Muscle Synergies Modify Static Optimization Estimates of Joint Stiffness during Walking.

Abstract

Because of its simplicity, static optimization (SO - also called inverse dynamic optimization) is frequently used to resolve the muscle redundancy problem. However, SO minimizes antagonistic co-activation and therefore joint stiffness, which may not be physiologically realistic. This study explores how imposing a synergy structure on the muscle activations estimated by SO (termed "synergy optimization," or SynO) affects calculated lower body joint stiffnesses during walking. Because a synergy structure limits the achievable muscle activations and couples all time frames together, it provides a potential mechanism for reducing indeterminacy and improving physiological co-activation but at the cost of a larger optimization problem. To compare joint stiffnesses produced by SynO (2 through 6 synergies) and SO, we used both approaches to estimate lower body muscle activations and forces for sample walking data obtained from the Knee Grand Challenge Competition. Both optimizations used a custom Hill-type muscle model that permitted analytic calculation of individual muscle contributions to the stiffness of spanned joints. Both approaches reproduced inverse dynamic joint moments well over the entire gait cycle, though SynO with only 2 synergies exhibited the largest errors. Maximum and mean joint stiffnesses for hip and knee flexion in particular decreased as the number of synergies increased from 2 to 6, with SO producing the lowest values. Our results suggest that SynO increases joint stiffness by increasing muscle co-activation, and furthermore, that walking with a reduced number of synergies may result in increased joint stiffness and thus stability.