Frequency response model of skeletal muscle and its association with contractile properties of skeletal muscle

The aims of the present study were to develop a mathematical model of the skeletal muscle based on the frequency transfer function, referred to as frequency response model, and to presume the relationship between the model elements and skeletal muscle contractile properties. Twitch force in elbow flexion was elicited by applying a single electrical stimulation to the motor point of biceps brachii muscles, and then analyzed visually by the Bode gain and phase diagram of the force signal. The frequency response model was represented by a frequency transfer function consisting of five basic control elements (proportional element, dead time element, and three first-order lag elements). The model element constants were estimated by best-fitting to the Bode gain and phase diagram of the twitch force signal. The proportional constant and the dead time in the frequency response model correlated significantly with the peak torque and the latency in the actual twitch force, respectively. In addition, the time constants of the three first-order lag elements in the model correlated strongly with the contraction time and the half relaxation time in the actual twitch force. The results suggested a possibility that the individual elements in the frequency response model would reflect the biochemical and biomechanical properties in the excitation–contraction coupling process of skeletal muscle.