Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip

Abstract

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error approximately 0.5mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.

Figure 1

Cross-sections through femur with bone (light gray) and cartilage (dark gray). A- orientation of plane used to define section through FE model of femur, B- subject-specific model, C- subject-specific bone model with constant cartilage thickness (Model 1), D- subject-specific bone model with varying cartilage thickness based on the best-fit radius of joint space midline (Model 3), E- best-fit sphere model with constant cartilage thickness (Model 4), and F- best-fit conchoid model with constant cartilage thickness (Model 5). Rigid bone model not shown (Model 2).

Figure 2

Conchoid schematic. Left) two radii: a and b (dashed lines) and θ define a conchoid with center C_CONCH according to the general equation: r = a + b cosθ. Right) the best fit conchoid (solid line) for the subject-specific bone/cartilage interface (dotted line) was calculated by optimizing C_CONCH, a, and b along the direction of n. The central rotation axis, n, was calculated as the average orientation of all vectors (dotted arrows) that originated from the center of a best fit sphere (C_SPHERE) and ended at each surface node representing the native bone/cartilage interface.

Figure 3

Comparison of acetabular cartilage pressures between the subject-specific model (first column) and all simplified models (adjacent columns) for each loading scenario analyzed (rows). Pressures were slightly elevated when a constant cartilage thickness was assumed to cover subject-specific bone geometry (column 2). Pressures were substantially elevated and distributed over a smaller area when bones were assumed rigid (column 3). Assuming smooth articulating cartilage topology covering subject-specific geometry (column 4) and fitting the bone/cartilage interface to both spheres (column 5) and conchoids (column 6), with constant cartilage thickness, resulted in a substantial decrease in pressures, with contact distributed over a larger area.

Figure 4

Comparison of FE predicted peak pressures between the subject-specific model and all simplified models. Top) peak pressures increased when a constant cartilage thickness was assumed to cover subject-specific bone geometry and when bones were assumed rigid. Peak pressures were less than half those of the subject-specific model when cartilage topology was simplified to conform to a best-fit radius, sphere or conchoid. Middle) average pressures followed a similar trend as peak pressure. Error bars indicate standard deviations in pressure for elements that predicted pressures > 0.1 MPa. Bottom) comparison of FE predicted contact areas. As expected, contact areas followed a trend opposite to predictions of peak and average pressure.