Phase-Space Dynamics Reveal Structured and Chaotic Motility in Human Sperm via DTW Clustering

Abstract

BackgroundTraditional sperm motility metrics often fail to reflect the dynamic complexity of motion patterns. Here, we present an unsupervised framework combining dynamic time warping (DTW) clustering with phase-space and fatigue-sensitive descriptors to uncover latent motility phenotypes. MethodsWe analyzed 1,176 sperm tracks from the VISEM dataset using DTW distance matrices applied to velocity time series, followed by agglomerative hierarchical clustering (n = 2). After cluster assignment, we extracted phase-space features--recurrence rate, spectral entropy, fractal index, and Lyapunov approximation--and computed fatigue metrics such as VSL slope. ResultsDTW clustering revealed two well-separated motility phenotypes with a mean silhouette score of 0.861. Chaotic-like tracks exhibited higher spectral entropy (4.45 vs. 2.58), elevated fractal index (0.079 vs. 0.434), and increased local instability as reflected by the Lyapunov approximation (0.131 vs. 0.009; all p < 0.001). Recurrence rate showed no significant difference. VSL slope was markedly more negative in Chaotic-like tracks, indicating a stronger fatigue component. ConclusionsOur pipeline stratifies sperm motility into biologically interpretable dynamic classes using raw temporal profiles--without relying on predefined scalar indices. This approach may enhance phenotypic analysis in reproductive diagnostics by capturing structural and fatigue-driven variability in sperm motion.