Study of calcium overload in one-dimensional cardiac model. role of spatial distribution of pathology

The premature ventricular contractions are relatively common clinical diagnosis. Ventricular activation initiated from an ectopic focus in the heart ventricles results in the premature contraction. Pathophysiology of this disease is related to calcium overload in cardiomyocytes when delayed after depolarization aroused due to spontaneous calcium release from sarcoplasmic reticulum. This could lead to myocardium activation from an ectopic focus and premature ventricular contraction. In our work, we study calcium overload in cardiomyocytes using one-dimensional monodomain electrophysiological model of the myocardium. Calcium overload in cardiomyocytes is simulated by inhibition of Na$^+$/K$^+$ exchanger and SERCA-pump within the Noble98 cell model. We propose an algorithm to automatically detect premature activation in the one-dimensional model. The main goal of our study is to evaluate the effect of a spatial distribution of pathology on the frequency of premature myocardium excitations. Model simulation showed that an ectopic activation is usually initiated in a region of the maximum pathology. However, if the function of a spatial distribution of pathology had a discontinuity, then an ectopic activation initiated from the region of discontinuity of a function. Also, we study changes in action potential generation in the pathology region. We obtained a nonlinear and a nonlocal relationship between spatial distribution of pathology and the degree of sarcoplasmic reticulum overload in the one-dimensional model.