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Novel stand-off pads for ultrasound-CT registration and elastography Kingma, Raoul Jacob 2012

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Novel Stand-off Pads for Ultrasound-CT Registration and Elastography by Raoul Jacob Kingma B.Eng., McMaster University, 2009 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) March 2012 c© Raoul Jacob Kingma 2012 Abstract Laparoscopic surgery has many advantages including reduced patient mor- bidity and improved recovery times, but has the drawback of a very limited field of view. Thus improvements in image guidance in laparoscopic surgery are highly desirable, especially in highly technical operations such as robot- ically assisted laparoscopic partial nephrectomies (RALPN). In RALPN, image guidance can be enhanced by bringing pre-operative computed tomography (CT) and intra-operative ultrasound images into the surgeon’s field of view, depicting underlying anatomy. Multiple tracking and registration steps with inherent trade-offs of accuracy and convenience are normally required to display the images in the camera view. In this thesis, a new tracker-less method is developed for the step of registering pre-operative 3D CT to pre-operative 3D ultrasound which uses a novel fiducial stand-off pad. The pad contains fiducial markers visible in both modalities which are matched to obtain the registration parameters. The fiducial stand-off pad is tested in a controlled phantom study to determine registration accuracy and in a small clinical study to determine clinical feasibility. The fiducial stand- off pad is capable of similar registration accuracies to incumbent approaches without the need for external tracking equipment, and is easily integrated into medical imaging protocols. A second enhancement of RALPN image guidance is the integration of ultrasound elastography to display mechanical properties of the tissue. Elas- tography has been in development for over two decades, but further improve- ments are required to improve quantitative estimations of tissue properties. In this thesis, a stand-off pad is used as a method of measuring ultrasound transducer contact force distributions, which will allow force measurements to be used in solving for local tissue elasticities. Forces are obtained by measuring displacements in the stand-off pad and converting them to forces using a finite element model. The accuracy of displacement estimates is tested, and the force computation process is validated. As well, a force measurement system is implemented for use with a three-dimensional linear array transducer. The results show that this is a feasible force measurement method, providing approximately 10% error in force measurements. ii Preface This thesis is based on two manuscripts which are the result of the collabo- ration of multiple researchers. A version of Chapter 3 was published in Computer Aided Surgery in March 2011: R. Kingma, R.N. Rohling, and C. Nguan, “Registration of CT to 3D ultrasound using near-field fiducial localization: A feasibility study.” Com- puter Aided Surgery, 2011;16(2):54-70. The paper was co-authored with Drs. Rob Rohling and Chris Nguan. Dr. Rohling provided the conceptual idea of using a fiducial stand-off pad as a registration tool. The author’s contribution was developing the main con- cept, fabricating fiducial stand-off pads and the testing phantom, arranging CT and ultrasound scans, obtaining patient CT and ultrasound data, com- pleting the numerical analysis, and preparing the manuscript. Dr. Rohling also contributed many suggestions and improvements to the methods used, and was also the primary editor of the manuscript. Dr. Nguan also edited the manuscript, and was instrumental in arranging the patient study (Ethics Certificate H08-02798) and in providing feedback on the clinical aspects of the research. Chapter 4 was written in collaboration with Drs. Tim Salcudean, Rob Rohling, Reza Zahiri-Azar and M.A.Sc. candidate Eric Pospisil. Dr. Sal- cudean provided the concept of using an elastic pad as a force sensor for 2D and 3D ultrasound transducers, which is the basis of this chapter. He also provided the suggestion of using a scattering medium to track motion in the stand-off pad. The author’s contribution was then developing this concept, manufacturing and procuring the stand-off pads, designing the experimental setup and performing data collection, analyzing the data. Dr. Salcudean then suggested the used of a finite element model in recovering forces. The author created the finite element model, completed validation experiments, implemented a working system and prepared the manuscript. Dr. Rohling provided various suggestions throughout the research, and both he and Dr. Salcudean offered editing suggestions for the manuscript. Dr. Zahiri-Azar contributed the motion-tracking algorithms used in this research, and aided iii Preface in solving motion-tracking difficulties. Eric Pospisil provided the software which was used as the foundation for the final implementation of the force measurement system, and gave suggestions for modifying the software for the purposes of this research. iv Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xiv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 CT to US Registration . . . . . . . . . . . . . . . . . . . . . 7 2.2 Ultrasound Elastography . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Motion Estimation . . . . . . . . . . . . . . . . . . . 12 2.2.2 Tissue Property Reconstruction . . . . . . . . . . . . 15 3 Rigid Registration of 3D CT to 3D Ultrasound Using a Fidu- cial Stand-off Pad . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Stand-off Pad Construction . . . . . . . . . . . . . . . 21 3.2.2 Ultrasound Image Quality . . . . . . . . . . . . . . . 21 v Table of Contents 3.2.3 Controlled Phantom Study . . . . . . . . . . . . . . . 23 3.2.4 Clinical Study . . . . . . . . . . . . . . . . . . . . . . 26 3.2.5 Lever Arm Effect Error . . . . . . . . . . . . . . . . . 28 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.1 Ultrasound Image Quality . . . . . . . . . . . . . . . 29 3.3.2 Controlled Phantom Study . . . . . . . . . . . . . . . 29 3.3.3 Clinical Study . . . . . . . . . . . . . . . . . . . . . . 39 3.3.4 Lever Arm Effect Error . . . . . . . . . . . . . . . . . 42 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4.1 Ultrasound Image Quality . . . . . . . . . . . . . . . 42 3.4.2 Fiducial Localization Error . . . . . . . . . . . . . . . 43 3.4.3 Fiducial Registration Error . . . . . . . . . . . . . . . 43 3.4.4 Target Registration Error . . . . . . . . . . . . . . . . 43 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4 Force Profile Measurements Using a Compliant Stand-off Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Stand-off Pad Development . . . . . . . . . . . . . . . . . . . 53 4.3 Methods - Stand-off Pad Properties . . . . . . . . . . . . . . 54 4.3.1 Stand-off Pad Speed of Sound . . . . . . . . . . . . . 54 4.3.2 Stand-off Pad Elasticity . . . . . . . . . . . . . . . . . 57 4.4 Results and Discussion - Stand-off Pad Properties . . . . . . 58 4.4.1 Stand-off Pad Speed of Sound . . . . . . . . . . . . . 58 4.4.2 Stand-off Pad Elasticity . . . . . . . . . . . . . . . . . 59 4.5 Methods - Displacement Tracking Validation . . . . . . . . . 61 4.5.1 Displacement Tracking of Experimental Data . . . . . 61 4.5.2 Experimental Repeatability and Hysteresis . . . . . . 65 4.5.3 Simulated Compression of RF Signal . . . . . . . . . 65 4.5.4 3D Finite Element Model of Stand-off Pad Deforma- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.5.5 Extrapolation of Pad-Tissue Interface Displacement Measurements . . . . . . . . . . . . . . . . . . . . . . 67 4.6 Results and Discussion - Displacement Tracking Validation . 69 4.6.1 Displacement Tracking of Experimental Data . . . . . 69 4.6.2 Experimental Repeatability and Hysteresis . . . . . . 72 4.6.3 Simulated Compression of RF Signal . . . . . . . . . 78 4.6.4 3D Finite Element Model of Stand-off Pad Deforma- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 vi Table of Contents 4.6.5 Extrapolation of Pad-Tissue Interface Displacement Measurements . . . . . . . . . . . . . . . . . . . . . . 89 4.7 Methods - Obtaining Force Measurements from Displacement Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.7.1 Simulation of a Look-up Based Force Recovery with 2D Transducer . . . . . . . . . . . . . . . . . . . . . . 93 4.7.2 Simulation of Direct Force Recovery via FEM with 3D Transducer . . . . . . . . . . . . . . . . . . . . . . . . 95 4.7.3 Experimental Validation of Direct Force Recovery with 3D Transducer . . . . . . . . . . . . . . . . . . . . . . 100 4.7.4 Spatial Resolution of Force Measurements with 3D Transducer . . . . . . . . . . . . . . . . . . . . . . . . 105 4.7.5 Implementation of Stand-off Pad Force Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.8 Results and Discussion - Obtaining Force Measurements from Displacement Data . . . . . . . . . . . . . . . . . . . . . . . 107 4.8.1 Simulation of a Look-up Based Force Recovery with 2D Transducer . . . . . . . . . . . . . . . . . . . . . . 107 4.8.2 Simulation of Direct Force Recovery via FEM with 3D Transducer . . . . . . . . . . . . . . . . . . . . . . . . 108 4.8.3 Experimental Validation of Direct Force Recovery with 3D Transducer . . . . . . . . . . . . . . . . . . . . . . 111 4.8.4 Spatial Resolution of Force Measurements with 3D Transducer . . . . . . . . . . . . . . . . . . . . . . . . 114 4.8.5 Implementation of a Stand-off Pad Force Measure- ment System . . . . . . . . . . . . . . . . . . . . . . . 115 4.9 Discussion of Viscoelastic Behavior of the Stand-off Pad . . . 116 4.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5 Conclusions and Future Research . . . . . . . . . . . . . . . . 118 5.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.2.1 Fiducial Stand-off Pad for Image Registration . . . . 119 5.2.2 Force Measurement Stand-off Pad for Elastography . 120 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 vii Table of Contents Appendices A Expanded Patient Study for Fiducial Stand-off Pad . . . . 132 B Experimental Displacement Profiles in the Stand-off Pad 133 C Repeatability of Displacement Measurements . . . . . . . . 139 D Comparison of Displacement Tracking Results with a 1D Linear Deformation Model . . . . . . . . . . . . . . . . . . . . 145 D.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 D.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 E Mean and Standard Deviation of Displacement Extrapola- tion Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 viii List of Tables 3.1 The ultrasound acquisition settings used for image quality testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Ultrasound acquisition parameter sets used in phantom study. 25 3.3 Effect of stand-off pad thickness on axial resolution of ultra- sound images . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4 Effect of stand-off pad thickness on lateral resolution of ul- trasound images . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5 Effect of stand-off pad thickness on elevational resolution of ultrasound images . . . . . . . . . . . . . . . . . . . . . . . . 32 3.6 Effect of stand-off pad thickness on image contrast of ultra- sound images . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.7 Summary of errors in phantom testing. . . . . . . . . . . . . . 33 3.8 RMS FRE for three patients . . . . . . . . . . . . . . . . . . . 39 3.9 RMS TRE for three patients . . . . . . . . . . . . . . . . . . 40 4.1 Applied frequencies for shear rheometry testing . . . . . . . . 58 4.2 The speed of sound in the Blue Phantom stand-off pad com- puted from four trials. . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Maximum residual errors for polynomial fits . . . . . . . . . . 89 4.4 Maximum extrapolation errors . . . . . . . . . . . . . . . . . 90 4.5 Summary of objects used in experimental force measurement validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.1 RMS FRE for six additional patients . . . . . . . . . . . . . . 132 A.2 RMS TRE for six additional patients . . . . . . . . . . . . . . 132 ix List of Figures 1.1 Overview of laparoscopic surgery . . . . . . . . . . . . . . . . 1 1.2 The da Vinci Si Surgical System by Intuitive Surgical. Image courtesy of Intuitive Surgical (www.intuitivesurgical.com). . . 3 2.1 Methodology for registering pre-operative CT to intra-operative ultrasound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 A schematic of the calibration and tracking steps in the con- ventional tracked ultrasound method for CT-to-US registra- tions performed at the time of the CT. . . . . . . . . . . . . . 9 2.3 Overview of an ultrasound transducer as used in elastography 13 2.4 Overview of time delay estimators . . . . . . . . . . . . . . . 14 2.5 A sample elastogram . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 An example of a time-of-flight ultrasonic force sensor . . . . . 18 3.1 Typical ultrasound beam pattern for a linear array transducer. 20 3.2 The prototype fiducial stand-off pad containing five fiducial markers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 A schematic of the testing phantom . . . . . . . . . . . . . . 24 3.4 Patient positioning and setup used during the clinical study . 27 3.5 An illustration of the lever arm effect . . . . . . . . . . . . . . 28 3.6 Sample images used for determining stand-off pad effect on image quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.7 Sample image of line features used in calculation of elevational resolution effects . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.8 Sample images of the testing phantom . . . . . . . . . . . . . 33 3.9 FLE plotted against the various ultrasound parameters used . 34 3.10 RMS FRE plotted against the various ultrasound parameters used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.11 Absolute FRE for phantom test datasets . . . . . . . . . . . . 36 3.12 RMS TRE plotted against the various ultrasound parameters used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.13 Absolute TRE for phantom test datasets . . . . . . . . . . . . 38 x List of Figures 3.14 Sample images from the clinical study. . . . . . . . . . . . . . 39 3.15 Overlays of clinical data after registration . . . . . . . . . . . 41 3.16 Histograms of lever arm effect errors . . . . . . . . . . . . . . 42 4.1 Illustration of force measurement stand-off pad functionality . 49 4.2 Illustration of the region of interest in the force measurement stand-off pad . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3 An illustration of a general mechanical loading scenario . . . 53 4.4 The prototype Blue Phantom force measurement stand-off pad 54 4.5 Photos of the experimental setup . . . . . . . . . . . . . . . . 56 4.6 Shear and elastic moduli of the stand-off pad . . . . . . . . . 60 4.7 Applied displacements used in motion-tracking validation . . 62 4.8 Example displacement curve for a single RF line . . . . . . . 62 4.9 Effect of window size on maximum tracking depth with TDPE 64 4.10 Finite element model of the stand-off pad . . . . . . . . . . . 67 4.11 The pad-tissue interface location relative to the ultrasound transducer as found in the ultrasound signal . . . . . . . . . . 68 4.12 Displacement profiles at the transducer centerline for different motion-tracking methods . . . . . . . . . . . . . . . . . . . . 71 4.13 Experimental repeatability based on the repeatability of dis- placement measurements between trials . . . . . . . . . . . . 73 4.14 Experimental hysteresis curves based on displacement mea- surements at the bottom boundary of the ROI . . . . . . . . 76 4.15 Experimental hysteresis magnitudes along the transducer cen- terline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.16 Displacement curves for simulated compression of the trans- ducer centerline for different motion-tracking methods . . . . 81 4.17 The bias effect of signal amplitude on displacement measure- ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.18 The uncompressed signal for the transducer centerline . . . . 83 4.19 Comparison of unfiltered and filtered motion-tracking results for ST and TDPE-ST Hybrid motion-tracking algorithms ap- plied to simulated data . . . . . . . . . . . . . . . . . . . . . . 84 4.20 The completed FEM simulation showing axial displacements 85 4.21 Displacement curves from the FEM model and the experi- mental data for each motion-tracking method . . . . . . . . . 87 4.22 Displacement error curves when comparing the FEM model to the experimental data for each motion-tracking method . . 88 4.23 Residuals of a cubic polynomial fit to the displacement data . 91 xi List of Figures 4.24 Residuals of a fourth order polynomial fit to the displacement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.25 Simulation models for look-up based force measurement ap- proach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.26 A 3D linear array transducer . . . . . . . . . . . . . . . . . . 96 4.27 Images of the FEM model used in simulating the stand-off pad for a 3D linear array . . . . . . . . . . . . . . . . . . . . . 98 4.28 Displacement profile applied to the stand-off pad . . . . . . . 99 4.29 Experimental apparatus used in force validation experiments 101 4.30 Photos of the objects used in force measurement validation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.31 The pad-tissue interface for the 3D linear array transducer . . 103 4.32 Images of the FEM model used in force measurement validation104 4.33 The experimental apparatus for resolution testing . . . . . . . 106 4.34 Measured forces and errors in force measurements . . . . . . 108 4.35 The ideal and computed displacement profiles for the simula- tion of a flat stand-off pad imaged with a 3D transducer . . . 109 4.36 The ideal and obtained force profiles for the simulation of a flat stand-off pad imaged with a 3D transducer . . . . . . . . 110 4.37 Force profile errors in a 3D simulation of a flat stand-off pad 110 4.38 The displacement and force profiles for each object in exper- imental validation . . . . . . . . . . . . . . . . . . . . . . . . 112 4.39 Force measurement errors in experiments . . . . . . . . . . . 113 4.40 Spatial resolution of force measurements . . . . . . . . . . . . 114 4.41 Screen capture of working force measurement system . . . . . 115 B.1 Displacement profiles in the stand-off pad with TDPE motion- tracking (window size 0.5 mm) . . . . . . . . . . . . . . . . . 134 B.2 Displacement profiles in the stand-off pad with TDPE motion- tracking (window size 1.0 mm) . . . . . . . . . . . . . . . . . 135 B.3 Displacement profiles in the stand-off pad with TDPE motion- tracking (window size 2.0 mm) . . . . . . . . . . . . . . . . . 136 B.4 Displacement profiles in the stand-off pad with the ST algorithm137 B.5 Displacement profiles in the stand-off pad with the TDPE-ST Hybrid algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 138 C.1 Repeatability of displacement measurements in the stand-off pad with TDPE motion-tracking (window size 0.5 mm) . . . 140 C.2 Repeatability of displacement measurements in the stand-off pad with TDPE motion-tracking (window size 1.0 mm) . . . 141 xii List of Figures C.3 Repeatability of displacement measurements in the stand-off pad with TDPE motion-tracking (window size 2.0 mm) . . . 142 C.4 Repeatability of displacement measurements in the stand-off pad with the ST algorithm . . . . . . . . . . . . . . . . . . . 143 C.5 Repeatability of displacement measurements in the stand-off pad with the TDPE-ST Hybrid algorithm . . . . . . . . . . . 144 D.1 Comparison of estimated displacements to a 1D linear dis- placement model . . . . . . . . . . . . . . . . . . . . . . . . . 146 D.2 Difference between tracked displacements and 1D linear model displacements in the stand-off pad with TDPE motion-tracking (window size 0.5 mm) . . . . . . . . . . . . . . . . . . . . . . 148 D.3 Difference between tracked displacements and 1D linear model displacements in the stand-off pad with TDPE motion-tracking (window size 1.0 mm) . . . . . . . . . . . . . . . . . . . . . . 149 D.4 Difference between tracked displacements and 1D linear model displacements in the stand-off pad with TDPE motion-tracking (window size 2.0 mm) . . . . . . . . . . . . . . . . . . . . . . 150 D.5 Difference between tracked displacements and 1D linear model displacements in the stand-off pad with the ST algorithm . . 151 D.6 Difference between tracked displacements and 1D linear model displacements in the stand-off pad with the TDPE-ST Hybrid algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 D.7 Difference between tracked displacements and 1D linear model displacements at the transducer centerline for different motion- tracking methods . . . . . . . . . . . . . . . . . . . . . . . . . 153 E.1 Mean and standard deviation of extrapolation errors for all motion-tracking methods at each frame . . . . . . . . . . . . 155 E.1 Mean and standard deviation of extrapolation errors for all motion-tracking methods at each frame (cont.) . . . . . . . . 156 xiii List of Abbreviations 1D One Dimensional 2D Two Dimensional 3D Three Dimensional CT Computed Tomography EBRT External Beam Radiation Therapy FEM Finite Element Model FLE Fiducial Localization Error FRE Fiducial Registration Error FWHM Full Width at Half Maximum LPN Laparoscopic Partial Nephrectomy MRI Magnetic Resonance Imaging LSE Least Squares Estimate PET Positron Emission Tomography PVA Polyvinyl Alcohol PVC Polyvinyl Chloride RALPN Robotically Assisted Laparoscopic Partial Nephrectomy ROI Region of Interest SOS Speed of Sound SNR Signal-to-Noise Ratio ST Sample Tracking TDPE Time Domain Cross-Correlation with Prior Estimates TRE Target Registration Error US Ultrasound ZCT Zero-Crossing Tracking xiv Acknowledgments I would like to thank my supervisors, Drs. Rob Rohling and Tim Salcud- ean, for their guidance, support and patience throughout the duration of my research, and for encouraging me to bring the research to a thorough completion. I would also like to thank Mahmoud Ansari of the Chemical Engineering department for taking the time to perform rheometry tests for this research. A hearty thank-you also goes out to the rest of the Robotics and Control Lab. In particular, I would like to thank Reza-Zahiri Azar, Hani Eskandari, Ali Baghani and Orcun Goksel for contributing suggestions and for being willing to help solve the difficulties that arose throughout the research. I’d also like to thank Caitlin Schneider for her unending help in supplementing my lack of coding expertise, and for being an excellent soundboard for research ideas. Jeff Abeysekera is thanked for providing insights into ultrasound elastography and providing feedback and various useful algorithms. Eric Pospisil is thanked for providing his software and for willingly answering related questions. Not to be forgotten, thank-you to all members of the RCL who made the lab into a never-ending adventure - the jokes, pranks, summer lunches, baking, laughter and interesting smells will not be forgotten anytime soon! Lastly, thank-you my wonderful family for their unending support and prayers. And thank-you to my darling Sara, who stood by me through the stress and frustration and triumphs, always willing to help and cheer. xv — “So I saw that there is nothing better than that a man should rejoice in his work, for that is his lot. Who can bring him to see what will be after him?” — Ecclesiastes 3:22 xvi Chapter 1 Introduction 1.1 Motivation Laparoscopy is a minimally invasive surgical technique in which small in- cisions are made in the skin of the abdomen, followed by the insertion of specialized ports. Long tools and a camera are inserted through the ports to access the surgical site (see Fig. 1.1). The advantages of laparoscopy include lower patient morbidity and post-operative pain, reduced infection rates, shortened hospital stays, and faster recovery [54]. Many surgical pro- cedures can now be performed laparoscopically, such as cholecystectomy, appendectomy, esophagectomy and nephrectomy surgeries, to name just a few [23], [28], [35]. (a) (b) Figure 1.1: Overview of laparoscopic surgery. (a) Typical laparoscopic tools. Image courtesy of LUT (www.lut-endoscopy.com). (b) Schematic of laparo- scopic surgery, where small incisions are made and a camera and tools are inserted through the incisions. Image courtesy of www.beltina.org. Of particular interest is partial nephrectomy surgery, which is a surgical treatment of renal (kidney) cancer. Kidney cancer is the sixth most diag- nosed malignancy, responsible for 2.6% of cancer related deaths in Canada. 5100 diagnoses are expected in Canada in 2011, with 1650 patients expected 1 1.1. Motivation to succumb to the disease (Canadian Cancer Statistics 2011: www.cancer.ca). When a patient is suspected of having renal cancer, a diagnostic computed tomography (CT) scan is obtained [33]. The CT images are used to verify the tumor presence, to select the appropriate surgical option, and to aid in sur- gical planning. The surgical options are radical or partial nephrectomy. In partial nephrectomy surgery, the tumor is removed from the affected kidney, while in radical nephrectomy surgery the entire kidney is removed. Partial nephrectomy is the preferred option because it removes the cancer while pre- serving renal function, and it is currently a standard of care for tumors under 4 centimetres in size [19], [28], [33]. When performed laparoscopically, it is a very technically challenging operation, requiring intra-corporeal suturing. As well, surgeons have only 30 minutes of warm ischemia time (no blood flow to the kidney) to complete resection of the tumor and reconstruction of the surgical site, further compounding the technical challenge [33]. The operation also suffers from the general laparoscopic limitations of reduced surgeon dexterity and a limited field of view [60]. Due to its complex nature, there are a limited number of centers that offer this surgical option for renal cancer treatment [38]. Overcoming these limitations requires the use of emerging technology in the areas of robotics and medical imaging. Robotic assistance with the da Vinci Si surgical robot (Intuitive Surgical, Sunnyvale, California) can pro- vide surgeons with improved dexterity through 7 degree-of-freedom (DOF) robotic tools [53]. The system (Fig. 1.2) offers precise motion by filtering tremors in the surgeon’s hand and by offering motion scaling for very deli- cate movements. As well, the system’s stereo cameras provide surgeons with a 3D view of the surgical site. However, information about the sub-surface anatomy remains unavailable. This information could improve guidance significantly by giving the surgeon information about underlying structures including the location of major blood vessels, nerves and tumors. This could in turn improve the outcomes and availability of robotically assisted laparo- scopic partial nephrectomy (RALPN). Improving surgical guidance in RALPN surgery involves bringing vari- ous medical images of the kidney anatomy into the surgical field of view of the surgeon. CT images show the kidney anatomy and pathology in great detail, with low noise and excellent contrast. They are already obtained pre-operatively for diagnostic purposes [33], but cannot be obtained intra- operatively. These images are currently used for surgical guidance, although they cannot show changes in the position of the anatomy (due to patient positioning) or in the tumor size that occurred since the diagnosis. Ultra- sound (US) can be taken both pre-operatively and intra-operatively, being 2 1.1. Motivation Figure 1.2: The da Vinci Si Surgical System by Intuitive Surgical. Image courtesy of Intuitive Surgical (www.intuitivesurgical.com). a portable and real-time imaging modality, and shows different aspects of anatomy and pathology. Ultrasound images have the drawback of increased noise and a smaller field of view than CT. A combination of real-time ultra- sound and pre-operative CT would greatly improve image guidance during surgery, accounting for tissue shifts via ultrasound and showing the anatomy in great detail via CT. This motivates the development of improved CT-to- ultrasound registration algorithms which align the pre-operative 3D CT im- ages and the intra-operative 3D ultrasound images. A third imaging modal- ity of interest is ultrasound elastography, which displays the mechanical properties of the tissue being imaged (elasticity and viscosity). This is par- ticularly useful in identifying tumor margins because the stiffness of tumors generally differs significantly from surrounding tissue [57]. Elastography is still in the research stage, and improvements to the methods of obtaining elastographic images are needed to make elastography clinically feasible for a variety of applications. In particular, methods of measuring contact forces at the interface between the ultrasound transducer and the tissue would be very beneficial in solving the inverse problem of calculating tissue stiffness from displacement measurements. The three imaging modalities of ultrasound, CT and ultrasound elastog- raphy are key ingredients for improving image guidance in RALPN. Con- ventional ultrasound can provide real-time images during surgery, and CT 3 1.2. Thesis Objectives can be fused with the ultrasound to show more detailed information about the anatomy. The ultrasound can at the same time provide elastography images which show the stiffness of the tumor and surrounding tissue, de- picting tumor margins more clearly. The goal of this research work is to contribute to integrating ultrasound, CT, and ultrasound elastography into RALPN surgery. This will enable surgeons to perform RALPN surgery more accurately and efficiently, improving patient outcomes, and contributing to improved health-care. 1.2 Thesis Objectives The objective of this thesis is to contribute to the areas of CT-to-US regis- tration and ultrasound elastography through the use of modified ultrasound stand-off pads. Stand-off pads are commonly used for imaging superficial structures in ultrasound. The stand-off pad is placed between the ultra- sound transducer and the patient’s skin, increasing the distance between the two. This provides better quality images of structures located near the skin’s surface, which would otherwise be too close to the transducer to im- age properly. Currently they are not widely used for any other purpose. Our goal is to use stand-off pads to create a rigid registration algorithm for CT-to-US registration and to create a force profile sensor for ultrasound elastography. More specifically: 1. A stand-off pad containing fiducials is hypothesized to be a practical alternative to existing CT-to-US rigid registration techniques which take place at the time of the CT. This registration will form part of the first step in the registration of pre-operative CT to intra-operative ultrasound (see Fig. 2.1 in Chapter 2). The performance of this ap- proach is studied and compared to the incumbent tracker-based reg- istration approach. The fiducial stand-off pad should provide similar accuracy to the tracker-based method, while at the same time being easier to use and to integrate into medical imaging protocols. 2. A stand-off pad containing a scattering medium is hypothesized to be able to provide a pressure/force profile measurement at the interface of the ultrasound transducer and the tissue. These measurements can improve elastography images by providing absolute values of tissue elasticity and can provide more inputs to the problem of solving for tissue elasticities. The displacement in the stand-off pad under an ap- plied force is extracted, and converted to a force profile through the 4 1.3. Thesis Outline use of finite element models. The feasibility of this force profile sensor is tested by validating our ability to track motion within the stand-off pad, by simulating the stand-off pad in use for force measurements, by validating force measurement accuracy in experiments, and by imple- menting a complete force measurement system on existing ultrasound machine architecture. 1.3 Thesis Outline This thesis is presented in a manuscript-based style as per the guidelines of the Faculty of Graduate Studies at the University of British Columbia. Each research chapter represents a body of work that has been or is ready for submission to a peer-reviewed publication. Each research chapter con- tains a brief introduction to the research presented, a description of the methodology used, results and discussion of experiments and conclusions. The contributions of each chapter are as follows: 1. Chapter 2 contains a relevant literature review of CT-to-US regis- tration, discussing the current techniques and applications. It also contains a pertinent introduction to ultrasound elastography, tissue motion-tracking algorithms and the use of force measurements in elas- tography. This background shows the current state of technology and demonstrates where stand-off pad based methods will fit in. 2. Chapter 3 contains the overview, methodology, results and discussion of implementing a novel image registration technique using a fiducial stand-off pad. A stand-off pad containing fiducials is attached to a patient during CT and ultrasound scans. The fiducials are aligned between the 3D image sets to register the images. The results of a controlled study using tissue-mimicking phantom are presented, which demonstrate suitable registration accuracies. The results of a small pa- tient study are included that demonstrate its clinical usefulness and practicality. The fiducial stand-off pad registration technique shows comparable accuracy to incumbent tracker-based CT-to-US registra- tions. 3. Chapter 4 contains the overview, methodology, results and discus- sion of implementing a stand-off pad based force measurement system for ultrasound elastography. A stand-off pad containing a scattering medium is located between the ultrasound transducer and the under- lying tissue. The stand-off pad is compressed and decompressed in 5 1.3. Thesis Outline a controlled study, and the motion of the scatterers is tracked using various speckle tracking algorithms. FEM models and ultrasound field simulations are used to validate this force measurement system, and the force measurement accuracy is also found via experiments. The force measurement errors of this approach are approximately 10%. 4. In Chapter 5, the thesis is summarized and major contributions are highlighted. The strengths and weaknesses of the research in both registration and elastography are presented, as well as future research directions and possibilities. 6 Chapter 2 Background 2.1 CT to US Registration Image registration is the process by which different images (2D or 3D) of the same object are properly aligned (e.g. CT and ultrasound images of the kidney) and is central to improving image guidance in RALPN. CT-to-US registration is of particular importance, as it is a first step in the larger goal of bringing pre-operative 3D CT and real-time 3D ultrasound images into the field of view of a surgeon. An overview of this entire procedure is as follows: pre-operative CT is registered to intra-operative ultrasound, and the intra-operative ultrasound is registered to the robot’s stereo cameras (which constitute the surgeon’s view). This first step of registering pre- operative CT and intra-operative ultrasound is also broken into two steps. First, pre-operative CT is registered to the pre-operative ultrasound, and then the pre-operative ultrasound is registered to intra-operative ultrasound during the actual surgery (Fig. 2.1). Figure 2.1: Methodology for registering pre-operative CT to intra-operative ultrasound. The pre-operative 3D CT is registered to pre-operative 3D US (at the time of the CT), and then the pre-operative US is registered to intra-operative US (at the time of surgery). The first step (highlighted) is the focus of the work in this thesis. 7 2.1. CT to US Registration The advantage of this approach is that a less complex mono-modality reg- istration (US-to-US) is performed during the surgery, leaving the more chal- lenging task of multi-modality registration to the pre-operative stage when time constraints are of less importance. An alternative to this two-stage approach is to attempt a more difficult direct registration of pre-operative CT to intra-operative ultrasound. The first step in the proposed approach is the registration of pre-operative CT to pre-operative ultrasound. This registration is essential in ensuring that the final registration is accurate, and is the focus of the image registration research in this thesis. The conventional approach to such a CT-to-US registration is based on tracking the position of the ultrasound probe in space with an optical or elec- tromagnetic tracking system [13], [32], [64]. To perform a registration, the ultrasound images are calibrated with respect to the ultrasound probe, which is tracked in space using, for example, infrared LEDs attached to the probe which are visible to a trinocular camera system [64]. The CT images are calibrated with respect to the tracking system reference frame. The steps of ultrasound-to-probe calibration, probe tracking and tracker-to-CT calibra- tion are combined to realize the CT-to-US registration transformation (see Fig. 2.2). Tracker-based registrations are susceptible to organ motion (from, for example, respiration). In one study, registration errors were found to be 13 millimeters for landmarks inside the body in abdominal scanning [32], due mainly to respiration. As well, this approach requires a tracking sys- tem to be set up in the CT scanning area, which can be cumbersome and undesirable. Patient motion in the interval between the ultrasound and CT scans also introduces errors, although these might be mitigated by adding trackers to the patient. A similar registration approach is used in External Beam Radiation Therapy (EBRT) for the treatment of prostate cancer. A B-mode Acquisi- tion and Targeting ultrasound system (BAT) is used to acquire ultrasound images of the prostate [12], [34]. The ultrasound probe is attached to a positioning arm which tracks its 3D position. The arm and CT scanner are calibrated to a global reference frame using a docking station for the BAT system. The registration is performed using these calibrations and ultra- sound probe positioning, in a similar manner to the external tracking case described above. Refinements to the registration are made manually by vi- sually aligning the prostate boundaries. In a study of 35 patients [34], this system gave registration errors between the CT and ultrasound of up to 7.0 millimeters in the anterior/posterior direction, 6.4 millimeters in the lateral direction, and 6.7 millimeters in the superior/inferior direction. The com- bined multi-modality pre-operative registration and mono-modality intra- 8 2.1. CT to US Registration Figure 2.2: A schematic of the calibration and tracking steps in the conven- tional tracked ultrasound method for CT-to-US registrations performed at the time of the CT. operative registration (Fig. 2.1) has also been explored for EBRT with a mean target registration accuracy of 2.5 millimeters [69]. Point-based or fiducial-based registration methods are similar to tracker- based methods in that they provide a rigid registration to align image sets. In these registrations, markers are implanted or attached to the patient and point-to-point matching is used to align two sets of images. The markers are referred to as fiducials or fiducial markers, and come in many forms. They may be intrinsic, including distinct anatomical features (e.g. a bone feature), or may be extrinsic, including hollow cylinders, wires, beads or even surgical staples, which are embedded in or attached to the patient [22], [31], [37], [42]. Fiducial based registrations have been most widely used in neurosurgery, hip surgery and radiotherapy, where the anatomy is essentially rigid [20]. Typically the fiducials are attached directly to the patient, by embedding them in the patient’s skull for example, and standard medical image volumes are obtained (MR, CT, US). During surgery, the fiducial markers are touched with a position sensor to register the images to the surgical space. Fiducial- based methods are not widely used for the registration of soft tissue because soft anatomy is subject to deformation and shifts. In some cases, it may be possible to achieve registration by simply align- ing the anatomical features in the CT and ultrasound images (known as feature-based registration). Many such registration algorithms have been reported in the literature, including some specifically for CT-to-US registra- 9 2.1. CT to US Registration tion. Brendel et al. [10] registered CT and ultrasound datasets of the spine by matching surfaces and bone structures, with an accuracy of 0.5 millime- ters. Maes et al. [40] used mutual information to successfully register CT, magnetic resonance (MR), and positron emission tomography (PET) im- ages with an accuracy of 1 millimeter, and Rusinek et al. [56] aligned 3D brain scans (various modalities) using the centroid and principal axes of the brain, with an accuracy of 1–2 millimeters. Algorithms differ with respect to the amount of user interaction, the need for initialization, the speed of registration, the organ of interest and the dimensions of the image data (i.e., 2D or 3D). Image-based multi-modality registration is a difficult problem, especially if it is required to operate reliably on a wide range of patients in a clinical setting, and research in this area is therefore ongoing. Most feature-based registration methods require initialization to work effectively. Iterative Closest Point (ICP) is a well-known algorithm used to match point clouds extracted from 3D images [8], and its use in medical image registration has been widely reported [25]. Initialization with an ap- proximate alignment is required to ensure that the true optimum is reached since it is an iterative procedure and susceptible to local minima. A similar but more robust algorithm is the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which finds the true optimum more reliably, though at the expense of increased computational cost [24]. Again, initialization of the registration is useful. Capture ranges (i.e. the required accuracy of the initialization) can vary for feature-based methods. ICP works well with less than 30 degrees and 30 millimeters of misalignment [73]. Another exam- ple, which used simulated ultrasound images to register CT and ultrasound (via CMA-ES), required 15 millimeters or less of initial misalignment for the algorithm to work reliably [74]. In a third example, where ultrasound datasets were registered using mutual information, the capture range was 24–44 millimeters [59]. The capture range and registration accuracy depend on many factors, including the complexity of the shape of the surface, errors in surface localization, and the registration algorithm. Some systems use a marker or tracker-based registration to initialize the subsequent feature-based registration procedure. One example is the registration of bone surfaces between pre-operative CT and intra-operative ultrasound [3]. The registration is initialized using anatomical landmarks (which are easily determined with bone structures), and ICP is used to fine- tune the registration. In another example, tracked ultrasound is used to initialize a feature-based approach which uses simulated ultrasound images for the registration of soft tissue [71]. Such a combination may be necessary to account for organ motion due to breathing which is difficult to estimate 10 2.2. Ultrasound Elastography with external trackers. In such cases, the errors in the tracker-based regis- tration are acceptable so long as they fall within the capture range of the subsequent feature-based registration. The fiducial stand-off pad method- ology will provide a simpler method of obtaining this rigid-body CT-to-US registration which can be used to initialize feature-based registrations. 2.2 Ultrasound Elastography Elastography is an emerging imaging modality which displays tissue dis- placements, strains and mechanical properties rather than visible features. This is of particular importance in cancer diagnoses, where the mechanical properties of soft tissue are affected by the presence of cancer [46]. The difference in stiffness between the tumor and the surrounding tissue is the basis of palpation, which is widely used for diagnoses of breast and prostate cancer [11], [43]. However, palpation is generally limited to large super- ficial tumors, and its effectiveness has come into question [7]. With the advent of various imaging modalities (mammography, CT, and MRI), med- ical imaging began to play an important role in the diagnoses of cancer. Mammography is used widely in breast cancer screening, using x-rays to achieve high resolution images. CT is used for a variety of cancer diagnoses, including lung, pancreatic and kidney cancers [21], [33], [62]. Both mam- mography and CT expose the patient to radiation, which can be linked to carcinogenesis, though the benefits often outweigh the risks [44], [61]. MRI is used for the diagnosis of a wide variety of cancer types without any ra- diation exposure risk to the patient. However, it is expensive and therefore not widely used for cancer screening. All of the above modalities are not well-suited for real-time imaging during cancer surgery. Ultrasound elastog- raphy has the advantages of low cost, no radiation exposure and portability, making it suitable both as a diagnostic tool and for use in real-time surgical guidance for cancer surgeries. This includes, of course, renal cancer and partial nephrectomies, which are the focus of this work. Elastography is based on measuring the motion of tissue while it moves from an undeformed to a deformed state. This is done by applying either a static pressure (quasi-static elastography) or vibration (vibro-elastography) to the tissue and measuring the resulting tissue motion using common imag- ing modalities [6], [36], [46], [55]. The two modalities that are most often used are MRI and ultrasound, each with benefits and drawbacks. MRI provides a high signal-to-noise ratio (SNR), and offers equal resolution of motion estimates regardless of direction [47], while ultrasound is portable, 11 2.2. Ultrasound Elastography inexpensive, and is simpler to set up and use. This has made ultrasound elastography more widely studied than MRI elastography [17], [46], [66], [68]. 2.2.1 Motion Estimation Ultrasound imaging works by measuring the echo response of an ultrasonic pulse transmitted from an ultrasound transducer. The echo response is recorded over time, with the received signal corresponding to scatterers in the imaged material that are encountered by the transmitted pulse as it propagates from the transducer. The 1D echo signal is called a radio- frequency (RF) line, since the frequency is in the mega-Hertz range. Dis- placements are typically measured along the axial direction of the ultrasound transducer (Fig. 2.3), though the complete displacement field would also re- quire measurements in the lateral and elevational directions. When a particular scatterer moves by some amount in the axial direction (due to tissue compression), the position of the echo response of that scat- terer shifts by a proportional amount in the received RF signal (Fig. 2.4). Since the size of the shift is measured in units of time, estimators which exploit this property to measure displacements are known as time delay estimators. Tracking of displacements in the lateral direction of the trans- ducer is also possible, but has much lower spatial resolution (to compare, the axial spatial resolution is 20 microns, while the lateral resolution is 300 microns, as in Fig. 2.3). Improvements have been made to the reso- lution of lateral tracking through spatial compounding of the ultrasound signal [50], and through the use of two ultrasound transducers mounted per- pendicularly to each other [1]. Tissue deformation results in a change of shape of the signal along with the shift, causing it to either compress or stretch. In order to overcome this and improve the displacement estimates, stretching algorithms (both global and adaptive) have been proposed and implemented [2], [67]. The most common methodology for displacement tracking finds the max- imum or minimum of a pattern-matching function to match segments of a reference signal with the time-delayed signal (Fig. 2.4). The reference sig- nal is divided into equally sized, equally spaced overlapping windows. The pattern-matching function is then used to find the location of the best match between a reference window and the time-delayed signal. Common pattern matching techniques are to find the peak of the cross-correlation function of the two signals [46], [76], or sum absolute differences [9]. Furthermore, neighboring windows generally have similar displacements, which can be ex- ploited to speed up the motion estimation. This has been implemented in 12 2.2. Ultrasound Elastography Figure 2.3: Overview of an ultrasound transducer as used in elastography. Shown are the principal directions of the transducer, two sample RF lines (a typical transducer will have 128), and the relative spatial resolutions in the axial and lateral directions. an algorithm called Time Domain Cross-Correlation with Prior Estimates (TDPE) [76], which is used extensively in the research work in this thesis. With window-based algorithms, the number of displacement measure- ments is much lower than the number of data points. Several feature-based algorithms have been developed which produce a higher measurement reso- lution by tracking the motion of features. These include the zero-crossings of the signal, each individual sample in the signal, or the peaks of the sig- nal [16], [77]. With sample tracking (ST) and zero-crossing tracking (ZCT), the reference RF signal is interpolated using splines and the location of each sample or zero-crossing in the compressed signal is found using the spline coefficients. With peak-tracking, a continuous wavelet transform of 13 2.2. Ultrasound Elastography Figure 2.4: Overview of time delay estimators. (a) A window of the uncom- pressed signal with the corresponding window in the compressed signal. (b) The cross-correlation function used to determine the time delay. the reference signal is taken, and the peak locations tracked [16]. The mea- surement resolution of each of these methods is as high as the number of features available. However, these methods are generally more sensitive to noise in the data [77]. A combination of window and feature-based algo- rithms is also possible, with the window-based method providing a course displacement measurement, and the feature-based algorithm used to fine- tune the measurements. An example of this is the combination of TDPE and ST [77]. Each motion-tracking algorithm allows tissue motion to be tracked along each RF line individually, for all of the RF lines in an ultrasound transducer (typically 128). Thus an axial displacement field is obtained for a region 14 2.2. Ultrasound Elastography of interest (ROI) in the imaged tissue, which can be further analyzed to reconstruct local mechanical properties. 2.2.2 Tissue Property Reconstruction A number of methods are used to obtain estimates of the local tissue prop- erties from the displacement data, with the results typically displayed to the user as an elastogram (see Fig. 2.5 for an example). In the simplest case, the motion estimates are used to calculate local strains by taking the spatial gradient of the displacement data. The local strains are related to the Elastic Modulus (EM) using Hooke’s Law of elasticity by assuming a uniform stress field (i.e. a direct mapping of strain to elasticity). However, the image will contain artifacts wherever the uniform stress assumption does not hold. In order to obtain absolute values of elasticity, the magnitude of the stress field must be known. Because it is assumed constant, this can be done by measuring a stress profile at the boundary of the material being imaged. Figure 2.5: A sample elastogram which displays the stiffness of the tissue. A circular occlusion is visible in the tissue which has a higher stiffness than the surrounding tissue. A more accurate method is to use the displacement measurements and boundary conditions as inputs to an inverse problem which outputs the local elasticities. This takes the non-uniform stress field present in the tissue into account, giving more accurate estimates of elasticity. The inverse problem is so-called because there is no closed-form solution to find the local elastic- ities. It corresponds to the forward problem which finds local displacements 15 2.2. Ultrasound Elastography based on a known stress field and known local elasticities. A variety of algo- rithms have been developed and implemented to solve the inverse problem. One method models the tissue in the axial direction as a series of Voigt elements (spring-damper), and extracts the transfer functions between ele- ments based on measured local displacements and applied frequency. The transfer functions are analyzed to obtain elasticity and viscosity [17], [66]. In this approach, one of the elements is set as a reference, and all elastici- ties are found relative to the reference element. If a force measurement is available at the surface of the tissue, absolute values of elasticity can be found. There are also a number of finite element model (FEM) based meth- ods that have been developed [18], [79]. The tissue is modeled with finite elements, and the elasticity and viscosity is found by minimizing an objec- tive function such that predicted displacements (based on known boundary and loading conditions) match measured displacements as closely as possi- ble. This approach gives absolute values of elasticity, and requires either displacement or force measurements at the boundaries of the tissue. In the method presented by Zhu et al. [79], the only boundary condition required is the surface force at the compressor. Force arrays are suggested as the means to obtain the measurements, but this has not been implemented in their work. In the work of Liu et al. [39] and Wang et al. [70], reconstruc- tions of the breast are performed based on a non-linear FEM model, where boundary forces at the surface are again used as the boundary condition input in the inverse problem. MEMS pressure sensors are suggested for ob- taining the force measurements, though, as with the previous case, this has not been implemented in their work. Another methodology to find local tissue elasticities, called mechanical imaging, has been developed for reconstructing the properties of the breast and prostate [14], [15]. A force sensor array is pressed against the breast or prostate, thereby mimicking palpation. The number of sensors in the array depends on the application, with 192 used for the breast, and 128 used for the prostate. Coupled with a priori knowledge of the organ shape, size and location, elasticity images are displayed in real time. This approach does not use ultrasound imaging at all, but force measurements are the backbone of this technique, so advancements in force measurement methods would be useful. It is clear that there are a wide variety of elastography algorithms in which accurate force measurements are useful for either improving results, or serve as the main inputs to the algorithm. In relation to this, there has been some work done in measuring boundary pressures or forces in ultrasound for 16 2.2. Ultrasound Elastography use in elastography. The first method is to use pressure or force sensors or arrays at or around the ultrasound transducer. A very simple version of this is presented by Yuan et al. [75], where the ultrasound transducer was centered in a plate containing force sensors. The force distribution on the probe face was found by interpolating the force sensor data. The 3D stress field throughout the tissue was estimated based on these measurements. This approach yielded a low spatial resolution force profile, as only ten force sensors were used. Another example is the film-type pressure sensor developed by Tsubai et al. [65]. The thin pressure sensors could be mounted directly to the face of an ultrasound transducer, with a small trade-off in signal quality. The spatial resolution of this force profile was also low, with only eight sensing elements across the transducer. The second method used for measuring force is a compliant layer of known stiffness placed between the transducer and the underlying tissue. This is used in industrial and research settings for robotic tactile sensors. In these applications, an ultrasonic transducer measures the distance between the transducer and the edge of the compliant layer, based on the time of flight (Fig. 2.6), and Hooke’s Law is used to compute the force. By pro- ducing an array of transducers, a tactile sensor can be manufactured, which is capable of giving a force profile over a larger area [27]. The reported measurement resolution of displacement of the rubber layer was 6.8 to 16.8 microns, depending on the material used [27]. These sensors depend on a large change in acoustic impedance between the compliant layer and the force-causing object, and thus are well suited to hard objects that would be encountered in an industrial setting. However, when objects of similar acoustic impedance to the compliant layer are used, much of the transmitted ultrasound enters the object, reducing the power of the received signal and hindering acquisition of accurate displacement measurements. This compliant layer approach was first mentioned with regards to elas- tography by Ophir, who wished to use it as an estimation of the stress field in tissue, assuming an axially constant stress field [46]. However, it was not implemented in his work. This idea was utilized by Matsumura et al. [41], who created a tissue phantom containing a layer of known elasticity in or- der to obtain absolute values of elasticity in elastograms. The displacement resolution reported in this compliant layer was 2 microns (corresponding to 0.02% strain). This information was used to solve the inverse problem by as- suming constant stresses along the axial direction of the ultrasound beams. The local elasticities were then calculated using Hooke’s Law, with the pres- sure estimate at the surface of the phantom and local strain estimates as inputs. 17 2.2. Ultrasound Elastography Figure 2.6: An example of a time-of-flight ultrasonic force sensor. The compliant layer has known stiffness, and deforms under applied force. The time of flight of the ultrasonic pulse determines the change in thickness, and thus the applied force. As apparent from the literature, force measurements at the ultrasound transducer would be very useful in solving the inverse problem for ultrasound elastography. However, there are few examples of working systems where a force measurement system has been implemented in conjunction with the elastography system. The use of a compliant layer is more easily integrated into various reconstruction algorithms than force sensors since a simpler setup is involved. As well, it is conceivably more reliable, since there are no sensors or additional electronics involved. The compliant layer could be used to provide a reference elasticity in the elastogram, to gage the overall stress in the material (assuming constant stress), or to provide more information about boundary conditions by giving the force distribution at the transducer. Thus it is clear that a stand-off pad based force measurement system would have significant benefits to elastography. 18 Chapter 3 Rigid Registration of 3D CT to 3D Ultrasound Using a Fiducial Stand-off Pad 3.1 Introduction This chapter presents a novel solution to the problem of registering 3D CT to 3D ultrasound at the time of the CT scan. This is an important step towards enabling registration of pre-operative CT to intra-operative ultra- sound, which could greatly improve surgical guidance in RALPN. Though there are many incumbent approaches for CT-to-US registration (see Sec- tion 2.1), there are two main drawbacks seen. In the case of tracked ultra- sound, there is a need for complex and bulky external equipment, such as optical tracking systems, to be located in the CT facility. As well, these registrations are multi-step, requiring two calibration steps and a tracking step. With current fiducial-based methods, the fiducials have to be phys- ically implanted in the patient. In the case of feature-based registrations (which are generally more accurate), the main drawback is the need for a reasonably accurate initial alignment to enable the registration. The solu- tion to these drawbacks can be found in the novel proposed fiducial stand-off pad to perform a rigid CT to ultrasound registration. The fiducial stand-off pad will directly register 3D CT and 3D ultrasound volumes with a rigid-body transformation in a single step. In the proposed paradigm, a stand-off pad containing fiducial markers visible in CT and ultrasound is attached to the patient during pre-operative scanning. These fiducial markers are aligned between the two image sets to obtain the rigid registration parameters (three translations and three rotations). This use of fiducials to register ultrasound and CT is not completely new, as seen in Chapter 2. Lewis et al. demonstrated ultrasound detection of fiducials for surgical navigation more than a decade ago [37]. The pro- posed technique differs in that it places the fiducials in the near-field of a 19 3.1. Introduction 3D ultrasound transducer, and uses a reusable stand-off pad to secure the fiducials to the patient. This eliminates the need to implant fiducials into the anatomy, which increases the ease of use and level of patient comfort. As well, fiducial-based methods have not been widely used in soft tissue registration up until now. This method is most well-suited to use with 3D ultrasound transducers, which have gained popularity in recent years, by allowing registration with a single acquisition of 3D ultrasound and 3D CT image volumes. This approach will also eliminate the need for bulky exter- nal equipment, and can provide the initialization necessary for subsequent feature-based registrations. The accuracy of this registration technique depends strongly on how well the fiducials can be localized in the 3D ultrasound. The localization accuracy may be negatively affected by placing the fiducials in the near-field of the ultrasound beam as planned. When traditional array transducers are used, the ultrasound beam is narrowest at the focal depth, while it is wider in the near and far fields (Fig. 3.1). In other words, the resolution in the lateral and elevational directions varies with depth, with much lower resolution in the near field. Although the focal point can be moved closer to the near field, there is a compromise between improving the image quality of the near field and maintaining the image quality of the far field of the image. Multiple transmit focal points can be used to maximize image quality in both near and far fields at the cost of decreased imaging speed. Figure 3.1: Typical ultrasound beam pattern for a linear array transducer. Localizing near-field fiducials has been shown by Poon et al. [48] to be feasible for use in calibrating tracked ultrasound. Small plastic beads were placed against the face of the ultrasound transducer as fiducial markers, and were successfully localized. The result was a system capable of calibra- tion accuracies of 5.1 to 5.5 millimeters (RMS). This shows promise for the localization of near-field fiducials for CT-to-US registrations. 20 3.2. Methods 3.2 Methods 3.2.1 Stand-off Pad Construction The registration of 3D volumes requires a minimum of three non-collinear fiducial markers visible in both CT and ultrasound. To improve the accu- racy of the registration and to allow for some undetected fiducials in the ultrasound image data, two extra fiducials were placed in the stand-off pad, for a total of five. The pattern also places two of the fiducials close together to make the pattern more obviously asymmetric, which allows corresponding fiducials between the two modalities to be easily determined (see Fig. 3.2). Polyvinyl chloride (PVC) was chosen as the pad material because of its durability and flexibility, so that it could conform well to a patient’s body. To create the stand-off pad, the PVC (Super Soft Plastic, Zeiner’s Bass Shop, Wichita, KS) was heated to 180 degrees Celsius in a beaker, while being constantly stirred with a magnetic stir rod. When transparent, a base layer of PVC was poured into a mold and allowed to cool. The thickness of this base layer was used to determine the total thickness of the pad. Five metal spheres (1 millimeter diameter) were placed in the desired pattern on the base layer as the fiducial markers. A thin layer (2–3 millimeters) of PVC was poured over the fiducials, sealing them inside the stand-off pad. A prototype stand-off pad with the chosen fiducial pattern is shown in Fig. 3.2. Because of the manufacturing process, some air bubbles unavoidably became trapped within the stand-off pad, which may cause artifacts in ultrasound images of the pad. The stand-off pad was also enclosed in a latex-free ultrasound probe cover (GE Healthcare, Waukesha, WI) to prevent contact between the PVC and the patient’s skin due to the toxicity of PVC. Ultrasound coupling gel was liberally distributed inside the probe cover to prevent an air barrier from forming between the PVC and cover. Two stand-off pads were fabricated using this technique, with total thicknesses of 12 and 20 millimeters which were then used for image quality testing. 3.2.2 Ultrasound Image Quality The effect of each manufactured stand-off pad on ultrasound image quality was quantified to determine which stand-off pad to use for further testing. A thicker stand-off pad places the fiducials closer to the focal point, which should increase the accuracy of localization. However, it also causes in- creased attenuation leading to degraded image quality in the far-field where the organ of interest is located. A thinner stand-off pad results in less atten- uation, but the fiducials become harder to visualize, and the stand-off pad 21 3.2. Methods Figure 3.2: The prototype fiducial stand-off pad containing five fiducial markers. becomes more difficult to fabricate. A general purpose quality assurance ultrasound phantom (Computer Imaging Reference Systems Inc., Norfolk, VA, USA) containing point tar- gets and occlusions was used to measure the image quality. Each stand-off pad was placed on the phantom and images were taken by imaging through the stand-off pad. These images were compared to an image of the phantom taken with no stand-off pad. The lateral and axial resolution degradation was calculated by comparing the width and height of nine point features in the phantom located at different depths. The full width at half of maxi- mum (FWHM) was used in these calculations. The elevational resolution was calculated using nine line features in reconstructed ultrasound volumes. The line features were achieved by scanning the nine phantom point fea- tures perpendicular to the lateral/axial scan, so that the point features now appear as lines. The width (i.e. blurring) of the line features was measured in the reconstructed 3D ultrasound volumes and compared to compute the degradation in elevational resolution. Contrast ratios were calculated using three occlusion features in the phantom. The appearance of the feature as compared with the surround- ing background was used to compute the contrast ratio. The ultrasound machine parameters used for these tests are summarized in Table 3.1. 22 3.2. Methods Machine Parameter Setting Probe Frequency 5 MHz Focal Depth 7.6 cm Depth 15 cm Gain 48% Table 3.1: The ultrasound acquisition settings used for image quality testing. 3.2.3 Controlled Phantom Study Phantom Design A tissue-mimicking phantom was designed in order to obtain measures of the fiducial localization error (FLE), the fiducial registration error (FRE) and the target registration error (TRE). The phantom was made of agar gel because of its ease of fabrication. The gel was composed of 1.17% high gel-strength agar, 4% glycerol, 0.25% bleach and 94.58% water (by mass). The amount of glycerol is such that the speed of sound in the agar was 1540 metres per second, matching the speed of sound in tissue. The phantom contained eight phantom target fiducials, located 60 millimeters from the top of the phantom, well into the far-field of the ultrasound, approximating the location of the kidney. Metal spheres (1 millimeter diameter) were used as the target fiducial markers. During testing, the stand-off pad was secured to the top of the phantom and a layer of ultrasound coupling gel was deposited between the stand-off pad and the phantom to provide sufficient acoustic coupling. A schematic of the testing phantom is shown in Fig. 3.3. Data Acquisition A 3D CT scan of the testing phantom with the fiducial stand-off pad secured to the top was obtained using an Aquilion 64-slice CT scanner (Toshiba Med- ical Systems, Tustin, CA, USA). Then, with the stand-off pad still secured, 3D ultrasound volumes of the phantom were obtained using a Sonix RP ul- trasound system (Ultrasonix Medical Corporation, Richmond, BC, Canada). A 3D ultrasound transducer (4DC7-3/40), with 76 frames per volume, gave a field of view of approximately 55 degrees. The parameters of frequency, focal depth, gain and depth were varied between different ultrasound scans to verify that the registration process would be reliable regardless of what imaging parameters were used. The ultrasound parameter sets used during the experiments are summarized in Table 3.2. 23 3.2. Methods Figure 3.3: A schematic of the testing phantom with the fiducial stand-off pad secured to the top. The position of the ultrasound transducer is also indicated. CT-to-US Registration The first step of the registration was to manually select the centers of the stand-off pad fiducials (Cartesian coordinates) in both CT and ultrasound volumes using ITK-Snap software (University of Pennsylvania, Philadelphia, PA, USA). These coordinate points were used to calculate rigid registration parameters with the method of Horn et al. [26], implemented in MATLAB (MathWorks, Natick, MA, USA). Four stand-off pad fiducials were used to calculate the rigid registration parameters. The coordinates of the phantom target fiducials were also manually selected, and their positions recorded in both CT and ultrasound. Measures of the FLE, FRE and TRE were calculated using the fiducial locations and registration parameters. Descriptions of these errors are as follows. The FLE is a measure of how accurately the stand-off pad fiducials are located in ultrasound as compared with their true positions, without any registration step involved. Normally, the fiducial locations would be found 24 3.2. Methods Varied Parameter Varied Parameter Other Parameter Settings Settings (Constant) Focal Depth (4 cm) Probe Frequency (MHz) 2.5, 3.3, 4, 5 Gain (48%) Depth (15 cm) Frequency (5 MHz) Focal Depth (cm) 2, 4, 6, 8, 10 Gain (48%) Depth (15 cm) Frequency (5 MHz) Gain (%) 48, 51, 57, 63 Focal Depth (4 cm) Depth (15 cm) Frequency (5 MHz) Depth (cm) 9, 11, 13, 15 Focal Depth (4 cm) Gain (48%) Table 3.2: Ultrasound acquisition parameter sets used in phantom study. with respect to a global reference frame, and compared to their known global positions. Since there was not an easy way to do this in these experiments, the positions of the fiducials as found in CT were considered the true posi- tions, and a measure of the FLE was calculated using inter-fiducial distances. The distance between each of the stand-off pad fiducials was compared be- tween the CT and US data to indicate how well the stand-off pad fiducials can be localized in the lateral and elevational directions in ultrasound. The distances between each stand-off pad fiducial and all phantom target fidu- cials were compared between CT and US to indicate how well the fiducials can be localized in the axial direction. The mean and standard deviation in each direction (lateral/elevational and axial) were reported for each of the ultrasound parameter sets in Table 3.2 to show the effect of ultrasound parameters on the FLE. As well, a mean and standard deviation for all of the collected data was calculated to indicate the overall FLE. This measure of FLE is a relative measure, simply comparing how well the fiducials are localized in ultrasound as compared with CT. The FRE is a measure of how accurately the stand-off pad fiducials are aligned after the registration and was found by comparing the coordinates of the stand-off pad fiducials in the US volume with their positions in the registered CT volume. The root mean square (RMS) FRE for each ultra- sound parameter set is reported to show the effect of varying the ultrasound 25 3.2. Methods parameters. As well, the absolute FRE (mean and standard deviation) in each principal direction of the ultrasound transducer was found using all of the collected measurements. The TRE is a measure of how accurately the image as a whole is aligned and is usually the accuracy reported for any given registration method. It was calculated by comparing the Cartesian coordinates of the eight phantom target fiducials in the ultrasound volumes and in the registered CT volumes. RMS errors are computed for each parameter set to demonstrate the effect of US parameters on the TRE. The absolute TRE (mean and standard devi- ation) in each principal direction of the ultrasound transducer are reported (computed using data from all ultrasound parameter sets) to indicate the overall accuracy of the registration method. 3.2.4 Clinical Study An initial clinical study of three patients was undertaken to validate the reg- istration paradigm for kidney registrations in a clinical setting.1 In the initial study, the stand-off pad manufactured in Section 3.2.1 was used, while in the additional study a new stand-off pad was created that contained multiple fiducial patterns. This was meant to provide the sonographer with increased freedom in locating the transducer, since the entire stand-off pad now had fiducials. The study was done at Vancouver General Hospital after approval by the Clinical Research and Ethics Board. Subjects were recruited using signed consent from a list of patients scheduled for nephrectomy surgery. There were no exclusion criteria for subject participation. To obtain the necessary images, the subject was positioned in the flank position in the CT scanner and the stand-off pad secured to the subject’s side, near the kidney, using medical grade tape. Ultrasound volumes of the kidney were obtained by imaging through the stand-off pad (Fig. 3.4). The ultrasound machine parameters were optimized for a clear image of the pa- tient’s kidney, and the field of view of the ultrasound transducer was set to 75 degrees. Upon completion of the ultrasound scan, a standard diagnos- tic CT scan was taken, with the patient in the exact same position. The subject was requested to maintain a breath-hold on inspiration during the ultrasound scans and again during the CT scan to attempt to minimize respiratory movement of the kidney. The patient setup, stand-off pad place- ment and ultrasound imaging added an average of 10 minutes to the total 1Six additional patients were later added to the study, and the results of this work are found in Appendix A. 26 3.2. Methods time required of the patient in the clinic compared with only obtaining the diagnostic CT. Figure 3.4: Patient positioning and setup used during the clinical study. The patient is in the flank position and the stand-off pad is attached to the patient’s side above the kidney. The kidney is imaged through the stand-off pad with ultrasound, after which a standard diagnostic CT is taken. After the data acquisition was complete, the fiducials were segmented in both modalities using Stradwin 3.8 software [63]. The centroids of each fiducial were then computed based on the segmentation. The kidney was also manually segmented in both modalities using Stradwin 3.8, the segmen- tations read into MATLAB and the centroid of each kidney found. Either four or five fiducials were used for performing the registration, depending on how many fell into the ultrasound field of view. The rigid registration parameters were obtained in the same manner as in the phantom study. Us- ing these parameters, the CT image data was registered to the ultrasound coordinate frame and overlays of the kidney in ultrasound and in registered CT were generated and displayed. The quality of the registration could be qualitatively assessed by viewing the alignment of the renal structures. As well, a measure of the TRE for clinical data was obtained by calculating the displacement between the kidney centroids in ultrasound and registered CT. 27 3.2. Methods 3.2.5 Lever Arm Effect Error In this registration paradigm, the lever arm effect is a potentially significant error source. This results from the placement of the fiducials near the face of the ultrasound transducer, at the top of the image volumes. Therefore a small angular error in the fiducial registration, caused by errors in locating the stand-off pad fiducials, can result in large TRE values near the phantom target fiducials or near the kidney as illustrated in Fig. 3.5. Figure 3.5: An illustration of the lever arm effect. The white fiducials represent true locations; black fiducials represent locations with localization error. A small angular error in the fiducial registration can result in a large registration error of the target point. In determining the magnitude of the lever arm effect error, the worst case scenarios are considered, where each of the five stand-off pad fiducials is localized with the maximum FLE. The computation to quantify the lever arm effect was as follows. The positions of the stand-off pad fiducials as found in CT are considered to be the true positions. The centroid of the stand-off pad fiducials was calculated by averaging the fiducial coordinates, and a plane of best fit containing the centroid was found using least-squares regression. Then a target point was placed in line with the centroid and displaced in a direction perpendicular to the plane (see Fig. 3.5 as a guide). Two displacements of the target point from the plane were used; a displace- ment of 60 millimeters simulated the phantom study and a displacement 28 3.3. Results of 80 millimeters simulated the patient study. The fiducials were then per- turbed by the maximum FLE in each principal direction. For example, the maximum axial FLE (positive direction) and maximum lateral/elevational FLE (positive direction) constituted one perturbation. All combinations were applied for a total of 8 perturbations of each fiducial. The target point coordinates were recalculated for all combinations of perturbations, for a total of 32768 computations. The distance between the target point before and after perturbation was reported as the lever arm effect error for each case. This formulation is very conservative in assuming that each fiducial is always located with the maximum FLE. 3.3 Results 3.3.1 Ultrasound Image Quality Sample images used for calculating axial and lateral resolution and contrast are shown in Fig. 3.6, with the numerical results shown in Tables 3.3, 3.4 and 3.6. A sample image of the line features used to calculate the elevational resolution is shown in Fig. 3.7, with the numerical results shown in Table 3.5. When compared with the case of no stand-off pad, the axial resolution was degraded by 11% for the 12 millimeter pad, and by 32% for the 20 millimeter pad. The lateral resolution was degraded by 13% for the 12 millimeter pad and by 29% for the 20 millimeter pad. Finally, the elevational resolution was degraded by 6% for the 12 millimeter pad and by 7% for the 20 millimeter pad. Contrast was degraded by 5% for the 12 millimeter pad, and by 6% for the 20 millimeter pad. In both cases, the fiducials could be located without difficulty, and based on these results, the 12 millimeter pad was chosen to be used for the phantom and clinical studies. 3.3.2 Controlled Phantom Study Sample images of the phantom as seen in CT and ultrasound are shown in Fig. 3.8, showing the appearance of the stand-off pad and target fiducials in each modality. Fiducial Localization Error (FLE) The results for FLE are displayed in Fig. 3.9. These box and whisker plots show the minimum, maximum, median and 25th/75th percentiles of the er- ror measurement data. The FLE computed using inter-fiducial distances 29 3.3. Results Figure 3.6: Sample images used for determining stand-off pad effect on image quality. From left to right: CIRS phantom with no stand-off pad, with the 12 millimeter stand-off pad, and with the 20 millimeter stand- off pad. Ultrasound acquisition settings were used as per Table 3.1. The arrow indicates point feature target 1, with 2–9 below it in sequence; the circle indicates occlusion feature 1, with 2–3 below diagonally below it in sequence. Point Feature Axial FWHM (#pixels) No Pad 12-mm Pad 20-mm Pad 1 1.349 1.537 1.932 2 1.180 1.363 1.720 3 1.743 1.851 2.360 4 1.756 1.787 2.706 5 1.740 2.033 2.059 6 1.765 1.852 2.215 7 1.617 2.221 2.349 8 1.723 1.799 2.225 9 2.118 2.133 1.872 Mean Degradation N/A 11% 32% Table 3.3: Effect of stand-off pad thickness on axial resolution of ultrasound images. Ultrasound acquisition settings used are summarized in Table 3.2. Point feature numbering is indicated in Fig. 3.6. between the stand-off pad fiducials had a mean error of 2.38±0.93 millime- ters, giving a measure of the lateral and elevational FLE. The FLE computed using inter-fiducial distances between the stand-off pad and phantom target fiducials had a mean error of 1.34±0.80 millimeters, giving a measure of the 30 3.3. Results Figure 3.7: Sample image of line features used in calculation of elevational resolution effects. The arrow shows line feature 1, with 2–9 below it in sequence. Point Feature Lateral FWHM (#pixels) No Pad 12-mm Pad 20-mm Pad 1 3.763 4.252 4.038 2 3.170 3.796 5.391 3 5.103 6.169 7.727 4 5.206 5.688 6.492 5 4.753 5.263 6.393 6 5.281 5.520 5.797 7 4.822 5.296 5.799 8 4.928 5.450 6.241 9 5.119 5.898 6.010 Mean Degradation N/A 13% 29% Table 3.4: Effect of stand-off pad thickness on lateral resolution of ultra- sound images. Ultrasound acquisition settings used are summarized in Ta- ble 3.2. Point feature numbering is indicated in Fig. 3.6. axial FLE. There was no notable dependence of the FLE on the ultrasound machine parameters used. 31 3.3. Results Point Feature Elevational Feature Width (mm) No Pad 12-mm Pad 20-mm Pad 1 8.67 8.33 8.07 2 6.26 6.07 6.40 3 4.88 5.24 5.53 4 3.72 4.95 4.14 5 4.21 4.48 4.63 6 3.54 3.69 3.86 7 5.24 5.52 5.72 8 4.26 4.49 4.65 9 4.67 4.75 4.87 Mean Degradation N/A 6% 7% Table 3.5: Effect of stand-off pad thickness on elevational resolution of ul- trasound images. Ultrasound acquisition settings used are summarized in Table 3.2. Point feature numbering is indicated in Fig. 3.7. Occlusion Feature Contrast Ratio No Pad 12-mm Pad 20-mm Pad 1 0.202 0.279 0.362 2 0.374 0.294 0.255 3 0.503 0.340 0.175 Mean Degradation N/A 5% 6% Table 3.6: Effect of stand-off pad thickness on image contrast of ultrasound. Ultrasound acquisition settings used are summarized in Table 3.2. Point feature numbering is indicated in Fig. 3.6. Fiducial Registration Error (FRE) The RMS FRE results are shown in Fig. 3.10. The box and whisker plots in Fig. 3.11 show the minimum, maximum, median and 25th/75th percentiles of the FRE in each principal direction of the ultrasound probe. As with the FLE, there was no notable dependence of the FRE on the ultrasound ma- chine parameters used. The absolute mean FRE was 1.08±0.29 millimeters in the lateral direction, 0.46±0.33 millimeters in the axial direction, and 0.90±0.71 millimeters in the elevational direction. 32 3.3. Results (a) (b) Figure 3.8: Sample images of the testing phantom. (a) CT. (b) Ultrasound. Target Registration Error (TRE) The RMS TRE is shown in Fig. 3.12. The box and whisker plots in Fig. 3.13 show the minimum, maximum, median and 25th/75th percentiles of the TRE in each principal direction of the ultrasound probe. As with the FLE and FRE, there was no notable dependence of the TRE on the ultrasound ma- chine parameters used. The absolute mean TRE was 0.89±0.76 millimeters in the lateral direction, 1.84±0.95 millimeters in the axial direction, and 3.31±1.97 millimeters in the elevational direction. Controlled Phantom Study Results Summary The results for the phantom study are summarized below in Table 3.7. Lateral (mm) Axial (mm) Elevational (mm) Error Norm (mm) FLE 2.38±0.93 1.34±0.80 2.38±0.93 3.62 FRE 1.08±0.29 0.46±0.33 0.90±0.71 1.48 TRE 0.89±0.76 1.84±0.95 3.31±1.97 3.89 Table 3.7: Summary of errors in phantom testing in each principle direction. 33 3.3. Results (a) (b) (c) (d) Figure 3.9: FLE plotted against the various ultrasound parameters used. For each panel, the left plot indicates lateral/elevational errors (N=6) and the right plot indicates axial errors (N=32). (a) FLE vs. probe frequency. (b) FLE vs. focal depth. (c) FLE vs. gain. (d) FLE vs. depth. 34 3.3. Results (a) (b) (c) (d) Figure 3.10: RMS FRE plotted against the various ultrasound parameters used. (a) FRE vs. probe frequency. (b) FRE vs. focal depth. (c) FRE vs. gain. (d) FRE vs. depth. 35 3.3. Results Figure 3.11: Absolute FRE in the lateral, axial and elevational directions for all phantom test datasets (see Table 3.2). 36 3.3. Results (a) (b) (c) (d) Figure 3.12: RMS TRE plotted against the various ultrasound parameters used. (a) TRE vs. probe frequency. (b) TRE vs. focal depth. (c) TRE vs. gain. (d) TRE vs. depth. 37 3.3. Results Figure 3.13: Absolute TRE in the lateral, axial and elevational directions for all phantom test datasets (see Table 3.2). 38 3.3. Results 3.3.3 Clinical Study Samples of typical images obtained during the patient study are shown in Fig. 3.14, highlighting the stand-off pad fiducials as well as the patient’s kidney. Figure 3.14: Sample images from the clinical study, with CT shown on the left, and ultrasound on the right. Fiducial Registration Error The RMS FRE for each of the initial three patients is shown in Table 3.8, with the mean RMS FRE being 0.98±0.46 millimeters in the lateral direc- tion, 0.38±0.28 millimeters in the axial direction, and 1.61±0.45 millimeters in the elevational direction. The FRE values corresponded well with the re- sults of the phantom study. Patient RMS FRE (mm) Lateral Axial Elevational 1 1.21 0.70 2.09 2 1.29 0.25 1.19 3 0.45 0.19 1.56 Mean 0.98 0.38 1.61 Table 3.8: RMS FRE for three patients. 39 3.3. Results Target Registration Error The absolute TRE for each of the initial three patients is shown in Table 3.9, with overlays of the segmented ultrasound and registered CT kidneys shown in Fig. 3.15. The mean TRE in each of the principal directions was 7.64±6.91 millimeters in the lateral direction, 10.64±2.02 millimeters in the axial di- rection, and 1.48±0.85 millimeters in the elevational direction. Patient Kidney Centroid Displacement (mm) Lateral Axial Elevational Total 1 14.34 11.99 1.00 18.72 2 8.05 8.29 2.46 11.81 3 0.53 11.54 0.99 11.59 Mean 7.64 10.64 1.48 14.04 Table 3.9: RMS TRE for three patients. 40 3.3. Results (a) (b) (c) Figure 3.15: Overlays of clinical data for three patients after registration using the fiducial stand-off pad. The CT data is shown in blue and the ultrasound data in red. (a) Patient 1. (b) Patient 2. (c) Patient 3. 41 3.4. Discussion 3.3.4 Lever Arm Effect Error The lever arm effect errors are shown in Fig. 3.16. In the case simulating the phantom study, shown in Fig. 3.16(a), the mean lever arm error was 4.96 millimeters, and the maximum error was 17.16 millimeters. For the case simulating the clinical study, shown in Fig. 3.16(b), the mean lever arm error was 6.42 millimeters and the maximum error was 22.72 millimeters. The histograms in Fig. 3.16 show the error distribution for all tested per- turbations of the fiducials, indicating the low frequency of the maximum error. (a) (b) Figure 3.16: Histograms of lever arm effect errors. Bin size = 1 mm; N = 32768. (a) Lever arm effect errors for a target point 60 mm from the fiducials (simulates phantom study). (b) Lever arm effect errors for a target point 80 mm from the fiducials (simulates clinical setting). 3.4 Discussion 3.4.1 Ultrasound Image Quality The stand-off pad fiducials were clearly visible in the CT and ultrasound images, and were easily distinguished from any air bubbles trapped within the pad. Both the phantom target fiducials (controlled phantom study) and kidney (patient study) were still clearly visible despite the decrease in reso- lution and contrast. These decreases were caused by increased attenuation because of the pad as well as a speed of sound mismatch between the stand- off pad and quality assurance phantom (PVC has a speed of sound of 1420 42 3.4. Discussion m/s while the phantom speed of sound is 1540 m/s). The image degradation could be reduced with improvements to the stand-off pad construction. This would include using commercial stand-off pad techniques to eliminate the gel-filled cover around the pad, and to better match the acoustic impedance of the pad to that of the tissue. The decrease in image quality caused by the stand-off pad may be acceptable for this registration task. 3.4.2 Fiducial Localization Error The FLE results are smallest in the axial direction, as expected, since the resolution of ultrasound is the best in the axial direction. Conversely, the higher lateral/elevational error is due to poorer resolution in these direc- tions. This is especially true for the elevational direction where the fiducials appear oblong because of the wide beam width in the near field, making them more difficult to localize. The methodology used to calculate the FLE overestimates the error because it does not measure the FLE of each fidu- cial independently; rather, each error measurement is affected by the FLE of two fiducials. Additionally, as noted, the FLE does not depend strongly on the ultrasound parameters used, meaning these results are valid for typical usage of the ultrasound machine. This also implies that the FRE and TRE should be consistent across all ultrasound parameter sets since FRE and TRE depend on FLE. 3.4.3 Fiducial Registration Error The FRE computed in the controlled phantom study was also consistent with respect to the various ultrasound parameters, as expected based on the FLE results. Furthermore, the FRE is consistent between the controlled phantom study and the patient study. This is also expected because the FRE is not affected by underlying anatomy. This result confirms that in clinical usage, where the pad is secured to a patient, the fiducials are localized and registered with the same accuracy as in the controlled study. Lastly, the axial FRE is smallest because the ultrasound resolution is highest in this direction. 3.4.4 Target Registration Error The TRE computed in the controlled phantom study was also consistent across all the ultrasound parameter sets, as expected based on the FLE results. In the controlled phantom study, the lateral TRE was the smallest rather than the expected axial TRE. This is because the phantom target 43 3.4. Discussion fiducials showed some reverberation in the axial direction in the ultrasound images. This reduced the axial localization accuracy of the phantom target fiducials, causing a slight increase in the axial TRE. Aside from this, a combination of the fiducial localization in ultrasound and lever arm effect is the main source of TRE in the controlled phantom study. In the initial patient study, the error sources were more complex, re- sulting in much higher TRE values, particularly in the lateral and axial directions. As seen in Tables 3.7 and 3.9, the elevational TRE was similar to the phantom study. However, the axial error was consistently higher (ap- proximately 10 millimeters), and the lateral error showed a large variation between the data sets (0.5 to 14 millimeters).2 A portion of this lateral error (which was aligned with the long axis of the kidney) was a result of respira- tory motion of the kidney between the time of the ultrasound and the time of the CT. This also explains why there was so much variation in the lateral error between data sets, since the respiratory motion can vary greatly. A breath-hold was requested (after inspiration) to reduce respiratory move- ment of the kidney, but the consistency of the breath-hold taken at the time of the ultrasound and the breath-hold taken at the time of the CT is essen- tial, yet hard to manage. Incumbent CT-to-US registration methods based on trackers suffer from similar errors due to respiration. The paradigm used by Kaspersen et al. [32] produced a similar amount of TRE (13 millimeters), and respiration was cited as the largest error source. Moerland et al. [45] found that the kidney moves between 10 and 86 millimeters under forced respiration, and a similar study by Schwartz et al. [58] showed kidney mo- tion of 4-43 millimeters for deep respiration (both studies placed the patient in the supine position). Thus the amount of kidney motion caused by an inconsistent breath-hold can be significant. To improve the consistency of the breath-hold, a respiratory belt transducer could be used to synchronize image acquisition with a particular respiratory stage, such as full expiration. Other more complex solutions, such as predictive respiration gating could be used as well [52]. An additional source of error is the deformation of the stand-off pad un- der pressure from the transducer. This causes the stand-off pad to conform to the convex shape of the transducer, potentially changing the orientation of the fiducials when compared to the undeformed position at the time of the CT. In the phantom study and initial patient study, a single fiducial pattern was placed in the pad (see Section 3.2.1), meaning the transducer 2In the additional patient study (see Appendix A), the lateral errors show a similar range, from 5 to 18 millimeters. 44 3.4. Discussion had to be located directly above the fiducial pattern during imaging. This prevents the fiducials from changing their orientation when the transducer pressure is applied. However, in the additional patient study, multiple fidu- cial patterns were placed in the stand-off pad to provide the sonographer with more freedom in locating the transducer. This meant that fiducials not directly under the transducer were imaged and used for the registration. These fiducials are more susceptible to a change in orientation with applied transducer pressure, which can result in a large lever arm error. In particu- lar, this may have led to the higher elevational errors seen in the additional patient study, and the larger variation between patients. Based on these results, the single fiducial pattern is recommended in further work on this registration method. A large portion of the axial error is caused by compression of the tissue because of the applied pressure of the ultrasound transducer. This causes the skin-to-kidney distance to differ between the ultrasound and CT scans, lead- ing to an increase in the axial TRE. The amount of compression is dependent on patient physiology and the amount of pressure applied by the sonogra- pher, yet it explains the consistently large error in the axial direction found in the patient study. Comparison of the skin-to-kidney distance between the CT and ultrasound images in the initial study showed an approximate difference of 8 millimeters for Patient 1, and 10 millimeters for Patient 2 and 3.3 Therefore the probe pressure should be reduced if practical, or the alignment of the CT and ultrasound images should be adjusted according to the difference in the skin-to-kidney distance measurement. This registration paradigm is sensitive to respiration and probe pressure because it assumes that both the kidney and stand-off pad fiducials do not move between the CT and ultrasound. Traditional tracker-based approaches assume that only the kidney does not move. Since the probe motion is tracked, the tissue compression is accounted for, and only respiration is left as a major factor. With the stand-off pad method, this error is significant but consistent, and can thus potentially be adjusted for. Lever Arm Effect Error The results from the lever arm effect calculations (Fig. 3.16) indicate that this was the main source of target registration errors in the controlled phan- tom study. However, in this controlled case, the computed TRE is less than the average lever arm error. This is because the lever arm errors were cal- 3A similar situation occurred in the additional patient study (Appendix A) where the axial error was an average of 12 millimeters. 45 3.5. Conclusions culated with the assumption that each fiducial is always located with the maximum FLE. This very conservative methodology overestimates the lever arm effect. The lever arm effect was not predominantly seen in the initial clinical study results. The major misalignments in the registration were consistently along the long axis of the kidney (lateral direction of the probe) and in the axial direction of the ultrasound probe, as explained previously. None of the axial error is caused by the lever arm effect since the lever arm and axial direction are parallel. Concerning the long axis of the kidney, the direc- tion of misalignment should not be so consistent if these errors were caused by a lever arm effect. The stand-off pad is placed in different orientations with each patient, and the lever arm effect is not limited to a single direc- tion. The lever arm effect errors could be further reduced by performing the registration with a larger number of fiducials. In the additional patient study, lever arm effect was seen as evidenced by the larger registration errors in the lateral and elevational directions. However, as discussed above, this is likely the result a physical change in the orientation of the fiducial pattern caused by the deformation of the stand-off pad, as opposed to fiducial localization error alone. 3.5 Conclusions A simple and effective fiducial stand-off pad has been developed for regis- tering CT and ultrasound image volumes of the kidney, providing an FRE less than 2.5 millimeters in each principal direction. The trade-off is a small decrease in image quality, which can be mitigated with improvements in stand-off pad construction, including choice of material. The target reg- istration accuracy depends strongly on respiratory motion of the kidney, as well as the deformation of tissue boundaries. However, this registration paradigm is easily integrated into a clinical setting, since minimal additional equipment and setup is required, and the fiducials are attached to the patient with little effort. Thus it is also suitable for other applications of CT-to-US registration. The results of the initial and additional patient study show that the in-vivo registration accuracy is within the capture ranges of a number of de- formable or feature-based registration approaches introduced previously [8], [24], [59]. For these, the 12-29 millimeters of misalignment obtained with the fiducial stand-off pad registration is sufficient to initialize each approach. Additional work that will result in improvements to the registration accuracy 46 3.5. Conclusions and which will make this registration paradigm more versatile are presented in Chapter 5. This rigid registration of CT to ultrasound is one step towards providing surgeons with improved CT image guidance for RALPN procedures. Going beyond this conventional type of image guidance is the use of ultrasound elastography to show the mechanical properties of the tissue. The following chapter will discuss the contributions of using a stand-off pad in ultrasound elastography for improving elastography images. 47 Chapter 4 Force Profile Measurements Using a Compliant Stand-off Pad 4.1 Introduction This chapter presents the feasibility study of using a stand-off pad containing scatterers as a force profile measurement tool for elastography. Elastogra- phy enables the visualization of the mechanical properties of tissue, which can be very useful in cancer imaging [46]. As shown in Chapter 2, there are many available methods of solving for tissue properties to produce such im- ages. Several of these either depend on, or may benefit from, contact force measurements between the tissue and the ultrasound transducer. However, a force measurement system has been implemented in very few of these, with implementations of the algorithms tested only in simulations [39], [70], [79]. Two approaches are seen in the cases where a force-measurement imple- mentation has been achieved. The first is to use commercially available force sensors attached to the ultrasound probe, which requires either that the ultrasound beam passes through the sensors, or that the sensors are placed around the transducer face instead of on it. This will either degrade the image quality [65] or the force measurement accuracy at the transducer face [75]. The second approach is to use a compliant layer of known elastic- ity between the tissue and transducer in which the deformation is measured, and force measurements are computed using Hooke’s Law. This was the ap- proach suggested by Ophir [46], and implemented by Matsumura et al. [41]. In that implementation, the compliant layer was constructed as part of a testing phantom. It was not designed as a reusable device to be applied in various applications, and did not look at the challenges of using such a force measurement approach in a more realistic clinical setting. The compliant- layer approach has also been used for industrial ultrasonic tactile sensors which are best suited for contact with hard objects [27]. 48 4.1. Introduction The proposed force measurement stand-off pad is a reusable compliant layer that enables force profile measurements using a medical ultrasound system, and which may be used for a range of applications such as breast and liver elastography. There are two main benefits given by the stand-off pad approach. First, absolute measures of tissue properties can be obtained more easily, since the stand-off pad provides a fixed and known reference for elasticity and viscosity. Second, it will enable the inclusion of force measurements as a boundary condition for solving the inverse problem of calculating tissue stiffness from displacement measurements. The stand-off pad functions as follows. Compression is applied to the stand-off pad with the ultrasound transducer, and the stand-off pad deforms according to the amount of deformation applied and the properties of the underlying tissue, as illustrated in Fig. 4.1. Figure 4.1: Illustration of force measurement stand-off pad functionality. The deformation at each RF line is measured, from which a force profile can be computed using Hooke’s Law. A representation of the resulting force profile is also shown. In the simplest model, each RF line obtained from imaging the stand-off pad is treated as a 1D linear spring. If the stand-off pad stiffness and the deformation of the pad at each RF line are known, the force at each RF line can be computed using Hooke’s Law: 49 4.1. Introduction F = −k∆x, (4.1) where F = applied force (Newtons), k = spring stiffness (Newtons/meter), and ∆x = deformation of material (meters) Hooke’s Law can also be normalized, with the stress proportional to the strain along each RF line. This general linear stress-strain relationship is: σ = E, (4.2) where σ = stress/pressure (Pascals), E = material elasticity or Young’s modulus (Pascals), and  = strain With this methodology, the pad-tissue interface displacement must be tracked as force is applied, in a manner similar to industrial ultrasonic force sensors. However, this is not practical in a medical imaging application be- cause the typical pad-tissue interface produces a saturated echo in the RF signal, which hinders motion-tracking algorithms. Lowering the acoustic power of the ultrasound transducer negates this, but also severely degrades the image quality in the underlying tissue, rendering the images useless for elastography. Another option is to alternatively fire high and low power pulses which would be used for image generation and force measurement respectively. However, the problem may be compounded by the use of ul- trasound coupling gel at the pad-tissue interface, which moves and displaces under applied force from the transducer. Thus the echoes due to coupling gel cannot be distinguished from those caused by the interface, effectively obscuring the motion and behavior of the interface. In order to avoid the effects of tracking this interface alone, the stand-off pad is filled with a scat- tering medium which enables motion tracking throughout the stand-off pad. A region of interest (ROI) of each RF line is then selected to be up to but not including the saturated pad-tissue interface echo. This is illustrated in Fig. 4.2. Axial displacements are tracked throughout the ROI, and the dis- placement at the pad-tissue interface can be obtained by extrapolating this 50 4.1. Introduction displacement data. If required, axial strain can be computed by calculating the spatial gradient of the displacement data. (a) (b) Figure 4.2: Illustration of the region of interest in the force measurement stand-off pad. The pad-tissue interface creates a saturated response in the RF signal, so the RF signal is truncated just before the pad-tissue interface. (a) Schematic of the region of interest for a single RF line. (b) Entire region of interest shown in a B-mode image. In reality, the stand-off pad deforms in three dimensions as a function of the applied force, boundary conditions, and the material properties of the stand-off pad. This 3D deformation may also affect how the stand-off pad deforms in the axial direction, and may imply that the Hooke’s Law model for each RF line (mentioned above) is not suitable. The simplest model of 3D deformation is an isotropic material acted upon by compressive forces in a homogeneous manner. The resulting stresses and strains can be related by a 3D extension of Hooke’s Law, which indicates that deformation along one axis of a material will cause deformation along the other axes: i = 1 E [σi(1 + ν)− ν(σx + σy + σz)], (4.3) 51 4.1. Introduction where i = x, y, or z (three principle directions), and ν = Poisson’s ratio This can be further generalized to include the contributions of shear forces: ij = 1 E [σij(1 + ν)− νδijσkk], (4.4) where i, j = indices which indicate direction (see Fig. 4.3), σkk = σx +σy +σz = σ11 +σ22 +σ33, and δij = Kronecker delta function Similarly, in the more general case where an object is subject to a variety of loads and constraints (Fig. 4.3), the stress and strain at any point within the object can be described using second order tensors, shown in Eqns. 4.5 and 4.6. σ =  σ11 σ12 σ13σ21 σ22 σ23 σ31 σ32 σ33  (4.5)  =  11 12 1321 22 23 31 32 33  (4.6) In some cases, it is possible to simplify the 3D model to a 2D model through appropriate plane stress or plane strain assumptions. The plane stress case is used where one dimension of an object is much smaller than the others, and the loading is such that the principal stress along this dimension is approximately equal to zero. The plane strain case is used where one dimension of the object is constrained, so the principal strain along this dimension is assumed to be equal to zero. The use of these assumptions depends on the geometry of the object and the loading conditions that it is subjected to. Understanding and modelling the actual 3D deformation of the stand-off pad is essential to creating a feasible force sensor. 52 4.2. Stand-off Pad Development Figure 4.3: An illustration of a general mechanical loading scenario. 4.2 Stand-off Pad Development As mentioned, the force measurement stand-off pad must contain scatterers which enable motion-tracking algorithms. Typically, this requires a scatterer density of 40 scatterers/mm3 [51] to provide fully developed speckle in the ultrasound images. As well, the material used must be durable and stable to ensure reusability, meaning its mechanical properties must not change over time. Common tissue-mimicking materials used in phantom construc- tion were considered, including agar, gelatin, poly-vinyl alcohol (PVA) and poly-vinyl chloride (PVC). Agar and gelatin were ruled out because of their tendency to crack when compressed. PVA is non-toxic and easy to manu- facture, but its properties depend on how wet or dry the material is at a given time, requiring the stand-off pad to be sealed in plastic for stability, which may affect the mechanical behavior. PVC is toxic, but is stable and durable. Due to the toxicity, a transducer cover and a layer of coupling gel are necessary to protect the ultrasound transducer (and patient) from the material, similar to the fiducial stand-off pad used in Chapter 3. In- troducing coupling gel between the transducer and stand-off pad can affect the manner in which motion is transmitted from the transducer to the pad (since the gel displaces under compression), making it unsuitable in this force-measurement application. In place of common tissue-mimicking materials, a custom-designed stand- off pad was manufactured by Blue Phantom (Redmond, WA, USA) from their proprietary tissue-mimicking material. This material is durable and 53 4.3. Methods - Stand-off Pad Properties non-toxic so that the ultrasound transducer can come into direct contact with the pad, and its properties are stable over time. The speed of sound was specified to match the speed of sound in tissue, 1540 m/s, and this was verified by further testing (see Section 4.3.1). The finalized stand-off pad contains the required level of scatterers to enable motion-tracking and has dimensions of 125 by 65 by 12 millimeters (see Fig. 4.4). Unless otherwise noted, this particular stand-off pad geometry was used in all experiments described in the following sections. The mechanical properties of this material are also an important factor in using the stand-off pad to obtain force measurements. It is a heavily cross-linked elastomer exhibiting viscoelastic behavior, meaning that there is a transient response of the material to mechanical loading. As well, the material is isotropic and nearly incompressible (Poisson’s ratio, ν, is nearly 0.5). Elastomers also exhibit non-linear elasticity over large deformations (greater than 15% strain), and are typically hysteretic between the loading and unloading stages of a deformation due to the dissipation of energy as the material is loaded. Nevertheless, under certain conditions (e.g. small loads), a simple static model of mechanical properties can suffice. Figure 4.4: The prototype Blue Phantom force measurement stand-off pad. A photograph of the 125 by 65 by 12 millimeter stand-off pad (left) and its appearance in an ultrasound B-mode image (right) are shown. 4.3 Methods - Stand-off Pad Properties 4.3.1 Stand-off Pad Speed of Sound The speed of sound (SOS) of the Blue Phantom material is used for con- verting the units of tracked displacements from samples to microns (see Eqn. 4.7), which is an essential step in obtaining force measurements based on stand-off pad deformation. It is noted that displacement in samples are 54 4.3. Methods - Stand-off Pad Properties real numbers, not only whole integers. This conversion is also required for all validation experiments for displacement estimation. Because of its im- portance, the speed of sound was verified with the following experiment. The relation between samples and displacement is: d = sv 2f , (4.7) v = 2fd s , (4.8) where v = speed of sound (m/s), f = sampling frequency of ultrasound machine (MHz), d = applied displacement (microns), and s = estimated displacement (samples) Experimental Apparatus The following apparatus allows the application of controlled displacements to an ultrasound transducer in contact with the stand-off pad. A L14-5/38 linear array transducer was mounted to a rotary motion stage (Parker Model 10000, Irwin, PA, USA) which controlled the transducer’s lateral tilt. This apparatus was secured to the z-axis of a three-axis manual linear motion stage (Newport 462 Series, Irvine, CA, USA) which controlled the verti- cal displacement of the transducer with 2-micron resolution. The linear stage was bolted to an optical table (Newport, Irvine, CA, USA) to ensure a secure mounting of the apparatus. The stand-off pad was placed on a smooth Plexiglas surface and the transducer was brought into contact with the stand-off pad so that the pad was properly visualized in the B-Mode image (as in Fig. 4.4). It is noted that the interface between the stand-off pad and Plexiglas will be referred to as the pad-tissue interface for consis- tency with terminology in the rest of the thesis. The transducer’s horizontal alignment was achieved by using the B-Mode image as a guide to making necessary adjustments with the manual rotary motion stage. A Sonix Touch ultrasound system (Ultrasonix, Richmond, BC, Canada) was connected to the transducer and used for data acquisition, with a transmit frequency of 10 MHz and a sampling frequency of 40 MHz. The focal depth was set to 5 millimeters (the approximate center of the stand-off pad) and the aperture 55 4.3. Methods - Stand-off Pad Properties size of the transducer was set to 32, a typical value for ultrasound imag- ing (the aperture refers to how many of the 128 piezoelectric elements in the transducer are used in obtaining a single RF line). Photos of the ex- perimental setup are shown in Fig. 4.5. This apparatus was used for data collection in the speed of sound experiment, but is also used to collect data for motion-tracking validation experiments (Section 4.5). (a) (b) Figure 4.5: Photos of the experimental setup. (a) The linear and rotary mo- tion stages are shown, with the mounted ultrasound transducer contacting the force measurement stand-off pad, which has been placed on the Plex- iglas. (b) The Sonix Touch ultrasound system used in data acquisition. Image courtesy of Ultrasonix (www.ultrasonix.com). Experimental Procedure Compressions of 0.5 and 1.0 millimeters were applied to the stand-off pad using the experimental apparatus. Two datasets were obtained for each magnitude of applied displacement for a total of four datasets. The acoustic power of the ultrasound transducer was set to the lowest setting so that the pad-tissue interface was clearly seen without saturation of the signal. The displacement of the interface in each RF line was found using a version of a cross-correlation based motion-tracking algorithm [76], which was modified to track only the motion of the interface. With a known applied displacement and a computed tracked displacement, the speed of sound can be calculated using Eqn. 4.8. The mean speed of sound from all RF lines in each trial as well as the mean and standard deviation of the speed of sound from all four trials is 56 4.3. Methods - Stand-off Pad Properties reported in Section 4.4.1. Using the standard deviation, the effect of a small variation in the speed of sound on displacement measurements can be found as a percentage of the nominally computed displacement using: δd = derror dnominal = nδv 2f nv 2f = δv v (4.9) where δd = uncertainty in displacement after conversion, derror = error in displacement due to SOS Error, dnominal = displacement calculated using nominal SOS, δv = uncertainty in SOS, and v = SOS 4.3.2 Stand-off Pad Elasticity The elasticity of the stand-off pad is required in recovering contact forces from applied displacements, regardless of what model of the stand-off pad is used. A Kinexus shear rheometer (Malvern Instruments Ltd., Malvern, Worcestershire, UK) with parallel serrated disks (to avoid slippage) was used to characterize the Blue Phantom material. The storage and loss moduli (G′ and G′′ respectively) were obtained at 10 different oscillation frequencies us- ing a stress-controlled test with an applied stress of 1 Pascal. The oscillation frequencies used are summarized in Table 4.1. Two samples of Blue Phan- tom material were tested, with the first sample undergoing three trials and the second undergoing two trials. From these results, the shear modulus, G∗, could be computed using Eqn. 4.10. Subsequently, the elastic modulus, E∗, could be computed using Eqn. 4.11 and the Poisson’s ratio (ν) of 0.5. The mean and standard deviation of the shear modulus and elastic modu- lus (for each sample individually and for the results from all five trials) are reported in Section 4.4.2. (G∗)2 = (G′)2 + (G′′)2, (4.10) where 57 4.4. Results and Discussion - Stand-off Pad Properties G∗ = shear modulus (Pa), G′ = storage modulus (Pa), and G′′ = loss modulus E∗ = 2G∗(1 + ν), (4.11) where E∗ = elastic modulus (Pa), and ν = Poisson’s ratio Frequency (rad/s) 0.1354 0.2916 0.6283 1.354 2.916 6.283 13.54 29.16 62.83 135.4 Table 4.1: Applied frequencies for shear rheometry tests. 4.4 Results and Discussion - Stand-off Pad Properties 4.4.1 Stand-off Pad Speed of Sound The speed of sound in the Blue Phantom material computed from each of the four trials is presented in Table 4.2. The speed of sound of the Blue Phantom material is found to be 1540.1±2.6 m/s. Using the uncertainty formulation presented in Section 4.3.1, the uncer- tainty of ±2.6 m/s will cause a 0.17% error in the converted displacement 58 4.4. Results and Discussion - Stand-off Pad Properties Dataset Applied Displacement Speed of Sound (microns) (m/s) 1 500 1536.9 2 500 1539.3 3 1000 1542.8 4 1000 1541.5 Average — 1540.1±2.6 Table 4.2: The speed of sound in the Blue Phantom stand-off pad computed from four trials. magnitudes (as a percentage of the nominal displacement), meaning this small variation in the speed of sound will have little effect on the computed displacements (e.g. 0.42 microns error for a 250 micron applied displace- ment). 4.4.2 Stand-off Pad Elasticity The results obtained using rheometry testing are shown in Fig. 4.6, where the mean and standard deviations are presented for each tested sample and for the combined results. When the stand-off pad is used for force mea- surements, the low frequency results will be used for further calculations (to simulate a quasi-static scenario). At the lowest tested frequency, the elastic modulus was 35.11±1.27 kPa for the first sample, 24.64±3.69 kPa for the second sample, and 28.83±6.33 kPa for the mean of both samples. The large standard deviation in the combined results is due to the difference between the two tested samples (see Fig. 4.6(a)). This combined result is within the range of the stiffness of both healthy and cancerous soft tissues, such as the liver (10–15 kPa) [5], and breast (3 kPa) [78], and breast tumours (18–94 kPa) [72]. If desired, the stiffness of the stand-off pad could be optimized for the specific tissue in an elastography application. 59 4.4. Results and Discussion - Stand-off Pad Properties (a) (b) Figure 4.6: Shear and elastic moduli of the stand-off pad. (a) Individual results for each sample. (b) Combined results from both samples. 60 4.5. Methods - Displacement Tracking Validation 4.5 Methods - Displacement Tracking Validation 4.5.1 Displacement Tracking of Experimental Data Accurate displacement measurements are essential to producing accurate force measurements, and so methods of tracking motion in the stand-off pad were validated. The motion-tracking occurs close to the transducer face, where the RF signal quality may be degraded by the near-field effects of the ultrasound beam, and it must be verified that the motion-tracking in this situation is feasible. Data Collection Datasets for displacement tracking validation were obtained using the same experimental apparatus described in Section 4.3.1. Displacements were ap- plied with the z-axis of the motion stage according to Fig. 4.7 and 50 sets of RF data were captured at each displacement magnitude. This RF data was time-averaged at each applied displacement before any displacement track- ing was performed in order to filter out noise from the environment. The averaged RF data obtained for a given applied displacement is referred to as a frame in all further discussion of the motion-tracking validation exper- iments. The range of applied displacements (Fig. 4.7) correspond to a range of strains in the stand-off pad from 0% to approximately 2%, applied in a cycle of compression followed by decompression. This cycle was repeated four times to obtain four complete data sets, or trials. Motion-tracking Algorithms Time Domain Cross-Correlation with Prior Estimates (TDPE) and Sample Tracking (ST) were the fundamental algorithms used to track motion in the stand-off pad [76], [77]. TDPE is a window-based motion-tracking method, while ST tracks the motion of each sample in the RF signal (for further details, refer to Chapter 2). For each frame, axial motion was tracked along each RF line. This produced a displacement curve corresponding to each RF line, similar to the sample displacement curve shown in Fig. 4.8. 61 4.5. Methods - Displacement Tracking Validation Figure 4.7: Applied displacements used in motion-tracking validation. Dur- ing compression, 0 to 20 microns (2 micron increments) and 20 to 250 mi- crons (10 micron increments) were applied. During decompression, the same displacements were applied in reverse, for a total of 67 applied displacements corresponding to 67 RF frames. Figure 4.8: Example displacement curve for a single RF line. The dis- placements are measured relative to the transducer interface, and therefore increase in magnitude with increased distance from the transducer. 62 4.5. Methods - Displacement Tracking Validation Several variations and combinations of TDPE and ST motion-tracking were tested, and these were as follows: 1. TDPE Motion-Tracking Standard TDPE motion-tracking was performed using the initial frame (0 microns of applied displacement) as the fixed reference from which displacements were measured. Each RF line was divided into equally sized, equally spaced windows of 0.5, 1.0 and 2.0 millimeters in length (26, 52 and 104 samples in length), which is approximately equal to 3, 6 and 12 wavelengths of the transmitted ultrasound pulse. The win- dow spacing was set to one sample, resulting in the maximum overlap possible between adjacent windows. Normally a smaller window over- lap would be used (e.g. 50% overlap), but to be able to compare the effect of window size effectively, the maximum is used. The number of windows per RF line was then 597, 584 and 558 corresponding to the window sizes of 0.5, 1.0 and 2.0 millimeters. As the windows increase in size, fewer windows are able to fit into the ROI. The ROI also lim- its the maximum depth at which different window sizes are able to produce a displacement measurement; as the window size increases, the maximum depth of tracking decreases, as is illustrated in Fig. 4.9. Lastly, because TDPE is a window-based method, it may be affected by stretching or compression (change of shape) of the RF signal which occurs as the stand-off pad is deformed (especially for large applied displacements). 2. ST Motion-Tracking Sample tracking is less susceptible to stretching or compression of the RF signal, but is more sensitive to noise. Furthermore, ST is not suit- able for measuring large displacements, meaning that motion-tracking cannot be performed relative to the initial RF frame. Instead, track- ing is done with respect to the previous frame (called relative tracking or changing reference tracking), and the displacements between sub- sequent frames are summed to obtain measurements relative to the initial frame. This may lead to an accumulation of tracking errors over time as more frames are added. 3. TDPE-ST Hybrid Motion-Tracking A combination of TDPE and ST may provide the best aspects of both methods. TDPE is used to find a course displacement, and ST is used to fine-tune the measurements. This allows a fixed reference frame to 63 4.5. Methods - Displacement Tracking Validation Figure 4.9: Effect of window size on maximum tracking depth with TDPE. No RF data outside the ROI is used, and the center of a window is the location of a particular displacement measurement. Therefore with the large window size, the maximum depth (i.e. distance from transducer) of the last possible displacement measurement is much less than with a small window size. be used, and eliminates the effects of the stretching or compression of the RF signal. TDPE with a window size of 0.5 millimeters was used to find the course displacements, and ST was applied to each window to fine-tune the displacement of each sample within the window. All variations of motion-tracking were used to track displacements in the experimental data, to compare the feasibility and accuracy of each method. The algorithms were applied to the RF data that fell within the ROI (refer to Fig. 4.2). In addition, a median filter (kernel size: 5 samples by 60 samples) was applied to each frame to filter out false peaks in the displacement data. The motion-tracking results along the transducer centerline for the first trial are presented in Section 4.6.1. 64 4.5. Methods - Displacement Tracking Validation 4.5.2 Experimental Repeatability and Hysteresis The compression/decompression experiment described in Section 4.5.1 must exhibit strong repeatability if the stand-off pad is to be used for accurately measuring forces. In other words, the motion-tracking algorithms must yield the same displacement measurements for the same applied displacement, which would result in the same contact force being computed. Theoretically, repetition of the same experiment should yield the same RF signal data, and thus the same displacement profiles for each of the four trials. For each motion-tracking algorithm, at each frame (i.e. amount of ap- plied displacement), the standard deviation (i.e. repeatability) of the dis- placement measurements from the four trials was calculated at each location throughout the ROI. From this, the mean repeatability in the ROI was com- puted for each frame, and these results are presented in Section 4.6.2. Experimental hysteresis may have also been present in the experiments, and its significance must also be determined. The main source of hysteresis is the viscoelastic behavior of the stand-off pad as it is compressed and de- compressed. Since the material takes some time to restore its original shape after a deformation, some hysteresis is likely to occur during the approxi- mately 20 minutes of time taken for each trial. To illustrate the hysteresis, representative hysteresis curves were created using displacement data from the transducer centerline. The displacements at the bottom boundary of the ROI for this RF line were plotted for compression and decompression to create the curves (for a single trial with each motion-tracking method). The magnitude of the hysteresis was calculated at each location along the transducer centerline for each frame by comparing the magnitudes of the displacements obtained for the compression and decompression stages. The results of hysteresis magnitude for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns are presented in Section 4.6.2. 4.5.3 Simulated Compression of RF Signal A simulated compression of the RF signal was analyzed to determine the cause of various features seen in the displacement tracking results (Sec- tion 4.6.1). This analysis can help determine if artifacts (in the form of pe- riodic features) in the motion-tracking are inherent in the motion-tracking algorithm, or are a result of experimental noise or ultrasound near-field ef- fects. The simulated dataset was created using the RF signal at the transducer centerline (the initial frame), so that the results of the simulated compression 65 4.5. Methods - Displacement Tracking Validation are a fair comparison to the displacement tracking results from the exper- iment. The section of RF signal corresponding to the stand-off pad was compressed in a linear fashion by re-sampling the RF signal using MAT- LAB. The simulated compression magnitudes corresponded to the applied displacements in the compression stage of the experimental procedure (see Fig. 4.7). This simulated compression yields RF data that will exhibit per- fect 1D linear compression, is free of any near-field effects of the ultrasound, and does not contain experimental noise. The TDPE, ST and TDPE-ST Hybrid algorithms were applied to find the displacements along this RF line at each of the 34 simulated frames, with the results displayed in Section 4.6.3 for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns. 4.5.4 3D Finite Element Model of Stand-off Pad Deformation A finite element model (FEM) of the stand-off pad was created and analyzed using ANSYS 12.1 (ANSYS Inc., Canonsburg, PA, USA) to validate the motion-tracking algorithms and ensure that the displacement results were capturing the realistic behavior of the stand-off pad. Referring to the results in Section 4.6.1, it is clear that the displacement profile as produced by the motion-tracking algorithms has an S-shape.4 This may be the result of the 3D deformation of the stand-off pad, which is not easily visualized. The experimental setup was simulated in the FEM, with the boundary conditions set such that the bottom of the pad (pad-tissue interface) was constrained in all directions (no slip in x, y and z). The contact area with the transducer was constrained in both x and y (i.e. no slip between the transducer face and the stand-off pad). The no-slip condition was chosen because the stand-off pad material provides a large amount of friction be- tween itself and adjacent surfaces, and no coupling gel was present during experiments, which would provide added lubrication. For the simulation, the material was assumed to be linear, since the range of applied strains is small (approximately 2–3%). As well, the material is approximated as elastic, which ignores the transient response of the material under compression. However, the model will be able to establish whether or not the shape of the deformation curves is an accurate representation of the actual deformation when compressed. Because the stand-off pad and transducer are symmetric, the problem was reduced to modeling one quarter of the stand-off pad using symmetry 4A formal comparison of the displacement results of Section 4.6.1 to a 1D linear defor- mation model can be found in Appendix D. 66 4.5. Methods - Displacement Tracking Validation assumptions. The shape of the transducer face was assumed to be a flat quadrilateral, and a model of the stand-off pad was created based on the actual physical dimensions of the pad. A mesh of 780 brick elements was applied to the 3D model of the quarter stand-off pad. In the area of the pad directly under the transducer, a higher resolution mesh was used to give a higher resolution measurement of the mechanical response in this area. This is illustrated in Fig. 4.10. Displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns were applied to the stand-off pad, and the axial displacements along the location of the transducer centerline were obtained. The results of the simulation are presented in Section 4.6.4. Figure 4.10: Finite element model of the stand-off pad. This model shows one quarter of the entire stand-off pad and transducer contact, taking ad- vantage of symmetry. 4.5.5 Extrapolation of Pad-Tissue Interface Displacement Measurements As noted in Section 4.1, the ROI of the stand-off pad does not include the pad-tissue interface. However, the axial displacements in the region of the stand-off pad outside the ROI are required in order to obtain forces at the pad-tissue interface using displacements, no matter which model is used. It is therefore necessary to extrapolate displacements in this region as accurately as possible. The first step was to find the exact location of the pad-tissue interface at 67 4.5. Methods - Displacement Tracking Validation each RF line when the stand-off pad is in the uncompressed state. This was accomplished by obtaining a single RF frame with the lowest acoustic power setting on the ultrasound machine, where the interface could be seen clearly. The maximum intensity location of the interface signal was obtained as the true pad-tissue interface location for each RF line. The interface location across the transducer face is shown in Fig. 4.11. A profile is seen where the stand-off pad is approximately 100 microns thicker in the center of the transducer, due to the transducer geometry - the transducer face has a slight convex shape which is visible to the naked eye. As well, a misalignment of the transducer with respect to the stand-off pad is noticeable, with the pad- tissue interface location approximately 20 microns closer to the transducer on the right side of the transducer as compared with the left (corresponding to 0.03 degrees of horizontal misalignment). Figure 4.11: The pad-tissue interface location relative to the ultrasound transducer as found in the ultrasound signal. With the true location of the pad-tissue interface known, polynomials were used to model the displacement curve at each RF line, and these poly- nomials could then be used for extrapolation. Based on the results of Sec- tion 4.5.4, a linear model is not suitable (because it cannot account for the S-shape of the displacements of Section 4.6.1), so higher order models are used. The least squares method was used to fit the models to the data, and the quality of each model was calculated using the residuals of least 68 4.6. Results and Discussion - Displacement Tracking Validation squares fit. The models were then used to extrapolate the pad-tissue inter- face displacement at each RF line, and this extrapolation was compared to the known applied displacement at each frame to quantify the error. The different models are summarized here. In models 1(a) and 2(a), a polynomial of the specified order was fitted to the displacement data within the ROI of each RF line, using least squares. The polynomial coefficients were used to extrapolate the displacement at the pad-tissue interface location. In models 1(b) and 2(b), a polynomial of the specified order was fitted to the displacement data, as before. However, to avoid the effects of the high curvature of higher order polynomials, the slope of the polynomial at the bottom of the ROI was calculated from the polynomial coefficients, and used to linearly extrapolate the displacement at the pad-tissue interface location. 1. (a) Cubic Extrapolation (CE) (b) Cubic Polynomial Fit with Linear Extrapolation (CLE) 2. (a) 4th Order Extrapolation (4thOE) (b) 4th Order Polynomial Fit with Linear Extrapolation (4thOLE) The results of the error in the extrapolation as well as the residuals of the polynomial fits are shown in Section 4.6.5. 4.6 Results and Discussion - Displacement Tracking Validation 4.6.1 Displacement Tracking of Experimental Data The displacement curves along the transducer centerline for each motion- tracking method are shown in Fig. 4.12, in which a number of specific fea- tures can be noted.5 With all motion-tracking methods, a slight hysteresis in the displacement magnitudes is noted, which is quantified and discussed in Section 4.6.2. Each method also causes a variety of artifacts in the displace- ment curves, which may be caused by limitations of the motion-tracking 5Additional results showing the displacement profiles throughout the entire stand-off pad for a single trial, for each of the motion-tracking methods, are found in Figs. B.1 to B.5 (Appendix B). Those results indicate that the S-shaped displacement profiles are consistent for all the RF lines of the ROI. They also show a slight trend across the stand- off pad, where the displacements at a given depth decrease from left to right in the ROI, which corresponds to the horizontal misalignment of the transducer (see Fig. 4.11). 69 4.6. Results and Discussion - Displacement Tracking Validation algorithms. This is examined more closely and discussed in Section 4.6.3. Lastly, the displacement curves exhibit an S-shape, which may be the result of the 3D deformation of the stand-off pad. This is explored and discussed in Section 4.6.4. 70 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.12: Displacement profiles at the transducer centerline for different motion-tracking methods. The applied displacements shown are 0, 10, 20, 50, 100, 150, 200 and 250 microns in compression (blue) and decompression (red). (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 71 4.6. Results and Discussion - Displacement Tracking Validation 4.6.2 Experimental Repeatability and Hysteresis The average repeatability versus frame for each motion-tracking method is shown in Fig. 4.13, where an approximately linear trend of worsening repeatability versus frame is seen.6 This is a result of the viscoelasticity of the Blue Phantom material, which causes the stand-off pad to experience relaxation under continued compression. During the experiments, there was a significant amount of time between the first and last frames (on the order of 20 minutes or so), due to the process of applying compression and recording data. This time between frame acquisitions was not well-controlled, so each trial had different amounts of transient time between frames. Therefore, for higher frame numbers, there is an increase in the variability of how much the stand-off pad has responded to the applied compression. This explains the trend of worsening repeatability with increasing frame number. All variations of TDPE motion-tracking resulted in similar repeatability, regardless of window size, indicating that the repeatability is not affected by the change in window size. The repeatability was a maximum of ±1.01 microns, ±1.00 microns, ±0.99 microns for window sizes of 0.5, 1.0 and 2.0 millimeters respectively. The TDPE-ST hybrid algorithm had a similar result, with a maximum repeatability of ±1.02 microns, while the ST algo- rithm performed the most poorly, with a maximum repeatability of ±1.28 microns. The repeatability of both the TDPE-ST hybrid and ST algorithms is affected by the appearance of a large amount of false peaks in the data, which are removed with a median filter. However, the filtering process does not completely eliminate all of the false peaks, resulting in errors in the motion tracking (this is further discussed in Section 4.6.3). This is further compounded in the ST algorithms where a changing reference is used. Ab- solute displacements are obtained by summing the relative displacements, meaning the motion-tracking and filtering errors accumulate from frame to frame, and these errors may differ significantly from trial to trial.7 6The repeatability of displacement measurements throughout the entire ROI is shown in Figs. C.1 to C.5 of Appendix C. These figures indicate a trend of worsening repeatability from left to right in the ROI, which corresponds with the horizontal misalignment of the transducer (see Fig. 4.11). This trend may be caused by unpredictable lateral forces on the surface of the stand-off pad (from the misalignment, due to the lack of lubrication between pad and transducer). These forces would cause increased unpredictable deformation on the right side of the ROI where the stand-off pad is thicker, increasing the variability between trials. 7This is particularly apparent in Fig. C.4 of Appendix C, where there are two regions in the stand-off pad where the repeatability is much worse than the surrounding areas, indicating that at these locations the filtering algorithm was particularly ineffective. 72 4.6. Results and Discussion - Displacement Tracking Validation Figure 4.13: Experimental repeatability based on the repeatability of dis- placement measurements between trials. The results for each motion- tracking method are shown. The experimental hysteresis curves for displacement are shown in Fig. 4.14. The magnitude of displacement obtained during compression is larger than the magnitude obtained during decompression for a given amount of applied displacement, implying a small amount of hysteresis. The magnitude of the hysteresis along the transducer centerline is shown in Fig. 4.15, and several trends are noted. The hysteresis magnitude is roughly proportional to depth into the stand- off pad, meaning the hysteresis is roughly proportional to the stand-off pad displacement at a given depth (compare Fig. 4.15 with Fig. 4.12). As well, the hysteresis magnitudes are generally largest at an applied displacement of 0 microns, and decrease to zero at an applied displacement of 250 microns (see Fig. 4.15). The applied displacements of 0 microns correspond to the beginning and end of the compression/decompression cycle, and the applied displacement of 250 microns corresponds to the exact middle of the cycle (see Fig. 4.7). In other words, the hysteresis magnitude increases with increased time between the compression and decompression frames for a given applied displacement. As well, the hysteresis magnitude increases with an increasing amount of total deformation between the compression and decompression frame for a 73 4.6. Results and Discussion - Displacement Tracking Validation given applied displacement. For example, between the initial frame and the last frame (Fig. 4.7), the pad has compressed 250 microns and decompressed 250 microns. Between the 33rd and 35th frames, the pad has compressed only 10 microns and decompressed 10 microns. Another notable result is that the hysteresis magnitude at small depths is relatively large (see Figs. 4.15(a) to 4.15(c) for the most dramatic exam- ples of this). Up to a depth of approximately 1 millimeter, the hysteresis magnitude decreases as a result of interactions between the transducer face and the stand-off pad. The stand-off pad surface conforms to the transducer face during compression, and tends to hold this shape as the compression is removed, creating more complex behavior at the surface of the stand-off pad. This is compounded by a limited amount of slip at the transducer face. This trend is less clear in the ST results due to the higher hysteresis values overall. The hysteresis results from different motion tracking algorithms can also be compared. The three TDPE motion-tracking variations performed con- sistently, with a maximum hysteresis values of 3.96, 3.64, and 3.15 microns for window sizes of 0.5, 1.0, and 2.0 millimeters respectively (when com- paring an applied displacement of 0 microns between compression and de- compression). All three variations have similar hysteresis results along the centerline, with a smoother centerline results curve for a larger window size. The TDPE-ST Hybrid algorithm produced a similar result to the TDPE tracking, with a maximum hysteresis of 3.40 microns, though the hysteresis shows a less consistent trend along the centerline. As mentioned earlier, this is due to a large number of false peaks in the data which are difficult to filter out effectively, and cause errors in the displacement data. The ST algorithm resulted in the largest hysteresis magnitudes, with two noticable spikes in the hysteresis at depths of 3.5 and 7 millimeters where the hysteresis reached 35 microns. At the maximum depth, the hysteresis was approximately 15 microns. These two spikes in hysteresis correspond to two spikes in the displacement curves at the same depths (see Fig. 4.12(d)). False matches in the displacement data at these locations were persistent from frame to frame, and were such that the median filtering could not completely remove them. The use of a changing reference with the ST algorithm means that displacements from frame to frame are summed to obtain the absolute displacements, meaning the displacement errors are also summed and accumulate. At these two locations, this leads to an extremely large hysteresis, since a large amount of error has accumulated between the compression and decompression frame for a given applied displacement. The higher hysteresis error overall with this motion-tracking algorithm is also a 74 4.6. Results and Discussion - Displacement Tracking Validation result of the accumulation of error in the ST algorithm (further discussion on this accumulation of error is found in Section 4.6.3). 75 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.14: Experimental hysteresis curves based on displacement measure- ments at the bottom boundary of the ROI. The results are representative, showing only the centerline displacements for a single trial. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 76 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.15: Experimental hysteresis magnitudes along the transducer cen- terline. The hysteresis between compression and decompression for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns are shown. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 77 4.6. Results and Discussion - Displacement Tracking Validation 4.6.3 Simulated Compression of RF Signal The results for tracking displacements as the RF data of the transducer centerline was artificially compressed are shown in Fig. 4.16. These plots are compared with Fig. 4.12 of Section 4.6.1. The biggest difference between the expermental and simulation results is the overall shape of the displacement curves, where the curves from the simulation are linear (as expected, because a linear compression was applied), while the experimental curves have an S-shape. This is likely due to the 3D deformation of the stand-off pad which occurred during the experiment, and is explored in Section 4.6.4. The displacement results from TDPE motion-tracking have similar fea- tures in both the simulation and experimental data, especially with larger applied displacements. With TDPE motion-tracking and an applied dis- placement of 250 microns, a 2.0 millimeter window causes a large amplitude periodic trend along the displacement curve (Fig. 4.12(c)), where three sig- nificant peaks along the displacement curve are noted. With a window size of 1.0 millimeters, the amplitude of this effect decreases but remains, and the 0.5 millimeter window has several small peaks in both the experimental and simulated data (Fig. 4.12(a)). The periodicity seen in the experimental results could be recreated in the simulation, so the artifacts are a result of the TDPE motion-tracking algorithm. These artifacts do not reflect true displacements in the stand-off pad, nor are they a result of the ultrasound beam-forming. Because the periodic artifacts are larger when larger displacements are applied indicates that this is a result of RF signal de-correlation. This de-correlation is caused by the change of shape as it is compressed. This signal de-correlation is compounded by a variation in magnitude of the RF signal along a single RF line. Because there is de-correlation in the signal, the compressed signal can- not be matched exactly to the original uncompressed signal with cross- correlation. As a result, the cross-correlation calculation biases towards locations with higher signal amplitudes, since the calculation involves mul- tiplying the uncompressed and compressed signals together. This effect was clearly demonstrated through a simple test. A single window of data for each window size was created that contained a sine wave, and this window was compressed by approximately 4%. Then one wavelength of the signal was amplified by factors of 1 to 10. In the first case, the left-most section of signal was amplified, and in the second case the right-most section was amplified, as demonstrated in Figs. 4.17(a) and 4.17(b). For each factor of amplification, the displacement of the window was computed using TDPE, 78 4.6. Results and Discussion - Displacement Tracking Validation with the expected displacement magnitudes known. The results are shown in Figs. 4.17(c), where it is clear that if one wavelength of signal has an amplitude of 5 times that of the rest of the window, the bias will be between 5 and 25 microns (depending on the window size), which is significant and certainly accounts for the artifacts seen in the displacement data. A large window size results in a larger bias, because the change in signal shape is more pronounced in a larger window. This biasing effect is what caused the peaks in the period artifacts of the displacement measurements with TDPE motion-tracking, which roughly correspond to the three areas of higher signal amplitude highlighted in the original RF signal (Fig. 4.18). This is a drawback of TDPE motion-tracking, though, as seen in Fig. 4.16(a), a small window produces relatively few artifacts. With the ST motion-tracking results, errors develop in the simulated re- sults at depths of approximately 6, 7.5 and 9.5 millimeters (Fig. 4.16(d)). A similar trend occurs in the experimental data, where apparent errors appear at depths of 3, 7, 8 and 10 millimeters. This is caused by the susceptibility of the ST algorithm to noise and the limitations of median filtering in remov- ing this noise. In Figs. 4.19(a) and 4.19(b), the relative displacement curves are shown for the simulated data set, both before and after median filtering. The 1D median filter was applied to each displacement curve with a kernel size of 60 samples. Each line on each plot represents a relative displacement curve obtained from subsequent frames in the RF data. Though the median filtering removes the majority of the false peaks in this data, it does not do this perfectly, and spikes consistently persist at depths of 6, 7.5 and 9.5 millimeters. These relative displacements are summed to obtain absolute displacements relative to the initial frame. This means that an error in the displacement curve at frame N carries through all subsequent frames. If the median filter is ineffective at the same depth into the stand-off pad for several subsequent frames, the error may even increase (see Fig. 4.16(d)). With the TDPE-ST hybrid method, the results appear to be similar to those from TDPE tracking with a 0.5 millimeter window. Though there is no accumulation of error with this algorithm (because a fixed reference frame is used), the results may still contain a high level of noise before median filtering is applied, as is illustrated in Figs. 4.19(c) and 4.19(d). As with the ST algorithm, the median filter is effective but not perfect, and may leave small artifacts in the displacement curve at locations with a large number of false peaks. However, as shown in Fig. 4.19(d), no large spikes remain in the displacement curves after the filtering operation. This simulation confirms that the artifacts in the displacement curves 79 4.6. Results and Discussion - Displacement Tracking Validation are a limitation of the various motion-tracking methods used. Based on the simulated and experimental motion-tracking results, TDPE (0.5 millimeter window) and TDPE-ST Hybrid appear to be the best choices for motion- tracking in the stand-off pad application. 80 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.16: Displacement curves for simulated compression of the trans- ducer centerline for different motion-tracking methods. The displacements corresponding to applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns are shown. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 81 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) Figure 4.17: The bias effect of signal amplitude on displacement measure- ments. (a) A sample of the sine-wave signal (uncompressed), with one wave- length amplified by various factors. (b) The magnitude of the bias caused by the amplification of one wavelength in the window. 82 4.6. Results and Discussion - Displacement Tracking Validation Figure 4.18: The uncompressed signal from the transducer centerline. Areas of high signal magnitude which negatively affect the motion-tracking are highlighted. 83 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) Figure 4.19: Comparison of unfiltered and filtered motion-tracking results for ST and TDPE-ST Hybrid motion-tracking algorithms applied to simu- lated data. The results corresponding to applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns are shown. A 1D median filter with a kernel size of 60 samples was used to detect false peaks in the displacement data. (a) ST - Unfiltered (relative displacements). (b) ST - Filtered (relative displacements). (c) TDPE-ST Hybrid - Unfiltered. (d) TDPE-ST Hybrid - Filtered. 84 4.6. Results and Discussion - Displacement Tracking Validation 4.6.4 3D Finite Element Model of Stand-off Pad Deformation An image of the resulting axial displacements in the stand-off pad quar- ter model is shown in Fig. 4.20. As well, the displacement curves for the transducer centerline are plotted against the experimental displacements in Fig. 4.21. As seen from these plots, the FEM model recreates the S-shaped displacement curves of the experimental data, though the experimental dis- placements do not follow the model exactly. Figure 4.20: The completed FEM simulation showing axial displacements in the stand-off pad quarter model. The errors between the FEM displacements and the experimental data are shown in Fig. 4.22. From these plots, it is clear that the TDPE-ST Hybrid algorithm most closely matches the simple FEM model, with maxi- mum residual errors less than 8 microns, compared with 10–12 microns for TDPE, and greater than 15 microns for the ST algorithm. TDPE-ST does not suffer from accumulated error, as in the case of the ST algorithm, in which the experimental data underestimates displacements. The window- based TDPE method finds a displacement across a whole window, which, as shown in Section 4.6.3, can lead to skewed results based on fluctuations in the RF signal. Additional errors between the FEM model and experimental data are caused by differences between the assumed and actual boundary conditions. There is likely a limited amount of slip possible at the pad-tissue interface and at the transducer contact region that was ignored by choosing no-slip conditions. Ignoring the viscoelasticity may have also had an effect, since the 85 4.6. Results and Discussion - Displacement Tracking Validation stand-off pad would experience some amount of relaxation at each amount of applied displacement that was not accounted for in the model. However, as seen in Fig. 4.20, the stand-off pad deformation is approximated well with the linear elastic FEM model. 86 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.21: Displacement curves from the FEM model and the experimental data for each motion-tracking method at the transducer centerline. The displacements corresponding to applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns are shown. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE- ST Hybrid. 87 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.22: Displacement error curves when comparing the FEM model to the experimental data for each motion-tracking method at the transducer centerline. The displacements corresponding to applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns are shown. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 88 4.6. Results and Discussion - Displacement Tracking Validation 4.6.5 Extrapolation of Pad-Tissue Interface Displacement Measurements The residual errors indicating how well the CE and 4thOE models fit the displacement data of each motion-tracking method are shown in Figs. 4.23 and 4.24. For each RF line, the RMS error between the polynomial fit and the data along the entire line is calculated, and the mean error from all four trials is reported (giving an error value at each RF line and each frame). The maximum errors tabulated in Table 4.3 and the errors displayed graphically in Figs. 4.23 and 4.24 indicate that the 4thOE model is a slightly higher quality fit to the displacement data than the CE model. The quality of the fit also differs when using displacement data from different motion-tracking methods. With TDPE motion-tracking, the quality of fit deteriorates with an increase in window size, corresponding to the decrease in the quality of the displacement tracking (see Section 4.6.3). ST motion-tracking resulted in the highest residuals, owing to the high level of noise in the data, while TDPE-ST Hybrid produced a similar quality fit to the TDPE (1.0 millimeter window) motion-tracking. Motion-tracking Cubic Fit Fourth Order Fit Method Max. Error Max. Error (microns) (microns) TDPE (0.5 mm window) 2.93 2.35 TDPE (1.0 mm window) 2.99 2.99 TDPE (2.0 mm window) 6.19 6.19 ST 7.64 7.64 TDPE-ST 3.79 2.98 Table 4.3: Maximum residual errors for each motion-tracking method and each polynomial fit. The maximum error and maximum error variance with which each model predicts the pad-tissue interface displacement is summarized in Table 4.4.8 The fourth order extrapolation (4thOE) performed well, with the best accu- racy in three of five cases. This method resulted in large errors when used with displacement data from the ST and TDPE (2.0 millimeter window) algorithms, and small errors when used with data from the TDPE (0.5 and 1.0 millimeter windows) algorithms. The ST algorithm results in displace- 8The error and error variance versus frame are shown in Fig. E.1 of Appendix E for each motion-tracking method. A brief discussion of those results is also found there. 89 4.6. Results and Discussion - Displacement Tracking Validation ments with larger error and noise, while TDPE (2.0 millimeter window) has a large extrapolation distance (see Fig. 4.9) and a poorer polynomial fit (see Fig. 4.24). From these results, the 4thOE method with either TDPE (0.5 or 1.0 millimeter windows) or the TDPE Hybrid algorithm are recommended. Motion-tracking CE CLE 4thOE 4thOLE Method (microns) (microns) (microns) (microns) TDPE (0.5 mm) 6.98±2.25 5.85±2.25 2.70±2.44 3.38±1.72 TDPE (1.0 mm) 7.51±2.87 5.03±2.82 2.70±3.15 2.20±1.77 TDPE (2.0 mm) 8.89±6.80 2.52±6.08 6.98±14.32 11.14±4.60 ST 16.25±1.75 14.98±1.68 12.32±1.71 13.39±1.15 TDPE-ST 6.45±2.07 6.22±2.08 2.69±2.30 2.79±1.87 Table 4.4: Maximum extrapolation errors for each motion-tracking method and each extrapolation method. 90 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.23: Residuals of a cubic polynomial fit to the displacement data for each motion-tracking method. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 91 4.6. Results and Discussion - Displacement Tracking Validation (a) (b) (c) (d) (e) Figure 4.24: Residuals of a fourth order polynomial fit to the displacement data for each motion-tracking method. (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE- ST Hybrid. 92 4.7. Methods - Obtaining Force Measurements from Displacement Data Based on the results of all the motion-tracking validation experiments, TDPE motion tracking with a 0.5 millimeter window is the suggested motion- tracking algorithm for this application. It contains relatively minor artifacts compared with the other methods, and follows the expected displacement profile (according to the FEM) of the stand-off pad quite closely. When used in conjunction with a 4th order polynomial model (4thOE) for ex- trapolations of pad-tissue interface displacement, it produces an accuracy of 2.70±2.44 microns or better, and has a repeatability of ±1.01 microns. Furthermore, the TDPE method is not susceptible to noise, making it a more desireable option. These results demonstrate that motion-tracking within the stand-off pad is feasible, and now methods of converting these deformation measurements into force measurements are required. 4.7 Methods - Obtaining Force Measurements from Displacement Data Now that displacement estimation within the stand-off pad has been shown to be feasible and accurate, attention is now turned to devising a method to convert experimentally tracked displacements to reaction force measure- ments. The proposed methods use FEMs of the stand-off pad to return forces, either by using the FEM to generate a look-up table of forces cor- responding to pad-tissue interface displacements, or by direct use of the FEM. 4.7.1 Simulation of a Look-up Based Force Recovery with 2D Transducer The first approach to recovering forces from displacements is a look-up based method, most suitable for use with a 2D ultrasound transducer. An FEM of the stand-off pad under some approximation of typical boundary condi- tions is generated, and various displacements are applied to the transducer in simulation. The reaction forces corresponding to the various displace- ments are stored for each location across the transducer face. In subsequent experiments, the pad-tissue interface displacement at each RF line can be used to look up the corresponding force. The FEM of the stand-off pad was created using ANSYS 12.1, using the geometry and experimental conditions described in Section 4.3.1. In particular, a no-slip condition was assumed at the pad-tissue interface and at the face of the transducer, and the material was again approximated as 93 4.7. Methods - Obtaining Force Measurements from Displacement Data linear and elastic. Displacements of 2 to 300 microns (2 micron increments) applied by the ultrasound transducer were simulated, and the corresponding reaction forces were found at the location of each RF line of the transducer. The applied displacement and reaction force information was stored in a look-up table. Next, simulations of two models were used to test the accuracy of such an approach. In both cases, the reaction forces generated in the simulation of each model are defined as the true reaction forces. Schematics of the two models are shown in Fig. 4.25, and are described as follows. • Model 1 The stand-off pad was simulated using the same conditions as were used to create the look-up (see above). Displacements of 60, 120, 180 and 240 microns were applied to the stand-off pad (corresponding to strains of 0.5, 1.0, 1.5 and 2.0%). • Model 2 A new FEM was created in which the stand-off pad was placed on a slab of underlying tissue of dimensions 125 by 65 by 10 millimeters. As well, an inclusion of size 10 by 10 by 5 millimeters was included in the center of the tissue slab. Displacements of 110, 220, 330 and 440 microns were applied to the setup (corresponding to overall strains of 0.5, 1.0, 1.5 and 2.0%). For both models, positions and amplitudes of scatterers were distributed randomly throughout the stand-off pad, based on a scatterer density of 40 scatterers/mm3. The FEM results were then interpolated to obtain the dis- placement and position of each scatterer at each stage of the compression. With the initial and compressed positions of the scatterers in the stand-off pad known, a simulated ultrasound signal could be obtained. Field II, a program developed for the simulation of ultrasound transducer fields and ultrasound imaging using linear acoustics was used to produce the ultra- sound signal [29], [30]. With this software, the L14-5/38 transducer used in motion-tracking validation experiments was approximated, with a center frequency of 10 MHz, a center-to-center element spacing of 304.8 microns, and an elevational focus of 16 millimeters. 96 RF lines were simulated using an aperture size of 32 elements (the full 128 elements were not simulated to avoid edge effects of aperture imaging). Motion-tracking was then performed on the ultrasound signal data from each model, and the pad-tissue interface displacements at each RF line were found using the 4thOE method described in Section 4.5.5. Reaction forces corresponding to these pad-tissue interface displacements were returned us- ing the look-up table, and compared to the known reaction forces to deter- 94 4.7. Methods - Obtaining Force Measurements from Displacement Data (a) (b) Figure 4.25: Simulation models for look-up based force measurement ap- proach. (a) Model 1. (b) Model 2. mine a force measurement error, reported as a percentage of the true force. The results for Model 1 and 2 (force measurements and force measurement errors) are found in Section 4.8.1. 4.7.2 Simulation of Direct Force Recovery via FEM with 3D Transducer The look-up based method of the previous section suffers because of a lack of knowledge of the stand-off pad boundary conditions during compression, because a 2D ultrasound transducer and large stand-off pad are used. In other words, the pad-tissue interface displacement can only be determined for the area of stand-off pad directly below the transducer face. A better method of recovering reaction forces at the pad-tissue interface is one where 95 4.7. Methods - Obtaining Force Measurements from Displacement Data the boundary conditions of the entire pad are known. This can be accomplished through the use of a 3D linear array transducer (see Fig. 4.26), where the stand-off pad could be attached as a cover for the transducer face. When compression is applied, the pad-tissue interface could be obtained across the entire stand-off pad, instead of only a small portion of it. This displacement profile could then be used as the input into an FEM which computes the reaction forces at the surface. Figure 4.26: A 3D linear array transducer. An FEM simulation in ANSYS 12.1 was used as a preliminary validation of this force recovery approach. The purpose of the simulation was to verify that forces can be accurately recovered if the stand-off pad geometry and pad-tissue interface displacements (across the entire pad) are known. To simplify the simulation, the curvature of the 3D transducer face was ignored. Instead, a flat stand-off pad was simulated, assumed to be attached to a flat 3D transducer with no-slip allowed between the pad and transducer. The stand-off pad as modelled is shown in Fig. 4.27. A sinusoidal axial displacement profile was applied along the z-axis (cor- responding to the lateral direction of the probe), across the entire length of the pad, as shown in Fig. 4.28. The pad-tissue interface surface of the stand-off pad was free to move in the lateral and elevational directions (slip- condition), and the material was approximated as linear and elastic. The obtained FEM deformation of the stand-off pad was used to compute the displacements of scatterers within the stand-off pad, and to obtain the true reaction forces at the pad-tissue interface. These scatterer positions and displacements were input into Field II to simulate the ultrasound signal re- ceived. The 3D probe was moved in increments of 1 millimeter across a 96 4.7. Methods - Obtaining Force Measurements from Displacement Data range of 43 millimeters in the x-direction (Fig. 4.27), simulating the eleva- tional motion of the transducer. The pad-tissue interface axial displacements were obtained by processing the ultrasound signal as described in previous sections. The pad-tissue interface displacement profile obtained by processing the ultrasound signal was input to the FEM, and the corresponding reaction forces were determined. The mean and standard deviation of the error between the true forces and the experimentally determined forces are shown in Section 4.8.2. 97 4.7. Methods - Obtaining Force Measurements from Displacement Data (a) (b) Figure 4.27: Images of the FEM model used in simulating the stand-off pad for a 3D linear array. (a) Isometric view of the stand-off pad with Cartesian coordinate frame noted. (b) Side view of the stand-off pad with the fixed transducer surface and the applied displacement surface noted. 98 4.7. Methods - Obtaining Force Measurements from Displacement Data (a) (b) Figure 4.28: Displacement profile applied to the stand-off pad in the FEM simulation. (a) Displacement profile along the z-direction (lateral direction of transducer). (b) Displacement profile applied across the entire stand-off pad. 99 4.7. Methods - Obtaining Force Measurements from Displacement Data 4.7.3 Experimental Validation of Direct Force Recovery with 3D Transducer Experimental Apparatus For this experimental validation, a new stand-off pad was manufactured that fits on the ultrasound transducer (i.e. curved shape), and enables imaging of the entire pad. This pad is shown in Fig. 4.29, having been secured to the ultrasound transducer. The dimensions of the stand-off pad were as follows: a width of 32 millimeters, a thickness of 12 millimeters, an inner radius of 82.85 millimeters, and a sweep of 18 degrees. A 4DL14-5/38 transducer (Ultrasonix, Richmond, BC, CA) was mounted vertically using a custom mounting bracket, and the stand-off pad was se- cured to the face of the transducer using removable latex rubber (Fig. 4.29). A volume of RF data corresponding to the uncompressed stand-off pad was obtained to be used as a fixed reference. Various objects of known mass were then applied to the stand-off pad, and RF volumes were obtained. For each object, five datasets comprising an uncompressed and compressed RF volume were obtained. The objects used are summarized in Table 4.5, with pictures shown in Fig. 4.30. The masses were determined using an Ex- cell BH-600 precision balance (Excell Precision Co., Ltd., Hsin-Tien, Taipei Hsien, Taiwan). The first object was a washer with four bearings (2 millime- ter diameter) glued to the underside (Fig. 4.30(a)) so that point forces were applied to the stand-off pad. The second object was the same washer object, but with a 9.5 millimeter bearing providing added weight (Fig. 4.30(b)). The third object was two of the washers placed side-by-side, with an additional weight applied to one of the washers (Fig. 4.30(c)). Object Description Mass (grams) 1 Washer 1.59 2 Washer with bearing 5.11 3 Two washers (one has small added weight) 4.54 Table 4.5: Summary of objects used in experimental force measurement validation. Displacement Tracking and Force Recovery Using the RF volumes obtained from the uncompressed state and each com- pressed state, displacements could be found at the pad-tissue interface (the 100 4.7. Methods - Obtaining Force Measurements from Displacement Data Figure 4.29: Experimental apparatus used in force validation experiments. upper boundary of the stand-off pad in Fig. 4.29). This required that the location of the pad-tissue interface be found at each location in the volume. The pad-tissue interface caused a large spike in the RF signal (as in previous experiments), and the maximum intensity location was identified as the true interface location. In this calculation, the computed distance is relative to the crystals of the ultrasound probe. The results are shown in Fig. 4.31, where the dome-like appearance of the pad-tissue interface is due to the geometry and curvature of the transducer face, to which the stand-off pad conforms. Next, the motion-tracking was performed, and the 4thOE extrapolation (Section 4.6.5) was used to extract the pad-tissue interface displacement. These displacements were then used as the input into an FEM in ANSYS 12.1. The FEM mimicked the geometry of the stand-off pad, which was modeled as a section of thick-walled cylinder with an inner radius of 82.85 millimeters, a thickness of 12 millimeters, a width of 32 millimeters, and a sweep of 18 degrees. A maximum mesh size of 1 millimeter is applied to the model. The material properties of the Blue Phantom material are also added to the model (see Section 4.4.2), though the material was assumed to be linear elastic. Screen captures of the FEM model are shown in Fig. 4.32. Displacement and force profile results (at the pad-tissue interface of the stand-off pad) from these validation experiments are shown in Section 4.7.3. 101 4.7. Methods - Obtaining Force Measurements from Displacement Data (a) (b) (c) Figure 4.30: Photos of the objects used in force measurement validation experiments. (a) Object 1. (b) Object 2. (c) Object 3. 102 4.7. Methods - Obtaining Force Measurements from Displacement Data Figure 4.31: The pad-tissue interface for the 3D linear array transducer, relative to the transducer crystal array. 103 4.7. Methods - Obtaining Force Measurements from Displacement Data (a) (b) Figure 4.32: Images of the FEM model used in force measurement validation. (a) Isometric view of the stand-off pad with cylindrical coordinate frame noted. (b) Side view of the stand-off pad with the fixed transducer surface and the applied displacement surface noted. 104 4.7. Methods - Obtaining Force Measurements from Displacement Data Force Measurement Error The force measurement error was quantified by computing the difference between the sum of the recovered forces across the stand-off pad surface and the known weight of the object that was applied to the stand-off pad. The error was computed as a percentage of the true force (see Eqn. 4.12), and the results are shown in Section 4.8.3.  = 100( ∑ FFEM −W ) W , (4.12) where  = force measurement error (%), and∑ FFEM = summation of forces obtained from FEM, W = known weight of the applied object 4.7.4 Spatial Resolution of Force Measurements with 3D Transducer The spatial resolution with which force measurements can be obtained is limited by the lateral and elevational resolutions of the 3D transducer, and the mesh refinement used in the FEM to recover forces. A measure of this resolution was obtained by applying a point force at known locations in both the lateral and elevational axes, and measuring the locations as they appear in the force profile maps produced by the force measurement pad method. The experimental setup shown in Fig. 4.33 was used to obtain measures of the lateral and elevational resolution. A 2 mm ball bearing was used as a point force applicator, and was attached via an aluminum arm to a 3 axis linear motion stage (Newport 462 Series, Irvine, CA, USA). The location of the point force was moved using the motion stage by increments of 50 microns over a range of 4 millimeters (-2 mm to 2 mm), in both the lateral and elevational directions. The movement was also measured in the force profile images by resolving the centroid of the point force. Comparing the known positions of the point force (as applied with the motion stage) with those obtained experimentally gave an indication of the resolution with which point forces can be resolved. The results for this experiment are shown in Section 4.8.4. 105 4.7. Methods - Obtaining Force Measurements from Displacement Data Figure 4.33: The experimental apparatus for resolution testing. An alu- minum arm connects the motion stage to a 2 mm bearing used to apply a point force to the stand-off pad. 4.7.5 Implementation of Stand-off Pad Force Measurement System A single functional force measurement system was created where the com- putations of the previous sections were done online, suitable for displaying contact forces to a user. The system was implemented on a Sonix RP ultra- sound system (Ultrasonix, Richmond, BC, Canada), with the software based on both the work of Pospisil et al. [49] and the Propello ultrasound inter- face developed by Ultrasonix. The basic functionality of the program was to display and continually update contact forces at the pad-tissue boundary to the user when scanning with a 3D linear transducer. The program com- bines all the steps that have been established and examined in the previous sections. The user requests the software to begin scanning, and then stores a volume RF data corresponding to the uncompressed state of the stand-off pad. As the system runs, it continues to collect RF data, and measures displacements relative to the reference volume using TDPE motion-tracking with a 0.5 millimeter window size. The displacements are used to extrapo- late the pad-tissue boundary displacement using the 4thOE method. These displacements are interpolated so that they are suitable for input into the 106 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data FEM model. The program then calls ANSYS 12.1 to compute the contact forces (based on displacements) using the same FEM as used in the force measurement validation experiments (Section 4.7.3). These forces are dis- played to the screen in the form of a color map. Sample screen-captures of the working system are shown in Section 4.8.5. 4.8 Results and Discussion - Obtaining Force Measurements from Displacement Data 4.8.1 Simulation of a Look-up Based Force Recovery with 2D Transducer The force measurements and FEM-generated true forces for Model 1 are shown in Fig. 4.34(a), and the force measurement errors (in percentage) are displayed in Fig. 4.34(b). The look-up based method worked well with this model, resulting in force measurement errors less than 1.5%. The force measurements and FEM-generated true forces for Model 2 shown in Fig. 4.34(c), and the force measurement errors (in percentage) are displayed in Fig. 4.34(d). With this model, the look-up based method performed much more poorly than Model 1, with errors near 17%. The results show a distinct area (between lines 50 and 80 of Fig. 4.34(c)) of increased force at the location of the inclusion, while in the true force profile this is not seen. The small error in recovering the force from the look-up table for Model 1 is a result of motion-tracking error and error in the extrapolation of the pad- tissue interface. At larger applied displacements, the extrapolation error was also larger, as indicated in Section 4.6.5. Despite this, when the assumed conditions in the FEM (used to generate the look-up table) are a match to the experimental conditions, forces will be accurately recovered. In both cases, the linear elastic assumption used in modeling the material had no effect, since the same FEM material properties were used in generating the deformation and in recovering the forces. The shortcomings of a look-up based method are clear with Model 2. Be- cause soft tissue is located underneath the stand-off pad, the stand-off pad experiences a large change in overall shape as well as a compression at the transducer location. This complex 3D deformation of the entire stand-off pad drastically alters the force magnitudes and distribution at the trans- ducer face. In an actual imaging scenario, the boundary conditions used to generate the look-up table will always differ from the actual boundary 107 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data (a) (b) (c) (d) Figure 4.34: Measured forces and errors in force measurements. (a) Model 1 force measurements. (b) Model 1 force measurement errors. (c) Model 2 force measurements. (d) Model 2 force measurement errors. conditions in the imaging scenario. 4.8.2 Simulation of Direct Force Recovery via FEM with 3D Transducer The displacement profile obtained from the simulated ultrasound data is shown next to the original applied displacement profile in Fig. 4.35. The displacement error when comparing these two profiles is 3.26±0.31 microns across the entire stand-off pad surface (RMS error of 7.90 microns). The displacement error is due to the motion-tracking algorithms used, and from the extrapolation of pad-tissue interface displacements. 108 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data The true force profile and the experimentally obtained force profile are shown in Fig. 4.36. Qualitatively there is a good match between the two. The force error at each point across the stand-off pad is shown in Fig. 4.37, where high errors are found at the edges of the stand-off pad (due to edge effects). The mean force error across the entire stand-off pad is 31.29±10.62 micro-Newtons, or 0.5±1.7%. The force measurement errors result from the displacement errors, which have a compounding effect. This is because an error in the applied displace- ment at one location results in force errors in a region surrounding that same location. The assumption of a linear elastic material had no effect on these results, since the same FEM material properties were used in generating the deformation and in calculating the reaction forces. The magnitudes of the errors and the comparison of the ideal and experimental force profiles indi- cates that this method is feasible for recovering the force profile across the stand-off pad. Furthermore, this method is more robust than the look-up based approach. (a) (b) Figure 4.35: The ideal and computed displacement profiles for the simulation of a flat stand-off pad imaged with a 3D transducer. (a) Ideal displacement profile. (b) Displacement profile computed from simulated ultrasound data. 109 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data (a) (b) Figure 4.36: The ideal and obtained force profiles for the simulation of a flat stand-off pad imaged with a 3D transducer. (a) Ideal force profile. (b) Force profile obtained based on simulated ultrasound data. (a) (b) Figure 4.37: Force profile errors in a 3D simulation of a flat stand-off pad. (a) Error values (µN). (b) Error percentages. 110 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data 4.8.3 Experimental Validation of Direct Force Recovery with 3D Transducer Displacement Tracking and Force Recovery The displacement and force profiles at the surface of the stand-off pad for each object are shown in Fig. 4.38. Qualitatively, the expected profiles for each object are obtained. For objects 1 and 2, the largest displacements are found at the locations of the four bearings which apply the load. For object 3, eight contact points can be determined, with four of the points having a higher force (i.e. the heavier of the two washers placed on the stand-off pad). In all cases, a region larger than the region of contact is displaced. The force profiles reflect the displacement profiles, with areas of larger displacement corresponding to areas of higher reaction forces in the stand-off pad. Force Measurement Error The overall force measurement errors for each object are shown in Fig. 4.39. The overall error averaged from the three objects was 10.6±5.5% error, with the smallest error occurring with Object 3, and the largest with Object 1. There are a number of error sources that contribute in this system. First of all, motion tracking between corresponding frames (uncompressed and compressed) is affected by decorrelation caused by motor positioning. This could be improved through better motor control of the 3D transducer which would ensure that the exact same position is used for corresponding frames. Also, characterizing the elasticity of the material (see Section 4.4.2) resulted in a ±20% variation in the elasticity, which creates a level of uncertainty in the results. Furthermore, the stand-off pad was secured to the transducer using latex rubber, meaning there is a thin layer of soft material between the pad and transducer, which is not accounted for in the FEM model. Some of these issues could be rectified by implementing improved motor control in the transducer, by a more thorough characterization of the stand-off pad material properties, and by improving the stand-off pad design and the manner in which it is attached to the transducer. Another potential error source is the assumption that the material was linear elastic, which ignores the transient behavior of the material. The FEM does not consider the effect of material relaxation or hysteresis on the reaction force, though this would inevitably have some effect. If the material relaxes under compression, the displacement would increase while the total force remains the same. A more complex model could take this into account. 111 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data (a) (b) (c) (d) (e) (f) Figure 4.38: The displacement and force profiles for each object in experi- mental validation. (a) Object 1 - Displacement profile. (b) Object 1 - Force profile. (c) Object 2 - Displacement profile. (d) Object 2 - Force profile. (e) Object 3 - Displacement profile. (f) Object 3 - Force profile. 112 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data Figure 4.39: Force measurement errors in experiments for each object ap- plied to the stand-off pad. The mean and standard deviation of five trials is shown. 113 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data 4.8.4 Spatial Resolution of Force Measurements with 3D Transducer Plots showing the true point force positions versus the experimental posi- tions in the lateral and elevational directions are shown in Fig. 4.40. In the lateral direction, the experimental positions have an associated uncertainty of ±0.2 millimeters, meaning a change in the lateral position of a point force smaller than 0.2 millimeters cannot be resolved with certainty. In the ele- vational direction the experimental positions have a measurement noise of ±0.4 millimeters, so a change in the elevational position force smaller than 0.4 millimeters cannot be resolved with certainty. (a) (b) Figure 4.40: Spatial resolution of force measurements. The resolution is indicated by the noise in the experimental data, indicated by the ±2σ limits (2 standard deviations). (a) Lateral direction. (b) Elevational direction. The lateral resolution is better than the elevational resolution, which is expected, since the ultrasound transducer’s resolution is higher in the lateral direction. The element spacing is approximately 300 microns, as compared to the approximately 700-800 micron frame spacing in the elevational direc- tion. Furthermore, the element spacing is always fixed, while the elevational spacing is also affected by the motor movement of the transducer. In other words, the frame spacing is not perfectly consistent, leading to increased noise when determining positioning in the elevational direction. 114 4.8. Results and Discussion - Obtaining Force Measurements from Displacement Data 4.8.5 Implementation of a Stand-off Pad Force Measurement System A screen-capture of the graphical user interface of the working contact force system is shown in Fig. 4.41. The force profile obtained using Object 2 (see Section 4.7.3) is displayed to the user. The current system provides contact force updates every 20 seconds, due to the memory requirements of the displacement calculations and ANSYS. A working implementation of a stand-off pad based force measurement system has been achieved, which can be improved in subsequent versions through the use of Graphical Processing Units, and faster processors. Figure 4.41: Screen capture of working force measurement system, with the force profile from Object 2 shown. 115 4.9. Discussion of Viscoelastic Behavior of the Stand-off Pad 4.9 Discussion of Viscoelastic Behavior of the Stand-off Pad Throughout the development and validation of the force measurement stand- off pad, the viscous properties of the material were ignored in various mod- els (see Sections 4.6.4, 4.7.1, 4.7.2, and 4.7.3). However, these effects were clearly present, seen most obviously in the hysteresis observed in the dis- placement tracking validation experiments (Section 4.6.2). The linear elastic model of the stand-off pad remains a good model to use in this first iteration of force measurement system design. The applied com- pressions were small, and the resulting hysteresis magnitudes were also small (e.g. a hysteresis of 3 microns resulting from a compression and decompres- sion of 250 microns). As well, the elasticity measurement alone had a large amount of uncertainty (±20%), which is likely a more significant source of uncertainty than ignoring the viscous effects. Lastly, the experimental validations were not based on a repeated compression and decompression cycle where the hysteresis and viscous effects would be expected to play a larger role. In summary, the linear elastic model was sufficient in the ex- periments performed, and would also be suitable for a quasi-static scenario where compression is applied in stages, with no decompression in between. In a real-world imaging scenario, the compression of the stand-off pad could be cycled multiple times, meaning the viscous effects will play a much larger role. The central way to reduce these effects is to use a different stand-off pad material which exhibits a reduced viscous response. The best method would be to implement a more complex FEM which is capable of modeling visco-elastic behavior, such as that developed by Areias et al. [4]. In this case, the visco-elastic material could be characterized and accounted for completely. Before this is attempted, however, issues such as accurate material testing and ultrasound transducer motor control should be addressed, as these are also important contributors to accurate force measurements. Another issue that arises from the visco-elasticity of the material is that the RF signal can possibly drift and change slightly over time. This means that the reference signal, used to compute displacements and thus forces, can no longer be correlated well. If improvements in accounting for the visco- elastic behavior are not sufficient, the system may also have to contain a maximum number of volumes that can be processed before the experiment should be restarted, with a new reference volume. The viscous behavior of the stand-off pad is an important consideration 116 4.10. Conclusions in an accurate force measurement system. Viscous effects were ignored in validation experiments based on appropriate assumptions about the behav- ior, but as the system is developed further, this must be taken more fully into account. 4.10 Conclusions A force measurement stand-off pad containing a scattering medium has been developed which is suitable for measuring force when used with a 3D ultra- sound transducer. Axial displacements are tracked throughout the stand-off pad and used to obtain the displacement profile at the pad-tissue interface. Motion-tracking extrapolation methods were validated for this purpose, with accuracies of better than 3 microns. The force recovery via FEM was vali- dated to be accurate to within 10% of the true forces. Furthermore, a fully functional force measurement system has been implemented on an ultra- sound system. This force measurement method is simple to implement in that it re- quires no additional sensors or electronics to operate. As well, the use of the force measurement system will enable the inclusion of force measure- ments in elastography algorithms. This system is another step in improving elastography images, which will contribute to improved image guidance in RALPN, and in other applications. 117 Chapter 5 Conclusions and Future Research This final chapter of this thesis highlights the contributions of the completed research in light of the thesis objectives, and indicates future research direc- tions. In summary, the research work in the areas of CT-to-US registration and ultrasound elastography are two important steps in improving image guidance for RALPN. The image registration work is a first step in pre- senting a fusion of ultrasound and CT to the surgeon for surgical guidance, while enabling force measurements in elastography will improve solutions of the inverse elastography problem. In the long term, these steps to improved image guidance will contribute to improved surgical efficiency, outcomes and patient well-being. 5.1 Contributions In Chapter 3, a fiducial stand-off pad for rigid registration has been de- signed and proven to work for clinical CT-to-US registrations at the time of the CT. It is capable of registration accuracies of 14-20 millimeters in clinical applications. These accuracies are slightly worse than the 13 mil- limeter accuracy of the incumbent tracked ultrasound approach, but this trades off against a simplified registration technique. In controlled studies, the accuracy is better than 4 millimeters, meaning this method also has sig- nificant promise in applications where the imaged tissue is not susceptible to movement. Furthermore, this technique provides suitable accuracy for the initialization of several other registration approaches, which were found to have capture ranges between 15 and 44 millimeters, depending on the technique. Lastly, it has been proven to be simple to implement in a clinical setting, since only the stand-off pad is required, as opposed to the optical tracking system required by the incumbent approach. The fiducial stand-off pad registration is simple and reliable, providing an excellent alternative to existing CT-to-US registrations that take place at the time of the CT. 118 5.2. Future Work In Chapter 4, a force measurement stand-off pad containing a scattering medium has been manufactured and validated for use as a force sensor when used with a 3D ultrasound transducer. In simulations, the force measure- ment accuracy of the stand-off pad was within 0.5% of the applied force. In experiments, the force measurement accuracy was within 10%. Further- more, a working force measurement system was implemented on existing ultrasound machine architecture, which opens the door to force measure- ments being integrated into elastography algorithms. The objectives of the thesis in formulating a novel CT-to-US image reg- istration algorithm, and in contributing to improvements in ultrasound elas- tography through novel force measurement techniques have been met. How- ever, in both areas of work, much of the research was done to establish feasibility, and there is much future research possible. 5.2 Future Work 5.2.1 Fiducial Stand-off Pad for Image Registration 1. Stand-off Pad Manufacturing Methods Other materials that pro- vide the durability and resilience of PVC without the toxicity should be explored for the fiducial stand-off pad. This will negate the need for a probe cover and ultrasound gel in enclosing the pad, likely im- proving the image quality when the pad is in use. It will also provide a more elegant fiducial stand-off pad both in ease of use, aesthetics and ability to obtained necessary ethical approvals. Options for mate- rials include PVA, Zerdine (trademark material of CIRS Inc., Norfolk, VA), or Blue Phantom material (Blue Phantom, Redmond, WA). Op- timally, a stand-off pad which is able to acoustically couple to the skin with little need for coupling gel will be produced. With little or no coupling gel between the pad and patient, motion of the pad between the time of the ultrasound and the time of the CT would be further reduced, and would increase the comfort level of the patient. 2. Fiducial Pattern Improvements In the initial study, a small num- ber of fiducials were included in the pad so that fiducial correspon- dence was easily determined between CT and ultrasound. Since the pad is secured to the patient but the fiducials must remain visible in the ultrasound volumes, there is a relatively small window where the ultrasound transducer can be located, which can lead either to part of the fiducial pattern being missed in the volume, or to a less than 119 5.2. Future Work optimal image of the kidney. In the additional patient study, multiple patterns were used to allow greater freedom in locating the transducer, but this can lead to more severe lever arm errors due to a change in fiducial orientation when the pad deforms. An improved design would be to secure the pad to the ultrasound transducer (with the fiducials directly in front of the transducer) until the kidney is found, and then, once in the optimal position, detached from the ultrasound transducer and secured to the patient. Another option is to create a pocket in the stand-off pad above the fiducials that conforms to the shape of the ultrasound transducer. This would consistently locate the probe relative to the fiducial stand-off pad to prevent missing fiducials in the image volumes, and to ensure that the fiducials are directly un- der the transducer to prevent changes in fiducial orientation due to transducer pressure. As well, an optimal number of fiducials will be determined which provides a balance of low FRE values and ease of fiducial matching. 3. Integration with Feature-Based Registrations This thesis fo- cused only on a portion of a pre-operative CT to pre-operative ultra- sound registration. The next logical step is to integrate this method with subsequent feature-based registrations capable of higher accura- cies, such as the simulated ultrasound method [74]. This would create a complete registration system which takes as inputs the pre-operative CT and pre-operative ultrasound datasets and the fiducial stand-off pad information, and outputs accurately registered datasets that are ready to use for registration to intra-operative ultrasound. The tar- get registration error and computation time for the complete system should be evaluated to optimize the complete CT-to-US registration. This system should be implemented in a user-friendly interface on the ultrasound machine that enables the registration to be performed ef- ficiently. This would complete the first step of pre-operative CT to intra-operative ultrasound registration for use in surgical guidance. 5.2.2 Force Measurement Stand-off Pad for Elastography 1. Optimization of Stand-off Pad Design and Properties The stand-off pad used with the system can be improved by using a dedi- cated mold in order to achieve the desired shape. As well, the thickness and stiffness of the pad could be optimized to provide the best combi- nation of force sensitivity and range of forces that can be sensed. At 120 5.2. Future Work the same time, the stand-off pad could be adapted to different imaging scenarios. Furthermore, a better method of attaching the pad to the probe should be devised, which will allow the pad to be sufficiently coupled to the transducer to facilitate imaging (with known bound- ary conditions), and will also allow the pad to be easily applied or removed. 2. FEM Improvements In the work presented, the stand-off pad ma- terial was assumed to be linear elastic, and a quasi-static scenario was assumed. However, the viscous effects of the material were ignored. The model could be improved by including the hysteresis and non- linearity of the material, as well as exploring dynamic models. 3. Improve Force Measurement System Software The force mea- surement methodolgy as a whole suffered because of poor transducer motor control, which affects the displacement data in the elevational direction. Poor motor control leads to worsened correlation in motion- tracking and poorer spatial elevational resolution of force measure- ments. Implementing better motor control as part of the force mea- surement system would improve displacement measurements and force measurements, and would improve force measurement repeatability with the 3D transducer. Additionally, the current update rate of the force measurement system is one frame every 20 seconds, which is far slower than the desired real- time system. The system speed can be increased by implementing a built-in FEM into the software, rather than calling ANSYS from the main program, and by adapting the code for parallel computations on a graphical processing unit (both in the FEM and in the displacement tracking). This will significantly increase the rate at which a force profile can be obtained using the system. This will also enable the system to be smoothly integrated into a complete system which would use the force measurements to calculate tissue properties. 4. Incorporate Stand-off Pad Force Data in Solving the Inverse Problem In this thesis, the stand-off pad was not implemented in solving the inverse problem for elastography. It should be incorporated into algorithms which provide relative measures of elasticity, using the known properties of the stand-off pad to calibrate the results and validate the effectiveness of this approach. As well, methods which are able to use force measurements as inputs should also be tested for improvements in the accuracy of results, the ease of use, the sensitivity 121 5.2. Future Work to noise in the force measurements and so on, establishing the benefits of using force measurements as boundary conditions. Once established in phantom work, the effectiveness of using the force measurement stand-off pad on patient data can be explored as well. 5. 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Patient RMS FRE (mm) Lateral Axial Elevational 4 1.18 0.88 1.64 5 0.93 0.54 1.39 6 0.53 0.30 1.20 7 1.16 0.90 1.51 8 0.48 0.43 1.33 9 0.87 0.54 1.83 Mean 0.86 0.60 1.48 Table A.1: RMS FRE for six additional patients Patient Kidney Centroid Displacement (mm) Lateral Axial Elevational Total 4 12.99 15.13 12.51 23.54 5 5.00 13.32 4.84 15.03 6 17.57 8.06 21.03 28.56 7 9.27 9.79 5.79 14.67 8 14.18 11.92 15.80 24.35 9 8.71 13.55 4.44 16.71 Mean 11.29 11.96 10.74 20.48 Table A.2: RMS TRE for six additional patients 132 Appendix B Experimental Displacement Profiles in the Stand-off Pad 133 A p p en d ix B . E x p erim en tal D isp lacem en t P rofi les in th e S tan d -off P ad Figure B.1: Displacement profiles in the stand-off pad with TDPE motion-tracking (window size 0.5 mm). The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings. 134 A p p en d ix B . E x p erim en tal D isp lacem en t P rofi les in th e S tan d -off P ad Figure B.2: Displacement profiles in the stand-off pad with TDPE motion-tracking (window size 1.0 mm). The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings. 135 A p p en d ix B . E x p erim en tal D isp lacem en t P rofi les in th e S tan d -off P ad Figure B.3: Displacement profiles in the stand-off pad with TDPE motion-tracking (window size 2.0 mm). The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings. 136 A p p en d ix B . E x p erim en tal D isp lacem en t P rofi les in th e S tan d -off P ad Figure B.4: Displacement profiles in the stand-off pad with the ST algorithm. The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline at each point is highlighted with ’o’ markings. 137 A p p en d ix B . E x p erim en tal D isp lacem en t P rofi les in th e S tan d -off P ad Figure B.5: Displacement profiles in the stand-off pad with the TDPE-ST Hybrid algorithm. The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline at each point is highlighted with ’o’ markings. 138 Appendix C Repeatability of Displacement Measurements 139 A p p en d ix C . R ep eatab ility of D isp lacem en t M easu rem en ts Figure C.1: Repeatability of displacement measurements in the stand-off pad with TDPE motion-tracking (window size 0.5 mm). The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings. 140 A p p en d ix C . R ep eatab ility of D isp lacem en t M easu rem en ts Figure C.2: Repeatability of displacement measurements in the stand-off pad with TDPE motion-tracking (window size 1.0 mm). The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings. 141 A p p en d ix C . R ep eatab ility of D isp lacem en t M easu rem en ts Figure C.3: Repeatability of displacement measurements in the stand-off pad with TDPE motion-tracking (window size 2.0 mm). The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings. 142 A p p en d ix C . R ep eatab ility of D isp lacem en t M easu rem en ts Figure C.4: Repeatability of displacement measurements in the stand-off pad with the ST algorithm. The dis- placement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline at each point is highlighted with ’o’ markings. 143 A p p en d ix C . R ep eatab ility of D isp lacem en t M easu rem en ts Figure C.5: Repeatability of displacement measurements in the stand-off pad with the TDPE-ST Hybrid algorithm. The displacement profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline at each point is highlighted with ’o’ markings.144 Appendix D Comparison of Displacement Tracking Results with a 1D Linear Deformation Model D.1 Methods The simplest model of the stand-off pad would be to treat each RF line as 1D spring. In order to validate that this is a feasible approach, the displacement results of Chapter 4, Section 4.6.1 (further results also dis- played in Appendix B), were compared to a 1D linear deformation model. This model was constructed by setting the displacement equal to zero at the transducer face and equal to the applied displacement at the pad-tissue interface, and linearly interpolating displacements between these two end points. The displacements along each RF line were compared to this model, in the manner shown in Fig. D.1. The results of this comparison are found in Section D.2. The exact location of the pad-tissue interface at each RF line in the uncompressed state is required to perform this comparison. A description of how this interface location was computed is found in Chapter 4, Section 4.5.5 (see especially Fig. 4.11). D.2 Results The comparison between the motion-tracking results for each motion-tracking method and the assumed 1D linear deformation model is shown in Figs. D.2 to D.6, with the centerline comparison shown in Fig. D.7. These figures show that the displacements differ from the model in a consistent manner. In the top half of the ROI (nearest the ultrasound transducer face), the displacement magnitudes are less than those predicted by the model, with the maximum difference from the model equal to approximately 5% of the applied displacement. In the bottom half of the ROI (nearest the pad-tissue 145 D.2. Results Figure D.1: Comparison of estimated displacements to a 1D linear displace- ment model. The displacement profile according to the model for a single RF line goes through zero displacement at the transducer face and the ap- plied displacement amount at the pad-tissue interface. The deviation of the actual displacements from this model is computed. interface), the displacement magnitudes are higher than those predicted by the model, with the maximum difference from the model equal to approxi- mately 17% of the applied displacement. This pattern is consistent for all frames, with the magnitude of the non-linearity increasing proportionally to the magnitude of the applied displacement. The plots in Figs. D.2 to D.6 also display a small lateral trend, where the cross-over point between positive and negative errors shifts upwards on the right side of the ROI. This corresponds to the horizontal misalignment of the ultrasound transducer, and which was also seen in the results in Appendix B. The comparison to the 1D model indicates that the stand-off pad does not follow closely to a 1D deformation model. Furthermore, a change in boundary conditions or stand-off pad geometry may cause even more com- plex displacement curves and profiles in the stand-off pad. Therefore un- 146 D.2. Results derstanding the 3D deformation of the stand-off pad in any application is essential. 147 D .2. R esu lts Figure D.2: Difference between tracked displacements and 1D linear model displacements in the stand-off pad with TDPE motion-tracking (window size 0.5 mm). The difference profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings.148 D .2. R esu lts Figure D.3: Difference between tracked displacements and 1D linear model displacements in the stand-off pad with TDPE motion-tracking (window size 1.0 mm). The difference profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings.149 D .2. R esu lts Figure D.4: Difference between tracked displacements and 1D linear model displacements in the stand-off pad with TDPE motion-tracking (window size 2.0 mm). The difference profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings.150 D .2. R esu lts Figure D.5: Difference between tracked displacements and 1D linear model displacements in the stand-off pad with the ST algorithm. The difference profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings.151 D .2. R esu lts Figure D.6: Difference between tracked displacements and 1D linear model displacements in the stand-off pad with the TDPE-ST Hybrid algorithm. The difference profiles for applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns (in both compression and decompression) are shown. The transducer centerline is highlighted with ’o’ markings.152 D.2. Results (a) (b) (c) (d) (e) Figure D.7: Difference between tracked displacements and 1D linear model displacements at the transducer centerline for different motion-tracking methods. The differences correspond to applied displacements of 0, 10, 20, 50, 100, 150, 200 and 250 microns in both compression (blue) and decom- pression (red). (a) TDPE (0.5 mm window). (b) TDPE (1.0 mm window). (c) TDPE (2.0 mm window). (d) ST. (e) TDPE-ST Hybrid. 153 Appendix E Mean and Standard Deviation of Displacement Extrapolation Errors There are two trends that are noted in the results presented here. The first is that both error and error variance are roughly proportional to the applied displacement. This is caused by more pronounced artifacts in the displace- ment curves for higher applied displacements and poorer polynomial fits for these curves. The second is that the effect of hysteresis can be observed by comparing the error at the first and last frames in each sub-figure of Fig. E.1. For example, the magnitude of the hysteresis for TDPE motion-tracking re- sults was 3–4 microns at an applied displacement of 0 microns (see Chapter 4, Section 4.6.2, Figs. 4.15(a) to 4.15(c)). In Figs. E.1(a) to E.1(e), the error is near 0 microns at the beginning of the compression/decompression cycle (0 microns applied displacement), and approximately 3 microns at the end of the cycle (0 microns applied displacement). These error results indicate that displacements can be tracked with a high degree of accuracy within the stand-off pad. 154 Appendix E. Mean and Standard Deviation of Displacement Extrapolation Errors (a) (b) (c) (d) Figure E.1: Mean (left) and standard deviation (right) of extrapolation er- rors for all motion-tracking methods at each frame. The mean and standard deviation at each frame were computed using the errors from all RF lines and all trials. (a),(b) Mean and standard deviation of errors (TDPE - 0.5 mm window). (c),(d) Mean and standard deviation of errors (TDPE - 1.0 mm window). 155 Appendix E. Mean and Standard Deviation of Displacement Extrapolation Errors (e) (f) (g) (h) (i) (j) Figure E.1: (continued) (e),(f) Mean and standard deviation of errors (TDPE - 2.0 mm window). (g),(h) Mean and standard deviation of errors (ST). (i),(j) Mean and standard deviation of errors (TDPE-ST Hybrid). 156

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