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Three-dimensional Kinematic Analysis of Spine Motion

Permanent Link: http://ufdc.ufl.edu/UFE0041210/00001

Material Information

Title: Three-dimensional Kinematic Analysis of Spine Motion
Physical Description: 1 online resource (117 p.)
Language: english
Creator: Conrad, Bryan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: biomechanics, computer, graphics, image, kinematics, registration, spine
Biomedical Engineering -- Dissertations, Academic -- UF
Genre: Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: THREE-DIMENSIONAL KINEMATIC ANALYSIS OF SPINE MOTION Motion is an important function of the human spine and accurate measurement of that motion is critical to assessing spinal health and the effect of treatments. There is a great need for tools that allow accurate 3D intervertebral spine motion to be measured in vivo. The purpose of this study is to develop a method for registering a 2D radiograph with a 3D CT scan for the purpose of measuring 3D motion in the spine. This goal was achieved in three phases. The first phase of this project evaluated the accuracy of a fluoroscopic object recognition technique to measure the 3D position and orientation of a cervical disc arthroplasty implant. Although the experimental uncertainties of the proposed technique have been extensively analyzed with respect to the measurement of knee implant motions, the size, geometry, and type of motion of spine implants requires that these uncertainties be determined specifically for spine components. These uncertainties were determined using a cadaver model. The second phase of this project developed and evaluated the static accuracy and capture range of a novel 2D/3D image registration methodology using existing gold standard data. Digitally reconstructed radiographs were used in the registration algorithm to take advantage of the internal contours and density variation of the bony anatomy. In the third phase of this project, the uncertainties of measuring dynamic 3D kinematics of cervical vertebrae were determined. The tools developed in this project will allow clinicians and researchers to accurately quantify the performance of the normal spine as well as new implants designed to restore motion to the spine. This methodology also has applications for other joints, such as the shoulder, ankle, knee and hip.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Bryan Conrad.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Banks, Scott A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041210:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041210/00001

Material Information

Title: Three-dimensional Kinematic Analysis of Spine Motion
Physical Description: 1 online resource (117 p.)
Language: english
Creator: Conrad, Bryan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: biomechanics, computer, graphics, image, kinematics, registration, spine
Biomedical Engineering -- Dissertations, Academic -- UF
Genre: Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: THREE-DIMENSIONAL KINEMATIC ANALYSIS OF SPINE MOTION Motion is an important function of the human spine and accurate measurement of that motion is critical to assessing spinal health and the effect of treatments. There is a great need for tools that allow accurate 3D intervertebral spine motion to be measured in vivo. The purpose of this study is to develop a method for registering a 2D radiograph with a 3D CT scan for the purpose of measuring 3D motion in the spine. This goal was achieved in three phases. The first phase of this project evaluated the accuracy of a fluoroscopic object recognition technique to measure the 3D position and orientation of a cervical disc arthroplasty implant. Although the experimental uncertainties of the proposed technique have been extensively analyzed with respect to the measurement of knee implant motions, the size, geometry, and type of motion of spine implants requires that these uncertainties be determined specifically for spine components. These uncertainties were determined using a cadaver model. The second phase of this project developed and evaluated the static accuracy and capture range of a novel 2D/3D image registration methodology using existing gold standard data. Digitally reconstructed radiographs were used in the registration algorithm to take advantage of the internal contours and density variation of the bony anatomy. In the third phase of this project, the uncertainties of measuring dynamic 3D kinematics of cervical vertebrae were determined. The tools developed in this project will allow clinicians and researchers to accurately quantify the performance of the normal spine as well as new implants designed to restore motion to the spine. This methodology also has applications for other joints, such as the shoulder, ankle, knee and hip.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Bryan Conrad.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Banks, Scott A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041210:00001


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THREE-DIMENSIONAL KINEMATIC ANALYSIS OF SPINE MOTION By BRYAN PRESTON CONRAD A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORID A IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1

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2009 Bryan Preston Conrad 2

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To my girls 3

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ACKNOWLEDGMENTS I thank my committee for providing thoughtful feedback and insight. Dr. Horodyski has helped to keep the project focused on the clinical goals and applications of measuring spine motion and has also shared her extensive experience with statistical analysis. In every interaction I have had with him, Dr. Fregly has been a source of inspiration and encouragement. I also appr eciate his background in optimization techniques and for letting me borrow three co mputers and a corner of his lab to do several thousand registrations this past summ er. Dr. Zheng has given me a great deal of advice on many aspects of kinematics, image analysis and computer programming. The many interactions I have had with him in the Biomechanics and Motion Analysis lab have gone a long way in shaping my underst anding of how to apply engineering principles in a medical environment. I thank Dr. Banks for giving me the opportunity to work on an interesting, significant and challe nging project. His arrival at UF when I was desperately seeking a thesis advisor and proj ect was serendipitous I am incredibly grateful that he suggested that it might be interesting to st udy spine kinematics; despite the challenges (or maybe because of t hem), I cannot imagine working on a more rewarding project. I also appreciate the interaction and frequent feedback from my fellow graduate students. Bo, JD and Dr. David have done an excellent job of representing the engineering contingent in t he OSMI. The development of my image registration code was greatly assisted by the contributions of Shang, who laid the groundwork with JointTrack 2.0. I also appreciate the various insights and suggestions of Nick, Tim, Ben, and the many undergraduate st udents that have worked in t he lab over the years. 4

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I also thank my high school calc ulus teacher Anastasia Bilotta, who infected me with a passion for math and a zeal for solving difficult problems. I thank my family for the support and encouragement they have provided during my exceedingly long tenure as a graduate student. I started this journey the same year I married Suzanne and I assured her when we got married that there was no possibility of me ever pursuing a doctorate degree. Al though this was not part of the bargain when she married me, she has been a constant s ource of encouragement and help at every step of the process. She has displayed an incredible level of selflessness in giving me the time necessary to complete this wo rk, I could not have completed this degree without her help. Along the way we have be en blessed with two daughter s. Adeline is very curious about this book I am writing and would like me to read it to her when I am done. Esther has taken a keen interest in my laptop and has been trying to help me by typing a few lines for me every time I turn my back on her. 5

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TABLE OF CONTENTS page ACKNOWLEDG MENTS..................................................................................................4 TABLE OF CO NTENTS..................................................................................................6 LIST OF TABLES............................................................................................................8 LIST OF FI GURES..........................................................................................................9 LIST OF ABBR EVIATIONS...........................................................................................12 ABSTRACT ...................................................................................................................13 CHAPTER 1 INTRODUC TION....................................................................................................15 Clinical Moti vation...................................................................................................15 Spine Anat omy.......................................................................................................16 Hypothes is..............................................................................................................17 Specific Aims..........................................................................................................18 2 MEASUREMENT OF CERVICAL DISC REPLACEMENT KINEMATICS USING MODEL TO IMAGE REGISTRAT ION.....................................................................19 Introducti on.............................................................................................................19 Clinical Moti vation............................................................................................19 Purpos e............................................................................................................20 Methods ..................................................................................................................22 Image Registra tion Tool...................................................................................22 Experimental Setup..........................................................................................23 Data Anal ysis...................................................................................................24 Result s....................................................................................................................25 Discussio n..............................................................................................................31 3 VALIDATION OF A METHOD TO REGISTER A 3D CT VOLUME TO A SINGLE PLANE 2D FLUOROSCOPIC IMAGE USING DIGITALLY RECONSTRUCTED RADIOGRAPH S.....................................................................................................34 Introducti on.............................................................................................................34 Clinical Moti vation............................................................................................34 Medical Image Re gistrati on..............................................................................34 Purpos e............................................................................................................35 Methods ..................................................................................................................37 Digitally Reconstruc ted Radiog raphs...............................................................37 6

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Perspective Projection Geom etr y.....................................................................43 Registration Algorit hm......................................................................................44 Image Metric.....................................................................................................45 Mean squa res............................................................................................46 Normalized correla tion metr ic....................................................................48 Normalized cross correlati on......................................................................50 Gradient corre lation ...................................................................................51 Gradient diffe rence....................................................................................55 Mutual info rmation.....................................................................................57 Mutual information and gr adient corre lation ...............................................59 Optimize r..........................................................................................................61 Starting Po sitions .............................................................................................62 Result s....................................................................................................................63 Discussio n..............................................................................................................67 Conclusi on..............................................................................................................72 4 MEASUREMENT OF SPINE KINEMA TICS BY REGISTERING LATERAL FLUOROSCOPY IMAGES TO DIGITALLY RECONSTRUCTED RADIOGRAPH S.....................................................................................................73 Introducti on.............................................................................................................73 Review of Current Methods fo r Measuring Sp ine Motion.................................74 Purpos e............................................................................................................76 Methods ..................................................................................................................77 Specimen Prepar ation......................................................................................77 Experimental Protoc ol......................................................................................77 Imaging Prot ocol..............................................................................................80 Data Anal ysis...................................................................................................81 Software Deve lopment.....................................................................................82 Result s....................................................................................................................85 Discussio n............................................................................................................104 5 CONCLUS ION......................................................................................................108 LIST OF REFE RENCES.............................................................................................109 BIOGRAPHICAL SKETCH .......................................................................................... 117 7

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LIST OF TABLES Table page 2-1 RMS errors for image based measur ements compared to marker based measurem ents....................................................................................................25 2-2 Precision for image based measur ements compared to marker based measurem ents....................................................................................................26 2-3 Bias for image based measurem ents compared to marker based measurem ents....................................................................................................26 3-1 Analysis of registration e rrors for each pos e paramet er.....................................66 3-1 Specimen pr operties ...........................................................................................81 4-1 Average RMS Errors for translati ons................................................................102 4-2 Average RMS Errors for rotati ons.....................................................................102 4-3 Average bias for translations ............................................................................102 4-4 Average bias fo r rotations.................................................................................103 4-5 Average precision fo r translati ons....................................................................103 4-6 Average precision for rotati ons.........................................................................103 8

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LIST OF FIGURES Figure page 2-1 CAD model of the Synt hes Pro-Disc C cervical ar throplasty implant..................24 2-2 Absolute segmental rotation (in degrees) of the superior impl ant.......................26 2-3 Absolute segmental rotation (in degrees) of the superior impl ant.......................27 2-4 Rotation errors (in degrees ) of the superio r implant ...........................................28 2-5 Absolute segmental rotation (in degrees) of the infe rior impl ant.........................29 2-6 Absolute segmental rotation (in degrees) of the infe rior impl ant.........................30 2-7 Rotation errors (in degrees) of the inferior implant .............................................31 2-7 Surface model projections of a cervical spine arthropl asty impl ant....................32 2-8 Surface model projections of a cervical spine arthropl asty impl ant....................33 3-1 Diagram of the work flow dur ing the registra tion proc ess...................................35 3-2 Diagram of the radiogr aphic projection geometry...............................................39 3-3 Diagram of the DRR projection geom etry...........................................................40 3-4 Texture mapping. ................................................................................................41 3-5 DRRs of a thoracolumbar spine s pecimen .........................................................42 3-6 DRRs of a cervical spine spec imen....................................................................42 3-7 Example of a fluoroscopic image of the thoracol umbar sp ine............................43 3-8 The projection geomet ry of the radiographic imaging equipment.......................44 3-9 Schematic diagram of the registration process...................................................45 3-10 Plots of the MS metric function vers us pos e.......................................................47 3-11 Plots of the NC metric function vers us pos e.......................................................49 3-12 Plots of the NCC metric function vers us pos e....................................................51 3-13 Changing the amount of image blur. ...................................................................52 3-14 An example of edge images fr om the fluoroscopic im age..................................53 3-15 Plots of the NCC metric function vers us pos e....................................................54 9

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3-16 Plots of the GD metric function vers us pose.......................................................56 3-17 Example of Mut ual informa tion. ..........................................................................58 3-18 Plots of the MI metric function vers us pos e........................................................59 3-19 Plots of the GC+MI metr ic function ve rsus pos e.................................................60 3-20 Percentage of successful registrations. ..............................................................64 3-21 For registrations t hat were su ccessful................................................................65 3-22 Three orthogonal views of a surface model a spi nal vert ebrae..........................68 4-1 Definition of the motion capture refer ence fram e................................................78 4-2 Definition of the anatom ical referenc e frame......................................................79 4-3 Image of the fluorosc opic testing setup..............................................................79 4-4 Screen capture of pyTrack so ftware. ..................................................................83 4-5 Diagram of the pyTr ack data stru cture...............................................................84 4-6 Segmental rotation (in degrees) of the superior vertebrae.................................86 4-7 Segmental rotation (in degrees ) of the superio r vertebrae.................................87 4-8 Segmental rotation (in degrees) tracking errors of the superior vertebrae..........88 4-9 Segmental translation (in mm) of the superio r vertebr ae....................................89 4-10 Segmental translation (in mm) of the superior vertebrae ....................................90 4-11 Segmental translation tracking errors (in mm) of the super ior vertebrae............91 4-12 Segmental rotation (in degrees) of the inferior vertebr ae...................................92 4-13 Segmental rotation (in degrees) of the inferior vertebr ae...................................93 4-14 Segmental rotation tracking errors (i n degrees) of the inferior vertebrae............94 4-15 Segmental translation (in mm) of the inferior vertebr ae......................................95 4-16 Segmental translation (in mm) of the inferior vertebr ae......................................96 4-17 Segmental translation tracking errors (in mm) of the infe rior vertebrae..............97 4-18 Relative joint angles (in deg) calc ulated from image bas ed motion data............98 10

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4-19 Relative joint angles (in deg) calc ulated from marker based motion data...........99 4-20 Relative joint translations (in mm) ca lculated from image based motion data..100 4-21 Relative joint translations (in mm) calculated from marker based motion data.101 4-18 Lateral bending motion presents challenges with a lateral fluoroscopic view...104 11

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LIST OF ABBREVIATIONS 3D Three Dimensional CT Computerized Tomography DRR Digitally Recons tructed Radiograph MRI Magnetic Resonance Imaging PET Positron Emission Tomography SPECT Single Photon Emission Computed Tomography US Ultrasound MSE Mean Square Error NCC Normalized Correlation Coefficient GD Gradient Difference GC Gradient Correlation MI Mutual Information ACDF Anterior Cervical Discectomy and Fusion mTRE mean Target Registration Error 12

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Abstract of Dissertation Pr esented to the Graduate School of the University of Fl orida in Partial Fulf illment of the Requirements for t he Degree of Doctor of Philosophy THREE-DIMENSIONAL KINEMATIC ANALYSIS OF SPINE MOTION By Bryan Preston Conrad December 2009 Chair: Scott A. Banks Major: Biomedical Engineering Motion is an important function of the human spine and accurate measurement of that motion is critical to a ssessing spinal health and the effe ct of treatments. There is a great need for tools that allow accurate 3D intervertebral spine motion to be measured in vivo The purpose of this study is to develop a method for registering a 2D radiograph with a 3D CT scan for the purpose of measuring 3D motion in the spine. This goal was achieved in three phases. T he first phase of this project evaluated the accuracy of a fluoroscopic object recognition technique to measure the 3D position and orientation of a cervical disc arthropl asty implant. Although the experimental uncertainties of the proposed technique have been extensively analyzed with respect to the measurement of knee implant motions, the size, geometry, and type of motion of spine implants requires that these uncertainties be dete rmined specifically for spine components. These uncertainties were determined using a cadaver model. The second phase of this projec t developed and evaluated the static accuracy and capture range of a novel 2D/3D image registration methodology using existing gold standard data. Digitally reconstructed radiographs were used in the registrati on algorithm to take advantage of the internal contours and density variation of the bony anatomy. In the 13

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14 third phase of this project, the uncertainties of measuring dynamic 3D kinematics of cervical vertebrae were determined. The tools developed in this project will allow clinicians and researchers to accurately quant ify the performance of the normal spine as well as new implants designed to restore moti on to the spine. This methodology also has applications for other joints, such as the shoulder, ankle, knee and hip.

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CHA PTER 1 INTRODUCTION Clinical Motivation The purpose of the h uman musculoskeleta l system is to support the body and allow motion. If we didnt need to move, we would have roots and photosynthesize.(1) Motion is a critical function of the body. Measuring motion is important to understanding the function of the joints of the body. There are many di sabilities that can adversely affect joints in the body and understanding t he motion of those joints can provide an avenue to restore the proper func tion of the joint. Range of jo int motion often is used as an indicator of the extent of disability caus ed by joint disease. Likewise, changes in motion provide a valuable outcome measure to assess the effectiveness of clinical interventions. Although many orthopaedic ther apies attempt to re store normal joint motion, in some cases it is not clear how to measure or even evaluate normal joint motion. The situation of c linically measuring spine kine matics is so muddled that not only is there disagreement over how much motion is des irable, but there is also controversy over how to define whether any motion exists at all. Some authors have suggested that less than 2-4 deg of motion constitutes a fusion, while others hold that a fusion must be demonstrat e less than 1 deg of motion. These differences are likely attributable to the large uncertainties associated with currently available motion measurement tools. There are numerous challenges that must be addresse d to perform accurate measurements of skeletal motion. Most joints must be ev aluated in 3-dimension (3D) motion to fully appreciate their full function. While it can be convenient and useful to sometimes model them as su ch, joints generally do not behave as simple mechanical 15

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linkages lik e a hinge, ball-socket or universal joint. The most complete model of joint motion requires that it be modeled as a 6-degree of freedom joint. It is also difficult to measure skeletal motion externally due to th e paradoxical motion of the overlying soft tissue. While these challenges ar e encountered when performing kinematic measurements for every joint in the body t hey are perhaps most acute when measuring spine motion. The fundamental purpose of this project is to develop, validate and utilize a method to accurately measure spinal motion. There are three specific requirements that drive this research project: Intervertebral motion it is critical to measure motion at each functional spinal unit, between adjacent vertebrae, so t hat dysfunction and treatments can be evaluated at the point of application. Three-dimensional it is necessary to measure spine motion in three dimensional space, so that the full functional range of motion of the spine can be evaluated. in vivo it is important to measure spine motion in a clinical setting using noninvasive methods, so that the full physi ological environment (including active muscle forces) can be tested. Spine Anatomy A brief review of spine anatomy as it rela tes to the purpose of this research study is presented below, much more detailed works (such as (2)) are av ailable with greater depth than is possible here. The human spine is a unique st ructure consisting of 24 indiv idual bones. Of these 24 bones there are seven cervical vertebrae, twelve thoracic vertebrae and five lumbar vertebrae. While the vertebrae in each region share common characteristics, each bone has a uni que geometry that def ines the type and amount of motion is allowable at that level. In the upper cervical spine, C1 and C2 differ significantly in structure and function from the rest of the cervical spine and are 16

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generally treated separately. C1, also called t he atlas, articulates wit h the occiput of the skull and allows only flexion and extens ion mo tions. The C2 vertebra, also known as the axis, forms a pivot which articulates with C1 to allow nearly planar axial rotation. The remainder of the cervical, thoracic and lu mbar vertebrae (C3-L5), have three points of motion between each level, the intervertebr al disc and the right and left facets. At each level the angle of the facet joints di ctates the amount and direction of motion allowed. Oblique in the cervical spine to allow freedom for flexion-extension, lateral bending and axial rotation; nearly vertical and para llel to the frontal plane in the thoracic spine to restrict all motion except for lateral bending; and nearly vertical and oriented parallel to the sagittal plane in the lumbar spine to allow flexion-extension. The articulations in the spine present a comp lex kinematic environment where motions are coupled. For example: as the cervical spi ne rotates axially, it also bends laterally. When cervical spine motion is being evaluated, it is therefore valuable to account for motions in all three dimensions. Becaus e the individual vertebrae reside deep within surrounding soft tissue, there are very few external landmarks that can be used to quantify intervertebral motion, which limits the use of exte rnal sensors for measuring intervertebral spine motion. Hypothesis The purpos e of this project is to quantify the 3D motions of the human spine for both normal anatomy as well as for implanted devices. The specific hypothesis that drives this work is that model to image r egistration can be used to accurately measure the kinematics of the spine. The conception of this pr oject was inspired from the following observations. First, single pla ne fluoroscopy and 2D/3D registration have been used for over 15 years to quantify the in vivo motions of knee arthroplasty 17

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component s(3-12). Second, more recently, th is technique has been extended so that not only can metallic objects be registered, but bone models can be tracked as well. Third, advances in imaging and computing allow higher resolution images to be acquired, which is critical for tracking the relatively smaller bones of the spine. The specific aims are designed to provide a co mprehensive evaluation of the accuracy of applying a 2D/3D registration algorit hm to measuring spine motion. Specific Aims The specific aims of this research project were: Specific Aim 1. Determine the accu racy of a fluoroscopic object recognition technique to measure the 3D position and orientation of a cervical disc arthroplasty implant using existing model based registration methods. Although the experimental uncertainties of the proposed technique have been extensively analyzed with respect to the measurement of knee implant motions, the size, geometry, and type of motion of spine implants requires that these uncertainties be determined specifically for spine compon ents. A cadaver model was used to quantify the uncertainty of this method. Specific Aim 2. Determine the accu racy of a fluoroscopic model registration technique to measure the 3D position and ori entation of the vertebrae. Digitally reconstructed radiographs were used in the registration algorithm to take advantage of the internal contours and dens ity variation of the bony anatomy. This phase of the research pr oject developed of a set of software tools that enable 2D/3D registration of spin al vertebrae. The experi mental uncertainties for registering static images were determined for the image regist ration process. Existing static gold standard data were used for this phase of the project. Specific Aim 3. Characterize the 3D motion of vertebrae during dynamic motion. The final aim is to demonstrate an in vitro application of a 2D/3D registration algorithm for measuring dynamic spine mo tions and to evaluate the uncertainties of measuring vertebral kinematics usi ng image registration. The technique developed in Specific Aim 2 was utilized in a cadaver study to measure dynamic intervertebral kinematics in the spine. T he ultimate results of this project is to generate a unique set of tool s that can be used to measure 3D segmental spine motion in vivo. 18

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CHA PTER 2 MEASUREMENT OF CERVICAL DISC RE PLACEMENT KINEMATICS USING MODEL TO IMAGE REGISTRATION Introduction Clinical Motivation Anterior cervical discectomy and fusion (A CDF) currently are the gold standar d for treating the symptoms of radiculopathy and myelopathy. Although ACDF has favorable short-term results, recent data suggests that in the longterm, fusion adversely affects adjacent vertebral levels. It is suspected that by eliminating motion at one level, increased stress and motion is induced at adjacent levels, which leads to degeneration. Cervical arthroplasty has been introduced as an alternative to fusion to preserve motion at operated levels. Although several clinic al trials are underway to evaluate the effectiveness of various cervical disc repl acement implants, im portant biomechanical parameters remain to be addressed. The co mbination of concern over the long-term consequences of spinal arthrodesis and the pr oliferation of motion preserving spinal technology has created an acute need for accu rate measurements of 3-dimensional spine motion. Symptoms of cervical spondylosis include pain and motor dysfunction caused by impingement of the nerve roots (radiculopathy) or spinal cord (myelopathy). Patients with cervical spondylosis are typically treated conservatively at first. If the patients symptoms are unresponsive to conservative tr eatment, surgery may be indicated, in which case, ACDF can be used to provide decompression to the nerves and spinal cord. Although excellent 2 year clinical results have been reported for ACDF, recent results from longer term studies are soberin g. Hillibrand has documented a cumulative 2.9% per year rate of repeat ed operation at segments adjacen t to a fusion resulting in 19

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approximately 26% of patients r equiring an additional fusion by 10 years(13). Goffin(14) recently reported that 92% of patients with cervical inter body fusion eventually displayed signs of adjacent segment degeneration (follow-up 60187 months). While the mechanism responsible for adj acent level degeneration has not been clearly defined, it is often postulated to be a result of altered biomechanics of the spine caused by the fusion(15). Another widely held theory is that t he adjacent degeneration is a continuation of the natural history of the disease process(16). However, in the study by Goffin et al.(14), younger trauma patients without histor y of pre-existing degenerative disc disease had similar rates of adjacent degeneration to older patients with spondylosis or disc herniat ion. This finding suggests that biomechanical factors play an important role in understanding an d potentially alleviating adjacent disc degeneration. Cervical disc replacements have been designed to maintain motion in the cervical spine while allowing decompression of nerve roots and the spinal cord. The goal of cervical arthroplasty is to maintain norma l neck kinematics, thereby avoiding increased stresses on levels adjacent to the surgery. Although several clinical trials are underway to evaluate the effectiveness of various cervical disc replacement implants(17-21), important biomechanical parameters remain to be addressed. Purpose Motion measurement is critical for evaluat ing clinic al modalities. The increasing use of motion preserving devices in the sp ine has highlighted the need for accurate kinematic measurement tools to evaluate the performance of these new implants. Single plane fluoroscopy has been used for over 15 years to quantify the in vivo motions of total knee replacement impl ants, with reported accuracies of 0.5-1.0 deg for rotations. 20

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The purpos e of this phase of the research project was to determine the accuracy and feasibility of using a fluoroscopic image registration technique to measure the 3D position and orientation of a cervical disc arthroplasty implant. 21

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Methods Image Registration Tool We propose to utilize techniq ues that we have previously implemented and validated on numerous studies of knee implants (8,12,22-27) to measure 3D motion of spinal arthroplasty components in the cerv ical spine. Radiographic images are produced when x-rays pass through space and ar e attenuated by the patients anatomy before striking a sensitive medium to cause a c hemical or electrical reaction. The x-ray beam emanates from a single point in space, creating a perspective projection of the object. The location of the x-ray source with respect to the image plane can be measured and the same projection can be r eproduced on a computer. Computer aided design (CAD) models of implant designs ca n be obtained from t he manufacturer or reverse engineered and used to create proj ections of the implant based on a perspective projection model. The position and orientati on of the CAD model can be modified until the computer generated projections of th e model match the views obtained from patients thus determining the position and orientation of the objects in 3D space. A number of groups around the world have used shape matching techniques for determining implant motion from singl e-plane radiographic views, studying a range of joints and activities including gait (4) stair-climbing(3), and deep knee bends(7). Although the details of the methods vary measurement precis ion for each moving segment is typically 0.5mm-1.0mm for im plant motions parallel to the image plane and 0.5-1.0 for all rotations(22). For the current experiment, used an existing tool developed in our laboratory to measur e spine arthroplasty kinematics. 22

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Experimental Setup A four-camera optical motion capture system (Motion Analysis Corp, Santa Rosa, CA) was used to establish the true position and orientation of each cervical vertebrae during the dynamic test. In our lab, th is motion capture system has demonstrated a positional accuracy of less than 0.2 mm for a volume of 1 m3. Three reflective tracking fiducial markers were attached to specif ic anatomical landmarks on each cervical vertebrae to allow them to be visualized with the optical motion capture system. Three cadaveric cervical spines that have been implanted with a cervical disc arthroplasty were obtained for this experime nt. Three dimensional CAD surface models of the cervical disc arthroplasty implants we re obtained from the manufacturer (Figure 2-1). Each cadaver spine was manually m anipulated through a range of motions while simultaneously recording both fluoroscopic images and optical motion capture of the spine. The position and or ientation of each cervical vertebrae and the implant was determined using both the optical system and the fluoroscopic technique. For the fluoroscopic data, the positi on and orientation of the implants was determined using existing model to image registration software (J ointTrack 1.0, previously developed in our lab). The accuracy of the position and or ientations determined by the fluoroscopic measurements were evaluated against the tr ue values obtained from the optical motion capture system. 23

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Figure 2-1. CAD model of the Synthes Pro-Disc C cervical arthroplasty implant that was evaluated for this experiment. Data Analysis For the error analysis, the absolute position and orientation of the two vertebrae was calculated for both measurement techniques The position and orientation at each frame, i, w as determined with respect to the neutral pose, which was defined as the first frame of the trial. Where A is a 4 x 4 homogenous transformation matrix. These absolute poses were determined for both the mocap and fluorosc opic techniques, and used to calculate the uncertainties between the two measurement systems. Motion capture data was collected at a rate of 60 frames/s and the fluoroscope captured images at a rate of 7.5 frames/s. To ensure that the motion capture and fluoroscopic data are comparabl e in terms of temporal re solution, the fluoroscopic 24

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results were resampled at a rate of 60 Hz using an inter polation algorithm. The da sets were temporally synchronized by performing a linear regression between the mocap and fluoroscopic data. The fluoroscopic data was shifted in the time dom until the R2 of the linear regression was ta ain maxi miz ed. This method optimized the align rmine (RMS) e rrors were calculated to determine the experimental uncertain ties. r ental and -1.95 3.36o for 2-1. RMS ed mpared t measurements. l Flexion Extension (dLateral Be nding (deg) Axial Rotation (deg) ment between the two data sets.. Experimental errors w ere determined by measuring the deviation of the fluoroscopic calculated absolute position and orientation data from the motion capture values. Differences were calculated for each frame of data and averaged to dete mean errors. Root mean square Results The disc replacement implants were placed a t three different levels in the cervical spine (C3-C4, C4-C5, C6-C7). The absolute rotations of each implant were calculated during each motion trial (flexion-extension tria l, lateral bending trial, and axial rotation trial) using both the image based measurement technique (F igures 2-1 and 2-4) and fo the marker based gold-standar d technique (Figures 2-2 and 2-5) The experim uncertainties for calculating the absolute range of motion of each implant were 0.23 1.68o for flexion-extension, 0.13 1.73o for lateral bending axial rotation. (Tables 2-1 to 2-3, and Figures 2-3 and 2-6). Table errors for image bas measurements co o marker based Tria eg) AR 1.49 1.70 4.42 FE 2.17 1.50 1.59 LB 2.19 3.54 8.03 Grand Total 1.95 2.25 4.68 25

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Table 2-2. Precision for image based measurements compared to marker based measurements. Trial Flexion Extension (deg) Lateral Bending (deg) Axial Rotation (deg) AR 1.16 1.33 4.18 FE 2.11 0.96 1.40 LB 1.78 2.90 4.50 Grand Total 1.68 1.73 3.36 Table 2-3. Bias for image based m easurements compared to marker based measurements. Trial Flexion Extension (deg) Lateral Bending (deg) Axial Rotation (deg) AR 0.53 0.28 0.62 FE -0.08 0.51 -0.47 LB 0.24 -0.39 -6.01 Grand Total 0.23 0.13 -1.95 Figure 2-2. Absolute segmental rotation (in degrees) of the superior implant of each spine specimen in primary direction of motion (white background) and the offaxis motions (grey background), measured using optical marker based motion tracking. 26

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Figure 2-3. Absolute segmental rotation (in degrees) of the superior implant of each spine specimen in primary direction of motion (white background) and the offaxis motions (grey background), measured using optical marker based motion tracking. 27

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Figure 2-4. Rotation errors (in degrees) of the superior implant of each spine specimen in primary direction of motion (white background) and the off-axis motions (grey background), calculated by subtract ing the optical marker based results from the image based results. 28

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Figure 2-5. Absolute segmental rotation (in degrees) of the inferior implant of each spine specimen in primary direction of motion (white background) and the offaxis motions (grey background), measured using image based motion tracking. 29

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Figure 2-6. Absolute segmental rotation (in degrees) of the inferior implant of each spine specimen in primary direction of motion (white background) and the offaxis motions (grey background), measured using optical marker based motion tracking. 30

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Figure 2-7. Rotation errors (in degrees) of the inferior implant of each spine specimen in primary direction of motion (white background) and the off-axis motions (grey background), calculated by subtract ing the optical marker based results from the image based results. Discussion While analyzing the data for th is exp eriment, it was discovered that the size and geometry of the implant made axial rota tion and lateral bending pose estimations unreliable. The implant models are fairly symmetric in these planes and large changes in the rotation of the implant were not r eadily discernable from the projection image (Figures 2-7 and 2-8). In t hese two figures, the implant wa s rotated from -5 to +5 degrees about the X and Y axes. These changes in orientation have very little affect on the shape of the projection and make it very difficult to accurately match the implant shape to the fluoroscopic projection. The sma ll size (63 x 26 pixels ) of the implant with 31

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respect to the full fluoroscopic field of view (1024 x 1024 pixels) als o make it difficult to detect measure the motion of the implant. These results demonstrate that single plane fluoroscopy can be a useful tool for quantifying the dynamic fl exion-extension motion of spinal implants. However, there are limitations to this method that make it unfeasible for evaluating axial rotation and lateral bending from a single sagittal plane fluoroscopic image. In addition to the problems in measuring X and Y rotations, this method r equires surface models for registration, which make it difficult to apply to tracking vertebrae. Figure 2-7. Surface model projections of a cervical spine arthropl asty implant rotated about the X-axis (axis oriented toward the right). The top left image is at -5 deg, and the bottom right image is at +5 deg of rotation. 32

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Figure 2-8. Surface model projections of a cervical spine arthroplasty implant rotated about the Y-axis (axis ori ented up). The top left im age is at -5 deg, and the bottom right image is at +5 deg of rotation. 33

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CHA PTER 3 VALIDATION OF A METHOD TO REGISTER A 3D CT VOLUME TO A SINGLE PLANE 2D FLUOROSCOPIC IMAGE USING DI GIT ALLY RECONSTRUCTED RADIOGRAPHS Introduction Clinical Motivation The ability to accurately track the motion of the spi ne is a valuable tool for diagnosing the extent of spi nal disorders and assessing the functi onality of motion preserving implants. Howe ver, a standardized method for quantifying spine motion has not yet been embraced by the clinical or research communities. Medical Image Registration The rapid development of new functional and anatomical imaging modalities, has presented clinicians and resear chers with the challe nge of integrating a wide array of data into a useful format. Images can be acquired using CT, MRI, positron emission tomography (PET), single photon emission computed tomography (SPECT), Ultrasound (US), X-Ray, video (from arthroscope, la ryngoscope, or laparoscope). Depending on the imaging modality, the di mensionality of the images c ould be 2D, 3D (spatial), 3D (temporal sequence of 2D images), or 4D (temporal sequence of 3D images). Furthermore, the images may be acquired from t he same patient at di fferent times, from different patients, or even from an atlas of standard images. Further complexity is introduced due to the fact that the images ar e often captured at different resolutions, have different fields of view and have different geometric distortions based on the imaging equipment. A number of excellent and thorough revi ews have been written on the topic of medical image registration, for example Va ndenelsen(28), Maintz(29) and Hill(30). For different applications of image registration, the problem statement is unique and will 34

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dictate the nature of the soluti on. One of the most common applic ations is for alignment and integration of two or more 3D images ac quired using different imaging modalities. Another area of active research is the c hallenge of aligning 3D CT image to a 2D fluoroscopic image. This problem has severa l applications in the intraoperative setting, where it can be used to visualize anatomic structures as well as to guide instruments and radiation therapy. We describe a te chnique for applying 2D/3D image registration to measure the position and or ientation of spinal vertebrae, which can be used to measure dynamic motion in the spine. Purpose A diagram of the work flow for the im age registration process is presented in Figure 3-1. Figure 3-1. Diagram of the work fl ow during the registration process. 35

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In this chapter, we will describe a method that will allow the 3D kine matics of an individual vertebrae to be measur ed from single plane latera l fluoroscopic images. The key element of this method is to use digita lly reconstructed radiographs (DRRs) created from a computed tomography (CT) volume to register the fluoroscopic images. When the CT volume is optimally aligned, t he DRR image has a maximum similarity to the fluoroscopic image. Although the ultimate intention is to use this tool for the measurement of dynamic spine motion, the goal of this phase of the research project is to assess the uncertainties of measuring the position and orientation of static images. In the next chapter, we will evaluate the uncertainties associated with measuring dynamic spine motion. The required accuracy for clinical use is highly dependent on the application. Based on similar studies in the literature, a threshold for clinical accuracy was set at 2mm in-plane mean Tar get Registration Error (mTRE) for this study. We chose mTRE as an outcome meas ure because it provides a scalar value that represents the position and orientation errors of the 3D volumes transformed into 2D position distances in the projection plane. While it is represented as a distance, it is a function of the position and orie ntation of the 3D volume. 36

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Methods The requirements of the curr ent project are to develop, validate and utilize a pose estimation tool that can: Measure position and orientation in 3D Measure position and orientat ion of individual vertebrae Have sufficient accuracy for clinical and research use (<2mm mTRE errors) Be non-invasive, and appropriate for in vivo populations Digitally Reconstructed Radiographs DRRs hav e been used in clinical applications for surgical planning since at least 1990(31). They have also been utilized extensivel y in surgical navigation to register a pre-operative CT scan to an intra-operative fl uoroscopic image(32-38), thus allowing the location of internal anatomic structures to be determined relative to external landmarks. Motion analysis can then be used to track in struments that are introduced to the operative field and allow the surgeon to visualize their position and orientation with respect to internal anatomy. DRRs are created by projecting a 3D image volume onto a 2D image plane (Figures 3-2 and 3-3). There are several methods for performing this projection. Raycasting, for example, is a fairly common pr ojection algorithm. Ray-casting works by calculating a series of lines or rays that or iginate from each pixel location in the image plane and travel through the volume, toward the perspective focus. Along the path of the ray, each pixel value encountered in t he volume is summed to determine the pixel value at the location where the ray originat es from the imaging plane. Ray-casting can produce images that look very similar to ac tual radiographs because the computational method is analogous to the physical process of creating radiographic images. 37

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Radiographs are produced by emitting photons from a point source and detecting the amount of energy received by the image detector. Any objec ts that are encountered by the photons along their path attenuate the beam and result in lower energy being detected at the image in tensifier. While ray-casting can produce high-qual ity, realistic images, the calculation is com putationally int ensive, especi ally for large images. An alternative to ray-casting is to use 3D texture mapping(39) methods which can take advantage of hardware accelerated graphics (40-43) processing units on modern graphics cards. Texture mappi ng calculates a 2D image slice from any different viewpoint, reorienting the volume to the desired position and orient ation, and then reslicing the volume along the direction of projection (Figure 3-4). By using hardware accelerated texture mapping, the generat ion of DRR images can be accomplished significantly faster than the CPU based ray-casting method. Render speed affects image registration since, at each new pos e, a new DRR image must be rendered. Texture mapping results in some image artifacts that are not present in ray-cast images, but for the current research project, these artifacts were determined to be acceptable (Figure 3-5 and Figure 3-6), w hen compared to fluoroscopic images (Figure 3-7). The use of texture mapping to produce DRRs allowed us to achieve reasonable performance (each registration took approximately 60-90s). 38

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Figure 3-2. Diagram of t he radiographic projec tion geometry. The object being imaged, a thoracolumbar spine in this example, is placed between the x-ray source and the detector, or image intensifier, wh ich forms the image plane. By using a calibration procedure, the imaging geometry of a specific radiography device can be obtained. 39

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Figure 3-3. Diagram of t he DRR projection geometry. Usi ng the projection geometry derived from the calibration of the x -ray device, a computer graphics scene can be constructed to produc e DRRs with matching perspective projections to the x-ray images. The differences between this virtual setup and the radiographical setup described in Figur e 3-3 is that instead of an x-ray source, an openGL camera is used, and instead of an anatomical object being imaged, a projection is created digitally from an existing CT scan. The pixel spacing and dimensions of the DRR are controlled to match the x-ray image. A comparison of the render time for ra y-casting and texture mapping algorithms was performed by rendering the same 3D vo lume 20 times and calculating the average time required to project a 512x512 pixel image. On an Intel Core Duo CPU T5550 running at 1.83GHz with a NVIDIA GeForce 8400M GS graphics card, ray-casting took an average time of : 0.84 0.22 seconds (average frame rate: 1.26 0.27 frames/second) and texture mapping took: an average time of: 0.15 0.04 seconds (average frame rate: 7.18 1.41 frames/second). On an Intel Core Duo CPU T9400 running at 2.53GHz with a NVIDIA Quadro FX 770M graphics card, ray-casting 40

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took an average time of : 0.37 0.01 seconds (average frame rate: 2.73 0.08 frames/second) and texture mapping took: an average time of: 0.03 0.01 seconds (average frame rate: 30.41 3.86 frames/second). The raycasting rendering, which is performed on the CPU, scales roughly with t he speed of the processor (1.83GHz vs. 2.53GHz), where the 2. 53GHz processor rendered the volume 2.2 times faster than the 1.83GHz processor. H owever, the text ure mapping rendering which is performed on the graphics card scales with GPU performance (1033 vs. 5297 in 3DMark06 benchmark), where the Quadro FX 770M card rendered the volume 4.2 times faster than the 8400M GS card. Figure 3-4. Texture mapping reslices the CT volume, so that the resulting grid is parallel to the image plane. The image data is interpolated and mapped onto the resampled grid and the contribut ion of each voxel to the image is calculated using the graphics hardware. Texture mapping is significantly faster than using software based ray-cast ing methods to render a 3D volume. 41

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A B Figure 3-5. DRRs of a thoracolumbar sp ine specimen generated using two different rendering techniques. A) Ray-casting B) Texture mapping. In the texture mapped image, there are sli ght wood grain artifacts due to interpolation between pixels. The mean frame rate for 20 renderings using the ray-cast mapper was 1.85 +/0.10 fps, the mean fr ame rate for 20 renderings using the texture mapper wa s: 8.15 +/0.37 fps A B Figure 3-6. DRRs of a cervical spine s pecimen generated using two different rendering techniques. A) Ray-casting B) Text ure mapping. In the texture mapped image, there are slight wood grain artifacts due to in terpolation between pixels. 42

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A B Figure 3-7. Example of a fl uoroscopic image of the thoracolumbar spi ne A) lateral view and B) anterior view. Perspective Projection Geometry In order for DRR imag es to match fluorosc opic images, it is critical that the perspective projection param eters are established. The parameters that need to be determined from the radiographic imaging eq uipment in order for the DRR images to have the same geometrical projections as the radiographic image s are the principal point, principal distance and pixel spacing(44) (Figure 3-8). T he principal distance is the length of the line from the x-ray source to the image pl ane, perpendicular to the image plane. The principal point is the point in the image plane at which a perpendicular line extending from the image plane will intersect the x-ray source. Pixel spacing is the physical size of the image pixels in t he horizontal and vertical directions. 43

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Figure 3-8. The projection geometry of the radiographic imaging equipment. The principal distance, x and y offset and pi xel size are required to create DRR projections that match the images c aptured from the fluoroscopic system. Registration Algorithm The registration algorithm ties toget her the necessary component s of the registration and manages the flow of data from DRR, metric, transform, and optimizer. A basic framework for the registration algorit hm used in this work is presented below (Figure 3-9). The process begins with the two input images that are to be registered, a 2D image from the fluoroscopic device and a 3D CT (or MRI) volume. 44

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Fluoroscopic image Figure 3-9. Schematic diagram of the registration process (a dapted from the ITK Software Guide(45)). The five basic components are: Input images, metric, DRR, optimizer and transform. Image Metric A key step in the registration of a 3D volume to a 2D image is defining a measure that returns a value which represents the si mi larity between two images. This measure is called a similarity measure or image metric, and the two terms will be used interchangeably. For this proj ect the similarity measurem ent is calculated on two 2D images (fluoroscopic image and DRR image). T he inputs to the metr ic function are the two images and the output is a scalar value representing the sim ilarity of the two images. The most important characteristic of the image metric functi on is that it returns a minimum value when the two images are opt imally aligned. A wide variety of image similarity metrics have been described in t he literature[31,32,48,49,80,83,84,85] for different image registration applications. The choice of an image metric heavily depends on the details of the r egistration being performed. Fa ctors that can affect the CT Image Metric Optimizer DRR Transform Transform Parameters Similarity Measure 45

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image metric include: image resolution, image size and imaging modality (CT, MRI, ultrasound, etc). The ability of the metric to accurately quantif y spatial alignment between two images depends on the in trinsic properties of the im ages. An ideal metric is sensitive to differences in structural posit ion, but robust to noise and occlusions. All of the image metrics considered for this proj ect use the pixel intens ity values from the fixed and DRR images as inputs. The different image metrics that were considered for this experiment are presented below. Mean squares One of the simplest image si milarity measures is the mean squares (MS) metric (52,45). Where: Ai is the i-th pixel in the fixed image Bi is the i-th pixel in the DRR image N is the total number of pixels considered The mean squares metric is equal to 0 when t he two images are identical. This metric has a fairly large capture range(45), but doe s not perform well when images are taken from different modalities, because it assumes that the pixel intensities between two homologous points in the compared images matc h exactly. This measure has been shown to be the optimum similarity metric when two images differ only by Guassian noise(53). 46

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Figure 3-10. Plots of the MS metric func tion versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. 47

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Normalized correlation metric The normalized correlation (NC) metric(45) accommodates linear shifts in pixel intensity between two images by calculating the product of two homologous pixels and normalizing it by the geometric mean of t he sum of squares for each image. Where: Ai is the i-th pixel of the fixed image Bi is the i-th pixel of the DRR image N is the number of pixels considered NC is a better choice than MS when there is a shift in pixel intensities between two images, because the pixel magnit ude is normalized for each image. 48

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Figure 3-11. Plots of the NC metric functi on versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. 49

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Normalized cross correlation The normalized cross correlation (NCC) (54) metric is very similar to NC, except that each image is first normalized to its mean pixel value befor e determining the product between the two images. Where: Ai is the i-th pixel of the fixed image Amean is the mean intensit y of the fixed image Bi is the i-th pixel of the DRR image Bmean is the mean intensity of the DRR image N is the number of pixels considered 50

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Figure 3-12. Plots of the NCC metric function versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. Gradient correlation The gradient correlation (GC) metric has been demonstrated in previous studies to be a useful measurement for comparing DR R images to fluoroscopic images( 33). The 51

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GC metric uses edge information from the im age by calc ulating an image gradient using the Sobel filter and Gaussian blur with a standard deviation of 1. 4. The GC metric is the same as the NCC, except the i nput images are gradient images. Where: Ai is the i-th pixel of the gradient of the fixed image Amean is the mean pixel intensity value for the gradient of the fixed image Bi is the gradient ima ge from the DRR image Bmean is the mean pixel intensity val ue for the gradient of the DRR image N is the number of pixels considered For this study, a Gaussian blurring filter (Figure 3-13) was applied to the images before calculating the gradients, a standard deviation of 1.4 was chosen based on preliminary testing. An example of a gradient image of one vertebrae is shown in Figure 3-14. Figure 3-13. Changing the amount of im age blur before calcul ating the edge image accentuates different featur es of the image. All im ages were blurred with a Gaussian filter and then a Sobel edge det ecting algorithm was applied in the horizontal and vertical directions. From left to right, the images were blurred with a kernel size of: 1, 2, 4, 8, 16. 52

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Figure 3-14. An example of edge images fr om the fluoroscopic image (left) and the DRR image (right) for a vertebrae in opt imal alignment. A standard deviation of 1.4 was used in the Gau ssian filter for these images. 53

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Figure 3-15. Plots of the NCC metric function versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. 54

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Gradient difference The gradient difference (GD)(54) metric computes the difference between two edge images, using a scale parameter to adjust the intensit y between the two images. Where: Aedge is the edge enhanced fixed image Bedge is the edge enhanced DRR image scale is the a scalar parameter (see text for detail) Idiff is the difference image created from Aedge and Bedge is the variance of the Idiff N is the number of pixels in Idiff The scale parameter is include d in the image difference calculation to compensate for different ranges of intensity values in the images being compared. The scale is optimized using brute force over the range ma x(A)/max(B)/100 to ma x(A)/max(B) to find the value that minimizes the metric result. Edge images were calculated using a Sobel gradient filter, which was applied in both the horizontal and vertical dimensions. 55

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Figure 3-16. Plots of the GD metric func tion versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. 56

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Mutual information Mutual information (MI)(53,48) is an example of a class of similarity metrics based on statistical descriptions of intensity probability distributions. The concept of MI is that the information contained in two images is maximized when the images are perfectly aligned. Specifically, this metr ic calculates the uncertainty of knowing the pixel value in one image given a value in the other image. For example, if the two images are completely independent, the mu tual information would be 0, that is knowing one pixel would yield no information about the other image. If the two images are identical, then knowing one pixel would allow the correspondi ng pixel in the other image to be known exactly, and the mutual info rmation would be high (Figure 3-9). The benefit of using statistical descriptors of the im age is that they ar e insensitive to shifts or inversion (as with MRI and CT) of pixel intensities. Where: p(A) is the probability density f unction for the fixed image P(B) is the probability dens ity function for DRR P(A,B) is the joint probability density f unction for the fixed image and DRR N is the number of pixels considered 57

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Figure 3-17. Example of Mutual informati on as applied to a fluoroscopic image and DRR image in optimal alignment. Mutual information is calculated from the probability density functions of each im age, which are simply the normalized histograms of the images. The joint histogram is a plot of each images individual histogram, with the fluoroscopic image on the x-axis and the DRR image on the y-axis. The product of marginal entropy is a measure of the total amount of information contained withi n both images. Mutual information is the probability of knowing a pixel in one image, given the intensity value for the other image. 58

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Figure 3-18.. Plots of the MI metric function versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. Mutual information and gradient correlation A third image metric w as created by combini ng the MI and GC metric into a single similarity measure (MI+GC), with the theory that the unique characteristics of each would synergistically improve the performance of the combined metric (Figure 3-19). 59

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Figure 3-19.. Plots of the GC+MI metric function versus pose. Dimensions 0-2 correspond to X, Y and Z translations, and dimensions 3-5 correspond to rotations about the X, Y and Z axes. Translations are in mm, and rotations are in radians. 60

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The plots of the metric function versus pose provide us eful information on the characteristics of the metric. For example, the ratio of the highest value to the lowest value determines the sensitivity of the metric to small changes in pose. The slope of the metric is also important: if the metric begins to slope downward further from the optimimal pose, then it indicates the metric has a large capture range. Based on the results of the metric function versus pose analysis, we chose to use three different metrics (MI, GC, GC+MI) for the remainder of the experiments in this chapter. Optimizer The image similarity metric defines the co st function that should return a minimum value when the images are aligned. The choice of an optimizer for finding the minimum value for the cost function has a significant impact on the results of the registration algorithm. The optimizer takes as an input the value of the cost function from which it generates a new pose vector to evaluate in the cost function. The challenge of the optimizer is to relatively quickly desc end into the global minimum without getting trapped in spurious local minimum. For this study, a global optimizer, simulated annealing ( SA), was initially chosen. SA was selected because its global characteristics would potentially allow for a very large capt ure range, meaning relatively poor starting poses would still converge to the true solution. The principle of the SA algorithm is to take random parameter steps in the region around the current guess. If a step improves the cost function, it is acc epted and used as the starting guess for the next iteration. A fraction of the steps that have a worse cost function value are also accepted since the cost function might need to go uphill to escape a local minimum. At each iteration, the step size is reduced (quenched), until it reaches a minimum value. Initial testing with the SA optimizer demonstrated t hat the stochastic nature of the algorithm made tuning 61

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the parameters very difficult, since sometimes the same parameter set would result in a successful registration and sometimes it would not converge. The second optimizer that was consider ed was the regular st ep gradient de scent optimizer (RSGD). The RSGD optimizer calcul ates a finite-difference gradient of the parameter space at each it eration and takes a step along each parameter dimension proportional to the gradient for that parameter. Because the RGSD optimizer is deterministic, it was easier to determine a parameter se t that would consistently converge the optimizer. Ultimat ely, the RSGD optimizer was used in the registration algorithm. The following param eters were chosen based on pilot testing from a small subset of different starting poses. The si ze of the step taken at each iteration was reduced by a factor of 0.75 each time the gradient changed sign. The stopping conditions for the optimizer were: step size was less than 0.1, more than 100 iterations or gradient change of less than 1e-4. The op timizer was repeated for five runs, with the best result of the previous run being used as the starting point for the next run. The initial maximum step size was 4 and was reduced by a factor of 0.618 after each run. Starting Positions A standard set of starti ng positions prov ided with the gold-st andard dataset were used as initial guesses for the optimizer. Starting positions are described by the mean target registration error (mTR E), which defines the average displacement error (in mm) over a grid represent ing the volume of one vertebral body(51). A total of 150 starting positions were uniformly distributed over the range of 0-15 mm mTRE, so that the capture range of the registra tion algorithm could be determined. Registration success was defined as mTRE in the plane of fluor oscopic image within 2mm. The mTRE is calculated by transforming a grid of points using the pose being evaluated. The mean 62

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distance of these points from the true position is the mT RE, and therefore the error measure is a function of both rotation and translation errors. Results A total of si x vertebral bodies, three each fr om two spines, were registered. Each vertebral body was registered at each of the 150 starting posit ions, so that there were a total of 900 registrations performed for each si milarity metric. Th e starting positions were grouped into 1 cm bins for this anal ysis, such that each bin contained 60 registrations with which to gauge the success of the algorithm (10 star ting positions x 6 vertebrae). A registration wa s deemed successful if the in-plane mTRE was less than 2mm. The combined gradient correlation an d mutual information similarity metric produced successful registrations 88% of the time when starting within 4mm mTRE (Figure 3-11), compared to 75% successful registrations with the standard gradient correlation metric and 30% successful registrations with the standard mutual information metric over the same range of starting posit ions. For the registrations that were successful, the error was consistently between 1.2-1.6mm regardless of starting position or metric used (Figure 3-12). For evaluating the accuracy at matching each pose parameter (translation and orientation), we defined 1.2 mm and 1.2 deg (for translations and rotations, respectively) as t he threshold for success for that parameter. This value was chosen because it represent s approximately the overall accuracy of the algorithm as measured in mTRE (Figure 3-12). The percentage of successful final results for individual pose parameters is pr esented in Table 3-1. X translations are approximately (they represent global axes t hat are not aligned wit h the anatomic axes) out of the fluoroscopic plane and are therefore expected to be less accurate than the other parameters. 63

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Figure 3-20. Percentage of successful registrations plotted against the amount of error in the starting position. Both the GC and combined GC+MI metric had similar results, with the success rate at approx imately 80% when the starting position is within 4 mm mean target registration error (mTRE). Successful registration was defined as within 2mm mTRE for in-plane errors. 64

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Figure 3-21. For registrations that were successful, the average in-plane mTRE was invariant to the amount of starting error. 65

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Table 3-1. Analys is of registration e rrors for each pose parameter when using the combined MI+GC metric. For individual parameters, success was defined as being within 1.2 mm or 1.2 deg of the opt imum value at the final registration pose. Axes are global and are not a ligned with anatomic reference system. Cells that are greater t han 95% are highlighted in green, those between 8095% are yellow and those less than 80% are red. % of final parameters within 1.2mm/1.2deg Starting Error (mTRE) Xtrans YtransZtransXrot Yrot Zrot 0-1 70% 100% 100% 100% 100% 80% 1-2 90% 100% 100% 100% 100% 87% 2-3 80% 100% 100% 100% 100% 77% 3-4 97% 100% 100% 100% 100% 79% 4-5 83% 100% 93% 100% 100% 73% 5-6 74% 100% 93% 100% 100% 74% 6-7 60% 93% 87% 93% 90% 60% 7-8 70% 87% 90% 80% 77% 53% 8-9 63% 90% 80% 80% 80% 73% 9-10 76% 55% 83% 59% 55% 66% 10-11 57% 83% 73% 83% 77% 53% 11-12 73% 60% 73% 77% 80% 43% 12-13 47% 77% 70% 43% 67% 67% 13-14 63% 50% 80% 80% 53% 73% 14-15 57% 70% 77% 87% 50% 70% 66

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Discussion One of the requirements of this res earch project was to develop an image registration methodology that could be used to measure the position and orientation of vertebrae. Previous work in our lab has made extens ive use of 3D CAD models to register to 2D fluoroscopic images. This technique has worked well for tracking large non-symmetric implants, but ear ly experience demonstrated that surface models of the vertebrae would be insufficient to determine the bone pose. While surface models have proven to be very useful for matching bones with uniform density and minimal internal detail, this is not the case for spinal vert ebrae. Figure 3-22 shows a surface model of a spinal vertebra that was created from a CT scan. While the surface model is a high fidelity representation of the anatom ical structures, it is not ve ry effective for matching to a 2D radiographic image. In the spine there are a number of internal features that can provide useful landmarks for model to image regi stration. In particular the areas around the facet joints, pedicles and lateral mass/tr ansverse processes are obscured when the spine is in a neutral position. When the sp ine rotates about one of the axes parallel to the image plane, there is more overlap of th e vertebral bodies as well as the facets, lamina, pedicles. It is difficu lt to accurately visualize this overlapping region using surface models of the bone. The result is that there is a large uncertainty in finding the true position of the bone model that will genera te the unique projection observed in the fluoroscopic image. For this reason we chose to use DRRs for this project so that we would be able to generate projections of t he bone volume that were closely matched to the actual fluoroscopic images. 67

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We have previous ly used a surface model based technique for tracking the motion of cervical spinal arthroplasty implants. Be cause of the small size of the implants and their symmetrical shape, rotations and transla tions out of the plane of motion could not be accurately measured. The current te chnique provides several advantages over tracking the implants alone. Since CT scans are used as models for registration, nonoperated vertebrae can be tracked in addition to implants. This is critical for the important application of tracking moti on of non-operated vertebrae adjacent to an implant. If it is assumed that the implant is rigidly fixed to the bone it is anchored to, then the vertebrae and implant structure can be used for im age registration, which will provide significantly more geometrical in formation than using the implant alone. Figure 3-22. Three orthogonal views of a surface model a spinal vertebrae with an implant compared to DRR renderings of the same vertebrae. A) Anterior surface model, B) Lateral surface model, C) Axial surface model, D) Anterior DRR, E) Lateral DRR, F) Axial DRR 68

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Previous research by Penney(33) evaluated 6 different similarity measures for 2D/3D image registration of lumbar spi ne images. They found gradient difference, gradient correlation and pattern intensity to have the best results, with rotational RMS errors of 0.2-0.5 deg and translation RMS erro rs of 0.3-0.5 mm in plane and 4-5 mm out of plane. They also found that mutual information had the largest errors, for the particular images used in the investigation. This result is contrary to previous data that suggests mutual information to be highly ac cu rate for 3D to 3D registration. The difference is possibly due to the nature of the images being registered. Mutual information utilizes statistical descriptors of the images, sampling more pixels will generally result in less variability of the probability distribution function. Therefore including more pixels, such as is the case for 3D/3D volumes, can increase its effectiveness. Our results co rroborate the observation of Penney(33) in that we found mutual information alone to be less accurate t han gradient correlation, but this could be because the region of interest in our registra tion was relatively small (approximately 75 x 150 pixels). The gold-standard data used in this study was originally produced and described by Van De Kraats(51). Their investigation ev aluated two different similarity metrics, a gradient based method and an intensity based method (gr adient difference). The results presented in this chapter are in good agreement with the dat a reported in their investigation for CT to singl e plane fluoroscopy for capture region, however we did observe slightly larger errors than they r eported for the intensity based method (0.6 mm 69

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compared to 1.2 mm). This difference could be due to differences in generating the DRR imag es and in the optimizers that were implemented. In a similar study of 3D/2D CT and MRI to x-ray image r egistration in the lumbar spine, Tomazevic(55) reported average mT RE values of 0.2-0.5mm (depending on vertebral level) for biplane registration using CT volumes. For their biplane registration setup, they determined a capture region of approximately 6mm mTRE. As in the current study, they also observed a rapid dr op-off in successful registrations beyond the capture region. This is in contrast to resu lts in the same paper that show as a steady, almost linear, drop in successful r egistrations for MR I to x-ray. One novel contribution of the current re search was the evaluation of a unique image similarity metric, by combining the results of gradient correlation and mutual information into a single measurement. The theory behind this metric is that the two different functions would be sensitive to different features in the image and by combining them, the resulting metric would be more robust than either of the individual components alone. Our results demonstr ate that when com pared head-to-head the gradient correlation metric was significantly more accurate than mutual information alone. Even still, there seem s to be a modest synergistic e ffect by combining the two measures and that the combined metric has a slightly higher success rate. The time duration of each registration is not as critical for our intended application of tracking kinematics compar ed to the surgical navigati on application. However, increasing the speed can facilitate user interact ion during the registration process. For example, if each registration can be completed in a few minutes or less, then a user can oversee the optimizer and stop the registration process and restart it with a new initial 70

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guess if the optimizer is not converging. The generation of DRRs is the bottleneck for our registration algorit hm, and this can be significantly sped up with high performance graphics cards. For these experiments, relatively modest consumer graphics cards were used (Nvidia GEForce 9400 GT, Nvidia GEForce 8400 GS and Nvidia GeForce 8600 GT), based on benchmarks, it is expected that a high end graphics card (Nvidia Geforce GTX 285) could increase the speed of DRR generation by at least a factor of 4. Also with the recent introduction of graphics hardware specifically designed for general purpose computing (eg Nvidia Tesla) it mi ght be possible to achieve even greater increases in registration speed. 71

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Conclusion These results demonstrate that single pl ane fluoroscopy can be a useful tool and accurate tool for measuri ng 3D position and orientation of spinal vertebrae when a staring position within 4mm mTRE can be s upplied by the user. The range of the capture region could possibly be increased by modifying the image metric or the optimizer. Since all three of the metrics evaluated in this study seem to have a similar drop-off in capture range around 4 mm, it is possible that this is an artifact of the optimizer used. By modifying the optimizer to search a larger region, it might be possible to increase the capture region. We are in the process of exploring additional global optimization options that can be implemented effi ciently without requiring an excessively high number of iterations to conv erge. The next step in this project is to apply this image registration technique to measure vertebral motion in dynamic fluoroscopic image series. 72

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CHA PTER 4 MEASUREMENT OF SPINE KINEMA TICS BY REGISTERING LATERAL FLUOROSCOPY IMAGES TO DIGITALLY RECONSTRUCTED RADIOGRAPHS Introduction It is widely recognized that many sp inal disor ders have a biomechanical component which is often manifest in either a loss of motion or hyper-motion (instability). The American Medical Associ ation recommends measuring spine range of motion using a goniometer or inclinom eter to document permanent impairment associated with chronic low ba ck pain(56). In response to this proposal by the AMA, Nitschke(57) investigated the practical usef ulness of these instruments and reported poor reliability when using a goniometer or dual inclinometer to measure thoracolumbar flexion, extension, lateral bending and axial ro tation. Clinicians are therefore presented with the dilemma of having a mandate to meas ure spine motion, but the available tools are unreliable. At a more basic level, ther e are still questions regarding the in vivo 3D kinematics of the normal spine. The challenge lies in measuring complex 3D motion of a series of individual non-superficial vertebrae in vivo Most of the solutions available to date fail at least one of these criteria. Numerous methods have been proposed and implemented for quantifying in vivo spine mo tion. In the following sect ion, we explore the current options and demonstrate t hat there is a critical need for a technique that can accurately, reliably and non-invasively measure the in vivo intervertebral kinema tics of the cervical and lumbar spine. 73

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Review of Current Methods for Measuring Spine Motion Optical motion tracking is often used for tracking the motion of the whole body (or even multiple bodies) through a large capture volume. Such systems have proven to be very useful for measuring gait mechanics and sports activities, but are inadequate for measuring the motion of individu al vertebrae in the spine. There are several limitations to optical motion capture technology. Mark ers placed on the skin surface suffer from errors due to soft tissue artifact when the so ft tissues movement does not coincide with the underlying bone motion. Even in areas of the body where bony landmarks are relatively superficial, such as the medial and lateral condyles of the knee, large deviations between bone motion and marker motion have been docu mented. In the spine, it is not possible to attach external skin based markers in a way that would allow accurate measurements of the 3D movements of individual vertebrae. Electromagnetic systems(58-61) have also been used to measure spinal ROM. Our lab has made extensive use of this methodology in cadavers(62-69) where the sensors can be rigidly and invasively attached to the vertebrae. However, for in vivo measurements, this techniqu e is generally limited to external skin based attachment and like optical motion tracking, it suffers fr om the errors due to soft tissue artifact. Other specialized systems have been devel oped to attempt to measure spine motion using externally attached linkages (CA 6000) (70,71) or a series of inclinometers and magnets(72) (CROM) or accelerometers(73,74) (Spinal Mouse). However, these devices only allow the global motion of the spine to be accurately measured and are not able to determine the amount of motion occurri ng at each individual segment. To asses the extent of spinal disease, it is critical that motion is m easured at individual functional spinal units, so that the appropr iate levels can be treated. In measuring outcomes, it is 74

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also important to determine whether motion is occurring at the operated level or at adjacent levels. Another common method for measuring spinal motion that is widely accepted in the clinical environment is by evaluating two dimensional static radiographs at the extents of the range of motion (e g. flexion-ext ension films). Spine motion that occurs in the plane of the image can be measured direct ly from the image, however care must be taken when measuring translati ons that the appropriate reference frames are taken into account and that consistent landmarks are chosen as the basis for measurements. While this method is able to measure the maximum range of motion (ROM), it is not able to describe the dynamic motion of the spine. Two-dimensional lateral flexion-extensi on radiographs alone are inadequate to be used as a clinical outcome measure, and have been shown to give limited information on the underlying pathologic condition. (75) The uncertainty associated with measuring flexion-extension ROM from radiographs is estimated at 3-5 deg and fusion is generally defined as motion less than 2-4 deg(76-78) There has been a great deal of controversy clinically over how to define how much measured motion is relevant since difference between a completely fused spine and normal motion can be as little as 6 deg of ROM. An interesting new technique that coul d potentially facilitate measuring dynamic kinematics is 4D (3D volume over time) im aging using either MR I(79) or CT(80). However, 4D imaging equipment is still in an early st age of development and not yet capable of tracking in vivo spine motions. Dynamic CT has been used in a cadaver study to capture a 3D image at the extent of motion, due to space limitations within the 75

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CT, it would be challenging to perform functi onal activiti es while being imaged.(81) During the time required to obtain each 3D im age, the subject must remain completely static during the acquisition of the image, or the image will contain motion blur. It is also possible that the kinematics of the joints will be differ ent because of the static requirements than what would be observed during dynamic motion. Some researchers have used invasive techniques to attach motion sensors tospinous processes using k-wires(82). The in vasive nature of this technique makes it unlikely to gain widespread acceptance for measur ing motion in healthy individuals. It is also possible that the insertion of pins into the spine might have an affect on an individuals ability to move normally. Radiostereometric analysis (RSA) provides accurate measurements, but requires invasive surgery to implant metallic beads in the bone. Because it is an invasive technique it is only used in subjects who are already undergoing surgery, in which case the surgeon would have access to the nece ssary anatomical landmarks to place the beads. In the cervical spine, some invest igators have experienced difficulty in using RSA, due to the relatively small size of the vertebral body not allowing sufficient distribution of the beads.(83) Purpose There is a critical need for a technique that can accurately, reliably and noninvasiv ely measure the in vivo intervertebral kinematics of the cervical and lumbar spine. The increasing use of motion preservi ng devices in the spine has highlighted the need for accurate kinematic measurement tools to evaluate the performance of these new implants. Furthermore, a fundamental need exists for accurate measurements of 76

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normal and pathologic motion to better inform clinic ians, researchers, and implant designers. Single plane fluoroscopy has been us ed for over 15 years to quantify the in vivo motions of total knee replacem ent implants, with r eported accuracies of 0.5-1.0 deg for rotations in the image plane. This methodol ogy has been modified to incorporate the additional capabilities of regi stering DRR projection images and shown accuracy of 1.2 mm mTRE for in-plane motion (Chapter 3). The purpose of this project was to determine the accuracy of using an image based 2D/3D registration technique to measure the 3D segmental kinematics of a cervical spine during dynamic motion. Methods Specimen Preparation Three fresh frozen human cadaveric cervic al spines were obtained instrumented with a Synthes ProDis c-C total disc replacement (Synthes Spine, West Chester, PA). For specimen 1, the intervertebral implant was placed at C4-C5, for specimen 2 the implant was placed at C6-C7 and for spine 3 t he implant was placed at C3-C4. The two vertebrae at the operated level (superior and inferior) were used for the 2D/3D image registration kinematics measurements. Experimental Protocol To establis h the Ground Tr uth motion of the implant s, a four-camera optical motion analysis system (Motion Analysis Co rp, Santa Rosa, CA) was used to measure the 3D position of markers attached to anatomic landmarks (Figure 4-1). Three markers were attached to both the superior and inferior vertebrae at the operated level. The anatomic coordinate system for the fluorosc opic system was defined by identifying three landmarks in the CT image: left and right mid-pedicle, and the mo st anterior point of the 77

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vertebral body at the mid-pedicle level. T he origin of th e coordinate system is the midpoint between the right and left pedicle mark ers. The X-axis is defined between the right and left mid-pedicle points a nd positive to the right. The Y-axis is in the plane of the three landmarks pointing anteriorly. T he Z-axis is perpendicular to the Xand Yaxes and is positive in the crani al direction (Figure 4-2). The cranial and caudal ends of the spine we re potted in polystyrene resin (Bondo Inc, Atlanta, GA). The caudal end of the spine specimen was secured in a vice clamp and positioned in the fluoroscopic devices so that a lateral image could be obtained (Figure 4-3). A manipulator handle was attached to the crani al end of the specimen so that the spine could be manually maneuvered thorough a range of mo tion, while limiting radiation exposure to the in vestigator. Each spine wa s then moved through a passive range of motion in orthogonal planes: flexio n-extension, lateral bending and axial rotation. A B C Figure 4-1. Definition of the motion captur e reference frame. A) superior view, B) lateral view, C) anterior view. 78

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A B C Figure 4-2. Definition of the anatomical refe rence frame in the CT volume. A) superior view, B) lateral view C) anterior view. Figure 4-3. Image of the fluoroscopic test ing setup. The optical motion tracking markers are visible on the spine specimen. 79

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Imaging Protocol A Siemans AXIOM-artis fluoroscope was utilized, with the peak energy set to73 kVp, exposure time of 6 ms and frame rate of 7.5 frames/second. The full fluoroscopic images were 1024x1024 pixels, with a pixel size of 0.34x0 .34 mm. For analysis, the images were cropped to 512x512, which allo wed the vertebrae C3-C7 to be visible during the entire motion sequence. Fluorosc opic images were captured concurrently with the optical motion capture data. Fo llowing the motion test, a CT (Siemans, Sensation 16) scan was acquired for each spi ne. For the CT scan the peak energy was set to 140 kVp and the slice thickness was 0.5 mm, with 0.25 mm overlap between slices. Details of the specimen pr operties are presented in Table 3-1. After the CT scans were acquired, the images were processed (ImageJ, National Institutes of Health, USA) to removed overla pping vertebrae, so that a volume could be created which included one and only one vertebr a. The volume was cropped to the bounding box of the vertebra. An image mask was created by using a threshold value that removed the soft tissue from the CT images, while leaving the cortical and cancellous bone intact. The mask was applied to the image, leavi ng the raw intensity values for the bone while eliminating the ba ckground and soft tissue. In each image slice, adjacent vertebra were manually airb rushed out of the image using the spraycan tool. 80

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Table 3-1. Specimen properties. Specimen CT Pixel Spacing (mm/pixel) Tested Levels Spine 1 (0.164, 0.164, 0.5) C4-C5 Spine 2 (0.279, 0.279, 0.5) C6-C7 Spine 3 (0.193, 0.193, 0.5) C3-C4 Data Analysis In order to measure motion of individual verebra, an anat omical coordinate system was defined for each bone. For the CT volu me used in the image registration method this was performed by identifying anatomical landmarks on the image slices. For the motion capture data, the mark ers themselves were attached to specific anatomic locations s o that they would define a comparable re ference system to the image registration method. Kinematics were calcul ated for each individual bone by aligning the dynamic pose to an initial static image at the beginning of each trial. The motion capture data was collected at a rate of 60 Hz, and the fluoroscopic data was collected at 7.5 Hz. To obtain data on the same time scale, the fluoroscopic data was interpolated to 60 Hz. The dat a between the two systems was synchronized in the temporal domain by optimizing the lin ear regression between the motion capture data and the fluoroscopic data. The fluorosc opic data series was shifted in the time domain by one frame, and the linear regression was calculated. The frame which returned the largest R2 value from the linear regression was chosen as the first frame of the fluoroscopic data. Errors were defined by subtracting the fluoroscopic kinematics from the motion capture kinemat ics. RMS errors were calculated for each motion. Bias 81

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and precision were als o measured by calc ulating the mean and standard deviation of the error measurements. The relative joint angles between the proximal and distal vertebral body were also calculated. While these data were not utilized in the uncertainty analysis because of the low magnitude, they provide insight into the accuracy of using a fluoroscopic measurement tool for clinic al segmental ROM evaluations. The kinematics of the intervertebral motion are calculated as follows: Likewise, for the optical motion capture (mocap) measurements: Software Development One of the challenges of image registration is to obtain a good initial pose for the 3D volume to match to the 2D fluoroscopic image. To facilit ate this process, a graphica l user interface (pyTrack) was built for the image registration algorithm described in the previous chapter. The software was writt en in the Python programming language using QT for the user interface. This interface a llows the user to manipulate the 3D position and orientation of the CT volume and obser ve the DRR projection overlaid on the fluoroscopic image (Figure 4-13). The user in terface provides controls for navigating the data, adjusting the image and DRR di splay parameters, managing region of interests (ROIs), and for performing image regist ration. The interface provides several tools to assist the user in determining an in itial pose for the CT volume, setting up the registration and viewing the resu lts of the optimization: 82

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Charts for each pose parameter to allow t he user to visualize the trends in motion. Windowshade tool that allows the user to interactively split the screen so that the DRR and fluoroscopic image can be viewed at the same time. A checkerboard tool that creates a checker pattern alternating between patches of the DRR image and patches of t he fluoroscopic image. Kinematics charts that display the re lative joint angles between any two CT models loaded in the project. An ROI tool for interactively drawi ng, moving and storing region of interest information. An optimizer report tool that displays the cost function eval uations and parameter adjustments over the course of the optimization. In addition to providing a user interface, the pyTrack software also implements a data architecture (Figure 4-14) that allows all of the parameter s (data paths, object poses, parameter settings, ROIs, centers of ro tation, etc.) related to a project to be saved to an XML file. Figure 4-4. Screen capture of pyTrack so ftware user interface for performing 2D/3D DRR image registration. 83

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Figure 4-5. Diagram of t he pyTrack data structure. 84

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Results The rotations and translations of two cerv ical vertebrae were measured in each of three spine specimens using both marker based motion capture and 2D/3D image registration. The kinematics were calculated relative to the starting static pose of each vertebrae. In the figures bel ow, the results for each trial (flexion-extension, lateral bending and axial rotation) are presented in co lumns and the measured motions in each anatomical plane are presented in rows. Figures 4-6 to 4-6 present the rotation and translation results for the superior vertebrae, for marker based, image based and relative errors, respectively. Figures 47 to 4-12 present the rotation and translation results for the inferior vertebrae, for marker based, image based and relative errors, respectively. In the rotati on figures, the background for c harts of the primary motion direction is colored white, while off-axis motions are shaded gray. As expected for each motion trial, the la rgest motions were measured in the direction of motion; however some off-axis, coupled motions were also measured. For example: axial rotation (p rimary range of motion: 17 deg) was accompanied by a smaller amount of lateral bending (4 deg) and a small amount of axial rotation (8 deg) was measured during lateral bending (pri mary range of motion: 12 deg) tests. In all planes of motion, there was less e rror when measuring the inferior vertebrae compared to the superior vertebrae. This difference was statistically significant for inferior-superior translation (p=0.021), flexio n-extension (p=0.026), and axial rotation (p=0.015). 85

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Figure 4-6. Segmental rotation (in degrees) of the superior vertebrae of each spine specimen in primary direction of moti on (white background) and the off-axis motions (grey background), m easured using marker based optical motion tracking. 86

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Figure 4-7. Segmental rotation (in degrees) of the superior vertebrae of each spine specimen in primary direction of moti on (white background) and the off-axis motions (grey background), measured using image based 2D/3D registration. 87

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Figure 4-8. Segmental rotation (in degrees) tracking errors of the superior vertebrae of each spine specimen in primary direct ion of motion (white background) and the off-axis motions (grey background). Errors are calculated by subtracting the image based motion from the marker based motion. 88

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Figure 4-9. Segmental translation (in mm) of the superior vertebrae of each spine specimen, measured using marker based optical motion tracking. 89

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Figure 4-10. Segmental translation (in mm) of the superior vertebrae of each spine specimen, measured using image based 2D/3D registration. 90

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Figure 4-11. Segmental translation tracking errors (in mm) of the superior vertebrae of each spine specimen, measured using ma rker based optical motion tracking. Errors are calculated by subtracting the image based motion from the marker based motion. 91

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Figure 4-12. Segmental rotation (in degrees) of the inferior vertebrae of each spine specimen in primary direction of moti on (white background) and the off-axis motions (grey background), measured using marker based optical motion tracking. 92

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Figure 4-13. Segmental rotation (in degrees) of the inferior vertebrae of each spine specimen in primary direction of moti on (white background) and the off-axis motions (grey background), measured using image based 2D/3D registration. 93

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Figure 4-14. Segmental rotation tracking errors (in degrees) of the inferior vertebrae of each spine specimen in primary direct ion of motion (white background) and the off-axis motions (grey background). Errors are calculated by subtracting the image based motion from the marker based motion. 94

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Figure 4-15. Segmental translation (in mm) of the inferior vertebrae of each spine specimen, measured using marker based optical motion tracking. 95

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Figure 4-16. Segmental translation (in mm) of the inferior vertebrae of each spine specimen, measured using image based 2D/3D registration. 96

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Figure 4-17. Segmental translation tracking errors (in mm) of the inferior vertebrae of each spine specimen, measured using ma rker based optical motion tracking. Errors are calculated by subtracting the image based motion from the marker based motion. 97

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Figure 4-18. Relative joint angles (in deg) calculated from image based motion data. 98

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Figure 4-19. Relative joint angles (in deg) calculated from marker based motion data. 99

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Figure 4-20. Relative joint translations (in mm) calculated from image based motion data. 100

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Figure 4-21. Relative joint translations (i n mm) calculated from marker based motion data. 101

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Table 4-1. Average RMS Errors for translations, average over 3 spines and 2 vertebral bodies. Trial Medial Lat eral Translation (mm) Anterior Posterior Translation (mm) Inferior Superior Translation (mm) AR Trial 1.84 0.78 0.60 FE Trial 0.70 0.94 0.68 LB Trial 1.90 0.67 0.86 Grand Total 1.48 0.80 0.71 Table 4-2. Average RMS Errors for rotations, average over 3 spines and 2 vertebral bodies. Trial Flexion Extension (deg) Lateral Bending (deg) Axial Rotation (deg) AR Trial 1.63 2.19 1.73 FE Trial 0.84 1.70 1.12 LB Trial 1.34 2.97 2.05 Grand Total 1.27 2.29 1.63 Table 4-3. Average bias for translations, average over 3 spines and 2 vertebral bodies. Trial Medial Lateral Translation (mm) Anterior Posterior Translation (mm) Inferior Superior Translation (mm) AR Trial 0.32 -0.21 -0.18 FE Trial 0.20 -0.19 0.12 LB Trial -0.68 -0.44 0.18 Grand Total -0.05 -0.28 0.04 102

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Table 4-4. Average bias for rotations, average over 3 spines and 2 vertebral bodies. Trial Flexion Extens ion (deg) Lateral Bending (deg) Axial Rotation (deg) AR Trial -1.02 -0.57 0.05 FE Trial -0.21 -0.64 0.02 LB Trial -0.44 -0.49 -0.58 Grand Total -0.56 -0.57 -0.17 Table 4-5. Average precision for translations, average over 3 spines and 2 vertebral bodies. Trial Medial Lateral Translation (mm) Anterior Posterior Translation (mm) Inferior Superior Translation (mm) AR Trial 1.74 0.68 0.46 FE Trial 0.60 0.90 0.62 LB Trial 1.56 0.41 0.62 Grand Total 1.30 0.66 0.57 Table 4-6. Average precision for rotations, average over 3 spines and 2 vertebral bodies. Trial Flexion Extension (deg) Lateral Bending (deg) Axial Rotation (deg) AR Trial 1.21 2.07 1.56 FE Trial 0.67 1.15 1.01 LB Trial 1.03 2.30 1.65 Grand Total 0.97 1.84 1.41 103

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Discussion Smaller errors were observed for the infe rior vertebrae compared to the superior vertebrae. Different vertebrae were measured in each spine: C4-C5 for spine 1, C6-C7 for spine 2, and C3-C4 for spine 3, howev er there are general trends in the anatomy that might explain the difference in errors. From cranial to caudal, the vertebral bodies become larger and the spinous process becom es more prominent, two features which could be useful for image registration. Howeve r, the overall results for the three spines did not follow this pattern, as spine 3 (C3-4) had the smallest errors and spine 1 (C4-5) had the highest errors. Because the caudal end of the spine specimen was fixed to the ground while the cranial end was moved, th e more superior vertebrae experienced greater motion than more inferior vertebrae. There is a trend that during larger ranges of motion the errors are higher, and could explain the differences in errors between the superior and inferior vertebrae. A B Figure 4-18. Lateral bending motion present s challenges with a lateral fluoroscopic view. A) DRR projection of C6-C7 vertebrae at peak lateral bending pose, B). corresponding fluoroscopic image of the bones in the same pose. 104

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The most common application of 2D/3 D image registration for measuring kinematics has been tracking implant motion. There are several differences between tracking implants versus tracking bones. Firs t, while implant CAD models are availab le from their manufacturer, bone models must be derived from imaging studies. The preferred method for generating t hese models is through CT scans, however, it has also been demonstrated that slightly less accu rate models can be built from magnetic resonance imaging (MRI) scans(5). Second, since implants are constructed from dense, radiopaque, metallic materials, their inte rnal contours (if present) are not easily visible during fluoroscopic evaluation. However, bone has the property of radiolucency that allows internal contours of the structures to be visualized with fluoroscopy. By taking advantage of this additional geometric info rmation, it is theoretically possible to improve image registration results by using DRR projection images, which are a closer match to the fluoroscopic image than a surface model projection. Accuracy of measurement of spine motions is important clinically, where even small motions can be clinically relevant. Fo r example, the lower limit for normal spine intervertebral spine motion is approximat ely 7 deg, and fusion is often defined as an intersegmental ROM of less t han 3-5 deg. However, many existing methodologies are only accurate to within 2-3 deg, which can lead to a high proportion of mistakes in quantifying fusion success rates. The resu lts of the present study demonstrate improved uncertainties compared to existing methodologies. One commonly used technique for intervert ebral motion analysis in the spine is a 2D quantitative motion analysis (QMA) softwar e program produced by Medical Metrics. This software has been used in a number of clin ical trials to asses lumbar and cervical 105

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ROM after disc replac ement(19,84,21) or arthrodesis(85). In cadaver testing, Zhou etal(86), report rotati onal errors of 0.47+/-0.24 deg fo r flexion extension motions. Although their results demonstr ate excellent accuracy and repr oducibility, the test setup was constrained to allow only motion in the sagittal plane and the specimen was carefully aligned with the imaging plane. In a clinical scenario, it might be difficult to reproduce that same control ov er patient alignment, which would decrease the accuracy of this method. Also, this is purely a 2D measurement tool and makes no attempt to quantify axial rotation, or lateral bending. Despite these limitat ions, the number of studies that utilize this software highlights the critical need for intervertebral motion measurements in the spine. Tashman has previously reported usi ng DRRs to perform model-based bone tracking using a custom designed high-spe ed bi-plane fluoroscopy system(87). Their group has published results of tr acking glenohumeral(88) and knee motion(50,89,90,87). As in this projec t, their early papers used DRRs generated directly from CT data using the VTK 3D te xture mapping function(87). Some of their more recent studies have made use of a clus ter of 24 computers running in parallel to generate ray-traced DRRs(89). Using biplane-fluoroscopy and RSA as a gold standard, they have demonstrated accuracy of 0.385 mm RMS error for sca pula tracking and 0.374mm RMS for humerus tracking. There are some limitations to this study. It is not possible to judge whether the motions evaluated in this study are represent ative of kinematics that would be produced in vivo during active muscle activation. Howeve r, the motions evaluated in this study were intended to cover a normal passive range of motion for the spine, and for the 106

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purpose of evaluating the meas urement methodology, should be similar to the types of motions that would be observed clinically. The use of single plane lateral fluoroscopy inherently presents difficulties in measuring out of plane motion. For the cervical spine, this factor i s most problematic during lateral bending motion. In addition to the insensitivity to out of plane motion, latera l bending also produces significant occlusions between adjacent vertebra (Figure 4-13). It is possible that the use of bi-plane fluoroscopy would allow increased accuracy in measuring lateral bending and mediallateral translation. The presence of motion capture markers in the fluoroscopic views (Figure 4-13B) also creates occlusions wit h the bones and could decrease the accuracy of image registration, however, during clinical use these markers woul d not be present. 107

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108 CHAPTER 5 CONCLUSION Measuring 3D inter-segmental motion in t he spine is a challenging task, but one which can have a significant im pact on the clinical care of the spine. Three distinct clinical applications that c an directly benefit from improved motion measurements are: Diagnosis of disease early in the dis ease process when conservative therapies might be most advantageous Document the level of disability Evaluate the effectiveness of treatments This research project has presented a new methodology for measuring spine motion and reported the measurement uncertainties using both static and dynamic goldstandard data. This method was applied to measuring the 3D motion of an intervertebral cervical disc replacement implant. Several contributions were made during the c ourse of this work. The feasibility of using surface models to track cervical ar throplasty implants was documented. A new measurement tool was developed which facilit ated image registration of CT volumes to fluoroscopic images using DRRs. This is t he first reported work that has applied this technique to measuring motion in the cervical spine. A novel image metric was derived and characterized for performing 2D 3D image registration. The next steps in this line of resear ch are to continue to improve the image similarity metric and optimizer to make them more robust to poor image quality and occlusions. Although the present study has focused exclusively on measuring spine kinematics, this technique can readily be applie d to other joints such as the shoulder, knee and ankle.

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LIST OF REFERENCES 1. Banks S. Personal Communication. 2. Morris H. Human anatomy: A complete systematic treatise. Churchill; 1966. 3. Banks SA, Hodge WA. 2003 Hap Paul Award paper of the International Society for Technology in Arthroplasty Design and activity dependence of kinematics in fixed and mobile-bearing knee ar throplasties. The Journal of arthroplasty. 2004;19(7):809-816. 4. Banks SA, Fregly BJ, Boniforti F, Reinschmidt C, Romagnoli S. Comparing in vivo kinematics of unicondylar and bi-unicondyla r knee replacements. Knee Surg Sports Traumatol Arthrosc. 2005; 5. Moro-oka T, Hamai S, Miur a H, Shimoto T, Higaki H, Fr egly BJ, et al. Can magnetic resonance imaging-derived bone models be used for accurate motion measurement with single-plane three-dimensional s hape registration? Journal of Orthopaedic Research. 2007;25(7). 6. Bellemans J, Banks S, Victor J, Vandenneucker H, Moemans A. Fluoroscopic analysis of the kinematics of deep flexion in total knee arthroplasty. Influence of posterior condylar offset. J Bone Joint Surg Br. 2002;84(1):50-3. 7. Kanekasu K, Banks SA, Honjo S, Nakata O, Kato H. Fluoroscopic analysis of knee arthroplasty kinematics during deep flexion kneeling. The Journal of arthroplasty. 2004;19(8):998-1003. 8. Banks SA, Hodge WA. Implant design affe cts knee arthroplasty kinematics during stair-stepping. Clin Orthop Re lat Res. 2004;(426):187-93. 9. Banks S, Bellemans J, Nozaki H, Whiteside LA, Harman M, Hodge WA. Knee motions during maximum flexion in fixed and mobile-bearing arthroplasties. Clin Orthop Relat Res. 2003;(410):131-8. 10. Banks SA, Harman MK, Bellemans J, Hodge WA. Making sense of knee arthroplasty kinematics: news you can us e. J Bone Joint Surg Am. 2003;85-A Suppl 4:64-72. 11. Banks SA, Harman MK, Hodge WA. Mechani sm of anterior impingement damage in total knee arthroplasty. J Bone Joint Surg Am. 2002;84-A Suppl 2:37-42. 12. Banks SA, Markovich GD, Hodge WA. T he mechanics of knee replacements during gait. In vivo fluoroscopic analysis of tw o designs. Am J Knee Surg. 1997;10(4):2617. 109

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BIOGRAPHICAL SKETCH The author is married to Suzanne Shunk Conrad and has two lovely daughters, Adeline Ross Conrad ( ) and Esther Maeve Conrad ( He was raised by two wonderful loving parents and molded by an encouraging sister. 2mce ) 117