Ligament Forces at the Knee during Isometric Quadriceps Contractions

Abstract

A mathematical model of the knee in the sagittal plane was used to investigate the ligament forces resulting when a posteriorly directed external force, applied to the tibia, resists extension of the knee under increasing isometric quadriceps contractions. The model is based on simple geometric representations of the bones, ligaments and muscles at the knee. An elementary mechanical analysis was used to predict which ligament, the anterior or posterior cruciate, was loaded at a given flexion angle and known line of action of the external force. Ligament force, as a proportion of the external force, was calculated first assuming the ligaments to be represented by single, inextensible lines. Modelling the ligaments as continuous arrays of extensible fibres then showed that tibio-femoral translations and ligament forces increased non-linearly with increasing muscle forces and approached asymptotic values which depended on flexion angle. In most positions of the joint, the calculated asymptotic ligament force values were less than the reported ultimate strength of human ligament, despite quadriceps forces of over three times body weight. The possibility of these asymptotic values of ligament force may explain why, at certain flexion angles, large forces can be developed by the muscles at the knee without ligament rupture.