2.1 Geometric characteristics of the finite element model
A 24-year-old healthy male volunteer who was 175 cm tall and weighed 70 kg was enrolled. X-ray examination showed no foot or lower limb fracture, no tumors, and no deformities, and the patient had no history of surgery. A computed tomography scan was taken of the right foot and ankle by Siemens computed tomography (CT) system (Sensation 64, Siemens Healthcare, Germany) with a slice thickness of 0.6 mm in our hospital. The newly developed foot and ankle brace [15] was used to maintain a neutral position during scanning. A total of 261 2D tomographic images were collected and saved in DICOM format. The scanned computed tomography (CT) file was then imported into the medical 3D modeling software Mimics (Materialise, Leuven, Belgium), and the three-dimensional geometric point clouds of the tibia and the talus were obtained by threshold segmentation and manual segmentation. To reduce the computational complexity, the reverse engineering software Geomagic (Geomagic studio 10.0, Geomagic, Research Triangle Park, NC) was used to homogenize the point clouds and encapsulate them into a triangular mesh surface for softening, repairing, and removing spikes. The surface was converted into a NURBS surface and then imported into 3D CAD software SolidWorks (Dassault Systems, France) to form a solid model in which the talus was moved up 1.8 mm along the longitudinal axis of the tibia to fill the joint space and the articular surface of the distal tibia was trimmed to match the trochlea of talus as the ankle arthrodesis required removal of the articular cartilage and a good fit between the tibia and the talus. Considering that the diameter of cancellous screws commonly used in ankle arthrodesis is generally less than 8 mm, in this study, the three cancellous bone screws were simplified into cylinders with a diameter of 8 mm and added to the tibia-talus fusion model (see Figure 1 for a schematic diagram).
Figure 1: Schematic diagrams of the modeling and analysis procedure.
2.2 Exploring possible screw configurations
SolidWorks software was used by clinicians (XM, XW) with experience in ankle arthrodesis surgery to explore the possible configurations of three screws through which the following four goals could be achieved. First, there was no collision of screws, and the portion of screws within bone was as long as possible. The positions where screws passed through the articular surface were evenly distributed on the trochlea of the talus. Finally, no screws penetrate the contralateral bone cortex.
Ankle arthrodesis models of various screw configurations were then imported into the finite element analysis software ANSYS Workbench (ANSYS Inc., Canonsburg, PA, USA) for material property assignment, meshing, interaction relationship definition, and boundary condition setting and calculation.
2.3 Material properties, meshing, and interaction relationship definition of the finite element model
The tissues were set as an isotropic linear elastic material, and the material parameters for bone and screw were assigned in accordance with the literature [14, 16]. The Young's modulus of the tibia and the talus was defined as 837 MPa and 13,000 MPa, respectively, and Poisson's ratio was 0.3 [16]. Screws were regarded as incompressible material, Young's modulus was defined as 110,000 MPa, and Poisson's ratio was 0.4. Bones were divided by quadratic four-node tetrahedron elements, and cylinder screws were divided by hexahedron elements. A 1.5-mm mesh size was used determined by a mesh convergence test. The interaction of bones and screws is listed in Table 1.
Table 1: Interaction definition [14]
Contact
|
Interaction type
|
Tibia and talus
|
Frictional, coefficient of friction is 0.1
|
Screws and tibia
|
Tie
|
Screws and talus
|
Frictionless
|
2.4 Loading and boundary settings
The mid-stance phase was simulated in these models. Vertical loads that were half weight were applied to the upper tibia surface. The plantar surface of the talus was completely fixed. Meanwhile, the effect of external force on primary stability was evaluated for early postoperative patients with plaster [13]. We applied a uniform pressure distribution of 50 MPa perpendicular to the top surface of each screw to simulate the external force [14]. Additionally, 10 Nm torque was applied in different directions to the upper tibia surface to simulate the load of dorsiflexion, internal rotation, and external rotation[9] (Figure 1).
In this study, a finite element model based on 3D reconstruction of CT scan images was used to simulate biomechanics after ankle arthrodesis. The maximum and mean von Mises stress values at both the tibia and the talus were calculated to evaluate the stress distribution and stress transition to the screws. The maximum and mean micromotion at the fused articular surface were analyzed to evaluate the primary stability following ankle arthrodesis. We simulated four common clinical ankle stress scenarios (standing weight-bearing, dorsiflexion, internal rotation and external rotation), and calculated the maximum and average von Mises stress values at bones and the maximum and average micromotion of the articular surface.