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

心脏电活动可以由一个反应-扩散系统来数学描述，该系统将来自细胞膜离子通道的生物数据整合到器官解剖学中。折返是沿着心肌中稳定或不稳定的回路传播的电波，从而启动并维持复杂的自我维持活动。心房的解剖结构创造了一种底物，当细胞到细胞之间的耦合减少或不均匀时，当各向异性很强时，它就会促进这些折返。折返电路的长度区分了宏观折返(例如，在解剖障碍周围)和微观折返(例如，在以细胞高度去耦合为特征的慢传导区域)。我们的总体目标是建立一个多尺度的心房模型，它结合了近细胞的空间分辨率(&lt；100微米)和器官尺度(10厘米)，同时保留了一些3D解剖特征(心房间纤维束、小梁结构、心内膜差异)，并能够模拟从离子通道(S 10微米)到折返活动(S 10微米)的时间尺度。我们将开发软件，根据基于图像的心房解剖和纤维定位描述，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微观和宏观折返之间的相互作用。有数值证据表明，大规模的连续模型不能捕捉到微观异质性引起的传导减速的细节，这对宏观传播有影响。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，微观结构的异质性是心律失常的机制基础。我们的工作将让我们深入了解微观缺陷是如何产生复杂的动力学的。

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.