Bone surface models of the reoriented hip joints are imported into ScanIP software (Simpleware Ltd., Exeter, UK). While patient-specific cartilage models are essential in biomechanical simulation, it has been previously reported in [14] that the predicted optimal alignment of the acetabulum was not significantly sensitive to the choice of cartilage thickness distribution over the acetabulum. Therefore a 3D dilation operation was performed on femoral head and acetabular surfaces to create femoral and pelvic cartilage layers with a constant thickness as has been done in [1]. Reconstructed surfaces were smoothed with a recursive Gaussian filter to remove segmentation artifacts (Fig. 3a, c).

Surfaces were discretized using tetrahedral elements (Fig. 3b, d). Since the primary concern was focused on the joint contact, a finer mesh was employed for the cartilage than for the bone. Refined tetrahedral meshes were constructed for the cartilage layers using ScanFE module (Simpleware Ltd., Exeter, UK). Cortical bone surfaces were discretized using coarse tetrahedral elements. Trabecular bone was not included in the models, for it has little effect on predictions of contact stress as reported in [1]. Tied and sliding contact constraints were used in Abaqus/CAE 6.10 (Dassault Systmes Simulia Corp, Providence, RI) to define the cartilage-to-bone and cartilage-to-cartilage interfaces, respectively. It has been reported in [5] that the friction coefficient between articulating cartilage surfaces is very low, on the order of 0.01–0.02 in the presence of synovial fluid. Therefore, it is reasonable to neglect frictional shear stresses between contacting articular surfaces.

Pelvic and femoral cartilages were modeled as homogeneous, isotropic, and linearly elastic material with Young’s Modulus E = 15 MPa and Poissons ratio = 0. 45. Cortical bone of pelvis and femur were modeled as homogeneous, isotropic material with elastic modulus E = 17 GPa and Poissons ratio = 0. 3 as has been used in [20].

The loading and boundary conditions used in this paper resemble those used by Phillips et al. [15] (Fig. 3e). The top surface of pelvis and pubic areas were fixed, and the distal end of the femur was constrained to prevent displacement in the body x and y directions while being free in vertical z direction (Fig. 3e). The center of femoral head derived from a least-square sphere fitting was selected to be the reference node. The nodes of femoral head surface are constrained by the reference node via kinematic coupling. The fixed boundary condition model was then subjected to a loading condition as published in [4], representing a single leg stance situation with the resultant hip joint contact force acting at the reference node. Although CT scan was performed in the supine orientation and the loading condition of our biomechanical simulation is based on one-leg stance situation [4], previous work [14] has shown that there is no significant difference between the contact pressure in the Bergmanns reference frame and those in the supine reference frame. In addition, as pointed out by Armiger et al. [3], it is not an infrequent clinical practice to use the supine frame as an estimate of the standing frame. Therefore we believe our model makes good use of valuable, available data from Bergmanns work [4]. Following the loading specification in [15], the components of joint contact force along three axes are given as 195, 92, and 1,490 N, respectively, by assuming a constant body weight of 650 N for all subjects to remove any scaling effect of body weight on the absolute value of the contact pressure. The resultant force is applied based on anatomical co-ordinate system described in Bergmann et al. [4], whose local coordinate is defined with the x axis running between the centers of the femoral heads (positive running from the left femoral head to the right femoral head), the y axis pointing directly anteriorly, and the z axis pointing directly superiorly.