Rhythmic Dynamics and Synchronization via Dimensionality Reduction: Application to Human Gait

Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system.Author Summary: Complex physiological rhythms arise from a large variety of biological systems that include natural pacemakers as well as feedback mechanisms, from the heartbeat to the rhythmic movement of human walking. Accurately extracting and characterizing the fluctuations underlying the biological rhythms is a fundamental problem which holds the key to understanding the mechanisms that govern the dynamics of biological systems. Usually such signals demonstrate certain oscillatory patterns, with each period displaying irregular fluctuation, or nontrivial dynamics, over time. This renders traditional spectral methods and nonlinear techniques less effective. We propose a novel approach to highlight the intrinsic fluctuations masked by the periodic component and noise through advanced dimension-reduction techniques, and apply it to human gait data from healthy subjects and diabetics. We find that this approach is capable of extracting the intrinsic dynamics and identifying the subtle synchronization pattern between knee and ankle. We find that although the two groups of individuals demonstrate remarkable differences in the dynamics of ankle movement and ankle-knee synchronization, the knee movement of both groups show similar dynamics. These results suggest that sensory feedback from a peripheral nerve system (like the feet) does not play an important role in regulating the motor control of human walking.