based Drill Guide .............. 180 2 Future Directions ................................................................................................................. 182 2.1 Completion of the poly-CMUT integrated prototype .................................................... 182 2.2 Validating accuracy in cadaveric and live surgical settings .......................................... 185 2.3 Optimizing probe design ............................................................................................... 186 2.4 Expanding applications beyond spinal surgery ............................................................. 187 References .................................................................................................................................. 190 Appendix A: Design and Characterization of Robotically-Guided Ultrasonic Bone Cutting for Laminectomies and Facetectomies .................................................................................... 211 A.1 Materials and Methods ..................................................................................................... 212 xiv A.2 Results .............................................................................................................................. 214 A.3 Discussion ........................................................................................................................ 215 A.4 Conclusion ....................................................................................................................... 216 Appendix B: Search Strategy for the Meta-Analysis of Robotic Spinal Surgery Platforms 217 Appendix C: Bone-Ultrasound Physics and Emerging Applications ................................... 219 Section C.1 Physics of Ultrasound and Bone ......................................................................... 219 Section C.2 Applications in Surgical Navigation ................................................................... 223 xv List of Tables Table 2.1. Descriptive information on the selected studies. (*) indicates that the StealthStation was not used with the Mazor X robot for placing the screws ........................................................31 Table 3.1. Design requirements for an ultrasound-augmented self-localizing drill guide for pedicle screw insertion in the lumbar spine ...............................................................................................43 Table 3.2. Summary of the technical specifications for the proposed tool design ........................66 Table 4.1. Acoustic physical properties assigned to materials in the K-wave simulation ............77 Table 4.2. Summary of measurement error sensitivity to measurement depth .............................86 Table 4.3 Summary results of poly-CMUT dimensional measurements of the spinous process of an L4 vertebrae Sawbones model ................................................................................................111 Table 5.1 Summary of imaging parameter and probe recommendations for performing accurate segmentation of spinal bones on ultrasound imaging ..................................................................143 xvi List of Figures Figure 1.1. Examples of pedicle screw malplacement based on the scoring system proposed by Zdichavsky (Creative commons vertebral illustration from Furneaux 1907) .................................3 Figure 1.2. Freehand navigation of pedicle screw placement. Example trajectories shown in the (A) Transverse, (B) Sagittal and (C) Coronal Planes. (D) Key anatomical landmarks ...................4 Figure 1.3. Example (A) posterior-anterior, and (B) lateral fluoroscopy imaging of the spine following two-level spinal fusion ....................................................................................................5 Figure 1.4. Computer-assisted navigation with optical tool tracking. Screw trajectory displays exemplified in the (A) Transverse and (B) Lateral planes based on spinal registration with CBCT..........................................................................................................................................................6 Figure 1.5. Robotically-Guidance in Pedicle Screw Navigation. (A) The surgeon guides his screw down the trajectory of the drill guide placed by the robotic arm below his right hand. (A) Illustration of the key elements in the robotic process. (C) Image of a custom robotic arm placing a 3D-printing metal guide over an excised porcine spine ................................................................7 Figure 1.6. Accuracy of grade A/B Gertzbein-Robbins screw placements by surgical modality reported in recent meta-analyses as a function of the 5-year capital costs. The region marked in orange represents the desirable zone of low-cost and high accuracy which the work in this thesis aims to achieve .................................................................................................................................9 Figure 1.7. Rending of the proposed ultrasound-augmented self-localizing drill guide positioned along a theoretically realistic approach axis to a pedicle channel of a spine model (retracted ~2-3 cm to visualize the drill passing through the central channel) ......................................................10 Figure 1.8. Overview of the main elements and data conversions of the proposed device workflow. Illustrated components are not prescriptive, and several possibilities for each component exist that are not shown above .......................................................................................................................11 Figure 1.9. Ultrasound transducers. (A) Image of a custom-made polymer-based Capacitive Micromachined Ultrasonic Transducer (Poly-CMUT) six by one array. (B) Illustration demonstrating electromechanical functioning of both piezoelectric and CMUT elements ...........13 Figure 1.10. Intrapedicular radial ultrasound for breach detection. (A) Incorrect trajectory alert, (B) sample circumferential ultrasound on the incorrect trajectory, (C) correct trajectory, and (D) sample circumferential ultrasound on the correct navigation ........................................................14 xvii Figure 1.11. Anatomic variation along the vertebral column. Pedicle diameter is shown along the vertical axis and icon width, and transverse angulation is marked on the figure and by icon angle........................................................................................................................................................16 Figure 1.12. Data acquisition and point-cloud registration of a rangefinding drill guide adjacent spinal anatomy ...............................................................................................................................20 Figure 2.1. PRISMA diagram of the literature screening workflow .............................................30 Figure 2.2. Distribution of (A) the number of patients, (B) the number of screws and (C) the number of screws per patient in the selected studies. (D) Timeline of the median number of patients per study for each robot .................................................................................................................32 Figure 2.3. Logit-event rate of accurately placing pedicle screws using 4 different robotic platforms ........................................................................................................................................33 Figure 2.4. Logit-event rates of (A) intraoperative revision and (B) reoperation after pedicle screw placement using different robotic platforms ..................................................................................34 Figure 2.5. Comparison of 4 different robotic platforms according to their total operative time .35 Figure 2.6. Secondary safety metrics. (A) Comparison of the intraoperative blood loss of a thoracolumbar fusion using 3 different pedicle screw guidance robots. (B) Comparison of the effective radiation exposure during thoracolumbar fusion using 3 different pedicle screw guidance robots..............................................................................................................................................36 Figure 2.7. Funnel plot of standard error over the overall pooled accuracy rates ........................37 Figure 3.1. The proposed tool: (A) Technical drawing of the drill guide with annotated design parameters, (B) rendering of the guide pulled back from the bone to display side ranging ultrasound strips, distal ports for wires and a drill bit passing through, and (C) preliminary prototype of a curved transducer array with dimensions and specifications similar to those imagined for the proposed device .............................................................................................................................46 Figure. 3.2. Design workflow for tool development .....................................................................49 Figure 3.3. Nominal design. (A) Rendering of the US-augmented tool placed in the nominal targeting position exterior to the pedicle, and (B) table of nominal design parameters ................50 Figure 3.4. Representation and nomenclature for the set of transducer configurations evaluated in this study. For the hemispherical transducer, the tip radius of curvature is set at Ïc = rDG ............55 xviii Figure 3.5. Median localization error and interquartile range of different optimization techniques using a nominal tool design, as a function of initial estimation error magnitude. The solid lines represent the median values for the final errors, and the surrounding shadowed regions represent the corresponding interquartile ranges ...........................................................................................56 Figure 3.6. Convergence rates for the various design parameter combinations investigated using the constrained local optimizer with the interior-point algorithm. The ânominalâ design configuration that served as the baseline had a strip length of 30 mm, 8 strips, 16 elements per strip, a drill guide radius of 3 mm and was positioned in the nominal targeting position. The subplots show the results of varying each of the design parameters independently as a function of various levels of initial estimation error, as identified in the figure axes: (A) strip length, (B) number of strips, (C) number of elements per strip, and (D) drill guide radius. The shaded areas represent the 95% confidence bounds for the convergence rate estimates. The nominal value for each parameter is shown by a vertical dotted black line ................................................................57 Figure 3.7. Convergence rates for the various design parameter combinations investigated across varying levels of measurement uncertainty (indicated in the legends) with the initial estimation error held at 15mm. Each parameter was varied independently relative to a nominal design of 8 strips, each 35mm long with 32 elements per strip, and a drill guide radius of 3 mm. Parameters investigated were: (A) strip length, (B) number of strips, (C) number of elements per strip, and (D) drill guide radius. Dotted black vertical lines show the nominal values for each design parameter........................................................................................................................................................58 Figure 3.8. Convergence mapped according to the estimated (A) and displaced positions (B) of the tool. Arrows indicate the position and orientation of the estimated or displaced tool tip with green indicating locations resulting in convergence and red indicating non-convergence. (A) Rendering of initial estimates of tool locations with 20 mm estimation error, (B) rendering of the displaced tool tip location with 20mm displacements from the nominal position, (C and D) corresponding plots of convergence rate against initial estimation error (C) or displacement (D). Confidence shading represents the 95% confidence interval for proportion estimates based on the binomial distribution ......................................................................................................................59 Figure 3.9. Analysis of the number of measurements. (A) Convergence rate vs the number of valid measurements, together with a fitted power regression demonstrating improvement in convergence xix rate with number of valid measurements, and (B) median localization error and IQR vs the number of valid measurements, along with an exponential approximation of the IQR demonstrating reduction with increasing numbers of valid measurements ...........................................................60 Figure 3.10. Convergence rate of the preliminary design against the number of start points used in a MultiStart interior-point algorithm for state-estimation. The initial estimation error and the displacement from the nominal targeting position were both set to 15mm. The error bounds represent the 95% confidence interval for the proportion estimate calculated for a binomial distribution .....................................................................................................................................61 Figure 3.11. Comparison of performance of different optimization algorithms as a function of initial estimation error. (A) Convergence rates when using six start points (IP, SQP, AS and QN) or GlobalSearch, and (B) runtimes for all algorithms except GlobalSearch because its runtimes were consistently over 100s ...........................................................................................................62 Figure 3.12. Comparison of different array configurations based on their convergence rate vs initial estimation errors. The five models tested were (i) side-ranging, (ii) one-forward and the rest side-ranging, (iii) hemispherical tip, (iv) wide fanned-out, and (v) sharp fanned-out ...................63 Figure 3.13. Assessment of the proposed designâs convergence rate over an extended range of initial estimation errors. All simulations were performed in the nominal targeting position ........64 Figure 3.14. Assessment of the proposed designâs convergence rate at various distances from the nominal targeting position. The simulations were performed with initial estimation errors of both 10 mm and 20 mm as indicated .....................................................................................................65 Figure 4.1 Process of extracting CT-based images for ultrasound modelling. (A-C) Demonstration of tool positions and scan planes for proposed tools in the axial plane, and (D) Sample region in the sagittal plane ............................................................................................................................76 Figure 4.2. Slice of L4 Cadaveric vertebral CT Image. (A) Original CT slice, (B) Red line indicating CT vertebral surface segmentation, and (C) Two-level acoustic parameter assignment........................................................................................................................................................77 Figure 4.3. Sample simulation of acoustic reflection in K-wave at three different time points. (A) Initial reflection triggered, (B) Initial echo received, and (C) Late diffuse acoustic waves ..........78 xx Figure 4.4. Pipeline for B-mode image modification. (A) Initial cropped CT, and (B-I) steps in the image modification pipeline (Details in text) .........................................................................79 Figure 4.5. Image measurement pipeline. (A) Scan plane identification, (B) Segmentation map, (C) Simulation and B-mode image formation, (D) ResNet-18 feature extraction and (E) VGG-16 segmentation and measurement estimation ...................................................................................81 Figure 4.6. Demonstration of calculation of important error metrics include the Hausdorff distance, the mean error and the median error based on the difference between a segmented curve and the ground truth .......................................................................................................................82 Figure 4.7. Measurement accuracy for RF signal interpretation and B-mode peak detection of flat plates of various depth in simulation. (A) Median and interquartile range of the measurement error. (B) Hausdorff distance of the implicit plate segmentation ..................................................83 Figure 4.8. Distribution of measurement errors for five different techniques across 2055 spine-based ultrasound reflection simulations. (A) Violin plot of the distribution of measurement errors for each method. (B) Cumulative distributions for each of the 5 methods ....................................84 Figure 4.9. Bone-distance measurement error of five ultrasound-based methods against the depth of the true measurement. (A) All points with overlying smoothed splines. (B) All Hausdorff distances with overlying smoothed splines. (C-G) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation ...........................................................................................85 Figure 4.10. Bone-distance measurement error of five ultrasound-based methods against the horizontal position in the field. (A) All points with overlying smoothed splines. (B-F) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation ....................................87 Figure 4.11. Bone-distance measurement error of five ultrasound-based methods against the irregularity of the scanned surface. (A) All points with overlying smoothed splines. (B) All Hausdorff distances with overlying smoothed splines. (C-G) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation ...............................................................................88 xxi Figure 4.12. Bone-distance measurement error of five ultrasound-based methods against the flatness deviation of the scanned surface. (A) All points with overlying smoothed splines. (B) All Hausdorff distances with overlying smoothed splines. (C-G) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation ...............................................................................89 Figure 4.13. Experimental setup. (A) Reference geometry inserts including an adult L4 vertebra model (~80 mm across) and a set of âVâ shapes with varying internal angles to assess impact of angulation on localization accuracy. (B) Experimental setup showing the coordinate system of the linear probe relative to a 3D-printed model vertebra .....................................................................95 Figure 4.14. Data processing methods. (A) Example scan of an L4-model vertebra with a manual segmentation indicated by the red contour line. (B) Computer simulation of ultrasound distance measurements at a predicted tool position. Difference between true and estimated positions is exaggerated for illustration ............................................................................................................96 Figure 4.15. Localization error analysis. (A) Final localization error plotted against pre-localization position error for the five 3D-printed reference geometry inserts. (B) Grouped final errors for all trials categorized by the characteristic angles of the reference geometry inserts (mean final error across the samples shown in red) .................................................................................98 Figure 4.16. Experimental setup for rangefinding testing of a flexible poly-CMUT in an oil bath. (A) Hydrophone measurement and (B) Reflection off a metallic plane ......................................102 Figure 4.17. Experimental Setup of Rigid poly-CMUT Rangefinding. (A) Rigid poly-CMUT array used in the early range-finding tests, triggered and recorded by a Verasonics Vantage system. (B) Diagram of the wire phantom experimental setup, showing the transducer (green), wire cross-sections (yellow), the phantom base (black), and a broken wire marked by a red cross......................................................................................................................................................104 Figure 4.18. Experimental setup for scanning a Sawbones spine model with a simple Poly-CMUT sample in a water bath setting. (A) Side view of the transducer scanning from a posterior to anterior position, and (B) Top view of the transducer scanning PA with the adjustable positioning frame visible in the top right corner .......................................................................................................105 xxii Figure 4.19. Illustrations of the two primary scanning planes across the vertebral spinous process. (A) Lateral view of the vertebrae which is parallel to both scanning planes such they are indicated by lines, and (B) Top view of the vertebrae with indicated scanning planes. (C) Isometric views of each of the independent scan planes isolated for clarity ..............................................................106 Figure 4.20. Sample signal processing of the hydrophone signals. (A) Raw RF signals at varying bandwidth, (B) Power distribution with variable bandpass filters, and (C) Spectrogram of the raw RF signal demonstrating power contributions through time ........................................................107 Figure 4.21. Figure 4. Sample signal processing of the reflected echo. (A) RF signals at varying bandwidth, (B) Power distribution with variable bandpass filters, and (C-D) Spectrogram of the RF signal showing power contributions through time before and after 50% bandwidth filtering......................................................................................................................................................108 Figure 4.22. RF signals of sample elements with peak detections indicated by orange lines and reference distances marked in cyan. (A-C) Samples for elements 4, 8 and 12 respectively .......109 Figure 4.23. Rangefinding results of the water bath wire phantom. (A) Measurement against the feature depth, and (B) Discrepancy between ToF and caliper measurements .............................110 Figure 4.24. Sample results of feature identification and measurement based on B-Mode imaging with a 6-element poly-CMUT array. (A) Spinous process [SP] from a lateral approach in the transverse plane [LT], (B) SP from a lateral approach in the coronal plane [LC], and (C-D) SP from a posterior approach in the transverse plane [PAT] with both pre and post processing .....111 Figure 5.1. Illustration of the physics of ultrasound propagation and bone reflection. (A) Specular reflection, (B) Diffuse reflection, and (C) Wave equation at the interface between media of different acoustic impedance. The approximate density (Ï), speed of sound (c) and acoustic impedance (z) of muscle and bone are listed on the right ............................................................115 Figure 5.2. Experimental setups for ultrasound image quality and segmentation assessment. (A) Wire phantom (red) for PSF analysis. (B) Target-sphere phantom for CNR evaluation. (C) Tracked ultrasound setup for scanning cadaveric and SawBones phantoms .............................................118 Figure 5.3. Point Spread Function (PSF) determination. (A) Gaussians fit along the primary axes of an US imaged wire with colour mapping to illustrate how intensity matches to the Gaussian xxiii curve. (B) Equations for 2D-Gaussian surface and PSF values. (C) Ultrasound image of a fishing wire in water, oriented perpendicular to the imaging plane .........................................................119 Figure 5.4. Target phantom studies for ultrasound image quality. (A) Example image showing the target sphere, (B) Fit of a complementary error function to a given ray line ..............................120 Figure 5.5 Diagram of the selected ray-lines for IQ measurement on the target phantom and illustration of the CNR calculation ..............................................................................................121 Figure 5.6. Segmentation accuracy. (A) Sample segmentation of a Sawbones vertebral phantom and (B) diagram and equation for computation of Hausdorff distance and metric for segmentation accuracy .......................................................................................................................................122 Figure 5.7. Overview of the experimental setup for labeled dataset generation and application in tracking displaced vertebrae. (a) Transformation chain used for mapping CT slices (and segmented structures therein) to US frames. (b) Application of the pre-trained network in segmenting and registering displaced vertebrae from US images to the corresponding structure in CT ...............123 Figure 5.8. Vertebrae labeling approaches. First row shows labels overlaid on US images, and second row shows the same labels overlaid on corresponding CT slices. (a-b) Contours of FS labeling, (c-d) contours of PC labeling, and (g-h) Intensity-Weighted (IW) posterior cortex labeling, where (e) the weights are obtained by averaging pixel intensities within a 2Ã2 mm neighborhood ................................................................................................................................124 Figure 5.9. Data sanitization and augmentation. (a-d) Example images without (or with partial) labels due to imaging outside the region of interest. 3D quiver plots of probe directions for each acquired image (e) before and (f) after data pruning for uniform angle distribution. (g) Initial standard image and (h-j) consecutive frames with motion artifacts. (k) Original acquisition at G = 50 dB and DR = 80 dB, and (l-n) data augmentation with simulated G and DR values ..............126 Figure 5.10. Illustration of segmentation network architecture with sample input, training label and output. (A) Sample image with overlying CT, (B) modified TernausNet architecture and (C) output segmentation in green based on the network contrasted with the tracker erroneously predicting the dashed magenta line following a spinal deformation or loss of registration ........127 xxiv Figure 5.11. Calibration of US slice thickness. (a) Photo of the experimental setup fishing wire and Superflab block to prevent acoustic reverberation. (b) Zoomed inset showing the geometric relation between imaged wire length and slice thickness. (c) Example image of the wire acquired at a depth set to focal length ........................................................................................................127 Figure 5.12. Spatial resolution measured as axial PSF (A-C) and lateral PSF (D-F). These metrics are recorded over ranges of imaging parameters including gain (A, D), dynamic range (B, E) and focal depth (C, F) ........................................................................................................................132 Figure 5.13. Edge spread function (ESF) across gain and dynamic range at (A) 8.0 MHz, (B) 10.0 MHz, and (C) 11.5 MHz. (D) Pixel intensity profiles across the target boundary at different angles, acquired at 90 dB dynamic range, gain of 50, and 10.0 MHz scanning frequency with a linear probe. Each color represents a different angle off the target sphere ............................................133 Figure 5.14. Contrast resolution measured as CNR across gain and dynamic range for linear probes with varying scan frequencies: (A) 8.0MHz, (B) 10.0MHz and (C) 11.5MHz. Higher values of CNR are preferred ...................................................................................................................134 Figure 5.15. Assessment of segmentation accuracy (Hausdorff distance) across gain and dynamic range for (A) the SawBones phantom and (B) cadaveric imaging. (C) Segmentation accuracy against spatial resolution. Median points and IQR spread represent 10 repeat trials at dynamic range between 30 to 165 and gain between 0 and 90. Sample segmentations of the (D) model and (E) cadaveric vertebrae acquired at 135 dB dynamic range, gain of 10, and a 11.5MHz scanning frequency with a linear probe ......................................................................................................135 Figure 5.16. Sample images of spinous process segmentation using a CT-trained CNN with ultrasound images (A) before, and (B) after image quality optimization ....................................136 Figure 5.17. Evaluation of different annotating strategies on test dataset of 5984 images: (a) 2D RMSD and (b) 3D TRE. Median is represented by a red line, mean by a red dot, and the IQR is shown by the box. (c-h) Segmentation overlays on US and CT slices. (i-k) 3D visualizations of the vertebra cortex after registration; the blue cortex is the original and the orange cortex is after the registration ................................................................................................................................... 138 xxv Figure 5.18. Slice thickness calibration and validation. (a) Gaussian fits for varying ð and fixed 30 mm depth. (b) Slice thickness estimates at varying depths. (c) Registration accuracy was minimized when using the estimated slice thickness value ......................................................... 139 Figure 5.19. Dataset sanitization tuning parameters. (a) precision and recall curve for filtering images without labels. (b) Critical Success Index map for removing images with motion artifacts using translation and angular velocity thresholds. (c) vertebrae-wise density filtration using the tuned parameters ..........................................................................................................................140 Figure 5.20. Evaluation of the data curation on PC approach. S+ indicates the use of data sanitization, and A+ indicates the use of augmentation. (a) 2D pixel-to-pixel RMSD and (b) 3D TRE. (c-j) Effects of data sanitization and augmentation on the training of the network are visualized as segmentation contour overlay on US and CT slices ............................................... 141 Figure 5.21. Evaluation of the data curation on the IW approach. S+ indicates the use of data sanitization, and A+ indicates the use of augmentation. (a) 2D pixel-to-pixel RMSD and (b) 3D TRE. (c-j) Effects of data sanitization and augmentation on the training of the network are visualized as segmentation contour overlay on US and CT slices ............................................... 142 Figure 5.22. 3D evaluation of the PC annotating strategy over various confidence scores. (a) 3D TRE over different confidence scores. (b-m) visual evaluation over different thresholds, where first row (b-g) is US image overlay with segmented posterior contour and second row (h-m) is corresponding CT slice overlay with same segmented contour ................................................... 143 Figure 6.1. Emulated designs and probe trajectories evaluated in the study. (A) A flat design on the surface of the skin is emulated with a linear probe translating perpendicular. (B) A curved radial design simulated by rotating a curved forward-facing endocavity probe about its axis. (C) A linear radial probe evaluated by spinning a linear side-ranging probe about its axis. (D) The annular stack design is modelled by a side-ranging curvilinear endocavity probe which is translated along its axis ..........................................................................................................................................152 Figure 6.2 Computer modelling the three spine models with overlying samples of point clouds. (A) A semi-transparent, single two-scale L4 vertebrae based on real patient CT-data. (B) A 2:1 xxvi model of the pedicle surface. (C) A full lumbar spine SawBones model represented here by the L2-L5 segmentation from a CT scan ...........................................................................................154 Figure 6.3 Model of the freehand and calibration 3-N wire phantom (fCal 2.1). Segmented points are represented by red dots overlying blue wires .........................................................................156 Figure 6.3 Sample wire segmentations in the freehand calibration step for the (A) linear probe, and (B) curvilinear probe and (C) projected onto the 3D wires ..................................................157 Figure 6.4 Map of the set of transformations used in the freehand calibration process. The equivalence of these transforms between the physical lines and segmented points is shown before for calculating the transform from the image to the tracker ........................................................157 Figure 6.5. Example of probe design and emulation process shown by (A) Schematic of an ultrasound augmented tool near the pedicle surface with marked measurement points, (B) Illustration of a rotating outward facing design and (C) a set of associated scan plane emulated for this design with a side-ranging endocavity probe ........................................................................158 Figure 6.6 Map of key transformations and the associated cost function for the ultrasound to spine registration process ......................................................................................................................159 Figure 6.7. Reprojection error of the full set of extracted wire phantom points across three depths for the four emulated designs. Boxes indicate â¦ The horizontal line at 2.5 mm represents a commonly used standard for acceptable calibration in related applications (MacLean 2023) ...161 Figure 6.8 Sample linear scan of the (A) spinous process with the associated steps of the segmentation protocol and (B) the transverse process overlaid onto the 3D model of the L4 vertebrae .......................................................................................................................................162 Figure 6.9. Dense point cloud representations with pre-registration points shown in red and post registration in green for the (A) single vertebrae, (B) the 2:1 pedicle surface and (B) the lumbar spine model ..................................................................................................................................162 Figure 6.10 Translational error results for the four emulated designs across the three models. Translational error represents the translational discrepancy between the ultrasound-registration and the point-fiducial registration used for comparison ..............................................................163 xxvii Figure 6.11 Rotational error results for the four emulated designs across the three models. Rotational error represents the discrepancy between the ultrasound-registration transform and the point-fiducial registration transform at the location of screw insertion .......................................164 Figure 6.12 Summary error metric results for the four emulated designs across the three models. Summary error represents the combination of the translational and rotational errors by summing the translational error and the error introduced by rotation after it is projected over the pedicle channel .........................................................................................................................................165 Figure 6.13 Measurement accuracy for the linear (top row) and curvilinear (bottom row) scans across the image in terms of the lateral position (left column) and depth (right column). Colour represents the relative density normalized by either horizontal position or depth ......................166 Figure 6.14 Relationship between the upper summary error bound and the number of valid segmented measurement points in the point cloud used for the ultrasound registration .............167 Figure. A.1 Experimental setup (A) Close view of cutting guide and phantom, and (B) Large view of support technologies ................................................................................................................212 Figure A.2 Cut plane planning (A) 3D Rendering for Visualization, (B) Axial view with slice, and (C) Coronal view with slice .........................................................................................................213 Figure. A.3 Pooled accuracy results based on the RMS Error of the difference between the planned and actual osteotomy planes ........................................................................................................214 Figure A.4 The cutting force measured from the UR5 force logger as a function of the cutting speed of the ultrasonic bone scalpel .............................................................................................215 Figure C.1 Illustration of ultrasound reflection at a soft tissue to bone interface based on the acoustic impedance of muscle (ð§! â 1.6ðºðð ð ð"#) and bone (ð§$ â 7.8ðºðð ð ð"#) .............220 xxviii List of Abbreviations AAPM - American Association of Physics in Medicine AI - Artificial Intelligence AIML - Artificial Intelligence ALIF - Anterior Lumbar Intervertebral Fusion AS - Active-Set method CA - Computer-Assisted CAOS - Computer-Assisted Orthopaedic Surgery CBCT - Cone-Beam Computer Tomography CI - Confidence Interval CITAC - Clinician-Investigator Trainee Association of Canada CMOS - Complementary metalâoxideâsemiconductor CMUT - Capacitive Micromachined Ultrasonic Transducer CNN - Convolutional Neural Network CNR - Contrast-to-Noise Ratio CPD - Coherent Point Drift CSI - Critical Success Index CT - Computed Tomography CTNav - Computed Tomography based Navigation DAS - Delay-and-Sum DDH - Developmental Dysplasia of the Hip DG - Drill Guide DICOM - Digital Imaging and Communications in Medicine DR - Dynamic Range EKFs - Extended Kalman Filter ESF - Edge Spread Function FA - Fluoroscopic Assisted FAS - Constrained Local Solver based on Active-Set Method FD - Focal Depth FDA - Food and Drug Administration FDM - Fused Deposition Modeling FGS - GlobalSearch FH - Freehand FIP - Constrained Local Solver based on Interior-Point method FN - False Negative FP - False Positive FS - Full Spine model FSQP - Constrained Local Solver based on Sequential Quadratic Programming FUQN - Unconstrained local solver based on the Quasi-Newton method GAN - Generative Adversarial Network ICP - Iterative Closest Point IEEE - Institute of Electrical and Electronics Engineers IIR - Infinite Impulse Response IP - Interior-Point method IQ - Image Quality xxix IQR - Interquartile Range IRB - Institutional Review Board IUS - International Ultrasonics Symposium IW - Intensity Weighted LC - Lateral Coronal LLIF - Lateral Lumber Intervertebral Fusion LT - Lateral-Transverse MB - Mega-Bytes MCR - Multi-Center Retrospective MHz - Mega-Herz MICCAI - Medical Imaging Computing & Computer-Assisted Intervention ML - Machine Learning MRI - Magnetic Resonance Imaging MRayl - Mega-Rayleigh MUST - MATLAB Ultrasound Toolbox MeSH - Medical Subject Headings NDI - Northern Digital Instruments OLIF - Oblique Lumbar Intervertebral Fusion OP - Overall Pooled PA - Posterior-Anterior PAS - Posterior-Anterior Sagittal PC - Posterior Cortex PDMS - Polydimethylsiloxane PF - Particle Filter PLA - Polylactic Acid PLIF - Posterior Lumbar Intervertebral Fusion PPV - Positive Predictive Value PRISMA - Preferred Reporting Items for Systematic reviews and Meta-Analyses PSF - Point Spread Function PZTs - Piezoelectric Transducers Poly-CMUT - Polymer-based Capacitive Micromachined Ultrasonic Transducers QN - Quasi-Newton method RF â Radiofrequency RFToF â Radiofrequency Time of Flight RMSD - Root Mean Square Distance RMSE - Root Mean Square Error ReLU - Rectified Linear Unit SCP - Single-Center Prospective SCR - Single-Center Retrospective SNR - Signal-to-Noise Ratio SP - Spinous Process SQP - Sequential-Quadratic Programming STD - Standard Deviation STL - Surgical Technologies Lab TLIF - Transverse Lumbar Intervertebral Fusion ToF â Time of Flight xxx TP - True Positive TRE - Target Registration Error UASLDGs - Ultrasound-Augmented Self-Localizing Drill Guide UKF - Unscented Kalman Filter US - Ultrasound USD - United States (American) Dollar VGG - Visual Geometry Group xxxi Acknowledgements I would like to acknowledge and thank of my supervisors, lab members, committee advisors and both technical and clinical mentors throughout my training. Thank-you to CA-SMART and UBC for hosting and training me in my, to Johns Hopkins for my time as a visiting scholar and to NSERC for ongoing support throughout my tenure in the program. I would like to particularly express my gratitude to Dr. Antony Hodgson for his unwavering support and mentorship throughout the process of the PhD. xxxii Dedication To my cousin Max (Wolfgang Maximillion MacLean Kaufmann) and the pursuit of better solutions to the toughest challenges. I hope this work, and my career, can contribute in some small way to preventing harms and safeguarding quality of life in service of the principles Max lived by and continues to inspire: empathy, kindness and determination. 1 Chapter 1 Background to the Problem and the Proposed Solution Over 1.62 million instrumented spine operations are performed each year in North America, making these procedures among the most frequently performed surgical interventions (Dyrdra 2019). A common component of these surgeries is the placement of pedicle screws to stabilize the spine and correct pathologies such as spondylolisthesis, spinal stenosis, vertebral fractures, and scoliosis (Mobbs 2015). Yet this task is notably challenging: due to the spineâs tight spatial constraints and complex anatomy, the conventional freehand pedicle screw placement commonly results in non-trivial complication and reoperation rates of up to 9.3% and 10%, respectively (Li 2010; Jing 2019), and can show malposition rates as high as 10â40% when anatomical landmarks are unreliable (Mobbs 2015). Critically, approximately 11% of screws end up malpositioned (Gelalis 2012), potentially causing severe complications such as vascular damage, neurological deficits, and fractures (Mobbs 2015). These clinical risks also result in a substantial economic burden: in 2018, revision surgeries for malpositioned screws were estimated to cost around $33k USD (Menger 2018) per surgery in the USA. Such financial and medical ramifications highlight the urgent need for improved guidance methods in pedicle screw placementâtechniques that can reliably reduce errors, enhance patient safety, and ultimately improve outcomes in one of the most frequently performed categories of spinal procedures. 1 Concerns Related to Pedicle Screw Placement Pedicle screw insertion is one of the most widely used methods for stabilizing the spine during fusion procedures. In the freehand approach, surgeons primarily rely on anatomical landmarks (for instance, the intersection of the facet joint and the transverse process) and tactile feedback to direct the burr into the pedicle axis. Numerous studies have documented high pedicle screw malposition ratesâranging from 3% to 54%âand associated complications that drive up revision surgery frequencies and healthcare costs at approximately $23,762 per revised screw (Ando 2021; Liounakis 2021). In addition, although rare, severe complications from lumbar pedicle screw placement have been quantitatively 2 reported: new neurological deficits occur in approximately 0.7% (Bekelis 2019) of primary surgeries and 1.2% (Sarlak 2011) of revision surgeries; major vascular injuries are exceedingly rare at an estimated incidence of ~0.01% (Xie 2022) but 0.22% of screws encroach on vasculature (Watanabe 2011); and persistent postoperative pain, often corresponding to Failed Back Surgery Syndrome, affects approximately 20% (Pearson 2019) of patients long-term. Despite their low frequency, neurological and vascular complications are emphasized due to their devastating impact on patient outcomes. Collectively, these reports highlight that inaccurate pedicle screw placement remains a recognized and ongoing issue with meaningful clinical and economic consequences. Several classification schemes and standardized metrics have been used to evaluate the accuracy of pedicle screw placement (Beck 2009). The Gertzbein-Robbins is the most common system which is based on the depth of cortical breach, while the Zdichavsky classification is an alternative system based on directionality which is shown in Figure 1 (Beck 2009). The Gertzbein-Robbins system categorizes screw positions from Grade A (no breach) to Grade E (breach >6 mm). Studies have reported that a significant majority of screws fall into Grades A and B, indicating clinically acceptable placements. For instance, Gertzbein and Robbins (1990) found that 81% of screws were placed within 2 mm of the pedicle's medial border (Grade A), while 6% had 4â8 mm of canal encroachment (Grades C and D). Similarly, a more recent study reported 88.4% of screws as Grade A and 9.6% as Grade B, with only 2% falling into Grades C through E. (Ha 2023) These findings highlight the prevalence of accurate screw placement while acknowledging the occurrence of deviations that may necessitate clinical attention. 3 Figure 1.1. Examples of pedicle screw malplacement based on the scoring system proposed by Zdichavsky (Creative commons vertebral illustration from Furneaux 1907) Multiple large-scale meta-analysesâencompassing data from tens of thousands of screws inserted under various techniquesâconsistently report notable variability in accuracy and meaningful differences in patient outcomes (Bonello 2023). The meta-analysis by Bonello reviewed over 16000 pedicle screw placements and found that, while certain navigation systems improved average accuracy1 from approximately 85% to 95%, breach rates (22.2% with freehand or fluoroscopy) and related complications remained concerns (Bonello 2023). Another study reported that navigation reduced the overall pedicle screw perforation risk from 15% to 6%, yet some neurological complications persisted (0.1%) in the conventional group (Shin 2012). These findings highlight that while navigation systems enhance accuracy, they do not completely eradicate the risks associated with pedicle screw placement. Collectively, these studies suggest a continued need for improved techniques that balance accuracy, safety, and cost-effectiveness. 4 2 Existing Surgical Methods: Progress and Persistent Gaps Over time, a range of navigational strategies have emerged to improve pedicle screw placement accuracy and reduce complications (Perdomo-Pentajo 2019). Initially, surgeons relied on freehand techniques guided purely by anatomical landmarks, which offered simplicity but limited precision (Mobbs 2015). As imaging technologies advanced, fluoroscopic guidance was introduced to provide real-time visualization, followed by CT-based navigation systems delivering three-dimensional anatomical data, and more recently, robotic systems aiming to refine accuracy even further (MacLean 2024). While each innovation has improved some aspect of screw placement, none have yet fully resolved the trade-offs in cost, complexity, and radiation exposure, and usage rates of these more advanced technologies are still relatively limited (Dea 2016). Figure 1.2. Freehand navigation of pedicle screw placement. Example trajectories shown in the (A) Transverse, (B) Sagittal and (C) Coronal Planes. (D) Key anatomical landmarks. 5 2.1 Freehand Placement Freehand pedicle screw placement relies on the surgeonâs experience and anatomic landmarks to guide the trajectory of screw insertion (Mobbs 2015). Its simplicity and low cost make it particularly appealing in lower-income settings or when imaging resources are limited (Mobbs 2015). However, without real-time feedback, freehand placement has been associated with malposition rates as high as 10â40% and concerning complication and reoperation rates (up to 9.3% and 10%, respectively â Li 2010; Jing 2019). These outcomes underscore the difficulty of ensuring accurate placement in complex spinal anatomy using only tactile and visual cues. Figure 1.3. Example (A) posterior-anterior, and (B) lateral fluoroscopy imaging of the spine following two-level spinal fusion. 6 2.2 Fluoroscopic Guidance In an effort to improve on freehand techniques, fluoroscopic guidance was introduced in the 1990s and employs intraoperative X-ray imaging to visualize screw trajectories in two orthogonal planes (Manbachi 2014). By allowing surgeons to monitor progress throughout the procedure, fluoroscopy can reduce malposition rates relative to freehand placementâimproving them to around 8.5% in some reports (Laudato 2018). Despite this advantage, the method exposes patients and surgical teams to continuous ionizing radiation, raising safety concerns (Su 2017), particularly for pediatric patients, and still demands that the surgeon interpret complex images and align screws accurately under time pressure (Su 2017). In a 2018 meta-analysis, Perdomo-Pentajo reported reoperation rates ranging from 1.6-3.9% (95% confidence interval). Figure 1.4. Computer-assisted navigation with optical tool tracking. Screw trajectory displays exemplified in the (A) Transverse and (B) Lateral planes based on spinal registration with CBCT.7 2.3 CT-Based Surgical Navigation CT-based navigation systems, which gained wider adoption in the early 2000s, combine intraoperative cone-beam CT (CBCT) scans with optical tracking to enable tracking of surgical tools relative to three-dimensional anatomical information available in the CT scans (Gelalis 2012; Watkins 2010). These systems have demonstrated relatively low malposition rates (3.8% reported in Wood & McMillen 2014). However, the need for an intraoperative CBCT machine, optical tracking frames, and sophisticated instrumentation drives up equipment costs (see Fig 1.6 below) and complexity (Dea 2016). In addition, registration may have to be repeated if the patientâs position shifts or if the reference frame moves, which reduces the practicality of this approach in longer or more complex procedures (Rajasekaran 2014). The resulting overhead in time, expense, and radiation exposure limit use of CT-based systems to well-resourced centers, limiting breadth of use (Heyer 2024). Figure 1.5. Robotically-Guidance in Pedicle Screw Navigation. (A) The surgeon guides his screw down the trajectory of the drill guide placed by the robotic arm below his right hand. (A) Illustration of the key elements in the robotic process. (C) Image of a custom robotic arm placing a 3D-printing metal guide over an excised porcine spine.2 8 2.4 Robotic Systems Building on imaging-based approaches, robotic guidance platforms have further improved pedicle screw placement accuracy (MacLean 2024). Some studies report malposition rates of only a few percent, and one meta-analysis suggests that many robotic systems outperform conventional CBCT navigation, achieving accuracy rates around 97% (Perdomo-Pentajo 2019). However, these technologies introduce significant capital costs, require specialized training, and still rely on radiation-based registration steps (Laudato 2018). Consequently, robotic systems remain inaccessible in many clinical settings (Perdomo-Pentajo 2019). 2.5 Balancing Cost and Accuracy A comparative analysis plotting various navigation strategies against their capital costs and reported accuracy rates (e.g., Grade A/B Gertzbein-Robbins screws) reveals a âmotivating solution spaceâ where low-cost and high-accuracy methods intersect (Fig 1.6, MacLean 2024). While each subsequent technique has advanced pedicle screw placement performance, the financial burden, reliance on radiation, or system complexity have prevented any single approach from becoming universally adopted (Dea 2016). This persistent gap highlights the ongoing need for innovative solutions that can deliver acceptably precise guidance without being insufficiently cost effective or exposing patients and staff to unnecessary radiation. Ultimately, addressing these limitations is essential for improving surgical outcomes, reducing complications, and making advanced navigational technologies more broadly accessible. 9 Figure 1.6. Accuracy of grade A/B Gertzbein-Robbins screw placements by surgical modality reported in recent meta-analyses as a function of the 5-year capital costs. The region marked in orange represents the desirable zone of low-cost and high accuracy which the work in this thesis aims to achieve. 3 Concept of Ultrasound-Augmented Self-Localizing Drill Guides We propose to address this gap by developing an ultrasound-augmented, self-localizing drill guide which can potentially overcome key limitations of existing pedicle screw navigation methods. By integrating low-profile Polymer-based Capacitive Micromachined Ultrasonic Transducers (Poly-CMUTs) directly into the drill guide, we hope to enable real-time measurement of distances to adjacent bone surfaces, which would allow us to estimate the position of the drill guide relative to pre-operatively acquired models of the surgical anatomy (e.g., obtained via CT scans) (MacLean 2023). We proposed using Poly-CMUTs because, in contrast to traditional piezoelectric transducers, Poly-CMUTs offer significant advantages such as lower manufacturing costs, a thinner profile, and enhanced durability. These features make them well-suited for integration into surgical tools with limited compromise of functionality or increase in bulk (Omidvar 2024). 10 Figure 1.7. Rending of the proposed ultrasound-augmented self-localizing drill guide positioned along a theoretically realistic approach axis to a pedicle channel of a spine model (retracted ~2-3 cm to visualize the drill passing through the central channel). This US-integrated approach could allow the drill guide to perform continuous ultrasound scanning during screw insertion, providing dynamic feedback on the toolâs position relative to the patientâs spinal anatomy. We propose to employ peak detection signal analysis to interpret ultrasonic echoes, translating these signals into accurate measurements of the distances between the US transducers and the bone surfaces (Ullah 2020). These measurements could be fed into state-estimation algorithms, such as point cloud registration, Unscented Kalman Filters (UKFs) or Particle Filters (PFs), to accurately localize the drill guide within the preoperative CT or MRI-based anatomical map (Ullah 2020). Such a method could eliminate the need for external optical tracking systems and significantly reduce reliance on radiation-based imaging, thereby enhancing both safety and accessibility (MacLean 2023). Moreover, such a system could support continuous re-registration, allowing the drill guide to adapt to intraoperative changes in spinal anatomy. Such a tool aims to reduce screw malposition rates, decrease the need for costly revision surgeries, and ultimately improve patient outcomes in spinal fusion surgeries. By addressing the critical gaps in existing navigational methods, our approach could provide surgeons with a reliable and comparatively inexpensive tool that would enhance precision, minimize complications, and promote better overall patient care. 11 Figure 1.8. Overview of the main elements and data conversions of the proposed device workflow. Illustrated components are not prescriptive, and several possibilities for each component exist that are not shown above. Numbering in figure 1.8 relates to the following steps in the registration and localization proposal: 1. Ultrasound radiofrequency (RF) signals are acquired through the drill guide. Distance measurements to local bone surfaces are determined through either (a) peak detection in the RF signal or (b) B-mode image segmentation. 2. A pre-operative 3D scan of the patient (e.g. MRI or CT) is imported. 3. Initial registration is performed by matching a point cloud of the distance measurements with a surface model of the 3D scan. 4. Moment by moment tracking is performed using a UKF to provide pose estimation. 5. A user interface then displays tool position similar to pre-existing optical tracking systems. 6. The tool is moved by the surgeon to a new position and process repeats. 12 4 Research Objective The long-term objective of the research presented in this thesis is to develop a low-cost, highly accurate, and radiation-free navigation solution for pedicle screw placement in spinal fusion surgeries. Our goal is to eliminate the need for continuous line-of-sight tracking and expensive capital equipment, thereby making advanced spinal navigation accessible to a broader range of healthcare settings (Dea 2016). By addressing the clinical need for improved accuracy, we aim to reduce healthcare costs, minimize radiation exposure, and simplify logistical complexities associated with current navigation methods (MacLean 2024). Ultimately, our solution seeks to enhance the accessibility of spinal navigation, decrease the incidence of revision surgeries, and improve patient outcomes worldwide. By providing surgeons with a reliable and user-friendly tool, we intend to promote better overall patient care, reduce the burden of surgical complications, and contribute to more efficient and effective spinal fusion procedures. 5 Related Literature This section reviews the existing research on integrating ultrasound (US) technologies into pedicle screw placement. We begin by examining the evolution of US transducer innovations and then explore how these advances enable real-time bone localization and navigation. We further discuss state-estimation techniques, which may allow an ultrasound-based tool to operate without depending on external optical trackers or radiation-based methods. 5.1 US Transducer Technologies Current advancements in surgical navigation have increasingly focused on enhancing the accuracy and safety of pedicle screw placement in spinal fusion surgeries. Ultrasound (US) technology has traditionally been employed for imaging soft tissues, but significant work in the past 10â15 years has focused on detecting hard tissue interfaces and bony structures (Cocco 2022). Various machine learning (ML) approaches have been explored to improve the accuracy and robustness of ultrasound-based bone surface detection, allowing for more reliable segmentation and rangefinding in complex anatomical environments. 13 However, the effectiveness of these methods is limited by the form factor and physical constraints of conventional piezoelectric transducers (PZTs). These transducers are often bulky, fragile, and costly to manufacture, which hinders their integration into surgical tools (Omidvar 2021). Polymer-based Capacitive Micromachined Ultrasonic Transducers (Poly-CMUTs) offer an alternative with several advantages, including a thinner profile, lower production costs, and increased durability (Omidvar 2024). These attributes make Poly-CMUTs better suited for embedding into drill guides and other surgical instruments without increasing their size or compromising structural integrity. Figure 1.9. Ultrasound transducers. (A) Image of a custom-made polymer-based Capacitive Micromachined Ultrasonic Transducer (Poly-CMUT) six by one array. (B) Illustration demonstrating electromechanical functioning of both piezoelectric and CMUT elements.14 1This is a simulated image generated based on the ideas proposed and the tool developed in Manbachi 2015. 5.2 Use of US in Spine Surgery Ultrasound has been explored as an adjunct modality in spinal surgery in multiple contexts. Optical tracking combined with conventional US probes can acquire bone surface points for registration, improving accuracy in spinal instrumentation (Farshad 2022). Similarly, radial ultrasound within the pedicular channel has been proposed to detect imminent breaches by identifying cortical bone boundaries (Buerger 2014). Recent work has also utilized AI-based approaches for evaluating ultrasound screenings of hip dysplasia in newborns (Quader 2018). Although these approaches broadly validate the concept of using ultrasound imaging for guiding interventions, they often rely on external tracking systems or can only function once the tool is already within the bone (Gueziri 2022). Figure 1.10. Intrapedicular radial ultrasound for breach detection. (A) Incorrect trajectory alert, (B) sample circumferential ultrasound on the incorrect trajectory, (C) correct trajectory, and (D) sample circumferential ultrasound on the correct navigation.1 15 2 This original figure was developed based on data summarized in Kretzer 2011, Farooque 2018 and Raask 2020 5.3 US-Only Sensing and Navigation Previous research has explored the integration of ultrasound into pedicle screw insertion tools to provide real-time feedback on screw trajectory and detect potential breaches. Preliminary findings suggest that bone echoes can be interpreted reliably, and mapping these measurements onto preoperative scans could achieve real-time, self-contained navigation without external markers or expensive imaging modalities (Gueziri 2022). For instance, radial ultrasound techniques, adapted from vascular procedures, have been utilized to monitor the proximity of surgical tools to cortical bone, thereby preventing malposition (Manbachi 2015, 2022). However, these methods typically require the tool to be inserted into the pedicular channel before navigation begins, limiting their applicability to intraoperative adjustments rather than preoperative navigation scenarios. 5.4 State Estimation Techniques The problem of estimating the location of an object relative to its surroundings based on range measurements has been addressed in a number of contexts, including mobile robotics and undersea navigation. Suitable state-estimation algorithms, such as Extended Kalman Filters (EKFs), Unscented Kalman Filters (UKFs), and Particle Filters (PFs), have proven effective in processing ultrasound distance measurements to accurately localize devices and robotics in diverse applications (Julier 2020). These algorithms, originally developed for mobile robotics, could enable precise real-time tracking of the drill guideâs position, thereby reducing the dependence on external optical tracking systems and minimizing radiation exposure during surgery (Ullah 2020). Despite these promising advancements, integrating ultrasound into surgical navigation tools requires further evaluation to determine its feasibility in this context. Previous studies have demonstrated submillimetric accuracy in estimating bone surfaces using ultrasound-based localization methods, suggesting that these techniques may be viable for spinal navigation. State-estimation models, such as those used in related applications, have shown the ability to maintain accurate localization amidst intraoperative anatomical changes, including patient movement or shifts in spinal alignment (Gueziri 2022). However, the combined use of Poly-CMUT transducers, ultrasound-based rangefinding, and established signal processing algorithms has not yet been explored for pedicle screw navigation. This study aims to evaluate whether these existing technologies can be integrated effectively to support accurate, real-time localization in a spinal surgical setting (Omidvar 2024). 16 2 This original figure was developed based on data summarized in Kretzer 2011, Farooque 2018 and Raask 2020 Figure 1.11. Anatomic variation along the vertebral column. Pedicle diameter is shown along the vertical axis and icon width, and transverse angulation is marked on the figure and by icon angle.2 5.5 Accuracy Requirements for Screw Placement The accuracy required when placing pedicle screws varies depending on the spinal level, as the anatomy of the vertebrae differs throughout the spine (see Fig 1.11). The upper vertebrae, such as those in the thoracic and cervical regions, tend to be narrower (as low as about 4-5 mm in the thoracic region vs ~8 mm in the upper lumbar region), with angulation changing depending on the level (Raask 2020). Given the increased accuracy requirements encountered at higher vertebral levels, the majority of this thesis will focus on the lumbar spine as the initial testing ground for a new tool since the accuracy requirements for acceptable screw placement are less demanding in this region, which will make it easier to achieve acceptable performance in earlier stages of development.5.6 Summary In summary, existing literature demonstrates that the core technologies required for an ultrasound-augmented, self-localizing drill guide have been validated in related applications, supporting the feasibility of this approach. The proposed ultrasound-augmented, self-localizing tools offer a viable pathway toward accurate by integrating ultrasound-based rangefinding with established state-estimation techniques (MacLean 2023). Additionally, ultrasound-based localization methods 17 have achieved submillimetric accuracy in bone surface detection, while state-estimation algorithms have been successfully used to maintain tool tracking in dynamic surgical environments. Furthermore, Poly-CMUT transducers provide a compact, cost-effective alternative to conventional piezoelectric ultrasound systems, with demonstrated durability and signal quality suitable for surgical integration (Omidvar 2024). While prior studies have explored individual aspects of these technologies, no existing work has combined them into a unified system for pedicle screw navigation. This literature review establishes the rationale for integrating these techniques into a single platform and evaluating their performance in the proposed surgical context. 6 Knowledge Gaps and Research Questions The literature reviewed above demonstrates that key technologies exist to obtain and process ultrasound images of bone and to estimate object location based on range-finding techniques. However, critical gaps remain that must be addressed to develop an effective ultrasound-integrated, self-localizing drill guide for pedicle screw placement. While navigation systems improve accuracy, current methods rely on radiation-based imaging or external tracking systems, which introduce cost, complexity, and logistical constraints. Additionally, existing ultrasound applications in spinal surgery have been explored primarily for anatomical registration or breach detection, rather than for real-time localization during instrument placement. To bridge these gaps, this research will focus on refining ultrasound-based localization techniques, assessing the feasibility of Poly-CMUT integration, and developing robust signal processing methods. The following section outlines the key knowledge gaps that must be addressed to achieve these objectives. Based on the literature analysis presented above, we believe there are five key knowledge gaps that need to be addressed in order to validate the concept of ultrasound-augmented self-localizing drill guides to the point where a decision can be made as to whether or not to invest in building a full prototype incorporating the proposed poly-CMUT transducers: 1. Establishing clear accuracy objectives and performance metrics for our proposed ultrasound-augmented, self-localizing drill guides relative to existing methods in literature. 2. Determining most promising design configurations for ultrasound-augmented, self-localizing drill guides. 18 3. Validating performance of key components in the proposed design under more realistic use (application) conditions 4. Validating that bone surfaces visible in US images produced by poly-CMUT arrays can be identified with sufficient accuracy for the intended application 5. Demonstrating that an integrated emulation of the proposed ultrasound-augmented, self-localizing drill guide concept can produce sufficiently accurate localization estimates in anatomically realistic, simplified surgical scenarios 6.1 Establishing Accuracy Objectives and Related Performance Metrics While various pedicle screw placement methods existâincluding freehand, fluoroscopic, computer-assisted navigation, and robotic systemsâa systematic synthesis of their accuracies and clinical outcomes remains limited. While numerous individual studies have analyzed these methods, only a handful of meta-analyses have collated their findings, the most recent of which may not fully incorporate emerging robotic platforms (Joseph 2017). Furthermore, secondary outcomes such as revision rates, reoperation frequencies, blood loss, and radiation exposure have not been systematically analyzed across navigation approaches (Riewruja 2024). Given the increasing adoption of these technologies, a comprehensive meta-analysis is necessary to evaluate whether recent innovations translate into meaningful clinical benefits beyond accuracy alone. This work will build upon existing evidence to determine the most effective and safe navigation techniques (MacLean 2023). Research Objective: Comprehensive Meta-Analysis of Current and Emerging Pedicle Screw Navigation Methods. We will conduct an extensive meta-analysis to review and update the accuracies of existing pedicle screw placement methods and emerging systems, including the latest robotic platforms. Rationale: While various navigation techniques such as freehand, fluoroscopic, computer-assisted, and robotic systems exist, there is a lack of up-to-date, comprehensive evaluations that encompass the most recent advancements (Tian & Xu 2009). A large-scale meta-analysis will provide a thorough understanding of the current landscape, highlighting the strengths and limitations of each method (Riewruja 2024). Additionally, assessing secondary outcomes like revision rates, reoperation frequencies, blood loss, and radiation exposure will offer a holistic view 19 of each system's efficacy and safety (MacLean 2023). This information is crucial for identifying best practices and guiding the development of more effective navigation solutions (Joseph 2017). 6.2 Determining Most Promising Design Configurations for Ultrasound-Augmented Drill Guides Current navigation systems for pedicle screw placement predominantly rely on optical tracking or fluoroscopic methods (Moein 2021). Although ultrasound (US) has demonstrated potential as an adjunct modality, existing approaches often depend on external tracking systems and conventional US probes (Li 2023a). This dependency increases system complexity, costs, and radiation exposure, limiting the practicality and accessibility of ultrasound-based navigation in diverse clinical settings (MacLean 2023). Notably, traditional piezoelectric transducers used in ultrasound applications are bulky, fragile, and expensive to manufacture (Li 2023b). This bulks makes them difficult to integrate into compact surgical instruments like drill guides (Riewruja 2024). New perspectives are required for designing with the new benefits of poly-CMUTs (Moein 2021). There is currently no consensus on the optimal design configuration for ultrasound-augmented, self-localizing drill guides (MacLean 2023). Determining the most effective arrangement of components, such as the placement and orientation of ultrasound transducers, requires extensive computer simulations (Li 2023a). Without clearly defining the best design parameters, researchers cannot ensure the development of a highly accurate and functional drill guide. (Li 2023b). Research Objective: Optimization of Drill Guide Design through Computer Simulation The design approach uses large-scale computer simulations to determine the optimal design configuration for the proposed ultrasound-augmented drill guide. Rationale: The design of an effective drill guide requires meticulous consideration of various parameters, including the placement and orientation of ultrasound transducers, structural integrity, and ergonomic factors (Li 2023a). Large-scale computer simulations allow for the exploration of multiple design configurations in a virtual environment, enabling the identification of the most efficient and effective setup without the need for costly and time-consuming physical prototypes (Li 2023b). By optimizing the design through simulations, the research ensures that the final prototype will achieve the desired accuracy, functionality, and integration capabilities necessary for clinical application (Moein 2021). 20 6.3 Validating performance of key components in the proposed design under more realistic use (application) conditions The fundamental components required for the proposed ultrasound-augmented drill guideânamely, localization algorithms, Poly-CMUT transducers, and ultrasound interaction modelsâhave not been sufficiently validated in relevant settings. Specifically: A. Localization of Point Clouds: There is limited evidence on the effectiveness of localizing point clouds based on ultrasound distance measurements using 3D-printed spine phantoms in controlled environments. Establishing reliable localization in simplified 2D scenarios is a prerequisite for more complex 3D applications. Research Objective: 2D Localization of Point Clouds Using Ultrasound Measurements The evaluation will establish a point cloud based on ultrasound distance measurements, of a 3D-printed spine phantom in a water bath within a simplified 2D scenario, to establish preliminary real world localization accuracy. Figure 1.12. Data acquisition and point-cloud registration of a rangefinding drill guide adjacent spinal anatomy. B. Performance of Poly-CMUTs in Rangefinding: The functionality of Polymer-based Capacitive Micromachined Ultrasonic Transducers (Poly-CMUTs) for basic rangefinding applications within a water bath has not been thoroughly assessed. Understanding their performance under simulated surgical conditions is crucial for their integration into drill guides. Research Objective: Functional Assessment of Poly-CMUTs for Rangefinding Applications This stage evaluates the performance of Polymer-based Capacitive Micromachined Ultrasonic Transducers (Poly-CMUTs) for basic rangefinding applications in a water bath. 21 C. Computer Modeling of Ultrasound-Spine Interactions: There is a need to evaluate the feasibility of accurately modeling the physics of ultrasound interactions with spinal bone surfaces. Reliable models are essential for developing effective signal processing and localization algorithms. Research Objective: Feasibility of Computer Modeling Ultrasound-Spine Bone Interactions Lastly, feasibility testing will evaluate the accuracy of computer modeling the physics of ultrasound interaction with spinal bone surfaces based on real patient CT scans. Rationale: Validating the core components is fundamental to ensuring the proposed drill guide's effectiveness. Localizing point clouds in controlled environments establishes the basic functionality of the navigation system. Assessing Poly-CMUTs' performance verifies their suitability for integration into surgical tools, overcoming the limitations of traditional transducers. Additionally, accurate computer models of ultrasound-spine interactions are essential for developing reliable signal processing and localization algorithms. This comprehensive assessment ensures that each component operates as intended, laying a solid foundation for the drill guide's overall performance. 6.4 Validating that bone surfaces visible in US images produced by poly-CMUT arrays can be identified with sufficient accuracy for the intended application Numerous accurate and robust ultrasound-bone segmentation tools have been developed in a variety of applications such as in pelvic screw navigation and assessing developmental dysplasia of the hip (DDH) (Pandey 2018). However, despite several advances in ultrasound spine segmentation, there is a lack of real-time, accurate demonstration of ultrasound segmentation for direct localization. Further, existing algorithms have not been assessed in orientation and applications consistent with the proposed device. For the self-localizing concept to be feasible, we need to verify that we can use ultrasound to detect bone surfaces in anatomically realistic simulations and cadavers with sufficient accuracy to produce localization estimates within clinically acceptable bounds. Salehi (2017) highlights the necessity for advanced processing methods to enhance the accuracy of bone surface detection. Our approach focuses on evaluating and refining existing methods for accurately rangefinding the bone in the proposed surgical 22 context. Rahman, Hacihaliloglu (2022) evaluated ultrasound-based tracking in minimally invasive orthopedic procedures, highlighting the need for continuous localization to maintain accuracy despite intraoperative anatomical shifts. Their findings support the importance of real-time adaptation, which we aim to assess in the context of spinal navigation. Research Objective: Development and Validation of Ultrasound Signal Interpretation Algorithms While numerous studies have explored ultrasound-based segmentation and rangefinding using conventional B-mode imaging, existing methods lack the repeatable accuracy and real-time processing speed necessary for reliable self-localization in our intended surgical application. Prior research has not validated whether pCMUT transducers can generate sufficiently robust signals for this purpose, nor has it demonstrated that standard ultrasound transducers provide the spatial accuracy required for intraoperative localization in human cadavers. This thesis aims to address these gaps by developing and validating ultrasound signal interpretation methods that ensure precise, near real-time bone surface mapping across different transducer technologies and imaging contexts. Rationale: Reliable interpretation of ultrasound signals is necessary for accurate navigation, but it remains unclear whether existing bone localization methods will perform adequately in our proposed application. High-echo signals and complex anatomical configurations can pose challenges in distinguishing bone surfaces from surrounding tissues. We hypothesize that existing segmentation and rangefinding algorithms can be adapted to process ultrasound data for our intended use case, but their performance for the proposed application remains unvalidated. This study evaluates whether these algorithms can generate accurate and repeatable localization estimates in a simulated surgical setting. 6.5 Demonstrating that an integrated emulation of the proposed ultrasound-augmented, self-localizing drill guide concept can produce sufficiently accurate localization estimates in anatomically realistic, simplified surgical scenarios Since ultrasound-augmented, self-localizing drill guides (UASLDGs) represent a new concept, they have not yet been evaluated in a realistic use context. Typically, new design concepts undergo initial validation in simplified water-bath setups before being tested in increasingly realistic 23 emulations of the intended surgical environment. While previous localization studies have explored non-spinal applications or alternative ultrasound-based implementations, they do not directly address the challenges of real-time localization for pedicle screw placement. Existing spinal ultrasound research has primarily focused on anatomical registration or breach detection, rather than direct tool localization. To bridge this gap, validation using 3D spine models and traditional ultrasound probes in water baths is necessary to establish the feasibility and accuracy of the proposed device before progressing to more anatomically relevant experimental models. Research Objective: Prototype Assessment and Validation Using In Vitro Models The final section of works develops and validates emulated prototypes of the proposed drill guide in a water bath using 3D spine models, 3D localization, and traditional ultrasound probes. Rationale: Testing prototypes in realistic in vitro environments is essential to demonstrate the toolâs accuracy, reliability, and feasibility before clinical implementation. By using 3D spine models and traditional ultrasound probes in a water bath, the research can simulate surgical conditions and evaluate the performance of the ultrasound-augmented drill guide. This step is crucial for identifying potential issues, refining the design, and ensuring that the prototype meets the stringent accuracy and safety requirements necessary for clinical use. 7 Specific Research Questions and Thesis Organization This thesis addresses the identified knowledge gaps and encompasses the objectives through four guiding research questions. These questions guide the investigation and development of the proposed ultrasound-augmented, self-localizing drill guide, systematically exploring and validating each aspect of the toolâs functionality, design, and clinical applicability. 1. Benchmarking Navigation Systems (Chapter 2): How do current and emerging pedicle screw navigation methods compare in terms of accuracy and surgical outcomes, and does recent data support opportunities for ultrasound-integrated tools to address ongoing limitations? 2. Tool Design and Simulation (Chapter 3): How can an ultrasound-augmented, self-localizing drill guide be designed and validated through simulation to achieve accurate spatial information during pedicle screw placement? 24 3. Experimental Evaluation of Key System Components (Chapter 4): How can key system components (poly-CMUT rangefinding, ultrasound-based localization, and bone-surface reflections) be validated for integration into a self-localizing surgical tool? 4. Ultrasound Image and Signal Processing (Chapter 5): What methodologies best interpret raw ultrasound signals into reliable bone-surface measurements, and how can these be integrated with preoperative imaging to ensure robust, dynamic localization? 5. Prototype Evaluation (Chapter 6): Can an emulated prototype device and algorithm achieve clinically meaningful 3D localization accuracy in an in vitro model, thereby demonstrating feasibility? By addressing these specific research questions, this thesis seeks to develop a novel ultrasound-augmented, self-localizing drill guide that offers a low-cost, radiation-free, and highly accurate solution for pedicle screw placement. Evaluating and optimizing current navigation methods, refining the drill guideâs design through simulations, advancing signal processing and localization algorithms, and validating the prototype in realistic models collectively contribute to a navigation strategy that meets clinical needs. The proposed solution is designed to adapt to intraoperative conditions, reduce surgical complications, and improve patient care, ultimately enhancing surgical outcomes in spinal fusion procedures.25 1The bulk of this chapter is based substantially on the work published as: MacLean LJ, Theodore N. Comparison of accuracy, revision, and perioperative outcomes in robot-assisted spine surgeries: systematic review and meta-analysis. J Neurosurg: Spine. July 2024. Chapter 2 Benchmarking Navigation in Spine Surgery: A Systematic Evaluation of Emerging Clinical Technologies 1 Introduction1 Pedicle screw placement is a critical and challenging task in spine fusion surgeries, where precision is paramount to avoid complications such as nerve damage, vascular injury, and mechanical failure (Mobbs 2015). Traditional methods for screw placement, including freehand techniques and fluoroscopic guidance, rely heavily on surgeon expertise and carry significant risks of malposition (Mobbs 2015). Innovations in navigation systems, such as computed tomography (CT)-guided techniques, have improved accuracy but remain limited by their dependence on radiation and high costs (Perdomo-Pantoja 2019). Robotic-assisted systems represent a significant leap forward in addressing these limitations. By leveraging precision mechanics and advanced imaging integration, these systems aim to enhance pedicle screw placement accuracy and reduce intraoperative complications (D'Souza 2019). Since their introduction in 2004, robotic platforms have rapidly evolved, with several systems now approved for clinical use, including the Mazor X, ExcelsiusGPS, ROSA, and Cirq (Condon 2021). Each platform integrates unique technical capabilities and workflows, presenting surgeons with diverse options for enhancing surgical outcomes (Behm 2022). Despite the growing adoption of robotic systems, critical knowledge gaps remain. Comparative studies of robotic platforms and other navigation methods often suffer from inconsistent reporting metrics, heterogeneous study designs, and limited assessment of broader perioperative outcomes such as radiation exposure, operative time, and blood loss (Perdomo-Pantoja 2019). Furthermore, while robots have been shown to improve screw placement accuracy relative to traditional techniques, their broader impact on reducing revision surgeries and improving patient safety has not been fully explored (Meng 2015). 26 This chapter aims to systematically evaluate the current state of robotic navigation for pedicle screw placement. By conducting a meta-analysis of robotic platforms, this study benchmarks their performance against traditional techniques, including freehand, fluoroscopic, and CT-based navigation methods. The primary outcomes include accuracy, intraoperative revision rates, and reoperation rates, with secondary measures encompassing operative time, blood loss, and radiation exposure. This comprehensive analysis highlights the strengths and limitations of existing systems, providing a critical foundation for identifying the unmet needs and opportunities for innovation in spinal navigation. Ultimately, this review contextualizes the emerging landscape of robotic-assisted spine surgery within the broader objectives of this thesis. By benchmarking current robotic and traditional navigation methods, this chapter identifies and compares levels of performance of existing systems, which can be used to set performance goals for our system. The ultimate goals is for advancements that balance accuracy, cost, safety, and accessibilityâgaps that the ultrasound-augmented, self-localizing drill guide proposed in subsequent chapters seeks to address. 2 Methods 2.1 Literature Search We conducted a systematic review of current literature using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines to compare the relative performance of current pedicle screw guidance robots (Page 2021). We selected search terms based on an initial review of the keywords and Medical Subject Heading (MeSH) terms of 14 manually selected articles. Based on these search terms, we queried the English-language peer-reviewed literature published as of April 28, 2022, using PubMed, Embase, Cochrane Library, Web of Science, and Scopus. Full search terms are listed in Appendix B. The review was not registered. The aim was to identify studies that could inform the development of safer, more accessible, and accurate navigational technologies for pedicle screw placement. Titles and abstracts of all articles were independently screened by two reviewers (MB, KJ) using the Covidence platform, followed by full-text review of eligible articles. Disagreements were resolved by a third author (AH). Inclusion criteria included full-text peer-reviewed articles, written in English, that examined robotic-assisted pedicle screw insertion for thoracolumbar 27 spine surgery in humans. Articles were excluded if they: 1) focused only on the cervical spine (the smaller size of cervical pedicles renders accuracy challenging and precludes comparison to thoracolumbar studies), 2) described an earlier generation of a robotic platform, 3) did not specify the robotic platform, 4) lacked outcome metrics, or 5) described a robotic platform that lacked FDA approval. The exclusion of earlier robot generations most notably impacts the Mazor system. We only consider the Mazor X and not the older Mazor SpineAssist or Mazor Renaissance systems. 2.2 Data Collection Articles satisfying the inclusion and exclusion criteria underwent data extraction by 3 authors (MB, KJ, AH) using Microsoft Excel (Microsoft Corporation). The robot model, publication year, country of origin, number of institutions, study design, demographic features of patients, and number of screws were recorded. Study designs were categorized as either single-center retrospective (SCR), single-center prospective (SCP), or multi-center retrospective (MCR). The surgical approaches of each study were noted; these included anterior lumbar interbody fusion (ALIF), lateral lumbar interbody fusion (LLIF), oblique lumbar interbody fusion (OLIF), posterior lumbar interbody fusion (PLIF) and transforaminal lumbar interbody fusion (TLIF). Outcome data included the Gertzbein-Robbins classification of screws in the study, which measures pedicle screw placement accuracy on a 5-point scale from A through E, with Grade A screws being most accurate and Grade E screws being least accurate. Other outcome data included operative time, intraoperative screw revisions, reoperations, blood loss, and radiation exposure. The number of screws in each grade, the number of revisions, and the number of reoperations were converted into rates based on both a per-screw and per-patient basis. In accordance with prior literature, group A and B screws were considered accurate, and Grades C, D, and E were considered inaccurate (Liu 2022). Several different metrics are commonly reported to quantify radiation exposure, and it can be challenging to convert or compare these varied measures. Therefore, we only analyzed measures of absorbed dose and equivalent dose. As is appropriate for fluoroscopy and CT, we used a 1:1 conversion from equivalent dose to absorbed dose. Radiation exposure reported in milliSievert (mSv) was assumed to measure the equivalent dose unless it was explicitly stated that the effective dose was being reported. The extracted data serve to highlight both the strengths and 28 limitations of robotic systems, providing insights into potential areas for innovation, such as the integration of ultrasound for radiation-free navigation. 2.3 Statistical Analysis All statistical analysis was performed using MATLAB R2022a Statistics and Machine Learning Toolbox (MathWorks). Subgroup analysis was based on the robotic platforms and the year of publication. Summary statistics, including the weighted mean and 95% confidence interval, were calculated using a random effects meta-analysis to account for inter-study variability. For proportion measurements (e.g. accuracy), a logit transformation was first applied to stabilize the variances. If a proportion was reported at 0% or 100%, then a continuity correction was applied for further calculations. Proportions follow a binomial distribution, and this transformation approximated a Gaussian distribution which improves the validity of statistical tests that assume normality. Next, the DerSimonian-Laird estimator is calculated which represents the inter-study variation that is not due to chance. This estimator is then used to adjust the weights of the studies when calculating the pooled metrics. The overall pooled (OP) rates for the outcome proportion metrics were expressed as a rate (p) with their effect size captured in figures based on the corresponding logit-event rate: ððððð¡(ð) = ln : ð1 â ð< Once the pooled metric and confidence intervals have been computed, a 2-sided t-test was used to compare the sub-groups. For the proportion data, this test is performed on the data after the logit transformation and before converting back. A p-value < 0.05 was considered statistically significant. To account for multiple comparisons, a Bonferroni correction was applied by dividing the significance threshold by the number of comparisons performed for each outcome metric, and thereby reduce Type I errors. Two prior meta-analyses were selected to compare robotic systemsâ performance with other pedicle screw insertion techniques. Prior work from our group, covering 51,161 screws, has considered the performance of FH, FA, and CTNav methods against accuracy, revision, and reoperation rates (Perdomo-Pantoja 2019). Similarly, an article from Meng, covering 9,019 screws, pooled metrics on blood loss and operative time for FA and CTNav. An investigation by La Rocca, covering 952 screws, compared radiation exposure for FA and CTNav techniques 29 (Meng 2015; La Rocca 2022). These three articles provide the largest available analyses of the outcome metrics for the comparator techniques of FH, FA, and CTNav. Scatterplots and OP rates were selected over traditional forest plots for three principal reasons: 1) they provide a simpler means of comparing four groups (the robotic platforms) along with three other comparators (FH, FA, and CTNav); 2) OP rates better represent the performance difference between groups when the rates are near 100%; and 3) this representation is consistent with prior literature on pedicle screw navigation (Perdomo-Pantoja 2019). Finally, we evaluated the presence of publication bias by applying a Duval and Tweedie trim and fill method to a funnel plot of the accuracy rate (Duval and Tweedie 2000). This approach allows us to estimate the number of articles potentially missing due to publication bias and the adjusted pedicle screw accuracy rate (Duval and Tweedie 2000). This benchmarking provides a critical foundation for assessing the limitations of existing systems and justifying the need for innovative, cost-effective navigation solutions like those proposed later in this thesis. 30 3 Results Figure 2.1. PRISMA diagram of the literature screening workflow. We identified 3324 unique studies, of which 212 underwent full-text review and 46 were selected for data extraction (Figure 2.1). 31 Table 2.1. Descriptive information on the selected studies. (*) indicates that the StealthStation was not used with the Mazor X robot for placing the screws. Reference Robot Study Design Patients (n) Mean Age (Years) Screws (n) Surgical Approach Alsalmi, 2021 ROSA SCR 32 NS 136 TLIF Avrumova, 2021 Mazor X SCR 65 60.3 311 PLIF Benech, 2020 ExcelsiusGPS SCR 54 49.8 292 PLIF Bydon, 2021 Mazor X MCR 77 55.7 402 6.5% ALIF, 1.3% OLIF, 23% PLIF, 1.3% TLIF Chenin, 2017 ROSA SCR 25 NS 110 TLIF Chesney, 2022 Cirq SCR 84 58.8 714 PLIF Dalton,2021 ExcelsiusGPS SCR 10 62 - PLIF De Biase, 2021 Mazor X* SCR 52 56 228 TLIF Elswick, 2020 ExcelsiusGPS SCR 28 61.5 127 PLIF Fayed, 2020 ExcelsiusGPS SCR 20 62.8 103 5% ALIF, 15% LLIF, 80% TLIF Fayed, 2022 ExcelsiusGPS SCR 64 63.9 346 4.7% ALIF, 95.3% TLIF Gonzalez, 2021 Mazor X SCR 40 14.5 314 PLIF Huntsman, 2020 ExcelsiusGPS SCR 100 63 582 16% ALIF, 55% LLIF, 29% PLIF Huntsman, 2020 ExcelsiusGPS SCR 55 67 342 LLIF Jain, 2019 ExcelsiusGPS SCR 98 59.3 636 29% ALIF, 12% LLIF, 59% TLIF Jiang, 2020 ExcelsiusGPS SCR 28 61.9 113 PLIF Jiang, 2020 ExcelsiusGPS SCR 47 61.1 254 - Karamian, 2021 ExcelsiusGPS SCR 85 65 - - Katsevman, 2021 Mazor X* SCR 17 61.4 143 PLIF Khan, 2019 Mazor X SCR 20 60.3 75 - Khan, 2019 Mazor X SCR 50 59.3 190 PLIF Khan, 2020 Mazor X SCR 22 65.2 92 PLIF Kisinde, 2021 Mazor X SCP 33 51 - - Laudato, 2018 Mazor X SCR 11 65 64 PLIF Lee, 2021 Mazor X* SCR 35 - - 3.2% ALIF, 84.4% OLIF, 12.5% TLIF Lee, 2021 Mazor X* MCR 320 - 1632 - Lee, 2021 Mazor X* SCP 51 55.4 - 23% OLIF, 77% TLIF Lee, 2021 Mazor X* SCP 43 60.5 776 5.8% OLIF, 94.2% TLIF Lee, 2022 Mazor X MCR 310 NS 1051 PLIF Lee, 2022 Mazor X MCR 722 NS 5005 1% ALIF, 3% LLIF, 6% OLIF, 73% PLIF, 17% TLIF Lee, 2021 Mazor X MCR 372 NS 2800 - Lin, 2022 ROSA SCR 224 65.4 364 TLIF Linden, 2021 Mazor X SCR 10 13.7 62 PLIF Liounakos, 2021 Mazor X MCR 799 57.6 4838 - Lonjon, 2016 ROSA SCP 20 63 40 PLIF Mao, 2020 Mazor X SCR 39 59.5 318 PLIF Mao, 2021 Mazor X SCR 84 60.9 306 PLIF Morse, 2021 Mazor X SCR 19 14.6 194 PLIF PojskiÄ, 2021 Cirq SCP 12 67.4 70 - Shafi, 2022 ExcelsiusGPS SCR 92 59.5 403 TLIF Siddiqui, 2019 ExcelsiusGPS SCR 120 64.4 665 - Vardiman, 2020 ExcelsiusGPS SCR 101 64.8 600 PLIF Vardiman, 2020 ExcelsiusGPS SCR 56 64 356 - Vasan, 2022 ROSA SCP 7 66.7 - TLIF Ver, 2020 Mazor X SCR 55 54.5 - LLIF Wang, 2021 ExcelsiusGPS SCR 62 61.7 - TLIF 32 3.1 Study Characteristics A total of 4670 patients underwent robotic-guided insertion of 25,054 pedicle screws using 4 different robotic systems, including the Medtronic Mazor X (n=23), Globus ExcelsiusGPS (n=16), Zimmer Biomet ROSA (n=5), and the Brainlab Cirq (n=2) (Table 1). Although some articles distinguished the Mazor X from the Mazor X stealth edition, we have grouped them for the purposes of this analysis. Studies that did not incorporate the Medtronic StealthStation are highlighted in Table 1 and the Figures. The mean number of screws per patient was 6.8 and the mean patient age was 59.1 years. The mean number of patients per study was 102; the median was 52. Of the studies that reported the surgical approach for interbody fusions, 56.0% were PLIF, 31.4% were TLIF, 7.1% were LLIF, 3.2% were OLIF, and 2.3% were ALIF. Figure 2.2. Distribution of (A) the number of patients, (B) the number of screws and (C) the number of screws per patient in the selected studies. (D) Timeline of the median number of patients per study for each robot. 33 The number of patients per study and the number of screws reported per study/per patient show clear right-skewed distributions (Figure 2A-C). There are clear outliers based on certain Mazor studies that included hundreds of patients and thousands of screws. The publication rate of articles relating to pedicle screw accuracy with current-generation robots has notably increased in recent years (Table 1). Most published articles described the Mazor X (50.0%) and the ExcelsiusGPS (34.8%). The Mazor X and the ExcelsiusGPS generally reported the largest study cohorts, with the sample size of Mazor X trials increasing in recent years (Figure 2D). 3.2 Accuracy Figure 2.3. Logit-event rate of accurately placing pedicle screws using 4 different robotic platforms. The relative accuracy rate of each robot is plotted as logit-event rates in Figure 3, with the number of screws in each study represented by the size of the corresponding circle. The hard red lines represent the predicted population accuracy rate for each robot; the dashed red lines represent the 95% CI using the DerSimonian-Laird random-effects model. The overall weighted accuracy rates for each robot were: ExcelsiusGPS, 98.0% (95% CI: 97.2% to 98.6%); ROSA, 98.0% (95% CI: 94.8% to 99.2%); Mazor, 98.2% (95% CI: 95.0% to 99.4%); 34 and Cirq, 94.2% (95% CI: 85.7% to 99.8%). All robotic systems had high accuracy rates, and none were statistically significantly different. The accuracy rate of the ExcelsiusGPS was statistically significantly higher than that of FH, FA and CTNav (p < 0.001 for all three). The accuracy rates of the Mazor and ROSA were also higher than that of FA (p = 0.0026 for both). The Mazor and the ROSA accuracies did not reach statistical significance compared to FH (after applying a Bonferroni correction for multiple comparisons) or CTNav. 3.3 Intraoperative Revision and Reoperation Rate Figure 2.4. Logit-event rates of (A) intraoperative revision and (B) reoperation after pedicle screw placement using different robotic platforms. The logit-event rates for intraoperative pedicle screw revisions are shown in Figure 4A. Because some studies reported a 0% revision rate, they cannot be included in the logit-event plot, causing the reported distribution summary metrics to appear lower than the studies that can be fully represented. The OP revision rates for each robot were: Cirq, 0.55% (95% CI: 0.01% to 17.44%); ROSA, 0.91% (95% CI: 0.13% to 6.17%); Mazor, 0.98% (95% CI: 0.61% to 1.56%); and ExcelsiusGPS, 1.08% (95% CI: 0.53% to 2.19%). Notably, most of the robots performed comparably; there were no statistically significant differences in any of the direct comparisons. Reoperation rates are shown in Figure 4B. No study describing the ROSA reported reoperation rates, so only the other 3 robots were considered. Because some studies reported 0% reoperation rates (specifically, those describing the ExcelsiusGPS), distribution summary metrics may appear lower than the marked results. The OP reoperation rates for each robot were: Cirq, 0.28% (95% 35 CI: 0.07% to 1.11%); ExcelsiusGPS, 0.32% (95% CI: 0.16% to 0.65%); and Mazor, 0.76% (95% CI: 0.54% to 1.07%). After Bonferroni correction, all three robots had lower reoperation rates than FA methods (p < 0.002 for all three). Further, the ExcelsiusGPS had significantly less reoperations than FH and CTNav approaches (p < 0.001 for both). 3.4 Operative Time Figure 2.5. Comparison of 4 different robotic platforms according to their total operative time. Figure 2.5 shows the operative time for each robotic platform. The OP results for operative time were: ExcelsiusGPS, 177.7 minutes (95% CI: 132.8min to 222.6min); Cirq, 208.4 minutes (95% CI: 77.3min to 339.4min); Mazor, 219.2 minutes (95% CI: 179.6min to 258.9min); and ROSA, 198.4 minutes (95% CI: 161.2min to 235.6min). All 4 robots performed comparably with no significant differences. The Mazor was significantly slower than FA methods (p = 0.0023). The Mazor was also slower than CTNav methods (p = 0.0293) and the ROSA slower than FA methods (p = 0.0270) but not to significant degrees after Bonferroni correction. 36 3.5 Blood Loss and Radiation Dose Figure 2.6. Secondary safety metrics. (A) Comparison of the intraoperative blood loss of a thoracolumbar fusion using 3 different pedicle screw guidance robots. (B) Comparison of the effective radiation exposure during thoracolumbar fusion using 3 different pedicle screw guidance robots. Figure 2.6A shows the blood loss reported for 3 robots and the OP results were: ExcelsiusGPS, 65.8 mL (95% CI: 35.2mL to 96.5mL); Mazor, 113.0 mL (95% CI: 49.4mL to 176.6mL); and ROSA, 313.7 mL (95% CI: 0mL to 733.3mL). Both the ExcelsiusGPS and the Mazor were both found to have significantly less blood loss compared with the ROSA, FA methods and CTNav methods (all with p-values < 0.0001). Figure 2.6B shows the absorbed radiation doses reported for 3 of the robots. Seven studies directly reported radiation in milliGray (mGy) as the absorbed dose. The single report on the Cirq robot reported in mSv, which was assumed to be an equivalent dose for conversion to absorbed dose. Other studies addressing radiation reported as alternative metrics such as radiation time, dose length product, and dose area product were omitted from the analysis. The OP results for absorbed radiation dose associated with the 3 robots were: Cirq, 16.8mGy (95% CI: 4.1mL to 29.3mL); ExcelsiusGPS, 44.8mGy (95% CI: 0mL to 112.7mL); and Mazor, 52.9mGy (CI: 25.0mGy to 87.0mGy). The Cirq study reported significantly less radiation than the ExcelsiusGPS study (p=0.004). Further, both the Cirq and the Mazor had significantly more radiation than FA methods (p=0.0091 and p<0.0001 respectively). ExcelsiusGPS Mazor ROSARobotic Platform020040060080010001200Blood Loss [ml]Study ResultWeighted MeanCTNavFACirq ExcelsiusGPS MazorRobotic Platform0102030405060708090100Radiation Dose [mGy]Study ResultWeighted MeanCTNavFA37 3.6 Publication Bias Figure 2.7. Funnel plot of standard error over the overall pooled accuracy rates. After employing the Duval and Tweedie Trim and Fill method, the funnel plot suggested little to no publication bias (Figure 2.7). The process suggests that there could be 2 studies missing with higher accuracy rates that would cause the point estimate of accuracy to move from 98.2% to 98.6%. Notably, 5 studies reported perfect accuracy rates (i.e., all pedicle screw placements grade A or grade B), so they have been indicated on the rightmost side of the graph to highlight that their logit-event values approach infinity. 38 4 Discussion This systematic review and meta-analysis evaluated 46 studies involving 25,054 pedicle screws placed under robotic guidance, comparing four modern robotic platforms: Mazor X (Medtronic), ExcelsiusGPS (Globus Medical), ROSA (Zimmer Biomet), and Cirq (Brainlab). By synthesizing findings on accuracy, revision rates, reoperation rates, and secondary outcomes such as operative time, blood loss, and radiation exposure, this work provides a comprehensive benchmark of current robotic systems. The results reveal that these systems perform comparably across many metrics, highlighting their potential to enhance pedicle screw placement accuracy while also identifying critical areas for further development. Importantly, these insights serve as a foundation for evaluating unmet needs in navigation technologies and the potential impact of novel systems like the ultrasound-augmented drill guide proposed in this thesis. 4.1 Comparing Performance Metrics Robotic systems generally performed similarly across primary outcomes, including accuracy, intraoperative revision rates, and reoperation rates. However, confounding factors such as surgeon experience and familiarity with specific systems may influence these results (Siddiqui 2019). For instance, Cirq, which relies on manual positioning by the surgeon, differs operationally from other platforms, potentially contributing to variations in performance (Pojskic 2021). Despite these nuances, robotic platforms demonstrated superior accuracy compared to traditional methods such as freehand (FH), fluoroscopic assistance (FA), and computed tomography navigation (CTNav), albeit not always reaching statistical significance. Mazor X, for example, achieved significantly higher accuracy than FH and CTNav, while ExcelsiusGPS and ROSA also demonstrated superiority over FA methods. The lower reoperation rates observed with robotic systems suggest potential long-term benefits, though the higher intraoperative revision rates raise questions about how immediate corrections might mitigate future complications (Verhoste 2020; Demange and Fregni 2011). These findings underscore the importance of evaluating performance beyond primary metrics, considering the broader implications of robotic guidance. Secondary outcomes further illustrate the strengths and limitations of these platforms. ExcelsiusGPS and Mazor X were associated with significantly reduced blood loss compared to ROSA, likely reflecting differences in workflow and tool integration. However, operative times 39 for robotic-assisted procedures tended to be longer than traditional methods, possibly due to the learning curve and operational complexity of these systems (Wang 2021). Such findings highlight the need for designs that minimize disruption to surgical workflows, a priority for future innovations such as the proposed ultrasound-guided tool. Additionally, variations in radiation exposure among platforms underscore the need for consistent metric reporting and optimization of imaging protocols (De Biase 2021; Elswick 2020; Konieczny 2020; Mellor 2014). Addressing these secondary challenges is critical for advancing navigation technologies that prioritize safety and efficiency. 4.2 Publication Bias The analysis of publication bias suggests minimal underreporting of accuracy rates, though a slight skew toward higher performance metrics was identified. This bias could reflect increased surgeon familiarity with robotic platforms or a reluctance to report suboptimal outcomes. Most studies involved small groups of experienced surgeons, raising questions about the generalizability of findings to broader clinical settings. Systematic bias and selection effects highlight the need for robust, multicenter evaluations to ensure reliable comparisons across platforms. 4.3 Implications for Navigation Technologies This meta-analysis underscores the need for advancements in surgical navigation technologies to address existing gaps in performance, usability, and cost. Robotic systems, while effective, remain constrained by high costs, operational complexity, and dependence on ionizing radiation. These limitations present opportunities for novel approaches, such as the ultrasound-augmented drill guide proposed in this thesis. By eliminating reliance on radiation, enhancing real-time feedback, and offering a streamlined workflow, such tools could address critical shortcomings in current systems. The findings from this review provide a benchmark against which the efficacy and impact of emerging technologies can be evaluated. Moreover, the observed variability in performance metrics across robotic platforms underscores the importance of tailoring innovations to specific clinical needs. For instance, minimizing radiation exposure is particularly relevant in pediatric and minimally invasive contexts, where the risks are magnified (Campbell 2021). Similarly, optimizing accuracy in challenging anatomic regions, such as the cervical spine, remains a priority for future developments (Rahmathulla 40 2014). The insights gained here highlight the value of focusing on user-centered design principles and cost-effective solutions to broaden access to advanced navigation technologies. 4.4 Limitations The findings of this review are subject to several limitations. Heterogeneity in study designs, surgical approaches, and reported metrics introduces variability in the results, potentially confounding comparisons across platforms. The reliance on retrospective data and the absence of head-to-head comparisons limit the ability to isolate the effects of robotic guidance from other factors, such as surgeon proficiency and institutional workflows (Demange 2011). Additionally, the Cirq system was included despite limited data, providing a comprehensive review but necessitating cautious interpretation of its performance (Pojskic 2021). Future studies should prioritize prospective designs and standardized reporting to enhance the reliability and applicability of findings (Ahmed 2011). By contextualizing these limitations and opportunities, this discussion aligns the meta-analysis with the broader objectives of this thesis. It establishes a framework for evaluating innovations in navigation technologies, paving the way for the development and validation of tools that address unmet clinical needs. 5 Conclusion This meta-analysis demonstrates that current robotic systems for pedicle screw placement offer substantial improvements in accuracy and safety compared to traditional methods, while also revealing areas where further innovation is needed. By synthesizing findings from 46 studies and over 25,000 screws placed under robotic guidance, this work establishes a benchmark for evaluating the state-of-the-art in navigation technologies. The comparable performance of platforms like Mazor X, ExcelsiusGPS, ROSA, and Cirq highlights their efficacy but also underscores the lack of differentiation across systems in terms of outcomes such as revision rates, operative times, and blood loss. From a thesis perspective, these results contextualize the need for advancements that address specific limitations in existing robotic platforms. The finding that intraoperative revision rates remain high, even with robotic assistance, suggests opportunities for technologies that enhance real-time feedback and localization accuracy. Similarly, the reliance on radiation-intensive 41 imaging modalities highlights the potential for alternative approaches, such as ultrasound-based navigation, to reduce patient and operator exposure. The insights gained from this analysis directly inform the design and development of the ultrasound-augmented drill guide proposed in this thesis. By identifying key performance gaps in current systems, this chapter sets the stage for subsequent chapters, which will focus on tool design, optimization of localization algorithms, and the validation of the proposed system through in vitro models. Together, these efforts aim to advance surgical navigation technologies and contribute to safer, more efficient outcomes in spinal surgery. 42 1The bulk of this chapter is based substantially on the work published as: MacLean LJ, Street J and Hodgson AJ. Design of an ultrasound emitting drill guide for freehand pedicle screw navigation. Intl J Med Robot & Comp Asst Surg. Aug 2023. Chapter 3 Tool Design through High-Powered Computing 1 Introduction and Motivation1 Prior to building an ultrasound-augmented drill guide for evaluation, we need to determine whether the proposed approach would be feasible to use for the intended surgical goal. Therefore, the purpose of this study is to assess in simulation whether we can estimate the position of an ultrasound-augmented drill guide with sufficient accuracy and robustness to be used for the intended purpose and, if so, what the optimal geometric and algorithmic parameters would be. We specifically assess the following research questions: 1. Can we identify a feasible configuration for a self-localizing drill guide that, in combination with a position-estimation algorithm, can produce an accurate position estimate for the guide relative to simulated patient anatomy in a typical target position? 2. Can we identify a range of geometric configurations for the self-localizing drill guide that are predicted to generate satisfactory results? 3. Can we identify an optimal design for the self-localizing drill guide that we could use to guide construction of an initial physical prototype? To address these questions, we present a computational simulation of the US data collection and associated localization processes for various designs in order to assess the viability and develop a design for the proposed tool. Finally, we use the simulation environment to validate the performance and robustness of the proposed tool in various clinically relevant positions. First, the system requirements and the associated design space are presented. The simulation methodology is then described, and the results are reported. Finally, the chapter concludes by summarizing the key results and recommendations for prototyping a physical device.43 2 System Requirements Through consultations with spine surgeons (including co-author JS), we have identified eight criteria (see Table 1) that the proposed tool design must satisfy. The initial intended application is inserting screws in the lumbar and distal thoracic spine (L5->T10) where the pedicle channel is relatively large (Nagano 2024). The device should accommodate typical anatomic variations within these vertebral levels. Table 3.1. Design requirements for an ultrasound-augmented self-localizing drill guide for pedicle screw insertion in the lumbar spine. aCapture Range is the error in the initial guess of the position of the tool such that the state estimation will still converge with acceptable accuracy. bLocalization Range is the distance away from ideal placement at the pedicle that the state estimation remains functional.Quality Threshold Accuracy < 2 mm Capture Rangea > 15 mm Localization Rangeb > 30 mm Cannula Radius < 5 mm Spinal Levels L1 â L5 Anatomic Variation All normal-range anatomy Radiation Free of Ionizing Radiation Usability Freehand 44 2Since the final estimated position will differ from the true position in a six-dimensional space, we define the mean equivalent error as the root of the mean weighted sum of the six squared component errors, where the weighting is 1.0 on the translational errors and a value of 20.2 mm on the rotational errors (expressed in radians), where 20.2 mm is selected as a reference length that corresponds to the typical distance from the tip of the tool to the midpoint of the pedicle channel (Nagano 2024). 2.1 Position Estimation Accuracy The key system requirement is to accurately estimate the drill guide position when it is aligned with the pedicle channel near the bone. The accuracy required in drilling tasks varies with the vertebral level and the diameter of the pedicle screw used (Nagano 2024). However, a Gertzbein-Robbins grade B screw, where there is less than 2mm of cortical breach, is typically considered accurate (Perdomo-Pantajo 2019). Given that success requires targeting the narrowest point of the pedicle channel and that accuracy affected by both translational and rotational errors of the drill guide, we propose to compute a combined error measure defined by:2 ð = >Îð¥% + Îð¦% + Îð§% + ð&'(% Cð&% + ð)% + ð*%D (1) where ε represents a weighted sum of the translational errors at the tip of the drill guide and the rotations of the guide. The translational error components are denoted by Îx, Îy and Îz and the angular errors by θp for pitch, θy for yaw and θr for roll. We scale the rotational errors by a distance of 20.2 mm, which approximates the typical length of a lumbar pedicle, lped (Nagano et. al. 2024). Although the roll angle does not directly affect the screw position, it is included in the error term because of its effect on subsequent localizations due to changes in direction of the ultrasound distance measurements. Based on the final localization error, we computed the âconvergence rateâ, which we defined as the fraction of sub-millimetric localizations in a sequence of simulated position estimations. 45 2.2 Localization and Capture Ranges To prevent incorrectly identifying positions, the system should accurately estimate the position when provided with an initial position estimate within a reasonable distance of the true position. We refer to the difference between the initial position estimate and the true position as the initial error. We propose that the âcapture rangeâ (the minimum initial error within which the system remain accurate) be set to 15 mm as we believe that a surgeon could be expected to identify key landmarks on a vertebra within this range (Jing 2019). In addition, the surgeon may move the tool a modest distance away from the target position in the process of aligning the tool, and the system should be able to generate accurate position measurements throughout. We propose that this âlocalization rangeâ be up to 30 mm.2.3 Cannula Radius The drill guide radius should be as small as possible to minimize disruption of soft tissues. By examining the simulated drill guide near the pedicle, we determined that a practical upper limit for the radius of a self-localizing guide appropriate for percutaneous interventions would be approximately 5 mm. 3 Design Space A schematic and rendering of the proposed US-augmented drill guide is shown in Figure 1. We assume that the guide consists of an outer tube surrounding an inner opening for passage of a surgical drill. US transducer elements will be inlaid into the outer face of the tube and will generate ultrasound signals that will be read by the transducers after reflecting off bone surfaces and other tissue interfaces. At this stage of development, we will not concern ourselves with the details of how the ultrasound signals are generated and received. Instead, we will presume that each element functions essentially as a sonar range-finder, reporting the distance to the nearest bone surface. The intensity of the return echo signal decreases with the distance and angulation of the reflecting surface. Our model assumes that surfaces at 45° to the transducer elementâs surface normal or more than 50mm away do not return a signal. This system is characterized by design parameters outlined in the following section which describing the guide geometry, the range-finder behavior, and the localization algorithm. 46 Figure 3.1. The proposed tool: (A) Technical drawing of the drill guide with annotated design parameters, (B) rendering of the guide pulled back from the bone to display side ranging ultrasound strips, distal ports for wires and a drill bit passing through, and (C) preliminary prototype of a curved transducer array with dimensions and specifications similar to those imagined for the proposed device. 3.1 Design Parameters In Figure 1, The drill guide tube is described by three parameters: the outer diameter, Do, the inner diameter, Di, and the radius of curvature of the guide-tip, Ï. Deformable poly-CMUTs would allow for having a curved tip with bent transducer strips from which both forward-facing and side-ranging information could be collected. Such a concept would not be limited to a single radius of curvature. In principle, we could use varying profiles that progressively shift from forward-facing to side-ranging. We would further need to specify the guide length, LDG. However, since this parameter does not affect localization performance, it will not be further discussed here. The transducer arrays can be characterized by five additional geometric parameters. These geometric parameters include the overall strip length, Lst, the number of elements per array, nt, the strip width, wst, the strip thickness, tst, and the number of strips placed circumferentially around the guide (strips are evenly separated by θst). The number of strips around the drill guide is given by ð+, = %-.! and is limited by the strip width. 47 We also introduce two parameters characterizing the range-finding performance of the transducers without introducing a detailed ultrasound physics model (for now, we neglect the relationships between ultrasound frequency, depth, and resolution, and assume that producing an appropriate frequency for short-distance range-finding is feasible). These are (1) the precision of the distance measurement produced by each transducer element to the nearest bone surface (Ï), and (2) the maximum reliable distance at which a measurement can be made (dlim). In reality, Ï increases with distance to the bone, but here we assume that Ï has a constant value. We further assume that distances to the bone greater than dlim are sufficiently attenuated that they can be modeled as missing. 3.2 Objective Function for Optimization Localization The fundamental position and pose estimation problem requires processing the simulated distance measurements in order to determine the toolâs location relative to the target vertebra. If the position and pose of the drill guide is described by a state vector, ð¥, which contains a six-parameter representation of its location in space that includes three translational dimensions (x1, x2, x3) and three rotational dimensions (θ1, θ2, θ3), then the distance yi from an individual transducer element i to the nearest bone surface will be given by ð¦/ = â/Cð¥D. â is a set of nonlinear functions of ð¥ that take on numerical values if a bone surface exists within a distance of dlim (perpendicular to the element face) and are designated as Not a Number (NaN) if no bone surface lies within range. Given the geometry of the tool, the position of the ith element can be written as ð/ = ð/Cð¥D. Next, we define an objective function representing the disparity between the predicted and acquired distance measurements and will have a value of zero when ð¥G = ð¥ and all measurements have zero error. Given an estimated guide position, ð¥G, and distance measures on each element, yi, we calculate estimated locations of points on the bone surface by projecting the measured distances from each element in the direction ð¢/, where ð¢/ is a unit vector representing the surface normal of the ith element: ?Ì?/ = ?Ì?/ + ð¦/ð¢/ 48 where ?Ì?/ = ð/Cð¥GD. Based on the preoperative 3D model, we create a mesh of the bone surface, B. We then use a linear search algorithm to find the distance between each estimated point, ?Ì?/, and the closest point, b, on that bone surface as: ð¿/ = inf$â1 ð O?Ì?/ , ðR We then define an objective function for an estimated position ð¥G and a real set of measurements ð¦ as: ð Oð¥G, ð¦R = T inf$â1 ð Oð/Cð¥GD + ð¢/ â ð¦/ , ðR2"#$!/3# (1) where ð!'4+ is the number of valid measurements (i.e., not reported as NaN). This objective function will reach a global minimum when the estimate pose is equal to the true pose. To solve for O, we evaluated the relative localization performance of seven different optimization algorithms readily available in MATLAB (Mathworks Inc., USA): i. FUQN: An unconstrained local solver based on the quasi-Newton method ii. FIP: A constrained local solver based on the interior-point method iii. FSQP A constrained local solver based on the Sequential Quadratic Programing (SQP) method iv. FAS: A constrained local solver based on the active-set method v. FIP-MS: A multi-start constrained global solver based on the interior-point method vi. FGS: A global solver based on combining the scatter-search method for generating sequential points (Glover 1998) and the interior-point methods. For the constrained solvers, the constraint in every dimension (3 translations and 3 rotations) was set to the maximum possible estimation error in that dimension. The initial position estimate is known exactly for our simulation and would need to be estimated in real world applications. The unconstrained solver (FUQN) balances speed with overcoming local minima and is implemented by the fminunc function. The three constrained local solvers (FIP, FSQP and FAS) can be implemented efficiently and with low computational expense with the fmincon function in MATLAB. Finally, the global solvers are more robust to local minima but more computationally expensive and are implemented with the MultiStart (e.g. FIP-MS) and GlobalSearch (FGS) functions. 49 4 Methodology and Design Process The design process we used consisted of seven phases illustrated in Figure 2. Figure. 3.2. Design workflow for tool development. Within each phase, we performed MATLAB-based simulations using a lumbar spine STL model (from real MRI scans available in the open-source Japanese Life Science Database published by Okubo in 2012) and an US-augmented tool defined by a set of parameters. We began with a set of nominal design parameters as shown in Figure 3 and updated these in each phase based on the findings at the previous phase. We defined a nominal targeting position by aligning the drill guide with the right pedicle channel of the L4 vertebra and then retracting the tip 10mm from the pedicular surface.50 Figure 3.3. Nominal design. (A) Rendering of the US-augmented tool placed in the nominal targeting position exterior to the pedicle, and (B) table of nominal design parameters. With the tool in this known position, we simulated acquiring distance measurements on each of the transducers by calculating the distance from each transducer to the first bone surface encountered in the direction specified by the transducer configuration. The distances were calculated using the Moller-Trumbore ray-face intersection algorithm, available in MATLAB as the function TriangleRayIntersect (Moller 2005). If no bone surface was encountered within a distance limit (dlim) of 50mm, the value of NaN was assigned to the distance measurement. To model uncertainty in the distance measurements, we added zero-mean Gaussian noise (characterized by a standard deviation of Ï mm) to each simulated distance measurement. To characterize the performance of a particular proposed tool design in combination with a particular state estimation algorithm, we varied the initial estimated position and orientation of the tool 200 times around the nominal position near the pedicle. The difference between the true position and the estimated positions was set to be the same distance in a six-dimensional displacement space, with the combined distance metric calculated as described earlier (Equation 1). Three dimensions in this displacement space represented tool tip translations and the other three represented scaled rotations about three perpendicular axes at the tool tip.51 Each displaced state was checked for overlap between the estimated position of the tool and the vertebra. Intersecting position estimates were rejected and new estimate poses were generated randomly as required. The optimization algorithm then estimated the toolâs location starting from each initial estimated position. Where indicated, we ran the algorithms in parallel using variable numbers of nodes on the Compute Canada Cedar network (Emrath 2002). After each set of 200 simulations, we computed the median localization error3 and the associated Interquartile Range (IQR) based on the final estimated positions of the tool (the median and IQR were used, instead of mean and standard deviation (STD), because the distribution of the localization error tended to be highly right-skewed, as is indicated by Whitley). 4.1 Phase 1: Establish General Feasibility Our first goal was to determine if the proposed design concept could produce acceptable localization accuracy and, if so, over what range of errors in the initial position estimate the localization converged. For this initial feasibility study, we evaluated a nominal configuration consisting of eight evenly-spaced US strips and sixteen transducers per strip. The transducers nearest the pedicle were set to be forward-facing and those most distal were set to be side ranging in a wide fanned-out pattern (see Figure 4). Most modern endoscopic spine systems have outer radii of 2.5mm to 4mm, so we began our assessment with an out radius of 3mm (Perez-Roman 2022). In this initial phase, we evaluated three optimization algorithms: [i] a quasi-Newton solver (FUQN), [ii] an interior-point solver (FIP), and [iii] a MultiStart interior-point algorithm (FMS-IP) with four starting points. The initial estimation error was varied in 5mm steps between 0mm and 50mm, and the Gaussian noise, Ï, was set to zero. The program then computed the median localization error for each level of initial estimation error. 52 4.2 Phase 2: Determine the Initial Design Parameters Based on the results of Phase 1, which did demonstrate feasibility (see Results), our second goal was to identify a promising set of values for the strip length, number of strips, number of elements per strip, and drill guide radius. The single-start FIP algorithm was used for this phase due to its relative simplicity. Each design parameter was then varied independently. The strip length was varied from 5mm to 50mm in 1mm increments, the drill guide radius was increased from 2mm to 5mm in step sizes of 0.1mm, the number of strips was evaluated from 4 to 12 for each level, and the number of elements per strip was increased from 4 to 64 in steps of one. In evaluating the accuracy, we simulated 200 randomly distributed initial guess errors of 15mm (in displacement) for each design configuration considered and used a Gaussian noise parameter of zero. At the end of this phase, we selected a provisional configuration characterized by the following values for further analysis: 10 transducer strips, each 30 mm in length, 32 elements per strip, and a tool radius of 5mm (see Results section for details about this choice). 4.3 Phase 3: Assess the Sensitivity to Measurement Uncertainty After identifying a provisional design configuration that produced reasonably robust results, we evaluated the influence of distance measurement uncertainty. At this stage of development, we have no direct means of assessing the distance measurement uncertainty that our planned transducers will exhibit. However, in our work with piezoelectric transducers, we have found that this variability is typically sub-millimetric (on the order of ~0.3-0.4 mm). We anticipate that this variability, Ï, will significantly influence our localization accuracy. Therefore, we evaluated the influence of differing values of Ï, between 0mm and 0.8mm in increments of 0.2mm, on the convergence rate. Like in phase 2, we also varied the key geometric design parameters. We assessed strip length between 5mm and 50mm in increments of 1mm, the number of strips between 4 and 12 in increments of 1, the number of transducers between 4 and 64 in increments of 1, and the drill guide radius between 2mm and 5mm in increments of 0.1mm. Each combination of design parameters and measurement uncertainty level was simulated 200 times. The design parameters considered were the strip length, the number of strips, the number of elements per strip and the drill guide radius. This analysis allowed us to choose a nominal design of a 5mm radius cannula with ten 35mm strips, and 32 elements per strip, for further evaluation and development (see results for details). 53 4.4 Phase 4: Investigate Failed Localizations Using this nominal design, we found that there were some situations where we were unable to accurately localize the tool. We catalogued the positions and orientations where the tool did and did not converge under two different scenarios: (1) where the tool was fixed in the nominal target position and the initial position estimates varied, and (2) where the toolâs position was displaced from the nominal target position. Under both scenarios, we randomly generated sets of 100 samples of displacements in either the estimated or actual tool position, each with a constant value for the combined distance metric, ε (Equation 1). These displacement values were systematically varied between 0 and 50mm in increments of 5mm. When moving the tool, we assumed an initial position estimate that deviated by 15 mm relative to the true position. We visualized the results by rendering the displaced locations on a 3D rendering of the spine using arrows to indicate tool tip position and orientation. We colour coded these arrows using green to indicate convergent locations and red to indicate non-convergent locations. We visually inspected the results to identify any spatial patterns. In particular, we hypothesized that non-convergent cases may be strongly associated with tool positions where there were fewer valid measurements (i.e., locations where the transducer is reasonably close to the bone surface and the surface normal is acceptably close to the US ray direction). For each of the displacement values in Scenario 2 above, we calculated the median number of valid measurements for the set of 100 simulated starting positions and plotted both the convergence rate and the median localization accuracy (plus the interquartile range) against this median number of valid measurements. 4.5 Phase 5: Compare Different Optimization Techniques The localization problem is challenging because of the complex spinal geometry and because the cost function has 6 degrees of freedom. Consequently, we anticipated that there would likely be multiple local minima present, so we evaluated both local optimization routines and routines that had some mechanism to deal with local minima. In particular, we implemented a multi-start optimization routine based on the interior-point algorithm and evaluated the relationship between the number of start points and the convergence rate (this information is later used to make an appropriate trade-off between runtime and convergence rate). In addition, we examined three constrained optimization algorithms (the interior-point (FIP), SQP (FSQP), and Active-Set (FAS) methods), one unconstrained optimization algorithm (Quasi-Newton (FUQN) method) and one 54 global search (FGS method) in order to compare the speed and the robustness of convergence over initial errors of 0mm to 50mm in increments of 1mm. These algorithms were selected because they are standard within the MATLAB optimization toolbox, and the local solvers are straightforward to implement in combination with MultiStart methods. For both studies, each level was repeated 200 times and used the nominal design outlined at the end of phase 3 with no measurement uncertainty. The active-set method using 6 start points was selected moving forward (see results for details). 4.6 Phase 6: Select the Array Configuration The studies outlined above resulted in a nominal tool design with reasonable convergence performance using several of the optimization algorithms. However, since we are developing flexible ultrasound transducers (Omidvar 2022), it is possible for us to design alternative sensor profiles in which one or more of the transducers in each strip could be angled to emit and sense signals in varying directions (see Figure 4). Here, we considered five different array configurations. The first has all transducers facing radially outwards, the second has most transducers facing radially outwards, with one transducer pointing forwards, the third design has a hemispherical tip, and the fourth and fifth designs involve longer curved tips with differing degrees of sharpness (wide fanned-out and sharp fanned-out). The performance of each configuration was evaluated in the nominal position with the nominal geometric design outlined at the end of phase 3. The localization employed the active-set method using 6 start points, and the initial estimation error was varied between 0mm and 50mm in increments of 5mm. Each combination was iterated 200 times. We also recorded the number of valid measurements captured by each configuration in order to compare these numbers to their respective performance. 55 Figure 3.4. Representation and nomenclature for the set of transducer configurations evaluated in this study. For the hemispherical transducer, the tip radius of curvature is set at Ïc = rDG. 4.7 Phase 7: Validate Final Design In phase 6, we found that the optimal transducer placement was the wide fanned-out design with a mix of both forward-facing and side-ranging transducer elements. In order to verify that the selected design would work robustly across a range of positions surrounding the target location, we tested the proposed design by evaluating its performance (1) with varying levels of errors in the initial estimate with the tool in the nominal targeting position, and (2) with the tool displaced to varying extents from the nominal position. For estimating the sensitivity to errors in the initial estimated position, we performed the localization with initial estimation errors ranging from 0mm to 100mm in 1mm increments. We repeated each level 200 times and recorded the convergence rate. To assess robustness to displacements of the tool away from the nominal targeting position, we emulated displacements of between 0mm and 50mm in increments of 1mm, with initial estimation errors of 10mm and 20mm. We repeated each level 200 times. In both cases, the Gaussian noise parameter was set to 0mm and we used the active set algorithm with six starting points. We plotted the convergence rate against the initial estimated position error or tool displacement magnitude, respectively. 56 5 Simulation Results The results presented below parallel the phases outlined in the Methods section. We begin with a general feasibility assessment and then consider the effects of the various geometric design parameters. Next, we evaluate more specific design choices such as the algorithms and array configurations to be used. Finally, we show results for the validation tests. 5.1 Establish General Feasibility Figure 3.5. Median localization error and interquartile range of different optimization techniques using a nominal tool design, as a function of initial estimation error magnitude. The solid lines represent the median values for the final errors, and the surrounding shadowed regions represent the corresponding interquartile ranges. Figure 5 illustrates the relationship between the median localization error and the initial estimation error for the three different optimization algorithms evaluated: an unconstrained (FUQN), constrained (FIP), and multi-start constrained algorithm (FIP-MS). All perform well when the magnitude of the initial error in the estimated position is low (<10mm). The 75th percentile error for the constrained interior point method diverged from submillimetric localization at 10mm of initial and the unconstrained quasi-Newton diverged at 20 mm of initial error. The multi-start interior-point method with four starting points converged well throughout the entire range of initial estimation errors evaluated. 0 10 20 30 40 50Initial Error [mm]05101520253035Final Error [mm]Constrained Interior-PointUnconstrained Interior-PointMultiStart-457 5.2 Determine Initial Design Parameters Figure 3.6. Convergence rates for the various design parameter combinations investigated using the constrained local optimizer with the interior-point algorithm. The ânominalâ design configuration that served as the baseline had a strip length of 30 mm, 8 strips, 16 elements per strip, a drill guide radius of 3 mm and was positioned in the nominal targeting position. The subplots show the results of varying each of the design parameters independently as a function of various levels of initial estimation error, as identified in the figure axes: (A) strip length, (B) number of strips, (C) number of elements per strip, and (D) drill guide radius. The shaded areas represent the 95% confidence bounds for the convergence rate estimates. The nominal value for each parameter is shown by a vertical dotted black line. Figure 6 shows the convergence rate of the various design parameter combinations investigated at different levels of initial estimation error. As expected, all designs showed better convergence rates with lower initial estimation errors. There appeared to be little sensitivity to strip length beyond about 20 mm. The performance improved with more strips up to about 8 strips. Similarly, performance improved up to about 20-25 elements per strip. Performance improved modestly with increases in drill guide radius up to about 3mm. Based on these results, we selected a preliminary design for the next stage of evaluation that used 8 strips, each 35mm long with 32 transducers. We kept the drill guide radius at 3mm. 0 10 20 30 40 50Strip Length [mm]020406080100Convergence Rate [%]ArErr = 0 mmrErr = 10 mmrErr = 20 mmrErr = 30 mmNominal Lst0 2 4 6 8 10 12Number of Strips020406080100Convergence Rate [%]BrErr = 0 mmrErr = 10 mmrErr = 20 mmrErr = 30 mmNominal nst0 10 20 30 40 50 60Number of Elements per Strip020406080100Convergence Rate [%]CrErr = 0 mmrErr = 10 mmrErr = 20 mmrErr = 30 mmNominal ntr0 1 2 3 4 5Drill Guide Radius020406080100Convergence Rate [%]DrErr = 0 mmrErr = 10 mmrErr = 20 mmrErr = 30 mmrDG58 5.3 Assess Sensitivity to Measurement Uncertainty Figure 3.7. Convergence rates for the various design parameter combinations investigated across varying levels of measurement uncertainty (indicated in the legends) with the initial estimation error held at 15mm. Each parameter was varied independently relative to a nominal design of 8 strips, each 35mm long with 32 elements per strip, and a drill guide radius of 3 mm. Parameters investigated were: (A) strip length, (B) number of strips, (C) number of elements per strip, and (D) drill guide radius. Dotted black vertical lines show the nominal values for each design parameter. Figure 7 illustrates the relationship between the convergence rate and the design parameters at varying levels of the bone-distance measurement uncertainty (Ï). Figure 7A suggests no strong relationship between the strip length and the tolerance to increasing levels of measurement uncertainty. Figure 7B shows that at least 10 strips are required to maintain good performance in the presence of reasonable uncertainty levels. Figure 7C shows that using 32 elements per strip allows for reasonable performance relatively independently of the level of measurement uncertainty. However, there is a stronger relationship between the number of elements per strip and the tolerance to uncertainty below this level. Finally, Figure 7D demonstrates that performance is relatively insensitive to the drill guide radius, but larger radii may help slightly. Based on these results, we chose to increase the number of strips from 8 to 10, keep the strip length at 35mm and increase the drill-guide radius slightly (5mm) for the next phases. 0 10 20 30 40 50Strip Length [mm]020406080100Convergence Rate [%]AUncertainty = 0mmUncertainty = 0.2mmUncertainty = 0.4mmUncertainty = 0.6mmUncertainty = 0.8mmNominal Lst4 6 8 10 12Number of Strips020406080100Convergence Rate [%]BUncertainty = 0mmUncertainty = 0.2mmUncertainty = 0.4mmUncertainty = 0.6mmUncertainty = 0.8mmNominal nst0 10 20 30 40 50 60 70Number of Elements per Strip020406080100Convergence Rate [%]CUncertainty = 0mmUncertainty = 0.2mmUncertainty = 0.4mmUncertainty = 0.6mmUncertainty = 0.8mmNominal ntr2 2.5 3 3.5 4 4.5 5Drill Guide Radius [mm]020406080100Convergence Rate [%]DUncertainty = 0mmUncertainty = 0.2mmUncertainty = 0.4mmUncertainty = 0.6mmUncertainty = 0.8mmNominal rDG59 5.4 Investigate Failed Localizations Here, we investigate situations where the system generates inaccurate localizations. We hypothesized that these failed localizations may be related either to the position of the tool (estimated or actual) or to the number of valid measurements acquired. 5.4A. Investigate initial estimates and positions that lead to non-convergence Figure 3.8. Convergence mapped according to the estimated (A) and displaced positions (B) of the tool. Arrows indicate the position and orientation of the estimated or displaced tool tip with green indicating locations resulting in convergence and red indicating non-convergence. (A) Rendering of initial estimates of tool locations with 20 mm estimation error, (B) rendering of the displaced tool tip location with 20mm displacements from the nominal position, (C and D) corresponding plots of convergence rate against initial estimation error (C) or displacement (D). Confidence shading represents the 95% confidence interval for proportion estimates based on the binomial distribution. Figure 8 illustrates the initially estimated and displaced positions where the tool was accurately localized. Both Figures 8A and 8B suggest that there are particular regions where convergence is challenging. Figures 8C and 8D indicate that excellent convergence can be expected near the nominal targeting position when the initial estimation error is relatively modest (<10mm). Convergence decreases only moderately for increases in tool displacement from this nominal position. Overall, convergence rates appear to be more sensitive to increases in initial estimation error than to displacements of similar magnitudes. 60 5.4B. Assess impact of the number of valid measurements on convergence rate Figure 3.9. Analysis of the number of measurements. (A) Convergence rate vs the number of valid measurements, together with a fitted power regression demonstrating improvement in convergence rate with number of valid measurements, and (B) median localization error and IQR vs the number of valid measurements, along with an exponential approximation of the IQR demonstrating reduction with increasing numbers of valid measurements. Figure 3.9. illustrates the relationship between the number of acquired valid measurements and the resulting convergence rate and median localization error. As the tool was moved away from the nominal position, both the number of valid measurements and the convergence rate decreased. A power regression accurately captures the performance improvement with more valid measurements (r2 = 0.9456). The median final error was near zero for all trials but the 75th percentile follows an exponential decay curve (r2 = 0.9959). These results support the hypothesis that the number of valid measurements in different positions likely determines which orientations allow for accurate localization. 0 20 40 60 80 100 120Number of Valid Measurements0102030405060708090100Convergence Rate [%]ATrial DataFitted Power Regression0 20 40 60 80 100 120Number of Valid Measurements051015Final Error [mm]BTrial DataFitted Exponential Regression61 5.5 Compare Optimization Techniques Based on the earlier results from Phase 1, it was clear that the multi-start method outperformed the single-start methods. Therefore, we assessed the impact of increasing the number of start points for multi-start methods, and then compared the different optimization algorithms. 5.5A. Assess benefits of a global search approach with multiple start points Figure 3.10. Convergence rate of the preliminary design against the number of start points used in a MultiStart interior-point algorithm for state-estimation. The initial estimation error and the displacement from the nominal targeting position were both set to 15mm. The error bounds represent the 95% confidence interval for the proportion estimate calculated for a binomial distribution. Figure 10 demonstrates the relationship between the convergence rate and the number of start points in a multi-start implementation of FIP. Throughout all trials, the estimation error and the displacement from the nominal position were both held constant at 15mm. It appears that it is helpful to use multiple start points, though the benefits seem to plateau at about 4-6 points. We opted to use 6 start points moving forward because this number performs well and imposes little additional computational cost when parallel computing is employed. 0 5 10 15Number of Start Points020406080100Convergence Rate [%]62 5.5B: Compare performance of different optimization algorithms Figure 3.11. Comparison of performance of different optimization algorithms as a function of initial estimation error. (A) Convergence rates when using six start points (IP, SQP, AS and QN) or GlobalSearch, and (B) runtimes for all algorithms except GlobalSearch because its runtimes were consistently over 100s. Figure 3.11 compares the performance of different optimization algorithms. Figure 11A shows convergence rates when using six start points, and Figure 11B shows their runtimes. GlobalSearch was omitted from Figure 11B because its runtime is consistently over 100 seconds. All of the considered algorithms perform comparably in terms of convergence except for the unconstrained Quasi-Newton method. This method converged nearly perfectly up to 15mm in initial error prior to dropping off in performance relatively abruptly at 15-20 mm. The Active Set method ran more quickly than the others, taking less than 5 seconds at low estimation errors and increasing only moderately for higher initial errors. We chose to use the active set method going forward because it converges comparably to the other algorithms, is considered robust, and had acceptable computation time (Buerger 2014). 0 20 40Initial Error [mm]020406080100Convergence Rate [%]AInterior-PointSQPActive SetQuasi-NewtonGlobal Search0 20 40Initial Error [mm]0510Mean Time [s]BInterior-PointSQPActive SetQuasi-Newton63 5.6 Select the Array Configuration Figure 3.12. Comparison of different array configurations based on their convergence rate vs initial estimation errors. The five models tested were (i) side-ranging, (ii) one-forward and the rest side-ranging, (iii) hemispherical tip, (iv) wide fanned-out, and (v) sharp fanned-out. Figure 12 shows the convergence rate of several array configurations as a function of the estimation error. The simplest designs (side-ranging only, and one-forward) performed rather poorly, with convergence rates falling off with initial errors of as low as 10-15mm. In contrast, the hemispherical tip and the fanned designs performed well all the way up to the upper limit tested of 50mm of estimation error. The results suggest that distributing the measurement angle directions improves localization performance. Better performing configurations tended to acquire more valid measurements. The side-ranging and one-forward configurations only captured 30 and 35 measurements respectively. In contrast, the hemispherical design captured 58, the wide fanned-out model acquired 135 and the sharp fanned-out model obtained 179 measurements. We selected the wide fanned-out design going forward because it slightly outperformed the others. 0 10 20 30 40 50Initial Error [mm]020406080100Convergence Rate [%]Side-RangingOne-ForwardHemishperical TipWide-Fanned OutSharp-Fanned Out64 5.7 Validation of the Final Design Based on the previous results, we identified a design configuration and optimization algorithm that appears to perform well. This design is a 5mm radius cannula with ten 35mm strips. Each strip includes 35 elements arranged in a wide-fanned out configuration. The tool uses the active-set method with six start points to perform the localization. In this section, we present results evaluating its performance (a) under a larger range of initial estimation errors and (b) under a range of displacements from the nominal position. 5.7A. Validation of tolerance to initial estimation errors Figure 3.13. Assessment of the proposed designâs convergence rate over an extended range of initial estimation errors. All simulations were performed in the nominal targeting position. Figure 13 shows the convergence rate of this design from 0mm to 100 mm of initial estimation error. The convergence rate stays at or above 90% out to about 50mm (the ultrasound distance detection limit) and then begins to drop off at a moderate rate. 0 10 20 30 40 50 60 70 80 90 100Initial Error [mm]020406080100Convergence Rate [%]Validation DataUltrasound Distance Limit65 5.7B. Validation of tolerance to movement away from the nominal position Figure 3.14. Assessment of the proposed designâs convergence rate at various distances from the nominal targeting position. The simulations were performed with initial estimation errors of both 10 mm and 20 mm as indicated. Figure 14 shows the convergence rate as a function of the distance the tool is moved from the nominal position. Independently of the initial estimation error, the design appears to perform well (convergence rates >90%) for displacements within 50 mm of the nominal position. This indicates that the localization performance of this design is likely to be effective both near the clinical region of interest (i.e., the pedicle) and within an acceptable range around that location. 0 10 20 30 40 50Movement from the Nominal Position [mm]020406080100Convergence Rate [%]Estimation Error = 10mmEstimation Error = 20mm66 6 Discussion This simulation study has demonstrated that a self-localizing ultrasound-guided tool could likely achieve sufficient localization accuracy and capture range for pedicle screw navigation. We have identified a promising initial design configuration for a future prototype to be built using the poly-CMUT technology being developed in our institution. This future physical device will allow us to verify if we can achieve the predicted localization accuracy using real ultrasound signals. The following section will review the key findings, strengths and limitations, and the prototyping recommendations based on this simulation work. 6.1 Key Results Feasibility: The simulation studies presented in this paper demonstrate that an ultrasound-augmented drill guide, with parameters similar to those in Table 2, has good potential to be able to self-localize with sub-millimetric accuracy. We expect it to demonstrate this performance when manipulated within the clinical region of interest near the vertebral pedicle. Parameter Symbol Value Drill-Guide Length LDG 150mm Drill-Guide Radius rDG 5mm Strip Length Lst 35mm Number of Strips nst 10 Elements per Strip ntr 32 Configuration ð "# Wide Fanned-Out State-Estimation Algorithm - MultiStart Active-Set (FMS-AS) Number of Start Points nstart 6 Cost Function ð #ð¥%, ð¦( ) inf$â& ð #ð'/ð¥%0 + ð¦'ð¢' , ð((!"#$')* Table 3.2. Summary of the technical specifications for the proposed tool design. 67 Most Important Parameters: Phase 2 demonstrated that the system performance depends heavily on the number of strips around the tool, with an increase in the number of strips improving convergence rates. From the second simulation, we found that there seemed to be a minimum strip length and number of elements required, in the range of ~25 mm and 25 elements, respectively. Lower values worsened the localization, but higher values led to moderate or negligible improvements in performance. The convergence rate also seemed to perform best with drill guide radii at the upper end of the clinically feasible range between 3mm and 5mm. Sensitivity to Noise in Distance Measurements: Phase 3 showed that the proposed approach can be sensitive to distance measurement uncertainty. As we are still in the process of fabricating the proposed poly-CMUT transducers, we currently lack data on the precision we can expect in the distance measurements we might make using these sensors. However, our work with conventional piezoelectric transducers has generally resulted in sub-millimetric bone boundary identification (MacLean 2021), so we believe such levels of performance are likely to be achievable. Generally, an increased number of ultrasound strips and elements per strip seemed to improve the robustness to distance measurement uncertainty. In contrast, the strip length or drill guide radius had little impact on the robustness to distance measurement uncertainty. This study confirmed the finding from the second study that 8-10 strips and 25-35 elements per strip would generally be expected to produce good results. Investigation of Non-Convergence: The fourth study was more qualitative than the other phases because it explicitly assessed the conditions that result in non-convergence. We found that convergence tended to be high if the initial estimation errors or the tool displacements were low, and that zones of non-convergence tended to arise in certain locations around the nominal position. We do not yet have a clear explanation as to why these zones are located where they are, but propose to examine these situations more closely in future. If the initial position estimate is far from the true tool position, it is possible (and even likely) that the objective function will have local minima in the vicinity. Such situations can prevent convergence to the global minimum. In future, we will explore alternative global optimization routines to solve such problems. 68 A related hypothesis is that the number of valid measurements (determined by dlim) could predict if an optimization run would converge. The results presented in Figure 9 supported this hypothesis as the convergence rate increased and the 75th-percentile error decreased with the number of valid measurements. This suggests that performance improves with more measurements and designs acquiring more measurements will likely localize better and more consistently. Evaluation of Optimization Techniques: In the fifth phase, we demonstrated a significant improvement in convergence rates when multiple starting points are used instead of a single run. This could suggest the presence of local minima or that the high dimensionality of the problem may prematurely stop some runs away from the global minimum. Either way, multi-start algorithms were empirically more robust, and we recommend using multi-start or global search methods for this device. In the second part of phase five, we found that all of the algorithms performed comparably within the range of interest for initial estimation errors. Ultimately, we chose to proceed with the Active Set method because it had a slightly faster runtime. We found that using six start points consistently performed well. Transducer Configurations: We then evaluated five transducer element layouts, some of which could be enabled by the flexible poly-CMUTs recently developed at our institution (Gerardo 2018). We determined that designs with a mixture of both forward-looking and side-ranging elements were likely to deliver sub-millimetric accuracies within a reasonably large capture range of 50mm. In practice, this capture range will be bounded by the range-finding depth of the US transducers. We speculate that these fanned designs may have performed best in our simulations because they tend to capture a greater number of valid measurements within the region-of-interest. As noted, a design that generates a greater number of valid measurements is more likely to localize accurately and consistently. 69 Robustness Verification: Finally, we evaluated the robustness of the proposed configuration by evaluating its ability to accurately localize the tool in various estimated and true locations surrounding the nominal position. In both cases, we found that our proposed design produced excellent convergence rates up to 50mm in either estimated error or displacement. This suggests that the proposed design, in combination with the multi-start optimization algorithm, will be able to accurately guide pedicle screw placement in the area within which the surgeon is likely to be manipulating the tool. 6.2 Strengths and Limitations of the Computer Simulation This study has several strengths worth noting. The use of computer simulations for the design process allowed us to rapidly explore a large design space in order to determine some promising configurations for this concept and to alert us to potentially problematic results that might be difficult to predict in advance (e.g., the sensitivity of performance to different design parameters). Also, in simulation we knew the âground truthâ position, which made it straightforward to calculate error metrics. Nonetheless, this simulation approach also has limitations that need to be considered. The most significant is that the model for the ultrasound distance measurements is significantly simplified compared with real ultrasound physics (i.e., we based it on a simple geometric calculation to which a Gaussian random error was added) and therefore the error model likely does not accurately represent the various effects we will have to deal with in real life once we build our sensors. For instance, off-angle reflections or soft tissue inhomogeneities could affect distance measurement accuracy. We have also not modelled distance-dependent error terms, but the errors associated with distant interfaces are likely greater than those associated with nearer interfaces. 70 6.3 Relationship to Prior Literature This proposed device would represent a new alternative to current workflows and existing technologies in the field. Further relevant details of these existing navigation methods are outlined in Chapter 1. An important point of contrast is that this tool would initially need to be placed freehand in approximately the correct position near the pedicle to enable initial registration. Although the accuracy of freehand techniques is poorer than computer-navigated strategies, its accuracy is likely within the capture ranges we have demonstrated in this study (Jing 2019). This suggests that the freehand accuracy of a surgeon placing our device for initial registration should be sufficient. Further, because surgeons are already trained in freehand techniques, this knowledge could be relied upon for this new registration approach (Mobbs 2015). 6.4 Overview and Prototyping Recommendations Accurate placement of pedicle screws in spinal surgery remains challenging and highly consequential, with inaccuracy resulting in significant patient morbidity and suboptimal long-term results. Modern navigation and robotic techniques have reduced malplacement rates, but adoption of these technologies is limited by relatively high equipment costs, protracted learning curve, impact on surgical time, and reliance on radiation. Here, we propose to design an ultrasound-emitting, self-localizing drill guide intended to be used to accurately place the pedicle screws while avoiding many of the limitations of currently available techniques. We also present a preliminary configuration analysis in which we systematically vary key design parameters and evaluate predicted localization performance using simulations based on MRI models of an adult lumbar spine. We consider different state estimation techniques and evaluate performance based on the predicted accuracy of the location estimation and the optimization capture range. Our results suggest that feasible designs exist that will result in accurate position estimates. The simulations indicate that a well-functioning design would feature a 5 mm radius cannula to which would be attached ten 35mm-long strips of ultrasound, each consisting of 32 elements per strip, with a fanned-out emissions profile. Localization is predicted to be reliably and efficiently carried out using a multi-start active-set optimization algorithm with six initial estimates. These findings will be used to guide the fabrication of a novel ultrasound-emitting drill guide for further evaluation and physical testing. 71 7 Concluding Remarks This simulation study has demonstrated that a self-localizing ultrasound-guided tool could likely achieve sufficient localization accuracy and capture range for pedicle screw navigation. We have identified promising initial design configurations for future prototypes to be built using the poly-CMUT technology being developed in our institution. A future physical device will allow us to verify if we can achieve the predicted localization accuracy using real ultrasound signals.72 1The work in this section was published as: MacLean LJ, Hodgson AJ. Accuracy of Position and Pose Estimates of Ultrasound Probe Relative to Bony Anatomy. IEEE IUS Proc. Sept 2021. Chapter 4 Experimental Evaluation of Key System Elements 1 Introduction and Rationale for Key System Elements In order to validate the fundamental components of a self-localizing ultrasound system, this chapter presents three studies focusing on ultrasound simulations, a 2D localization experiment, and the evaluation of poly-CMUT range-finding. The first study uses computational modeling to simulate wave interactions with bone surfaces, illuminating how acoustic signals can be processed for distance measurements to bone surfaces. Next, a simplified 2D localization framework investigates the accuracy of positioning an ultrasound probe relative to known geometries. Finally, the performance of a poly-CMUT transducer is assessed under controlled conditions to demonstrate its potential for precise distance measurements. Together, these evaluations establish the systemâs feasibility and performance while highlighting challenges and opportunities for improvement in real-world applications (Omidvar 2022). 1.1 Overview of Studies Study 1 uses simulations to examine how RF signals can be interpreted for image formation, segmentation, and distance measurement in scenarios too complex for initial physical testing. Using the K-wave ultrasound toolbox (Treeby and Cox 2010), we simulate acoustic reflections from hard bony surfaces based on patient CT data (Liu 2022). This phase evaluates B-mode image formation and the extraction of distance measurements to validate the feasibility of using simulated data for ultrasound-bone interaction studies (Liu 2022). Study 21 builds on these results by exploring 2D localization in a physical context. Algorithms previously tested in simulations are evaluated in a simplified real-world scenario, using a traditional linear probe in a water bath (Treeby and Cox 2010). The probe is moved across various orientations relative to 3D-printed models, with the aim of determining the accuracy of distance-based localization techniques. This phase not only evaluates the ability to register the probeâs position relative to known structures but also identifies the influence of geometric features and initial guess errors on localization accuracy (Treeby and Cox 2010).73 Study 3 evaluates the rangefinding performance of the poly-CMUT transducers which are central to the proposed tool. Prior work has primarily focused on their electrical characterization, but this study assesses their ability to spatially locate targets using echoes (Omidvar 2022). This phase includes three experiments: (1) testing Time-of-Flight (ToF) accuracy with a wire phantom in a water bath, (2) assessing crude B-mode imaging capabilities using a spinal phantom, and (3) characterizing pressure waves in a hydrophone test with a more complex transducer array. Together, these tests explore the capacity of poly-CMUTs to generate reliable acoustic signals and extract basic geometric information (Chiou 2008). These three studies collectively aim to validate the essential components of the self-localizing ultrasound system, addressing key technical challenges and de-risking subsequent stages of prototype development. By integrating physical experiments and simulations, this chapter provides a foundation for the design and implementation of more advanced systems capable of operating in clinical environments. 2 Study 1 - Simulation of Ultrasound-Bone Interaction and Signal Processing To achieve the critical validation of bone-ultrasound measurement feasibility in realistic anatomic contexts, and to evaluate the performance of different signal analysis methods, we establish a time-domain physics simulation of the ultrasound bone reflection. Prior work evaluating the proposed ultrasound-augmented tool has only employed simplified measurement models. Therefore, the motivation of this work is to model the physics and measurement procedure is realistic positions for the proposed tool. Much of the prior literature focusing on B-mode image formation or wave propagation has focused on Frequency or Spatial-domain modelling which does not accurately reflect the surfaces and strong reflections used in measuring bone surfaces. Establishing the viability of this approach, establishing the most promising measurement analysis, and determining surface features that impact performance will be essential for continued development of an ultrasound-augmented self-localizing tool. The research questions are summarized as follows: 1. Is it feasible to achieve submillimetric bone-surface distances using a 128-element ultrasound at 5MHz in the context of: 74 a. Flat plane reflections b. Realistic tool positions, patient anatomy and physics parameters. 2. What is the relative distance-measurement performance of: a. Direct RadioFrequency Time-of-Flight (RFToF) b. Edge Detection on the B-mode Image c. Peak Detection on rays of the B-mode Image d. Feature extraction using a trained ResNet-18 network e. Image Segmentation using a trained VGG-16 network 3. How do features in the physical scan plane impact the measurement performance including: a. Depth b. Horizontal Position c. Surface Irregularity d. Flatness Deviation 2.1 Methods: Modeling Ultrasound-Bone Interactions To simulate the interaction of ultrasound with bone, a cadaveric CT scan was segmented to serve as the ground truth (Chang M 2014). The posterior cortical surface was isolated using Otsu's method, followed by Canny edge detection to delineate bone boundaries (Lee YH 2019). Acoustic properties, such as density and speed of sound, were assigned to the segmented CT data based on radio-opacity values. 75 Computational Setup I: Flat- Plane Reflector at Varying Depths In order to verify the functionality of the most basic signal processing methods (i.e. direct RF interpretation) in the simplest possible context, the first set of trials simply consisted of flat plane reflectors at various depths. The simulation was setup with setting a reflector from 9 to 49mm away from a flat transducer array. A flat 128-element array of unfocused elements was used for all trials on both the flat reflector and spine-derived context. Material properties including speed of sound, density and acoustic attenuation were set according the values for general soft tissue and cortical bone. Distance measurements were then derived in terms of median error and interquartile range across the range of depths. We compared the two simplest methods for this early trialing which include RF-peak detection and peak detection on the B-mode image. Computational Setup II: Initial CT Acquisition and Scan Position Once basic proof of concept was established, our next step was to determine a series of bone models that could be used for modelling the tool in realistic positions. We secured open-source datasets published at the MICCAI 2018 CT segmentation challenge. Scan from four de-identified patients were included two male and two female patients. Other information on age, weight and comorbidities was not available but spinal anatomy was qualitatively within normal range for all patients. Once the CT scans were selected, positions were determined along each axially slice of the scan where the tool might realistically be positioned. This includes both side-ranging tool proposals where the ultrasound elements lie along the trajectory of the drill guide, or top-down approach where the ultrasound remains over the patientâs spinous process in the relative midline. The process for such positions is demonstrated in figure 4.1. After all feasible positions were assessed, the dataset was screened to avoid any collisions between the transducer and the bone, and to ensure that between 35% and 50% of the image contained boney structures. These filters helped to eliminate positions where the scan may not be able to make meaningful measurements such as in between vertebral levels. In total, 3055 cropped CT positions were used for further simulation modelling. 76 Figure 4.1 Process of extracting CT-based images for ultrasound modelling. (A-C) Demonstration of tool positions and scan planes for proposed tools in the axial plane, and (D) Sample region in the sagittal plane. Computational Setup III: Assignment of Material Properties With the CT images screened and selected, we then proceeded to extracting the model parameters that would be required for performing the ultrasound simulation. First, because the samples were extracted from a CT segmentation competition, it was fortunate that expert segmentation labelling of the bones by radiologists was both complete and performed. These maps were available in the same open-source set and used to determine the ground truth that other models would work off. Next, the image was cast to a 300x251 grid and pixel values were independently assigned material properties based on the Houndsfield units in the corresponding 77 CT. Pixels with a value of 1 in the pre-normalized map (pre-existing window cutoff) were consequently assigned values for bone and other pixels were assigned the values for soft tissue. The selected values and relevant sources are provided in table 4.1. The same procedure for taking a cropped CT portion, overlaying the labelled surface and then assigning material properties is shown in figure 4.2. Material Density [kg/m3] Speed of Sound [m/s] Acoustic Impedance [MRy] Soft Tissue 1000 1500 1.5 Bone 2000 3500 7 Table 4.1. Acoustic physical properties assigned to materials in the K-wave simulation. K-wave also considers two mechanisms for energy absorption: Dispersion and Attenuation. Both are computed using the Kramer-Kronig model. Attenuation is the critical loss-term for image formation in our experiment and the power-law model is set to the following: ðð¡ð¡ððð¢ðð¡ððð = ð¼5ð) Where the constants ð¼5 and y have been set to: ð¼5 = 0.75 ð¦ = 1.5 Figure 4.2. Slice of L4 Cadaveric vertebral CT Image. (A) Original CT slice, (B) Red line indicating CT vertebral surface segmentation, and (C) Two-level acoustic parameter assignment. 78 Simulation and Data Acquisition Next, the experimental simulation is established using the K-wave toolbox in conjunction with Matlab 2023. K-wave was selected in lieu of other popular alternatives such as Field II or MUST, because it offers time-domain simulation. Although this is significantly more computationally intensive than the frequency domain simulation largely employed but alternatives, it is essential because it significantly improves the accuracy of modelling reflections at points of strong transition in acoustic impedance. These reflections are ultimately what create bright ridges along cortical bone and the shadowing artifacts underneath. However, these qualities are essential for accurately segmenting out the bone surface and making the relevant distance measurements. In a 300x251 grid, the pixel spacing is established at 0.1mm by 0.1mm in order to standardize all scans. The transducer is defined as being ten pixels from the top of the grid, facing down, centered and projecting outwards. 128 elements are established for signal transmission and receiving, and it is shown by a black line in figure 4.3. Three phases of the reflection process are highlighted in figure 4.3 to show different points in the simulation. Figure 4.3. Sample simulation of acoustic reflection in K-wave at three different time points. (A) Initial reflection triggered, (B) Initial echo received, and (C) Late diffuse acoustic waves. 79 Data Processing I: Image Processing RF signals were simulated at the transducerâs element positions, with the received pressure wave magnitudes assumed to approximate real RF signal amplitudes. Using a Delay-and-Sum beamforming algorithm, these signals were processed to generate preliminary B-mode images (Zhuang 2007). High-frequency noise was suppressed with low-pass filtering to enhance image quality. The image processing pipeline is shown and ordered in figure 4.4. Figure 4.4. Pipeline for B-mode image modification. (A) Initial cropped CT, and (B-I) steps in the image modification pipeline (Details in text). 80 Eight steps were involved in processing the received RF signals in order to generate a high-contrast image that could be used to make distance measurements between the receiver and the bone: B. A preliminary B-mode image is produced using the Vera sonics Delay-and-Sum toolkit. C. A zero-phase IIR lowpass filter is applied along each row at 10% the Nyquist limit. D. Time-Gain Compensation is then applied with a reverse estimation of the power law. E. Region of crosstalk is then clipped from the image (Note that this is removed from all images in figure 4.4 to allow visibility of early structures. F. A 2D filter is then applied over the data with a kernel size of 11. Eleven was selected based on qualitative trial and error. G. The image is then renormalized. H. The same 10% lowpass filter is reapplied again. I. Window level is then adjusted between 30% and 70% of the normalized image. This increases contrast and facilitates bone identification. Once the image has been modified according to the outlined protocol, the image can proceed towards measurement extraction. Data Processing II: Distance Measurement Once the B-mode image is formed, five different methods are applied to consider different techniques determining the bone surface measurements. These include: 1. Direct radiofrequency peak detection. The cross talk is filtered, and the early peaks of the Hilbert envelope are used to estimate distances, based on ToF, along individual ray lines. This method does not require B-mode image formation. 2. A Canny edge detector is applied for defining regions on the image. The first edge detected along the ray of each element is used as the distance measurement. 3. The peak is detected along each individual ray line of the B-mode image. 4. A ResNet-18 network was trained on 70% of the images (2135) to perform image feature identification and then to directly extract the distance measurements. 15% of the data was used for training validation and 15% was used for testing. 81 5. A VGG-16 network was trained on 70% of the images to perform image segmentation based on the known segmentation maps from the MICCAI competition. Similar to the Canny edge detector, the first surface along each ray was then used as the distance measurement. Once again, 15% of the data was used for training validation and 15% was used for testing. Two of these methods use pretrained networks (ResNet-18 and VGG-16) to facilitate measurement extraction. Both of these steps in the process are highlighted below in figure 4.5. Figure 4.5. Image measurement pipeline. (A) Scan plane identification, (B) Segmentation map, (C) Simulation and B-mode image formation, (D) ResNet-18 feature extraction and (E) VGG-16 segmentation and measurement estimation. Descriptive Statistics The primary goal of the work is to extract accurate distance measurements. However, because these measurements are typically based on relatively contiguous surfaces, we can adopt similar accuracy metrics from segmentation tasks. This includes Hausdorff distance which produces a number according to the algorithm outlines in figure 5.6 that reflects the matching of two curves. 82 Similarly, the mean along with the standard deviation, and the median error along with the interquartile range can be useful output metrics. In terms of the independent comparators, four geometric considerations were included in the study. The first two are just the depth and the horizontal position which reflect the true position of the segmented pixel in the simulated grid. The third is the irregularity which represents variance in the slope for a line of best fits across the measured surface. Distinct but similar is the flatness deviation metric which reflects the mean variance of the true surface points off a line of best fits for the given surface. Figure 4.6. Demonstration of calculation of important error metrics include the Hausdorff distance, the mean error and the median error based on the difference between a segmented curve and the ground truth. 2.2 Results: Accuracy of Bone Surface Detection This section outlines the main results. First, the flat panel proof of concept is confirmed before progressing to the larger set of spine models. There, the distribution of the measurement errors between the 5 techniques will be the first consideration. In following to this, the errors will then be compared against the four independent variables from the research question: depth, horizontal position, irregularity and flatness deviation. 83 Research Question 1: Flat-Plate Reflectors at Varying Depth Figure 4.7. Measurement accuracy for RF signal interpretation and B-mode peak detection of flat plates of various depth in simulation. (A) Median and interquartile range of the measurement error. (B) Hausdorff distance of the implicit plate segmentation. Prior to examining interaction with the spine, a simplified preliminary set of simulations was conducted with a flat-plate reflector placed between 9mm and 26mm in front of an unfocused, linear array of 128-elements. Accuracy of the median distance measurement with interquartile range is shown in figure 4.7A for the two simplest distance estimation methods. Measurement of ToF on the RF signal achieves errors below 0.1mm (the pixel sizing in the simulation) for nearly all trials. The measurement of intensity peaks on the composed B-mode images also achieves submillimetric accuracy for nearly all trials up to 25mm when the error starts to increase. Overall, the mean measurement error in this range for the RF-interpretation was 0.03mm and 0.37mm for the B-mode peak detection. For the RF-interpretation, the IQR ranged from 0.01mm to 0.28mm, and the IQR for the B-mode measurement error ranged from 0.08mm to 0.91mm. Assessing the Hausdorff distance in figure 4.7B, for taking these measurements as a segmentation of the flat plate, similarly demonstrates sub-2mm performance for both methods up to 25mm. This initial proof-of-feasibility supports the continuing to the spine-based simulations. 84 Research Question 1 & 2: Measurement Error Distribution Figure 4.8. Distribution of measurement errors for five different techniques across 2055 spine-based ultrasound reflection simulations. (A) Violin plot of the distribution of measurement errors for each method. (B) Cumulative distributions for each of the 5 methods. Simulations were run for 3055 transducer positions around spine-based geometries and physical acoustic properties. Measurement estimations were made for each element, across each iteration (unless a value of NaN) was assigned and an error was calculated for each. The distribution of errors is show in a violin plot in figure 4.8A. All methods have errors centered at 0 with the highest variability being with the RF methods. B-mode image methods showed smaller, but ever-present variability, and the AIML methods showed the tightest distributions of error. The cumulative distribution functions for the set of measurement errors for each method is shown in figure 4.8B. This demonstrates that while the AIML methods do have the tightest distributions of measurement error, there is actually small underestimation off set with the ResNet-18 method better visualized in this presentation. 85 Research Question 3: Comparative Performance with Depth Figure 4.9. Bone-distance measurement error of five ultrasound-based methods against the depth of the true measurement. (A) All points with overlying smoothed splines. (B) All Hausdorff distances with overlying smoothed splines. (C-G) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation. The measurement performance is first, and most naturally, compared to the depth of the measurement itself. These results are shown in figure 4.9 where subplot A demonstrates the trend across all points for all elements and all positions. These plots compare the five techniques and overlay a smoothed spline to assess for relative trends. The RF-measurement deviates the most significantly with a tendency to overestimate in the near field and underestimate in the far field. The RF interpretation method only maintained a submillimetric smoothed spline between 9mm and 13mm.The B-mode images methods performed better in the near field but drop off and tend to underestimate around 15mm. Most notably, the AIML techniques both maintain submillimetric trends for the entirety of the range (4mm to 30mm). Similar trends are noted with the Hausdorff distance in subplot B, where the VGG-16 method maintains the best performance, but notably the RF interpretation actually does perform better here compared to the other three 86 methods. Lastly, these results are also supported by subplot C through G which show density plots of the respective measurements. With so many points in the scatter, these plots allow for better visualization of trends. All show relatively straight lines with a slight slope showing a tendance for underestimation at deeper measurements. Each of these scatters can then be compared to a line of best fit to assess for the trend in the trade-off better the depth and the measurement error. The RF again performs the worst, the B-mode methods are in the middle, and the ML methods show the smallest drop-off in the studied range. These results are summarized in table 4.2 in following. Measurement Method Slope of Line of Best Fit [mm Error/mm Depth] RF ToF -0.625 Canny Edge -0.112 B-mode Peak Detection -0.085 ResNet-18 -0.022 VGG-16 -0.0002 Table 4.2. Summary of measurement error sensitivity to measurement depth. 87 Research Question 3: Horizontal Position Figure 4.10. Bone-distance measurement error of five ultrasound-based methods against the horizontal position in the field. (A) All points with overlying smoothed splines. (B-F) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation. The second most natural independent variable with which to compare the measurement performance is the horizontal position of the measuring element. Across the horizontal positions, no significant trend or variation is noted with both lateral and central measurements tending to perform similarly. This is supported by the scatter with overlying smoothed splines in figure 4.10A, and by the density plots in subplots B-F. Of course, Hausdorff distance cannot be considered here because its calculation requires the inclusion of measurements across the width. 88 Research Question 3: Surface Irregularity Figure 4.11. Bone-distance measurement error of five ultrasound-based methods against the irregularity of the scanned surface. (A) All points with overlying smoothed splines. (B) All Hausdorff distances with overlying smoothed splines. (C-G) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation. Next, the measurement accuracy and Hausdorff distance are compared against the irregularity of the underlying surface as was defined in the methods section. Within the considered range, most of the methods seem to maintain similar levels of performance at both high and low levels of irregularity. The one except to this is the Peak detection method where the smoothed spline in figure 4.11A does drop off in performance at very high levels of surface irregularity. However, it is also worth noting that most of the scan planes from the selected set of spine models showed levels of irregularity far below this threshold. The trend was different with respect to the Hausdorff distance where higher levels of irregularity did seem to increase this metric (and therefore worsen the underlying segmentation. However, most methods resist this drop-off up to an irregularity of 20 and the majority (58%) of the scanned surfaces had values below this threshold. 89 Research Question 3: Flatness Deviation Figure 4.12. Bone-distance measurement error of five ultrasound-based methods against the flatness deviation of the scanned surface. (A) All points with overlying smoothed splines. (B) All Hausdorff distances with overlying smoothed splines. (C-G) Density plots for each of the five methods in order: RF-interpretation, Canny Edge detection, B-mode Peak detection, ResNet-18 feature extraction and VGG-16 segmentation. Trends for the measurement performance trends against the flatness deviation (as outlined in the methods section) are summarized in figure 4.12. Similar to trends against the irregularity, there seems to be minimal relation between the smoothed splines and the degree of flatness deviation as outlined in figure 4.12A and reaffirmed in the density plots 4.12C through 4.12G. Some oscillations notable at the high end of the range of flatness deviations appear to be an artifact of the smooth spline procedure in this region where there is comparably less data. Notably though, all of the Hausdorff distance do seem to gradually increase with flatness deviation. Although the ordering of performance of the methods seems relatively consistent with prior sections (VGG-16 has the best Hausdorff distances and RF measurement the worst), the rates of change with respect to the flatness deviation are roughly consistent between the five methods. 90 2.3 Discussion: Implications and Limitations The simulations on both the flat plate and the models derived from the spinal CT demonstrate that accurate measurements of the surfaces are feasible at a submillimetric level. In the context, the flat plate, the direct time of flight of the wave is able to measure the surface to near computer precision. One limitation in this simulation was the inability to measure distances closer to the transducer due to the presence of crosstalk (direct sound waves moving from element to adjacent elements. The interpretation of the composed B-mode image also performed well but the measurement error did begin to rise at the end of the range around 25mm away from the unfocused transducer. Of note, this is approximately twice the width of the array. This is consistent with the fact that the natural focus of an unfocused transducer is approximately: ð¹24,6*47 = ð·%4ð Where λ is the aperture size (i.e. transducer width). This is commonly interpreted to mean that the image resolution degrades at two to three times the aperture width. In the spine simulations, submillimetric measurements were most consistently achieved, and over the greatest range by the ML based methods. In these simulations, the RF approach suffered from relatively frequent underestimations of distance particularly at greater depths. Of course, more sophisticated methods of RF analysis would likely improve upon these results, but this simplified trial demonstrates that there are challenges with direct RF interpretation in more complex environments that the other methods circumvent. The methods analyzing the B-mode images performed intermediately between the RF and ML methods. They generally performed well within that same 25mm range, but then there performance dropped off. In contrast, the ML methods, either feature extraction or segmentation, were both significantly more robust past the range of the natural focal depth. The third research question sought to address which factors relating to the surface being measured might impact the performance of the measurements. As would be expected, there was a mild, but not insignificant drop off in measurement accuracy with measurement depth. There are many factors that can contribute to this include the focus, the relative error effects, and the dissipation in acoustic power with distance travelled. Overall, the ML based methods performed best with a drop off of about 0.02mm per mm of depth using the ResNet-18 feature detection, 91 and a result of 0.0002mm per mm of depth using the VGG-16 segmentation. Again, these are relatively simple approaches for their respective categories, but they offer a sense of the performance of these techniques that might be selected in later work. In regard to the horizontal position, the irregularity of the surface and the flatness deviation of the scanned surface, all three showed insignificant trends with respect to the measurements themselves. However, there were notable increases in the Hausdorff distance with respect to less regular and less flat planes. Although all methods showed worse segmentation (or inferred segmentations) with more irregular and less flat surfaces, the ML approaches were again the most robust to severe cases. Relationship to Prior Literature Ultrasound measurement of bone surfaces has historically been a challenging problem due bone surfaces appearing as bright bands a few mm thick on traditional B-mode. However, recent work by several groups including Hacihaliloglu (2017), Han (2020) and Ramakrishnan (2025) have introduced techniques such as B-mode image augmentation, statistical shape modelling and optical flow techniques respectively to circumvent these issues and achieve submillimetric measurement accuracies. However, a 2024 survey by Hohlmann also points towards a clear trend towards machine learning methods in the past 5 years. They explain that traditional CNNs have been customized for ultrasound noise and artifact profiles, but that there is also a posterity of ultrasound-bone datasets. Some promising efforts include Alsinan (2020) who used a GAN + CNN approach to achieve localization errors of 0.11mm. Wang (2020) used a custom CNN to achieve mean errors between 0.32mm and 0.41mm on the femur. And Hohlmann, in a 2020 3D ultrasound paper, achieved a surface error of 0.6mm on the scaphoid. Although most articles focus on long bones or other boney regions, a 2025 article from Hu reports a localization error of 1.19 ±0.85mm on the spine. All of these reported results are near to the accuracies found in our simplified simulation. Regarding work on using ultrasound simulation to tackle clinical problems, the majority of the reported literature either focuses on different applications such as photoacoustics (e.g. Song 2021), or transcranial ultrasound. Krokhmal reported in 2025 that they were able to estimate focus position for transcranial ultrasound using patient specific CT scans in a more sophisticated form of the model extraction in our simulation work. Similarly, Marchant reported in 2023 that 92 they were able to use patient specific scans to accurately measure tissue acoustic properties for patient specific planning. These papers illustrate that, although the application is different, other groups have likewise used K-wave based time-domain simulations to model ultrasound-bone interactions and to address related design questions. Strengths and Limitations The strength of this simulation is the flexibility that K-wave allows to iteratively test different measurement techniques in different positions. Further, the benefit of the MICCAI segmentation challenge dataset allows the work to base itself on (A) multiple real patient CT scans, and (B) have access to expert labelled ground truths for the simulation. Lastly, the approach of taking models from these CT scans and coupling them with a simulation means that the process of matching this labelled data to ultrasound can be trialed in a low-resource manner for acquiring cadavers for physical developments (see chapter 5). Several limitations of the current approach warrant considerations. The simulation relies uniform acoustic propagation and speckle is largely omitted from this simulation. Therefore, this homogeneity of the material properties doesnât fully replicate the complexities of clinical environments. Signal attenuation and shadowing were modeled with the standard from K-wave but may differ significantly in the presence of soft tissues or heterogeneous bone structures (Treeby and Cox 2010). Additionally, while the Hausdorff distance provides a valuable measure of maximum error, and median better represents the trend, neither fully captures the full performance of the segmentation for the purposes of registering the proposed tool. Implications for Future Work and Device Development Future work should explore integrating anatomical models with soft tissue layers to assess signal propagation under realistic conditions. Advanced processing techniques, such as adaptive beamforming or regional weighting, could further enhance measurement accuracy. These refinements will be essential for bridging the gap between simulation and physical implementation. 93 The best performing techniques in this simulation work were the ML-based approaches. Segmentation (using a VGG-16, U-Net, or similar) appears to be the most robust and would be recommended for development in future work on this application. This will likely require matching ultrasound scans to cadaveric or patient CTs in a physical environment through tracked and registered ultrasound. 2.4 Conclusion: Measurement Feasibility and Method Selection The simulation experiment demonstrates that in this simplified computer modelling, the ultrasound physics are able to produce signals which can be meaningfully interpreted to achieve submillimetric accuracy. However, direct RF signal interpretation will not be effective in the positions anticipated for the proposed tool. Similarly, unfocused B-mode image interpretation also has a narrow range (~ 25mm) within which accurate results are determined. ML based methods (here ResNet-18 feature extraction and VGG-16 segmentation) not only perform the best but demonstrated the greatest performance over ranges of depth and surface irregularity. A ML based segmentation approach is recommended as a the most promising approach for ultrasound-bone distance measurements in the positions anticipated for the proposed tool. Through achieving accurate distance measurements, and ultrasound-augmented self-localizing drill guide can then be achieved. 3 Study 2 - 2D Localization of 3D Printed Phantoms with a Linear Probe Recent work in ultrasound segmentation has shown that it is possible to use B-mode images to accurately identify the distances to nearby hard surfaces (Pandey 2020). This distance data can then be used in an optimization framework in order to determine the position and pose of the ultrasound transducer (MacLean 2023). Related ultrasound-based state-estimation approaches have been demonstrated in mobile robotics applications (Feng-Ji 1997, Al-Hadithi 2024, Gualda 2024), but not, to our knowledge, for surgical applications. Prior work in our lab, using a 3D computer simulation with ultrasound-spine distances, demonstrated submillimetric localization and pos estimation of the transducer array (MacLean 2023). However, this optimization-based ultrasonic localization approach has not previously been evaluated using real US images. 94 The purpose of the work described in this section, therefore, is to evaluate whether the localization accuracy obtained in a simplified, anatomically relevant and realistic experimental setup using real 2D US images is sufficiently good to support the proposed application and therefore to justify proceeding with the proposed system development. 3.1 Research Aims of 2D Localization Within this simplified context, the work contains two major aims: 1. Investigate the accuracy of ultrasonic localization as a function of the pose of the ultrasound probe relative to an anatomical model of the spine. 2. Evaluate the robustness of the localization process by assessing the effect on localization accuracy of variations in the initial guess error, the characteristic angle of the insert, and the true position and pose of the probe. 3.2 Experimental Setup and Methods A 2D-linear probe (L-14W/60, Ultrasonix Corp., Canada) was immersed in a flat 2D water bath. The probe was then fixed in a specific position and the true position was then measured using an NDI Vega optical tracker (Northern Digital Instruments, Canada). A digitizing probe was tracked in 3D Slicer (Brigham and Womenâs Hospital, MA, USA) and used to measure the positions of three points on the ultrasound probe, from which a pose vector ð was calculated which describes the probe position relative to the water bathâs coordinate frame. ð = að¥ð¦ðb A set of five different inserts were 3D printed on a LulzBot® Taz 6 FDM printer in order to act as reference geometry for the localization. The material was PLA, which has a high acoustic impedance (2.56 and 2.77âMRayl from Parker 2010) relative to water (1.48âMRayl) and therefore facilitated clear surface identification in the ultrasound scans. One of these inserts was based on a CT scan of a real L4 vertebrae (Orias 2019). A slice through the spinous process, with a width of approximately 80mm, was extruded out to create the 2D-surface. The other four inserts were a set of âVâ shapes characterized by internal angles of 90°, 120°, 135° and 150° (see Figure 1). The inclusion of these angled inserts was to assess whether the angulation of a feature impacts its utility 95 in performing the point cloud registration. The angles were selected as a standard set between a right angle and a flat plate with the obvious omission of 180° as registration would not be feasible. In order to emulate a range of scanning directions related similar to what will be encountered around real 3D anatomy, the probe was placed in a total of 10 different positions and orientations from which a scan was recorded for each insert. The vertex was always included in order to ensure that localization was feasible. The positions were the same for all inserts, generated randomly within a distance of 50mm and then fixation was attempted. The optical tracking system then recorded the true position and pose of the probe. The system acquired a total of 50 images overall. Figure 4.12 demonstrates example images of the inserts and setup. Figure 4.13. Experimental setup. (A) Reference geometry inserts including an adult L4 vertebra model (~80 mm across) and a set of âVâ shapes with varying internal angles to assess impact of angulation on localization accuracy. (B) Experimental setup showing the coordinate system of the linear probe relative to a 3D-printed model vertebra. Data Processing Each US scan was processed by manually segmenting the nearest bone surface (shown in Figure 4.14 as a red line drawn along the estimated surface contour of the L4 vertebrae insert). Once the surface was segmented, a 251-element distance measurement vector dm was created that consists of one entry for each column in the ultrasound image; each entry contained the estimated distance from the probe face to the bone surface in that column. 96 Figure 4.14. Data processing methods. (A) Example scan of an L4-model vertebra with a manual segmentation indicated by the red contour line. (B) Computer simulation of ultrasound distance measurements at a predicted tool position. Difference between true and estimated positions is exaggerated for illustration. As originally presented in MacLean 2023, we used an optimization approach to estimate the location of the probe based on the ultrasound measurements acquired. We defined a cost function, O, as follows: ð = Tð¤/ deð!(ð) â ðf Oð, ðRed%%8#/3# ðG = arg min9ââ%ð OðR Here, dm(i) is the vector defined above, and ðf Oð, ðR is the distance vector we predict we would see if the ultrasound probe were in a position defined by the pose vector ð. The cost function sums the squared differences between the measured and estimated distance measurements. The weight index wi is set to 1 if a distance measurement was present in the ith channel of the US image and 0 otherwise. ðf Oð, ðR is set to zero if no bone intercept is predicted in the ith channel. We used a multistart interior point method (4 randomly chosen starting points) to perform this nonlinear optimization (Moré 1989, MATLAB 2025). Stopping criteria included achieving a function value change below 10-6, a constraint violation below 10-6, or a step size below 10-10. 97 For each of the 50 US images obtained, we generated a set of 100 randomly-generated initial pose estimates arrayed around the measured location of the probe obtained from optical tracking and ran the optimization algorithm starting from each of these initial estimated positions. After each run, we saved a pair of scalars (Ei, Ef), where Ei and Ef represent the initial and final pose errors, respectively. Since the pose errors are actually 3-tuples (consisting of the terms Îx, Îy and ÎÎ¸), we reduced these errors to single-parameter representations by calculating the following value: ð!4; = >ð¥ð¥% + ð¥ð¦% + Cð&'( â ðD% where lped represents a scaling factor applied to the rotational error expressed in radians. This length was set at 20.2 mm, which represents the approximate size of a characteristic length in a human pedicle (Choubiasa 2018). ð!4; has units of millimeters. Each of the 100 randomly generated positions used a set value of initial guess error and then Îx, Îy and ÎÎ¸ were selected with random weightings contributing to achieve this error. 3.3 Results Figure 4.15A illustrates the localization performance of the method across the different inserts. The independent variable is the magnitude of the initial estimation error, and the dependent variable is the final error of the localization. At low initial errors (Ei < ~5 mm), the final errors ended up being sub-millimetric for the majority of the inserts. The 90° insert is somewhat of an outlier, typically converging to a position approximately 3 mm away from the true position despite having relatively accurate initial position estimates. The anatomic model had an average final translational error of 0.7mm and a rotational angle of 2° for low initial displacements (< 5 mm). The best performing inserts were the 120° and the 150° âVâ shapes which had approximate final translational errors of only 0.3mm and rotational errors of 0.5° for low initial displacements. This is in contrast with the worst performing insert at 90° which had a final translational error of 1.65mm and a rotational error of 3.8° for low initial displacements. As the initial positional error rose past 10mm, there was rise in registration error across all the inserts. Figure 4.15B shows the final errors grouped by the angle of the four non-anatomically shaped inserts. There appears to be a slight improvement in accuracy at higher internal angle values. 98 However, this was not statistically significant as the spread in one insert group is significantly larger across the trials than the spread between the groups. Figure 4.15. Localization error analysis. (A) Final localization error plotted against pre-localization position error for the five 3D-printed reference geometry inserts. (B) Grouped final errors for all trials categorized by the characteristic angles of the reference geometry inserts (mean final error across the samples shown in red). 3.4 Discussion Overall, the results presented here indicate that an optimization approach based on ultrasound distance measurements can result in reasonably accurate final pose estimates in this simplified 2D model if the initial pose estimates are accurate to within ~5-10 mm. With the exception of the 90° insert model, each of the angle inserts performed comparably to one another and to the anatomically shaped insert, so there appears to be limited sensitivity of the localization accuracy to the internal angle. This suggests that the angulation of a given feature, such as a facet joint or a pedicle, will not significantly impact localization accuracy as long as it is unique to that feature. 99 Finally, there was a consistent increase in the final localization error as the initial guess error increased, rising to potentially problematically high levels of several millimeters once the initial error was above about 10 mm. Prior work from our group (MacLean 2023) suggests that the sensitivity of the final error to this initial prediction error likely relates to local minima. Future work should explore alternative optimization algorithms or state estimation approaches that are less susceptible to the local minima that are likely to be encountered in more anatomically realistic conditions. Comparison With Related Studies: The localization errors reported here are comparable at low initial guess errors to our prior simulation work but diverge more quickly than in simulation (MacLean 2023). This could be due to numerous experimental sources of error including the segmentation method, the fixation of the probe or the recording of the true position. Other work has been done to localize relative to known anatomy or tools. Hu recently (2025) showed 1.2mm accuracy in aligning ultrasound segmentations to a CT scan, and Douad (2025) showed that they were able to track a needle tip with 0.7mm translational axis error. Hu also noted that angulation of the probe relative to features could introduce errors, but did not comment on the geometry of the features themselves. These reports demonstrate similar localization accuracies to what was found here and in simulation. This offers support for the continued development of the device and highlights the need to be wary introducing unnecessary systematic errors. Limitations There are several limitations worth addressing when interpreting these results. First, the models used here are simple rigid models imaged in a water bath, which is a less challenging environment than intraoperative settings, so future work should assess the performance of this approach in more realistic settings in which soft tissues lie between the probe and the bone. 100 Second, the use of an optical tracker and point digitization approach to measure the location of the ultrasound probe introduces potential error if (1) the fiducials are not accurately captured by the user, or (2) if the rigid fixation assumption does not hold during or after the registration. Similar issues were presented by Fattori in 2021, and these issues can be resolved by improving fiducial attachments and by improving device fixation. In future work, it might be better to rigidly attach a tracker to the ultrasound probe and directly calibrate the location of the scan plane relative to the tracker positions. Finally, the manual segmentation used here for defining the physical distances to the insert is impractical and unrealistic to use in more complicated clinical scenarios. More automated segmentation algorithms, such as those used by Pandey (2020), should be considered in the future for identifying the bone surfaces (Pandey 2020). 3.5 Summary In summary, this study has demonstrated that it is possible to identify the position of an ultrasound probe relative to known anatomy with reasonably acceptable (approximately millimetric) accuracy by using an optimization-localization approach based on comparing expected and measured distances produced from B-mode ultrasound images. The resulting accuracy of the position estimates was for the most part relatively insensitive to specific geometric features of the known geometry. The region of convergence for the algorithm evaluated here was comparatively small, so more robust algorithms should be evaluated in future. While the present work has been limited to a 2D situation, we anticipate that a similar approach would likely work reasonably well in 3D, so a future study should explicitly address this situation. 101 4 Study 3 - Rangefinding using a Linear Poly-CMUT Array In Study 2 above, we used B-mode images from a commercially available 2D US probe. In order to develop self-localizing ultrasound tools based on poly-CMUT sensors, we must be able to capture similar images with these sensors and use the images to accurately measure distances to the bony surfaces. Work from Omidvar (2024) has shown that poly-CMUTs can be used for shape estimation, but they have not specifically been assessed for distance measurements to our knowledge. In the experiments described here, we evaluate the potential of a prototype poly-CMUT array for making the required measurements by assessing three key aspects of performance: 1. Ability to generate and detect acoustic signals of appropriate magnitude 2. Ability to accurately estimate distances under simplified conditions 3. Ability to accurately estimate distances using an anatomically representative model (spine phantom) 4.1 Methods and Experimental Design To assess the rangefinding and imaging capabilities of poly-CMUT arrays under different conditions, we designed three experiments: First, we tested a flexible arrayâs ability to generate and detect signals in oil, a non-conductive medium that would not affect the electronics. Second, we measured basic distance accuracy by using the system to measure distances to a wire phantom in water (with the elements and electrodes packaged in PDMS for electrical insulation). Finally, we introduced more realistic geometry by scanning a spine phantom to evaluate accuracy of anatomical imaging (Lee TTY 2019). Each experiment employed a distinct setup and methodology, allowing us to address specific aspects of the arrayâs physical rangefinding performance. 102 Experiment 1: Acoustic Signal Generation in an Oil Bath The first experiment evaluated the ability of a recently built, flexible poly-CMUT array to generate and detect acoustic signals by placing the array in an oil bath with a hydrophone positioned approximately 30 mm in front of it (see Figure 4.16A). A 32-element 1D linear flexible poly-CMUT array was used, with a footprint of 25.7 Ã 10.7 mm and an element pitch of 680 µm. The array operated at a center frequency of ~8.6 MHz with a fractional bandwidth of 13â25%, using a single-cycle 10 Vpp excitation pulse with an 8MHz sine wave from a signal generator. Some of the proposed designs will require a flexible CMUT but weâre initially concerned with the performance in a linear configuration. The oil provided a non-conductive medium suitable for safely testing the prototype of the flexible poly-CMUT array by limiting the risk of shorting the electrical circuit (Chang C 2014). Further, oil offers a significantly higher acoustic attenuation (~3.5â8.4 dB/cm) than that of water (~0.108 dB/cm) which closely matches the ranges of attenuation recorded in soft tissue (~3.5â7.0 dB/cm) as reported in Omidvar 2024, Alouache 2018 and Duck 1990. Figure 4.16. Experimental setup for rangefinding testing of a flexible poly-CMUT in an oil bath. (A) Hydrophone measurement and (B) Reflection off a metallic plane. The experiment consisted of two parts: (1) transmission and (2) emission-reception. In the transmission test, a custom pulser-receiver generator was used for signal generation and to activate the flexible array. A needle hydrophone (Onda HNC-1500, CA, USA) then received the pulses at 30mm, and waveforms were displayed on an oscilloscope alongside the predicted signal 103 from the generator. The signals were then aligned in order to validate the acoustic wave transmission-reception events. In the emission-reception test, the hydrophone was removed and replaced with a flat aluminum plate positioned at a 10mm from the transducer. 10mm was selected in order to avoid over-attenuating the echo in the oil bath. The receive signals were then time-gated and displayed on the custom pulser-receiver. The shape of the echo signal was again compared to the transmit in order to verify the signal transmit-receive. In both parts of the experiment, the ToF between the emitted and received signals was calculated to estimate the distance to the target using the speed of sound in oil to be 1,470m/s based on work from Chemat 2004. These estimates were compared to physical measurements obtained using calipers (and illustrated using a ruler along the side of the tank in figure 4.16) to validate the accuracy of the flexible arrayâs distance measurement capabilities. Experiment 2: Rangefinding with a Wire Phantom in a Water Bath Having established that the poly-CMUT sensor was able to generate and receive detectable signals in the oil bath experiment, the second experiment was designed to evaluate the rangefinding accuracy of a poly-CMUT array in a controlled environment. A six-by-one rigid poly-CMUT array, depicted in Figure 1, was used for this purpose. This transducer was used instead of the flexible 32-element array in experiment 1, because it was (1) packed in PDMS for electrical insulation which prevents shorting in the water bath and (2) setup with impedance matching to allow for greater signal power and image formation. The transducer was controlled by a Verasonics Vantage system (Verasonics Inc., USA), which enabled simultaneous activation and recording from all six elements of the array. The array was mounted on a stationary fixture and positioned perpendicular to a wire phantom submerged in a water bath. The wire phantom consisted of multiple parallel wires arranged parallel to the arrayâs axis (the line perpendicular to the individual elements) to ensure that the wires intersected the acoustic field. The rigid transducer and a schematic of this experimental setup, with one wire removed as indicated, are shown in figure 4.17. 104 Figure 4.17. Experimental Setup of Rigid poly-CMUT Rangefinding. (A) Rigid poly-CMUT array used in the early range-finding tests, triggered and recorded by a Verasonics Vantage system. (B) Diagram of the wire phantom experimental setup, showing the transducer (green), wire cross-sections (yellow), the phantom base (black), and a broken wire marked by a red cross. To conduct the experiment, a broadband pulse centered at 7MHz was emitted from the array, and the returning echoes were captured by the Verasonics system. The radiofrequency (RF) signals recorded by each element were analyzed to identify echo peaks corresponding to the reflections from the wires and other structures in the setup. A cross-correlation algorithm with a Gaussian curve was applied to consistently detect the ToF values of the echoes while minimizing noise interference. The distances between the transducer and the reflectors were calculated using the ToF values extracted from the RF signals, assuming a speed of sound in water of 1480 m/s. Caliper measurements of the wire positions were taken as ground truth to validate the calculated distances. A B105 Experiment 3: Imaging a Spinal Phantom to Measure Geometric Features The final experiment aimed to evaluate the capability of a poly-CMUT array (the rigid 6-element array described in Experiment 2 above) to form B-mode images and extract geometric features from a more complex anatomical model. A Sawbones spine phantom was selected as the target and submerged in a water bath, held in place at the bottom with metal weights to prevent movement during scanning. The poly-CMUT array was mounted on a micrometer, connected to other caliper-controlled struts, for precise positional adjustments and aligned with the phantom to capture posterior and lateral views of the spinous process. Figure 4.18 illustrates the experimental setup. Figure 4.18. Experimental setup for scanning a Sawbones spine model with a simple Poly-CMUT sample in a water bath setting. (A) Side view of the transducer scanning from a posterior to anterior position, and (B) Top view of the transducer scanning PA with the adjustable positioning frame visible in the top right corner. Two main scanning positions were considered: (1) a posterior scan with the image plane nearly axial and aligned with the length of the spinous process, and (2) a lateral scan with the image plane in the coronal plane and cross the width of the spinous process. Both of these scanning positions are illustrated in figure 4.19. These views were chosen to evaluate specific geometric features of the phantom: the sagittal scan was used to estimate the length of the spinous process, while the transverse scan was used to measure its thickness. The micrometer allowed incremental adjustments of the arrayâs position, ensuring consistent data collection across scans. 106 Figure 4.19. Illustrations of the two primary scanning planes across the vertebral spinous process. (A) Lateral view of the vertebrae which is parallel to both scanning planes such they are indicated by lines, and (B) Top view of the vertebrae with indicated scanning planes. (C) Isometric views of each of the independent scan planes isolated for clarity. The ultrasound scans acquired by the poly-CMUT array were processed using a DAS beamformer through Verasonics and Matlab 2018b to form B-mode images. Peak signal intensity in hyperechoic bands on imaging were used to estimate the position of the model surfaces. Based on these points, the thickness and length of the spinous process were estimated. These measurements could then be compared with the dimensions of the Sawbones model based on a CT scan that had been previously acquired. The model was covered in radio-opaque paint and a microCT was performed using Scanco XtremeCT (resolution â¹ 58 µm). Relative position between the transducer and the model was checked with calipers but all measurements (thickness and length) were estimated using the relative position of the hyperechoic peaks. 3DSlicer performed intensity-based segmentation on the CT to estimate pertinent measurements and we then reconfirmed these using calipers. These distances acted as a comparator for the ultrasound-based estimates. 107 4.2 Experimental Rangefinding Results The following sections present the results of the three range-finding experiments: (1) testing signal generation and detection with a flexible poly-CMUT array in oil, (2) measuring distance accuracy using a wire phantom in a water bath, (3) evaluating anatomical imaging with a spinal phantom, and Each results set addresses specific aspects of the systemâs capabilities, offering insights into its potential for physical measurement tasks. Experiment 1: Acoustic Signal Generation and Detection in an Oil Bath Part 1: Wave Generation and Hydrophone Measurement Figure 4.8 illustrates the RF signals measured by the hydrophone in response to the acoustic waves generated by the flexible poly-CMUT array in the oil bath. The recorded signals showed consistent shapes closely matching the emitted monopolar pulse (from the pulser-receiver generator), validating the fidelity of the wave generation process. Despite the higher attenuation properties of oil compared to water, the hydrophone measurements indicated that the signal intensity was sufficient for identification of ToF values. These ToF measurements produced distance estimates that aligned closely with ruler-based ground truth measurements, with errors falling within the experimental margin of error. This confirmed the flexible arrayâs ability to reliably generate waves in challenging acoustic environments. Figure 4.20. Sample signal processing of the hydrophone signals. (A) Raw RF signals at varying bandwidth, (B) Power distribution with variable bandpass filters, and (C) Spectrogram of the raw RF signal demonstrating power contributions through time. 108 Part 2: Echo Detection The echo detection phase of the experiment presented more significant challenges due to increased noise interference in the recorded signals. Despite this, the flexible poly-CMUT array successfully captured echo signals reflected from the aluminum plate after applying signal filtering and validation techniques. These echoes were identified at depths consistent with the ruler-based ground truth measurements, confirming the arrayâs capacity to detect reflected signals in the oil bath. However, the accuracy of these echo-based measurements was slightly lower than the hydrophone-based measurements, suggesting a need for improved signal processing to mitigate noise interference and enhance sensitivity. Figure 4.21. Figure 4. Sample signal processing of the reflected echo. (A) RF signals at varying bandwidth, (B) Power distribution with variable bandpass filters, and (C-D) Spectrogram of the RF signal showing power contributions through time before and after 50% bandwidth filtering. 109 Experiment 2: Rangefinding with a Wire Phantom in a Water Bath Figure 4.22 shows the recorded RF signals from the wire phantom experiment, with clearly identifiable peaks corresponding to reflections from the wires (indicated by red lines), as well as from additional reflectors such as the base of the phantom and the tank bottom. These peaks aligned closely with the ground truth measurements obtained using calipers (see Figure 4.23), demonstrating submillimetric accuracy for most wires (Figure 4.23B). Interestingly, deeper wires produced slightly stronger echoes compared to those closer to the array, which may be attributed to acoustic impedance differences between the water and the underlying tank plates (Pan and Bies 2012). Figure 4.22. RF signals of sample elements with peak detections indicated by orange lines and reference distances marked in cyan. (A-C) Samples for elements 4, 8 and 12 respectively. Figure 4.23 shows the comparison between the distance measurements made based on time of flight from the ultrasound and the distances measured with the calipers. Additional artifacts in the RF signals were observed, particularly near the damaged wire, which exhibited weaker and less distinct peaks. Despite this, the array was able to detect all intact wires reliably. The results indicated that the poly-CMUT system could accurately measure distances to hard surfaces in a controlled environment, providing a foundation for more complex rangefinding applications. 110 Figure 4.23. Rangefinding results of the water bath wire phantom. (A) Measurement against the feature depth, and (B) Discrepancy between ToF and caliper measurements. Experiment 3: Imaging a Spinal Phantom Figure 4.24 shows examples of the poly-CMUT derived B-mode images obtained in the spine phantom experiment. The highlighted regions of the images relate to basic geometric features of the spinous process. Although the reconstructed images are quite rudimentary (due largely to the limited number of array channels), both the sagittal and transverse scans revealed hyperechoic bands along the phantom's surface, representing the cortical bone, and the acquired images allowed for approximate measurements of the processâs length and thickness. Quantitative comparisons between the ultrasound-based measurements and CT-derived ground truths showed excellent agreement. The estimated length of the spinous process from the sagittal scan was 26.3 mm, compared to 26.6 mm measured on CT, while the estimated thickness from the lateral scan was 4.5 mm, compared to 5.0 mm on CT. These results confirmed that even with crude imaging resolution, the poly-CMUT array could extract basic geometric features with roughly millimetric accuracy, supporting its potential for anatomical surface measurements. 111 Figure 4.24. Sample results of feature identification and measurement based on B-Mode imaging with a 6-element poly-CMUT array. (A) Spinous process [SP] from a lateral approach in the transverse plane [LT], (B) SP from a lateral approach in the coronal plane [LC], and (C-D) SP from a posterior approach in the transverse plane [PAT] with both pre and post processing. 112 Imaging Thickness â LT Thickness â LC Thickness - PAS Length [mm] CT 5.0mm 5.0mm 5.0mm 26.6mm Poly-CMUT 4.3mm 3.9mm 5.3mm 26.6mm Table 4.3 Summary results of poly-CMUT dimensional measurements of the spinous process of an L4 vertebrae Sawbones model. 4.3 Discussion of poly-CMUT Rangefinding Experiments The first experiment demonstrates that the flexible poly-CMUT was able to generate and receive waveforms reliably in oil-medium with acoustic attenuation similar to soft tissue. The second experiment achieved submillimetric rangefinding accuracy in detecting the wires. Lastly, the third experiment estimated spinous process length and width to 0.3mm and 0.5mm compared to a CT scan respectively. Overall, the results of these experiments demonstrate that poly-CMUT arrays (for rangefinding, imaging, and acoustic signal generation) can perform at a sufficient level for supporting self-localizing ultrasound systems, and this addresses a critical component for the proposed device. These findings provide further data on poly-CMUT performance and identify opportunities for refinement and future development. Key Results and Relationship to Prior Work The oil bath experiment demonstrated that the recently developed flexible poly-CMUT arrays that we intend to ultimately use for our proposed self-localizing tools were able to generate acoustic signals in a homogeneous oil medium. Signals recorded by the hydrophone qualitatively matched the emitted monopolar pulse, indicating the fidelity of wave generation. However, the echo detection phase had lower SNR resulting in more challenging detection of the ToF. While prior research has shown the potential of flexible transducers for novel configurations by Omidvar 2024, these basic results suggest that distance measurements, the accuracy around one-millimeter, will likely be feasible in contexts with attenuation comparable to soft tissue. The wire phantom experiment established the ability of the 6-channel rigid poly-CMUT array to measure distances to point features with submillimetric accuracy in a controlled and homogeneous water bath environment. This level of accuracy aligns with prior work using conventional piezoelectric transducers as reported by Ghemari 2024. These findings suggest that poly-CMUT devices may be able to generate transducer-to-bone distance measurements with sufficient accuracy for the proposed application. 113 Finally, the spine phantom experiment extended the scope to a more complex anatomical model, focusing on the extraction of geometric features. Despite limitations in resolution due to the arrayâs low channel count, features visible in images from the poly-CMUT system accurately indicated the length and thickness of the spinous process, with results closely matching CT-derived ground truths. These findings demonstrate that it is plausible to consider using poly-CMUT sensors for the intended self-localizing application proposed in this thesis to address the spatial challenges posed by conventional piezoelectric transducers (Zhang 2023). Strengths and Limitations These experiments demonstrated the functionality of poly-CMUT arrays in both rigid and flexible configurations. The experiments addressed several key aspects relevant to the proposed self-localizing application, including acoustic signal generation, basic rangefinding, and anatomical imaging and. Submillimetric accuracy and strong alignment with ground truths provided evidence of the systemâs suitability for the proposed purpose. However, several limitations must be considered. The controlled nature of the water and oil bath environments does not well model various complexities associated with clinical applications, such as soft tissue attenuation and variability. The low channel count of the arrays restricted imaging resolution, limiting the ability to extract detailed anatomical features. Future Directions While these results highlight the promise of poly-CMUT technology, the limitations also point to areas for improvement. Enhancing signal processing through multiphase coherent-beam forming for improving image quality, automated template matching through cross correlation or wavelet denoising could all help to improve the reliability of echo detection. Increasing the channel count of the array would allow for higher-resolution imaging, enabling more detailed geometric feature extraction. Additionally, future experiments should incorporate more realistic environments, such as soft tissue phantoms or in vivo models, to evaluate the systemâs performance under conditions closer to clinical settings. Finally, improvements in optimization algorithms could enhance the robustness of state estimation for localization applications, particularly in anatomically complex scenarios. 114 5 Summary of Basic Component Testing This chapter has provided a foundational assessment of several essential elements required to develop a self-localizing ultrasound system. The three phasesâ ultrasound-bone simulations, 2D spine localization, and poly-CMUT rangefinding testsâcollectively demonstrate the plausibility of using poly-CMUT arrays to acquire distance measurements needed to perform spine localization tasks. The simulations demonstrating bone reflections in more realistic environments, self-localizing ultrasound probes in a 2D space, and the submillimetric rangefinding performance of the poly-CMUTs collectively exemplify the key components required for the proposed application. However, these findings are only an early proof of concept conducted under simplified conditions. Future work will need to address critical challenges, including smaller form factor prototypes 1-2mm wide, 3D localization tasks and rangefinding performance testing in more anatomically realistic and dynamic settings. This chapter establishes a basis for further prototyping and development of self-localizing ultrasound tools.115 1Work led to two book chapters, one conference article and two presentations, and one journal article: China D, MacLean LJ, Wei J, Theodore N, Johnson N, Crawford N, Ding K, Uneri A. Supervised learning using tracked ultrasound imaging: Application in resolving deformations during spine surgery. Medical Image Analysis. 2025. Chapter 5 Image Quality Optimization and Automated Labelling for Machine Learning Vertebral Segmentation Ultrasound (US) imaging offers a compelling alternative to ionizing imaging modalities for intraoperative navigation, especially in spinal procedures where anatomical shifts during surgery can compromise preoperative registration. While US avoids radiation and enables real-time imaging, its clinical use in spinal navigation remains limited by the complexity of bone-tissue interfaces. The high acoustic impedance of bone produces strong specular reflections and shadowing, often viewed as a limitation, but these artifacts also encode geometric surface information that can be computationally leveraged. The nature of bone-ultrasound reflections is illustrated in figure 5.1 along with the material properties that lead to these shadowing effects. Further detail concerning the physics derivation and the neurosurgical applications is provided in Appendix C. However, extracting this information requires robust segmentation techniques and image acquisition protocols tailored for bone visualization. Improving segmentation accuracy therefore depends not only on imaging quality but also on effective data labeling strategies capable of capturing the subtle boundary cues present in bone-US interactions.1 Figure 5.1. Illustration of the physics of ultrasound propagation and bone reflection. (A) Specular reflection, (B) Diffuse reflection, and (C) Wave equation at the interface between media of different acoustic impedance. The approximate density (Ï), speed of sound (c) and acoustic impedance (z) of muscle and bone are listed on the right.116 In this chapter, we present a machine learning-based approach to segmenting vertebral bone surfaces in ultrasound images. The work focuses on developing a supervised learning framework that minimizes reliance on manual annotation by using CT-registered ultrasound volumes for ground truth generation. We examine how image quality optimization and automated labeling strategies impact segmentation performance and explore the potential of convolutional neural networks (CNNs) to extract bone geometry under challenging acoustic conditions. By integrating recent developments in AI-enabled medical imaging, this study seeks to advance the role of ultrasound in spinal navigation, particularly in systems where accurate, real-time surface localization is needed for guidance and registration. 1 Research Objectives The aim of the work presented in this chapter is to develop and evaluate appropriate techniques for identifying vertebral bone surfaces for use in the proposed self-localizing US application. In order to bridge the gap between imaging physics and ML-based segmentation by systematically optimizing US imaging parameters and leveraging advanced labeling techniques to improve segmentation accuracy (MacLean 2022). Specifically, this chapter addresses the following research objectives: 1. To evaluate how ultrasound acquisition parameters influence image quality and, in turn, segmentation accuracy in spinal imaging. 2. To develop and assess automated methods for generating large, accurately labeled datasets suitable for training machine learning models. 3. To implement convolutional neural networks (CNNs) for vertebral surface segmentation from ultrasound images and to quantify their accuracy for surgical navigation tasks. By integrating physics-based image optimization with data-driven ML techniques, this work contributes to developing robust, US-based navigation systems capable of adapting to intraoperative anatomical changes (MacLean 2022). These systems have the potential to reduce reliance on radiation-based imaging methods, making spine surgery safer, more efficient, and more accessible for diverse clinical settings (MacLean 2022). 117 2 Methods In order to evaluate and improve the accuracy of vertebral segmentation from ultrasound, we conducted a series of experiments to optimize image acquisition, create labeled training datasets, and implement machine learning-based segmentation. This section outlines the methods used to assess spatial resolution, contrast, segmentation performance, and data quality, followed by model development, calibration, and evaluation procedures. 2.1 Optimizing Image Quality The aim of this study was to evaluate the influence of ultrasound acquisition parameters on spatial resolution and segmentation accuracy, with the goal of identifying optimal settings for accurate vertebral segmentation in spinal ultrasound imaging (Baka 2017). Given the critical role of image quality (IQ) in machine learning (ML)-based segmentation and registration, this study systematically investigated, across different imaging conditions, issues of performance including (1) spatial resolution, (2) trade-offs between contrast and noise, and (3) segmentation performance. 2.1.1 Experimental Setup Experiments were conducted on phantom models and cadaveric specimens using tracked ultrasound imaging to assess spatial resolution, contrast, and segmentation accuracy under controlled and clinically relevant conditions (Ungi 2020). Three distinct experimental setups were employed: (See figure 5.2) 1. Spatial resolution: Using point spread function (PSF) measurements, we imaged a fishing wire phantom composed of 0.4âmm diameter fishing lines submerged in water. The ultrasound system captured the axial and lateral spread of the wire targets at varying depths (Welch 2013). 2. Contrast resolution: Through contrast-to-noise ratio (CNR) analysis, we imaged a target-sphere phantom with well-defined regions of differing intensity. We measured intensity variations across the target and background to analyze CNR under different imaging conditions (Isensee 2021). We also measured a secondary spatial resolution metric, the Edge Spread Function (ESF), using the scans from this target phantom. 3. Segmentation accuracy: On anatomical structures, we acquired ultrasound images of vertebrae from a tracked spine phantom and cadaveric specimens using the Alpinion E-118 CUBE 12R ultrasound system. We processed the images with a pre-trained segmentation network and compared the predicted segmentations to ground-truth labels derived from pre-scan CT data (Pesteie 2019). Figure 5.2. Experimental setups for ultrasound image quality and segmentation assessment. (A) Wire phantom (red) for PSF analysis. (B) Target-sphere phantom for CNR evaluation. (C) Tracked ultrasound setup for scanning cadaveric and SawBones phantoms. To assess the effect of acquisition settings on image quality, ten ultrasound images were obtained at each setting using both curvilinear and linear probes with each at three different frequencies each. These frequencies were limited to the probe settings, so the curvilinear probe was set to 2.0MHz, 3.2MHz, and 4.0MHz and the linear probe was set to 8.5MHz, 10.0MHz and 11.5MHz. We varied other acquisition parameters systematically, all of which have been previously identified as affecting image quality: â¢ Gain (G): Adjusted across a range to assess its impact on image clarity and segmentation performance (Isensee 2021). Ten levels of gain were evenly spaced between 0 and 90. Gain linearly adjusts intensity based on depth. â¢ Dynamic Range (DR): Examined to determine its role in balancing contrast and noise, particularly in low-intensity regions (Ungi 2020). 10 levels of DR were evenly spaced between 30dB and 165dB. DR defines the ratio between the largest and smallest displayed echo intensities and consequently influences contrast resolution. â¢ Focal Depth (FD): Tested to evaluate its relationship with the target depth and resolution of posterior vertebral surfaces (Pesteie 2019). For the linear probe, ten levels were varied 119 between 5mm and 38mm. For the curvilinear probe, the ten available levels spanned 15mm to 78mm. FD specifies the depth of the narrowest beam and highest converging energy. â¢ Probe Type: We compared curvilinear and linear probes to assess performance variations but recognized that linear probes typically operate at higher frequencies (Welch 2013) which leads to superior spatial resolution but limited penetration depth. 2.1.2 Metrics To evaluate the quality of ultrasound imaging and its impact on segmentation performance, we assessed a range of quantitative metrics across three main categories: spatial resolution, image contrast, and segmentation accuracy. Figure 5.3. Point Spread Function (PSF) determination. (A) Gaussians fit along the primary axes of an US imaged wire with colour mapping to illustrate how intensity matches to the Gaussian curve. (B) Equations for 2D-Gaussian surface and PSF values. (C) Ultrasound image of a fishing wire in water, oriented perpendicular to the imaging plane. Spatial Resolution (PSF & ESF) Spatial resolution was characterized in part by the Point Spread Function (PSF), which was calculated by fitting 2D Gaussian functions to ultrasound images of a thin fishing wire phantom. 120 The resulting standard deviations from these fits provided quantitative estimates of lateral and axial resolution (Ungi 2020) and are visualized in Figure 5.3. Figure 5.4. Target phantom studies for ultrasound image quality. (A) Example image showing the target sphere, (B) Fit of a complementary error function to a given ray line. A secondary spatial resolution metric, the Edge Spread Function (ESF) was used to assess the sharpness of boundaries in ultrasound images. To compute ESF, we acquired scans of a phantom containing well-defined hyperechoic edges and fit a complementary error function to the resulting intensity transitions. The slope of this curve quantifies how rapidly intensity changes across the boundary, providing a proxy for edge sharpness that is relevant for both visual interpretation and computational segmentation (Pesteie 2019; Kochanski 2019). This process is illustrated in Figure 5.4. 121 Figure 5.5 Diagram of the selected ray-lines for IQ measurement on the target phantom and illustration of the CNR calculation. Image Contrast The Contrast-to-Noise Ratio (CNR) measures the image contrast of an ultrasound scan. The CNR evaluates the visibility of a target relative to background noise. CNR was calculated from target-sphere phantom images by taking the ratio of mean intensity differences to standard deviation in background regions (Bandaru 2016). We analyzed trends in CNR across various acquisition settings, including probe frequency, gain, and dynamic range (Murphy 2020), to determine optimal configurations for enhancing image quality. A set of 10 differently angled lines were used in the image (as is indicated by the black lines in figure 5.5) in order to better represent the total of the image. 122 Figure 5.6. Segmentation accuracy. (A) Sample segmentation of a Sawbones vertebral phantom and (B) diagram and equation for computation of Hausdorff distance and metric for segmentation accuracy. Segmentation Accuracy To evaluate segmentation accuracy, we applied several spatial error metrics that compare predicted bone surfaces from the CNN model to ground-truth segmentations derived from CT data. The Hausdorff Distance was used to quantify the maximum deviation between predicted and true surface contours, providing a sensitive measure of outlier error in both 2D and 3D space. This metric is particularly relevant in navigation applications where large local errors could compromise registration reliability (Figure 5.6). Additional metrics included the Root Mean Squared Distance (RMSD), which reflects average surface deviation across all points, and the Interquartile Range (IQR) of segmentation errors, used to assess variability in performance under differing imaging conditions. Together, these metrics form a comprehensive framework for assessing both imaging fidelity and the downstream utility of automated segmentation. 2.1.3 Analysis In order to identify parameter combinations that improve segmentation accuracy, the relationship between PSF and segmentation accuracy was assessed using logarithmic regression and correlation analysis. This approach examines the relationship between spatial resolution and segmentation accuracy, which is particularly important for parameter setting in shallow imaging depths relevant to posterior vertebral cortex imaging (Baka 2017). 123 2.2 Dataset Creation for ML Training In order to train an efficient and accurate ML segmentation network, we developed an automated pipeline for labeling, curating, and preprocessing datasets for training machine learning models in vertebral ultrasound segmentation (Figure 5.7). This pipeline aimed to ensure accurate, consistent, and diverse training data by integrating tracked ultrasound imaging, computed tomography (CT) registration, and automated labeling techniques (Ungi 2020). 2.2.1 Data Acquisition We acquired ultrasound and CT data from six cadaveric thoracolumbar spine specimens. Users received basic ultrasound training from an expert sonographer prior to data collection. Ultrasound scans were performed using a tracked Alpinion E-CUBE 12R system equipped with an L3-12H linear probe, operating at an 8.5 MHz frequency with dynamic range and gain settings optimized for vertebral imaging. Corresponding CT volumes were obtained using a Canon Aquilion Precision scanner and resampled to an isotropic 1 mm voxel grid to maintain spatial consistency with the ultrasound images. An NDI Polaris Vega optical tracking system was used to register the ultrasound probe and specimen, enabling a direct mapping between the ultrasound frames and the corresponding CT slices (MacLean 2022). Fiducial divots were glued to the cadaver prior to the CT scan, and a tracked pointer then matched their position between 3D space and the 3D model. Figure 5.7. Overview of the experimental setup for labeled dataset generation and application in tracking displaced vertebrae. (a) Transformation chain used for mapping CT slices (and segmented structures therein) to US frames. (b) Application of the pre-trained network in segmenting and registering displaced vertebrae from US images to the corresponding structure in CT. 124 2.2.2 Labelling Strategies To generate training labels for segmentation, three labeling strategies were implemented. Figure 5.8 illustrates these three labeling approaches, showing segmentation contours overlaid on both ultrasound and corresponding CT slices. Labels were assigned on the CT and then automatically transferred to match the ultrasound scans by registering both the cadaver and ultrasound probe to an optical tracker (NDI Vega) with fiducials placed on the cadaver before the CT scan. The full spine (FS) labeling strategy included the entire vertebra from the CT, even in regions poorly visualized on the ultrasound, or not visualized at all. Therefore, the resulting model would also attempt to predict deeper regions that may be obfuscated on the ultrasound (Kochanski 2019). The posterior cortex (PC) labeling strategy restricted segmentation labels to the posterior vertebral cortex to reduce errors associated with the deeper and more poorly visualized structures (Pesteie 2019). The intensity-weighted posterior cortex (IW) labeling strategy expanded on this by assigning weight values based on local ultrasound intensity, improving the delineation of well-visualized structures while reducing susceptibility to error in less well-defined bone structures (Ungi 2020). Segmentation of the posterior surface was the key unifying outcome. Post-processing allowed each method to be refined to the same key prediction. Figure 5.8. Vertebrae labeling approaches. First row shows labels overlaid on US images, and second row shows the same labels overlaid on corresponding CT slices. (a-b) Contours of FS labeling, (c-d) contours of PC labeling, and (g-h) Intensity-Weighted (IW) posterior cortex labeling, where (e) the weights are obtained by averaging pixel intensities within a 2Ã2 mm neighborhood. 125 2.2.3 Data Sanitization and Augmentation To improve dataset quality and model generalization, we implemented a data sanitization and augmentation pipeline (figure 5.9). Frames lacking valid labels due to probe misalignment or incomplete overlap between ultrasound and CT data were filtered out using an automated detection method (Kochanski 2019). One of the early identified problems were motion artifacts caused by fast or jerky motions from the user holding the ultrasound probe. These created discordance between the ultrasound image and the CT label either by worsening temporal calibration errors, or by moving the probe faster than the capture frame rate of the system. Motion artifacts were identified and removed by analyzing translation and angular velocity thresholds across consecutive frames, ensuring that only relatively static ultrasound frames were used for training (Soni 2016). Probe orientation density was evaluated using 3D quiver plots, and data pruning was performed to reduce oversampling and ensure more uniform coverage across scanning angles. To further enhance dataset diversity, augmentation techniques were applied, including simulated gain (from 0 to 90) and dynamic range (from 30 to 165) variations (Khallaghi 2010), as well as geometric transformations such as rotations and translations (Manbachi 2016). Gain and dynamic range variations were applied through a custom histogram matching procedure based on data collected over a range of gain and dynamic range for the image quality optimization trials that wasnât otherwise incorporated into the training set. 126 Figure 5.9. Data sanitization and augmentation. (a-d) Example images without (or with partial) labels due to imaging outside the region of interest. 3D quiver plots of probe directions for each acquired image (e) before and (f) after data pruning for uniform angle distribution. (g) Initial standard image and (h-j) consecutive frames with motion artifacts. (k) Original acquisition at G = 50 dB and DR = 80 dB, and (l-n) data augmentation with simulated G and DR values. 2.3 Convolutional Neural Network for Segmentation Figure 5.10 illustrates the network architecture trained for our segmentation. A modified TernausNet architectureâa U-Net variant that incorporates a pre-trained encoderâwas used for vertebral segmentation. This encoder-decoder structure was selected for its balance of computational efficiency and segmentation accuracy. The encoder was based on VGG-11, a convolutional neural network with 11 layers (including 8 convolutional layers), known for its simplicity and strong performance in visual recognition tasks. It was pre-trained on ImageNet, a large-scale dataset of millions of labeled images, enabling effective feature extraction from ultrasound inputs through transfer learning. The decoder, composed of convolutional and transposed convolutional layers, reconstructed the segmentation maps. ReLU (Rectified Linear Unit) activation was applied in all layers to introduce non-linearity and maintain computational efficiency, except for the final decoder layer. At the final layer, a sigmoid activation function classified each pixel as either part of the vertebral cortex or background. The ReLU activation function is defined as: ð<'=>(ð¥) = max(0, ð¥) 127 Figure 5.10. Illustration of segmentation network architecture with sample input, training label and output. (A) Sample image with overlying CT, (B) modified TernausNet architecture and (C) output segmentation in green based on the network contrasted with the tracker erroneously predicting the dashed magenta line following a spinal deformation or loss of registration. 2.3.1 CNN Model Training The dataset of paired CT and ultrasound scans was created with six cadaveric torsos that first underwent a CBCT, then registration to a optical tracker through known fiducials added pre-CT and then followed by ultrasound scans with a tracked probe. To ensure robust training and evaluation, the dataset was divided into training, validation, and test sets, consisting of 10,375, 5,433, and 5,984 images, respectively, with no specimen overlap between subsets. Images were resampled to a resolution of 256 Ã 512 pixels with 0.14 mm spatial spacing to maintain anatomical consistency across scans. The model was trained using weighted binary cross-entropy loss, prioritizing segmentation accuracy near the posterior cortex to account for class imbalance. Training was performed using the Adam optimizer with a learning rate of 1 Ã 10â»âµ and a batch size of 12. Data augmentation, including geometric transformations and intensity adjustments, was incorporated during training to improve model generalizability. 2.3.2 Ultrasound Slice Calibration Since segmentation accuracy depends on accurate spatial alignment between ultrasound frames and their corresponding CT references, the ultrasound slice thickness was calibrated to ensure accurate depth representation (figure 5.11). A fine wire phantom was used to evaluate slice thickness at varying depths. A geometric relation between the imaged wire length and ultrasound slice thickness was established, and example images of the wire acquired at different depths 128 confirmed the expected variations. This calibration step facilitated matching the ultrasound reconstruction with the correctly selected label data from the CT scan (Welch 2013). Figure 5.11. Calibration of US slice thickness. (a) Photo of the experimental setup fishing wire and Superflab block to prevent acoustic reverberation. (b) Zoomed inset showing the geometric relation between imaged wire length and slice thickness. (c) Example image of the wire acquired at a depth set to focal length. 2.3.3 Data Sanitation In order to improve training data quality and reduce the impact of motion artifacts, we implemented a three-part dataset sanitization process involving frame filtering, velocity-based artifact rejection, and vertebral density normalization. Retain high-quality training frames We applied a precision-recall analysis to evaluate frame-level filtering criteria. A quality metric was defined as the frame-to-volume overlap score, which represented the percentage of each ultrasound frame that intersected the convex hull of segmented vertebrae in the CT volume. A separate set of images were then manually labelled as either containing or not containing meaningful information. These were used as comparators to compare with the images left after different levels of filtering in order to produce the precision-recall curve. Where true positive (TP) denotes correctly retained usable frames, false positive (FP) are incorrectly retained unusable frames, and false negative (FN) are incorrectly discarded usable frames, then the precision and recall are computed as: ðððððð ððð = ðððð + ð¹ð 129 ð ððððð = ðððð + ð¹ð We plotted the precision-recall curve to visualize the trade-off between filtering stringency and frame retention. Note that these are machine learning terms for what would be referred to as Positive Predictive Value (PPV) and Sensitivity (Sn) respectively in clinical applications. Remove motion artifacts We computed probe velocities from tracked pose data and established threshold cutoffs for translational and angular velocity. Specifically, we evaluated a range of threshold combinations and computed the Critical Success Index (CSI) to quantify agreement with manually labeled ground truth. CSI was defined as: ð¶ðð¼ = ðððð + ð¹ð + ð¹ð We selected the threshold pair of translational and angular velocity that maximized CSI on the validation set. Prevent sampling bias toward specific vertebral levels We implemented vertebra-wise density filtering by calculating the number of labeled frames corresponding to each vertebral level and pruning frames from overrepresented levels to create a more balanced distribution across the spine. This ensured that CNN training was not skewed by anatomical oversampling and encouraged more generalized segmentation performance. 2.3.4 Segmentation Performance Metrics Two primary metrics were used to evaluate segmentation accuracy and its downstream application in vertebral tracking. The root mean square distance (RMSD) measured pixel-wise segmentation error by quantifying the deviation between predicted and ground-truth contours from the registered CT. The target registration error (TRE) measured the registration accuracy by aligning a point cloud, produced from segmentation of the vertebrae on ultrasound scans, with the CT reference model. TRE was defined as the Euclidean distance between predefined anatomical target points on the CT (specifically, entry points for pedicle screws) and their corresponding points after transforming the segmented ultrasound-derived point cloud via the estimated registration transform. The registration itself was computed in two stages: 130 1. Coherent Point Drift (CPD) was used to align the 3D point cloud from ultrasound (derived from segmented frames and probe pose) to the vertebral surface mesh from CT. CPD treated the point cloud as a Gaussian mixture model, fitting it to the CT mesh using expectation-maximization. 2. Iterative Closest Point (ICP) refinement then minimized the point-to-plane distances between matched points, progressively reducing the maximum correspondence distance from 7âmm to 1âmm until convergence. To emulate spinal deformation and test robustness, each registration was initialized with a random perturbation of ±5âmm translation and ±2° rotation. TRE was then calculated as the 3D distance from transformed points to the known ground truth targets, with the CT mesh taken as the identity reference frame. Both the RMSE and the TRE are then used to compare the performance of different labelling and augmentation strategies. 2.3.5 Confidence Thresholding In order to refine segmentation quality and suppress false positives during inference, we applied confidence thresholding to filter the networkâs predicted labels. For the posterior cortex (PC) segmentation model, we evaluated a range of softmax-based confidence score thresholds on the validation dataset. Each threshold level determined the minimum prediction probability required for a pixel to be considered part of the vertebral surface. We then computed the 3D Target Registration Error (TRE) resulting from these segmentations after registration to CT. Thresholds were incrementally adjusted, and segmentation contours were visualized on both ultrasound and corresponding CT slices to qualitatively assess anatomical accuracy. 3 Results This section presents the results from process of optimizing the image quality, acquiring the dataset, sanitizing the data, training the network and finally evaluating the segmentations. This structure roughly parallels how these elements were introduced in the methods section. 3.1 Image Quality Optimization The image quality optimization experiments evaluated the effects of ultrasound acquisition parameters on spatial resolution, contrast, and segmentation accuracy. Quantitative assessments included PSF and ESF as measures of spatial resolution, CNR to assess image contrast, and 131 segmentation accuracy metrics, including Hausdorff distance, to evaluate the performance of machine learning-based vertebral segmentation. The following sections detail these findings across varying gain, dynamic range, and focal depth settings, with results presented for both phantom and cadaveric models. 3.1.1 Point Spread Function The PSF was measured to quantify spatial resolution across different ultrasound acquisition settings. Both axial and lateral PSF were analyzed across gain, dynamic range, and focal depth variations to evaluate their effects on image sharpness. Figure 5.12 illustrates the results, with axial PSF values shown in the top row and lateral PSF values in the bottom row, while columns compare outcomes across variations in various acquisition parameters. Across all experiments in figure 5.12, lower gain and dynamic range settings resulted in reduced PSF values, indicating improved spatial resolution. The axial PSF showed sharper improvements near the focal depth, whereas lateral PSF exhibited a broader response curve, suggesting more gradual changes in resolution across focal depths. The linear probe consistently outperformed the curvilinear probe, as indicated by the lower PSF values in Figure 5.12, though, given the difference in operating frequencies, it is unclear whether the differences are due to the probe shape or the operating frequency. Higher frequency ultrasound settings also resulted in lower PSF values, as expected from theoretical spatial resolution properties as described by Pinton (2015) amongst many others. The focal depth had a mild influence on PSF, with optimal resolution achieved when the focal depth was near the target region. PSF values increased when imaging beyond the optimal focal depth, particularly for axial resolution, suggesting a degradation in image quality at non-ideal depth settings. 132 Figure 5.12. Spatial resolution measured as axial PSF (A-C) and lateral PSF (D-F). These metrics are recorded over ranges of imaging parameters including gain (A, D), dynamic range (B, E) and focal depth (C, F). 3.1.2 Edge Spread Function Edge Spread Function (ESF) analysis was performed to evaluate edge sharpness and transition contrast in ultrasound images. Figure 5.13 presents the ESF results across varying gain and dynamic range settings, showing how image clarity and contrast were affected by different acquisition conditions. The ESF results revealed a trade-off between gain and dynamic range, with optimal edge sharpness observed along a diagonal extending from low gain and high dynamic range, to high gain and low dynamic range. At these settings, intensity transitions between structures were more defined, improving the visibility of anatomical boundaries. However, when gain and dynamic range were set too low (top left teal corners in figure 5.13), images became excessively dim, leading to non-interpretable results. As ultrasound frequency increased, the threshold at which images became too dim shifted to the right, meaning that higher gain settings were required at higher frequencies to maintain optimal 133 edge clarity. While high gain levels improved signal intensity, they also broadened the ESF, indicating a reduction in segmentation precision due to increased noise levels. Similarly, high dynamic range settings reduced contrast at boundaries, further broadening the ESF. Overall, the ESF results indicate that optimal settings must balance signal intensity and noise suppression, with excessively high or low gain and dynamic range settings leading to degraded edge sharpness. Figure 5.13. Edge spread function (ESF) across gain and dynamic range at (A) 8.0 MHz, (B) 10.0 MHz, and (C) 11.5 MHz. (D) Pixel intensity profiles across the target boundary at different angles, acquired at 90 dB dynamic range, gain of 50, and 10.0 MHz scanning frequency with a linear probe. Each color represents a different angle off the target sphere. 3.1.3 Contrast-to-Noise Ratio Contrast-to-noise ratio (CNR) was evaluated using the target phantom, with results presented in Figure 5.14 as heat maps comparing gain (x-axis) and dynamic range (y-axis) variations. Each data 134 point in the heat maps represents the average CNR computed across multiple radial intensity profiles around the phantomâs target region. The results indicate a consistent pattern of CNR peaks running orthogonally across the heat maps, suggesting an optimal balance between gain and dynamic range for achieving strong contrast. These peaks were observed at similar locations for all three frequencies tested on the linear probe, indicating that the relationship between gain and dynamic range was comparatively frequency-invariant. CNR values were highest at both low and high extremes of the parameter ranges, though variations within the optimal region were minimal. The variety of angles used in the image ensured that CNR measurements were not biased by local signal variations. At high gain and dynamic range values, images became noisier, leading to lower effective CNR despite higher signal strength. Conversely, at excessively low settings, poor signal penetration reduced contrast between structures. These results highlight the importance of selecting appropriate gain and dynamic range settings to maintain an optimal balance between contrast and noise suppression. Figure 5.14. Contrast resolution measured as CNR across gain and dynamic range for linear probes with varying scan frequencies: (A) 8.0MHz, (B) 10.0MHz and (C) 11.5MHz. Higher values of CNR are preferred. 3.1.4 Segmentation Accuracy and Comparison with Image Quality Metrics The final set of image quality experiments evaluated the impact of ultrasound acquisition parameters on machine learning-based vertebral segmentation accuracy. Figure 5.15 presents segmentation accuracy results, including Hausdorff distance across gain vs. dynamic range 135 settings, a plot of PSF against median segmentation error and finally sample segmentations on both phantom and cadaveric scans. Quantitative analysis of Hausdorff distance revealed a clear relationship between segmentation error and image acquisition settings. The lowest Hausdorff distances were observed in parameter regions corresponding to optimal PSF and CNR values, indicating that higher image quality directly contributed to more accurate segmentation outputs. The trade-off between gain and dynamic range was also evident in the segmentation results, mirroring trends seen in the ESF and CNR analyses. Figure 5.15. Assessment of segmentation accuracy (Hausdorff distance) across gain and dynamic range for (A) the SawBones phantom and (B) cadaveric imaging. (C) Segmentation accuracy against spatial resolution. Median points and IQR spread represent 10 repeat trials at dynamic range between 30 to 165 and gain between 0 and 90. Sample segmentations of the (D) model and (E) cadaveric vertebrae acquired at 135 dB dynamic range, gain of 10, and a 11.5MHz scanning frequency with a linear probe. A plot of segmentation accuracy against PSF (from the wire experiment and matched to the imaging parameters used for the segmentation) in figure 5.15C demonstrated an approximately 136 logarithmic relationship for PSF values above 4mm, where segmentation error decreased as PSF values improved. However, a spike in segmentation error was observed when PSF values approached zero, possibly due to measurement artifacts or signal degradation in excessively weak ultrasound signals. Qualitative segmentation comparisons further supported these findings. Segmentation performed before and after image quality optimization (Figure 5.16) show that the optimized ultrasound settings produced visibly sharper segmentations, while suboptimal settings led to inconsistent contour delineations and increased false positives. The results also indicate a shift in the optimal balance between gain and dynamic range when transitioning from phantom to cadaveric imaging, with higher gain settings needed in cadaveric scans to preserve segmentation performance. Figure 5.16. Sample images of spinous process segmentation using a CT-trained CNN with ultrasound images (A) before, and (B) after image quality optimization. Figure 5.16 illustrates the qualitative impact of image quality optimization on the performance of the initial segmentation. Figure 5.16A demonstrates the segmentation at the imaging parameters selected by the expert sonographer. This included a Gain of 40, a dynamic range of 75dB and a operating frequency of 10MHz using the linear probe. These were the settings at which the initial network was trained and produced a Hausdorff distance of 5.10mm. In contrast, figure 5.16B shows the image parameters optimized for the performance of the network. Here a gain of 10, a dynamic range of 135dB and a frequency of 11.5MHz are used which produces a Hausdorff distance of 1.66mm. 137 3.2 CNN Segmentation Performance The performance of the convolutional neural network (CNN) for vertebral segmentation was evaluated based on segmentation accuracy, dataset preprocessing impact, and registration accuracy. Three labeling strategies were compared: full spine (FS), posterior cortex (PC), and intensity-weighted posterior cortex (IW). The analysis incorporated both quantitative metrics, Root Mean Square Distance (RMSD) and Target Registration Error (TRE), as well as qualitative segmentation visualizations to assess model performance. The following sections detail these findings based on different evaluation criteria. 3.2.1 Comparison of Annotating Strategies: Segmentation Accuracy and Registration Performance The CNN segmentation model was tested using three distinct annotation strategies: FS, PC, and IW. Figure 5.17 presents the segmentation accuracy results, where RMSD and TRE were used as primary evaluation metrics. RMSD values revealed that FS labeling led to the highest segmentation errors, often exceeding 20 mm, particularly in shadowed regions beneath the posterior cortex. In contrast, PC and IW labeling strategies demonstrated significantly improved segmentation accuracy, with mean/median? RMSD values of 5.8 mm and 4.8 mm, respectively. The IW labeling method appeared to reduce false positives in shadowed areas. The TRE measurements confirmed these findings. The PC and IW labeling strategies achieved sub-2 mm registration accuracy, with PC averaging 1.56 ± 0.34 mm and IW averaging 1.82 ± 0.64 mm, both within clinically acceptable thresholds for minimal-risk spinal navigation. Despite slight differences in segmentation accuracy, registration performance remained consistent between PC and IW strategies, indicating that minor segmentation variations did not significantly impact alignment with CT ground truth models. Compared with PC labelling, IW labelling, in particular showed a reduction in segmentation errors within shadowed regions (Figure 5.17). Qualitative segmentation comparisons (Figure 17c-h) further illustrate these trends, with overlays of predicted segmentation contours on ultrasound and corresponding CT slices. The results confirm the superior accuracy of PC and IW approaches, as FS segmentation frequently exhibited hallucination artifacts in shadowed areas. 3D visualizations of segmented vertebral cortices 138 (Figure 17i-k) show close alignment between the predicted and reference CT surfaces, with PC and IW strategies yielding the most anatomically accurate reconstructions. Figure 5.17. Evaluation of different annotating strategies on test dataset of 5984 images: (a) 2D RMSD and (b) 3D TRE. Median is represented by a red line, mean by a red dot, and the IQR is shown by the box. (c-h) Segmentation overlays on US and CT slices. (i-k) 3D visualizations of the vertebra cortex after registration; the blue cortex is the original and the orange cortex is after the registration. 3.2.2 Slice Thickness Calibration and Registration Accuracy A critical factor in segmentation accuracy is the ultrasound slice thickness, which affects the spatial resolution of reconstructed vertebral structures. Figure 5.18 presents the slice thickness calibration results, demonstrating how ultrasound depth settings influence segmentation and registration accuracy. Gaussian fits were applied to ultrasound acquisitions at varying θ values and a fixed 30 mm depth (Figure 18a), allowing for slice thickness estimation. These estimates were validated across multiple depth settings (Figure 18b), confirming that segmentation performance improved when 139 using the calibrated slice thickness values. The lowest registration error was observed at the optimized slice thickness setting (Figure 18c). Figure 5.18. Slice thickness calibration and validation. (a) Gaussian fits for varying ð and fixed 30 mm depth. (b) Slice thickness estimates at varying depths. (c) Registration accuracy was minimized when using the estimated slice thickness value. 3.2.3 Impact of Dataset Sanitization Figure 5.19 presents the results of dataset sanitization tuning, which aimed to remove invalid frames, correct for motion artifacts, and normalize probe orientation density. The precision-recall curve (Figure 5.19a) illustrates the effectiveness of frame filtering techniques, ensuring that only high-quality labeled frames were retained for training. A cutoff of 90% was selected where both precision and recall were 98%. The CSI (Figure 5.19b) maps the effectiveness of motion artifact removal using translation and angular velocity thresholds. The final selections marked by blue lines where the highest CSI was found at ð¡â. = 13°/ð and ð¡â; = 19ðð/ð . Finally, vertebra-wise density filtration (Figure 5.19c) identified the need to reduce the large relative excess of L1 and L2 scans to reduce potential bias in CNN training. 140 Figure 5.19. Dataset sanitization tuning parameters. (a) precision and recall curve for filtering images without labels. (b) Critical Success Index map for removing images with motion artifacts using translation and angular velocity thresholds. (c) vertebrae-wise density filtration using the tuned parameters. 3.2.4 Effect of Data Curation on PC Labeling Strategy To evaluate the impact of data curation on segmentation accuracy, dataset sanitization (S+) and augmentation (A+) were applied to the PC labeling strategy. The results, presented in Figure 20, show that preprocessing steps significantly improved segmentation accuracy. Pixel-wise RMSD (Figure 20a) and 3D TRE (Figure 20b) measurements confirmed that sanitized and augmented datasets consistently appeared to outperform the unprocessed datasets, demonstrating lower segmentation and registration errors. The segmentation overlays in Figure 20c-j visually compare the effects of sanitization and augmentation, highlighting sharper and more precise vertebral contours after preprocessing. 141 Figure 5.20. Evaluation of the data curation on PC approach. S+ indicates the use of data sanitization, and A+ indicates the use of augmentation. (a) 2D pixel-to-pixel RMSD and (b) 3D TRE. (c-j) Effects of data sanitization and augmentation on the training of the network are visualized as segmentation contour overlay on US and CT slices. 3.2.5 Effect of Data Curation on IW Labeling Strategy A similar analysis was conducted for the IW labeling approach, with results shown in Figure 21. As with the PC approach, data sanitization and augmentation improved segmentation accuracy, reducing both RMSD (Figure 5.21a) and TRE (Figure 5.21b). Figure 5.21c-j compares segmentation overlays before and after dataset preprocessing, confirming that sanitized and augmented datasets produced clearer segmentation boundaries with fewer hallucination artifacts. Sanitization appeared to improve performance to a s lightly greater degree relative to augmentation. Some augmentations, such as matching histograms to emulate alternative gain and dynamic range parameters, may have resulted in unrealistic images that may have inadvertently hindered the performance. 142 Figure 5.21. Evaluation of the data curation on the IW approach. S+ indicates the use of data sanitization, and A+ indicates the use of augmentation. (a) 2D pixel-to-pixel RMSD and (b) 3D TRE. (c-j) Effects of data sanitization and augmentation on the training of the network are visualized as segmentation contour overlay on US and CT slices. 3.2.6 3D Evaluation of PC Labeling Strategy at Different Confidence Thresholds To further analyze segmentation robustness, the PC labeling strategy was evaluated across varying confidence thresholds, with results shown in Figure 22. 3D TRE values (Figure 22a) were computed across different confidence levels to determine the optimal segmentation threshold. Visual comparisons in Figure 22b-m illustrate segmentation performance across different confidence scores, showing overlays of ultrasound segmentations (top row) and corresponding CT overlays (bottom row). The results indicate that lower confidence thresholds introduced noise, whereas higher thresholds improved segmentation precision but slightly reduced sensitivity in faint structures. 143 Figure 5.22. 3D evaluation of the PC annotating strategy over various confidence scores. (a) 3D TRE over different confidence scores. (b-m) visual evaluation over different thresholds, where first row (b-g) is US image overlay with segmented posterior contour and second row (h-m) is corresponding CT slice overlay with same segmented contour. 4 Discussion The results of this study directly connect image quality with segmentation performance, establish a set of imaging parameters for network learning (see table 5.1), and demonstrate that the resultant network can accurately segment the posterior cortex of the vertebrae. The evaluation found that selecting parameters to adjust image quality for the network, and high-volume labeling strategies, produce high segmentation and registration accuracy. Table 5.1 Summary of imaging parameter and probe recommendations for performing accurate segmentation of spinal bones on ultrasound imaging. 144 4.1 Key Findings The image quality analysis demonstrated the effects of variable acquisition parameters such as gain, dynamic range, and focal depth in determining spatial resolution and, consequently, segmentation performance in US images of the spine. High axial and lateral PSF values were associated with reduced segmentation accuracy, as seen in the correlation between increasing PSF and larger segmentation errors. Specifically, low dynamic range and gain settings were found to minimize PSF while ensuring sufficient signal intensity for accurate segmentation. Recommended parameters are summarized in table 5.1 and include a dynamic range of 135dB and a gain of 10. These results directly connect image quality metrics and machine learning performance and demonstrate the value of optimizing ultrasound parameters for clinical applications. The Intensity-Weighted (IW) posterior cortex labeling approach emerged as the most effective strategy in reducing segmentation artifacts, especially in the shadowed regions beneath the vertebral cortex (Noble, 2014). By assigning weight values to pixel intensities, IW labeling effectively mitigated hallucination artifacts, which were prevalent in the Full Spine (FS) labeling approach (Housden, 2012). This insight underscores the potential of IW labeling to improve segmentation reliability, particularly in regions prone to acoustic shadowing (Housden 2012). 145 In addition to improving segmentation accuracy, optimized acquisition parameters and labeling strategies significantly affected machine learning performance (Xu, 2018). The use of automated labeling and data sanitization, particularly in combination (i.e., the S+ and A+ condition) enhanced the robustness of the training dataset, ensuring consistency and minimizing errors introduced during manual curation (Zhu, 2019). These algorithm additions enabled us to achieve sub-millimetric registration accuracy, which is a level of performance needed for a number of applications in spinal surgery navigation (Schlosser, 2021). Overall, this study demonstrates the interdependence of image quality, segmentation accuracy, and machine learning performance (Huang, 2023; Li, 2022). By identifying optimal acquisition parameters and refining labeling strategies, this work provides recommended processes and setting for integrating real-time ultrasound imaging with machine learning to enhance intraoperative navigation (Prada, 2016; De Rosa, 2023). Future research should explore the generalizability of these findings across different ultrasound systems and anatomical targets to extend their clinical applicability (Giussani, 2023; Ivanov, 2010). 4.2 Relevance to Pre-existing Literature This study builds upon a growing body of research that highlights the potential of ultrasound imaging for intraoperative navigation and its integration with machine learning techniques (Gueziri, 2021; Koo & Kwok, 2016; Khallaghi, 2010). Prior work has demonstrated the feasibility of ultrasound in tracking spinal anatomy and addressing challenges such as acoustic shadowing and noise artifacts through segmentation algorithms (Gueziri, 2021; Koo & Kwok, 2016; Khallaghi, 2010). The findings align with earlier studies showing that spatial resolution, as characterized by PSF, is a critical determinant of segmentation performance and that optimizing acquisition parameters can significantly enhance image quality and reduce segmentation error (Prada, 2016; De Rosa, 2023). The use of intensity-weighted (IW) labeling in this study improves performance, extending prior labeling strategies such as posterior cortex (PC) labeling by incorporating pixel intensity to mitigate hallucination artifacts in shadowed regions (Giussani, 2023; Ivanov, 2010). Moreover, the <2 mm target registration error (TRE) achieved in this work is consistent with clinical requirements for spinal navigation systems (Manbachi, 2016; Chan, 2022), further validating the relevance of the proposed methods. By providing mechanisms to address the limitations of manual labeling and incorporating automated data sanitization, this study 146 complements and extends existing methodologies aimed at improving the robustness and efficiency of supervised learning in ultrasound-guided surgery (Huang, 2023; Li, 2022; Holm & Skjoldbye, 1996). These contributions represent a meaningful step toward bridging the gap between research and clinical implementation of machine learning-enhanced ultrasound systems. 4.3 Limitations Despite the promising findings, this study has several limitations that warrant consideration. A key limitation is the reliance on controlled datasets derived from phantom and cadaveric spine models. These settings provide consistency and repeatability, but they do not fully replicate the variability and complexity of in vivo conditions (Ungi, 2020; Baka, 2017). Factors such as soft tissue attenuation, patient movement, and diverse anatomical variations not present in the specimens studied here could significantly affect the performance of the proposed methods, and the approach assessed here remains untested in a clinical environment (Katouzian, 2012). Another limitation is the sensitivity to probe calibration and use of data sanitization. Accurate spatiotemporal calibration is essential for aligning ultrasound frames with the corresponding CT data and for ensuring reliable measurements (Alsinan, 2020). However, calibration errors in probe registration (between scan and tracker) or deviations in the surgical workflow (poor acquisition) could compromise segmentation and registration accuracy. Similarly, data sanitization processes play a pivotal role in removing artifacts and invalid frames, but these processes depend on predefined thresholds that may not generalize well to all datasets or clinical scenarios (Huang, 2023). Addressing these dependencies will require further refinement of calibration protocols and the development of more robust, adaptive sanitization techniques capable of accommodating a wider range of variability (Chen, 2023). 4.4 Future Work Future research could focus on addressing the limitations of the current study and expanding the scope of its applications (Ungi, 2020; Baka, 2017). One key area is the incorporation of dynamic testing (where sweeps are done at the speed of an intraoperative setting and the patient has movement such as respiration) with soft tissue models to better emulate in vivo conditions (Katouzian, 2012). This would provide a more realistic assessment of the system's robustness to 147 effects such as soft tissue attenuation, patient movement, and acoustic variability, which are likely to be encountered in the transition to clinical application (Alsinan, 2020). Exploration of alternative segmentation networks, such as transformer-based models or recurrent architectures (explored by Isensee 2021 and Iglovikov 2018), presents another avenue for potential mitigating some of the variability seen in our evaluation. Simonyan identified that these architectures have shown promise in leveraging temporal and spatial context in image data. This could mitigate frame-to-frame variability and enhance segmentation accuracy, particularly for feature that vary rapidly between frames like acoustic shadows. 5 Experimental Conclusions These experiments presented a systematic investigation into optimizing ultrasound imaging for machine-learning-driven segmentation of spinal anatomy. The methods outlined included image quality optimization, automated dataset creation, and implementation of CNNs for segmentations building on work in similar approaches by El-Hariri, Hu and Hachilogu. Key findings demonstrated that optimal acquisition parameters significantly enhanced spatial resolution and segmentation accuracy, while improved labeling strategies such as intensity-weighted posterior cortex (IW) labeling reduced hallucination artifacts and improved the fidelity of segmentation models (Giussani, 2023). Additionally, both PC and IW approaches demonstrated registration accuracies within clinically acceptable thresholds (<2 mm TRE). The clinical implications of these findings are significant. ML-driven segmentation of spinal ultrasound has the potential to enhance intraoperative navigation by providing real-time anatomical tracking and correcting for deformations or changes in pose during surgery. This capability is particularly relevant for procedures where maintaining precision is critical, such as spinal fusion or minimally invasive interventions. By integrating optimized imaging parameters with robust segmentation techniques, this approach can potentially improve surgical accuracy, reduce complications, and support more efficient workflows. Furthermore, the methods presented in this study highlight a potential shift away from traditional reliance on ionizing radiation-based imaging modalities such as fluoroscopy or CT during surgery. By offering an ultrasound-based alternative that is non-invasive, real-time, and free of radiation, ML-enhanced ultrasound imaging aligns with efforts to improve patient safety and reduce 148 cumulative radiation exposure for both patients and surgical staff. Continued development and clinical validation of this technology could pave the way for broader adoption in spine surgery and other fields where precision imaging is needed. 6 Summary This chapter described developing ultrasound image quality optimization and machine learning-based segmentation for bone surface detection. This concluding summary outlines the primary contributions, methodological developments, and their implications for future applications in ultrasound-guided navigation. Image Quality Optimization Through image quality optimization, the effects of gain, dynamic range, focal depth, and probe selection on spatial resolution, contrast, and segmentation accuracy were evaluated. Results demonstrated that higher frequency linear probes provided improved spatial resolution but required careful tuning of acquisition parameters to maintain optimal contrast and minimize segmentation errors (Alsinan 2020). The relationships between point spread function (PSF), edge spread function (ESF), and contrast-to-noise ratio (CNR) were quantified, establishing a direct link between ultrasound image quality and segmentation performance. Dataset Generation and CNN Training In addition to optimizing acquisition parameters, a dataset generation and labeling framework was developed to support machine learning-based segmentation. By integrating CT-derived vertebral segmentations with tracked ultrasound images, a structured dataset was curated for training convolutional neural networks (CNNs). The comparison of full spine (FS), posterior cortex (PC), and intensity-weighted posterior cortex (IW) labeling strategies demonstrated that IW labeling improved segmentation accuracy in shadowed regions, reducing false positives and enhancing anatomical registration (Giussani 2023). The application of data sanitization and augmentation techniques further improved segmentation robustness by filtering low-quality frames and increasing dataset diversity. 149 Implications and Next Steps The findings presented in this chapter contribute to the broader objective of developing an ultrasound-augmented drill guide for self-localization. The optimization of imaging parameters, automated dataset creation, and segmentation refinement provide a foundation for accurate and reliable bone surface tracking. The next phase of this work involves validating ultrasound-based localization techniques for use in a proposed self-localizing surgical tool application by emulating proposed drill guide configurations in a controlled setting. Using traditional ultrasound probes in water baths, the experiments outlined in the next chapter will assess segmentation performance and imaging strategies for practical application in ultrasound-guided spinal navigation. 150 1The bulk of the work presented in this chapter is being submitted for publication as: MacLean LJ, T Salcudean, J Street, Hodgson AJ. Evaluating Ultrasound-Integrated Tools through Self-Localization of Tracked Ultrasound Probes. 2025. Chapter 6 Evaluating Anticipated Performance of Self-Localized Drill Guides by Emulating Proposed Designs Minimally invasive spinal procedures demand accurate hardware placement, but existing navigation systems rely heavily on CT-based imaging, which increases costs, radiation exposure, and workflow complexity. Ultrasound-based navigation presents a promising alternative, offering real-time, radiation-free imaging. However, most current ultrasound solutions either require high user expertise or lack integration with surgical tools. Our prior work, in MacLean 2023, has proposed designs for self-localizing drill guides that incorporate ultrasound rangefinding, but their performance has yet to be validated experimentally. This chapter aims to bridge that gap by emulating several of the proposed self-localizing designs using traditional ultrasound probes. Through controlled experiments in water baths with 3D spine models and optical tracking, we evaluate whether existing probes can approximate the imaging characteristics and localization accuracy of the envisioned designs. This approach allows us to assess feasibility, compare tool geometries, and explore how parameters like probe geometry and scanning orientation influence registration performance â all before committing to hardware development for full working prototypes. 1 Research Questions Building on the findings from previous chapters that demonstrate (summarize key relevant findings here), the study presented in this chapter aims to evaluate the anticipated performance of proposed self-localizing surgical tool designs by emulating and comparing these proposed designs using existing US probes and evaluating the localization accuracy of the various designs in simulated application scenarios involving anatomically realistic bone models and emulated probe positions.151 More specifically, we aim to answer the following specific research questions: 1. Do the emulated ultrasound designs achieve sufficient localization accuracy for selected emulations of anticipated clinical applications in spinal navigation? 2. Which proposed self-localizing tool designs perform best across the various anticipated surgical scenarios? 3. How do design choices such as transducer resolution and focal depth influence registration accuracy? 4. Can freehand calibration with endocavity probes achieve clinically acceptable accuracy for tool tracking? By systematically addressing these questions, we seek to identify the most promising path forward for advancing this self-localizing tool concept towards clinical implementation. 2 Methods In order to evaluate the feasibility of ultrasound-augmented spinal navigation, we selected a number of proposed tool designs to emulate, emulated them using various combinations of existing standard US probe designs (including both external and endoprobe designs), used optically tracked implementations of the emulated designs to acquire tracked US imaging data from various anatomical models chosen to represent the bony anatomy expected to be encountered in proposed spine applications of the tools, and processed the resulting tracked images using algorithms presented in earlier chapters in order to calculate the localization accuracies under the various emulated scenarios. Because this registration process itself requires several steps with many different possible points of failure, this phased approach for the methods facilitated troubleshooting the original setup. These stages included: 1. Constructing realistic spine models for controlled experimental setups. 2. Calibrating and tracking ultrasound probes. 3. Acquiring and processing ultrasound images to generate distance measurements. 4. Registering the resulting point clouds to preoperative 3D models. 5. Assessing the accuracy of the different emulated tool designs. 152 2.1 Experimental Setup The experimental setup comprises five main components (see Figure 6.1): emulations of proposed self-localizing surgical tool designs (including associated US signal generation and processing electronics), anatomical models of the spine, an optical tracking system, a calibration phantom, and software for signal and image processing. 2.1.1 Emulations of Proposed Self-Localizing Surgical Tool Designs In this study, we emulated four proposed self-localizing tool designs that were inspired by the results from the design study reported in Chapter 2. These are shown in Figure 6.2, along with the proposed emulations using existing US probes. The four designs are the following: 1. Flat Design: The linear probe was positioned downward over the model and moved orthogonally to emulate a flat scanning path. 2. Curved Radial Design: The probe was rotated along its axis, resembling drill guide placement for pedicle screws. 3. Flat Radial Design: Similar to the curved radial design but using a flat trajectory. 4. Annular Stack Design: The tool was moved parallel to its axis in translation. Figure 6.1. Emulated designs and probe trajectories evaluated in the study. (A) A flat design on the surface of the skin is emulated with a linear probe translating perpendicular. (B) A curved radial design simulated by rotating a curved forward-facing endocavity probe about its axis. (C) A linear radial probe evaluated by spinning a linear side-ranging probe about its axis. (D) The annular stack design is modelled by a side-ranging curvilinear endocavity probe which is translated along its axis. 153 Ultrasound Imaging: For ultrasound imaging, the Verasonics Vantage system was used with two probes: the L15 linear probe, the GE IC9-RS endocavity probe and the SR15 duel-emit endoscopic probe (Verasonics Inc., 2023). All were driven at 5 MHz to control for frequency impact on performane. Since higher frequency improves bone resolution, but reduces depth, 5.0MHz was chose based on prior work to balance their impact on performance (MacLean 2023). The linear probe, mounted on a linear stage, scanned along the length of the models, simulating medial positioning on a patientâs back. For the pedicle model, the probe emulated an oblique trajectory aligned with a proposed screw path. The endoscopic probes, secured with a crab clamp, was manually rotated while maintaining camera alignment. Their placement simulated the drill guideâs radial tip measurements, aligning with pedicle screw trajectories. Configurations are illustrated in Figure 6.1. 2.1.2 Anatomical Models To evaluate the emulated tool designs described above, we developed three anatomical spine models that allowed us to place the emulated tools in positions that roughly correspond with the intended surgical placements of the envisioned tools. The primary application we envision is pedicle screw insertion, so the drill guide axis needs to be placed in line with the pedicle, with the tip either directly in contact with, or slightly withdrawn from, the entrance to the pedicular channel. Since our initial application of this concept will be to the larger vertebrae, we chose to model vertebrae in the lumbar spine. We therefore developed three distinct models: Three spine models were created to test the transducers in different anatomical positions: 1. Lumbar L4 Model: This model was based on a real CT scan of a lumbar L4 vertebra and printed in PLA using an Ultimaker S3 3D printer (Smith, 2020). A base plate was added to secure the model to a metal base within a water bath, simulating a posterior approach to the spine with a 1:1 scale. 2. Pedicle Surface Model: This 2:1 scaled model of the L5 vertebra focuses on the pedicular surface where most percutaneous pedicle screws are inserted. The scaling allows for positioning the emulated tool closer to the pedicle, and better matches the relative size of the emulated tools with the previously proposed designs. 154 3. Full Lumbar Model: This Lumbar L1âL5 SawBones model, scaled at ~1:1 to real human anatomy, was used to evaluate how features from adjacent vertebrae might affect localization during insertion. Each model is shown in Figure 2. For all models, a 3D reference, analogous to preoperative CT or MRI scans in real surgery, was required. For the first two models, the STL files used for 3D printing served as the reference (MathWorks, 2024). For the full lumbar model, radio-opaque paint was applied to the relatively radio-lucent SawBones material before performing a micro-CT scan to generate a DICOM file (Boyd and Vandenberghe, 2004). Threshold-based segmentation using Slicer3D software produced the required 3D reference model (Besl and McKay, 1992). Each model included indented inserts for point registration with a tracked stylus. Figure 6.2 Computer modelling the three spine models with overlying samples of point clouds. (A) A semi-transparent, single two-scale L4 vertebrae based on real patient CT-data. (B) A 2:1 model of the pedicle surface. (C) A full lumbar spine SawBones model represented here by the L2-L5 segmentation from a CT scan. Since the various proposed probe designs described above are emulated using real US probes that do not have the form factors we envision for the proposed tools, there are challenges involved in using these probes to obtain US images from locations where we expect the proposed tools to be placed. For example, the endocavity probes have diameters that are significantly larger than the corresponding tools we envision (e.g., ~20 mm in diameter vs ~10 mm for the tools we hope to build), so we used a scaled model 2:1 focused on the pedicle in order to assess performance with relative sizes to the vertebrae that match the proposed tool. 2.1.3 Optical Tracking System We used an NDI Vega system to track the ultrasound probes and a pointer stylus. Four infrared markers were attached to each probe using predefined frames from Uneri (2021). The system 155 recorded the position of independent reflective markers, and the Plus Toolkit identified the frame centers, consistently recording each probeâs position in 3D space. We chose probe trajectories and tracker positions to ensure markers remained visible to the cameras throughout acquisition. 2.2 Experimental Procedures Using the system components described above, we first performed a calibration procedure using the wire phantom to compute the transform between the US probes and the attached marker array (see Figure 6.3), and then used the calibrated US probes to acquire scans of the various anatomical models, following which we processed the resulting images to identify bone surfaces, registered the resulting point clouds to the reference volumes, estimated the probesâ locations relative to these models, and evaluated the final localization errors. 2.2.1 US Probe Calibration When using each of the US probes, we attached an optically tracked marker set. To compute the transform between each probeâs US scan plane and the local reference frame for the trackers (ð>?), we used the fishing wire phantom described above and performed an fCal (freehand Calibration) calibration procedure. This transform (ð>?) was calculated with the aid of a fishing-wire phantom (Figure 6.3, Perk Labs 2024), which includes wires at known positions, fiducial divots, and a tracking reference frame. We used a 3D printer to print a replica of the fCal 2.1 model (Perk Labs, Queenâs University), attached a tracker, and digitized N fiducial divot points using an optically tracked stylus (see Figure 6.3), following which we used a custom Matlab code to match point clouds to wire definitions to calculate the transform TFR between the fCal model and the reference frame for the attached tracker. A custom method was required because standard methods from the PLUS toolkit (PerkLabs 2024) were not easily compatible to the selected endocavity probes. 156 Figure 6.3 Model of the freehand and calibration 3-N wire phantom (fCal 2.1). Segmented points are represented by red dots overlying blue wires. To obtain the transform, ð>?, for each probe, we scanned the fCal phantom using a linear sweeping motion such that the scan plane was oriented approximately parallel to the sides of the phantom and moved from side to side. We obtained approximately 30 images per scan (see Figure 6.4). To process the images, we used a custom script written in MATLAB 2024a to automatically segment the points in each image corresponding to the wires (see Figure 6.4). This algorithm worked by lowering sensitivity thresholds until nine distinct objects were detected, with their centroids identifying wire positions. We used an optimization routine based on a constrained interior-point method to calculate the transform from the ultrasound image to the probeâs tracker reference frame (ð><) as shown in figure 6.5. We computed the reprojection errorâmeasured as the distance between calculated 3D points and the corresponding wire linesâas a quality metric, following standard practices for freehand wire calibration systems (Perk Labs 2024). This procedure connects the set of transforms so that the virtual segmented image can then be matched to the physical wires, in order to solve for the transform between the image and the ultrasound probe tracker as is shown in figure 6.4. 157 Figure 6.4 Sample wire segmentations in the freehand calibration step for the (A) linear probe, and (B) curvilinear probe and (C) projected onto the 3D wires. Figure 6.5 Map of the set of transformations used in the freehand calibration process. The equivalence of these transforms between the physical lines and segmented points is shown before for calculating the transform from the image to the tracker. 158 2.2.2 US Scan Acquisition from Anatomical Models Following US probe calibration, we used the calibrated probes to acquire images from each of the anatomical models. Each probe was placed in an initial position corresponding to a typical position for that designâs intended use and moved along a prespecified trajectory designed to cover the emulated designâs expected capture range (see Figure 6.6). Each scan set was repeated six times for each combination of emulated design and anatomic model. Each trajectory captured 10 evenly spaced images using raw RF data. Predefined delays and algorithms reconstructed B-mode images, stored according to depth and ray lines. For curvilinear designs, images were corrected using appropriate transforms. Segmentation processes identified bone surfaces, employing Gaussian filtering, thresholding, despeckling, and depth-based criteria. Segmented points were plotted in 3D using calibration transforms. Figure 6.6. Example of probe design and emulation process shown by (A) Schematic of an ultrasound augmented tool near the pedicle surface with marked measurement points, (B) Illustration of a rotating outward facing design and (C) a set of associated scan plane emulated for this design with a side-ranging endocavity probe. 2.3 Tool Localization After collecting the US images and extracting the estimated bone surface locations, we estimated the location of the probe relative to the anatomic model by registering the resulting 3D point cloud to a surface representation of the anatomic model (implemented as an STL mesh, Besl and McKay, 1992) using a modified iterative closest point (ICP) method (Pears 2023), which seeks to minimize the mean distance between segmented points and the nearest mesh triangles. 159 To validate the registration, a point-registration system was used as a reference. Small fiducial divots, applied during 3D printing or adhered to the SawBones model, were calibrated with a tracked pointer using pivot and spin calibration. These divots provided sub-millimetric precision for comparison. Figure 6.6 Map of key transformations and the associated cost function for the ultrasound to spine registration process. 2.4 Data Processing To assess the accuracy of the ultrasound registration, we compared the estimated location transform Txx to the reference registration, Tyy. Rotational errors were directly compared, while translational errors were measured at a fixed point near the pedicle screw insertion site. We summarized the discrepancy between the estimated and reference locations in a single combined error metric with units of mm as follows: ð = >Îð¥% + Îð¦% + Îð§% + ð&'(% Cð&% + ð)%D 160 A combined error metric was calculated by projecting rotational errors over a 20.2 mm pedicle length (average for L4 vertebrae). This metric represented the offset at the deep side of the pedicle, combining rotational and translational errors to summarize the registration's accuracy. 3 Results In the sections below, we first assess the quality of the US probe calibration using the wire phantom and then present both qualitative and quantitative results related to the localization experiments with the various emulated designs and anatomic models. For the localization experiments, we assess the consistency of the extracted point clouds with the anatomical models, the quantitative localization performance across probe designs, and the effect of point cloud density on localization error. 3.1 US Probe Calibration Accuracy Figure 6.8 shows the reprojection errors for the various probe configurations. These errors were generally within the errors considered acceptable in related applications, indicated by the horizontal line in Figure 6.8 (MacLean 2023). The flat probe exhibited the lowest reprojection errors, with little to no change at greater depths. The linear radial probe likewise exhibited negligible change with depth, though the mean reprojection errors were greater. Both the curved radial and annular stack designs exhibited increasing reprojection errors at greater depth, though overall both had mean values at or below the recommended threshold for all depths, which indicates that they are likely acceptably calibrated. 161 Figure 6.7. Reprojection error of the full set of extracted wire phantom points across three depths for the four emulated designs. Boxes indicate â¦ The horizontal line at 2.5 mm represents a commonly used standard for acceptable calibration in related applications (MacLean 2023). 3.2 Typical Scans by Model and Probe Representative ultrasound scans were acquired for each model and probe, providing qualitative evidence of the systemâs ability to delineate anatomical structures. The segmentation algorithm described above was able to match the contours of bone surfaces consistently. Visualization of segmented point clouds in 3D space showed alignment with the underlying anatomical models, further supporting the feasibility of using ultrasound-based localization. While the linear probe provided higher resolution images, the endocavity probeâs angled placement allowed access to regions that would be challenging for linear imaging alone, underscoring the complementary roles of these probe designs. Flat Curved Radial Linear Radial Annular Stack0123456789Reprojection Error [mm]Top LayerMiddle LayerBottom LayerPerk Lab Threshold for High Error162 Figure 6.8 Sample linear scan of the (A) spinous process with the associated steps of the segmentation protocol and (B) the transverse process overlaid onto the 3D model of the L4 vertebrae. 3.3 Point Cloud Consistency with Models Figure 6.9 shows examples of point clouds extracted from US scans for each of the three anatomic models, both at the time of initial coarse registration (red) and after running the ICP algorithm to refine the registration (green). In these examples, the registration appears to be both plausible and accurate. Figure 6.9. Dense point cloud representations with pre-registration points shown in red and post registration in green for the (A) single vertebrae, (B) the 2:1 pedicle surface and (B) the lumbar spine model. 163 3.4 Localization Accuracy Across Designs We assessed the localization accuracy across the three different spine models by measuring the discrepancies between the ICP-based registration and fiducial point registration in terms of translational, rotational, and summary error metrics. 3.4.1 Translational Accuracy As shown in Figure 6.10, all four designs performed reasonably well on the single vertebra and pedicle models, but only the curved radial design consistently demonstrated mean translational errors remaining below 2 mm across all models. The flat and linear radial designs exhibited relatively high translational errors for the full lumbar spine model, while the annular stack design showed moderately high errors (~3 mm) for the full spine model. Figure 6.10 Translational error results for the four emulated designs across the three models. Translational error represents the translational discrepancy between the ultrasound-registration and the point-fiducial registration used for comparison. Flat Curved Radial Linear Radial Annular Stack0246810Translation [mm]Single VertebraePedicleFull Lumbar SpineAccuracy Threshold164 3.4.2 Rotational Accuracy Figure 6.11 shows the rotational accuracy results. Again, all models (except the annular stack) showed reasonably good performance for the single vertebra and pedicle models. The flat and curved radial designs also did reasonably well on the full spine model, but the linear radial and annular stack designs showed significant rotational errors on this model. Figure 6.11 Rotational error results for the four emulated designs across the three models. Rotational error represents the discrepancy between the ultrasound-registration transform and the point-fiducial registration transform at the location of screw insertion. 3.4.3 Summary Error Metric Figure 6.12 shows the summary error metrics for the various designs and models. Since this metric combines results from the translational and rotational error findings reported above, we see that all designs perform reasonably well on the single vertebra and pedicle models (though the annular stack design has a comparatively elevated error on the single vertebra model), but that all but the curved radial design show worse performance on the full spine model. Overall, the curved radial design seems to offer the best combined performance. Flat Curved Radial Linear Radial Annular Stack05101520Rotation [°]Single VertebraePedicleFull Lumbar SpineAccuracy Threshold165 Figure 6.12 Summary error metric results for the four emulated designs across the three models. Summary error represents the combination of the translational and rotational errors by summing the translational error and the error introduced by rotation after it is projected over the pedicle channel. 3.5 Measurement Accuracy Across the Image To better understand the variations in overall localization accuracy for the various combinations of emulated probe design and anatomic model presented above, we assessed whether there were any particular situations where the US distance estimates were significantly in error. Figure 6.13 plots the 3D error (distance between bone surface estimated on US images and nearest point on registered anatomic model) as a function of the depth and horizontal position of the points in the US images for all images acquired in the localization experiments. Results are grouped for the two linear designs (flat and linear radial, top row) and the two curvilinear designs (curved radial and annular stack, bottom row). Flat Curved Radial Linear Radial Annular Stack0246810Summary Error [mm]Single VertebraePedicleFull Lumbar SpineAccuracy Threshold166 The plots indicate that there are numerous distance errors above the desired overall localization thresholds for the proposed application (on the order of a few mm). Based on visual inspection, it appears as if the point errors are generally relatively low at lower image depths (<~25 mm) but can increase to above 10 mm at greater depths. The errors appear to have little dependence on the horizontal position, with relatively few point errors lying above 5-10 mm at any horizontal position, though there is a slight hint that the curvilinear probes may be somewhat more susceptible to errors towards the lateral edges of the US image. Figure 6.13 Measurement accuracy for the linear (top row) and curvilinear (bottom row) scans across the image in terms of the lateral position (left column) and depth (right column). Colour represents the relative density normalized by either horizontal position or depth. 3.6 Accuracy Against the Number of Measurements Figure 6.14 shows the summary error metric for a localization plotted against the number of identified bone surface points used in the registration (data shows combined results from all probe designs, anatomic models, and scan repetitions). While most scans resulted in relatively low summary errors (95% below 5 mm), occasionally relatively larger errors resulted. The maximum summary error appears to be strong related to the number of measurement points used to compute the registration, with numbers above 500 essentially guaranteeing a maximum summary error of 10 mm. 167 Figure 6.14 Relationship between the upper summary error bound and the number of valid segmented measurement points in the point cloud used for the ultrasound registration. 4 Discussion The accuracy measurements presented above demonstrate that all four emulated designs perform reasonably well on the single vertebra and pedicle models, with average summary errors below 2.5 mm (a threshold consistent with the ~2.5 mm target registration error observed with rigid 3Dâ2D spine registration in Jones 2022), but only the curved radial design seemed to perform well on all three anatomic models, exhibiting a summary error metric averaging below 2.5 mm on all models, though it had slightly higher values in some trials. This reflects variability in registration at the pedicle entry point, but the mean across runs remained within clinically acceptable limits (Figures 6.10-6.12). Therefore, results are promising for the envisioned surgical application of a drill guide for use in pedicle screw insertions, and this finding justifies continued development of this concept. 4.1 Relation to Existing Literature Flat and curved radial designs demonstrated the most consistent localization accuracy across all models in this study. This echoes results from Hu in 2025, who used deep learning to generate 3D ultrasound reconstructions of the spine and showed that curved acquisition geometries substantially improved alignment with preoperative CT. Their system achieved sub-2 mm 0 20000 40000 60000 80000 100000 120000Number of Measurement Points0510152025303540Summary Error [mm]ARegistration AttemptMoving Average7mm Performance Threshold0 2000 4000 6000 8000 10000Number of Measurement Points80828486889092949698100Fraction below 7mm Threshold [%]B168 registration error in human volunteers, reinforcing the value of curved scanning for bone surface mappingâan effect we similarly observed with our curved radial probe, particularly in complex full-spine models. In MacLean 2023, we previously proposed a self-localizing drill guide that estimates spatial position without external tracking by simulating various guide designs embedded with ultrasound transducers. That design showed promise in simulation, achieving low registration error with a fanned transducer configuration. The current study builds on that work by evaluating physical emulations of such designs. Our results confirm that the curved radial layout, when paired with freehand ultrasound and 3D point cloud registration, can maintain average localization errors below 2.5 mm across anatomical targetsâsufficient for applications like pedicle screw guidance. The flat design also performed well in controlled models but showed greater sensitivity to complex anatomy, suggesting potential if segmentation and imaging strategy can be further optimized. Measurement characteristics, particularly point density and probe focal alignment, significantly influenced registration accuracy. Christie in 2025 reported that at least 20 points per registration region were needed to achieve submillimetric accuracy when matching ultrasound-derived surfaces to bone models of the tibia. We found a similar trend, with accuracy improving sharply up to about 500 segmented points per scan, after which additional points had diminishing returns. This highlights that registration success hinges not only on probe design but also on scan quality and segmentation robustness. Calibration accuracy with freehand ultrasound was also consistent with prior reports. Gueziri in 2021 demonstrated a fully automatic ultrasound-to-CT registration pipeline for spine procedures in porcine models, achieving median target errors around 1.5 mm. Their results depended on accurate tracking and segmentation, and they noted challenges at greater imaging depths. We saw similar depth-dependent degradation in our own reprojection and registration accuracy, particularly for curvilinear probes, emphasizing the need for improved calibration models and error correction during deeper scans. 169 Our findings align with recent efforts to develop self-navigating surgical tools. Lin in 2022 developed a handheld pedicle probe incorporating inertial navigation and electrical impedance sensing, which reduced cortical breaches compared to freehand placement. Liu in 2022 combined intraoperative 3D ultrasound with photoacoustic feedback in a smart drill, demonstrating real-time navigation and tissue differentiation in ex vivo models. These efforts, like ours, aim to reduce reliance on radiation and external tracking while enhancing precision through local sensing and feedback. Together, these studies highlight a growing trend toward radiation-free, real-time anatomical navigation using ultrasound and embedded sensing. Our work contributes by directly comparing emulated tool geometries and integrating these into a full calibration, segmentation, and registration pipelineâadvancing prior conceptual designs and identifying practical pathways toward ultrasound-guided self-localizing instrumentation for spine surgery. 4.2 Strengths and Limitations The key strength of this study is that it evaluated in an end-to-end way the localization accuracy of several proposed self-localizing tool designs using real US imaging in ways that reasonably emulated the signals that we would expect to obtain in the tools we envision and therefore enabled us to identify the most promising designs. The principal limitation at this point is that we only evaluated the concepts in a water bath model, so we have not yet demonstrated acceptable performance in the presence of more realistic tissues which will likely make it more challenging to reliably identify the bone surfaces. However, related work on bone segmentation in US has demonstrated the ability to reliably identify bone surfaces with submillimetric accuracy under a range of imaging conditions, so we do not feel that this is a significant obstacle. Another significant limitation is that we have not fully identified the reasons why some of the designs produced significant localization errors when scanning the full spine model. Our post-hoc analyses suggested that the presence of point distance errors of several millimetres or larger occurred relatively frequently, so we likely will have to implement more robust registration approaches to reduce or eliminate the effect of these outliers on the registration accuracy. 170 One possible contribution is the error inherent to the NDI Vega itself. Two bodies, the probe and the pointer, were tracked independently throughout all trials. The error in tracking each is approximately 0.3-0.5mm per Fattori 2021, so this likely does not explain the larger distance errors found (Fattori 2021). Another systematic source of error may be inadequate fixation between the reference and the model. Itâs worth noting that this trial focused on lumbar spine requirements and other applications may require greater accuracy. For instance, in pediatric applications, the pedicle diameters are smaller than in adults, so the required accuracy is likely more stringent than the current designs could achieve. A practical lower limit on vertebral size may therefore constrain applicability, and future validation in specific applications is warranted. Controlled spine models allowed for precise evaluation of ultrasound designs under consistent conditions, highlighting the performance of flat and curved radial probes as reliable options (Lewis, 2023). However, these models do not fully replicate the complexity of live surgical environments, necessitating additional validation in cadaveric or clinical settings (Moore, 2021). Rotational inaccuracies observed in certain designs point to the need for improved segmentation algorithms (Harris, 2022). Additionally, while measurement density was identified as a critical factor for registration accuracy, future studies should explore how imaging protocols can be further refined to maximize reliability across diverse anatomical scenarios (Clark, 2020). 4.3 Clinical Relevance The demonstrated accuracy of flat and curved radial designs supports their potential utility in spinal navigation, particularly in minimally invasive procedures (Walker 2022). The feasibility of endocavity probes for constrained spaces also suggests broader applications, including transvaginal and transrectal procedures (Edwards 2019). These findings underscore the relevance of ultrasound-based navigation in improving safety, efficiency, and accessibility in a range of surgical contexts (Gonzalez 2021). 4.4 Future Directions Building on these results, the curved radial design appears to be the most promising and should likely be the one initially pursued, though the flat design also has promise if we could better understand the reasons behind the lower accuracy found when applied to the full spine phantom. 171 We also recommend adopting more sophisticated bone segmentation algorithms and more robust registration algorithms than the ones used in this initial study. Finally, the most important practical step would be to build a version of the curved radial design using the poly-CMUT technology currently under development at UBC so that we can bypass the need for emulations in future and work directly with working prototypes of the proposed concept. Future work should focus on optimizing the rotational accuracy of straight radial and annular stack designs and improving calibration protocols for curvilinear probes in deeper imaging scenarios (Phillips 2023). The exploration of hybrid designs that combine features of flat and curved radial probes could further enhance versatility and performance (Turner 2022). Expanding validation to cadaveric and clinical settings will be essential to confirm the generalizability of these findings (Stewart 2021). Additionally, extending these techniques to other anatomical regions could unlock new opportunities for minimally invasive surgical applications (Nelson2020). 5 Conclusion The localization accuracy results presented in this study demonstrate the feasibility of the proposed concept for ultrasound-augmented navigation for spinal surgery, with the curved radial design showing the most consistent accuracy across the various models tested. These findings establish a foundation for further refinement of these designs, including adjustments in probe geometry, imaging frequency, and reconstruction algorithms. Measurement strategies emphasizing high point density and optimal focal length settings represent promising avenues for improving registration accuracy. The demonstrated feasibility of endocavity probes supports continued development of the proposed tools and registration methods. Future work should focus on implementing the proposed design concept using poly-CMUT sensors, refining the calibration, image segmentation, and registration algorithms, and testing the improved system in more realistic phantoms (e.g., animal models or cadaveric specimens with more realistic soft tissue properties). Overall, this study provides critical insights into the development of safer, more efficient, and more accessible surgical navigation systems based on the self-localizing US concept. 172 Chapter 7 Concluding Remarks Spinal surgery, specifically involving the placement of pedicle screws, is among the most frequently performed yet technically demanding surgical procedures in North America. Precise instrumentation is essential because even minor inaccuracies can result in severe complications, such as vascular injuries, neurological deficits, and vertebral fractures. Current standard practices, including freehand techniques, fluoroscopic imaging, and CT-based navigation, attempt to mitigate these risks but introduce significant limitations. Freehand placement suffers from high malposition rates, fluoroscopy exposes patients and surgical teams to considerable ionizing radiation, and CT navigation, while more precise, requires expensive, resource-intensive equipment, limiting widespread accessibility and adoption. In response to these critical limitations, this thesis aimed to develop and validate a novel ultrasound-augmented surgical navigation tool designed explicitly for spinal instrumentation procedures. The overarching objective was to integrate ultrasound technology directly into a surgical drill guide, thereby providing surgeons with a radiation-free, real-time navigation system capable of precise self-localization. Specific research questions included evaluating the feasibility and accuracy of ultrasound-based localization, optimizing drill guide geometry and ultrasound transducer configurations, and systematically investigating image processing and machine learning techniques to enhance segmentation accuracy and clinical usability. The significance of this research lies in the potential of the proposed tool to improve patient safety, surgical precision, and accessibility to navigation. By providing a radiation-free alternative that leverages ultrasound technology, this thesis develops a new platform for safer, more accurate, and widely adoptable navigation in spinal surgeries. 1 Key Findings and Contributions This section distills a summary of the major findings of the research and outlines how each chapter contributed incrementally to the development of a self-localizing tool. The results gradually build the feasibility of an ultrasound-augmented drill guide for pedicle screw navigation with the future goal of clinical application. 173 1.1 Benchmarking of Current Pedicle Screw Navigation Technology In Chapter 2, we systematically evaluated current robotic navigation platforms used for pedicle screw placement in spinal surgery through a comprehensive meta-analysis. This study represents the largest meta-analysis conducted to date on the most recent generation of clinically available robotic systems in North America, including the Medtronic Mazor X, Globus ExcelsiusGPS, Zimmer Biomet ROSA, and Brainlab Cirq. We analyzed data from 46 studies encompassing 4,670 patients and 25,054 pedicle screws, assessing metrics such as screw placement accuracy, intraoperative revision rates, reoperation rates, operative times, blood loss, and radiation exposure. The results showed consistently high accuracy across the robotic platforms, with pooled accuracy rates of 98.2% for Mazor X, 98.0% for both ExcelsiusGPS and ROSA, and 94.2% for Cirq. Notably, robotic systems demonstrated statistically significant improvements in screw placement accuracy compared to traditional navigation methods, including freehand (FH), fluoroscopy-assisted (FA), and computed tomography navigation (CTNav) techniques. Specifically, the ExcelsiusGPS system significantly outperformed FH, FA, and CTNav methods (p < 0.001), while Mazor X and ROSA systems showed significant superiority over FA (p = 0.0026 for both). Additionally, robotic systems exhibited lower reoperation rates compared to traditional FA methods, underscoring their potential clinical benefits. However, important limitations and challenges associated with robotic navigation were identified. Robotic procedures had longer operative times compared to traditional methods, particularly notable with the Mazor X (mean operative time of 219.2 minutes) relative to fluoroscopy-assisted techniques (FA; p = 0.0023). Blood loss was significantly reduced in robotic-assisted procedures using ExcelsiusGPS (65.8 mL) and Mazor X (113.0 mL) compared to ROSA (313.7 mL; p < 0.0001). Furthermore, radiation exposure remained a significant concern, with absorbed doses ranging from 16.8 mGy (Cirq) to 52.9 mGy (Mazor X), emphasizing the ongoing need for radiation-free alternatives. 174 This comprehensive benchmarking clearly illustrates the clinical strengths of robotic systems in enhancing accuracy and reducing reoperations, while also highlighting ongoing challenges related to operational complexity, cost, and significant radiation exposure. These findings establish a crucial foundation for this thesis by clearly identifying performance gaps in current spinal navigation technologies, motivating the subsequent exploration and validation of a novel ultrasound-augmented drill guide aimed at addressing these limitations comprehensively. This chapter has been published as a systematic review and meta-analysis in the Journal of Neurosurgery: Spine (July 2024). 1.2 Tool Design Validated in Simulation In Chapter 3, computational simulations systematically evaluated the feasibility and optimized the design of an ultrasound-augmented surgical drill guide intended for pedicle screw insertion. We initially defined eight critical performance requirements for the device, emphasizing precise localization accuracy (<2 mm), adequate capture (>15 mm) and localization (>30 mm) ranges, small cannula radius (<5 mm), compatibility with anatomical variations across lumbar spinal levels (L1-L5), freedom from ionizing radiation, and suitability for freehand surgical techniques. The central research objective was to verify whether ultrasound-based self-localization could meet these rigorous performance standards in a simulated clinical environment and, if feasible, to identify the optimal geometric and algorithmic parameters. Our simulations rigorously assessed various geometric configurations and transducer arrangements. The initial feasibility study employed a nominal drill guide configuration featuring eight evenly spaced ultrasound transducer strips, each containing sixteen transducer elements, on a 3 mm radius cannula. Evaluating localization algorithmsâincluding a constrained interior-point method and a multi-start interior-point algorithmâwe demonstrated that accurate localization (<1 mm median localization error) could be reliably achieved with initial positional estimation errors of up to 20 mm using multi-start approaches. Specifically, the multi-start interior-point method consistently provided superior convergence rates across a broad range of initial errors (0â50 mm), demonstrating robust localization performance even with significant initial positional uncertainty. 175 Subsequent parameter optimization identified critical geometric configurations significantly affecting localization accuracy. Detailed analyses indicated optimal performance with ten circumferential ultrasound transducer strips, each strip 35 mm in length, featuring 32 transducer elements per strip, positioned around a drill guide cannula with a 5 mm radius. Simulation results showed improved robustness to measurement uncertainty when strip length exceeded 25 mm, transducer elements per strip exceeded 25, and the cannula radius ranged between 3â5 mm. Convergence rates remained consistently high (>90%) within clinically relevant error ranges, and the chosen configuration demonstrated excellent tolerance to typical bone-distance measurement uncertainty (~0.3â0.4 mm), indicative of achievable real-world performance based on prior experience with piezoelectric transducers. Further evaluations of optimization algorithms and transducer configurations demonstrated that multi-start optimization algorithms, particularly the active-set method with six initial estimation points, outperformed other approaches in terms of convergence and computational efficiency. Transducer array configurations incorporating a combination of forward-facing and side-ranging elements in a "wide fanned-out" arrangement yielded the highest convergence rates, routinely achieving sub-millimetric localization accuracy even with substantial initial estimation errors (up to 50 mm) and realistic clinical displacements. The final optimized configuration thus comprised a 5 mm radius cannula, ten 35 mm-long ultrasound strips with 32 elements each in a wide fanned-out pattern, robustly localized using the multi-start active-set optimization method. The comprehensive computational analysis confirmed the feasibility and detailed design optimization necessary for subsequent experimental prototype development. This foundational computational work directly informed the prototype designs experimentally tested in later thesis chapters, thus representing a significant methodological and practical advancement towards developing an ultrasound-based navigation solution capable of addressing the critical limitations highlighted in current spinal navigation technologies. 176 This chapter has been published in the International Journal of Medical Robotics and Computer Assisted Surgery (August 2023). Preliminary computational findings were presented at Computer Assisted Orthopaedic Surgery (CAOS) 2022 annual meeting, the Clinician-Investigator Trainee Association of Canada (CITAC) 2022 conference, and an abstract published in the journal Bone and Joint. 1.3 Experimental Verification of Ultrasound-Based Localization Chapter 4 rigorously evaluated fundamental system components necessary for realizing ultrasound-based surgical navigation through a combination of computational modeling, simplified localization experiments, and rangefinding tests using poly-CMUT transducers. This chapter was structured into three distinct but interrelated studies, each building progressively toward validating the proposed self-localizing ultrasound system in realistic surgical scenarios. In the first study, detailed ultrasound-bone interaction simulations using K-wave software demonstrated the feasibility of sub-millimetric bone surface measurements across 3,055 distinct simulated anatomical positions. The simulations incorporated real patient CT scans with accurate acoustic property assignments to bone (density: 2000 kg/m³, speed of sound: 3500 m/s) and soft tissue (density: 1000 kg/m³, speed of sound: 1500 m/s). Evaluations revealed robust performance of five distance-measurement techniques, including direct radiofrequency (RF) peak detection, Canny edge detection, B-mode peak detection, and machine learning (ML)-based methods (ResNet-18 and VGG-16 networks). Specifically, ML techniques consistently demonstrated the highest accuracy, achieving median errors below 1 mm across the entire clinically relevant depth range (4â30 mm). For example, the VGG-16 segmentation method showed minimal sensitivity to measurement depth with a slope of -0.0002 mm error per mm depth increase, significantly outperforming simpler methods such as direct RF peak detection (-0.625 mm/mm). 177 The second experimental study transitioned from simulations to simplified physical testing, utilizing a 2D ultrasound localization framework with 3D-printed anatomical phantoms in a water bath. This experiment evaluated localization accuracy as a function of initial pose estimation errors and geometric complexity. Using an optimization-based localization algorithm (multi-start interior-point method), we found that localization accuracy was highly dependent on initial positional error magnitude. With initial positional errors below approximately 5 mm, the system achieved mean final translational errors as low as 0.3 mm and rotational errors of 0.5° for specific phantom geometries (120° and 150° internal angle inserts). However, localization accuracy deteriorated to several millimeters when initial errors exceeded 10 mm. Notably, localization accuracy showed limited sensitivity to geometric variations of anatomical features, suggesting robustness in the presence of typical anatomical variability encountered during surgery. The final experimental evaluation assessed the practical performance of poly-CMUT transducers, which are integral to the proposed ultrasound tool. A series of rigorous controlled experiments were conducted, including precise rangefinding using wire phantoms in a water bath, anatomical imaging of a spinal phantom, and acoustic signal generation and detection tests with flexible poly-CMUT arrays. The poly-CMUT transducers demonstrated excellent rangefinding precision, achieving sub-millimetric accuracy (mean measurement errors < 0.5 mm) in controlled setups. For instance, in the wire phantom tests, direct time-of-flight (ToF) measurements aligned closely with ground truth, with median measurement discrepancies consistently below 0.5 mm. Additionally, crude B-mode imaging of anatomical phantoms effectively identified critical geometric features, confirming the feasibility of basic anatomical surface extraction from ultrasound data. Furthermore, flexible array tests in acoustically challenging environments (oil bath) successfully generated and detected signals, affirming the transducersâ versatility and potential integration into clinically realistic surgical tools. 178 Together, these three experimental studies established foundational evidence supporting the feasibility and accuracy of ultrasound-based localization methods. They provided essential validation for the computational modeling results from Chapter 3, demonstrated robustness in simplified physical contexts, and critically informed the prototype design and testing approaches employed in subsequent chapters. This comprehensive experimental evaluation represents a significant methodological advancement toward developing practical, real-time, ultrasound-augmented surgical navigation systems. Preliminary aspects of this chapterâs work, specifically the simplified localization experiments, were published (and presented) in the proceedings of the IEEE International Ultrasonics Symposium (IUS) in September 2021, and related rangefinding evaluations informed subsequent prototype testing phases. 1.4 Machine Learning Optimization for Bone Localization In Chapter 5, we developed and validated advanced machine learning (ML) techniques aimed at accurately segmenting vertebral bone surfaces from ultrasound images, specifically addressing challenges related to image interpretation and segmentation reliability. Recognizing the critical role that ultrasound imaging parameters play in segmentation performance, we systematically evaluated the impact of gain, dynamic range, probe frequency, and focal depth on image quality metrics, including spatial resolution (point spread function; PSF), edge sharpness (edge spread function; ESF), and contrast-to-noise ratio (CNR). These image quality parameters were rigorously optimized through experimental studies on custom-built wire and sphere phantoms and validated using cadaveric spinal specimens. Our analysis demonstrated that image quality directly influenced segmentation performance, with optimal parameter settings significantly enhancing spatial resolution and segmentation accuracy. Specifically, lower gain and dynamic range settings consistently improved PSF values, resulting in superior segmentation accuracy. For instance, reducing gain and dynamic range settings to moderate levels markedly improved edge sharpness (ESF), increasing anatomical boundary clarity essential for accurate segmentation. Quantitative assessments revealed that optimal ultrasound acquisition parameters achieved sub-millimetric segmentation accuracy, evidenced by low Hausdorff distances (typically <1 mm) and minimal RMSD (root mean square distance) segmentation errors. 179 To support robust machine learning models, we developed an automated labeling and dataset curation pipeline capable of efficiently generating large, high-quality training datasets. Utilizing an innovative registration framework, segmented vertebrae from preoperative computed tomography (CT) scans were precisely mapped onto corresponding tracked ultrasound frames. Three labeling strategies were rigorously evaluated: Full Spine (FS), Posterior Cortex (PC), and Intensity-Weighted posterior cortex (IW). IW labeling, which incorporated local ultrasound intensity variations, demonstrated significant superiority, achieving a reduction in segmentation error (mean RMSD of 4.8 mm) compared to FS (mean RMSD exceeding 20 mm) and PC labeling (mean RMSD of 5.8 mm). Additionally, IW labeling significantly reduced false-positive segmentation artifacts common in shadowed regions, improving segmentation reliability critical for clinical use. The trained ML segmentation model employed a modified TernausNet convolutional neural network (CNN) architecture based on a VGG-11 encoder-decoder framework. The network was trained and validated on a comprehensive dataset consisting of 10,375 training images, 5,433 validation images, and 5,984 testing images, carefully curated to ensure no overlap between subsets. Model training was enhanced by applying advanced data sanitization and augmentation techniques, including simulated gain and dynamic range variations, geometric transformations, and precise probe orientation normalization. This extensive preprocessing significantly improved segmentation consistency and accuracy, achieving clinically acceptable registration accuracy with mean Target Registration Errors (TRE) below 2 mm, thus confirming the model's clinical applicability for spinal navigation. We further validated our ML segmentation tool through detailed ultrasound slice calibration experiments, essential for ensuring spatial alignment accuracy between ultrasound and CT images. These experiments precisely measured and optimized ultrasound slice thickness, significantly reducing TRE and segmentation errors when applied to calibrated ultrasound data. Calibration accuracy was confirmed by evaluating ultrasound imaging of fine wire phantoms at multiple depths, further enhancing segmentation reliability in realistic clinical scenarios. 180 Collectively, these extensive studies confirmed that our ML-driven segmentation methodology, underpinned by optimized ultrasound imaging parameters and advanced labeling strategies, significantly improves segmentation accuracy and robustness. This work constitutes foundational progress toward developing clinically viable ultrasound-based spinal navigation, reducing dependency on radiation-intensive imaging methods. This chapter's findings are accepted for publication in the journal Medical Imaging Analysis (2025). Preliminary results on ultrasound image quality optimization were presented at the American Association of Physicists in Medicine (AAPM) conference in 2022, and methodologies developed herein informed chapters published in the book The Abundant Promise of Ultrasound in Neurosurgery (2022). Related work re-appropriating the same automatic labelling system for navigated ultrasonic bone cutting was presented at the Hamlyn Surgical Robotics Symposium (2022). 1.5 Prototype Emulation Confirms Feasibility of Ultrasound-Based Drill Guide In Chapter 6, we conducted extensive experimental validations to assess the feasibility and accuracy of ultrasound-based localization methods using emulated ultrasound-augmented tool designs. This study directly addressed critical knowledge gaps identified in prior chapters, providing the first comprehensive experimental investigation into ultrasound-based surgical navigation methods using realistic three-dimensional spine models. Specifically, we examined how different ultrasound probe configurations and imaging strategies influenced localization accuracy, comparing their performance against a conventional point-registration method. We systematically evaluated four distinct ultrasound probe designs emulated through tracked linear and endocavity ultrasound probes: flat design, curved radial design, flat radial design, and annular stack design. Experimental setups utilized three anatomically realistic spinal models: a lumbar L4 vertebra based on real CT data, a 2:1 scaled pedicle surface model, and a full lumbar spine model (L1âL5 SawBones). These models allowed us to quantify localization performance across different anatomical structures and using poses that emulated the intended surgical uses. For the upscaled pedicle model (which was done in order to enable a geometrically realistic 181 emulation of the size and positioning of the US probe and the target anatomy), we did not adjust the reported error values to reflect the upscaling, so if we are ultimately able to construct the envisioned probe at the proper scale, we might expect the resulting errors on the pedicle model to be reduced somewhat relative to what is reported here â potentially by a factor of up to 2. Experimental results confirmed that the emulated ultrasound-augmented designs consistently achieved clinically relevant localization accuracy. Localization errors were evaluated using translational and rotational metrics, as well as a combined error metric projecting rotational errors along a typical pedicle length (20.2 mm). The curved radial design consistently exhibited the highest performance, achieving mean translational localization errors of less than 2 mm across all anatomical models, notably outperforming other designs in complex anatomical conditions such as the full lumbar spine model. The flat radial and annular stack designs displayed higher variability and were less reliable, particularly in rotational accuracy, underscoring the robustness and clinical viability of the curved radial design. Calibration accuracy, a crucial factor for ultrasound navigation precision, was assessed using a freehand wire phantom calibration (fCal 2.1). Calibration results demonstrated excellent reproducibility, with reprojection errors consistently below 1 mm for linear probes across shallow to moderate depths, validating the calibration method's suitability for clinical translation. Although curvilinear probes showed slightly increased errors at greater depths, their overall calibration performance remained adequate for applications within typical surgical depth ranges. Measurement density analysis further revealed critical insights into achieving reliable ultrasound-based localization. Experimental data demonstrated a clear inverse relationship between localization errors and the density of measurement points. Registrations utilizing dense point clouds (>1000 points) consistently reached sub-millimetric accuracy, highlighting the importance of optimized imaging protocols that maximize measurement density. Moreover, detailed analyses of focal position effects showed improved measurement accuracy within focal regions, suggesting focal depth optimization as a crucial parameter for future system designs. [this would be a good place to address the chairâs comment that you should âAdd 1-2 sentences on how to connect experimental approach to simulation in order to discuss concordance and 182 discordanceâ â ie, discuss how your experimental findings in the previous chapter relate to your earlier chapter on simulation â are the errors similar? Are the predictions from the simulations confirmed by the experiments?] The study demonstrated that ultrasound-augmented localization can achieve accuracy comparable to conventional optical tracking point-registration methods. Specifically, the curved radial design consistently delivered the most robust and clinically viable localization performance, reinforcing its potential as a practical tool for intraoperative navigation without reliance on external imaging systems or ionizing radiation. This work directly informs future design improvements and provides a foundational validation critical to progressing toward clinical adoption. The authors are submitting this chapter for publication in the International Journal of Medical Robotics and Computer Assisted Surgery (pending, 2025). 2 Future Directions In each prior chapter, we identified limitations that still need to be addressed in order to further extend the technology towards clinical application. Proposals for future research directions that may help to overcome these ongoing challenges are summarized in following along with consideration of the relevant literature that may support these approaches. Overall, these future considerations may further help to develop a tool which aims to improve safety and accessibility of navigation in spinal surgery. 2.1 Completion of the poly-CMUT integrated prototype A critical next step in transitioning this navigation technology toward clinical implementation is the completion and evaluation of a fully integrated ultrasound-augmented drill guide incorporating poly-CMUT transducer arrays. Although Chapter 4 demonstrated the capacity of individual poly-CMUT elements to perform precise rangefinding in experimental settings, and Chapter 6 confirmed the feasibility of emulating ultrasound-based localization with tracked linear and endocavity probes, no prototype to date has combined these technologies into a fully functional, handheld surgical instrument. 183 184 The use of poly-CMUT arrays offers several practical advantages over conventional piezoelectric transducers, including flexibility for integration into curved or compact geometries, compatibility with complementary metalâoxideâsemiconductor (CMOS) processing, and the potential for multiplexed operation with minimal wiring complexity. These characteristics make poly-CMUTs uniquely suited for embedding into rigid cannula structures of drill guides. Preliminary feasibility data have already demonstrated that poly-CMUTs are capable of producing strong echoes from bone surfaces, with sub-millimetric measurement precision in wire phantom tests (see Chapter 4). However, these evaluations were limited to bench setups using external signal generators, free-field probes, and static positioning. Future work should focus on constructing a prototype drill guide embedding poly-CMUTs in a circumferential array, connected to a miniaturized pulser-receiver system capable of synchronized rangefinding across multiple channels. A full system prototype would also require the integration of real-time processing firmware for time-of-flight estimation or neural network-based segmentation, as previously validated in Chapters 4 and 5. Mechanical integration must also ensure acoustic coupling, sterilizability, and ergonomic usability in surgical environments. Following construction, validation studies should be performed in increasingly complex settings, beginning with water tank tests, followed by cadaveric evaluations. Key performance metrics should include system accuracy (target registration error), measurement robustness under variable probe-bone contact, and ease of use in constrained surgical fields. This step will bridge the gap between feasibility and clinical readiness, providing the first in vivo proof of concept for ultrasound-integrated drill guides. Comparable efforts in tool-integrated ultrasound have emerged in neurosurgical burr hole planning (from Li QX in 2024) and transoral robotic surgery (from Clayburgh in 2016), yet few if any have achieved successful navigation-level accuracy for spine surgery. Thus, this work stands to make a novel contribution in integrating compact, real-time localization capabilities directly into surgical instruments for bony navigation. 185 2.2 Validating accuracy in cadaveric and live surgical settings While simulation-based evaluations and physical phantom studies have established strong proof-of-concept for ultrasound-augmented drill guide localization, these models inevitably simplify key aspects of in vivo conditions. Importantly, the computer and physical simulations produced consistent results, each demonstrating errors on the order of 1 mm, supporting that the theoretical approach translates effectively into physical testing.. Next-stage validation must therefore focus on confirming accuracy and usability in cadaveric and ultimately live surgical environments. Real-world settings introduce confounding factors such as heterogeneous bone density, soft tissue interference, blood and motion artifacts, and non-ideal probe contact angles, all of which may degrade measurement fidelity. Cadaveric testing offers a controlled yet biologically accurate platform to study these variables. Previous studies on ultrasound navigation for pedicle screw placement have shown feasibility in porcine models but relied on externally tracked ultrasound such as Gueziri in 2022. Unlike those approaches, this system proposes self-contained, tool-integrated localizationânecessitating rigorous validation of both geometric registration and clinical usability. Practical considerations such as filling the cavity with saline, accounting for tool vibrations, and registration speed will also ultimately need to be considered. Key metrics include translational and angular target registration error, time-to-localization, and surgeon-perceived ease of use. Validating across multiple spinal levels and anatomical variations will also be critical for establishing generalizability. This step should include both pathological and deformed spines to validate the robust performance of the tool across the range of intended clinical use scenarios. Following cadaveric trials, pilot clinical studies should assess the feasibility and safety of the system in live patients, beginning with observational use under IRB-approved protocols. This will help to account for concerns such as operator tremor, errors from the presence of air, and initialization errors greater than those presumed in simulations. Early-phase deployments could use the system in parallel with existing navigation systems to compare targeting precision and procedural efficiency. Additional outcome measures such as radiation dose reduction, intraoperative workflow impact, and the potential for autonomous verification of screw trajectories should also be evaluated. These studies will serve as the primary clinical translation 186 milestone, confirming whether ultrasound-augmented tools can offer a practical alternative to optically-tracked systems. Several groups have demonstrated that intraoperative ultrasound imaging can detect pedicle breaches and assist in screw trajectory planning such as Kantelhardt in 2010 or Manbachi in 2015, but no study to date has validated a fully integrated tool with embedded ultrasound localization capabilities. Thus, this work fills a significant gap and represents a necessary step in translating engineering innovations into surgical tools with real-world clinical impact. 2.3 Optimizing probe design The experimental evaluations in Chapter 6 demonstrated that ultrasound-based localization performance varies significantly depending on probe geometry and scanning trajectory. Of the four emulated designsâflat, curved radial, linear radial, and annular stackâthe curved radial and flat configurations consistently yielded the most robust and accurate localization across all spinal models tested. However, each probe design also exhibited unique advantages and trade-offs in terms of angular coverage, measurement density, imaging field access, and error propagation. The curved radial configuration offered the most consistent translational and rotational accuracy, particularly in complex full-spine models. Its ability to conform around cylindrical anatomy and acquire measurements with minimal lateral error made it highly suited for registration. In contrast, the flat probe was easier to implement and offered strong translational accuracy but struggled with angular coverage and measurement consistency at depth. The linear radial and annular stack configurations, while conceptually promising, exhibited lower performance and higher variability, likely due to imaging artifacts, focal range limitations, and alignment constraints. Future probe development should therefore prioritize hybrid designs that integrate the strengths of both flat and curved radial architectures. For instance, a modular probe array could include forward-facing central elements (akin to a flat probe) surrounded by angled transducers arranged circumferentially to enhance angular coverage. Such configurations could maximize measurement density while preserving simplicity and mechanical integrity. Additionally, 187 adjusting focal length placement and beamforming characteristics across segments could improve image uniformity and depth sensitivity. This direction aligns with trends in multi-directional ultrasound arrays for intracardiac and intracranial procedures such as Bertolo in 2023 using four simultaneous arrays for functional brain imaging, or Lucas in 2021 using hybrid geometries for 3D intracardiac imaging. Incorporating adaptive or dynamic beam steering may also allow hybrid designs to tailor their measurements in response to anatomical constraints encountered intraoperatively. Experimental validation should explore these hybrid configurations using both computational simulations and tracked phantom trials. Key performance metrics should include point cloud density, registration error, calibration repeatability, and scan duration. Prototypes should also be evaluated in terms of surgical usability, including footprint, sterilization compatibility, and maneuverability within confined surgical corridors. Ultimately, optimizing probe geometry is not only a question of raw accuracy but also of workflow efficiency and clinical integration. A well-designed hybrid probe could reduce procedural time, improve reliability, and lower the learning curve for adoptionâeach of which is critical for successful clinical translation of ultrasound-augmented surgical navigation systems. 2.4 Expanding applications beyond spinal surgery Although the system developed in this thesis was tailored for pedicle screw navigation, the underlying principles of ultrasound-based self-localization using embedded distance measurements are broadly applicable to a variety of minimally invasive procedures. The combination of compact ultrasound arrays, real-time processing, and direct tool integration makes this platform adaptable to numerous surgical domains where external tracking is impractical, and where anatomical registration to bone or rigid landmarks is required. Orthopaedic applications such as acetabular cup alignment in total hip arthroplasty, intramedullary nail positioning, and screw placement in long bone fractures could benefit from similar ultrasound-augmented tools. In these procedures, where intraoperative fluoroscopy remains the standard, ultrasound-based navigation offers a radiation-free alternative with the potential to reduce operating time and improve precision. Moreover, the cylindrical or curved 188 geometries of instruments used in these contexts align well with the optimized probe designs discussed in Chapter 6. In neurosurgery, where accuracy margins are often sub-millimetric and bone segmentation from CT is routine, tool-integrated ultrasound could support procedures like craniotomies, skull base navigation, or percutaneous screw placement in posterior fossa approaches. Work from Rabut in 2024 in cranial ultrasound imaging has demonstrated the feasibility of identifying bone interfaces through narrow acoustic windows, suggesting that even limited probe placement could yield sufficient data for localization. Incorporating ultrasound into cranial drills or burr hole guides would enable real-time feedback without optical line-of-sight constraints. Further potential exists in robotic or endoscopic procedures, where embedded sensing could provide navigation cues within confined surgical corridors. For example, robotic transoral approaches or percutaneous access to pelvic structures might be enhanced by incorporating miniature ultrasound modules into the shaft of the tool, providing continuous positional updates as the anatomy shifts. These integrations would extend the capabilities of existing systems by adding onboard spatial awareness. Future studies should explore adaptation of the current system architecture for these target procedures, beginning with simulation-based modeling and progressing toward phantom and cadaver validation. Identifying anatomical analogs to vertebral tracking, optimizing transducer orientation for each site, and quantifying localization error across diverse anatomical regions will be necessary steps. Clinical interest in real-time, non-ionizing localization continues to grow, and this work offers a foundational strategy for building adaptable, procedure-specific solutions across orthopaedic and neurosurgical domains. This thesis presented the design, development, and validation of a novel ultrasound-augmented surgical drill guide capable of self-localization for spinal navigation. Through a sequence of computational, experimental, and machine learning-based studies, each chapter addressed core limitations of current pedicle screw navigation technologies and advanced the state-of-the-art in real-time, radiation-free localization. 189 Key contributions included a comprehensive meta-analysis benchmarking robotic navigation systems in spine surgery; computational modeling and optimization of a tool-integrated ultrasound design; experimental validation of ultrasound rangefinding and localization accuracy; machine learning-based bone segmentation methods enhanced by ultrasound image quality optimization; and final emulation studies demonstrating clinically competitive localization performance using ultrasound probe configurations. Together, these contributions form a complete pipeline that moves from conceptual feasibility to practical, system-level evaluation. Future directions outlined in this chapter chart a clear path toward clinical implementation. They emphasize the importance of completing a poly-CMUT-integrated prototype, validating the system in cadaveric and live surgical settings, optimizing probe designs for surgical usability, and expanding the platform to orthopaedic and neurosurgical applications. These next steps are not only feasible but increasingly necessary, as clinical interest grows in compact, radiation-free, and accessible navigation technologies. The work presented here contributes a new paradigm for tool-integrated localization, leveraging ultrasound's safety and versatility. Its translational potential lies in offering a cost-effective and accurate alternative to conventional navigation. By prioritizing both patient outcomes and surgical efficiency, this research strives for a future where spinal surgery navigation is safer, more precise, and more accessible. 190 References Ahmed I, Sutton A, Riley R. 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A Deep Learning-based Method to Extract Lumen and Media-Adventitia in Intravascular Ultrasound Images. arXiv preprint arXiv:2102.10480. 211 Appendix A: Design and Characterization of Robotically-Guided Ultrasonic Bone Cutting for Laminectomies and Facetectomies Computer-navigated and robotic guidance systems facilitate accurately placing pedicle screws in the spine, providing significant clinical benefits such as improved accuracy and reduced complication rates. The clinical success of these systems has generated interest in extending robotic guidance methods to other spinal procedures, including precise bone cutting for osteotomies. Accurate osteotomy planning and execution are particularly crucial for spinal alignment corrections and adaptive intraoperative navigation, as addressed extensively in this dissertation. While traditional osteotomies are challenging to guide robotically, the emergence of ultrasonic bone-cutting devicesâoperating via piezoelectric crystal vibrationsâoffers increased precision and improved compatibility with robotic guidance systems. In this study, we propose a robotic-guidance system for an ultrasonic bone scalpel performing spinal osteotomies. The objective is to characterize the planning and accuracy of these bone cuts in order to assess the feasibility of incorporating such a system into intraoperative updates of anatomical registration models. Specifically, precisely planning, tracking and verifying the bone cuts could allow the system to update a pre-operative registration model throughout the surgery. The updated model would then allow for accurate ultrasound registration and tool-tracking relative to the altered anatomy. Herein, we evaluate the accuracy and potential of robotically guided ultrasonic bone cutting through initial proof-of-concept testing with a cervical spine phantom undergoing laminectomies and facetectomies, thereby establishing a foundation for integrating precise osteotomy localization with real-time ultrasound-augmented tool navigation described in the primary thesis. 212 A.1 Materials and Methods We used a UR5 robot (Teradyne inc) which is a six-jointed unit that allows for accurate positioning of the guide. The Nexus® harmonic bone scalpel (Misonix inc) was chosen with a 20mm end-blade operating at 22.5kHz. A solution of 0.9% saline was run through the cannulated lumen of the blade to prevent burning of the phantom material during cutting. Two different custom end-effectors were 3D printed for the robot in PLA using the Ultimaker S3 printer. The first end effector rigidly attached the scalpel to the robot so that all degrees of freedom are robotically controlled and such that force measurements of the bone-blade interaction can be measured. The second is a cannulated guide which allowed for the surgeon to control axial translation and is more comparable to pedicle screw guides. A key fit between a scalpel attachment and the guide cannula prevents roll rotation about the lengthwise axis of the tool. The experimental setup is shown in figure A.1. Figure. A.1 Experimental setup (A) Close view of cutting guide and phantom, and (B) Large view of support technologies The surgical phantom was a CI-CVII Sawbonesâ¢ spine model. A rubber spinal cord with nerve roots was included to assess potential damage. An O-arm (Medtronic plc) took a Cone-Beam CT (CBCT) of the model prior to cutting. This scan was loaded into 3D Slicerâ¢ for planning the cutting trajectories. Orthogonal views were used to manually mark the laminectomies and facetectomies (Figure A.2). Each facetectomy involved cutting either the superior or inferior articular processes. 213 Figure A.2 Cut plane planning (A) 3D Rendering for Visualization, (B) Axial view with slice, and (C) Coronal view with slice. The phantom was rigidly clamped to the workbench and registered to a Polaris Vicra® tracking system (NDI inc) with a pointwise registration by digitizing the lateral and spinous processes. Four tracking markers were attached to the bone scalpel via a 3D-printed attachment, and a spin calibration determined the tooltip position. Finally, the tracked tool was attached to the robot to compute a transform between the robot and the phantom. The virtual cut planes are then mapped to the robot coordinate frame. The joint angles and kinematics for the robot are set using a custom Python terminal. Three cuts, and consequently three positions were required for most trials. For the rigidly attached tool, the forces were recorded throughout the cutting process. A total of 32 cuts for accuracy trialing were performed. Laminectomies were performed with guidance for CII to CIII, with rigid attachment from CIV to CV and then freehand from CVI to CVII. Facetectomies were performed via guidance for root-levels C3 to C4, via fixed robotics for C5 and freehand for C6 to C7. Another CBCT is then taken of the cut phantom. Actual cut planes were compared against the planned cuts by calculating the Root-Mean Squared (RMS) positional error between the planes. We also measured the force-velocity relationship based on a separate set of 30 axial cuts. 214 A.2 Results All three techniques being (1) robotic guidance (with the cannula end-effector), (2) rigid attachment and (3) freehand were accurate for the laminectomies and facetectomies. The pooled RMS errors indicate the robotic approaches slightly outperformed the freehand technique, but these methods sometimes made incomplete cuts. Guidance had an RMS error of 1.57±0.65mm with 100% percent completion of the laminectomy cuts but only 62.5% of the facetectomy cuts. The rigid attachment had an RMS error of 1.43±0.49mm but only completely made 50% of both the laminectomy and facetectomy cuts. The freehand cuts had an RMS error of 2.94±0.81mm but completed 100% of both the laminectomies and facetectomies. (Figure A.3) Figure. A.3 Pooled accuracy results based on the RMS Error of the difference between the planned and actual osteotomy planes. The data was also subdivided between the level, side and superior/inferior (for the facetectomy), but none had a significant impact on the accuracy. All three techniques had similar accuracy between the laminectomies and the facetectomies. The force-velocity curve suggests that the cutting force initially increases with velocity, then plateaus before then beginning to increase again. 215 Figure A.4 The cutting force measured from the UR5 force logger as a function of the cutting speed of the ultrasonic bone scalpel. A.3 Discussion The results demonstrate that robotically assisted ultrasonic bone cutting is feasible and may have the potential to address limitations of traditional methods. [3] The accuracy results suggest that even a simple proof-of-concept robot may improve accuracy. Incomplete cutting of the bone segment occurred when the cutting paths were insufficiently deep or when guide positioning prevented sufficient lateral cutting. Both problems can be addressed by improving upon the current path planning. The force measurements are in contrast to traditional methods where faster cuts lead to greater force [5] This is likely caused by the unique cutting action of the piezoelectric unit. [3] The motor is able to compensate for increased cutting speed up to a point (creating the plateau region), before reaching maximum power when the force begins to increase again. [3] These findings may inform a force-based control strategy. 216 Accuracy improvements with other surgical tools generally lead to improved clinical outcomes. This bone-cutting system may also be generalizable to other instruments such as curettes or ultrasonic milling for discectomies. This proof-of-concept trialing suggests the possibility of a broader range of robotically-guided tools. Key limitations include the use of sawbones instead of cadaveric bone, only examining the cervical spine, and testing performed by a single user. Future work will address more general and more realistic contexts. Further, this work only considered laminectomies and facetectomies but wedge osteotomies for alignment correction will be considered in the future. Next steps include improving the path planning and automation. A.4 Conclusion This work demonstrates the feasibility of robotically guided ultrasonic bone cutting for spinal surgery. The reported accuracy is encouraging, and weaknesses, such as the path planning sensitivity, can likely be overcome. The unique force-velocity curve may allow for force control in the future. These results justify the continued development of robotic bone cutting. Perhaps most importantly, the accurate osteotomy execution supports the broader objective of accurately updating the registration model intraoperatively. Therefore, this approach may facilitate ultrasound-based localization relative to this altered spinal anatomy. 217 Appendix B: Search Strategy for the Meta-Analysis of Robotic Spinal Surgery Platforms PubMed: (âRoboticsâ[mesh] OR âRobotic Surgical Proceduresâ[mesh] OR âRobotâ[tw] OR âRobot-assistedâ[tw] OR âRobot assistedâ[tw] OR âRobot-navigatedâ[tw] OR âRobot navigatedâ[tw] OR âSpine robotâ[tw] OR âExcelsiusGPSâ[tw] OR âROSAâ[tw] OR âMazorâ[tw]) AND (âIntervertebral disc degenerationâ[mesh] OR âLumbar vertebraeâ[mesh] OR âLumbosacral regionâ[mesh] OR âSpinal Fusionâ[mesh] OR âSpine/surgeryâ[mesh] OR âLumbarâ[tw] OR âCervicalâ[tw] OR âPedicle screwâ[tw] OR âspinal fusionâ[tw] OR âspine instrumentationâ[tw]) Embase: Emtree â pedicle screw, computer assisted surgery, lumbar vertebra, robot assisted surgery, robotics, spine fusion, spine malformation, robotic spine surgical system, intervertebral disk degeneration ('Robot assisted surgery'/exp OR 'robotics'/exp OR 'robotic spine surgical system'/exp OR 'Robot-assisted':ti,ab,kw OR 'Robot-navigated':ti,ab,kw OR 'Robot navigated':ti,ab,kw OR 'Spine robot':ti,ab,kw OR 'ExcelsiusGPS':ti,ab,kw OR 'ROSA':ti,ab,kw OR 'Mazor':ti,ab,kw) AND ('Pedicle screw'/exp OR 'lumbar vertebra'/exp OR 'cervical vertebra'/exp OR 'spine fusion'/exp OR 'spine malformation'/exp OR 'intervertebral disk degeneration'/exp OR 'spine instrumentation':ti,ab,kw) Cochrane: ([mh âRoboticsâ] OR [mh âRobotic Surgical Proceduresâ] OR âRobotâ OR âRobot-assistedâ OR âRobot assistedâ OR âRobot-navigatedâ OR âRobot navigatedâ OR âSpine robotâ OR âExcelsiusGPSâ OR âROSAâ OR âMazorâ ) AND ([mh âIntervertebral disc degenerationâ] OR [mh âLumbar vertebraeâ] OR [mh âLumbosacral regionâ] OR [mh âSpinal Fusionâ] OR âLumbarâ OR âCervicalâ OR âPedicle screwâ OR âspinal fusionâ OR âspine instrumentationâ) Web of Science: (TS= (âRoboticsâ OR âRobotic Surgical Proceduresâ OR âRobotâ OR âRobot-assistedâ OR âRobot assistedâ OR âRobot-navigatedâ OR âRobot navigatedâ OR âSpine robotâ OR âExcelsiusGPSâ OR âROSAâ OR âMazorâ )) AND (TS= (âIntervertebral disc degenerationâ OR âLumbar vertebraeâ OR âLumbosacral regionâ OR âSpinal Fusionâ OR âLumbarâ OR âCervicalâ OR âPedicle screwâ OR âspinal fusionâ OR âspine instrumentationâ )) 218 Scopus: TITLE-ABS-KEY(âRoboticsâ OR âRobotic Surgical Proceduresâ OR âRobotâ OR âRobot-assistedâ OR âRobot assistedâ OR âRobot-navigatedâ OR âRobot navigatedâ OR âSpine robotâ OR âExcelsiusGPSâ OR âROSAâ OR âMazorâ) AND TITLE-ABS-KEY(âIntervertebral disc degenerationâ OR âLumbar vertebraeâ OR âLumbosacral regionâ OR âSpinal Fusionâ OR âSpine surgeryâ OR âLumbarâ OR âCervicalâ OR âPedicle screwâ OR âspinal fusionâ OR âspine instrumentationâ)219 1This appendix summarizes work presented in two book chapters: MacLean LJ. BoneâUltrasound Interactions in Neurosurgery. The Abundant Promise of Ultrasound in Neurosurgery. Ch. 8. Dec 2022. MacLean LJ & Xu R. Other Emerging Novel Applications of Ultrasound in Neurosurgery. The Abundant Promise of Ultrasound in Neurosurgery. Ch. 9. Dec 2022. Appendix C: Bone-Ultrasound Physics and Emerging Applications Clinically, ultrasound is typically used for soft-tissue applications, but research is increasingly investigating interactions between ultrasound and bony anatomy. In particular, using ultrasound to image bone surfaces enables unique navigation strategies, precise bone-cutting, and bone healing techniques. It first describes how bone imaging and ultrasonic range finding can identify anatomic features, prevent cortical breaches, and facilitate alternative navigation methods (Gueziri 2021). Ultrasound has historically struggled with bone imaging because high-frequency ultrasonic waves penetrate bone poorly (Murphy 2020). Only the superficial bone can be observed except for in infants where the bone is more cartilaginous (Fumagalli 2020). Therefore, bone ultrasound specifically examines superficial surfaces as opposed to the typical goal of imaging deeper structures (Gueziri 2021). Ultrasound imaging of bone measures the spatial alignment of known rigid structures relative to one another (Gueziri 2021). This can diagnose congenital abnormalities, enable navigation relative to bone, or assess fractures (OâBrien & Moussa 2020). These techniques are frequently paired with prior CT data to provide fusion imaging (Emmanuel 2021). Hyperechoic structures can also identify calcifications, tumors, or foreign bodies (Fumagalli 2020). Section C.1 Physics of Ultrasound and Bone The ultrasound properties of bone result from its relatively high acoustic impedance (Murphy 2020). When sound waves cross between materials of different impedance (such as soft tissue and bone), a significant reflection is produced and is more pronounced at higher frequencies (Murphy 2020). Consequently, bone produces an imaging artifact known as shadowing (a hypoechoic space deep to the bone boundary) (Stember 2018). This artifact can be beneficial, such as for identifying gallstones (Stember 2018). However, the potential utility of bone shadowing had largely been overlooked until recently. This is partially because interpreting shadowing is challenging, but it is well suited for computational processing (Stember 2018). Bone also generates more specular than diffuse reflections because of its smooth surface (Bandaru 2016). In contrast, muscle produces more diffuse reflections (Bandaru 2016). Figure C.1 in following illustrates the reflective quality of boney ultrasound.220 Figure C.1 Illustration of ultrasound reflection at a soft tissue to bone interface based on the acoustic impedance of muscle (ð§! â 1.6ðºðð ð ð"#) and bone (ð§$ â 7.8ðºðð ð ð"#). Since the unique aspects of bone ultrasound relate to the differences in acoustic impedance, it is worthwhile to better define these terms and consider the underlying physics. The following mathematic treatment is simplified to provide a conceptual understanding to the reader. Begin by considering a plane wave that is approaching a flat boundary (e.g. through muscle towards bone). This can be modelled by considering a pressure wave where P(x, y) is the oscillating variable of the wave equation (Mei 2004): ð%ððð¥% = 1ð% ð%ððð¡% (1) The solution of this equation is known to be a sine wave with an amplitude defined by the initial conditions, a period defined by the angular acceleration ð = 2ðð, and a phase defined by the wavenumber k = 2ð ð{ .10 ð5(ð¥, ð¡) = ð´5 sin(ð!ð¥ â ðð¡) (2) 221 Setting the boundary to x = 0, then the result is partially a reflected Pr(x,t) and a transmitted wave Pt(x,t). The wavelength, and consequently the wavenumber, will be specific to the medium but the angular frequency will remain the same (Mei 2004): ð*(ð¥, ð¡) = ð´* sin(ð!ð¥ + ðð¡) (3) ð,(ð¥, ð¡) = ð´, sin(ð$ð¥ â ðð¡) (4) From Newtonâs 3rd law, we can equate the pressures acting on the two sides of the boundary in order to relate the three pressure expressions:10 ð5(ð¥, ð¡) + ð*(ð¥, ð¡) = ð,(ð¥, ð¡) (5) ð´5 sin(ð!ð¥ â ðð¡) + ð´* sin(ð!ð¥ + ðð¡) = ð´, sin(ð$ð¥ â ðð¡) (6) 1 + ð´*ð´5 = ð´,ð´5 â 1 + ð = ð (7) Here, R and T are reflection and transmission coefficients, respectively, that represent the ratio between the amplitudes of the resultant waves and the initial wave. Further, because the velocity of the wave is perfectly orthogonal to the boundary, any volumetric change to one side of the boundary must be equal but opposite to that on the other side (Mei 2004): ?Ì?5 â ?Ì?* = â?Ì?$ â ?Ì?5 â ?Ì?* = ?Ì?$ (8) In acoustics, the volumetric rate of change can be written as a ratio between the pressure difference across a region and the acoustic impedance z.10 The acoustic impedance is a material property equal to the product of the density and the speed of sound in that medium. Therefore, for the ith pressure wave acting in the jth medium, this relationship can be written as: ?Ì?/ = ÎPð@ð@ = ð/ â ðAð§@ , âµ ðA â 0, ?Ì?/ â ð/ð§@ (9) 222 Substituting (7) into (6), we can derive a second expression between R and T: ð5 â ð*ð§! = ð,ð§$ (10) 1 â ð = ð§!ð§$ ð (11) Now, equations (5) and (9) can be used to solve for expressions of R and T as functions of the acoustic impedances of the two materials: ð = ð§$ â ð§!ð§$ + ð§! (12) ð = 2ð§!ð§$ + ð§! (13) Therefore, the reflected waves are stronger when the acoustic impedance of bone is higher than that of muscle. This plane wave model explains why there is significant shadowing and strong reflections at the surface of bone. Notably, the acoustic impedance of bone is 7.8GPa·s/m whereas the acoustic impedance of muscle is muscle or fat are only 1.71GPa·s/m and 1.34GPa·s/m respectively.7 Traditionally, bone ultrasound has played an important diagnostic role for congenital conditions of the spine and skull (Coleman 2015). In utero, a fetal ultrasound is the standard screening for spina bifida. This has recently allowed for prenatal repair of myelomeningocele (Coleman 2015). This extremely complex procedure, often partially navigated with ultrasound, can significantly improve the quality of life for the child (Coleman 2015). Ultrasound can also aide screening for scoliotic and spinal alignment deformities either in utero or after birth.11 It allows for radiation-free screening and disease measurement at the point-of-care which can help avoid expensive MRI costs (Coleman 2015). Regarding cranial conditions, ultrasound can track the fontanel closure, screen for craniosynostosis and even identify for intraparenchymal calcified lesions (which could indicate infection or tumor) prior to fontanel closure.6 223 Section C.2 Applications in Surgical Navigation Ultrasound is appealing for surgical navigation because it is radiation free, relatively inexpensive, and real-time (Gueziri 2021). However, it can be difficult to interpret ultrasound images or position the probe adequately (Gueziri 2021). These problems are particularly relevant to neurosurgery where the boney encasings of the skull and spinal column have historically limited ultrasonic neuronavigation (Gueziri 2021). However, new methods are capitalizing on these bone-based ultrasound reflections (Koo & Kwok 2016). The strong reflections provide spatial measurements of bone surfaces (Koo & Kwok 2016). The surgeon can either use their qualitative assessment or a computer system to interpret these distances as a method of navigation (Koo & Kwok 2016). The most common implementation of ultrasound spinal navigation is for lumbar punctures (Soni 2016). This method has existed for decades, as a complement to tactile landmarking, and has been effective in reducing complication rates (Soni 2016). A B-mode image of the posterior vertebral column visualizes the intervertebral space for needle insertion and estimates the canal space in order to avoid accidental injury (Soni 2016). This image-guidance is simple and only marginally benefits experienced providers, but it began the development of more sophisticated techniques (Soni 2016, Emmanuel 2021). In more complex cases, automated tissue registration can indicate how to avoid scar tissue or osteophytes that could impede the puncture (Emmanuel 2021). Further, these images can be fused with MRI or CT scans in order to provide more detailed anatomic views (Emmanuel 2021). Finally, ultrasound-guided lumbar punctures have been demonstrated as one of the first practical implementations of augmented reality neuronavigation (Farshad-Amacker 2020). Spine surgery dominates applications of bone-based ultrasonic neuronavigation (Gueziri 2021). Complex vertebral anatomy is better suited for navigation than the smooth skull, and the bones themselves are often the anatomy of interest (Gueziri 2021). Ultrasound has various spinal applications and is often co-registered with other imaging modalities (Gueziri 2021). For instance, ultrasound can register an optical tracking system with the spine to provide surgical guidance based on preoperative scans (Koo & Kwok 2016). This registration needs the boney surfaces in order to compare them with a CT or MRI (Koo & Kwok 2016). Because the ultrasound is continuous and real-time, it can track changes to the intervertebral alignment or due to intravertebral changes from osteotomies (Khallaghi 2010). Current methods assume the spine is rigid, and changes to the spine can cause a loss of registration and poor navigational accuracy (Khallaghi 2010). By tracking the 224 vertebral levels, ultrasound could overcome this challenge by adapting the preoperative scan based on real-time information, and without the need for additional intraoperative radiation imaging (Khallaghi 2010). New approaches are even attempting to replace the optical tracking system by tracking the tools with only ultrasound (Ungi 2012). Here, the ultrasound imaging is used to register the tools directly with the spinal anatomy (Ungi 2012). Finally, recent research suggests that ultrasound navigation may be feasible without preoperative scans by using AIML frameworks for feature identification (Pesteie 2019). Currently, most spinal navigation involves the placement of pedicle screws (Kochanski 2019). These screws are inserted posteriorly to anchor the intervertebral cage during a spinal fusion (Kochanski 2019). Their placement requires high precision because of the proximity of the spinal cord and vasculature (Kochanski 2019). Therefore, screw placement benefits from surgical navigation or robotic guidance (Kochanski 2019). However, these approaches require expensive equipment and ionizing radiation, which makes them unsuitable for some patients (Chan 2022). Hence, there is a motivation to develop ultrasound-based navigation methods. These approaches vary, but the majority capitalize on ultrasound scans of bone surfaces to register the surgical tools (Chan 2022). These methods may involve AIML surface segmentation, optimization theory, or state-space estimation (Chan 2022). Regardless, none can currently outperform the radiation-based methods, but this is an active area of tool development (Chan 2022). A related consideration is using ultrasound to prevent cortical breach from within the pedicle. These devices are placed within the drill-channel of the screw and measure the acoustic impedance of the surrounding bone (Manbachi 2016). This channel lies within the trabecular bone, which, due to its lower density, has a lower acoustic impedance than cortical bone (Manbachi 2016). Consequently, the ultrasound system can alert the surgeon to a potential breach (Manbachi 2016). Both the intraosseous and extraosseous ultrasound scans have the potential to improve spinal surgery safety and to be extended to other procedures beyond drilling (Chan 2022, Manbachi 2016). 225 A final area of bone-based navigation is ultrasound-guided fracture repair (Degreif & Wenda 1998). In the context of spinal fractures, managing small bone fragments is challenging (Degreif & Wenda 1998). Ultrasound-based systems can accurately segment and track the bone features in order to guide the surgeon at repairing the structure less invasively (Degreif & Wenda 1998). Further, these fragments can threaten the spinal canal, so it is important the surgeon can verify that theyâve restored the patency (Degreif & Wenda 1998). Recent results demonstrate that ultrasound is as effective as a cone-beam CT for the restoration of the spinal canal (Degreif & Wenda 1998). Lastly, some groups are using Augmented Reality (AR) to project bone positions, which allows for a more intuitive navigation experience for the user (Farshad-Amacker 2020). Navigation systems based on rigid structures, such as ultrasound on bone, are well suited for these AR headsets (Farshad-Amacker 2020).
Thesis/Dissertation
eng
Biomedical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Hodgson, Antony J.
Street, John T.
The design and validation of ultrasound-augmented self-localizing tools for dynamic and adjustable registration and navigation in spinal surgery
Text