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 con- structed 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
Finite element model Simulation of the ligamentSimulation of the cartilage
Conversion from 2D images to 3D modelwith 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, Fig. 4.1 Steps performed to construct finite element model of the healthy wrist
34 4 Finite Element Modelling of the Healthy Wrist Joint
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 tri- angular 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.
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)
4.1 Bone Model Reconstruction 35
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).
Fig. 4.3 Steps performed to construct finite element model of the cartilage
36 4 Finite Element Modelling of the Healthy Wrist Joint
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)
4.1 Bone Model Reconstruction 37
Table 4.1 (continued)
Ligament Connection 1 Connection 2 Stiffness
specified (N/mm)
Dorsal intercarpal Trapezoid Trapezium 110 [5]
Dorsal intercarpal Trapezium and trapezoid
Triquetrum 128 [5]
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 Carpometacarpal
Trapezium 1MC lateral 100 [12]
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 (Testut)
Radius Scaphoid?lunate 50,75
Volar Radioulnar Radius Ulnar 50 [12]
38 4 Finite Element Modelling of the Healthy Wrist Joint