Mathématiques en biologie et médecine
Multistability and Automaticity during ischemia and adrenergic stimulation in ionic models of cardiac myocytes
Vinet, Alain, S. Bouchard and F. Grégoire-Lacoste
Université de Montréal

Cardiac arrhythmias are often triggered by the spontaneous firing of otherwise excitable cells. Such abnormal automaticity can occur in the ventricles during the early phase of ischemia or in the auricles following the activation of the cardiac sympathetic autonomic nervous system (CSAN). In ischemia, the concentration of potassium increases in the ischemic zone, resulting in a depolarization of the cells and the creation of an injury current flowing from the impaired to normal tissue. On the other hand, CSAN activation increases the conductance of K+ and Ca++ membrane currents. We show that these pairs of parameters can induce multi-stability and automaticity in an ionic model of the human ventricular myocyte and of canine atrial myocyte respectively, both describes by a high dimension differential algebraic system. The analysis of simplified models shows that, in both cases, the automatic regimes involve the interaction of a fast and a slow oscillator. The fast oscillator is driven by the K+ and Ca++ currents and their gate variables. The slow one implies either the spontaneous release of the Ca++ by the sarcoplasmic reticulum in the ventricular model, or the Na-Ca and Na-K exchanger in the atrial model. Each oscillator is associated to a pair of Hopf bifurcations whose relative locations vary as a function of the parameters, generating diverse complex scenarios of bifurcation. These can be understood by following the path follow by these bifurcations in the parameter plane.

Lundi, 17 juin, 11h30
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