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

Finite element models of the hip can predict cartilage pressures consistent with
experimental data when subject-specific bone and cartilage geometry are accurately
represented and bones are modeled as deformable [3-5]. Most published FE models,
however, do not model the complex geometry of the hip joint. Prior studies have
assumed spherical geometry and neglected cartilage [9] or assumed a constant cartilage
thickness [1, 10, 11]. Models that assume ideal geometry underestimate peak pressures
by 60%, average pressures by 21%, and overestimate contact area by 10% [4]. When
bone and cartilage geometry are reconstructed from high-resolution CT images, average
pressures are within 16% and contact areas are within 21% of those measured in-vitro.
However, the construction and analysis of FE models of the hip is time-intensive and
computationally expensive.
DEA (i.e. rigid body spring method) is a computationally efficient method for
calculating cartilage stresses [6-8, 12]. Bones are modeled as rigid bodies and the
cartilage surface is inferred to have thickness equal to the distance between bones,
represented as an array of springs [12]. Cartilage contact stress is quantified based on
the deformation of each spring. Previous DEA models have assumed concentric hip
joint geometry and constant cartilage thickness. These assumptions underestimate
cartilage contact stress and predict unrealistic, simplified contact patterns [4, 8]. It is
possible that DEA could provide realistic predictions of cartilage contact stress if
subject-specific bone and cartilage geometry were incorporated. The objectives of this
study were to develop and verify a DEA model that includes subject-specific bone and
cartilage geometry, and to compare DEA model predictions of cartilage contact stresses
with predictions from validated FEA models.
3. METHODS
High resolution CT image data (512×512, 320 mm field of view, resolution
0.625×0.625 mm 2 , 0.6 mm slice thickness) of a 25 year old male cadaveric hip were
segmented to determine cartilage thickness and the geometry of the bone-cartilage
interface for the acetabulum and femur [3]. A previously validated subject-specific
FEA model provided baseline geometry (cortical bone and cartilage surfaces) for both
the DEA and FEA analysis [3].
3.1 Discrete Element Analysis Implementation and Verification
A custom C++ program was used to perform the DEA analysis. As the DEA method
requires rigid bones, both the pelvis and femur were modeled as triangulated rigid
surfaces, with position dependent cartilage thickness values assigned to each node.
Nodal cartilage thicknesses were computed as the distance between subject-specific
cartilage and cortical bone surfaces projected along the surface normals. Cartilage was
represented by a distribution of compressive springs generated in the region of the
femoral head underlying the acetabulum. A spring was defined for each triangular
element of the acetabulum surface in this region. One end of the spring was attached at
the center of the triangle on the acetabulum. The other end was determined by
projecting the first point along the acetabulum surface normal onto the femoral head.
The total length of each spring accounted for the acetabular and femoral cartilage
thickness as well as the joint space (Fig 1). Each spring had an initial length defined as
the sum of acetabular cartilage thickness, femoral cartilage thickness, and joint space at