From micro- to macro-reentries in discrete multiscale mathematical models of atrial tissue

心脏电活动可以通过反应-扩散系统进行数学描述，该系统集成了细胞膜离子通道和器官解剖的生物数据。再入是沿着稳定或不稳定的心肌回路传播的电波，从而启动并延续一个复杂的自我维持的活动。当细胞间偶联减少或不均匀以及各向异性很强时，心房的解剖结构创造了促进这些再入的底物。重入回路的长度区分了宏观重入（例如绕过解剖障碍）和微观重入（例如在以高度细胞解耦为特征的慢传导区域）。挑战在于开发计算机模型，弥合微观和宏观尺度之间的差距，以模拟两种类型的再入。我们的总体目标是创建一个结合近细胞空间分辨率（< 100µm）和器官尺度（10 cm）的心房多尺度模型，同时保留一些3D解剖特征（心房纤维束、小梁结构、心外膜内差异），并能够模拟从离子通道（10µs）到再入活动（10 s）的时间尺度。我们将开发软件，根据心房解剖和纤维取向的图像描述，自动生成由相互连接的电缆组成的心房模型。在这个模型中，我们将研究包含传导缓慢或受损区域的组织中的微观和宏观再入之间的相互作用。有数值证据表明，大规模连续模型不能捕捉微观非均质性诱导的传导减速的细节，这对宏观传播有影响。我们的新模型将为研究离散传播的宏观影响和评估连续模型的局限性提供一个框架。离散传播在心脏组织中的重要性在于微观结构的异质性是心律失常的机制基础。我们的工作将深入了解复杂的动力学是如何从微观缺陷中产生的。

Cardiac electrical activity can be mathematically described by a reaction-diffusion system that integrates biological data from ion channels in cell membranes to organ anatomy. Reentries are electrical waves that propagate along stable or unstable circuits in the cardiac muscle, thereby initiating and perpetuating a complex self-sustained activity. The anatomical structure of the atria creates a substrate that promotes these reentries when cell-to-cell coupling is reduced or heterogeneous and when anisotropy is strong. The length of the reentrant circuits differentiates macro-reentries (e.g. around anatomical obstacles) from micro-reentries (e.g. in slow conduction regions characterized by a high degree of cell decoupling). The challenge is to develop computer models that bridge the gap between the micro- and macro-scales to simulate both types of reentries.  Our general objective is to create a multiscale model of the atria that combines near-cellular spatial resolution (< 100 µm) with organ scale (10 cm), while keeping some 3D anatomical features (interatrial fiber bundles, trabeculated structure, endo-epicardial differences) and enabling the simulation of time scales from ion channels (10 µs) to reentrant activity (10 s). We will develop software to automatically generate a model of the atria composed of interconnected cables from an image-based description of atrial anatomy and fiber orientation. In this model, we will study the interplay between micro- and macro-reentries in tissues incorporating regions of slow or impaired conduction. There is numerical evidence that large-scale continuous models fail to capture the details of microheterogeneity-induced conduction slowing, with implications on macroscopic propagation. Our new model will provide a framework to investigate the macro-scale influence of discrete propagation and assess the limitations of continuous models. The importance of discrete propagation in cardiac tissue is that microstructural heterogeneity is a mechanistic basis for arrhythmia. Our work will give insights into how complex dynamics arises from micro-scale defects.