Medical Biological Engineering Computing-2013

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ORIGINAL ARTICLE

Biomechanical analysis of the wrist arthroplasty in rheumatoidarthritis: a nite element analysis

M. N. Bajuri • Mohammed Raq Abdul Kadir •

Malliga Raman Murali • T. Kamarul

Received: 15 January 2012/ Accepted: 24 October 2012 / Published online: 3 November 2012 International Federation for Medical and Biological Engineering 2012

Abstract The total replacement of wrists affected byrheumatoid arthritis (RA) has had mixed outcomes in termsof failure rates. This study was therefore conducted toanalyse the biomechanics of wrist arthroplasty usingrecently reported implants that have shown encouragingresults with the aim of providing some insights for thefuture development of wrist implants. A model of a healthywrist was developed using computed tomography imagesfrom a healthy volunteer. An RA model was simulatedbased on all ten general characteristics of the disease. TheReMotion TM total wrist system was then modelled tosimulate total wrist arthroplasty (TWA). Finite elementanalysis was performed with loads simulating the statichand grip action. The results show that the RA modelproduced distorted patterns of stress distribution with ten-fold higher contact pressure than the healthy model. For theTWA model, contact pressure was found to be approxi-mately vefold lower than the RA model. Compared to the

healthy model, signicant improvements were observed forthe TWA model with minor variations in the stress distri-bution. In conclusion, the modelled TWA reduced contactpressure between bones but did not restore the stress dis-tribution to the normal healthy condition.

Keywords Arthroplasty Rheumatoid arthritis Biomechanics Finite element analysis

1 Introduction

One of the most common skeletal diseases that is com-monly associated with the wrist joint is rheumatoid arthritis(RA) [ 45]. The disease affects mostly synovial joints,resulting in considerable pain, loss of function and eventualdeformity. It is a life-long condition, and the diseaseactivity might change over time resulting in different ratesof pathological process progression [ 48].

In general, there are three characteristics which may beseen in the wrist as the result of RA—cartilage destruction,synovial proliferation and ligamentous laxity [ 48]. Damageto the cartilage which may result in signicant cartilagethinning may occur due to cytochemical effects which leadto the degradation and inhibition of new cartilage forma-tion [ 13]. Articular cartilage works as a wear-resistantsmooth surface, nearly frictionless with load-bearingcapability [ 26]. Thus, the absence of cartilage will result inhigh contact pressure due to non-uniform load transmissionthat is created within these denuded areas. Bone erosiondue to synovial proliferation resulted in sharp bony edgesthat cause high-stress concentration and could lead totendon rupture [ 43]. Laxity of the ligaments caused by thesynovial expansion will further alter physiological bonetranslation and displacement [ 48]. Occurring concurrently,

M. N. Bajuri M. R. Abdul Kadir ( & )Faculty of Health Science and Biomedical Engineering,Medical Implant Technology Group, Universiti TeknologiMalaysia (UTM), 81310 Johor Bahru, Johor, Malaysiae-mail: [email protected]

M. N. Bajurie-mail: [email protected]

M. R. Murali T. KamarulFaculty of Medicine, Tissue Engineering Group (TEG),Department of Orthopaedic surgery, National OrthopaedicCentre of Excellence in Research and learning (NOCERAL),University of Malaya, 50603 Lembah Pantai, Kuala Lumpur,Malaysiae-mail: [email protected]

T. Kamarule-mail: [email protected]

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Med Biol Eng Comput (2013) 51:175–186DOI 10.1007/s11517-012-0982-9



these changes will lead to biomechanical imbalances thatultimately result in visible deformity of the wrist [ 35].

Total wrist arthroplasty (TWA) is a treatment optionwhich is gaining popularity for treating severe deformity of the joint due to RA [ 21]. The use of TWA is intended torestore wrist joint motion while eliminating pain and jointstiffness. However, there are two reported problems asso-ciated with the use of TWA—implant loosening andmetacarpal perforation [ 11 ]. Loosening is more commonand it is attributed to the lack of bony support for theimplant [ 34]. A new total wrist arthroplasty system, theReMotion TM , was developed to resolve this issue whileensuring good joint stability. Two main concepts wereincorporated in the design: intercarpal fusion to avoidmetacarpal perforation and resurfacing the distal radiusregion to avoid implant loosening and dislocation [ 23].Short-term follow-up from a prospective study showedgood clinical track record demonstrating a high rate of satisfaction amongst patients, with minimal complicationsreported [ 23]. However, there appears to be paucity in theknowledge with regards to changes in the biomechanicalforces acting to the wrist joint following TWA in rheu-matoid patients. The signicant effect of bone graft forbetter bone fusion has also been reported by Zander et al.[11 ]. Such studies are important as it would provide addi-tional information that could benet researchers [ 50],practicing surgeons and implant manufacturers. Therefore,a study was performed to analyse stress distribution andcontact stresses in severe rheumatoid wrist after TWA byassessing and comparing the load transfer throughout the joint and contact pressure at the articulations. A healthywrist model was also constructed to compare the resultsbetween RA and TWA.

2 Methods

2.1 Geometry

Computed Tomography (CT) images of a healthy asymp-tomatic 53 years old male volunteer were used to construct3-dimensional (3D) model of the wrist joint. The scan wasperformed on the wrist in an extended (33.11 ) and devi-ated (17.34 ulnar) position, measured relative to the ana-tomically based radial coordinate system [ 29]. The CTimages ranging from the distal end of the long bones of theleft forearm—radius and ulna—to the proximal third of themetacarpals were captured. The scans with a total length of 102.3 mm have a slice thickness of 1.5 mm and a resolu-tion of 0.98 mm in plane. Semi-automatic segmentation viagrayscale value was used to virtually construct the corticalbone model (Mimics software, Materialise, Belgium). Theregion inside the cortical was automatically converted into

cancellous bone. The software’s marching cubes algorithmwas used to generate 3D triangular surface mesh of thewrist model for nite element analysis. The ratio of twicethe radius of the inscribed circle to the radius of theascribed circle of the triangle was used as normalizedindicator for mesh quality verication [ 32]. High qualitysurface mesh was produced by setting the correspondingvalue at 0.4 [ 18, 25]. In addition, an average element sizeof 0.4 mm was chosen to produce higher denition modelwith sufcient geometric description of the bone geometry,veried via an anatomy software [ 33]. The completed 3Dsurface mesh of the wrist bones was then converted intorst order linear tetrahedral elements (Marc.Mentat,MSC.Software, Santa Ana, CA), consisting of 828,888elements and 204,218 nodes.

Cartilage layers for the articulations between bones weremodelled by extracting proles of the articulating surfaceswith a thickness size half of the minimum distance betweentwo bones [ 16]. This resulted in a good geometrical rep-resentation and material distribution of the cartilage(Fig. 1), compared and checked with an anatomy software[33].

All 60 ligaments were modelled using linear mechanicallinks where the insertion points were estimated via ananatomy software [ 33] and a previous anatomical study[15]. Stiffness of the ligaments was varied from 40 to

Fig. 1 Finite element model of the healthy wrist showing thecartilage as extruded elements at the articulations between bones andligament as a set of mechanical links

176 Med Biol Eng Comput (2013) 51:175–186

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350 N/mm [ 7, 10 , 16 , 41, 42] as shown in Table 1. Thoseligaments with no previous reports of their material prop-erties were assigned with the properties of their adjacentligaments [ 17]. Numbers of links were varied according tothe distribution of the origin and insertion of the ligaments.

2.2 Modelling of the wrist affected by rheumatoid

arthritis

Past literatures have thoroughly addressed the followingten characteristics of the Type IIIa (disintegration type withmore ligamentous instability) of the RA wrist, and thuswere used to construct the model of the rheumatic wrist:

1. Destruction of the cartilage [ 49]. This was modelledby removing all cartilages, simulating worst-case scenario(Fig. 2, 1).

2. Loss of carpal height as a result of bone destruction[48]. The carpometacarpal (CMC) ratio of 0.4 which rep-resents severe rheumatic wrist was used in the simulation

[53]. It was simulated by translating metacarpals in10.1 mm proximally. As compared to the healthy modelwith a total carpal height of 32.45 mm (CMC = 0.55), theeffect of impaction in RA model could be seen as the totalcarpal height has reduced to 22.35 mm (CMC = 0.4)(Fig. 2, 2).

3. Dislocation of the carpus in the ulnar direction due toloss of tension of the radiotriquetral ligament, irrespectiveof the status of the ulnar head [ 48]. The rst gure showsthe dislocated carpus towards ulna. The simulation was

Table 1 Listing of ligaments modelled specifying their connectionsand dened stiffness parameters [ 7, 10 , 16 , 41 , 42 ]

Ligament Connection 1 Connection 2 Stiffnessspecied(N/mm)

Capitohamate Capitate Hamate 325 [ 42]

Capitotrapezial Capitate Trapezium 300 [ 42]

Dorsal carpometacarpal Capitate 4MC medial 300 [ 10]

Dorsal carpometacarpal Capitate 4MC lateral 300 [ 10]

Dorsal carpometacarpal Capitate 3MC medial 300 [ 10]

Dorsal carpometacarpal Capitate 3MC lateral 300 [ 10]

Dorsal carpometacarpal Trapezoid 2MC lateral 100 [ 10]

Dorsal carpometacarpal Trapezoid 2MC medial 50 [ 10]

Dorsal carpometacarpal Trapezium 2MC medial 48 [ 7]

Dorsal carpometacarpal Hamate 4MC 300 [ 10]

Dorsal carpometacarpal Hamate 5MC 300 [ 10]

Dorsal intercarpal Hamate Capitate 325 [ 42]

Dorsal intercarpal Capitate Trapezoid 300 [ 42]

Dorsal intercarpal Hamate Triquetrum 300 [ 10]

Dorsal intercarpal Hamate Lunate 150 [ 10]Dorsal intercarpal Capitate Lunate 150 [ 10]

Dorsal intercarpal Capitate Scaphoid 150 [ 10]

Dorsal intercarpal Scaphoid Trapezium 150 [ 10]

Dorsal intercarpal Trapezoid Trapezium 110 [ 16]

Dorsal intercarpal Trapeziumandtrapezoid

Triquetrum 128 [ 16]

Dorsal lunotriquetral Lunate Triquetrum 350 [ 42]

Dorsal 2MC1MC 2MC 1MC 100




Dorsal radioulnar Radius Ulna 50 [ 10]

Dorsal scapholunate Lunate Scaphoid 230 [ 42]

Dorsaltrapeziometacarpalcarpometacarpal

Trapezium 1MC lateral 100 [ 10]

Long radiolunate Lunate Radius 75 [ 42]

Palmar carpometacarpal Capitate 3MC 100 [ 10]



Palmar carpometacarpal Trapezium 3MC 88 [ 7]

Palmar carpometacarpal Trapezium 2MC 57 [ 7]

Palmar carpometacarpal Hamate 5MC 100 [ 10]

Palmar carpometacarpal Hamate 3MC 100 [ 10]Palmar carpometacarpal Pisiform 5MC 100 [ 10]

Palmar 1MC2MC 1MC 2MC 100




Palmartrapeziometacarpal

Trapezium 1MC 24 [ 7]

Pisohamate Hamate Pisiform 100 [ 10]

Radial arcuate Capitate Scaphoid 40 [ 42]

Table 1 continued

Ligament Connection 1 Connection 2 Stiffnessspecied(N/mm)

Radial collateral carpal Radius Scaphoid 10 [ 41]

Radiodorsaltrapeziometacarpal

Trapezium 1MC medial 78 [ 7]

Radioscaphocapitate Radius Capitate 50 [ 42]

Palmar radiotriquetrum Radius Triquetrum 27 [ 41]

Dorsal radiotriquetrum Radius Triquetrum 27

Scaphotrapezial Scaphoid Trapezium 150 [ 42]

Scaphotriquetrum Scaphoid Triquetrum 128

Short radiolunate Lunate Radius 75 [ 42]

Ulnolunate Ulna Lunate 40 [ 42]

Ulnar arcuate Capitate Triquetrum 40 [ 42]

Ulnar collateral Triquetrum Ulna 100 [ 10]

Ulnar collateral Pisiform Ulnar 100 [ 10]

Ulnotriquetral Triquetrum Ulna 40 [ 42]

Volar lunotriquetral Lunate Triquetrum 350 [ 42]

Volar radioscapholunate(testut)

Radius Scaphoid ? lunate 50,75

Volar radioulnar Radius Ulnar 50 [ 10]

Med Biol Eng Comput (2013) 51:175–186 177

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done by rotating 10 of all carpus towards ulnar where thecenter of the radius used as the center of rotation (COR).The next gure shows the simulated loss of tension(in circular) of the radiotriquetral ligament where only onelink remained simulating worn ligaments (Fig. 2, 3).

4. Dislocation of theproximal carpalrow in thepalmar andulnar direction [ 48]. The simulation was done by translatingthe bones 2.76 mm palmarly and 7.61 mm towards ulnardirection, as shown in the superior view of Fig. 2, 4.

5. Scapholunar dissociation (SLD) with scapholunateadvanced collapse (SLAC) wrist arthritis stage 2 [ 48]. Thesimulation was performed by increasing the distancebetween the scaphoid and lunate from (1.98 mm, healthy)to (6.51 mm, RA). The weakened ligaments modelled withone link element (Fig. 2, 5).

6. Dislocation of the scaphoid in the palmar direction asa result of the radial insertion of the Testut ligamentsynovialitis [ 48]. The simulation was done by rotating thescaphoid radially (center of scaphoid as COR) and palm-arly (the proximal end ulnar direction as COR) for 16.8and 22.3 , respectively (Fig. 2, 6).

7. Hand scoliosis due to ruptured tendon. This mecha-nism resulted in a changed axis of the wrist to the ulna witha consecutive rotation of the metacarpal bones in the radialdirection [ 48]. It was simulated by dislocating 7.23 mm allcarpus excluding the scaphoid towards the ulnar and radi-ally rotating all metacarpals by 10 where the COR waspositioned at the center of the radius (Fig. 2, 7).

8. Reduction of contact between the lunate and radius[48]. It was simulated by translating 7 mm of the lunatetowards the ulnar (reference was positioned at the center of the distal ulna), resulting in the decreasing of the contactbetween the radius and the lunate (Fig. 2, 8).

9. Bone erosion [ 48]. It was simulated by Booleanoperation (subtraction) once the positions of the affectedbones were conrmed. Sharp edges due to bone erosionwere simulated by local smoothing algorithm tool (rightgure) (Fig. 2, 9).

10. Osteoporotic bone [ 48, 49]. This criterion was simu-lated by reducing the elastic modulus of the bones; 33 % forthe cortical bone and 66 % for the cancellous bone [ 38].

As the disease progresses, the effect of torn and stret-ched ligaments was simulated by reducing the number of links as described in Fig. 2. The simulated RA wrist modelwas then converted into solid tetrahedral mesh consistingof 1,115,599 elements and 233,570 nodes. The steps takento simulate the 1 to 9 characteristics are described in Fig. 2.

2.3 Modelling of the total wrist arthroplasty (TWA)model

The latest wrist implant for arthroplasty, ReMotionTM

pro-duced by Small Bone Innovations, wasused in the simulation

[24]. The model of the implant was constructed using CADsoftware, Solidworks 2009, and converted into surface tri-angular elements using MARC MENTAT software. Virtualpreparation of the bone for implantationwas carried out priorto insertion of the implant where the scaphoid, lunate andsome parts of the capitate and triquetrum were resected. Theimplant components werethenplaced in theirrespective boneand laterconverted intosolidtetrahedral meshwith1,305,415elements and 277,070 nodes. The steps are shown in Fig. 3.

2.4 Contact modelling

A deformable-to-deformable contact was selected betweenthe articulating surfaces. To approximate frictionless con-tact for the control model (healthy wrist), a small value of friction coefcient (0.02) was assigned [ 18]. For the RAmodel, an assumed friction coefcient of 0.3 was used dueto the relatively rougher surface of the contacted bones [ 4].Surface roughness of 0.8 was used at the carpal platecomponent in the TWA model simulating its rough surfaceto promote osseointegration [ 47]. The effect of screwthread was simulated by preventing any slippage at thecontacting surfaces [ 12]. The rest of the contacting bodieswere allowed to move physiologically.

2.5 Tissue properties modelling

Bones of the wrist were modelled with linear isotropicmaterial denition representing the cortical bone (healthymodel: E = 18 GPa, m = 0.2 [18] and RA and TWA model:E = 12 GPa, m = 0.2) and cancellous bone (healthymodel: E = 100 MPa, m = 0.25 [18] and RA and TWAmodel: E = 33 MPa, m = 0.25). All implant components(radius component, carpalplate, central pegand screws) wereassigned with properties simulating CoCrMo alloys(E = 210 GPa, m = 0.3) [46], whilst the carpal ball wasassigned with UHMWPE properties ( E = 1.4 GPa, m = 0.3[14]). The bone graft modulus was varied ( E = 0.1, 1 and 5GPa, m = 0.2 [54]) to analyse their effects on intercarpalfusion. Hyper-elastic material properties were assigned tosimulate the large deformation behaviour of the cartilage inthe healthy model [ 9], where the Mooney–Rivlin parametersof C10 = 4.1 MPa and C01 = 0.41 MPa [ 30] were used.

2.6 Simulations

As hand grip strength was a common indicator of assess-ment for both rheumatic and treated wrists [ 3, 11 , 39], theload simulating static gripping force of the wrist calculatedby Gislason et al. [ 17] was used in all simulated cases. Thestatic gripping force of the wrist calculated by Gislasonet al. [17] was used with a magnitude of the resultantcompression pressure of 7.33 MPa distributed over the ve


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metacarpals (Fig. 4a). Figure 4b–d shows the applied loadsand their distributions.

Constraints were applied at the proximal ends of theradius and ulna to assist convergence of the solution [ 18].

The carpometacarpal joint and the insertion of tendons(abductor pollicis longus muscle, exor carpi radialismuscle, exor carpi ulnaris muscle, extensor carpi ulnarismuscle, extensor carpi radialis brevis muscle, extensorcarpi radialis longus muscle) were xed to prevent motionat the x and y directions, thus enabling movements of allbones (excluding the radius and ulna) in the direction of applied loading [ 10]. These constraints through xation of the tendons at their insertion points were vital to achieveconvergence of the model [ 13].

3 Results

3.1 Bone stress distribution

The difference of stress distribution amongst the three caseswas clearly observed in Fig. 5. At the carpal complex, anuniform load transmissionwasfound at theTWAmodel withsmall variations of stress magnitude observed ranging from1.08 to 1.63 MPa (Fig 6a). In contrast, the correspondingbones of the RA model showed high variation of stressmagnitudes (ranging from 1.87 to 3.97 MPa), indicating anon-uniform load transmission. Stress distribution in theTWA model showed no similarity to that of the healthymodel. Amongst all the three models, the healthy model has

Fig. 2 Finite element model of the wrist joint affected by RAtogether with steps to simulatethe 1 to 9 characteristics


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the highest magnitude of stress per element (average2.49 MPa), followed by the RA model (average 1.99 MPa)and the TWA model (average 1.29 MPa).

3.2 Contact pressure

The simulated RA model has the highest contact pressure of almost ten times higher (average 3.9 MPa) than the healthymodel (average 0.40 MPa) (Fig. 6b). The high magnitudeobserved in the diseased model reduced to almost ve timeslower after TWA (average 0.75 MPa), which is almost sim-ilar to the magnitudes from the healthy model (47 % higher).

In general, the trapezium was observed as the most criticalbone (excluding the resected scaphoid) with the highestmagnitude of pressure found in all the three simulated cases,especially in the RA model (11 MPa).

3.3 Variation on bone graft modulus

It was observed that the bone graft modulus had signicantimpact on the stress distribution (Fig. 7a) as well as contactpressure (Fig. 7b) at the carpal complex. Increasing the bonegraft modulus to 5 GPa resulted in efcient load transmis-sion, prohibiting motion between bones, thus reducing

Fig. 3 3-dimensional niteelement model of the TWAwrist joint together with thesteps required to construct themodel


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contact pressure particularly in the carpal region. High uc-tuation pattern of graphs was found in the TWA modelengaged with bone graft modulus of 0.1 GPa, indicatinginconsistent stress and contact pressure magnitudes.

4 Discussion

4.1 Comparative analysis

The results from this study were compared with othernumerical and experimental works [ 17, 31, 37, 43] whereslight differences were observed due to variation in

anatomical conguration. Only the healthy wrist model canbe compared, because at the time of writing there were noreported works on simulated RA and TWA models. Themodel quality and reliability in terms of its mesh wasassessed based on surface element analysis where 90 % of the elements had a value greater than 0.80 (where unityrepresents an equilateral triangle).

Agreement was found for several aspects of stresstransfer highlighted in previous studies [ 8, 17–19, 28, 31,37]. Our study revealed that the load transmission at theradiocarpal joint transferred more to the scaphoid (63 %)than the lunate [ 37]. Macleod et al. [ 31] in their cadavericstudy reported that 68 % of the load at the forearm was

Fig. 4 Magnitudes of pressureapplied on the metacarpal bones(a ) [18] together with niteelement model assembly of thehealthy ( b ), RA ( c) and TWA(d ) model. From the gure, theproximal and tendon insertionxation and the loadingconditions can be seen.Pressures were applied alongthe metacarpal axis


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transferred to the radius, but Gislason et al. [ 17] reported

a range of 78.7 % to 92.8 % in their simulation studies.These ndings supported the fact that the radius is themost signicant load bearer in the wrist joint. Our studyalso shows similar ndings for the radius as the main loadbearer with 78 % of the load. The overall load wastransferred mostly to the radial side (63 %), and this issimilar to reports by Gislason et al. [ 18] and Givissis et al.[19].

The strain magnitudes of the radius bone were alsocompared with other studies performed on a healthy radius

bone [ 8, 28]. Bosisio et al. [ 8] in their study on apparent

elastic modulus of human radius using inverse nite ele-ment model, reported an ultimate strain value for the cor-tical radius of e u = 1.50 % and the yield strain of e

y = 0.90 %. Kerin et al. [ 28] conducted a study on thecompressive strength of articular cartilage and reported afailure strain value of cartilage under compression to be30 %. Our study shows average strain values for the car-tilage, cortical and cancellous bones were e = 1.40 %,e = 0.02 %, e = 0.17 %, respectively. These strain valueswere below the failure criteria reported in literature [ 8, 28].

Fig. 5 Stress distributioncontours for the healthy ( a ), RA(b ) and TWA model ( c) fromthe palmar ( left ) and dorsal(right ) view. Stress scales varyamongst gures to obtainmaximum image detail


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4.2 Biomechanical analysis on the efciencyof the total wrist arthroplasty (TWA) procedure

The pathogenesis of RA involved the destruction of softtissues such as the cartilage [ 48]. The cartilage functions asa nearly frictionless bearing and a shock absorbing mech-anism to uniformly and safely transfer loads to the under-

lying bone [ 26]. The absence of cartilage will thereforeresulted in higher stress concentration with high contactpressure generated at the articulation surfaces. Signicantalteration was, therefore, observed in the biomechanicalbehaviour of the rheumatic wrist joint with signicantlyhigher contact pressure of the bones. The high contactpressure was also due to the eroded bone surfaces with theexistence of sharp edges, as can be clearly seen on the RAmodel.

Imbalance load transmission was also observed in therheumatic model where lesser load was transferred radially(58 %) compared to the healthy model (63 %). One of thecauses for the imbalance is due to the dislocation of carpustowards ulnar which resulted in load distribution changes.In a rheumatoid joint, inammation of the synovial uidcould severely affect the ligaments through stretching ortearing with a potential eventual deformity [ 48]. Thiscondition distorts the constraint initially provided by theligaments and led to random translation, dislocation, androtation of the affected bones. Hand scoliosis conditionalso contributed to load transfer imbalance where theradially rotating metacarpals caused the direction of stresses to move towards the ulnar side.

As far as treatment is concerned, it is vital to solve twomain problems caused by RA as shown in this study; theeffect of high contact pressure and imbalance load trans-mission. The ReMotion TM implant used in our TWA modelproposed two main design concepts—intercarpal fusionand distal radius resurfacing to minimise motion that couldlead to metacarpal perforation and implant loosening. Ourresults conrmed the ability of this implant system toreduce high contact pressure in RA bones through inter-carpal fusion approach. This implant system fused theaffected bones via two screws, one central peg and bonegrafts, thus minimising stress concentration and reducingthe potential problem of wear at the articulation.

In terms of load transmission, the disproportionate pat-tern of stress distributions observed in the RA modelchanged to a more uniform pattern after TWA. This ndingcomplied with the implant design concept of intercarpalfusion to attain solid bony mass and, therefore, uniformpattern of loading [ 21]. Better fusion could be achieved bybone graft with a modulus close to the bone; our parametricanalysis showed that bone graft with a modulus of 5 GPaproduced more encouraging results in terms of uniformload transmission and lower contact pressure. This is in

Fig. 6 Average von Mises stress ( a) and contact pressure ( b ) in eachbone of the three models

Fig. 7 Average von Mises stress ( a) and contact pressure ( b ) in eachbone of the different bone graft modulus


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agreement with the concept of avoiding elasticity mismatch[36] to prevent unphysiological loading and unwarrantedbone remodelling. In clinical practice, there were varioussources of bone grafts with different modulus ranging from0.1 GPa (iliac crest) to 5 GPa (bula) [ 54].

The simulation of such an extremely complex joint of thewrist will be even more difcult and resource demandingwhen pathological conditions, such as RA, are taken intoaccount. Several assumptions were, therefore, incorporatedin the nite element model development and analysis toassist in the convergence of the solutions. Even though allthe ten characteristics of the RA wrist have been simulated,quantitative data are lacking. Carpometacarpal ratio of 0.4for severe RA was the only quantitative data reported inliterature. However, this ratio sufciently provided theupper and lower boundary of the carpal region. We haveassumed the position of the individual bones relative to eachother from clinical reports; for instance, hand scoliosis wassimulated by dislocating all carpus towards the ulnar, andradially rotate all metacarpals by 10 .

The material parameters used in this study have directinuence on the outcome of the analysis. We have simpli-ed the modelling of the articular cartilage with bulk solidproperties, where a more complex modelling approach mayhave been better to represent its real mechanical behaviour,specically for the rheumatic joint. Mathematical approachusing biphasic bril-reinforced composite models has beenreported to model the articular cartilage [ 27, 44, 51].However, this mathematical model, as far as the authors areaware, has not been fully utilised in any nite elementanalysis of human joints. It is important to note thatincorporating such mathematical formulation into a highlycomplex model of the wrist would be too prohibitive, atleast for our current computational capabilities.

We have also simplied the material properties for thebone, where an isotropic behaviour was assigned to thenormal and RA bones. This simplication has been widelyused in the biomechanics studies related to orthopaedics,even though the properties of bone changes due to theageing process and even more pronounced in those withskeletal disorders [ 1, 5, 6]. The abnormal alterations in thebone remodelling process, for example, resulted in dis-turbed bone homeostasis leading to bone resorption [ 2, 22].Patient specic analysis could be done by assigning theactual grayscale value (Hounseld unit) from CT images tothe associated elements.

The use of linear links to simulate the ligaments wasfound to be adequate as the outcomes of the analyses weresimilar to reported clinical works [ 37, 43]. However, futureworks are recommended to use non-linear viscoelasticproperties which are a better representation of ligaments[17] and may avoid unphysiological concentrated stress atthe tendon insertions observed at the carpal complex of the

healthy and RA model in this study. Prestress in ligamentscould be physiologically simulated if element based mod-elling was implemented [ 20] or physiological distributionof the insertion points of the ligaments [ 18] were used asthese would better mimic the anatomy of the wrist joint.

Most published work related to orthopaedic biome-chanics using the nite element method used the von Misesstress as the equivalent comparison of stresses in bones topredict potential failure [ 6, 18, 40]. However, there is arecent report where the principal stresses (and not vonMises) were used in the biomechanical analysis of aproximal hip. Orthotropic properties were used, where theauthors argued that this approach provided a better repre-sentation of the real bone [ 52]. However, this is very rel-evant in the analysis of the proximal femur in whichdirectional behaviour of the cancellous bones was obvious.It is also less time consuming to analyse a single body likethe proximal femur using orthotropic properties. In con-trast, our analysis was relatively more complex involving15 bones of the wrist with distinctly less directionalbehaviour of trabeculae. We have, therefore, simplied ouranalysis using isotropic behaviour and von Mises stress.

This study has presented several ndings that reafrmedthe good clinical outcome of a specic implant system forTWA as conrmed in a short-term follow-up study repor-ted by Herzberg [ 23]. We have provided further insightsinto the biomechanical aspects of RA wrist and the corre-sponding changes after TWA. Whilst long-term follow-upstudy is still required, this study strongly recommends theuse of TWA as a viable alternative to total wrist fusion inrheumatoid patients especially in case of bilateralinvolvement [ 49]. We believe that this is the rst everreported work that simulates the pathological conditions of the RA of the wrist joint as well as simulating the reli-ability of treatment via arthroplasty.

Acknowledgments The authors wish to thank Dedy Wicaksonofrom the Medical Implant Technology Group, Universiti TeknologiMalaysia and Iskandar Mohd Amin from the Orthopaedic Depart-ment, Hospital Universiti Sains Malaysia for their valuable commentsand supports.

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