Validation of optimization models that estimate the forces exerted by synergistic muscles

The purpose of this study was to validate the mathematical predictions of individual muscle forces obtained using optimization models. Mathematical muscle force predictions were made using linear and nonlinear optimization models proposed in the literature. Actual muscle forces were measured experimentally from soleus, gastrocnemius and plantaris muscles of an adult male cat during a variety of locomotor tasks. Mathematically predicted muscle forces did not agree well with the experimentally determined muscle forces, because changes in force sharing during given step cycles and for different locomotor speeds were largely ignored in the theoretical models tested. It is suggested that changes in force sharing during given step cycles may be caused by differences in force-velocity characteristics or small time delays of onset of activation between muscles; whereas changes in force sharing associated with different speeds of locomotion may be caused by corresponding changes in the magnitude of centrally controlled activation. Theoretical simulations testing the feasibility of these suggestions were encouraging. In view of the findings of this study, it is suggested that future models should be developed and validated based on experimental findings.