1. Establishment of the three-dimensional (3D) model
1.1 Establishment of the talar 3D model
A healthy male volunteer was selected who was 37 years old and had a height of 170 cm and a body weight of 65 kg; foot tumour, deformation and other lesions were excluded. The left foot and ankle scan was obtained from a cone-beam CT (CBCT) scan using a PedCAT scanner (Curvebeam, USA), and the 3D reconstruction of different parts was completed with Mimics software. Triangular mesh models of the talus were reconstructed using a visualization software package (Mimics 19.0 Materialise, Leuven, Belgium). A triangular meshed model was imported into reverse engineering software (Geomagic studio 10.0, Geomagic, Research Triangle Park, NC), and the triangle mesh surface was translated into the NURBS surface. Then, a solid model of the left talus was obtained, as shown in Fig. 1.
1.2 Establishment of 3D model of custom-made talar component
The talar 3D model was imported into Pro/Engineer software. The custom-made talar component for TAR was designed based on the talar 3D model. In reference to the design of the central peg of the talar component of the Salto Talaris total ankle prosthesis, two pins were designed in the posterior body of the prosthesis. The two pins were arranged in an isosceles triangle with the central peg.
2. Experimental Grouping and FEA
2.1 3D modelling and designing
Referring to the osteotomy concept of the TAR prosthesis and whether to perform osteotomy on the lateral articular facet of the talus, two kinds of custom-made talar components were used for the TAR implants: a 2-surface contact type (Type-1), as shown in Fig. 2, and a 3-surface contact type (Type-2), as shown in Fig. 3. At the same time, two kinds of talus models after osteotomy matched the 2-surface prosthesis (Fig. 4A) and the 3-surface prosthesis (Fig. 4B).
2.2 Model assembly
Taking Type-1 as an example, the details of the prosthesis and bone installation are shown in Fig. 5. With 3D CAD software (SolidWorks), the front contact surface and the back contact surface of the talus were assembled with the corresponding parts of the prosthesis, as shown in Fig. 6. The method used to set a Type-2 assembly was similar.
Taking the 3-surface prosthesis and talus as an example, the 2-surface types were similar (Fig. 7 and Fig. 8). The assembled solid model was imported into HyperMesh 14.0, and the mesh cell size was set at the edge of the contact area as the front contact surface (Area A) divided by the mesh unit size of 0.1; the main contact area was set as the back contact surface (Area B) divided by the mesh unit size of 0.6; the non-contact area was set as the lateral contact surface (Area C) divided by the mesh unit size of 1.0. The mesh information of the two modelling groups is shown in Table 1 and Table 2. The mesh assembly of the models was obtained as shown in Fig. 9.
2.4 Material properties and Interactions
HyperMesh 14.0 was used to import the mesh model into the finite element software Abaqus 6.13(Hibbitt, Karlsson & Sorenson, Inc., Providence, RI, USA); the properties were set to be isotropic, and Young's modulus and Poisson's ratio are shown in Table 3. Each contact surface was set as normal hard contact with no friction and tangential contact with friction. To ensure the static balance of loads, the friction coefficient of this model was set to 0.5. According to the requirements of the surgical installation, the main fixed connection parts (cylinder and pins) were set as TIE constraints. Then, there were two pairs of contacts and three TIE pairs for a 2-surface model and three pairs of contacts and three TIE pairs for a 3-surface model.
2.5 Boundary conditions and load
Fixing the lower surface of the talus means locking 3 translational degrees of freedom and 3 rotational degrees of freedom. According to the extended position of the contact force of the talus and tibia, this position is set as the application position of the contact resultant force point (Fig. 10), i.e., the reference point (RP). Then, the coupling method is used to constrain the reference point RP to the upper surface of the CoCrMo prosthesis. The contact force of the ankle joint in the main direction (axial), anterior-posterior direction, and medial-lateral direction under a complete gait was shown. The typical load time point, i.e., contact forces of 0.48 and 0.5, were selected on the transverse axis as the load (Fig. 11). Based on a body weight of 65 kg, the corresponding Newtonian force is obtained. Typical contact forces in the three directions are shown in Table 4 (Unit: BW, bodyweight) and Table 5 (Unit: N). The material of the prosthesis is calculated with an elastic modulus of 220 GPa under two types and two loads.