ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.2 Finite Element Analysis
Following a previously validated subject-specific FE model, bone was represented by
triangular shell elements and was modeled as rigid [3]. Using hexahedral elements,
cartilage was modeled as a neo-Hookean hyperelastic material using the following
relationship:
E
G
[3]
2(1 v)
where G is the shear modulus, E is the elastic modulus (11.85 MPa), and v is the
Poisson’s ratio (0.45). For strains less than 30%, the neo-Hookean hyperelastic material
provides equivalent properties to those used for the DEA implementation (Hooke’s
Law) [14]. FE models were analyzed using NIKE3D.
3.3 Loading and Boundary Conditions
The pelvis was assumed to be rigid and fixed in space. The femoral head was modeled
as rigid, but was only restricted to rotation (free to translate in all three axes). Loading
conditions and geometric orientation of the femur relative to the pelvis followed
previously published data for in-vivo hip loads [15]. Here, data collected from patients
with instrumented femoral implants were averaged to determine the equivalent hip joint
force and bone orientations at peak load. The average data specified the relative
positioning of the femur and acetabulum and magnitude/direction of applied force
assuming a body weight of 800 N. Walking (W), descending stairs (DS), and ascending
stairs (AS) were analyzed. Force was applied to the center of rotation of the joint,
which was determined as the centroid of the sphere fitted to the femoral head.
3.4 Prediction Comparisons
To facilitate the comparison between DEA and FEA results, DEA nodal results (defined
on the triangulated bone surfaces) were projected onto the articulating (quadrilateral)
surface of the FEA cartilage mesh and interpolated. Interpolation was done by finding
the closest point projection of each quadrilateral node onto the triangular bone surface.
Then, the value at the projection point was interpolated from the nodal values using
element shape functions. Predictions of peak contact stress, average contact stress, and
contact area were compared between DEA and FEA. 2.5
4. RESULTS
The convergence study demonstrated that ~20,000
springs were required to achieve