Makif YudAlef, Rishon Lezion, Israel.
Physics Department, Ben-Gurion University, Beer-Sheva, Israel.
Sci Rep. 2021 Jun 1;11(1):11441. doi: 10.1038/s41598-021-90892-2.
In the last several years, quite a few papers on the joint question of transport, tortuosity and percolation have appeared in the literature, dealing with passage of miscellaneous liquids or electrical currents in different media. However, these methods have not been applied to the passage of action potential in heart fibrosis (HF), which is crucial for problems of heart arrhythmia, especially of atrial tachycardia and fibrillation. In this work we address the HF problem from these aspects. A cellular automaton model is used to analyze percolation and transport of a distributed-fibrosis inflicted heart-like tissue. Although based on a rather simple mathematical model, it leads to several important outcomes: (1) It is shown that, for a single wave front (as the one emanated by the heart's sinus node), the percolation of heart-like matrices is exactly similar to the forest fire case. (2) It is shown that, on the average, the shape of the transport (a question not dealt with in relation to forest fire, and deals with the delay of action potential when passing a fibrotic tissue) behaves like a Gaussian. (3) Moreover, it is shown that close to the percolation threshold the parameters of this Gaussian behave in a critical way. From the physical point of view, these three results are an important contribution to the general percolation investigation. The relevance of our results to cardiological issues, specifically to the question of reentry initiation, are discussed and it is shown that: (A) Without an ectopic source and under a mere sinus node operation, no arrhythmia is generated, and (B) A sufficiently high refractory period could prevent some reentry mechanisms, even in partially fibrotic heart tissue.
在过去的几年中，文献中出现了相当多关于传输、曲折和渗流联合问题的论文，涉及到不同介质中各种液体或电流的通过。然而，这些方法尚未应用于心脏纤维化（HF）中的动作电位通过，这对于心脏心律失常问题至关重要，尤其是心房性心动过速和颤动。在这项工作中，我们从这些方面解决 HF 问题。使用元胞自动机模型来分析分布式纤维化损伤的类似心脏组织的渗流和传输。尽管基于相当简单的数学模型，但它导致了几个重要的结果：（1）表明，对于单个波前（如由心脏窦房结发出的波前），类似心脏矩阵的渗流与森林火灾情况完全相似。（2）表明，平均而言，传输的形状（这是与森林火灾无关的问题，涉及到动作电位通过纤维化组织时的延迟）表现为高斯分布。（3）此外，还表明，在接近渗流阈值时，这个高斯分布的参数以临界方式表现。从物理角度来看，这三个结果是对一般渗流研究的重要贡献。我们的结果与心脏学问题的相关性，特别是折返起始问题的相关性进行了讨论，并表明：（A）在没有异位源且仅在窦房结运行的情况下，不会产生心律失常，以及（B）足够高的不应期可以防止一些折返机制，即使在部分纤维化的心脏组织中也是如此。
