numerical modelling of the shoulder for clinical applications

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doi: 10.1098/rsta.2008.0282, 2095-21183672009Phil. Trans. R. Soc. A

Philippe Favre, Jess G. Snedeker and Christian GerberapplicationsNumerical modelling of the shoulder for clinical

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RE V I E W

Numerical modelling of the shoulderfor clinical applications

BY PHILIPPE FAVRE*, JES S G. SNEDEKER AND CHRISTIAN GERBER

Laboratory for Orthopaedic Research, Department of Orthopaedics, Balgrist,University of Zurich, Forchstrasse 340, 8008 Zurich, Switzerland

Research activity involving numerical models of the shoulder is dramatically increasing,

driven by growing rates of injury and the need to better understand shoulder jointpathologies to develop therapeutic strategies. Based on the type of clinical question theycan address, existing models can be broadly categorized into three groups: (i) rigid bodymodels that can simulate kinematics, collisions between entities or wrapping of themuscles over the bones, and which have been used to investigate joint kinematics andergonomics, and are often coupled with (ii) muscle force estimation techniques,consisting mainly of optimization methods and electromyography-driven models, tosimulate muscular action and joint reaction forces to address issues in joint stability,muscular rehabilitation or muscle transfer, and (iii) deformable models that account forstressstrain distributions in the component structures to study articular degeneration,

implant failure or muscle/tendon/bone integrity. The state of the art in numericalmodelling of the shoulder is reviewed, and the advantages, limitations and potentialclinical applications of these modelling approaches are critically discussed. This reviewconcentrates primarily on muscle force estimation modelling, with emphasis on a novelmuscle recruitment paradigm, compared with traditionally applied optimizationmethods. Finally, the necessary benchmarks for validating shoulder models, the emergingtechnologies that will enable further advances and the future challenges in the fieldare described.

Keywords: shoulder biomechanics; computer/numerical modelling;glenohumeral joint; muscle force estimation; rigid body model; finite element

1. Introduction

(a) Increasing interest in shoulder modelling

Historically, in orthopaedics, most numerical simulations have focused on the hipand the knee, with fewer on the shoulder. From a clinical perspective, the hip andknee have largely occupied the interests of clinical and industrial researchersbecause the vast majority of joint replacements are performed at these joints.

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One contribution of 15 to a Theme Issue The virtual physiological human: tools and applications I.

* Author for correspondence ([email protected]).

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From a modelling standpoint, the complexity of the shoulder joint itself may be adisincentive to modellers, who have to cope with intricate active and passivestabilizing mechanisms and an extremely large range of joint motions (Hogfors

et al. 1995). Upper extremity motions are by necessity more variable than thelocomotive movements of the lower limb (a well-defined cyclic motion), andwhile a two-dimensional analysis of gait can reasonably characterize legkinematics, such a simplified treatment of the shoulder is inadequate (Rauet al. 2000).

Shoulder problems are gaining research interest as 2030 per cent of thepopulation suffer from shoulder pain and 8.8 per cent suffer functionalimpairment (Lock et al. 1999; Makela et al. 1999). Furthermore, many majorclinical challenges of shoulder orthopaedics have proven to be persistent, and aneed for deeper understanding of shoulder pathology and treatment has become

clear. On the modelling side, lessons learned from other joints can now be appliedto the shoulder, and improvements in software and computational power havefacilitated the building and solving of ever more complex models. All thesefactors have driven the exponential increase in the number of publicationsinvolving numerical models of the shoulder (figure 1), the most clinically relevantof which we review here.

(b ) Essential clinical issues with potential to be addressed using models

Among the many shoulder problems encountered in daily clinical practice,

several concerns are of particular interest to the modeller. First, they correspondto some of the most challenging issues in shoulder orthopaedics. Second,numerical simulations offer unique potential to improve their treatment.

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(i) Glenohumeral instability

The glenohumeral joint is the most frequently dislocated major joint of thebody, affecting at least 1.7 per cent of people in the course of their lifetime(Hovelius 1982). The contribution of the glenohumeral surface shape, capsule

and ligaments to stability has been widely studied, although glenohumeral jointstability is primarily ensured by coordination of muscular actions (Lippitt &Matsen 1993; Veeger & van der Helm 2007). This is especially complex, as somemuscles may act as stabilizers, while others rather tend to destabilize the joint,depending on joint position (van der Helm 1994a; McMahon & Lee 2002; Werneret al. 2007; Favre et al. 2009). Our present knowledge fails to explain many casesof instability, owing to insufficient understanding of how the musclessimultaneously move the humerus and prevent glenohumeral dislocation(Kronberg et al. 1991; McMahon & Lee 2002; Veeger & van der Helm 2007).Here, muscle force estimation models can be considerably helpful in studyingactive stabilization mechanisms. Rigid body or deformable models can be used to

assess the influence of passive stabilizers and joint conformity in more depth.

(ii) Rotator cuff tears

The muscles of the rotator cuff maintain joint stability by pulling the humeralhead into the glenoid socket. Tears of the rotator cuff tendons are common andhave been shown to be present in over 50 per cent of asymptomatic people abovethe age of 60 (Sher et al. 1995), reflecting accumulated damage over the course ofa lifetime. These tears may progress to massive, symptomatic tears, eventuallyleading to irreversible changes in the physiology of the muscle and tendon

(Gerber et al. 2004), making surgical repair difficult. Torn cuff tendons can leadto pain, instability, dysfunction and osteoarthritis, and in the worst cases candegenerate to cuff tear arthropathy, in which the humeral head collapses (Neeret al. 1983). The pathogenesis of rotator cuff tears remains unclear, and the besttreatment for this common disorder remains a source of debate (Williams et al.2004). The evolution to a symptomatic tear is not well understood, and althoughmany other factors are involved (vascular, genetic, etc.), finite-element (FE)analyses can provide first insight into tendon-loading patterns (Luo et al. 1998;Wakabayashi et al. 2003; Sano et al. 2006) or could give guidelines to optimizethe mechanics of tendon repair. Interestingly, the functional deficits associatedwith rotator cuff tears are highly variable among patients, varying from normalrange of motion to pseudoparalysis, indicating that some patients are able tocope with the torn muscles, while others cannot. Here, muscle force estimationmodels could help us to understand how compensation involving the remainingviable muscles occurs and to define new rehabilitation strategies.

(iii) Shoulder arthroplasty

The number of partial and total shoulder replacements remains relativelysmall in comparison with that for the hip or knee, but has tripled in just 10 yearsin the USA, reaching 29 000 partial and total shoulder replacements in 2004

(Kozak et al . 2006). The two major complications associated withjoint replacement are loosening of the glenoid component and joint instability(Franklin et al. 1988; Wirth & Rockwood 1996).

2097Review. Numerical modelling of the shoulder

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Although the aetiology of glenoid loosening is not yet fully understood, it isgenerally believed to have several potential (and possibly interrelated) sources,notably implant design, implant wear and particle formation, surgical technique,poor bone quality and eccentric implant loading. Eccentric loading can be due tomigration of the humeral head (Franklin et al. 1988) or disadvantageous implant

positioning (Nyffeler et al . 2006). In their ability to explore mechanicalphenomena, FE simulations offer potential to understand these issues.

As with the normal glenohumeral joint, instability of the prosthetic joint is also aprimary concern. Because stability of the shoulder depends so heavily on the activemusculature, muscle force estimation models may improve our understanding of thestability changes induced by an implant. Constrained devices such as the reverseprosthesis (in which the ball is transposed to the scapula and the socket to thehumerus) provide increased intrinsic stability, but they have been associated withhigher rates of surgical revision (Matsen et al. 2007). Moreover, the geometric andkinematic changes induced by the reverse design present many questions to be

investigated (Boileau et al. 2005), and rigid body models may provide a tool forinvestigation. Generally, models may facilitate our quest for increased implantlongevity by helping the surgeon in choosing an appropriate size, type and positionof the prosthesis and guide in optimizing soft tissue tension and force balance.

(iv) Tendon transfer

Muscle transfer represents a viable treatment option to restore the lostfunction in a variety of difficult shoulder issues. The anatomical insertion of afunctioning muscle is detached and transferred to a different location to fulfil anew role and restore a lost function. For instance, the latissimus dorsi transfer

can restore external rotation in the case of irreparable rotator cuff tears (Gerber1992), or be further combined with arthroplasty (Gerber et al. 2007). However,the clinical outcome of muscle transfers is still difficult to predict, and thebiomechanical implications of such procedures are only beginning to beunderstood (Magermans et al. 2004a,b; Favre et al. 2008a). Rigid body modelssimulating muscle wrapping can provide first information on the muscle path andmoment arm of the transferred muscle. Muscle force estimation models can thenhelp in understanding how the changes induced by the transferred muscleinfluence the distribution of muscle forces over the whole joint. Generally,simulations should provide guidelines (choice of muscle to transfer, optimal

insertion site and muscle training) to maximize the functional potential.

2. Numerical models of the shoulder

Simulations performed with numerical models allow investigation of aspectsthat are otherwise difficult or impossible to quantify, overcoming technicallimits (deterioration of tissues, adequate placement of sensors, etc.) andethical limits (invasiveness and short supply of specimens) on direct in vivo orin vitro measurements.

Depending on the aspect of shoulder function to be investigated, various

modelling approaches can be selected. Because the clinical question generallydictates the kind of model to be used, in the current review we categorize the modelsbased on the type of output they generate, and thus the type of clinical question they

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can address (table 1). This classification is not exhaustive, largely allows foroverlapping between categories and focuses on the clinical issues described above.

Accordingly, the available models can be broadly categorized into three maingroups: (i) rigid body models that can simulate kinematics, collisions betweenentities or wrapping of the muscles over the bones, and which have been used toinvestigate joint kinematics and ergonomics, and have very often been coupledwith (ii) muscle force estimation techniques, consisting mainly of optimization

methods and electromyography (EMG)-driven models, to simulate muscularaction (inverse dynamics) and joint reaction forces to address issues in jointstability, muscular rehabilitation or muscle transfer, and (iii) deformable modelsthat account for stressstrain distributions in the component structures, andwhich can be used to study articular degeneration, implant failure or muscleintegrity. This review does not intend to provide an exhaustive list of allpublished shoulder models but points out several key models that have beenspecifically tailored to address clinical questions.

(a) Rigid body models

Rigid body models idealize a system as consisting of solid bodies connected bykinematic constraints, and in which deformations of the bodies are neglected.

Table 1. Potential of different numerical model types to address the most pressing shoulder clinicalissues, as defined in this review. (Each clinical issue is subdivided into respective relevant researchtopics. A cross means that the output delivered by the numerical model type could be or has beenimplemented to address them directly. This list is not exhaustive.)

clinical issue research topic

shoulder model type

rigid bodymuscle forceestimation deformable

glenohumeralinstability

passive stabilization ! !muscular stabilization !joint conformity/constraint ! !

rotator cufftears

muscle overload ! !pathogenesis of tear ! !compensation/rehabilitation !tendon repair ! !

shoulderarthroplasty

implant type or design ! ! !fixation !range of motion !implant component positioning ! ! !cement thickness !shoulder function !implant intrinsic stability ! !

tendontransfer

choice of muscle to transfer ! !prediction of functional outcome !

post-operative muscle training !optimize insertion site ! !



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In applying this approach to the shoulder, the bones are represented as rigidsegments, and the muscles as adjustable length segments that link their originand insertion. Kinematics, collisions between entities or wrapping of the musclesover the bones can be simulated. Because deformations are not considered, thenecessary computational power is considerably less than that required for

deformable models, and useful information can often be extracted from relativelysimple models that run quickly on low-cost computational hardware.

Rigid body models have been used in kinematics studies (i.e. to describe motionof the rigid segments, without consideration of the causes leading to movement)to assess the range of shoulder motions in rehabilitation and ergonomicsapplications (Johnson & Gill 1987; Engin & Tumer 1989; Klopcar et al. 2007).As an example of a model specifically tailored to address a clinical question, weimplemented a rigid body model to investigate whether malpositioning ofconventional shoulder implant components can cause impingement, leading to thenotching observed in patients, finally inducing eccentric loosening and possible

glenoid loosening (figure 2; Favre et al. 2008b). In an inverse dynamics approach,such models have been used to estimate joint moments in the whole upper limbduring a specific motion (Barker et al. 1997).

(a) (b)

Figure 2. (a) Notching of the humerus at the level of the inferior glenoid border in patients with a

conventional shoulder implant and (b) rigid body model to investigate whether malpositioning ofimplant components can cause this notching through impingement, eventually leading to eccentricloading of the glenoid component and its loosening.

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Most often, rigid body models have been used for rigid body dynamics, incombination with muscle force optimization techniques (described in detail in2b later). Here, the rigid body models provide anatomical data, specifically themuscle moment arms and lines of action, as input to a coupled muscle forceestimation method. Such models have been shown to predict accurately muscle

moment arms of the rotator cuff in comparison with experimentally measuredvalues (Gatti et al. 2007), supporting the use of rigid body models for calculationof moment arms, with the advantage that these can be easily computed for anyposition of the joint at any time, as opposed to those measured experimentally.In turn, the determined muscle forces may then be used to drive the rigid bodykinematics in a forward dynamics approach. Here, the rigid body model servesfor visualization of an induced motion, making muscle force estimation softwaremore intuitive and facilitating user interaction with the model (Dickerson et al.2007). Commercially available models for the whole musculoskeletal system(AnyBody Technology A/S, Aalborg, Denmark; SIMM, MusculoGraphics Inc.,

Santa Rosa, CA, USA) also incorporate muscle force optimization algorithms.These packages have been customized and used in several shoulder studies(Holzbaur et al. 2005; Langenderfer et al. 2005; Charlton & Johnson 2006).

While rigid body models are useful for many applications, they do havelimitations. Most published rigid body models of the shoulder are limited by asimplified representation of the glenohumeral joint as an ideal joint, withpredefined degrees of freedom. It has been approximated as consisting of threehinges with defined axes of rotation (Barker et al. 1997; Klopcar et al. 2007) or bydefining it as an ideal ball-and-socket joint (van der Helm 1994b; Garner &Pandy 1999; Maurel & Thalmann 1999; Favre et al. 2008b). These simplificationsprevent translations at the glenohumeral joint and thus limit studies on jointstability. Furthermore, the problem of muscle wrapping requires someimprovement. Accounting for physical contact between muscles and bones, orbetween muscles and other soft tissues, is a complicated issue that can limitaccuracy in modelling muscle actions over large ranges of motions. This is amajor problem as it directly affects the muscle moment arm and line of action(Charlton & Johnson 2001). It is sometimes solved artificially by definingso-called via points through which the muscle is forced to pass or by replacingthe complex bony geometry with simpler shapes (van der Helm et al. 1992;Garner & Pandy 2000; Holzbaur et al. 2005); but these techniques do not mirrorthe in vivo behaviour. More recent methods model the entire muscle volume

using the FE method (Blemker et al. 2007). As a final limitation, rigid bodymodels neglect tissue deformation and cannot be used to address some veryimportant questions of shoulder biomechanics (such as arthroplasty, wherequantifying mechanical bone stresses are important). However, these sacrificesin realism do yield a significant advantage in smaller requirements forcomputational power, allowing larger models of not only the shoulder but alsooften the entire upper limb or torso. This is essential in efficiently studyingbi-articular muscles and the coupling between multiple joints.

(b ) Muscle force estimation

Estimation of muscle loading is critical in predicting when tendon tears willoccur. When tears have already been diagnosed, this information is required to



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develop strategies for safely reconstructing them, or to optimize rehabilitation byfocusing on the remaining viable muscles. It is also necessary to understand howthe central nervous system controls the musculoskeletal system during specifictasks in order to best treat neurological or muscular deficiencies. Finally,accurately estimating the forces at the joint contact interface is fundamental to

prosthesis design in preventing accelerated implant wear and premature failure.In order to simulate how muscles are coordinated to move the arm or to hold it

in a certain position, two parameters must be defined: first, an appropriate set ofactive muscles (muscle recruitment) and second, the distribution of forceamongthese muscles to reach equilibrium. Early models of shoulder muscle forcebalance were two-dimensional systems that considered only a few muscles, andcould be solved by simple analytical methods (Inman et al. 1944; De Luca &Forrest 1973; Poppen & Walker 1978; Bassett et al. 1990). While these modelswere limited to a simple arm movement (elevation) and included a restrictedset of muscles, they nonetheless delivered important insights into some basic

working principles of shoulder function. More importantly, they provided atechnical foundation on which later three-dimensional models could be built toaddress more complex questions, necessitating the use of computers.

When comprehensively modelling the muscular forces at the shoulder, themain hurdle is of a mathematical nature. In the simplified case in which theglenohumeral joint is represented as a ball-and-socket joint (thus removing/constraining the three translational degrees of freedom), the system is governedby three equations describing the equilibrium in each rotational degree offreedom. The muscle forces are treated as unknowns in these equations.This system of three equations would have one unique solution only if no more

than three unknowns were present. In actuality, the many muscles that cross theglenohumeral joint present a much less defined system. Muscles with largeorigins are often subdivided to allow for a differentiated action, as moment armlength and direction of tendon action can vary considerably within an individualmuscle (van der Helm & Veenbaas 1991; Favre et al. 2005, 2009), so that manyshoulder models regularly include more than 20 muscle segments. This yields amathematically indeterminate system comprising more unknowns thanequations and is characterized by an infinite number of possible solutions. Themain issue is to find a method that systematically isolates a suitable solutionamong these infinite number of solutions.

Most computational methods tackle the indeterminacy issue using mathemat-ical optimization. The forces are distributed among muscles in such a way that achosen cost function is minimized, while ensuring that these forces satisfy givenphysical constraints. The cost function can be based upon muscle stress, force,energy, fatigue, etc., and the constraints usually dictate that the muscle forcescan apply tension only, must satisfy the equilibrium equations and fall withinreasonable upper (tetanic muscle force) and lower (negligible force) muscle forcelimits (Karlsson & Peterson 1992). The first optimization models were developedto simulate muscular load sharing at other joints (Penrod et al. 1974; Seireg &Arvikar 1975), and the shoulder represents a more recent application. The first

three-dimensional model of shoulder muscle force estimation was extensivelydescribed by Karlsson & Peterson (1992) and was later followed by the mostfrequently cited and implemented model to date (van der Helm 1994b).

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One of the major problems in optimization techniques is the choice of anappropriate cost function. Comparisons with EMG activity have shown thatsome cost functions predict onoff muscle recruitment patterns better thanothers, but it is not yet clear what principles would dictate how muscles arerecruited in vivo (Karlsson & Peterson 1992; van der Helm 1994a; Erdemir et al.

2007). Furthermore, muscle load sharing strategy is likely to differ betweensubjects, depending to some extent on the type of activity and varying in response tofatigue, mental demands and visual feedback or in the presence of musculoskeletaldisorders, such as rotator cuff tears (Kronberg et al. 1991; Jensen et al. 2000;Steenbrink et al. 2006). Finally, co-contraction of antagonistic muscles can bepredicted (Jinhaa et al. 2006), but it has been shown to confound conventionaloptimization-based models (Cholewicki et al. 1995; Dickerson et al. 2008).

In an attempt to overcome the drawbacks of analytical optimizationtechniques, experimentally based, EMG-driven models that were first developedfor the lower back (McGill 1992) have been extended to the shoulder (Koike &

Kawato 1995; Laursen et al. 1998; Langenderfer et al. 2005). In such models, theset of active muscles is identified in recordings of EMG activity for isolatedshoulder positions. The muscle force is then estimated by assuming a linearrelationship between EMG and force under isometric conditions. One advantageis that the recruitment of a particular muscle is directly indicated by the EMGmeasurements, and realistic muscle recruitment patterns can be immediatelyimplemented in the model. In this way, co-contraction of antagonistic musclesmay be directly accounted for and simulated. The main weakness of such modelsis that reliable EMG recordings of all relevant muscles must be available for thesimulated position. This is technically demanding (even if possible) and bringswith it the well-known difficulties inherent in EMG signal measurement andprocessing (De Luca 1997).

All muscle force estimation models are limited in their ability to beindividualized, owing to the variability in anatomy and neuromuscular control,and this restricts the general applicability of a single model. Despite the limitationsof these methods, and the difficulties in validating such models (to be discussed in3b later), muscle force estimation models have been applied successfully toinvestigate a variety of clinical questions. They have been used to evaluate theinfluence of a prosthesis on the muscular forces (de Leest et al. 1996), to assessthe influence of scapular neck malunion on shoulder function (Chadwick et al.2004), to test tendon transfers (Magermans et al. 2004a,b) and to prevent overload

injuries in wheelchair design and propulsion (van der Helm & Veeger 1996; Veegeret al. 2002; Lin et al. 2004; van Drongelen et al. 2005, 2006). Because muscle forceestimation models must necessarily entail a muscle recruitment strategy, they giveexplicit insight into the manner in which the central nervous system drives themusculoskeletal system. Changes in the applied cost function or recruitmentcriteria directly affect the prediction of recruited muscles and can be varied toexplore neuromuscular control hypotheses. The effect of a neurological or musculardeficiency can be assessed by scaling the allowed maximum relative force ofselected muscles (van Drongelen et al. 2006). In a forward dynamics approach,muscle forces can be used to calculate joint torques and trajectory using the

dynamics equations (Koike & Kawato 1995), and combined with rigid body modelswith the previously described advantage of motion visualization. Finally, suchmodels are useful for investigating how joint stability is achieved, by considering



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the intersection of the resultant force with the glenoid, with the joint remainingstable as long as the resulting joint force falls within the glenoid boundaries(van der Helm 1994b; Favre et al. 2005).

(i) A new paradigm for muscle force estimation

In an effort to avoid the previously described limitations that accompanytraditional muscle force estimation methods (choice of an appropriate costfunction, co-contraction prediction and requirements for EMG measurements),we have developed an algorithm to predict the muscle forces required forshoulder joint equilibrium. This algorithm implements a novel recruitmentstrategy that focuses on selecting muscles with a relative mechanical advantage,and a corresponding set of muscles that counterbalance secondary jointmoments. Because the recruitment process is central to the new method, wedescribe it here briefly. A more comprehensive description of the entire algorithmcan be found elsewhere (Favre et al. 2005).

In this muscle recruitment paradigm (figure 3), an external moment atthe joint centre of rotation is decomposed into three orthogonal components. TheAlgorithm for Shoulder Force Estimation (ASFE) first recruits the muscles that

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Figure 3. Muscle recruitment paradigm in the Algorithm for Shoulder Force Estimation (ASFE):(a) external moment components and (b) muscle potential moment components. The threeexternal moment components (grey bars in (a), shown as dotted or dashed lines in (b)) are assessedto recruit muscles from two groups. Muscles from group 1 oppose the greatest external momentcomponent only (here, the y-component of the external moment, shown in dashed lines, is

counteracted by the y-component of the muscle, shown with black fill), disregarding the other twocomponents (shown with grey fill). Muscles from group 2 concurrently oppose all three externalmoment components simultaneously (external moment components shown in dashed lines, musclemoment components shown with black fill).

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have the largest potential mechanical advantage in offsetting the greatest of thethree external moment components, without any regard for the other twocomponents (group 1). Here, potential mechanical advantage is defined by themuscle lever arms for the current position (Favre et al. 2009) multiplied bymuscle cross section. In order to offset the two remaining components of the

external moment, muscles that simultaneously oppose all three externalcomponents are recruited (group 2). Muscles that do not fit within these twogroups are not active in the current loop (but may become active in later loops,thus allowing simulation of co-contraction, depending on which component of theremaining external moment becomes the greatest). The equilibrium forceequations then attribute forces to the set of recruited muscles in proportion toeach muscles cross-sectional area (thereby making the system mathematicallydeterminate). The boundary conditions ensure that the assigned muscle forcesare physiological (range in tension from zero to the tetanic muscle force) and theresultant muscle forces from this loop are then arbitrarily scaled down (typically

by 95%) to ensure that the model converges and the external moment is notovershot. The whole process is iteratively repeated using the remaining externalmoment as input to the next loop, until all three components of the externalmoment are balanced. At the end, the resultant force is determined, and if thejoint reaction force points outside of the glenoid (unstable joint), the simulationis restarted, but first giving all rotator cuff muscles a supplementary force.

This method has been shown to deliver realistic muscle recruitment patternsin comparison with EMG measurements (Favre et al. 2005). In order to validatethe obtained joint reaction force, the performance of the ASFE and otheroptimization criteria, in comparison with the instrumented shoulder implant(Bergmann et al. 2007), is described in 2b(ii) below for a classic example.

(ii) Abduction in the scapular plane

Abduction was simulated with the ASFE at 0, 45, 90 and 1208 with respect tothe torso in the scapular plane. The arm weight (35 N) was applied at the middleof the arm (0.3 m from humeral head centre). Because the ASFE considers afixed scapula, the rotation of the scapula was taken into account by rotating theexternal force vector according to a scapulohumeral rhythm ratio of 1 : 2.

Figure 4 shows the joint reaction force predicted by the ASFE and compares itwith the reaction force reported from other studies (Poppen & Walker 1978;

van der Helm 1994a; Terrier et al. 2008). Deviations in predicted joint resultantforces up to 908 can be explained by differences in model geometry (musclesegmentation, humeral head size, muscle size, muscle origin and insertion site) andrecruitment strategy. The large deviation after 908 abduction is due tothe ASFE incorporation of muscle co-contraction, which cannot be consideredin the other models. Muscles of the rotator cuff and the deltoid, which representthe totality of muscles included by Poppen et al. and Terrier et al., also showeda decreased activity past 908 in the ASFE, except for the posterior deltoidsegment. The rise in joint resultant force above 908 is due to other muscles.At 1208 abduction, the majority of abductors externally rotate the humerus

(table 2). Only the cranial segments of the subscapularis and pectoralis majorcan counterbalance external rotation, but they are also strong forward flexors.Here, other muscles such as teres major are activated to help balance these



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components, even if such a muscle is a very strong adductor. Interestingly,in vivo measurements using instrumented shoulder prostheses (Bergmann et al.2007) recently presented at the meeting of the European Society ofBiomechanics have indicated that joint reaction forces increase as abduction

exceeds 908 (Nikooyan et al. 2008). Although the ASFE is able to replicate thistrend, it does not necessarily mean that the muscle forces found herecorrespond to an in vivo muscular contribution during abduction, as manyphysiologically plausible muscle force patterns can lead to a similar jointreaction force. Experimental measurements of muscular activity in posturesabove 908 of abduction are now required. However, it may indicate thatco-contraction is a very important aspect of shoulder biomechanics, which hasthus far been widely neglected.

(c) Deformable models

The FE method can simulate the deformations of complex systems that areotherwise difficult to assess and has been used to address a broad range ofproblems in the field of biomechanics and orthopaedics (Huiskes & Hollister1993). FE modelling opens up a vast range of possibilities for simulating complexmaterial phenomena such as nonlinear elastic and viscoelastic behaviours, plasticdeformation, creep and fatigue failure behaviours.

Most FE models of the shoulder have been developed to specifically investigateglenoid fixation and loosening, generally relating excessive bone or cementstresses to failure. The influence of implant design parameters, such as peg orkeeled glenoid anchorage (Lacroix et al. 2000), shape of implant components

(Lacroix & Prendergast 1997; Buchler & Farron 2004; Terrier et al. 2006) orunconventional fixation type (Murphy & Prendergast 2005), has been studiedusing FE models. Finally, the FE method has been implemented in comparisons

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Figure 4. Joint reaction force during abduction in the scapular plane obtained by different models

(triangles, Poppen & Walker 1978; circles, van der Helm 1994a; diamonds, Terrier et al. 2008). Forthe ASFE (squares, Favre et al. 2005), the input data (muscle moment arms and lines of action)were measured in prior experiments so that only four positions are currently available in thescapular plane (0, 45, 90 and 1208 torso-humeral elevation). The grey arrow shows the tendency ofthe measurements obtained with the instrumented shoulder implant in two patients able to abducttheir arm higher than 908 (correspondence with Prof. G. Bergmann).

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between cemented and uncemented prosthesis fixation (Gupta et al. 2004b,c),and testing the influence of cement thickness (Couteau et al. 2001; Terrier et al.2005) or implant positioning on bone and cement stresses (Hopkins et al. 2004;Farron et al. 2006).

Shoulder FE studies addressing other clinical shoulder questions are fewer.Interesting two-dimensional studies have considered the stress pattern in thesupraspinatus tendon, trying to understand the mechanical origin of tears (Luoet al. 1998; Wakabayashi et al. 2003; Sano et al. 2006). Another study tried toquantify the influence of the shape of the humeral head on the stress distribution inthe scapula with the intent to compare a normal with an osteoarthritic shoulder

(Buchler et al. 2002). Finally, relative kinematics of implant components havebeen simulated using the FE method to study implant intrinsic stability (Hopkinset al. 2006, 2007).

Table 2. Muscle segment moment arms at 1208 abduction. (Abduction (C) or adduction (K)moment arms are given in the first column, forward (C) or backward (K) change in plane ofelevation in the second, and internal (C) or external (K) axial rotation in the third column. Thefourth column displays the forces attributed by the ASFE.)

moment arm components

force (N)elevation (mm)plane of elevation(mm)

axial rotation(mm)

anterior supraspinatus 17.19 14.21 K2.63 18.56posterior supraspinatus 21.53 2.58 K5.24 18.56cranial subscapularis 2.86 22.17 1.43 4.42middle subscapularis K1.72 21.28 5.52 11.85caudal subscapularis K11.23 14.32 8.75 11.85cranial infraspinatus 20.05 K4.20 K10.61 18.28

middle infraspinatus 13.01 K11.73 K11.63 18.28caudal infraspinatus 4.77 K13.76 K12.23 18.28cranial teres minor K4.30 K15.76 K10.46 0.00caudal teres minor K8.59 K14.06 K14.32 0.00anterior deltoid 22.33 28.65 0.00 187.15anterior middle deltoid 27.16 5.17 0.00 63.11middle middle deltoid 25.78 K9.79 0.00 85.60posterior middle deltoid 13.64 K25.04 0.00 85.60posterior distal deltoid 7.16 K37.34 0.00 126.92posterior proximal deltoid 2.81 K30.23 0.00 99.35triceps K20.06 K14.30 0.00 0.00

coracobrachialis 2.86K

30.08 0.00 23.93teres major K25.78 K7.16 3.44 62.90cranial latissimus dorsi K31.51 2.88 7.16 7.63middle latissimus dorsi K40.11 2.88 7.16 7.63caudal latissimus dorsi K42.97 0.00 2.86 12.90cranial pectoralis major 5.73 31.09 4.30 58.61middle pectoralis major K1.43 50.13 5.73 12.11caudal pectoralis major K37.24 54.43 11.46 12.11biceps caput longum 2.91 17.19 K10.02 22.13biceps caput breve 2.91 31.51 0.00 30.63





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The main limitations of deformable models usually lie in the definitions ofboundary conditions and material properties that are employed. Measuring anddescribing the material properties of biological tissues is not at all simple, andmost models necessarily implement idealized material properties. With regard toboundary conditions, in vivo forces have been simulated by applying the joint

resultant force only (Stone et al. 1999; Couteau et al. 2001; Andreykiv et al.2005). In more elaborate FE models (Lacroix et al. 2000; Gupta et al. 2004b,c;Hopkins et al. 2005, 2007; Murphy & Prendergast 2005), individual musclecontributions were assigned according to van der Helm (1994b). Axial rotation ofthe humerus has been simulated by applying a gradually imposed displacementat a chosen muscle insertion and by restricting unwanted motions through non-physiological boundary constraints at the distal extremity of the humerus (Buchleret al. 2002). In a later extension of the same model, this artificial boundarycondition was removed, but the model was restricted to a two-dimensionalrepresentation and to the deltoid and rotator cuff muscles (Terrier et al. 2008).

Finally, investigating glenoid loosening requires a profound understanding of thefailure mechanisms. FE models can predict mechanical factors such as bone-implant micromotion, wear or excessive stress, but the induced biological responseis extremely complex and remains not yet fully understood.

Despite these limitations, results obtained from deformable models can still bedirectly transferred to clinical practice by defining the relative influence ofsurgically adaptable parameters (choice of implant, components positioning, useof cement, etc.) on the investigated consequence (stress shielding, asepticloosening, etc.).

3. Model validation

To efficiently address scientific and clinical questions through a modellingapproach, the goal is not to build a perfectly realistic model, but to create asufficiently accurate representation of the aspect to be investigated. Thecomplexity of a biological system, such as the shoulder, is such that somesimplifications must be made in the modelling process, although each assumptionintroduces a potential source of error. To ensure that the imposed simplificationsdo not diminish the veracity of the simulation, validation is essential. Thevalidation process confronts simulation results with reality, or, when this is not

directly possible, with controlled experiments that approximate reality.Simulation results are compared against measurable parameters with the aimto identify inappropriate assumptions or simplifications that can then beadjusted to improve the fidelity of the model.

(a) Validating rigid body models

Simulated rigid body motion can be compared with experimentally measuredkinematic data. For instance, the simulated reachable workspace of the arm canbe validated against actual measurements of range of motions (Klopcar et al.2007). Rigid body models used for the quantification of moment arms can also be

directly compared with in vivo or in vitro measurements (Garner & Pandy 2001;Gatti et al. 2007). Finally, when combined with muscle force estimation, in vivomeasurements of maximum isometric muscle torques exerted at the joint and/or

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the resultant kinematics can be used for comparison, although these onlyvalidate the global simulation quality and do not yield specific information onindividual muscle forces (Garner & Pandy 2001).

(b ) Validating muscle force estimation models

In an indeterminate system of equations, it falls on the modeller to restrict thenumber of considered solutions to those that can realistically occur in vivo. Asdescribed above, muscle force estimation models deliver two main pieces ofinformation: the set of recruited muscles and the force that these exert. EMGsignals can be used to compare the timings of the muscle activities (Happee &van der Helm 1995) and to verify that the model activates a reasonable set ofmuscles (Karlsson & Peterson 1992; Happee 1994; van der Helm 1994b; Happee &van der Helm 1995; Nieminen et al. 1995; Niemi et al. 1996; Favre et al. 2005), orthey could also allow comparison of paralysis experiments (either pathological orneurotoxin induced) against model behaviour when specific muscles are removedfrom consideration. On the other hand, we are currently limited in our ability toquantify individual muscle force magnitude since no in vivo muscular forcemeasurement devices are currently available (Erdemir et al. 2007), and EMGamplitude is a poor measure for validating the forces obtained by musculo-skeletal models (Inman et al. 1952; van der Helm 1994b). Given the lack ofreliable muscle force measurement techniques, results have generally beencompared with those obtained with previous models. However, this approachcannot be considered a valid muscle force validation, but merely serves as anindication that two models represent reality in a similar way. Since this approachcannot root out problems with widely held assumptions, there is obviously a

pressing need for better techniques to quantify in vivo muscle forces.

(c) Validating deformable models

In the most straightforward validations of FE models, modelling results(surface strain patterns) have been directly compared with experimentsperformed under similar loading conditions, using an in vitro strain gaugemeasurement (Couteau et al. 2001; Gupta et al. 2004a; Maurel et al. 2005) orphotoelastic techniques (Murphy & Prendergast 2005). As an example of clinicalvalidation, bone formation around a retrieved specimen confirmed that the bonestress predicted by the model (disregarding other important factors) was withinacceptable values (Ahir et al. 2004). For a proper validation of an FE model,strict guidelines and best practices have been suggested (Viceconti et al. 2005).Unfortunately, the validation step is very often neglected in deformable models.

(d) Emerging technologies for model validation

In the past, validation often compared model results with experimentsperformed on cadavers. Emerging technologies now allow direct comparison withselected in vivo measurements, bringing the models to a higher level of accuracy.Their use for validation of shoulder models is nascent (Dubowsky et al. 2008;

Terrier et al. 2008), but is destined to increase. Rapid progress in the field ofmedical imaging opens new possibilities to measure rotation and translation ofthe glenohumeral joint during in vivo movements using standard fluoroscopic





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sequences (Pfirrmann et al. 2002), open magnetic resonance imaging (MRI;Graichen et al. 2000) and biplanar X-rays (Bey et al. 2008). These quantitiesprovide useful global criteria for a partial assessment of model performance ofrigid body or contact models. Validation of the forces predicted by numericalmusculoskeletal models of the shoulder has now been improved with direct

measurements of glenohumeral contact forces using an instrumented implant(Bergmann et al. 2007) as well as enhanced techniques to measure in vivo muscleactivity (Praagman et al. 2003, 2006; de Groot et al. 2004).

4. Outlook in numerical shoulder modelling

Implementation of more realistic modelling approaches to investigate stabilizationof the glenohumeral joint is imperative (Veeger & van der Helm 2007). Sincetranslations may no longer be small in comparison with rotations in the unstable

shoulder, modellers may have to deviate from the simplification of the shoulderjoint as a perfect ball-and-socket (Hopkins et al. 2006). If a priori (artificial)restrictions on translations are to be avoided, muscle force estimation models canplay a valuable role in introducing muscle-driven stabilization of the joint.

Owing to the great individual variability in anatomy, patient-specific modelsmay be needed to study specific skeletal deformities, and altered bone and softtissue material properties, or for individual diagnosis and surgical planning.With semi-automatic extraction of anatomy from computed tomography andMRI images, models of individual patients are now plausible (Young et al.2008). For studies on loosening of the glenoid component in shoulderarthroplasty, a more realistic representation of the underlying bone micro-architecture may improve the representation of the interface mechanics andforce transmission in the bone, enhancing failure risk prediction (Ulrich et al.1997; Pistoia et al. 2002). Also, long-term predictions of implant fixation couldbe improved by including bone mechanical adaptation laws into FE models(Beaupre et al. 1990; Cowin et al. 1992; Prendergast & Taylor 1994; Huiskeset al. 2000). Such FE models for the shoulder do exist but have been limited totwo-dimensional analyses of the glenoid (Andreykiv et al. 2005; Sharma et al.2007). Simulation of fibrous tissue interposition between the implant and bonecould also be added (Weinans et al. 1990).

In this paper, shoulder models were treated as belonging to three main groups.

Although these categories sometimes overlap already, as seen with the couplingof rigid body and muscle force estimation models, an integrated modellingapproach can combine the advantages of the different models, offering newpossibilities. For example, when studying the influence of implant componentpositioning (table 1), the integrated modelling approach would provide a tool toaddress simultaneously the interconnected implications in range of motions andanatomy (which could be investigated with a rigid body model), the changes inmuscle activity and contact forces (which is studied with muscle force estimationmodels) and the deformations of the implant interface and implant fixation(information typically delivered by an FE model). In an effort to reduce

computational expense, FE models rarely represent the shoulder as a whole.When possible, parts of the system are simplified (or neglected) and substitutedwith approximate boundary conditions. However, this can lead to erroneous

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conclusions (Gupta & van der Helm 2004; Hopkins et al. 2005). For FE, in

general, the benefits of relying on fully balanced external load regimes have beendemonstrated (Duda et al. 1998; Speirs et al. 2007). Explicit incorporation oftissue deformations and failure further allow investigations into how these factorscan affect segment motions and muscle force activity. Thus, through anintegrated modelling approach, more realistic conditions can be implemented,yielding more reliable results. To this end, we see the FE method as the mostpromising framework. Modern commercial FE software packages allowsimulation of large motions, and can implement the simplifying aspects of rigidbody assumptions in a hybrid fashion, permit simultaneous inclusion of muscleforce estimation and recruitment strategies, and allow determination of

component deformations in critical locations. To this end, we are currentlydeveloping a model that combines the ASFE with an anatomically precise FEmodel of the glenohumeral joint (figure 5).

muscle force

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model of the glenohumeral joint: (a) FE (rigid body), (b) ASFE and (c) FE (deformable). Here, onlya few muscle segments are represented on the three-dimensional model of the shoulder. Thedeformable muscles can wrap on the bones, relying on detection of contact in the FE software.The moment arms and lines of action of the muscles are computed in this position and sent to theASFE. The muscle forces are returned as boundary conditions to the FE model. The infinitesimalmotion of the arm is simulated within the FE model and the positional error between the obtainedand the target positions is determined. This loop is reiterated until the positional error is less thana predefined value. Results obtained with this model will be validated against EMG patterns,glenohumeral contact forces for given activities, and clinical cases of muscle insufficiency.





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In conclusion, numerical models of the shoulder have proven to be useful in awide range of clinical applications. In the future, given our growing under-standing of shoulder mechanics, advances in modelling methods and increases incomputer power, numerical models should enable researchers to address evermore complex clinical questions and ultimately improve patient care.

References

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Chadwick, E. K. J., van Noort, A. & van der Helm, F. C. T. 2004 Biomechanical analysis ofscapular neck maluniona simulation study. Clin. Biomech. (Bristol, Avon) 19, 906912.(doi:10.1016/j.clinbiomech.2004.06.013)

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