Impulse-momentum analysis shows that walking on a split-belt treadmill was energetically optimal after adaptation

Abstract

1) Background and aim Asymmetric walking, especially walking on a split-belt treadmill, has been applied to the study of walking disabilities such as hemiparesis. These studies have reported that the large asymmetry observed in kinematic features at the early stage of split-belt walking gradually changes to being more symmetric as the walking continues due to a process of adaptation. We hypothesized that an energetic perspective may provide important insights into this locomotor adaptation. Human walking is known to be energetically optimal by impulse-momentum analyses such as a gravitational impulse model. In this study, we examined whether asymmetric walking adaptation on a split-belt treadmill could be explained in terms of energetics using impulse-momentum analysis. 2) Methods To examine whether the energetics of gait adaptation occurred in an optimal manner in split-belt walking, we analyzed the impulse-momentum of step-to-step transitions for split-belt walking using the impulse model. The impulse model consists of a point mass and two massless rigid legs. To represent the asymmetric features of split-belt walking, especially the leg angle, we introduced the leg length change into the impulse model for each step-to-step transition. In addition, the momentum difference relative to two belts was introduced to represent the difference of speed between two belts. Model parameters were leg angle and the amplitude of the gravitational impulse which were set from the angle of impulses and the duration of double support phase respectively, based on experimental data. Optimal push-off which minimized work done throughout a stride could be obtained from the work-energy relationship for each belt. To validate the model, we obtained the kinetic and kinematic data from a split-belt walking experiment on nine subjects who signed the informed consent form approved by IRB of Georgia Tech. They walked in baseline periods with tied belts (0.5 and 1.5 m/s), the adaptation period with split-belt (0.5:1.5 m/s) and the post-adaptation period with tied belt again (0.5 m/s). Impulses and work were calculated by integrating forces and power, which were obtained as product of force and velocity of the center of mass relative to each belt. 3) Results In early adaptation, subjects could not generate optimal push-off impulse so that the push-off impulse could not compensate the collision loss, and this result showed that gait during the early adaptation was not energetically optimal. Gait during the late adaptation, however, was energetically optimal so that optimal push-off was generated to compensate collision loss fully as consistent with the model prediction. 4) Conclusions The results imply that adaptation during split-belt treadmill walking occurred to optimize energetics and it could be explained in terms of energetics by an impulse-moment analysis.