Department of Physiology and Institute of Biomedical Engineering, Université de Montréal, Montreal, Quebec, Canada.
Chaos. 2011 Mar;21(1):013108. doi: 10.1063/1.3544470.
Atrial fibrillation (AF), arising in the cardiac atria, is a common cardiac rhythm disorder that is incompletely understood. Numerous characteristics of the atrial tissue are thought to play a role in the maintenance of AF. Most traditional theoretical models of AF have considered the atrium to be a flat two-dimensional sheet. Here, we analyzed the relationship between atrial geometry, substrate size, and AF persistence, in a mathematical model involving heterogeneity. Spatially periodic properties were created by variations in times required for reactivation due to periodic acetylcholine concentration [ACh] distribution. The differences in AF maintenance between the sheet and the cylinder geometry are found for intermediate gradients of inexcitable time (intermediate [ACh]). The maximum difference in AF maintenance between geometry decreases with increasing tissue size, down to zero for a substrate of dimensions 20 × 10 cm. Generators have the tendency to be anchored to the regions of longer inexcitable period (low [ACh]). The differences in AF maintenance between geometries correlate with situations of moderate anchoring for which rotor-core drifts between low-[ACh] regions occur, favoring generator disappearance. The drift of generators increases their probability of disappearance at the tissue borders, resulting in a decreased maintenance rate in the sheet due to the higher number of no-flux boundaries. These interactions between biological variables and the role of geometry must be considered when selecting an appropriate model for AF in intact hearts.
心房颤动（AF）起源于心脏心房，是一种常见的心脏节律紊乱，目前尚未完全了解。许多心房组织的特征被认为在维持 AF 中发挥作用。大多数传统的 AF 理论模型都将心房视为二维平板。在这里，我们在涉及异质性的数学模型中分析了心房几何形状、基质大小和 AF 持续时间之间的关系。由于周期性乙酰胆碱浓度[ACh]分布导致再激活所需时间的变化，产生了空间周期性特性。在中等不可兴奋时间（中间[ACh]）梯度下，发现平板和圆柱几何形状之间的 AF 维持差异。几何形状之间的 AF 维持最大差异随着组织尺寸的增加而减小，当基质尺寸为 20×10cm 时，最大差异减小到零。发生器有倾向于固定在更长不可兴奋周期的区域（低[ACh]）。几何形状之间的 AF 维持差异与中等锚固情况相关，其中转子核心在低[ACh]区域之间漂移，有利于发生器消失。发生器的漂移增加了它们在组织边界消失的概率，从而由于通量边界的数量增加，平板中的维持率降低。在选择完整心脏 AF 的合适模型时，必须考虑这些生物变量之间的相互作用和几何形状的作用。
