This proposal addresses five major aspects of research that will be carried out to elucidate the mechanism underlying normal/abnormal cardiac rhythms. The first part is to perform a comprehensive investigation of the phenomenon associated with phase-resetting and annihilation of single cardiac rhythm in response to external stimuli. In order to study such a phenomenon, computer simulations and bifurcation analysis will be carried out on the (previously published) cardiac electrical models. The second part is to (i) minimize the number of differential equations in these models and (ii) unified them so that one set of equations can describe electrical activity of any cardiac pacemaker cell. To obtain a simpler mathematical model we will try to find a relationship among the gating dynamic variables; to formulate a unified model we will consider the role of intracellular Ca2+ and Na+ ions and the Ca+ -buffering power of the intracellular stores, in addition to extracellular K+ compartmentation. The third part is to (i) stimulate on a computer the propagation of an impulse along a string of pacemake cardiac cells and (ii) extend it to a 2- and 3-dimensional network of excitable cells. To simulate impulse propagation on a string, we will use the mathematical model obtained in the second part; to simulate that on a 2- and 3-dimensional network, we will use a 2- variable FitzHugh-Nagumo type model. This part of research is intended to further identify the cause of cardiac arrhythmias. In the fourth part, we will examine periodic doubling and chaos that have been observed, both experimentally and theoretically, in electrical activity of the heart. To do this, we intend to construct the Poincaire first return maps and to carry out a bifurcation and power spectrum analysis using the mathematical cardiac models. From our results, we will try to identify a possible relationship between the bifurcation phenomenon and arrhythmias in the heart. In the fifth part, we will make a detailed comparison between the computer predictions and those provided by experimental sources. This will verify our simulation to be realistic and relevant to cardiophysiology.
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