The variation in the orientations and moment arms of the knee extensor and flexor muscle tendons with increasing muscle force: A mathematical analysis

Abstract

The orientations and moment arms of the knee extensor and flexor muscle tendons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal plane was used to define the motion of the joint in the unloaded state during 0-120 degrees flexion. The cruciate and collateral ligaments were represented by arrays of elastic fibres, which were recruited sequentially under load or remained buckled when slack. A bi-articular model of the patello-femoral joint was used. Simple straight-line representation was used for the lines of action of the forces transmitted by the model muscle tendons. The effects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the maximum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degree flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tendon was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the maximum change in moment arm of the hamstrings tendon was 8 per cent at 60 degrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum change for the gastrocnemious tendon was 3 per cent at 0 degree. The orientations of the flexor muscle tendons in this range of force either remained constant or changed by 1 degree or less at any flexion angle. The general trend at any flexion angle was that, as the muscle force was increased, the moment arms and the orientations approached nearly constant values, showing asymptotic behaviour. It is concluded that experimental simulations of knee muscle action with low values of the externally applied load, of the order of 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.