Stresses in the human knee joint

Abstract

Analytical and experimental techniques for determining contact stresses between the bones of human knee joints (femur and tibia) are developed. The techniques presented allow for rational analysis of stresses that act in diseased or deformed joints and can provide insight into rational design of artificial joints. Analytical contact conditions are developed in terms of displacements, rigid body degrees of freedom, and force equilibrium of the bodies. The problem of contact between the femur and tibia is formulated as a quadratic programming problem. Force-deformation relations for the the two bodies were generated with a general purpose structural analysis program, NASTRAN. A numerical technique based on Wolfe's Algorithm is applied to solve the quadratic programming problem. Analytical results are verified by two-dimensional photoelastic experimentation. A three-dimensional stress-freezing photoelastic technique is employed to determine the contact stresses on the condyles of the femur and tibia, under normal loading. A model was constructed of epoxy resin and photo-elastic techniques were employed to determine the stress field in the model, hence the contact stresses. Results show that about 75% of the projected area of the condyles can be in contact, in the standing position.