Institute of Biomedical Engineering, Department of Pharmacology and Physiology, Faculty of Medicine, Université de Montréal, C.P. 6128, succ. Centre-ville, Montreal, Quebec H3C 3J7, Canada.
Chaos. 2022 Apr;32(4):043113. doi: 10.1063/5.0082763.
Gap junctions exhibit nonlinear electrical properties that have been hypothesized to be relevant to arrhythmogenicity in a structurally remodeled tissue. Large-scale implementation of gap junction dynamics in 3D propagation models remains challenging. We aim to quantify the impact of nonlinear diffusion during episodes of arrhythmias simulated in a left atrial model. Homogenization of conduction properties in the presence of nonlinear gap junctions was performed by generalizing a previously developed mathematical framework. A monodomain model was solved in which conductivities were time-varying and depended on transjunctional potentials. Gap junction conductances were derived from a simplified Vogel-Weingart model with first-order gating and adjustable time constant. A bilayer interconnected cable model of the left atrium with 100 μm resolution was used. The diffusion matrix was recomputed at each time step according to the state of the gap junctions. Sinus rhythm and atrial fibrillation episodes were simulated in remodeled tissue substrates. Slow conduction was induced by reduced coupling and by diffuse or stringy fibrosis. Simulations starting from the same initial conditions were repeated with linear and nonlinear gap junctions. The discrepancy in activation times between the linear and nonlinear diffusion models was quantified. The results largely validated the linear approximation for conduction velocities >20 cm/s. In very slow conduction substrates, the discrepancy accumulated over time during atrial fibrillation, eventually leading to qualitative differences in propagation patterns, while keeping the descriptive statistics, such as cycle lengths, unchanged. The discrepancy growth rate was increased by impaired conduction, fibrosis, conduction heterogeneity, lateral uncoupling, fast gap junction time constant, and steeper action potential duration restitution.
缝隙连接表现出非线性的电学特性，这些特性被假设与结构重构组织中的心律失常有关。在 3D 传播模型中大规模实现缝隙连接动力学仍然具有挑战性。我们的目的是量化在左心房模型中模拟心律失常期间非线性扩散的影响。在存在非线性缝隙连接的情况下，通过推广以前开发的数学框架来实现传导特性的均匀化。解决了一个电导率随时间变化且取决于跨连接电位的单域模型。缝隙连接电导由具有一阶门控和可调时间常数的简化 Vogel-Weingart 模型得出。使用具有 100μm 分辨率的左心房双层互连电缆模型。根据缝隙连接的状态，在每个时间步重新计算扩散矩阵。在重构组织基质中模拟窦性节律和心房颤动发作。通过降低耦合和弥漫性或串珠状纤维化来诱导缓慢传导。从相同的初始条件开始，用线性和非线性缝隙连接重复模拟。量化线性和非线性扩散模型之间的激活时间差异。结果在很大程度上验证了传导速度>20cm/s 时的线性近似。在非常缓慢的传导基质中，在心房颤动期间，差异随着时间的推移而累积，最终导致传播模式的定性差异，同时保持描述性统计信息（如周期长度）不变。传导障碍、纤维化、传导异质性、侧向去耦、快速缝隙连接时间常数和动作电位时程恢复斜率增加都会导致差异增长率增加。
