Modeling the length dependence of isometric force in human quadriceps muscles

Functional electrical stimulation is used to restore movement and function of paralyzed muscles by activating skeletal muscle artificially. An accurate and predictive mathematical model can facilitate the design of stimulation patterns that produce the desired force. The present study is a first step in developing a mathematical model for non-isometric muscle contractions. The goals of this study were to: (1) identify how our isometric force model's parameters vary with changes in knee joint angle, (2) identify the best knee flexion angle to parameterize this model, and (3) validate the model by comparing experimental data to predictions in response to a wide range of stimulation frequencies and muscle lengths. Results showed that by parabolically varying one of the free parameters with knee joint angle and fixing the other parameters at the values identified at 40° of knee flexion, the model could predict the force responses to a wide range of stimulation frequencies and patterns at different muscle lengths. This work showed that the current isometric force model is capable of predicting the changes in skeletal muscle force at different muscle lengths.