Anatomy and Embryology

, Volume 189, Issue 6, pp 545–552

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

  • Felix Eckstein
  • Beat Merz
  • Peter Schmid
  • Reinhard Putz
Original Articles

DOI: 10.1007/BF00186828

Cite this article as:
Eckstein, F., Merz, B., Schmid, P. et al. Anat Embryol (1994) 189: 545. doi:10.1007/BF00186828

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/mm2 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/mm2). 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.

Key words

Incongruity Joint loading Load distribution Finite element method Joint geometry 

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Felix Eckstein
    • 1
  • Beat Merz
    • 2
  • Peter Schmid
    • 2
  • Reinhard Putz
    • 1
  1. 1.Anatomische Anstalt der Ludwig Maximilians Universität MünchenMünchenGermany
  2. 2.Institut für Biomedizinische Technik und Medizinische Informatik der ETH ZürichZürichSwizzerland