title: Bifurcations, sustained oscillations and torus bursting involving ionic concentrations dynamics in a canine atrial cell model.
abstract: Atrial fibrillation is a disorganization of the electrical propagation in the atria often initiated by ectopic beats. This spontaneous activity might be associated with the appearance of sustained oscillations in some portion of the tissue. Adrenergic stress and specific gene polymorphisms known to promote atrial fibrillation are notably related to calcium and potassium channel conductances. We performed codimension-one and two bifurcation analysis along these conductances in an ionic canine atrial myocyte model. Two Hopf bifurcations were found, related to two distinct mechanisms: (1) a fast calcium gating-driven oscillator, and (2) a slow concentration-driven oscillator. These two mechanisms interact through a double Hopf bifurcation (HH) in a neighborhood of which a torus (Neimark-Sacker) bifurcation leads to bursting. A complex codimension-two theoretical scenario was identified around HH, through systematic comparison with the attractors found numerically. The concentration oscillator was further decomposed to reveal the minimal oscillating subnetwork, in which the Na(+)/Ca(2+) exchanger plays a prominent role.
authors: Institut de Génie Biomédical, Department of Physiology, Faculty of Medicine, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal H3C 3J7, Canada.
authors: François
authors: F
authors: Grégoire-Lacoste
authors: Institut de Génie Biomédical, Department of Physiology, Faculty of Medicine, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal H3C 3J7, Canada; Centre de Recherche, Hôpital du Sacré-Coeur de Montréal, Canada.
authors: Vincent
authors: V
authors: Jacquemet
authors: Institut de Génie Biomédical, Department of Physiology, Faculty of Medicine, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal H3C 3J7, Canada; Centre de Recherche, Hôpital du Sacré-Coeur de Montréal, Canada. Electronic address: alain.vinet@umontreal.ca.
authors: Alain
authors: A
authors: Vinet
mesh_terms: D000200:Action Potentials; D000818:Animals; D001281:Atrial Fibrillation / Q000209:etiology / Q000378:metabolism; D020013:Calcium Signaling; D004285:Dogs; D055724:Electrophysiological Phenomena; D015640:Ion Channel Gating; D055641:Mathematical Concepts; D008955:Models, Cardiovascular; D032383:Myocytes, Cardiac / Q000378:metabolism*; D015221:Potassium Channels / Q000378:metabolism; D015222:Sodium Channels / Q000378:metabolism; D019831:Sodium-Calcium Exchanger / Q000378:metabolism
chemical_list: D015221:Potassium Channels; D015222:Sodium Channels; D019831:Sodium-Calcium Exchanger
keywords: Atrial myocyte ionic model; Double-Hopf bifurcation; Minimal oscillator; Sustained oscillations; Torus bursting