Mathematical modelling of the contribution of mechanical inhomogeneity in the myocardium to contractile function.

Earlier we developed a mathematical model of the cardiac muscle that allowed for inactivation through the effects of cooperativity of contractile proteins. In the present work we used the model to analyze the mechanical function of an inhomogeneous myocardium. To simulate the latter we chose, as the simplest sytstem, a duplex in which muscles with different mechanical properties were connected in series and in parallel. Numerical experiments showed that the basic effect due to the inhomogeneity consists in the non-additivity of the mechanical characteristics of the muscle, e.g., of the relationship between end-systolic length and end-systolic force (Les - Pes). As a rule, non-additivity consists in a negative inotropic effect. The analysis showed that the cause of non-additivity is redistribution of loads between muscles (in a parallel duplex), redistribution of lengths (in a serial duplex), changes in the rate of contraction of each muscle compared to contraction that when working separately, shifts in time to Les. Also, the model predicts that additional inactivation of contractile proteins in a muscle within a duplex against isolation is the substantial mechanism of enhanced non-additivity. Among the factors of inhomogeneity studied the basic determinants are difference in amplitudes between isometric tensions developed by each muscle in isolation and the asynchronism in the development of these tensions.