Citation
Patient Specific Computational Modeling to Assess Reverse Shoulder Arthroplasty

Material Information

Title:
Patient Specific Computational Modeling to Assess Reverse Shoulder Arthroplasty
Creator:
Walker, David R
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (123 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering
Mechanical and Aerospace Engineering
Committee Chair:
BANKS,SCOTT ARTHUR
Committee Co-Chair:
FREGLY,BENJAMIN J
Committee Members:
SARNTINORANONT,MALISA
WRIGHT,THOMAS W,JR
Graduation Date:
8/9/2014

Subjects

Subjects / Keywords:
Arthroplasty ( jstor )
Deltoid muscle ( jstor )
Electromyography ( jstor )
Geometry ( jstor )
Kidnapping ( jstor )
Kinematics ( jstor )
Modeling ( jstor )
Muscles ( jstor )
Shoulder ( jstor )
Shoulder joint ( jstor )
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
biomechanics -- dynamics -- moment -- muscle -- orthopaedics -- reverse-total-shoulder
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Mechanical Engineering thesis, Ph.D.

Notes

Abstract:
Reverse Total shoulder arthroplasty (RTSA) isutilized to restore shoulder function in patients with osteoarthritis androtator cuff deficiency. The purpose of this study was to assess the behaviorof RTSA shoulder subjects as compared to healthy shouldered subjects. Scapulohumeral rhythm (SHR) of patients withRTSA during unloaded shoulder abduction and deltoid muscle activity duringactive shoulder abduction, flexion and external rotation were measured to giveinsight into the function of RTSA shoulders compared to normal shoulders. We studied 33 subjects at least 6 months postunilateral reverse total shoulder arthroplasty. Seventeen subjects (11-medial,6- lateral) performed shoulder abduction (elevation and lowering) duringfluoroscopic imaging. SHR was calculated from the slope of the humeral andscapular elevation angles. Subjects then performed both weighted (1.5kg) andun-weighted abduction (coronal plane) and forward flexion (sagittal plane), andun-weighted external rotation. Activation of the anterior, lateral andposterior aspects of the deltoid and upper trapezius muscles were recordedbilaterally using bipolar surface electrodes. Motion capture using passivereflective markers was used to quantify three-dimensional motions of bothshoulders. Forabduction above 40 degrees, shoulders with RTSA exhibited an averageSHR of 1.2:1. There were significant differences in SHR between medial andlateral offset groups of RTSA shoulders (p During abduction, lateral deltoid activity wassignificantly higher in implanted than in non-implanted shoulders for themedial group. During flexion, the anterior deltoid was significantly moreactive in the lateral group during weighted and un-weighted flexion. Posteriordeltoid was not activated over 40percent of MVIC. SHR in RTSA shoulders is significantly different from normal shoulders. Significantdifferences also occur between RTSA groups (medial/lateral). The musclerecruitment data suggest reverse total shoulder arthroplasty simplifiesdeltoid muscle activation. We observed higher muscle activation in the portionof the deltoid directly in line with the task, but reduced muscle function inthe out-of-line portions of the muscle. This information will be useful toguide refinement in the geometric design of the prosthetic components, surgicalalignment of the implants, intraoperative soft-tissue tensioning, and thedesign of muscle strengthening programs. This thesis seeks to assess the momentgenerating capacity of muscles in the shoulder after reverse shoulder jointreplacement. The information collected in the previous experimental studieswill be used to calibrate and validate patient-specific computational models toassess muscle soft-tissue tensioning. An upper extremity model will bedeveloped in this study to address two current limitations of upper extremitymodeling. (1) Current models are limited because they do not incorporatesubject-specific geometric changes (joint centers) to observe musclelengthening/tensioning changes in the shoulder. (2) The other limitation liesin the motion of the shoulder girdle where the motion of the clavicle andscapula are constrained to move as a function of humeral motion only in theelevation plane. Kinematics and subject-specific data were collected to addressthese limitations. This enhanced subject-specific model framework will be usedto assess the effects of reverse total shoulder arthroplasty (RTSA) on themoment generating capacity of muscles crossing the shoulder girdle. Patient-specific muscle moment arm measurementswill be calculated from simulations that are driven by data taken from clinicalstudies. A novel method was also developed to calculate patient-specificmusculotendon parameters and likewise muscle recruitment and forcecontributions over abduction and scaption activities. The predictions developedgive a better understanding implant choice and placement for reverse shoulderarthroplasty. ( en )
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.
Thesis:
Thesis (Ph.D.)--University of Florida, 2014.
Local:
Adviser: BANKS,SCOTT ARTHUR.
Local:
Co-adviser: FREGLY,BENJAMIN J.
Statement of Responsibility:
by David R Walker.

Record Information

Source Institution:
UFRGP
Rights Management:
Copyright Walker, David R. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Classification:
LD1780 2014 ( lcc )

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1 PATIENT SPECIFIC CO MPUTATIONAL MODELING TO ASSESS REVERSE SHOULDER ARTHROPLASTY By DAVID R . WALKER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FO R THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2014

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2 © 2014 David R. Walker

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3 ACKNOWLEDGMENTS I would like to thank first and foremost my Lord Jesus Christ for keeping me and sustaining my strength for this process. It is t hrough his strength that I had the ability to accomplish such a formidable task. I would then like to thank my advisor Dr. Scott Arthur Banks for all his undying help over the last 6 .5 years. He has been instrumental in guiding and developing my skills. It was his ability to trust in my ability to run the studies being presented in this thesis that allowed me to persevere and accomplish this task. I would then like to thank Dr. Thomas Wright for also trusting in my ability to accomplish the task of running these studies. Dr. Wright also served as a mentor in understanding the shoulder anatomy as well as the reverse prosthesis function. I would like to also thank Aimee Struk for her instrumental recruitment and aiding to test all of the subjects. She has been a pleasure to work with and instrumental to getting this studies complete. I would like to thank Dr. Bryan Conrad for all his assistance and mentorship. His training of use of the motion capture lab was instrumental in the successful completion of the stu dies presented. I would like to thank Dr. Bo Gao who mentored and was instrumental in the development of the initial analysis tools for both kinematic and EMG analysis. I would like to thank my undergraduate mentee team (Karen Steiner , Lyneesha Sweeney, Co urtney Cox, Mpho Sello, and Adori ) for their hard work in shape matching images for kinematic analysis. I would like to thank Ms. Jennifer Jones for her instrumental help in digitizing motion data captured by the motion capture system. Lastly I would like to thank my mother (Ms. Audrey Fisher) for her encouraging words and support through this whole process. She has been instrumental in strengthening my character in the precepts of Jesus Christ so that I would be by the power of Jesus Christ our Lord.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 3 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 ABSTRA CT ................................ ................................ ................................ ................................ ... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 14 Shoulder Anatomy ................................ ................................ ................................ .................. 14 Shoulder Joi nt Injuries ................................ ................................ ................................ ............ 14 Reverse Total Shoulder Arthroplasty ................................ ................................ ..................... 14 Scapulohumeral Rhythm (SHR) ................................ ................................ ............................. 15 Muscle Activation and Function ................................ ................................ ............................. 16 Patient specific Muscle Moment Force Analysis ................................ ................................ ... 17 2 SCAPULOHUMERAL RHYTHM OF REVERSE TOTAL SHOULDER ARTHROPLASTIES DURING NON WEIGHTED SHOULDER ABDUCTION .............. 21 Abstract ................................ ................................ ................................ ................................ ... 21 Scapulohumeral Rhythm for RTSA ................................ ................................ ........................ 22 Participants ................................ ................................ ................................ ............................. 23 Image acquisition and 3D modeling ................................ ................................ ....................... 24 Statistica l Methods ................................ ................................ ................................ .................. 25 Source of Funding ................................ ................................ ................................ ................... 25 SHR Results ................................ ................................ ................................ ............................ 25 SHR Discussion ................................ ................................ ................................ ...................... 26 3 REVERSE TOTAL SHOULDER ARTHROPLASTY MUSCLE FUNCTION DURING ABDUCTION, FLEXION AND EXTERNAL ROTATION ................................ 32 Abstract ................................ ................................ ................................ ................................ ... 32 Electromyography of RTSA ................................ ................................ ................................ ... 33 EMG Results ................................ ................................ ................................ ........................... 36 EMG Discussion ................................ ................................ ................................ ..................... 37 4 DELTOID MOMENT ARMS DURING ABDUCTION: A SUBJECT SPECIFIC MUSCULOSKELETAL MODELING STUDY IN HEALTHY SHOULDERS AND SHOULDERS WITH RTSA ................................ ................................ ................................ .. 43 A bstract ................................ ................................ ................................ ................................ ... 43

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5 Moment Arms for RTSA ................................ ................................ ................................ ........ 44 Overview ................................ ................................ ................................ ................................ . 46 Kinematic Data ................................ ................................ ................................ ....................... 46 RTSA Joint Configuration ................................ ................................ ................................ ...... 47 Joint Definition ................................ ................................ ................................ ....................... 47 Muscle Definiti ons ................................ ................................ ................................ .................. 48 Patient Specific Model Scaling ................................ ................................ ............................... 48 Model Moment Arm Analysis ................................ ................................ ................................ 49 Statistical Methods ................................ ................................ ................................ .................. 49 Moment Arm Results ................................ ................................ ................................ .............. 49 Moment Arm Discussion ................................ ................................ ................................ ........ 50 5 HOW SENSITIVE IS THE DELTOID MOMENT ARM TO JOINT CENTER CHANGES WITH RTSA? ................................ ................................ ................................ ..... 5 9 Abstract ................................ ................................ ................................ ................................ ... 59 Moment Arm Sensitivity ................................ ................................ ................................ ........ 60 Overview ................................ ................................ ................................ ................................ . 62 Data Collection ................................ ................................ ................................ ....................... 62 Model Definition ................................ ................................ ................................ .................... 63 Shoulder Joint Geometry ................................ ................................ ................................ ........ 63 Sensitivity Study ................................ ................................ ................................ .............. 63 Moment Arm Sensitivity Resu lts ................................ ................................ ............................ 64 Moment Arm Sensitivity Discussion ................................ ................................ ...................... 65 6 A NOVEL APPROACH TO ESTIMATION OF PATIENT SPECIFIC MUSCLE STRENGTH WITH REVERSE TO TAL SHOULDER ARTHROPLASTY ........................ 75 Abstract ................................ ................................ ................................ ................................ ... 75 Patient Specific Muscle Strength Calibration ................................ ................................ ........ 76 Model Definition ................................ ................................ ................................ .................... 77 Arm Abduction Angles ................................ ................................ ................................ ........... 78 Moment Arm Calculations ................................ ................................ ................................ ..... 78 Muscle Parameter Estimation ................................ ................................ ................................ . 78 Muscle Force and Activation Data ................................ ................................ ......................... 78 Muscle parameter Estimation ................................ ................................ ................................ . 79 Phase 1 Patient Specific Muscle Strength Calibration ................................ ........................ 80 Phase 1A Optimizer Cost Function ................................ ................................ ............... 80 Phase 1A: MVIC Moment Calibration ................................ ................................ ............ 80 Phase 1B Optimizer Cost Function ................................ ................................ ............... 82 Phase 1B: MVIC EMG Calibration ................................ ................................ ................. 82 Phase 2 Muscle Activation and Performance Prediction ................................ ..................... 83 Patient Specific Muscle Strength Calibration Results ................................ ............................ 83 Phase 1: Patient Specific Muscle Strength Calibration ................................ ................... 83 Phase 2: Patient Specific Muscle Performance Prediction ................................ ............. 84 Muscle Strength Calibration Discussion ................................ ................................ ................ 85

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6 7 HOW SENSITIVE IS DELTOID PERFORMANCE TO JOINT CENTER CHANGES WITH RTSA? ................................ ................................ ................................ ......................... 95 Abstract ................................ ................................ ................................ ................................ ... 95 Muscle Activation and length Sensitivity ................................ ................................ ............... 96 Model Definition ................................ ................................ ................................ .................... 97 Clinical Data Collection ................................ ................................ ................................ ......... 98 Joint Space Sampling and Data Inputs ................................ ................................ ................... 98 Pati ent Specific Muscle Strength Calibration ................................ ................................ ......... 99 Muscle Performance Prediction ................................ ................................ ............................ 100 Muscle Activation and Length Sensitivity Results ................................ ............................... 100 Muscle Activation and Length Sensitivity Discussion ................................ ......................... 101 8 CONCLUSION ................................ ................................ ................................ ..................... 111 Muscle Moment Arm ................................ ................................ ................................ ............ 112 Muscle Force ................................ ................................ ................................ ........................ 113 REFERENCES ................................ ................................ ................................ ............................ 115 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 123

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7 LIST OF TABLES Table page 5 1 Peak variation of muscle moment arms due to joint center variation (All in Patient C). ................................ ................................ ................................ ................................ ....... 69 6 1 Optimized Maximum Activations from Tracked EMG at 90° (Phase 1A) ....................... 89 6 2 Normalized Values of Muscle Parameters Compared to Initi al Estimates ........................ 89 7 1 Joint Center variation ................................ ................................ ................................ ....... 105 7 2 Peak variation of muscle activation to joint center variation changes ............................. 105 7 3 Peak variation of muscle normalized length to joint center variation changes ................ 105

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8 LIST OF FIGURES Figure page 1 1 The human shoulder girdle consists of the humerus, scapula and clavicle. 1 ..................... 18 1 2 The shoulder musculature is multilayered and complex. For RTSA shoulders, the muscle s of greatest functional importance are the deltoid and trapezius. Sagittal (A) and posterior coronal views (B). 1 ................................ ................................ ...................... 19 1 3 Torn rotator cuff tendon. Diagnosis for rotator cuff arthropathy ................................ ....... 20 2 1 3D 2D model registration for RTSA subject. ................................ ................................ .... 29 2 2 Humeral and scapula coordinate system definitions in accordance with the Intern ational Society of Biomechanics standards. ................................ ............................. 30 2 3 Scapulohumeral rhythm during unweighted abduction. Blue: Normal data set, Orange: Reverse shoulder population. ................................ ................................ ............... 31 2 4 Scapulohumeral rhythm during weighted abduction. Blue: Normal data set, Orange: Reverse shoulder population. ................................ ................................ ............................. 31 3 1 Surface electromyography placement. P hoto provided by David R Walker at the orthopaedic sport and medical institute. ................................ ................................ ............ 40 3 2 Muscle activation for weighted flexion.. ................................ ................................ ........... 41 3 3 Muscle activation for weighted flexion.. ................................ ................................ ........... 41 3 4 Muscle activation of the posterior deltoid during weighted abduction .............................. 42 3 5 M arker placement for motion analysis in upper extremity ................................ ................ 42 4 1 ................................ ................... 54 4 2 Bone a nd implant coordinate definitions (A) Humeral stem, Glenosphere (B) Humerus and scapular bones. ................................ ................................ ............................ 54 4 3 Implemented bone and implant configurations. Implant (dark grey) and Bone (white transpare nt) ................................ ................................ ................................ ........................ 55 4 4 Three dimensional bone and implant meshes (orange and blue) registered to two dimensional fluoroscopy x rays ................................ ................................ ......................... 56 4 5 Del toid moment arms varied over the arc of shoulder abduction. ................................ ..... 57 4 6 Three dimensional bone and implant meshes (orange and blue) registered to two dimensional fluoroscopy x rays ................................ ................................ ......................... 58

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9 4 7 Joint center (JC) and Humeral Offset (HO) for normal and reverse total shoulder arthroplasty patients. ................................ ................................ ................................ .......... 58 5 1 Three dimensional bone and imp lant meshes (orange and blue) registered to two dimensional fluoroscopy x rays ................................ ................................ ......................... 70 5 2 Description of native humeral head offset (HO) and implant joint center of rotation (JC) relative to the na tive glenoid center (NG). Implants are shown in dark grey and bones in transparent white. ................................ ................................ ................................ 70 5 3 Variation of deltoid muscle moment arms as a function of joint geometry changes. Top: Patient A, small; Middle: Patient B, medium; Bottom: Patient C, large. .................. 71 5 4 Variation of anterior deltoid moment arm as a function of changes in joint geometry. Blue Anterior/Posterior shifts of join t center; Red Superior/Inferior shifts of joint center; Green Medial/Lateral shifts of joint center. ................................ ........................ 72 5 5 Variation of lateral deltoid moment arm as a function of changes in joint geometr y. Blue Anterior/Posterior shifts of joint center; Red Superior/Inferior shifts of joint center; Green Medial/Lateral shifts of joint center.. ................................ ....................... 73 5 6 Variation of posterior deltoid moment arm as a function of changes in joint geometry. Blue Anterior/Posterior shifts of joint center; Red Superior/Inferior shifts of joint center; Green Medial/Lateral shifts of joint center.. ................................ . 74 6 1 Normalized force length relationships for each muscle. 82 ................................ ................. 89 6 2 Isometric joint moment predictions from Phase 1 muscle strength calibration. Black experimentally measured moments; Re d predicted moments. ................................ .... 90 6 3 Predicted muscle activations for Phase 1 muscle strength calibration. ............................. 90 6 4 Predicted normalized mu scle lengths for isometric trials. ................................ ................. 91 6 5 Phase 2 moment tracking for dynamic abduction (Black Experimental joint moments, Red moment summation from muscle contributions). ................................ ... 92 6 6 Phase 2 muscle activation prediction for dynamic abduction. ................................ ........... 93 6 7 Phase 2 muscle normalized length regions for dynamic abduction. ................................ .. 93 6 8 Phase 2 muscle activation predictions for dynamic abduction ................................ .......... 94 6 9 Phase 2 muscle activation predictions from modified moment arms f or dynamic abduction. ................................ ................................ ................................ ........................... 94 7 1 Three dimensional bone and implant meshes (orange and blue) registered to two dimensional fluoroscopy x rays ................................ ................................ ....................... 105

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10 7 2 Implemented bone and implant configurations. Implant (dark grey) and Bone (white transparent) ................................ ................................ ................................ ...................... 106 7 3 Variation of deltoid activation as a function of changes in the joint confi guration.. ....... 107 7 4 Variation of deltoid activation as a function of changes in the joint configuration. ........ 108 7 5 Variation of delto id normalized length as a function of changes in the joint configuration. ................................ ................................ ................................ ................... 109 7 6 Variation of reserve actuation as a function of changes in the joint configuration. t ..... 110

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11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requir ements for the Degree of Doctor of Philosophy PATIENT SPECIFIC COMPUTATIONAL MODELING TO ASSESS REVE RSE SHOULDER ARTHROPLASTY By D avid R. Walker August 2014 Chair: Scott Arthur Banks Major: Mechanical Engineering Reverse Total shoulder arthroplasty (RTSA) is utilized to restore shoulder function in patients with osteoarthritis and rotator cuff defic iency . The purpose of this study was to assess the behavior of RTSA shoulder subjects as compared to healthy shouldered subjects . Scapulohumeral rhythm (SHR) of patients with RTSA during unloaded shoulder abduction and deltoid muscle activity during activ e shoulder abduction, flexion and externa l rotation were measured to give insight into the function of RTSA shoulders compared to normal shoulders. We studied 33 subjects at least 6 months post unilateral reverse total shoulder arthroplasty. Seventeen su bjects (11 medial, 6 lateral) performed shoulder abduction (elevation and lowering) during fluoroscopic imaging. SHR was calculated from the slope of the humeral and scapular elevation angles . Subjects then performed both weighted (1.5kg) and un weighted abduction ( coronal plane ) and forward flexion ( sagittal plane ) , and un weighted external rotation. A ctivation of the anterior, lateral and posterior aspects of the deltoid and upper trapezius muscles were recorded bilaterally using bipolar surface electrod es. Motion capture using passive reflective markers was used to quantify three dimensional motions of both shoulders.

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12 For abduction above 40 , shoulders with RTSA exhibited an average SHR of 1.2:1. There were significant difference s in SHR between medial and lateral offset groups of RTSA shoulders (p< <0 .05). Durin g abduction, lateral deltoid activity was significantly higher in implanted than in non implanted shoulders for the medial group. During flexion, the anterior deltoid was significantly mor e activ e in the lateral group during weighted and un weighted flexion. Posterior deltoid was not activated over 40% of MVIC. SHR in RTSA shoulders is significantly different from normal shoulders. Significant differences also occur between RTSA groups (medial/lat eral) . The muscle recruitment data suggest reverse total shoulder arthroplasty simplifies deltoid muscle activation. We observed higher muscle activation in the portion of the deltoid directly in line with the task, but reduced muscle function in the out o f line portions of the muscle . This information was useful to guide refinement in the geometric design of the prosthetic components, surgical alignment of the implants, intraoperative soft tissue tensioning, and the design of muscle strengthening programs. This thesis developed a computational framework using clinical data to predict muscle performance post RTSA . The information collected in the previous experimental studies was used to calibrate and validate patient specific computational models to assess muscle soft tissue tensioning. An upper extremity model was developed in this study to address two current limitations of upper extremity modeling. (1) Current models are limited because they do not incorporate subject specific geometric changes (joint ce nters) to observe muscle lengthening/tensioning changes in the shoulder. (2) The other limitation lies in the motion of the shoulder girdle where the motion of the clavicle and scapula are constrained to move as a function of humeral motion only in the ele vation plane. Kinematics and subject specific data

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13 were collected to address these limitations. This enhanced subject specific model framework was used to assess the effects of reverse total shoulder arthroplasty (RTSA) on the moment generating capacity of muscles crossing the shoulder girdle. Patient specific muscle moment arm measurements was calculated from simulations that are driven by data taken from clinical studies. A novel method was also developed to calculate patient specific musculotendon parame ters and likewise muscle recruitment and force contributions over dynamic abduction. T he predictions developed give a better understanding implant choice and placement for reverse shoulder arthroplasty.

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14 CHAPTER 1 INTRODUCTION Shoulder Anatomy The shou lder joint is comprised of three bones, the humerus, the sca pula and the clavicle ( 1 1). The shoulder is contr olled by a variety of muscles ( 1 2). 1 The rotator cuff muscles, the trapezius and the deltoid serve to lift and stabilize the arm. The joint achieves great mobility under coordinated control of these muscles. An irreparable tear of the rotator cuff muscles may functionally immobi lize the shoulder. There are several different disorders that lead to immobilization of the shoulder. Shoulder Joint Injuries Shoulder joint related problems are a common reason for visits to the Orthopaedic surgeon. In 2003 , 14 million people in the Unit ed States visited a doctor for a shoulder related i njury. 2 These people suffered from a variety of disorders such as rotator cuff arthropathy ( 1 3) , frozen shoulder, and shoulder impingement syndrome. Irreparable tears of the rotator cuff muscles (Teres minor, supraspinatus, infraspinatus, and subscapularis) will cause the development of osteoarthritis (1 3) and impairment of motion of the shoulder [ref] . In the event of an irreparable rotator cuff ( 1 3) the Reverse Total Shoulder Arth roplasty (RTS A) is an increasingly popular option to restore mobility in the shoulder . Reverse Total Shoulder Arthroplasty The Reverse Total Shoulder Arthroplasty (RTSA) Paul Grammont , who developed the principles lead ing to succ essful reverse and total sho ulder prostheses . 1 A reverse prosthesis is comprised of a glenosphere, a hu meral stem, and a humeral cup ( 1 4 ). The reverse prosthesis possesses several potential advantages. In a normal shoulder with an irreparable r otator cuff tear, patients often experience pain and dislocation of the humeral

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15 head. RTSA obviates the need for rotator cuff muscles by fixing the center of rotation (COR) of the humerus relative to the scapula. This allows for stabili zation of the COR without need for dynamic muscular stabilization of the joint . The implant defined COR also allows for manipulation of the deltoid moment arm. RTSA ca n alleviate pain while restoring motion to shoulders with irreparable rotator cuff injuries or failed total shoulder replacements ( 1 3 ) . The optimal amount of lateral offset in RTSA remains the subject of current study and debate . 3 Three designs of RTSA were available to study for this thesis, with each adopting a different philosophy for how far laterally the COR should be placed (medial, neutral and lateral, Figure 1 4) . 4,5 Improper placement of the COR can lead to possible implant failure by glenoid loosening, and impingement syndrome . 6 Therefore, information on reverse shoulder joint behavior with reference to normal shoulders is vital to identify ideal placement of the CO R and minimize implant failure . The measurement of motion and muscle function in RTSA shoulders is the primary motivation for the studies that comprise C hapters 2 and 3. The measurement of motion of the humerus and scapula was used to calculate a paramete r known as the scapulohumeral rhythm (SHR) Scapulohumeral Rhythm (SHR) The coordinated motion of the humerus and scapula has been defined as a ratio between how each of the bodies move, hence the scapulohumeral rhythm (SHR). SHR was first reported to be a constant 2:1 (humerus : scapula) ratio by Inman et al . for normal healthy subjects. 7 Many researchers have since measured SHR in normal and pathological shoulders . 8,9 To date, there has been no report of SHR for RTSA patients. Alterations in the position and movement of the scapula, called scapular dyskinesia, change the SHR and likely manifest in various shoulder

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16 disorders, such as rotator cuff tears, impingement syndrome, frozen shoulder, osteoarthritis, t hrowing injuries and instability. 9 It is vital to know the SHR of the RTSA popu lation in determining if RTSA SHR differs from normal shoulders and to assess possible points of failure for the implan t. Calculating SHR of RTSA subjects during shoulder abduction will help assess how the RTSA shoulder functions with respect to a normal shoulder. Muscle Activation a nd Function Muscles are the actuators of the shoulder joint. They produce tension that i s applied to the bone s via tendon s to drive motion . In RTSA patients , the primary muscles that perf orm lifting of the arm are the d eltoi ds and the upper trapezius ( 1 2) . 1 0 How these muscles are recruit ed is vital to understand ing the function of the RTSA shoul der. It is likely that c hange s in RTSA geometry directly affect the function of these muscles. Measurements of muscle activity during abduction , flexion and exte rn al rotation was presented in Chapter 3 . By measuring muscle activity during t hese activities, a model of how muscle recruit ment varies with different RTSA designs can be developed . These measurements can be used to assess ideal placement of the COR to opt imize function in RTSA shoulders. This thesis seeks to assess the moment generating capacity of muscles in the shoulder after reverse shoulder joint replacement. The information collected in the previous experimental studies was used to calibrate and valid ate patient specific computational models to assess muscle soft tissue tensioning. An upper extremity model was developed in this study to address two current limitations of upper extremity modeling. (1) Current models are limited because they do not incor porate subject specific geometric changes (joint centers) to observe muscle lengthening/tensioning changes in the shoulder. (2) The other limitation lies in the motion of the shoulder girdle where the motion of the clavicle and scapula are constrained to m ove as a

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17 function of humeral motion only in the elevation plane 11 16 Kinematics and subject specific data were collected to address these limitations. This enhanced subject specific model framework was used to assess the effects of reverse total shoulder arthroplasty (RTSA) on the moment generating capacity of muscles crossing the shoulder girdle. Patient specific Muscle Moment Force Analysis A nested optimization was also developed to calculate pat ient specific musculotendon parameters to likewise muscle recruitment and force contributions over dynamic abduction. The predictions developed will give a better understanding implant choice and placement for reverse shoulder arthroplasty.

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18 Figure 1 1. The human shoulder girdle consists of the humerus, scapula and clavicle . 1

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19 Figure 1 2. The shoulder m usculature is multilayered and complex . For RTSA shoulders, the muscles of greatest functional importance are the delt oid and trapezius. Sagittal ( A ) and posterior coronal views ( B ) . 1 A B

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20 Figure 1 3. Torn rotator cuff tendon. Diagnosis for rotator cuff arthropathy

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21 CHAPTER 2 SCAPULOHUMERAL RHYTH M OF REVERSE TOTAL S HOULDER ARTHROPLASTI ES DURING NON WEIGHTED SHOULDER AB DUCTION Abstract Little is known about kin ematic function of the reverse total shoulder arthroplasty (RTSA). Scapulohumeral rhythm (SHR) is a common metric for assessing muscle function and shoulder joint motion. Understanding how RTSA affects shoulder function may help refine implant design, surg ery, and rehabilitation strategies. The purpose of this study was to compare SHR in shoulders with RTSA to normal shoulders. Twenty eight subjects were recruited for an institutional review board approved study. Subjects were more than six months post u nilateral RTSA. Subjects performed arm abduction in the coronal plane with and without a 3 lb. hand held weight. Three dimensional model image registration techniques were used to measure orientation and position for the humerus and scapula from fluoroscop ic images. ANOVA and Tukey tests were used to assess group wise and pair wise differences. SHR in RTSA shoulders (1.3:1) was significantly lower than in normal shoulders (3:1). Below 30° abduction, RTSA and normal shoulders show a wide range of SHR, varyin g from 1.3:1 to 17:1. Above 30° abduction, SHR in RTSA shoulders was 1.3:1 for unweighted abduction and 1.3:1 for weighted abduction. Maximum RTSA shoulder abduction in weighted trials was lower than in unweighted trials. SHR variability in RTSA shoulders decreased with increasing arm elevation. RTSA shoulders show kinematics that are significantly different from normal shoulders. SHR in RTSA shoulders was significantly lower than in normal shoulders, indicating RTSA shoulders utilize much more scapulotho racic motion, and much less glenohumeral motion, to elevate the arm. With these observations it may be possible to improve rehabilitation protocols,

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22 with particular attention to the periscapular muscles, and to improve implant design or placement to optimi ze functional outcomes in shoulders with RTSA. Level of Evidence: The study is a level III case control therapeutic study. Key words: reverse total shoulder arthroplasty; rehabilitation; implant design; surgical technique; shoulder motion; scapulohumeral r hythm. Scapulohumeral Rhythm for RTSA Reverse total shoulder arthroplasty (RTSA) have become a widespread treatment option for patients with rotator cuff arthropathy. RTSA studies have yielded promising results not only in the relief of chronic pain due motion during functional activities. Despite good clinical outcomes potential issues still occur post RTSA that are associated with deltoid tensioning and joint range of motion. Potentia l instability, scapular notching, and polyethylene wear may lead to significantly decreased functional outcomes and increased risk of RTSA failure. 5,17,18 Better knowledge of shoulder joint motion is critical to understanding how shoulders with RTS A function. With a better understanding of reverse shoulder motion, optimal design and configuration of the implants can be achieved to increase functional outcomes and lower RTSA failure rates. This study quantifies the kinematics of shoulders with RTSA a nd compares these results with kinematics of young healthy shoulders studied with identical methodology. Altered scapular kinematics are often associated with shoulder disorders. 7 Scapulohumeral rhythm (SHR) has been used to quantify the relative motion o f the scapula and humerus, and is a sensitive measure of shoulder dysfunction. 8 There have been many methods developed to measure shoulder motion and SHR, of which most are noninvasive and require

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23 placement of markers on the skin. 19 As with any methods using markers that are not rigidly fixed to the bones, there can be significant soft tissue movement that affects the measurement. 20 Fluoroscopic imaging and model image registration techniques have been used for over 20 years to quantify the motions of implants and bones in vivo, including the shoulder. 19 These radiographic methods quantify implant or bone motion directly, and are unaffected by motions of the surrounding skin or soft tissues. A lthough studies have been performed to assess the maximum range of shoulder motion with RTSA, there is no information directly quantifying scapulothoracic and scapulohumeral motion in these shoulders. The goal of this study was to quantify SHR in shoulders with RTSA during abduction with and without a hand held weight, and to compare these measures with those previously obtained from healthy young shoulders using the same protocol and methods. Participants Twenty eight subjects with RTSA gave written inf ormed consent to participate in this IRB approved study. They were an average of 37 months post unilateral RTSA (range 12 63 months) and had an average age of 73. The RTSA group was comprised of 23 females and 5 males. Each RTSA subject had at least two ro tator cuff tendon tears that were deemed non repairable by the surgeon as well as secondary arthritis. These RTSA patients were treated with three different implant designs. Seven RTSA subjects received implants with a glenosphere center of rotation within 2mm of the glenoid face, and a medialized humeral design having a line of action within the humerus (Aequalis ® , Tornier, Edina, MN). Sixteen RTSA subjects received implants with a glenosphere center of rotation at least 6mm lateral to the glenoid face an d a medialized humeral design (Reverse ® Shoulder Replacement, DJO Surgical, Austin, Tx,). Ten RTSA subjects received implants with a medial center of rotation glenosphere and a lateralized

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24 humeral design (Equinoxe ® , Exactech, Gainesville, FL). Each variati on of prosthetic shoulder geometry is intended to provide mechanical advantage to the deltoid . 3 5,17,21,22 Subjects with all three implant designs comprised the RTSA study cohort. Image acquisition and 3D modeling Single plane Fluoroscopic images of the shoulder during coronal plane abduction w ere captured at 7.5 Hz. Motions were performed so that one cycle required approximately 15 seconds to complete, moving from the arm at the side to maximum abduction and returning to arm at the le during elevation and lowering of the arm, with specific attention to keeping their torso upright in a standing posture. Subjects performed unweighted trials and weighted trials with a 3 lb. hand held weight. Subjects rested for 2 minutes between trials to minimize the potential for fatigue. Subjects were positioned so that their coronal plane was p erpendicular to the x ray beam. Fluoroscopic images were undistorted using custom software (Mathworks) and three dimensional (3D) to two dimensional (2D) mode l image registration techniques were used to determine the 3D motions of the implants from the undistorted images. 19 Subject specific implant mode ls for the humeral and glenoid components were created so that measured implant rotations corresponded to anatomic shoulder motions. These 3D implant models were projected onto the undistorted fluoroscopic images and their 3D pose was adjusted to match the implant silhouette in the fluoroscopic image, providing humeral and scapular component kinematics ( Figure 2 1). 19 Elevation of the humeral and sc apular components in the coronal plane were determined ( Figure 2 2), and a third order polynomial was fitted to a plot of scapular elevation (ordinate) versus humeral elevation (abscissa) to permit resampling at equal intervals of humeral elevation. Scapul

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25 registration technique was found to be 1 mm for translations and .5 degrees for rotat ions. 19 We use our previously reported results for healthy young shoulders as the basis for quantitative comparison of RTSA shoulder function. 8 These normal shoulders were studied using the same methods and calculations. Statistical Methods Comparison of RTSA shoulders with healthy young shoulders was performed using t wo way repeated measures ANOVA with t he level of significance of 0.05. Significant Di fference was used to perform pair wise post hoc comparisons at specific humeral elevation angles. Source of Funding A research grant from the American Shoulder and Elbow Surgeons was received in partial support of this work. Funds from an unrestricted res earch grant from DJO, LLC, were used to support the research assistantship of DW.Geometric models of implants were received from the companies marketing those devices. Neither the funding agency nor the commercial entities played any role in the study desi gn, recruitment of subjects, interpretation of data, or preparation of this manuscript. SHR Results For abduction above 30 , shoulders with RTSA exhibited an average SHR of 1.3:1 during unweighted abduction (Figure 2 3). There was no significant SHR differ ence between abduction with and without 3 kg handheld weights (1.3:1 weighted) (Figure 2 4), nor was there a significant difference between elevation and lowering. SHR was highly variable for abduction less than 30 , with SHR ranging from 2:1 to 17:1. The mean SHR for normal shoulders was 3:1

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26 (Figure 2 3, 2 4). Maximum unweighted abduction averaged 150° for normal shoulders, 110° for unweighted abduction in RTSA shoulders, and 90° for weighted abduction in RTSA shoulders. SHR Discussion RTSA is an increasin gly important treatment option for severe trauma and degeneration of the shoulder. There is active debate on the best implant geometric configurations to restore shoulder function, but very little quantitative in vivo data to guide this debate. We perform ed this study to determine if shoulders with RTSA show close to normal scapulohumeral rhythm and found that shoulders with RTSA exhibit low SHR values, or less glenohumeral motion, as the arm moves through the abduction arc. Two study limitations need to b e considered, both related to the fact that the primary implant used for RTSA changed over time. First, we enrolled subjects with three different RTSA implant designs, presenting a range of geometric configurations. We did not detect significant difference s in SHR between these three subgroups and present the data as a single inclusive RTSA group. It is possible that comparisons of larger groups of subjects would reveal significant differences in SHR between implant types. Second, the postoperative follow u p interval was different for subjects receiving each of three different RTSA designs. It is possible that differences in SHR will be manifest when subjects receiving the three designs are all studied at the same postoperative intervals. SHR is an important and widely documented parameter to describe coordinated motion in healthy and diseased shoulders. SHR in young normal shoulders has been reported to average 3:1 8 while SHR in RTSA shoulders has been reported to average 1.3:1. 23,24 Matsuki et al. showed differences in scapular motions between dominant and non dominant shoulders in healthy young subjects, but the SHR values did not differ (2.6:1 and 2.7:1, respectively). 8 Our study of 28 shoulders with RTSA showed SHR averaging 1.3:1 for unweighted abduction and 1.3:1 for

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27 weighted abduction. Consistent with p revious reports, we found SHR in shoulders with RTSA is consistently lower than in healthy shoulders. At arm elevation angles less than 30 , SHR in shoulders with RTSA is highly variable. This is consistent with the scapular setting phase described in pre vious studies. 8,23,25 At higher elevation angles, SHR in shoulders with RTSA (1.3:1) is much more consistent and is lower than SHR in normal shoulders (roughly 3:1). Reduced glenohumeral motion with RTSA may result from a combination of muscular and articular mechani sms. Shoulders with RTSA lack a competent rotator cuff and this may contribute to reduced glenohumeral motion. In particular, without the supraspinatus and infraspinatus, the shoulder lacks the intrinsic muscles that can assist the deltoid in raising and l owering the arm against gravity. 10,26 Cuff dysfunction may also elicit deltoid inhibitory signals , further reducing the ability of the deltoid to provide glenohumeral motion. 27 In addition, the RTSA articulation and implants may restrict glenohumeral motion. Imposing a fixed center of rotation on the glenohumeral joint, especially if it is different from the natural anatomy, may change the relationship between the torque elevating the humerus and the reaction forc es acting on the glenoid, and these altered mechanics may affect glenohumeral motion. Implant impingement, as has been observed in numerous studies, is an obvious factor in restricting glenohumeral motion. 28 Efforts to improve postoperative function in shoulders with RTSA should focus attention on reduced glen ohumeral motion, and seek to understand how these muscular and articular factors contribute. Greater scapular motion is observed in shoulders with RTSA. An SHR of 1.3 is consistent with previous reports and implies greater activity in the trapezius. 23,25 This sam e cohort of RTSA study subjects was also observed using electromyography (EMG) and motion capture during arm abduction, and their upper trapezius EMG activity was found to be

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28 significantly higher than in normal age and gender matched subjects. 29 Increased scapulothoracic motion may have profound clinical implications, as periscapular muscle pain, subscapular bursitis, acromioclavicular joint pain, and scapular spine stress fractures have all been observed in shoulders with RTSA. 23 Shoulder rehabilitation following RTSA may benefit from focused strengthening of the periscapular muscles to facilitate these increased demands for scapular movement. Improving function in should ers with RTSA is an increasingly important pursuit with the growing utilization of this treatment. Shoulders with RTSA, by definition, have suffered from severe mechanical insult and/or disease, and they do not show normal scapulohumeral coordination after surgery. Our results suggest two important fronts for improving clinical and functional results with RTSA. First, the interplay of altered musculature and joint geometry must be further studied so that treatments can be objectively designed to achieve the best possible glenohumeral motion with RTSA. Second, there are greater demands for scapular motion after RTSA, and rehabilitation strategies should increasingly focus on strengthening the periscapular muscles to enhance function and avoid common complicat ions.

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29 Figure 2 1 . 3D 2D model registration for RTSA subject.

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30 Figure 2 2 . Humeral and scapula coordinate system definitions in accordance with the International Society of Biomechanics standards.

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3 1 Figure 2 3: Scapulohumeral rhythm during unweigh ted abduction. Blue: Normal data set, Orange: Reverse shoulder population. Figure 2 4 . Scapulohumeral rhythm during weighted abduction. Blue: Normal data set, Orange: Reverse shoulder population.

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32 CHAPTER 3 REVERSE TOTAL SHOULDER ARTHROPLAST Y MUSCL E FUNCTION DURING ABDUCTION, FLEXION A ND EXTERNAL ROTATION Abstract Little is known about muscle activation after reverse total shoulder arthroplasty (RTSA). Understanding how RTSA affects shoulder function may help refine its design and use. This study so ught to evaluate deltoid and upper trapezius muscle activity during shoulder abduction, flexion, and external rotation in RTSA subjects. 50 subjects were recruited for an institutional review board approved study. We studied and gender matched control group. RTSA subjects were divided into three groups accordin g to implant design. Subjects performed weighted and un weighted abduction in the coronal plane, forward flexion in the sagittal plane, and un weighted external rotation. Electromyography activation of the anterior, lateral, and posterior aspects of the d eltoid and the upper trapezius muscles were recorded bilaterally using bipolar surface electrodes. Motion capture using passive reflective markers quantified three dimensional motions of both shoulders. During abduction and flexion, deltoid and upper trap ezius activity was significantly increased in RTSA shoulders. Posterior deltoid activation was highest in shoulders with the medial glenosphere/lateral humerus implant design. Shoulders with the medial glenosphere/medial humerus were most similar to the co posterior deltoid muscle activation during weighted flexion. RTSA increases muscle activation compared to normal shoulders. RTSA often restores stability and motion, but does not restore normal deltoid or upper trapeziu s activation levels. Increased muscle activation in shoulders with RTSA suggests they are less efficient. RTSAs with lateral or medial glenosphere centers of rotation had mostly similar muscle activation.

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33 Electromyography of RTSA Reverse total shoulder ar throplasty (RTSA) is an effective treatment option for patients with symptomatic glenohumeral arthritis and a deficient rotator cuff. RTSA has been reported to produce early satisfactory clinical outcomes in pain relief and restoration of active forward fl exion and abduction. 22,30 However, associated deltoid tensioning and potential instability, scapular notching, and polyethylene wear may l ead to significantly decreased functional outcomes and incre ased risk of RTSA failure. 5,18,31 Better knowledge of muscle activity after RTSA is critical to understanding how shoulders with RTSA function, and how to address associated chal lenges to improve functional outcomes and longevity. Most RTSA research has focused on improving the design and biomechanics of reverse prostheses.2,5,10,14 5,32 34 Few studies have focused on the deltoid, which becomes the primary mover in the rotator cuf f deficient shoulder and RTSA. 35 We currently lack a fundamental understanding of how deltoid tension and activity relates to functional outcomes, such as range of motion (ROM), arm strength, and functional scores with RTSA. Insufficient deltoid tension may lead to prosthetic instability, whereas excessive deltoid tension may result in acromial fra ctures; 33 other factors may also play a role. 36 Deltoid tension is thought to directly affect the activ ation pattern and active force generating ability of the muscle such that active ROM and shoulder function depend on the interplay between RTSA geometry and deltoid length and tension. 32 34 In a rotator cuff deficient shoulder, muscle tension is required to dynamically stabilize the glenohumeral joint and to move the arm. RTSA provides conforming joint surfaces that may reduce the need for dynamic muscular stabilizers and allow for more efficient recruit ment of shoulder muscles compared to the rotator cuff deficient shoulder, but this has not been demonstrated in vivo. The purpose of this study was to determine shoulder muscle activation in

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34 patients with three RTSA implant designs. We studied deltoid and upper trapezius muscle activity in RTSA shoulders and normal shoulders in age and gender matched controls during both weighted and unweighted shoulder abduction and flexion, and unweighted external rotation. In this study we compared muscle activation pa tterns of the deltoid and trapezius between shoulders with RTSA and shoulders in age and gender matched controls. Fifty subjects (34 females and 16 males between the ages of 60 and 85) gave written informed consent to participate in this IRB approved stud y. Seventeen healthy subjects (indicating no history of shoulder pathology or complaints) made up of 11 females and 6 males with an average age of 73 comprised the age and gender matched control group. Thirty three subjects with RTSA made up the RTSA grou p. They were an average of 37 months post unilateral RTSA (ranging 12 63 months) and had an average age of 73. The RTSA group was comprised of 24 females and 9 males. Each RTSA subject had at least two rotator cuff tendon tears that were deemed non repaira ble by the surgeon as well as secondary arthritis. RTSA subjects were divided into three groups according to implant design. Seven subjects in Group 1 received implants with a glenosphere center of rotation within 2mm of the glenoid face, and a medialized humeral design having a line of action within the humerus (Aequalis®, Tornier, Edina, MN, Figure 3 1 ). Sixteen subjects in Group 2 received implants with a glenosphere center of rotation at least 6mm lateral to the glenoid face and a medialized humeral de sign (Reverse® Shoulder Replacement, DJO Surgical, Austin, Tx, Figure 3 1 ). Ten subjects in Group 3 received implants with a medial center of rotation glenosphere and a lateralized humeral design (Equinoxe®, Exactech, Gainesville, FL, Figure 3 1 ). Each var iation of prosthetic shoulder

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35 Constant Murley Shoulder Score (CMS) preoperatively was 18. The average RTSA subject normalized CMS a t th e time of the study was 73 . weighted abduction, weighted and un weighted flexion, and un weighted external rotation. Motions were performed so that one cycle required approximately 15 seco nds. Weighted trials used a 1.5 kg hand held weight. Subjects rested for 2 minutes between activities to minimize the effects of fatigue. A twelve camera motion capture system was used to record the motions of fifteen skin mounted retro reflective markers at 60 Hz (Figure 3 2). 9,37 Skin surface electromyography (EMG) was collected simultaneously at 1200 Hz using bipolar electrodes placed bilaterally on the anterior, lateral, and posterior aspects of the deltoid and on the upper trapezius (Telemyo 2400, Noraxon USA Inc., Scottsdale, AZ). Maximal voluntary isometric contraction (MVIC) data were used to normalize the EMG signals. 38 A hand held dynamometer was used to measure the maximum force generated at the wrist joint during MVIC trials. Reflective marker kinematics were determined using standard software (EvaRT, Motion Analysis Corporation, Santa Rosa, CA) and filtered using a fourth order, zero phase shift, low pass Butterworth filter with a 12 Hz cutoff frequency. A custom program was used to compute shoulder abduction, flexion, and external rot ation angles using an abduction flexion external rotation sequence. 31 EMG data were mean filtered and fitted spline curves were used to determine the EMG signal magnitude at specific arm angles. Statistical Methods

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36 Comparisons between shoulders with RTSA and controls were performed using two way repeated estly Significant Difference was used to perform pair wise post hoc comparisons. EMG Results All shoulder groups exhibited increasing muscle activity with increasing abduction or flexion, and activation was higher for weighted activities. In general, shou lders with RTSA showed higher muscle activation than healthy controls. Shoulders with RTSA typically did not abduct or flex to the same extent as healthy controls (150°) and their abduction and flexion was typically less during weighted activities (85°). G roup 3 shoulders (medial glenosphere/lateral humerus) showed significantly higher posterior deltoid activity than the other groups. Group 2 (lateral glenosphere/medial humerus) and Group 3 (medial glenosphere/lateral humerus) shoulders showed significantly higher anterior deltoid activation than Group 1 (medial glenoshpere/medial humerus) or control shoulders during un weighted abduction ( Figure 3 3 a). All groups of RTSA shoulders showed significantly higher anterior deltoid activation during weigh ted abduction than controls (Figure 3 3 a). RTSA Group shoulders showed higher deltoid, and upper trapezius activation during weighted abduction tha n control shoulders (Figure 3 3 ). Deltoid and upper trapezius activity was higher in the RTSA shoulders than in healthy controls during un weighted and weighted flexion ( Figure 3 4). Group 3 shoulders showed generally higher muscle activation than all other groups du ring flexion activities (Figure 3 4 ), with significant differences during weighted fle xion compared to Controls (all muscles), Group 1 (posterior deltoid), and Group 2 (posterior deltoid and upper trapezius). Group 1 shoulders showed muscle activation most similar to Controls during flexion.

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37 Average posterior deltoid activation did not exce ed 20% of MVIC for any group during un weighted external rotation and differences between groups were small (<5% MVIC, Figure 3 5). EMG Discussion Deltoid muscle function is critical to shoulder function following RTSA, yet there is little objective info rmation about deltoid function in these patients. We found muscle activity in RTSA shoulders was significantly different from healthy controls. In replaced shoulders, deltoid activity is increased compared to normal control shoulders. The increase in delto id and trapezius muscle activation demonstrates that these muscles work harder to elevate the arm after RTSA. As expected, muscle activity increased during weighted trials in both RTSA and normal control shoulders. 39 Our results suggest muscle activation increases in RTSA shoulders in order to compensate for the rotation being fixed to the scapula. Some degree of altered muscle function likely persists from the preoperative state, but this requires experimental confirmation. The abnormality of RTSA muscle function highlights new opportunities to advance this treatment through additional study of implant design, surgical technique, musculoskeletal function, and rehabilitation. This study included 33 subjects with unilateral RTSA. We used th gender distribution to recruit 17 matched, healthy subjects with no prior history of shoulder pain, pathology or functional deficiency as the Control group. Control shoulders were able to achieve full normal ranges of abduction, flexio n and external rotation. Gender matched controls were chosen to standardize muscle volume differences between men and women. Age matched healthy controls were chosen to represent optimal shoulder function relevant to RTSA subjects. The contralateral should ers of the RTSA subjects were also studied and found to be statistically different from the Control shoulders.

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38 Our equipment was limited to eight channels of EMG (four placed bilaterally), so it was not possible to record muscle activity for teres minor ( if present) or other important shoulder muscles. We attempted to minimize experimental variability by: (1) having a single examiner prepare and place the EMG electrodes for all subjects; (2) coaching subjects on how to perform the MVIC trials to get the be st possible activation levels for normalization; and (3) saving for analysis only trials in which the subject maintained the correct upright posture. Despite these steps, EMG data are variable and it is possible our cohort does not represent the full range of EMG patterns found in the population of patients who have undergone RTSA. Our primary finding is higher muscle activation in RTSA shoulders than in age and gender matched controls. Muscle activation for shoulders with RTSA was characteristically simil ar, although several statistically significant differences were observed. These differences were typically smaller between RTSA groups than those between RTSA shoulders and healthy controls. There is ongoing debate regarding the merits of increasing latera lization with RTSA, typically citing improved deltoid moment arms or optimal deltoid muscle fiber lengths. 28 For the range of lateralization tested, the effects on deltoid muscle activation appear limited. Similarly, there have been several reports emphasizing the importance of the posterior deltoid as the key mover for external rotation. 40,41 For external rotation without resistance, we observed no more than 20% MVIC activation of the posterior deltoid, although this could change dramatically in MVIC trials evaluating external rotation against resistance. In heal thy shoulders the primary arm abductors are the del toid and upper trapezius. 42 44 Increased deltoid activity in cuff deficient shoulders leads to instability and upward humeral migration. Our data show all aspects of the deltoid were significantly more active in RTSA shoulders than in healthy controls, not just in those primarily in line with the mechanical

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39 demand. RTSA patients may develop a wh ole deltoid contraction strategy preoperatively as a means to dynamically stabilize their unstable and cuff deficient shoulder which may persist after RTSA implantation. Further exploration of muscle activation in shoulders with cuff tear arthropathy would provide a better idea of pre RTSA shoulder function and help to identify therapeutic opportunities for post RTSA rehabilitation. The synergy between the deltoid and upper trapezius is evident in the EMG data from RTSA shoulders (Figs. 3 and 4). For both a bduction and flexion motions, deltoid activity reaches a plateau mid motion and the upper trapezius activation increases linearly with greater abduction or flexion. These patterns of muscle activation suggest an increasing contribution of scapular rotation to overall motion at greater abduction/flexion angles, or a decreasing scapulohumeral rhythm. The muscle activity coincides with greater glenohumeral motion at low angles with increasing scapular thoracic motion above 40 degrees as the upper trapezius bec omes more active in the RTSA shoulders. We conclude that deltoid and upper trapezius activation in RTSA shoulders is abnormal. The muscles appear to be working harder to provide arm abduction and flexion after RTSA. RTSA shoulders labor more and yet do not achieve the range of motion of a healthy subject. This calls into question whether current designs are optimal to increasing range of motion, especially when the arm is load bearing. Our observations support further research to identify the physiologic an d/or mechanical basis for the changes in muscle activation in order to optimize RTSA treatments. Based upon the external rotation data, there appears to be little value in a strengthening program directed at the posterior deltoid.

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40 Figure 3 1. Surface e lectromyography placement . Photo provided by David R Walker at the orthopaedic sport and medical institute.

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41 Figure 3 2. Muscle activation for weighted flexion . A) Anterior deltoid during weighted abduction, B) Lateral deltoid during weighted abduct ion, C) Posterior deltoid during weighted abduction, D) Upper trapezius during weighted abduction. Figure 3 3. Muscle activation for weighted flexion . A) Anterior delto id during weighted flexion, B) Lateral delto id during weighted flexion, C) Posterior d elto id during weighted flexion, D) Upper trapezius during weighted flexion.

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42 Figure 3 4. Muscle activation of the posterior deltoid during weighted abduction Figure 3 5 . Marker placement for motion analysis in upper extremity

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43 CHAPTER 4 DELTOID MOMENT ARMS DURING ABDUCTION: A SUBJECT SPECIFIC MUSCULOSKELETAL MODELING STUDY IN HEALTHY SHOULDERS AND SHOULDERS WITH RTSA Abstract Reverse total shoulder arthroplasty (RTSA) is increasingly used in the United States since approval by the FDA in 2003. R TSA relieves pain and restores mobility in arthritic rotator cuff deficient shoulders. Though many advantages of RTSA have been demonstrated, there still are a variety of complications (implant loosening, shoulder impingement, infection, frozen shoulder) m aking apparent much still is to be learned how RTSA modifies normal shoulder function. A better understanding of shoulder motion and muscle function post RTSA surgery will support improved implant designs, surgical techniques and rehabilitative strategies for RTSA. The goal of this study was to assess how RTSA affects deltoid muscle moment generating capacity post surgery using a subject specific computational model driven by in vivo kinematic data. A subject specific 12 degree of freedom (DOF) musculoskel etal model was use d to analyze the shoulders of 24 subjects (14 RTSA, 12 Normal). The model was modified from the work of Holzbaur et al. to directly input 6 DOF humerus and scapula kinematics obtained using fluoroscopy. Model geometry was scaled according vivo abduction kinematics for each subject were input to their subject specific model and muscle moment arms for the anterior, lateral and posterior aspects of the deltoid were measured over the arc of motion. S imilar patterns of muscle moment arm changes were observed for normal and RTSA shoulders. The moment arm of the anterior deltoid was positive with the arm at the side and decreased monotonically, crossing zero (the point at which the muscle fibers pass acr oss the joint center) between 50° 60° glenohumeral abduction. The average moment arm of the lateral deltoid

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44 was constant and positive in normal shoulders, but showed a decreasing trend with abduction in RTSA shoulders. The posterior deltoid moment arm was negative with the arm at the side, and increased monotonically to a positive value with increasing glenohumeral abduction. Subject specific moment arm values for RTSA shoulders were highly variable compared to normal shoulders. Two way repeated measures AN OVA showed significant differences between RTSA and normal shoulders for all three aspects of the deltoid moment arm, where the moment arms in RTSA shoulders were smaller in magnitude. Shoulder functional capacity is a product of the moment generating abil ity of the shoulder muscles which, in turn, are a function of the muscle moment arms and muscle forces. Placement of implant components during RTSA can directly affect the geometric relationship between the humerus and scapula and, therefore, the muscle mo ment arms in the RTSA shoulder. Our results show RTSA shoulders maintain the same muscle moment arm patterns as healthy shoulders, but they show much greater inter subject variation and smaller moment arm magnitudes. These observations show directly how RT SA configuration and implant placement affect deltoid moment arms, and provide an objective basis for determining optimal implant configuration and surgical placement to maximize RTSA function in a patient specific manner. Moment Arms for RTSA Reverse Tota l Shoulder Arthroplasty (RTSA) increasingly is being used in the United States since its approval by the FDA in 2003. 45 RTSA serves to restore some mobility in rotator cuff deficient shoulders while relieving the pain of osteoarthritis. Although several advantages of reverse shoulder arthroplasty have been reported (e.g. treatment of rotator cuff arthropathy, treatment rheumatoid arthritis with patients with an irreparable cuff tear, proximal humeral tumors and proximal humeral fractures with anterosuperior escape), 5,17 , 4,18 there still are a variety of complications (e.g., implant loosening, acromial fracture, scapula notching, frozen

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45 shoulder, glenoid morphology) making it apparent much remains to be learned how RTSA modifies normal shoulder function. 2,6 ,46 48 A better understanding of shoulder motion and muscle function post RTSA will support improved design rationales and surgical implementation of this treatment. Fundamentally, the ability of a muscle to move the shoulder is a function of two factors, the muscle moment arm and the muscle force generating capacity, 49 52 and sev eral cadaver studies have reported how changes in RTSA geometry affect shoulder muscle moment arms. 3,11 13,32 34,53,54 These studies provide some insight to how muscle moment arms change in a limite d set of cadaveric joints, but they do not capture the full variation of morphology, size and motion that would be encountered in a RTSA clinical cohort. There are few reports of direct in vivo measurements of RTSA shoulder muscle moment arms due to the di fficulty of measuring these parameters non invasively. 55 Computational modeling provides a powerful method to analyze human biomechanics and advanced models of the upper extremity have been developed for a variety of applications. 3,11 13,32 34,53,54 , 56 59 , 60 62 Detailed muscle properties input to these musculoskeletal models typically are derived from cadaver studies. 49 52 For example, Holzbaur et al. used a musculoskeletal model based upon cadaveric measurements of muscle properties to determine muscle moment arms and joint moments, and found their results compared well to experimental data. 58 Ling et al. used computational models to assess muscle tendon transfers in the shoulder. 63 Other investigators have used similar musculoskeletal models to study RTSA biomechanics during active abduction. 12,13 Common to all of these u pper extremity models is the use of generic muscle properties (origin and insertion geometry, tendon slack lengths, optimal fiber lengths, etc.), and the assumption of a constant scapulohumeral rhythm fixing scapular upward rotation to humeral elevation. 49 52,56,57 , 58 This generic approach is useful for quantifying broadly the

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46 geometric and moment generating relationships of the shoulder muscles, but it would be difficult to use to muscle configuration and shoulder rhythm could be very different from an average idealized individual. Recent studies of sho ulders with RTSA have shown much greater scapular movement, or a smaller scapulohumeral rhythm, than is observed in healthy shoulders, 24,64 and a much wider range of joint center locations relative to the glenoid. 65 These two factors suggest subject specific shoulder geometry and movement patterns may significantly alter the muscle moment arms after RTSA. Therefore, the goal of this study was to use subject specific geometric and kinematic data for both healthy shoulders and shoulders with RTSA to implement subject specific musculoskeletal models and determine the range of shoulder muscle moment arm variation for arm abduction. These models will establish how current RTSA shoulders affect muscle moment arms relative to healthy shoulders, and provide objective relationships between surgical placement of the RTSA implant comp onents and the resulting muscle moment arms. Overview Previously collected kinematic data for healthy shoulders and shoulders with RTSA 26,27 were used to scale, configure and drive subject specific computational models. The patient specific models were us ed to simulate dynamic abduction and muscle analyses were performed to determine the muscle moment arms of the anterior, lateral and posterior aspects of the deltoid. 55,58 Kinematic Data We previously performed two fluoroscopy studies to quantify the kinematics of the humerus and scapula in healthy shoulders and shoulders with RTSA. 8,29 These three dimensional (3D) kinematics and subject specific bone and implant geometry data were used to configure and

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47 drive each patient specific model. Body segment lengths collected from motion capture were used to scale the thorax, scapula and humerus of each subject specific model. 29 RTSA Joint Configuration In our previous studies we utilized 3D reconstr uctions of bone from CT (Figure 4 1, 4 2) and 3D surface meshes of implants (provided by manufacturers) to perform 3D 2D i mage registration to measure either bone or implant positions and orientations during movement (Figures 4 4). 19 In shoulders with RTSA, we used th e same technique to measure 3D kinematics of the bones and implants in the same images. Since the implants are rigidly fixed to the bones, the relative position/orientation of the implants, corresponding to their surgical placement, can be determined as an average of the displacement over a series of fluoroscopic images (Figure 4 4 ,4 5). 65 computational mode rhythm of scapular motion linked to humeral motion. All measurements of joint geometry were taken from the center of the native glenoid (NG). The humeral offset (HO) defines the dist ance from the center of the native humeral head to NG, and the joint center (JC) defines the distance from the RTSA glenosphere implant center to NG (, Figure 4 3 , 4 6 and 4 7 ). The joint center change post RTSA was measured as the distance (JC HO). The hu meral offset for both normal and RTSA was measured as the distance HO NG. Thus changes of HO in the medial/lateral direction would be considered HO M/L (Figure 4 3 ,4 6 ). Joint Definition The OpenSim shoulder joint defined by Holzbaur et al. 55,58 was modified and defined as a twelve degree of freedom system in which both the scapula and humeru s were modeled as six degree of freedom universal joints with respect to the thorax. 58 The thorax was defined as the

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48 fixed reference frame. This assumption originally was made because the patients were instructed not to bend during fluoroscopy data collection. Each moving body rotational order was defined as a 3 1 2 sequence. Each degr ee of freedom was driven by the kinematic data collected for each patient. Following collection of the fluoroscopy data, it was found the radiology technician performing examinations of RTSA patients continuously moved the c arm gantry vertically to keep the shoulder joint view centered during patient movement. In order to re establish the trunk as a fixed frame of reference, a consistently identifiable bone landmark (apex of a rib) was tracked in all fluoroscopic images, and the vertical translations of a ll bodies were corrected for this motion of the reference system. Muscle Definitions The shoulder model consisted of 16 muscle actuators. Muscle attachment points, via 55,58 and were modified to include only the muscles that span the shoulder girdle, including anterior deltoid, lateral deltoid, posterior deltoid, supraspinatus, latisimus dorsi, rotator cuff muscles (infraspinatus, supraspinatus, teres minor, and subscapularis), pectoralis major, coracobrachialis. The lateral deltoid wrapping surface was modified to be a cylinder instead of an ellipse to increase the robustness of the model when the joint center is changed. All modifications of wrapping geometry remained consistent with the Holzbaur et al. 58 Patient Specific Model Scaling The modified OpenSim model was scaled for each of the 14 RTSA subjects using their in vivo motion capture marker data. Ma rker placement defined the humeral length, which was used to uniformly scale the upper extremity segments according to the long axis of the humerus. 58 All scaling was performed using the scaling tool in OpenSim. 55

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49 Model Moment Arm Analysis Arm abduction was simulated using the humeral and scapular 3D kinematic data collected in previous work. 8,29 The joints in RTSA subject specific models were configured to each arm pose during abduction for each subject and muscle moment arms were calculated. Statisti cal Methods Comparison of RTSA cohort and normal cohort deltoid moment arm means and standard deviations were performed using t wo way repeated measures ANOVA with t he level of significance chosen to be 0.05. to perform pair wise post hoc comparisons. Moment Arm Results JC in RTSA shoulders varied over a much greater range than in native shoulders ( F i gure 4 7 ). JC lateral offset in RTSA shoulders was at least 6 mm smaller than the smallest humeral head center la teral offset in the healthy shoulders. The center of rotation in RTSA shoulders was more inferior than in healthy shoulders. The range of anterior/posterior placement of the rotation center for RTSA shoulders was bounded by the range for normal shoulders. Similar patterns of muscle moment arm changes were observed for normal and RTSA shoulders, but the moment arms were statistically different between groups (Figure 4 4 and 4 5). The moment arm of the anterior deltoid was positive with the arm at the side a nd decreased monotonically, crossing zero (the point at which the muscle fibers pass across the joint center) between 40° 60° glenohumeral abduction (Figure 4 4, 4 5 ). The average moment arm of the lateral deltoid was nearly constant and positive in normal shoulders, but showed a decreasing trend with abduction in RTSA shoulders (Figure 4 4, 4 5 ). The posterior deltoid moment arm was negative with the arm at the side, and increased monotonically to a positive value with

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50 increasing glenohumeral abduction (Fi gure 4 4, 4 5 ). There were significant pair wise differences between normal and RTSA shoulder moment arms at 45 ° glenohumeral abduction for the anterior deltoid, 15 ° 45 ° for the lateral deltoid, and at all compared angles except 15 ° for the posterior delto id. Subject specific moment arm values for RTSA shoulders were highly variable compared to normal shoulders. Moment Arm Discussion The incidence of complications with RTSA has been reported between 19% to 68%. 2,6,48 A better understanding of how su rgical placement of RTSA implants changes muscle moment arms and muscle performance may aid in refinement of implant design and surgical technique to improve clinical and functional outcomes. 3,11 13, 32 34,53,54 However, there have been few direct shoulder muscle moment arm measurements reported after RTSA. 12,13,49 This paucity of measures in clinical cohorts motivated our study assessing deltoid muscle moment arms in 14 RTSA patients and 12 normal shoulders. We found deltoid muscle moment arms in shoulders with RTSA exhibited similar patterns of change over the arc of glenohumeral abduction, but that RTSA shoulders typically had lower deltoid muscle moment arms. As with a ny computer modeling study, a number of simplifications and limitations are important to state. First, we had the scapular and humeral bone (or implant) geometry in each bility to identify all of the muscle origins and insertions for each muscle on each bone. Thus, it was 58 OpenSim shoulder model, animated with subject specific humeral and scapular kinematics. The use of this scaled generic model may produce different muscle moment arms than a t ruly subject specific set of shoulder geometry. Second, we found the lateral deltoid muscle wrapping surface in the original model 58 produced

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51 discontinuous muscle moment arms when the joint center was moved according to the surgical cylindrical wrapping surface was developed for the lateral deltoid providing a surface that was more robust to joint configuration changes. This change in wrapping surface geometry had very limited effect on muscle moment arms for arm abduction movements, but will need to be carefully evaluated if the model is used for forward flexion or combined arm movements. Indeed, exploring how best to define custom wrapping surfaces for joints with geometry that differs significantly from the nominal model is an important area for future studies. We found that the center of rotation in RTSA shoulders varied over a much greater range than in natural shoulders, and that most variation was in the coronal plane ( F igure 4 7 ). Subject specific joint configurations were input to our computational m odel so direct relations between joint center location and muscle moment arms could be determined. Muscle moment arms in the RTSA group were significantly different (p<.05) from the normal group for the anterior, lateral and posterior deltoid, with some mo ment arms varying by more than 20mm across the RTSA group. In general, we found a more medial, inferior or anterior RTSA joint center resulted in a larger muscle moment arm, while a more lateral, superior or posterior RTSA joint center resulted in a smalle r muscle moment arm for the arm abduction activity. Comparing healthy with RTSA shoulder geometry, Boileau characteristically shifted in an inferior/medial direction and the change in C OR varies depending 17 . Our measurements of RTSA joint centers and humeral offsets are consistent with these earlier findings. We also provide joint center geometry in a normal shoulder cohort, which may provide useful reference values when considering how to reconstruct

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52 the joint geometry in diseased shoulders where cuff deficiency and osteoarthritis can alter the natu ral joint center. 65 The reported values for shoulder muscle moment arms vary widely. In normal shoulders, Holzbaur et al. experimentally measured anterior deltoid moment arms of 15 20 m m, while our healthy subject specific model analyses showed an average 24 mm anterior deltoid moment arm for abduction at 60°. In RTSA shoulders, Ackland 11 and Kontaxis et al. 28 found anterior deltoid moment arms of 13 mm, while our models showed an averag e 37 ± 15 mm anterior deltoid moment arm with the arm at the side. For the lateral deltoid in RTSA shoulders, previous studies have reported moment arms of 14 mm, Quental 20 mm, Ackland 40mm, Ackland 50 mm, Terrier 52 mm, van der Helm and 59 mm De Wilde as compa red to 22±7 mm from our models. It is likely that differences in measurement methods account for differences in moment arm values between our work and previous reports. For example, we used subject specific shoulder joint geometry and in vivo kinematics fo r each case, while previous work has used either simplified models of shoulder motion, e.g. an assumed scapulohumeral rhythm, or generic shoulder joint geometry. The goal of the study was to assess the effect of RTSA on deltoid muscle moment arms on a pat ient specific basis. We observed significant variation in deltoid muscle moment arms as a function of joint center changes, and also that RTSA shoulders generally showed smaller deltoid muscle moment arms than healthy shoulders. These two observations supp ort a conclusion that it may be possible to enhance deltoid muscle moment arms by placing the RTSA joint center in a patient optimized position to provide the best muscle moment generating capacity. Further studies are required to determine the sensitivity of muscle moment arm changes to changes in joint geometry, how moment arms vary over different functional motions, and how joint center changes affect shoulder muscle force production potential. Our study findings

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53 provide some objective relationships betw een reconstructed joint geometry and deltoid muscle moment arms that may be used to improve shoulder implant design, surgical techniques and rehabilitation strategies.

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54 Figure 4 1. Figure 4 2. Bone and implant coordinate definitions (A) Humeral stem, Glenosphere (B) Humerus and scapular bones.

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55 Figure 4 3. Implemented bone and implant configurations. Implant (dark grey) and Bone (white transparent)

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56 Figure 4 4. Three dimensional bone and implant meshes (orange and blue) registered to two dimensional fluoroscopy x rays

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57 Figure 4 5. Deltoid moment arms varied over the arc of shoulder abduction. (a) The anterior deltoid showed a decreased trend in both healthy and RTSA moment ar ms were significantly smaller by mid abduction. (b) The lateral deltoid was almost constant across the abduction arc in healthy shoulders, but was decreasing and smaller magnitude in RTSA shoulders. (c) The posterior deltoid moment arm increased from the i nitial negative values, but the magnitude was always greater in the healthy shoulders. The mean ±1 stdev is shown for normal (orange) and RTSA (blue) shoulders and pairwise differences are denoted by open circles.

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58 Figure 4 6 . Three dimensional bone and implant meshes (orange and blue) registered to two dimensional fluoroscopy x rays Figure 4 7 . Joint center (JC) and Humeral Offset (HO) for normal and reverse total shoulder arthroplasty patients.

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59 CHAPTER 5 HOW SENSITIVE IS THE DELTOID MOM ENT ARM TO JOINT CENTER CHANGES WITH RTSA? Abstract Reverse total shoulder arthroplasty (RTSA) is an increasingly common treatment for osteoarthritic shoulders with irreparable rotator cuff tears. Although very successful in alleviating pain and restoring some function, there is little objective information relating geometric changes imposed by the reverse shoulder and arm function, particularly the moment generating capacity of the shoulder muscles. Recent modeling studies of reverse shoulders have shown s ignificant variation in deltoid muscle moment arms over a typical range of joint center locations in shoulders with RTSA. The goal of this study was to investigate the sensitivity of muscle moment arms as a function of varying the joint center in three rep resentative RTSA subjects that spanned the anatomical range from our previous study cohort. We hypothesized there may exist a more beneficial joint implant placement, measured by muscle moment arms, compared to the actual surgical implant configuration. A 12 degree of freedom, subject specific model was used to represent the shoulders of three patients with RTSA for whom fluoroscopic measurements of scapular and humeral kinematics during abduction had been obtained. The computer model used subject specific in vivo abduction kinematics and systematically varied joint center locations over 1521 different perturbations from the surgical placement to determine moment arms for the anterior, lateral and posterior aspects of the deltoid muscle. The joint center wa s varied from its surgical position ±4 mm in the anterior/posterior direction, ±12mm in the medial/lateral direction, and 10 mm to 14 mm in the superior/inferior direction. The anterior deltoid moment arm varied up to 20 mm with center of rotation variat ions, primarily in the medial/lateral and superior/inferior directions. Similarly, the lateral deltoid

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60 moment arm demonstrated variations up to 13 mm, primarily with joint center changes in the medial/lateral and superior/inferior directions. The posterior deltoid moment arm varied up to 15mm, primarily in early abduction, and was most sensitive to changes of the joint center in the superior/inferior directions. The goal of this study was to assess the sensitivity of the deltoid muscle moment arms as a fun ction of joint configuration for existing RTSA subjects. High variations were found for all three deltoid components. Variation over the entire abduction arc was greatest in the anterior and lateral deltoid, while the posterior deltoid moment arm was mostl y sensitive to joint center changes early in the abduction arc. Moment arm changes of 13 20 mm represent a significant amount of the total deltoid moment arm. This means there is an opportunity to dramatically change the deltoid moment arms through surgica l placement of the joint center of rotation. Computational models of the shoulder may help surgeons optimize subject specific placement of RTSA implants to provide the best possible muscle function, and assist implant designers to configure devices for the best overall performance. Moment Arm Sensitivity Reverse total shoulder arthroplasty (RTSA) has become a popular treatment for shoulders with osteoarthritis and severe cuff tear arthropathy, but complication rates ranging from 19% to 68% (for implant loos ening, acromial fracture, scapular notching, frozen shoulder, dislocation, etc.) are still reported. 6 2,48 Different RTSA designs have now been developed by changing implant joint geometry to address these complications. 4,5,46,66 For example, the Grammont type design (e.g. Delta III, DePuy, Warsaw, IN) places the center of rotation medial and inferior to improve the deltoid moment arm, while the Frankle type design (RSP, DJO Surgical, Austin, TX) lateralizes the joint center with a more neutral glenosphere place ment. Clinical and biomechanical studies have been performed to support each design theory, but there is still a

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61 need for quantitative work to relate joint center changes and clinical/functional out comes. 3,12,13,49,67 Many cadaver and computational biomechanical studies have evaluated the influence of RTSA joint geometry changes on muscle moment arms and range of motion. 13,49 51 For example Roche et al. assessed the relationship between reverse shoulder design parameters and range of motion, impingement and stability. 3 Guti rrez reported a series of studies evaluating implant design and surgical factors on shoulder mechanics during different motions. 54,68 Henninger et al. made the case for in vitro biomechanical studies, stating computational models, cadaveric studies include the effects of soft tissue tension, patient 49 51,62 This type of study has the specific advantage of being able to precisely manipulate the joint geometry and to measure resulting changes in muscle moment arms. However, these studies are limited in that they were largely performed in typically healthy shoulders (which would not capture the anatomical characteristics of the diseased shoulder); they typically only f ocused on a single implant device within a study (so the range of joint variation was typically small); they assume a fixed pattern of movement between the humerus and scapula that may not represent what happens in cuff tear shoulders; and they typically u se implant placements that do not reproduce surgical placement in actual patients. In an effort to address some of these limitations, we sought to assess the sensitivity of deltoid muscle moment arms using patient specific data sets and models. Implant de signers and previous biomechanical studies agree that changing the joint center changes the shoulder muscle moment arms. The challenge remains to determine how the shoulder joint center should be placed in a specific patient to obtain the best possible mus cle moment arms for a range of activities. Therefore, the goal of this study is to use subject specific

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62 models of three RTSA patients to determine the sensitivity of their deltoid muscle moment arms to changes in RTSA joint configuration over the anterior/ posterior, medial/lateral and superior/inferior directions of the joint. Overview A 12 degree of freedom (DOF) patient specific three dimensional model was used to simulate dynamic abduction for 1521 surgical implementations for three different RTSA patie nts that spanned the range of patient body sizes from our previous work (small patient was 89% nominal size, medium patient was 98% nominal size, large patient was 105% nominal size). 58 Three dimensional kinematic fluoroscopy and motion capture data collected from our previous work was used to define the nominal joint geometry and to p rescribe humeral and scapular motions in each of the three subject specific RTSA models. 8,29 Each model was scaled according the humeral stem offset a long the medial/lateral, superior/inferior, and anterior/posterior directions. Deltoid moment arms were predicted and their sensitivity assessed in the medial/lateral, superior/inferior, and anterior/posterior directions. Data Collection Kinematic data we re collected using fluoroscopy and model image registration for each of our RTSA subjects performing arm abduction. 19,29 In addition, three dimensional motion capture data were collected for each subject performing a variety of activities. 29 These kinematic data were used to scale, configure and drive the subject specific computational models. 55,58 Subject A received an Equinoxe reverse implant with a medialized glenoshpere (Equino x, Exactech, Gainesville, FL) 3,4 , and Subjects B and C received a Reverse Shoulder Prosthesis with a lateralized glenoshpere (RSP, D JO Surgical, Austin, TX). 3,4 The model for each patient was

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63 scaled by their humeral length relative to the humeral length of the gen eric model (Subject A 89%, Subject B 98%, Subject C 105%). 58 Model Definition Our subject specific model was adapted from Holzbaur et al., 58 and consisted of a 12 degree of freedom shoulder model with 11 muscle actuators for the upper extremity. The fluoroscopic kinematic data were used to drive the motions of the humerus and scapula, making it unnecessary to assume any relationship between scapular and humeral motion. Shoulder Joint Geometry We utilized three dimensional (3D) reconstructions of bone and 3D meshes of the implants (provided by manufacturer, DJO surgical, Exactech Inc ) to perform 3D 2D image registration and measure the bone and implant positions and orientations (Figure 5 1). 4,19,69 4,70 These data were used to define the 3D placement of the implants in the bones, and also how the bones moved during dynamic shoulder abduction (Figure 5 2). 65 Having 3D motion data for each specific in vivo motions. All measurements of joint geometry were referenced to the native glenoid (NG). We defin ed two other points; the humeral offset (HO) measured the vector from the center of the native humeral head to NG, and the joint center (JC) measured a vector from the RTSA glenosphere center to NG ( Figure 5 2). The joint center change post RTSA w as measured as the difference between NG and JC (JC HO). The joint center for the normal was measured as the NG and HO (NG HO). Sensitivity Study A total 1521 variations in joint geometry were modeled and analyzed for each of three shoulders. The nominal j oint geometry represented the surgical placement of the RTSA implants

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64 in each shoulder. The humeral offset was varied from its nominal position ±4 mm in the anterior/posterior direction, ±12 mm in the medial/lateral direction, and 10 mm to +14 mm in the s uperior/inferior direction. Joint center variation ranges were based on the range of joint geometries measured in 14 RTSA subjects in our previous work. Dynamic abduction was simulated for each case and the deltoid moment arms were computed. 55 Moment Arm Sensitivity Results Moment arm variation was significant for all three heads of the deltoid over the 1521 different joint geometries and in all three RTSA patients (Figure 5 3). The anterior deltoid moment arm showed at least 10 mm variation, at least 6mm variation in the lateral de ltoid moment arm, and at least 10 mm variation of the posterior deltoid moment arm in each RTSA subject (Figure 5 3). Moment arm variations resulted from joint geometry changes in all directions, with the greatest variations observed in the largest subject , Patient C, and for superior/inferior variation of the joint center (Table 5 1). At initial glenohumeral elevation all patients showed at least 2mm variation in deltoid moment arms for each direction of joint center change. Anterior deltoid moment arm var iation was 5 6 mm in the anterior/posterior direction, 8 11 mm in the medial/lateral direction and 2 4 mm in the superior/Inferior direction across patients (Figure 5 4). All three patients showed the same pattern of moment arm change, with the greatest mo ment arms in early abduction and a decrease with increasing abduction. Note: Patients B and C show an abrupt change in anterior deltoid moment arm at 30° 40° glenohumeral abduction which likely results from an irregular interaction of the musculotendon u nit with the virtual wrapping surface in the Opensim model. Lateral deltoid moment arms varied 2 5 mm with anterior/posterior joint center changes, 2 7 mm with medial/lateral joint center changes, and 2 10 mm with superior/inferior joint center changes in the three RTSA subjects at initial glenohumeral abduction (Figure 5 5). All three

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65 subjects showed significant variation of lateral deltoid moment arm with joint center changes, but each subject appeared to have a different overall pattern of moment arm cha nge: Patient A showed an increasing then decreasing moment arm over the abduction arc, Patient B showed an almost monotonic decrease of moment arm over the abduction arc, and Patient C showed an almost constant lateral deltoid moment arm (Figure 5 5). The posterior deltoid moment arm varied 3 20mm with anterior/posterior joint center changes, 3 5 mm with medial/lateral joint center changes and 4 8 mm with superior/inferior joint center changes across RTSA subjects (Figure 5 6). All three arms showed increas ing posterior deltoid moment arms with increasing abduction, but the pattern of variation with joint center changes was different: Patient A showed greatest variations in early abduction, Patient B showed greatest changes in later abduction, and Patient C showed large variations in posterior deltoid moment arm over the entire abduction arc (with greatest variations due to AP joint center changes). Moment Arm Sensitivity Discussion Changes in RTSA implant designs have been shown to affect clinical outcomes. 3,4,49 51,71,72 But to date, n either biomechanical nor clinical studies have described the influence of joint geometry changes on the deltoid muscle moment arm the prime mover of the shoulder after d to such basic implantation methods and prosthesis design principles reflects the level of uncertainty 72 It is imperative to provide surgeons and implant designers with information to better understand the effects implant geometry and surgical placement have on deltoid moment arms to improving muscle performance and clinical outcomes in patients with RTSA. Many biomechanical studies have been reported, but most have been performed using generic configuratio ns or cadavers

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66 without incorporating patient specific information. 49,54,62,67,72 75 A recent assessment of healthy and implanted shoulders showed there was large inter subject deltoid moment arm variation for both normal and RTSA patients, highlighting the subject specific nature of shoulder mechanics and the opportunity for optimizin g individual treatments. This study was performed to quantify the sensitivity of deltoid moment arms to changes in RTSA joint geometry. We show that the deltoid moment arms are very strongly affected by the joint center location, supporting the prospect of subject specific treatment planning with sufficiently robust and validated shoulder modeling tools. This musculoskeletal modeling study has a number of important limitations to consider. First, the musculotendon wrapping surfaces defining the shoulder geo metry in the generic Opensim model were tuned for a specific joint center location and were not robust to the large joint center changes implemented in this study. 58 We modified the wrapping surface for the lateral deltoid so that it would maintain anatomic wrapping geometry that was robust to 1521 joint center changes. This modificati on was consistent for all three patients. This modification may have introduced regions of discontinuity (Figure 5 5), which also were dependent upon the with changing joint centers will likely provide more robust and accurate results. Second, our study assumes joint kinematics would remain the same and that all joint center variations would be clinically feasible for all joint center variations tested. Due to muscle pre tensioning, as well as other anatomic constraints, some of the simulated joint configurations may not be clinically achievable. Third, this study evaluated variations of deltoid moment arms only for arm abduction. Obviously, other arm motions ar e important for shoulder function and will need to be evaluated as part of a more comprehensive approach to optimal joint center location. Finally,

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67 although we may be able to predict implant configurations that provide increased deltoid moment arms, this a nalysis does not predict how shortening or lengthening the deltoid will affect its ability to generate force. Thus, a specific joint center may provide enhanced muscle moment arms, but lengthen the muscle beyond its effective region on the length/tension c urve. Deltoid muscle moment arms can be changed by varying the joint center in the anterior/posterior, medial/lateral, and superior/inferior directions. The anterior deltoid moment arm varied 2 11 mm over all joint center changes and subjects (Figure 5 4). Most of the variation occurred with superior/inferior and anterior/posterior joint shifts. Consistent with previous studies, the highest moment arms were produced by moving the joint center more medial and inferior. 3,5,17,51,76 The lateral deltoid moment arm varied most with superior/inferior and medial/lateral joint center shifts, and also was maximized with a medial and infe rior joint center placement. The posterior deltoid moment arm varied most with anterior/posterior and superior/inferior joint center shifts, and was maximized with an anteriorly and inferiorly placed joint center. The pattern of deltoid moment arm variati on was not consistent across the three subjects, suggesting shoulder size, initial joint center location, and subject specific kinematics may all have affected moment arms. For example, the largest lateral deltoid moment arm was found in the medium sized P atient B with the medialized RTSA design. Additional studies with a wider range of patient variation and a variety of activities will be required to identify how specific factors affect deltoid moment arms. Nevertheless, our analysis of a single activity w ith three subjects showed patterns of moment arm variation that were generally consistent with the literature, as medialized joint centers generally increased the deltoid moment arms, 5 and deltoi d moment arms at 0° abduction were consistent previous reports. 12,13,77 .

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68 Previous cadaveric studies and generic musculoskeletal models have provided objective information for understanding shoulder function and contributing to RTSA implant design. 3,12,16,32,46,49,50,52,67,71,72 The subject specific modeling capability we report permits variational studies to determine obje ctively the implant placement or configuration that will optimize the shoulder muscle moment arms for a range of relevant activities. This geometric analysis can be augmented to determine how muscle length changes will affect their force generation propert ies, so that both muscle moment arms and muscle forces can be chosen to provide the best joint moment capabilities. Ultimately, this type of tool could be used to support o each specific patient.

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69 Table 5 1. Peak variation of muscle moment arms due to joint center variation (All in Patient C). Muscle Anterior/Posterior (mm) Medial/Lateral (mm) Superior/Inferior (mm) Anterior Deltoid 8 @ 28° 5 @ 32° 20 @ 30° Lateral D eltoid 8 @ 33° 10 @ 31° 12 @ 45° Posterior Deltoid 15 @ 33° 6 @ 33° 15 @ 33°

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70 Figure 5 1. Three dimensional bone and implant meshes (orange and blue) registered to two dimensional fluoroscopy x rays Figure 5 2 . Description of native humeral he ad offset (HO) and implant joint center of rotation (JC) relative to the native glenoid center (NG). Implants are shown in dark grey and bones in transparent white.

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71 Figure 5 3. Variation of deltoid muscle moment arms as a function of joint geome try changes. Top: Patient A, small; Middle: Patient B, medium; Bottom: Patient C, large. (A) (B) (C)

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72 Figure 5 4. Variation of anterior deltoid moment arm as a function of changes in joint geometry. Blue Anterior/Posterior shifts of joint center; Red Superio r/Inferior shifts of joint center; Green Medial/Lateral shifts of joint center. Top: Patient A, small; Middle: Patient B, medium; Bottom: Patient C, large. (A) (B) (C)

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73 Figure 5 5 . Variation of lateral deltoid moment arm as a function of changes in joint geomet ry. Blue Anterior/Posterior shifts of joint center; Red Superior/Inferior shifts of joint center; Green Medial/Lateral shifts of joint center. Top: Patient A, small; Middle: Patient B, medium; Bottom: Patient C, large. (A) (B) (C)

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74 Figure 5 6. Variation of posterior deltoid moment arm as a function of changes in joint geometry. Blue Anterior/Posterior shifts of joint center; Red Superior/Inferior shifts of joint center; Green Medial/Lateral shifts of joint center. Top: Patient A, small; Middle: Patient B, medium; Bottom: Patient C, large. (A) (B) (C)

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75 CHAPTER 6 A NOVEL APPROACH TO ESTIMATION OF PATIENT SPECIFIC MUSCLE STRENGTH WITH REVERSE TOTAL SHOULDER ARTHROPLASTY Abstract Modern musculoskeletal modeling techniques have been used to simulate shoulders with reve rse total shoulder arthroplasty and study how geometric changes resulting from implant placement affect shoulder muscle moment arms. These studies do not, however, take into account how changes in muscle length will affect the force generating capacity of muscles in their post operative state. The goal of this study was to develop and calibrate a patient specific shoulder model for subjects with RTSA in order to predict muscle activation during dynamic activities. Patient specific muscle parameters were es timated using a nested optimization scheme calibrating the model to isometric arm abduction data at 0°, 45° and 90°. The model was validated by comparing predicted muscle activation for dynamic abduction to experimental electromyography recordings. A twelv e degree of freedom model was used with experimental measurements to create a set of patient specific data [three dimensional kinematics, muscle activations, muscle moment arms, joint moments, muscle lengths, muscle velocities, tendon slack lengths, optima l fiber lengths, peak isometric forces] estimating muscle parameters correspond measured strength. The optimization varied muscle parameters to minimize the difference between measured and estimated joint moments and muscle activations . This optimization yields a set of patient specific muscle parameters corresponding to the for a range of dynamic activities. The model calibration/optimization procedure was performed on arm abduction data for a subject with reverse total shoulder arthroplasty. Muscle activation predicted by the model ranged

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76 between 3% and 90% of maximum. The maximum joint moment produced was 20 Nm. The model replicated measured joint moments accurately (R 2 > 0.99). The optimized muscle parameter set produced feasible muscle moments and muscle activations for dynamic arm abduction, when calibrated using data from isometric force trials. Current modeling techniques for the upper e xtremity focus primarily on geometric changes and their effects on shoulder muscle moment arms. In an effort to create patient specific models, we have developed a framework to predict subject specific muscle parameters. These estimated muscle parameters, in combination with patient specific models that incorporate the dynamic muscle activation in novel tasks and, for example, predict how joint center changes with re verse total shoulder arthroplasty may affect muscle function. Patient Specific Muscle Strength Calibration Reverse total shoulder arthroplasty (RTSA) has grown in popularity since its approval for use in the United States in 2004. 45 There are now several RTSA designs on the market. 4,5,17,45,66,71 Ch anges in implant design are said to improve muscle efficacy. 4,5,72 Although biomechanical studies have assessed some of these claims using generic computer simulation and cadaveric models, the findings are limited in their clinical application as they do not incorporate patient specific anatomical information. 11,12,14,58,61,64,78 80 Recently developed musculoskeletal model s have shown significant subject to subject variation in shoulder muscle moment arms with RTSA ( ref Walker Chapter 4 and 5 ), suggesting the actual muscle lengths and activations may be similarly subject specific, and of interest to optimize placement of sh oulder implants. Previous studies have used musculoskeletal models and kinematic data to estimate muscle strength in the normal shoulder. 11,12,61,78 Zajac et al. developed a now popular Hill type

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77 model paper 81 of the musculotendon actuator that can be tuned to specific muscles by specifying five parameters (peak muscle force and the corresponding fiber length, pennation angle, maximum sho rtening velocity, and tendon slack length). 11,14,58,79,80 This model is commonly used but tuning the muscle parameters on a subje ct specific basis remains challenging, 14,61,64,79 and there only ar e a few reports using in vivo data with optimization methods to calibrate muscle parameters to patient specific data. 11,61,78,82 Advanced numerical optimization techniques using quadratic programming, nested optimization and non linear least squares have been used to estimate m uscle force generation and have shown great promise to address problems of this nature. 14,78,79 The goal of this study was to develop an optimization scheme to calibrate a subject specific musculoskeletal model to predict how changes in shoulder joint geometry affect the deltoid muscle, and its force gene ration and recruitment during arm abduction. A patient specific calibration method for tuning muscle parameters using static isometric force and electromyography data is described. The converged musculoskeletal model is then validated with experimental dat a for dynamic arm abduction. Predicted muscle activations and normalized lengths are used to demonstrate the model predictions are physiologically reasonable. Model Definition The three dimensional musculoskeletal model from the previous chapters 58 was simplified to include only the muscles and degrees of freedom (DOF) necessary to p erform dynamic abduction, resulting in a two DOF model (humeral abduction angle and flexion moment) including eight muscles: anterior deltoid (DELT1), lateral deltoid (DELT2), posterior deltoid (DELT3), teres minor (TMIN), teres major (TMAJ), and latissimu s dorsi (LAT1, LAT2, LAT3). A Hill type muscle model was used to represent each of the muscle segments. 58,82 The simplified upper extremity model was used to generate input parameters (muscle lengths, muscle

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78 velocities, muscle moment arms and joint moments) used in the muscle parameter estimation optimization. The exemplar patient used for the simu lation received a reverse shoulder prosthesis with a laterally offset glenosphere (RSP, DJO Surgical, Inc.). Arm Abduction Angles Joint angles for the shoulder girdle were specified from experimental fluoroscopic data and included the humerus and scapula moving relative to the thorax. 8,19 This is distinct from other reported models, where scapular motions were estimated or fixed to humeral motions. 11,14,58,61,78,79 Presumably, having the patient specific measured humera l and scapular motions will provide more accurate estimates of muscle moment arms for the abduction activity. Moment Arm Calculations Muscle moment arms were calculated using Opensim and then assumed constant when solving for joint moments within the opti mization framework. Muscle moment arms were specified for all 8 muscles during MVIC and dynamic abduction simulations. Muscle Parameter Estimation Initial muscle parameter values were taken from Holzbaur et al. and modified within our estimation framework . 58,83 Muscle lengths and velocities were calculated using the Opensim software using the subject speci fic kinematics for arm abduction. 55 Muscle Force and Activation Data Maximum voluntary isometric contraction (MVIC) forces (at the wrist) were measured using a dynamometer at 0°, 45°, and 90° of arm abduction. 29 Each trial was performed three times while force, arm position and EMG were recorded for the anterior, lateral and posterior aspects of the deltoid. 29 Shoulder kinematics data and MVIC loads were used to drive the subject specific model in Opensim, and the corresponding inverse dynamics moments were calculated. 55,58 A rigid tendon model was used to calculate the force for ea ch muscle. 84 These

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79 joint loads served as the experimental moments being tracked in Phase 1 of the muscle parameter estimation process. Inverse dynamics loads corresponding to experi mental dynamic abduction data were also calculated in Opensim and used in our Phase 2 muscle performance prediction validation step. Muscle parameter Estimation An optimization loop was created to systematically vary muscle activations and muscle paramet ers ( to reproduce the experimental abduction moment and track the EMG of three deltoid heads for Opensim simulation of the MVIC task. Initial parameters input to the optimization included muscle parameters (peak isometric force, optimal fiber length, tendon slack length, maximum shortening velocity, pennation angle, musculotendon length, musculotendon velocity), eight muscle moment arms, and the inverse dynamics abduction moment. The total shoulder moment, , was a summation over all eight muscles of the vector product of the muscle moment arm ( ) and muscle force ( ). 78 Muscle forces were determined from their predicted activations (Phase 1A) and muscle contractile dynamics. The inner level (Phase 1A) parameter estimation ut ilized quadratic programming to determine the set of muscle activations minimizing the difference between experimental and predicted joint moments for isometric abduction at 0°, 45° and 90°. 78 The outer level (Phase 1B) optimization utilized non linear least squares to vary muscle parameters to track experime ntal EMG data while matching experimental and predicted joint moments. 61 Once these constraints determined. To validate this muscle parameter optimization approach, we predicted the

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80 activa tion and force generation (Phase 2) of each muscle during dynamic abduction and compared the predicted activations with the experimentally measured activations for the subject. Phase 1 Patient Specific Muscle Strength Calibration Phase 1A: Optimization of muscle activations to reproduce joint moments calculated from experimental data. Utilizes quadratic programming. Phase 1B: Optimization of muscle parameters to minimize the difference between the predicted and experimental muscle activations during d ynamic abduction. Utilizes non linear least squares. Phase 1A Optimizer Cost Function Phase 1A of the optimization utilized the quadratic programming optimizer to find a vector x (muscle activation) that minimizes the quadratic function (1), subject to the linear constraint ; such that the experimental joint moments were reproduced. Quadratic programming provides a global solution for our problem. This solution was deemed physiologically feasible once the predicted activation for each muscle was betw een 0 and 1. Reserve actuation was implemented to guarantee that a numer ically feasible solution was always achieved. Phase 1A: MVIC Moment Calibration Initial muscle activations were predicted in phase 1A using quadratic programming as shown above. The q uadratic function (1) was a surrogate for minimization of metabolic cost. The P hase 1A optimization was able to solve for a feasible solution ( muscle activations between 0 and 1, normalized muscle lengths of 0.5 1.5 , and within 2.5 times of initial muscle parameters). Initial guesses for the peak isometric force, optimal fiber length and tendon slack length were taken from Holzbaur et al. 83 Note that the muscle parameters, inverse dynamics moments, ( 6 1)

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81 muscle moment arms, muscle lengths and muscle velocities were passed into quadratic programming as constants and were not varied within in the P hase 1A optimization . To ensure that the muscles were operating within their optimal length they were bounded to stay between 0.5 and 1 . The stereotypic muscle force length curve (Figure 6 1) captures the active and passive force generating capability of a muscle, 61,82 and shows the active force generating capability of a muscle occurs with normalized lengths between 0.5 and 1 . The summation of our predicted moments ) to equate our experimental moments ( ) was a linear equality that was satisfied in our optimization (6 2) . T he predicted joint moment is calculated 6 3 where muscle activations ( ), p eak isometric force ( , optimal fiber length and tendon slack length are the known muscle moment arms, lengths and velocities. Muscle contraction dynamics wer e governed by Hill type muscle properties. 81 The excitation to activation dynamics were performed by using new excitation activation co nversion technique that incorporated a time delay and a nonlinear segment which was represented as a nonlinear first order differential equation. 85 I n order to sum forces a muscle contraction dynamics model using a rigid tendon model was used to convert our activations to force. 82 Once an optimized numerically feasible solution was found with quadratic programming, muscle activations then served as inputs into phase 1B optimization. = (6 2) (6 3)

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82 Phase 1B Optimizer Cost Function Phase 1B outer level optimization estimated muscle parameters that correspond to linear cost function (4) that was minimized; where is a non linear function. Non linear least squares allowed us to vary multiple muscle parameters while constraining the activations of the deltoid muscle to track the experimental data. Our cost function minimized the difference between meas ured and predicted deltoid activations, penalized non cost lowering variations of muscle parameters, and minimized reserve actuation. This optimizer was chosen so that the lower and upper bounds for muscle parameters could be specified to guarantee physiol ogical predictions of the muscle parameters (5). Phase 1B: MVIC EMG Calibration Phase 1B optimization serves as the outer loop of the nested optimization. The Phase 1B cost function guarantees that each muscle parameter estimate satisfies the cost funct ion (5) and has a feasible solution of muscle activation predictions (0 to 1 muscle activation). The cost function (5) was minimized to solve for an ideal set of muscle parameters corresponding to the allows us to track the MVIC EMG activations where is the predicted activation from the optimizer, is the expression was used to penalize changes of the muscle parameters that do not affect the overall cost function, and are reserve actuators (6 4) = + (6 5)

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83 for each joint moment built into our optimization to guarantee a feasible solution for our nested optimization. Phase 1 optimization yields a set of muscle parameters that corresponds to the predictions. Phase 2 Mus cle Activation and Performance Prediction Using the inner level optimization developed previously , quadratic programming was run to predict activations for dynamic abduction while tracking the joint moments ( equation 1 and 2; Trial not used in our calibrat ion process). The predictions were then compared to experimental measurements to validate our optimization scheme. Four optimization schemes were performed to eliminate the need for reserve actuation to track both abduction and flexion joint moments (Fig ures 6 5 and 6 7). Abduction and flexion joint moments were tracked to different levels of accuracy. The optimized set of muscle parameters was used for each of the four cases. Case 1 modified the model inputs to our optimization to only use the deltoid m uscles to track the abduction joint moment (Top Left). Case 2 modified the model inputs to only use the deltoid muscles to track the abduction and flexion joint moments (Top Right). Case 3 modified the model inputs to use the deltoids, teres minor, teres m ajor, and latissimus dorsi to track abduction joint moment (Bottom Left). Case 4 modified the model inputs to to use the deltoids, teres minor, teres major, and latissimus dorsi to track abduction and flexion joint moments (Bottom Right). This was perform ed to account for possible loss of muscle force generation due to the removal of certain muscles. Patient Specific Muscle Strength Calibration Results Phase 1: Patient Specific Muscle Strength Calibration Joint moment predictions for phase 1A matched the experimental data (R 2 =0.99, Figure 6 2 ). All predicted muscle activations were within the physiologically feasible bound ( 0 to 1 ,

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84 Figure 6 3). Predicted maxi mum muscle activations for the anterior and lateral deltoid muscles closely match the ir correspon ding experimental measure ments (Table 6 1). The predicted normalized muscle lengths also fell within the optimal performance region ( 0.5 and 1 , Figure 6 3 ) . Reserve actuator compensa tion did not exceed 1.2 Nm for P hase 1 optimization. Maxi mum shoulder joint abduction moment produced for isometric trials was 30 Nm. Muscle parameter predictions varied from their initial guesses as tuned by the p hase 1B optimization , while p eak isometric force fixed at 2.5 times literature values across all m uscles (Table 6 2) . 58 All converged values were between the physiological bounds set within the optimization (Table 6 2). Phase 2: Patient Specific Muscle Performance Prediction Four different optimization predictions were performed to best account for abduction and flexion moment tracking (Figure s 6 5 and 6 7). Muscle activations for dynamic abduction were predicted using the converged muscle pa rameters from the P hase 1 optimization (Figure 6 8). The max imum dynamic abduction moment was found to be 19.1 Nm. Joint moment tracking for cases 1 to 4 showed a variation in the accuracy of th e muscle activation predictions to reproduce the abduction and flexion moments (Figure 6 5). The best tracking of joint moments w as achieved in Case 3, when tracking only the shoulder abduction moment with the eight muscle model (R 2 =0.99, Figure 5 , B ottom left ). Muscle activations for Cases 1 to 4 were within the feasible range (0 to 1, Figure 6). Normalized muscle operating lengths were found to be in the optimal range ( 0.5 and 1 , Figure 6 7). Muscle activation for the heads of t he deltoid were comparable to experimental data (Figure s 6 8 and 6 9). Initial trends between the lateral and posterior deltoid seemed to correlate well with the experimental activation s (Figure 6 8). Correlations with predicted and experimental muscle activations with modified muscle moment

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85 arms yielded more consistent results (Figure 6 9). Adding the latissimus dorsi contributed minimally to o verall joint moment summation ( Figure 6 5 B ottom, <.3 Nm). Reserve actuation was utilized at no more than 10% of the overall joint moment (max reserve = 1.95 Nm). Muscle Strength Calibration Discussion Shoulder muscle performance after RTSA induced length and tension changes is a topic of high cur rent interest. Current methods for predicting muscle function utilize theoretical kinematic and kinetic data and optimization techniques to estimate patient specific muscle strength. 14,58,61,78,79,86 In validating the Delft Shoulder and Elbow Model for two shoulder hemi arthroplasty patients, Nikooyan et al. showed model scaling changed their dynamic task results by up to 23%. 79 Clearly, to best predict muscle function for a specific patient, we must have a method to calibrate our model to that patient. No framework currently exists to estimate muscle performance post RTSA on a patient specific basis. Our study focused on using measured patient data and computational methods to calibrate a model for predicting patient specific shoulder muscle activity after RTSA. Several assumptions and limitations are relevant to the results of this study, including the use of a single subject example, a limited set of isometric calibration poses, a limited set of dynamic test activities, and a number of simplifying model assumptions. All of these limitations can be addressed with additional data or effort and have little influence on the technical merits of the study. The major technical limitation of the study relates to the construction of the basic musculoskeletal model. We adapted for this project a generic model originally developed with many anatomical properties derived from cadavers. 11,13,51,53,58 We modified this model by uniformly scaling it to a spec specific kinematic and kinetic information. Uniform scaling affects all of the muscle and soft tissue properties, musculotendon wrapping surfaces and muscle origin/insertion sites. 58,83 This

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86 scaled anatomy approach is commonly used 11,13,14,58,79 because determining the details of subj ect specific anatomy is prohibitively time consuming and costly. Of particular relevance for this study, musculotendon wrapping surfaces are scaled according to subject size but they are not shifted relative to the bones with the RTSA joint center. This ma y shift the muscle moment arm patterns and introduce discontinuities when joint centers are moved far from their normal anatomic locations. For example, the model was able to track inverse dynamics joint moments over much of the abduction activity, but fa iled to track joint moments in the middle of the dynamic abduction motion when deltoid muscle moment arms were small and muscle moments could not balance joint loads. As a result, we were forced to employ reserve actuators in the model to ensure complete t racking of the joint moments. These observations make clear the need to explore methods for enhancing musculotendon wrapping surfaces, moving them with non anatomic joint centers, and validating the associated muscle moment arm calculations in future work. Validation of musculoskeletal models is often qualitative and indirect. Charlton et al. dimensional model of the upper limb and shoulder girdle. In the absence of in vivo experime ntal data this is restricted 14 Nikooyan et al. validated their model by comparing predicted and in vivo measured joint reaction loads, 79 but they could not provide a direct comparison of their predicted muscle activations with measured values. In this st udy, we 29 The Phase 1 patient specific muscle strength calibration yielded a calibrated set of muscle parameters and activations MG (Table 6 2). We were able to track both humeral joint moments and match the EMG for isometric abduction at 0°, 45°, 90° (Figure 6 2, Table 6 1). We

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87 predicted anterior and lateral deltoid, and upper trapezius muscle activations that compared closely with t he experimental isometric EMG measurements (Table 6 1). The predicted activation for the posterior deltoid did not match well, suggesting it may be useful to add different postures over the gamut of arm motions to provide a more robust tuning method. Normali zed muscle lengths for the isometric tasks were within the optimal region (Figure 6 4). Maximum isometric moments (28 40 Nm) were consistent in magnitude with Holzbaur et al., who reported 50 75 Nm moments for isometric abduction at 0°, 45°, and 90° in vit ro with anatomically normal specimens and assumed scapulohumeral kinematics. 58,83 The model was able to determine feasible solutions to reproduce joint moments for dynamic abduction for the four cases using different muscles and inverse dynamics loads (Figure 6 5). Predicted muscle activation was found to vary based on the moments tracked as well as the n umber of muscles included within the optimization (Figure 6 6 ). Predicted normalized muscle lengths were all within the optimal force production range (Figure 6 7). Our predicted activations for lateral and posterior deltoid matched the initial trend of th e experimental EMG data (up to 50% of abduction activity), but there were dramatic differences between predicted and measured muscle activity in the middle of arm abduction (Figure 6 8). 29 This nonphysiologic behavior resulted from the deltoid muscle moment arms crossing zero, prompting overactuation of other muscles to balance the inverse dynamics loads. This behavior likely results from the use of generic deltoid wrapping objects and may be improved by refinement of the wrapping surfac es. Patient specific wrapping surfaces are not easily measured, so the location and shape of the wrapping surfaces may need to be added design variables in the Phase 1B optimization framework to produce muscle moment arms and lengths that are robust to joi nt center changes. The generic wrapping surfaces can be used to obtain initial moment arm estimates with our

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88 patient specific joint configuration and kinematic data. As an example, the wrapping surfaces were manually adjusted to provide better moment arms and more physiologic muscle activation predictions were obtained (Figure 6 9). A nested optimization approach was developed to calibrate a musculoskeletal shoulder patient specific data to tune muscle parameters while satisfying dynamic constraints. This framework uses patient specific data (muscle moment arms, lengths, velocities, etc.) to calibrate a model that can then be used to estimate shoulder muscle performa nce in different activities. Further model refinements will improve muscle activation predictions, but the basic framework has been developed to calibrate the model to patient specific inputs (Figure 6 8 ,6 9). By automating this approach to subject specifi c musculoskeletal modeling, we hope to reliably and robustly predict muscle performance changes as a function of shoulder implant design and surgical placement to provide surgeons with objective information to enhance their treatments.

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89 Table 6 1. Optim ized Max imum Activations from Tracked EMG at 90° (P hase 1A ) Muscle Initial Experiment Optimized Anterior Deltoid .03 .73 .76 Lateral Deltoid .22 .96 .98 Posterior Deltoid .24 .32 .05 Upper Trapezius .18 .82 .82 Table 6 2. Normalized Values of Muscl e Parameters Compared to Initial Estimate s Muscle Anterior Deltoid 250% 119% 128% Lateral Deltoid 250% 113% 85% Posterior Deltoid 250% 93% 92% Teres Minor 250% 99% 99% Teres Major 250% 126% 127% Upper Trapezius 250% 1 33% 86% Figure 6 1. Normalized force length relationships for each muscle . 82

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90 Figure 6 2. Isometric joint moment predictions from P hase 1 muscle strength calibration. Black e xperimental ly measured moments ; Red predicted moments. Figure 6 3. Pr edicted muscle activat ions for P hase 1 muscle strength calibration.

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91 Figure 6 4. Predicted normalized muscle length s for isometric trials.

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92 Model Z moment tracking Z X moment tracking Deltoid M uscles Anterior Deltoid 1 Lateral deltoid 2 Posterior deltoid 3 Teres m inor Teres major Latissimus dorsi Figure 6 5. Phase 2 moment tracking for dynamic abduction (Black Experimental joint moments, Red moment summation from muscle contributions). Top left 3 muscles, abduction moment, Top right 3 muscles, abducti on and flexion moment, Bottom left 8 muscles, abduction moment, Bottom right 8 muscles, abduction and flexion moment

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93 Model Z moment tracking Z X moment tracking Anterior Deltoid 1 Lateral deltoid 2 Posterior deltoid 3 Anterior Deltoid 1 La teral deltoid 2 Posterior deltoid 3 Teres minor Teres major Latissimus dorsi Figure 6 6 . Phase 2 muscle activation prediction for dynamic abduction. Top left 3 muscles, abduction moment ; Top right 3 muscle s, abduction and flexion moment; Botto m left 8 muscles, abduction mome nt; Bottom right 8 muscles, abduction and flexion moment . Model Z moment tracking Z X moment tracking Anterior Deltoid 1 Lateral deltoid 2 Posterior deltoid 3 Teres minor Teres major Latissimus dorsi Figure 6 7. Phase 2 muscle normalized length regions for dynamic abduction.

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94 Figure 6 8. Phase 2 muscle activation predictions for dynamic abduction Figure 6 9. Phase 2 muscle activation predictions from modified moment arms for dynamic abduction.

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95 CHAPT ER 7 HOW SENSITIVE IS DELTOID PERFORMANCE TO JOINT CENTER CHANGES WITH RTSA? Abstract Reverse Total shoulder arthroplasty (RTSA) has become an increasingly used solution to treat osteoarthritis and cuff tear arthropathy. Though successful there are still 1 0 to 65% complication rates reported for RTSA. Complication rates range over different reverse shoulder designs but a clear understandi ng of implant design parameters that cause complications is still lacking within the literature. In efforts to reduce com plication rates (Implant fixation, range of motion, joint stiffness, and fracture) and im prove clinical/functional outcom es having to do with proper muscle performance we have employed a computational approach to assess the sensitivity of muscle performan ce to changes in RTSA implant geometry and surgical placement . The goal of this study was to assess how changes in RTSA joint configuration affect deltoid performance. performance. This approach was automated to assess changes in muscle performance over 1521 joint configurations for an RTSA subject . Patient specific muscle moment arms, muscle lengths, muscle velocities, and muscle parameters served as inputs into the muscle predicti on scheme. We systematically varied joint center locations over 1521 different perturbations from the in vivo measured surgical placement to determine muscle activation and normalized operating region for the anterior, lateral and posterior aspects of the deltoid muscle. The joint center was varied from ±4 mm in the anterior/posterior direction, ±12mm in the medial/lateral direction, and 10 mm to 14 mm in the superior/inferior direction (Table 6 2). Overall muscl e activity varied over 1521 different implant configurations for the RTSA subject . For initial elevation the RTSA subject showed at least 25 % deltoid activation sensitivity

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96 in each of the directions of j oint configuration change. P osterior deltoid showed a maximal activation variation of 84 % in the superior/inferior direction . Deltoid activation variations lie primarily in the superior/inferior and anterior/posterior directions. An increasing trend was seen for the anterior, lateral and posterior deltoid ou tside of the discontinuity seen at 28°. Activation remained below 4Nm . The most optimal deltoid normalized operating length was implemented by changing the joint con figuration in the superior/inferior and medial/lateral directions. Current shoulder models utilize cadaver information in their assessment of generic muscle strength. In adding to this literature we performed a sensitivity study to assess the effects of RT SA joint configurations on deltoid muscle performance. With this information improvements can be made to the surgical placement and design of RTSA to improve functional/clinical outcomes while minimizing complications. Muscle Activation and length Sensi tivity Reverse total shoulder arthroplasty (RTSA) remains a difficult surgery to implement due to the lack of information provided to assess overall placement of the implant and its corresponding effects on muscle performance. 2 Misplacement of the implant may lead to a variety of mechanical complications (scapular notching, acromial fracture, glenoid loosening, etc ) . 48 . Furthermore specific complications are arising related to impl ant type such as disassembly of humeral or glenoid component, and dissociation of the polyethylene humeral plate. 6 Cheung et al . states that they believe knowledge of various design affects may be an important factor in avoiding and managing RTSA. 2 To that point knowledge of how deltoid performance is affected by RTSA implant changes has the potential to improve functional/clinical outcomes while minimizing complications.

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97 Current literature lacks information that can assess deltoid muscle balancing as it relates to geometric changes in RTSA . Current biomechanical studies assess deltoid moment arms post RTSA in a cadaver or computational framework setting. 3,13,16,49,51,87 While t aking the insight gained from these studies it was noted that a patient specific sensitivity study to assess deltoid muscle balance had not been performed. Literature has foreshadowe d the need for patient specific computational modeling to improve i mplant design and surgical practice. 3,51,68,72,79,87,88 Although this is clear a clinical data set that is ideal to calibrate and valida te a shoulder model to a patient was still not found for a cohort size larger than 2. 79 Nikooyan et al. shows much promise in performing patient specific modeling but still has a high overall cost of implementation and is highly invasive for the patient. Our previous work devel oped a novel approach to calibrate patient specific muscle mom ent arms and muscle strength to predict muscle performance post RTSA during dynamic abduction for a given patient . We now seek to assess the sensitivity of the deltoid muscle performance to changes in joint configuration for the same RTSA patient. Proper deltoid balancing (tensioning/lengthening) is key to improving functional/clinical outcomes post RTSA. Being able to predict deltoid muscle performance as a function of joint configuration changes post RTSA provides useful information in placement and choi ce of the implant pre RTSA . The goal of this study was to assess how changes in RTSA joint configuration affect the sensitivity of deltoid performance (recruitment and force production). Model Definition A three dimensional computational model that was m odified from Holzbaur et al . to mode l a subject with a reverse shoulder prosthesis (RSP). 4,58 The model had 6 m uscle actuators and 2 degrees of freedom (DOF). The model incorporated muscle actuators to represent the anterior deltoid, lateral deltoid, posterior deltoid, teres minor, teres major and the upper

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98 trapezius. A Hill type muscle was used to represent each actuator. 81 The abduction and flexion DOF were incorporated within the model. The model was subject specific in nature as it was scaled, configured and driven using patient specific fluoroscopy and motion capture data. In efforts to model real life motion we measured both scapular and humeral kinematics in vivo in our previo us studies (ref chapter 2, 3) . The model was used to generate the muscle moment arms, experimental joint moments, muscle length, muscle velocity as inputs for our muscle performance prediction. 55 Clinical Data Collection Maximal voluntary isometric contraction (MVIC) torque curves were measured usin g a dynamometer. 29 The torque angle curves were col lected for abduction at 0° , 45 ° , and 90 °. Each trial was performed three times. Using our previous kinematic data in conjunction with the MVIC loads t he activity was si mulated in Opensim and corresponding i nverse dynamics moments were calculated for the experimental data set 55,58 . These loads served in our previous . Inverse dynamics loads corresponding to our experimental dynamic abduction data were also calculated and used in our muscle performa nce predictions. Muscle excitations for the anterior, lateral, and posterior deltoid were measured using electromyography for 0, 45, 90 MVIC abduction and dynamic abduction. 29 Joint Space Sampling and Data Inputs Original patient joint configuration for the RTSA patient was measured using three dimensional to two dimensional registration techniques(Figure 7 1). 19,29 A 1521 joint our previous work ( ref chapter 4, 5; Figure 7 1 and 7 2). The humeral offset was varied from its surgical position ±4 mm in the anterior/posterior direction, ±12mm in the medial/lateral

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99 direction, and 10 mm to 14 mm in the superior/inferior direction (Table 7 1). Dynamic abduction was then simulated for each of the 1521 RTSA subject joint configurations to predict deltoid mus cle moment arms, lengths, velocities, and inverse dynamics loads as a function of each joint configuration using the Opensim software 55 . These parameters served as inputs into our muscle performance estimation script. Patient Specific Muscle Strength Calibration An optimization appr oach was developed in our previous work to systematically vary muscle activations and muscle parameters ( to reproduce the maximal voluntary isometric contractions (MVIC) moments for 0°, 45°, 90° abduction and track the EMG of the deltoid heads for isometric abduction (ref chapter 6). Inputs to the optimization consisted of musc le parameters (peak isometric force, optimal fiber length, and tendon slack length, max shortening velocity, and pennation angle, musculotendon length, musculotendon velocity), muscle moment arms (anterior deltoid, lateral deltoid, posterior deltoid, teres minor, teres major, upper trapezius), experimental abduction and flexion moments. A rigid tendon model was used to calculate the forces for each muscle. 82 Activation dynamics were used to compare experimental EMG to predicted activations. 85 The inner level optimization utilized quadratic programming optimizer to estimate muscle activations to minimize the difference between experimental and predicted MVIC joint moments for isometri c abduction at 0, 45, 90°. 78 The outer level optimizat ion utilized the non linear least squares optimizer to vary muscle parameters within our optimization to track experimental EMG data for the patient. 61 After running our optimization scheme we were able to e strength (ref chapter 6). The corresponding muscle parameters were held constant as inputs to the muscle performance prediction framework for each of the 1521 different perturbations of joint configuration post RTSA .

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100 Muscle Performance Prediction Muscl e activation and normalized length were predicted for the 1521 RTSA joint configurations during dynamic abduction in an optimization scheme using quadratic programming. The quadratic function (6 1 ) was minimized to simulate the minimization of metabolic c ost. The peak isometric force, optimal fiber length and tendon slack length were taken from our patient specific muscle strength calibration described above. Note that the muscle parameters, inverse dynamics moments, muscle moment arms, muscle lengths and muscle velocities were passed into quadratic programming as constants and were not varied within in the optimization. Muscle activations were varied to minimize the quadratic function. The summation of our predicted moments ( ) to equate our experimental moments ( ) was a linear equality that was satisfied in our optimization: = ( 6 2). The predicted joint moment is calcul ated as ( 6 3) where muscle activations ( ), Peak isometric force ( , optimal fiber length and tendon slack length , are the known muscle moment arms, lengths and velocities . Our optimization yielded 1521 different muscle activation ( ) and normalized operating lengths profiles to now assess how changes in RTSA joint configuration affect muscle performance. Muscle Activation and Length Sensitivity Results Overall muscle activity varied over 1521 different implant configurations for the RTSA subject (Table 7 2, Figure 7 3 and 7 4). At initial glenohumeral elevation at least 25 % in variation for the deltoid acti vation sensitivity was observed across joint configuration directions . Anterior deltoid maximal activation variation was 70 % in the anterior/posterior direction (Figure

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101 7 3, Table 7 2). The maximal Lateral deltoid activation variation was 60 % in the anteri or/posterior direction during dynamic abduction (Table 7 2, Figure 7 3, 7 4 ). The anterior/posterior and medial/lateral directions were the primary source of variation in the lateral deltoid. The posterior deltoid maximal activation variation was 84 % acros s directions of joint configuration change (Figure 7 3, 7 4). Deltoid a ctivation sensitivity were found primarily in the superior/inferior and medial/lateral directions . An increasing trend was seen for the deltoid outside of the discontinuity seen at 28°. experimental data (Figure 7 3, Blue line). Reserve actuation was minimally used (<1 Nm) for all joint angles except at 28° and 45 ° . After observing deltoid activation changes it was necessary to see how t he deltoid normalized operating length (performance) varied as a function of RTSA joint configurations (Table 7 3). The Anterior deltoid normalized length variation ranged .05 .08 across joint configurations changes. The lateral deltoid normalized length var iation was .10 across joint configuration changes. The posterior deltoid normalized length variation range d .08 .10 across the joint configuration (Figure 7 5). The most optimal normalized length was implemented by changing the joint configuration in the s uperior/inferior and medial/lateral directions. Muscle Activation and Length Sensitivity Discussion There is a growing need for insight into how RTSA joint configuration changes (geometry and placement) affect musc le performance so improvements can be mad e to implant design and surgical placement . Current cadaveric and computational shoulder studies have focused on assessing range of motion, muscle moment arms and other mechanical factors to predict possible clinical/functional outcomes . 12,49 51,54,71 These studies have provided useful support for the design and placement of RTSA implants. For example Gutiérrez et a l . found that a more lateral center of rotation promotes an increased impingement free range of motion during

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102 abduction. 54 To add to the clinical understanding a computational sensitivity study was performed using a subject specific mode l in conjunction with a previously validated optimization approach to predict the variation of the deltoid muscle activation and normalized operating length to changes in RTSA joint configuration. In performing the study several limitations had to be cons idered. First we note that generic wrapping objects represent ative of soft tissue wrapping were scaled and used to assess muscle moment arm predictions in a patient . Although this is the current state of the art in computational biomechanics it would be i deal to be able to measure in vivo wrapping surface changes within that patient . This limitation was found to yield a discontinuity at 28° of glenohumeral motion in our predictions . This was not critical to the overall prediction s of deltoid activation and normalized operating length. We also were limited by imploring the use of reserve actuation in our optimization scheme to ensure complete tracking of the experimental joint moments within our optimization scheme (Figure 7 6) . Reserve actuation did not e xceed 20% (4 Nm) of the experimental moments being tracked. We also most note that our experimental moments were calculated from experimental kinematics using the inverse dynamics tool within Opensim . 55 An assumption was also made that all 152 1 positions could be reach ed within sur gery. Thi . Considering these limitations gave a better understanding of our results. Deltoid muscle activation was predicted during dynamic abduction for each of our 1521 simulated surgical joint configurations . The anterior deltoids activation sensitivity primarily lied in the anterior/posterior directions and superior/inferior directions. This is expected as most of the muscle fibers of the anterior deltoid lie in the sagittal plane. Alth ough the muscle activation increased as a function of varying the joint configuration in the anterior direction , variations of

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103 22 % of the normalized activation are still notable in other directions of joint configuration change (Table 7 2). The anterior delt oid activated from 35 % to 1 00% in the last third of the activity to compensate for losses in lateral and posterior deltoid activation (Figure 7 3A). The lateral deltoid showed increased activation as the joint configuration was more laterally placed. Altho ugh that was observed the primary sensitivity of lateral deltoid activation was the superior/inferior direction (Figure 7 3B). Aside from the discontinuity in our data at 28° the lateral deltoid had an overall increasing trend and was compared to the trend of what we observed from our experimental deltoid measurements ( ref chapter 6; Figure 3B; Blue line). 29 The posterior deltoid also showed this same behavior while primarily having its variation in the superior/inferior and medial/later al directions (Figure 7 3C) . Trends of our muscle activation predictions were semi consistent with our nominal experimental deltoid activation measurements for the subject (Figure 7 3, Blue line) . The largest opportunity for variation of muscle recruitment was found in the lateral and posterior deltoid (.84 and .7). Minimizing activation to perform a task would be the ideal criteria for finding the ideal joint configuration suited for the subject to accomplish dynamic abduction. To utilize the most effectiv e muscle activation the normalized lengthening variations for each muscle were predicted. The anterior deltoid showed a shortening trend over abduction and varied primarily as a function of anterior/posterior and medial/lateral changes. The lateral deltoi d normalized length trend behaved much the same but showed a variance .10 with less of a negative sloped trend. Differing from t he anterior and lateral deltoid, the posterior deltoid normalize length had a slight lengthening trend. It ranged from .08 .10 i n variation across any given direction of RTSA joint configuration change. Muscle normalized length predictions for the deltoid showed that increased force production corresponds to superior/inferior and medial/lateral joint configuration changes. Our norm alized deltoid

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104 operating length predictions were comparable to literature as Pandy et al . found normalized deltoid operating lengths to fall within 0.5 to 1 for a healthy subject. 61 Note that we modeled the shoulder of an RTSA subject in 1521different configurations so compariso n to literature was unachievable as a comparable data set did not exist. The sensitivity of the deltoid muscle activation and performance was predicted as a function of joint configuration changes for an RTSA subject. Current lite rature has not focused to assess deltoid performance over the RTSA joint space and thus revealed an opportunity to grow understanding in deltoid performance post RTSA. 3,49,51,79 By implementing our framework we were able to assess d eltoid muscle performance over 1521 simulated s urgical im plantations of RTSA . Although this study has provided useful insights we found that improving soft tissue wrappin g will improve the confidence of our findings. The deltoid activation and normalized operating length displayed a discontinuity at 28° and 40° as a cause of this limitation. Despite this limitation the overall reproduction of our experimental joint moments at best was while having low reserve actuation at no higher than 4 Nm (Figure 7 6). Our reserve actuation was minimal (>1Nm) for all joint angles except at 28° and 45 ° . It should also be noted that moving the RTSA joint configurations in the medial and inferior directions drastically lowered the need for reserve actuation as well as lowered the deltoid muscle activations. Our findi ngs showed that there were more ideal solutions than the surgical implementation. Our current predictions bring insight into how RTSA surgical p lacement and implant choice affect the deltoid activation and performance . It is our inference that this framewo rk can be applied to optimize deltoid balancing to improve muscle performance on a patient specific basis to ideally promote better clinical/functional outcomes and minimize complications.

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105 Table 7 1. Joint Center variation 1521 configurations Anterior/Po sterior (mm) Medial/Lateral (mm) Superior/Inferior (mm) Joint Variation 4 mm 4mm 12 mm 12mm 10mm 14mm Table 7 2. Peak variation of muscle activation to joint center variation changes Muscle Anterior/Posterior ( ) Medial/Lateral ( ) Superior/Inferior ( ) Anterior Deltoid .70 .25 .58 Lateral Deltoid .60 .4 1 Posterior Deltoid .40 .5 .84 Table 7 3. Peak variation of muscle normalized length to joint center variation changes Muscle Anterior/Posteri or ( ) Medial/Lateral ( ) Superior/Inferior ( ) Anterior Deltoid .08 .08 .05 Lateral Deltoid .10 .10 .10 Posterior Deltoid .10 .10 .08 Figure 7 1. Three dimensional bone and implant meshes (orange and blue ) registered to two dimensional fluoroscopy x rays

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106 Figure 7 2 . Implemented bone and implant configurations. Implant (dark grey) and Bone (white transparent)

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107 Figure 7 3. Variation of deltoid activation as a function of changes in the joint co nfiguration. Blue Anterior/Posterior joint configuration changes. Red Superior/Inferior joint configuration changes. Green Medial/Lateral joint configuration changes. Subject scale: A Anterior Deltoid, B Lateral Deltoid, C Posterior Deltoid. Blue In vivo experimental data for RTSA subject. ( A) (B) (C)

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108 Figure 7 4. Variation of deltoid activation as a function of changes in the joint configuration. (A) Anterior/Posterior changes in joint configuration. (B) Medial/Lateral changes in joint configurati on. (C) Superior/Inferior joint configuration changes. ( A) (B) (C)

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109 Figure 7 5. Variation of deltoid normalized length as a function of changes in the joint configuration. Blue Anterior/Posterior changes in joint configuration. Red Superior/Inferior changes in joint configuration. Green Medial/Lateral joint configuration changes. A Anterior Deltoid , B Lateral Deltoid , C Posterior Deltoid ( A) (B) (C)

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110 Figure 7 6 . Variation of reserve actuation as a function of changes in the joint configuration. Blue Anter ior/Posterior changes in joint configuration. Red Superior/Inferior changes in joint configuration. Green Medial/Lateral joint configuration changes. A Abduction Moment , B Flexion moment ( A) (B)

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111 CHAPTER 8 CONCLUSION Understanding the function of the Reve rse Total shoulder Arthroplasty (RTSA) during motion is critical to the design of preclinical plans for the placement of the implant. The studies behave like normal s scapulohumeral kinematics and muscle functio n. Chapters 4 7 assessed deltoid muscle moment arm, activation and length post RTSA. In Chapter 2 it was found that SHR at low abduction angles in both healthy and RT SA shoulders is highly variable . SHR in RTSA shoulders decreases dramatically with abduction, such that mostly scapular elevation is observed at the extreme of abduction. Rotator cuff deficient arthritic shoulders treated with RTSA do not move like healthy young shoulders ( 2 4, 2 5, 2 6) . Further, Medial and Lateral RTSA populations had significantly different SHR (p=0.0002341). In Chapter 3 it was found that the lateral deltoid functioned as the primary abductor of the arm and the an terior deltoid functioned as the primary flexor of the arm (s 3 4, 3 5). Posterior deltoid activity in all activities averaged less than 40% of MVIC (s 3 6, 3 7, 3 8). It was seen that there was a significant difference in activation between the Medial and Lateral Groups of the RTSA population. For abduction the Lateral RTSA Group had higher lateral deltoid activity in the implanted shoulder for early abduction. Beyond 70° elevation, the contralateral shoulders showed higher lateral deltoid activation than the implanted Lateral Group shoulders. Conversely the Medial Group did not show this behavior; the implanted side displayed a higher activation for the lateral deltoid for all degrees of elevation than the non implanted side.

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112 For flexion the Medial Group had higher anterior deltoid activity in the implanted side for early angles of flexion. Above 50° degrees elevation, anterior deltoid activation for the Medial Group was higher in the contralateral shoulders than the implanted shoulders. Conversely, the L ateral Group did not show this behavior; the implanted shoulders displayed higher anterior deltoid activation for all degrees of elevation compared to the non implanted shoulders. This muscle activation pattern is also seen in weighted and un weighted tria ls of flexion in the anterior deltoid (AD: p<0.05). The findings on shoulder muscle activation with and without RTSA provide context for assessing how geometric changes in implant design affect shoulder motion and muscle recruitment. It was found that the muscle function and kinematics of the RTSA are significantly different from normal shoulders. These insights may lead to the development of preclinical plans for placement of the implant, improved implant design, and modification of rehabilitative strategi es to improve outcomes and optimize quality of life for patients who undergo RTSA. Muscle Moment Arm RTSA. A 12 degree of freedom, subject specific model was used to repre sent the shoulders of three patients with RTSA for whom fluoroscopic measurements of scapular and humeral kinematics during abduction had been obtained. The computer model used subject specific in vivo abduction kinematics and systematically varied joint c enter locations over 1521 different perturbations from the surgical placement to determine moment arms for the anterior, lateral and posterior aspects of the deltoid muscle. The joint center was varied from its surgical position ±4 mm in the anterior/poste rior direction, ±12mm in the medial/lateral direction, and 10 mm to 14 mm in the superior/inferior direction.

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113 The anterior deltoid moment arm varied up to 20 mm with center of rotation variations, primarily in the medial/lateral and superior/inferior dir ections. Similarly, the lateral deltoid moment arm demonstrated variations up to 13 mm, primarily with joint center changes in the medial/lateral and superior/inferior directions. The posterior deltoid moment arm varied up to 15mm, primarily in early abduc tion, and was most sensitive to changes of the joint center in the superior/inferior directions. The goal of this study was to assess the sensitivity of the deltoid muscle moment arms as a function of joint configuration for existing RTSA subjects. High v ariations were found for all three deltoid components. Variation over the entire abduction arc was greatest in the anterior and lateral deltoid, while the posterior deltoid moment arm was mostly sensitive to joint center changes early in the abduction arc. Moment arm changes of 13 20 mm represent a significant amount of the total deltoid moment arm. This means there is an opportunity to dramatically change the deltoid moment arms through surgical placement of the joint center of rotation. Computational mode ls of the shoulder may help surgeons optimize subject specific placement of RTSA implants to provide the best possible muscle function, and assist implant designers to configure devices for the best overall performance. Muscle Force the activation and lengthening of the deltoid muscles as a function of RTSA joint configuration. a pproach was automated to assess changes in muscle performance over 1521 joint configurations for an RTSA subject . Patient specific muscle moment arms, muscle lengths, muscle velocities, and muscle parameters served as inputs into the muscle prediction sche me. We systematically varied joint center locations over 1521 different perturbations from the in vivo measured surgical

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114 placement to determine muscle activation and normalized operating region for the anterior, lateral and posterior aspects of the deltoi d muscle. The joint center was varied from the RTSA ±4 mm in the anterior/posterior direction, ±12mm in the medial/lateral direction, and 10 mm to 14 mm in the superior/inferior direction (Table 7 2). Overall muscle activ ity varied over 1521 different implant configurations for the RTSA subject . For initial elevation the RTSA subject showed at least 25 % deltoid activation sensitivity in each of the directions of j oint configuration change. P osterior deltoid showed a maxima l activation variation of 84 % in the superior/inferior direction . Deltoid activation variations lie primarily in the superior/inferior and anterior/posterior directions. An increasing trend was seen for the anterior, lateral and posterior deltoid outside o f the discontinuity seen at 28°. Activation remained below 4 Nm . The most optimal deltoid normalized operating length was implemented by changing the joint configurat ion in the superior/inferior and medial/lateral directions. Current shoulder models utilize cadaver information in their assessment of generic muscle strength. In adding to this literature we performed a sensitivity study to assess the effects of RTSA join t configurations on deltoid muscle performance. With this information improvements can be made to the surgical placement and design of RTSA to improve functional/clinical outcomes while minimizing complications.

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123 BIOGRAPHICAL SKETCH David W alker is from the island of J amaica. He is the only child of A udrey F isher. D avid attended the U niversity of F lorida where he received his Bachelor of Science i n M echanical E ngineering . He received his Master of Science in M echanical E ngineering from the University of Florida in spri ng 2012. He received his Ph.D. from the U niversity of Florida in A ugust of 2014 . He has spent his life in pursuit of true meaning and purpose which he found in his relationship in 2008.