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

The orientations and moment arms of the knee extensor and flexor muscle ten dons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal p lane was used to define the motion of the joint in the unloaded state durin g 0-120 degrees flexion. The cruciate and collateral ligaments were represe nted by arrays of elastic fibres, which were recruited sequentially under l oad or remained buckled when slack. A bi-articular model of the patello-fem oral joint was used. Simple straight-line representation was used for the l ines of action of the forces transmitted by the model muscle tendons. The e ffects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the max imum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degrees flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tend on was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the m aximum change in moment arm of the hamstrings tendon was 8 per cent at 60 d egrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum chang e for the gastrocnemious tendon was 3 per cent at 0 degrees. The orientatio ns of the flexor muscle tendons in this range of force either remained cons tant or changed by 1 degrees or less at any flexion angle. The general tren d at any flexion angle was that, as the muscle force was increased, the mom ent arms and the orientations approached nearly constant values, showing as ymptotic behaviour. It is concluded that experimental simulations of knee m uscle action with low values of the externally applied load, of the order o f 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.