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，该系统将细胞膜中的离子通道的生物数据整合到器官解剖结构中。折返是沿着心肌中稳定或不稳定的回路沿着传播的电波，从而启动并维持复杂的自我维持活动。心房的解剖结构产生了一种基质，当细胞与细胞的耦合减少或不均匀时，以及当各向异性很强时，这种基质会促进这些折返。折返回路的长度将宏观折返（例如，在解剖学障碍物周围）与微观折返（例如，在以高度细胞去耦为特征的慢传导区域中）区分开。目前的挑战是开发计算机模型，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心房的多尺度模型，该模型将近细胞空间分辨率（< 100 µm）与器官尺度（10 cm）相结合，同时保留一些3D解剖特征（心房纤维束，小梁结构，心内膜-心外膜差异），并能够模拟从离子通道（10 µs）到折返活动（10 s）的时间尺度。我们将开发软件，根据心房解剖结构和纤维方向的基于图像的描述，自动生成由互连电缆组成的心房模型。在这个模型中，我们将研究组织中的微观和宏观折返之间的相互作用，包括缓慢或受损的传导区域。有数值证据表明，大规模的连续模型未能捕捉微观不均匀性引起的传导减慢的细节，与宏观传播的影响。我们的新模型将提供一个框架来研究离散传播的宏观影响，并评估连续模型的局限性。心脏组织中离散传播的重要性在于微结构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如何从微观缺陷中产生。

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.