The Wrist Joint

SpringerBriefs in Applied Sciences and Technology

Computational Mechanics

Series Editors Andreas Öchsner Holm Altenbach Lucas F. M. da Silva

For further volumes: http://www.springer.com/series/8886 Mohd Nazri Bajuri Mohammed Raﬁq Abdul Kadir

Computational Biomechanics of the Wrist Joint

123 Mohd Nazri Bajuri Mohammed Raﬁq Abdul Kadir Department of Biomechanics and Department of Biomechanics and Biomedical Materials Biomedical Materials Universiti Teknologi Malaysia Universiti Teknologi Malaysia Johor Johor Malaysia Malaysia

ISSN 2191-5342 ISSN 2191-5350 (electronic) ISBN 978-3-642-31905-1 ISBN 978-3-642-31906-8 (eBook) DOI 10.1007/978-3-642-31906-8 Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2012943372

Ó Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com) Preface

The wrist joint is engaged in virtually every human functional activity and as such, exposed to high number of traumatic injuries, primary osteoarthritis, and secondary degenerative disease. One of the most common skeletal diseases associated with the wrist joint is rheumatoid arthritis (RA). The disease affects mostly synovial joints, resulting in considerable pain, loss of function, and eventual deformity. It is a life-long condition, and the disease activity might change over time. As compared to the hip and knee joints, this disease was identiﬁed to easily affect the wrist joint. There are three main symptoms of wrist with RA—cartilage destruction, synovial proliferation, and ligamentous laxity. Cartilage destruction caused by thinning occurs due to cytochemical effects resulting in degradation and inhibition of new cartilage. Additionally, bone erosion due to the synovial proliferation may cause sharp bony edges which might lead to tendon rupture. The laxity of the ligaments caused by the synovial expansion led to unphysiological bone translation and displacement. The pathological process of the RA starts with synovial inﬂammation primarily at the ulnar side of the wrist. It then spreads to the adjacent area including the radiocarpal joint, known as a critical region for the load transfer and joint motion. The adjacent cartilages, ligaments, and tendons degenerate accordingly. In severe cases, tendon rupture occurs with a consequence of kinematic changes of the wrist resulting in periarticular bones disruption at the articular surface. All the mentioned symptoms lead to the degeneration of both soft and hard tissues, and ultimately cause instability and mutilation of the joint. For severe cases of RA, arthroplasty as an alternative to bone fusion treatment (arthrodesis) has an advantage in preserving the joint motion. It is, however, reported in numerous literature that this procedure is the most unsuccessful arthroplasty as compared to the knee and the hip arthroplasty. Two main causes were addressed, the implant loosening and metacarpal perforation. It is noteworthy to mention that to date, however, there are designs reported to obtain good clinical outcome for a short-term evaluation. Follow up procedures are still running assuring the reliability of the implant for long-term clinical application.

v vi Preface

As one of established methods for prediction, finite element method was chosen to reaffirm those facts. Considering the inconsistent information on the reliability of the existing implant design, series of finite element analyses were performed to investigate the following aspects: 1. The biomechanical behaviours of the rheumatic wrist. 2. The biomechanical performance of the TWA procedure. This monograph is devoted to emphasize and analyse these two main concerns in supporting better clinical treatment for patients with RA. The information is recommended for biomedical engineers and researchers interested in computational works, medical practitioners dealing with the determination of understanding the RA disease as well as its treatment, from both clinical and engineering perspectives.

Skudai, May 2012 Mohd Nazri Bajuri Mohammed Raﬁq Abdul Kadir Contents

1 The Wrist Joint ...... 1 1.1 Anatomy of the Wrist Joint ...... 1 1.2 Bone Structure ...... 3 1.3 Cartilage Structure...... 4 1.4 Ligament Structure ...... 7 1.5 Kinematics ...... 8 References ...... 11

2 Biomechanical Properties and Behaviours of the Wrist Joint..... 13 2.1 Contact Surfaces and Load Transmission ...... 13 2.2 Biomechanical Consideration of the Cartilage Structure ...... 14 2.3 Biomechanical Consideration of the Ligamentous Structure . . . . 15 2.4 Current Trends in Biomechanical Modelling...... 17 2.4.1 Rigid Body Spring Method ...... 17 2.4.2 Finite Element Method ...... 17 References ...... 22

3 The Wrist Joint Affected by Rheumatoid Arthritis ...... 25 3.1 Pathology ...... 25 3.2 Rheumatoid Arthritis ...... 26 3.3 Treatment ...... 30 References ...... 31

4 Finite Element Modelling of the Healthy Wrist Joint ...... 33 4.1 Bone Model Reconstruction ...... 33 4.2 Modelling of Cartilages ...... 39 4.3 Modelling of Ligaments ...... 39 References ...... 40

vii viii Contents

5 Finite Element Analysis of the Wrist Joint Affected by Rheumatoid Arthritis ...... 41 5.1 Finite Element Model Construction of the Rheumatic Wrist . . . . 41 5.1.1 Simulation of Cartilage Destruction...... 42 5.1.2 Simulation of Loss of Carpal Height ...... 43 5.1.3 Simulation of Dislocation of the Carpus in the Ulnar Direction ...... 43 5.1.4 Simulation of Dislocation of the Proximal Carpal Row in the Palmar and Ulnar Directions ...... 43 5.1.5 Simulation of Scapholunate Dissociation and Scapholunate Advanced Collapse ...... 45 5.1.6 Simulation of Dislocation of the Scaphoid in the Palmar Direction ...... 46 5.1.7 Simulation of Hand Scoliosis ...... 46 5.1.8 Simulation of Reduction of Contact Between the Lunate and the Radius ...... 47 5.1.9 Simulation of Bone Erosion ...... 47 5.2 Finite Element Analysis: Pre-Processing Procedures ...... 48 5.3 Biomechanical Behaviours of the Rheumatic Wrist Joint ...... 50 5.3.1 Comparative Analysis ...... 50 5.3.2 The Biomechanical Effect of Symptoms and Pathophysiological Characteristics...... 52 References ...... 56

6 Finite Element Analysis of the Wrist Arthroplasty in Rheumatoid Arthritis...... 59 6.1 Total Wrist Arthroplasty...... 59 6.2 Finite Element Modelling of the Total Wrist Arthroplasty . . . . . 60 6.3 Finite Element Analysis: Pre-Processing Procedures ...... 60 6.4 Finite Element Analysis ...... 65 6.4.1 Mechanical Stress Distribution Within the Bones ...... 66 6.4.2 Mechanical Contact Pressure Within the Bones ...... 67 6.4.3 Biomechanical Analysis of Different Moduli of Bone Graft ...... 67 6.4.4 Biomechanical Assessment of the Total Wrist Arthroplasty Procedure ...... 67 References ...... 68

Summary ...... 71

Index ...... 73 Abbreviations

BRM Biologic response modiﬁer C Capitate CD Compact disc CT Computed tomography CTS Carpal tunnel syndrome DMARD Disease-modifying anti-rheumatic drug exp Exponential FE Finite element FEM Finite element method GPa Giga pascal H Hamate HC Hamitocapitate HTq Hamitotriquetral L Lunate LTq Lunotriquetral max. Maximum MC Metacarpal min Minute mm Millimeter MPa Mega pascal MR Magnetic resonance MRI Magnetic resonance imaging N Newton NMR Nuclear magnetic resonance No. Number NSAID Non-steroidal anti-inﬂammatory drug P Pisiform PRC Proximal row carpectomy RA Rheumatoid arthritis RBSM Rigid body spring method RC Radiocapitate

ix x Abbreviations

RT Radiotriquetrum S Scaphoid sec Second SL Scapholunate SLAC Scapholunate advanced collapse SLD Scapholunate dissociation STd Scaphotrapezoid STm Scaphotrapezium STq Scaphotriquetrum TCL Transverse carpal ligament TFCC Triangular ﬁbrocartilage complex THA Total hip arthroplasty TKA Total knee arthroplasty TNF Tumor necrosis factor TP Trapezium TWA Total wrist arthroplasty TZ Trapezoid Notations

Variable Explanation l Friction coefﬁcient E Young’s modulus m Poisson’s ratio x, y, z Cartesian coordinates % Percentage r Stress ° Degree k Stiffness

xi Chapter 1 The Wrist Joint

Abstract In this chapter, information on the wrist anatomy, kinematics and its mechanical behaviours is presented. It commences with a brief explanation on the complexity of the joint, which covers the structure of its hard and soft tissues. All the eight bones constructing the joint were categorized into several groups according to their respective positions. The associated tendons together with five main muscles were well identified in the literature, and thus sufficiently presented in this chapter. This complex joint with numerous articulations appears with many articular cartilages, thus the function are thoroughly explained in this chapter. Further details are presented in the following subsections, which cover description on the structure of each bone, the elements constructing the articular cartilage together with the associated pathology condition and the ligamentous structure. All of these components are essential to bring functions to the joint, allowing its mobility and sustainability. Information on the kinematics of the joint is presented in the last sub-section. This chapter provides sufficient information to assist understanding for the subsequent chapters.

Keywords Wrist joint Á Carpal bones Á Articular cartilage Á Ligamentous structure Á Kinematics

1.1 Anatomy of the Wrist Joint

The wrist joint complex consists of multiple articulations of the eight carpal bones with the distal radius, the structure within the ulnocarpal space, the metacarpals, and each other. The eight carpal bones are hamate, capitates, trapezoid, trapezium, triquetrum, pisiform, lunate and scaphoid, which together are also referred to as the carpus. The soft tissue structures surrounding the carpal bones include the tendons that cross the carpus or attach to it and the ligamentous structures that connect the carpal bones to each other and the bony elements of the hand and forearm [1].

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 1 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8_1, Ó Springer-Verlag Berlin Heidelberg 2013 2 1 The Wrist Joint

Fig. 1.1 Schematic drawings for palmar view of the wrist joint complex showing the eight carpal bones and their articulations with the distal radius, distal ulna, the metacarpal bones of the hand and each other. H hamate, C capitates, TZ trapezoid, TP trapezium, TQ triquetrum, P pisiform, L lunate, S scaphoid. The arrows indicate the line of the joints. a carpometacarpal; b midcarpal; c radiocarpal. The light brown surfaces indicate the articular cartilages [8, 9]

The carpus is divided into the proximal and distal row. The bones of the distal row from the radial to ulnar side are the trapezium, trapezoid, capitate and hamate. The distal carpal row forms a relatively immobile transverse unit that articulates with the metacarpals to form the carpometacarpal joint. All four bones in the distal row fit tightly against each other and are held together by stout interosseous ligaments [1, 2]. The more mobile proximal row consists of the scaphoid, lunate, and triquetrum. This row articulates with the distal radius to form the radiocarpal joint (scaphoid fossa of radius, 46 %; lunate fossa of radius, 43 %; ulnar soft tissue structures, 11 %). The scaphoid connects anatomically and functionally both rows, and articulates in part with the radius. The lunate articulates in part with the ulnar soft tissue structures. The eighth carpal bone, the pisiform is a sesamoid bone that mechanically enhances the wrist’s most powerful motor, the flexor carpi ulnaris, and forms its own small joint with the triquetrum. Between the proximal and distal rows of carpal bones is the midcarpal joint, and between adjacent bones of these rows are the intercarpal joints. The wrist consists of three main joints; distal radioulnar joint, the radiocarpal joint, and the midcarpal joint. The palmar surface of the carpus as a whole is concave, constituting the floor and walls of the carpal tunnel. The complete anatomy of the wrist joint is illustrated in Fig. 1.1. The radiocarpal joint, which is arguably the most critical articulation in the wrist joint [2–4] consists of 75 % of the articulation between proximal carpal bones and the distal radius, whereas the remaining 25 % is the ulnacarpal or in particular, triangular fibrocartilage complex (TFCC) together with two main facets: elliptical scaphoid facet and spherical lunate facet [5]. There is a 1.1 Anatomy of the Wrist Joint 3

Fig. 1.2 The radiocarpal joint from distal [2]. Illustrated are the two fossae for the scaphoid and lunate bone

fibrocartilage ridge separating these two facets, known as the interfacet promi- nence. Concavity with declination 10–15o palmarly and 15–25o ulnarly is also observed at the distal articular surface of the radius [6]. TFCC, which functions as a buffer between the triquetrum and the distal tip of the ulna during ulnar deviation, consists of many components. Fibrocartilaginous disc, dorsal radioulnar and palmar ligaments, ulnocarpal ligaments, and the tendon sheath of the extensor carpi ulnaris form the TFCC [7]. Figure 1.2 illustrates the radiocarpal joint. There are five main muscles associated with the motion of the wrist joint [8]. Radial deviation motion is performed by the extensor carpi radialis brevis, which is inserted onto the proximal end at the dorsal surface of the third metacarpal bone. Another tendon with the same function namely extensor carpi radialis longus is also inserted onto the proximal end at the dorsal surface of the second metacarpal bone. The last of the three muscles acting on the radial side, namely the flexor carpi radialis contributes to radial deviation and flexion of the wrist joint. The insertion is found at the palmar side of the base of the second metacarpal. The flexor and extensor carpi ulnaris muscles which are found at the ulnar side, flex and extend the wrist joint respectively. Both of them are acting together to perform ulnar deviation motion. There are three insertion points for the tendon of the flexor carpi ulnaris, where one of them is found at the pisiform. The remaining two are connected via ligaments onto the hamate and fifth metacarpal bone.

1.2 Bone Structure

Bones at the wrist joint have unique structure, and therefore names were given according to their shape or structure (Fig. 1.3). For instance, the name of the second largest carpal bone, the scaphoid is derived from the Greek ‘‘scaphe’’ which has the same meaning as ‘‘rowing boat’’ since it shaped like a boat [8]. 4 1 The Wrist Joint

Fig. 1.3 Exploded conﬁguration for palmar view of the wrist joint complex showing different bone structures of the eight carpal bones. H hamate, C capitates, TZ trapezoid, TP trapezium, TQ triquetrum, P pisiform, L lunate, S scaphoid [8, 9]

As aforementioned, there are eight carpal bones where each of their names was given according to their shape. Table 1.1 provides information on the structure for each bone of the wrist joint.

1.3 Cartilage Structure

Cartilage comprises of a dense network of collagen fibers embedded in a gel-like component of the ground substance namely chondroitin sulfate [11]. It lacks blood vessels, lymphatics and nerves [8]. There are three types of cartilages: hyaline cartilage, fibrocartilage and elastic cartilage. Articular cartilage which is composed from hyaline cartilage is mainly located at the ends of long bones. It promotes flexibility, support as well as smooth surfaces to assist movements of joints [11]. Four layers exist as shown in Fig. 1.4 with the topmost layer namely superficial zone which has the greatest importance. Since articular cartilage functions as a nearly frictionless bearing while uniformly transferring loads on underlying bone preventing high stress concentrations [12], this layer acts by supporting more than 90 % of the compressive loads. This corresponding surface also functions to resist shear forces generated by the joint movement. The fluid and collagen content in the cartilage differ, which subsequently lower in the intermediate, deep and cal- cified zones of articular cartilage. The collagen fibers determine its strength and its resilience, which is an ability to restore its original shape after deformation attributed to the presence of chondroitin sulfate. There were numerous reports on works related to pathological condition of the cartilage. One of them was a study on its poor capacity of repair and healing thus resulted in cartilage degeneration [13]. This study has demonstrated that the onset and progression of the disease was due to perturbation in underlying bone through acute injuries [14]. It was expected that local alterations in the subchondral bone 1.3 Cartilage Structure 5

Table 1.1 Description on the different structures of the eight carpal bones Bone Description Scophoid The scaphoid can be divided into three main regions: the proximal pole, the waist and the distal pole. Several characteristics of the scaphoid have been identiﬁed, which include a single convex distal surface for articulation with the trapezium and trapezoid, a large concave distal capitate surface, a ﬂat semilunar lunate surface medially and a large convex radial articular area extending dorsally [8]

The next bone wedged between the scaphoid and triquetrum with its crescent shape is the lunate. This bone articulates laterally with the Lunate scaphoid via its ﬂat semilunar facet. The medial part, on the other hand articulates with the triquetrum through its square surface. The radius, on its proximal region is articulated via convex facet. Distally, its convex surface articulates with the capitate Triquetrum The most medial bone of the proximal row carpal bone is the triquetrum. This small and irregularly shaped bone has distal concavo-convex surface which articulates with the hamate. At the anterior side of the bone, its oval convex palmar facet articulates with the pisiform whilst radially, the lunate is articulated with a square surface of the triquetrum

The sesamoid bone of the tendon of the ﬂexor carpi ulnaris, which is the pisiform has a single ﬂat oval articular facet. This facet allows Pisiform articulation with the triquetrum on its dorsal surface [10]

Hamate The wedge shape bone, hamate has articular surfaces for the capitate and triquetrum on either sides. For articulation with the ﬁfth and fourth metacarpals, there is a ridge at the distal articular surface, functions as a divider between medial and lateral facets. A hook on its palmar side, also known as hamulus, functions as an attachment point for certain ligaments. This criterion gives the hamate its distinct shape [8]

Capitate The largest carpus namely the capitate which lies in the center of the wrist has a convex surface of its proximal part which is articulated with the lunate. Meanwhile, its lateral surface articulates with the trapezoid and scaphoid, and medial surface with the hamate. A concave distal strip on its lateral part is for articulation with the second metacarpal base whilst the third metacarpal base was articulated via a concavo-convex distal facet. The name of capitate is derived from the Latin word ‘capitãtus’ which means ‘containing head’ due to a rounded head-shaped on its surface

(continued) 6 1 The Wrist Joint

Table 1.1 (continued) Bone Description Trapezoid A relatively smaller bone namely the trapezoid, on the other hand is articulated medially with the trapezium via a flat facet surface. On its proximal side, the scaphoid is articulated through a slightly concave surface whilst on its medial side, the capitate is articulated via a flat facet surface. Distally, the second metacarpal is articulated via a convex triangular surface [8] Trapezium The trapezium is located between the first metacarpal distally and the scaphoid proximally. For the articulation with the first metacarpal, it has a saddle shaped distal articular surface

Fig. 1.4 The articular cartilage which consists of four existing layers: superﬁcial, intermediate, deep and calciﬁed [19]

plate stiffness do affect stresses and deformations in the adjacent articular cartilages. Overgrowth of the subchondral plate, known as bone boss [15], as well as softening following either bone bruises [16] or degeneration [17] were commonly detected in the wrist joint especially following subchondral hematomas in distal radius fractures [18]. 1.4 Ligament Structure 7

Fig. 1.5 View of the wrist joint with the major ligaments. The ligamentous structure can be divided into two groups; deep ligaments (a palmar view, b dorsal view) and superﬁcial ligaments (c palmar view, d dorsal view). SL scapholunate ligament, LTq lunotriquetral ligament, HC hamitocapitate ligament, STd scaphotrapezoid ligament, STm scaphotrapezium ligament, HTq hamitotriquetral ligament, RC radiocapitate ligament, STq scaphotriquetrum ligament, RT radiotriquetrum ligament. Image taken and adapted from interactive Hand CD (Primal Pictures) [8]

1.4 Ligament Structure

The stability of the wrist does not only rely on the multi-articulation geometry and muscle support through tendinous structure, but also vitally resolute by the reliability of the ligamentous structure (Fig. 1.5). It functions as a constraint (mainly as tensile resistance) and a stabilizer during motion and loading of the wrist joint [11]. Previous studies have addressed several aspects throughout the complexity of 8 1 The Wrist Joint the ligaments structure including the histology, shape and the composition. The general nomenclature was also identified; where the names of the ligaments were given based on the bones they connect, from proximal-to-distal and radial-to-ulnar paths. Potential biomechanical functions have also been considered to summarise the ligaments of the wrist [5, 20]. Significantly, previous studies have showed variability in sizes and structures of the ligaments in the wrist joint. In a study by Nowalk et al. [21] revealed that the cross-sectional area of 12 investigated radiocapitate ligaments was 8 mm2 (standard deviation of 1.3 mm2) and the length was 10 mm (standard deviation of 1 mm). In a study on 90 cadaveric wrists, it was demonstrated that the ligaments seem to have large range of size [22]. For instance, the dorsal radiocarpal ligaments range in width at the proximal end between 5.5 and 17.8 mm and in length between 13.8 and 29.4 mm. They also addressed three distinct shape categories for the dorsal intercarpal ligament and four distinct shape categories for the dorsal radiocarpal ligament [22]. Thus, these findings induced a noteworthy conclusion, where there should be no standardisation to define the kinematics of the wrist joint due to huge existing variability found in the ligamentous structure.

1.5 Kinematics

In comparison with other common joints like the knee and the hip, the wrist is an extremely mobile organ. Two main factors lead to its great mobility; multi-planar geometry of the articulation surfaces and complex ligamentous interactions [5]. The principle of ‘‘variable geometry’’ is naturally implemented which enable the great range of motion of the wrist joint. This concept caused the multi-directional relative motion between individual carpal bones. Kinematic behaviour of both static and dynamic postures through planar (in both sagittal and coronal planes) and non-planar motions has been thoroughly examined in previous reports. As far as the kinematics of the wrist joint was concerned, it was vital to identify of the center of rotation for the primary axes of flexion–extension or radial–ulnar deviation. There were studies attempted to tackle this issue, however, to date, none of them have successfully established the exact location, thus came with several assumptions. The head of the capitate was assumed to be the center of rotation, the axis connecting the styloid process of the radial and ulnar was assumed as the axis of flexion–extension whereas for the radial–ulnar deviation, the axis was assumed to be oriented orthogonal to the flexion–extension axis [23–28]. Out of these complete ranges, its lesser functional range of motions has also been suggested to range from 40o extension to 40o flexion in the sagittal plane, and the arc of motion for radioulnar deviation in the coronal plane of 40o [7]. There were studies performed on the nature and direction of the carpal bones. One of the findings was that a single functional model of the wrist was not likely to be determined [29, 30]. There were also no significant differences found in a gender-based analysis performed in a study by Wolfe et al. [31]. This finding was 1.5 Kinematics 9

Fig. 1.6 Images of three-dimensional reconstructed wrist motions in radial deviation (a), neutral (c and i), ulnar deviation (e), extension (g) and flexion (k)[35] further supported by several kinematic studies investigating similar wrist kinematics [32, 33]. Motion of the wrist joint can be divided into three groups: flexion–extension, radial–ulnar deviation and forearm pronation–supination. A combination of these motions, namely circumduction, were found to have reduction of 17 % for flexion–extension and of 11 % for radial–ulnar deviation than for planar motion [33]. The wrist motions were found to have unique ranges. For flexion and extension, the normal range was 65–80o of flexion and 55–75o of extension [28]. A study on 40 subjects (20 for each gender; age ranged from 20 to 60 years) has revealed an average maximum ranges of wrist motion of 59o extension to 79o flexion (138o arc of motion). Generally, due to slight palmar tilt of the distal radius surface, the flexion normally exceeds extension by an average of 10o. An approximation has been made in conjunction with the contribution of proximal and distal carpal rows to the total arc of flexion and extension [28]. During flexion, 40 % occurs at the radiocarpal joint while the remaining 60 % occurs at the midcarpal joint. The same percentage occurred during extension, however the locations of occurrences were switched: 40 % at the midcarpal and 60 % at the radiocarpal joint. Previous studies have determined that movement between the capitate and third metacarpal was small, thus it has been suggested that these two bones in relative with the radius to be the axis in determining movements of the wrist joint [32, 34]. Motions at the coronal plane involved out of plane movements. During radial deviation, the scaphoid flexed with rotation of its distal pole towards palmar due to the intruded styloid process of the distal radius. All the proximal carpal bones are 10 1 The Wrist Joint

Fig. 1.7 The double-V system conﬁguration during neutral (a), radial (b) and ulnar deviation (c) by the ulnolunate and radiolunate ligaments and the palmar intercarpal ligament [28, 36] connected via ligaments, therefore the translation of the scaphoid also affecting the other bones of the same row, which in this case resulted in ﬂexed proximal row of carpal bones. During ulnar deviation, these carpal bones will reverse towards extension. The triquetrum found to be displaced palmarly due to the proximal 1.5 Kinematics 11

Table 1.2 Wrist range of Wrist motion Range of motion motion Flexion–extension [28] Flexion: 65–80o Extension: 55–75o Radial–ulnar deviation [26, 27] Radial deviation: 15–25o Ulnar deviation: 30–45o Forearm Pronation: 60–80o pronation–supination [28] Supination: 60–85o migration of the hamate. This motion leads to the extension of the lunate. Fig- ure 1.6 illustrates the images of reconstructed wrist motions during an in vivo study. Largely, the three motions were dictated by a double-V system, where the proximal V consisted of the radiolunate (lateral arm of the proximal) and the ulnolunate (medial arm of the proximal) ligaments. The mechanisms for each motion are as depicted in Fig. 1.7 [28]. Forearm pronation and supination motions were mainly occurred at the elbow joint, despite small motions also observed at the wrist joint. Average values for range of motion have been identiﬁed, where a range of 60–80o found during pronation and 60–85o during supination (150o arc of motion). The axis for these motions lies obliquely passing through the center of the humeral capitulum and the midpoint of the head of ulna [27, 28] (Table 1.2).

References

1. Netter FH (2003) Atlas of human anatomy, 3rd edn. Icon Learning Systems, Teterboro 2. Gislason MK, Nash DH, Nicol A, Kanellopoulos A, Bransby-Zachary M, Hems T, Condon B, Stansfield B (2009) A three-dimensional finite element model of maximal grip loading in the human wrist. Proc Inst Mech Eng 223(7):849–861 3. Ulrich D, van Rietbergen B, Laib A, Rüegsegger P (1999) Load transfer analysis of the distal radius from in vivo high-resolution CT-imaging. J Biomech 32(8):821–828 4. Polikeit A, Nolte LP, Ferguson SJSJ (2004) Simulated influence of osteoporosis and disc degeneration on the load transfer in a lumbar functional spinal unit. J Biomech 37(7):1061–1069 5. Schmitt R (2006) Funktionelle Anatomie und Biomechanik des Karpus. Der Radiologe 46(8):638–648 6. Berger RA (1996) The anatomy and basic biomechanics of the wrist joint. J Hand Ther 9(2):84–93 7. An K, Berger RA (1991) Biomechanics of the wrist joint. Springer, New York 8. McGrouther DA. HP interactive hand-anatomy CD, Primal Pictures, v.1.0 9. Margareta Nordin VHF (2001) Basic biomechanics of the musculoskeletal system, 3rd edn edn. Lippincott Williams and Wilkins, Philadelphia 10. Berger RA (2001) The anatomy of the ligaments of the wrist and distal radioulnar joints. Clin Orthop Relat Res 383:32–40 11. Gerard J, Tortora BD (2009) Principles of anatomy and physiology, 12th edn. Wiley, USA 12. James CB, Uhl TL (2001) A review of articular cartilage pathology and the use of glucosamine sulfate. J Athl Train 36(4):413–419 12 1 The Wrist Joint

13. Buckwalter JA, Mankin HJ (1998) Articular cartilage: degeneration and osteoarthritis, repair, regeneration, and transplantation. Instr Course Lect 47:487–504 14. Radin EL, Rose RM (1986) Role of subchondral bone in the initiation and progression of cartilage damage. Clin Orthop Relat Res 213:34–40 15. Henderson IJP, La Valette DP (2005) Subchondral bone overgrowth in the presence of full- thickness cartilage defects in the knee. Knee 12(6):435–440 16. Meyer EG, Baumer TG, Slade JM, Smith WE, Haut RC (2008) Tibiofemoral contact pressures and osteochondral microtrauma during anterior cruciate ligament rupture due to excessive compressive loading and internal torque of the human knee. Am J Sports Med 36(10):1966–1977 17. Boyd SK, Müller R, Zernicke RF (2002) Mechanical and architectural bone adaptation in early stage experimental osteoarthritis. J Bone Miner Res 17(4):687–694 18. Lindau T, Adlercreutz C, Aspenberg P (2003) Cartilage injuries in distal radial fractures. Acta Orthop Scand 74(3):327–331 19. Heinegard D, Saxne T (2011) The role of the cartilage matrix in osteoarthritis. Nat Rev Rheumatol 7(1):50–56 20. Berger RA (1997) The ligaments of the wrist. A current overview of anatomy with considerations of their potential functions. Hand Clin 13(1):63–82 21. Nowalk MD, Logan SE (1991) Distinguishing biomechanical properties of intrinsic and extrinsic human wrist ligaments. J Biomech Eng 113(1):85–93 22. Viegas SF, Yamaguchi S, Boyd NL, Patterson RM (1999) The dorsal ligaments of the wrist: anatomy, mechanical properties, and function. J Hand Surg 24(3):456–468 23. Brumbaugh RB, Crowninshield RD, Blair WF, Andrews JG (1982) An in vivo study of normal wrist kinematics. J Biomech Eng 104(3):176–181 24. Landsmeer JM (1961) Studies in the anatomy of articulation. I. The equilibrium of the ‘‘intercalated’’ bone. Acta Morphologica Neerlando-Scandinavica 3:287–303 25. Macconaill MA (1941) The mechanical anatomy of the carpus and its bearings on some surgical problems. J Anat 75(Pt 2):166–175 26. Volz RG, Lieb M, Benjamin J (1980) Biomechanics of the wrist. Clin Orthop Relat Res 149:112–117 27. Youm Y, McMurthy RY, Flatt AE, Gillespie TE (1978) Kinematics of the wrist. I. An experimental study of radial-ulnar deviation and flexion-extension. J Bone Joint Surg 60(4):423–431 28. Nordin Margareta, Frankel VH (2001) Basic biomechanics of the musculoskeletal system, 3rd edn. Lippincott Williams & Wikins, Pennsylvania 29. Feipel V, Rooze M (1999) Three-dimensional motion patterns of the carpal bones: an in vivo study using three-dimensional computed tomography and clinical applications. Surg Radiol Anat 21(2):125–131 30. Moojen TM, Snel JG, Ritt MJPF, Venema HW, Kauer JMG, Bos KE (2003) In vivo analysis of carpal kinematics and comparative review of the literature. J Hand Surg 28(1):81–87 31. Wolfe SW, Neu C, Crisco JJ (2000) In vivo scaphoid, lunate, and capitate kinematics in flexion and in extension. J Hand Surg 25(5):860–869 32. Neu CP, Crisco JJ, Wolfe SW (2001) In vivo kinematic behavior of the radio-capitate joint during wrist flexion-extension and radio-ulnar deviation. J Biomech 34(11):1429–1438 33. Salvia P, Woestyn L, David JH, Feipel V, Van S, Jan S, Klein P, Rooze M (2000) Analysis of helical axes, pivot and envelope in active wrist circumduction. Clin Biomech 15(2):103–111 34. Patterson RM, Nicodemus CL, Viegas SF, Elder KW, Rosenblatt J (1998) High-speed, three- dimensional kinematic analysis of the normal wrist. J Hand Surg 23(3):446–453 35. Moojen TM, Snel JG, Ritt MJPF, Venema HW, den Heeten GJ, Bos KE (2001) Pisiform kinematics in vivo. J Hand Surg 26(5):901–907 36. Taleisnik J (1984) Classification of carpal instability. Bulletin Hosp Joint Dis Orthop Inst 44(2):511–531 Chapter 2 Biomechanical Properties and Behaviours of the Wrist Joint

Abstract Previous experimental and computational studies have outlined several properties and behaviours of the wrist joint. This chapter compiled relevance inputs associated with the biomechanical considerations of the joint, consisting of contact analyses at the articulations and load transmission throughout the joint. The succeeding sections present information on the biomechanical properties of the cartilages and ligamentous structure. It was addressed that due to difficulties in accessing the articulations in the wrist joint, investigations on the articular cartilages were mainly done through computer simulations. For the ligaments, a typical stress strain curve was used to mimic its mechanical behaviour. The principal load behaviour of ligaments with respect to their elongation during constant elongation- rate has evident the existence of the toe-regions, thus addressing its viscoelastic behaviour. Information on current methods in biomechanical modelling—rigid body spring and finite element—is also presented. Greater emphasize was given to the finite element method due to its appropriateness in performing contact analysis in the wrist joint. Facts and findings from previous finite element studies were included to support future understanding.

Keywords Load transfer Contact surface Viscoelastic Stress–strain curve Rigid body spring Finite element

2.1 Contact Surfaces and Load Transmission

The application of pressure sensitive ﬁlms to investigate the articulating surface loads transmission of the wrist joint has proved to be possible based on several previous experimental works. However, not all of the articulations could be inserted by ﬁlms attributed to relatively smaller gaps compared with the thickness

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 13 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8_2, Ó Springer-Verlag Berlin Heidelberg 2013 14 2 Biomechanical Properties and Behaviours of the ﬁlm and the difﬁculties in accessing those articulations. As an alternative, pressure transducer was used by Short et al. [1] to analyse pressures in the ulnocarpal and radiocarpal joints. Despite easier accessibility, considerably high percentage of error, 11 % was found. It was also revealed that the compressive forces to the radius were mainly transferred through the scaphoid and lunate. Another cadaveric study has reported that the radius was the greatest load bearer, which was subjected with 82 % of loads at the neutral position and 63–87 % of loads during radial-ulnar deviation and pronosupination, respectively [2]. In conjunction with the load transfer to the radius in the neutral position, 60 % of the load was transferred via the scaphoid [3]. Additionally, the radioscaphoid articulation was also found to have wider contact area, contributes approximately 50 % larger as compared to the radiolunate articulation [4]. There was also a study performed to investigate load transfer at the midcarpal and radiocarpal joints [3]. It was found that the stress at the midcarpal joint was well-distributed, 20 % through the hamotriquetral articulation, 29 % through the capitolunate articulation, 28 % through the scaphocapitate articulation and the remaining 23 % through the scaphotrapeziumtrapezoid articulation. It was also found that 20–40 % of the available articulations were occupied during physiological loading condition [3].

2.2 Biomechanical Consideration of the Cartilage Structure

Despite extensive experimental studies on the interactions between cartilage and its underlying support [5], the relative importance of subchondral injuries and their likely effects on load transfer of both articular cartilage and bone remains not well quantified. Due to difficulties in controlled experimental studies of such injuries in the subchondral region and their detection by joint images, computational simulation has been recognized as a feasible tool to simulate perturbed conditions and to determine their effects on the mechanical environments of the joint. The success of such attempts, however, depends on the accuracy of the computational model used. In earlier computational investigations of articular cartilage, biphasic fibril- reinforced composite models were introduced [6] and validated. It consists of non- fibrillar solid matrix and collagen fibrils, and their properties and mechanical functionality have also been simulated [7, 8]. Such composite models have extensively employed in recent knee model studies [9, 10]. Alternatively, collagen fibrils have been implicitly taken into consideration in constitutive models of the solid matrix [11]. 2.3 Biomechanical Consideration of the Ligamentous Structure 15

Fig. 2.1 The principal load behaviour of ligaments with respect to their elongation during constant elongation- rate [13–15]

2.3 Biomechanical Consideration of the Ligamentous Structure

Besides of the anatomical structure of the ligaments, several studies were also performed to investigate its mechanical properties [13–15]. Viscoelastic stress relaxation, nonlinear stress–strain behaviour, hysteresis and rate dependent stress– strain behaviours were successfully found under constant or cyclic loadings [12]. Based on the typical stress–strain (force–elongation) curves during constant elongation rate obtained from various carpal ligaments, three main subsequent phases were found. It starts with a ‘‘toe region’’, followed by a quasi-linear region, and ended up with a failure region (Fig. 2.1). Characterization of the curves has been made based on ligament stiffness in both the quasi-linear region and ultimate strengths. There was also a report on the dependencies of these characterizing values on elongation rate which also consisted of the load relaxation behaviour over the course of time (Fig. 2.2)[14]. It was shown that after preconditioning at low loads, the specimens were elongated to 50 N at 50 mm/min. The specimens were held at a speciﬁc elongation, and the relaxation behaviour of the ligaments over a period of 100 s was obtained. After that, the specimens were elongated at 100 mm/min until failure. An issue was arisen as the presented results were problematic due to various measurement techniques applied. For instance, a study performed on the scapholunate ligament to investigate the slope of the quasi-linear region (related to ligament stiffness) used elongation rate of 50 mm/min [14], whereas an elongation rate of 100 mm/min was applied purposely in another study to determine the slope of various ligaments [16]. As the previous two studies were independent, another biomechanical study made the elongation rate to be dependent on the ligament length resulted in a rate ranging from 5 to 25 mm/s [17]. 16 2 Biomechanical Properties and Behaviours

Fig. 2.2 The mechanical sequence for the scapholunate ligament [14]

Investigation on the effect of preconditioning routine has also been performed in previous studies. It was found that the preconditioning routine by stretching the ligaments enables averaging approach to the measurements [17–19]. This finding was proven to be logical as in the first ten load cycles, the restraint force of ligament for a given strain will decrease continually [19]. There was also a study with no preconditioning performed, which resulted in high variability of the results obtained [20]. Repeatable comparable data was one of the aims of these experi- ments. Out of these experimental studies, it was addressed that many difficulties faced due to the complexity of the carpal ligaments (the dimensions and shapes as well as the structures of the bones and articulations), and also the results obtained were incomparable with findings from knee ligaments experimental works [17–19]. Stiffness as one of the critical parameters has been addressed and its elastic modulus was found possible to be calculated once the physical dimensions of the ligaments were obtained. The stiffness of the extrinsic carpal ligaments has been discovered in previous works. It was found that the magnitude for the corresponding ligaments range from 10.9 to 46.4 N/mm [17]. It was also discovered that in neutral posture of the wrist, some of the ligaments were actually in tension [19]. Despite of the complex structure of the intrinsic ligaments which has thus far received little attention, their mechanical properties as found in several studies were profound and sufficient to be utilised in future studies. The stiffness of these intrinsic ligaments which range from 40 to 350 N/mm was obviously higher as compared to the extrinsic carpal ligaments. This difference was therefore showed that the mechanical properties of ligaments were highly dependent on its physiological location. Overall, previous studies have progressively investigated the behaviour and properties of the ligaments associated with the wrist joint. A wide range of variability was reported, not only among different studies, but also among specimens within a given study comparing the same ligament. Despite these inconsistencies, the reported works significantly provide constructive fundamentals for specifying ligament behaviours, assisting better understanding on the static and kinematics of the wrist joint. 2.4 Current Trends in Biomechanical Modelling 17

2.4 Current Trends in Biomechanical Modelling

Previous works had shown progress of modelling techniques, started with as simple as two-dimensional modelling with only a few bones involved, then progressively become more complicated and highly efﬁcient attributed to the existing of high-end computational technology. However, due to the complexity of the wrist joint as compared to other joints, reported studies on the wrist modelling were still focused at the very early stage of its model development.

2.4.1 Rigid Body Spring Method

The patterns of load distributions, the kinematics, the effect of constraints as well as unique cases related to pathological conditions were aspects analysed in the previous studies [21–24]. Several approaches have been introduced to tackle aforementioned matters. In comparison with other available methods, rigid body spring method (RBSM) was commonly used to analyse multiple body contact forces as well as to perform kinematics analysis. This technique applied rigid body elements representing the bones, whereas the cartilages and ligaments were modelled using spring elements [24]. This method has also been utilised to investigate load transfer. In accordance to a two-dimensional study on 120 normal wrists, percentage of load transfer at the radiocarpal and ulnacarpal joints has been successfully unfolded [24]. 55 % of loads were transferred through radioscaphoid articulation, 35 % through radiolunate articulation whereas the remaining 10 % through the ulnacarpal articulation. Total load of 10 N simulating grasp action was applied at the five metacarpals. The cartilage with a stiffness of 15 MPa was simulated via compressive springs with stiffness of 200 N/mm each whereas tensile spring elements were used to model 28 ligaments. This study suggested that improvements should be taken into consideration in future studies especially regarding contact area between bones. A more recent study implemented three-dimensional RBSM wrist modelling sufficiently simulating the wrist joint kinematics and the findings were validated experimentally [25].

2.4.2 Finite Element Method

The finite element (FE) method is a computational numerical analysis technique, which is combined with computational modelling to obtain stress and strain patterns in modelled bodies, and has been widely used as solutions to engineering problems [26]. Variety of shapes and models can be analysed using FE method, either from as simple as a sphere, up to more complex and complicated design, such as an aeroplane. It can be defined as a tool used to predict behaviour of a 18 2 Biomechanical Properties and Behaviours complex problem, in which the structures are divided into smaller pieces so that complex mathematics formula can be occupied to calculate and simulate the required problems [27]. In other words, it uses a complex system of points called nodes which make a grid known as mesh. The mesh elements are connected to their adjacent nodes to react upon conditions assigned, including the material properties, the contact modelling as well as the boundary condition representing the real condition of that particular problem. This section has information on some aspects in FE analysis used to study the behaviours of the wrist, which covers types of mesh element and von Mises stress criterion. Information on findings and procedures used in previous studies on FE analyses were sufficiently provided in the following sections.

2.4.2.1 Mesh Element Types

There are two main types of element that have been widely used: tetrahedral and hexahedral. Tetrahedral with tetrahedron shape of elements can be either first order (with 4 nodes) or second order (with 10 nodes), and is preferable to model cur- vatures. Hexahedral, on the other hand, found to have better accuracy due to its nature of having relatively more degrees of freedom [28]. This brick shaped of element could also be categorized into first order (with 8 nodes) and second order (with 16 nodes) [29]. Despite of having greater accuracy, this type of element found to have less efficiency in performing contact analysis due to high number of nodes resulted in more tendency to distort. Therefore, tetrahedral was the better option for contact analysis.

2.4.2.2 Von Mises Yield Criterion

To analyse ductile material, it was often suggested to use von Mises stress which was formulated from a theory named the von Mises stress yield criterion [27]. This theory used to describe plasticity, and has been widely employed in material science and engineering field. Usually, prediction on yielding of material under any loading conditions was made based on this theory. The von Mises stress is calculated by combining stresses in the dimensions (x-, y- and z-directions) at any point on a structure, see Eq. (2.1). It was useful not only to determine the level of plastic deformity, but also to investigate the fatigue strength. Based on the theory, the material said to yield when the von Mises stress reaches the yield strength. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 2 2 rvm ¼ pffiffiffi ðÞr1 r2 þðÞr2 r3 þðÞr3 r1 ð2:1Þ 2 2.4 Current Trends in Biomechanical Modelling 19

2.4.2.3 Past Finite Element Studies

The FE method has been widely used to study various human joints such as the hip and knee [30–39], and has been accepted by medical researchers as one of the important assistive tools in surgical planning [31, 32, 40–44]. Previous studies have shown its superior in varieties of analyses: pathomechanics, load transfer behaviour, contact analysis and also in investigation to assess viability of joints replacements including arthroplasty and arthrodesis. Although this method has been used for simulation of various human joints, the number of literatures related to the wrist was fairly limited with mostly reported on the model development [25, 44–48]. In the hip joint, only two bones were involved compared with 15 bones in the wrist joint, thus resulted in much more complicated analyses need to be done. Contact analysis of this multi-articulation joint proves to be especially tricky. In addition, the huge number of ligaments associated with the wrist joint make the analyses become much more challenging. For instance, wrong properties and locations of insertions resulted in unphysiological alterations of kinematics and dynamic of the joint. Additionally, solution convergence has been addressed as another main concern in finite element analysis of the wrist joint concerning the stability of the constructed FE models. Accurate and precise bone geometrical shape, articulations and the ligamentous structure are vital assuring successful analysis [46]. Therefore, of these few studies, there were lot of assumptions and simplifica- tions made. For instance, the computational investigation of the wrist was started with two-dimensional FE analysis [49]. This study was performed to undertstand the behaviour of the Kienbock’s disease treated using ceramic lunate replacement method. In this study, the complexity of the joint was simplified by grouping bones into proximal, distal and forearm and excluding ligamentous constraint. It was quantified that contact analysis for the actual wrist joint could not be performed due to limited articulations. A more recent study on three-dimensional finite element analyses have been carried investigating static carpal load transfer [50]. This study sufficiently includes the whole wrist joint, consisted of separated 8 carpal bones, the radius and ulna which emphasised more at the radiocarpal joint. Non- physiological constraints were applied to achieve solution convergence. Similarly, studies by Cheng et al. [51] and Troy et al. [52] which partially analysed the behaviour of the wrist joint by having investigation on the distal radius fracture. To the best of the authors knowledge, there were none of previous studies successfully investigated the behaviour of the whole complete structure of the wrist joint without performing non-physiological constraint as well as wide range of parametric studies. Regarding three-dimensional finite element studies on the pathological condition of the wrist, only a few numbers of works were found. There was a study performed to analyse the biomechanical effects of different position of Kirschner wires to provide initial stability of scaphoid fractures [48]. This study modelled the scaphoid whereas the adjacent bones were represented via articular cartilages with the thickness of 1 mm, assumed to be constant for each articulation. Another study 20 2 Biomechanical Properties and Behaviours on the biomechanical effect of the transverse carpal ligaments (TCL) release for surgically treated carpal tunnel syndrome (CTS) has been performed considering a complete model of the wrist joint. The TCL was constructed as a bundle of elements (not as springs which other studies used). It was found that due to the TCL release, the carpal bones at the radius side (the trapezium, trapezoid and scaphoid) displaced more towards radius during loading. This abnormal translation was doubt to be one of the implications of the postoperative surgery of the TCL release. Of these few studies on the diseased wrist joint, there was none made on the wrist joint affected by RA.

2.4.2.4 Ligaments Modelling

Tension-only spring elements were mainly used in the previous studies to simulate ligament. Despite the nature of the ligaments with nonlinear viscoelastic properties, due to simplification as well as limited resources, the issue on the linearity of the ligaments varied among previous studies. Linear properties of cables were used in a study by Ezquerro et al. [48] where different positions of Kirschner wires for scaphoid fracture fixation were analysed. However, most of them were used non-linear properties of springs to simulate the ligaments [25, 44, 46, 47]. The load-deflection behaviour discussed in Sect. 2.3 was used, governed by the superposition of a linear and exponential function: e f ðÞ¼e k l ðÞþe 0:03 0:03 k l exp ð2:2Þ o o 0:03 l lo e ¼ ð2:3Þ lo with k is the linear ligament stiffness, l is the momentary spring element length defined by the distance between the two element connections, and lo being the specified initial length of each ligament. Each spring element starts to exert nonlinear tensile force after crossing the specified initial ligament length lo. The initial length represents a variable model parameter. Regarding number of ligaments, previous study has shown that not all ligaments could be modelled. Since springs element were used, it was not possible to model the wrapping of ligaments. For instance, a study by Carrigan et al. [47] modelled 29 ligaments out of 64 ligaments available. Similarly, in a more recent study by Fischli et al. [25], a bit more ligaments of 32 were developed. In addition, number of springs used to model each ligament was also varied. There was a study where only one spring was used to simulate one ligament for their kinematics study [25]. Another study performed to analyse the carpal load transmission used two springs [47] and the others used multiple springs in parallel [44, 46]. 2.4 Current Trends in Biomechanical Modelling 21

2.4.2.5 Cartilage Modelling

The cartilage impacts the kinematics of the wrist joint due to its functions in intermediating load transfer between bones. Several ways were found in previous study in order to model the cartilage. Biphasic, transversely isotropic material properties was one of the methods used [53]. It is however was less utilised as compared to the less complex [57] linear elastic material properties [22, 24, 37, 54–56]. Additionally, there were more modelling methods that have been investigated; rigid body spring method, finite element method, Hertzian theory and an elastic solution [57]. They found that the finite element method had the advan- tages, which enable micromotion and stress distribution study to be performed within the contacted bodies, including the cartilage layer. Regarding elastic solution, hyperelastic material model has been chosen in previous studies to represent the cartilage [58–60]. Models can be classified as: Neo-Hookean model [27]

W ¼ C10ðÞI1 3 ð2:4Þ Mooney-Rivlin model [27]

W ¼ C10ðÞI1 3 +C01ðÞI2 3 ð2:5Þ Polynomial form [27]

XN i j W ¼ CijðÞI1 3 ðÞI2 3 ð2:6Þ i¼0;j¼0

Yeoh model [27]

XN i W ¼ Ci0ðÞI1 3 ð2:7Þ i¼0 Ogden model [27]

Xn l ÀÁ W ¼ i kai þ kai þ kai 3 ð2:8Þ a 1 2 3 i¼1 i where Cij, and li, are material stiffness constants corresponding to Young’s modulus in linear material. Above models except from the Ogden are based on the principle invariants and the strain energy function is depend on ﬁrst and second principle invariants, i.e. W = W(I1,I2) due to incompressibility. The Ogden model is directly based on principle stretch ratios, k. 22 2 Biomechanical Properties and Behaviours

References

1. Short WH, Werner FW, Fortino MD, Mann KA (1997) Analysis of the kinematics of the scaphoid and lunate in the intact wrist joint. Hand Clin 13(1):93–108 2. Werner FW (1995) Principles of musculoskeletal biomechanics-wrist. In: Peimer CA (ed) Surgery of the hand and upper extremity. McGraw-Hill, Toronto, pp 31–42 3. Viegas SF, Patterson RM (1997) Load mechanics of the wrist. Hand Clin 13(1):109–128 4. Patterson RVS (1995) Biomechanics of the wrist. J Hand Ther 8(2):97–105 5. Karsdal MA, Leeming DJ, Dam EB, Henriksen K, Alexandersen P, Pastoureau P, Altman RD, Christiansen C (2008) Should subchondral bone turnover be targeted when treating osteoarthritis? Osteoarthr Cartil 16(6):638–646 6. Goldsmith AAJ, Hayes A, Clift SE (1996) Application of finite elements to the stress analysis of articular cartilage. Med Eng Phys 18(2):89–98 7. Shirazi R, Shirazi-Adl A (2005) Analysis of articular cartilage as a composite using nonlinear membrane elements for collagen fibrils. Med Eng Phys 27(10):827–835 8. Li LP, Soulhat J, Buschmann MD, Shirazi-Adl A (1999) Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model. Clin Biomech 14(9):673–682 9. Julkunen P, Wilson W, Jurvelin JS, Rieppo J, Qu C-J, Lammi MJ, Korhonen RK (2008) Stress-relaxation of human patellar articular cartilage in unconfined compression: prediction of mechanical response by tissue composition and structure. J Biomech 41(9):1978–1986 10. Wilson W, van Donkelaar CC, van Rietbergen B, Ito K, Huiskes R (2004) Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J Biomech 37(3):357–366 11. Soltz MA, Ateshian GA (2000) A Conewise Linear Elasticity mixture model for the analysis of tension-compression nonlinearity in articular cartilage. J Biomech Eng 122(6):576–586 12. Hingorani RV, Provenzano PP, Lakes RS, Escarcega A, Vanderby R (2004) Nonlinear viscoelasticity in rabbit medial collateral ligament. Ann Biomed Eng 32(2):306–312 13. An K, Berger RA (1991) Biomechanics of the wrist joint. Springer, New York 14. Johnston JD, Small CF, Bouxsein ML, Pichora DR (2004) Mechanical properties of the scapholunate ligament correlate with bone mineral density measurements of the hand. J Orthop Res 22(4):867–871 15. Viegas SF, Patterson RM, Hokanson JA, Davis J (1993) Wrist anatomy: incidence, distribution, and correlation of anatomic variations, tears, and arthrosis. J Hand Surg 18(3):463–475 16. Nowalk MD, Logan SE (1991) Distinguishing biomechanical properties of intrinsic and extrinsic human wrist ligaments. J Biomech Eng 113(1):85–93 17. Savelberg HH, Kooloos JG, Huiskes R, Kauer JM (1992) Stiffness of the ligaments of the human wrist joint. J Biomech 25:369–376 18. Bettinger PC, Smutz WP, Linscheid RL, Cooney WP, An K-N (2000) Material properties of the trapezial and trapeziometacarpal ligaments. J Hand Surg 25(6):1085–1095 19. Savelberg HH, Kooloos JG, Huiskes R, Kauer JM (1993) An indirect method to assess wrist ligament forces with particular regard to the effect of preconditioning. J Biomech 26(11):1347–1351 20. Savelberg HH, Kooloos JG, Huiskes R, Kauer JM (1992) Strains and forces in selected carpal ligaments during in vitro flexion and deviation movements of the hand. J Orthop Res 10(6):901–910 21. Genda E, Horii E (2000) Theoretical stress analysis in wrist joint—neutral position and functional position. J Hand Surg (British Eur Vol) 25:292–295 22. Iwasaki N, Genda E, Barrance PJ, Minami A, Kaneda K, Chao EYS (1998) Biomechanical analysis of limited intercarpal fusion for the treatment of Kienböck’s disease: a three- dimensional theoretical study. J Orthop Res 16(2):256–263 References 23

23. Manal K, Lu X, Nieuwenhuis MK, Helders PJM, Buchanan TS (2002) Force transmission through the juvenile idiopathic arthritic wrist: a novel approach using a sliding rigid body spring model. J Biomech 35(1):125–133 24. Schuind F, Cooney WP, Linscheid RL, An KN, Chao EYS (1995) Force and pressure transmission through the normal wrist. A theoretical two-dimensional study in the posteroanterior plane. J Biomech 28(5):587–601 25. Fischli S, Sellens RW, Beek M, Pichora DR (2009) Simulation of extension, radial and ulnar deviation of the wrist with a rigid body spring model. J Biomech 42(9):1363–1366 26. Hutton DV (2004) Fundamentals of finite element analysis. McGraw Hill: Higher Education, New York 27. Donald BJM (2007) Pratical stress analysis with finite element. Glasnevin P, Ireland 28. Lo SH, Ling C (2000) Improvement on the 10-node tetrahedral element for three-dimensional problems. Comput Methods Appl Mech Eng 189(3):961–974 29. Yoshimura S, Wada Y, Yagawa G (1999) Automatic mesh generation of quadrilateral elements using intelligent local approach. Comput Methods Appl Mech Eng 179(1–2): 125–138 30. Abdul-Kadir MR, Hansen U, Klabunde R, Lucas D, Amis A (2008) Finite element modelling of primary hip stem stability: the effect of interference fit. J Biomech 41(3):587–594 31. Anderson AE, Ellis BJ, Maas SA, Weiss JA (2010) Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J Biomech 43(7):1351–1357 32. Janssen D, Mann KA, Verdonschot N (2008) Micro-mechanical modeling of the cement-bone interface: the effect of friction, morphology and material properties on the micromechanical response. J Biomech 41(15):3158–3163 33. Kayabasi O, Ekici B (2007) The effects of static, dynamic and fatigue behavior on three- dimensional shape optimization of hip prosthesis by finite element method. Mater Des 28(8):2269–2277 34. Teoh SH, Chan WH, Thampuran R (2002) An elasto-plastic finite element model for polyethylene wear in total hip arthroplasty. J Biomech 35(3):323–330 35. Bendjaballah MZ, Shirazi-Adl A, Zukor DJ (1997) Finite element analysis of human knee joint in varus-valgus. Clin Biomech 12(3):139–148 36. Boyd SK, Müller R, Zernicke RF (2002) Mechanical and architectural bone adaptation in early stage experimental osteoarthritis. J Bone Miner Res 17(4):687–694 37. Li G, Lopez O, Rubash H (2001) Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis. J Biomech Eng 123(4):341–346 38. Peña E, Calvo B, Martínez MA, Doblaré M (2006) A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Biomech 39(9):1686–1701 39. Peña E, Calvo B, Martínez MA, Doblaré M (2007) Effect of the size and location of osteochondral defects in degenerative arthritis. A finite element simulation. Comput Biol Med 37(3):376–387 40. Kim S-H, Chang S-H, Jung H-J (2010) The finite element analysis of a fractured tibia applied by composite bone plates considering contact conditions and time-varying properties of curing tissues. Compos Struct 92(9):2109–2118 41. Varga P, Baumbach S, Pahr D, Zysset PK (2009) Validation of an anatomy specific finite element model of Colles’ fracture. J Biomech 42(11):1726–1731 42. Radev BR, Kase JA, Askew MJ, Weiner SD (2009) Potential for thermal damage to articular cartilage by PMMA reconstruction of a bone cavity following tumor excision: a finite element study. J Biomech 42(8):1120–1126 43. Guo X, Fan Y, Li Z-M (2009) Effects of dividing the transverse carpal ligament on the mechanical behavior of the carpal bones under axial compressive load: a finite element study. Med Eng Phys 31(2):188–194 24 2 Biomechanical Properties and Behaviours

44. Gislason MK, Nash DH, Nicol A, Kanellopoulos A, Bransby-Zachary M, Hems T, Condon B, Stansfield B (2009) A three-dimensional finite element model of maximal grip loading in the human wrist. Proc Inst Mech Eng 223(7):849–861 45. Gislason MK, Nash DH, Stansfield B (2008) In vivo contact stresses at the radiocarpal joint using a finite element method of the complete wrist joint. J Biomech 41(Suppl 1):S147–S147 46. Gislason MK, Stansfield B, Nash DH (2010) Finite element model creation and stability considerations of complex biological articulation: the human wrist joint. Med Eng Phys 32(5):523–531 47. Carrigan SD, Whiteside RA, Pichora DR, Small CF (2003) Development of a three- dimensional finite element model for carpal load transmission in a static neutral posture. Ann Biomed Eng 31(6):718–725 48. Ezquerro F, Jiménez S, Pérez A, Prado M, de Diego G, Simón A (2007) The influence of wire positioning upon the initial stability of scaphoid fractures fixed using Kirschner wires: a finite element study. Med Eng Phys 29(6):652–660 49. Oda M, Hashizume H, Miyake T, Inoue H, Nagayama N (2000) A stress distribution analysis of a ceramic lunate replacement for Kienböck’s disease. J Hand Surg (British Eur Vol) 25:492–498 50. Carrigan S (2002) Development of a static carpal load transmission model using finite element method. Queen’s University, Kingston 51. Cheng H-YK, Lin C-L, Lin Y-H, Chen AC-Y (2007) Biomechanical evaluation of the modified double-plating fixation for the distal radius fracture. Clin Biomech 22(5):510–517 52. Troy KL, Grabiner MD (2007) Off-axis loads cause failure of the distal radius at lower magnitudes than axial loads: a finite element analysis. J Biomech 40(8):1670–1675 53. Donzelli PS, Spilker RL, Ateshian GA, Mow VC (1999) Contact analysis of biphasic transversely isotropic cartilage layers and correlations with tissue failure. J Biomech 32(10):1037–1047 54. Blankevoort L, Kuiper JH, Huiskes R, Grootenboer HJ (1991) Articular contact in a three- dimensional model of the knee. J Biomech 24(11):1019–1031 55. Ledoux P, Lamblin D, Targowski R (2001) Modifications to the mechanical behavior of the wrist after fracture of the scaphoid. Modeling by finite element analysis. Acta Orthop Belg 67(3):236–241 56. Li G, Gil J, Kanamori A, Woo SLY (1999) A validated three-dimensional computational model of a human knee joint. J Biomech Eng 121(6):657–662 57. Li G, Sakamoto M, Chao EYS (1997) A comparison of different methods in predicting static pressure distribution in articulating joints. J Biomech 30(6):635–638 58. Li Z, Kim JE, Davidson JS, Etheridge BS, Alonso JE, Eberhardt AW (2007) Biomechanical response of the pubic symphysis in lateral pelvic impacts: a finite element study. J Biomech 40(12):2758–2766 59. Trabelsi O, del Palomar AP, López-villalobos JL, Ginel A, Doblaré M (2010) Experimental characterization and constitutive modeling of the mechanical behavior of the human trachea. Med Eng Phys 32(1):76–82 60. Swieszkowski W, Ku DN, Bersee HEN, Kurzydlowski KJ (2006) An elastic material for cartilage replacement in an arthritic shoulder joint. Biomaterials 27(8):1534–1541 Chapter 3 The Wrist Joint Affected by Rheumatoid Arthritis

Abstract This chapter begins with information on the pathological conditions associated with the wrist joint. The following section discussed in detail on the rheumatoid arthritis, as it is the most critical disease affecting the joint. Generally, there are three main symptoms: synovial proliferation, cartilage destruction and ligaments laxity. The disease progresses with several cascade events known as pathophysiology. Scapholunate advanced collapse (SLAC) and the destruction of the capitolunate articulation were among of them. The severity of the disease differs according to several categories or classiﬁcations established by previous researcher—Larsen-Daale-Eek, Wrightington, Simmen and Hubber. As far as the treatment was concerned, the most problematic option is the wrist arthroplasty attributed to the loosening of the implant and metacarpal perforation, despite of its advantage in preserving joint motion. This option, thus less preferred by medical practitioners as compared to the arthrodesis or bone fusion. However, as the technology progresses, the designs of the implants for arthroplasty were found to be better and better, promising a more reliable treatment for the rheumatic wrist.

Keywords Wrist joint Á Rheumatoid arthritis Á Wrist arthroplasty Á Wrist arthrodesis Á Scapholunate advance collapse Á Scapholunate dissociation

3.1 Pathology

Viegas et al. [1] through their cadaveric study have demonstrated valuable insights into several different symptoms and characteristics of diseases associated with the wrist joint. This study involved 393 cadaver wrists ranging from fetal to 99 years old, with an average age of 67. Several diseases have been meticulously investigated, including the arthrosis, chondromalacia and soft tissue damaged. Athrosis

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 25 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8_3, Ó Springer-Verlag Berlin Heidelberg 2013 26 3 The Wrist Joint Affected by Rheumatoid Arthritis

Fig. 3.1 Patient affected by rheumatoid arthritis with severe dislocation of both wrists [10]

was defined as worn off of the articular cartilage in any portion of the bones which gives exposure to the subchondral bone. This study has reported that 58 % of the specimens suffered with arthrosis; 21 % of them were identified at the radiocarpal joint whereas 46 % was observed at the midcarpal joint. 24 % of the dissected specimens were found to have chondromalacia, which were found to have disabnormalities of softening and fibrillation associated with articular cartilage. Out of that, 4 and 22 % were affected by the disease at the radiocarpal and midcarpal joints, respectively. All of these reported findings showed high frequency of tissue damages, thus significantly indicate that numerous wrist joints are over worn or overloaded during their lifetime. This phenomenon is worsening as the aging population is increasing thus leading to higher demands in the future. However, treatments’ options are fairly limited and less efficient due to the weak understanding towards the biomechanical behaviour of the wrist, as well as limited computational and experimental resources. Carpectomy, partial or complete arthrodesis and arthroplasty are examples of available treatments [2–9]. Each of them nonetheless has their own weaknesses. For instance, the limited motions due to bone fusions in arthrodesis resulted in less independencies of the patient. The arthroplasty as another option experiences high failure rates [8].

3.2 Rheumatoid Arthritis

One of the most common skeletal diseases associated with the wrist joint is rheumatoid arthritis (RA) [10, 11]. The disease affects mostly synovial joints, resulting in considerable pain, loss of function and eventual deformity as shown in Fig. 3.1.It is a life-long condition, and the disease activity might change over time. Rheu- matoid arthritis is a chronic, systemic, inﬂammatory disease that results from an autoimmune disorder causing the damage of the joint [12, 13]. Swelling and inﬂammation of the joint are as a result of lymphocytes effect in the synovium, leads to mutilation of the joint. RA as a symmetrical disease is normally attacks 3.2 Rheumatoid Arthritis 27

Fig. 3.2 A posterior photograph of patient with rheumatoid arthritis hands (a), note axial deviation of the wrist and clearer observed as seen in X-ray of the right (b) and left (c) wrist [13] both sides of the limb (Fig. 3.2). It can either be the same joint in both limbs or different joints of the same limb. For instance, patient with RA in the wrist has the same symptoms in the ﬁngers of the same hand. In conjunction with the pathomechanics of the RA, there are cascade of events behind it. The disease process commences by mainly affecting the soft tissues including the adjacent articular cartilage (chondrolysis) then followed by the hard tissues (bone resorption), thus resulting in severe deformities [12, 13] of the joint. 28 3 The Wrist Joint Affected by Rheumatoid Arthritis

Table 3.1 Radiographic staging according to Larsen-Daale-Eek [12, 14] Larsen score Radiographic changes 0 Normal joint, no changes 1 Osteoporosis and swelling 2 Joint space narrowing and erosion 3 Signiﬁcant erosion, moderate destruction

Table 3.2 Wrightington classiﬁcation [13, 15] Score Radiographic ﬁnding Therapy 1 Osteoporosis, cysts, erosion Synovectomy 2 Carpal Instability Soft tissue stabilization/partial arthrodesis 3 Destruction, subluxation Arthroplasty/arthrodesis 4 Severe radial destruction Arthrodesis

Table 3.3 Simmen and Hubber classiﬁcation [12, 16] Type Natural course of the disease I Also known as ankylosing type, where spontaneous fusion of the wrist as the indicator II It comes together with arthritic and degenerative changes. This also known as osteoarthritic type showing both the osteoporosis as well as subchondral sclerosis which affects stabilization III The wrist with progressive disintegration and instability (luxation, progredient bone loss and mutilation) can be categorized under this disintegrative type. There are two subtypes: IIIa with more ligamentous instability IIIb with complete loss of carpal anatomy due to marked destruction of the bone

To efficiently examine the severity of the RA deformities, previous reports have introduced several classifications according to their own reliable approaches. Larsen et al. classification used radiologic changes for scoring system with the basis of 5 grades, in which the degree of joint and cartilage destructions used as the primary indicators (Table 3.1)[12, 14]. Combination between radiologic findings and therapeutic options were used in the Wrightington classification, with the basis up to four grades (Table 3.2)[13, 15]. Simmen and Huber on the contrary established a classification method purely based on the natural course of the disease, without considering any radiologic inflammatory destruction [12, 16]. This classification distinguished the courses into three types. Table 3.3 provides information on these three classifications of RA. There are three main characteristics of the wrist affected by RA: cartilage destruction, synovial proliferation and ligamentous laxity [10, 17]. Cartilage destruction of thinning was occurred due to cytochemical action, which resulting in degradation of existing cartilages and inhibition of new cartilage formation [17]. The synovial proliferation may cause bone erosion with sharp edges which might lead to tendon rupture [10, 18]. Ligamentous laxity caused by stretching attributed 3.2 Rheumatoid Arthritis 29

Fig. 3.3 Radiograph of the wrist with SLD (a)[20] and SLAC (b)[7] to synovial expansion, results in ulnar translation and carpal supination. The pathological process begins with inflammation of the synovial, affects commonly at the ulnar side of the wrist joint [10, 12]. It then spreads to adjacent area of the wrist including the radiocarpal joint. The neighbouring tissues which consist of the cartilages, ligaments and tendons degenerate subsequently. In severe cases, tendon rupture occurs with a consequence of kinematic changes of the joint, resulting in disruption of the periarticular bones and the articular surfaces [9, 19]. On the whole, these three symptoms have critically caused degeneration of both soft tissues and bones, hence eventually mutilated and unstable wrist joint. Trieb et al. [13] have successfully identified the pathophysiological characteristics of the wrist with RA. Ligamentous laxity for both the intrinsic and extrinsic ligaments has resulted in unphysiological bones movements. This was evident as loss of tension of the radiotriquetral ligament caused dislocation of the carpus in the ulnar direction. Scapholunar dissociation (SLD) due to the increased distance between the scaphoid and lunate is primarily occur because of deteriorated intrinsic ligaments: scapholunar and luno-triquetral which caused by synovial inflammation [20] (Fig. 3.3a). Progression of this SLD will also lead to a more severe deformation of the joint, known as scapholunate advanced collapse (SLAC) (Fig. 3.3b). Another pathophysiology characteristic is the dislocation of the proximal carpal row in the ulnar and palmar directions. Ulnar dislocation of the bones was attributed to the weakened radiotriquetral ligament and destructed capitolunate joint, thus resulted in relatively greater load being transferred to the lunate. The reduction of contact between the lunate and the radius was also found in rheumatic wrist due to the dislocation of lunate in the ulnar direction. The scaphoid as the most problematic carpal bone was commonly found to be dislocated palmarly due to deteriorated radioscapholunate ligament. The impaction or loss of carpal height was due to bone erosion and the unphysiological bones dislocations which worsen 30 3 The Wrist Joint Affected by Rheumatoid Arthritis

Fig. 3.4 Arthrodesis of the wrist affected by rheumatoid arthritis. Stanley pin is used for fusion, together with excision of the distal ulna (Darrach’s procedure) [21] the functionality and stability of the wrist joint. Hand scoliosis could also be observed in the rheumatic wrist. This was occurred as a result of ruptured tendon, which has led to a changed axis of the wrist to the ulnar, and the rotation of metacarpal in the radial direction.

3.3 Treatment

Treatments are given according to levels of severity of the diseased wrist. Syn- thetic narcotics, opiods, Non-steroidal anti-inflammatory drugs (NSAIDs) and cortisone are examples of medication given to the patients who are considered under less severe level of pain. To prevent bacterial infections, antibiotics are used. Joint inflammation could be inhibited with Biologic Response Modifiers (BRMs) which targets the immune system preventing activation of tumor necrosis factor (TNF). Similarly, Disease-Modifying Anti-Rheumatic Drugs (DMARDs) has also given encouraging effects in reducing the pain. For severe cases, surgical procedures are usually employed, which were categorised into two main objectives: motion eliminating and motion preserving procedures. Arthrodesis or wrist fusion as depicted in Fig. 3.4 is performed to relief pain by fusing affected bones, partially or completely, established through plates and screws fixations. This procedure obtained patients’ satisfaction as it promotes 3.3 Treatment 31

Fig. 3.5 ReMotion (Small Bone Innovations, Morrisville, PA) used in this arthroplasty as a treatment for severe wrist affected by rheumatoid arthritis [25] relief of pain while promising joint stability. Despite of its benefits, this procedure will not be recommended for patients with both limbs affected, as it prohibits motions of the limbs. It wills definitely causing difficulties to perform their daily activities. To circumvent this problem, motion-preserving procedure has been introduced. Designed to preserve joint motions, total wrist replacement (Fig. 3.5) or total wrist arthroplasty (TWA) was established [22]. Similar to other joints, it requires removal of some portions of the affected joint to place the implant. Despite of promoting benefits, this technique resulting in high failure rate, primarily due to metacarpal perforation and loosening of the implant [22]. Although numerous attempts through designs of better implants and more efficient procedure were given to improve this option, there are still many complications reported [6, 8, 23, 24].

References

1. Viegas SF, Patterson RM, Hokanson JA, Davis J (1993) Wrist anatomy: incidence, distribution, and correlation of anatomic variations, tears, and arthrosis. J Hand Surg 18(3):463–475 2. Dacho AK, Baumeister S, Germann G, Sauerbier M (2008) Comparison of proximal row carpectomy and midcarpal arthrodesis for the treatment of scaphoid nonunion advanced collapse (SNAC-wrist) and scapholunate advanced collapse (SLAC-wrist) in stage II. J Plast Reconstr Aesthet Surg 61(10):1210–1218 3. Elhassan B, Shin AY (2009) Management of wrist arthritis secondary to advanced Kienbock disease. Tech Orthop 24(1):27–31 4. Hogan CJ, McKay PL, Degnan GG (2004) Changes in radiocarpal loading characteristics after proximal row carpectomy. J Hand Surg 29(6):1109–1113 32 3 The Wrist Joint Affected by Rheumatoid Arthritis

5. Cavaliere CM, Chung KC (2008) A systematic review of total wrist arthroplasty compared with total wrist arthrodesis for rheumatoid arthritis. Plast Reconst Surg 122(3):813–825 6. Cavaliere CM, Chung KC (2008) Total wrist arthroplasty and total wrist arthrodesis in rheumatoid arthritis: a decision analysis from the hand surgeons’ perspective. J Hand Surg 33(10):1744–1755 7. Mastella DJ, Ashmead DI, Watson HK (2009) Scapholunate advanced collapse wrist arthritis. Tech Orthop 24(1):13–18 8. Adams BD (2006) Total wrist arthroplasty for rheumatoid arthritis. Int Congr Ser 1295:83–93 9. Huang KM, Naidu SH (2002) Total wrist arthroplasty: is there a role? Curr Opin Orthop 13(4):260–268 10. Simmen BR, Kolling C, Herren DB (2007) The management of the rheumatoid wrist. Curr Orthop 21(5):344–357 11. Stegeman M, Rijnberg WJ, van Loon CJM (2005) Biaxial total wrist arthroplasty in rheumatoid arthritis. Satisfactory functional results. Rheumatol Int 25(3):191–194 12. Trieb K, Hofstätter S (2009) Treatment strategies in surgery for rheumatoid arthritis. Eur J Radiol 71(2):204–210 13. Trieb K, Hofstätter S (2009) Rheumatoid arthritis of the wrist. Tech Orthop 24(1):8–12 14. Larsen A, Dale K, Eek M (1977) Radiographic evaluation of rheumatoid arthritis and related conditions by standard reference films. Acta Radiol Diagn (Stockh) 18(4):481–491 15. Hodgson SP, Stanley JK, Muirhead A (1989) The Wrightington classification of rheumatoid wrist X-rays: a guide to surgical management. J Hand Surg (British Eur Vol) 14(4):451–455 16. Simmen BR, Huber H (1994) The wrist joint in chronic polyarthritis—a new classification based on the type of destruction in relation to the natural course and the consequences for surgical therapy. Handchir Mikrochir Plast Chir 26(4):182–189 17. Cush JJ, Lipsky PE (1991) Cellular basis for rheumatoid inflammation. Clin Orthop Relat Res 265:9–22 18. Ertel AN, Millender LH, Nalebuff E, McKay D, Leslie B (1988) Flexor tendon ruptures in patients with rheumatoid arthritis. J Hand Surg 13(6):860–866 19. Tomé-Bermejo F, Lara-Escobar F, Sánchez-Infante JL, Navarro-Maeso J, Madruga-Sanz JM (2008) Total wrist arthroplasty in patients with rheumatoid arthritis. Evaluation of preliminary results. Revista Española de Cirugía Ortopédica y Traumatología (English Edition) 52(4):199–205 20. De Smet L, Degreef I (2007) Bilateral osteochondroma of the scaphoid causing scapholunate dissociation: a case report. Chirurgie de la Main 26(3):141–142 21. Broadbent MR, Hayton MJ (2010) The hand and wrist in rheumatoid arthritis and osteoarthritis. Surgery (Oxf) 28(2):89–94 22. Anderson MC, Adams BD (2005) Total wrist arthroplasty. Hand Clin 21(4):621–630 23. Menon J (1998) Universal total wrist implant: experience with a carpal component fixed with three screws. J Arthroplast 13(5):515–523 24. Stegeman M, Rijnberg WJ, van Loon CJ (2005) Biaxial total wrist arthroplasty in rheumatoid arthritis. Satisfactory functional results. Rheumatol Int 25(3):191–194 25. Gupta A (2008) Total wrist athroplasty. J Orthop Res 37:12–16 Chapter 4 Finite Element Modelling of the Healthy Wrist Joint

Abstract The ﬁnite element method was used to perform contact analysis in the wrist joint, thus requires its model construction preceding any analyses. The steps and procedures are as explained in this chapter. The three-dimensional model of the healthy wrist was constructed from the CT images of a healthy volunteer. Segmentations were performed on CT images selecting the regions of the cortical and the cancellous bone. The completed three-dimensional model was then constructed consisting of solid linear ﬁrst order tetrahedral elements. As no soft tissues appeared in CT images, manual constructions of it were performed. The articular cartilages were modelled by extruding the articulating surfaces with a thickness size half of the minimum distance between the two bones. Set of links were used to simulate the ligamentous structure. The model was then compared with anatomical software for precision, assuring its reliability for future consumption.

Keywords Healthy wrist Á Finite element model Á Simulation of the ligament Á Simulation of the cartilage Á Conversion from 2D images to 3D model

4.1 Bone Model Reconstruction

A three-dimensional (3D) model of the healthy wrist joint was reconstructed from computed tomography (CT) images of a healthy asymptomatic male, 53 years old volunteer with no radiological signs of pathology. The scans were taken from the whole upper limb of a healthy human body in extended (33.11o) and deviated (17.34o ulnar) wrist positions, measured relative to anatomically based radial coordinate system [1]. The radiograph images of the wrist, ranging from the distal end of the long bones of the left forearm—radius and ulna- to the proximal third of the metacarpals were then cropped. The total length of the scans was 102.3 mm

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 33 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8_4, Ó Springer-Verlag Berlin Heidelberg 2013 34 4 Finite Element Modelling of the Healthy Wrist Joint

Fig. 4.1 Steps performed to construct ﬁnite element model of the healthy wrist with a resolution of 0.98 mm in plane and the slice thickness was 1.5 mm. Semi- automatic segmentation was performed using Mimics software (Materialise, 4.1 Bone Model Reconstruction 35

Fig. 4.2 The R-in/R-out as the quality parameter used to determine the quality of mesh (a). The software which indicates the location of the quality parameters (b)

Belgium) on each CT image to select the cortical region. The inner surface of this region was then used as the outer layer for the cancellous bone. The 3D models of the wrist were constructed using AMIRA software (Mercury Computer Systems, Inc., San Diego, CA) where an automatic compilation through the software’s marching cubes algorithm was applied, which generates a 3D triangular surface mesh. An average element size of 0.4 mm was chosen which resulted in an accurate geometric description of the bone geometry. The created models were compared with an anatomy software [2], and were considered acceptable to mimic the healthy wrist joint. Boolean operations were occupied to check for any intersecting bodies. 36 4 Finite Element Modelling of the Healthy Wrist Joint

Fig. 4.3 Steps performed to construct ﬁnite element model of the cartilage

Marc.Mentat (MSC.Software, Santa Ana, CA) software was used to convert the completed model to 3D solid linear ﬁrst order tetrahedral elements. This resulted in FE model of the healthy wrist consisting of 828,888 elements and 204,218 nodes. The steps performed were shown in Fig. 4.1. The ratio of twice the radius of the inscribed circle to the radius of the ascribed circle of the triangle was used as the normalised indicator to determine the mesh quality (Fig. 4.2a) [3]. The value was set at 0.4 to produce a high quality of surface mesh [4]. An assessment made on the model quality based on surface element conﬁrming its reliability where the ratio of twice the radius of the inscribed circle to the radius of the ascribed circle of the triangle for 90 % of elements was greater than 0.80 (where unity represents an equilateral triangle (Fig. 4.2b). 4.1 Bone Model Reconstruction 37

Fig. 4.4 Finite element model of the healthy wrist. The cartilage elements (a) can be seen as the extruded elements at the articulations between bones (b)

Table 4.1 Listing of ligaments modelled specifying their connections and deﬁned stiffness parameters Ligament Connection 1 Connection 2 Stiffness speciﬁed (N/mm) Capitohamate Capitate Hamate 325 [7] Capitotrapezial Capitate Trapezium 300 [7] Dorsal carpometacarpal Capitate 4MC medial 300 [12] Dorsal carpometacarpal Capitate 4MC lateral 300 [12] Dorsal carpometacarpal Capitate 3MC medial 300 [12] Dorsal carpometacarpal Capitate 3MC lateral 300 [12] Dorsal carpometacarpal Trapezoid 2MC lateral 100 [12] Dorsal carpometacarpal Trapezoid 2MC medial 50 [12] Dorsal carpometacarpal Trapezium 2MC medial 48 [9] Dorsal carpometacarpal Hamate 4MC 300 [12] Dorsal carpometacarpal Hamate 5MC 300 [12] Dorsal intercarpal Hamate Capitate 325 [7] Dorsal intercarpal Capitate Trapezoid 300 [7] Dorsal intercarpal Hamate Triquetrum 300 [12] Dorsal intercarpal Hamate Lunate 150 [12] Dorsal intercarpal Capitate Lunate 150 [12] Dorsal intercarpal Capitate Scaphoid 150 [12] Dorsal intercarpal Scaphoid Trapezium 150 [12] (continued) 38 4 Finite Element Modelling of the Healthy Wrist Joint

Table 4.1 (continued) Ligament Connection 1 Connection 2 Stiffness speciﬁed (N/mm) Dorsal intercarpal Trapezoid Trapezium 110 [5] Dorsal intercarpal Trapezium and Triquetrum 128 [5] trapezoid Dorsal lunotriquetral Lunate Triquetrum 350 [7] Dorsal 2MC1MC 2MC 1MC 100 Dorsal 3MC2MC 3MC 2MC 100 Dorsal 4MC3MC 4MC 3MC 100 Dorsal 5MC4MC 5MC 4MC 100 Dorsal radioulnar Radius Ulna 50 [12] Dorsal scapholunate Lunate Scaphoid 230 [7] Dorsal Trapezometacarpal Trapezium 1MC lateral 100 [12] Carpometacarpal Long radiolunate Lunate Radius 75 [10] Palmar Carpometacarpal Capitate 3MC 100 [12] Palmar Carpometacarpal Capitate 2MC 100 [12] Palmar Carpometacarpal Capitate 4MC 100 [12] Palmar Carpometacarpal Trapezium 3MC 88 [9] Palmar Carpometacarpal Trapezium 2MC 57 [9] Palmar Carpometacarpal Hamate 5MC 100 [12] Palmar Carpometacarpal Hamate 3MC 100 [12] Palmar Carpometacarpal Pisiform 5MC 100 [12] Palmar 1MC2MC 1MC 2MC 100 Palmar 2MC3MC 2MC 3MC 100 Palmar 3MC4MC 3MC 4MC 100 Palmar 4MC5MC 4MC 5MC 100 Palmar Trapeziometacarpal Trapezium 1MC 24 [9] Pisohamate Hamate Pisiform 100 [12] Radial arcuate Capitate Scaphoid 40 [7] Radial collateral carpal Radius Scaphoid 10 [10] Radiodorsal Trapeziometacarpal Trapezium 1MC medial 78 [9] Radioscaphocapitate Radius Capitate 50 [10] Palmar Radiotriquetrum Radius Triquetrum 27 [10] Dorsal Radiotriquetrum Radius Triquetrum 27 Scaphotrapezial Scaphoid Trapezium 150 [7] Scaphotriquetrum Scaphoid Triquetrum 128 Short radiolunate Lunate Radius 75 [7] Ulnalunate Ulna Lunate 40 [7] Ulnar arcuate Capitate Triquetrum 40 [7] Ulnar collateral Triquetrum Ulna 100 [12] Ulnar collateral Pisiform Ulnar 100 [12] Ulnotriquetral Triquetrum Ulna 40 [7] Volar lunotriquetral Lunate Triquetrum 350 [7] Volar Radioscapholunate Radius Scaphoid ? lunate 50,75 (Testut) Volar Radioulnar Radius Ulnar 50 [12] 4.2 Modelling of Cartilages 39

Fig. 4.5 Finite element model of the healthy wrist. The ligaments can be seen as sets of links connecting bones

4.2 Modelling of Cartilages

Cartilage layers in the articulations between the solid geometry were modelled by manually identifying the articulating surfaces between bones (Fig. 4.3). To form the cartilage, extracted proﬁles representing the surfaces of the cartilage distribution were extruded with a thickness size half of the minimum distance between two bones [5], resulted in a good geometrical representation and material distribution of the cartilage (Fig. 4.4). In total, there were 35 cartilages constructed. The distribution of the cartilage was compared and considered acceptable according to an anatomy software [2].

4.3 Modelling of Ligaments

All 60 ligamentous constraints as shown in Fig. 4.5 were modelled using linear link elements [6], and the positions of their insertion points were estimated based on previously published anatomical studies [2, 4]. The stiffness of the ligaments varied widely between 40 and 350 N/mm as were reported in previous experimental works (Table 4.1)[5, 7–10]. For ligaments that did not have published material parameters, it was assumed that the properties of the neighbouring 40 4 Finite Element Modelling of the Healthy Wrist Joint ligaments would apply [11]. To simulate distribution of the origin and insertion of the ligaments, parallel multiple links were applied [4, 11].

References

1. Coburn JC, Upal MA, Crisco JJ (2007) Coordinate systems for the carpal bones of the wrist. J Biomech 40(1):203–209 2. McGrouther DA. HP interactive hand-anatomy CD, Primal Pictures, v.1.0 3. Materialise (2008) Mimics help manual. Materialise version 12.1 4. Gislason MK, Stansfield B, Nash DH (2010) Finite element model creation and stability considerations of complex biological articulation: the human wrist joint. Med Eng Phys 32(5):523–531 5. Fischli S, Sellens RW, Beek M, Pichora DR (2009) Simulation of extension, radial and ulnar deviation of the wrist with a rigid body spring model. J Biomech 42(9):1363–1366 6. Ezquerro F, Jiménez S, Pérez A, Prado M, de Diego G, Simón A (2007) The influence of wire positioning upon the initial stability of scaphoid fractures fixed using Kirschner wires: a finite element study. Med Eng Phys 29(6):652–660 7. Schuind F, Cooney WP, Linscheid RL, An KN, Chao EYS (1995) Force and pressure transmission through the normal wrist. A theoretical two-dimensional study in the posteroanterior plane. J Biomech 28(5):587–601 8. Carrigan SD, Whiteside RA, Pichora DR, Small CF (2003) Development of a three- dimensional finite element model for carpal load transmission in a static neutral posture. Ann Biomed Eng 31(6):718–725 9. Bettinger PC, Smutz WP, Linscheid RL, Cooney WP, An K-N (2000) Material properties of the trapezial and trapeziometacarpal ligaments. J Hand Surg 25(6):1085–1095 10. Savelberg HH, Kooloos JG, Huiskes R, Kauer JM (1992) Stiffness of the ligaments of the human wrist joint. J Biomech 25:369–376 11. Gislason MK, Nash DH, Nicol A, Kanellopoulos A, Bransby-Zachary M, Hems T, Condon B, Stansfield B (2009) A three-dimensional finite element model of maximal grip loading in the human wrist. Proc Inst Mech Eng Part H J Eng Med 223(7):849–861 12. Carrigan S (2002) Development of a static carpal load transmission model using finite element method. Queen’s University, Kingston Chapter 5 Finite Element Analysis of the Wrist Joint Affected by Rheumatoid Arthritis

Abstract This chapter presents the information on the biomechanical analysis of the rheumatic wrist using the finite element method. This study was designed to better understand the biomechanical behaviour of the diseased wrist, thus assuring better future treatments. The three-dimensional model of the wrist affected by rheumatoid arthritis was constructed from CT images of the healthy volunteer, by considering ten characteristics involving three main symptoms and seven pathophysiology criteria of the disease. Comparison was made between the simulated healthy wrist which functions as control and the rheumatic wrist model. Both models were assigned with the same loading simulating static hand grip action. It was revealed from the finite element analyses that the RA model produced ten times higher contact pressure at the articulations in comparison with the healthy model. Additionally, normal physiological load transfer changed from primarily through the radial side to an increased load transfer of 5 % towards the ulnar. These significant findings recommend that future treatments should be able to avoid any unphysiological impacts as addressed in this study.

Keywords Finite element analysis Rheumatoid arthritis Computational modelling High contact pressure Unphysiological load direction

5.1 Finite Element Model Construction of the Rheumatic Wrist

Based on past literatures (see Chap. 3), symptoms and the pathophysiology of rheumatoid arthritis (RA) were well-identiﬁed. Type IIIa (disintegration type with more ligamentous instability according to Simmen and Hubber classiﬁcation) of RA was simulated, wherein 10 criteria were included:

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 41 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8_5, Ó Springer-Verlag Berlin Heidelberg 2013 42 5 Finite Element Analysis

Fig. 5.1 Modelling of the cartilage destruction

1. Cartilage destruction [1–3]. 2. Loss of carpal height due to bone destruction [2, 4]. 3. Dislocation of the carpus in the ulnar direction [2]. 4. Dislocation of the proximal carpal row in the palmar and ulnar direction [2]. 5. Scapholunar dissociation (SLD) with scapholunate advanced collapse wrist arthritis (SLAC) stage 2 [2, 5]. 6. Dislocation of the scaphoid in the palmar direction due to the radial insertion of the Testut ligament synovialitis [2]. 7. Hand scoliosis due to ruptured tendon. This mechanism ends in a changed axis of the wrist to the ulna with a consecutive rotation of the metacarpal bones in the radial direction [2]. 8. Reduction of contact between the lunate and radius [2]. 9. Bone erosion [2, 3, 6–8]. 10. Osteoporotic bone [2, 3]. This criterion was simulated by reducing the elastic modulus of the bones; 33 % for the cortical bone and 66 % for the cancellous bone [9–15]. All these ten characteristics were utilised as a whole to construct the model of the rheumatic wrist. The succeeding sections explained steps performed to simulate each characteristic.

5.1.1 Simulation of Cartilage Destruction

The cartilage destruction was modelled by removing all the articular cartilages to simulate worst-case scenario (Fig. 5.1). It was thus resulted in existence of gaps 5.1 Finite Element Model Construction of the Rheumatic Wrist 43

Table 5.1 Information on the carpometacarpal ratio used in this study in comparison with the literature Literature [4] Current study Simulation Healthy: Healthy: Translation of metacarpals CR = 0.54 ± 0.03 32:45 10.1 mm proximally to simulate CR = 0:55 ¼ 0:55 Severe RA: Severe RA: severe RA model CR = 0.40 22:35 CR ¼ 0:55 ¼ 0:38

between bones. In real clinical environment, the adjacent anatomical of the joint makes these gaps ‘removed’ by physiologically connecting the related bones.

5.1.2 Simulation of Loss of Carpal Height

The reduction of gaps has resulted in loss of carpal height. Carpometacarpal ratio (CR)—the ratio between the distance from the distal radius to the base of the third metacarpal with the length of the third metacarpal [4]—was utilised to simulate this condition. Further details were mentioned in Table 5.1 and the simulated loss of carpal height was shown in Fig. 5.2.

5.1.3 Simulation of Dislocation of the Carpus in the Ulnar Direction

Dislocation of the carpus in the ulnar direction occurs due to loss of tension of the radiotriquetral ligament, irrespective of the status of the ulnar head [2]. The entire carpus excluding the scaphoid was involved in the simulation. Figure 5.3a depicts the dislocated carpus towards ulnar. The simulation was done by rotating 10° of carpus towards ulnar with the center of the radius used as the center of rotation (COR). Figure 5.3b shows the simulated loss of tension (in circular) of the radiotriquetral ligament where only one link remained mimicking weakened ligaments.

5.1.4 Simulation of Dislocation of the Proximal Carpal Row in the Palmar and Ulnar Directions

Dislocation of the proximal carpal row in the palmar occurred physiologically as during ulnar deviation (either due to physiological movements or as a results of disease), the scaphoid, lunate, and triquetrum rotate palmarly [16]. In the 44 5 Finite Element Analysis

Fig. 5.2 Simulated loss of carpal height due to bone destruction (b). As compared to the healthy model (a) (total carpal height of 32.45 mm), the simulated impaction in RA model was seen to have total carpal height reduced to 22.35 mm

Fig. 5.3 The dislocated carpus towards ulna (a). The RA bones are in red and the transparent bones represent the normal healthy wrist. Weakened ligaments were simulated by remaining one link (b). The ligament in circle was the simulated loss of tension of the radiotriquetral ligament rheumatic wrist, the occurrence of SLAC (stage 3), SLD and the weakened radio- triquetrial ligaments has resulted in the dislocation of carpus towards ulnar direction [2]. These situations induced greater load subjected to the lunate thus ultimately destruct the capitolunate joint [5]. Figure 5.4 illustrates the simulated palmar (2.76 mm) and ulnar dislocation (7.61 mm) of the proximal carpal bones. 5.1 Finite Element Model Construction of the Rheumatic Wrist 45

Fig. 5.4 Superior view of the proximal row carpal bones. The ﬁgure shows its dislocation towards palmar and ulnar directions. The RA bones were in red and transparent bones represent the normal healthy bones

Fig. 5.5 The simulated SLD and SLAC were shown in (a) where the RA bones were in red and the transparent bones represent the healthy bones. The simulated effect of weakened and torn ligaments was also shown (b)

5.1.5 Simulation of Scapholunate Dissociation and Scapholunate Advanced Collapse

The SLD was simulated by increasing distance between the scaphoid and the lunate, from 1.98 to 6.51 mm. The worn and torn intrinsic ligaments as results from the synovitis effect [2, 5] were simulated by utilising one link. As stated by Trieb et al. [2], the scapholunar and lunotriquetral ligaments are commonly effected as the disease progresses, thus this condition subsequently destruct the scapholunate articulation [9, 17, 18]. This circumstance was even worse as the high mobility of the scaphoid has resulted in imbalance load transfer from the distal to the proximal through the joint [16], and even pronounced as the capitate dissociates the scaphoid and the lunate further. SLAC was then diagnosed as the disease progressed. This condition incorporates the triquetrum, and its distance from the lunate was also reduced. Again, the synovitis leads to the dislocation of the triquetrum and the lunate towards distal ulnar. The simulated characteristic is as shown in Fig. 5.5. 46 5 Finite Element Analysis

Fig. 5.6 Information from literature on the rotatory subluxation of the scaphoid, producing incongruent loading at the radioscaphoid facet [5] was used to perform the simulation (a).The simulated scaphoid dislocation in the palmar direction from sagittal view (b) and palmar view (c). The RA bones were in red and the transparent bones represent the healthy bones

5.1.6 Simulation of Dislocation of the Scaphoid in the Palmar Direction

Dislocation of the scaphoid in the palmar direction was due to the radial insertion of the Testut ligament synovialitis has caused bone loss and the possibility of so-called Mannerfelt crypt [2]. This is also one of the criteria of the SLAC [5]. The simulation (Fig. 5.6) was performed by rotating radially the scaphoid (center of scaphoid as COR) and palmarly (the proximal end ulnar direction as COR) for 16.8 and 22.3°, respectively.

5.1.7 Simulation of Hand Scoliosis

Hand scoliosis occurs due to tendon rupture. This mechanism ends in a changed axis of the wrist to the ulna with a consecutive rotation of the metacarpal bones in the radial direction [2]. Hand scoliosis was simulated by dislocating 7.23 mm all carpus excluding the scaphoid towards ulnar and rotating radially 10° of all metacarpals with the center of the radius as the COR. This mechanism resulted in a changed axis of the wrist to the ulnar [2] (Fig. 5.7). 5.1 Finite Element Model Construction of the Rheumatic Wrist 47

Fig. 5.7 The dislocation of carpus towards ulnar and rotation of metacarpals radially due to tendon rupture resulted in hand scoliosis. The RA bones were in red while transparent bones depicting the normal healthy wrist

5.1.8 Simulation of Reduction of Contact Between the Lunate and the Radius

As revealed by Trieb et al., the contact between the lunate and the radius was decreased in rheumatic wrist [2]. It was due to the dislocation of the proximal row or the carpal bones towards ulnar. This condition was simulated through translation of 7 mm of the lunate towards ulnar direction (reference was positioned at the center of the distal ulna) resulting in decreasing of the contact between the radius and the lunate (Fig. 5.8).

5.1.9 Simulation of Bone Erosion

Bone erosion was simulated by using Boolean operation (subtraction) after assuring accuracy of the bone’s position (Fig. 5.9). Sharp edges due to eroded bone were manually simulated by utilising local smoothing algorithm tool. Bone erosion was regularly occurred in the rheumatic wrist attributed to the inﬂammation of the synovial ﬂuid and deterioration of the joint constraint [1–3, 6–8]. The differences of volumes between the healthy and the RA bones were summarised in Table 5.2. 48 5 Finite Element Analysis

Fig. 5.8 The palmar view of the carpus where the RA bones were in red while transparent bones depict the normal healthy wrist. The ﬁgure shows the translation of the lunate towards ulnar direction resulting in the decreasing of the contact between the radius and the lunate

Fig. 5.9 The effect of bone erosion was shown in this exploded view of the RA model (left)

5.2 Finite Element Analysis: Pre-Processing Procedures

As aforementioned, the healthy model was used as control, and was compared with the RA model created. Finite element analyses were occupied with the following pre-processing procedures. For contact modelling, each of the contact body was deﬁned as deformable [19]. In total, there were 51 contact bodies in the healthy model and 16 contact bodies in the RA model existed. Two different conditions were set for the RA and the healthy models. For the healthy model, frictionless 5.2 Finite Element Analysis: Pre-Processing Procedures 49

Table 5.2 Information on the difference between the healthy and RA wrist after simulated bone erosion No. Bone Healthy (mm3) RA (mm3) Bone Erosion (%) 1 1MC 3852.1 3766.0 2.2 2 2MC 2423.8 2312.0 4.6 3 3MC 2946.1 2600.1 11.7 4 4MC 1678.9 1603.6 4.5 5 5MC 2414.8 2223.2 7.9 6 Trapezium 1646.6 1336.9 18.8 7 Trapezoid 1177.1 926.5 21.3 8 Capitate 2450.7 1809.5 26.2 9 Hamate 1887.7 1784.3 5.5 10 Scaphoid 2346.5 1763.0 24.9 11 Lunate 1438.3 1054.5 26.7 12 Triquetrum 1679.9 1480.7 11.9 13 Radius 9666.3 9487.3 1.9 14 Ulna 5689.4 5528.5 2.8 MC Metacarpal contact was assumed to ensure that no shear stresses occurred at the articulation surfaces. Friction coefficient of 0.02 was applied as suggested by previous researchers [20, 21]. However, this free motion of the bones should be relatively restricted to achieve convergence, and separation of the bones once contact had been made must be avoided [18]. For the static gripping task simulated in this study, there will be no relative movement between the metacarpals due to the stout ligaments connecting the metacarpals to each other and to the distal row. The carpometacarpal joint was therefore restricted by assigning glue type of contact to prevent any forms of articulations [22, 23]. The geometrical shape of the carpometacarpal joint also plays a role in joint stability where the second and third metacarpals are relatively more rigid than the fourth and fifth metacarpals [16]. For the RA model, friction coefficient of 0.3 was applied due to the relatively rougher surface of the contacted bones [24]. The bone parts of the wrist were modelled using linear isotropic material representing the cortical (healthy model: E = 18 GPa, v = 0.2 and RA model: E = 12 GPa, v = 0.2) and the cancellous bone (healthy model: E = 100 MPa, v = 0.25 and RA model: E = 33 MPa, v = 0.25) [20, 25–27]. The cartilages in the healthy model was assigned with hyper-elastic material properties due to its large deformation behaviour [27]. Mooney-Rivlin modelling was used to perform the hyperelastic behaviour with coefficients of C10 = 4.1 MPa and C01 = 0.41 MPa [28]. The elastic modulus assigned was 10 MPa [19]. The load simulating the gripping force of was used in this study (Fig. 5.10). The magnitude of the resultant compression pressure was 7.33 MPa distributed over the five metacarpals. All the applied loads and the placement of the loading were mentioned in Table 5.3. To assist convergence of the solution, the proximal ends of the radius and ulna are fully constrained [20]. The carpometacarpal joint and the 50 5 Finite Element Analysis insertion of the tendons (abductor pollicis longus muscle, flexor carpi radialis muscle, flexor carpi ulnaris muscle, extensor carpi ulnaris muscle, extensor carpi radialis brevis muscle, extensor carpi radialis longus muscle) were fixed prohib- iting motion at the x and y directions, to enable movements of all bones (excluding the proximal ends of the radius and ulna) in the direction of the applied loading [19]. All these settings worked as input of the FE analyses using Marc. Mentat (MSC.Software, Santa Ana, CA) software.

5.3 Biomechanical Behaviours of the Rheumatic Wrist Joint

5.3.1 Comparative Analysis

As far as the reliability of the results and model created were concerned, comparison was made between literatures and findings from our study. Results from finite element analyses were used (Fig. 5.11). It was addressed that all of the five aspects of stress transfer emphasized in the previous studies were in agreement with our investigation [18, 20, 29–33]. One of them was the percentage of load transmission through the radiocarpal and midcarpal joints as reported by Patterson et al. They have found that the scaphoid sustained 60.0 % of the load and the other 40.0 % by the lunate [29]. The same finding was observed in our study where the scaphoid was subjected with the higher load as compared to the lunate, 63.4 and 65.3 % for the healthy and RA models, respectively. In their cadaveric studies, Macleod et al. [30] have revealed that 68.0 % of the load through the forearm was transferred to the radius, whereas Gislason et al. [18] have came out with a range of 78.7–92.8 % from his simulation studies. These studies notably addressed the role of the radius as a major load bearer in the wrist joint. Our study presents similar findings where 77.8 % of the load was transferred to the radius and the remaining to the ulna. For the RA model, a higher percentage of 87.3 % of the load was transferred to the radius thus leads to imbalance of stress distribution. This study revealed that the load was transferred radially throughout the wrist joint, similar to the simulation studies by Gislason et al. [20] and experimental work by Givissis et al. [31]. In comparison with the RA model, higher stress concentration was found at the radial side of the healthy model (63.34 %), whereas a lower percentage of loads (60.99 %) were found at the RA model. Comparison was also made on the strain magnitude of the radius bone. Bosisio et al. [32] have addressed an ultimate strain value for the cortical radius (eu = 1.5 ± 0.1 %) as well as the yield strain (ey = 0.9 ± 0.2 %). Another study by Kerin et al. [33] have reported a failure strain value of the cartilage under compression to be 30 %. In this study, analyses at the diaphysis of the distal radius showed that the strain value of the cartilage of the healthy model was on average e = 1.4 %. The corresponding value for the cortical bone of the healthy and RA 5.3 Biomechanical Behaviours of the Rheumatic Wrist Joint 51

Fig. 5.10 The loading condition applied simulating static hand gripping action

Table 5.3 Magnitudes of pressure applied on the metacarpal bones Thumb Index Long Ring Little Cross-sectional area (mm2) 126.30 77.00 84.15 57.60 80.20 Load (N) [20] 255.60 120.30 106.40 88.00 77.30 Pressure (MPa) 2.02 1.56 1.26 1.53 0.96 52 5 Finite Element Analysis

Fig. 5.11 Equivalent von Mises (EQV) stress plot for the healthy and RA model models was e = 0.02 and 0.06 %, respectively. The cancellous bone for the healthy and RA model have relatively higher strain value, e = 0.17 and 0.15 %, respectively. All values from our study were found to be below the failure criteria as mentioned by the previous researchers.

5.3.2 The Biomechanical Effect of Symptoms and Pathophysiological Characteristics

The worsened mechanical properties of the associated tissues and physiological functions of the wrist affected by RA [2] were simulated. Discussion on the effect of the pathophysiology will be presented separately. As one of the characteristics, the osteoporotic RA bones analysed here were found to have 20 % lower stress in comparison with the healthy bones (Fig. 5.12). This condition was signiﬁcantly mimicking the condition where the rheumatic patients tend to underutilise their hands. As the condition progresses, there is high tendency to be affected by bone atrophy as a result of slow generation of the bone cells [34]. Soft tissues are destructed at the early stage of the RA mechanism [7]. This study has signiﬁcantly evident the effect of this situation towards biomechanical behaviour of the joint. The absence of the articular cartilage resulted in unphysiological changes to the contact pressures within bones and compressive stress within the cartilages layers, which were addressed in this study and further supported by work done by Carrigan et al. [19]. Ten times higher contact pressure in 5.3 Biomechanical Behaviours of the Rheumatic Wrist Joint 53

Fig. 5.12 Histogram of average EQV stress in each bone of the Healthy and RA model the RA model as compared to the healthy (Fig. 5.13) has vitally conveyed the significance of having cartilage at the articulation areas. The nature of the cartilage—hyper-elastic and frictionless—makes it imperative in preventing high stress concentration at the underlying bones. Additionally, the generation of the high contact pressure was also attributed to the existence of the sharp edges due to bone erosion, as clearly evident in the RA model (Fig. 5.14b). In contrast, the healthy model with smoother bone surfaces (Fig. 5.14a) showed a well distribution of stress. Potential eventual deformity of the ligaments of the rheumatic wrist was attributed to the inflammation of the synovial fluid. The ligaments were stretched and torn, indicating ligaments laxity [2]. This condition distorts the constraint initially provided by the ligaments and led to the random translation, dislocation, and rotation of the affected bones. As prescribed in this study, the dislocation of carpus towards ulnar were found to cause biomechanical alteration to the wrist joint. It was evident that the load was transmitted more through the ulnar side of the RA model (42 %) as compared to the healthy model (37 %) (Fig. 5.15). The change in the load direction was also due to the hand scoliosis condition, in which the radially rotated metacarpals caused the direction of the stresses to concentrate ulnarly. This is the result of having the highest stress at the first metacarpal located at the lateral side of the wrist joint, which pushed the bones towards ulnar direction. Stage 2 of scapholunate advance collapse (SLAC) with scapholunate dissociation (SLD) may even be the additional causes of the altered loading direction (Fig. 5.16). As the distance between the scaphoid and lunate has increased due to SLD, it was addressed that the load was dominantly subjected to the lunate. The simulated collapse had clearly illustrated that the capitolunate joint was unable to 54 5 Finite Element Analysis

Fig. 5.13 The average contact pressure in each bone of the healthy and RA model

Fig. 5.14 Stress distribution in the forearm (the radius and ulna) for the healthy (a) and RA model (b). Two critical articulations were identiﬁed; radioscaphoid and radiolunate. It was also observed that existence of sharp edges at the RA model resulted in high stress concentration 5.3 Biomechanical Behaviours of the Rheumatic Wrist Joint 55

Fig. 5.15 Von Mises stress distribution for the palmar aspect of the healthy and the RA models

physiologically sustain the applied load, thus resulted in high stress concentration at this destructed articulation. It was noteworthy to highlight that the SLAC and SLD in rheumatic wrist were also led to high contact pressure found at the radiocarpal articulation with a maximum pressure of 116 MPa at the radiolunate joint. In comparison with the healthy 56 5 Finite Element Analysis

Fig. 5.16 The dorsal view of the load distribution at the capitolunate and capitoscaphoid articulations

Fig. 5.17 The transverse view of the contact pressure plot at the radiocarpal joint model, a very less pressure was generated with a maximum pressure of 21 MPa found at the radioscaphoid joint (Fig. 5.17). Structure based argument was made, whereby the scaphoid is naturally at risk as its articulation was found to have elliptical shape. Therefore, axial rotation of the scaphoid as the diseases progresses has significantly generating high contact pressure at the articulation due to reduction of the contacted area subjected with loads [5]. All findings presented and discussed in this chapter have brought to a conclusion, which was biomechanical alteration of the healthy joint has significantly occurred in the rheumatic wrist joint. We believed that the outcomes presented here could notably provide insights to better understand the disease, and thus come with much more encouraging treatments for future benefits.

References

1. Cush JJ, Lipsky PE (1991) Cellular basis for rheumatoid inﬂammation. Clin Orthop Relat Res 265:9–22 2. Trieb K, Hofstätter S (2009) Rheumatoid arthritis of the wrist. Tech Orthop 24(1):8–12 References 57

3. Trieb K, Hofstätter S (2009) Treatment strategies in surgery for rheumatoid arthritis. Eur J Radiology 71(2):204–210 4. Youm Y, Flatt AE (1980) Kinematics of the wrist. Clin Orthop Relat Res 149:21–32 5. Mastella DJ, Ashmead DI, Watson HK (2009) Scapholunate advanced collapse wrist arthritis. Tech Orthop 24(1):13–18 6. Ertel AN, Millender LH, Nalebuff E, McKay D, Leslie B (1988) Flexor tendon ruptures in patients with rheumatoid arthritis. J Hand Surg 13(6):860–866 7. Simmen BR, Kolling C, Herren DB (2007) The management of the rheumatoid wrist. Curr Orthop 21(5):344–357 8. McKee A, Burge P (2010) The principles of surgery in the rheumatoid hand and wrist. Orthop Trauma 24(3):171–180 9. Polikeit A, Nolte LP, Ferguson SJSJ (2004) Simulated influence of osteoporosis and disc degeneration on the load transfer in a lumbar functional spinal unit. J Biomech 37(7):1061–1069 10. Andresen R, Haidekker MA, Radmer S, Banzer D (1999) CT determination of bone mineral density and structural investigations on the axial skeleton for estimating the osteoporosis- related fracture risk by means of a risk score. British J Radiol 72(858):569–578 11. Homminga J, Weinans H, Gowin W, Felsenberg D, Huiskes R (2001) Osteoporosis changes the amount of vertebral trabecular bone at risk of fracture but not the vertebral load distribution. Spine 26(14):1555–1561 12. Schaffler MB, Burr DB (1988) Stiffness of compact bone: effects of porosity and density. J Biomech 21(1):13–16 13. Augat P, Link T, Lang TF, Lin JC, Majumdar S, Genant HK (1998) Anisotropy of the elastic modulus of trabecular bone specimens from different anatomical locations. Med Eng Phys 20(2):124–131 14. Lang T, Augat P, Majumdar S, Ouyang X, Genant HK (1998) Noninvasive assessment of bone density and structure using computed tomography and magnetic resonance. Bone 22 (5, Suppl 1):149S–153S 15. Rice JC, Cowin SC, Bowman JA (1988) On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 21(2):155–168 16. Gerard J, Tortora BD (2009) Principles of anatomy and physiology, 12th edn. Wiley, USA 17. Ulrich D, van Rietbergen B, Laib A, Rüegsegger P (1999) Load transfer analysis of the distal radius from in vivo high-resolution CT-imaging. J Biomech 32(8):821–828 18. Gislason MK, Nash DH, Nicol A, Kanellopoulos A, Bransby-Zachary M, Hems T, Condon B, Stansfield B (2009) A three-dimensional finite element model of maximal grip loading in the human wrist. Proc Inst Mech Eng Part H J Eng Med 223(7):849–861 19. Carrigan SD, Whiteside RA, Pichora DR, Small CF (2003) Development of a three- dimensional finite element model for carpal load transmission in a static neutral posture. Ann Biomed Eng 31(6):718–725 20. Gislason MK, Stansfield B, Nash DH (2010) Finite element model creation and stability considerations of complex biological articulation: the human wrist joint. Med Eng Phys 32(5):523–531 21. Wright V, Dowson D (1976) Lubrication and cartilage. J Anat 121(Pt 1):107–118 22. Kauer JMG (1986) The mechanism of the carpal joint. Clin Orthop Relat Res 202:16–26 23. Viegas SF, Patterson RM, Todd PD, McCarty P (1993) Load mechanics of the midcarpal joint. J Hand Surg 18(1):14–18 24. Alkan I, Sertgöz A, Ekici B (2004) Influence of occlusal forces on stress distribution in preloaded dental implant screws. J Prosthet Dent 91(4):319–325 25. Bajuri MN, Kadir MRA, Raman MM, Kamarul T (2012) Mechanical and functional assessment of the wrist affected by rheumatoid arthritis: a finite element analysis. Med Eng Phys (in press) 26. Rho J-Y, Tsui TY, Pharr GM (1997) Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 18(20):1325–1330 58 5 Finite Element Analysis

27. Brown CP, Nguyen TC, Moody HR, Crawford RW, Oloyede A (2009) Assessment of common hyperelastic constitutive equations for describing normal and osteoarthritic articular cartilage. Proc Inst Mech Eng Part H J Eng Med 223(6):643–652 28. Li Z, Kim J-E, Davidson JS, Etheridge BS, Alonso JE, Eberhardt AW (2007) Biomechanical response of the pubic symphysis in lateral pelvic impacts: a finite element study. J Biomech 40(12):2758–2766 29. Patterson RM, Viegas SF, Elder K, Buford WL (1995) Quantification of anatomic, geometric, and load transfer characteristics of the wrist joint. Semin Arthroplast 6(1):13–19 30. Macleod NA, Nash DH, Stansfield BW, Bransby-Zachary M, Hems T (2007) Cadaveric analysis of the wrist and forearm load distribution for finite element validation. In: In sixth international hand and wrist biomechanics symposium, Tainan, Taiwan, Republic of China, 29–30 June 2007, p 11 31. Givissis PK, Antonarakos P, Vafiades VE, Christodoulou AG (2009) Management of posttraumatic arthritis of the wrist with radiolunate fusion enhanced with a sliding autograft: a case report and description of a novel technique. Techniques in Hand & Upper Extremity Surgery 13(2):90–93 32. Bosisio MR, Talmant M, Skalli W, Laugier P, Mitton D (2007) Apparent Young’s modulus of human radius using inverse finite-element method. J Biomech 40(9):2022–2028 33. Kerin AJ, Wisnom MR, Adams MA (1998) The compressive strength of articular cartilage. Proc Inst Mech Eng Part H J Eng Med 212(4):273–280 34. McMaster PE (1937) Bone atrophy and absorption: experimental observations. J Bone Joint Sur 19(1):74–83 Chapter 6 Finite Element Analysis of the Wrist Arthroplasty in Rheumatoid Arthritis

Abstract This chapter presents information on finite element analyses (FEA) of stress distribution and contact pressure with the carpal articulation following total wrist arthroplasty (TWA) for rheumatoid arthritis (RA) of the wrist. Results from the previous analyses on the healthy and rheumatic wrist were used for comparison. A TWA model was developed based on parameters of a wrist implant named ReMotionTM total wrist system, and was then applied with the same boundary condition (static hand grip action) as the other two models. FEA has revealed that the contact pressure for the TWA model was five times lower than the RA model. Despite this encouraging finding, small variations in the amount of stress distribution were still present when compared to the healthy model. This comes to a conclusion that the used of TWA could reduces the high contact pressure induced in the RA model thus improving the diseased condition, however, there are rooms for improvement for TWA procedure to restore the biomechanical behaviour of the healthy wrist joint.

Keywords Wrist joint Á Rheumatoid arthritis Á Total wrist arthroplasty Á Contact pressure Á Stress Á Finite element analysis

6.1 Total Wrist Arthroplasty

Total wrist arthroplasty (TWA) for a rheumatic wrist has been designed to preserve motion of the joint, thus found to be a superior alternative to wrist arthrodesis (bone fusion). Despite of this privilege, there were issues with regards to its success rates. Based on literature reports on clinical studies, it was addressed that this wrist replacement has higher failure rates as compared to hip and knee arthroplasty [1–7]. In total hip arthroplasty (THA) procedure where the affected areas at the femoral head and neck are dissected, it was reported as the most reliable arthroplasty to

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 59 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8_6, Ó Springer-Verlag Berlin Heidelberg 2013 60 6 Finite Element Analysis date [8]. Similarly, the total knee replacement (TKR) procedure possessed sub- stantially high success rates due to the existence of sufficient bony support to provide stability [9]. In total wrist arthroplasty (TWA) procedure, despite of resecting all the affected regions at the bones as observed in THA and TKR, the TWA requires several bones to be remained assuring sufficient bony support (Fig. 6.1). The existing bony support which consists of small bones of carpus; normally the distal row is likely to experience micromotion [10]. This explains why solid bony supports at the carpal regions of the joint become extremely problematic. Consequently, a study to investigate the behaviour of this motion is prudent, par- ticularly during pre (RA) and post surgery (after TWA). Therefore, this chapter was presented to highlight the efforts performed to investigate the biomechanical behaviours of the rheumatic wrist during pre and post surgery, using finite element analysis.

6.2 Finite Element Modelling of the Total Wrist Arthroplasty

In this simulation, the latest wrist joint replacement, ReMotionTM produced by Small Bone Innovations, was occupied [11]. CAD software, SolidworksÒ 2009 was used to model the implant, whereas MARC.MENTAT software used to convert the model into surface triangular elements. Similar to the real surgical procedure, the scaphoid, lunate and some parts of the capitate and triquetrum were resected, and followed by the installation of the implant component to their respective bones. All parts were then converted into solid tetrahedral mesh with 1,305,415 elements and 277,070 nodes. These steps are illustrated in Fig. 6.2.

6.3 Finite Element Analysis: Pre-Processing Procedures

For contact modelling, articulating surfaces were established with deformable-to- deformable contact. Surface roughness at the carpal plate component was set at 0.8 simulating its rough surface to support osseointegration [15]. The effect of screw thread in preventing any slippage at the contacting surfaces was simulated [16]. Physiological movements are allowed for the remaining contacting bodies. Bones of the wrist in the TWA were modelled as having the same properties as the RA model (the cortical bone; E = 12 GPa, m = 0.2 and the cancellous bone; E = 33 MPa, m = 0.25). They were modelled to incorporate linear elastic, isotropic and homogenous properties. Implant components (radius component, carpal plate, central peg and screws) were assigned with properties simulating CoCrMo alloys (E = 210 GPa, m = 0.3) [17], whereas the carpal ball was assigned with UHMWPE properties (E = 1.4 GPa, m = 0.3 [18]). The bone graft modulus was varied (E = 0.1, 1 and 5 GPa, m = 0.2 [19]) to analyse their effects in performing intercarpal fusion. These parameters are summarised in Table 6.1. 6.3 Finite Element Analysis: Pre-Processing Procedures 61

Fig. 6.1 The radiographic images of the healthy joint (left) and its replacement (right) for the hip (a), knee (b) and wrist joint (c). It was clearly depicted that for the total hip arthroplasty [12](a), the affected parts of femur including its head and neck are removed, whereas for total knee replacement [13] (b), only affected surfaces are removed. These two procedures have received great satisfaction from patients and surgeons. However, for total wrist arthroplasty [14](c), some affected bones are still remained. Even though bone grafts and screws are used to obtain bony support for stability, its effectives were still questionable 62 6 Finite Element Analysis

Fig. 6.2 Steps to construct the model of total wrist arthroplasty (TWA)

The load simulating static gripping force of the wrist calculated by Gislason et al. [20] was used. The magnitude of the resultant compression pressure was 7.33 MPa distributed over the ﬁve metacarpals, as shown in Table 6.2. All the applied loads and their distributions are presented in Fig. 6.3. 6.3 Finite Element Analysis: Pre-Processing Procedures 63

Table 6.1 Material properties of the reconstructed 3D models Materials Young’s modulus, E (MPa) Poisson ratio, m Cortical bone 12,000 0.20 Cancellous bone 33 0.25 Implant components (CoCrMo) 210,000 0.30 Carpal ball (UHMWPE) 1,400 0.30 Bone graft 100 0.20 1,000 5,000

Table 6.2 Relative loading on the metacarpal bones Thumb Index Long Ring Little Cross-sectional area (mm2) 126.30 77.00 84.15 57.60 80.20 Load (N) 255.60 120.30 106.40 88.00 77.30 Pressure (MPa) 2.02 1.56 1.26 1.53 0.96

Fig. 6.3 Applied boundary condition simulating static hand grip action 64 6 Finite Element Analysis

Fig. 6.4 Stress distribution contours for the healthy, RA and TWA model

The proximal ends of the radius and ulna were fully constrained to assist convergence of the solution [21]. Additional constraints were occupied by fixing the carpometacarpal joint and the insertions of tendons (abductor pollicis longus muscle, flexor carpi radialis muscle, flexor carpi ulnaris muscle, extensor carpi ulnaris muscle, extensor carpi radialis brevis muscle, extensor carpi radialis longus muscle). All the components (excluding the radius and the ulna) were only allowed to move at the z direction similar to the direction of the applied loading [22]. 6.4 Finite Element Analysis 65

Fig. 6.5 Average stress per element for the three different cases

Fig. 6.6 Average contact pressure for the three different cases

6.4 Finite Element Analysis

Comparison was made between the three cases: the healthy, the diseased (rheumatoid arthritis) and the wrist after treatment (TWA). Two parameters were used; stress and contact pressure. The efﬁciency of the TWA procedure was then evaluated based on the comparative analyses performed. 66 6 Finite Element Analysis

Fig. 6.7 Average stress (a) and contact pressure (b) for three different moduli of the bones graft

6.4.1 Mechanical Stress Distribution Within the Bones

The difference of stress distribution among the three cases was clearly evident in Fig. 6.4. A uniform load transmission was found at the carpal complex in the TWA model with small variations of stress magnitudes ranging from 1.08 to 1.63 MPa (Fig. 6.5). The corresponding bones in the RA model however showed high variation of stress magnitudes ranging from 1.87 to 3.97 MPa, thus indicating a non-uniform load transmission. In comparison with the healthy model, stress distribution in the TWA model showed no similarity. Among all the three models, the healthy model have the highest magnitude of stress per element (average 6.4 Finite Element Analysis 67

2.49 MPa), followed by the RA model (average 1.99 MPa) and the TWA model (average 1.29 MPa).

6.4.2 Mechanical Contact Pressure Within the Bones

Contact pressure within the bones has shown that the high magnitude found in the RA model (average 3.9 MPa) was reduced to almost ﬁve times lower after TWA (average 0.75 MPa). This advantage however was not restoring the pressure of the healthy model (average 0.4 MPa). It was also evident that the trapezium could be considered as the most critical bone as high magnitude of pressure was always found in this bone for all three simulated cases, with the highest pressure found at the RA model (11 MPa) (Fig. 6.6).

6.4.3 Biomechanical Analysis of Different Moduli of Bone Graft

It was observed that the modulus of the bone graft had significant impact on the stress distribution (Fig. 6.7a) and contact pressure (Fig. 6.7b), which were found significantly at the carpal complex. Increasing the bone graft modulus to 5 GPa resulted in efficient load transmission. High fluctuation pattern of graphs was found in the TWA model engaged with bone graft modulus of 0.1 GPa, indicating inconsistent stress and contact pressure magnitudes.

6.4.4 Biomechanical Assessment of the Total Wrist Arthroplasty Procedure

As far as treatment is concerned, it is vital to solve two main problems caused by RA as shown in the previous chapter; which were the effect of high contact pressure and imbalance load transmission. The ReMotionTM implant used in the TWA model anticipated two main design concepts—distal radius resurfacing and intercarpal fusion—to minimize motion that could cause metacarpal perforation and implant loosening. FEA results have confirmed the ability of this implant system to reduce high contact pressure in RA bones through intercarpal fusion approach. This implant system fused the affected bones using two screws, one central peg and bone grafts, thus has resulted in minimised stress concentration and therefore reduced the potential problem of wear at the articulation. In terms of load transmission, the disproportionate pattern of stress distributions observed in the RA model changed to a more uniform pattern after TWA (Fig. 6.5). This finding complied with the implant design concept of intercarpal fusion to 68 6 Finite Element Analysis attain solid bony mass and therefore uniform pattern of loading [23]. Better fusion could be achieved by using bone graft with a modulus close to the bone; our parametric analyses showed that bone graft with a modulus of 5 GPa produced more encouraging results in terms of uniform load transmission and lower contact pressure (Fig. 6.7). This is in agreement with the concept of avoiding elasticity mismatch [24] to prevent unphysiological loading and unwarranted bone remod- elling. In clinical practice, there were various sources of bone grafts with different modulus ranging from 0.1 (iliac crest) to 5 GPa (fibula) [19]. This chapter has presented several findings that reaffirmed the good clinical outcome of a specific implant system for TWA as confirmed in a short term follow-up study reported by Herzberg [25]. We have provided further insights into the biomechanical aspects of rheumatic wrist and the corresponding changes after TWA. As long term follow-up study is still required, this study strongly recom- mends the use of TWA as a viable alternative to total wrist fusion in patients with rheumatoid arthritis especially in case of bilateral involvement [26].

References

1. Bajuri MN, Kadir MRA, Raman MM, Kamarul T (2012) Mechanical and functional assessment of the wrist affected by rheumatoid arthritis: a finite element analysis. Med Eng Phys (in press) 2. MacCullough MBA (2006) Clinical and biomechanical analysis of total wrist arthroplasty devices. Dissertation, University of Iowa, Iowa 3. Bajuri MN, Kadir MRA (2010) Biocomputational comparative study of Rheumatoid Arthritis of the wrist joint before and after arthroplasty; carpal stability analysis. In: Biomedical Engineering and Sciences (IECBES), 2010 IEEE EMBS conference on 30 Novemb 2010–2 Dec 2010, pp 270–275 4. Lorei MP, Figgie MP, Ranawat CS, Inglis AE (1997) Failed total wrist arthroplasty. Analysis of failures and results of operative management. Clin Orthop Relat Res 342:84–93 5. Huang KM, Naidu SH (2002) Total wrist arthroplasty: is there a role? Curr Opin Orthop 13(4):260–268 6. Adams BD (2010) Complications of wrist arthroplasty. Hand Clin 26(2):213–220 7. Anderson MC, Adams BD (2005) Total wrist arthroplasty. Hand Clin 21(4):621–630 8. Abdul-Kadir MR, Hansen U, Klabunde R, Lucas D, Amis A (2008) Finite element modelling of primary hip stem stability: the effect of interference fit. J Biomech 41(3):587–594 9. Dewan A, Bertolusso R, Karastinos A, Conditt M, Noble PC, Parsley BS (2009) Implant durability and knee function after total knee arthroplasty in the morbidly obese patient. J Arthroplast 24 (6, Suppl 1):89–94, e83 10. Menon J (1998) Universal total wrist implant: experience with a carpal component fixed with three screws. J Arthroplast 13(5):515–523 11. Innovations SB (2009) Surgical technique, ReMotionTM Total Wrist Implant System. Small Bone Innovations, New York 12. Mont MA, Seyler TM, Ragland PS, Starr R, Erhart J, Bhave A (2007) Gait analysis of patients with resurfacing hip arthroplasty compared with hip osteoarthritis and standard total hip arthroplasty. J Arthroplast 22(1):100–108 13. Rahman WA, Garbuz DS, Masri BA (2010) Randomized controlled trial of radiographic and patient-assessed outcomes following fixed versus rotating platform total knee arthroplasty. J Arthroplast 25(8):1201–1208 References 69

14. Adams BD (2006) Total wrist arthroplasty for rheumatoid arthritis. Int Congr Ser 1295:83–93 15. Tajdari M, Javadi M (2006) A new experimental procedure of evaluating the friction coefficient in elastic and plastic regions. J Mater Process Technol 177(1–3):247–250 16. Cheng H-YK, Lin C-L, Lin Y-H, Chen AC-Y (2007) Biomechanical evaluation of the modified double-plating fixation for the distal radius fracture. Clin Biomech 22(5):510–517 17. Sun D, Wharton JA, Wood RJK (2009) Micro-abrasion-corrosion of cast CoCrMo—effects of micron and sub-micron sized abrasives. Wear 267(1–4):52–60 18. Dowson D, Fisher J, Jin ZM, Auger DD, Jobbins B (1991) Design considerations for cushion form bearings in artificial hip joints. ARCHIVE: Proc Inst Mech Eng Part H J Eng Med 1989–1996 203–210, 205(28):59–68 19. Zander T, Rohlmann A, Klöckner C, Bergmann G (2002) Effect of bone graft characteristics on the mechanical behavior of the lumbar spine. J Biomech 35(4):491–497 20. Gislason MK, Nash DH, Nicol A, Kanellopoulos A, Bransby-Zachary M, Hems T, Condon B, Stansfield B (2009) A three-dimensional finite element model of maximal grip loading in the human wrist. Proc Inst Mech Eng Part H J Eng Med 223(7):849–861 21. Gislason MK, Stansfield B, Nash DH (2010) Finite element model creation and stability considerations of complex biological articulation: the human wrist joint. Med Eng Phys 32(5):523–531 22. Carrigan SD, Whiteside RA, Pichora DR, Small CF (2003) Development of a three- dimensional finite element model for carpal load transmission in a static neutral posture. Ann Biomed Eng 31(6):718–725 23. Gupta A (2008) Total wrist athroplasty. J Orthop Res 37:12–16 24. Murali P, Bhandakkar TK, Cheah WL, Jhon MH, Gao H, Ahluwalia R (2011) Role of modulus mismatch on crack propagation and toughness enhancement in bioinspired composites. Phys Rev E 84(1):015102 25. Herzberg G (2011) Prospective study of a new total wrist arthroplasty: short term results. Chirurgie de la Main 30(1):20–25 26. Trieb K, Hofstätter S (2009) Treatment strategies in surgery for rheumatoid arthritis. Eur J Radiol 71(2):204–210 Summary

This monograph has sufficiently presented outcomes from finite element analyses of the simulated healthy, diseased and treated wrist joint, and they could be summarised as follows: 1. The absence of the cartilage, the abnormal dislocations of bones with sharp edges and the laxity of the ligaments in the rheumatic wrist have resulted in significant unphysiological alteration of the biomechanical behaviours of the wrist joint, as shown and elucidated in this monograph. TWA was then proving to provide improvement in reducing contact pressure and assuring balance load transmission. However, there were rooms for enhancements as the ultimate goal to restore the function of the healthy wrist still not absolutely achieved. 2. Efforts in simulating the complex wrist joint experienced various difficulties and it was even pronounced when dealing with the pathological conditions and its treatments. Therefore, the finite element model development and analyses mentioned here were performed under certain level of uncertainty and assumptions. Quantification was found to be very challenging as the available information is fairly limited. For the RA model construction, for instance, there was only one out of 10 characteristics has been quantified which was the carpometacarpal ratio. The remaining characteristics were simulated by making relevance assumptions according to clinical reports. 3. Technical aspects of the model development need to be further explored. Issues on linearity (linear or non-linear) of the simulated ligaments, material properties (isotropic, othotropic etc.) order of elements element type (tetrahedral– hexahedrals), contact modeling and also effect of sharp gradient between two material properties, require further explorations.

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 71 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8, Ó Springer-Verlag Berlin Heidelberg 2013 Index

A F Arthrodesis, 30 Fatigue, 18 Arthroplasty, 59, 60, 67 Force, 4, 14–16, 20, 49, 62 Atrophy, 52 Forearm, 1, 9, 11, 19, 33, 50

B H Bone graft, 60, 63, 67, 68 Hamate, 1–3, 5, 11, 37, 38, 49 Hip, 8, 19, 59

C Cancellous, 33, 35, 42, 49, I 52, 60, 63 Impaction, 29, 59 Capitate, 1, 2, 5, 8, 9, 14, 37, 45, 60 Carpal, 1–5, 8–10, 15, 16, 19, 20, 29, 42–45, 47, 60, 63, 66, 67 K Carpometacarpal, 2, 43, 49, 64, 71 Kienbock’s, 19 Carpus, 1, 2, 5, 29, 43, 53, 60 Knee, 8, 14, 16, 19, 59, 60 Cartilage, 4, 14, 21, 28, 38, 42 Contact pressure, 52–56, 65, 67 Cortical, 33, 35, 42, 49, 50, 60, 63 L Ligament, 2, 3, 5, 7, 8, 11, 15, 20, 29 Linear, 15, 20, 36, 39, 49, 60 D Load transmission, 13, 20, 66–68 Distal, 1, 2, 5, 6, 8, 9, 19, 33, 43, 45 Lunate, 1, 2, 19, 29, 45, 47, 60

E M Elastic modulus, 49 Metacarpal, 1–3, 5, 9, 17, 25, 30, 31, 33, 43, Erosion, 28, 29, 42, 47, 53 46, 49, 53, 62, 64, 67

M. Nazri Bajuri and M. R. Abdul Kadir, Computational Biomechanics of the Wrist Joint, 73 SpringerBriefs in Computational Mechanics, DOI: 10.1007/978-3-642-31906-8, Ó Springer-Verlag Berlin Heidelberg 2013 74 Index

M (cont.) S Micromotion, 21, 60 Scaphoid, 29, 42, 43, 45, 46, 50, 56 Muscle, 1, 3, 7, 50, 64 Scapholunar dissociation, 42, 45 Scapholunate advanced collapse, 29, 42 Scoliosis, 30, 42, 46, 53 P Segmentation, 33, 34 Pisiform, 1–3, 5, 38 Spring, 17, 20, 21 Proximal, 2, 3, 8, 10, 33, 42, 43, 46 Subchondral, 4, 6, 14, 26, 28

R T Radiocarpal, 2, 3, 8, 14, 17, 19, 26, 29, 50, 55 Tendon, 1, 3, 5, 18–30, 42, 46, 50, 64 Radioscaphoid, 14, 17, 56 Tetrahedral, 18, 36, 60 Radius, 2, 5, 9, 14, 20, 33, 36, 43, 46, 49, 50, Toe Region, 15 64 Trapezium, 1, 2, 5, 6, 20, 37, 38, 49, 67 Rheumatoid arthritis, 26, 41, 68 Trapezoid, 1, 2, 5, 6, 20, 37, 38, 49 Rigid body spring, 17, 21 Triquetrum, 1–3, 5, 10, 37, 38, 43, 45, 60