How Gait Nonlinearities in Individuals Without Known Pathology Describe Metabolic Cost During Walking Using Artificial Neural Network and Multiple Linear Regression

Abstract

This study uses Artificial Neural Networks (ANNs) and multiple linear regression (MLR) models to explore the relationship between gait dynamics and the metabolic cost. Six nonlinear metrics—Lyapunov Exponents based on Rosenstein’s algorithm (LyER), Detrended Fluctuation Analysis (DFA), the Approximate Entropy (ApEn), the correlation dimension (CD), the Sample Entropy (SpEn), and Lyapunov Exponents based on Wolf’s algorithm (LyEW)—were utilized to predict the metabolic cost during walking. Time series data from 10 subjects walking under 13 conditions, with and without hip exoskeletons, were analyzed. Six ANN models, each corresponding to a nonlinear metric, were trained using the Levenberg–Marquardt backpropagation algorithm and compared with MLR models. Performance was assessed based on the mean squared error (MSE) and correlation coefficients. ANN models outperformed MLR, with DFA and Lyapunov Exponent models showing higher R2 values, indicating stronger predictive accuracy. The results suggest that gait’s nonlinear characteristics significantly impact the metabolic cost, and ANNs are more effective for analyzing these dynamics than MLR models. The study emphasizes the potential of focusing on specific nonlinear gait variables to enhance assistive device optimization, particularly for hip exoskeletons. These findings support the development of personalized interventions that improve walking efficiency and reduce metabolic demands, offering insights into the design of advanced assistive technologies.