Instability of spiral and scroll waves in the presence of a gradient in the fibroblast density: the effects of fibroblast–myocyte coupling

Abstract

Fibroblast-myocyte coupling can modulate electrical-wave dynamics in cardiac tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous, so there can be gradients in the fibroblast density (henceforth we call this GFD) especially from highly injured regions, like infarcted or ischemic zones, to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to arrhythmias, so it is important to understand the effects of GFD in the formation and sustenance of arrhythmic reentrant waves, like spiral or scroll waves. Therefore, we investigate the effects of GFD on the stability of spiral and scroll waves of electrical activation in a state-of-the-art mathematical model for cardiac tissue in which we also include fibroblasts. By introducing GFD in controlled ways, we show that spiral and scroll waves can be unstable in the presence of GFDs because of regions with varying spiral-or scroll-wave frequency ω, induced by the GFD. We examine the effects of the resting membrane potential of the fibroblast and the number of fibroblasts attached to the myocytes on the stability of these waves. Finally, we show that the presence of GFDs can lead to the formation of spiral waves at high-frequency pacing.lead to the fragmentation of the electrical waves [16,17] and even waveblock [17]. Many studies have investigated the effects of fibroblasts on wave dynamics in cardiac tissue [16][17][18][19][20]. Some of these studies model the fibroblasts as inexcitable obstacles [19][20][21]; others take into account the fibroblast-myocyte coupling and consider either (a) a random distribution of fibroblasts, with an average density that is uniform in space [16][17][18], or (b) localized fibroblast inhomogeneities [18]. However, in real diseased hearts the distribution of fibroblasts may not be uniform, even on average, but, rather, there may be a gradient in fibroblast density (GFD), as has been observed in aged-rabbit hearts [6]. Moreover, in hearts that have been injured, say because of myocardial infarction, the fibroblast density may vary from a high value in the infarcted region to a lower value in the normal region of the heart [22,23], with intermediate values in interfaces between these regions. It is important, therefore, to understand what role such GFD can play in inducing and then, perhaps, destabilizing re-entrant waves, like spiral or scroll waves.We show that a state-of-the-art mathematical model for cardiac tissue, based on the O'Hara-Rudy model (ORd) for a human ventricular cell [24], provides us with a natural platform for (a) incorporating fibroblastmyocyte interactions and (b) imposing GFD in a controlled way so that we can study, exclusively, its effects on spiral-and scroll-wave dynamics, without other complicating factors that can be present in real cardiac tissue, such as scars, which lead to conduction inhomogeneities [25]. We carry out such a controlled study of the effects of GFD by using the ORd model, for a human ventricular cell [24], with passive fibroblasts, as in the model of MacC...

Ca2+ Cycling Impairment in Heart Failure Is Exacerbated by Fibrosis: Insights Gained From Mechanistic Simulations

“…This value is within the range of 0.3–8 nS measured in cultured myocyte–fibroblast pairs ( Rook et al, 1992 ). In our simulations, an elevated degree of fibrosis was considered by setting a myocyte–fibroblast ratio of 1:5, obtained by increasing G gap fivefold ( Mayourian et al, 2016 ; Zimik and Pandit, 2016 ). In the absence of fibrosis, G gap is 0, and the myocyte is not coupled to fibroblasts.…”

Anisotropic shortening in the wavelength of electrical waves promotes onset of electrical turbulence in cardiac tissue: An in silico study

“…We have also observed the drift of spiral waves towards the large-APD region (see Fig 8) in the initial time before the waves break up. A study by Zimik, et al, [35] finds that spatial gradients in ω, induced by gradients in the density of fibroblasts, can precipitate a spiral-wave instability. However, none of these studies provides a clear understanding of the mechanisms underlying the onset of spiral-and scroll-wave instabilities, from a fundamental standpoint.…”

“…We use the standard values for all parameters [33], except for the parameter k. We write k = g × k o , where g is a multiplication factor and k o is the control value of k. In 2D simulations we introduce a spatial gradient (a linear variation) in the value of k along the vertical direction of the domain. To mimic the electrophysiology of a human ventricular cell, we perform similar studies using a slightly modified version of the ionically-realistic O'Hara-Rudy model (ORd) [34,35]. Here, the transmembrane potential V is governed by the ODE…”

“…For the numerical implementation of the diffusion term in Eq (6), we follow Refs. [35,36]. We construct our anatomically realistic simulation domain with…”

Reentry via high-frequency pacing in a mathematical model for human-ventricular cardiac tissue with a localized fibrotic region

“…In particular, it has been shown that fibroblasts, distributed randomly in a monolayer with myocytes, can cause fragmentation of waves 25 , 43 and even complete waveblock 25 . The presence of local 26 and global 27 gradients in the density of fibroblasts has also been shown to induce spiral waves. Other studies have investigated the effects of fibroblast on the stability of spiral waves 28 – 31 .…”