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A New Soft Tissue Artifact Compensation Technique in Human Motion Analysis and Clinical Applications

Permanent Link: http://ufdc.ufl.edu/UFE0041214/00001

Material Information

Title: A New Soft Tissue Artifact Compensation Technique in Human Motion Analysis and Clinical Applications
Physical Description: 1 online resource (175 p.)
Language: english
Creator: Gao, Bo
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: acl, analysis, anterior, artifact, biomechanics, cruciate, fluoroscopy, kinematics, knee, ligament, motion, orthopaedics, soft, sta, tissue
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: Human motion analysis plays an important role in understanding normal function as well as pathological abnormalities of human musculoskeletal systems. Among different motion analysis techniques, skin marker-based stereophotogrammetry is the one used most widely in the biomechanical community. A major limitation of this technique is that motion-tracking markers are attached to skin surface of body segments and these markers can move relative to the underlying bone during activities. The relative movement between skin markers and the underlying bones is usually referred to as soft tissue artifact (STA) and it has been proved to be a major source of error of the technique. Much effort has been devoted by the research community to developing techniques to compensate for STA effects and improve motion analysis accuracy. However, the problem has not yet been solved satisfactorily. In the framework of this dissertation, a new STA compensation method was developed based on in vivo soft tissue movements and inter-subject similarities. First, it was demonstrated that soft tissue deformation on the lower extremity has inter-subject similarities, which was a new insight contrary to the prevailing opinion. Second, a simultaneous fluoroscopy and stereophotogrammetry study was conducted to assess STA in vivo on six subjects who had total knee arthroplasty (TKA), during a series of knee flexion movements and a step-up activity. Both inter-subject similarity and inter-motor-task similarity were observed on the STA results. Based on these similarities, a ?universal? STA model was constructed using multilinear regression on the STA measurements obtained from multiple subjects and multiple activities. Third, from the ?universal? STA model, a new STA compensation concept was implemented in two methods: an STA deduction (STAD) method and a directional weighted optimization (DWO) method. The performance of the two methods was evaluated on the in vivo knee joint kinematics. Both methods demonstrated improvement over the conventional rigid body optimization (RBO) method, and the STAD method exhibited the best performance. Overall, the STAD method reduced analysis errors by 37% to 75% for different kinematic variables. Finally, the newly developed STA compensation technique was applied clinically to investigate three-dimensional (3D) knee joint kinematics of patients after anterior cruciate ligament (ACL) injury and reconstructive surgery. 3D knee joint kinematics of ACL-deficient patients and ACL-reconstructed patients were investigated during level walking and compared to a group of healthy subjects who had bilateral ACL-intact knees. Significant reduction of extension was observed in the ACL-deficient knees during midstance and in the ACL-reconstructed knees during swing phase. Greater varus and internal tibial rotation were identified in the ACL-deficient knees. The kinematics of the ACL-reconstructed knees exhibited some improvement, but had not been fully restored to a normal level.
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 Bo Gao.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Zheng, Naiquan.
Local: Co-adviser: Banks, Scott A.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041214:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041214/00001

Material Information

Title: A New Soft Tissue Artifact Compensation Technique in Human Motion Analysis and Clinical Applications
Physical Description: 1 online resource (175 p.)
Language: english
Creator: Gao, Bo
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: acl, analysis, anterior, artifact, biomechanics, cruciate, fluoroscopy, kinematics, knee, ligament, motion, orthopaedics, soft, sta, tissue
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: Human motion analysis plays an important role in understanding normal function as well as pathological abnormalities of human musculoskeletal systems. Among different motion analysis techniques, skin marker-based stereophotogrammetry is the one used most widely in the biomechanical community. A major limitation of this technique is that motion-tracking markers are attached to skin surface of body segments and these markers can move relative to the underlying bone during activities. The relative movement between skin markers and the underlying bones is usually referred to as soft tissue artifact (STA) and it has been proved to be a major source of error of the technique. Much effort has been devoted by the research community to developing techniques to compensate for STA effects and improve motion analysis accuracy. However, the problem has not yet been solved satisfactorily. In the framework of this dissertation, a new STA compensation method was developed based on in vivo soft tissue movements and inter-subject similarities. First, it was demonstrated that soft tissue deformation on the lower extremity has inter-subject similarities, which was a new insight contrary to the prevailing opinion. Second, a simultaneous fluoroscopy and stereophotogrammetry study was conducted to assess STA in vivo on six subjects who had total knee arthroplasty (TKA), during a series of knee flexion movements and a step-up activity. Both inter-subject similarity and inter-motor-task similarity were observed on the STA results. Based on these similarities, a ?universal? STA model was constructed using multilinear regression on the STA measurements obtained from multiple subjects and multiple activities. Third, from the ?universal? STA model, a new STA compensation concept was implemented in two methods: an STA deduction (STAD) method and a directional weighted optimization (DWO) method. The performance of the two methods was evaluated on the in vivo knee joint kinematics. Both methods demonstrated improvement over the conventional rigid body optimization (RBO) method, and the STAD method exhibited the best performance. Overall, the STAD method reduced analysis errors by 37% to 75% for different kinematic variables. Finally, the newly developed STA compensation technique was applied clinically to investigate three-dimensional (3D) knee joint kinematics of patients after anterior cruciate ligament (ACL) injury and reconstructive surgery. 3D knee joint kinematics of ACL-deficient patients and ACL-reconstructed patients were investigated during level walking and compared to a group of healthy subjects who had bilateral ACL-intact knees. Significant reduction of extension was observed in the ACL-deficient knees during midstance and in the ACL-reconstructed knees during swing phase. Greater varus and internal tibial rotation were identified in the ACL-deficient knees. The kinematics of the ACL-reconstructed knees exhibited some improvement, but had not been fully restored to a normal level.
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 Bo Gao.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Zheng, Naiquan.
Local: Co-adviser: Banks, Scott A.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041214:00001


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A NEW SOFT TISSUE ARTIFACT COM PENSATION TECHNIQUE IN HUMAN MOTION ANALYSIS AND CLINI CAL APPLICATIONS By BO GAO 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 Bo Gao 2

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To the mentors who guided me to the world of scientific reasoning and creative exploring; and to my family who prov ided me constant support and encouragement, making this milestone possible 3

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ACK NOWLEDGMENTS I thank Professor Nigel Zheng and Professor Scott Banks for their direct mentoring on my program study and research work, and Professor B.J. Fregly and Professor MaryBeth Horodyski for thei r guidance along my progress. I thank Bryan Conrad for his numerous help during my daily work. I thank Judith Barry, Shang Mu, Brooke Organ, Jason Bouwkamp, David Walker, Alexander Bennett, Poorya Shidfar, Bing Xiao, Hongsheng Wang for their assistance in data collection and post-processing. I thank Dr. Peter Gearen, Dr. Peter Indelicato, Dr. Mi chael Moser, Butch Landsiedel, Mieko Dunn for their assistance in subject recruitm ent, and all the research subjects who participated in my study. I also thank my parents and wife for their loving encouragement, which motivated me to where I am today. 4

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TABL E OF CONTENTS page ACKNOWLEDGMENTS ..................................................................................................4 LIST OF TABLES ............................................................................................................8 LIST OF FIGURES ..........................................................................................................9 LIST OF ABBREVIATIONS AND ACRONYMS .............................................................14 ABSTRACT ...................................................................................................................17 CHAPTERS 1 BACKGROUND AND INTRODUCTION .................................................................19 Human Motion Analysis ..........................................................................................19 Skin Marker-Based Stereophotogrammetry ............................................................19 Soft Tissue Artifact (STA) .......................................................................................20 STA Compensation Techniques .............................................................................22 Anterior Cruciate Ligament (A CL) Injury and Knee Osteoarthritis ...........................27 2 DOES SOFT TISSUE MOVEMENT HAVE INTER-SUBJECT PATTERNS? ..........31 Introduction .............................................................................................................31 Design and Methods ...............................................................................................32 Subjects ............................................................................................................32 Marker Placement ............................................................................................33 Experimental Setup ..........................................................................................34 Analysis Method ...............................................................................................34 Results ....................................................................................................................36 Inter-Subject Similarity ......................................................................................36 Soft Tissue Movement Behavior .......................................................................39 Gender Differences ..........................................................................................42 Discussions .............................................................................................................42 Conclusions ............................................................................................................46 3 IN VIVO ASSESSMENT OF SOFT TISSUE ARTIFACT ........................................47 Introduction .............................................................................................................47 Design and Methods ...............................................................................................50 Subjects ............................................................................................................50 Experimental Setup ..........................................................................................51 Marker Placement ............................................................................................52 Motor Tasks ......................................................................................................53 Test Procedure .................................................................................................55 5

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Image Processing .............................................................................................59 Spatial and Temporal Synchronization .............................................................61 STA Computation .............................................................................................64 Results ....................................................................................................................65 STA on the Thigh and Shank of a Representative Subject ..............................65 Inter-Subject Common Patterns of STA on the Thigh ......................................69 Inter-Subject Common Patterns of STA on the Shank .....................................73 Discussions .............................................................................................................77 4 DEVELOPMENT OF NEW METHOD S FOR SOFT TISSUE ART IFACT COMPENSA TION...................................................................................................82 Introduction .............................................................................................................82 Development of a Universal STA Model ...............................................................82 STA in a Two-Dimensional Joint Angle Space .................................................82 Mathematical Expression of STA .....................................................................88 Inter-Motor-Task Similarity of STA ...................................................................94 A Universal STA Model of All Subjects ..........................................................99 Two New Methods for STA Compensation ...........................................................111 STA Deduction (STAD) Method .....................................................................111 Directional Weighted Optimization (DWO) Method ........................................113 Results and Discussions .......................................................................................114 Evaluation Approach ......................................................................................114 Kinematic Results ...........................................................................................115 Analysis Error Comparison .............................................................................122 5 THREE DIMENSIONAL KINEMATICS OF ACL-DEFICIENT AND ACLRECONSTRUCTED KNEES ................................................................................131 Introduction ...........................................................................................................131 Design and Methods .............................................................................................134 Subjects ..........................................................................................................134 Experimental Setup ........................................................................................135 Marker Placement ..........................................................................................136 Test Procedure ...............................................................................................136 Analysis Methods ...........................................................................................136 Results ..................................................................................................................139 Spatiotemporal Parameters ............................................................................139 Key Events during a Gait Cycle ......................................................................140 Joint Kinematics .............................................................................................141 Comparison between STAD method and RBO method .................................142 Discussions ...........................................................................................................148 6 SUMMARY AND CO NCLUSION S ........................................................................156 Novelties and Key Points ......................................................................................156 Methodological Novelties of this Study ...........................................................156 6

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Key Points Learned from this Study ...............................................................159 Limitations and Future Direction ...........................................................................162 Limitations of this Study ..................................................................................162 Future Study Suggestions ..............................................................................163 LIST OF REFERENCES .............................................................................................165 BIOGRAPHICAL SKETCH ..........................................................................................175 7

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LIST OF TABLES Table page 2-1 Subject information. ............................................................................................32 2-2 Variables that showed statisti cal differences between gender groups. ...............42 3-1 TKA subject information. ....................................................................................50 4-1 Coefficient matrices of th igh markers for all subjects. .......................................109 4-2 Coefficient matrices of shank markers for all subjects. .....................................110 5-1 Subject information. ..........................................................................................135 5-2 Initial knee joint angles at the st ati c standing posture and spatiotemporal variables during gait. ........................................................................................139 6-1 Summary of studies about soft ti ssue movement on human lower extremity and the analysis scopes. ..................................................................................158 8

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LIST OF FIGURES Figure page 2-1 Marker placement on the thigh and shank. .........................................................33 2-2 Inter-marker soft ti ssue movement calculation. ..................................................35 2-3 Inter-marker translations on the thigh during walking. ........................................37 2-4 Inter-marker translation s on the shank during walking. ......................................38 2-5 Inter-marker rotations during walking. ................................................................39 2-6 Maximums and minimums of inter-mark e r translations and rotations in a gait cycle. ..................................................................................................................41 3-1 Simultaneous fluoroscopy and stereophotogrammetry setup. ............................51 3-2 Marker placement on the thigh and shank. .........................................................53 3-3 A subject performing knee flexion/extens ion movement at -15 of hip flexion. ...54 3-4 A subject performing knee flexion/ext ens ion movement at 45 of hip flexion. ....54 3-5 L-frame used for spatial synchronization. ...........................................................56 3-6 X-ray image of the L-frame. ................................................................................57 3-7 Stereophotogrammetric image of the L-frame. ...................................................57 3-8 Standing posture on a control plate. ...................................................................58 3-9 Fluoroscopic and stereophotogrammetr ic images on the standing posture. .......58 3-10 Program used to obtain parameters of the fl uoroscopy and correct edge distortion of fluoroscopic images. .......................................................................60 3-11 JointTrack used to determine the 3D poses of the TKA prostheses at each fluoroscopic image. .............................................................................................61 3-12 Shape-matching between marker clus ters and the fluoroscopic image.. ............62 3-13 Temporal synchronization bet ween the fluoroscopic and the stereophotogrammetri c trajectori es of the target marker. ...................................64 3-14 The movements of ma rkers and the underly ing bones were transformed to a uniform spatiotemporal space thus the relative movements can be analyzed. ...65 9

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3-15 STA on the thigh and shank of a repres entative subject during knee flexion at -15 of hip flexion. ...............................................................................................66 3-16 STA on the thigh and shank of a repres entative subject during knee flexion at 15 of hip flexion. ................................................................................................67 3-17 STA on the thigh and shank of a repres entative subject during knee flexion at 30 of hip flexion. ................................................................................................67 3-18 STA on the thigh and shank of a repres entative subject during knee flexion at 45 of hip flexion. ................................................................................................68 3-19 STA on the thigh and shank of a repres entative subject during knee flexion at 60 of hip flexion. ................................................................................................68 3-20 STA on the thigh and shank of a repr esentative subject during step ping up. .....69 3-21 Mean curves and standard deviations of thigh STA across all subjects during knee flexion at -15 of hip flexion. .......................................................................70 3-22 Mean curves and standard deviations of thigh STA across all subjects during knee flexion at 15 of hip flexion. ........................................................................70 3-23 Mean curves and standard deviations of thigh STA across all subjects during knee flexion at 30 of hip flexion. ........................................................................71 3-24 Mean curves and standard deviations of thigh STA across all subjects during knee flexion at 45 of hip flexion. ........................................................................71 3-25 Mean curves and standard deviations of thigh STA across all subjects during knee flexion at 60 of hip flexion. ........................................................................72 3-26 Mean curves and standard deviations of thigh STA across all subjects during stepping up. ........................................................................................................72 3-27 Mean curves and standard deviations of shank STA across all subjects during knee flexion at -15 of hip flexion. ............................................................74 3-28 Mean curves and standard deviations of shank STA across all subjects during knee flexion at 15 of hip flexion. .............................................................74 3-29 Mean curves and standard deviations of shank STA across all subjects during knee flexion at 30 of hip flexion. .............................................................75 3-30 Mean curves and standard deviations of shank STA across all subjects during knee flexion at 45 of hip flexion. .............................................................75 3-31 Mean curves and standard deviations of shank STA across all subjects during knee flexion at 60 of hip flexion. .............................................................76 10

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3-32 Mean curves and standard deviations of shank STA across all subjects during stepping up. .............................................................................................76 4-1 3D plot of marker T1s STA (SI co mponent) of a representative subject over hip and knee flexion angles. ...............................................................................84 4-2 2D plot showing the hip and knee angle coverage by the series of knee flexion movements of a representative subject. ..................................................84 4-3 2D plot showing the relationship between the STA component and hip flexion angle. ..................................................................................................................85 4-4 2D plot showing the relations hip between the STA component and knee flexion angle. ......................................................................................................85 4-5 3D plot of marker S4s STA (SI co mponent) of a representative subject over ankle and k nee flexion angles. ...........................................................................86 4-6 2D plot showing the ankle and knee angle cov erage by the series of knee flexion movements of a representative subject. ..................................................87 4-7 2D plot showing the relations hip between the STA component and ankle plantarflexion angle. ...........................................................................................87 4-8 2D plot showing the relations hip between the STA component and knee flexion angle. ......................................................................................................88 4-9 Multilinear regression on the data point s of the SI component of T1s STA. ......90 4-10 2D projections of the regression model showing the dependency of the SI component of T1s STA to hip and knee joint angles. .........................................91 4-11 Multilinear regression on the data point s of the SI component of S4s STA. ......92 4-12 2D projections of the regression model showing the dependency of the SI component of S4s STA to ankle and knee joint angles. .....................................93 4-13 Measured and predicted AP component of thigh ST A during stepping-up activity. ...............................................................................................................95 4-14 Measured and predicted SI component of thigh STA dur ing stepping-up activity. ...............................................................................................................95 4-15 Comparison between the prediction residuals and the STA of thigh markers along AP direction during stepping-up activity. ...................................................96 4-16 Comparison between the prediction residuals and the STA of thigh markers along SI dir ection during stepping-up activity. ....................................................96 11

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4-17 Measured and predicted AP component of shank STA during stepping-up activity. ...............................................................................................................97 4-18 Measured and predicted AP component of shank STA during stepping-up activity. ...............................................................................................................97 4-19 Comparison between the prediction residuals and the STA of shank markers along AP direction during stepping-up activity. ...................................................98 4-20 Comparison between the prediction residuals and the STA of shank markers along SI dir ection during stepping-up activity. ....................................................98 4-21 3D plot of marker T1s STA (SI component) of all subjects over hip and knee flexion angles. ...................................................................................................100 4-22 2D plot showing the hip and knee angle coverage by the series of knee flexion movements for all subjects. ...................................................................100 4-23 2D plot showing the relationship between the STA component and hip flexion angle for all subjects. ........................................................................................101 4-24 2D plot showing the relations hip between the STA component and knee flexion angle for all subjects. ............................................................................101 4-25 3D plot of the marker S4s STA (SI component) of all subjects over ankle and knee flexion angles. ..........................................................................................102 4-26 2D plot showing the ankle and knee angle cov erage by the series of knee flexion movements for all subjects. ...................................................................102 4-27 2D plot showing the relations hip between the STA component and ankle plantarflexion angle for all subjects. ..................................................................103 4-28 2D plot showing the relations hip between the STA component and knee flexion angle for all subjects. ............................................................................103 4-29 Multilinear regression on the data points of the SI component of T1s STA for all subjects. .......................................................................................................105 4-30 Multilinear regression on the data points of the SI component of S4s STA for all subjects. .......................................................................................................105 4-31 2D projections of the regression model showing the dependency of the SI component of T1s STA to hip and knee joint angles for all subjects. ...............106 4-32 2D projections of the regression model showing the dependency of the SI component of S4s STA to ankle and knee joint angles for all subjects. ...........107 12

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4-33 Kinematic results obtained using different methods for the stepping-up trial of a representative subject. ..................................................................................116 4-34 Kinematic results obtained using different methods for the knee flexion trial at 15 of hip flexion of a representative subject. ...................................................117 4-35 Kinematic results obtained using different methods for the knee flexion trial at 30 of hip flexion of a representative subject. ...................................................118 4-36 Kinematic results obtained using different methods for the knee flexion trial at 45 of hip flexion of a representative subject. ...................................................119 4-37 Kinematic results obtained using different methods for the knee flexion trial at 60 of hip flexion of a representative subject. ...................................................120 4-38 RMS kinematic errors of all subjects during stepping-up. .................................123 4-39 RMS kinematic errors of all subjects during knee flexion at 15 of hip flexion. .124 4-40 RMS kinematic errors of all subjects during knee flexion at 30 of hip flexion. .125 4-41 RMS kinematic errors of all subjects during knee flexion at 45 of hip flexion. .126 4-42 RMS kinematic errors of all subjects during knee flexion at 60 of hip flexion.. 127 5-1 An ACL-D subject in test. .................................................................................135 5-2 Definition of anatomical coordina te systems on the femur and the tibia. ..........137 5-3 Timings of key events in the gai t cycle for ACL-I, ACL-D and ACL-R groups. ..141 5-4 The 3-D joint rotations during walking of ACL-I, ACL-D and ACL-R knees.. ....144 5-5 The 3-D joint translations during walk ing of ACL-I, ACL-D and ACL-R knees ..145 5-6 Comparison of 3-D knee joint ro tations obtained using STAD method and RBO method. ....................................................................................................146 5-7 Comparison of 3-D knee joint transl ations obtained using STAD method and RBO method. ....................................................................................................147 13

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LIST OF ABBREVIAT IONS AND ACRONYMS ACL Anterior cruciate ligament ACL-D ACL-deficient ACL-I ACL-intact ACL-R ACL-reconstructed AP Anterior/posterior BMI Body mass index CHS Contralateral heel strike CT Computed tomography CTO Contralateral toe off DWO Directional weighted optimization FE valley Minimum knee flexion during midstance GCS Global coordinate system HS Heel strike IRB Institutional review board LCS Local coordinate system LCSRT Local coordinate systems of the reference triad ML Medial/lateral MRI Magnetic resonance imaging PCT Point cluster technique RBO Rigid body optimization ROM Range of motion RMS Root-mean-square SI Superior/inferior STA Soft tissue artifact 14

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STAD STA deduction STD/SD Standard deviation TKA Total knee arthroplasty TO Toe off UF University of Florida 1st FE peak Maximum knee flexion during the stance phase 2nd FE peak Maximum knee flexion during the swing phase 2D Two-dimensional 3D Three-dimensional ankle Ankle plantarflexion angle hip Hip flexion angle knee Knee flexion angle )( ifavg The average of a variable at i % gait cycle across all subjects )(ifstd The STD of a variable at i% gait cycle across all subjects boneO Position vector of the bone RTO Position vector of the reference triad in GCS ip The ith markers position in GCS at a dynamic instant dynanicg ip_ The global position of a ma rker at a dynamic instance initial ip The ith markers position in LCSRT at the initial standing posture staticl ip_ Local position of a marker in t he anatomical reference system at the static neutral posture boneR Orientation matrix of bone RT iR A triads orientation matrix in LCSRT 15

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jR The jth triads orientation matrix in GCS at a dynamic instant RTR Orientation matrix of the reference triad in GCS RT iV A markers translation vector in LCSRT i shankSTAV_ A shank markers STA vector i thighSTAV_ A thigh markers STA vector iiiwzwywx Weight vect or for marker i 16

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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 A NEW SOFT TISSUE ARTIFACT COM PENSATION TECHNIQUE IN HUMAN MOTION ANALYSIS AND CLINICAL APPLICATIONS By Bo Gao December 2009 Chair: Nigel Zheng Cochair: Scott Banks Major: Biomedical Engineering Human motion analysis plays an important role in understanding normal function as well as pathological abnormalities of human musculoskeletal systems. Among different motion analysis techniques, ski n marker-based stereophot ogrammetry is the one used most widely in the biomechanical community. A major lim itation of this technique is that motion-tracking marker s are attached to skin surface of body segments and these markers can move relati ve to the underlying bone during activities. The relative movement between skin ma rkers and the underlying bones is usually referred to as soft tissue arti fact (STA) and it has been proved to be a major source of error of the technique. Much effort has been devoted by the research community to developing techniques to compensate for STA effects and improve motion analysis accuracy. However, the problem has not yet been solved satisfactorily. In the framework of this dissertati on, a new STA compensation method was developed based on in vivo soft tissue movements and inter-subj ect similarities. First, it was demonstrated that soft tissue deformati on on the lower extremity has inter-subject similarities, which was a new insight cont rary to the prevailing opinion. Second, a 17

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18 simultaneous fluoroscopy and stereophotogra mmetry study was conducted to assess STA in vivo on six subjects who had total knee arthroplasty (TKA), during a series of knee flexion movements and a step-up activity Both inter-subject similarity and intermotor-task similarity were observed on the ST A results. Based on t hese similarities, a universal STA model was constructed using multilinear regression on the STA measurements obtained from multiple subjects and multiple activities. Third, from the universal STA model, a new STA compens ation concept was implemented in two methods: an STA deduction (STAD) method and a directional weighted optimization (DWO) method. The performance of t he two methods was evaluated on the in vivo knee joint kinematics. Both methods demonstrated improvement over the conventional rigid body optimization (RBO) method, and t he STAD method exhibited the best performance. Overall, the STAD method r educed analysis errors by 37% to 75% for different kinematic variables. Finally, the newly developed STA compensation technique was applied clinically to investigate threedimensional (3D) knee joint kinematics of patients after anterior cruciate ligament (ACL) injury and reconstructive surgery. 3D knee joint kinematics of ACL-deficient pati ents and ACL-reconstructed patients were investigated during level walking and compared to a group of healthy subjects who had bilateral ACL-intact knees. Significant reduction of extension was observed in the ACLdeficient knees during midstance and in t he ACL-reconstructed knees during swing phase. Greater varus and internal tibial rotation were identified in the ACL-deficient knees. The kinematics of the ACL-reconstr ucted knees exhibited some improvement, but had not been fully restored to a normal level.

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CHA PTER 1 BACKGROUND AND INTRODUCTION Human Motion Analysis The major function of human musculoskeleta l system is to generate motion. As a quantitative tool, human motion analysis pl ays an important ro le in understanding normal function and abnormities of human mu sculoskeletal systems (Andriacchi and Alexander, 2000). It has been widely utilized in the areas of biomechanical research, clinical assessment, sports performance ev aluation, and orthopedi c prosthesis design optimizations (Banks and Hodge, 2004; Benoit et al., 2006; Dennis et al., 2005; Noyes et al., 1996). Many different techniques have been developed and used in various applications of human motion analyses. These techniques include video cameras (Rowe, 1996), electrogoniometers (Martelli, 2003), inertial motion recorder (Elble, 2005), stereophotogrammetry (Cappozzo et al ., 2005), electromagnetic tracking system (Meyer et al., 2008), Roentgen stereophotogramme tric analysis (Adam et al., 2004), single plane and biplane fluoroscopy (Banks et al., 1997; Li et al., 2005), magnetic resonance imaging (MRI) (Patel et al., 2004) computed tomography (CT) (Feipel and Rooze, 1999), etc. Each of these techniques has its own strengths and limit ations and is suitable for certain applications. Skin Marker-Based Stereophotogrammetry Among different motion analysis techniques, skin marker-based stereophotogrammetry has the feat ures of being non-invasive, radiation-free, flexible and easy to implement, suitable for measur ing high speed movement and movement occurring in large spatial volumes. Benef iting from these advantages, skin markerbased stereophotogrammetry is cu rrently the most widely used technique in human 19

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motion analyses. Sinc e mid 1970s, ster eophotogrammetry has been used as an analysis tool in biomechanical research for over 30 years (A ndriacchi and Alexander, 2000). With the significant improvement of hardware and software performance during the past decade, modern commercial systems can usually achieve an accuracy of better than one millimeter in 3D marker tracking with hundr eds of frames captured per second (Chiari et al., 2005). However, there is a major issue rela ted to this technique and it largely limits the applications for accurate skeletal movement measurement. Since human body segments are not rigid bodies, markers attached to skin surface cannot perfectly follow the bone movement dur ing activities. Thus when skin marker trajectories are used to determine skeletal move ment, soft tissue move ment will result in analysis errors. Soft Tissue Artifact (STA) In the biomechanical research community the movement of skin markers with respect to the underlying bones is usually refe rred to as soft tissue artifact (STA). STA can be caused by a combination of muscle contraction, skin stretc hing and sliding, inertial effects of markers, and other experimental errors ( Leardini et al., 2005). STA has been proved as a major source of erro r associated with skin marker-based motion analysis, and the error caused by STA is usua lly significantly larger than instrument errors (Leardini et al., 2005). In gait analysi s, STA is especially disruptive in secondary rotational and translational components of k nee kinematics, but t hese small kinematic components are considered of high interest in detecting gait deficiencies (Croce, 2006). As reported in one study, during level walking i ndividual markers STA can be up to 30 mm and the resultant peak-to-peak error in bone orientation can be up to 20 for the femur and 10 for the tibia (Cappozzo et al., 1996). Be cause the accuracy of skin 20

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marker-based motion analys is is largely limited by the effects of STA, other invasive or radiation-involved techniques have to be considered when high accuracy is required (Fleming et al., 2001; Lafortune et al., 1992; You et al., 2001). To understand the behavior of STA and to evaluate its influence on skeletal motion analysis, many studies were conducted during the past twenty years. As STA is the relative movement between skin markers an d bones, the position and orientation of bones need to be measured. For this purpose, invasive devices were most commonly used. These devices including intracortical bone pins (Benoit et al., 2006; Fuller et al., 1997; Reinschmidt et al., 1997a; Reinschmidt et al., 1997b), external fixators (Cappozzo et al., 1996) and percutaneous trackers (Holden et al., 1997; Manal et al., 2000), can be rigidly fixed to bones. By tracking trajectori es of markers fixed on the invasive device and markers attached to the skin surfac e, both bone motion and skin motion can be measured. Thus STA and its re sultant errors on joint kinematic determination can be evaluated. These invasive devices provide a direct and reliable meas urement of skeletal motion, but they could potentially constrain or alter the free movement of soft tissues. Pain and/or anesthesia involv ed in the test may also affect the normal skeletal motion pattern. To overcome these shortcomings of invasive techniques, a few studies used non-invasive radiographic techniques includ ing two-dimensional (2D) X-ray and 3D fluoroscopy to investigate STA on the lowe r extremity (Sati et al., 1996; Stagni et al., 2005). These techniques made it possible to measure bone pose and unconstrained skin marker positions simultaneously. Because of the limited fluoroscopic field of view, the motor tasks that are studied usually need to be confined in a relatively small space. 21

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Because of the diversities of techniques, motor tasks, marker placements, and subjects in the previous studies, the repor ted STA results had cons iderable variability. But some basic characteristics of STA are consistent for most studies: 1) STA for individual markers is usually in the magnitude of millimeters to centimet ers; 2) the errors caused by STA are much larger than instrum ent errors of motion analysis systems; 3) STA is skin location specific, i.e., markers on different skin locations have different movement relative to the bone during an ac tivity. Although joint landmarks are often selected as marker placement locations in clinical motion analysis, these locations could have larger STA than other areas on the segmen t; 4) STA is motor task specific, i.e., a marker on the same location may have different STA during different activities; 5) For the lower extremity, STA is usually larger on the thigh than on the shank; 6) STA imposes larger influence on those kinematic variables that have smaller range of motion (such as translations and axial rotations of the knee joint), which often leads to low reliability of the analysis on these variabl es; 7) STA usually has similar frequency content with skeletal movement, which reflects the inherent influence of muscle contraction and joint position on STA. This also indicates the impossibility to isolate STA effects from bone motion simply by using a frequency filtering process. STA Compensation Techniques Since STA is a critical issue in skelet al motion analysis, much effort has been devoted by biomechanical researchers to look ing for solutions for the problem. Various STA compensation techniques have been proposed to improve the motion analysis accuracy (Alexander and Andr iacchi, 2001; Andriacchi et al., 1998; Cappello et al., 1997; Cappello et al., 2005; Cheze et al ., 1995; Lu and O'Connor, 1999; Soderkvist and Wedin, 1993; Spoor and Veldpaus, 1980). 22

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In clinical gait analysis and many other appl ications, usually only a small number of skin markers are placed on joint landmarks to track the movement of body segments. This practice is based on the theory that three non-collinear markers are adequate to determine the 3D pose of a rigid-body s egment. However, human body segments are not rigid bodies, and STA at joint landmarks is even more prominent than at other locations on the body segments (Cappozzo et al., 1996). To reduce the effect of STA on 3D bone pose determination, a reasonable approach is to employ redundant skin markers. On each body segment, more than three markers could be used and distributed on the skin surface. With more markers covering a larger area of the segment, it is expected that the marker cluster as a whole will represent a better approximation of the bony segment in pose measurement. To derive the bone pose from the position of the marker clusters, different calculation algorithms have been proposed and can be generally divided into tw o categories: rigid body optimization (Soderkvist and Wedin, 1993; Spoor and Veldpaus, 1980) and non-rigid body optimization (Alexander and A ndriacchi, 2001; Andriacchi et al., 1998). In the first category, a segment is considered as a rigi d frame plus perturbation, and each markers local coordinates in the anatomical reference system are considered constant during the activities. Then a best-fit solid frame will be determined at each time instant to minimize the overall spatial perturbation. Typically a least squares method is used to solve this over-determined question. A similar experimental solidificat ion approach often used in motion labs is to attach a rigid shell with no less than three markers to each body segment. These shells serve as a rigid r epresentation of the bony segment but their efficacy compared with other marker sets is debated (Manal et al ., 2000). In non-rigid 23

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optimizatio n approaches, a body segment will be allowed to deform in the models, and the local coordinates of each marker in its anatomical reference system are nonconstant with time. A representative met hod is called point cluster technique (Andriacchi et al., 1998). This technique uses eigenvalues of the inertia tensor of each marker cluster to determine the non-rigid body poses, based on the fact that the eigenvalues will remain constant if the marker cluster is rigid. A virtual mass as a weight factor is assigned to each marker at each time frame, and the mass will be adjusted so that a lower mass will be assigned to a point wit h larger displacement relative to the segment reference frame. Al though the concept of this non-rigid body optimization approach seems more realistic, their effe ctiveness compared to traditional rigid optimization methods remains controversial (Cereatti et al., 2006; Gao et al., 2007; Taylor et al., 2005). One major limitation of both rigid and non -rigid optimization approaches is that they can only compensate for internal deformation within marker clusters but do nothing on the overall shift of the marker cluster rela tive to the bone. All these methods have no effect if the whole mark er cluster shifts relative to the bone. The anatomical structures of soft tissue and the relationship between the behaviors of soft tissue movements and skeletal positions are not taken into account in these approaches. STA is treated as a random noise, and the optimizations aim in geometrically smoothing the noise off. However, muscle and skin movement is not random in nature but related to the ske letal position and adjacent joint angles (Cappozzo et al., 1996). STA is also not geomet rically uniform. It could be larger at some locations and smaller at others. Withou t including physiological and anatomical 24

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information of soft tissue movement, the e ffectiveness of pure geomet rical optimizations is limited. To overcome the aforementioned limitations, a few ot her techniques have been proposed in order to i nclude subject-specific physiological informa tion of soft tissue movement. Cappello et al introduced a double calibration method which utilized two extremes of expected range of motion as reference postures and calibrated each markers local coordinates at these two postures (Cappello et al., 1997). The instantaneous local coordinat es of each skin marker were computed by linear interpolation between the two reference in stants along time. The time-varying local coordinates of markers were finally used to determine the bone pose at each instant. This method was tested on a subject with exte rnal fixator on the femur. The results showed that root-mean-square (R MS) errors of the femur or ientation and position were reduced from about 5 and 7 mm to less than 4 and 4.5 mm. More recently, the same group applied a linear interpolat ion STA model with knee flexion angle to several nonambulation activities and demonstrated its effe ctiveness in error redu ction (Cappello et al., 2005). One of our studies al so demonstrated that using multiple reference postures can reduce the STA errors during simu lated level walking (Gao and Zheng, 2006). Another similar but different technique propose by Lucchetti et al is called dynamic calibration (Cappello et al., 1997). Rather than selecting a few discrete instants as the reference postures, a continuous relationshi p between the soft tissue movement on the thigh and the hip joint angles was measured. This was achieved by pre-analyzing kneelocked hip rotation trials under the assumpti on that STA on the shank is negligible. The relationship between STA and hip joint fl exion/extension, abduction/adduction, and 25

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internal/external rotation angles were described as an STA table which was later used in the analy sis for other trials. This dynamic calibration method was tested on a patient wearing a single degree of freedom (DOF) knee prosthesis and the RMS errors of knee joint translations and rotations were reduc ed from 14 mm and 6 to 6 mm and 3. The multiple reference posture approaches (Cappello et al., 1997; Cappello et al., 2005; Gao and Zheng, 2006) and dynamic calibra tion approach (Lucchetti et al., 1998) achieved better STA compensation effectivene ss because of the inclusion of subject anatomical information and specific motor task information into the method. This is a substantial improvement from previous geometrical optim ization algorithms. Since skin and muscle movement is related to skeletal movement, the strategies of these methods are more reasonable. However, apparent limitations also ex ist for these methods. For the multiple reference posture approach, only a few discrete postures are calibrated and interpolation has to be used for other postures in between. Even at the calibration postures, the anatomical landmark misplacement could lead to considerable errors in determination of markers local coordinates (Della Croce et al., 2005). The dynamic calibration method overcomes this shortcom ing by obtaining a continuous relationship between markers local coordinates and the hip angles. But a large simplification in this method is the assumption that STA on the thigh is only related to hip joint angles but not knee joint angles. STA on the thigh is dependent on both hip and knee joint angles (Cappozzo et al., 1996), but this is not reflec ted in the dynamic calibration method. In addition, both dynamic calibration and multiple calibration methods require extra trials during the test, which prolongs the test procedure in clinic situations. 26

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To pursue more effective and convenient ST A compensation techniques, there is a basic question that needs to be answer ed: does STA have inter-subject similarity? The answer of this question will guide us to di fferent directions. If the answer is NO and STA is totally a subject-specific movem ent, we will have to pursue subject-specific models to describe and compensate for STA; but if the answer is YES and STA does have inter-subject similarity, it will be po ssible to develop generic or semi-generic models from the data of a sm all population and use them for a larger population. Considering most people have similar anatomical structures and limb coordination during the same motor task, it will be reasonabl e to expect that STA has certain intersubject similarities. If this is true, the problem could be solved by the second approach discussed above. In the framework of this dissertation, we will explore the behavior of soft tissue movement and demonstrate that STA has inter-subject sim ilarity, which is contrary to the prevailing opinion. Based on this funding, a universal STA model will be developed using in vivo STA data from six different subjec ts. This STA model will be used in an evidence-based strategy to formulate a more effective and convenient STA compensation technique for ski n marker-based motion analysis. Anterior Cruciate Ligament (ACL) Injury and Knee Osteoarthritis The human anterior cruciate ligament (ACL) plays an important ro le in controlling knee joint stability, not only by limiting tibia anterior translation but also by controlling knee axial rotation and varus movement (Andersen and Dyhre-Poulsen, 1997; Markolf et al., 1995). Rupture of the ACL is a common knee injury in athletic and young population, especially in females. Every year, approximately 80,000 to 250,000 ACL injuries occur in the United States (Griffin et al., 2006). The vast majo rity of the affected 27

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indiv iduals are aged from 15 to 45 years old (Griffin et al., 2000), and more than 50% of all those sustaining ACL injury are in young at hletes from 15 to 25 years old (Griffin et al., 2006). Female athletes are even more vul nerable to ACL injury, with epidemiological data showing that females are two to eight ti mes more likely than males to sustain such an injury (Arendt and Dick, 1995). Both contact and noncontact mechanism during sport participation can result in ACL injury, and th e latter one is considered with even higher incidence (Griffin et al., 2000). After the rupt ure of the ACL, knee joint stability and loadbearing pattern between contact joint surfaces could be altered, resulting in abnormal loading on the cartilage during activities (Chaudhari et al., 2008; Li et al., 2006). This biomechanical environment change has been associated wit h cartilage degeneration and progressive development of knee joint osteoarthritis (Andriacchi et al., 2006; Andriacchi and Mundermann, 2006; Stergiou et al., 2007; Wu et al., 2000). The theory has been supported by both animal and human studi es (Baliunas et al., 2002; Brandt et al., 1991; Neyret et al., 1993; Papaioannou et al., 2004; Pond and Nuki, 1973). For untreated ACL-deficient (ACL-D) knees, the ri sk of knee osteoarthritis development has been reported as high as 44% after eleven years (Noyes et al., 1983), and over 50% of cases have led to total knee arthroplasty before age 63 (Nebelung and Wuschech, 2005). To restore the knee joint stability and function after ACL injury, ACL reconstructive surgery typically is recommended. However, the effectiveness of ACL reconstruction in preventing cartilage d egeneration and osteoarthritis devel opment remains controversial (Jones et al., 2003; Lohmander and Roos, 1994). Studies have found that even after constructive surgery, early cartilage degeneration cannot be successfully prevented and 28

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premature knee osteoarthritis can still develop (Asano et al., 2004; Daniel et al., 1994; Lohmander et al., 2004; Seon et al., 2006). T hese studies evaluated the articular cartilage of ACL-reconstructed (ACL-R) knees with sample sizes of from 41 to 105 patients. The results showed a high prevalence of knee osteoarthritis after a period of 5 to 12 years post surgery, and a significant degeneration of cart ilage was observed as early as 15 months after surgery. These findi ngs indicated that current reconstructive surgeries are not able to effectively reduce the risk of early cart ilage degeneration and osteoarthritis development for ACL-D knees, which has been considered by many researchers as a consequence of that knee jo int kinematics has not been fully restored through the reconstructive surgeries and fo llowing rehabilitation programs (Brandsson et al., 2002; Papannagari et al., 2006). The re sidue abnormalities of joint motion and the resultant contact pattern change between arti cular surfaces could lead to progressive cartilage degeneration with millions of cycles of joint loading during daily activities. And any existing traumatic damage on articular cartilage or menisci accompanying the ACL injury would deteriorate the situation and speed up the mechanicalbiological dynamics even more. But on the other side, in most motion analysis studies, abnormal kinematics and kinetics were often observed in ACL-D knee s but not in ACL-reconstructed (ACL-R) knees. Many studies found the motion and loading patterns of ACL-R knees are close to normal knees (Ferber et al., 2002; Georgoulis et al., 2003). There is an inconsistency between motion analysis data and clinic outcome s. One possible explanation is that although the reconstruction does not fully restore the normal kinematics of ACL-D knees, the difference between ACL-R knee s and healthy knees are small and not easy 29

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30 to be detected by measurem ents without enough accuracy. T he kinematics change of ACL-D knees is usually of several millim eters in translation and several degrees in rotation. The differences between ACL-R k nees and the healthy could be even smaller. This small difference is not easily identifi ed using ordinary skin marker-based motion analysis, whose errors caused by STA can ea sily be greater than 10 mm and 5. This assumption was also supported by two studi es which identified abnormal kinematics of ACL-R knees using radiographic techniques (Brandsson et al., 2002; Papannagari et al., 2006). In these studies, the knee moti on was investigated dur ing non-ambulatory activities. To identify the abnormal moti on during daily activities, radiographic techniques are not suitable and other techniques which can measure motion in a large spatial volume with adequate accuracy are needed. With the new STA compensation technique that will be developed in this study, we expect skin marker-based stereophotogrammetry will be a qualif ied approach to achieve this challenging aim.

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CHA PTER 2 DOES SOFT TISSUE MOVEMENT HAVE INTER-SUBJECT PATTERNS? Introduction As introduced in the first chapter, soft tissue artifact (STA), which is the relative movement between skin marker s and the underlying bone, repr esents a major source of errors in skin marker-based motion anal ysis (Leardini et al., 2005). Because the accuracy of skin marker-based stereophotogramme try is largely limited by STA, other invasive or radiation-invo lved techniques have to be used when a higher accuracy is required (Fleming et al., 2001; Lafortune et al., 1992; You et al., 2001). In order to effectively compensate for the effects of STA and improve the accuracy of skin markerbased motion analysis, it is critical to well understand the behavior and characteristics of soft tissue movement during activities. Several studies have been conducted to examine human soft tissue movement during different motor tasks. Among them, in vasive approaches were most frequently used including intracortical bone pins (Benoit et al., 2006; Fuller et al., 1997; Reinschmidt et al., 1997a; Reinschmidt et al., 1997b), external fixators (Cappozzo et al., 1996) and percutaneous trackers (Holden et al., 1997; Manal et al., 2000). These invasive devices provide a direct and reliable measurement of bony segment movement, but they may constr ain and/or alter free soft tissu e motion. To overcome this limitation, a few studies used non-invasive radiographic techniques including twodimensional (2D) X-ray and 3D fluoroscopy (S ati et al., 1996; Stagni et al., 2005). These techniques made it possible to measure bony segment pose and unconstrained skin marker positions at the same ti me. But the limited field of view of fluoroscopy is difficult to examine ambulatory motor tasks. Consequently, few studies have used a non31

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invasiv e approach to investigate soft tissue movement during walki ng, while walking is one of the most important human daily activities and the focu s of clinical gait analysis. The purpose of the study in this chapter was to investigate soft tissue deformation on the thigh and shank during level walking using a non-invasive approach on twenty healthy subjects. With the meas urement of skin marker cl usters, soft tissue deformation during walking was quantified as inter-marker translations and rotations, which reflected the positional and orientati onal change between different skin locations. By using marker triads in addition to single marker s, both rotations and translations of skin surface were analyzed. Inter-subject similarity of the translation and rotation patterns was also evaluated, as well as gender effects on soft tissue deformation magnitudes. Design and Methods Subjects Twenty healthy subjects (ten males and ten females) without previous injuries on lower extremities were recruited for this study (Table 2-1). Informed consent was obtained from each subject and the test was conducted under an Institutional Review Board (IRB) approved protocol. Table 2-1. Subject information. Gender Number Age (year) Height (mm) Weight (kg) Body Mass Index (kg/m2 ) Male 10 22.2 (SD 2.9) 182.1 (SD 4. 3) 77.0 (SD 10.8) 23.2 (SD 2.8) Female 10 21.0 (SD 1.1) 162.0 (SD 6. 0) 54.7 (SD 7.8) 20.8 (SD 2.2) Total 20 21.6 (SD 2.2) 172.1 (SD 11. 5) 65.9 (SD 14.7) 22.0 (SD 2.8) 32

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Marker Placement To track ski n motion on the thigh and shank, a cluster of retro-reflective markers and triads was attached to each segment. For each leg, seven single markers and four triads were placed on the anterolateral si de of the thigh and femoral epicondyles; six single markers and four triads were placed on the anterolateral side of the shanks and tibial plateau ridges and malleoli (Figure 2-1). The markers and triads were placed approximately at the same locations on each subject. Triads were small rigid triangular plates made of thermoplastic material with th ree markers fixed on the vertices. With the three vertex markers, each triads rotation can be determined for skin surface rotation analysis. On the other hand, a triad has the same skin attachment area as a single marker, thus the center position of the three vertices can be used for skin surface translation analysis. A single marker has a ma ss of about 4 grams and a triad of about 7 grams. All retro-reflective ma rkers are about 10 mm in diameter. Figure 2-1. Marker placement on the thi gh and shank. Seven single markers and four triads were placed on the anterolateral side of the thigh. Six sing le markers and four triads were placed on the anterolateral side of the shanks. Each triad with three vertex markers was consi dered as one entity. Marker labels are illustrated for the right leg and are s agittally mirrored for the left leg. [Reprinted with permission fr om Gao, B., and Zheng, N., 2008, Investigation of soft tissue movement during level walking: Translations and rotations of skin markers: Journal of Biomechanics, v. 41, no. 15, p 3190, Fig.1] 33

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Experimental Setup An 11-camera stereophotogrammetric syste m (Motion Analysis Corp., CA) was used to record marker motion at 60 Hz. T he average marker tracking error in the 3D measurement space (5.0 m 2.0 m 2.5 m) was less than 1 mm after calibration. After a static posture at neutral standing being ac quired for anatomical frame definition, each subject was instructed to walk through t he measurement space at his/her normal cadence. Five repeated walking trials were collected for each subject. Analysis Method The deformation of soft tissue on the thigh and shank was analyzed by quantifying the relative movement between different markers on each segment. One triad on each segment was specified as the reference tr iad and the movement of other markers with respect to the reference triad was computed. Any triad can serve as the reference triad in principle and the results will reflect a same systematic movement. Here thigh triad T7 and shank triad S3 were selected as the refer ence triads respectively (Figure 2-1). At the neutral standing posture, local coordina te systems of the reference triads ( LCSRT) were defined to parallel with the anatomical reference frames. During walking, other markers movements relative to the refe rence triad were expressed as translation vectors and rotation matrices in LCSRT (Figure 2-2). A markers translation vector RT iV and a triads rotation matrix RT iR in LCSRT can be expressed as: inital i RTi RT RT ipOpRV )(][1 (2-1) ][][][1 j RT RT jRRR (2-2) 34

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where RTO and RTR are the position and orientation of the reference triad in the global coordinate system ( GCS) respectively; ip is the ith markers position in GCS at a dynamic instant; initial ip is the ith markers position in LCSRT at the initial neutral standing posture; and jR represents the jth triads orientation matrix in GCS at the same dynamic instant. Translation and ro tation of each marker relati ve to the reference triad were decomposed into three directional components. Projection method was used to decompose rotation matrices into three angles in order to avoid the rotation sequence asymmetry. Figure 2-2. Inter-marker soft tissue move ment calculation. [Reprinted with permission from Gao, B., and Zheng, N ., 2008, Investigation of soft tissue movement during level walking: Translations and ro tations of skin markers: Journal of Biomechanics, v. 41, no. 15, p 3191, Fig.2] All variables were normalized to a gait cycl e (from heel strike 0% to heel strike 100%) and then averaged on multiple trials and on left and right legs for each subject. 35

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For each variable at an instant of a gait cycle ( i %), the average and standard deviation of all subjects (n = 20) were ca lculated. Root mean square (RMS) of over a gait cycle represents the average variability of the variable among the subjects. A variable with a strong inter-subject similarity would have similar curves for all subjects, and the maximum and minimum values in a gait cycle would be at the similar timing for all subjects. Ther efore, the difference between the maximum and minimum of the averaged curve would be greater. The ratio between the range of and RMS of over a gait cycle was used to assess the inter-subject similarity: )(ifavgf)(ifstd)(ifstd)(ifstd)(iavg 100 )( ))(min())(max(100 1 2 i std avg avgif ifif r (2-3) For an r value greater than 2, it could be cons idered that the inter-subject average pattern was not overshadowed by the inter-s ubject variability, i.e., a definite intersubject similarity existed. Overall translation/rotation magnitude of a markers/triad was quantified in the form of 222 zyxRRRR where ,, were the magnitudes in each spatial direct ion. The effects of gender on each marker/triad's ov erall translation/rotation magnitude were examined using one-way analysis of variance (SPSS, Chicago, IL). xRyRzRResults Inter-Subject Similar ity The inter-marker movement over a gait cycle was illustrated as mean curves and standard deviations of all subjects (Figure 23 to Figure 2-5). Although variability existed 36

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across subjects who had different genders and body heights/weights, inter-subject similarities were definit e for most variables. For the thigh, all 30 translation variables and 8 out of 9 rotation variables had definite in ter-subject similarities (Figure 2-3, 2-5); for the shank, 23 out of 27 translation variab les had definite inter-subject similarities (Figure 2-4). Figure 2-3. Inter-marker transla tions on the thigh during walking. Triads T7 was specified as the reference triad and other markers translations relative to it are illustrated as three directional components. The three numbers inside each small graph are the r values which indicate the prominence of intersubject similarities. Horizontal axis of each graph represents 0~100% gait cycle (from heel strike to heel strike). An terior, lateral, and superior directions are shown as positive. [Reprinted wit h permission from Gao, B., and Zheng, N., 2008, Investigation of soft tiss ue movement during level walking: Translations and rotations of skin marker s: Journal of Biomechanics, v. 41, no. 15, p 3190, Fig.3] 37

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Figure 2-4. Inter-marker translations on t he shank during walking. Triads S3 was specified as the reference triad and other markers translations relative to it are illustrated as three directional components. The three numbers inside each small graph are the r values which indicate the prominence of intersubject similarities. The horizontal ax is of each graph represents 0~100% gait cycle (from heel strike to heel strike). An terior, lateral, and superior directions are shown as positive. [Reprinted wit h permission from Gao, B., and Zheng, N., 2008, Investigation of soft tiss ue movement during level walking: Translations and rotations of skin marker s: Journal of Biomechanics, v. 41, no. 15, p 3192, Fig.4] 38

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Figure 2-5. Inter-marker rotations during walk ing. Triads T7 and S3 were specified as the reference triads on the thigh and shank, respectively. Other markers rotations (_rot) relative to the reference triads are illustrated as three components. The three numbers in side each small graph are the r values which indicate the prominence of inter-subject similarities. Horizontal axis of each graph represents 0~100% gait cycle (f rom heel strike to heel strike). Positive directions are illustrated in the diagram as arrows on the reference triad axes. [Reprinted with permission from Gao, B., and Zheng, N., 2008, Investigation of soft tissue movement during level walking: Translations and rotations of skin markers: Journal of Biomechanics, v. 41, no. 15, p 3192, Fig.5] Soft Tissue Movement Behavior From the inter-marker translations and ro tations, a 4D image of the soft tissue deformation (3D space and time) on the thigh and shank during a gait cycle can be perceived, with translations showing skin stretching and rotations showing skin tilting between two surface locations. For example, from T1's translations (Figure 2-3) and rotations (Figure 2-5), it can be seen that the skin translation between T1 and T7 occurred mostly in superior/inferior (SI) di rection and rotation occurred mainly in the 39

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transverse plane. While a gait cycle progre ssed, the skin surface be tween the two locations was elongated in SI direction from heel strike to maximum knee flexion and then was shortened until the next heel strike; meanwhile, it also rotated externally during the first half of the gait cycle and then rotated back internally after that. The elongation/shortening range bet ween T1 and T7 was about 13 mm in SI direction and the rotation range was about 18 in the trans verse plane. Similar information can be read for every marker on both thigh and shank. Soft tissue deformation on the thigh exhibited similar pa tterns for markers on a same vertical column (Figure 2-3). Translation patterns of T3 were si milar to those of T6 and T9; translation patterns of T2 were si milar to those of T5 and T8; and translation patterns of T1 were similar to those of T4. But these three subgroups were not similar to each other. Such features also existed for rotations: T3 had simila r rotation patterns to T9 but not to T1 (Figure 2-5). No such trends were apparent for shank markers (Figure 2-4). Soft tissue deformation was generally larger on the thigh than on the shank. Intermarker translations and rota tions occurred in all three di rections but the magnitudes were not uniform along all directions (Figur e 2-6). For thigh markers (average of 20 subjects), the maximum range of motion (R OM) of translation reached 19.1 mm in anterior/posterior (AP) direction, 9.8 mm in lateral/medial (LM) di rection, and 13.0 mm in SI direction; the maximum ROM of rotation was 5.9 in the frontal plane, 12.0 in the sagittal plane, and 19.6 in the transvers e plane. For shank markers, the maximum ROM of translation was 9.3 mm in AP direction, 4.4 mm in LM direction, and 6.9 mm in SI direction; the maximum ROM of rotations was 2.7 in the frontal plane, 2.6 in the 40

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sagittal plane, and 8.6 in the transverse plane. Translations were relatively larger in AP and SI directions than in LM direction; rotati ons were greater in transverse plane than in frontal and sagittal planes. Markers placed on joints (T10, T11, S1, S2, S9, and S10) generally exhibited larger movement than other markers. Figure 2-6. Maximums and minimums of inte r-marker translations and rotations in a gait cycle. The zero line corresponds to the neutral standing posture. [Reprinted with permission from Gao, B., and Zheng, N., 2008, In vestigation of soft tissue movement during level walking: Translations and rotations of skin markers: Journal of Biomechanics v. 41, no. 15, p 3193, Fig.6] 41

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Gender Differences For most translation and rotation variables no significant differences between males and females were detected. The fe w variables detected with statistical differences between gender groups included translations of T10 and T11, and rotation of T1 and T3 (Table 2-2). Females ex hibited smaller inter-marker translations but larger inter-marker rotations. Table 2-2. Variables that showed st atistical differences between gender groups (* P <0.05, ** P <0.01). Variable Male Female P Trans_T10 30.1 5.3 24.4 6.4 Trans_T11 29.6 6.1 20.9 3.3 ** Rot_T1 20.4 4.7 24.2 2.9 Rot_T3 23.3 5.2 28.5 5.1 Discussions The purpose of this chapter was to inve stigate soft tissue movement on the thigh and shank during level walking using a noninvasive approach. This purpose was achieved using a novel analysis method. By quantifying inter-marker translations and rotations on each segment, the soft tissue deformation was depicted in a 4D picture. The results revealed quantitative informa tion about morphological dynamics of soft tissue profile during walking in forms of positional and orientational changes between different skin locations. Compared with STA repor ted in a previous study (Stagni et al., 2005), the inter-marker translations measured in the present study were of similar magnitudes. Little data has been published previously to which our results of skin marker rotations during walki ng can be compared. Inter-marker rotations were found to 42

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be up to 5.9, 12.0, and 19.6 in the frontal sagittal and transverse planes on the thigh, respectively, and up to 2.7, 2.6, and 8.6 on the shank, respectively (Figure 2-6). Soft tissue deformation occurred in all three directions but the distri bution was not uniform. Translational movement s were often more prominent in AP and SI directions than in ML direction. Rotational movements we re greater in the transverse plane than in the other two planes, especially for the thigh. These features could be explained by the muscular structures of lower extremity. Most muscles on the thigh and shank orient along SI direction. During their shortening and lengthening, length change of muscle fibers causes skin markers to move along SI di rection; the rotations in both frontal and sagittal planes are small. Meanwhile, t he cross-sectional ar ea of muscle bundles increases during shortening and decreases during lengthening. The circumference change of muscle bundles could lead to both translational and rotational movement of skin markers in the transverse plane. Another interesting feature found in this study was that soft tissue movement on the thigh ex hibited "longitudinal" similarity. For both translations and rotations, markers on the same vertical column (such as T3-T6-T9, T2T5-T8, or T1-T4) had similar movement patterns. When the quadriceps contracted during the swing phase, T1 and T4 shifted in feriorly, medially, posteriorly and rotated internally; T2, T5 and T8 shifted inferiorly, laterally, and anteriorly; T3, T6 and T9 shifted superiorly, laterally, and rotated externally. T hese findings indicated the primary role of quadriceps muscle in soft tissue movement on the anterior-lateral thigh. No such trends were apparent for shank markers. This study analyzed the inter-marker mo vement on the thigh and shank, but did not directly measure STA which is marker s movement relative to the bone. The 43

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adoption of this alternative approach was partially a result of technical limitations and the nature of the probl em. Currently only invasive devices and fluoroscopic techniques can achieve direct measurement of bony segment movement. But invasive methods have the potential to alter free soft tissue mo vement and are not appr opriate for a large healthy subject population. Fluoroscopy is not easy to be used for measuring large ROM motor tasks like ground walking. Another limitation of this study was the narrow range of subject age and BMI. The BMI of the healthy subjects tested in this step of study was in the lower bound of general pat ient population. With only young healthy subjects, some findings from this study may vary for other age and/or BMI groups. The influences of age and BMI on soft tissue movement behaviors need further investigation. Another important finding in this study wa s that soft tissue deformation exhibited inter-subject similarity, i.e., most inter-mark er translations and rotations showed similar patterns across different subjects (Figur e 2-3 to Figure 2-5). Since inter-marker movement represents the differ ence of two markers STA, this result indicates the possibility that markers STA may also have inter-subject similarity Considering that most people have similar muscular structures and joint coordination manners during the same activity, this finding is not surprising. However, little related evidence had been reported previously and the current preva iling opinion about STA is that it has no similarity among different people (Leardini et al., 2005). We consider that three possible reasons may go far in explaining the absence of similar findings in previous studies. The first is the study purpose. Many previous studies focused on the evaluation of joint kinematic errors caused by STA rather t han STA itself which is the movement of 44

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indiv idual markers (Benoit et al., 2006; Ho lden et al., 1997; Manal et al., 2000; Reinschmidt et al., 1997a; Reinschmidt et al., 1997b). Kinematic errors caused by STA are not equivalent to STA itself and could be influenced by more factors. Any variation in marker numbers, marker placement lo cations, and calculation methods of joint kinematics could result in different joint ki nematic errors even fo r the same intrinsic STA. The second reason involves sample size. Most previous studies included no more than seven subjects with unilateral test (Cappo zzo et al., 1996; Fuller et al., 1997; Sati et al., 1996; Stagni et al., 2005). With su ch few subjects, similarity could be overshadowed easily by variability. The th ird factor concerns the experimental and analysis methods. Very few studies had used a non-invasive method to examine the movement of individual ma rkers. In two such studies, one tested two total knee replacement patients (Stagni et al., 2005) and the other tested three healthy knees (Sati et al., 1996). Both studies examined the ov erall ROM of skin markers but did not analyze the time/joint angle related patterns nor perform inter-subject comparison. In the present study, twenty healthy subjects were tested bilaterally during walking without any constraint on free soft tissue movement. Th is was, to our knowledge, the first study to measure movement of individual skin markers in 4D space using a non-invasive approach and to evaluate their inter-subject similarities. One importance of that STA has inter-subject similarity is that this may provide a new strategy for STA effect compensati on and motion analysis a ccuracy improvement, as one persons STA profile can possibly be predicted from that of other persons of similar ages and body conditions. Compared with current STA compensation techniques which treat STA as a random or arbitrary noise (Alexander and Andriacchi, 45

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46 2001; Andriacchi et al., 1998; Cheze et al., 1995; Lu and O'Connor, 1999; Soderkvist and Wedin, 1993; Spoor and Veldpaus, 1980), this may lead to more efficient STA compensation methods by allowing constructi on of generic or semi-generic STA models from a small group of people and to apply to a large population. Although results in this work indicate the potential of this approach, further studies on direct STA measurement and inter-subject assessment will be needed to completely prove the hypothesis and explore the efficacy. Conclusions By using a non-invasive approach to analyze skin marker movement in a relatively large, healthy subject sample, the study in this chapter provided detailed 4D information of soft tissue deformation on the thigh and shank during level walking. Both qualitative and quantitative information is helpful in understanding STA behavior and exploring better marker configurations fo r gait analysis. Contrary to the prevailing opinion, this study also suggested the possibility that soft tissue movement has inter-subject similarity. This new finding may lead to mo re effective strategies for STA effect compensation and accuracy improvement in skin marker-based moti on analysis. In the next two chapters, we will further explore the behavior of STA in vivo using a simultaneous fluoroscopic and stereophotogramme tric experiment. The findings from these studies will lead us to a new strategy of STA compensation.

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CHA PTER 3 IN VIVO ASSESSMENT OF SOFT TISSUE ARTIFACT Introduction In the previous chapter we demonstrated that soft tissue movement is not a random noise but is a natural movement and has inter-subject similarity. This indicates that soft tissue artifact (STA), which is the relative movement between the markers and the underlying bone, is also not a r andom artifact. Similar to soft tissue deformation or inter-marker movement whic h was studied in the previous chapter, STA may also have certain patterns which are rela ted to adjacent joint positions and motor tasks. If these natural patterns of STA can be directly i dentified, we can use this information to develop more specific STA co mpensation techniques, which will be much more effective than current compensation techniques that treat STA as random noise. However, to directly assess STA, t he movement of both skin markers and the underlying bone needs to be measured at t he same time. Comparing to the measurement of skin marker movement, th e measurement of bone motion is much more challenging. As being discussed in Ch apter 2, most studies that measured in vivo bone movement used invasive/sem i-invasive methods, including intracortical bone pins (Benoit et al., 2006; Fuller et al., 1997; Rein schmidt et al., 1997a; Reinschmidt et al., 1997b), external fixators (Cappozzo et al., 1996) and percutaneous trackers (Holden et al., 1997; Manal et al., 2000), etc. For the purpose of assessing STA behavior, intracortical bone pin method has apparent disadvantages. First, the invasive pins can cause significant discomfort and potential infection risk to the tested subjects. Second, the pins could constrain and alter the free movement of the soft tissue, and the discomfort could even alter normal skeletal movement. External fixators have similar 47

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drawbacks. They could produce even more c onstraint on free soft tissue movement than intracortical pins. Percutaneous trackers are less invasive, but they can only be used to measure tibial movement, where t he effect of STA is much less than on the thigh. So far only a few studies used non-invasive techniques to evaluate free soft tissue movement relative to the underlying bone in living people (Garling et al., 2007; Sangeu x et al., 2006; Sati et al., 1996; Stagni et al., 2005). These studies used medical imaging techniques to measure the bone position, including magnet ic resonance imaging (MRI) and fluoroscopy. MRI provides a radiati on-free option for marker and bone pose tracking, but it is not suitable for dynamic measurements due to t he low speed of image acquisition. Fluoroscopy techniques have been widely used in the biomechanical community to measure in vivo poses of orthopedic prostheses and/or bones during different motor tasks (Banks et al., 2003; Komi stek et al., 2003; Kozanek et al., 2009; Stiehl et al., 1995). This dynamic X-ra y technique can usual ly reach an imaging acquisition rate of 7 to 30 fr ames per second, which is mu ch faster than MRI imaging and is sufficient for many low or middle sp eed activities. However, unlike MRI or computer tomography (CT), fluoroscopy only produces a series of 2D images but does not directly provide the 3D pose measurem ent. To obtain the 3D pose of the tested object from the 2D images, a 2D-3D registra tion is needed. This registration could be achieved using an edge based matching (Ban ks and Hodge, 1996) or image intensity based matching (Penney et al., 2001). With su ch a registration, even a single view fluoroscopy can be used to obtain the 3D pos e of the tested object. This technique has been validated and shown the capability to ac hieve an accuracy of about 1 and 1 mm 48

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for in-plane motion measurement. The out -plane motion measurement accuracy is lower when using a single plane fluorosc opy technique. More recently, double plane fluoroscopy has also been implemented to reduce out-plane motion measurement errors (Bingham and Li, 2006; Li et al., 2006) Because of its non-invasive nature and the capability to measure skeletal pose in a dynamic manner, fluoroscopic technique provides a suitable approach for the aim of our study. To track skin marker motion along wit h tracking bone pose using fluoroscopic technique, there are two options: using fluorosc opy itself (Garling et al., 2007; Sati et al., 1996) or using a separate stereophotogramme tric system (Akbarshahi et al., 2009; Stagni et al., 2005). Using fluoroscopy itself to track the marker pos ition simplifies the experimental configuration to using only one system, but it is diffi cult to track many markers distributed on a large area of the body segment due to the limited view field of fluoroscopy. Using a separate stereophotogrammetr ic system to track marker positions is a more flexible approach. It allows the measurement of large num ber of markers in a large space. But both spatial and te mporal synchronizations between the stereophotogrammetric system and the fluoro scopic system need to be achieved. Then the movement of the markers and t he bone can be expressed in a uniform spatiotemporal space, and relative movement (STA) can be analyzed. For the purpose to assess free movement of large number of skin markers relative to the underlying bone, a simultaneous fl uoroscopy and stereophotogrammetry method was used in this chapter. Six male subjects who had total knee arthroplasty (TKA) prostheses were tested during a series of knee flexion/extension movements and a stepping-up activity. 49

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Design and Methods Subjects With the permission of the institutional re view board (IRB) of the University of Florida (UF ), six male subjects who had acc epted a primary TKA sur gery were recruited in this study (Table 3-1). Table 3-1. TKA subject information. Subject # 1 2 3 4 5 6 Age (year) 60 69 64 67 65 65 Height (m) 1.74 1.68 1.64 1.79 1.78 1.70 Weight (kg) 95 75 81 95 78 80 Body mass index (kg/m^2) 31.4 26.6 30.1 29.6 24.6 27.7 TKA side Right Left Left Right Right Left Time after surgery (months) 52 35 25 42 12 60 Top Thigh Circumference (cm) 68 52 56 58 53 50 Mid Thigh Circumference (cm) 60 48 48 50 45 44 Maximum Calf Circumference (cm) 43 39 39 40 39 35 Thigh skinfold thickness (cm) 35 11 28 26 15 8 Shank skinfold thickness (cm) 24 16 13 17 6 9 The inclusive criteria of subject recruitment were: Gender: male Being younger than 70 years old Being active in daily life and having no difficulties to perform daily activities Body mass index (BMI) less than 32 Completion of the TKA surgery at leas t one year before parti cipating in this study 50

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A signed c onsent form was obtained from ea ch subject and the test was conducted using an IRB approved protocol. Experimental Setup A fluoroscopic system (SIEMENS AXIO M-Artis) in the Orthopaedics and Sports Medicine Institute of UF & S hands Hospital was used to reco rd the radiographic images of knee joint movement. The images were captured at a frequency of 7.5 Hz and the shutter speed was 10 ms. The fluoroscopic system has an image intensifier of 14 inch and the image size was 1024-by-1024 pixels. The distance between the X-ray source and the intensifier was about 1.1 m (Figure 3-1). Figure 3-1. Simultaneous fluoroscopy and stereophotogrammetry setup. A stereophotogrammetric system with five Eagle cameras (Motion Analysis Corp., CA, USA) was set up around the functional spac e of the fluoroscopic system to capture 51

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the movement of reflective markers (Figur e 3-1). The 3D residue of marker position tracking of the ster eophotogrammetric system was less than 0.4 mm after calibration. The stereophotogrammetric system was running at 60 Hz and shutter speed was 1 ms. Marker Placement The subject was required to wear an athletic short that allowed good exposure of both thigh and shank and had little constraint on the movement of skin markers. On the TKA side of the subject, eleven retro-reflective markers (10 mm in diameter) were attached to the thigh (Figure 3-2). Nine mark ers (T1 to T9) were placed to cover the anterolateral side of the thigh, and another two markers (T10 and T11) were placed on the medial and lateral epicondyles of the fe mur. Eleven markers were attached to the shank (Figure 3-2). Two markers (S1 and S2) were placed on the medial and lateral ridges of the tibial plateau. Six markers (S3 to S8) were placed on the anterolateral side of the shank. Two markers (S9 and S10) were placed on the medial and lateral malleoli. Another marker (S11) was placed on the tibi al tubercle. These markers were used to measure the skin motion at 22 locations. Four markers were placed on the pelvis (Figure 3-1). These markers were used to measure the pelvic orientation and to ca lculate hip flexion angle during movement. Since the pelvic markers were not used to m easure skin motion, their specific positions were not critical. They were usually placed on the locations that had no large displacement and had good exposure to the stereophotogrammetric cameras. Another marker was placed on the patella to facilitate the temporal synchronization between the fluoroscopic and stereophotogramme tric systems (see next se ctions for details). In addition, four markers were attached to the image intensifier and five markers were attached to the C-arm of the fluoroscopic unit. These markers were used to track the 52

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movement of C-arm during te st and to determine the spatial sync hronization between the fluoroscopic and stereophotogrammetric syst ems (see next sections for details). Figure 3-2. Marker placem ent on the thigh and shank. Motor Tasks Due to the limited field of view of the fl uoroscopy, it was not suitable to measure motor tasks occurring in a large space like ground walking. Thus, we designed a series of knee flexion movements at different hi p flexion angles to cover the sagittal-plane range of motion (ROM) of both hip and knee jo ints during basic daily activities. Five knee flexion trials were performed by the su bject, with a hip flexion angle at -15, 15, 30, 45, and 60 respectively (for description convenience, we referred hip extension to as -15 hip fl exion in this manuscript). At each knee flexion trial, the subject performed a few repeats of knee extension-flexion-extension movements, while maintaining the hip flexion angle which was instructed by a researcher using a goniometer. Figures 3-3 and 3-4 illust rate a subject performing the knee flexion/extension movements at -15 and 45 of hip flexion. Ot her trials were essentially similar. 53

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Figure 3-3. A subject performing knee flexion/ex tension movement at 15 of hip flexion. Figure 3-4. A subject performing knee flexion/ex tension movement at 45 of hip flexion. 54

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With the series of knee flexion/extensi on movements, a combination ROM of hip flexion angle (about from -15 to 60 in a discrete manner) and knee flexion angle (about 0 to 90 in a continuous manner) co uld be covered. Ankle flexion angle was not intentionally controlled considering its low influence on s hank STA (Cappozzo et al., 1996). Retrospective analysis showed that the ankle plantarflexion angle covered in the series of movements was about -10 to 30. From these trials, ST A on the thigh and its dependency on hip and knee flexion angles could be analyzed. STA on the shank and its dependency on knee and ankle flexion angles could be analyzed. In addition to the five knee flexion/ext ension movements, a stepping-up activity was also performed by each subject (Figur e 3-1). This activity was tested as an example of functional moto r task during daily living. The step was about 25 mm in height. In the stepping-up trial, the tested subject slowly stepped hi s foot of the TKA side onto the step, and follo wed by the other foot. Test Procedure First, the fluoroscopic unit was configur ed for knee joint imaging and the C-arm was positioned horizontally. A custom-built calibration jig was assembled onto the image intensifier of the C-arm and an X-ra y image was taken. This image was used to obtain the calibration parameter s of the fluoroscopy (e.g. pi xel size, source-intensifier distance, image center position) and to corr ect geometric distortion of the fluoroscopic images. The stereophotogrammetric cameras were positioned around the testing space and the positions of the cameras were adjus ted to reach a good coverage on the TKA side of the tested subject. The stereophotog rammetric system was then calibrated with a seed calibration followed by a wand calibration. 55

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Four markers were attached to the image in tensifier plane of the fl uoroscopic unit, and another five markers were attached to the C-arm (Figure 3-5). These markers were used to track the C-arm position during test and to facilitate spatial synchronization between the two systems. A custom-built L-fr ame which had four markers attached to a rigid plate was mounted on a tripod and plac ed between the C-arm (Figure 3-5). An X-ray image was taken on the L-frame by the fluoroscopic system (Figure 3-6), and the 3D positions of all these markers were ta ken by the stereophotogra mmetric system at the same time (Figure 3-7). The 4 marker s on the L-frame and the 4 on the intensifier panel were seen by both the fluoroscopi c and stereophotogrammetric systems thus could be used to spatially synchronize t he two systems. The same procedure was repeated three times, with the Lframe at three different posit ions and orientations. The three trials were averaged to provide a more reliable synchronizati on result. After the spatial synchronization procedure, the L-fr ame was taken out of the functional space and the system was ready for test. Figure 3-5. L-frame used for spatial synchronization. 56

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Figure 3-6. X-ray image of the L-frame. Figure 3-7. Stereophotogrammetr ic image of the L-frame. Reflective skin markers were placed on the subject and the test started with a static trial, while the subjec t was standing still on a pre-design ed plate. His foot distance and orientation were controlled by two bars on the plate (Figure 3-8). Both fluoroscopic 57

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and stereophotogrammetric images were taken for thi s standing posture (Figure 3-9). This trial was used to define the initial an atomical coordinate systems and the initial position of each skin marker relative to the underlying bone. The s patial relationships between the geometrical coordinate systems of the prostheses and the anatomical coordinate systems of the bone were al so obtained from this trial. Figure 3-8. Standing posture on a control plate. Figure 3-9. Fluoroscopic and stereophotogrammetric images on the standing posture. 58

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After the static trial, the subject perfo rmed the series of k nee flexion/extension movements. The subject stood on his non-tested foot and was instructed to lift his thigh of the TKA side to a position where the hip fl exion angle was measured by a researcher using a goniometer. The subject maintained the hip angle and flexed/extended his knee slowly for several repeats. Enough practice was given before each tr ial until the subject felt completely comfortable to perform t he required task. Hand s upport was sometime provided to help the subject per form the task, especially for t he -15 trial (Figure 3-3). For all the trials, the flexion/extens ion movement was performed in a slow-speed manner to accommodate to the frame rate of fluoroscopy (7.5 Hz). During data collection of each trial, the stereophotogrammetric system was turned on first and then the fluoroscopic system. Temporal synchro nization was not implemented during the experimental stage but in data processi ng stage (see next sections). At least one complete flexion/extension cycle was recorded by both system s for each trial (each hip flexion angle). After the five knee flexion/ extension trials, the stepping -up trial was performed by the subject. The subject slowly stepped his foot (TKA side) onto the 25 mm high step, and followed by the other f oot. The fluoroscopic and stereophotogrammetric data were collected in a similar manner as t he flexion/extension movements. Image Processing All the fluoroscopic images were first c onverted from DICOM format to TIFF format using a MATLAB (MathWorks Inc., MA, USA) program. The fluoroscopic calibration image was used to compute the major parameters of the fluoroscopy (e.g. pixel size, source intensifier distance, image center pos ition, distortion coefficients) by another MATLAB program developed by former students in the lab (Figure 3-10). These 59

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parameters were then used to process all the fluoroscopic images for geometric distortion correction, and in la ter shape-matching proc edure. Figure 3-10. Program used to obtain parameters of the fluor oscopy and correct edge distortion of fluoroscopic images. 3D models of both femoral and tibial com ponents of the TKA pr ostheses in STL format were imported into a custom-developed software (JointTrack, Mu, University of Florida). Controlled by the calibration param eters obtained from the previous step, the 2D projections of the model s were generated. With the undistorted fluoroscopic images on the background, an edge-based shape-matc hing procedure was performed to determine the 3D poses of the prostheses at each fluoroscopic im age (Figure 3-11). 60

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Figure 3-11. JointTrack used to determine the 3D poses of the TKA prostheses at each fluoroscopic image. Spatial and Temporal Synchronization The stereophotogrammetric and fluoroscopi c images recorded at the spatial synchronization trials (Figures 3-5 to 3-7) were used to determine the spatial relationship between the coordinate systems of the two systems. For each trial, the 3D positions of the eight mark ers (4 on the image intensifie r panel and 4 on the L-frame) were first determined from the stereophotogrammetric system (Figure 3-7). An STL model of the eight markers was created and imported into JointTrack. A shapematching process was performed between the marker cluster model and the fluoroscopic image (Figure 3-12). Differing to the method only using markers on the image intensifier for spatial synchronization (Stagni et al., 2005), we also included the Lframe markers to form the ma rker cluster model. By invo lving markers spreading along the in/out image plane axis, this modified approach resulted in more reliable spatial 61

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synchroniz ation. As shown on the left pictur e of Figure 3-12, the four markers on the image intensifier seem to be matched well with the fluoroscopi c image, but from the four markers on the L-frame we can tell the match was not precise. On the right picture of Figure 3-12, all the eight mark ers are matched well and the re sults are more reliable. From the matching result, the marker clus ters 3D pose in the fluoroscopic space was obtained. Since the marker clusters 3D pose in the stereophotogrammetric space was also known, the spatial relations hip between the fluoroscopic space and the stereophotogrammetric space was able to be det ermined. The average result was taken from the three spatial synchr onization trials. The eight-marker spatial synchronization method demonstrated good repeatabili ty for the multiple tria ls. The standard deviation (STD) of spatial synchronization results obtai ned from the three trials were usually less than 0.2 for rotations and 0.6 mm for in-plane translations and 3 mm for out-plane translation. Figure 3-12. Shape-matching between marker clusters and the fluoroscopic image. Left: only the four markers on the image intensifier being matched; Right: all the eight markers being matched. 62

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Since the spatial relationship bet ween t he fluoroscopic coordi nate system and the markers fixed on the C-arm was constant during the test, the spatial relationship between the fluoroscopic coordinate system and the stereophotogramme tric coordinate system was able to be determined by tracking the markers attached to the C-arm even the C-arm moved during the test. Temporal synchronization betwe en the fluoroscopic and the stereophotogrammetric systems wa s achieved by using a single target marker, which was usually the patella marker or the tibial tubercle marker (depending on the fluoroscopic images of a specific trial). Si nce the target marker was tracked by the stereophotogrammetric system and it was also visible in the fluoroscopic image, the motion trajectory of this marker determined by both systems provided direct information to synchronize the two systems temporally Because the shape-matching process on a sphere shaped single marker lacks good accura cy along the in/out plane direction, we only used the in-plane movement of the target marker to determine the time alignment. The 3D trajectory of the target marker measured fr om the stereophotogrammetric system was transformed to the fluoroscopic space and projected ont o the image plane. Each of the two components of the project ed trajectory (X: horizontal component; Y: vertical component) was used to compare to the X or Y translation measured directly from the fluoroscopy (Figure 313). The optimization metric used to align the time axes of the two systems was the STD of the difference betwe en the two translational trajectories measured from t he two systems. This optimization metric was sensitive to the shape misalignment of the curves but insensitive to the vertical offset between the curves. Since the stereophotogrammetric system had a higher frequency than the 63

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fluoroscopy (60 Hz vs 7.5 Hz), down -sampling (1:8) was applied on the stereophotogrammetric curve in order to perform the curve matching. This method demonstrated good synchronization reliability. Fo r all the trials in this study, the difference between the synchronization re sults using X and Y components was always no more than one stereophotogrammetric frame (i.e. 1/60 second). Figure 3-13. Temporal synchronizati on between the fluoroscopic and the stereophotogrammetric trajectori es of the target marker. STA Computation Once the spatial and temporal synchronizations between the stereophotogrammetric and fluoroscopic system s were determined for each trial, the movement of both skin mark ers and prostheses/bone could be analyzed in a uniformed spatiotemporal space. The movements of indi vidual markers relative to the underlying bone were determined, and expre ssed in the anatomical coor dinate system of femur or tibia (Figure 3-14). 64

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Figure 3-14. The movements of markers and the underlying bones were transformed to a uniform spatiotemporal space thus the relative movements can be analyzed. The anatomical coordinate syst ems of the femur and tibial were defined based on the standing posture. The origin of tibia was defined as the midpoint of the medial and lateral ridges of the tibial plateau. The origin of femur wa s defined as the midpoint of the medial and lateral epicondyles of the femur. The coordinate axes of both femur and tibia were defined parallel to the global coordinate systems at t he standing posture, thus all joint angles (hip, knee and angle) were init ialized as zero at the neutral standing posture. The dynamic pose of the anatomical coordinate systems of femur/tibia during movement was determined from t he fluoroscopic measurement. Results STA on the Thigh and Shank of a Representative Subject Figures 3-15 to 3-20 show the STA (individu al markers displacement relative to the bone) of a representative subject during k nee flexions at -15, 15, 30, 45, 60 of 65

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hip flexion and during stepping up. The marker names can be found in Figur e 3-2. The horizontal axis of each subplot is along time. Fo r the knee flexion trials it starts from an extension position and ends at t he peak flexion that followed (u sually larger than 90). For the stepping-up trial, it starts from the knee entering the fluoroscopic view and ends when the movement concluded with the knee fully extended. In some trials some markers were not tracked by the stereophotogrammetric system at some frames. This usually happened on some shank markers and medial knee and ankle markers when the knee joint reached high flexion. The missing data points were not interpolated or extrapolated in these figures, thus the result s showing below are truly from experimental data. Figure 3-15. STA on the thigh and shank of a representative subject during knee flexion at -15 of hip flexion. 66

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Figure 3-16. STA on the thigh and shank of a representative subject during knee flexion at 15 of hip flexion. Figure 3-17. STA on the thigh and shank of a representative subject during knee flexion at 30 of hip flexion. 67

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Figure 3-18. STA on the thigh and shank of a representative subject during knee flexion at 45 of hip flexion. Figure 3-19. STA on the thigh and shank of a representative subject during knee flexion at 60 of hip flexion. 68

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Figure 3-20. STA on the thigh and shank of a representative subjec t during stepping up. Inter-Subject Common Patterns of STA on the Thigh Figures 3-21 to 3-26 show the mean curves and STD of every thigh markers STA across all the six subjects, during knee flexions at -15, 15, 30, 45, 60 of hip flexion and during stepping up. For the knee flexion trials, the STA was firstly expresses along knee flexion angle; then the average across all subjects was taken over the range from 10 to 90 of knee flexion. For the steppingup trial, the average across subjects was taken over time from the frame when the knee entered the fluoroscopic view until the frame when the movement concluded with the knee extended on the step. Due to the larger error of out-plane tr anslation measurement of single view fluoroscopy technique, the STA along medial/l ateral (ML) direction is not reliable and not presented. In each of the following figures, subplots of STA along anterior/posterior 69

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(AP) direction (_X) are show n on the top row, with anterior as positive; subplots of STA along superior/inferior (SI) di rection (_Z) are shown on the bottom row, with superior as positive. Figure 3-21. Mean curves and standard deviati ons of thigh STA across all subjects during knee flexion at -15 of hip flexion. Figure 3-22. Mean curves and standard deviati ons of thigh STA across all subjects during knee flexion at 15 of hip flexion. 70

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Figure 3-23. Mean curves and standard deviati ons of thigh STA across all subjects during knee flexion at 30 of hip flexion. Figure 3-24. Mean curves and standard deviati ons of thigh STA across all subjects during knee flexion at 45 of hip flexion. 71

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Figure 3-25. Mean curves and standard deviati ons of thigh STA across all subjects during knee flexion at 60 of hip flexion. Figure 3-26. Mean curves and standard deviati ons of thigh STA across all subjects during stepping up. 72

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Inter-Subject Common Patterns of STA on the Shank Figure 3-27 to 3-32 show the mean curv es and STD of each shank markers STA across all the six subjects, during knee flexions at -15, 15, 30, 45, 60 of hip flexion and during stepping up. The marker names c an be found in Figure 3-2. For the knee flexion trials, the STA was firstly expresses along the k nee flexion angle; then the average across all subjects was taken over t he range from 10 to 90 of knee flexion. For the stepping-up trial, the average across subjects was taken over time from the frame when the knee entered the fluoroscopic view until t he frame when the movement concluded with the knee extended on the step. The STA along ML direction are not presented due to the lower accuracy of outplane translation measurement of single view fluoroscopy. In each of the following six figures, subplots of STA along AP direction (_X) are shown on the top row, with anterior as positive; subplots of STA along SI dire ction (_Z) are shown on the bottom row, with superior as positive. In the trials at -15 of hip flexion, some skin mark ers on the shank were not completely tracked during the whole movement by the stereophotog rammetric cameras, thus there are some incompletion or disc ontinuities showing on the curves. For most other trials, this was not an issue. 73

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Figure 3-27. Mean curves and standard deviations of shank STA across all subjects during knee flexion at -15 of hip flexion. Figure 3-28. Mean curves and standard deviati ons of shank STA across all subjects during knee flexion at 15 of hip flexion. 74

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Figure 3-29. Mean curves and standard deviations of shank STA across all subjects during knee flexion at 30 of hip flexion. Figure 3-30. Mean curves and standard deviati ons of shank STA across all subjects during knee flexion at 45 of hip flexion. 75

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Figure 3-31. Mean curves and standard deviations of shank STA across all subjects during knee flexion at 60 of hip flexion. Figure 3-32. Mean curves and standard deviati ons of shank STA across all subjects during stepping up. 76

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Discussio ns In this step of study, the STA of indivi dual markers on both thigh and shank was measured in vivo without any constraints by invasive apparatus. At a very first glance, it is apparent that STA is not random noise but is systematic movement that related to the activity and joint positions. For the knee fl exion/extension movem ents, STA increased with increasing knee flexion ( deviating from the standing pos ture where the markers initial local positions were determined). Fo r the stepping-up activity, STA started with large values when the knee first entered the fluoroscopic view field (usually at over 70 of knee flexion and over 50 of hip flexi on); STA decreased as the knee extended and finally reached close to zero when the move ment concluded at k nee extension. From Figures 3-15 to 3-32, it can be seen that STA on the thigh was generally much larger than STA on the shank. A skin markers move ment on the thigh relative to the femur sometimes can be over 30 mm at high flexion. STA on the shank was usually less than 15 mm in any direction. This observation was expected considering the muscular structures on the thigh and the shank. The magnitudes and profiles of STA varied along different anatomical directions. STA was generally larger along SI direction than along the other two directions, and this feature was more prominent on the thigh. On the thigh, STA along SI direction exceeded 20 mm for many markers at high flexion, while STA along AP direction was usually less than 15 mm. STA along ML dire ction was not able to be reliably measured due to the relatively low accuracy of out -plane translation measurement using single view fluoroscopy. Based on the ML results we obtained, STA along ML direction was lower than along SI direction, but a littl e higher than along AP direction for most 77

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markers. On the shank, STA along AP direction was usually less than 10 mm for most markers, and was a little larger along SI direction. STA was not uniformly distributed on different markers at different locations. On the thigh, most markers shi fted slightly posteriorly whil e the knee flexed, but the two markers on the femoral epicondyles (T10 and T11) exhibited much larger posterior displacement than other markers. The thr ee markers on the anter ior side (T1, T4 and T7) exhibited the smallest anterior displace ment. All the thigh markers except for T10 and T11 moved inferiorly during knee flexion, while T10 and T11 moved in the superior direction. Among T1 to T9, the three mark ers on the lateral side (T3, T6 and T9) exhibited the smallest inferior displacemen t, while the three markers on the anterior side (T1, T4 and T7) exhibited the largest inferi or displacement. Overall, the markers on bone landmarks (T10 and T11) showed larger STA than other thigh markers. Anterior markers (T1, T4 and T7) were more reliable in AP direction, while lateral markers (T3, T6 and T9) were more reli able in SI direction. On the shank, most markers tended to sli ghtly shift anteriorly during knee flexion except for the marker on the lateral ridge of the tibial pl ateau (S1), which moved in the posterior direction. The marker on the medial ridge of tibial plateau (S2) exhibited larger anterior displacement than most other markers. All shank ma rkers except for the one on the tibial tubercle (S11) moved inferiorly during knee flexion. The two markers on the ridges of tibial plateau (S1 and S2) exhibited the largest infe rior displacement. The three markers on the anterior tibia (S3, S5 and S7) showed the smallest inferior displacement (less than 2 mm). Overall, S3, S5 and S7 had small STA on both AP and SI directions. S11 had small STA on AP direction but not on SI direction. The commonly used bone 78

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landmarks (S1, S2, S 9, and S10) did not exhibited smaller STA than other shank markers. Another interesting observation was that STA exhibited si milar patterns for markers that were on a same column (ver tical line). This was very prominent on the thigh. The nine markers on the anterolateral thigh (T1 to T9) can be categorized into three subgroups: 1) T1, T4 and T7; 2) T2, T5 and T8; and 3) T3, T6 and T9. The three markers in each subgroup showed similar STA patterns along both AP and SI directions. But the similarity for markers on a same row (horizontal line) was lower. Such similarity was also visible for markers on the shank, although less prominent. Markers S3, S5, and S7 exhibit ed similar STA patterns, as well as the subgroup S4, S6 and S8. This observation is consistent with t he findings in Chapter 2, and is reasonable considering most muscles c ontraction directions are generally along SI direction during knee flexion movement. STA patterns exhibited inter-subject simila rity, which can be seen in Figures 3-21 to 3-32. Although there was some variability, STA on most markers was in similar profiles across subjects. The similarity is most prominent for STA along SI direction, which showed clear mean curves and small STD across subjects. The common patterns along AP direction had higher STD than along SI direction, but still apparent. Because there were unavoidable marker plac ement inconsistency on different subjects, and the STA was more sensitive to loca tion change along AP dire ction than along SI direction (based on the findings in the previous paragraph), the higher STD on AP direction could result more fr om the marker placement incons istency than from the real inter-subject variability of STA. The effect of location sensitivity on the STA variability 79

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was more evidenc ed by the epicondyle mark ers (T10 and T11). Since the location sensitivity of STA is higher close to the jo int where large amount soft tissue deformation occurs during knee flexion, the STA pattern s of T10 and T11 exhibited higher intersubject variability than other markers. C onsidering subjects ant hropometric variability and marker placement inconsistency on di fferent subjects, the observed common patterns across subjects strongly demonstr ated that STA is not totally subjectdependent. This study is the first, to our knowledge, to provide direct evidence supporting this concept. This finding indicate s the possibility that STA models can be developed from some subjects and used for others, with major behaviors being reflected. In addition to that STA has inter-subject si milarity which was demonstrated in this study, another widely accepted conc ept that STA is totally motor task-dependent is also being challenged by the findings in this study. First, from Figures 3-21 to 3-32 it can be easily identified that the STA patterns were similar during the series of knee flexion movements, with small differences likely caus ed by the difference of hip flexion angles. In addition, for the stepping up activity, the STA exhibited comparable behavior to the knee flexion movements if we consider the movement of adjacent joints. For example, the SI components of thigh ST A during stepping up are genera lly consistent with those during knee flexion at 60 of hip flexion, imaging that the knee join t angle changed from 90 to 0. Based on this observation, we hypothesized that a large portion of STA is determined by the joint position or simply the adjacent joint angles. If the relationship between STA and the adjacent joint angles can be determined, a universal STA model could be developed for different motor tasks. If this hypothesis is proved, we no longer 80

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have to pursue STA models for each specific motor task. Rather than this, the universal STA model will be sufficient to r epresent the basic beha vior of STA during different motor tasks. In the next chapter, we will validate this hypothesis and demonstrate that STA also has inter-motor-ta sk similarity in addition to inter-subject similarity. Based on this knowledge, a universal STA model will be developed and two new evidence-based STA compensation methods will be implemented and their effectiveness over conventional method will be evaluated. 81

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CHA PTER 4 DEVELOPMENT OF NEW METHOD S FOR SOFT TISSUE ARTIFACT COMPENSATION Introduction In the previous chapter, we demonstrated that soft tissue artifa ct (STA) has intersubject similarity, and proposed the hypothesis that STA is not totally motor-taskdependent but mainly related to adjacent joint angles. In this chapter, we will test this hypothesis and demonstrate that a large portion of STA c an be predicted by adjacent joint position. Further, we wi ll develop a universal STA model that reflects the common patters multiple subjects. This STA model that can be represented as functions of adjacent joint angles will be established based on the in vivo STA data obtained from the previous chapter. From this model, tw o new evidence-based STA compensation methods will be developed and their performance will be evaluated by comparison to the conventional method. Development of a Universal STA Model STA in a Two-Dimensional Joint Angle Space In the last chapter, the STA during each of the series of knee flexion movements has been determined. By combining the results of the series of knee flexion trials (5 trials) together, we are able to obtai n an STA map over a wide coverage of combinations of adjacent joint angles. S pecifically, the hip, knee and ankle flexion angles during each of the 5 trials were calculated along with t he STA measurement. STA on the thigh was examined over hip and knee flexion angles, and STA on the shank was examined over ankle and knee flexion angles. For example, Figure 4-1 illustrates a 3-dimensional (3D) plot of T1s STA along superior/inferior (SI) direction of a repres entative subject, over hip and knee flexion 82

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angles. This plot contains all the data points from the 5 trials of knee flexion movements of this subject. Each dot in the plot represents one fluoroscopic image. A top 2dimensional (2D) view of this plot reveals the hip and knee angle ranges that were covered by the 5 trials (Figure 4-2). For this subject, the 5 trials covered a hip fle xion range about from 10 to 50, and a knee flex ion range about from 0 to 100. It was noted that the actual hip flexi on angles during these trials may deviate from the intended value (i.e., -15, 15, 30, 45, and 60). Espec ially for the -15 trial, the actually hip flexion angle was positive but not negative. This phenomenon happened on almost every subject. The cause was retrospectively identified as that when the subject performed this motor task his pelvis usually tilted forward and th is reduced the intended hip extension angle (the forward pelvic titling can be observed in Figure 3-3). Reasonable amount of hip angle fluctuation during individual trials was also observed (Figure 4-2). A left view of Figure 4-1 shows the relationship between this STA component and hip flexion angles (Figure 4-3) With hip flexion angle increased, STA increased along negative direction (i.e., mark er T1 moved inferiorly). The spread along vertical axis in Figure 4-3 indicates this STA component was not purely related to hip flexion angle but also knee flexion angle. This is shown in Figure 4-4 which is a front view of Figure 4-1. Figure 4-4 clearly reveals a negative slope between this STA component and knee flexion angle (i.e. with k nee flexed more, marker T1 shifted inferiorly more). Figures 4-3 and 4-4 demonstrate that the SI compone nt of T1s STA is related to both hip and knee fl exion angles. 83

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Figure 4-1. 3D plot of marker T1s STA (SI component) of a representative subject over hip and knee flexion angles. Figure 4-2. 2D plot showing the hip and k nee angle coverage by the series of knee flexion movements of a representative subject. 84

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Figure 4-3. 2D plot showing the rela tionship between the STA component and hip flexion angle. Figure 4-4. 2D plot showing the rela tionship between the STA component and knee flexion angle. 85

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Similar procedures can be performed on shank STA to examine it s relationship to both ankle and knee flexion angles. Figure 4-5 illustrates the 3D plot of the SI component of S4s STA of the same subject, over ankle and knee flexion angles. A top view of Figure 4-5 reveals the ankle and kn ee angle ranges that were covered by the series of trials (Figure 4-6). It shows t he trials covered an ankle flexion range of about from 10 dorsiflexion to 35 plantarflexi on. A left view of Figure 4-5 shows the relationship between this STA component and ankle flexion angle (Figure 4-7). A slight positive trend indicates marker S4 tended to shift superiorly while the ankle plantarflexed. Differing to this weak corre lation with the ankle joint angle, a more prominent correlation between this STA co mponent and knee joint angle was observed (Figure 4-8). A clear negative trend can be s een, indicating that marker S4 tended to move inferiorly while the knee flexed. Figure 4-5. 3D plot of marker S4s STA (S I component) of a representative subject over ankle and knee flexion angles. 86

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Figure 4-6. 2D plot showing the ankle and knee angle coverage by the series of knee flexion movements of a representative subject. Figure 4-7. 2D plot showing the rela tionship between the STA component and ankle plantarflexion angle. 87

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Figure 4-8. 2D plot showing the rela tionship between the STA component and knee flexion angle. Mathematical Expression of STA To express the relationship between STA and adjacent joint angles mathematically, multiple linear regression was used to constr uct the 2-variable function for each directional component of each marker s STA. To perform the multiple linear regression, there are many different options to design the terms of independent variables (here the independent variables are the adjacent joint angles). We have tested linear and quadratic options for this process. Due to the acceptable effectiveness and the simplicity, we decided to use linear terms in this step. Another ben efit of using linear models is the intuitiveness of mathematical description. Ea ch of the three coefficients obtained from the regression has an intuitive meaning in a li near model. The first two 88

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coefficients are the slopes of the STA to each adjacent joint angle, while the third coefficient is an offset value at t he neutral position in the model. Specifically a thigh markers STA vector i thighSTAV_ was modeled as a multilinear function of hip and kn ee flexion angles (hip and knee ), and a shank markers STA vector i shankSTAV_ was modeled as a multilinear functi on of ankle and knee flexion angles (ankle and knee ): 1333 222 111 knee hip i thighSTAcba cba cba V (4-1) 1333 222 111 knee ankle i shankSTAcba cba cba V (4-2) The number index (1, 2, or 3) represents each of the three directional components of the STA vector: anterior/posterior (AP), medial/lateral (ML) and SI. Coefficient and reflects the sensitivities of the STA component to each of the two adjacent joint angles, and coefficient is an offset. The 2-variable function shows geometrically as a plane in 3D. By using this model, the relationship between each markers STA and the adjacent joint angles can be fully described simply by us ing a 3-by-3 matrix. On ce this matrix is determined, the 3D STA vector of the specific marker at any combination of adjacent joint angles can be predicted. abc As an example, by running the multilinear regression on the data points shown in Figure 4-1 (SI component of T1 marker s STA), we obtained for marker T1: 8.6165.0181.0333 cba (4-3) 89

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The R-squared value was 0.89 and the root -mean-square (RMS) residual error was 2.06 mm. Thus the SI component of T1s STA as a function of the adjacent joint angles can be expressed as: 8.6 165.0 181.01 3__knee hip thighSTAV (4-4) The intuitive explanation of Equation 4-4 is: for each degree of hip flexion increase, the marker T1 tended to move inferiorly by 0.181 mm; for each degree of knee flexion increase, the marker T1 tended to move infe riorly by 0.165 mm. The small offset (6.8 mm) could come from both modeling devia tion and the actual difference between dynamic movement and the static standing pos ture. Figure 4-9 geometrically shows this function in 3D. Figure 4-10 shows the 2D proj ections of the 3D plane to demonstrate its dependency on hip and knee joint angles. From these figures, it can be seen the multilinear STA model provides as a good repr esentation of experimental data points. Figure 4-9. Multilinear regre ssion on the data points of the SI component of T1s STA. 90

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Figure 4-10. 2D projections of the regression model showi ng the dependency of the SI component of T1s STA to hip and knee joint angles. 91

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Similarly, by performing the multilinear regression on the data points shown in Figure 4-5 (SI component of marker S4 s ST A), we obtained for marker S4: 55.0092.0061.0333 cba (4-5) The R-squared value was 0.87 and the RMS re sidual error was 1.36 mm. Thus the SI component of T1s STA as a function of ankle and knee angles can be expressed as: 55.0 092.0 061.04 3__knee ankle shankSTAV (4-6) The intuitive explanation of Equation 4-6 is: for each degree of ankle plantarflexion increase, the marker S4 tended to move superiorly by 0.061 mm; for each degree of knee flexion increase, the marker S4 tended to move inferiorly by 0.092 mm. The offset is almost zero. Figure 4-11 geometrically shows this function in 3D. Figure 4-12 shows the 2D projections of the 3D plane to illustrate its dependency on ankle and knee joint angles. Figure 4-11. Multilinear regression on the data points of the SI component of S4s STA. 92

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Figure 4-12. 2D projections of the regression model showi ng the dependency of the SI component of S4s STA to ankle and knee joint angles. 93

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The same procedures were then performed on every component of every marker, and a series of 3-by-3 matrices were obt ained for the thigh markers and the shank markers. Thus a complete set of STA model s was established for this representative subject. Inter-Motor-Task Similarity of STA In the beginning of this chapter, we hypot hesized that STA is not totally motortask-dependent and a large portion of STA can be determined by the angles of the adjacent joints. In this section, we will te st this hypothesis by using the STA models established based on the data from the series of knee flexion movements, to predict the STA in the stepping-up trial and compare the predicted STA to the experimental measurements. To perform this comparison, the hip, knee, and ankle flexion angles during the stepping-up trial of the same subject were first computed. Then at each frame of the stepping-up trial, the instant hip and knee flexion angles were used to compute the predicted STA for every thigh marker; the ankle and knee flexion angles were used to compute the predicted STA for every shank marker. The computation was performed using Equations 4-1 and 4-2 and the matric es determined in the previous step. Figures 4-13 and 4-14 show the comparis ons of predicted STA (dashed lines) and the experimentally measured STA (solid lines ) of thigh markers during the stepping-up trial, along AP and SI directions, respectively It can be seen that the predicted STA successfully reflect the major patterns of real STA. The trends and the distributions among different markers of t he predicted STA are fairly cl ose to the experimentally measured results. The prediction residual erro rs are much smaller than the STA itself. In Figures 4-15 and 4-16, the prediction residuals (dashed lines ), which are the 94

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differences between the predicted STA and the measured STA, are plotted against the original ST A (solid lines). The prediction re siduals are usually less than 10 mm for most markers. This comparison indicates the feasibility of using the STA models established from the knee flexion movements to compensate for STA in the steppi ng-up movement. Figure 4-13. Measured (solid lines) and predi cted (dashed lines) AP component of thigh STA during stepping-up activity. Figure 4-14. Measured (solid lines) and pr edicted (dashed lines) SI component of thigh STA during stepping-up activity. 95

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Figure 4-15. Comparison between the predict ion residuals (dashed lines) and the STA of thigh markers along AP direction (so lid lines) during stepping-up activity. Figure 4-16. Comparison between the predict ion residuals (dashed lines) and the STA of thigh markers along SI direction (solid lines) during stepping-up activity. Figures 4-17 and 4-18 show the comparis ons of predicted STA (dashed lines) and the measured STA (solid lines) of shank markers during the stepping-up movement, along AP and SI directions, respectively. 96

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Figure 4-17. Measured (solid lines) and predicted (dashed lines) AP component of shank STA during stepping-up activity. Figure 4-18. Measured (solid lines) and predicted (dashed lines) AP component of shank STA during stepping-up activity. 97

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Figure 4-19. Comparison between the predict ion residuals (dashed lines) and the STA of shank markers along AP direction (solid lines) during stepping-up activity. Figure 4-20. Comparison between the predict ion residuals (dashed lines) and the STA of shank markers along SI direction (solid lines) during stepping-up activity. Again, the predicted STA reflected major tr ends and the distributions of real STA for many markers. Because the STA magnitu des on the shank are much smaller than on the thigh, similar amount of prediction e rrors could cause the predicted STA looks 98

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less alik e the measured STA. This phenom enon was more or less prominent for different markers. However, prediction resi duals are still smaller than the original STA magnitudes. Figures 4-19 and 420 plot the prediction residua ls (dashed lines) against the original curves of STA (solid lines). The prediction residuals for shank markers are usually less than 5 mm. Figures 4-13 to 4-20 revealed the in ter-motor-task similarity of STA and demonstrated the possibility to predict STA during a motor task based on data obtained from other motor tasks. A Universal STA Model of All Subjects So far we have demonstrated that STA has both inter-subject and inter-motor-task similarities. Based on this knowledge, a universal STA model could be established based on multiple subjects data. As examples comparable to Figures 4-1 to 4-8, the SI componen t of marker T1s STA of all the six subjects are plotted over hip and knee angles (Fi gures 4-21 to 4-24); the SI component of marker S4s STA of al l subjects are plotted over ankle and knee angles (Figures 4-25 to 4-28). In these figur es, each color represents each subject. 99

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Figure 4-21. 3D plot of marker T1s STA (SI component) of all subjects over hip and knee flexion angles. Figure 4-22. 2D plot showing the hip and kn ee angle coverage by the series of knee flexion movements for all subjects. 100

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Figure 4-23. 2D plot showing the relati onship between the STA component and hip flexion angle for all subjects. Figure 4-24. 2D plot showing the relati onship between the STA component and knee flexion angle for all subjects. 101

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Figure 4-25. 3D plot of the marker S4s STA (SI component) of all subjects over ankle and knee flexion angles. Figure 4-26. 2D plot showing the ankle and knee angle coverage by the series of knee flexion movements for all subjects. 102

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Figure 4-27. 2D plot showing the relati onship between the STA component and ankle plantarflexion angle for all subjects. Figure 4-28. 2D plot showing the relati onship between the STA component and knee flexion angle for all subjects. 103

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From Figures 4-21 to 4-28, it can be seen the relations hips between STA and adjacent joint angles are not exactly the same for all subjects. But the basic trends of these relationships are similar. If we used a ll the data points from all subjects to perform the multilinear regression proced ure described in earlier sections, the resultant functions should be an overall representati on of all the six subjects. For the example in Figure 4-21, by r unning the multilinear regression on all data points from six subjects for the SI component of T1 mark ers STA, we obtained for marker T1: 0.9137.0099.0333 cba (4-7) The R-squared value was 0.53 and the RMS resi dual error was 4.46 mm this time. Thus the SI component of T1s STA as a function of the adjacent joint angles for all six subjects can be expressed as: 0.9 137.0 099.01 3__knee hip thighSTAV (4-8) For the example of Figure 4-25, by r unning the multilinear regression on all data points from six subjects for the SI component of S4 markers STA, we obtained for marker S4: 951.0091.0136.0333 cba (4-9) The R-squared value was 0.72 and the RMS resi dual error was 2.10 mm this time. Thus the SI component of S4s STA as a function of the adjacent joint angles for all six subjects can be expressed as: 951.0 091.0 136.04 3__knee ankle shankSTAV (4-10) 104

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Figure 4-29. Multilinear regression on the data points of the SI co mponent of T1s STA for all subjects. Figure 4-30. Multilinear regression on the data points of the SI co mponent of S4s STA for all subjects. 105

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Figure 4-31. 2D projections of the regression model showi ng the dependency of the SI component of T1s STA to hip and knee joint angles for all subjects. 106

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Figure 4-32. 2D projections of the regression model showi ng the dependency of the SI component of S4s STA to ankle and knee joint angles for all subjects. 107

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After assembling all subjects together, t he universal models wer e not as good representations as subject-specific m odels. This can be seen by the decreased R-squared values and the increased RMS resi dual errors. However, the universal models are still able to reflect major common patterns of STA on the group of subjects (Figures 4-29 to 4-32). By repeating the multilinear regression procedure on every component of every marker on the thigh and shank, a series of 3-by -3 matrices that descr ibe the relationship of the STA and adjacent joint angles for all the subjects could be obtained (Tables 4-1 and 4-2). These coefficient matrices mathem atically represent the universal STA models of every marker for all the si x subjects (Equations 4-1 and 4-2). In Tables 4-1 and 4-2, indices 1, 2, and 3 represent AP, ML, and SI components respectively. From the matrices in the tables, it can be seen on the thigh the AP components of most markers STA are more sens itive to hip flexion angle, while the SI components of most markers STA are more sensitive to knee flexion angle. Most c values (offsets in the multilinear model) are smaller than 10 mm. A few markers ML components resulted in large c values (greater than 10 mm), which could be caused to large errors in ML STA m easurements. On the shank, a and b values are generally smaller than those on the thigh, reflecting t he smaller magnitudes of shank STA. All the c values for shank markers are generally small (less than 7 mm). 108

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Table 4-1. Coefficient matrices of thigh markers for all subjects. Marker Component a (mm/deg) b (mm/deg) c (mm) RSquared RMS residual (mm) 1 -0.136 -0.104 8.232 0.23 7.27 2 0.608 0.023 -17.518 0.44 8.57 T1 3 -0.099 -0.137 -9.002 0.53 4.46 1 0.222 -0.091 1.727 0.14 9.30 2 0.360 -0.006 -13.984 0.21 8.44 T2 3 -0.018 -0.186 -5.697 0.69 4.09 1 0.350 -0.111 -0.654 0.21 10.35 2 0.092 -0.031 -3.723 0.04 7.40 T3 3 0.083 -0.134 -1.864 0.71 2.76 1 -0.050 -0.057 2.571 0.08 6.99 2 0.498 -0.005 -13.626 0.41 7.29 T4 3 0.012 -0.185 -6.954 0.66 4.30 1 0.208 -0.072 -0.224 0.14 8.04 2 0.309 -0.014 -11.297 0.21 7.42 T5 3 0.047 -0.202 -5.468 0.72 4.10 1 0.279 -0.076 -2.626 0.17 8.88 2 0.121 -0.069 -3.163 0.12 6.83 T6 3 0.086 -0.137 -1.923 0.68 3.02 1 0.056 -0.058 -1.690 0.06 7.57 2 0.298 -0.008 -8.509 0.25 6.29 T7 3 0.019 -0.248 -3.914 0.79 4.18 1 0.202 -0.061 -3.243 0.14 7.52 2 0.192 -0.012 -6.692 0.13 6.07 T8 3 0.074 -0.209 -6.040 0.69 4.47 1 0.181 -0.057 -3.285 0.13 6.98 2 0.119 -0.088 -2.427 0.19 6.35 T9 3 0.091 -0.104 -2.429 0.46 3.73 1 0.181 -0.198 -10.880 0.28 10.44 2 0.088 -0.043 -0.028 0.08 5.67 T10 3 0.095 0.105 -4.556 0.20 7.44 1 -0.189 -0.280 5.251 0.76 5.57 2 0.034 0.023 -0.787 0.02 5.66 T11 3 -0.032 0.251 -3.444 0.50 8.15 109

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Table 4-2. Coefficient matrices of shank markers for all subjects. Marker Component a (mm/deg) b (mm/deg) c (mm) RSquared RMS residual (mm) 1 0.046 -0.069 2.702 0.32 3.31 2 0.148 -0.064 1.365 0.24 4.99 S1 3 0.077 -0.111 -0.265 0.53 3.46 1 0.046 0.120 -0.911 0.44 4.36 2 0.089 -0.077 1.034 0.23 4.63 S2 3 -0.138 -0.087 1.721 0.32 4.86 1 -0.043 0.016 1.654 0.08 2.54 2 0.175 -0.036 0.981 0.22 4.80 S3 3 0.066 -0.010 -0.601 0.20 1.86 1 -0.008 0.003 0.596 0.00 3.37 2 0.142 -0.046 0.781 0.16 5.26 S4 3 0.136 -0.091 -0.951 0.72 2.10 1 -0.032 0.017 1.801 0.04 3.33 2 0.123 -0.011 0.370 0.09 5.22 S5 3 0.069 -0.028 -0.453 0.37 1.67 1 0.019 0.043 -0.029 0.13 3.78 2 0.211 -0.024 1.400 0.20 5.76 S6 3 0.129 -0.060 -0.675 0.50 2.51 1 -0.079 0.031 2.834 0.09 4.49 2 0.110 0.005 -1.045 0.06 5.53 S7 3 0.032 -0.035 0.061 0.43 1.39 1 -0.031 0.046 0.620 0.09 4.86 2 0.125 -0.013 0.596 0.07 6.13 S8 3 0.128 -0.035 -0.529 0.39 2.47 1 -0.243 0.047 2.270 0.21 6.75 2 0.108 -0.005 -0.874 0.04 6.84 S9 3 0.149 -0.025 -2.986 0.37 2.72 1 -0.108 0.023 5.337 0.07 5.80 2 0.132 -0.009 -1.745 0.06 6.60 S10 3 0.016 -0.016 0.561 0.04 2.73 1 0.000 0.012 1.428 0.02 2.36 2 0.214 -0.078 1.656 0.39 4.70 S11 3 0.018 0.049 1.225 0.27 2.64 110

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In addition to the multilinear coeffici ents, the R-squared value and the RMS residual error from each regression are also s hown in T ables 4-1 and 4-2. For the thigh STA models, over 84% variables showed at least small correlation (R-squared > 0.1), about 40% showed at least moderate corre lation (R-squared > 0.3), and about 30% showed large correlation (R-squared > 0.5) For the shank STA models, over 60% variables showed at least small correlati on (R-squared > 0.1), about 33% showed at least moderate correlation (R-squared > 0.3), and about 10% showed large correlation (R-squared > 0.5). The average RM S residual error was 6.53 mm for thigh models, and 4.05 mm for shank models. These RMS residual errors were much smaller than the STA itself, indicating the effectiveness of using this universal STA model to compensate for STA effects. Two New Methods for STA Compensation With Tables 4-1 and 4-2 and Equations 4-1 and 4-2, the overall STA patterns of all the subjects under any given combinations of joint angles can be obtained. With this information, we developed two new evidence-based methods for STA compensation: a STA deduction (STAD) method and a dir ectional weighted opt imization (DWO) method. STA Deduction (STAD) Method If a human body segment (thigh or shank) is a rigid body, a skin markers global position at a dynamic instant can be expressed as staticl ibone bone dynamicg ipRO p_ _][ (4-11) where and are the position and or ientation of the bone; boneOboneRstaticl ip_ is the local position of the marker in the anatomical refe rence system at the static neutral posture. 111

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dynanicg ip_ is the global position of the marker in the laboratory coordinate system at a dynamic instance. But if the body segment is not a rigid body, the equation will not hold: staticl ibone bonepRO_][ dynamicg ip_ (4-12) The cause of the inequity is markers relative movement in the anatomical coordinate system, i.e. STA. It can be expressed as: staticl i bone dynamicg i bonepO p_ _1) (] STA iRV[ STA iV_ dynamicg ip (4-13) If is known, a new equation can be set up in a similar form of Equation 4-11: ) ]([_ STA i staticl ibone boneVpRO (4-14) Since static_l ip and dynanicg ip_ are also known, boneO and boneR can be solved using the same approach solving Equation 4-11. This is basic rationale of the STAD method. To implement this method to solve jo int kinematics, the STA vectors will be estimated using our universal STA model. Firs t, hip, knee and ankle flexion angles will be computed at each instant. At this step, the flexion angles do not need to be highly accurate and can be determined using any c onventional rigid body optimization method or simply using including angles between co nnections of specific markers. After determining joint angles at every instant of the trial, the STA models in Tables 4-1 and 4-2 will be used along with Equations 4-1 and 42 to compute the STA vector for every skin marker. Then the STA vectors will be app lied into Equation 4-14 for multiple markers. If there are no less than 3 markers at that frame, boneO and can be solved. boneR 112

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Directional Weighted Op timization (DWO) Method The concept of the DWO method can be explained as the following. In a conventional rigid-body optimization, each marker is considered having the same importance (weight). However, we have lear ned that different markers have different magnitudes of STA during an activity. In an equally-weighted optimizatio n, a marker that has large STA generates larger contribution to analysis errors than a marker that has small STA does. It is logical to assign diffe rent weights to different markers in the optimization. Further, even fo r the same marker, the ST A components along different directions are also not the same. One mark er may have a large STA along AP direction but a small STA along SI direction, as demon strated in the last c hapter. Thus, it would be more effective to assign different weights to different directional components of each marker. The weights will be determined by STA magnitudes, and this approach represents a non-rigid body optimization. The implementation of the DWO method can be expressed as the following: Search for and which minimize boneOboneR smar i staticl i bone dynamicg i bone iiipO pRwzwywxker 1 2 _1)) (]([. (4-15) where is the weight vector for marker i and iiiwzwywx STA i iiiV wzwywx/.111 (4-16) where is the STA vector for the same mark er at the specific frame, which is determined based on adjacent joint angles and the universal STA models. STA iV Although the basic concept of this DWO method is similar to some other non-rigid optimization algorithms such as the point cluster technique (PCT) (Andriacchi 113

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et al., 1998), a fundamental difference in our approach is that the weights are evidencebased instead of pure mathemat ical estimation. In addition, since the weights are determined based on continuous STA functions, the result ant kinematics would not have frequent discontinuities that ar e seen in using the PCT method. Results and Discussions Evaluation Approach To evaluate the performance of STAD and DWO methods, the in vivo knee joint kinematic data collected in Chapter 3 were used. We collected data on six subjects. In order to fairly test the ST A compensation methods, at this step we only used 5 of the 6 subjects data to construct the univers al STA models, and used the STA models to implement STAD and DWO methods and test their performance on the 6th subject. This procedure was repeatedly applied to each of t he six subjects. For example, the STA models established based on the data from subj ects #2, #3, #4, #5, and #6 were used to analyzed the kinematics of subject #1; the STA models established based on the data of subjects #1, #3, #4, #5, and #6 were used to analyzed subject #2; and so on. Thus six sets of evaluation were performed. The kinematic results obtained from a c onventional rigid body optimization (RBO) method (Spoor and Veldpaus, 1980), the ST AD method, and the DWO method were compared with the kinematics measured usi ng the fluoroscopic technique. The RMS errors of each of the three skin mark er-based methods were evaluated. In addition to analyzing the errors in knee jo int kinematics, the errors in femur and tibia kinematics were also evaluated. This was achieved by computing knee joint kinematics using one segments motion det ermined using skin markers, and another segments motion determined using fluoroscopy For example, the comparison between 114

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1) knee joint kinematics computed using the femur moti on determined using skin markers and the tibia motion determined usi ng fluoroscopy; and 2) knee joint kinematics computed using femur and tibia motion both det ermined using fluoroscopy; provides an evaluation of the errors caused by femur motion analysis. Similarly, the comparison between 1) knee joint kinematics computed using the femur motion determined using fluoroscopy and tibia motion determined us ing skin markers; and 2) knee joint kinematics computed using femur and tibia motion both determined using fluoroscopy; provides an evaluation of the errors caused by tibia motion analysis. Kinematic Results As examples, Figures 4-33 to 4-37 show the kinematic results of subject #3. The STA models were constructed based on the dat a from subjects #1, #2, #4, #5, and #6. In these figures, the solid black lines are knee joint kinematics measured from fluoroscopy, and each other color represent s one skin marker-based method (red: RBO; blue: STAD; green: DWO). For each skin mark er-based method (each color), thick solid lines are joint kinematics; thin solid lines are femur-based kinematics (femur motion determined using skin markers and tibia mo tion determined using fluoroscopy); thin dashed lines are tibia-based kinematics (tib ia motion determined using skin markers and femur motion determined using fluoroscopy). 115

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Figure 4-33. Kinematic results obtained using different methods for the stepping-up trial of a representative subject. 116

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Figure 4-34. Kinematic results obtained using di fferent methods for the knee flexion trial at 15 of hip flexion of a representative subject. 117

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Figure 4-35. Kinematic results obtained using di fferent methods for the knee flexion trial at 30 of hip flexion of a representative subject. 118

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Figure 4-36. Kinematic results obtained using di fferent methods for the knee flexion trial at 45 of hip flexion of a representative subject. 119

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Figure 4-37. Kinematic results obtained using di fferent methods for the knee flexion trial at 60 of hip flexion of a representative subject. 120

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From these kinematic results, we can see the conventional RBO method has low errors when the joint i s in a position that is close to the standing posture (joint angles are small). However, with t he joint position deviated more and more from the standing posture, the RBO results also deviated mo re and more from the true skeletal motion (fluoroscopic results). When the knee joint hi ghly flexed, the kinematic errors in RBO method were prominent. This phenomenon was es pecially apparent for SI translation, flexion/extension, and varus/valgus meas urements. For SI translation, the RBO methods may have an error of over 20 mm w hen the knee was highly flexed. Based on the findings in Chapter 3, t he underestimation of SI transl ation by the RBO method was mainly caused by the large inferior STA of thigh markers during knee flexion. The RBO method also underestimated knee flexion angle at high flexion, and the error could be as high as 8. For the AP translation results of knee flexion movements (Figures 4-34 to 4-37), the RBO method failed to characteri ze the femoral roll back behavior during high flexion. By comparing the femur-based and tibia-based kinematics, it can be seen the tibia-based results were close to the ske letal motion while femur-based results were close to skin marker-derived joint kinematics. This observation once again emphasized that major portion of analysis error in knee joint kinematics comes from thigh STA effects. Both STAD and DWO methods exhibited im provement over the RBO method. On Figures 4-33 to 4-37, the blue and green curves are much closer to the black curves than the red curves. Especially for SI trans lation and flexion/extension measurements, the STAD and DWO significantly reduced errors compared to the RBO method. The performance of STAD method was overall more consistent than the DWO method, 121

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which som etimes produced larger error than the RBO method. In the AP translation results of knee flexion movements (Fi gures 4-34 to 4-37), the STAD method successfully characterize the femoral roll ba ck behavior during high flexion. For all the three methods, tibia-based kinematics were much more accurate than femur-based kinematics. Analysis Error Comparison Figures 4-38 to 4-42 show the RMS kinematic errors for all the six subjects, during each specific motor task. In each subplot of these figures, the three bars of the STAD method and the three bars of t he DWO method were compared accordingly to the three bars of the RBO method. The va riables that resulted in st atistical differences were marked using asterisks (* P <0.05; ** P <0.01). Overall, the STAD method exhibited the best performance among the three, and it demonstrated significant improvement over the conventional RBO method. Compared to the RBO method, the STAD method on av erage reduced analysis errors by 49% for AP translation ( P <0.01), 68% for SI translation ( P <0.01), 75% for flexion/extension ( P <0.01), 37% for internal/external rotation ( P <0.05), and 45% for varus/valgus measurements ( P <0.05). 122

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AP Translation Errors0 2 4 6 8 10(mm)* SI Translation Errors0 10 20 30(mm)** ** ** ** RBO RBO_fem Flexion/Extension Errors0 5 10(deg)RBO_tib ** ** ** **STAD STAD_fem Int/Ext Rotation Errors0 2 4 6 8 10(deg)STAD_tib ** **DWO* DWO_fem Varus/Valgus Errors0 5 10 15(deg)* **DWO tib Figure 4-38. RMS kinematic errors of all s ubjects during stepping-up. The results of the STAD method and the DWO method we re compared to the RBO method accordingly Variables that had statis tical differences were marked using asterisks (* P <0.05; ** P <0.01). 123

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AP Translation Errors0 5 10 15(mm)** ** ** SI Translation Errors0 5 10 15 20 25(mm) RBO** ** **RBO_fem RBO_tib Flexion/Extension Errors0 5 10(deg)STAD ** ** ** **STAD_fem STAD_tib Int/Ext Rotation Errors0 2 4 6(deg)DWO DWO_fem DWO tib Varus/Valgus Errors0 1 2 3 4(deg)* Figure 4-39. RMS kinematic errors of all s ubjects during knee flexion at 15 of hip flexion. The results of the ST AD method and the DWO method were compared to the RBO method accordingl y. Variables that had statistical differences were marked using asterisks (* P <0.05; ** P <0.01). 124

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AP Translation Errors0 5 10 15 20(mm)** ** ** SI Translation Errors0 5 10 15 20 25(mm) RBO** ** **RBO_fem *RBO_tib Flexion/Extension Errors0 5 10(deg)STAD **STAD_fem** ** **STAD_tib Int/Ext Rotation Errors0 2 4 6 8(deg)DWO DWO_fem DWO tib Varus/Valgus Errors0 1 2 3 4 5(deg) Figure 4-40. RMS kinematic errors of all s ubjects during knee flexion at 30 of hip flexion. The results of the STAD method and the DWO method were compared to the RBO method accordingl y. Variables that had statistical differences were marked using asterisks (* P <0.05; ** P <0.01). 125

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AP Translation Errors0 2 4 6 8 10 12(mm)* ** ** SI Translation Errors0 5 10 15 20 25(mm) ** ** ** **RBO RBO_fem Flexion/Extension Errors0 5 10(deg)RBO_tib STAD** ** ** ** STAD_fem Int/Ext Rotation Errors0 2 4 6 8(deg)STAD_tib DWO DWO_fem DWO tib Varus/Valgus Errors0 2 4 6(deg) ** Figure 4-41. RMS kinematic errors of all s ubjects during knee flexion at 45 of hip flexion. The results of the STAD method and the DWO method were compared to the RBO method accordingl y. Variables that had statistical differences were marked using asterisks (* P <0.05; ** P <0.01). 126

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127 AP Translation Errors0 2 4 6 8 10 12(mm) ** ** SI Translation Errors0 5 10 15 20 25(mm)** ** ** ** **RBO RBO_fem Flexion/Extension Errors0 5 10(deg)RBO_tib ** *STAD STAD_fem Int/Ext Rotation Errors0 2 4 6 8 10(deg)STAD_tib DWO *DWO_fem Varus/Valgus Errors0 2 4 6 8 10(deg)DWO tib ** Figure 4-42. RMS kinematic errors of all s ubjects during knee flexion at 60 of hip flexion. The results of the STAD method and the DWO method were compared to the RBO method accordingl y. Variables that had statistical differences were marked using asterisks (* P <0.05; ** P <0.01).

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On average, the RMS errors of STAD me thod were 3.9 mm for AP translation, 4.7 mm for SI translation, 1.6 for flexion/extension, 3.1 for in ternal/external rotation, and 2.4 for varus/valgus measurements. It sh ould be noted these error magnitudes were obtained in motor tasks that involved large r anges of knee/hip flexion. As we observed, the kinematic errors of skin marker-derived measurements are highly related to joint position. Thus the actual errors occurring in some other motor tasks that involved smaller ranges of knee/hip flexion, such as le vel walking, are very likely to be lower than the errors observed in this study. As evidence to this opinion, the kinematic errors from RBO method shown in this study were about 2 to 3 times higher than those identified in a previous study performed on cadaveric kn ee specimens (Gao et al., 2007). In that previous study, knee flexion angles of the specimens were usually less than 60. This could be a main reason for the lower error m agnitudes identified in the previous study, in addition to stiffer soft tissues in cadaver ic specimens. In addition, the BMI of the TKA patients tested in this study (about 28 in av erage) was higher than that of many other sports injury patients, such as anterior cruc iate ligament injury patients. Thus the STA magnitude found in this study is expec ted to be an upper bound representation of general patient population. The STAD method exhibited its best error reduction capability in SI translation and flexion/extension measurement s. These error reductions resulted mainly from the compensation of major patterns of AP and SI components of thigh STA in the STAD method. The compensation also benefited more accurate measurements of other kinematic variables. The error reduction capabi lity of the STAD method was relatively lower on internal/external rotation and varu s/valgus measurements. A possible reason 128

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was that we were not able to obtain relia ble ML STA patterns in the current S TA models, because of the limitation of single view fluoroscopic technique. In addition to ML translation measurement, the ML STA could also affect axial rotation and varus/valgus measurements. Future work aiming to obtain more reliable ML STA assessment (for example, using a bi-plane fluoroscopic study design) could benefit further accuracy improvement on these secondary kinematic measurements. The relatively small sample size of subj ects in our study could also limit the effectiveness of the universal STA model and the performance of the STAD method. Only 6 (5 in evaluation) subjects STA data were included to establish the universal STA model. The variability in the small samp le could reduce the effectiveness of the STA model in representing the common patterns of a general population. With more subjects data being included in future studies, it is expected that the universal STA model would be more robust and more represent ative. As a result, the STAD method may be even more effective. Also because of the small subject sample size, the anthropometric parameters of individual subject were not taken into account in the STA models. With a larger subject sample size, it might be possible to des ign the STA models which incorporate the anthropometric characteristics of different subject, such as BMI, limb circumference, skin-fold thickness, etc. Since the primary aim of this study is to demonstrate the feasibility and effectiveness of the STA compensation concep t, a simple multilinear model was used to construct the STA models. The simple ma thematical model provided an intuitive expression of the STA-joint angle rela tionship, and worked well for many 129

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130 components/markers. However, for some components/markers (such as the T10 and T11), it is apparent that a linear model mi ght not be the best option (Figures 3-20 to 323). It is likely with more complex mathematic al functions (higher-order or piecewise), the STA models will be more reliable. All thes e aspects leave the possibilities for future methodological improvement.

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CHA PTER 5 THREE DIMENSIONAL KINEMATICS OF ACL-DEFICIENT AND ACLRECONSTRUCTED KNEES Introduction The human anterior cruciate ligament (ACL) plays an important ro le in controlling knee joint stability, not only by limiting tibia anterior translation but also by controlling knee axial rotation and varus movement (Andersen and Dyhre-Poulsen, 1997; Markolf et al., 1995). After ACL injury, knee joint stability and load-beari ng patterns between joint surfaces can be altered, resulting in abnormal loadings on the cartilage during functional activities (Chaudhari et al., 2008; Li et al., 2006). This change in biomechanical environment has been associated with cart ilage degeneration and progressive development of knee joint ost eoarthritis (Andriacchi et al., 2006; Andriacchi and Mundermann, 2006; Stergiou et al., 2007; Wu et al., 2000). This model has been supported by both animal and human studies (Ba liunas et al., 2002; Brandt et al., 1991; Neyret et al., 1993; Papaioannou et al ., 2004; Pond and Nuki, 1973). For untreated ACL-deficient (ACL-D) knees, the risk of knee osteoarthritis development has been reported as high as 44% after 11 years (Noy es et al., 1983), and over 50% of cases have led to total knee arthroplasty bef ore age 63 (Nebelung and Wuschech, 2005). ACL reconstructive surgery is typically recommended to restore the knee joint stability and function after ACL injury. However, the effectiveness of ACL reconstruction in preventing cartilage degeneration and osteoarthritis development remains controversial (Jones et al., 2003; Lohmander and Roos, 1994). Studies have shown that even after constructive surgery, early cartilage degeneration cannot be successfully prevented and premature knee osteoarthriti s can still develop (Asano et al., 2004; Daniel et al., 1994; Lohmander et al., 2004; Seon et al., 2006). These studies evaluated 131

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the articular cartilage of ACL-reconstructed (ACL-R) knees with sample sizes from 41 to 105 knees, and the results showed a high prev alence of knee osteoarthritis 5 to 12 years post surgery. A signifi c ant degeneration of cartilage was observed as early as 15 months after surgery (As ano et al., 2004). These finding s indicated that current reconstructive surgeries may not effect ively reduce the risk of early cartilage degeneration and osteoarthritis development in ACL-R knees. Researchers have suggested this could be a consequence of t he knee joint kinematics that have not been fully restored by the reconstructive su rgery and the rehabilitation that follows (Brandsson et al., 2002; Papannagari et al., 2006). The residual abnormalities of joint motion and the resultant contact pattern change between articular surfaces could lead to progressive cartilage degeneration under millions of cycles of joint loading during daily activities. If the articular cartilage or menisci had suffered traumatic damage at the time of the ACL injury, the situation c ould deteriorate and have negative impact on the mechanical-biological dynami cs more than would have result ed from the ACL injury alone. Although ACL injury usually occurs duri ng more intensive joint maneuvers, the cartilage degeneration and osteoar thritis development after the injury is considered a progressive process which happens under cyclic loading from less intensive but more frequent activities of daily living (Chaudhari et al., 2008; Miyazaki et al., 2002). In order to identify the risk factors that contribute to the biomechanical environment change after ACL injury, it is critical to understand the three-dimensional (3-D) joint kinematics of ACL-D and ACL-R knees during daily activi ties. Ground walking is the most common and frequently performed ambulatory activity Quite a few studies have been performed 132

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to evaluate joint kinematics of ACL-D/ACL-R knees during walk ing (A lkjaer et al., 2003; Andriacchi and Dyrby, 2005; Bush-Joseph et al., 2001; Georgoulis et al., 2003; Gokeler et al., 2003; Hurd and Snyder-Mackler, 2007; Knoll et al., 2004b; Kvist, 2004; von Porat et al., 2006). Most of these studies focus ed on joint movement in the sagittal plane. However, the knee joint has secondary movement other than that in the sagittal plane, and the secondary movement is considered to be clinically significant (Mundermann et al., 2005). In the handful studies that examin ed knee kinematics during walking in a full 3-D and 6 degree of freedom, reduced anterior tr anslation and tibial external rotation before heel strike were observed in AC L-D knees (Andriacchi and Dyrby, 2005). In addition, more internal tibial rotation during the initial swing phase was reported in ACLD knees compared to healthy knees (Georgou lis et al., 2003). So far little has been reported about kinematic alterations of front al plane movement in ACL-D knees or about secondary movement in ACL-R knees during level walking. The purpose of this chapter was to examine in 3-D the effects of ACL deficiency and reconstruction on the knee joint kinematics during walking. We hypothesized that ACL-D knees would ex hibit altered joint kinematics in 3-D, and the kinematics of ACL-R knee s that received reconstructi ve surgery would not been fully restored to a normal level. In order to test the hypothesis, we examined 3-D knee joint kinematics during walking in three subject groups: ACL-D, ACL-R and healthy controls with bilateral ACL-intact (ACL-I) knees. Kinematic variables of the three rotations and three translations of the knee joint were obtained using the STA compensation method developed in the prev ious chapter, and compared between the ACL-D and the ACL-I groups, as well as between the AC L-R and the ACL-I groups. 133

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Design and Methods Subjects Three groups of subjects (ACL-D, ACL-R, and ACL-I) were recruited and tested in this study (Table 5-1). Fourteen subjects who had sustained a unilat eral ACL injury were tested as the ACL-D group, including 11 ma les and 3 females. All ACL-D subjects were tested within one year after ACL injury (average 3 months) and the A CL ruptures were confirmed with MRI examination. Fourteen subjects w ho had undergone a unilate ral, primary ACL reconstruction were tested as the ACL-R gr oup. This group was composed of 12 males and 2 females. Three types of grafts had been used in these ACL-R knees (7 hamstrings tendon autografts, 5 bone-patellar tendon-bone allografts, and 2 Achilles tendon allografts). All ACL-R subjects were tested at least 3 months post reconstruction (typically within 12 months), and had co mpleted the postoperative rehabilitation programs before participating in this study The ACL-D and ACL-R subjects included had no accompanying damage to the posterior cruciate and collat eral ligaments, no more than 30% of the meniscus removed, no injuries on the contralateral limb, and no difficulty or pain in performing activities of daily living including walk ing. As the control group, 15 healthy subjects who had bilateral ACL-I knees and no history of musculoskeletal diseases on the lower extr emities were included. The ACL-I group consisted of 12 males and 3 females. The age, height, and weight distributions of the ACL -I group were not significantly different from those of the ACL-D and ACL-R groups ( P > 0.05). The protocol was approved by the institutional review board for human subject research and each subject gave informed consent. 134

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Table 5-1. Subject information. Group Number Age (year) Height (m) Weight (kg) Body mass index (kg/m^2) ACL-I 15 (12m & 3 f) 22.8 (SD 2.6) 1.81 (SD 0.10) 76.8 (SD 16.4) 23.3 (SD 3.2) ACL-D 14 (11m & 3 f) 26.7 (SD 8.6) 1.78 (SD 0.12) 82.7 (SD 22.0) 25.3 (SD 3.6) ACL-R 12 (12m & 2 f) 25.1 (SD 5.9) 1.80 (SD 0.07) 82.5 (SD 15.0) 25.8 (SD 4.8) Experimental Setup Motion data were collected using an 11-camera stereophotogrammetric system (Motion Analysis Corp., Santa Rosa, CA, USA) at 60 Hz. The measurement space was about 5.0 m 2.0 m 2.5 m and the 3-D residue of marker position tracking was lower than 1 mm after system calib ration. Sphere-shaped reflec tive markers 10 mm in diameter were attached to bone landmarks and body segments of the subject to track body movements (Figure 5-1). Figure 5-1. An ACL-D subject in test. 135

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Marker Placement Five markers were placed on the left and right anterior superior iliac spines, the left and right posterior superior iliac spines, and the sacrum. On each leg, eight markers were placed on the medial and lateral femoral epicondyles, the medial and lateral ridges of the tibial plateau, the medi al and lateral malleoli, the second metatarsal head and the heel. Another 17 and 14 markers were placed on the anterolateral si de of the thigh and the shank, respectively. The marker set used in this study was more complete than configurations commonly used in gait analyses such as the Helen Hayes marker set. The purpose of employing more markers to co ver a larger region of body segments was to reduce errors caused by soft tiss ue artifact (Leardini et al., 2005). Test Procedure The test started with a static trial while the subject stood with feet shoulder width apart and toes facing forwards. This static tr ial was used for initial anatomical frame definition. After adequate practice, the s ubject was commanded to walk through the measurement space at his/her self-selected speed while the motion capture system recorded at least one gait cycle for each leg. Two force platforms (AMTI, MA, USA) embedded in the floor were used to record gr ound reaction force to fa cilitate gait event detection. At least five good walking tria ls were recorded for each subject. Analysis Methods From the static standing trial, anatomic al frames on the femur and tibia were defined based on bone landmarks (Figure 5-2. a). Tibial origin was defined as the midpoint of the medial and lateral ridges of the tibial plateau. The midpoint of the transepicondylar line was considered the femoral origin. The midpoint of the medial and lateral malleoli was identified as the ankle joint center. Hip joint center was defined 136

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using a predictive method (Bell et al., 1990) The axes of the femoral and tibial coordinate systems were then described (Figure 5-2.a): points from the femoral origin to the hip joint center ; parallels to the cross product of and the vector from the heel to the second metatarsal head; fZfYfOhOfYfZf fZX points from the ankle joint center to the tibial origin ; parallels the cross product of and the vector from the heel to the second metatarsal head; tZaOtOtYtZt tZXtY b) Calculation of the 3D knee joint angles (Figure 5-2b). is the flexi on/extension angle, is the varus/valgus angle, is the axial rotation angle, is the projected vector of on the sagittal plane, is the projected vector of on the transverse plane, and is the projected vector of on the frontal plane. xzfXfYfXfYxy fY yz fY Figure 5-2. Definition of anatomical coordina te systems on the femur and the tibia. A fourth order Butterworth low-pass filter (cut-off frequency 6 Hz) with zero lag was applied to smooth original ma rker position data. The 3-D dynamic poses of the thigh 137

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and shank during walk ing were determined using the STA deduction (STAD) method developed in Chapter 4. Joint kinematics were then computed and described as the positional and orientational cha nge of the femur relative to the tibia (Figure 5-2 translations were derived from the movement of the femoral origin in the tibial coordinate system. In order to avoid rotational sequence dependency, the projec method was used to describe the joint rotations. A custom-developed MATLAB (MathWorks Inc., Natick, MA, USA) progr am was used to perform the kinematic analysis. As a comparison, another set of kinematics solv .b). The tion ed using conventional rigid body cycle optimization (RBO) method were also presented. The 3-D knee joint mo tion data during walking was normalized into each gait (from heel strike 0% to heel strike 100%). Each of the six kinematic curves (three rotations and three translations) for five trials was ensemble averaged for each subject across the whole gait cycle. Spatiotemporal variables including step/stride length and speed, durations of double and single support phases, and timing of key events inside the gait cycle were examined. Six key events between two sequential heel strikes were selected, including contralate ral toe off (CTO), maximum knee flexion during the stance phase (1st FE peak), minimum knee flexion during midstance (FE valley), contralateral heel strike (CHS), toe off (TO), and maximum knee flexi on during the swing phase (2ndFE peak). For each of the three rotational and three translational c omponents of knee joint kinematics, 101 discrete points correspo nding to 0~100% gait cycle at 1% interval were extracted using one-dimensional interpol ation for statistical analysis. Measures of each spatiotemporal variable as well as each discrete kinematic point were compared between ACL-D, ACL-R and ACL-I knees us ing a one-way analysis of variance (SPSS 138

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Inc., IL, USA). A significance level of = 0.05 was used in the st atistical analysis. For tests that resulted in a si gnificant omnibus F result, post hoc analysis was performed using the Tukeys honestly signific ant difference (HSD) procedure. Results Spat tical differences were detected between the patient and control roups (Table 5-2). Table 5-2. f t phase was from the toe off of the non-in jurevolv whil ingle support phase started fro f re l) ) ) nce 05) iotemporal Parameters At static standing pos ture, the initial knee joint angles were small for all the subjects and no statis g Initial knee joint angles at t he static standing posture and spatiotemporal variables during gait. For ACL-D and ACL-R subjects, the step length/speed was unilateral measurement on the injur ed or involved limb, while the stride length/speed was bilateral measurement on a complete gait cycle. For ACL D/ACL-R subjects, the 1st double support phase started fr om the heel strike o the injured/involved limb, while the 2nd double support phase was from the heel strike of the non-inju red/non-involved limb; the 1st single suppor d/non-in ed limb, e the 2nd s imb. m the toe o f of the inju d/in volved ACL-I mean (SD ACL-D mean (SD ACL-R mean (SD Statistical Differe (P < 0. Flexion @ static (deg) 0.5 (4.4) 2.4 (5.1) 2.7 (5.0) None Tibial Internal Rot @ static (deg) -0.2 (0.4) -0.1 (0.4) 0.2 (0.6) vs ec) vs m) ) ) ) vs 2nd Single Support phase (% gait cycle) 42.7 (1.8) 41.7 (1.7) 40.9 (1.8) ACL-I vs ACL-R None None Varus @ static (deg) -1.8 (2.6) -0.7 (2.9) -0.5 (3.7) Step Speed (m/sec) 1.23 (0.09) 1.12 (0.13) 1.15 (0.16) ACL-I ACL-D None Stride Speed (m/s 1.23 (0.08) 1.14 (0.14) 1.15 (0.17) Step Length (m) 0.69 (0.04) 0.65 (0.04) 0.67 (0.05) ACL-I ACL-D None Stride Length ( 1.38 (0.08 1.31 (0.09 1.34 (0.11 1st Double Support phase (% gait cycle) 7.9 (1.5) 9.1 (1.7) 8.7 (2.1) None 1st Single Support phase (% gait cycle) 42.0 (1.5) 40.7 (1.7) 41.8 (2.1) ACL-I ACL-D 2nd Double Support phase (% gait cycle) 7.4 (1.7) 8.5 (1.4) 8.6 (2.2) None 139

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The ACL-D knees showed a slower st ep speed and a shorter step length compared to the ACL-I knees ( P < 0.05). The difference was about 0.1 m/sec i n speed and 3 to 4 cm in each step. The speed and step length reduction trends were also visible in the ACL-R knees, but not statisti cally significant. The ACL-D and ACL-R knees exhibited shortened single support phas es and prolonged double support phases compared to the ACL-I knees. The timing of fset was about 1% gait cycle and it reached statistical significance on the 1st single support phase betw een the ACL-D and ACL-I groups, and on the 2nd single support phase between the ACL-R and ACL-I groups (Table 5-2). Key Events during a Gait Cycle In the gait cycle from the 1st heel strike (HS) to the 2nd HS, key events CTO, 1st FE peak, FE valley, CHS, TO, and 2nd FE peak occurred in sequence at about 8%, 12%, 38%, 50%, 58% and 72% of the gait cycle fo r the ACL-I subjects (Figure 5-3). Significant timing abnormalities were det ected on the ACL-D and ACL-R groups. The occurrences of the 1st FE peak and FE valley of the ACL-D group was delayed by about 2% gait cycle compared to the ACL-I group ( P < 0.05). The occurrences of TO and 2nd FE peak of the ACL-R group was delayed by about 2% compared to the ACL-I group ( P < 0.01) (Figure 5-3). 140

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Figure 5-3. Timings of key events in the gait cycle for ACL-I, ACL-D and ACL-R groups. The gait cycle was normalized from one heel strike (0%) to the next heel strike (100%). The key events examined in this study included contralateral toe off (CTO), maximum knee fl exion during the stance phase (1st FE peak), minimum knee flexion during midstance (F E valley), contralateral heel strike (CHS), toe off (TO), an d maximum knee flexion during the swing phase (2nd FE peak). Significant statistical di fferences were marked with asterisks (* P < 0.05, ** P < 0.01). Joint Kinematics Kinematic differences during walking we re observed in 3-D rotations between ACL-D, ACL-R and ACL-I knees (Figure 5-4). In the sagittal plane, the ACL-D knees were significantly less extended than t he ACL-I knees during a large portion of midstance (32% to 46% of gait cycle). The average FE valley during stance phase of the ACL-D knees was 15.3 (SD 6.3), which was significantly higher than the value of the ACL-I knees (9.0 (SD 3.3)) ( P < 0.01). The ACL-R knees exhibited improvement on this phenomenon and the ensemble curve did not differ significantly to the curve of 141

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ACL-I knees (Figure 5-4), but the average FE valley during stance phase (12.2 (SD 4.7)) was still hig her than that of the ACL-I knees. The ACL-R knees also showed a flexion offset during the second half of swing phase compared to the ACL-I knees ( P < 0.05). In the frontal plane, t here was a consistent offset between the curves of the ACLD knees and ACL-I knees. The ACL-D knees we re about 2 to 3 more varus than the ACL-I knees during the entire gait cycle, and this difference reached statistical significance during stance phase. A similar o ffset was also visible between the ACL-R and ACL-I knees although the difference was not statistically significant. A rotational offset was identified in the transverse plane. The ACL-D knees exhibited less tibial external rotation compared to the ACL-I k nees during most part of the gait cycle, and the difference reached statistical significance during a large portion of swing phase. This axial rotation offset was about 2 to 4 throughout the gait cycle and had not been eliminated in the ACL-R knees. The offset reached statistical significance at late stance phase and before TO on the ACL-R knees. No significant differences were observed on 3-D translati ons between ACL-D, ACL-R and ACL-I knees (Figure 5-5). Knee joint translations of the three subject groups exhibited similar patterns and the differences between groups were comparable to intragroup variability. Comparison between STAD method and RBO method Differences were observed in the ki nematics obtained using the new STAD method and using the conventional RBO met hod. For rotations, the RBO method underestimated knee flexion angle by about 3 compared to the STAD method (Figure 5-6). The RBO method also resulted in larger r ange of motion (ROM) for axial rotation measurement compared to the STAD method (Figure 5-6). For translations, the RBO 142

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method under-estimated anterior translation and the femoral roll-back behavior during the swing phase (Figure 5-7). After ST A compensation ( the STAD results), AP translation was closer to zero during stance phase and femoral roll-back was better characterized during swing phase. ML translati on was also closer to zero in the STAD results. The RBO method under-estimated super ior translation measurement by 5 to 10 mm (Figure 5-7). Although the kinematic results obtained using the two methods differed quantitatively, the qualitative comparisons betw een different subject groups (ACL-D and ACL-I, ACL-R and ACL-I) were similar. 143

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Figure 5-4. The 3-D joint rotations during walking of ACL-I, ACL-D and ACL-R knees. Ensemble curves of each subject group were normalized from heel strike to heel strike in a gait cycle. Segments wit h significant statistical differences ( P < 0.05) between the patients and the c ontrol groups were marked with asterisks. Flexion, varus, and external tibial rotation were illustrated as positive in the graphs. 144

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Figure 5-5. The 3-D joint translations during walking of ACL-I, AC L-D and ACL-R knees: anterior/posterior (AP), medial/lateral (ML), and superior/inferior (SI) translations. Ensemble curves of eac h subject group were normalized from heel strike to heel strike in a gait cycle. No significant statistical differences were observed between different s ubject groups. Anterior, medial, and superior translations (femur relative to tibia) were illustrat ed as positive in the graphs. 145

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Figure 5-6. Comparison of 3-D knee joint rotations obtained using STAD method (left) and RBO method (right). 146

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Figure 5-7. Comparison of 3-D knee joint translations obtained using STAD method (left) and RBO method (right). 147

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Discussio ns The purpose of this study was to examine the effects of ACL deficiency and reconstruction on the 3-D knee joint kinematics during walking. Findings of this study demonstrated significant alterations between the kinematics of the ACL-D knees and that of the ACL-I knees duri ng walking. After reconstructi ve surgery, some of the alterations had been improved, but normal joint kinematics and function had not been fully restored in the ACL-R knees. These observations supported the hypotheses that motivated this study. As spatiotemporal appearance, the ACL-D knees exhibi ted shorter step length and slower walking speed compared to the healthy knees. Similar phenomena have also been observed in another study (Knoll et al., 2004a). The reduction in step length and speed was also visible in the ACL-R knees, al though not as significant as in the ACL-D knees. The shorter step length of the ACL-D and ACL-R subjects could result from the knee not being fully extended during the st ance phase and at t he end of the swing phase (Figure 5-4). Given the fa ct that the stride length was almost twice the step length and the stride speed was almost equal to the step speed in these subjects, it can be concluded that the contralateral non-inju red/non-involved limb of the ACL-D/ACL-R subjects had developed compensatory motion patterns in order to adapt to the injured/involved limb. A decr eased duration of single support phase was visible on ACLD knees, as well as altered timing of key events in a gait cycle. The 1st FE peak and FE valley were postponed in ACL-D knees compar ed to the ACL-I knees. This reflects the increased time that the ACLD knees tended to stay in flexion before the knee reached maximum extension in order to accomplish a less abrupt weight shift. This adaptation mechanism was also demonstrated by an elec tromyographic study showing that ACL-D 148

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patients had extended firing of biceps femo ris and vastus medialis during the stance phase compared to healthy controls (Knoll et al., 2004a). The ACL-R knees showed an improved timing during stance phase, but a prolonged flexion period was obs erved during the swing phase. T hese phenomenological observati ons indicate the ACL-R knees have not been restored to a normal spatio temporal pattern. Significant kinematic alterations were obser ved in the sagittal plane, not only in the ACL-D knees but also in the ACL-R knees. The most striking abnormality was that the injured knees did not reach full extension at midstance. As a comparison, at the static standing posture, the av erage knee flexion angles of all th ree subject groups were small and there was no statistical difference betwe en them (Table 5-1). At midstance, the average FE valley of the ACL-I knees was clos e to the static standi ng posture, while the average FE valley of the ACL-D knees was si gnificantly higher than the angle at the static posture. Thus, the lack of full knee extension of the ACL-D subjects was not caused by anatomical differences compared to the control subjects but by functional deficit of the joint. Because one major functi on of the ACL is to limit anterior tibial translation when the knee is in extensi on, the ACL-D patients appeared to use the adaptation strategy of limit ing knee extension during movement to degrade the functional need for ACL. The kinematics had not returned to normal in the ACL-R knees. The average FE valley of the ACL-R k nees was still significantly higher than that of the ACL-I knees. The findings of the ext ension deficit were consistent with one study on ACL-D knees (Gokeler et al., 2003) and another on ACL-R knees during walking (Hurd and Snyder-Mackler, 2007). 149

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As one of the most important findings in th is study, kinematic alterations were also identified in secondary movem ent of both the ACL-D and ACL-R knees. In the frontal plane, the injured knees were more varus than the healthy knees Similar observations have been previously reported in ACL-R knees during downhill running (Tashman et al., 2004; Tashman et al., 2007), but little has been reported concerning level walking which is a much less intensive but more frequent ambul atory activity. In the transverse plane, an offset of internal tibial rotation wa s observed on both the ACL-D and ACL-R knees. This finding is consistent with the observa tions of two other studies on ACL-D knees during walking (Andriacchi and Dyrby, 2005; Georgoulis et al., 2003). From anatomical point of view, the ACL has an oblique medial or ientation from femur to tibia, thus a less functional ACL could result in a more interna lly rotated tibial position. The offsets of varus and internal tibial rotation observed in the ACL-D and ACL-R knees in this study were small in magnitude (about 2 ~ 4), but they were consistent throughout the whole gait cycle. With a more varus position, the lateral compartment of the knee joint tends to be more separated while the medial compartm ent of the knee contact tends to be more compressed. This could alter the normal lo ad distribution on the joint surface and generate much higher stresses on the medial compartment of cartilage and menisci. With a more internally rotated tibia pos ition, the contact location on the medial compartment of tibia plateau c ould shift to the anterior while the contact on the lateral compartment could shift to t he posterior. This axial posit ion alters both the contact location and contact stress on the cartilage, and could result in a more rapid cartilage thinning throughout the knee, especially in t he medial compartment (Andriacchi et al., 2006). Clinical studies have shown that in ACL-D and ACL-R knees, the medial 150

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compartment of the joi nt is more vulner able to cartilage degeneration and osteoarthritis development (Seon et al., 2006). This is cons istent with the kinematic abnormalities and risk factors we observed in t he present study. Overall, th e kinematics profiles of the ACL-R knees were closer to the ACL-D k nees than to the ACL-I knees (Figure 5-4). This finding reflected that the reconstruc tive surgery had not restored the joint kinematics of the ACL-D knees to a normal level. This could potentially explain the outcomes observed in clinic that early cartilage degeneration and progressive development of knee osteoarthritis were not effectively prevented even after ACL reconstruction (Asano et al., 2004; Daniel et al., 1994; Seon et al., 2006). The position of the ACL-R profiles in Figure 5-4 also indi cated that reconstructed ligaments in the ACL-R knees examined in this study were more likely to be under-functional rather than over-functional (e.g. over-tensioning). Some crosstalk like appearance was observed between varus/valgus and flexion/extension curves. It should be note that our varus/valgus angle was defined as the frontal projection of in cluding angle between femoral and tibial axis (Figure 5-2b). This angle is not the same thing as the angle between the contacting joint surfaces of the femur and tibia. Because the medial condyl e of femur is larger in radius than the lateral condyle of femur, a valgus angle wi ll always be observed fr om frontal projection during knee flexion even the joint surfaces keep contact. The magnitude of this valgus angle during swing phase (about 10) was consis tent to the results measured in the previous chapter using fluoroscopic technique (Figures 4-34 to 4-37). This indicated that the observed large valgus angle was not caused by analysis errors but mainly by the 151

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anatomical asymmetry of medial and lateral condyles of the femur. To fu rther examine the joint surface angle, image-based bone models have to be included. No significant differences of knee joint translations were observed during walking between ACL-D, ACL-R and ACL-I knees in this study, although it is well known that the primary function of the ACL is to control ti bial anterior translat ion and ACL deficiency could lead to excessive anterior tibial move ment during the passive knee laxity test (Bendjaballah et al., 1998). The observation could be possibly explained by active muscle functioning which is absent in a passi ve laxity test. During dynamic movement, antagonist and agonist muscles of ACL-D knees function and coordinate together to compensate for the deficiency of the ACL, which is the dominant stabilizer during the passive laxity test. Studies have revealed t hat static knee laxity evaluation does not correlate with dynamic knee joint function after ACL injury (Gokeler et al., 2003; Kvist et al., 2007; Patel et al., 2003), indicating that muscle compensation plays a significant role in dynamic knee joint stability. The compensation strategy could either be a stronger contraction of the hamstrings to pull the tibia posteriorly (K vist et al., 2007; Shelburne et al., 2005) or be a weaker contract ion of the quadriceps to avoid pulling the tibia anteriorly (Andria cchi and Birac, 1993). In the comparison between using STAD method and the conventional RBO method, we found that the kinematic resu lts differed quantitativ ely. The RBO method under-estimated flexion angles, over-estimated axial rotation ROM, under-estimated superior translation, and under-estimated anterior transla tion during the swing phase. These findings were consistent to the observa tions in the previous chapter (e.g. Figure 4-35), which indicated that the STA compensation used in the STAD method modified 152

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the kinematics obtained from RB O method to a correct direct ion. On the other hand, the qualitative comparisons between different subject groups we re similar for the results obtained using STAD and RBO methods. This suggest ed that STA error is more systematic rather than random. Its effect on individual s ubject was generally similar and might not alter the overall comparis ons between subject groups. Even though the conventional RBO method was not able to produc e quantitatively accurate results, it might still be able to provide an effective qualitative comparison between different subject groups. Several limitations need to be ack nowledged. First, the ACL-D and ACL-R subjects included in this study were not the same group of patients tested preand postoperatively. The current design was ade quate to provide meaningful comparison between each of the two patient groups and the healthy subject group, which was the aim of this study. But a preand postoperative matching desi gn would be more useful to directly assess the functional improvement af ter ACL reconstructive surgery. Second, the subject population in this step of study (ACL-D, ACLR and ACL-I subjects) differed to the subject population in the last chapter (total knee arthr oplasty patients) from which the STA model was constructed for the STAD method, in age and BMI. Thus there might be some errors when using the STA m odel developed from last chapter in the subject population examined in this chapter. Th ird, the subjects in all three groups included in this study were generally youn g, averaging 25 years of age. This sample was in general agreement wit h the epidemiological populatio n of ACL injury patients (Griffin et al., 2006), but would not be represent ative of all patient groups. Therefore the findings obtained from this study may not simply apply to populations with older ages. 153

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Fourth, the ACL-D patients test ed in this study were generally acutely injured (with one year), thus the findings in this study may not be the same for chronically ACL injured patients. Another limitation in this study was that we did not investigate the performance of different graft types s eparately. Three types of gr afts (bone-patella tendon-bone allograft, Achilles allograft and hamstri ng tendon autograft) were used in the ACL-R group, and there might be a functional differe nce associated with t he graft type although a systematic literature tends to support graft type may not play a primary role in the outcomes after ACL-R surgery (Spindler et al., 2004). Further research with larger subject sample size may be necessary to in vestigate these questions This study used a 3-D motion analysis and i dentified significant abnormalities of spatiotemporal performance and joint kinem atics during walking in the ACL-D knees. After reconstructive surgery and rehabilitatio n, the ACL-R knees exhibited improvement, but were not fully restored to a normal level. In addition to an extension deficit in the sagittal plane, both ACL-D and ACL-R knees exhi bited a varus offset in the frontal plane and a tibial internal rotation offset in the transverse pl ane, which were maintained throughout the whole gait cycle. The position change of varus and axial rotation of the knee joint could significantly alter the normal cartilage contact pattern and load distribution, causing different areas of ca rtilage to be newly lo aded or unloaded, or subjected to a change in magnitude of compre ssion or tension. Given the relatively low adaptation ability of mature cartilage, m illions of repeated abnormal loading cycles during daily activity could exaggerate the risky biomechanical factors and gradually lead to cartilage degeneration and pr emature osteoarthritis in ACL-D and ACL-R knees. Identification of biomec hanical environment alterations that occur during daily activities 154

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in ACL-D and ACL-R knees could help us better understand clinic al outcomes, as well as provide guidance for improvement in su rgical technique and rehabilitative regimens for ACL injury treatment. 155

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CHA PTER 6 SUMMARY AND CONCLUSIONS Novelties and Key Points In the framework of this dissertat ion, we focused on a long existing and challenging problem faced by the biomechanical research community. By investigating soft tissue artifact (STA) on the thi gh and shank, this study provided better understanding and some new knowledge about the behavior of STA. This new information allowed us to develop a novel and evidence-based STA compensation technique for skin maker-based motion analysis. The new STA compensation technique demonstrated significant improvement in error reduction compared to the conventional best-performance method. The reduction of the major source of errors could make skin marker-based motion analysis a more pow erful tool, and benefit biomechanical and clinical applications. Methodological Novelties of this Study The new findings of this study are di rectly related to new experimental and analysis methods. First, we used non-invasive motion tracking methods through the study to ensure a measurement of free skin marker motion and STA. Majority of previous studies on STA utilized invasive devices to measure ske letal movement. The invasive devices (especially external fixators) could largely constrain free skin motion and alter the natural behavior of STA. Second, we used a large subject sample size in Chapter 2 and a relatively large sample size in Chapters 3 and 4, compared to previous studies of similar types. Only if more subjects are included, t he assessment of inter-subject similarity of STA behavior is 156

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possible. Using too small subject sample siz e could be one reason for that no previous studies reported inter-subject evaluation of STA. Third, most previous studies focused on assessment of analysis errors caused by STA by comparing skin marker derived kinematics and other gold standard method (invasive devices or medical imaging techni ques) derived kinematics, but did not focus on STA itself, which is individual skin marker s movement relative to the bone. The kinematic errors caused by STA is not t he same concept as STA itself. Kinematic errors can be influenced by many factors in addition to STA. One can get different kinematic errors by using a different mark er set or a different analysis method, even though the intrinsic STA is the same. Although our final goal is to reduce the kinematic errors caused by STA, we need to study STA it self in order to find the solution. This was the rationale of our study design. Fourth, no previous studies examined the relationship between STA and joint positions. Although a few studies examined indi vidual markers movement relative to the bone and measured STA magnitude of each marker, none further looked into the joint position dependence or time dependency (such as at different percentage of a gait cycle) of STA. Thus, the information obtained can only provide a diagnosis but not a treatment. In Chapter 2, we examined soft tissue move ment along a normalized time scope (gait cycles). And in Chapters 3 and 4, we further examined the relationship between STA and adjacent joint angles. These methodological improvements allowed us to reveal some new findings about STA behavior. Fifth, we performed inter-subject similari ty assessment on soft tissue movement (Chapter 2) and STA (Chapter 3), which had not been conducted before. This approach 157

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finally led to a new ins ight about STA behav ior and a non-subject-specific scheme for STA compensation (Chapter 4). Table 6-1 summarizes a comparison between previous studies and the present study on the above aspects. Table 6-1. Summary of studies about soft tissue movement on human lower extremity and the analysis scopes. Reference Non-invasive measurement of free skin motion? More than 3 Subjects? Examined individual marker movement? Examined marker's movement with time or joint angles? Performed inter-subject evaluation of marker movement? (Cappozzo et al., 1996) No Yes Yes Yes No (Sati et al., 1996) Yes No Yes No No (Fuller et al., 1997) No No Yes Yes No (Holden et al., 1997) No No No No No (Reinschmidt et al., 1997a) No Yes No No No (Reinschmidt et al., 1997b) No No No No No (Manal et al., 2000) No Yes No No No (Stagni et al., 2005) Yes No Yes No No (Benoit et al., 2006) No Yes No No No (Garling et al., 2007) Yes/ No Yes Yes No No (Akbarshahi et al., 2009) Yes Yes Yes No No The present study Yes Yes Yes Yes Yes 158

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Key Points Learned from this Study STA is a systematic and natural movement, not random noise. Soft tissue artifact is not really an a rtifact but more a natural motion produced by muscles and skin movement. Any compensation methods t hat treat STA as r andom noise will have limited effectiveness. STA has inter-subject similarity. Due to the fact that most people have similar muscular structure and coordination during acti vities, soft tissue movement has intrinsic similarities between different people. A large portion of STA is related to the joint position, thus STA also has some inter-motor task similarity. Although muscle contraction and skin stretch (in addition to other types of STA causes, like i nertial effects) are not exactly the same during different motor tasks, a large portion of the soft tissue movement is similar if the joint is at a same position. Thus, an ST A model based on adjacent joint angles is effective across different motor tasks. STA generally increases with increasing joint angles. Since the markers anatomical positions are usually defined at a neutral standing posture (where STA is zero), the magnitudes of STA (markers location deviation from the init ial position) increase if the body posture deviates furt her from the neutral standing posture. STA on the thigh plays a dominant role in determining knee kinematic errors. If the STA effects on the thigh can be successfully compensated, knee joint kinematics will have much lower errors ev en without compensating for the STA effects on the shank. The largest STA on the thigh occurs along the superior/inferior (SI) direction. The STA magnitudes along SI direction are generally higher than those along 159

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anterior/posterior (AP) and medial/lateral (ML) directions, and can be over 25 mm for some mark ers. Most markers on the anterolateral side of the thigh tend to move posteriorly and inferiorly when the knee flexes. Exceptions: the marker s on the medial and lateral femoral epicondyles tend to move anteriorly and superiorly. The markers on the lateral side exhibited the smallest SI disp lacement, while the markers on the anterior side exhibited the smallest AP displacement. Most markers on the anterolateral side of the shank tend to move anteriorly and inferiorly when the knee flexes. Exceptions: the marker on the lateral ridge of tibial plateau along AP direction, and the marker on the tibial tubercle along SI direction. The markers on the anterior side of tibia exhi bited small displacement along both SI and AP directions. STA exhibited similar patte rns for markers that are on a same vertical line. This was very prominent on the thigh, but al so visible on the shank. The reason behind is that lower extremity muscles genera lly contract along SI direction. The markers placed on commonly used bone landmarks did not show smaller STA than other markers. The markers on femoral epico ndyles, ridges of tibial plateau, and malleoli exhibited larger STA than many other markers due to the large skin stretch near the joints. 160

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The AP component of thigh STA is mo re sensitive to hip flexion angles, w hile the SI component of thigh STA is more sensitive to knee flexion angles. This is generally true for most thi gh markers, while the markers on the femoral epicondyles behave differently. Among existing STA compensation algorit hms, the conventional rigid body optimization (RBO) method provid es overall the best result. Other non-rigid body optimization methods (inclu ding the point cluster technique) have not convincingly demonstrated their superior perfo rmance over the RBO method. The kinematic analysis errors derived from skin markers are not in a constant magnitude but are related to joint position. Skin marker derived kinematics (using the conventional method) could be fairly accurate if the joint angles are not too far away from the standing pos ture. But the errors can be si gnificantly larger at large joint angles. This is similar to the behavior of STA, which is the cause of kinematic errors. Both the STA deduction (STAD) method and the directional weighted optimization (DWO) method exhibited impr oved analysis accuracy compared to the conventional RBO method. The STAD method demonstrated the best performance in general. ACL-deficient (ACL-D) knees exhibited altered spatiotemporal parameters and 3D kinematics compared to ACL-i ntact (ACL-I) knees in gait, and these alterations had not been completely r estored to a normal level in the ACLreconstructed (ACL-R) knees. Both ACL-D and ACL-R knees exhibited reduced extension, a more varus and internally rota ted position compared to the ACL-I knees. 161

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Limitations and Future Direction Limitations of this Study As being discussed in each previous chapter, there were some limitations with this study. The ML component of STA was not reliably measured. This was mainly caused by the limitation of single view fl uoroscopy technique. Th is limitation would reduce the reliability of the uni versal STA model in its ML direction, and further reduce the effectiveness of STAD method in accu racy improvement on ML translation, axial rotation, and varus/valgus measurements. The subject sample size in the fluoroscopic study was still relatively small. Although 6 is already a relatively large samp le size comparing to many other studies with a similar type, more subjects wil l definitely enhance the robustness of the universal STA models and enhance the effectiveness of the STAD method. Only total knee arthroplasty (TKA) pa tients were included as subjects for in vivo STA measurement. Although we used special inclusive criteria in subject recruitment aiming to include only TKA subjec ts who had a physical condition closer to healthy population, there could be some differences between these TKA patients to other healthy/patient populations in terms of STA behavior. Only one functional motor task w as included in this study. Due to the purpose and scope of this study only a stepping up activity was included as an example of functional motor task to evaluate the new STA compensation method. Partially due to the limited subj ect sample size, the anthropometric information of the subjects was not included in the STA model. It is expected that 162

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STA behav ior is more or less related to a su bjects anthropometric condition. Taking this information into account could possibly ma ke the STA model more realistic. The multilinear model used in this st udy to construct the STA models was relatively simple. This simple model does have its advantages, such as being intuitively meaningful, and easy to implement and transfer. It is likely with more complex functions, the STA model could be more realistic. Future Study Suggestions Based on the limitations discussed above, there are options for future study advancement. To measure the ML component of STA more reliably. This can be achieved by either using a bi-plane fluoroscopy setup, or using a single-plane fluoroscopy in an AP view. Both approaches have extra challenges. By using a bi-plane fluoroscopy, the stereophotogrammetric cameras will have mo re obstructions and the skin marker tracking will be more difficult. Using a singleplane fluoroscopy in an AP view is also more difficult than using it in an ML view, considering the testing space and configuration. To include more subjects and h ealthy controls if possible. This will increase the scope of the research project and also need to get IRB approval. To study more ambulatory motor tasks and evaluate the STAD method performance. Level walking will be a good option for the next step, although it will require a fast shutter of the fluor oscopy to guarantee the image quality. To include subjects anthropometric in formation into the STA model, and to explore more complex mathemati cal expression of the STA model. To move into 163

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this step, it is the authors opinion that larger quantity of more reliable STA dat a has to be obtained first. 164

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BIOGRAPHICAL SKETCH Bo Gao was born in Baoji, China. He graduated from Baoji High School in 1998. He earned his B.S. degree in me chanical engineering from t he University of Science and Technology of China (USTC, Hefei, China) and entered the Graduate School of Chinese Academy of Sciences (GSCAS, Beijing, China) in 2002. Since August 2003, he worked as a research assistant in the N ano-Bioengineering Laborat ory, Institute of Mechanics of Chinese Academy of Sc iences, and earned his M.S. degree in biomechanics in 2005. In August 2005, he ent ered the Ph.D program of biomedical engineering in the University of Florida (UF). Since then he st arted working as a research assistant in the Biomechani cs and Motion Analysis Laboratory in the Orthopaedics and Sports Medicine Institut e (OSMI), UF & Shands. He earned his second M.S. degree in biomedical engineering in 2007, and is completing his Ph.D in 2009. 175