The characteristics method applied to the study of muscle dynamics (Q801835)

In the paper the macroscopic muscle dynamics is analyzed on the basis of the underlying microscopic contraction mechanisms. The contractile elements are the sarcomeres with their so-called cross-bridges as the microscopic force generators. These cross-bridges can exist in either of 2 states. The model of muscle fibre contains the contractile element of sarcomere in series with a passive visco-elastic element and in parallel with an element which accounts for the elasticity of the relaxed muscle. Assuming first-order kinetics for the actin-myosin bonding reaction a partial differential equation is posed for the probability distribution function n(x,t) of attached cross-bridges with displacement x at time t. The way of obtaining the analytical solution by the characteristics method is sketched in the general case, and the transient response of n(x,t) at a unit step activation is given. For the constant contractile velocity case and for the isometric contraction case the muscle dynamics is analyzed on the basis of the proposed model. The sum of the rate constants for unity displacement has been found to be the dominant contractile factor in determining the dynamic behavior of the muscle, and it has been quantitatively demonstrated how, during constant velocity release, the rise time of transient tension consistently decreases with increasing velocity.