Constrained optimization in human walking: cost minimization and gait plasticity

Abstract

As walking speed increases, consistent relationships emerge between the three determinant parameters of walking, speed, step frequency and step length. However, when step length or step frequency are predetermined rather than speed, different relationships are spontaneously selected. This result is expected if walking parameters are selected to optimize to an underlying objective function, known as the constrained optimization hypothesis. The most likely candidate for the objective function is metabolic cost per distance traveled, where the hypothesis predicts that the subject will minimize the cost of travel under a given gait constraint even if this requires an unusual step length and frequency combination. In the current study this is tested directly by measuring the walking behavior of subjects constrained systematically to determined speeds, step frequencies or step lengths and comparing behavior to predictions derived directly from minimization of measured metabolic cost. A metabolic cost surface in speed-frequency space is derived from metabolic rate for 10 subjects walking at 49 speed-frequency conditions. Optimization is predicted from the iso-energetic cost contours derived from this surface. Substantial congruence is found between the predicted and observed behavior using the cost of walking per unit distance. Although minimization of cost per distance appears to dominate walking control, certain notable differences from predicted behavior suggest that other factors must also be considered. The results of these studies provide a new perspective on the integration of walking cost with neuromuscular control, and provide a novel approach to the investigation of the control features involved in gait parameter selection.