The influence of geometry on the stress distribution in joints ? a finite element analysis

Abstract

Abstract. The incongruity of human joints is a phenomenon which has long been recognized, and recent CT-osteoabsorptiometric findings suggest that this incongruity influences the distribution of stress in joints during their normal physiological use. The finite element method (FEM) was therefore applied to five different geometric configurations consistent with the anatomy of articular surfaces, and a program with variable contact areas (Marc) was used to calculate the stress distribution for loads of 100 to 6 900 N. The assumption of congruity between head and socket results in a "bell-shaped" distribution of stress with a maximum value of 61.5 N/ram 2 in the depths of the socket, decreasing towards zero at its edges. In the model with a flatter socket the von Mises stresses are higher (max. 101.3 N/mm2); with a deeper socket, lower (max. 53.0 N/ram2). If the diameter of the head is greater, the stresses build up from the periphery of the socket and move towards its depths as the load increases. The combination of an oversized head and a deeper socket results in the most satisfactory stress distribution (max. 43.2 N/mm2). 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 advantageous, incongruous joint surfaces (oversized head and deepened socket) than in the congruous joint, and a better nutritive situation for the articular cartilage seems likely. The geometry of the joint is therefore a physiologically important and quantifiable factor contributing to an optimized transmission of forces in joints.

Computer simulation of subchondral bone adaptation to mechanical loading in an incongruous joint

“…This result extends earlier experimental (Eckstein et al, 1994a(Eckstein et al, , 1995bHillebrand et al, 1995) and computational (Eckstein et al, 1994b(Eckstein et al, , 1995c work in which the characteristic distribution pattern of subchondral bone density of the trochlear Fig. 4.…”

Modeling of Temporomandibular Joint Function Using MRI and Jaw-Tracking Technologies – Mechanics

“…Furthermore, we were able to quantify several aspects of the mechanical environment of the TMJ noninvasively, three-dimensionally and dynamically. Similar information is still unavailable for other synovial joints, although congruity variation and contact analysis between articular surfaces in other human and animal joints have been studied [Oberlander, 1978;Scherrer and Hillberry, 1979;Eckstein et al, 1994]. Nonetheless, most of these previous investigations were performed on cadavers or only under static conditions [Fujikawa et al, 1983;Warner et al, 1998;Reichle and Snaps, 1999], and therefore lack the active and spontaneous kinematic component peculiar to our method.…”

Morphomechanics of the humero‐ulnar joint: II. Concave incongruity determines the distribution of load and subchondral mineralization

“…Since articular surfaces need to be curved to provide the joints with a sufficient range of movement, the distribution of stress cannot possibly be uniform over the entire joint surface at every given load (Kummer, 1974;Bullough, 1981;Mockenhaupt, 1990;Eckstein et al, 1994a). Within a perfectly congruous (undeformable and frictionless) ball-and-socket joint the pressure ranges from a maximum in the depth of the joint to zero 0 1995 WILEY-LISS, INC. at its edges (Kummer, 1968).…”

“…These hypotheses have, however, been formulated in speculative and merely qualitative terms. In recent studies (Eckstein et al, 1994a) we have attempted to quantify the influence of geometric factors on the distribution of stress, but the articular cartilage layers were neglected in these models and no predictions of realistic joint pressures could therefore be put forward.…”