About weight factors in the non-linear objective functions used for solving indeterminate problems in biomechanics

A lot of non-linear objective criteria are applied for solving the indeterminate problems formulated for different biomechanical models--most of them can be covered by the expression [formula in text]. It might be noted, however, that most of the suggested criteria are not applicable if considerable antagonistic co-contractions exist. This could be an effect of treating the agonistic muscles and their respective antagonists in one and the same manner in the objective function. Using a completely inverse approach (the muscle forces are supposed to be known quantities) and a simple 1DOF model (actuated by three agonistic muscles and one corresponding antagonist) it has been shown which values of the weight factors c(i) may predict different levels of muscle forces from the two antagonistic groups. Three hypothetical border variants for magnitudes of the muscle forces are considered (flexor muscles are only active, extensor muscles are only active, considerable co-contraction of flexors and extensors exists). The main conclusions are: the signs of c(i) at agonistic muscles have to be opposite to the c(i) signs at their antagonists; the signs of the weight factors depend on the direction of the net external joint moment; the closer c(i) to zero, the bigger force will be predicted in the ith muscle.