Adiabatic Invariant of Center-of-Mass Motion during Walking as a Dynamical Stability Constraint on Stride Interval Variability and Predictability

SIMPLE SUMMARY: Human walking exhibits properties of both stability and variability. On the one hand, the variability of the interval of time between heel strikes is autocorrelated, i.e., not randomly organized. On the other hand, walking is highly stereotyped and arguments from general mechanics suggest that the stability of gait can be assessed according to invariant properties. This study aims at proposing one of those invariants. Participants walked for 10 min at a natural pace, with and without a metronome indicating participants’ preferred step frequency. In both cases, we use different parameters to assess both the variability and stability of walking. We verify a known result: the metronome strongly alters the variability of the motion. However, despite the large variability changes, our proposed adiabatic invariant is preserved in both conditions, demonstrating the stability of gait. It appears as though our model reveals dynamical constraints that are “hidden” beyond apparent walking variability. ABSTRACT: Human walking exhibits properties of global stability, and local dynamic variability, predictability, and complexity. Global stability is typically assessed by quantifying the whole-body center-of-mass motion while local dynamic variability, predictability, and complexity are assessed using the stride interval. Recent arguments from general mechanics suggest that the global stability of gait can be assessed with adiabatic invariants, i.e., quantities that remain approximately constant, even under slow external changes. Twenty-five young healthy participants walked for 10 min at a comfortable pace, with and without a metronome indicating preferred step frequency. Stride interval variability was assessed by computing the coefficient of variation, predictability using the Hurst exponent, and complexity via the fractal dimension and sample entropy. Global stability of gait was assessed using the adiabatic invariant computed from averaged kinetic energy value related to whole-body center-of-mass vertical displacement. We show that the metronome alters the stride interval variability and predictability, from autocorrelated dynamics to almost random dynamics. However, despite these large local variability and predictability changes, the adiabatic invariant is preserved in both conditions, showing the global stability of gait. Thus, the adiabatic invariant theory reveals dynamical global stability constraints that are “hidden” behind apparent local walking variability and predictability.