Finite Element Modelling of the Healthy Wrist Joint



Fig. 4.1
Steps performed to construct finite element model of the healthy wrist



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).

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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)



4.2 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].

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


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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)


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, 710]. For ligaments that did not have published material parameters, it was assumed that the properties of the neighbouring ligaments would apply [11]. To simulate distribution of the origin and insertion of the ligaments, parallel multiple links were applied [4, 11].

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



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

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Sep 26, 2016 | Posted by in ORTHOPEDIC | Comments Off on Finite Element Modelling of the Healthy Wrist Joint

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