Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to incorporate structural heterogeneities on small spatial scales, preventing a full understanding of the critical arrhythmogenic effects of conditions such as cardiac fibrosis. In this work, we explore the technique of homogenisation by volume averaging for the inclusion of non-conductive micro-structures into larger-scale cardiac meshes with minor computational overhead. Importantly, our approach is not restricted to periodic patterns, enabling homogenised models to represent, for example, the intricate patterns of collagen deposition present in different types of fibrosis. We first highlight the importance of appropriate boundary condition choice for the closure problems that define the parameters of homogenised models. Then, we demonstrate the technique’s ability to correctly upscale the effects of fibrotic patterns with a spatial resolution of $\text{10}\text{µm}$ into much larger numerical mesh sizes of 100-$\text{250}\text{µm}$. The homogenised models using these coarser meshes correctly predict critical pro-arrhythmic effects of fibrosis, including slowed conduction, source/sink mismatch, and stabilisation of re-entrant activation patterns. As such, this approach to homogenisation represents a significant step towards whole organ simulations that unravel the effects of microscopic cardiac tissue heterogeneities.

心脏电生理学中的计算模型因运行时间长而臭名昭著，限制了用于其解决方案的数值离散中的节点和网格元素的数量。这使得在小空间尺度上整合结构异质性变得特别具有挑战性，从而阻碍了对心脏纤维化等疾病的关键致心律失常影响的充分理解。在这项工作中，我们探索了通过体积平均进行均质化的技术，以较小的计算开销将非导电微结构纳入更大规模的心脏网格中。重要的是，我们的方法不限于周期性模式，使均质模型能够代表例如不同类型纤维化中存在的复杂胶原蛋白沉积模式。我们首先强调对于定义均质模型参数的闭合问题选择适当的边界条件的重要性。然后，我们证明了该技术能够以空间分辨率正确放大纤维化模式的影响 $\text{10}\text{微米}$成更大的数值网格尺寸 100-$\text{250}\text{微米}$。使用这些较粗网格的均质模型可以正确预测纤维化的关键促心律失常效应，包括传导减慢、源/汇不匹配以及重入激活模式的稳定。因此，这种均质化方法代表了向整个器官模拟迈出的重要一步，该模拟揭示了微观心脏组织异质性的影响。