Natural variability increases human walking metabolic costs and its implications to simulation-based metabolic estimation

Human walking contains variability due to small intrinsic perturbations arising from sensory or motor noise, or to promote motor learning. We hypothesize that such stride-to-stride variability may increase the metabolic cost of walking over and above a perfectly periodic motion, and that neglecting such variability in simulations may mis-estimate the metabolic cost. Here, we quantify the metabolic estimation errors accrued by neglecting the stride-to-stride variability using human data and a musculoskeletal model by comparing the cost of multiple strides of walking and the cost of a perfectly periodic stride with averaged kinematics and kinetics. We find that using an averaged stride underestimates the cost by about 2.5%, whereas using a random stride may mis-estimate the cost positively or negatively by up to 15%. As a further illustration of the cost increase in a simpler dynamical context, we use a feedback-controlled inverted pendulum walking model to show that increasing the sensory or motor noise increases the overall metabolic cost, as well as the variability of stride-to-stride metabolic costs, as seen with the musculoskeletal simulations. Our work establishes the importance of accounting for stride-to-stride variability when estimating metabolic costs from motion.