FACTORS AFFECTING THE STABILITY OF REVERSE SHOULDER ARTHROPLASTY

Transcription

1 FACTORS AFFECTING THE STABILITY OF REVERSE SHOULDER ARTHROPLASTY by Allison Loretta Clouthier A thesis submitted to the Department of Mechanical and Materials Engineering In conformity with the requirements for the degree of Master of Applied Science Queen s University Kingston, Ontario, Canada (December, 2011) Copyright Allison Loretta Clouthier, 2011

2 Abstract Reverse shoulder arthroplasty is a relatively new procedure that is used to treat shoulders with massive rotator cuff tears combined with arthritis, a condition that is not well managed using conventional shoulder arthroplasty. By reversing the ball-and-socket anatomy of the shoulder, the constraint of the joint can be increased. Despite the success of this prosthesis in improving pain and function, complication rates remain high and instability is often reported as the most commonly occurring complication. The mechanism of dislocation as well as factors that can be modified to decrease the risk of dislocation are not well understood for reverse shoulder arthroplasty. Therefore, the purpose of this study was to create a platform for examining the stability of reverse shoulder arthroplasty and use this to investigate factors affecting stability, including shoulder orientation (abduction and abduction plane angles), loading direction, glenosphere eccentricity and diameter, and humeral socket constraint. An anatomical shoulder simulator was developed using a synthetic bone model and pneumatically actuated cables to represent the three heads of the deltoid. A displacing force was applied to the humeral head by a material testing machine in an anterior, posterior, superior, or inferior direction. The force required to dislocate the joint was used as a measure of stability and the identified factors and the interactions between factors were examined using a half-fraction factorial design experiment. Increases in glenohumeral abduction or inferior-offset of the glenosphere were found to improve the stability of the prosthesis. Additionally, increased humeral socket depth resulted in greater stability for all loading directions, with the exception of inferior loading. Abduction plane angle and glenosphere diameter had no effect on the stability of reverse shoulder arthroplasty. ii

3 Co-Authorship This thesis contains the original work of Allison Clouthier, completed under the co-supervision of Dr. Kevin Deluzio and Dr. Tim Bryant. Chapter 3 was prepared as a manuscript to be submitted to the Journal of Shoulder and Elbow Surgery and co-authors include Markus Hetzler, Dr. Graham Fedorak, Dr. Tim Bryant, Dr. Kevin Deluzio, and Dr. Ryan Bicknell. Experiment design, data collection, data analysis, and writing of the manuscript were completed by the author with feedback on experiment design and editing of the manuscript by the co-authors. iii

4 Acknowledgements First and foremost, I would like to thank my supervisors Dr. Kevin Deluzio and Dr. Tim Bryant for all of your support, guidance, encouragement, advice, and senses of humour over the past two years. I have learned a huge amount from both of you over the past two years and am extremely grateful for the opportunity to work with you. Dr. Ryan Bicknell: thank you for providing me with such an interesting project to work on and for all of your insight along the way. Thanks to Steffani Vivani for your help in getting the project started. Thank you also to the rest of the shoulder group, Markus and Graham, for your feedback and help throughout this project. I would also like to thank all of the staff at the HMRC for being amazingly helpful with just about everything. I would be remiss if I didn t acknowledge the support of the members of JAM. Stacey, Yang, Qingguo, Erica, Brian, Renata, Ross, TT, Yvonne, Liz, and Lydia: thank you for your help trying to understand some tricky problems, for exposing me to so many areas of research, and for the fantastic snacks and company. I would like to specially thank Scott, for always being around to help me out and of course for making fun of me when I break things. To all of my teammates on Trogdor and the Disc Jockeys: the time spent both on and off the field (and in and out of the tube) certainly contributed to making my experience as enjoyable as it was. Finally, thank you to all of my friends and family who have encouraged me, inspired me, and helped me to get to where I am today. This work was supported by the National Sciences and Engineering Research Council and the Collaborative Research and Training Experience program. iv

5 Table of Contents Abstract... ii Co-Authorship... iii Acknowledgements... iv Chapter 1 Introduction The Shoulder Shoulder Simulators Reverse Shoulder Arthroplasty Biomechanical Advantages Instability of Reverse Shoulder Arthroplasty Clinical Findings Biomechanical Findings Factors Affecting Stability Summary Objectives Chapter 2 Shoulder Simulator Design Shoulder Simulator Design Bony Geometry and Implant Muscle Modelling Simulator Frame Displacing Force Kinematics and Force to Dislocate Kinematics Force to Dislocate Simulator Reliability Static Posture Repeatability Dislocation Repeatability Summary Chapter 3 Factors Affecting the Stability of Reverse Shoulder Arthroplasty: A Biomechanical Study Introduction Methods Joint Simulator v

6 3.2.2 Experimental Design Data Analysis Results Discussion Chapter 4 Discussion and Conclusions Shoulder Simulator Design Effect of Active Muscle Loading and Bony Geometry Stability Ratio Clinical Relevance Conclusions Limitations Future Work References Appendix A Detailed Experiment Design Appendix B Detailed Data Analysis Appendix C Instrumentation Specifications vi

7 List of Figures Figure 1.1: Bones of the glenohumeral joint Figure 1.2: Muscles of the glenohumeral joint... 3 Figure 1.3: Three heads of the deltoid... 3 Figure 1.4: Muscles crossing the glenohumeral joint Figure 1.5: Intrinsic shoulder simulator... 5 Figure 1.6: Simulator using synthetic bone... 6 Figure 1.7: Nylon webbing deltoid model... 8 Figure 1.8: Muscle cable load application Figure 1.9: A simulator that constrained the humerus to control arm posture... 9 Figure 1.10: Early reversed anatomy shoulder implants Figure 1.11: Grammont s reverse shoulder arthoplasty Figure 1.12: Advantage of medialized centre of rotation Figure 1.13: Changes in amount of deltoid available for abduction Figure 1.14: Biomechanical advantages of reverse shoulder arthroplasty Figure 1.15: Simulators used to examine intrinsic stability of reverse shoulder arthroplasty Figure 1.16: Cadaveric shoulder simulator used to investigate reverse shoulder arthroplasty Figure 2.1: Sawbone humerus and scapula used Figure 2.2: The DePuy Delta XTEND implant Figure 2.3: Ball joint rod end used to fix muscle cables to the humerus Figure 2.4: Cable wrapping point on scapula Figure 2.5: Calculation of ball joint insertion points Figure 2.6: Humeral casing used to fasten ball joints to the humerus Figure 2.7: Scapular fixture used to provide stiffness to the scapula Figure 2.8: L brackets used to mount scapula on frame Figure 2.9: Pneumatic actuators and load cells Figure 2.10: Simulator frame and Instron material testing machine Figure 2.11: Coordinate systems Figure 2.12: Additional scapular anatomical landmarks Figure 2.13: Shoulder angles Figure 2.14: Typical force vs. displacement plot Figure 2.15: Shoulder angles obtained for all trials Figure 2.16: Standard deviation of angles plotted against the averages vii

8 Figure 2.17: Correlation among trials for shoulder angles Figure 2.18: Mean muscle and displacing forces for reliability testing Figure 2.19: Mean force required to dislocate for four directions Figure 3.1: Glenohumeral joint simulator Figure 3.2: Coordinate systems Figure 3.3: Factors and levels investigated Figure 3.4: Force to dislocate by factor Figure 3.5: Interaction between loading direction and socket depth Figure 4.1: Friction in the muscle wrapping points Figure 4.2: Stability ratio parameters Figure 4.3: Stability ratio and joint reaction force Figure A.1: Comparison of ¼ fraction experiments performed on two different days Figure B.1: Normal probability plot of factors and all two factor interactions Figure B.2: Normal probability plot of residuals Figure B.3: Residuals plotted against predicted force to dislocate viii

9 List of Tables Table 1.1: Complication and dislocation rates in clinical studies Table 1.2: Factors affecting stability of reverse shoulder arthroplasty Table 2.1: Muscle force combinations tested Table 3.1: Forces applied to each muscle and resulting shoulder angles Table A.1: Factor codes and levels of each factor Table A.2: Design matrix used for first quarter-fraction experiment Table A.3: Design matrix used for second quarter-fraction experiment Table B.1: Effect estimates, sum of squares, and percent contributions Table B.2: 6-way ANOVA results Table B.3: 5-way ANOVA results ix

10 Chapter 1 Introduction 1.1 The Shoulder The shoulder is a complex joint that allows a high degree of mobility while successfully maintaining stability. It is one of the most mobile joints in the body, with a range of motion of 180 o vertically, 170 o horizontally, and 150 o in internal rotation (Rockwood, et al., 2009). The shoulder complex is actually comprised of four separate joints, which consist of the articulations between the scapula (shoulder blade), humerus (arm bone), clavicle (collar bone), and ribcage. The articulation that accounts for the majority of the shoulder s mobility is the glenohumeral joint. This joint is formed by the articulation between the humeral head and the glenoid of the scapula (Figure 1.1). These essentially form a ball-and-socket joint; however, the joint is often likened to a golf ball sitting on a tee (Rockwood, et al., 2009). The glenoid forms a small, shallow socket, meaning that the bones themselves, while allowing a large range of motion, do not provide much stability to the joint. 1

11 Scapula Anterior View Coracoid Humeral Head Humerus Acromion Glenoid Posterior View Scapular Spine Acromion Figure 1.1: Bones of the glenohumeral joint. Anterior (front) and posterior (back) views are shown for the scapula. The task of stabilizing the shoulder, therefore, is left to the muscles and ligaments of the joint. Most important among these is the rotator cuff, which consists of four muscles: supraspinatus, infraspinatus, subscapularis, and teres minor (Figure 1.2). While these muscles do contribute to motion of the shoulder, the main function of the rotator cuff is to keep the humeral head centred on the glenoid, resisting the shear forces created by larger muscles crossing the joint (Rockwood, et al., 2009). Illustrating this is the fact that damage to muscles of the rotator cuff often leads to shoulders that are prone to dislocation (Neviaser, et al., 1993). 2

12 Supraspinatus Supraspinatus Subscapularis Coracobrachialis Teres Minor Infraspinatus Teres Major Teres Major Anterior Posterior Figure 1.2: Muscles of the glenohumeral joint (rotator cuff, teres major, and coracobrachialis). The most important muscle to the function of the glenohumeral joint is the deltoid. This large muscle has three heads which insert on the clavicle, acromion, and spine of the scapula, as depicted in Figure 1.3. These are referred to as the anterior, middle, and posterior sections of the deltoid. Other muscles crossing the glenohumeral joint include: teres major, coracobrachialis pectoralis major, and latissimus dorsi (Figure 1.2, Figure 1.4). Clavicle Middle Anterior Posterior Figure 1.3: Three heads of the deltoid shown in a sagittal (side) view. The anterior head inserts onto the clavicle, the middle deltoid on the acromion, and the posterior deltoid on the spine of the scapula. 3

13 Deltoid Pectoralis Major Latissimus Dorsi Anterior Posterior Figure 1.4: Muscles crossing the glenohumeral joint. 1.2 Shoulder Simulators Understanding the biomechanics of a joint in vivo is a challenging problem. One method of circumventing this is to create a physical model of the joint that allows kinematics and kinetics of the joint to be more readily controlled and observed. For the shoulder, simulators have been developed to gain an understanding of shoulder biomechanics, including the investigation of shoulder injuries (Osterhoff, et al., 2011; Yamamoto, et al., 2009), muscle function (Ackland & Pandy, 2009; Itoi, et al., 1993), and arthroplasty (Shapiro, et al., 2007; Anglin, et al., 2000). These shoulder models generally fall into two categories: those that focus on the joint or prosthesis itself (intrinsic stimulators) and those that examine the joint under the influence of muscle loading (anatomical simulators). Simulators that focus on the joint are most often used to study intrinsic stability of the joint (Anglin, et al., 2000) or fixation of prosthesis components (Bicknell, et al., 2003). These generally include mechanisms that apply a compressive and displacing force either to implant 4

14 components (Harman, et al., 2005) or to a cadaveric specimen (Itoi, et al., 2000). If stability is of interest, then force to dislocate can then be measured, or if fixation is being examined, micromotion of components can be recorded. An example of a simulator used to investigate the intrinsic stability of total shoulder arthroplasty is shown in Figure 1.5. In this model, the glenoid component was implanted in a block of bone-substitute and compressed against the humeral component. The humeral component was then displaced and the force required to dislocate the joint was measured. In this study, the stability ratio, defined as the dislocating force (perpendicular to the centre-line of the concave component) divided by the compressive force (parallel to the centre-line of the concave component) (Rockwood, et al., 2009), was used as a measure of stability. Figure 1.5: Simulator used to examine the intrinsic stability of a total shoulder prosthesis. Compressive and dislocating forces are applied to the components and the force to dislocate recorded (Anglin, et al., 2000). While the aforementioned simulators are useful for studying the intrinsic stability of an implant or the shoulder, it is also important to understand shoulder biomechanics in a model that more closely replicates in vivo conditions. This requires the inclusion of active muscle loading, bony geometry, and soft tissue structures. Currently, a cadaver model is the closest physical 5

15 representation of in vivo conditions; however, use of cadaver specimens significantly complicates experimental protocols. Therefore, some authors have utilized synthetic bones (Osterhoff, et al., 2011; Favre, et al., 2008; Gutiérrez, et al., 2007) which allow active muscle loading and bony geometry to be modelled while maintaining a relatively simple model and experimental protocol (Figure 1.6). Figure 1.6: Simulator using synthetic bone. Braided cords were used to model muscles to which forces were applied by hanging weights. Changes to muscle moment arms following arthroplasty with latissimus dorsi transfer were investigated (Favre, et al., 2008). Although the shoulder complex consists of four articulations, shoulder simulators generally model only the glenohumeral joint. This is due to the difficulty involved in including all four articulations in the model and the fact that the glenohumeral joint provides the majority of the shoulder s mobility. Some simulators, however, have attempted to model scapular motion to some extent by mounting the scapula in such a way that it is able to be manually rotated to 6

16 roughly correspond to the in vivo scapular motion relative to the humerus (Smith, et al., 2006; Giles, et al., 2011). The most important feature of anatomical shoulder simulators is the inclusion of muscle loading. The majority of simulators include the deltoid and rotator cuff muscles. These are chosen as the rotator cuff is the primary stabilizer of the glenohumeral joint and the deltoid is the prime mover. Some simulators extend these to include other muscles crossing the glenohumeral joint such as pectoralis major, latissimus dorsi, and/or coracobrachialis (Ackland, et al., 2010; Favre, et al., 2008; Giles, et al., 2011; McMahon, et al., 2003). These may be modelled if influence of one of these muscles is being examined or simply to more closely replicate in vivo conditions. Since some of these muscles have much larger cross-sections than others, they are sometimes divided into sections and represented by more than one cable to capture this effect. This is commonly done with the deltoid muscle, which inserts in three locations on the scapula/clavicle and has sections that are recognized as performing different functions. However, some models have sectioned other large muscles as well (Favre, et al., 2008). Using multiple cables is not the only option for addressing this issue, although it is the most common. One simulator (Sharkey, et al., 1994) modelled the large cross-sectional area of the deltoid using a nylon webbing that distributed force along the entire deltoid insertion (Figure 1.7). 7

17 Figure 1.7: Nylon webbing used to model the wide insertion point of the deltoid (Sharkey, et al., 1994). Once desired muscle groups are selected, forces need to be applied to the muscles. In some cases this has been achieved using hanging weights (Gutiérrez, et al., 2007). In other models, weights were used for only the rotator cuff muscles to provide enough force to locate the humeral head on the glenoid (Bono, et al., 2001; Osterhoff, et al., 2011), as shown in Figure 1.8. Springs have also been used to apply muscle forces (Itoi, et al., 1993; Williams, et al., 2001). Most often, pneumatic (Kedgley, et al., 2007), hydraulic (Apreleva, et al., 2000), or linear actuators (Ackland, et al., 2010) are utilized for muscle force application as this allows for dynamic loading of muscles. A B Figure 1.8: A) A simulator that uses pneumatic actuators to load muscle cables (Kedgley, et al., 2007). B) A simulator utilizing hanging weights for the rotator cuff forces (Bono, et al., 2001). 8

18 Shoulder simulators also differ in their treatment of humeral constraint. In some cases, the humerus is free and its position is controlled only by the muscle forces (Kedgley, et al., 2007; Bono, et al., 2001; Sharkey, et al., 1994). However, in other models, the humerus is constrained in some fashion. This may be done to control the position of the humerus (Giles, et al., 2011; Makhsous, et al., 2004; Schamblin, et al., 2009), provide an axially directed force (Bryce, et al., 2010), or to apply a dislocating force to the distal portion of the humerus (McMahon, et al., 2003). An example of a simulator where the humerus is constrained is shown in Figure 1.9. Figure 1.9: A simulator that constrained the humerus to control arm posture (Schamblin, et al., 2009). As evidenced by the simulators discussed, there are various methods that can be employed to simulate the biomechanics of the shoulder. The choice of simulator design depends largely on the application for which it will be used. Intrinsic simulators are useful for determining the performance of the joint geometry or prosthesis components alone. However, anatomical simulators are necessary if the goal of the study is to understand the in vivo biomechanics of the joint. For anatomical simulators, there are varying techniques for modelling bony geometry, muscle loads, and shoulder function. Again, model parameters are selected based on the purpose 9

19 of the study, whether the function of the natural shoulder, shoulder injuries, or surgical procedures such as arthroplasty are to be investigated. 1.3 Reverse Shoulder Arthroplasty In 1893, the first documented shoulder arthroplasty was performed by French surgeon Jules Emile Péan to treat a case of tuberculosis (Péan, 1894). Since then, great advances have been made in shoulder arthroplasty and the procedure has been very successful in treating patients with arthritic shoulders (Barrett, et al., 1987; Norris & Iannotti, 2002). However, problems were encountered when the procedure was used in an attempt to treat patients with painful pseudoparalytic shoulders (Matsen, et al., 2007; Neer, et al., 1982). These patients have extreme loss of function in their shoulder due to massive rotator cuff tears compounded by other conditions such as arthritis or fracture. Although the joint surface was replaced, which sometimes relieved pain, the joint remained highly unstable and functional results were poor. The main stabilizers of the glenohumeral joint, the rotator cuff muscles, were largely absent in these patients, resulting in the shear forces generated by the deltoid being unopposed and an inability to keep the humeral head centred on the glenoid. As a result, when these patients attempt to elevate their arms, the force in the deltoid causes the humeral head to migrate upwards rather than pivoting on the glenoid. Problems with fixation were also encountered as the translating humeral head caused edge loading of the glenoid component resulting in a rocking-horse phenomenon that eventually loosened the glenoid component (Franklin, et al., 1988). This led to hemiarthroplasty (replacing the humeral joint surface only) becoming the standard treatment for these patients as it was possible to achieve some pain relief with this procedure. Functional results remained poor however, and the procedure was referred to as a limited goals prosthesis (Neer, et al., 1982). 10

20 In the 1970 s some surgeons began to experiment with the idea of reversing the ball-and-socket anatomy of the shoulder in an attempt to increase the constraint of the joint (Figure 1.10). The glenoid surface of the scapula is quite small and installation of a deeper socket on the glenoid is not feasible. It was therefore theorized that by reversing the anatomy, a more constrained socket could be installed on the humeral side. These initial attempts met with little success as excessive torque at the glenoid component-bone interface led to early failure, range of motion was limited, and instability was common (Broström, et al., 1992; Neer, 1990; Flatow & Harrison, 2011). These poor results led to the idea being abandoned. Figure 1.10: A) Neer s Mark I prosthesis. The implant was designed to be more constrained and had a large ball to increase range of motion, but this also prevented the rotator cuff from being reattached (Neer, 1990). B) The highly constrained Kessel prosthesis, developed in 1973, produced poor functional results (Broström, et al., 1992). Paul Grammont, a French orthopaedic surgeon, revisited the idea of reverse anatomy and designed a new reverse prosthesis in Grammont s first design featured 2/3 of a sphere cemented to the glenoid and a polyethylene humeral component (Figure 1.11A). This prosthesis 11

21 was successful in relieving pain, but functional results were variable (Grammont, et al., 1987). Therefore, Grammont revised his design in 1991 to include an uncemented half-sphere glenoid component (glenosphere) and a metal humeral stem with a polyethylene cup insert (Figure 1.11B). The prosthesis was designed to restore mobility and stability in a shoulder where the deltoid was the only functional muscle and was therefore dubbed the Delta III. Two year postoperative follow-ups found improvements in terms of both pain and function (Grammont & Baulot, 1993). Figure 1.11: A) Grammont s original design of his reverse prosthesis. B) The Delta III (Boileau, et al., 2005). Grammont style prostheses have been used in Europe since they were first developed and they gained FDA approval for use in the United States in The procedure has been very successful in improving function and relieving pain in patients with massive rotator cuff tears combined with glenohumeral arthritis a condition known as cuff tear arthropathy (Leung, et al., 12

22 2011; Boileau, et al., 2009; Cuff, et al., 2008). Due to the success experienced in cuff tear arthropathy, indications for the surgery have expanded to include conditions such as rheumatoid arthritis combined with rotator cuff deficiency (Holcomb, et al., 2010), revision of failed traditional arthroplasty (Flury, et al., 2010), fracture (Cazeneuve & Cristofari, 2010), and reconstruction after tumour (De Wilde, et al., 2011) Biomechanical Advantages There are several biomechanical advantages to reversing the anatomy of the shoulder. First and foremost, this allows a more constrained joint to be installed to address issues of humeral head translation and instability. However, Grammont s implant succeeded where others had failed due to features specific to his design. In Grammont s prosthesis, the glenoid component is a halfsphere and the centre of rotation is aligned with the glenosphere-bone interface. This prevents moments from being created at this interface (Figure 1.12) which contributed to loosening of the glenoid component in previous designs. A B M JRF JRF Figure 1.12: A) Initial attempts at installing a sphere on the glenoid had the centre of rotation (+) offset from the implant-bone interface with the result that the joint reaction force (JRF), which acts through the centre of rotation, causes a moment (M) at the interface. B) In Grammont s design, the centre of rotation is at the glenosphere-bone interface and therefore the JRF does not generate a moment at this interface. This medialization of the centre of rotation also increases the amount of the deltoid muscle that is available to contribute to abduction of the arm. By moving the axis of rotation closer to the centre 13

23 of the body, more deltoid fibres are outside of the axis of rotation and can therefore be recruited for abduction, as depicted in Figure Axis of Rotation Humeral Head Deltoid Scapula A B Figure 1.13: A transverse (overhead) view of the shoulder illustrating changes in the amount of deltoid that is available to contribute to shoulder elevation in the natural shoulder (A) and with a medialized centre of rotation following reverse shoulder arthroplasty (B). Because the axis of rotation is moved towards the centre of the body, more of the deltoid can contribute to elevation of the arm (shaded section) (Boileau, et al., 2005). While medializing the centre of rotation allows more of the deltoid to contribute to abduction, doing so also decreases the tension in the deltoid. To compensate for this, the centre of rotation is also distalized to restore some deltoid tension, as depicted in Figure The deltoid is further tensioned by the nonanatomic 155 o humeral component neck-shaft angle which lowers the humerus and, thus, the deltoid insertion point. In addition, the medialization and distalization of the centre of rotation increases the moment arm of the deltoid (Figure 1.14) and, therefore, less muscle force is required to generate shoulder movement. Finally, the large diameter glenosphere of the prosthesis increases the potential impingement free range of motion. 14

24 m d m d A B Figure 1.14: Centre of rotation (+), deltoid length (d), and deltoid moment arm (m) changes resulting from reverse shoulder arthroplasty. A) Natural shoulder. B) Reverse shoulder arthroplasty. The anatomical centre of rotation is superimposed on the reverse arthroplasty case (B) to highlight that it has been distalized and medialized. The deltoid moment arm and deltoid length are increased following reverse shoulder arthroplasty (d >d, m >m) Instability of Reverse Shoulder Arthroplasty Clinical Findings Despite the success of reverse shoulder arthroplasty in terms of pain relief and functional improvements, complication rates are high, ranging from 8 55% (Young, et al., 2009; Bufquin, et al., 2007; Werner, et al., 2005; Levy, et al., 2007; Wierks, et al., 2009). Common complications include erosion of the scapula due to impingement, infection, component failure, scapular fracture, and component loosening. In many studies, however, the most frequently occurring complication is dislocation (Cuff, et al., 2008; Cazeneuve & Cristofari, 2010; Zumstein, et al., 2011). Table 1.1 provides an overview of dislocation rates from a selection of clinical studies. In some cases, the direction of instability is documented based on x-rays or the cause of dislocation is theorized. However, the mechanism of dislocation is not well understood for reverse shoulder 15

25 arthroplasty as clinicians can only examine the shoulder after a dislocation event and attempt to determine how and why the instability occurred. Although investigating causes of dislocation in a clinical setting is difficult, some observations have been made. A correlation has been found between insufficiency of the subscapularis and shoulder dislocations (Edwards, et al., 2009; Gallo, et al., 2010). It is thought that if the subscapularis is intact, it is able to provide restraint to the joint and aid in preventing dislocations. Therefore, if the subscapularis is irreparable, the risk of dislocation is increased. Other authors have speculated that factors such as inadequate deltoid tension (Boileau, et al., 2005), inadequate soft tissue tension (Bicknell, et al., 2003), malpositioned components (Bicknell, et al., 2003), and impingement (Cazeneuve & Cristofari, 2010) may increase the likelihood of instability; however, little clinical data exists to validate these. 16

26 Table 1.1: Complication and dislocation rates in clinical studies. Indications for reverse shoulder arthroplasty are listed for each study and if a theorized mechanism of dislocation or direction of dislocation was discussed, this was included as well. An asterisk indicates dislocation was the most common complication in the study. Study Indication Complications Dislocations Theorized Mechanism of Dislocation (Boileau, et al., 2005) (Cazeneuve & Cristofari, 2010) (Cuff, et al., 2008) (De Wilde, et al., 2003) (Edwards, et al., 2009) (Gallo, et al., 2010) (Trappey IV, et al., 2010) (Wall, et al., 2007) 21 cuff tear 5 fracture sequelae 19 revision 10/45 (22%) 3 (7%) 36 fracture 8/36 (22%) 4 (11%) * 1 anterior due to humeral anteversion 3 superior due to impingement 37 cuff deficiency 9/94 (10%) 4 (4%) * 2 occurred due to a fall 33 previous cuff repair 23 revision 3 proximal humeral nonunion 13 tumour 5/13 (38%) 4 (31%) * 60 cuff tear arthropathy 33 revision 21 proximal humeral malunion 10 massive cuff tear and pseudoparesis 14 other 36 cuff tear arthropathy 18 revision 3 fracture sequelae 72 revision 119 cuff tear arthropathy 25 cuff tear and pseudoparalysis 25 fracture sequelae 16 acute fracture 5 rheumatoid arthritis 22 other 74 cuff tear arthropathy 54 revision 41 massive cuff tear 33 osteoarthritis 33 posttraumatic arthritis 5 other?/138 7 (5%) 16/57 (28%) 9 (16%) All anterior dislocations?/ (6%) 38/199 (19%) 15 (7.5%) 17

27 Biomechanical Findings To better understand the issues underlying reverse shoulder arthroplasty stability, some biomechanical investigations have been performed using shoulder simulators. Thus far, there have been two studies performed that examine the intrinsic stability of the implant and one performed in a cadaver model. Two studies have been conducted using simulators that apply a compressive force to the prosthesis components and then displace the components until they have dislocated (Figure 1.15). In one investigation, a simulator was created that utilized the glenosphere and polyethylene cup. A hierarchy of stability factors was sought, and it was determined that compressive force had the greatest effect on stability, followed by humeral socket depth (Gutiérrez, et al., 2008). Glenosphere diameter was found to have minimal effect of the force to dislocate. Another study employed a mechanism that allowed the orientation of the glenoid and humeral components to be modified (Favre, et al., 2010). For the humeral component, rotation about its long axis (version) was adjustable and anterior/posterior tilt was adjustable in the glenosphere. The compressive force was always applied in the medial direction and the displacing force in the anterior direction (Figure 1.15B). As expected, since it is symmetrical, tilting the glenosphere had little effect on force to dislocate. Version of the humeral component did affect stability however, as this changed coverage of the sphere by the socket. In this study, the stability ratio (dislocation force divided by compressive force (Rockwood, et al., 2009)) was used as a measure of stability as opposed to the dislocation force. Since this is a normalized measure, it can theoretically be easily compared with other studies which have not used the same compressive forces. 18

28 F D F D F C F C A B Figure 1.15: Shoulder simulators used to examine the stability of reverse shoulder arthroplasty. In each, a compressive (F C ) and displacing (F D ) force was applied and force to dislocate was recorded. A) This simulator was used to examine the effects of compressive force, socket depth, and glenosphere diameter (Gutiérrez, et al., 2008). B) This simulator was used to investigate the effect of component positioning by allowing the humeral and glenoid components to be rotated (angles α and β) (Favre, et al., 2010). Recently, the first investigation of reverse shoulder stability in a cadaver model was published (Henninger, et al., 2011). The effect of humeral component version and humeral socket thickness on a number of factors including anterior and lateral stability of the shoulder was examined. The anterior, middle, and posterior heads of the deltoid were modelled using pneumatically actuated cables and the subscapularis, supraspinatus, and infraspinatus/teres minor had constant loads applied by hanging weights (Figure 1.16). To test stability of the shoulder, a cable was fastened around the metaphysis of the humeral component and a force was manually applied either laterally or anteriorly while the elbow and wrist were restrained. For lateral loading, the arm was positioned in resting abduction and neutral internal rotation, while for anterior loading, the arm was manually held in 90 o external rotation and resting abduction. Lateral dislocation was said to occur when a ~5 mm gap formed between the humeral socket and glenosphere. It was found that lateral dislocations required less force than anterior dislocations. No significant differences were found between different levels of humeral component retroversion or humeral socket thickness. 19

29 Figure 1.16: Cadaveric shoulder simulator used to investigate lateral and anterior stability of reverse shoulder arthroplasty (Henninger, et al., 2011). It is noteworthy that the finding by Henninger et al. that humeral component version has little effect on stability contradicts the conclusions of Farve et al. using the intrinsic stability simulator. This demonstrates that biomechanics of the prosthesis are affected by biological factors such as muscle loads and bony geometry. Therefore, while understanding the intrinsic stability of the prosthesis is important, it is not sufficient and it is necessary to also examine stability in an anatomical model that replicates biological factors Factors Affecting Stability There are a large number of factors that have the potential to affect the stability of reverse shoulder arthroplasty. Some factors that have been previously investigated or discussed in the 20

30 literature as having an effect on stability are outlined in Table 1.2. As evidenced by the factors listed in this table, many have been identified as being potentially relevant to stability, but few have been studied biomechanically or clinically and even fewer have been studied in an anatomical model. Although this list contains factors discussed in the literature, it is certainly not exhaustive and it is likely that other variables exist that can be modified to improve the stability of this prosthesis. 21

31 Table 1.2: Some factors that may affect stability of reverse shoulder arthroplasty. For each factor, studies that have examined the factor biomechanically, found a correlation to stability clinically, or that have theorized that a factor has an effect without a formal clinical or biomechanical study are listed. Factor Biomechanical Study Category Factor Intrinsic Cadaver Implant Glenosphere diameter (Gutiérrez, et al., 2008) Surgical Biological Mode of Dislocation Glenosphere eccentricity Humeral neck-shaft angle Humeral socket constraint Humeral socket thickness Materials Component orientations Surgical approach Soft tissue condition Soft tissue tension Bony geometry Loading direction Load rate Arm position (Gutiérrez, et al., 2008) (Favre, et al., 2010) (Gutiérrez, et al., 2008) (Henninger, et al., 2011) (Henninger, et al., 2011) (Henninger, et al., 2011) Clinical Correlation (Edwards, et al., 2009) (Bicknell, et al., 2003) (Bicknell, et al., 2003) (Cuff, et al., 2008) Theorized (Gallo, et al., 2010) (Lädermann, et al., 2009) (Kalouche, et al., 2009) (Gallo, et al., 2010) (Gutiérrez, et al., 2008) (Boileau, et al., 2005) (Cazeneuve & Cristofari, 2010) (Molé & Favard, 2007) 1.4 Summary Reverse shoulder arthroplasty is a relatively new procedure used to treat shoulders with extreme rotator cuff deficiency, a complication not well managed using conventional arthroplasty. Despite the success of this prosthesis, complication rates remain high, with instability often being the 22

32 most common complication. This is concerning as it leaves the patient with a non-functioning, painful shoulder that may require additional surgery to repair. The underlying causes of instability in reverse shoulder arthroplasty are unclear; however, research has begun to illuminate the issue. A small number of factors have been investigated biomechanically using simulators. These studies determined that compressive force and humeral socket constraint have an important effect on stability. For some variables, such as subscapularis condition, correlations with stability have been found clinically and there are a large number of factors that have been theorized to be important for improving stability that have not been thoroughly investigated. In addition, some contradictions between experimentation methods have been found. Humeral component version was deemed to be important to intrinsic stability, but was found to have little effect when tested in a cadaver model. A larger glenosphere diameter has been theorized to improve stability as it should add tension to the deltoid, but in a test of intrinsic stability, it was found to have minimal effect. In other cases, factors theorized to be important have only been partially investigated. Clinically, it has been found that reverse arthroplasty shoulders can dislocate anteriorly, superiorly, posteriorly, or inferiorly. However, when loading direction was examined in a cadaver model, only anterior and lateral loading were examined. These examples indicate the necessity for more research in this area, particularly in a model that includes some of the active and passive constraints present in vivo. Since research into the large number of potential factors affecting stability of reverse shoulder arthroplasty has only just begun, screening experiments are an attractive option for identifying factors with the large effects on stability of reverse shoulder arthroplasty which can then be selected to be further investigated in detail. Factorial analysis techniques offer an excellent method for performing screening experiments of a large number of variables in a relatively small 23

33 number of experimental trials. This method has the additional benefit that interactions between the factors being screened can be investigated as well. This provides important information critical for fully understanding the biomechanics of this problem. Factors that have been identified previously form a starting point for inclusion in initial screening experiments of factors affecting stability. Limiting the experiment to include only factors that can be modified without reimplating the prosthesis can eliminate confounding biological factors such as anatomical variation between specimens and variations in component placement. Based on this, ideal factors for an initial screening experiment were defined as arm posture, loading direction, glenosphere diameter and eccentricity, and humeral socket constraint. These factors need to be examined in a model that includes active muscle loading and bony geometry to better replicate in vivo conditions and identifying significant interactions between factors is critical to fully understand factor effects. 1.5 Objectives 1. To design and develop a kinematic glenohumeral joint simulator that models bony geometry and active muscle loading. 2. To determine the reliability of positioning the shoulder using muscle loading. 3. To determine the reliability of measuring force to dislocate the shoulder. 4. To examine factors affecting reverse shoulder arthroplasty, including arm posture, loading direction, glenosphere diameter and eccentricity, and humeral socket constraint, and the interdependencies between these factors. 24

34 Chapter 2 Shoulder Simulator Design 2.1 Shoulder Simulator Design A kinematic glenohumeral joint simulator was developed to enable investigation of factors affecting the stability of reverse shoulder arthroplasty. The anatomical simulator modelled active muscle loading and bony geometry using a synthetic bone model Bony Geometry and Implant For this phase of the shoulder simulator, a Sawbones (Pacific Research Laboratories, Inc., Vashon, WA) humerus (Model #1028) and scapula (Model #1050) were used (Figure 2.1). Sawbones were chosen at this stage of testing to eliminate anatomical variation in samples as a confounding factor and to simplify the experimental protocol. Figure 2.1: Sawbone humerus and scapula used. This scapula model has a built in vise attachment. (Pacific Research Laboratories, 2011) 25

35 A Delta XTEND (DePuy Inc., Warsaw, IN) prosthesis, shown in Figure 2.2, was implanted according to the recommended surgical procedure (DePuy Orthopaedics Inc., 2010) by a senior orthopaedic resident. No lubrication was used at the joint for any of the testing performed as it was found that the friction between the UHMWPE humeral socket and the cobalt chrome glenosphere was not great enough to hamper movement of the arm. Since relative stability between conditions, and not the absolute value of force to dislocate, was of interest, lubrication of the joint was deemed unnecessary. Figure 2.2: The DePuy Delta XTEND implant (DePuy Orthopaedics Inc., 2010) Muscle Modelling The deltoid was the only muscle included in the model. Reverse shoulder arthroplasty is most often prescribed for patients who have massive rotator cuff tears (Matsen, et al., 2007; Sanchez Sotelo, 2009), so a worst case scenario was assumed and the entire rotator cuff was eliminated. Grammont named his prosthesis Delta as is was designed to provide stability and function using the deltoid alone (Boileau, et al., 2005) and the three heads of the deltoid together with a gravitational force create the minimum force complement required to control a three degree of freedom joint (Yanai, et al., 2001), such as the 26

36 glenohumeral joint. Therefore, no major issues of function or stability were anticipated in using the deltoid as the sole muscle. A 3.6 kg weight was attached to the distal portion of the humerus to simulate the weight of the arm (Zatsiorsky, 2002). The three heads of the deltoid, anterior, middle, and posterior (Rockwood, et al., 2009), were modelled separately using 1/16 diameter 7x7 galvanized aircraft cable to simulate active loading of muscles (Bono, et al., 2001). Cables were fixed to the humerus using three degree of freedom ball joint rod ends (Figure 2.3). Ball joints were utilized to ensure insertion points remained consistent for changing lines of action. The cables were passed through their insertion points on the scapula with a small piece of bicycle derailleur cable housing to reduce friction through the wrapping point (Figure 2.4). Bone Muscle cable Figure 2.3: Ball joint rod end used to fix muscle cables to the humerus. Cables had swaged ends that screw into the female end (McMaster Carr, 2011). 27

37 Figure 2.4: Cable wrapping point on scapula. A small piece of derailleur cable housing was utilized to reduce friction. To determine muscle insertion points and paths, data from a validated computer model of the shoulder (Holzbaur, et al., 2005) was used. For this model, made using SIMM (Musculographics Inc., Santa Rosa, CA), muscle insertion points were determined based on anatomical descriptions (Dalley & Moore, 1999) and muscle paths were determined by matching experimentally derived muscle moment arms (Liu, et al., 1997; Otis, et al., 1994). The model was first scaled to match the dimensions of the Sawbones humerus and scapula used in the simulator. The insertion points from the SIMM model were then recorded. For the scapula, these insertion points were used directly; however, for the humerus, because the ball joints have a centre of rotation that is offset from the surface of the bone, new insertion points for the ball joints were calculated. These were calculated by finding in three dimensions where the centre of the ball joint would intersect the muscle path given the known offset of the centre of the ball joint from the Sawbone surface, as shown in Figure 2.5. This was calculated for various arm positions and found to vary less than 1 cm, so locations calculated at a resting arm posture were used. 28

38 Humerus Muscle path Ball joint insertion Plastic Muscle insertion Figure 2.5: Cable insertion points using ball joints were calculated by considering where the centre of the ball joint would interest the muscle path. Plastic structures were designed to add stiffness to the foam Sawbones used and to accurately locate muscle insertion points. To ensure the ball joints would be securely screwed into the humerus, an approximately 5 mm thick plastic casing (Figure 2.6) was created using a three dimensional printer. The interior was the inverse of the Sawbone surface to ensure accurate alignment. Holes in the casing defined humeral insertion points based on their calculated locations. Three dimensional printing was also used to create a structure for the scapula that contained wrapping points for the deltoid cables (Figure 2.7). This structure was screwed onto the coracoid process and acromion of the scapula and was also fixed to the simulator frame to prevent the scapula from bending under applied muscle and displacing forces. 29

39 Figure 2.6: Humeral casing used to securely and accurately fasten ball joints to the humerus for muscle insertions. Figure 2.7: Scapular fixture used to provide stiffness to the scapula as well as guide the muscle cables through their insertion points on the scapula. 30

40 Force was applied to the muscle cables using 7/8 bore pneumatic actuators (068 DXP, Bimba Manufacturing Company, University Park, IL). Muscle forces were manually adjusted using precision regulators ( , Norgren Ltd., Littleton, CO). Inline, 100 lb capacity load cells (MLP 100, Transducer Techniques, Inc., Temecula, CA) were used to measure the forces in the muscle cables between the actuators and the scapular wrapping points. These were attached via inline ball joint linkages to the end of the actuator rods to ensure no shear loads were transferred to the load cells (Figure 2.9) Simulator Frame A frame for the simulator was created using modular extruded aluminum (80/20 Inc., Columbia City, IN). The Sawbone scapula used has a vise attachment which was screwed into a 3D printed plastic box and the frame using L brackets, as shown in Figure 2.8. The actuator mount for the frame was designed to be adjustable so that the actuators could be easily aligned with the cable wrapping points on the scapula to prevent bending moments from being transferred to the actuators (Figure 2.9). 31

41 Figure 2.8: The scapula was mounted to the frame using L brackets. The scapula was also attached to the top of the frame using the plastic deltoid guide to provide stiffness to the Sawbone. Figure 2.9: Pneumatic actuators and load cells. Actuator mounts were designed to allow adjustment of the horizontal and vertical position of the actuators. 32

42 2.1.4 Displacing Force A material testing machine (Model 1122, Instron, Norwood, MA) was used to apply a displacing force to the humerus. The simulator frame was bolted on to the base of the Instron to prevent movement between the two. Aircraft cable attached at the metaphysis of the humeral component and connected to the Instron was used to apply the displacement to the humerus. Pulleys allowed the displacement to be applied in the anterior, posterior, superior, or inferior directions relative to the scapula (Figure 2.10). An inline load cell (MLP 500, Transducer Techniques, Inc., Temecula, CA) was used to obtain the force in the displacing cable. Superior pulley Load cell Displacing force cable Instron Anterior pulley Inferior pulley Posterior pulley Figure 2.10: Simulator frame and Instron material testing machine. Aircraft cable routed using pulleys was used to apply a displacement in one of four primary directions relative to the scapula (anterior, posterior, superior, inferior). Anterior loading is shown. 33

43 2.2 Kinematics and Force to Dislocate Kinematics An Optotrak Certus motion capture system (Northern Digital Inc., Waterloo, ON) was used to record shoulder kinematics. One camera was used and tracking clusters were fixed to the scapula and the distal end of the humerus. An Optotrak Data Acquisition Unit (ODAU) II was used to collect analog data from the muscle and displacing force load cells. Shoulder kinematics were calculated according to the recommendations of the International Society of Biomechanics (Wu, et al., 2005). As shown in Figure 2.11, the humeral coordinate system was formed using the medial epicondyle (ME), lateral epicondyle (LE), and the glenohumeral rotation centre (GH). In this case, due to the reverse anatomy of the prosthesis used, GH was calculated by finding the centre of a sphere fit to the humeral cup, which corresponds to the centre of rotation. It should be noted that this is more medial than the centre of rotation would be in a natural shoulder. The origin of the coordinate system was at GH. was parallel to a line from GH to the midpoint of a line connecting ME and LE, pointing inferiorly, was normal to a plane formed by the three landmarks pointing anteriorly, and was the cross product of and pointing laterally. Note that because a left shoulder was used, pointed inferiorly rather than superiorly. The scapular coordinate system was based on the trigonum spinae (TS), inferior angle (IA), and acromion angle (AA). The origin was at AA. was parallel to a line from TS to AA pointing laterally, was normal to a plane formed by the three landmarks pointing anteriorly, and was the cross product of and pointing inferiorly. Again, due to the use of a left shoulder, was directed inferiorly rather than superiorly. 34

44 Zh Xh GH Zs Xs Yh AA Ys TS LE IA ME Figure 2.11: Coordinate systems used. ME = medial epicondyle, LE = lateral epicondyle, GH = glenohumeral rotation centre, AA = acromion angle IA = inferior angle, TS = trigonum spinae. Because the scapula Sawbone model used has a built in vise attachment (Figure 2.1), the anatomical landmarks TS and AI were not available. Therefore, in order to use this coordinate system, an intermediate coordinate frame was created using a Sawbone scapula with the full anatomy (Model #1021). This intermediate coordinate system was based on AA together with the scapular notch (SN) and coracoid process (CP), shown in Figure The transformation from the intermediate to the ISB recommended coordinate system was then calculated so that the ISB coordinate system could be obtained by digitizing AA, SN, and CP, which are all available on the Sawbone model used. 35

45 SN CP Figure 2.12: Additional scapular anatomical landmarks used to create an intermediate coordinate system for the scapula. SN = scapular notch, CP = coracoid process. Once these coordinate systems were established, the shoulder angles could be calculated according to a Y X Y Euler sequence. This process is outlined below. cos cos cos sin sin sin ϕ sin θ cos sin sin cos cos sin sin cos cos sin cos cos sin cos sin sin cos cos cos sin sin θ arctan 1,2 3,2 arccos 2,2 arctan 2,1 2,3 where and are the transformations from the scapula and humerus anatomical coordinates to global respectively, is the transformation from scapula to humerus anatomical coordinates, and is the coordinates of the origin of the scapula frame in humeral coordinates. The angles calculated are: = abduction plane angle, = abduction angle, and = internal rotation angle, which are explained in Figure

46 Figure 2.13: Shoulder angles used. Abduction plane angle is an initial rotation about the long axis of the humerus (Ys) that defines the plane abduction will occur in. Abduction is a rotation about an intermediate X axis. Internal rotation is a final rotation about Yh Force to Dislocate A typical plot of muscle and displacing forces versus displacement of GH for a superior dislocation is shown in Figure The peak displacing force was defined as the force to dislocate, which was used as a measure of stability for this study F D AD MD PD Force to dislocate Force (N) Displacement (mm) Figure 2.14: Muscle and displacing forces versus displacement of GH for a typical superior dislocation. FD = displacing force, AD = anterior deltoid force, MD = middle deltoid force, PD = posterior deltoid force. 37

47 2.3 Simulator Reliability Before the simulator was used for investigations of stability, experiments were carried out to determine its reliability. The only factor selected that had the potential for variation was shoulder posture (abduction plane and abduction angles) and the outcome measure of force required to dislocate the shoulder also had the potential for variable results. Therefore, two experiments were conducted with the goal of quantifying expected variation in these so as to provide context for future results, as well as face validity that the simulator functions as expected Static Posture Repeatability Using the shoulder simulator, a desired posture is attained by applying constant loads to the muscle cables. Therefore, in part due to friction, there is some variability in the posture resulting from a given muscle load. To examine the repeatability of statically positioning the shoulder, fifteen combinations of muscle forces were input manually and the resulting abduction plane and abduction angles were calculated. As internal rotation is not independently controllable using only the deltoid cables, it was not examined in this experiment. The muscle force combinations tested are shown in Table 2.1. Each combination was repeated five times and the trials were performed in a randomized order. 38

48 Table 2.1: Muscle force combinations tested. Middle Deltoid (N) Anterior Deltoid (N) Posterior Deltoid (N) The resulting abduction and abduction plane angles for each force input combination are shown in Figure One trial from the AD = 30 N, MD = 97 N, PD = 30 N combination was excluded from reliability calculations as the middle deltoid force was input incorrectly. 39

49 Abduction ( ) o [70,97,30] [30,97,30] [30,97,50] [30,87,30] [70,77,30] [60,77,30] [50,77,30] [40,77,30] [30,77,30] [30,77,40] [30,77,50] [30,67,30] [70,57,30] [30,57,30] [30,57,50] Abduction Plane ( o) Figure 2.15: Shoulder angles obtained for all trials. Muscle force combinations are shown in the legend as [AD force, MD force, PD force] in N. The repeatability of the abduction angle and abduction plane angle was calculated according to the methods of Bland and Altman (Bland & Altman, 1996). The estimated within subject standard deviation,, was determined by taking the square root of the mean square error term from a one way ANOVA. In this case, the subjects were the 15 force combinations. It can then be said that 95% of the time the difference between the resultant angles from two trials with the same force inputs is expected to be less than Using this method, it was determined that the difference between abduction angle for two replicate trials using will be less than 8.2 o, 95% of the time and the difference in abduction plane angle will be less than 10.1 o, 95% of the time. It was also confirmed that 40

50 the standard deviation of the five trials was not related to the magnitude of the angle achieved (Figure 2.16). Abduction Angle Standard Deviation ( ) o o Abduction Angle Mean ( ) Abduction Plane Standard Deviation ( ) o Abduction Plane Mean ( o) Figure 2.16: Standard deviation of angles obtained from five trials plotted against the average of the five trials. This confirms the standard deviation is not strongly related to the mean angles. The results obtained using the Bland Altman method were confirmed using an intraclass correlation coefficient (ICC). A two way model was used as this was a test retest experiment where trials were crossed with force combinations. A random model was selected as the force inputs chosen are only a sample of possible muscle force combinations that may be used. Therefore, ICC (2,1) was calculated as: 2,1 1 where is the error mean square, is the subjects mean square, is the trials mean square, is the number of trials, and is the number of combinations tested (Shrout & Fleiss, 1979). 41

51 An ICC of was found for the abduction angle and an ICC of was found for the abduction plane angle. These indicate excellent repeatability in that 92.3% and 98.2% of the variation in the data was intended variation due to different force inputs. However, the ICC should be interpreted with caution as larger ICC scores can be obtained by having greater spread in the data, an effect that can be observed here. The variance in the abduction plane angles was greater than for the abduction angles, as seen in the Bland Altman analysis; however, the ICC was greater for the abduction plane due to the larger range of angles tested. The correlation between trials is shown in Figure o Abduction Angle Trials 2-5 ( ) Abduction Angle Trial 1 ( o) Abduction Plane Trial 1 ( o) Figure 2.17: Correlation among trials for abduction angles and abduction plane angles. The correlation appears greater for the abduction plane angles due to a greater range of angles tested. o Abduction Plane Trials 2-5 ( ) Dislocation Repeatability As force to dislocate was to be used as a measure of stability for the simulator, it was also necessary to determine its repeatability. If the variation was found to be large, this could indicate the need to perform more replicates of the factorial experiment to account for noise. 42

52 In order to assess the repeatability of dislocating the reverse shoulder joint, the shoulder was dislocated five times in each direction (anterior, posterior, superior, inferior) in a randomized order. By applying 30.1 ±.5 N to the anterior deltoid, 77.1 ±.4 N to the middle deltoid, and 29.8 ±.5 N to the posterior deltoid, the shoulder was positioned in 12.5 ± 3.0 o abduction plane, 39.6 ± 1.8 o abduction, and 5.8 ± 2.3 o internal rotation. A displacing force was applied to the humeral component at 100 mm/min. The mean force versus displacement plots are shown for each loading direction in Figure As can be observed in this figure, standard deviations in forces were fairly small throughout the trials. The main feature of these plots used is the maximum displacing force, defined as the force to dislocate the shoulder. The mean force to dislocate for each direction is shown in Figure The reliability of the force to dislocate was also analyzed using the Bland Altman method and it was found that the difference between the force to dislocate for two replicate trials is expected to be less than 14.1 N, 95% of the time. This represents approximately 8 14% of the force to dislocate. 43

53 200 Anterior Dislocation 200 Posterior Dislocation Force (N) F D AD MD PD Force (N) F D AD MD PD Force (N) Displacement(mm) Superior Dislocation F D AD MD PD Force (N) Displacement(mm) Inferior Dislocation F D AD MD PD Displacement(mm) Displacement(mm) Figure 2.18: Mean muscle and displacing forces plotted against displacement of the glenohumeral joint centre (on the humerus) for five trials. FD = displacing force, AD = anterior deltoid force, MD = middle deltoid force, PD = posterior deltoid force. Standard deviations for each force are shown as shaded areas. 200 Force to Dislocate (N) Anterior Posterior Superior Inferior Figure 2.19: Mean force required to dislocate the shoulder joint for four loading directions. Standard error of the mean is shown with error bars. 44

54 2.4 Summary The simulator described in this chapter was created for the purpose of assessing the stability of reverse shoulder arthroplasty in an anatomical model and, therefore, design choices were made to allow this goal to be achieved. This simulator is one of the two simulators developed to investigate the stability of reverse shoulder arthroplasty in an anatomical model (Henninger, et al., 2011). The method of displacement application used was novel in that other anatomical simulators have used manual displacement application which is less precise in terms of rate and direction of application. The use of an unconstrained humerus positioned only by muscle forces was also unique and allowed for the modeling of in vivo conditions where the humerus would likely not be constrained in a given orientation. As a part of the development a prototype of the simulator was first created and used to test various options for muscle modelling, muscle wrapping and insertion points, and scapula and humeral fixtures. Once design parameters were decided upon, the simulator outlined here was created. The development of this testing platform required mechanical design of the simulator, establishing a procedure for motion tracking, and the creation of MATLAB (MathWorks, Natick, MA) scripts and GUIs used in force and motion data collection and analysis. There are a large number of factors that could potentially affect stability of reverse shoulder arthroplasty and, therefore, the shoulder simulator was designed for use in a screening experiment using a factorial design where several factors could be modified concurrently. Although the simulator was designed with this purpose in mind, it was also developed as a platform for studying shoulder biomechanics that will be expanded upon and used for future research in cadaver models of reverse shoulder biomechanics as well as other shoulder related issues. 45

55 Chapter 3 Factors Affecting the Stability of Reverse Shoulder Arthroplasty: A Biomechanical Study A paper submitted to The Journal of Shoulder and Elbow Surgery in December, Introduction Reverse shoulder arthroplasty was developed in 1987 by Paul Grammont to treat massive rotator cuff tear with glenohumeral arthritis, which results in a painful, functionally limited shoulder (Grammont, et al., 1987). This condition is not adequately managed using conventional shoulder arthroplasty (Matsen, et al., 2007; Neer, et al., 1982), yet reverse shoulder arthroplasty has been successful in reducing pain and improving function for these patients (Cuff, et al., 2008; Boileau, et al., 2006). With this procedure, the ball andsocket anatomy of the shoulder joint is reversed, allowing a more constrained joint to be implanted and increasing the deltoid moment arm, among other biomechanical advantages. The complication rate associated with reverse shoulder arthroplasty, however, remains high, with rates in clinical studies ranging from 8 55% (Wierks, et al., 2009; Werner, et al., 2005; Young, et al., 2009; Favard, et al., 2011; Gallo, et al., 2010). Often, the most common complication is cited as being instability or dislocation of the shoulder (Cuff, et al., 2008; Cazeneuve & Cristofari, 2010; De Wilde, et al., 2003; Zumstein, et al., 2011). This is concerning as management of instability is difficult and dislocation often results in a loss of shoulder function and the need for additional surgery. 46

56 Cadaveric and non cadaveric shoulder simulators that model muscle loading and bony geometry have been used to examine shoulder biomechanics, including shoulder injuries (Osterhoff, et al., 2011), muscle function (Ackland & Pandy, 2009), and traditional arthroplasty (Shapiro, et al., 2007). However, the use of such simulators in investigations of reverse shoulder arthroplasty stability has been rare. A recent exception found that humeral component version and humeral cup thickness have minimal effect on stability (Henninger, et al., 2011). This contradicts results found using only the implant components in a non anatomical simulator (Favre, et al., 2010), which implied that installing the prosthesis with some anteversion improved stability. This discrepancy indicates the need to examine reverse shoulder biomechanics in a physiological model to better understand behaviour of the prosthesis in vivo. In addition, most studies have examined single factors separately, neglecting interactions between factors which could provide better insight into the complicated problem of instability. There exists a large variety of factors which may contribute to stability of reverse shoulder arthroplasty. These are based on clinical results indicating that, for example, the reverse shoulder may be more prone to dislocation certain directions (Bicknell, et al., 2010) or that some arm positions may lead to instability (Molé & Favard, 2007). Other factors, such as compressive force and humeral socket depth (Gutiérrez, et al., 2008), have been found to have an effect on the intrinsic stability of the reverse prosthesis itself but have not been examined in a physiological model that accounts for the effect of active constraints, such as muscle loading, and passive constraints, such as bony geometry and soft tissue bulk. Additionally, some factors, such as glenosphere eccentricity (Lädermann, et al., 2009) and diameter (Gallo, et al., 2010), have been theorized to affect stability without any supporting 47

57 experimentation. None of these factors have been examined in a model that includes bony geometry and active muscle loading. Therefore, the objective of this study was to determine the effect of loading direction, arm posture, glenosphere diameter, glenosphere eccentricity, and humeral socket constraint on stability and the interactions between these factors in a simulator that includes active muscle loading and bony geometry. 3.2 Methods Joint Simulator Stability testing was performed using a custom glenohumeral joint simulator (Figure 3.1). Delta XTEND (DePuy Inc., Warsaw, IN) components were implanted in Sawbones (Pacific Research Laboratories, Inc., Vashon, WA) and the scapula was fixed to the simulator frame while the humerus was free to move. The three heads of the deltoid (anterior, middle, and posterior deltoid) were modelled using aircraft cable and muscle forces were applied using pneumatic actuators and recorded with in line load cells (Transducer Techniques, Inc., Temecula, CA). Muscle insertion points and paths were determined from previous anatomical studies (Dalley & Moore, 1999; Liu, et al., 1997; Otis, et al., 1994) and the cables were connected to the humerus using three degree of freedom ball joints. As the rotator cuff is often compromised in patients who receive this surgery, a worst case scenario was assumed and the deltoid was the only muscle included in the model. A 3.6 kg weight was attached to the distal humerus to represent the weight of the arm (Zatsiorsky, 2002). 48

58 Pneuma c Actuator Load cell MD PD Linear Actuator AD Marker Triad 3.6 kg Figure 3.1: Glenohumeral joint simulator. Force was provided to the anterior (AD), middle (MD), and posterior (PD) deltoid cables by pneumatic actuators. A material testing machine was used as a linear actuator to impose a displacing force which could be applied anteriorly, posteriorly, superiorly, or inferiorly through the use of pulleys. Optical marker triads on the humerus and scapula were used to capture shoulder kinematics. A material testing machine (Instron, Norwood, MA) provided the displacing force to the humeral head via a cable attached to the metaphysis of the humeral component. This location of force application has been used previously (Henninger, et al., 2011; Giles, et al., 2011) and was chosen as it is the closest to the centre of rotation that the force can be applied, thereby minimizing applied moments. Through the use of pulleys, the displacement could be directed in one of four primary directions relative to the scapula (anterior, posterior, superior, or inferior). Displacements were applied at 100 mm/min. Motion tracking was performed using an Optotrak Certus system (Northern Digital, Waterloo, ON). Shoulder angles were calculated based on the coordinate systems recommended by the International Society of Biomechanics (Wu, et al., 2005), as shown in 49

59 Figure 3.2. Shoulder angles were calculated based on a Y X Y Euler sequence, resulting in abduction plane, abduction, and internal rotation angles. Zh Xh GH Zs Xs Yh AA Ys TS LE IA ME Figure 3.2: Coordinate systems used. ME = medial epicondyle, LE = lateral epicondyle, GH = glenohumeral joint centre, AA = acromion angle, TS = trigonum spinae, IA = inferior angle. The origin of the humeral coordinate system is at GH, is the line from GH to the midpoint of LE and ME, is normal to the plane formed by ME, LE, and GH pointing anteriorly, and is the cross product of and. The origin of the scapular coordinate system is at AA, is the line pointing from TS to AA, is normal to the plane formed by AA, TS, and IA, and is the cross product of and Experimental Design Six factors were analyzed in this experiment: loading direction, abduction angle, abduction plane angle, socket depth, glenosphere diameter, and glenosphere eccentricity. Each factor was tested at a low and high level, with the exception of loading direction which had four levels. The factors and levels of each factor are shown in Figure 3.3. The angles were chosen to be the extremes of the shoulder s range of motion without impingement of the humeral socket on the scapula and were achieved by applying experimentally derived forces to the deltoid cables. 50

60 Loading Direction Abduction Abduction Plane Superior Anterior Posterior 45o 60o 55 o -15 o Inferior Frontal view Axial view Socket Depth Glenosphere Eccentricity Glenosphere Diameter Retentive 4mm High Mobility Standard 2mm Inferior-offset 36mm 42mm Figure 3.3: Factors and levels investigated. One replicate of a half fraction factorial design experiment (Montgomery, 2001) was carried out to examine these six factors in 64 trials. Due to implementation of a half fraction, as opposed to full, factorial design, there was aliasing between the following two factor interactions: loading direction/abduction angle and abduction plane/eccentricity, loading direction/abduction plane and abduction/eccentricity, and loading direction/eccentricity and abduction/abduction angle. As a result of this, if one of these interactions is found to be significant, its aliased interaction will show significance as well and it is difficult to determine which interaction is truly important. The experimental design is outlined in greater detail in Appendix A. 51

61 3.2.3 Data Analysis The displacing force required to dislocate the shoulder joint was used as a measure of stability for this investigation. Significant factors were determined using a normal probability plot of effect estimates (Montgomery, 2001) for the six factors and all two factor interactions. These were verified using a six way ANOVA and post hoc Tukey tests where p<0.05 was considered significant. 3.3 Results To determine how reliably the force to dislocate could be measured, the shoulder was dislocated five times in each direction, with the same arm posture and components each time. Based on the methods of Bland and Altman (Bland & Altman, 1996), it was determined that the force to dislocate in two replicate trials would be within 14.1 N of one another 95% of the time. Four shoulder postures were used in this experiment (two levels of abduction, two levels of abduction plane). The applied muscle forces and resulting shoulder angles for each posture used are shown in Table 3.1. Standard deviations were found to be less than 0.4 N for force inputs and 4.5 o for shoulder angles. 52

62 Table 3.1: Forces applied to each muscle and resulting shoulder angles for low and high levels of the abduction and abduction plane factors. Standard deviations are shown in brackets. (n = 16 for each posture) Factor Level ( o ) Muscle Force (N) Shoulder Orientation ( o ) Abduction Plane Abduction Anterior Deltoid Middle Deltoid Posterior Deltoid Abduction Plane Abduction Internal Rotation (0.09) (0.15) (0.19) (3.35) (3.25) (2.66) (0.10) (0.07) (0.17) (3.00) (3.17) (2.50) (0.11) (0.35) (0.10) (4.35) (3.48) (4.40) (0.29) (0.30) (0.28) (2.86) (4.47) (2.74) It was determined that abduction (p<0.0001), socket depth (p<0.0001), and glenosphere eccentricity (p<0.001) had a significant effect on force to dislocate the joint. In addition, the loading direction/socket depth interaction was deemed significant (p<0.001). Increasing glenohumeral abduction from 45 o to 60 o was found to increase force to dislocate by 59.5 N (30.5%) (Figure 3.4). Changing from a centred to an inferior offset glenosphere increased force to dislocate by 35.3 N (17.0%). Force to dislocate was not affected by changes in the abduction plane or the diameter of the glenosphere (p>0.05). Increasing the socket depth of the humeral component by changing from a high mobility cup to a retentive cup resulted in an increase in force to dislocate the joint as well, but it was dependent on loading direction (Figure 3.5). The increase in stability occurred for superior, posterior, and anterior loading, but not inferior. Force to dislocate was increased by N (88.0%), N (66.3%), and 70.5 N (35.9%) for superior, posterior, and anterior loading respectively. Also contributing to this interaction was the result that when using a retentive 53

63 humeral cup, force to dislocate was 69.1 N (29.8%) greater for superior loading than inferior loading. No other two factor interactions were found to be significant. Force to Dislocate (N) Ant Sup Post Inf Loading Direction * o 40 o 60 0 o -10 o 55 Abduction Abduction Plane Force to Dislocate (N) High Mobility Retentive Socket Depth * Standard Inf-Offset Glenosphere Eccentricity * mm 42mm Glenosphere Diameter Figure 3.4: Force to dislocate by factor. Modifying abduction, socket depth, and glenosphere eccentricity created significant changes in force to dislocate the shoulder. An asterisk indicates p< High Mobility Retentive Force to Dislocate (N) * * * * Anterior Posterior Superior Inferior Loading Direction Figure 3.5: Interaction between loading direction and socket depth. Increasing the socket depth from a high mobility cup to a retentive cup caused significant increases for all loading directions except inferior loading. There was also a significant difference in force to dislocate between superior and inferior loading when using a retentive cup. An asterisk indicates p<

64 3.4 Discussion Instability is often the most common complication following reverse shoulder arthroplasty and therefore understanding how to decrease the risk of dislocation is crucial for improving outcomes of this surgery. This study determined which factors influence force to dislocate in reverse shoulder arthroplasty and how they interact with one another. Increased glenohumeral abduction significantly improved stability independent of all other factors investigated. This effect was expected as increased abduction was a result of increased muscle forces, thus producing a larger joint reaction force. In a previous study of the intrinsic stability of reverse shoulder arthroplasty, compressive force was found to be the most important of the three factors affecting stability that were studied (Gutiérrez, et al., 2008). It is difficult to make recommendations for risky arm postures based on this as consistently maintaining high degrees of abduction is not practical. However, as this effect is likely due in part to the increased deltoid forces, it reiterates the suggestion that has been made previously that increasing deltoid tension may help to stabilize the joint (Boileau, et al., 2006; Grammont & Baulot, 1993). As the shoulder was found to be more stable when the muscle were more active, this also indicates that active rehabilitation may be more beneficial for patients than passive rehabilitation as the activity of shoulder muscles could reduce the risk of instability. Glenosphere eccentricity also had an impact on force to dislocate. One explanation for this may be that in vivo, an inferior offset glenosphere may increase deltoid tension. In addition, one mode that has been suggested for dislocation is impingement causing a levering 55

65 mechanism leading to dislocation of the joint (Gallo, et al., 2010) and another benefit of the inferior offset glenosphere is that it helps to prevent inferior impingement. Humeral socket depth was found to have a large effect on stability of the reverse prosthesis that was dependent on loading direction. The significant effect of humeral socket depth was expected as the deeper socket options exist specifically to increase the stability of the joint, and it has been found previously that this has a significant effect on stability (Gutiérrez, et al., 2008). However, due to the implementation of a factorial experiment design, the dependence of this effect on direction of dislocation was identified. This is due in part to the unconstrained nature of humerus during dislocations. Because of this, the applied displacing force often caused the humerus to rotate prior to subluxation, and therefore, in directions which allow greater range of motion (i.e. inferior, anterior), the humeral cup was rotated to a position where it covers less of the glenosphere, resulting in the increased socket depth becoming less effective. This reflects what could happen in vivo and indicates that although increased socket depth adds stability to the joint in general, it does depend on the mode of dislocation. It should also be noted that there is an associated trade off between mobility and stability as the retentive cups are more prone to impingement on the scapula and have a reduced theoretical range of motion (Gutiérrez, et al., 2009) and therefore, the decision to use a constrained humeral socket should be patient specific. The remaining factors, abduction plane and glenosphere diameter, had no impact on force to dislocate. The minimal effect of glenosphere diameter agrees with results found previously (Gutiérrez, et al., 2008). The lack of effect of abduction plane is likely due to the 56

66 unconstrained humerus in the experimental setup. However, it was felt that an unconstrained humerus better represented how dislocations may occur in vivo. There are some limitations associated with this experimental setup. Although this simulator models a more physiological setting than intrinsic simulators by including active muscle loading, the effect of soft tissue bulk is still not accounted for and this may also have an influence on the results. Therefore, further research should be undertaken to determine how this as well as other factors impact stability with various soft tissue structures in place. Additionally, the deltoid was the only muscle included in the model and reverse shoulder arthroplasty patients do generally have some of their rotator cuff intact, along with other muscles that cross the joint. For this study, a worst case scenario of complete rotator cuff deficiency was assumed; however, further work could further illuminate how various muscles influence stability. Another limitation is that dislocation was modelled by applying a force to the humeral head. This may not fully replicate the possible mechanisms of dislocation. However, it was felt that this would give a good representation of stability while simplifying and focusing the experiment. Finally, the aliasing of some two factor interactions was also a potential limitation as if one aliased interaction was found to be significant, its counterpart would show significance as well and it would be difficult to determine where the true significance lay. However, as none of the aliased interactions were significant, any such issues were avoided. This was the first study to investigate the effects of shoulder orientation and glenosphere eccentricity on the stability of reverse shoulder arthroplasty and the first to examine the effects of glenosphere diameter and humeral socket constraint using an anatomical 57

67 shoulder model, which is critical for understanding the biomechanics of the prosthesis under the influence of biological factors such as muscle loading and bony geometry. Another strength of this study lies in its factorial design which allows interactions between factors to be analyzed along with their main effects. Among the factors examined in this study, a dependency was found between humeral socket depth and loading direction. This demonstrates the importance of considering interactions in future studies as well. None of these factors operates in isolation in vivo, and therefore, it is essential to understand interactions between factors to fully understand the problem of instability in reverse shoulder arthroplasty. 58

68 Chapter 4 Discussion and Conclusions 4.1 Shoulder Simulator Design As outlined in Chapter 1, many different options exist for shoulder simulator design. The simulator developed here combined features of existing simulators in a way that enabled the evaluation of stability of reverse shoulder arthroplasty. As the objective of this work was to gain a better understanding of the stability of reverse shoulder arthroplasty in vivo, an anatomical simulator was chosen so that muscular loading and bony structures were included in the model. As with some previous simulators (Favre, et al., 2008; Osterhoff, et al., 2011), synthetic bones were used in the simulator as opposed to cadaver specimens, and as a result, no soft tissue structures, such as muscle bulk and ligaments, were included in this model. This was in part because this is the first phase of a larger project and was used to determine the viability of the simulator design, while still allowing clinically relevant data to be obtained. Additionally, the use of synthetic bone is advantageous in that specimens are nearly identical and, therefore, effects of the factors studied will not be confounded with anatomical variation between specimens. Another advantage is that there were no time constrains in using a specimen and by dividing the experiment between two days, a large number of trials could be completed with minimal changes to the experimental setup between days. Modelling of muscles in the simulator was implemented in a manner common to many previous shoulder simulators, including the use of pneumatically actuated cables (Kedgley, 59

69 et al., 2007; McMahon, et al., 2003) and representing the deltoid as three sections (Ackland, et al., 2010; Henninger, et al., 2011). This model differed from many existing simulators in that the deltoid was the only muscle included, but this was due to the specific purpose of examining reverse shoulder arthroplasty where most patients have significant rotator cuff deficiency. The strategy of eliminating the rotator cuff altogether has been used previously in software models (Terrier, et al., 2008) and represents a worst case scenario for available musculature available to stabilize and mobilize the joint. As a part of muscle modelling, wrapping points were created on the scapula to maintain lines of action for the shoulder muscles. In this simulator, the cables were essentially fed through holes in a plastic structure rather than over pulleys. This has been done in other simulators (Kelkar, et al., 2001; Favre, et al., 2008; Williams, et al., 2001) and was chosen as it allowed the wrapping points to be very close to the surface of the bone, the wrapping points maintained a consistent position, and the issue of keeping the cable passing correctly over the pulley despite changing lines of action is avoided. The disadvantage of not using pulleys, however, is that friction is generated in these wrapping points. A small piece of bicycle derailleur cable housing was used to alleviate some of the friction, but could not completely eliminate it. As the muscle forces were measured between the pneumatic actuators and the scapular wrapping points, friction in the wrapping points caused a discrepancy between the measured force, and the force that was applied to the humerus between the humeral insertion points and the scapular wrapping points. This is demonstrated in the free body diagram of the cable in Figure 4.1. The magnitude of this discrepancy was assessed by installing a load cell on either side of the wrapping point and comparing the measured forces for a variety of cable orientations. Doing so, the coefficient 60

70 of friction in the wrapping points was found to be approximately 0.14 which would result in a difference in forces of less than 10 N, with smaller differences for larger wrap angles (i.e. larger abduction angles). F 1 F f Wrapping point F N F 2 Figure 4.1: Free body diagram of a muscle cable. Friction in the muscle wrapping points ( ) caused a discrepancy between the force measured by the load cells ( ) and the force applied to the humerus ( ). is the normal force acting on the cable at the wrapping point. An important feature of this simulator was the manner in which the displacing force was applied to the joint. In some previous simulators, a displacing force has been applied manually (Giles, et al., 2011; Henninger, et al., 2011). Using a material testing machine to apply the displacing force, however, offers greater control over the force application. This allowed the rate of displacement as well as the direction of dislocation to be precisely controlled to ensure consistency of displacement application between trials. Overall, the design of the glenohumeral joint simulator combined established methods and novel features to model a physiological shoulder and assess stability following reverse shoulder arthroplasty. The simulator design possesses many advantages, including precision of displacing force application, accuracy of muscle insertion points, and inclusion of muscle loading and bony geometry. 61

71 4.2 Effect of Active Muscle Loading and Bony Geometry This was the first study to examine the effects of arm posture, glenosphere eccentricity and diameter, and humeral socket constraint on stability of reverse shoulder arthroplasty in an anatomical simulator. The effect of loading direction has been studied previously (Henninger, et al., 2011); however, only lateral and anterior loading were compared. While understanding the intrinsic stability of the components is important, knowledge of how the prosthesis behaves in vivo is also critical to preventing dislocation and anatomical shoulder simulators provide a method of representing these conditions in a controllable and observable way. Studying stability in the presence of these biological factors is important largely because of the role they play in providing stability or contributing to instability. Bony structures provide passive constraint in some cases, but if impingement between bones or between a bone and a component occurs, a levering mechanism may cause a dislocation. The forces generated by muscles, however, create active constraints that can stabilize or destabilize the joint, depending on their lines of action. Due to the inherent instability of the bones of the glenohumeral joint, the shoulder muscles are critical in maintaining stability. While it is possible to simplify this effect to the application of one compressive force, this does not fully represent the true in vivo conditions. The muscles of the shoulder pull in different directions and with different magnitudes which often means that the joint is being loaded asymmetrically. Depending on the direction of dislocation and the position of the arm, some muscles may be contributing more to dislocating the joint than to compressing it. Better replication of in vivo conditions is also achieved by positioning the shoulder through the application of appropriate muscle loads. In this way, the shoulder is not only positioned spatially, but the loading conditions 62

72 created by the muscles are also representative of the posture. This effect was observed in the results of this experiment where an increased abduction angle added stability to the shoulder as a combined result of increased compressive forces and the orientation of the shoulder. An anatomical shoulder simulator not only better replicates the true conditions of the shoulder, but also enables the investigation of a number of factors that cannot be examined in an intrinsic simulator. Any factors related to musculature or component placement can clearly best be studied if the model includes muscle and bones in which to install the prosthesis. However, these are not the only factors whose investigation is enabled. The results of this study demonstrated that glenosphere eccentricity can significantly improve stability of reverse shoulder arthroplasty. In a simulator that simply applies a compressive and displacing force to the components, an offset glenosphere would simply shift the entire system with no effect on the relationships between elements. Therefore, to gain an understanding of all of the factors affecting stability of reverse shoulder arthroplasty, it is necessary to utilize simulators that model more of the biological structures of the shoulder. 4.3 Stability Ratio The stability ratio is a measure that is sometimes used to quantify shoulder stability and has been used for the natural shoulder (Lippitt, et al., 1993; Yamamoto, et al., 2009), traditional arthroplasty (Anglin, et al., 2000; Karduna, et al., 1997), and reverse arthroplasty (Favre, et al., 2010). It is defined as the force required to dislocate the joint, perpendicular to the concave component centre line, divided by the compressive force applied parallel to the centre line (Rockwood, et al., 2009) (Figure 4.2). This measure is used because dislocation 63

73 force is known to be related to compressive force and by normalizing by compressive force, it is possible to compare stability between experiments where different compressive forces are used. Socket Centre Line Glenosphere Dislocating Force (FD) Stability Ratio = FD FC Humeral Socket Compressive Force (FC) Figure 4.2: Stability ratio parameters shown for reverse shoulder arthroplasty. If the compressive and displacing forces are not aligned parallel and perpendicular to the humeral socket centre line respectively, then the calculation of the stability ratio is more difficult. In this case, the joint reaction force should be calculated and split into compressive and dislocating components and then the ratio calculated from these. This is analogous to finding the tangent of the angle between the joint reaction force and the humeral socket centre line (Figure 4.3). 64

74 Joint Reaction Force FC 0 FD F 1 Humeral Socket Stability Ratio = FD FC = tan 0 F 2 Figure 4.3: The stability ratio can also be calculated from the angle between the JRF and the humeral socket centre line ( ). FD and FC are the dislocating and compressive components of the joint reaction force, F1 and F2 are applied forces. While this method is useful when examining the intrinsic stability of the shoulder or a prosthesis, it cannot adequately be used when incorporating effects not related to the geometry of the ball and socket joint. The stability ratio is related only to the geometry of the ball and socket and factors such as muscle loads, loading direction, component orientations, and glenosphere eccentricity will have no effect on the ratio. This is highlighted by the work of Guitérrez et al. who found the following mathematical formula for the stability ratio (Gutiérrez, et al., 2008): tan 1 tan, 2 atan 1 where FD is the force required to dislocate the prosthesis, FC is the compressive force, is the coefficient of friction between the components, is the depth of the humeral socket, and is the radius of the glenosphere. 65

75 The stability ratio was employed in a study of how component orientation affects stability of reverse shoulder arthroplasty and was found to change with component orientation (Favre, et al., 2010). In this case, the displacing and compressive forces were always applied in the anterior and medial directions while the components were rotated. These forces were then divided to get a ratio without considering that components of the displacing force were contributing to compression and vice versa. Therefore, the stability ratio was not calculated as outlined by Rockwood and this is actually a different measure, which may explain why it was found that the stability ratio varied with orientation of the components. For this reason, the stability ratio was not utilized in these experiments. Because of the inclusion of non geometrical elements such as muscle loading and arm posture, the force required to dislocate the joint will give a better indication of the stability of the prosthesis under the influence of these elements. 4.4 Clinical Relevance The purpose of this work was to gain an understanding of the factors affecting stability of reverse shoulder arthroplasty that will aid in the creation of guidelines that will decrease the risk of dislocation in reverse arthroplasty patients. It was determined that increased glenohumeral abduction resulted in an increase in stability of the joint. Although this may provide some insight into arm postures that are at increased risk of dislocation, it is obviously unreasonable to recommend that patients keep their arm abducted at all times. However, this is not the only conclusion that follows from this result. Increased abduction angles were achieved by increasing the deltoid forces, 66

76 particularly in the middle deltoid, which thereby increased the joint compressive force. It is therefore likely that the increase in stability is due, in part, to the increased compressive load, which has previously been shown to have a large effect on stability (Gutiérrez, et al., 2008). This also agrees with previous recommendations to increase deltoid tension to prevent dislocation of the prosthesis (Grammont & Baulot, 1993; Zumstein, et al., 2011). Deltoid tension can be increased in a number of ways, including using thicker polyethylene cups or using a spacer, distalizing the centre of rotation by using inferior offset glenospheres, and using larger diameter glenospheres (Boileau, et al., 2005). Care must be taken to not over tension the deltoid however, as this results in excess strain on the acromion which may lead to its fracture (Gallo, et al., 2010). Objective methods for determining optimal deltoid tension intraoperatively do not exist, although some recommendations have been made (Lädermann, et al., 2009). The other corollary of this result is that it may be beneficial for clinicians to prescribe active rehabilitation for patients as opposed to passive, as these results indicate that active musculature may decrease the risk of dislocation. Glenosphere eccentricity was another factor that was found to improve stability in reverse shoulder arthroplasty. The inferior offset glenosphere was created in accordance with recommendations that the glenosphere be positioned lower on the glenoid in order to reduce the risk of impingement of the humeral cup on the scapula (Nyffeler, et al., 2005). As a levering mechanism has been suggested for dislocation, prevention of impingement may also help to minimize the risk of dislocation. Additionally, as an eccentric glenosphere lowers the humerus, it should theoretically increase deltoid tension as well, thus further stabilizing the joint. 67

77 Finally, it was determined that increased humeral cup constraint increases stability, depending on the direction of loading. This increased stability was expected, as this is the purpose the retentive cup was designed for; however, the interaction with loading direction was interesting. Although the more constrained cup did not increase inferior stability, this may not be of much concern as inferior dislocations are rarely reported for reverse shoulder arthroplasty (Bicknell, et al., 2010; Cazeneuve & Cristofari, 2010). As the force to dislocate remained unchanged for inferior loading, in this experiment, use of a retentive cup was not detrimental to stability for any cases, but was simply more effective when loaded in some directions than others. Other measures need to be considered when using a more constrained humeral socket however. It has been shown that range of motion generally decreases when constraint is increased (Gutiérrez, et al., 2009) and therefore depending on patient specific parameters, such as anatomy and component placement, use of a constrained implant may or may not be warranted. While these factors have been shown to improve stability of reverse shoulder arthroplasty, there are many other considerations that need to be made to ensure these will improve overall results of the surgery. These include outcomes such as impingement, range of motion, component fixation, and stress in muscles and bones. An understanding of how some of these are affected by various factors does exist (Harman, et al., 2005; Gutiérrez, et al., 2008), but more work is required to determine conditions that will optimize all outcomes. This is a challenging problem, particularly because it is likely a patient specific one. 68

78 4.5 Conclusions An anatomical glenohumeral joint simulator was designed and developed using a synthetic bone model. The three heads of the deltoid were simulated using pneumatically actuated cables and a material testing machine applied a dislocating force to the humeral head. This simulator enabled the investigation of factors affecting the stability of reverse shoulder arthroplasty. The reliability of simulator shoulder orientations achieved by applying muscle forces was examined and the variation in angles for replicate trials was quantified. As force to dislocate was used as a measure of stability in this study, a similar experiment was performed to quantify the reliability of this measure. The variation in both of these quantities was found to be acceptable for the stability tests that were performed. The effect of arm posture (abduction and abduction plane angles), loading direction, glenosphere diameter and eccentricity, and humeral socket constraint on stability of reverse shoulder arthroplasty were investigated using the custom shoulder simulator. A factorial experiment design was implemented which allowed the interactions between factors to be examined as well. It was determined that glenohumeral abduction and glenosphere eccentricity both affect stability of the prosthesis and that humeral socket constraint affects stability, but is dependent on loading direction. This was the first study to examine the majority of these factors using an anatomical shoulder simulator and these results should provide insight into modifications that can be made intraoperatively to aid in reducing the risk of dislocation in reverse shoulder arthroplasty. 69

79 4.6 Limitations As with any study, the work presented here is not without limitations. Some of these have been discussed in section 4.1 Shoulder Simulator Design, including the use of synthetic bone and friction in the scapular wrapping points. Another limitation of this work is that only one mode of dislocation, a displacement applied to the humeral head, was explored. The mechanism of dislocation in vivo is unclear and it is likely that this method does not fully represent all potential mechanisms of dislocation. However, this is a method that has been used previously (Giles, et al., 2011; Henninger, et al., 2011) and gives a general reflection of how much force is required to dislocate the prosthesis, providing an accepted surrogate for stability. The shoulder is a complex joint, and in vivo, scapular motion contributes to the full range of motion of the joint. However, in this simulator, the scapula was fixed to the frame and all motion occurred at the glenohumeral joint. As the joint of interest in this study was the glenohumeral joint, theoretically, the only effect scapular motion would have had on the results would be due to a changing gravitational line of action. The ratio of glenohumeral to scapular rotation in abduction is generally modelled as being 2:1. Therefore, the abduction range of 15 o that was used implies that a 7.5 o change in scapular rotation should occur concurrently. As effects from this small amount of rotation would likely be small, it was deemed that inclusion of this small potential effect was not worth complicating the simulator design by incorporating scapular motion. 70

80 4.7 Future Work There are many avenues for next steps for this project. A number of factors remain that can be tested using the current simulator setup. Most important among these is component positioning. Due to the non anatomic nature of the prosthesis, component positioning is not obvious, and when suggestions exist for optimal component placement, these are not always supported by rigorous experimentation. For example, it has been suggested that tilting the glenosphere inferiorly may decrease the risk of impingement, but the effect of this on stability is yet to be determined. Humeral component anteversion is also often suggested. Although a recent cadaver study found this had little effect on force to dislocate, this study examined only lateral and anterior displacing forces and one arm posture. Therefore, more insight into the effect of version could be obtained by investigating interactions with more loading directions and various arm postures. The next phase of this work will involve extending the current shoulder simulator for use with cadaver specimens. This will create a more physiological model that includes effects of soft tissue structures, which likely play a role in providing passive stability. The addition of other muscles crossing the shoulder joint would allow better controllability of the shoulder and, again, create a more realistic model. This would also enable investigations into the function of individual muscles and soft tissue structures in terms of stability. Other improvements that can be made to the simulator include the addition of feedback control of the pneumatic actuators that provide muscle forces. This will enable more precision in applying these forces and decreased experiment time. Having this type of 71

81 muscle force control would also enable the modelling of situations with dynamic muscle loading. The end goal of this research is to implement computer assisted surgery for reverse shoulder arthroplasty. Before this can be realized, the biomechanics of reverse shoulder arthroplasty need to be better understood. In this project, a platform has been developed that will provide a means for investigation of this prosthesis. 72

82 References Ackland, D. C. & Pandy, M. G., Lines of action and stabilizing potential of the shoulder musculature. Journal of Anatomy, 215, pp Ackland, D. C., Roshan-Zamir, S., Richardson, M. & Pandy, M., Moment arms of the shoulder musculature after reverse total shoulder arthroplasty. The Journal of Bone & Joint Surgery, American Volume, 92(5), pp Anglin, C., Wyss, U. P. & Pichora, D. R., Shoulder prosthesis subluxation: Theory and experiment. Journal of Shoulder and Elbow Surgery, 9(2), pp Apreleva, M. et al., Experimental investigation of reaction forces at the glenohumeral joint during active abduction. Journal of Shoulder and Elbow Surgery, 9(5), pp Barrett, W. P. et al., Total shoulder arthroplasty. The Journal of Bone & Joint Surgery, American Volume, 69, pp Bicknell, R. T. et al., Does keel size, the use of screws, and the use of bone cement affect fixation of a metal glenoid implant? Journal of Shoulder and Elbow Surgery, 12(3), pp Bicknell, R. T., Matsen, F., Walch, G. & Nove-Josserand, L., Instability after reverse shoulder arthroplasty. The Journal of Bone & Joint Surgery, British Volume, 92-B Supp I, p. 34. Bland, J. M. & Altman, D. G., Measurement error. British Medical Journal, 313, pp Boileau, P. et al., Reverse total shoulder arthroplasty after failed rotator cuff surgery. Journal of Shoulder and Elbow Surgery, 18(4), pp Boileau, P., Watkinson, D., Hatzidakis, A. M. & Hovorka, I., Neer Award 2005: The Grammont reverse shoulder prosthesis: Results in cuff tear arthritis, fracture sequelae, and revision arthroplasty. Journal of Shoulder and Elbow Surgery, 15(5), pp Boileau, P., Watkinson, D. J., Hatzidakis, A. M. & Balg, F., Grammont reverse prosthesis: Design, rationale, and biomechanics. Journal of Shoulder and Elbow Surgery, 14(1, Supp 1), pp. S147 - S161. Bono, C., Renard, R., Levine, R. & Levy, A., Effect of displacement of fractures of the greater tuberosity on the mechanics of the shoulder. The Journal of Bone & Joint Surgery, British Volume, 83-B, pp

83 Broström, L.-Å., Wallensten, R., Olsson, E. & Anderon, D., The Kessel prosthesis in total shoulder arthroplasty: A five-year experience. Clinical Orthopaedics and Related Research, 277, pp Bryce, C. D. et al., A biomechanical study of posterior glenoid bone loss and humeral head translation. Journal of Shoulder and Elbow Surgery, 19(7), pp Bufquin, T., Hersan, A., Hubert, L. & Massin, P., Reverse shoulder arthroplasty for the treatment of three- and four-part fractures of the proximal humerus in the elderly: A prospective review of 43 cases with a short-term follow-up. The Journal of Bone & Joint Surgery, British Volume, 89-B(4), pp Cazeneuve, J.-F. & Cristofari, D.-J., The reverse shoulder prosthesis in the treatment of fractures of the proximal humerus in the elderly. The Journal of Bone & Joint Surgery, British Volume, 92(4), pp Cuff, D. et al., Reverse shoulder arthroplasty for the treatment of rotator cuff deficiency. The Journal of Bone & Joint Surgery, American Volume, 90, pp Dalley, A. F. I. & Moore, K. L., Clinically Oriented Anatomy. s.l.:lippincott Williams and Wilkins. De Wilde, L., Boileau, P. & Van der Bracht, H., Does reverse shoulder arthroplasty for tumors of the proximal humerus reduce impairment? Clinical Orthopaedics and Related Research, 469(9), pp De Wilde, L. et al., The reversed Delta shoulder prosthesis in reconstruction of the proximal humerus after tumour resection. Acta Orthopaedica Belgica, 69(6), pp DePuy Orthopaedics Inc., Delta XTEND Reverse Shoulder System. Design Rationale and Surgical Technique. Edwards, T. B. et al., Subscapularis insufficiency and the risk of shoulder dislocation after reverse shoulder arthroplasty. Journal of Shoulder and Elbow Surgery, 18(6), pp Favard, L. et al., Reverse prostheses in arthropathies with cuff tear: are survivorship and function maintained over time? Clinical Orthopaedics and Related Research, 469(9), pp Favre, P., Loeb, M. D., Helmy, N. & Gerber, C., Latissimus dorsi transfer to restore external rotation with reverse shoulder arthroplasty: A biomechanical study. Journal of Shoulder and Elbow Surgery, 17(4), pp

84 Favre, P., Sussmann, P. S. & Gerber, C., The effect of component positioning on intrinsic stability of the reverse shoulder arthroplasty. Journal of Shoulder and Elbow Surgery, 19, pp Flatow, E. L. & Harrison, A. K., A history of reverse total shoulder arthroplasty. Clinical Orthopaedics and Related Research, 469(9), pp Flury, M. P. et al., Reverse shoulder arthroplasty as a salvage procedure for failed conventional shoulder replacement due to cuff failure - Midterm results. International Orthopaedics, 35(1), pp Franklin, J. L., Barrett, W. P., Jackins, S. E. & Matsen, F. A., Glenoid loosening in total shoulder arthroplasty: Association with rotator cuff deficiency. The Journal of Arthroplasty, 3(1), pp Gallo, R. A. et al., Instability after reverse total shoulder replacement. Journal of Shoulder and Elbow Surgery, 4, pp Giles, J. W. et al., The effect of the conjoined tendon of the short head of the biceps and coracobrachialis on shoulder stability and kinematics during in-vitro simulation. Journal of Biomechanics, 44(6), pp Grammont, P. M. & Baulot, E., Shoulder update: Delta shoulder prosthesis for rotator cuff rupture. Orthopedics, 16, pp Grammont, P. M., Trouilloud, P., Laffay, J. & Deries, X., Etude et réalisation d'une nouvelle prothèse d'épaule. Rhumatologie, 39(10), pp Gutiérrez, S. et al., Hierarchy of stability factors in reverse shoulder arthroplasty. Clinical Orthopaedics and Related Research, 466(3), pp Gutiérrez, S. et al., Evaluation of abduction range of motion and avoidance of inferior scapular impingement in a reverse shoulder model. Journal of Shoulder and Elbow Surgery, 17(4), pp Gutiérrez, S. et al., Center of rotation affects abduction range of motion of reverse shoulder arthroplasty. Clinical Orthopaedics and Related Research, 458, pp Gutiérrez, S., Luo, Z.-P., Levy, J. & Frankle, M. A., Arc of motion and socket depth in reverse shoulder implants. Clinical Biomechanics, 24(6), pp Harman, M., Frankle, M., Vasey, M. & Banks, S., Initial glenoid component fixation in "reverse" total shoulder arthroplasty: A biomechanical evaluation. Journal of Shoulder and Elbow Surgery, 14(1, Supp 1), pp. S162 - S

85 Henninger, H. B. et al., Effect of deltoid tension and humeral version in reverse total shoulder arthroplasty: a biomechanical study. Journal of Elbow Surgery, [in press]. Holcomb, J. O. et al., Reverse shoulder arthroplasty in patients with rheumatoid arthritis. Journal of Shoulder and Elbow Surgery, 19(7), pp Holzbaur, K. R. S., Murray, W. M. & Delp, S. L., A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control. Annals of Biomedical Engineering, 33, pp Itoi, E. et al., Stabilising function of the biceps in stable and unstable shoulders. Journal of Bone & Joint Surgery, British Volume, 75-B, pp Itoi, E. et al., The effect of a glenoid defect on anteroinferior stability of the shoulder after bankart repair: A cadaveric study. The Journal of Bone & Joint Surgery, American Volume, 82, pp Kalouche, I. et al., Reverse shoulder arthroplasty: Does reduced medialisation improve radiological and clinical results? Acta Orthopaedica Belgica, 75(2), pp Karduna, A. R., WIlliams, G. R., Williams, J. L. & Iannotti, J. P., Joint stability after total shoulder arthroplasty in a cadaver model. Journal of Shoulder and Elbow Surgery, 6, pp Kedgley, A. E. et al., The effect of muscle loading on the kinematics of in vitro glenohumeral abduction. Journal of Biomechanics, 40(13), pp Kedgley, A. E. et al., In vitro kinematics of the shoulder following rotator cuff injury. Clinical Biomechanics, 22(10), pp Kelkar, R. et al., Glenohumeral mechanics: A study of articular geometry, contact, and kinematics. Journal of Shoulder and Elbow Surgery, 10(1), pp Lädermann, A. et al., Objective evaluation of lengthening in reverse shoulder arthroplasty. Journal of Shoulder and Elbow Surgery, 18(4), pp Leung, B., Horodyski, M., Struk, A. M. & Wright, T. W., Functional outcome of hemiarthroplasty compared with reverse total shoulder arthroplasty in the treatment of rotator cuff tear arthropathy. Journal of Shoulder and Elbow Surgery, [in press]. Levy, J., Virani, N., Pupello, D. & Frankle, M., Use of the reverse shoulder prosthesis for the treatment of failed hemiarthroplasty in patients with glenohumeral arthritis and rotator cuff deficiency. The Journal of Bone & Joint Surgery, British Volume, 89-B(2), pp

86 Lippitt, S. B. et al., Glenohumeral stability from concavity-compression: A quantitative analysis. Journal of Elbow Surgery, 2, pp Liu, J. et al., Roles of deltoid and rotator cuff muscles in shoulder elevation. Clinical Biomechanics, 12(1), pp Makhsous, M., Lin, F. & Zhang, L.-Q., Multi-axis passive and active stiffnesses of the glenohumeral joint. Clinical Biomechanics, 19(2), pp Matsen, F. A. et al., The reverse total shoulder arthroplasty. The Journal of Bone & Joint Surgery, American Volume, 88-A(3), pp McMahon, P. J. et al., A novel cadaveric model for anterior-inferior shoulder dislocation using forcible apprehension positioning. Journal of Rehabilitation Research and Development, 40(4), pp McMaster-Carr, McMaster-Carr. [Online] Available at: [Accessed 2011]. Molé, D. & Favard, L., Excentered scapulohumeral osteoarthritis [French]. Revue de Chirurgie Orthopédique et Traumatologique, 93(6 supp), pp Montgomery, D. G., Design and Analysis of Experiments. 5th ed. s.l.:john Wiley & Sons, Inc. Neer, C. S., Shoulder Reconstruction. Philadelphia: WB Saunders Co. Neer, C. S., Watson, K. C. & Stanton, F. J., Recent experience in total shoulder replacement. The Journal of Bone & Joint Surgery, American Volume, 64-A(3), pp Neviaser, R. J., Neviaser, T. J. & Neviaser, J. S., Anterior dislocation of the shoulder and rotator cuff rupture. Clinical Orthopaedics and Related Research, 291, pp Norris, T. R. & Iannotti, J. P., Functional outcome after shoulder arthroplasty for primary osteoarthritis: A multicenter study. Journal of Shoulder and Elbow Surgery, 11(2), pp Nyffeler, R. W., Werner, C. M. & Gerber, C., Biomechanical relevance of glenoid component positioning in the reverse Delta III total shoulder prosthesis. Journal of Shoulder and Elbow Surgery, 14(5), pp Osterhoff, G. et al., Medial support by fibula bone graft in angular stable plate fixation of proximal humeral fractures: an in vitro study with synthetic bone. Journal of Shoulder and Elbow Surgery, 20(5), pp

87 Otis, J. C. et al., Changes in the moment arms of the rotator cuff and deltoid muscles with abduction and rotation. The Journal of Bone & Joint Surgery, American Volume, 76-A(5), pp Pacific Research Laboratories, Sawbones. [Online] Available at: [Accessed 2011]. Péan, J. E., Des moyens prosthetiques destinés à obtenir la reparation des parties osseuses. Gaz des Hôp Paris, Volume 67, pp Rockwood, C. A., Matsen, F. A., Lippitt, S. B. & Wirth, M. A. eds., The Shoulder. s.l.:elsevier Health Sciences. Sanchez-Sotelo, J., Reverse total shoulder arthroplasty. Clinical Anatomy, 22(2), pp Schamblin, M. et al., In vitro quantitative assessment of total and bipolar shoulder arthroplasties: A biomechanical study using human cadaver shoulders. Clinical Biomechanics, 24(8), pp Shapiro, T. A. et al., Biomechanical effects of glenoid retroversion in total shoulder arthroplasty. Journal of Shoulder and Elbow Surgery, 16(3, Supp 1), pp. S90 - S95. Sharkey, N. A., Marder, R. A. & Hanson, P. B., The entire rotator cuff contributes to elevation of the arm. Journal of Orthopaedic Research, 12(5), pp Shrout, P. E. & Fleiss, J. L., Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), pp Smith, C. D. et al., A biomechanical comparison of single and double-row fixation in arthroscopic rotator cuff repair. Journal of Bone & Joint Surgery, American Volume, 88, pp Terrier, A., Reist, A., Merlini, F. & Farron, A., Simulated joint and muscle forces in reversed and anatomic shoulder prostheses. The Journal of Bone & Joint Surgery, British Volume, 90(6), pp Trappey IV, G. J., O'Connor, D. P. & Edwards, T. B., What are the instability and infection rates after reverse shoulder arthroplasty? Clinical Orthopaedics and Related Research, 469(9), pp Wall, B. et al., Reverse total shoulder arthroplasty: a review of results according to etiology. Journal of Bone & Joint Surgery, American Volume, 89, pp

88 Werner, C. M. L., Steinmann, P. A., Gilbart, M. & Gerber, C., Treatment of painful pseudoparesis due to irreparable rotator cuff dysfunction with the Delta III reverse-ball-andsocket total shoulder prosthesis.. Journal of Bone & Joint Surgery, American Volume, 87(7), pp Wierks, C., Skolasky, R. L., Ji, J. H. & McFarland, E. G., Reverse total shoulder replacement. Clinical Orthopaedics and Related Research, 467, pp Williams, G. R. et al., The effect of articular malposition after total shoulder arthroplasty on glenohumeral translations, range of motion, and subacromial impingement. Journal of Shoulder and Elbow Surgery, 10(5), pp Wu, G. et al., ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion--part II: shoulder, elbow, wrist and hand. Journal of Biomechanics, 38(5), pp Yamamoto, N. et al., Effect of an anterior glenoid defect on anterior shoulder stability: a cadaveric study. The American Journal of Sports Medicine, 37(5), pp Yanai, N., Yamamoto, M. & Mohri, A., Inverse dynamics analysis and trajectory generation of incompletely restrained wire-suspended mechanisms. Proceedings of the IEEE ICRA, 4, pp Young, S. W. et al., The SMR reverse shoulder prosthesis in the treatment of cuff-deficient shoulder conditions. Journal of Shoulder and Elbow Surgery, 18(4), pp Zatsiorsky, V. M., Kinetics of Human Motion. s.l.:human Kinetics. Zumstein, M. A., Pinedo, M., Old, J. & Boileau, P., Problems, complications, reoperations, and revisions in reverse total shoulder arthroplasty: A systematic review. Journal of Shoulder and Elbow Surgery, 20(1), pp

89 Appendix A Detailed Experiment Design Due to the wide variety of factors that have the potential to affect the stability of reverse shoulder arthroplasty, this investigation was a screening experiment designed to examine a large number of variables and identify important factors that warrant further investigation. To accomplish this, a factorial experiment design was implemented as this allows factors to be screened in relatively few trials by testing factors at low and high levels and varying all factors at the same time. The levels for each factor and letter codes used are listed in Table A.1. Table A.1: Factor codes and levels of each factor. Factor Code Factor Levels X Loading Direction Anterior Posterior Superior Inferior C Abduction Angle 45 o 60 o D Abduction Plane Angle 15 o 55 o E Socket Depth High Mobility Cup Retentive Cup F Glenosphere Eccentricity Standard Inferior Offset G Glenosphere Diameter 38 mm 42 mm The experiment was performed as two quarter fraction factorial designs, with each quarterfraction being carried out on a separate day. One replicate was performed using one Sawbone specimen. Since loading direction has four levels, the dummy factors A and B were used and combined to create factor X such that the effect estimate for X is the sum of effect estimates for A, B, and the AB interaction: l l l l. Each quarter fraction experiment was a 2 design with generators F = ABCD and G=±ABDE. The design matrices used for the two experiments are shown in Table A.2 and Table A.3. 80

90 Table A.2: Design matrix used for first quarter-fraction experiment performed with F = ABCD and G = ABDE. + and - indicate the low and high levels of each factor and x1-x4 indicate the four levels of loading direction (Factor X), where x1 = anterior, x2 = posterior, x3 = superior, x4 = inferior. Note that the runs listed here were performed in a randomized order. Run (A B) = X C D E F = ABCD G = ABDE x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

91 Table A.3: Design matrix used for second quarter-fraction experiment performed with F = ABCD and G = -ABDE. + and - indicate the low and high levels of each factor and x1-x4 indicate the four levels of loading direction (Factor X), where x1 = anterior, x2 = posterior, x3 = superior, x4 = inferior. Note that the runs listed here were performed in a randomized order. Run (A B) = X C D E F = ABCD G = -ABDE x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

92 Combining the two ¼ fraction experiments, a ½ fraction, 2 experiment was obtained with design generator F=ABCD. Due to the use of dummy variables A and B to create the four level factor X, some two factor interaction aliasing still exists between XC and DF, XD and CF, and between XF and CD. This is due to the following relationships: l l l l l l l l l l l l Average force to dislocate was compared from each of the 1/4 fraction experiments to check for bias between days (Figure A.1). No difference was found between days, so it was concluded that the data could be combined without introducing between day differences. 250 Force to Dislocate (N) Day 1 Day 2 Figure A.1: Comparison of ¼ fraction experiments performed on two different days. Error bars show standard error. Effect estimates were calculated for each factor and all factor interactions. Significant factors and interaction were identified by plotting the effect estimates on a normal probability plot and residuals were analyzed. These results were then confirmed using a 83

93 six way ANOVA. However, due to the aliasing between two factor interactions outlined previously, aliased interactions could not be analyzed using the ANOVA. Since abduction plane (D) was not found to have an effect on stability as a main factor or in any interactions, this factor was eliminated and a five way ANOVA was performed to allow analysis of the aliased interactions. Post hoc Tukey tests were then performed on identified interactions. Significance was defined as p<0.05. Normal probability plots, residual analysis, and ANOVA results can be found in Appendix B. 84

94 Appendix B Detailed Data Analysis Calculated effect estimates, sums of squares, and percent contributions for all factors and two factors interactions are shown in Table B.1. Table B.1: Effect estimate, sum of squares, and percent contribution for factor X = A + B, all other factors, and two factor interactions. Factor Effect Estimate Sum of Squares Percent Contribution X C D E F G XC XD XE XF XG CD CE CF CG DE DF DG EF EG FG A normal probability plot of the effect estimates for all factors and interactions was then created (Figure B.). Factors and interactions that deviate from a linear pattern are not 85

95 normally distributed and are therefore deemed to be significant. Factors E, C, F, and interaction XE were found to be significant. Normal Probability Plot F C E Normal Probability XE Effect Estimates Figure B.1: Normal probability plot of factors and all two factor interactions with X=A+B. The line indicates a pattern of normally distributed data. To confirm that factors C, E, F, and XE explain most of the variation in the data, force to dislocate was estimated for each trial using only these factors. l

96 where is the estimated force to dislocate, is the mean force to dislocate from all of the trials, l is the effect estimate of the significant factor, and is the coded variable (ie. 1 depending on if the factor is at the low or high level). The residuals ( ) for each k th trial and a normal probability plot was created to check that the residuals are normally distributed (Figure B.2). The residuals appear to be approximately normally distributed Normal Probability Figure B.2: Normal probability plot of residuals. The residuals were plotted against predicted force to dislocate ( ) to verify they did not grow with force to dislocate (Figure B.3) Residuals 87

97 Residuals Predicted Force to Dislocate (N) Figure B.3: Residuals plotted against predicted force to dislocate. There is no pattern apparent. An ANOVA was performed to confirm the results of the normal probability plot analysis. The results of the ANOVA are shown in Table B.2. However, as a result of two factor interaction aliasing, results are unavailable for CD, CF, and DF. To confirm that these were not significant, factor D was eliminated as it was not found to be significant as a main effect or in any interactions. A 5 way ANOVA was then performed (Table B.3). This eliminated any issues of aliasing in the ANOVA. Significant factors are shown in bold. 88

98 Table B.2: 6-way ANOVA results. Source of Variation Sum of Squares Degrees of Freedom Mean Square F o P Value X C < D E < F <0.001 G XC XD XE <0.001 XF XG CD CE CF CG DE DF DG EF EG FG Error Total

99 Table B.3: 5 way ANOVA results. As abduction plane was found to have negligible effects on its own or in interactions, it was eliminated to prevent aliasing problems in the ANOVA. Source of Variation Sum of Squares Degrees of Freedom Mean Square F o P Value X C < E < F <0.001 G XC XE <0.001 XF XG CE CF CG EF EG FG Error Total

100 Appendix C Instrumentation Specifications 91

101 MINI LOW PROFILE LOAD CELL UNIVERSAL / TENSION OR COMPRESSION MLP SERIES LOAD CELL CAPACITY RANGES: 10, 25, 50, 75, 100, 150, 200, 300, 500, 750, 1,000 LBS. The model MLP Series load cells were designed with economy as first priority. They are a scaled down version of our successful LPO Series Load Cells. MLP-10 through MLP-300 are anodized aluminum and the MLP-500 through MLP-1K are made from 17-4ph heat treated stainless steel. The unique low profile design of the MLP Series provides excellent stability for in line applications for tension and/or compression, while saving space at the same time. Options -CO Mini Gold Pin Connector System, male and female with 10' 4 cond. color coded shielded cable -DB Dual Bridge SPECIFICATIONS Rated Output (R.O.): 2 mv/v nominal Nonlinearity: 0.1% of R.O. Hysteresis: 0.1% of R.O Nonrepeatability: 0.05% of R.O. Zero Balance: 1.0% of R.O. Compensated Temp. Range: 60 to 160 F Safe Temp. Range: -65 to 200 F Temp. Effect on Output: 0.005% of Load/ F Temp. Effect on Zero: 0.005% of R.O./ F Terminal Resistance: 350 ohms nominal Excitation Voltage: 10 VDC Safe Overload: 150% of R.O. MODEL CAPACITY LBS. DIMENSIONS (INCHES) L L1 mwm W1 H THREAD THREAD DEPTH NATURAL RINGING FREQUENCY HZ DEFLECTION INCHES MLP , MLP / , MLP / , MLP / , MLP / , MLP / , MLP / , MLP / , MLP / , MLP / , MLP-1K 1, / , WT. OZS.

102 LORENZ MESSTECHNIK GmbH Presented By: A-Tech Instruments! Fax Mounting rail strain gauge amplifier Type GM 40 For control cabinet in-built, width only 23mm Direct connection to PLC 10V...30V DC supply, galvanic separation Easy operation Voltage-, and current output Function: The mounting rail amplifier type GM 40 gains the output of the sensors to conforming standard output signals. The narrow housing shape allows spacesaving mounting near to the sensors in control cabinets on standardized mounting rails. A galvanic separated supply voltage range of 10 to 30 V and the analog outputs of 0...±5/±10 V resp. optional current output allow the direct signal processing with an PLC-control. All control elements are obtainable on front side behind a detachable plexiglass panel. The adaption of the sensitivity of the sensor takes place on sight by DIL-switch. Base load (tara) can be aligned. Simulation of nominal signal possible with control-switch. Interference signals and settling processes of the measured signal can be alleviated with the input filter. The fine adjustment of the amplification and zero point as well as the filter is possible through potentiometer. SPECIFICATIONS: TYPE E-GM 40 Art. no Evaluation side Supply: Power supply voltage V DC Ripple < 10 % Power consumption 10V 150mA 24V 80mA Signal output: Output signal U-Out ± 5V/±10V, 2mA Voltage Ripple Gain drift Zero point drift Output resistance Limit frequency <20mV < 0,02 % / 10 K < 0,02 % / 10 K 10 Ω 10Hz - 1 khz 3dB Signal output: Current Output signal I-Out Ripple at 500R Gain drift Zero point drift Limit frequency mA an Ohm <20mV < 0,04 % / 10 K < 0,04 % / 10 K 10Hz...750Hz 3dB Sensor side Supply: Sensor supply 10V 30mA (Option 5V 15mA) TK supply voltage 25 ppm/ K Signal input: Sensor sensitivity 0,3mV/V...3,5mV/V Input resistance 10 9 Ω Other Nominal temperature range C Service temperature range C Storage temperature range C Dimension W x H x L 23 x 111x 76 Level of protection Clamping range of terminals Clamping rail profile IP 20 0,14 mm 2...1,5mm 2 DIN EN Options Type Art. no. Function E-GM40/I Current output mA E-GM40/I Current output mA E-GM40/I Current output 12±8mA E-GM40/I Current output 10±10mA E-GM40/S Sensor supply 5V 15mA E-GM40/N Neutral design sales@a-tech.ca Technical modification to reserve doc