Defining feasible bounds on muscle activation in a redundant biomechanical task: practical implications of redundancy.

Measured muscle activation patterns often vary significantly from musculoskeletal model predictions that use optimization to resolve redundancy. Although experimental muscle activity exhibits both inter- and intra-subject variability we lack adequate tools to quantify the biomechanical latitude that the nervous system has when selecting muscle activation patterns. Here, we identified feasible ranges of individual muscle activity during force production in a musculoskeletal model to quantify the degree to which biomechanical redundancy allows for variability in muscle activation patterns. In a detailed cat hindlimb model matched to the posture of three cats, we identified the lower and upper bounds on muscle activity in each of 31 muscles during static endpoint force production across different force directions and magnitudes. Feasible ranges of muscle activation were relatively unconstrained across force magnitudes such that only a few (0-13%) muscles were found to be truly "necessary" (e.g. exhibited non-zero lower bounds) at physiological force ranges. Most of the muscles were "optional", having zero lower bounds, and frequently had "maximal" upper bounds as well. Moreover, "optional" muscles were never selected by optimization methods that either minimized muscle stress, or that scaled the pattern required for maximum force generation. Therefore, biomechanical constraints were generally insufficient to restrict or specify muscle activation levels for producing a force in a given direction, and many muscle patterns exist that could deviate substantially from one another but still achieve the task. Our approach could be extended to identify the feasible limits of variability in muscle activation patterns in dynamic tasks such as walking.