Mutual information between joint angles and toe height in healthy subjects

Understanding the relationship between the position of the foot and the lower limb joint angles during normal gait is critical for the identification of the mechanisms involved in pathological gait. In this article, we introduce a novel framework that characterizes this relationship using mutual information in healthy subjects. The nonlinear connection between these variables is quantified using mutual information, and the MINE algorithm is used for precise estimation. Several simulations over Gaussian bivariate random variables reveal that overfitting is a critical factor affecting mutual information estimations by MINE, and we propose a simple methodology to address this issue when using gait signals. Our findings indicate that the statistical dependency between joint angles and toe height is symmetrical between the limbs for healthy subjects. Additionally, our results show that the ipsilateral knee angle holds the most significant amount of information regarding the toe height. In simpler terms, this knee angle serves as the most reliable predictor for toe height, and vice versa. To further enhance our understanding, we have developed a mutual information reference profile that enables the comparison of how the relationship between these biomechanical variables evolves under pathological conditions. The findings have significant implications for gait analysis and may aid in the identification and understanding of gait abnormalities in various contexts, contributing to the advancement of biomechanical research and clinical applications.