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One of the most common skeletal diseases associated with the wrist joint is rheumatoid arthritis (RA). The pathological process of RA begins with synovial inflammation mainly on the ulnar side of the wrist.

Anatomy of the Wrist Joint

Another tendon with the same function, the extensor carpi radialis longus, also inserts on the proximal end at the dorsal surface of the second metacarpal bone. The insertion is found at the palm of the base of the second metacarpal.

Bone Structure

The movement of the radial deviation is carried out by the extensor carpi radialis brevis, which inserts at the proximal end on the dorsal surface of the third metacarpal bone. There are three insertion points for the flexor carpi ulnaris tendon, one of which is on the pisiform.

Cartilage Structure

The medial part, on the other hand, articulates with the triquetrum through its square surface. Head The largest carpus, namely the head piece which lies in the middle of the wrist, has a convex surface of its proximal part which is articulated with the lunate.

Table 1.1 Description on the different structures of the eight carpal bones

Ligament Structure

Significantly, previous studies have shown variability in the dimensions and structures of the ligaments in the wrist joint. In a study of 90 cadaveric wrists, it was shown that the ligaments appear to have a wide range in size [22].

Kinematics

Abstract Previous experimental and computational studies have described several properties and behaviors of the wrist joint. Subsequent sections present information on the biomechanical properties of cartilage and ligamentous structure.

Contact Surfaces and Load Transmission

In conjunction with the load transfer to the radius in the neutral position, 60 % of the load was transferred through the scaphoid [3]. It was also found that 20-40% of the available articulations were occupied during physiological loading condition [3].

Biomechanical Consideration of the Cartilage Structure

It was also found that compressive forces in the radius were mainly transferred through the scaphoid and lunate. The stress at the mid-carpal joint was found to be well distributed, 20% through the hamotriquetral joint, 29% through the capitolun joint, 28% through the scaphocapitate joint, and the remaining 23% through the scaphotrapeziumtrapezoid joint.

Biomechanical Consideration of the Ligamentous Structure

It was also discovered that in the neutral position of the wrist, some of the ligaments were actually in tension [19]. Overall, previous studies have progressively investigated the behavior and properties of the ligaments associated with the wrist.

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

Current Trends in Biomechanical Modelling

Rigid Body Spring Method

Finite Element Method

Additionally, solution convergence has been addressed as another major concern in the finite element analysis of the wrist joint in relation to the robustness of the constructed FE models. 52] who partially analyzed the behavior of the wrist joint by investigating the fracture of the distal radius. Regarding three-dimensional finite element studies on the pathological condition of the wrist, only a small number of papers were found.

Cartilage affects the kinematics of the wrist joint due to its function of intermediate load transfer between bones. Peña E, Calvo B, Martínez MA, Doblaré M (2006) Three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint.

Pathology

Scapholunate advanced collapse (SLAC) and destruction of the capitolunate articulation were among them. In terms of treatment, the most problematic option is wrist arthroplasty attributed to implant loosening and metacarpal perforation, despite its advantage in preserving joint motion. However, as technology advances, arthroplasty implant designs are found to be better and better, promising a more reliable treatment for the rheumatic wrist.

24% of the dissected specimens were found to have chondromalacia, which was found to have softening and fibrillation disorders associated with articular cartilage. For example, restricted movements due to bone fusions in arthrodesis resulted in less patient independence.

Rheumatoid Arthritis

For example, a patient with RA in the wrist has the same symptoms in the fingers of the same hand. There are three main features of the wrist affected by RA: cartilage destruction, synovial proliferation, and ligament laxity [10, 17]. The pathological process begins with synovial inflammation, which usually affects the ulnar side of the wrist joint [10,12].

This was clearly evident as loss of tension of the radiotriquetral ligament caused dislocation of the carpal in the ulnar direction. Another pathophysiological feature is the dislocation of the proximal carpal row in the ulnar and palmar directions.

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]

Treatment

This occurred due to a ruptured tendon, which resulted in an altered axis of the wrist relative to the ulna, and rotation of the metacarpal in a radial direction. As with other joints, some parts of the affected joint must be removed to place the implant. Cavaliere CM, Chung KC (2008) A systematic review of total wrist arthroplasty compared with total wrist arthrodesis for rheumatoid arthritis.

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.

Fig. 3.5 ReMotion (Small Bone Innovations, Morrisville, PA) used in this arthroplasty as a treatment for severe wrist affected by rheumatoid arthritis [25]

Bone Model Reconstruction

The articular cartilage was modeled by extruding the articulating surfaces with a thickness equal to half the minimum distance between the two bones. Semi-automatic segmentation was performed using Mimics software (Materialise, Fig. 4.1 Steps performed to construct the finite element model of the healthy wrist. An average element size of 0.4 mm was chosen resulting in an accurate description geometric of the geometry of the bone.

The ratio between twice the radius of the inscribed circle and the radius of the inscribed circle of the triangle was used as a normalized indicator to determine the quality of the mesh (Figure 4.2a) [3]. Quality assessment of the model based on the surface element confirming its reliability, where the ratio of twice the radius of the inscribed circle to the radius of the inscribed circle of the triangle was greater than 0.80 for 90% of the elements (where the unit represents an equilateral triangle (Figure 4.2b).

Fig. 4.2 The R-in/R-out as the quality parameter used to determine the quality of mesh (a).

Modelling of Cartilages

Modelling of Ligaments

Coburn JC, Upal MA, Crisco JJ (2007) Coordination systems for the carpals of the wrist. Bettinger PC, Smutz WP, Linscheid RL, Cooney WP, An KN (2000) Material properties of the trapezoid and trapeziometacarpal ligaments. Savelberg HH, Kooloos JG, Huiskes R, Kauer JM (1992) Stiffness of the ligaments of the human wrist joint.

Abstract This chapter presents information on the biomechanical analysis of the rheumatic wrist using the finite element method. This study was designed to better understand the biomechanical behavior of the diseased wrist, thereby providing better treatments in the future.

Finite Element Model Construction of the Rheumatic Wrist

• Simulation of Cartilage Destruction
• Simulation of Loss of Carpal Height
• Simulation of Dislocation of the Carpus
• Simulation of Dislocation of the Proximal Carpal Row
• Simulation of Scapholunate Dissociation
• Simulation of Dislocation of the Scaphoid
• Simulation of Hand Scoliosis
• Simulation of Reduction of Contact Between the Lunate
• Simulation of Bone Erosion

Dislocation of scaphoid in palmar direction due to radial insertion of Testut ligament synovialitis [2]. Dislocation of the proximal carpal row in the palm occurred physiologically as during ulnar deviation (either due to physiological movements or as a result of disease), the scaphoid, lunate and triquetrum rotate the palm [16]. Again, synovitis leads to dislocation of the triquetrum and lunate towards the distal ulnar.

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 a so-called Mannerfelt crypt [2]. It was due to the dislocation of the proximal row or the carpal bones towards the ulnar.

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

Finite Element Analysis: Pre-Processing Procedures

However, this free movement of the bones should be relatively limited to achieve convergence, and separation of the bones once contact has been made must be avoided [18]. The geometric shape of the carpo-metacarpal joint also plays a role in joint stability, with the second and third metacarpals being relatively stiffer than the fourth and fifth metacarpals [16]. For the RA model, the friction coefficient of 0.3 was used due to the relatively rough surface of the contacted bones [24].

The cartilage in the healthy model acquired hyperelastic material properties due to its large deformation behavior [27]. To facilitate solution convergence, the proximal ends of the radius and ulna are completely clamped [20].

Biomechanical Behaviours of the Rheumatic Wrist Joint

Comparative Analysis

The Biomechanical Effect of Symptoms

Moreover, the occurrence of the high contact pressure was also attributed to the existence of sharp edges due to bone erosion, as clearly shown by the RA model (Fig. 5.14b). Possible eventual deformity of the ligaments of the arthritic wrist was attributed to the inflammation of the synovial fluid. Bajuri MN, Kadir MRA, Raman MM, Kamarul T (2012) Mechanical and functional assessment of the wrist affected by rheumatoid arthritis: a finite element analysis.

Patterson RM, Viegas SF, Elder K, Buford WL (1995) Quantification of anatomical, geometric, and load transfer characteristics of the wrist joint. Summary This chapter presents information on finite element analyzes (FEA) of stress distribution and contact pressure with the carpal articulation after total wrist arthroplasty (TWA) for rheumatoid arthritis (RA) of the wrist.

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

Total Wrist Arthroplasty

The results of preliminary analyzes on the healthy and rheumatic wrist were used for comparison. Despite this encouraging finding, there were still small differences in the amount of stress distribution compared to the healthy model. We conclude that the use of TWA could reduce the high contact pressure induced in the RA model, thus ameliorating the disease state, but there are opportunities for improvements in the TWA procedure to restore the biomechanical behavior of the healthy wrist joint.

This explains why rigid bony supports in the carpal areas of the joint become extremely problematic. Therefore, this chapter was presented to highlight the efforts made to investigate the biomechanical behavior of the arthritic wrist during pre- and post-operation, using finite element analysis.

Finite Element Modelling of the Total Wrist Arthroplasty

In a total wrist arthroplasty (TWA) procedure, despite the resection of all affected areas near the bones, as observed in THA and TKR, the TWA requires preservation of several bones to ensure adequate bone support (Fig. 6.1). Therefore, an investigation into the behavior of this movement is prudent, especially during pre- (RA) and post-operations (after TWA).

Finite Element Analysis: Pre-Processing Procedures

Similarly, the total knee replacement (TKR) procedure possessed significant success rates due to the existence of sufficient bony support to provide stability [9]. Although bone grafts and screws are used to obtain bone support for stability, its effectiveness was still questionable. The resultant compressive stress magnitude was 7.33 MPa distributed over the five metacarpals, as shown in Table 6.2.

The proximal ends of the radius and ulna were completely constricted to aid in convergence of the solution [21]. All the components (except the radius and ulna) were only allowed to move in the z-direction corresponding to the direction of the applied load [22].

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)

Finite Element Analysis

• Mechanical Stress Distribution Within the Bones
• Mechanical Contact Pressure Within the Bones
• Biomechanical Analysis of Different Moduli
• Biomechanical Assessment of the Total Wrist

It was found that the modulus of the bone graft had a significant effect on stress distribution (Figure 6.7a) and contact pressure (Figure 6.7b), which were found to be significant in the carpal complex. Bajuri MN, Kadir MRA (2010) A biocomputational comparative study of pre- and post-arthroplasty wrist rheumatoid arthritis; carpal stability analysis. Zander T, Rohlmann A, Klöckner C, Bergmann G (2002) Influence of bone graft characteristics on the mechanical behavior of the lumbar spine.

Abdul Kadir, Computational biomechanics of the wrist joint, SpringerBriefs in Computational Mechanics, DOI ÓSpringer-Verlag Berlin Heidelberg 2013. Abdul Kadir, Computational biomechanics of the wrist joint, SpringerBriefs in Computational Mechanics, DOI ÓSpringer-Verlag Berlin Heidelberg 2013.