Simulation of Ectopic Pacemakers in the Heart: Multiple Ectopic Beats Generated by Reentry inside Fibrotic Regions

Abstract

The inclusion of nonconducting media, mimicking cardiac fibrosis, in two models of cardiac tissue produces the formation of ectopic beats. The fraction of nonconducting media in comparison with the fraction of healthy myocytes and the topological distribution of cells determines the probability of ectopic beat generation. First, a detailed subcellular microscopic model that accounts for the microstructure of the cardiac tissue is constructed and employed for the numerical simulation of action potential propagation. Next, an equivalent discrete model is implemented, which permits a faster integration of the equations. This discrete model is a simplified version of the microscopic model that maintains the distribution of connections between cells. Both models produce similar results when describing action potential propagation in homogeneous tissue; however, they slightly differ in the generation of ectopic beats in heterogeneous tissue. Nevertheless, both models present the generation of reentry inside fibrotic tissues. This kind of reentry restricted to microfibrosis regions can result in the formation of ectopic pacemakers, that is, regions that will generate a series of ectopic stimulus at a fast pacing rate. In turn, such activity has been related to trigger fibrillation in the atria and in the ventricles in clinical and animal studies.

Nonlinear physics of electrical wave propagation in the heart: a review

“…Moreover, it is not yet clear if and how such fluctuations will become critical for the dynamics at the tissue or organ level. A first step maybe to employ discrete models of cardiac tissue that represent the dynamics of individual cells and are simple enough to be computationally feasible, see e. g. [170][171][172], with additional noise terms or a stochastic dynamics derived from detailed cellular models.…”

Reactive Interstitial and Reparative Fibrosis as Substrates for Cardiac Ectopic Pacemakers and Reentries

“…The detailed and discrete model of cardiac tissue was numerically solved [6] using the finite volume method. The reaction and diffusion parts of the discrete monodomain equations were split by employing the Godunov operator splitting Fig.…”

“…Therefore, this is a first order method. If the value of k, defined by equation (6), is close to zero we use the Euler method instead of equations (5) for the corresponding gating variable at that point of the simulation. The first order version of Sundnes et al method (SAST1) [23] extends the RL method for each and every differential equation of the model.…”

“…From this basic microscopic model we generate an equivalent discrete model [6] and presented in the bottom of Figure 1. With the discrete or network-like model we simulated reactive interstitial fibrosis by randomly removing a certain percentage of links between neighboring cells, φ l (see Figure 2); and to simulate reparative fibrosis we randomly removed a certain percentage of cells, φ c , from the network (see Figure 1).…”

“…In our previous works [1,6] we were able to generate an ectopic pacemaker in computer simulations of cardiac electrophysiology by assuming a single hypothesis for substrate: the existence of a region of microfibrosis, a mixture of excitable (healthy myocytes) and non-conducting (fibrosis) areas. The mechanism of this ectopic pacemaker is simple.…”