On the use of Hilbert transform for gait local dynamic stability analysis

• Published in: Research on biomedical engineering Vol. 39; no. 1; pp. 159 - 165
• Main Authors: Souza, Gustavo S. S., Andrade, Adriano O., Pereira, Adriano A., Vieira, Marcus F.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2023
• Subjects: Biomaterials; Biomedical Engineering and Bioengineering; Biomedical Engineering/Biotechnology; Engineering; Original Article; Hilbert transform; Non-linear gait analysis; Rosenstein algorithm; Local dynamic stability; State-space reconstruction
• ISSN: 2446-4740; 2446-4740
• DOI: 10.1007/s42600-023-00260-4

Purpose The Rosenstein algorithm is widely used for local dynamic stability (LDS) analysis of human gait to estimate the maximum exponent of Lyapunov. This algorithm needs two parameters to reconstruct the state-space that represents the original system: the time delay and the embedded dimension, which require the implementation of two other algorithms. These parameters vary according to the used dataset, which requires a new state-space reconstruction whenever the dataset changes. This study evaluates a method still unassessed in gait studies for state-space reconstruction to analyze LDS of human gait signals using Hilbert transform properties to reconstruct standardized state-spaces. This method does not require estimation of the aforementioned parameters for state-space reconstruction. Methods The proposed method, that we have called Hilbert Transform Reconstruction (HTR) method, is assessed and compared to the classical method using two different datasets from previous studies. Dataset A consisted of young adults aged 23.70 ± 5.30 years walking on a treadmill under 7 conditions related to backpack load and position (control condition: no backpack), while dataset B consisted of young adults aged 25.2 ± 5.1 years and older adults aged 69.3 ± 6.6 years walking on a treadmill at 7 inclinations (control condition: level inclination). The comparison was made using gait kinematic data collected by a 3D motion capture system. Results For dataset A, using the classical method, significant differences were only detected in one condition, while using the HTR method they were detected in four conditions when compared to the control condition. For dataset B, using the HTR method, significant differences were detected in five conditions, while using the classical method only in three conditions when compared to the control condition (5 vs 3 for young adults and 4 vs 2 for older adults). Overall, the results using the HTR method were consistent with the results reported in the corresponding previous studies obtained using the classical method: For dataset A, carrying heavy loads greater than 10% of body weight detrimentally affects gait LDS in a position-dependent manner, especially in the front part of the body. Bilateral back position with 10% of body weight is the safer condition, not significantly influencing gait LDS. Results for dataset B indicates that sloped surfaces impose an increasing challenge to gait the higher their inclination, especially in upward inclines. This same pattern is observed both in young and older subjects. Furthermore, the HTR method keeps better correlation with noise-added signals than the classical method up to 50 dB signal-to-noise ratio, indicating more robustness to noise. Conclusion The HTR method standardized the state-space reconstruction and was more sensitive to the evaluated conditions than the classical method. It is also slightly more robust to noise than the classical method.