Turbulent states and their transitions in mathematical models for ventricular tissue: The effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral- and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling Gⱼ and (2) the number Nf of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) Gⱼ is large or (b) the maximum possible number of fibroblasts per myocyte Nfᵐᵃˣ is large. We also observe that the minimum value of Gⱼ, for the transition from the ST to the RS state, decreases as Nfᵐᵃˣ increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) Gⱼ increases, with fixed Nfᵐᵃˣ, and (2) Nfᵐᵃˣ increases, with fixed Gⱼ. We obtain the boundary between ST and RS stability regions in the Nfᵐᵃˣ-Gⱼ plane. In particular, for low values of Nfᵐᵃˣ, the value of Gⱼ, at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as Nfᵐᵃˣ increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral- and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.