The phenomenological model of muscle contraction with a controller to simulate the excitation–contraction (E–C) coupling

We previously proposed a systematic motor model for muscle with two parallel Maxwell elements and a force generator P. The motor model showed the non-linear behavior of a muscle, such as the force–velocity relation and the force depression and enhancement, by using weight functions. Our newly proposed muscle model is based on the molecular mechanism of myosin cross-bridges. We assume that each parallel Maxwell element represents the mechanical properties of weak and strong binding of the myosin head to actin. Furthermore, we introduce a controller to simulate the excitation–contraction coupling of the muscle. The new muscle model satisfies all the properties obtained in our previous model and reduces the wasted energy of the viscous component to less than 5% of the total energy. The controller enables us to simulate contractions of slow and fast twitch muscles, which are driven by an artificial action potential or a processing electromyography signal despite their same mechanical components. The maximum velocities are calculated to be 3.4L0 m/s for the fast twitch muscle model and 2.5L0 m/s for the slow twitch muscle model, where L0 is the initial length of the muscle model.