Modeling the response of normal and ischemic cardiac tissue to electrical stimulation

Heart disease, the leading cause of death worldwide, is often caused by ventricular fibrillation. A common treatment for this lethal arrhythmia is defibrillation: a strong electrical shock that resets the heart to its normal rhythm. To design better defibrillators, we need a better understanding of both fibrillation and defibrillation. Fundamental mysteries remain regarding the mechanism of how the heart responds to a shock, particularly anodal shocks and the resultant hyperpolarization. Virtual anodes play critical roles in defibrillation, and one cannot build better defibrillators until these mechanisms are understood.;We are using mathematical modeling to numerically simulate observed phenomena, and are exploring fundamental mechanisms responsible for the heart's electrical behavior. Such simulations clarify mechanisms and identify key parameters.;We investigate how systolic tissue responds to an anodal shock and how refractory tissue reacts to hyperpolarization by studying the dip in the anodal strength-interval curve. This dip is due to electrotonic interaction between regions of depolarization and hyperpolarization following a shock. The dominance of the electrotonic mechanism over calcium interactions implies the importance of the spatial distribution of virtual electrodes.;We also investigate the response of localized ischemic tissue to an anodal shock by modeling a regional elevation of extracellular potassium concentration. This heterogeneity leads to action potential instability, 2:1 conduction block (alternans), and reflection-like reentry at the boarder of the normal and ischemic regions. This kind of reflection (reentry) occurs due to the delay between proximal and distal segments to re-excite the proximal segment.;Our numerical simulations are based on the bidomain model, the state-of-the-art mathematical description of how cardiac tissue responds to shocks. The dynamic LuoRudy model describes the active properties of the membrane. To model ischemia, the Luo-Rudy model is modified by adding ischemic-related ion currents and concentrations to mimic conditions during the initial phase of ischemia. The stimulus is applied through a unipolar electrode that induces a complicated spatial distribution of transmembrane potential, including adjacent regions of depolarization and hyperpolarization.;This research is significant because it uncovers basic properties of excitation that are fundamental for understanding cardiac pacing and defibrillation.