Minimum effort simulations of split-belt treadmill walking exploit asymmetry to reduce metabolic energy expenditure

Abstract

Walking on a split-belt treadmill elicits an adaptation response that changes the baseline step length asymmetry of the walker. The underlying causes of this adaptation, however, are difficult to determine. It has been proposed that effort minimization may drive this adaptation, based on the idea that adopting longer steps on the fast belt, or positive step length asymmetry (SLA), can cause the treadmill to exert net-positive mechanical work on a bipedal walker. However, humans walking on split-belt treadmills have not been observed to reproduce this behavior when allowed to freely adapt. To determine if an energy minimization motor control strategy would result in experimentally observed adaptation patterns, we conducted simulations of walking on different combinations of belt speeds with a human musculoskeletal model which minimized muscle effort. The model adopted increasing amounts of positive step length asymmetry and decreased its net metabolic rate with increasing belt speed asymmetry, up to +25.6% SLA and −14.3% metabolic rate at a 3:1 belt speed ratio, relative to tied-belt walking. These gains were primarily enabled by an increase of braking work and a reduction of propulsion work on the fast belt. The results suggest that a purely energy minimization driven split belt walking strategy would involve substantial positive SLA, and that the lack of this characteristic in human behavior points to additional factors influencing the motor control strategy, such as aversion to excessive joint loads, asymmetry, or instability.