Abaqus 6

The finite element simulation was carried out in Abaqus 6.11 (Dassault Systèmes, RI, USA). For the contact between the encapsulated soft tissue and ground, the coefficient of friction was set to 0.6 [35 (link)]. Two load cases were preceded for validation purpose. Firstly, the boundary and loading conditions simulated the axial compression test of a cadaveric study [6 (link)]. The proximal tibia and fibula, and the encapsulated soft tissue were fixed in all six degrees of freedom. An impactor would strike on the foot through a foot plate at 5.0 m/s (Fig 1). Since the mass of the impactor was not specified in the cadaveric study [6 (link)], it was approximated to 7 kg based on other similar studies [8 (link), 9 ]. The foot plate weighed 4.5 kg, comprised of a foam part and a rigid part. A compression force of 270N (half of body weight) would be applied once the foot plate hit and came into contact with the foot.
Another load case that included the Achilles tendon force would also be resembled. The Achilles tendon would be loaded 1.94kN and the same amount of force was also added to the compressive load [6 (link)]. A parametric analysis would then be carried out with the basic setting of the same cadaveric study [6 (link)], but simulated with different impact velocities (2.0 to 7.0 m/s).

Abaqus 6.11 (Dassault Systèmes Simulia Corporation, Providence, RI, USA) finite element package was used for FEM simulation. The 3D-FEM spinal cord model established in this study consisted of gray and white matter, as well as pia mater (Fig. 1). To simplify calculations in the model, the denticulate ligament, dura and nerve root sheaths were not included. The pia mater was included since it has been previously identified that the spinal cord with and without this component shows significantly different mechanical behavior (3 (link)). The spinal cord was assumed to be symmetrical around the mid-sagittal plane; therefore, only half the spinal cord required reconstruction and the whole model was integrated by mirror image. For computed tomography-myelography (CTM) measurement, the vertical length of the spinal cord was two vertebral bodies (~40 mm).
The lamina model was established by measuring CTM and magnetic resonance imaging (MRI) and simulated cervical OPLL. A rigid, wide trapezium body with a slope of 30° was used to simulate cervical OPLL by measuring the MRI of paper (Fig. 2) (1 (link)).

Before using this model to study the biomechanical response of facets, its calibration and validation had to be operated. The calibration procedure was conducted according to the method presented by Schmidt et al. [32 (link), 33 ]. The calibration factors of collagen fibers and ligaments were varied in order to obtain the optimal values (i.e., for which the range of motion (ROM) predicted by the model well matched the in vitro experimental results).
Validation was then undertaken by comparing the predicted data obtained by the current model with the results from the literature. The range of motion of each segment under moment loading in the three anatomic planes and the disc compression under a follower load of 1200 N were calculated and compared with the experimental and simulated data presented by Renner et al. [22 ]. The boundary conditions and loading were set to replicate the in vitro experiment. The surface-to-surface contact between facet joints was defined as frictionless during the entire validation simulation, as well as for the following biomechanical study of facet. All the simulation works were conducted in a commercial finite element package (Abaqus 6.11; Dassault Systèmes Simulia Corporation, Pennsylvania, USA).

ABAQUS-CAE was used to build the finite element meshes with 4-noded linear tetrahedrons. The optimal number of elements was chosen after simulating the convergence analysis to obtain sufficient accuracy in the results, then all simulations were performed using ABAQUS (ABAQUS 6.11, Dassault Systèmes, Vélizy-Villacoublay, France).