Parameter sensitivity of a mathematical model of the anterior cruciate ligament. - Toutoungi, D; Zavatsky, A; O'Connor, J (1997)
This paper presents the results of an investigation into parameter sensitivity of a mathematical model of the human anterior cruciate ligament (ACL). The model ACL comprised a continuous array of fibres mapped between part-elliptical attachment areas on the femur and tibia. Relative motion of the two bones was controlled by a planar four-bar linkage. Parameter modifications were: (a) an alternative set of values for the coordinates of the four-bar linkage joints; (b) rotation of the attachment areas of the ligament by +/- 30 degrees; and (c) variation of some mechanical properties. The alternative four-bar linkage parameter set produced extremely large changes in ACL force values, up to 130 per cent. Rotating the tibial attachment changed forces by less than 20 per cent, whereas rotating the femoral attachment changed forces by up to 100 per cent. Altering the mechanical parameters produced the smallest differences in force, under 15 per cent. These results highlight the importance, when using a theoretical model, of establishing the values of the parameters defining the model as accurately as possible and of carrying out a parameter sensitivity study. From a clinical viewpoint, they also suggest that, when reconstructing a ruptured ACL, one of the most important considerations must be to position the femoral attachment of the graft as accurately as is feasible.