Chemo-mechanical model for skeletal muscle contraction

Generation of force in skeletal muscle tissue depends on both chemical and mechanical phenomena. In this work, considering the kinetics of cross bridges, a one dimensional model has been proposed for predicting the isometric force according to the intracellular calcium ion distribution. Introduction The different ways of skeletal muscle activation lead to the formation of cross bridges (XB) according to the available calcium ion flow. XB kinetics is the cyclic connection between thin and thick filament at the sarcomere level to produce mechanical force. Since the Huxley model (Huxley 1974) can be considered as the first numerical muscle model considering XB kinetics, several works have developed different XB formulations (Razumova et al. 1999; Shorten et al. 2007). Recently, a more realistic 3D model (Heidlauf and Röhrle 2014) have appeared providing a chemo-mechanical approach to simulate complex muscle geometries. In this work, a new thermodynamically consistent model is proposed incorporating different scales to reproduce the force developed by muscle tissue. Material and Methods Cross bridge (XB) kinetics Mechanical force in skeletal muscle is produced during the well known power stroke, which is the transition step between chemical and mechanical energy. Consequently, a chemical model should be able to consider this event. Therefore, XB kinetics model of Razumova et al. 1999 (Fig. 1) has been used as the base of the chemical part. This model considers four states, including the preand postpower stroke. The first state (Roff) corresponds to the fraction of thin-filament regulatory units (RU) which are blocked by tropomyosin-troponin complex (TTC) (off position). In the second state (D) Ca has bound to TTC, RU changes to on position but there is no attachment. A1 and A2 states include cross bridge formation. Attached XB can be in two situations, preand post-power stroke. The fractions of these situations are defined respectively with A1 and A2. These states are in a cyclic dynamics and different rates (Fig. 1) control the number of XBs in the four situations. Kon and koff rates manage the on and off condition of RUs according to the calcium concentration level. The concentration of XBs in the four different situations can be found by solving a system of three ordinary equations as:                               t A g h t hA t A t A h f t A h t fD t A t D f k t gA t A f t R k t D off off on