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A fluoroscopy-based intraoperative tool for measuring alignments in spinal deformity correction surgery Amini, Mohammad 2016

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 A FLUOROSCOPY-BASED INTRAOPERATIVE TOOL FOR MEASURUING ALIGNMENTS IN SPINAL DEFORMITY CORRECTION SURGERY  by  Mohammad Amini  B.A.Sc., Sharif University of Technology, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in The Faculty of Graduate and Postdoctoral Studies (Biomedical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  July 2016  © Mohammad Amini, 2016  ii Abstract Spinal deformity is any abnormal formation, alignment, or shape of the vertebral column which can lead to pain and disability. In severe cases, corrective surgery is recommended for improving the spinal alignment with the goal of reducing pain and improving patient mobility. Although accurate intraoperative assessments of spinal alignments can highly influence patient outcomes, it still remains a technically challenging task due to the limited field of view or poor image quality of existing intraoperative tools. Therefore, the objective of this thesis is to develop a new intraoperative tool for radiographic assessment of long anatomies with a focus on spinal deformity correction surgery. An image-based technique is developed to produce long calibrated images on the surgical table. The system was validated by performing experiments on phantom objects and four cadaveric specimens. The sagittal and coronal radiographic parameters were measured on the generated long views and compared against the ground-truth data collected from computed tomography. The usability of the system, in terms of radiation exposure and the required time for image acquisition and processing, was compared against a long radiographic plain film method. Tests on the phantoms demonstrated localization accuracies of 3.9±2.3mm, and 0.6±0.7°, and stitching accuracies of 0.6±0.6mm and 2.5±1mm for coronal and sagittal views. From in-vitro experiments, on the coronal plane, the accuracies of radiographic measurements for spinal alignment angles and global spinal balance measurements were 1.1±0.7° and 0.9±0.7mm, respectively. On the sagittal plane, the Cobb angle measurement accuracy was 2.3±1.2°. The calculated radiation exposure and required time for image acquisition and processing were 2616mR and 12 minutes, which were 46% and 60% of the corresponding estimated values of long radiographic plain film method.  iii The introduced technique showed promising results for monitoring the spinopelvic alignments in both coronal and sagittal planes with accuracies within the clinically acceptable range  of <5mm and <5°, while the radiation exposure and time of image acquisition are kept lower than the corresponding values from competing methods. The proposed solution can potentially assist improve the outcomes of spinal deformity correction surgeries and similar surgical interventions where accurate assessment of long anatomies is critically important.   iv Preface The work presented in this thesis was performed by the author, Mohammad Amini, under the supervision of Dr. Shahram Amiri.   Preliminary results of the work reported here were presented at the 15th annual meeting of the International Society for Computer Assisted Orthopaedic Surgery (CAOS) in Vancouver, Canada, in June 2015.  The TC-arm platform (including the calibration process using IMU and the interface used for landmark localization), and the design of reference panel were available to the author at the beginning of the project. Some of the new improvements made to the interface of the system related to measurements on the long radiographic views, introduced in Chapter 3 of the study were made by other members of Dr. Amiri’s research group with some assistance from the author.  The author designed all of the phantoms associated with the evaluation of the system. Machining of the phantom components were fabricated by machine shop staff at the BC Cancer Agency Joint Engineering Centre. The cadaveric experiments are covered by the UBC clinical research ethics board (certificate H15-00695).     v Table of Contents  Abstract .......................................................................................................................................... ii	Preface ........................................................................................................................................... iv	Table of Contents ...........................................................................................................................v	List of Tables .............................................................................................................................. viii	List of Figures ............................................................................................................................... ix	List of Abbreviations .................................................................................................................. xii	Acknowledgments ...................................................................................................................... xiii	Chapter 1: Introduction ............................................................................................................... 1	1.1	 Significance of Spinal Deformities ............................................................................. 1	1.2	 Surgical Treatments and their Goals ........................................................................... 3	1.3	 Complications of Spinal Deformity Correction Surgery ............................................ 5	1.4	 Available Solutions for Reducing Postoperative Malalignment ................................. 6	1.5	 Commonly Available Intraoperative Imaging Tools .................................................. 7	1.6	 Tracked C-arm (TC-arm) System ............................................................................. 10	1.7	 Motivation of the Thesis ........................................................................................... 11	1.8	 Thesis Objectives ...................................................................................................... 12	1.9	 Thesis Outline ........................................................................................................... 12	Chapter 2: A New Fluoroscopy-Based Method for Generating Calibrated Large Bi-Planar Radiographic Images .................................................................................................................. 14	2.1	 Introduction ............................................................................................................... 14	2.1.1	 Currently Available Intraoperative Imaging ..................................................... 14	 vi 2.1.2	 Objectives of this Chapter ................................................................................. 18	2.2	 Methods..................................................................................................................... 20	2.2.1	 Proposed Kinematic Model of the C-arm ......................................................... 21	2.2.2	 Reference Panel ................................................................................................ 24	2.2.3	 Image Processing .............................................................................................. 25	2.2.4	 Image Stitching ................................................................................................. 36	2.2.5	 Validation Experiments .................................................................................... 43	2.3	 Results ....................................................................................................................... 48	2.3.1	 Landmark Localization Accuracies .................................................................. 48	2.3.2	 Bi-Planar Image Stitching Accuracies .............................................................. 49	2.4	 Discussion ................................................................................................................. 49	2.5	 Conclusion ................................................................................................................ 52	Chapter 3: Application of the Developed Method for Spinal Deformity Correction Surgery....................................................................................................................................................... 54	3.1	 Introduction ............................................................................................................... 54	3.1.1	 Radiographic Assessment of Spinal Alignments .............................................. 54	3.1.2	 Required Time and Radiation Exposure ........................................................... 58	3.1.3	 Objectives of this Chapter ................................................................................. 59	3.2	 Methods..................................................................................................................... 59	3.2.1	 Proposed Clinical Protocol ............................................................................... 60	3.2.2	 Bi-planar Image Acquisition ............................................................................. 61	3.2.3	 Sorting of Bi-planar X-rays and Localizing Landmarks ................................... 61	3.2.4	 Spinal Curvature Reconstruction ...................................................................... 62	 vii 3.2.5	 Validation .......................................................................................................... 64	3.3	 Results ....................................................................................................................... 73	3.3.1	 Localization of Vertebral Centroids .................................................................. 73	3.3.2	 Radiographic Assessment ................................................................................. 73	3.3.3	 Inter-Rater Reliability ....................................................................................... 75	3.3.4	 Comparison of the Image Quality ..................................................................... 76	3.3.5	 Radiation Exposure and Processing Time ........................................................ 78	3.4	 Discussion ................................................................................................................. 79	3.5	 Conclusion ................................................................................................................ 84	Chapter 4: General Discussions and Conclusions ................................................................... 86	4.1	 Contributions ............................................................................................................ 86	4.2	 Key Outcomes ........................................................................................................... 86	4.3	 Limitations ................................................................................................................ 88	4.4	 Technical Improvement Opportunities and Future Directions ................................. 90	4.5	 Conclusions ............................................................................................................... 91	References .....................................................................................................................................93	Appendices ..................................................................................................................................104 Appendix A: Landmark Digitization with Optotrak………………………………………..104 Appendix B: Radiographic Measurement…………………………………………………...110 Appendix C: Segmentation of CT Images…………………………………………………...116   viii List of Tables Table 2-1: Results of the translation and rotational accuracies, presented as mean and SD. ....... 48	Table 2-2: Results of the image stitching accuracies and parallax effects, presented as mean and SD. ................................................................................................................................................ 49	Table 3-1: The required time at each step for plain X-ray method to generate long radiographs. 58	Table 3-2: Specifications of the cadaveric specimens. ................................................................. 65	Table 3-3: Root mean square (RMS) and mean absolute difference (MAD) errors of vertebral centroid localization. ..................................................................................................................... 73	Table 3-4: Accuracies of manual measurements of radiographic parameters in both coronal and sagittal planes. ............................................................................................................................... 74	Table 3-5: Accuracies of automatic measurements of radiographic parameters in both coronal and sagittal planes. ........................................................................................................................ 75	Table 3-6: The ICC results between two observers. ..................................................................... 75	Table 3-7: Processing time, number of radiographs, and estimated radiation exposure. ............. 78	Table 3-8: Average time at each step of the plain X-ray and developed method to generate long radiographs. ................................................................................................................................... 78	Table A-1: Defined threshold for pivot parameters to ensure accurate data collection. ............. 107	Table C-1: Precision of the angular and balance measurement from CT images (3 trials). ....... 118	    ix List of Figures Figure 1-1: Abnormal spine curvatures. ......................................................................................... 2	Figure 1-2: (A) Preoperative and (B) postoperative views of spine views of the same spine. ....... 3	Figure 1-3: Description of the cone of economy. ........................................................................... 4	Figure 1-4: Sample of intraoperative (A) posteroanterior (PA) and (B) lateral radiographs. ......... 8	Figure 1-5: Demonstration of the Arcadic Orbic Iso-C C-arm parts. ........................................... 10	Figure 1-6: Tracked C-arm (TC-arm) configuration of sensors. .................................................. 11	Figure 2-1: Previously developed TC-arm system. ...................................................................... 18	Figure 2-2: Measurement of the sagittal balance. ......................................................................... 19	Figure 2-3: Overall workflow of the developed system. .............................................................. 21	Figure 2-4: Schematic view of DOF of a typical C-arm. .............................................................. 22	Figure 2-5: Arcadic Orbic Iso-C C-arm retrofitted with the new TC-arm setup. ......................... 24	Figure 2-6: The design of the reference panel. ............................................................................. 25	Figure 2-7: Demonstration of the steps for fiducial markers segmentation. ................................. 27	Figure 2-8: Designed method to determine the orientation of markers and remove the wrongly identified markers in the image. .................................................................................................... 28	Figure 2-9: Separation of the segmented fiducial markers into rows and groups. ....................... 29	Figure 2-10: The configuration of coordinate systems with respect to each other. ...................... 30	Figure 2-11: The calibration information calculated based on IMU data. .................................... 31	Figure 2-12: Location of the reference points on (A) X-ray image and (B) gantry local coordinate system (L). .................................................................................................................................... 32	Figure 2-13: The process for reconstructing the reference panel location. ................................... 34	Figure 2-14: Demonstration of the described landmark localization method. .............................. 38	 x Figure 2-15: Schematic diagram to find the anatomy-detector distance. ..................................... 39	Figure 2-16: Schematic diagram of depth-dependent image stitching process. ........................... 40	Figure 2-17: Demonstration of proposed image blending method. .............................................. 42	Figure 2-18: A custom-made phantom used for validation of landmark localization. ................. 44	Figure 2-19: Localization of fiducial landmarks based on bi-planar fluoroscopic views. ............ 45	Figure 2-20: A custom-made phantom used for validation of image stitching. ........................... 46	Figure 2-21: Generated long views from the phantom and demonstration of the method for calculating the accuracy of image stitching and parallax effects caused by an error in estimation of depth. ........................................................................................................................................ 47	Figure 3-1: Demonstration of the radiographic measurements. .................................................... 55	Figure 3-3: Proposed clinical protocol for intraoperative assessment of spine. ........................... 60	Figure 3-4: Custom graphical user interface (GUI) used for landmark localization. ................... 62	Figure 3-5: Inflection points of the spine. ..................................................................................... 64	Figure 3-6: Manual measurement of radiographic parameters. .................................................... 68	Figure 3-7: Automatic measurement of the radiographic parameters. ......................................... 69	Figure 3-8: Discrepancies between manual (A) and automatic (B) measurements of spinal alignments. .................................................................................................................................... 70	Figure 3-9: Experimental setup for acquiring the plain X-ray from a specimen. ......................... 72	Figure 3-10: Comparison of the (A) generated stitched long radiograph with (B) the images obtained from plain X-ray in a sagittal plane. ............................................................................... 77	Figure A-1: (A) OptoTrak Certus motion capture camera, (B) active markers used in this study...................................................................................................................................................... 104	Figure A-2: Digitizer spherical tip and the fiducial marker used during the experiments. ........ 105	 xi Figure A-3: (A) front and (B) side views of custom-made digitizing probe used for the experiments. ................................................................................................................................ 106	Figure A-4: Motion of a digitizing probe (side to side and front to back) to be collected during a pivot procedure. .......................................................................................................................... 108	Figure A-5: OptoTrak Certus System defaults coordinate system and axis directions. These axes used to report the precision of digitizing process. ...................................................................... 109	Figure B-1: Cobb angle measurements in the coronal plane. ..................................................... 111	Figure B-2: Measurement of coronal balance. ............................................................................ 112	Figure B-3: Cobb angle measurements in the sagittal plane. ...................................................... 113	Figure B-4: Measurement of pelvic incidence (PI) on the sagittal radiograph. .......................... 114	Figure B-5: Measurement of T1 pelvic angle (TPA) on the sagittal radiograph. ....................... 115	Figure C-1: The suggested method for the segmentation of endplates of a vertebra. ................ 116	Figure C-2: Segmentation of endplates of T3 in 3DSlicer from CT images. ............................. 117	Figure C-3: Segmentation of the right femoral head in 3DSlicer from CT images. ................... 118	 xii List of Abbreviations TC-arm Tracked C-arm DOF Degree(s) of freedom IMU Inertial measurement unit CAMC Camera-augmented C-arm SVA Sagittal vertical axis IM Image three-dimensional coordinate system L Local coordinate system G Global coordinate system SD Standard deviation OR Operating room RMM Radiographic measurement manual mR Milliroentgen CT Computed tomography CHVA Central hip vertical axis RMS Root mean square MAD Mean absolute difference ICCs Intra-class coefficients AP Anterior-posterior C7PL C7 plumb line CSVL Central sacral vertical line    xiii Acknowledgments I would like to thank my supervisor, Dr. Shahram Amiri for his priceless support and mentorship during my studies. This work would not have been completed without his valuable guidance. The knowledge and experience I have gained throughout this research was more than I could have ever imagined.   Many thanks are owed to Dr. Antony Hodgson, Dr. Carolyn Anglin, and Dr. Ganesh Swamy for their input and guidance. I would also like to thank the Smart-C team, student, faculty and staff of the Center for Hip Health and Mobility for making my graduate studies an amazing experience.  Finally, I would like to thank my truly amazing family and friends for their unbelievable supports throughout my life.     1  Chapter 1: Introduction 1.1 Significance of Spinal Deformities Spinal deformity is a complex three-dimensional abnormality of the spine that occurs in coronal, axial, and sagittal planes [1]. Depending on its severity, spine deformity can lead to various physical problems [2] such as uneven shoulder or hip, poor posture, weakness, pain, rotation of the rib cage that causes a rib prominence, and in severe cases difficulty of walking or breathing problems [3]. A recent study has shown that spinal problems affect health status as much as serious diseases such as cancer, diabetes, and heart disease [4]. Spinal deformity affects about 0.2% of the infantile and juvenile population [5], [6] and 2% to 3% of the adolescent population of United States, that accounts for an estimated 7 million cases [7]. For adults, the rate of spinal deformity is increasing with age [8]. In the United States, adult spinal deformity (ASD) affects about 8.5% of the population [9], [10]. Prevalence as high as 68% for adult population older than 60 years old has been reported [11]. The burden of spinal deformity includes health-care costs, pain management, therapy, and lost work days due to pain. The total hospital charges due to spinal deformity were $15 billion in 2011 that accounted for 20% of all hospital charges for spine disorders (in the United States) [12]. Spine deformity in children happens mostly between the ages of 10 to 15, but the condition also affects newborns and adults [7]. Scoliosis, defined as a side-to-side or lateral curvature of the spine in the coronal plane, is the most prevalent deformity of the spine (Figure 1-1-A) [7], usually classified according to the cause. The primary cause of scoliosis may in some situations be clearly detected, such as congenital abnormalities (those present from birth, due to failure of growth or segmentation of the vertebral bodies), or neuromuscular problems (caused by dysfunction of the central nervous system or CNS) [13],  or genetic conditions [14]. However, 2  in the majority of patients (about 80% [15]), the underlying causes are unknown, and the scoliosis is considered to be idiopathic [13]. Idiopathic scoliosis is sub-categorized as infantile (newborns less than three years of age), juvenile (from 3 to 10 years old), adolescent (older than ten years), or adult [13]. In the adults, the spine deformity can be caused either by the continuation of adolescent scoliosis or degeneration of the discs called de novo (new) scoliosis [16]. Adolescent Idiopathic Scoliosis (AIS) is the most prevalent form of scoliosis in both children and adults, covering more than eighty percent of idiopathic scoliosis [17]. While scoliosis is the main form of spine deformity (in terms of prevalence) [7], kyphosis (Figure 1-1-B) and lordosis (Figure 1-1-C) (abnormal curvatures of the thoracic and lumbar spine, respectively) in sagittal plane are the other types of spine curvature disorders [18].  Figure 1-1: Abnormal spine curvatures. (A) Scoliosis or lateral curvature of the spine. (B) Kyphosis or abnormal thoracic curvature. (C) Lordosis or abnormal lumbar curvature. ©Reproduced from [19] (figure 9-12) with permission from McGraw-Hill.  3  1.2 Surgical Treatments and their Goals The surgical and non-surgical (exercises and braces) treatment of spinal deformity is complex and depends on the severity of the curvature and skeletal maturity. Surgery is only suggested in severe cases due to the unbearable pain or where there is either a high possibility of progression or in patients where deformities would cause poor aesthetics as adults [15]. There are several techniques for scoliosis surgery such as posterior and anterior approach. These procedures use various instruments such as screws, hooks and rods for anchoring to the spine and creating a stable construct (Figure 1-2).   Figure 1-2: (A) Preoperative and (B) postoperative views of spine views of the same spine.  The postoperative views show the spine after the insertion of pedicle screws and rods. ©Reproduced from [20] with permission from Wolters Kluwer Health. Inc.   The main goals of spinal surgery are to stop the progression of the abnormality, as well as reducing pain and disability and improving the patient’s quality of life through achieving optimal spinal alignment [21]. The ideal spinal alignment provides a standing posture with minimal 4  muscular energy expenditure for an individual [22]. The importance of the ideal spinal alignment is illustrated in the “cone of economy” principle (Figure 1-3) [23]. In essence, the cone shows the area that the standing posture requires minimum energy expenditure. As the spinal alignment deviates from its normal shape in either coronal or sagittal planes, the body bend toward the outside of the defined cone, which requires additional effort and energy expenditure. Excessive deformity causes deviation from the cone which might lead to the inability of a patient to stand upright and results in falling. Deviation from the normal balance posture can also lead to overloading of the instrumentation and the adjacent anatomy leading to early failure of the implant or implant/bone interface [24]. Therefore, restoring spinal alignment in the surgery in both coronal and the sagittal plane is vital, to provide a standing posture within the cone and prevent further disability and complications [25], [26].   Figure 1-3: Description of the cone of economy. The figure shows the conical zone (from feet to the head) surround the individual as a stable area. Deviation from the center results in greater energy expenditure and ultimately deviation of the body outside the cone results in falling. © Reproduced from [22] with permission from Wolters Kluwer Health. Inc. 5  1.3 Complications of Spinal Deformity Correction Surgery Spinal deformity surgery is typically associated with a high rate of complications. Major complications of the surgery include: 1) issues related to blood loss or infection that can occur in any major surgery with long exposed wound and long OR time [1], and 2) issues related to spinal fusion surgery such as loss of normal spinal flexibility, unacceptable malalignments and post-surgery pain [27]. The rate of complications after multi-segmental spinal fusion surgery for spine deformity correction has been reported from 39% up to 78% [28], [29]. The variation of the rate is dependent on many factors such as different methods of treatment, patient factors, and the type of deformities [1]. Complications might lead to patients’ dissatisfaction [30] or even revision surgeries [1]. The overall rate of spine deformity revision surgeries reported between 10% - 17% [21], [31]. This rate of reoperation illustrates the financial burden by considering the estimated hospital costs that have been reported $100,000 for the primary and $67,000 for spine deformity revision surgeries (in the United States from 2005 to 2011) (revision surgery due to different issues – non-specific to malalignment) [32]. The immediate postoperative malalignment is a common cause for revision surgeries among the many risk factors such as curve progression, implant failure, and postoperative pain [33]. Immediate postoperative malalignment can be a generated by inadequate correction of deformity [34], and asymmetrical correction of deformity [33]. In the sagittal plane, inadequate correction of deformity is a major cause of postoperative spinal malalignment that may cause syndromes such as flatback, proximal junctional kyphosis (PJK), and proximal junctional failure (PJF) [33], [35]. Flatback refers to the loss of normal lordosis caused by the distraction instrumentation during deformity correction surgery [36]. Proximal junctional kyphosis (PJK) 6  refers to increase of segmental kyphosis above the fusion larger than 10° in comparison to preoperative measurement that in severe cases might lead to the fracture of the upper instrumented vertebrae (PJF) [35]. In the coronal plane, inadequate or asymmetrical correction of deformity can cause immediate postoperative malalignments such as shoulder asymmetry and leg-length discrepancy [33].  1.4 Available Solutions for Reducing Postoperative Malalignment It has been proposed that the chance of postoperative malalignment can be reduced by: 1) a reliable preoperative classification and planning methods [37] and also 2) accurate intraoperative execution of the plan and monitoring of curvature [33], [38]. These steps provide the tools that facilitate the decision-making process and aid the surgeon to reduce the chances of issues related to the radiographic complications and spine malalignment. The description of these steps is provided in the following: Preoperative classification and planning: The main purpose of preoperative classifications is to facilitate the surgical planning and reduce the variability of surgical approaches to improve the outcome. Several decision-making trees and preoperative planning methods have been developed for spine deformity surgery based on the available classification methods [37], [39]–[42]. However, the outcome of the surgery is still not satisfactory for all cases [43], and revision surgeries are still reported during follow-ups due to the parameters such as balance [44], [45]. Intraoperative execution of the plan and monitoring of curvature: Although preoperative planning remains vital in extremely complex surgeries like spine deformity, intraoperative monitoring of the curvature and spine alignment are important to finalize the plan successfully 7  and avoid immediate postoperative malalignment [33], [38]. Intraoperative radiographic appearance is reported as one of the predictors of postoperative outcome and health status [46]. Therefore, monitoring the spinal alignment while there is still possibilities for further modifications of the achieved correction can facilitate the achievement of optimal alignment and reduce the chance of postoperative complications associated with radiographic appearance [33], [38]. 1.5 Commonly Available Intraoperative Imaging Tools Imaging plays a significant role in the intraoperative monitoring of spinal curvature [47]. Intraoperative assessment of spine curvature and global alignment enables clinicians to modify the reconstructed alignment intraoperatively and reduce the chance of postoperative malalignment [38]. The commonly available intraoperative imaging tools are: 1) Plain radiographs and 2) Mobile C-arm. However, both of these have limitations in the convenience of use, required time for image acquisition, and inability to provide quantitative feedback. Plain radiographs represent the method for the assessment of radiographic parameters intraoperatively. Plain radiographs can be acquired using both CR (computed radiography) and DR (digital radiography) systems. CR (computed radiography) systems use cassettes to detect x rays which are scanned afterward using a scanner to generate digital radiograph. In DR systems, cassettes have been replaced by digital image detectors that can generate radiographs in real-time. For the intraoperative spine application, CR systems are more common due to the limited size of detectors in DR systems. However, the usability of cassettes is also limited due to their disadvantages such as poor quality and lengthy procedures. Intraoperative plain radiography requires long-length cassettes (Figure 1-4) which cause distortion that might alter the shape of anatomy and lead to a wrong assessment of radiographs. It also has a poor visualization due to 8  the same energy beam to different segments of the spine and pelvis with various amount of tissue and therefore underexpose and overexpose different areas results in artifacts [48]. The most commonly used radiographic film for spine surgeries is 36 inches long and 14 inches wide, which might not cover all of the required anatomical landmarks, like shoulders, femoral head, and cervical vertebra for adult patients due to its limited size [38]. Another main limitation of intraoperative X-ray is related to sagittal views [38]. Acquiring images from the sagittal view with high quality is very challenging due to the amount of tissue around the pelvic region and shoulder areas. The X-ray film also should be draped for sagittal images to avoid infection and this adds to the OR time. These described issues limits the monitoring of critical sagittal parameters such as global alignment intraoperatively.  Figure 1-4: Sample of intraoperative (A) posteroanterior (PA) and (B) lateral radiographs. They demonstrate 1) the inability of this method in visualizing the important anatomical landmarks (e.g., shoulder and femur heads in coronal view), 2) poor visualization due to the difficulty in obtaining correct exposures for different parts that have a different amount of tissue (femoral heads and endplates in the sagittal view. © Coronal view reproduced from [38] with permission from Wolters Kluwer Health. Inc. © Sagittal [49] view reproduced from with permission from Wolters Kluwer Health. Inc.  A B 9  A mobile C-arm fluoroscopy equipment is an X-ray machine that is extensively used during orthopaedic surgery for low radiation and convenience of the positioning mechanism. It consists of 1) an arc-shaped arm or gantry that holds an X-ray source at one end and an image detector at the other, 2) a control unit for gantry movement, 3) a base that provides a mechanical system for movement of the machine, and 4) a monitoring unit that visualizes the radiographs (Figure 1-5). C-arms have several advantages over plain X-ray imaging systems. The C-arm ability to move and rotate in different directions enables the surgeon to take X-rays from different viewing angles. Moreover, C-arm is categorized as a low-dose X-ray modality since it utilizes less radiation dose during fluoroscopic imaging in comparison to other X-ray devices, which is a critical fact for patient and clinical staff health [50]. Even though it is very broadly used, C-arm has some limitations. C-arm’s two-dimensional imaging modality is incapable of providing accurate long views of the anatomy due to its small field of view. Especially for spine deformity correction surgery, it is challenging to quantify the critically essential radiographic parameters such as coronal and sagittal balance on separated X-rays with a limited field of view. Therefore, there is a substantial need for an intraoperative imaging tool that provides reliable and accurate radiographs of the spine with sufficient field of view and high quality in both coronal and sagittal views. 10   Figure 1-5: Demonstration of the Arcadic Orbic Iso-C C-arm parts. Arcadic Orbic Iso-C C-arm (Siemens AG, Munich, Germany) parts include source, detector, gantry, control unit, base, and monitoring unit. The device was used for the experiments in this thesis.  1.6 Tracked C-arm (TC-arm) System A sensor-based tracking system (Tracked C-arm or TC-arm) has been developed by our research group to address the limitation of the C-arm and generate long intraoperative views [51]. This system utilizes two inertial measurement units (IMUs) attached to the gantry of the C-arm to measure orbit, tilt, wig wag, as well as two laser beam sensors to measure up-down and in-out movements of the gantry (Figure 1-6). This system calculates the pose of the source-detector set, for any configuration of the C-arm. This low-cost system is capable of determining an accurate estimate of the C-arm’s pose for any acquired fluoroscopic image and can track the center point of the gantry with better than 1.5±1.2 mm accuracy. The ability of the TC-arm in the generation of long views has been illustrated by Amiri et al. [51], however, this system requires an additional module to expand the tracking volume to longer lengths along the surgical table for 11  particular clinical applications including very long operative anatomies.  Figure 1-6: Tracked C-arm (TC-arm) configuration of sensors. The sensors calculate the gantry’s translations (up-down and in-out) and rotations (orbit, tilt, and wigwag). © Reproduced from [51] with permission from Springer.  1.7 Motivation of the Thesis This thesis is motivated by understanding the clinical need for a system that provides long radiographs of anatomy in both coronal and sagittal planes, using the widely-available imaging tool (C-arm). This thesis is organized into two parts. First, an add-on module to the previously developed TC-arm is proposed for expanding the tracking volume and providing calibrated images. The calibrated images acquired from the TC-arm system has been used to generate intraoperative long views of anatomy. Second, the capabilities of the developed system were validated for spine deformity surgery by defining a specific clinical protocol and performing tests on cadaveric specimens. 12  1.8 Thesis Objectives This thesis was motivated by the need for an accurate intraoperative tool for assessment of long anatomies for particular use in spinal deformity correction. This thesis follows two main objectives: 1. Development and validation of a technique for generating intraoperative long bi-planar radiographs of anatomy based on mobile C-arm fluoroscopy equipment 2. Evaluation of the developed technique for image quality, usability, and accuracy of radiographic measurements in the spinal deformity correction surgery 1.9 Thesis Outline Chapter 1 provides an overview of relevant literature about the significance and prevalence of spinal deformities, surgical treatments, and the role of intraoperative imaging tools for assessment of spinal alignments. Afterward, a brief description of the available intraoperative imaging systems and their limitations are provided. Motivation, as well as the objectives of the thesis, are also explained in this chapter.  Chapter 2 presents a framework that has been developed for the generation of intraoperative panoramic radiographs, followed by a description of the verification experiments and their results. Additional technical details are described in Appendix A. Chapter 3 details the clinical protocol that has been designed to facilitate the intraoperative assessment of the spine. The clinical application of the developed method is also validated by performing experiments on cadaveric specimens. The additional details of the validation process and measurements are listed in Appendix B and C. 13  Chapter 4 concludes with contributions of the proposed systems. Limitations, improvement opportunities, and future directions to make it ready for clinical use are also discussed in this chapter.  14  Chapter 2: A New Fluoroscopy-Based Method for Generating Calibrated Large Bi-Planar Radiographic Images 2.1 Introduction An intraoperative method that can provide accurate information about the shape of the long operative anatomy can be a useful resource for the surgical staff to assess the surgical objectives during the course of the operation, while there are chances for making necessary adjustments [33], [38]. Unfortunately, the current intraoperative imaging tools such as plain X-ray films and C-arm fluoroscopy are incapable of providing this information reliably due to the limited field of view or poor quality. As an alternative solution, in this chapter, an intraoperative assessment tool is introduced which is capable of visualizing the shape of long operative anatomies by utilizing mobile C-arm fluoroscopy equipment which is available in every OR. The desired system must be able to localize the locations of the landmarks and generate calibrated long radiographs in both coronal and sagittal planes.  In this chapter, a description of the proposed intraoperative imaging technique, followed by a detailed illustration of the validation experiments are provided. Additional technical details are detailed in Appendix A. 2.1.1 Currently Available Intraoperative Imaging The available imaging methods in literature can be classified into two broad groups: 1) X-ray film-based methods, and 2) fluoroscopy-based methods. As described below, each of these types of imaging groups has limitations such as poor quality of the image and small field of view. 15  2.1.1.1 X-ray Film-based Methods X-ray film-based methods utilize cassettes and films with extended lengths to visualize the spine in surgery [52]. For spine applications, even though long cassettes can provide a larger field of view, they might not be able to visualize all of the required anatomical landmarks that are necessary for complete radiographic assessment of alignment (e.g., cervical spine, shoulders, and femoral heads) particularly in adult patients [38]. This limitation necessitates the use of two images with sufficient overlapping areas which will increase the radiation exposure and operative time. A stitching software is also necessary to produce large views by matching visible features like radio-opaque references in the overlapping areas. The final image in this methods is prone to either miss or duplicate some parts of the anatomy [53]. The accuracy of stitching software has also been investigated and shown that 16% of digital scoliosis radiographs had stitching errors that could result in false diagnosis [48].  Besides the limitations associated with stitching of X-ray films, acquiring the intraoperative sagittal images with plain films are challenging, due to the poor quality of images around the areas with a large tissue thickness (e.g., pelvis and shoulder areas) (Figure 1-4-B) [38]. For the sagittal view, X-ray film should also be draped to avoid infection. Draping can add to the time required for preparation of the imaging system which introduces another limitation for this imaging method. 2.1.1.2 Fluoroscopy-based Methods Fluoroscopy-based methods have been suggested for producing panoramic views intraoperatively. In the normal use of a fluoroscopy equipment, X-rays with a small field of view are used by the surgeon to assess the spinal alignment. To expand the C-arm’s narrow field of view and to generate long radiographs, different methods were proposed. These methods can be 16  categorized into two main groups: 1) tracking-based methods and 2) fiducial-based methods, as described below. Tracking-based systems generate panoramic views by tracking the pose (position and orientation) of the C-arm’s source-detector set (full three-dimensional spatial coordinates of the detector and the corresponding position of the X-ray source). These methods can either rely on the visibility of fiducial markers in the X-ray image or utilize an external tracking device to estimate the parameters of the C-arm with respect to the global coordinate system. The calibration parameters with respect to the local coordinate system (gantry) can also be found using two main methods: 1) on-line methods and 2) off-line methods [54]. On-line methods determine the parameters using the presence of markers in the image. On the other hand, off-line methods determine the pose of the C-arm based on information obtained from a number projection views of a calibration phantom acquires in a previous step. The real-time (or intraoperative) pose parameters for each X-ray are then extracted based on the previously established off-line calibration. The required calibration information thereafter is recovered at each C-arm pose and for each X-ray shot (calibration information consisting of x, y, and z coordinates of the source and detector, pixel scale, and image orientation - for description see Figure 2-11)  Different intraoperative systems have been developed to estimate the pose of the C-arm and generate calibrated images. Calibrated images, from online or offline calibration, can be used to generate long radiographs. An example is a unique panel consisting of small markers that was built and used as a reference to estimate the pose of the C-arm [55]. In their proposed configuration, the large number of markers in the panel occluded the anatomical structures in the X-ray images and reduced the visibility of the anatomy. In another example, accelerometers were 17  used to recover the orientation of the C-arm with limitation in not being able to cover a large imaging volume [56]. The external tracking systems (optical tracking and magnetic tracking) have also been utilized as a mean of tracking for C-arm systems, but they are mostly limited by the requirement of line of sight or influence of magnetic fields [57], [58]. Camera-augmented C-arm (CAMC) is an another system that has been proposed more recently to recover the pose of the device [59]. This method incorporates a standard video camera along with the C-arm device to recover the pose of the C-arm. The main limitations of this system are the need for significant modifications to the C-arm machine as well as line-of-sight for sagittal views. Even though that the ability of CAMC system in providing long views has been demonstrated [60], [61], limitation of the system in producing sagittal views make then not useful for spine surgery. Fiducial-based systems estimate the image parameters based on the projection of fiducials in the image. Radio-opaque ruler has been utilized in different studies to generate long views [47], [62]. These systems first segment the graduations of the ruler on the X-ray and then determine the transformation between the images based on a feature-based alignment method. Radio-opaque custom-made panels also designed and proposed in different studies to align the images [63], [64]. These panels provide a unique pattern that can be used to generate a long view. The main limitations of reference-based systems are: 1) they assume the anatomy to be planar, 2) they assume that the image is parallel to the plane of anatomy, and 3) they assume a constant distance between the image and anatomy. During the spine deformity surgery, these limitations are not acceptable due to the curvature of the spine. 2.1.1.3 Tracked C-arm (TC-arm) system  The TC-arm is a fluoroscopy-based system that has been developed previously by our research group [51] (Figure 2-1). It utilizes off-line calibration methods to estimate the pose of the C-arm 18  using inertial measurement units (IMUs) and laser sensors to recover the orientation of the gantry and the up-down and in-out movement of the gantry. Complete three-dimensional spatial information of the X-ray source and image intensifier can be achieved using the calibration protocol for any arbitrary image acquired by the TC-arm system. This tracking system is an inexpensive method that can be added to any C-arm at low-cost and provides the intrinsic and extrinsic parameters for any collected fluoroscopic image collected by the system. The capability of TC-arm system in generating the long views by only rotating the C-arm gantry about the vertical axis of the device has been demonstrated [51]. However, the field of view of the system in the previous configuration is not sufficient for surgeries that require assessment of large anatomies such as the spine.   Figure 2-1: Previously developed TC-arm system. It consists of a sensor box and two inertial measurement units (IMUs) which communicate to a tracking PC and provides near-real-time measurements of the C-arm positions. © Reproduced from [51] with permission from Springer.  2.1.2 Objectives of this Chapter The objectives of this chapter are to: 1. Develop a fluoroscopy-based method for generating calibrated long bi-planar radiographs without limitation of the size of the anatomy 19  2. Conduct validation experiment on a custom phantom to evaluate if the proposed system has accuracy of 5mm or better for landmark localization 3. Conduct validation experiments on a custom phantom to quantify the parallax effect on the generated radiographic views In this study, a 5mm margin is suggested as an acceptable threshold for landmark localization error, based on a clinical experiment that evaluated the correlation between the sagittal balance (Figure 2-1) and health-related quality of life (HRQL) that shows self-reported pain and disability [22]. The sagittal balance is measured on long radiograph using two landmarks (C7 and posterior-superior corner of S1). Sagittal balance, also known as sagittal vertical axis (SVA), shows a distance between a vertical line from a center of C7 and the posterior superior corner of S1. Therefore, for landmark localization, a 5mm margin (10% of the proposed clinically acceptable threshold) was selected as an acceptable threshold in this study.  Figure 2-2: Measurement of the sagittal balance. The SVA (sagittal vertical axis) shows the sagittal imbalance, defined as the horizontal offset from the center of C7 to the posterior-superior corner of S1. The SVA < 50mm has proved to be correlated with a higher HQRL (health-related quality of life) score. © Reproduced from [22] with permission from Wolters Kluwer Health. Inc. 20  2.2 Methods In this study, a new image-based module has been developed as an add-on to the TC-arm system with the necessary software to generate the long views from individual X-rays. This module provides fully calibrated images along the length of the surgical table.  Development of the system included: 1) instrumenting the C-arm with an inertial measurement unit (IMU) and reference panel to encode the movements of each individual joint of the device; 2) developing a software to process the images and their corresponding calibration files (provided by the TC-arm system) to generate full three-dimensional spatial information of X-ray source and image intensifier in the global coordinate system, followed by, landmark localization and image stitching for creating the three-dimensional shape of anatomy and generating bi-planar long views.  The overall workflow (inputs, outputs, and computations) that has been designed for the intraoperative system to generate fully calibrated images are illustrated in Figure 2-3. In the designed workflow, for the coronal image, the pose of the image with respect to the local coordinate system is determined using the IMU data and the offline calibration lookup table that has been described in the literature (The IMU and calibration lookup table were available prior the start of the project) [51]. Subsequently, the pose of the image with respect to the surgical table (global coordinate system) is found using the designed image processing system and the projection of the reference panel in the image (The design of the reference panel was available prior the start of the project) . For the sagittal image, the calculated transformation between local and global coordinate frames in coronal view is used along with the IMU data in sagittal view to determining the pose of the image with respect to the surgical table. 21   Figure 2-3: Overall workflow of the developed system. This image explains the designed steps to generate bi-planar calibrated images. In the first step, the location of coronal images with respect to the local coordinate system is determined using the IMU information. After that, the location of coronal images with respect to the global coordinate system is found using the developed image processing unit. Finally, in the second step, global location of sagittal images is determined using the IMU information and the calculated transformation for the corresponding coronal image. In the flowchart, the boxes are color coded as follow: Orange: Inputs; Blue: processes; Green: Outputs.  2.2.1 Proposed Kinematic Model of the C-arm A typical mobile C-arm fluoroscopy has six degrees-of-freedom (DOF) (Figure 2-4). Three rotation parameters for the orientation of the gantry include: 1) wigwag (rotating the gantry, an arc-shaped arm, about the vertical axis or V-axis in Figure 2-4), 2) orbit (rotating the gantry about the horizontal axis or W-axis in Figure 2-4), and 3) tilt (rotating the gantry about the U-axis in Figure 2-4). Three translation parameters for the location include: 1) vertical (translating 22  the C-arm up and down along the V-axis), 2) horizontal (changing the length of the arm or movement of the base along the U-axis), and 3) along the table or the W-axis (Figure 2-4).  Figure 2-4: Schematic view of DOF of a typical C-arm. Joints configurations and degrees of freedom of a typical mobile C-arm equipment include three translations (in-out, up-down, and along the table) and three rotations (orbit, tilt, and wigwag) movements with respects to the global coordinate system.   In the proposed approach for tracking the mobile C-arm equipment, a custom-made ‘reference panel’ with an array of fiducial markers were used to calculate the movement of the base along the table (!") (Figure 2-4). In addition, this panel provides the wigwag rotation ($%), up-down (!%), and in-out movement (!&) information (total of 4 DOF). The gantry orientations (tilt and orbit) were calculated by employing one IMU attached to the gantry (2 DOF). Changes in the orientation of the gantry were detected using the angle-sensing ability of gyroscope and accelerometer in the IMU, and the magnetometer component of the sensor was disabled to avoid 23  errors due to proximity to metal objects. This configuration provides full 6 DOF tracking of the C-arm by transformation matrices that correspond to the above mentioned DOFs (Equation 2-1). T = T)*,),,)-,., . [T.*,.-] Equation 2-1 In the proposed kinematic model, the right side of the equation (Equation 2-1) that corresponds to the orbit and tilt of the C-arm’s gantry ([T.*,.-]) was calculated using the IMU data and interpolating based on an offline calibrated lookup table as published in the literature [51]. The left side of the equation (Equation 2-1) corresponds with location information of the base and gantry translational movements (!2&,!2%, and !2" in Figure 2-4), as well as rotation about the V-axis or wigwag (!3% in Figure 2-4). This component of the kinematic model was calculated using the reference panel and the developed image processing software that is described in the following sections. 24   Figure 2-5: Arcadic Orbic Iso-C C-arm retrofitted with the new TC-arm setup. This system consists of an inertial measurement unit (IMU) attached to the handrails of the gantry and a reference panel mounted under a radiolucent surgical table. The IMU provides the gantry’s orbit and tilt by communicating with tracking computer and the reference panel measures the translational movement of the device with respect to the surgical table as well as wigwag.  2.2.2 Reference Panel  The ‘reference panel’ holds an array of radio-opaque fiducials underneath the surgical table for the purpose of providing position information. The panel was previously designed by our research group and CNC machined from Delrin, a polymer known for its high stiffness, good X-ray transparency, and excellent dimensional stability (coefficient of linear thermal expansion = 5	×	109:	;</(;<℉)). The designed reference panel consists of a rectangular matrix (Figure 2-6-A), with a particular arrangement of ball bearings (1.6 mm in diameters) that forms a specific coding configuration (Figure 2-6-B). In this design, each two adjacent groups of ball bearings represent a unique location in the reference panel from which the unique row and column of ball bearings can be automatically detected by segmenting any radiographic projection of the panel. The reference panel is 1210 mm long and 420 mm wide which is sufficient for covering the 25  length of long operative anatomies such as spine and can be mounted under any conventional radiolucent surgical table. 2.2.3 Image Processing  A custom image processing software was developed to segment the fluoroscopic views, extract the panel information, and compute the spatial information of the coronal and sagittal views. The detailed technical description of each step is provided in the following sections. All the required software were developed in MATLAB (R2013a; MathWorks®, Natick, Massachusetts, US).  Figure 2-6: The design of the reference panel. (A) The reference panel, measuring 1210 by 420 mm in size, consist of 480 groups of ball bearings that represent unique locations on the table. (B) Sample arrangement of ball bearings in the design of the panel.  26  2.2.3.1 Segmentation of Fiducial Markers A series of image processing filters and image enhancement methods were incorporated to ensure robust and accurate detection of projections of the fiducial markers in the image (Figure 2-7). First, a contrast-limited adaptive histogram equalization (CLAHE) was applied to enhance the contrast of the grayscale image (with contrast enhancement limit of 0.02) and to enhance separation of the ball bearing projections from the background (Figure 2-7-A). Intensity adjustment then performed (with a gamma correction value of 0.55) to make a brighter output (Figure 2-7-B). In the next step, a Wiener two-dimensional adaptive filter (with a neighborhood size of 15×15) was applied to low-pass filter the grayscale image to reduce the effects of random noises in the image. Two-dimensional median filtering was then applied (with a 3×3 neighborhood) to enhance the performance of the edge detection (Figure 2-7-C). The Canny edge detection (with a σ value of 3) was performed subsequently to detect the sudden changes in intensity (Figure 2-7-D). Finally, the circular projections of fiducial markers were detected using the circular Hough transform (with a sensitivity of 0.9 and radius range between 4 and 20 pixels) (Figure 2-7-E) [65], [66]. For each image, the locations of the center of all projected fiducial markers (x, B) and their corresponding radii (r) were calculated (Figure 2-7). All of the described methods were performed using MATLAB image processing toolbox functions (R2013a; MathWorks®, Natick, Massachusetts, US). 27   Figure 2-7: Demonstration of the steps for fiducial markers segmentation. The X-ray image has been taken from a cadaveric pelvis with the presence of soft tissues and reference panel. This figure shows the implemented steps for accurate and robust segmentation of fiducial markers including results of: A) contrast enhancement, B) intensity adjustment, C) Wiener and median filters, D) Canny edge detection, E) detected circles using Hough transform, F) Final segmentation results plotted on the original image. 28  As shown in Figure 2-7, the process of segmentation was prone to error. To eliminate the wrongly detected markers, a specific process was designed to calculate the orientation of the markers in the image and to remove the wrongly identified markers. The orientation was found by passing lines with parametrically-defined angles through detected blobs and finding an angle of the line that is passing through the maximum number of circles (red lines in Figure 2-8). This method was followed by detecting and eliminating the false negative blobs that were identified wrongly during the Hough transform (blue triangle in Figure 2-8).  Figure 2-8: Designed method to determine the orientation of markers and remove the wrongly identified markers in the image. The process of removing the wrongly detected marker (blue triangle) by determining the orientation of the markers (red line).  2.2.3.2 Pattern Recognition A pattern recognition strategy was developed to find the row and column information of fiducial markers from the segmentation information. In this process, first, the circular projections separated into different rows (Figure 2-9-A) and groups (Figure 2-9-B) based on the calculated orientation in the previous step. Second, the unique row and column for each fiducial marker 29  were then identified by comparing the patterns of markers with the design of the panel (Figure 2-6).  Figure 2-9: Separation of the segmented fiducial markers into rows and groups. Detected and color coded (A) rows (green, red, and blue), and (B) groups in each row (yellow and magenta in the first row, red and green in the second row, and blue and black in the third row). Rows and groups are detected using the distances between them.  2.2.3.3 Pose Estimation of the Coronal View  The three-dimensional position and orientation of the coronal image with respect to the global coordinate system (defined with respect to the reference panel) were determined by finding the relationship between the image coordinate frame (IM) and the global coordinate frame (G). For this purpose, first, the transformation between the image coordinate system (IM) and the local coordinate system of the gantry (L) was found. Second, the transformation between a local coordinate system of the gantry (L) and the global coordinate system (G) was determined (Figure 2-10) (Equation 2-2). The local coordinate system of the gantry (L) stays fixed with respect to the global coordinate system when orbit and tilt angles of the C-arm were changing ($& and $" in Figure 2-4) but moves with respect to the global coordinate system as soon as other DOFs were changed. The details of this process are provided in the following paragraphs. 30  !DEF = 	!GF×!DEG  Equation 2-2  Figure 2-10: The configuration of coordinate systems with respect to each other.  The global coordinate system (G) is a fixed point on the corner of the reference panel. The local coordinate system (L) is located at the center of the X-ray cone, and the image coordinate system (IM) is located on the image plane.  The transformation between the image coordinate system (IM) and gantry local coordinate system (L) (!DEG ) was available through a method previously developed for offline calibration of the gantry. This method interpolates the intrinsic and extrinsic image parameters using IMU information [51]. The image parameters include coordinates of the X-ray source location, source to image distance, and the corresponding position and orientation of the image 31  detector all described with respect to an iso-centric point that does not change by tilt and orbit of the gantry (Figure 2-11).  Figure 2-11: The calibration information calculated based on IMU data. The image parameters include principal distance d (distance from the X-ray source to the image plane), the position of X-ray source relative to gantry local coordinate system, pixel size r (resolution), image normal vector XIM and image up vector YIM, vectors that indicate the planar orientation of the X-ray.  The coordinates of the segmented fiducial markers were translated from pixels to three-dimensional millimeter coordinates through the following equations (Equation 2-3,4,5,6). XIIJ = −dXMN +	XPQRSTUJ ; 	YIIJ = −dYMN +	YPQRSTUJ ; 	ZIIJ = −dZMN +	ZPQRSTUJ  Equation 2-3 X	axis:	XMN; 	Y	axis:	YMN; 	Z	axis:	XMN×YMN Equation 2-4 For a given measured pixel in image two-dimensional coordinate system (x]^, y]^), the corresponding three-dimensional coordinates were calculated as follows: xMN = x]^ − t 2 r, yMN = y]^ − t 2 r Equation 2-5 32  Where t is the size of the image (number of pixels along the Xb^	and	Yb^) and r is the pixel size (resolution). Each measured point was then transformed into the gantry local coordinate system (xJ, yJ, and	zJ): xJyJzJ = XMN. XJ YMN. XJ ZMN. XJXMN. YJ YMN. YJ ZMN. YJXMN. ZJ YMN. ZJ ZMN. ZJ ×xMNyMN0 + XIIJYIIJZIIJ  Equation 2-6 For calculating the transformation between local and global coordinate systems (!GF) three segmented fiducial markers with 90° separation angle were selected as the references (Figure 2-12-A). Corresponding three-dimensional coordinates of the reference points in the local coordinate system of the gantry were then calculated by using the Equation 2-6 (Figure 2-12-B).  Figure 2-12: Location of the reference points on (A) X-ray image and (B) gantry local coordinate system (L). (A) Two-dimensional X-ray of Sawbones model of a spine with detected reference points (yellow circles). (B) Corresponding three-dimensional location of reference points with respect to the image (IM) and local (L) coordinate systems (green circles).  33  At this stage, the position of the X-ray source with respect to the gantry local coordinate system (L) was known from an IMU-based information. Subsequently, the three-dimensional coordinate of the selected reference points on the panel (black circles in Figure 2-13) was computed using a constrained optimization algorithm. The objective function used for optimization moves the parametrically defined coordinates of the reference points along lines that connect the source to the projections and minimizes the difference of the angle between reference points and the physical design of the panel (90°). Let x n  indicate the parameterized vector location definition of the marker on the ray that connects the X-ray source to the three-dimensional coordinate of marker’s projection on the image plane (n = 0,1 , where n = 0 corresponds to the location of the source and n = 1 indicates the location of marker’s projection on the image plane) (Figure 2-13). Besides, let Vf and Vg denote the vectors that connect the reference points (Figure 2-13). The length of Vf and Vg and the angle between them was a priori information from the design of the reference panel (respectively 35 mm, 25 mm, and 90°). The optimization process converged to the three-dimensional location of the markers considering the constraints of the objective function, which was the angle (α) between the Vfand Vg minus 90 when the length of the Vf < 35.1 and Vg < 25.1 (Equation 2-7). f = argkl min	 α x(n) − 90 ; 	α n : the angle between Vf and Vg Equation 2-7 pf(<) −	pg(<) < 35.1pf(<) −	pq(<) < 25.1  34   Figure 2-13: The process for reconstructing the reference panel location. Three-dimensional location and orientation of the reference panel with respect to gantry local coordinate system are calculated by reconstructing rays (red lines) between the X-ray source and calculated reference points on the image plane for a single plane reconstruction process.  On the other hand, the coordinates of these points in the reference panel coordinate frame were known based on panel’s three-dimensional model. The rigid body transformation (TJr 	∈	ℝqkq) between the two coordinate systems (gantry local coordinate system and global coordinate system) was calculated by implementing the Singular Value Decomposition (SVD) method [67]. SVD calculates the parameters (3 rotations + 3 translations) that map the x, y, and z coordinate of fiducial markers in gantry local coordinate frame to the global coordinate frame for each image. These transformation parameters represent the image’s pose relative to the global coordinate system. Finally, the defined transformation matrices were applied for positioning the image with respect to the same global reference. The calculated transformation (TGF) inherently had the translation of the C-arm in all directions as well as wigwag (rotation around X axis) 35  (Equation 2-8). This can be used in the kinematic model of the C-arm (Equation 2-1) to determine the spatial coordinates of the X-ray source and image intensifier in space with respect to the global coordinate system which can be considered fixed to the surgical table. TGF = T)*,),,)-,.,  Equation 2-8 2.2.3.4 Pose Estimation of the Sagittal View The three-dimensional position and orientation of the sagittal image in the global coordinate system cannot be determined using a method that was described in the previous section since the reference panel is not visible in a sagittal view. To solve this issue, the sagittal image should be taken after acquiring the corresponding coronal X-ray by rotating the gantry ($" in Figure 2-4), while all of the C-arm joints are locked in place. This method keeps the local coordinate system stationary (the location of the local coordinate system in Figure 2-13) between the coronal and sagittal X-ray views. Therefore, the calculated transformation matrix between local and global coordinate systems stays the same (!GF  in Equation 2-2) for both coronal and sagittal views. The new transformation matrix for the sagittal view between the IM coordinate system and the local coordinate system (uvw;xxvy	!DEG  in Equation 2-9) was provided from the angle-sensing ability of IMU. The configuration and transformation corresponding to the sagittal view can be described by Equation 2-9. This protocol enabled the system to register the sagittal images as well as coronal images even without the presence of the reference panel. uvw;xxvy	!DEF = (Coronal	!GF)×(uvw;xxvy	!DEG ) Equation 2-9  36  2.2.4 Image Stitching  The transformation or homography (Hi) that maps the ith X-ray image to the plane of the first X-ray image was defined by Equation 2-10. In this equation, R	 ∈ 	ℝqkq describes the rotation, t	 ∈	ℝqdescribe the translation of gantry, n is the normal vector of the plane that contains anatomy, and d is the distance between the object and the image intensifier. K	 ∈ 	ℝqkq contains the intrinsic matrix of the camera and can be calculated by Equation 2-11, in which f represents camera focal length; (uÅ, vÅ) is an image origin coordinate, kR and kÑ are pixel scales along the horizontal and the vertical axis, and θ is an angle between image plane axis. Hi = KRK9f + 1dKtn)K9f Equation 2-10 Ü = −fkR fkRtan θ uÅ0 − fkÑsin θ vÅ0 0 1  Equation 2-11 The first part of the transformation in Equation 2-10 (KRK9f) fully defined from tracking and pose estimation. The second part (fá Ktn)K9f), however, depends on depths parameter d. To establish a valid homography for the images to create a panoramic image, the anatomy plane and its distance from the image intensifier is needed. The following sections describe how the depth parameters are estimated for generating stitched views. 2.2.4.1 Image Acquisition Protocol Following the workflow designed in Figure 2-3, the following image acquisition protocol was outlined: 37  1- Position the C-arm to take the first coronal X-ray that includes the area of interest while the C-arm wheels are locked. 2- Rotate the gantry 90° to take the corresponding sagittal X-ray from the area of interest while all other joints are locked. 3- Return the gantry to its coronal position. Unlock the wheels and move the C-arm to take another coronal X-ray shot such that the X-ray includes the next area of interest. 4-  Repeat the step 2 to acquire the sagittal view of the second area of interest. 5- Stop if the images cover the desired area, otherwise repeat the steps 3-4. 2.2.4.2 Landmark Localization The distance between anatomy and the detector can be determined by localizing landmarks along the length of the anatomy. After bi-planar image acquisition, the desired landmark was selected manually in each pair of images using the previously developed software that allows localization based on stereo radiographic views. The software localizes the position of the landmarks through a user interface that allows moving the projections of three-dimensional points on two views simultaneously as shown schematically in Figure 2-14. This process was performed manually for all of the required landmarks along the length of the anatomy. Afterward, the details of the structure were determined by employing the cubic spline interpolation that fills the shape of the anatomy between the selected landmarks. 38   Figure 2-14: Demonstration of the described landmark localization method. The three-dimensional coordinates of the desired landmark (red cross) can be calculated from two bi-planar X-rays by passing a ray through the source to the landmark on the image plane and finding the intersection between them.This was done by a previously developed graphical user interface.  2.2.4.3 Calculation of Anatomy to Detector Distance In the proposed approach, the distance between image intensifier and anatomy was considered variable and calculated using localized landmarks locations. To accurately estimate the distance between the anatomy and the detector, each image was broken down into a number of segments (Figure 2-15-B). To measure the distance, coordinates of corners of each segment were calculated based on fully determined image parameters in three-dimensions. Subsequently, the distance of each segment to the image was computed and the coordinates of segments’ corners in the anatomical height were calculated using linear perspective projection. The image segments were then mapped from image plane to anatomical plane by applying the projective transformation (Figure 2-15-A).  39   Figure 2-15: Schematic diagram to find the anatomy-detector distance. (A) The process of finding four corresponding corners on the image plane and anatomical plane (green box). The corners of the segments on the anatomical plane were calculated by passing a plane through the corners of X-ray and source and finding the intersection (red star). (B) Two-dimensional representation of the image segments and their corresponding locations in the height of anatomy (red dotted lines).  2.2.4.4 Depth-dependent Bi-planar Image Stitching To generate the bi-planar panoramic views of anatomy, the reference coronal and sagittal X-ray images were selected. These reference images were used as a reference frame to assemble the rest of the images. The previously mapped image segments in the height of anatomy were then projected and remapped on the reference image plane to generate long views (Figure 2-16). 40   Figure 2-16: Schematic diagram of depth-dependent image stitching process. It shows the generation of long views with a size close to the size of anatomy by back-projecting the image from the height of anatomy to the reference image plane. This can be repeated for all the radiographs.  2.2.4.5 Image Blending Smooth transition between the overlapping areas of images was necessary for generating high-quality long images. Otherwise, the different contrast between images, due to automatic contrast adjustment of the C-arm, influenced the quality of final panoramic view and created undesirable artifacts. To create a smooth transition between images, pixel values were weighted based on their distances (à) from the center of each image. After mapping the images on the reference frame, corresponding weighting mask (â) for each image was computed. The mask values decreased linearly from one (â = 1) at the center of the image (à = 0) to zero (â = 0) at the edges (à = $) (Equation 2-12). Subsequently, the mask was applied as the multiplier to each 41  image to weight the pixel values. This process was repeated for all of the images and finally, in the overlapping areas, the pixel values at same locations were computed and the highest pixel values were considered for the final panoramic view (Equation 2-13).  â = 1	 −	à$ Equation 2-12 äãåçéè = max 	(äfâf, ägâg) Equation 2-13 By performing the described image blending, the system generates the long stereo views of anatomy with a smooth transition in the overlapping areas by avoiding undesirable artifacts. Figure 2-17 demonstrates the described steps of image blending method for two sample X-rays. 42   Figure 2-17: Demonstration of proposed image blending method. Two sample X-rays from the cadaveric spinal column were collected in the presence of reference panel; after that, the corresponding weighting masks were created and used to blend the X-ray images to create a smooth transition between the overlapping fluoroscopic views. 43  2.2.5 Validation Experiments Validation of the developed system was conducted by designing and building specific phantoms to calculate the accuracy and precision of the system in landmark localization and image stitching. First, the accuracy of the system in landmark localization was evaluated by comparing the data from the developed method and optical tracking system as a reference. Second, the accuracy of the generated long views was assessed by analyzing the overlapping and non-overlapping areas on long radiographs. 2.2.5.1 Validation of Landmark Localization In this experiment, the accuracy of the system in landmark localization was assessed by performing five rounds of tests using a custom-designed phantom with known geometries. The coordinates of the markers obtained from the developed system were compared with the corresponding coordinates obtained from an optical tracking system as the ground-truth reference (Optotrak Certus Motion Capture system with an accuracy up to 0.1 mm) [68]. The phantom designed for this study consists of a base and four towers with different heights (Figure 2-18). A clear Polycarbonate sheet, 3/8ʺ thick, was selected as a base of the phantom for its X-ray transparency. Each tower consists of three parts: 1) Lower holder that connects the towers to the base by four bolts and nuts and two dowels. 2) Polycarbonate tube in different heights that sits inside the lower holder. 3) An upper holder that sits on the Polycarbonate tube with three square-shaped holes that hold three radio-opaque fiducial markers. To replicate the shape of spinal anatomy, the heights of the towers were selected at 15cm, 20cm, 10cm, and 5cm from left to right. The upper holder dimensions were designed in a way that all of the three fiducial markers can be captured in one X-ray shot. Both lower and upper holder were designed by dedicated software (SolidWorks, Traducao, Tennessee: Dassault Systems, 2015) and 44  were fabricated by a 3D printer (Ultimaker 2, Ultimaker B.V., Geldermalsen, Netherlands) and its software (Cura software, Version 15.04.2).  Figure 2-18: A custom-made phantom used for validation of landmark localization. Phantom consists of a clear radiolucent base, four towers with different heights to replicate the S-shape curvature of the spine, and twelve fiducial markers. © Spine drawing reproduced from www.mauriciokanno.daportfolio.com with permission from Mauricio Kanno, Sao Paulo, Brazil.  The ground-truth coordinates of the markers were collected by digitizing the markers’ locations using an Optotrak Certus Motion Capture system (NDI, Northern Digital Inc., Waterloo, Ontario, Canada) and by building a custom digitizer probe. The design of the probe has been described in Appendix A. During the experiments, the phantom was positioned on the surgical table (retrofitted with reference panel), and bi-planar images were collected from each tower. Automatic image analysis process and segmentation of the centers of the fiducial markers in each image were used for accurate localization of the landmarks and avoid subjectivity of the process. By uploading the X-rays and their corresponding calibration files, the image processing unit, first detected the two-45  dimensional centers of the circles by running a Hough transform circle detection code in a custom MATLAB program. After that, landmark localization method described in 2.2.4.2 was used to reconstruct the fiducial markers in three-dimensions (Figure 2-19).  Figure 2-19: Localization of fiducial landmarks based on bi-planar fluoroscopic views. The location of the landmarks found by passing rays through the X-ray source and projection of markers on bi-plane images (green circles) and finding the intersection of them.  A common coordinate system was defined for cross-referencing between Optotrak and image-based coordinates. The common coordinate system was aligned with main coordinates of the surgical table by setting the X-axis parallel to the length of the table, the Y-axis to align to the width of the table, and the Z-axis to be perpendicular to the table. The accuracy and precision of landmark localization were measured as the differences between the calculated locations from developed method and collected Optotrak data. The ability of the system in reconstructing the orientation of towers was also assessed by creating a coordinate system for each tower (based on available three markers on each tower) and finding the transformation matrix between the location of landmarks on each corresponding towers using the singular value decomposition (SVD) method [67]. Finally, the angles were recovered from the rotation matrix and the accuracy and precision were reported for each axis. The results were reported as the mean and standard deviation. 46  2.2.5.2 Validation of Bi-planar Image Stitching The accuracy of image stitching was assessed by conducting experiments on a custom-designed phantom (see 2.2.4.1). This phantom is composed of an S-shape steel wire, a helical wire, and hollow metal beads attached to the helical wire (Figure 2-20). The S-shape wire was formed to replicate the approximate shape of the spine and used as a reference for the stitching process. The helical wire was used around the reference wire to demonstrate the influence of ghosting effects in the image if the point of interest is not close to the initially selected landmarks. It also showed the effects of the wrong estimation of the depth on the accuracy of image stitching. The diameter of the helical wire was about 12cm. The hollow beads on the helical wire were used to represent common landmarks for the measurement on the long radiographs.  Figure 2-20: A custom-made phantom used for validation of image stitching. Phantom consists of 1) an S-shape wire to replicate the shape of the spine, 2) helical wire to demonstrate the ghosting effects if the desired landmark is not close to the registered anatomy and to show sensitivity of stitching to the estimation of the depth, and 3) fiducial markers tapped to helical wire that serves as a reference to calculate the errors in overlap areas.  47  Bi-planar long views of the phantom were generated using the proposed method (Figure 2-21-A). The accuracy of generated radiographs was determined by measuring the differences in thickness of the reference wire (S-shape) between the overlapping areas and non-overlapping areas (in pixels and millimeters, pixel scale = 0.2 mm) (Figure 2-21-B). Also, for the helical wire, the centroids of the corresponding beads on the overlapping areas were extracted and used to compute the ghosting effects (Figure 2-21-C). The measurements were performed at 12 different locations on the image and the results were reported as the mean and standard deviations (SD) of pixel and millimeter errors.   Figure 2-21: Generated long views from the phantom and demonstration of the method for calculating the accuracy of image stitching and parallax effects caused by an error in estimation of depth. (A) Generated coronal and sagittal radiographs from the phantom. (B) The measurement of differences between the diameter of the reference rod on overlapping areas and non-overlapping areas. (C) The distance between the centroid of corresponding beads on overlapping areas used to demonstrate the errors caused by ghosting effects. 48  Note that to compute the differences in overlapping areas, the described image blending method in section 2.2.4.5 was not used. Instead, a MATLAB built-in function for blending the images was used to facilitate the visualization of differences in the overlapping areas.  2.3 Results 2.3.1 Landmark Localization Accuracies The results from landmark localization demonstrate the ability of the system to localize the location of the landmarks with an overall error of 3.9 ± 2.3mm (Table 2-1). Also, the results of tower reconstruction show that the system was able to reconstruct the orientation of towers with an overall error of 0.6 ± 0.7° error. Table 2-1: Results of the translation and rotational accuracies, presented as mean and SD. (A) Translation accuracies (mean ± SD) calculated by comparing the TC-arm location against the optically digitized coordinates from Optotrak system. (B) Rotational accuracies (mean ± SD) of towers reconstruction found by decomposing the transformation matrix between the TC-arm and Optotrak data for each tower. (A) Translation Accuracy Mean ± SD of Error (mm) Along the Table (Tx) Across the Table (Ty) Perpendicular to the Table (Tz) 0.9 ± 0.7 1.6 ± 0.8 3.4 ± 2.1 (A) Overall Accuracy 3.9 ± 2.3 (B) Rotational Accuracy(°) Mean ± SD of Error (°) (Rx) (Ry) (Rz) 0.3 ± 0.3 0.5 ± 0.6 0.2 ± 0.3 (B) Overall Accuracy 0.6 ± 0.7   49  2.3.2 Bi-Planar Image Stitching Accuracies The results from bi-planar stitched long views of the reference wire demonstrate the ability of the system in stitching the images on coronal view with the accuracy of 3.2 ± 2.9 pixels (0.6 ± 0.6mm) and 12.5 ± 4.8 pixels (2.5 ± 1mm) for the sagittal view (Table 2-2). The accuracy of the stitched views in the overlapping area, calculated based on the helical wire, shows that the error in stitching can be up to 21.5 ± 5.3 pixels (4.3 ± 1.1mm) in the coronal and 33.6 ± 8.6 pixels (6.7 ± 1.7mm) in the sagittal view if the point of interest in the image is not close to the initially registered landmarks. Table 2-2: Results of the image stitching accuracies and parallax effects, presented as mean and SD. (A) Accuracies (mean ± SD) of generated panoramic images found by comparing the diameter of the reference wire (S-shape) on the overlapping areas against non-overlapping areas. (B) The errors (mean ± SD) in measurement due to the ghosting effects, found by extracting the centroid of corresponding beads on the overlapping areas.   (A) Reference Wire (B) Helical Wire pixels mm pixels mm Coronal Plane 3.2 ± 2.9 0.6 ± 0.6 21.5 ± 5.3 4.3 ± 1.1 Sagittal Plane 12.5 ± 4.8 2.5 ± 1 33.6 ± 8.6 6.7 ± 1.7  2.4 Discussion We proposed a novel method for generating bi-planar stitched long views in both coronal and sagittal planes and an accurate localization of the desired anatomical landmarks. The performance of the system was examined with two phantom-based experiments for landmark localization and image stitching to evaluate the accuracies of the developed methods. For the localization accuracy, the results show that the system is able to localize the three-dimensional location of landmarks with an overall error of less than 4mm. The calculated error seems promising and appears to satisfy the discussed 5mm acceptable margin of error (according 50  to the clinical needs as described in the objective of this chapter). It is not surprising that the results were different for different directions, with higher errors in the Z direction (perpendicular to the table) compared to the X and Y directions (along and across the table) (3.4 versus 0.9 and 1.6mm, respectively) (Table 2-1-A). The lower level of accuracy observed for up-down direction (compared to other directions) is inevitable due to the use of single-plane fluoroscopic views for pose estimation. Three-dimensional landmark localization accuracies also inherently showed the capability of the system in recovering the spatial coordinates of the X-ray source-detector set (full three-dimensional spatial coordinates of the image and the corresponding position of the X-ray source). Furthermore, the lower rotational accuracy for the Ry compared to the Rz (Table 2-1-B) was directly influenced by the lower three-dimensional localization accuracy in the Z (up-down) direction. For the long views, the result shows that the generated images have 3.2 pixels misalignment in coronal view and 12.5 pixels misalignment in sagittal view between images for the reference structure (S-shape wire) (Table 2-2). The lower accuracy in the sagittal views is expected to be also caused by the lower accuracy of landmark localization in the Z direction (Table 2-1). The coronal view result is comparable with the stitching method reported in Wang et al. [61] (1.9 pixels, only reported in coronal view) that used the CAMC system. However, it should be noted that the system proposed by Wang et al. requires a movement of the surgical table during the surgery which is not feasible in the intraoperative setting. Their system also does not generate the sagittal view due to the line of sight limitation of CAMC system [59]. This experiment also demonstrates that a deviation from 0 to 60mm (the estimated radius of helical wire) from the registered anatomy can cause about 4-7mm error in the overlapping areas and generate effects such as ghosting and misalignment on the long radiograph (Figure 2-21). This 51  finding is comparable with the reported finding in Wang et al. (13mm for 150mm error in depth measurement) [60] and Yaniv et al. (8.4mm for 50mm error in depth measurement) [62]. The discrepancies between the results of this study and the reported data in literature can be due to the fact that in the phantom used in this study the beads have different distances (heights) from the reference wire (0 to 60mm) which creates different amount of error in depth measurement for each bead (from 0 to 60mm compared to 150mm in Wang et al. and 50mm in Yaniv et al.). Therefore, the results on average are similar to the reported data in the literature. Another point of discussion is about the number of segments in each fluoroscopic view. We chose four segments for the purpose of image stitching. In coronal view, we observed that by decreasing the number of segments to one or two the error in the overlapping areas increased (by about one millimeter). On the other hand, the computational time increased significantly by increasing the numbers of segments (31, 49, and 64second for one, four and eight segment(s), respectively). As a general rule, the more numbers of segments led to more accurate stitched views. However, we observed that for more than four segments, the final accuracy of image stitching would not be sensitive to the number of segments. Thus, four segments were selected as an optimal number for the image stitching based on both accuracy and computational time. As another point in this experiment, the relationship between accuracy and number of segments was only investigated in the coronal view, since the distance between the anatomy and images does not change significantly in the sagittal view due to the design of the phantom. Therefore, better or the same level of accuracy is expected for the sagittal view compared to the coronal view by using the same number of segments (four).  One great advantage of this proposed method is the ability to generate calibrated panoramic in both coronal and sagittal planes, unlike the existing methods. The generated images 52  have close to 1:1 scale, true to life size, which can be used for intraoperative angular and length measurement without considering the scaling issue caused by the linear perspective projection of the C-arm X-ray images. These abilities provide long intraoperative images similar to the EOS® system for intraoperative purposes [69]. The proposed image fusion technique does not rely on overlapping X-ray regions and does not require a manual estimation of the distance between anatomy and reference panel. Another novelty of proposed image stitching system is its ability to compensate for the changes in the distance between image and anatomy by breaking down the images into numbers of segments. This ability allows enabling the system to generate long views with minimal artifacts in the overlapping areas. During the surgery, the generated long views can provide accurate quantitative intraoperative feedback to the surgeon with potential impact on reducing complications that stem from the lack of intraoperative evaluation tools [38]. The developed method in this study has a few limitations. One limitation is that the current image processing module can only process the images which have been taken from the reference panel with orbit and tilt angles close to zero (approximately less than ±5°), and could have difficulties in analyzing an oblique projection. However, for the purpose of long stitched images, coronal images with tilt and orbit angles close to zero are expected. Another limitation is that the images from reference panel cannot be processed right after the acquisition in the current version of the software, and they need to be post-processed after all the images are collected. 2.5 Conclusion The objectives of this chapter were achieved by developing a method for generating calibrated long bi-planar views of the anatomy using mobile C-arm fluoroscopy equipment. Accuracies of these methods were validated by custom-designed phantoms and demonstrated that the proposed module for the TC-arm system can accurately localize the anatomical landmarks and generate bi-53  planar stitched long views of anatomy in both coronal and sagittal planes with least artifacts. The results of the chapter support the promising potential of this new method for intraoperative assessment of long anatomies. 54  Chapter 3: Application of the Developed Method for Spinal Deformity Correction Surgery 3.1 Introduction It has been shown that the intraoperative spinal curvature after the spinal fusion is correlated with the postoperative shape of spine on standing radiographs [38], [46], [70]. Therefore, during the surgery, it is recommended that the shape of the spine assessed on radiographic views before finishing the surgery [33]. Assessment of spinal curvature is ideally performed on large radiographic views however, the conventional long plain films are difficult to use, are inaccurate, and expose to high radiation exposure. In the previous chapter, a new method has been developed to expand the utility of mobile C-arm fluoroscopy equipment for intraoperative evaluation of large anatomies. In this chapter, the ability of the developed method in providing an accurate visual intraoperative measurement of spinal alignments is determined as an effective tool for the above-mentioned issues. The usability of the developed method (in terms of time and radiation) is also assessed compared to plain X-ray methods. In this chapter, the currently available methods for a radiographic assessment of spinal anatomy are described, followed by the detailed illustration of the proposed clinical protocol for using the developed method in a clinical setting. Finally, the validation experiments on cadaveric specimens and the corresponding results are explained.  3.1.1 Radiographic Assessment of Spinal Alignments  The Cobb angle is the most commonly used technique for quantitative assessment of spinal curvature [71], [72]. This measurement represents the angulation between two particular levels of the spine by the lines drawn on a two-dimensional radiographic view, parallel to the superior 55  endplate of the superior vertebra and the other parallel to the inferior endplate of the inferior vertebra (Figure 3-1-A). Besides the Cobb angle, global alignment of the spine is measured using the spinal coronal and sagittal balance parameters. Coronal balance is calculated by drawing two vertical lines on a two-dimensional radiographic view from C7 (C7 plumb line) and S1 (central sacral vertical line). The horizontal deviation between these lines represents the coronal balance (Figure 3-1-B). Sagittal balance is also measured as the horizontal distance between the C7 plumb line and the posterior-superior corner of S1 endplate (Figure 3-1-C). Cobb angles and spinal balance are valuable and widely accepted measurements for diagnosis, planning of surgical procedures, intraoperative monitoring, and follow-up studies of patients with spinal deformity [73], [74].  Figure 3-1: Demonstration of the radiographic measurements. (A) Cobb method for measurement of the deviation of curves by drawing lines parallel to the superior endplate of the superior vertebra and the inferior endplate of the inferior vertebra. (B) Coronal balance measurement by calculating the distance between C7 plumb line (C7PL) and central sacral vertical line (CSVL). (C) Sagittal balance measurement by calculating the distance between C7 plumb line (C7PL) and the posterior superior corner of the S1 endplate. © Reproduced with permission from Medtronic. 56   The magnitude of the radiographic parameters is an important factor in the clinical decision-making process. Therefore, precise radiographic measurement is vital for assessment of spine deformity [75]. In terms of accuracy of the Cobb angle measurements, thresholds of error up to 5° have been suggested as an acceptable range [71], [76]. In terms of accuracy of coronal and sagittal balance measurements, as mentioned in Chapter 2, a 5mm margin is considered as an acceptable threshold of error in this study. This margin is 10% of a surgical goal (sagittal imbalance <50mm), that has been reported to be correlated with less pain and disability [22]. The variability of the radiographic measurement of the Cobb angles and balance has been assessed in different studies. Despite the simplicity of the measurement process, the variability of Cobb angle measurement has shown to be from 2° to 7° [77]–[83] and in the worst case, the reported variability was up to 9.5° [84]. The variability in the measurement of balance was also reported to be on the order of 3.8mm [75]. Several factors have shown to have an influence on measurement variability [78]. This includes variabilities in the selected landmarks that were used for the measurements as well as a level of experience of the observer in identifying the landmarks [77], [78], [85]. As another point, the false detection of the endplate orientation due to the anatomical deformity of the vertebra (e.g., the absence of endplate in patients with congenital scoliosis) is known as one of the source of error in Cobb angle measurements [86]. Digital Measurement of Radiographic Parameters  Computer-assisted measurement tools have been developed to address the variability in radiographic measurement and reduce error [75], [77], [79], [87]. Although the reliability of the radiographic measurements using digital methods has been reported to be higher than the manual measurements [75], [78], the impact of errors related to human subjectivity such as inconsistency 57  in determining the superior and inferior endplates and observer experience still remains as a source of error [88]. Automatic Measurement of Radiographic Parameters Automatic measurement methods have been proposed with the goal of eliminating all sources of error related to human subjectivity in radiographic measurements. Automatic systems use image processing algorithms to reconstruct the orientation of the endplates and measure the radiographic parameters. Detection of the edges of the vertebra using image processing methods has been suggested in the literature by Sardjono et al. [88]. This system uses three curve fitting methods to generate a smooth curvature between the detected edges of the vertebra on the radiograph so that the angles between the endplates could be determined more accurately. The Cobb angles were then calculated automatically by determining the angle between the tangential references at each point. In the aforementioned study, manual measurements were conducted as a reference for comparison and range of error from 3.9° to 7.4° was reported. In another study, the horizontal inclination of endplates of all vertebral bodies is automatically segmented from radiographs with an accuracy of 3° for Cobb angle measurements [86].  Although automatic methods led to an improvement in the measurement of Cobb angle and reducing the variability of measurements in comparison to manual methods [86], [88], these methods are not available for intraoperative assessment. The main challenge is the presence of metal screws and rods that can impair the process of automatic segmentation and lead to unreliable results. Therefore, manual and digital methods are still being used as the primary tools for measuring radiographic spinal parameters. 58  3.1.2 Required Time and Radiation Exposure Clinical usability of an intraoperative imaging tool is determined by 1) the time required for producing the radiograph during the surgery and 2) the radiation exposure to the patient and surgical staff. For the plain X-rays, the process of image acquisition and transferring of the image can take a considerable amount of time of the OR. Considering the number of required images (one or two images in each plane depending on the size of the patient) for both coronal and sagittal planes (total of two to four images), the image acquisition and processing might take up to 20 minutes (the estimated time stack for each step has been shown in Error! Reference source not found.). Alternatively, in a C-arm based method, the image acquisition and production can be reduced multiple folds. Table 3-1: The required time at each step for plain X-ray method to generate long radiographs. Plain X-ray method requires 3 steps to generate long radiographs. These steps include: 1) preparation of the patient and device, 2) image acquisition, and 3) post processing including scanning of the film and generation the radiographs.  Time (minutes) Steps Preparation Image Acquisition Post Processing Plain X-ray 8 2 10  The amount of radiation exposure has a direct influence on the long-term risks of cancer in patient and the surgical staff [89]. Radiation exposure levels from a single image of portable X-ray unit and C-arm (for both anterior-posterior and lateral projection) has been measured previously by creating a surrogate patient phantom to simulate the surgical scenario [90]. For a typical C-arm fluoroscopic image at the lumbar spine level, the patient radiation exposure was 59  reported to be 102mR1 and 116mR for a single anterior-posterior (AP) and lateral image. For the portable X-ray unit, the patient radiation exposure for a single coronal and sagittal radiograph was reported 2160mR (21 × C-arm) and 3435mR (30 × C-arm), respectively [90].  3.1.3 Objectives of this Chapter The overall objective of this chapter is to evaluate the feasibility of the developed method for spine deformity correction. The specific objectives are to:  1. Develop a clinical protocol for image acquisition and generation of bi-planar long radiographic views of the spine 2. Conduct in-vitro tests to validate the system for localizing the vertebral centroids, considering an acceptable 5 mm threshold of error as the goal 3. Conduct in-vitro tests to validate the manual and automatic options for measuring the spinal alignments, considering a threshold of error of 5° for angular and 5mm for balance measurements 4. Benchmark the developed system against equivalent plain X-ray methods for image quality, and usability in terms of radiation exposure and total image acquisition and processing time 3.2 Methods This section includes the description of the proposed clinical protocol for using the developed imaging system and the specific additional steps for assessment of the shape of the spinal anatomy, followed by the description of the validation experiments.                                                  1 milliroentgen (mR) is a measures of ionization produced by X-rays or gamma radiation in a cubic centimeter of air. 60  3.2.1 Proposed Clinical Protocol The clinical protocol describes a guideline for the practical steps in using the proposed system during the spinal deformity correction surgery. Figure 3-2 outlines the protocol that can be divided into two main preoperative preparation and intraoperative assessment steps.  Figure 3-2: Proposed clinical protocol for intraoperative assessment of spine. The first step (preoperative preparation) should be performed before the surgery. After that, the intraoperative assessment is being performed by generating the long radiographs. The designed method creates intraoperative bi-planar long views of the anatomy and provides a required visual feedback for measurement of radiographic parameters.  Preoperative Preparation Steps: 1- Registration of the inertial measurement unit (orientation sensor) as described in the literature [51]. 2- Mounting the reference panel under the surgical table.  Intraoperative Assessment Steps: 61  3- Image acquisition: Bi-planar (anterior-posterior and lateral) image acquisition (as described in Chapter 2). 4- Landmark localization: Three-dimensional localization of the centroids of the vertebral bodies using the custom-developed graphical user interface. 5- Spine curvature reconstruction and generation of long stereo X-rays. 6-  Radiographic measurement on the generated bi-planar long radiographs. The developed intraoperative assessment steps are explained in the following sections. 3.2.2 Bi-planar Image Acquisition Bi-planar fluoroscopic X-rays from the desired points of the anatomy were produced using the proposed imaging system described in the previous chapter. Having the matching posterior-anterior and lateral fluoroscopic views from the desired locations of the anatomy provided the ability to sort the bi-planar X-rays along the length of the anatomy. It also allowed localizing the landmarks incrementally in three-dimension from pairs of two-dimensional radiographic views.  3.2.3 Sorting of Bi-planar X-rays and Localizing Landmarks The designed interface uses calibration information from the developed system to sort the bi-planar images automatically. This ability provided more convenient imaging process that enables the surgical staff to acquire the bi-planar image without following any specific order. The three-dimensional location of the X-ray source and image were used to sort the images. This automatic process was performed after the image acquisition and before the three-dimensional localization of the landmarks. By sorting the images, the system was able to visualize the images in the correct order to facilitate the landmark localization. Three-dimensional location of the centroids was determined from stereo fluoroscopic views as previously described in Chapter 2. The designed interface provides an accurate tool for localizing and labeling of the various centroids 62  of the vertebral bodies (Figure 3-3) (The interface was previously designed by our research group and was available prior to the start of the project).  Figure 3-3: Custom graphical user interface (GUI) used for landmark localization. This interface provides a tool for vertebral centroid localization. The system is used to manually localize landmarks using stereo views simultaneously.  3.2.4 Spinal Curvature Reconstruction The spinal curvature, a continuous curve that passes through the localized centroids, is modeled by a spline function ‘f’ (Equation 3-1), in which parameter n shows the length along the curvature. ê < = p < , B < , ë(<)  Equation 3-1 A spline function has shown to be able to describe both the normal shape and scoliotic deformities of the spine appropriately [91], [92]. Since spine has three distinctive inflection points (i.e., the cervicothoracic junction, the thoracolumbar junction, and the lumbosacral junction) (Figure 3-4) [93], three cubic spline segments were suggested to form the spinal 63  curvature. These spline segments had a first and second order of continuity on connecting points and can be described by the following equations (Equation 3-2,3,4,5); where K is a degree of the spline and ví = ví,ì; î = 0, 1, … , 3 , vñ = vñ,ì; î = 0, 1, … , 3 , and vó = vó,ì; î =0, 1, … , 3  are the coefficients of splines p < , B < , ë < , respectively. Let the curve be parameterized by the spine curve parameters vã = ví vñ vó. The least-square fitting method was then used to obtain the optimal parameters (vãòôö) in each degree (K=1, 2, 3) by minimizing the sum of square residuals (r) between the localized centroids and the fitted spline (Equation 3-6). The selected non-constrained fitting method reduced the influence of error in manual centroid selection since direct spline interpolation of noisy data may result in a curve with undesirable oscillations. This strategy for curve fitting is expected to best fit a spline to both normal and deformed spines with different types and severity of the deformity. p < = ví,ì<õqúùf  Equation 3-2 B < = vñ,ì<ìqúùf  Equation 3-3 ë < = vó,ì<ìqúùf  Equation 3-4 ê < = ví,ì<ìqúùf , vñ,ì<ì,qúùf vó,ì<ìqúùf  Equation 3-5 S = üg Equation 3-6 64  The reconstructed curve was used to determine the distance between the anatomy and images for the purpose of long image generation (details described in section 2.2). Subsequently, for the automatic Cobb angle measurements, the three-dimensional shape of the curvature was projected onto both coronal and sagittal planes and used as a reference for determining the orientation of endplates (perpendicular to the tangent reference at any point along the length of the curvature).  Figure 3-4: Inflection points of the spine. The normal inflection points of the spine include cerviothoracic junction, thoracolumbar, and lumbosacral. © Spine drawing reproduced from www.mauriciokanno.daportfolio.com with permission from Mauricio Kanno, Sao Paulo, Brazil.  3.2.5 Validation The system was validated through a series of experiments to show the ability of the developed system for intraoperative assessment of a deformed spine. The aims of the experiments were: 1) to estimate the accuracy of the vertebral body localization. 2) To calculate the accuracy of 65  radiographic measurements using both manual and automatic methods against the data extracted from computed tomography (CT) images and to determine the inter-rater reliability to assess the sensitivity of the results to inter-rater effects. 3) To determine the quality of the stitched views compared to equivalent long plain films by imaging cadaveric specimens. 4) To determine the usability of the system by estimating the radiation exposure and the required time for image acquisition and production. In this study, four full-length cadaveric specimens (3 females and one male with the age of 83 ± 5 years) were used for the experiments. The specifications of the cadaveric specimens are listed in Table 3-2. During the experiments, the previously described clinical protocol (see section 3.3.1) was followed. For the purpose of comparison, the CT images of specimens were acquired (voxel size of 0.3	×	0.3	×	0.6	°°q) and analyzed in Slicer3D (version 4.3.1) to produce the ground-truth reference [94]. The illustration of the segmentation of the endplates and femoral heads is provided in Appendix C.  Table 3-2: Specifications of the cadaveric specimens. Information includes age, gender, body mass index, length, and type of spinal deformity.  Age Gender BMI Length of Specimen Type of Spinal Deformity #1 86 Female 16 T3 to mid-femur Scoliosis #2 81 Male 21 T2 to mid-femur Scoliosis #3 89 Female 30 Head to mid-femur Abnormal kyphosis (> 50°) #4 77 Female 17 Head to mid-femur (including arms) Scoliosis  3.2.5.1 Localization of Vertebral Centroids  The ability of the system in localizing the vertebral bodies was evaluated by comparing the three-dimensional location of the centroids of vertebral bodies from the proposed imaging system against the coordinates extracted from the CT images. The estimated accuracies were 66  reported as the root mean square error (RMS) (Equation 3-7) and mean absolute error (MAD) (Equation 3-8) using the following equations where ¢ is the number of points, °å is measurement values, and °å is reference values. $£u = 1¢ (°å − °å)g§åùf  Equation 3-7 £•à = 1¢ °å − °å§åùf  Equation 3-8 The coordinates of the points from CT images and large images were defined with respect to a common coordinate system to facilitate the interpretation of the data. For this purpose, centers of two femoral heads and center of the most superior vertebra were used to create a common coordinate system on both sets of images (CT and bi-planar radiographic views). 3.2.5.2 Radiographic Assessment  The Cobb angles in both coronal and sagittal radiographs and coronal balance measurements were conducted and compared with the ground-truth data produced from CT images. The measurement of the radiographic parameters performed using both manual and automatic methods. Manual Radiographic Assessment The radiographic parameters were digitally measured using the Surgimap software (Surgimap Spine Software, Nemaris Inc, New York, USA). The Surgimap provides radiographic measurement tools such as Cobb angle measurement and the balance analysis. On the coronal 67  radiograph, three Cobb angles (proximal thoracic, main thoracic and thoracolumbar/lumbar) and coronal balance were measured. On the sagittal radiograph, two Cobb angles (thoracic kyphosis and lumbar lordosis) and two pelvic parameters (pelvic incidence and T1 pelvic angle) were measured (Figure 3-5). For all measurements, Radiographic Measurement Manual (RMM) were used as the guideline (see Appendix B) [95]. Each radiograph evaluated four times, with an interval of at least a week between measurements. The error was calculated as the difference between manual calculation and extracted CT data. The accuracy and precision were reported as the average and standard deviation of the error for each radiographic parameter. Automatic Radiographic Assessment The automatic parameter measurement was performed using the three-dimensional spline curvature (described in 3.2.4). The projections of the curve onto the coronal and sagittal planes were used to determine the orientation of endplates, perpendicular to the tangential references at desired points [88], [96]. The endplate locations on the curve were assumed to be at the mid-distance between the two adjacent vertebral centroids. Subsequently, the Cobb angles were calculated automatically by determining the difference in the angle between the desired levels (Figure 3-6). The coronal balance was also calculated automatically by projecting the center of femoral heads and center of the C7 and S1 onto the coronal plane to determine the C7PL, CSVL using the described method in Appendix B (see Appendix B). The errors were calculated as the difference between automatic calculation and the CT-based measurements. The accuracy and precision of the measurements were calculated as the mean and standard deviation of the error for each radiographic parameter. Also, the discrepancies between manual and automatic measurements were also shown in Figure 3-7. 68   Figure 3-5: Manual measurement of radiographic parameters. The Cobb angles and coronal balance measurement in Surgimap software on (A) sagittal and (B) coronal radiographs. The radiographic measurement manual was used as a reference (see Appendix B). 69   Figure 3-6: Automatic measurement of the radiographic parameters. The Cobb angles were calculated by projecting the curvature onto long radiographs and finding the perpendicular line to the curve at the location of endplates. The coronal balance was measured by projecting the center of the C7 and calculating the distance from the central sacral vertical line (CSVL).   70   Figure 3-7: Discrepancies between manual (A) and automatic (B) measurements of spinal alignments. This figure shows the differences between manual(A) and automatic (B) measurements of main thoracic and thoracolumbar/lumbar angles in coronal view.   3.2.5.3 Inter-Rater Reliability The inter-rater reliability test was performed by recruiting a well-experienced spine surgeon as a second observer to repeat the measurements on the generated long views. The endplates of the curves were preselected using the Radiographic Measurement Manual (RMM) to decrease the variability in measurement. The second observer measured the parameters in 4 trials on all radiographs. The order of radiographs was altered randomly, and the observer was blinded to the previous measurements during the process. The average of the results from the second observer was then compared to the average of first rater’s results. The agreement between the two raters’ measurements identified by calculating the intra-class coefficients (ICCs) with a two-way 71  random effects model, single measures and absolute agreement approach [97]. The ICC value indicates the agreement between two raters in their measurements. The higher the ICC, the less variability exists between measurements of the two rates.  Each of the ICCs and their corresponding 95% confidence intervals was calculated using the SPSS software (IBM, Armonk, New York, USA) using a two-way random effects model. In addition, one-sided F-tests on the ICCs were carried out to test the null hypotheses that each ICC is equal to zero (significance level, P = 0.05). 3.2.5.4 Comparison of the Image Quality The qualitative assessment was performed by comparing the quality of the generated panoramic views against the equivalent plain X-rays. The ability of the two imaging systems (proposed method and plain X-ray) in visualizing the required anatomical landmarks (vertebrae endplates and femoral heads) were evaluated. The plain X-ray images were acquired by a portable X-ray unit (mobile 100-15, General Electric, Connecticut, USA) and a cassette (14"×17") (Figure 3-8). Posterior-anterior (PA) and lateral X-rays were acquired from two full-length frozen specimens during the experiment while the cassette was held under the table, at a distance of 30cm from the sample to replicate a typical clinical setup [38]. Voltage, current and time of exposure for each image were adjusted based on the recommended levels provided by Vancouver General Hospital (VGH) emergency. The same specimens were imaged in the lab using the proposed method and Arcadic Orbic Iso-C C-arm fluoroscopy equipment (Siemens AG, Munich, Germany).  72   Figure 3-8: Experimental setup for acquiring the plain X-ray from a specimen. (A) The specimen was located on the radiolucent table, and the cassette was located under the table. (B) The schematic illustration of experimental setup that shows the distances between the X-ray source, specimen, and the cassette.  3.2.5.5 Radiation Exposure and Processing Time The C-arm radiation exposures were calculated by counting the number of acquired images and using the published radiation exposure values reported for coronal and sagittal fluoroscopic imaging of the spine [90]. The values were compared with the equivalent values reported for a portable X-ray unit [90]. Note that the number of images in coronal and sagittal views were equal since bi-planar images were acquired in pairs from each level of anatomy (see 3.2.2). The processing time was also measured for three different steps: 1) image acquisition, 2) landmark localization, and 3) image stitching. All the computations and processes (landmark localization and image stitching) was performed using a computer with the following specifications: Intel® core TM i7 processor, 16 GB of memory and 64bit Windows 7 operating system. 73  3.3 Results 3.3.1 Localization of Vertebral Centroids The results of the vertebral body localization demonstrate that the system can calculate the three-dimensional location of the centroids of vertebrae at overall 4.3 ± 0.8mm RMS error and 4.0 ± 0.8mm MAD. Table 3-3 provides the calculated RMS and MAD error for each sample. Table 3-3: Root mean square (RMS) and mean absolute difference (MAD) errors of vertebral centroid localization. The results show the differences between the calculated three-dimensional coordinates of anatomical landmarks (centroid of vertebral bodies) from developed method and the data extracted from CT images. Specimen # RMS (mm) MAD (mm) 1 3.2 2.9 2 5.4 5.1 3 4.4 4.1 4 4.2 4.0 Overall  4.3 ± 0.8 4.0 ± 0.8  3.3.2 Radiographic Assessment Manual Radiographic Assessment For the manual measurements, in the coronal plane, the Cobb angles were at accuracies of 1.1 ± 0.7° (maximum error of 2.5°). The accuracy of the coronal balance was 0.9 ± 0.7mm (max error of 1.9mm). On the sagittal plane, the angular measurement had the accuracy of 2.3 ± 1.2° (maximum error of 4.9°) (Table 3-4).   74  Table 3-4: Accuracies of manual measurements of radiographic parameters in both coronal and sagittal planes. The error shows the difference between the manual measurement on the radiographs and the data collected from CT images. Plane Measurement Error Maximum Error Overall Error Coronal Proximal Thoracic (°) 0.6 ± 0.1° ** 0.7 1.1 ± 0.7° Main Thoracic (°) 1.0 ± 0.7° 1.9 Thoracolumbar/Lumbar (°) 1.3 ± 0.7° 2.5 Coronal Balance 0.9 ± 0.7mm 1.9 0.9 ± 0.7mm Sagittal Kyphosis (°) 2.0 ± 1.3° 4.4 2.3 ± 1.2° Lordosis (°) 2.1 ± 0.6° 2.9 Pelvic Incidence (°) 2.8 ± 1.3° 4.9 T1 Pelvic Angle (°) 2.4 ± 1.7° 4.4 ** Proximal thoracic was only measured for specimen #3 and #4 since T1 was not available for specimen #1 and #2.  Automatic Radiographic Assessment For the automatic measurements, the Cobb angle measurements in the coronal view were at accuracies of 4.2 ± 4.5° (maximum error of 13.4°). The accuracy of the coronal balance was 5.7 ± 5.1mm (maximum error of 11.1mm). On the sagittal plane, the angular measurements were at accuracies of 4.8 ± 3.9° (maximum error of 12.9°) (Table 3-5).     75  Table 3-5: Accuracies of automatic measurements of radiographic parameters in both coronal and sagittal planes. The Cobb angles were measured by finding the angle between tangential to the curvature of the spine at the location of endplates. The error shows the difference between the manual measurement on the radiograph and the data collected from CT images. Plane Measurement Error Maximum Error Overall Error Coronal Proximal Thoracic (°) 0.5 ± 0.3° ** 0.8 4.2 ± 4.5° Main Thoracic (°) 5.8 ± 4.7° 13.4 Thoracolumbar/Lumbar (°) 4.6 ± 4.3° 10.9 Coronal Balance 5.7 ± 5.1mm 11.1 5.7 ± 5.1mm Sagittal Kyphosis (°) 5.8 ± 4.0° 11.3 4.8 ± 3.9° Lordosis (°) 5.6 ± 3.4° 10.1 Pelvic Incidence (°) 5.7 ± 4.9° 12.9 T1 Pelvic Angle (°) 2.4 ± 0.7° 3.3 ** Proximal thoracic was only measured for specimen #3 and #4 since T1 was not available for specimen #1 and #2  3.3.3 Inter-Rater Reliability The radiographic parameters measured by the two raters showed the overall intra-class correlation (ICC) of 0.988. Table 3-6 reports the ICCs along with the 95% confidence intervals (CI) as calculated in SPSS for overall, frontal and sagittal measurements. Also, the F-tests all rejected the null hypothesis that each ICC is equal to zero (p-value of less than 0.05). Table 3-6: The ICC results between two observers. ICC was calculated using a two-way random effects model, single measures and absolute agreement. Significant level was set at p<0.05 for each ICC.  Overall Coronal Sagittal ICC 0.988 0.988 0.961 95% CI Lower Limit for ICC 0.975 0.965 0.890 95% CI Upper Limit of ICC 0.994 0.996 0.986  76  3.3.4 Comparison of the Image Quality The following images (Figure 3-9) shows the generated long views from proposed imaging method and plain X-rays in coronal and sagittal radiographs next to each other for one of the specimens studied in this work. As shown in sample images, there were clear visual differences between fluoroscopy-based and plain X-ray-based radiographs. The main differences were observed in the sagittal view. It was clear that the image generated by developed method has higher visibility of reference anatomical landmarks specifically around the pelvis and shoulders. The endplate visibility was also better in general in the radiographs that were generated by the proposed system in sagittal views. 77   Figure 3-9: Comparison of the (A) generated stitched long radiograph with (B) the images obtained from plain X-ray in a sagittal plane. The ability of the systems in better visualizing (C, D) the endplates around the shoulder area and (E, F) the femoral heads were used to compare the quality in a sagittal plane 78 3.3.5 Radiation Exposure and Processing Time During the experiments, an average of 24 fluoroscopic images were taken from each of the four cadaveric specimens (12 images per plane). The average calculated amount of radiation exposure was 1224mR and 1392mR for AP and lateral radiographs, calculated based on the reported exposure in the literature in which radiation exposure for a single exposure of C-arm was on average 102mR and 116mR for AP and lateral X-rays, respectively. The average image acquisition time was 7 minutes (between 5 to 10 minutes for different specimens), and the process of localization and image stitching took about 5 minutes (Table 3-7). The calculated times at each step were also reported in Table 3-8. Table 3-7: Processing time, number of radiographs, and estimated radiation exposure. The processing time was measured starting from the beginning of image acquisition to the end point of image processing and generation of long views. The number of X-rays was used to estimate the radiation exposure during the experiments. Specimen Required Time (minutes) Number of Images Estimated Radiation Exposure (mR) #1 11 20 2180 #2 10 20 2180 #3 13 26 2834 #4 15 30 3270 Overall 12 ± 2 24 2616  Table 3-8: Average time at each step of the plain X-ray and developed method to generate long radiographs. For the developed system, the time was calculated in three steps: 1) preparation, 2) image acquisition, and 3) post processing including landmark localization and image stitching.  Time (minutes) Steps Preparation Image Acquisition Post Processing Plain X-ray 8 2 10 C-arm based 0 7 5   79 3.4 Discussion In this chapter, we investigated the feasibility of the developed method (described in Chapter 2) for spine deformity correction surgery. For this purpose, we developed a specific clinical protocol and conducted series of experiments on four cadaveric specimens. The accuracy of the system was verified by performing landmark localization and radiographic measurement, considering the acceptable range of accuracy of 5mm for landmark localization, <5° for angular measurement, and <5mm for balance measurement. The quality of long radiographic images was compared against plain X-rays and showed a higher quality of the radiographs generated by the proposed method. The clinical usability of the system was evaluated in terms of radiation exposure and required time for image production compared to the commonly used plain X-ray method. In the first experiment, landmark localization accuracy was assessed by comparing the collected data with ground-truth information from CT images. The accuracy of the localization was important since the localized landmarks were used in the process of depth estimations for the purpose of stitching as well as curve reconstruction for the purpose of automatic radiographic assessment. The results of the centroid localization showed that the developed method can find the location of the landmarks with an overall RMS error of 4.3 ± 0.8mm and MAD error of 4.0 ± 0.8mm (Table 3-3). Previous methods in the literature are reported the mean absolute error (MAD) up to 3.4mm [73]. The error of the introduced system is slightly higher than the reported error in the literature which can be caused by: first, uncertainties in the spatial coordinates of the X-ray source-detector set (as described in section 2.4), and second, the manual selection of vertebral centroid on the X-rays without segmenting the corners of the vertebrae which can lead to inaccurate reconstruction. Localization can be improved by extracting the corners of the  80 vertebral bodies as described radiographic measurement manual (RMM) [95]. However, this will drastically increase the processing time which is undesirable for the intraoperative purpose.  The results of manual radiographic measurement show that the angular measurement error was < 1.1 ± 0.7° for coronal and < 2.3 ± 1.2° for sagittal planes and the balance measurement error was < 0.9 ± 0.4mm (Table 3-4). The maximum angular measurement was 4.9° for pelvic incidence angle which is close to the acceptable 5° threshold. The lower level of accuracy observed for the measurements around the pelvis in sagittal plane are inevitable due to a large amount of soft tissue and fat around the pelvis that occludes the S1 endplate and increases the chance of inaccurate detection. We also observed that for the measurement around the chest area on the sagittal plane, the presence of ribs can cause problems in detection of the endplates. In such cases, one possibility is using oblique X-rays instead of sagittal views to better visualize the sacral and vertebral endplates. The automatic radiographic parameters evaluation shows the error of < 4.2 ± 4.5° for coronal and < 4.8 ± 3.9° for sagittal plane Cobb angle measurements and error of < 5.7 ± 5.1mm for coronal balance measurements. However, the maximum error for most of the parameters passed the 5° threshold (Table 3-5). Therefore, we conclude that the developed automatic measurement cannot be used as an ultimate measurement tool. The error in automated assessment can be generated from two sources. First, the inaccuracy in a generation of the spinal curvature can lead to an error in the determination of the orientation of the endplates. Second, the assumption that the direction of the endplates is predictable from spline curve fitting is not accurate enough. Notably, the automatically calculated angles are still comparable with the automatic method introduced in literature (5.4 ± 5.1°) [88].  81 The inter-rater reliability showed a high degree of agreement between the measured radiographic parameters produced by the two raters, with ICC of > 0.96. We thus have statistical evidence to reject the null hypothesis that the two raters did not produce correlated results. The lower correlation in the sagittal plane (ICC of 0.961 for sagittal measurement compared to 0.988 for coronal measurement) is perhaps caused by the higher variation in the measurement of lumbar lordosis and pelvic incident angles due to the levels of uncertainties in the identification of sacral endplate in the radiographs. The measured ICC is comparable with the reported ICCs (between 0.93 to 0.99) in the literature for the other developed digital measurement methods [77], [98]–[100]. The inter-rater experiment suggests that the developed fluoroscopy-based imaging system can be reliably used by different observers to measure radiographic parameters with a close agreement with one another. It should be noted that we may not conclude from ICC whether the inter-rater differences were within the acceptable clinical range. However, the magnitude of difference in Cobb angle measurement between raters was 3.3° on average. This difference is smaller relative to the clinically acceptable error (5°), thus suggesting that the inter-rater differences would have a minor impact on the accuracy of measurement. However, it should be mentioned for one of the cadaveric specimens the difference between raters for lumbar lordosis was 18.3°. This large difference has resulted from the fact that the S1 endplate in the radiograph was not visible due to a large amount of soft tissue around the pelvis and poor image quality even in fluoroscopic view. The variance between readers was reported up to 31° in the literature [85]. The C-arm based method is expected to reduce the variance significantly since it provides better visualization of the landmarks. Comparison of the quality of generated radiographs views with plain X-rays shows that the images generated by C-arm based system can better visualize the required anatomical  82 landmarks around the areas with a large amount of soft tissue (e.g., femoral heads and shoulder) (Figure 3-9). The higher image quality of the introduced system stems from the fact that the amount of exposure and image contrast is tuned automatically by the C-arm according to the local thickness of soft tissue. The lower quality of the plain X-rays is because same energy beam crosses the anatomy along the length of the spine which under- and over- expose various points of the anatomy and significantly deteriorates the image quality and resulting in blurry images that can lead to difficulty in distinguishing the required landmarks. The calculated radiation exposure of this system (total of 2616mR) was %46 of the reported exposure from portable X-ray unit (total of 5596mR). During the experiments, besides the spine, we also took X-rays from the head of two specimens (#3 and #4) and shoulders for one of the specimens (#4) which increased the total number of images and subsequently radiation exposure, but it provides important additional references on both coronal and sagittal views. It is also important to mention that the images were acquired with a large amount of overlap during the experiments to demonstrate the capabilities of the system to create smooth overlapping areas. However, in the clinical setting, the radiation exposure can decrease by acquiring fewer images at desired levels only. For example, for the measurement of coronal balance, four anatomical landmarks can be enough for most basic evaluations (femoral heads, S1, and C7). The large radiographs can be generated to visualize the landmarks by only four bi-planar sets of X-rays (total of eight images) without any overlap. By considering these points, we conclude that the radiation exposure of the developed method is significantly lower than the portable X-ray units (~6 times less based on 4 views). The proposed image acquisition method took between 5 to 10 minutes based on the size of the specimen and the number of images required for covering the desired lengths. This is  83 comparable to the estimated time of the acquisition and production of X-ray films and can be decreased by taking less number of images with fewer overlapping areas. The landmark localization and image stitching also took about 5 minutes (Table 3-7). These post-processing steps can be done after image acquisition and after removing of the C-arm from the field of view so that the surgical staff can continue the surgery without waste of time. For the plain X-ray, the estimated image acquisition and production time in a real operative scenario is estimated to be up to 20 minutes, and therefore, we estimate that the developed system can be up to 1.7 times faster compared to the use of plain films.  This study has a few limitations. For the qualitative assessment, the C-arm device used during the experiments utilizes the automatic contrast adjustment which increases the quality of the individual images. Although this option is available in all modern C-arm equipment, this might not be available in very old models of the C-arms. Moreover, the presence of screw and rods potentially creates a metal artifact in the images acquired from C-arm which decreases the quality of the final image and obscures the visualization of the end plates. However, the same issues are expected to affect the quality of measurements based on standard radiographic films as well. Furthermore, a well-experienced radiation technologist might be able to optimize and adjust the imaging parameters (voltage, current, and time of exposure) for plain X-ray imaging to improve the image quality to some extends. Finally, we conclude that the quality of the panoramic images from TC-arm is comparable with the available plain X-ray systems. Another limitation is the accuracy of sagittal balance which was not reported in the measurements. Sagittal balance can be measured on the standing panoramic sagittal view by using the border of the image as a reference. However, the applicability of the same measurement in the prone position is questionable. The T1 pelvic angle (TPA) was used in this study instead of sagittal  84 balance as a global sagittal balance predictor which can account for both the spinal inclination and pelvic tilt [101]. As another general point, it is also important to mention that the curvature of the spine possibly changes between intraoperative and postoperative postures and affects the radiographic result (mostly in the sagittal plane) [49]. However, knowing the intraoperative measurement can help predict the postoperative alignments. As another related point, in the real surgical scenario, the severity of deformity can be more, compared to available cadaveric specimens in this study. This study also showed that high body mass index (BMI) is also a factor that can further reduce the quality of the images specifically around pelvis area. As another point, the sample size was also a limiting factor in this study and evaluation of the developed system with the larger and more diverse sample size could be helpful to demonstrate the potential of the system through more vigorous tastings. 3.5 Conclusion In this study, the feasibility of the proposed imaging system for intraoperative assessment of spinal alignments was determined. The potential application of the method for spinal deformity correction surgery was validated by experimenting on cadaveric specimens. The objectives of this chapter were achieved: 1) A protocol was developed for clinical application of the system that allows imaging both of the coronal and sagittal views of the patient on the surgical table. 2) The accuracy of the system in landmark localization was evaluated, and it was found within the acceptable range. 3) The accuracy of the manual and automatic options for the measurements of the radiographic parameters was evaluated, and it was found that manual evaluation of the radiographic views is the favorable choice. 4) Finally, the proposed system was benchmarked against the plain film imaging, and it was found that the proposed system has superior performances against the competing methods in terms of the quality of the radiographs, radiation  85 exposure, and the total image acquisition and processing time. Even though the developed automatic method had unacceptable errors compared to defined threshold, the results of the manual measurement showed that the developed system was able to provide the reliable intraoperative monitoring tool using C-arm fluoroscopy equipment with higher quality compared to plain X-ray method. Finally, the estimated radiation and the required time suggested the acceptable usability of the system.  86 Chapter 4: General Discussions and Conclusions This chapter provides further general discussions and conclusions by putting the results of the previous chapter into perspective. The contributions of the thesis are discussed, followed by the description of key outcomes and limitations of the developed system. The future directions to make the system ready for the clinical use, as well as opportunities for further technical improvement, are also explored in this chapter. 4.1 Contributions The work in this thesis was motivated by observing limitations in current imaging systems. The focus has been on spinal deformity correction application and developing an imaging tool for generating long radiographs intraoperatively. Given the importance of accurate assessment of spinal alignments in both coronal and sagittal planes as one of the important objectives of surgery [26], the intraoperative monitoring and assessment of the correction is still a limiting technical challenge due to the incapability of available intraoperative imaging modalities to provide radiographs with sufficient field of view. The two main general contributions of this thesis are: 1. Development and validation of a technique for generating intraoperative long bi-planar radiographs of anatomy based on mobile C-arm fluoroscopy equipment 2. Evaluation of the developed technique for image quality, usability, and accuracy of radiographic measurements in the spinal deformity correction surgery 4.2 Key Outcomes The first key outcome of this work is developing a technique for expanding the tracking volume of the previously developed TC-arm system. With the new module, it is now possible to generate full length coronal and sagittal views of the anatomy along the surgical table. The new module  87 also provides technical capabilities such as three-dimensional localization of the anatomy based on calibrated bi-planar views. The ability of the developed system for localization satisfied the 5mm defined acceptable threshold. The novel contribution of this technique is in incorporating an image-based reference and an automatic image processing unit for tracking the C-arm fluoroscopy equipment. Unlike the other methods that only use image-based references for the purpose of tracking, the developed technique is able to track the sagittal poses of the C-arm using IMU information. Compared to the external tracking systems such as optical localizers or electromagnetic trackers, the developed technique can provide the spatial coordinates without limitation of the line of sight obstructions or interference from metal objects. The second key outcome of this work is developing a method that can take individually calibrated fluoroscopy images from the tracking system to generate calibrated bi-planar long radiographs of anatomy with minimal parallax effects. The generated long radiographs can be used not only to visualize the long anatomy but also to measure the radiographic parameters for two-dimensional and possibly three-dimensional assessment. The accuracy of the generated radiographs was found similar to previously suggested methods in the literature. As another important point, the developed method can generate long radiographs without the need for overlapping areas between the images (e.g., coronal balance assessment that only femoral heads, S1, and C7 are required). This capability can potentially avoid unnecessary exposure (by ~6 times) and reduce the OR time and radiation to both patient and surgical staff.  The third key outcome of this work is the proof of the usability of the developed system (in terms of image quality, time, and radiation) in a simulated environment close to real life for spine deformity surgery. The radiographic assessment indicates that the generated radiographs can provide an intraoperative feedback for spine deformity assessment with better quality in  88 visualizing desired landmarks, less radiation exposure (54% less), and less required time for image acquisition and production (~1.7 times faster) compared to a current standard method (plain X-ray).  The fourth key outcome of this work is the versatility of the developed system that can be used for a broad range of surgical applications beyond spinal deformities. The idea described in this thesis can be expanded to other surgical procedures such as various osteotomies, lower limb reconstruction, and fracture fixation in which the accurate intraoperative assessment of the alignments and lengths are useful. Such a system could eventually help improve surgical outcome and reduce the postoperative complications in a wider spectrum of applications in orthopaedic surgery. 4.3 Limitations Limitations of the developed methods and the conducted experiments include: 1) the suggested image acquisition protocol requires frequent rotations of the C-arm between the coronal and sagittal views at each point along the length of anatomy, which can potentially add to the overall time of the surgery. 2) The position and orientation of sagittal images cannot be determined independently, and each sagittal view needs a matching coronal image to be taken. 3) In this study, the precision and accuracy of the system in tracking the location of the X-ray source and image detector was not explicitly measured. However, the landmark localization accuracy measurement inherently reflects the error induced from inaccuracies in tracking the X-ray source and detector positions. 4) The current pattern of markers in the reference panel showed a good robustness for the selected specimens. However, the presence of metal can block the markers and impair the process of segmentation in a more realistic spinal surgery application. Therefore, more robust patterns of markers might be needed to enable spatial tracking at the presence of  89 metal parts within the field of view. 5) In this study, one design and model of C-arm for the experiments was used. For other C-arms, the evaluation of accuracy and precisions might lead to different results due to the differences in image quality. The resolution of the image can influence the accuracy of marker detection and lead to different results (e.g., C-arms with flat panels can provide higher image resolution and higher tracking accuracies). 6) Finally, we have had a minimal geometric distortion since the available C-arm has the built-in distortion correction algorithm that eliminated the need for an undistortion procedure. For the cases that other C-arms are employed, there is a need for an additional distortion correction step, which can be implemented in the offline calibration process. Limitations associated with the clinical study include: 1) A limited number of cadaveric specimens used in the experiments. A larger group of specimens with different types of spinal deformities, ages, and severities are required to better demonstrate the abilities of the system completely. 2) The validation process was performed without the presence of the metal implants. Even though the reference panel and image processing module have been designed to work accurately in case that the small portion of the markers is occluded, there is room for redesigning a more robust panel to address this issue in the future. 3) In this study, the measurement of the radiographic parameters was conducted by only two observers. Even though the results showed a high correlation between the observers, to accurately demonstrate the variability of the measurement using the developed technique, more observers with different levels of expertise and more radiographs of various specimens are required. 4) The other limitation of this study is the assumption that the patient involuntary movement on the surgical table has negligible effects during the image acquisition. It is conceivable that even small movements as a result of breathing can create artifacts in the final image and lead to inaccurate radiographic assessment. Literature  90 reports the movement of 20mm for C7 relative to T12-L1 in an anterior-posterior direction for scoliotic spine (for patients aged 10-21 years) [102]. A rough calculation shows that in the worst case scenario the artifacts resulted from breathing and translational movement of vertebrae can lead to a maximum error of 4° in Cobb angle measurement and 2° in TPA measurement. This calculation is based on the following assumptions: C7 to T12-L1 distance: ~30cm, C7 to mid femur axis: ~60cm, and C7 anterior-posterior movement: 20mm, tan$% 2 30 = 3.8°, tan$% 2 60 = 1.9°. 4.4 Technical Improvement Opportunities and Future Directions There are several technical areas for potential improvement that may result in faster, more accurate, and more robust processing before using the technique in the clinical scenario. In this section, some of the technical improvement opportunities that could be explored are highlighted. Suggestions for technical improvements include: 1) Integrating the image processing module and IMU tracking to provide a closer to real-time calibration procedure. This process will decrease the intraoperative time requirement for transferring data between separate modules. 2) Employing machine learning algorithms to ensure robust and accurate extraction of the markers from fluoroscopic views once a sizable pool of images is available for training the system. 3) Development of automatic error detection system that can decrease a chance of wrong pose estimation during image processing. The automatic system analyzes the extracted data from the image and detects any chances of error. 4) Utilizing bi-planar views of endplate to improve repeatability of the Cobb angle measurements. This is particularly useful for identifying landmarks that are difficult to identify (e.g., S1 endplate). 5) Generating the global axial representation of the spine curvature, known as DaVinci representation [103], as a potential  91 output of the system. Providing the axial representation of the spinal column is in alignment with a future clinical needs for the diagnosis and treatment of spinal deformities [104]. Besides the technical improvement, some clinical experiments are required to further validate the system ready for the clinical use. 1) The suggested work beyond this thesis is to test the performance of the system in the presence of screw and rods to replicate the clinical scenario, and improving the design of the imaging reference to make the spatial tracking robust. 2) Performing inter-observer analysis using a larger number of samples and observers with different levels of expertise is also necessary to have a better evaluation of the reliability of the developed method. 3) Experimenting with larger and more diverse sample size with various deformity types and severities is crucial to assess the potentials of the developed system. 4) An accurate measurement of radiation exposure from the system by using the dosimeter can also be considered in future work. 5) Also as a recommendation, during the image acquisition the C-arm orientation can be manipulated to produce best visualization of the endplates for each individual image, for instance by making the gantry slightly oblique to the coronal or sagittal views (e.g., shoulder from lateral view). The image generated by our method in this situation can still generate long radiographs even when some of the views are not kept perfectly parallel. This can improve the visualization of the of all the anatomical landmarks in the long stitched view and potentially improve the corresponding radiographic assessments.  4.5 Conclusions The primary goal of this thesis was to develop an intraoperative method that provides tools for accurate assessment of long anatomies on the surgical table with a focus on spinal deformities. This goal has been accomplished through the achievement of two steps. First, a method for generating radiographs of long anatomy was successfully developed and validated in phantom- 92 based experiments. Second, the application of the developed technique was successfully demonstrated for spinal deformity correction surgeries. The promising results demonstrate the potential of the system for monitoring the alignment of the spine as well as pelvic parameters using a widely available imaging equipment in the OR (C-arm). The developed techniques in this thesis can ultimately be employed in a form of an intraoperative measuring tool that can assist the surgeon by providing real-time information about the shape of the anatomy during the course of the surgery. The results of this thesis can have potential impact in improving the surgical outcomes and preventing postoperative complications pertaining to the poor intraoperative evaluation of the operative anatomy in spinal deformity correction surgery.    93 References [1] H.-R. Weiss and D. Goodall, “Rate of complications in scoliosis surgery – a systematic review of the Pub Med literature,” Scoliosis, vol. 3, p. 9, 2008. [2] K. Freidel, F. Petermann, D. Reichel, A. Steiner, P. Warschburger, and H.-R. 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Shaffrey, S. Bess, and T. Errico, “The T1 pelvic angle, a novel radiographic measureof global sagittal deformity, accounts for both spinal inclination and pelvic tilt and correlates with health-related quality of life,” J. Bone Jt. Surg., vol. 96, no. 19, pp. 1631–1640, 2014. [102] J. C. Y. Leong, W. W. Lu, K. D. K. Luk, and E. M. Karlberg, “Kinematics of the chest cage and spine during breathing in healthy individuals and in patients with adolescent idiopathic scoliosis,” Spine (Phila. Pa. 1976)., vol. 24, no. 13, pp. 1310–1315, 1999. [103] A. P. Sangole, C. E. Aubin, H. Labelle, I. A. F. Stokes, L. G. Lenke, R. Jackson, and P. Newton, “Three-dimensional classification of thoracic scoliotic curves,” Spine (Phila Pa 1976), vol. 34, no. 1, pp. 91–99, 2009. [104] S. Donzelli, S. Poma, L. Balzarini, A. Borboni, S. Respizzi, J. H. Villafane, F. Zaina, and S. Negrini, “State of the art of current 3-D scoliosis classifications: a systematic review from a clinical perspective,” J. Neuroeng. Rehabil., vol. 12, no. 1, p. 91, 2015. [105] A. P. Sangole, C. E. Aubin, H. Labelle, L. G. Lenke, R. Jackson, P. Newton, and I. A. F. Stokes, “The central hip vertical axis: a reference axis for the Scoliosis Research Society three-dimensional classification of idiopathic scoliosis,” Spine (Phila. Pa. 1976)., vol. 35, no. 12, pp. E530–4, 2010. [106] D. J. Ryan, T. S. Protopsaltis, C. P. Ames, R. A. Hostin, E. O. Klineberg, G. M. Mundis, I. Obeid, K. M. Kebaish, J. S. Smith, O. Boachie-Adjei, D. C. Burton, R. A. Hart, M. Gupta, F. J. Schwab, and V. Lafage, “T1 pelvic angle (TPA) effectively evaluates sagittal deformity and assesses radiographical surgical outcomes longitudinally,” Spine (Phila. Pa.  103 1976)., vol. 39, pp. 1203–1210, 2014. [107] L. Humbert, J. A. De Guise, B. Aubert, B. Godbout, and W. Skalli, “3D reconstruction of the spine from biplanar X-rays using parametric models based on transversal and longitudinal inferences,” Med. Eng. Phys., vol. 31, no. 6, pp. 681–687, 2009.    104 Appendices Landmark Digitization with Optotrak This appendix provides information regarding a digitization of the phantom that has been used for landmark localization in chapter 2. The description of the custom-made digitizer probe that was built in this study is provided, followed by the experiments that have been conducted to 1) validate the accuracy of the probe, and 2) digitize the landmark locations on the phantom. A.1 Digitization of landmark locations The reference coordinates of the markers that were used for the three-dimensional localization in this study were collected by digitizing the fiducial markers’ three-dimensional positions. The digitization was performed using an Optotrak Certus Motion Capture System (NDI; Northern Digital Inc., Waterloo, Ontario, Canada). This optical measurement system is commonly used to track the positions of the infrared light-emitting diode (IRED) or active markers within a specific measurement volume using cameras (Figure A-1). It reports the three-dimensional coordinates of the markers relative to a global coordinate system with three-dimensional accuracy up to 0.1 mm, resolution of 0.01 mm and a maximum sampling rate (marker frequency) of 4600 Hz (Northern Digital, 2012a) [68]. The product specific software (NDI First Principles, version 1.2.4, © 2012 Northern Digital Inc.) was used for data acquisition.  Figure A-1: (A) OptoTrak Certus motion capture camera, (B) active markers used in this study.   105 A.2 Custom-made digitizing probe A digitizing probe provides the ability to localize both real and virtual markers. Real markers identify positions on a probe where markers can be attached. Alternatively, virtual markers help to calculate the three-dimensional coordinates of points where it is difficult to attach actual markers. The end tip of the probe can be used to determine the location of any point by placing the end tip of the tool at the desired point. The location of these points is recorded by their x, y and z coordinates. This is known as digitizing a point. A custom-made three-marker rigid body was fabricated to be used as a digitizing probe in this study to ensure accurate and precise digitization of the landmarks. The custom-made digitizer consists of 1) a spherical tip with the same size of the fiducial marker was used in this study (Figure A-2) that can sit inside of the holes of the upper holder, 2) smart marker rigid body that houses three smart markers to form a rigid body, 3) three smart markers, 4) a steel rod that connects the markers to the tip, and 5) a securing system to avoid any further movements between the markers and the rod (Figure A-3).  Figure A-2: Digitizer spherical tip and the fiducial marker used during the experiments.  The digitizer tip was fabricated by a 3D printer (Ultimaker 2, Ultimaker B.V., Geldermalsen, Netherlands) to represent a virtual marker during the digitization process.   106  Figure A-3: (A) front and (B) side views of custom-made digitizing probe used for the experiments. It consists of three smart markers, a rigid triangular body that houses smart markers, tip (virtual marker), steel rod that connects the virtual marker to a rigid triangular body and a lock system that ensures a rigid connection between the steel rod and the rigid body.  A.3 Validation Experiments Pivot procedure A pivot procedure was performed to use a custom-made rigid body as a digitizing probe with OptoTrak Certus System. This method creates the transformation that translates the origin of the rigid body to the pivot point. Different pivot pass parameters like maximum three-dimensional RMS error, maximum three-dimensional error, minimum minor, and the minimum major angle was defined to ensure accurate data collection. Table A-1 shows the thresholds that have been selected for the experiments.  107 Table A-1: Defined threshold for pivot parameters to ensure accurate data collection. The maximum three-dimensional RMS error is an acceptable threshold for three-dimensional RMS error produced by applying the final result of pivot procedure to each frame and calculating an overall RMS error. The maximum three-dimensional Error is an acceptable threshold for a three-dimensional error produced by applying the result of the final pivot procedure to each frame and calculate an error for that frame. The minimum minor and major angle define the acceptable threshold for minor and major angle (smallest and greatest angles the tool was moved during the pivot procedure) produced during a pivot. The minor angle is defined as being orthogonal to the plane of major angle. Pivot Parameters Defined Threshold Maximum three-dimensional RMS Error (mm) 0.5 Maximum three-dimensional Error (mm) 0.5 Minimum Minor Angle (°) 45 Maximum Major Angle (°) 45  The probe was sat inside one of the holes and pivoted in two perpendicular directions (side to side and then front to back) slowly and smoothly to create an accurate pivot data during the pivoting procedure, as mentioned in the device user guide (Figure A-4). This procedure determines the location of the probe tip (center of the ball) with respect to the origin of the tool. This is commonly known as a tip offset. By using the tip offset the origin of the probe is translated to the pivot point. After determination of the tip offset for the first time, the pivoting procedure was repeated before each test (five trials), and the maximum three-dimensional RMS were observed to test the robustness of the process.  108  Figure A-4: Motion of a digitizing probe (side to side and front to back) to be collected during a pivot procedure.  These motions provide required information to find the transformation between real markers and virtual marker (tip of the digitizer).  Phantom digitization Phantom digitizing experiments were performed with an OptoTrak Certus System using the custom-made digitizing probe and the phantom described in Chapter 2. The base of the phantom was firmly secured to the table to avoid any movements during the experiments. Experiments were repeated six times and the precision of the measurement in each direction was measured by calculating the standard deviation. A.4 Results Pivoting procedure The maximum observed three-dimensional RMS error (between five trials) for pivoting procedure (reported by NDI First Principles software) was 0.16 mm.    109 Phantom digitization precision The results of the experiments showed that the custom-made probe is capable of digitizing points with the precision of ± 0.2mm in X direction, ± 0.5mm in Y direction, and ± 0.2mm in Z direction with respect to OptoTrak Certus System default global coordinate system (Figure A-5).  Figure A-5: OptoTrak Certus System defaults coordinate system and axis directions. These axes used to report the precision of digitizing process.  A.5 Discussion and Conclusion In this appendix, we demonstrate the ability of a new digitizing probe in digitizing the three-dimensional location of landmarks. The results show that the digitizer had a reasonable precision (overall < 0.7mm) in digitizing points. It enables us to digitize the three-dimensional location of points where it is difficult to attach actual markers.    110 Radiographic Measurement The Spinal Deformity Study Group (SDSG) and Scoliosis Research Society (SRS) has identified 19 parameters and described them in a Radiographic Measurement Manual (RMM) [95]. The RMM guidebook provides a standardized measurement manual for the evaluation of curvature on radiographs for both adolescent idiopathic scoliosis (AIS) and adults’ deformity. In this thesis, seven parameters from the manual and one other parameter (total of eight) in coronal and sagittal views were used to determine the reliability of generated long views by the introduced system. This appendix provides an illustration of the measurements that has been used in this thesis. B.1 Coronal View  The following measurements from Radiographic Measurement Manual in the coronal view has been used: Proximal thoracic (PT) is defined as the angle between a line drawn from the superior endplate of T1 and a line drawn from the inferior endplate of T3 using the Cobb method (Figure B-1). Main thoracic (MT) is defined as the angle between a line drawn from the superior endplate of T3 and a line drawn from the inferior endplate of T12 using the Cobb method (Figure B-1). Thoracolumbar/lumbar (TL/L) is defined as the angle between a line drawn from the superior endplate of T12 and a line drawn from the inferior endplate of S1 using the Cobb method (Figure B-1).  111  Figure B-1: Cobb angle measurements in the coronal plane. Measurements including Proximal Thoracic (PT) between T1-T3, Main Thoracic (MT) between T3-T12, and Thoracolumbar/Lumbar (TL/L) between T12-L4. These parameters in coronal view have been used in this thesis for the measurements in Chapter 3. © Reproduced with permission from Medtronic.  Coronal balance (CB) is the distance between the C7 plumb line (C7PL), a vertical line dropped from the C7 vertebral body, and the coronal sacral vertical line (CSVL), the vertical line in a coronal radiograph that passes through the center of the sacrum (Figure B-2-A). For the standing radiographs, the lateral edge of the film represents a reference that shows the gravitational line and the C7PL and CSVL are drawn parallel to the edge of the radiograph. However, in the supine posture (intraoperative X-rays) since the direction of the gravitational line in unknown, the edge of the film is not reliable. Therefore, central hip vertical axis (CHVA) was used as a reference for a direction of the C7PL and CSVL in the prone posture. CHVA is a vertical line bisecting the line joining the centers of the femoral heads in coronal view (Figure  112 B-2-B) [105]. The coronal balance is measured as the distance between the center of C7PL and CSVL while they were drawn parallel to the direction of CHVA.  Figure B-2: Measurement of coronal balance. (A) Measurement of coronal balance using the C7 plumb line and central sacral vertical line in the standing posture. (B) Central hip vertical line (CHVA) on the coronal X-ray. CHVA can be found as a perpendicular line that bisecting the line joining the femoral heads centers. (A) © Reproduced with permission from Medtronic. (B) © Reproduced from [105] with permission from Wolters Kluwer Health, Inc.  B.2 Sagittal View The following measurements from Radiographic Measurement Manual in the sagittal view has been used in this thesis: Thoracic kyphosis (TK) is defined as the angle between a line drawn from the superior endplate of T2 and a line drawn from the inferior endplate of T12 using the Cobb method (Figure B-3-A).  113 Lumbar Lordosis (LL) is defined as the angle between a line drawn from the superior endplate of T12 and a line drawn from the superior endplate of S1 using the Cobb method (Figure B-3-B).  Figure B-3: Cobb angle measurements in the sagittal plane. Measurements including (A) Thoracic Kyphosis (TK) between T2-T12, and (B) Lumbar Lordosis (LL) between T12-S1. These parameters in sagittal view have been used in this thesis for the measurements in Chapter 3. © Reproduced from [22] with permission from Wolters Kluwer Health, Inc.  Pelvic incidence (PI) is defined as the angle between a line drawn from the center of the femoral head and the superior sacral endplate and a line drawn perpendicular to the center of the superior sacral endplate (Figure B-4-A). It is important to consider that in two-dimensional sagittal radiographs, it is usually impossible to obtain the superposition of the two femoral heads because of the projective characteristics of X-ray image acquisition. The reference point of the  114 measurements is therefore defined by the hip axis, represented by the midpoint of the line joining the centers of the circular acetabular edges (e.g. centers of the femoral heads) (Figure B-4-B) [95].  Figure B-4: Measurement of pelvic incidence (PI) on the sagittal radiograph. (A) Definition of pelvic incidence (PI) as an angle between the lines that connects the center of the femoral heads (o) to the center of sacral endplate (a). (B) Demonstrate the measurement of PI when the two femoral heads show up separately on the radiograph by using the mid-point of the hip axis (o) as the reference. © Reproduced with permission from Medtronic.  T1 pelvic angle (TPA) is defined as the angle between a line from the femoral heads to the center of T1 vertebral body and a line from the femoral heads to the center of the superior sacral endplate (Figure B-5). TPA demonstrate the global sagittal balance that accounts for both the spinal inclination and pelvic tilt [101]. This parameter has been used in this study instead of sagittal balance.   115  Figure B-5: Measurement of T1 pelvic angle (TPA) on the sagittal radiograph.  TPA is an angle between a line that connects center of T1 to center of femoral heads and a line that connects the center of the superior sacral endplate to the center of femoral heads. © Reproduced from [106] with permission form Wolters Kluwer Health, Inc.    116 Segmentation of CT Images This appendix provides information regarding the extraction of data from CT images that has been used as ground-truth information for radiographic measurements in chapter 3. For this study, CT images of the four (three females and one male) solid frozen scoliotic specimens with a voxel size of 0.3	×	0.3	×	0.6	223 acquired. The ground-truth data was generated by analyzing the images in 3DSlicer (version 4.3.1) [94]. The description of the method for segmentation of the endplates and femoral heads in this study is provided, followed by the repeatability results of the segmentation. C.1 Segmentation of Endplates The endplates of each vertebra were identified by manual selection of five points using a method described in the literature (Figure C-1) [107]. The centroids of the vertebral bodies were calculated as the average of the segmented points (ten points) on superior and inferior endplates (Figure C-2).   Figure C-1: The suggested method for the segmentation of endplates of a vertebra. This method finds four points on the circumference of the endplate and one point at the center of endplate (overall five points for each endplate). © Reproduced from [107] with permission from Elsevier.   117  Figure C-2: Segmentation of endplates of T3 in 3DSlicer from CT images. (A) Axial view of the superior endplate of the vertebra, (B) sagittal view, and (C) coronal view of the vertebra that shows the selected points on superior and inferior endplates. This method has been used for all of the specimens to find the direction of endplates and centroid of the vertebral bodies.  C.2 Segmentation of Femoral Heads Femoral heads were also used as reference anatomical landmarks. The surface of the femoral heads was segmented in the axial, sagittal and coronal images (more than 30 points were segmented) and the centers were determined by fitting a sphere to the segmented points using least-square method (Figure C-3).   118  Figure C-3: Segmentation of the right femoral head in 3DSlicer from CT images. (A) Axial, (B) sagittal, and (C) coronal views of the femoral head. The center of the femoral head was found by fitting a sphere to the segmented points.  The segmentation of the CT images for both endplate and femoral head segmentation was repeated three times to provide an accurate and reliable data. Reproducibility of the segmentation of CT images was evaluated by calculating the precision of Cobb angles in coronal and sagittal views and coronal balance (for parameter definitions see Appendix B).  C.3 Results Reproducibility The results of the Cobb angle and coronal balance measurements from CT images showed that the process is capable of measuring the Cobb angles with the precision of ±0.7° and coronal balance with the precision of ±0.6mm (Table C-1). Table C-1: Precision of the angular and balance measurement from CT images (3 trials). The results show the precision of the Cobb angle and coronal balance measurement.  Cobb angle (°) Coronal balance (mm) Precision (standard deviation) ±0.7 ±0.6   119 C.4 Discussion and Conclusion In this appendix, the method that was used for the segmentation of the CT images was demonstrated. The reproducibility of the proposed method for segmentation of the CT images was evaluated, and the results showed that the process could measure the Cobb angles with precision < 1° and coronal balance with precision < 1 mm. The calculated results are well within the acceptable range based on the defined threshold of 5° and 5mm for Cobb angle and balance, respectively. 

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