A Nonlinear Time Series Analysis on the Effect of Foot Injury on Gait Dynamics

The effects of foot injuries regarding bilateral asymmetry and gait dynamics are still poorly understood. Previous work discussed rehabilitation, postural control, and asymmetry, with the models being mainly validated for upper body translations and no or minimal assessment on rotation. The aim of this study was to assess the effect of foot injury on gait dynamics. For this, a wearable sensors system for data collection of the key variables of the of human movement was considered. The dynamics of motion – recorded in the plane of motion using a laser sensor – was assessed using a new projective method which considers the axial rotations, translation, and in-plane rotation patterns for normal human gait vs. simulated gait pathologies. A nonlinear timeseries analysis, along with a Poincare map, phase space, time delay, Lyapunov exponents, and false nearest neighbors (FNN) method have been considered in order to convey the periodicity of the data collected for a healthy individual with and without a simulated injury. The Lyapunov exponents which quantity the degree of separation of nearby trajectories are used to differentiate between the chaotic and non-chaotic behavior. The positive sign of the largest Lyapunov exponents for all data indicated “the exponential separation of nearby trajectories as time evolves”, that is, the chaotic behavior of the system.