Optimality principles for model-based prediction of human gait

Abstract

Although humans have a large repertoire of potential movements, gait patterns tend to be stereotypical and appear to be selected according to optimality principles such as minimal energy. When applied to dynamic musculoskeletal models such optimality principles might be used to predict how a patient's gait adapts to mechanical interventions such as prosthetic devices or surgery. In this paper we study the effects of different performance criteria on predicted gait patterns using a 2D musculoskeletal model. The associated optimal control problem for a family of different cost functions was solved utilizing the direct collocation method. It was found that fatigue-like cost functions produced realistic gait, with stance phase knee flexion, as opposed to energy-related cost functions which avoided knee flexion during the stance phase. We conclude that fatigue minimization may be one of the primary optimality principles governing human gait.

FIG. 1

Comparison of hip, knee and ankle angles on the left, and of vertical and horizontal ground contact forces on the right, obtained through predictive simulations using the family of cost functions in Eq. 9 with muscle volume-based weighting factors, ω_i = V_i.

FIG. 2

Comparison of hip, knee and ankle angles on the left, and of vertical and horizontal ground contact forces on the right, obtained through predictive simulations using the family of cost functions in Eq. 9 with unitary weighting factors, ω_i = 1.

FIG. 3

Stick figure of predicted gait patterns with p = 2 and ω_i = V_i (top), and p = 3 and ω_i = 1 (bottom). Note the difference in knee flexion during stance.

FIG. 4

Comparison of muscle activations predicted through the predictive simulations using the family of cost functions in Eq. 9 with the muscle volume-based weighting factors, ω_i = V_i, on the left and unitary weighting factors, ω_i = 1, on the right.