The electrical coupling between myocytes and fibroblasts and the spacial distribution of fibroblasts within myocardial tissues are significant factors in triggering and sustaining cardiac arrhythmias, but their roles are poorly understood. This article describes both direct numerical simulations and an asymptotic theory of propagation and block of electrical excitation in a model of atrial tissue with myocyte–fibroblast coupling. In particular, three idealized fibroblast distributions are introduced: uniform distribution, fibroblast barrier and myocyte strait—all believed to be constituent blocks of realistic fibroblast distributions. Primary action potential biomarkers including conduction velocity, peak potential and triangulation index are estimated from direct simulations in all cases. Propagation block is found to occur at certain critical values of the parameters defining each idealized fibroblast distribution, and these critical values are accurately determined. An asymptotic theory proposed earlier is extended and applied to the case of a uniform fibroblast distribution. Biomarker values are obtained from hybrid analytical-numerical solutions of coupled fast-time and slow-time periodic boundary value problems and compare well to direct numerical simulations. The boundary of absolute refractoriness is determined solely by the fast-time problem and is found to depend on the values of the myocyte potential and on the slow inactivation variable of the sodium current ahead of the propagating pulse. In turn, these quantities are estimated from the slow-time problem using a regular perturbation expansion to find the steady state of the coupled myocyte–fibroblast kinetics. The asymptotic theory gives a simple analytical expression that captures with remarkable accuracy the block of propagation in the presence of fibroblasts.

中文翻译：

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心肌细胞-成纤维细胞耦合心房组织模型中的动作电位传播和阻滞

肌细胞和成纤维细胞之间的电耦合以及成纤维细胞在心肌组织内的空间分布是触发和维持心律失常的重要因素，但它们的作用却知之甚少。本文描述了心肌细胞-成纤维细胞耦合心房组织模型中的直接数值模拟和传播和电激发阻滞的渐近理论。特别是，介绍了三种理想化的成纤维细胞分布：均匀分布、成纤维细胞屏障和肌细胞海峡——所有这些都被认为是现实成纤维细胞分布的组成部分。在所有情况下，通过直接模拟估计主要动作电位生物标志物，包括传导速度、峰值电位和三角测量指数。发现传播阻滞发生在定义每个理想化成纤维细胞分布的参数的某些临界值处，并且这些临界值是准确确定的。之前提出的渐近理论被扩展并应用于均匀成纤维细胞分布的情况。生物标志物值是从耦合的快时间和慢时间周期边界值问题的混合解析数值解中获得的，并且与直接数值模拟相比很好。绝对不应期的边界仅由快速时间问题确定，并且发现取决于肌细胞电位的值和传播脉冲之前钠电流的缓慢失活变量。反过来，这些量是从慢时问题估计的，使用规则的扰动扩展来找到耦合的肌细胞 - 成纤维细胞动力学的稳态。渐近理论给出了一个简单的分析表达式，该表达式非常准确地捕获了成纤维细胞存在时的传播阻滞。