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

Walking on a split-belt treadmill elicits an adaptation response that changes baseline step length asymmetry. 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 effort-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 that minimized muscle excitations and metabolic rate. The model adopted increasing amounts of positive SLA and decreased its net metabolic rate with increasing belt speed difference, reaching +42.4% SLA and -5.7% metabolic rate relative to tied-belt walking at our maximum belt speed ratio of 3:1. These gains were primarily enabled by an increase in braking work and a reduction in propulsion work on the fast belt. The results suggest that a purely effort 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.NEW & NOTEWORTHY Behavioral observations of split-belt treadmill adaptation have been inconclusive toward its underlying causes. To estimate gait patterns when driven exclusively by one of these possible underlying causes, we simulated split-belt treadmill walking with a musculoskeletal model that minimized its summed muscle excitations. Our model took significantly longer steps on the fast belt and reduced its metabolic rate below tied-belt walking, unlike experimental observations. This suggests that asymmetry is energetically optimal, but human adaptation involves additional factors.