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

Abstract

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 G_{j} and (2) the number N_{f} 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) G_{j} is large or (b) the maximum possible number of fibroblasts per myocyte N_{f}^{max} is large. We also observe that the minimum value of G_{j}, for the transition from the ST to the RS state, decreases as N_{f}^{max} 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) G_{j} increases, with fixed N_{f}^{max}, and (2) N_{f}^{max} increases, with fixed G_{j}. We obtain the boundary between ST and RS stability regions in the N_{f}^{max}-G_{j} plane. In particular, for low values of N_{f}^{max}, the value of G_{j}, at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N_{f}^{max} 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.

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

“…This increase of T is a consequence of the decrease of CV that is associated with a decrease of the upstroke velocity of a myocytefibroblast composite AP in its depolarization phase, as shown in Refs. [7,8,18]. Furthermore, we observe that the minimum value of N f , required for the ST-RS transition, decreases as G j increases, for the P2 parameter set.…”

“…The pseudocolor plot in Fig. 1(E), at time t = 8.8 s, shows such an ST state, which arises from the steep slope of the actionpotential-duration-restitution (APDR) plot [8,25]. In summary, then, in the absence of fibroblasts, the parameter sets P1 and P2 lead, respectively, to (a) an RS state and (b) an ST state in our 2D simulation domain.…”

“…2). Such an ST-RS transition is the consequence of the suppression of the steep APDR slope of a myocyte-fibroblast composite at the cellular level [8,33]. Once the ST state is suppressed, a single spiral in an RS state rotates periodically as shown Figs.…”

“…Such a decrease of W d is related to the shortening of the action-potential-duration (APD) of a myocyte-fibroblast composite that has been discussed in Refs. [7,8].…”

“…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.…”