THE LYAPUNOV EXPONENT IN GAIT ANALYSIS AND FALL RISK: A SCOPING REVIEW ON METHODOLOGIES, ATTRACTORS, AND CLINICAL APPLICATIONS

Dynamic Systems Theory (DST) and Chaos Theory (CT), when applied to human locomotor movements under quasistable conditions, can yield robust methodological strategies for identifying fall risk in older adults during walking or running. The Lyapunov Exponent (LE) is a mathematical measure [ou nonlinear metric] that quantifies the divergence of initially close trajectories within a dynamic system, such as human gait. Following a minor perturbation (e.g., uneven terrain), acceleration and angular velocity patterns can shift, signaling a drastic alteration in an older adult’s neuromotor control capacity, potentially leading to a fall. The objective of this scoping review was to discuss the implications of the LE regarding fall risk in older adults. Seminal articles and books in English were selected, prioritizing studies that employed DST and the Lyapunov Exponent in research concerning fall risk during gait. It was concluded that fall risk minimization strategies should focus on the older adult’s capacity—during walking and clinical interventions—to consolidate a satisfactory attractor. The goal is not to eliminate variability, but to ensure that the orbital divergence of trajectories never exceeds the critical threshold beyond which balance recovery becomes biomechanically impossible.