journal article·2026-04-18Open access

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

Arash Mohammadzadeh Gonabadi, Judith M. Burnfield

Applied Sciences· Volume 16· Issue 8

Abstract

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.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Balance, Gait, and Falls Prevention · Muscle activation and electromyography studies · Motor Control and Adaptation

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Research Institute, Madonna Rehabilitation Hospitals, Omaha, NE 68118, USA

Funding

U.S. Department of Education, National Institute on Disability and Rehabilitation Research · American Heart Association

References (66)

Show source-provided references
1. Human Movement Variability, Nonlinear Dynamics, and Pathology: Is There a Connection?10.1016/j.humov.2011.06.002 ↗
2. Mohammadzadeh Gonabadi, A., and Fallahtafti, F. (2025). Gait Stability Under Hip Exoskeleton Assistance: A Phase-Dependent Analysis Using Gait Tube Methodology. Appl. Sci., 15.10.3390/app15137530 ↗
3. Mohammadzadeh Gonabadi, A., Pipinos, I.I., Myers, S.A., and Fallahtafti, F. (2026). Gait Stability in Peripheral Artery Disease: A Phase-Dependent Analysis Using Gait Tube Methodology. Front. Rehabil. Sci., 7.10.3389/fresc.2026.1725201 ↗
4. Step Width Variability, but Not Step Length Variability or Step Time Variability, Discriminates Gait of Healthy Young and Older Adults during Treadmill Locomotion10.1016/j.jbiomech.2003.11.012 ↗
5. The Differences between Overground and Treadmill Walking in Nonlinear, Entropy-Based and Frequency Variables Derived from Accelerometers in Young and Older Women—Preliminary Report
6. Margin of Stability May Be Larger and Less Variable during Treadmill Walking Versus Overground10.3390/biomechanics1010009 ↗
7. Mohammadzadeh Gonabadi, A., Antonellis, P., Dzewaltowski, A.C., Myers, S.A., Pipinos, I.I., and Malcolm, P. (2024). Design and Evaluation of a Bilateral Semi-Rigid Exoskeleton to Assist Hip Motion. Biomimetics, 9.10.3390/biomimetics9040211 ↗
8. A System for Simple Robotic Walking Assistance with Linear Impulses at the Center of Mass10.1109/TNSRE.2020.2988619 ↗
9. Mohammadzadeh Gonabadi, A., Fallahtafti, F., and Burnfield, J.M. (2024). How Gait Nonlinearities in Individuals Without Known Pathology Describe Metabolic Cost During Walking Using Artificial Neural Network and Multiple Linear Regression. Appl. Sci., 14.10.3390/app142311026 ↗
10. McCamley, J., Denton, W., Arnold, A., Raffalt, P., and Yentes, J. (2018). On the Calculation of Sample Entropy Using Continuous and Discrete Human Gait Data. Entropy, 20.10.3390/e20100764 ↗
11. Ahmadi, S., Sepehri, N., Wu, C., and Szturm, T. (2018). Sample Entropy of Human Gait Center of Pressure Displacement: A Systematic Methodological Analysis. Entropy, 20.10.3390/e20080579 ↗
12. Comparative Study of Entropy Sensitivity to Missing Biosignal Data10.3390/e16115901 ↗
13. Balance and Mobility Training with or without Concurrent Cognitive Training Does Not Improve Posture, but Improves Reaction Time in Healthy Older Adults10.1016/j.gaitpost.2016.12.006 ↗
14. Effects of Short-Term Training on Heart Rate Dynamics in Individuals with Spinal Cord Injury10.1016/j.autneu.2009.03.012 ↗
15. Liu, A.-B., and Lin, C.-W. (2019). Multiscale Approximate Entropy for Gait Analysis in Patients with Neurodegenerative Diseases. Entropy, 21.10.3390/e21100934 ↗
16. Karmakar, C.K., Khandoker, A.H., Begg, R.K., Palaniswami, M., and Taylor, S. (2007). Understanding Ageing Effects by Approximate Entropy Analysis of Gait Variability. Proceedings of the 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE.10.1109/IEMBS.2007.4352703 ↗
17. A Comparative Study on Approximate Entropy Measure and Poincaré Plot Indexes of Minimum Foot Clearance Variability in the Elderly during Walking10.1186/1743-0003-5-4 ↗
18. Approximate Entropy of Motoneuron Firing Patterns during a Motor Preparation Task10.1016/j.jneumeth.2008.05.001 ↗
19. Determining Lyapunov Exponents from a Time Series10.1016/0167-2789(85)90011-9 ↗
20. Effect of Data and Gap Characteristics on the Nonlinear Calculation of Motion During Locomotor Activities
21. Selection Procedures for the Largest Lyapunov Exponent in Gait Biomechanics10.1007/s10439-019-02216-1 ↗
22. Length of Time-Series Gait Data on Lyapunov Exponent for Fall Risk Detection
23. Comparing Dynamical Systems Concepts and Techniques for Biomechanical Analysis10.1016/j.jshs.2016.01.013 ↗
24. Piergiovanni, S., and Terrier, P. (2024). Validity of Linear and Nonlinear Measures of Gait Variability to Characterize Aging Gait with a Single Lower Back Accelerometer. Sensors, 24.10.21203/rs.3.rs-4485214/v2 ↗
25. Kinematic Variability and Local Dynamic Stability of Upper Body Motions When Walking at Different Speeds10.1016/j.jbiomech.2004.12.014 ↗
26. Kuznetsov, N.A., and Rhea, C.K. (2017). Power Considerations for the Application of Detrended Fluctuation Analysis in Gait Variability Studies. PLoS ONE, 12.10.1371/journal.pone.0174144 ↗
27. Phinyomark, A., Larracy, R., and Scheme, E. (2020). Fractal Analysis of Human Gait Variability via Stride Interval Time Series. Front. Physiol., 11.10.3389/fphys.2020.00333 ↗
28. Detrended Fluctuation Analysis of Gait Dynamics When Entraining to Music and Metronomes at Different Tempi in Persons with Multiple Sclerosis10.1038/s41598-020-69667-8 ↗
29. Gait Dynamics, Fractals and Falls: Finding Meaning in the Stride-to-Stride Fluctuations of Human Walking10.1016/j.humov.2007.05.003 ↗
30. Tempting Long-Memory—On the Interpretation of DFA Results10.5194/npg-11-495-2004 ↗
31. Świtoński, A., Josiński, H., Polański, A., and Wojciechowski, K. (2024). Correlation Dimension and Entropy in the Assessment of Sex Differences Based on Human Gait Data. Front. Hum. Neurosci., 17.10.3389/fnhum.2023.1233859 ↗
32. The Effects of a Lower Body Exoskeleton Load Carriage Assistive Device on Oxygen Consumption and Kinematics during Walking with Loads10.1080/00140139.2010.512982 ↗
33. Estimation of Hurst Exponent for Sequential Monitoring of Clinical Trials with Covariate Adaptive Randomization10.1016/j.cct.2022.106887 ↗
34. Likens, A.D., Mangalam, M., Wong, A.Y., Charles, A.C., and Mills, C. (2023). Better than DFA? A Bayesian Method for Estimating the Hurst Exponent in Behavioral Sciences. arXiv.
35. Mylonas, V., Wiles, T.M., Kim, S.K., Stergiou, N., and Likens, A.D. (2026). Hurst-Kolmogorov Process Is a More Reliable and Statistically Powerful Alternative to Detrended Fluctuation Analysis for Estimating Hurst in Short Walking Trials. Ann. Biomed. Eng., 175.10.1007/s10439-026-04011-1 ↗
36. Walking Speed Influences on Gait Cycle Variability10.1016/j.gaitpost.2006.08.010 ↗
37. Kirchner, M., Schubert, P., Liebherr, M., and Haas, C.T. (2014). Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson ’ s Disease: Stitching Together Short Gait Trials. PLoS ONE, 9.10.1371/journal.pone.0085787 ↗
38. Investigating the Interaction between Heart Rate Variability and Sleep EEG Using Nonlinear Algorithms10.1016/j.jneumeth.2013.08.008 ↗
39. Nonlinear Time Series Analysis of Normal and Pathological Human Walking10.1063/1.1324008 ↗
40. Wolf, S.L. (1996). The Biomechanics of the Foot and Ankle, F.A. Davis. [2nd ed.].
41. Abnormal Foot Pressures Alone May Not Cause Ulceration10.1111/j.1464-5491.1989.tb01198.x ↗
42. NONAN GaitPrint: An IMU Gait Database of Healthy Young Adults10.1038/s41597-023-02704-z ↗
43. A Six Degrees-of-Freedom Marker Set for Gait Analysis: Repeatability and Comparison with a Modified Helen Hayes Set10.1016/j.gaitpost.2009.04.004 ↗
44. Federolf, P.A. (2013). A Novel Approach to Solve the “Missing Marker Problem” in Marker-Based Motion Analysis That Exploits the Segment Coordination Patterns in Multi-Limb Motion. PLoS ONE, 8.10.1371/journal.pone.0078689 ↗
45. Gap-Filling Approaches for Eddy Covariance Methane Fluxes: A Comparison of Three Machine Learning Algorithms and a Traditional Method with Principal Component Analysis10.1111/gcb.14845 ↗
46. Automated Gap-Filling for Marker-Based Biomechanical Motion Capture Data10.1080/10255842.2020.1789971 ↗
47. Gait Variability: Methods, Modeling and Meaning Example of Increased Stride Time Variability in Elderly Fallers Quantification of Stride-to-Stride Fluctuations10.1186/1743-0003-2-19 ↗
48. Fractal Dynamics in Physiology: Alterations with Disease and Aging10.1073/pnas.012579499 ↗
49. Jan, Y.-K., Lin, C.-F., Liao, F., and Singh, N.B. (2023). Editorial: Nonlinear Dynamics and Complex Patterns in the Human Musculoskeletal System and Movement. Front. Bioeng. Biotechnol., 11.10.3389/fbioe.2023.1339376 ↗
50. Mosaic Organization of DNA Nucleotides10.1103/PhysRevE.49.1685 ↗
51. Detection of a Long-Range Correlation with an Adaptive Detrending Method10.1103/PhysRevE.86.011135 ↗
52. Fractal Analyses for ‘Short’ Time Series: A Re-Assessment of Classical Methods10.1016/j.jmp.2006.07.004 ↗
53. Ihlen, E.A.F. (2012). Introduction to Multifractal Detrended Fluctuation Analysis in Matlab. Front. Physiol., 3.10.3389/fphys.2012.00141 ↗
54. Raffalt, P.C., Yentes, J.M., Freitas, S.R., and Vaz, J.R. (2023). Calculating Sample Entropy from Isometric Torque Signals: Methodological Considerations and Recommendations. Front. Physiol., 14.10.3389/fphys.2023.1173702 ↗
55. Approximate Entropy as a Measure of System Complexity10.1073/pnas.88.6.2297 ↗
56. Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy10.1152/ajpheart.2000.278.6.H2039 ↗
57. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets10.1016/0167-2789(93)90009-P ↗
58. Measuring the Strangeness of Strange Attractors10.1016/0167-2789(83)90298-1 ↗
59. Assessing the Stability of Human Locomotion: A Review of Current Measures10.1098/rsif.2012.0999 ↗
60. Kantz, H., and Schreiber, T. (2003). Nonlinear Time Series Analysis, Cambridge University Press.10.1017/CBO9780511755798 ↗
61. Stergiou, N. (2018). Nonlinear Analysis for Human Movement Variability, CRC Press.10.1201/9781315370651 ↗
62. Nonlinear Time-Series Analysis Revisited10.1063/1.4917289 ↗
63. An Improved Surrogate Method for Detecting the Presence of Chaos in Gait10.1016/j.jbiomech.2005.10.019 ↗
64. Locomotor Sensory Organization Test: How Sensory Conflict Affects the Temporal Structure of Sway Variability During Gait10.1007/s10439-015-1440-2 ↗
65. The Effect of the Walking Speed on the Stability of the Anterior Cruciate Ligament Deficient Knee10.1016/j.clinbiomech.2004.06.008 ↗
66. Temporal Structure of Variability Reveals Similar Control Mechanisms during Lateral Stepping and Forward Walking10.1016/j.gaitpost.2012.10.017 ↗