Dynamic Stability Analysis of Progressive Supranuclear Palsy Affected Gait Using Lyapunov Floquet Theory

Abstract

Progressive supranuclear palsy (PSP) is a neurodegenerative disease with severe gait and balance deficits. There are no effective ways to assess dynamic balance during walking in PSP. The Lyapunov Floquet (LF) theory has been utilized to study dynamic balance in healthy and pathologic gait but has not been applied to PSP affected gait. In the current study, the medio-lateral motion of the center of mass during gait for 40 patients with PSP (PSP group) and 33 healthy older adults (Control group) were studied. Metrics from LF theory, such as the maximal Floquet multiplier (FM), maximal long-term Lyapunov Exponent (LE ${}_{\text {L}}\text {)}$ , and maximal short-term Lyapunov Exponent (LE ${}_{\text {S}}\text {)}$ were used to study walking stability. Although all the gait dynamics for all the participants were stable and non-chaotic, the PSP group was observed to be closer to an unstable system and more susceptible to perturbations ( $\vert $ FM $\vert $ closer to 1 and LE_L closer to 0) than the Control group (p < 0.001). The control group’s stability deteriorated, and the gait system became more susceptible to perturbations with age. Such a trend was not observed in the PSP group. The risk of falls increased with increase in cadence in the PSP group (p < 0.001). These findings demonstrate the potential of LF theory measures to evaluate dynamic stability in patients with PSP and the need for future research using quantitative measures.