Grégoire-Lacoste François, Jacquemet Vincent, Vinet Alain
Institut de Génie Biomédical, Department of Physiology, Faculty of Medicine, Université de Montréal, CP 6128, Succ Centre-Ville, Montréal H3C 3J7, Canada.
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.
Math Biosci. 2014 Apr;250:10-25. doi: 10.1016/j.mbs.2014.01.010. Epub 2014 Feb 12.
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.
心房颤动是心房电传导的紊乱，通常由异位搏动引发。这种自发活动可能与组织某些部分持续振荡的出现有关。已知促进心房颤动的肾上腺素能应激和特定基因多态性与钙和钾通道电导显著相关。我们在犬类离子型心房肌细胞模型中沿着这些电导进行了一维和二维分岔分析。发现了两个霍普夫分岔，与两种不同机制相关：（1）快速钙门控驱动的振荡器，以及（2）缓慢浓度驱动的振荡器。这两种机制通过双霍普夫分岔（HH）相互作用，在其邻域内，一个环面（奈马克 - 萨克）分岔导致爆发。通过与数值发现的吸引子进行系统比较，在HH周围确定了一个复杂的二维理论场景。浓度振荡器进一步分解以揭示最小振荡子网，其中钠/钙交换器起着重要作用。
