Sudden cardiac death occurs when an unexpected ventricular arrhythmia degenerates into fibrillation, which prevents the heart from pumping blood through the body. Heart diseases such as heart failure are significant risk factors for arrhythmias and are characterized by severely altered calcium (Ca2+) handling in cardiac myocytes. However, the Ca2+-dependent mechanisms underlying cardiac arrhythmia initiation are not well understood.
In this work, mathematical models were developed to investigate the molecular mechanisms of pathological Ca2+ dynamics in ventricular cardiac myocytes. A biophysically-detailed three-dimensional model of a subcellular Ca2+ release site was used to study mechanisms of spontaneous spatially-confined Ca2+ release events, known as Ca2+ “sparks,” which underlie cell-wide Ca2+ release and arrhythmogenic Ca2+ waves. It revealed a correlation between Ca2+ spark frequency and the maximum eigenvalue of the adjacency matrix describing the Ca2+ release channel lattice. This relationship was further investigated using a mathematical contact network model describing the Ca2+ spark initiation process.
A multiscale model of a 1D fiber of myocytes was also developed to investigate the mechanisms of ectopic excitation of cardiac tissue. The model was used to study the stochastic variability of delayed afterdepolarizations caused by spontaneous propagating waves of Ca2+ sparks. Large delayed afterdepolarizations triggered ectopic beats probabilistically due to the stochasticity of Ca2+ release channel gating. A novel method was developed to estimate the probability of rare arrhythmic events
