Topological data analysis of postural sway: characterizing balance control during childhood development

Postural control matures through gradual refinement of sway organization, yet traditional CoP measures capture only variability and not the underlying geometric structure. Topological Data Analysis (TDA) offers a complementary approach by quantifying the persistence and complexity of sway dynamics. This study applied TDA to investigate developmental and task-related differences in CoP topology from childhood to adulthood.

A total of 460 healthy participants (ages 7-12 years and young adults) completed eight standing balance tasks that manipulated visual input, base of support (BoS), and cognitive load. For each 30-s CoP trial, Vietoris-Rips persistence diagrams were computed, and four H1-based TDA metrics were extracted: H1_Wasserstein distance, H1_TotalPersistence, Persistent Entropy, and H1_NumLongLoops. Mixed-design ANOVAs evaluated the effects of Age, Gender, Vision, BoS, and Cognitive Dual-Tasking (CDT) on each metric.

All TDA metrics exhibited strong age effects (all p < 0.001), with children showing greater persistence magnitudes and more long-lived loops than adults, reflecting less stable and more oscillatory sway organization. Vision significantly modulated H1_Wasserstein and Total Persistence (p < 0.001), with eye closure producing pronounced increases. Single-leg stance robustly amplified all TDA measures (p < 0.001). CDT induced moderate but significant alterations in several metrics, whereas Persistent Entropy remained insensitive to visual deprivation (p = 0.168). Gender differences were generally small but interacted with task difficulty for selected outcomes.

TDA revealed systematic developmental transitions in the topology of CoP dynamics, shifting from rich multi-loop structures in childhood to topologically simpler and more stable configurations in adulthood. These findings support TDA as a sensitive and physiologically meaningful approach for evaluating balance maturation and may aid in detecting atypical postural control patterns in clinical or developmental contexts.