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

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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.