Spiral-Wave Dynamics in a Mathematical Model of Human Ventricular Tissue with Myocytes and Fibroblasts

Abstract

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

The Effects of Fibroblasts on Wave Dynamics in a Mathematical Model for Human Ventricular Tissue

“…We check the accuracy of our numerical scheme, as in Ref. [28], by varying both δt and δx in a cable-type domain of myocytes [7,26] and by measuring CV of a plane wave, which is injected into the domain by stimulating its left boundary for 3 ms with a stimulus of strength 150 pA. With δx = 0.25 mm, CV increases by 1.1% when we change δt from 0.02 to 0.01 ms; if we decrease δx from 0.25 to 0.15 mm, with δt = 0.02 ms, then CV increases by 3.1%; these changes are similar to those found in other studies [22,26,28,29].…”

“…The full sets of equations for this model, including the ODEs for the ion-channel gating variables and the ion dynamics, are given in Refs. [7,26].…”

“…We use methods from these areas to solve the nonlinear, partial-differential equations for state-of-the-art mathematical models for cardiac tissue with myocytes and fibroblasts. We build on our earlier studies of this problem [7,8] to elucidate the role of two different forms of myocyte-fibroblast couplings on spiral-and scroll-wave dynamics in such models by using theoretical ideas from spatiotemporal chaos.…”

“…Zlochiver, et al [15] have shown the expression of Cx43 between fibroblasts and myocytes in a monolayer of myocytes and fibroblasts of neonatal rats; Miragoli, et al [16] have reported that Cx43 and Cx45 are expressed among fibroblasts and between fibroblasts and myocytes in cultured fibroblasts coated over rat-ventricular-myocyte strands. Both experimental and computational studies have shown that such coupling between myocytes and fibroblasts enhances electrical-signal propagation in cardiac tissue [7,[15][16][17][18]; this enhancement increases with N f , the number of fibroblasts that are attached to a myocyte. In cell-culture experiments, Miragoli, et al [16] have found that the conduction velocity (CV) decreases with an increase in the density of fibroblasts in cultured strands of neonatal-rat myocytes coated by fibroblasts; studies by McSpadden, et al [17] have found that CV decreases as the fibroblast number increases on the top of a myocyte layer in a monolayer of neonatal-rat cardiac myocytes, which are electrotonically loaded with a layer of cardiac fibroblasts.…”

“…Computational studies by Xie, et al, [18] have shown that CV decreases as they increase the gap-junctional coupling or the fibroblasts density in a 2D LR1 myocyte model [21], with either randomly attached or randomly inserted fibroblasts. In simulations with the 2D TNNP04 model (due to ten Tusscher, et al [22]), Nayak, et al [7] have found that CV either decreases or increases, with attached fibroblasts, as they increase the gap-junctional coupling. The experimental and computational investigations men-tioned above show that both the gap-junctional coupling and N f enhance CV and, therefore, they can play a crucial role in spiral-and scroll-wave dynamics in mathematical models for cardiac tissue.…”