IntroductionComputational models of cardiac conduction can play an important role in understanding the mechanisms of and developing treatments for fibrosis-induced cardiac arrhythmias. However, most studies investigating the arrhythmogenic role of cardiac fibrosis have modelled the myocardium as a locally homogenous continuum with increased conduction anisotropy in areas of fibrosis. While these continuum methods recreate simple planar conduction behaviour and allow for increased computational efficiency, it remains unclear how effectively they are able to model complex conduction patterns such as reentry. In 1981, Spach et al. [1] were the first to show that while cardiac conduction is continuous on the macroscopic scale, microscopic conduction is discontinuous and affected by the discrete cellular structure of the tissue. Since that time, many studies have used discrete microstructural cardiac models that incorporate individual cellular geometry [2]- [4]. Despite the discrete nature of cardiac conduction, many other studies have relied on continuum models that represent averaged electrical properties of cardiac tissue because these models decrease computational load and allow for large-scale simulations, including those of whole-heart conduction. While these continuous models, where the electrical properties are assigned to match macroscopic conduction properties and anisotropy, have been shown to reproduce simple conduction behaviours with high fidelity, it remains unclear if such models can account for the effects of fibrosis on the microscale.
Discrete versus continuous models
Modeling of fibrotic myocardiumThe most histologically accurate representation of fibrosis is as space-occupying features separating cells in discrete tissue models. Because collagenous septa are nonconductive, they can be more easily represented as the decoupling of transverse cellular connections [5].In continuous computational models, fibrosis is traditionally incorporated by decreasing conductivity values to reproduce experimentally observed conduction slowing and conduction anisotropy. While this approach reproduces the macroscopic conduction behavior, it does not capture the microscopic effects of fibrosis that could be implicated in arrhythmogenesis [6]. The more recent approach by Costa et al [7] of decoupling FEM elements to reproduce the effects of fibrosis is analogous to the approach of Spach et al. in the discrete model, and has shown promise in reproducing microscale conduction. However, it remains unclear how any of these approaches perform in the setting of reentry spiral wave behavior.In this manuscript, we elicit and compare spiral wave behavior in discrete models as well as in two types of equivalent continuous models to understand whether continuous computational models are sufficient to capture the details of reentry.
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