Is the Hénon map able to predict the interaction dynamics between the knee and hip joints emerged during sit-to-stand movement?

Abstract

In this study, the performance of a two-dimensional Hénon map in predicting the interactive dynamics of the knee and hip joints emerging during a normative sit-to-stand movement was evaluated. The instantaneous values of the knee and hip joints were the model inputs, and the next values of the knee and hip joints were predicted by the Hénon map. The map predicted the desired relative behavior of the joints, showing synergetic coordination between the joints. The experimental data were recorded from four healthy participants and used to identify the Hénon map via a genetic algorithm. Model performance was quantitatively assessed by computing the calculated prediction error and analyzing the behavioral dynamics of the state spaces reconstructed via the captured kinematic data. According to the results, there was an obvious similarity between the dynamics of the state space trajectories of the identified model and those of the recorded data, not only in terms of stretching and folding dynamics, but also concerning generalized synchrony. The acceptable performance of the proposed modeling solution can also be demonstrated through these results.

Keywords: Hénon map; dynamic similarity; kinematic synergy; sit-to-stand.