Effect of Data Length on Nonlinear Analysis of Human Motion During Locomotor Activities

Nonlinear analysis provides a framework for understanding the complexity and stability of human locomotion by capturing dynamic patterns beyond linear methods. This study examined the effect of data length on seven nonlinear measures: Sample Entropy (SpEn), Approximate Entropy (ApEn), Lyapunov Exponents using Wolf’s (LyEW) and Rosenstein’s (LyER) algorithms, Detrended Fluctuation Analysis (DFA), Correlation Dimension (CD), and the Hurst–Kolmogorov process (HK). A 3500-frame kinematic dataset from a healthy adult performing motor-assisted elliptical training and treadmill walking was segmented from 100 to 3500 frames in 10-frame increments. Data from treadmill and elliptical conditions were analyzed and presented in a combined manner to highlight general stabilization trends across locomotor tasks. Results revealed that increasing data length significantly affected all nonlinear metrics (p ≤ 0.0005). Stabilization occurred at varying minimum lengths: SpEn at ~4.5–8.8 s (540–1060 frames), ApEn at ~5.4–7.7 s (650–920 frames), LyEW at ~19.1–29.2 s (2290–3500 frames), LyER at ~1.3–1.5 s (150–180 frames), DFA at ~29.2 s (3500 frames), CD at ~1.7–15.9 s (200–1910 frames), and HK at ~9.1–9.8 s (1090–1180 frames). Notably, HK achieved stable estimates in approximately one-third of the time required for DFA and substantially less than LyEW, supporting its suitability for time-constrained or clinical settings. These findings suggest the need to tailor data collection to each nonlinear metric and to report data length explicitly to improve accuracy, reproducibility, and methodological rigor in gait variability research. However, these findings should be interpreted within the limitations of a single-participant, exploratory design.