Modeling the relationship between wrist angle and muscle thickness during wrist flexion–extension based on the bone–muscle lever system: A comparison study

A structural model of skeletal muscle based on the bone–muscle lever system is proposed to describe the relationship between wrist angle and thickness of the extensor carpi radialis muscle during the process of wrist flexion–extension. This model applied the cosine theorem to the expression for muscle length, in order to relate wrist angle to muscle thickness by the invariance of muscle volume, which was used to calculate the length of the extensor carpi radialis muscle from the muscle thickness. To validate the proposed model, wrist angles were also computed by other models based on regression, such as linear regressions, an artificial neural network, and a support vector machine. The results show that wrist angles are predicted well at different extension rates by our proposed model, with correlation coefficient (R2) greater than 0.94, standard root mean square error (SRMSE) less than 8.0 and relative root mean square error (RRMSE) less than 13%. These parameters show that the proposed model is better than the other regression-based models (p < 0.05). More importantly, this model can be clearly related to physiology. Thus, it can potentially be used to investigate the relationship between internal structural changes of skeletal muscle and external limb behaviors, and to develop prosthetic hands and functional electrical stimulation systems.