Spiral-wave Instability in a Medium with a Gradient in the Fibroblast Density: a Computational Study

Abstract

Fibrosis, a process of fibroblast proliferation in cardiac tissue, is a major concern for patients with diseases like ischemia, heart failure, and cardiomyopathy, because of its arrhythmogenic effects. Fibroblasts, in appreciable densities, are IntroductionThe occurrence of abnormal spatiotemporal patterns of electrical waves in cardiac tissue, in the form of spiral waves, has been associated with cardiac arrhythmias [1]. The existence of a single spiral wave is associated with tachycardia [2], and a multiple-spiral-wave state is associated with a life-threatening arrhythmia known as fibrillation [3]. A single-spiral-wave state can transition into a multiple-spiral-wave state if the spiral becomes unstable and breaks up, giving rise to many daughter spirals [1]. Given that fibrillation is a more lethal condition than tachycardia, it is important to understand the mechanisms of the transition process from a single-to a multiple-spiral-wave state. Here, we present a mechanism of spiral-wave instability in a medium with a gradient in fibroblast density (GFD).Fibroblasts are passive cells that are needed for the proper functioning of a heart, because they, along with other cells, form the extracellular matrix and ensure the structural integrity of the heart. However, the abnormal proliferation of fibroblasts because of diseases like ischemia, heart failure, and cardiomyopathy is considered to be arrhythmogenic [4]. Fibroblasts, if they form gapjunctional coupling, can change the electrophysiology of myocytes in cardiac tissue [5]. This, in turn, can affect the dynamics of electrical waves in cardiac tissue. Many studies have been performed to investigate the effects of fibroblasts on wave dynamics in cardiac tissue [6,7]; however, most of the studies, which consider fibroblast-myocyte (FM) coupling, deal with a homogeneous distribution of fibroblasts in the domain. But, the density of fibroblasts in a diseased cardiac tissue may not necessarily be homogeneous [8]. Therefore, it is important to study the effects of FM coupling on wave dynamics in a domain with heterogeneous distributions of fibroblast density.We investigate the effects of GFD on spiral-wave dynamics in a mathematical model for human-ventricular tissue. We find that GFD induces a spatial variation of the local spiral-wave frequency ω in the domain. This variation of ω in the domain leads to spiral-wave instability, and the degree of instability depends on the magnitude of the variation of ω. We also investigate the factors that modulate the variation of ω in the domain. We find that, for a given GFD, the resting membrane potential E f of the fibroblasts, and the number of fibroblasts N f that are coupled to a myocyte can change the spatial variation of ω in the domain. Finally, we also show that GFD can spontaneously initiate spiral waves via high-frequency pacing.