Reduction of pendular energy exchange at very slow human walking speeds reveals deviations from simple walking models

Walking can be modelled as a simple inverted pendulum, where the human body takes advantage of exchanging kinetic and gravitational potential energy to remain in motion. This exchange is well documented at normal speeds but could break down at very slow speeds. We examined energy transduction through the phase shift between potential and kinetic energy in human walking at a wide range of speeds (0.1-2.0 m s-1), specifically capturing very slow speeds (<0.6 m s-1). We measured phase shift with two different methods. One method used two classical phase shifts of α and β from ( Cavagna and Legramandi, 2020). The second method utilized cross-correlation across each stride. We calculated phase shift from a human gait study and from two simple inverted pendulum-type walking models ( Srinivasan and Ruina, 2006; Rebula and Kuo, 2015). Participants walked at 13 prescribed speeds between 0.1 and 2.0 m s-1 on a split belt instrumented treadmill. We found that phase shifts increased as speed decreased. However, at speeds slower than 0.3 m s-1, the phase shifts approached zero. The simple walking models were unable to demonstrate phase shift behaviour at any speed. Our study demonstrates that as speed slows, humans walk less similarly to the inverted pendulum models, and more complex models may be required to characterize walking at very slow speeds.