Finite Element Analysis of the Wrist Joint Affected by Rheumatoid Arthritis - Computational Biomechanics of the Wrist Joint - page 49

Table 5.2 Information on the difference between the healthy and RA wrist after simulated bone

erosion
No. Healthy (mm 3 ) RA (mm 3 ) Bone 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 carpo-
metacarpal 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 repre-
senting 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 defor-
mation behaviour [ 27 ]. Mooney-Rivlin modelling was used to perform the hyper-
elastic 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