A modeling study of mechanical energetic optimality in incline walking

To maintain steady level walking, collision loss is predominantly compensated for with push-off propulsion, and negligible additional work is performed during the single support phase. The observed energy balance during the double support phase is energetically optimal. However, unlike level walking, significant work proportional to the incline slope was observed during the single support phase, which raises the question of whether energetic optimality applies to incline walking. In this study, we examined the energetic optimality of incline walking using a simple work-energy relationship. Work performed by the leading and trailing leg over a gait cycle was estimated for various incline slopes, and the optimal push-off impulse that minimized the total work performed was calculated. The model prediction for least costly gait occurred when push-off propulsion provided all of the necessary work for raising or lowering the body center of mass (CoM) and collision compensation. When we assumed that the generation of optimal propulsion is gradually scaled to obey a feasible push-off constraint, which was estimated based on the allowable plantar flexor torque and the weight support of the trailing leg, the predicted slope-proportional increase in mechanical work done by the ground reaction force (GRF) during the single support phase was consistent with the empirical data. This result implies that the energetic optimality of incline walking can be described from a mechanical perspective and is subject to a feasible push-off propulsion constraint. However, the implication of the mechanical perspective of energetic optimality on the metabolic cost should be further examined and compared using empirical data.