THE INFLUENCE OF GEOMETRY ON THE STRESS-DISTRIBUTION IN JOINTS - A FINITE-ELEMENT ANALYSIS

The incongruity of human joints is a phenomenon which has long been re cognized, and recent CT-osteoabsorptiometric findings suggest that thi s incongruity influences the distribution of stress in joints during t heir normal physiological use. The finite element method (FEM) was the refore applied to five different geometric configurations consistent w ith the anatomy of articular surfaces, and a program with variable con tact areas (Marc) was used to calculate the stress distribution for lo ads of 100 to 6 900 N. The assumption of congruity between head and so cket results in a ''bell-shaped'' distribution of stress with a maximu m value of 61.5 N/mm(2) in the depths of the socket, decreasing toward s zero at its edges. In the model with a flatter socket the von Mises stresses are higher (max. 101.3 N/mm(2)); with a deeper socket, lower (max. 53.0 N/mm(2)). If the diameter of the head is greater, the stres ses build up from the periphery of the socket and move towards its dep ths as the load increases. The combination of an oversized head and a deeper socket results in the most satisfactory stress distribution (ma x. 43.2 N/mm(2)). These results extend previous photoelastic findings with incongruous joint surfaces. The calculated mechanical conditions show a relationship to the location of osteoarthritic changes, and are reflected by the distribution pattern of subchondral bone density. A more satisfactory stress distribution is found With functionally advan tageous, incongruous joint surfaces (oversized head and deepened socke t) than in the congruous joint, and a better nutritive situation for t he articular cartilage seems likely. The geometry of the joint is ther efore a physiologically important and quantifiable factor contributing to an optimized transmission of forces in joints.