The redundant nature of locomotor optimization laws

A sagittal-plane model of the lower limb, which considered the possibility of antagonistic and synergistic muscle action and took account of the load-bearing roles of the cruciate ligaments, was applied to a dynamic analysis of level walking. It was hypothesized that: (1) the simple, one-sided constraints that intra-articular contact forces must be compressive and muscle and ligament forces tensile substantially reduce the redundancy of the load-transmitting structures of the lower limb, (2) many previously proposed optimization laws for muscle selection yield equivalent results, when they are applied to a finite set of admissible limiting solutions, and (3) the aforementioned optimization laws, when applied to a finite set of admissible limiting solutions, do not adequately predict the co-contraction of antagonistic muscles during gait. The problem of indeterminacy was resolved by considering all possible limiting solutions of the system unknowns on the dynamic equations. Although 498 limiting solutions of nine unknowns could arise at each sampled point on the gait cycle, the aforementioned one-sided constraints ruled out the large majority of them. It was shown that of the 498 possible, the minimum number of simultaneous admissible solutions for any subject was as few as three and the maximum number was only 18. The Principles of minimal total muscle force, squared muscle force, muscle stress, intra-articular contact force and instantaneous muscle power predicted remarkably similar patterns of muscle activity over the gait cycle. Of the six tested performance criteria, the Principle of minimal total ligament force was the least successful in terms of selecting solutions that closely matched the EMG patterns. This result implied that the muscles do not always act to protect the knee ligaments during gait. Finally, each of the above minimum principles failed to predict any antagonistic quadriceps-hamstrings action at the knee and hip around the event of heelstrike, although such activity was indicated by electromyography.