Scaling properties of conduction velocity in heterogeneous excitable media

In silico study of multicellular automaticity of heterogeneous cardiac cell monolayers: Effects of automaticity strength and structural linear anisotropy

The biological pacemaker approach is an alternative to cardiac electronic pacemakers. Its main objective is to create pacemaking activity from added or modified distribution of spontaneous cells in the myocardium. This paper aims to assess how automaticity strength of pacemaker cells (i.e. their ability to maintain robust spontaneous activity with fast rate and to drive neighboring quiescent cells) and structural linear anisotropy, combined with density and spatial distribution of pacemaker cells, may affect the macroscopic behavior of the biological pacemaker. A stochastic algorithm was used to randomly distribute pacemaker cells, with various densities and spatial distributions, in a semi-continuous mathematical model. Simulations of the model showed that stronger automaticity allows onset of spontaneous activity for lower densities and more homogeneous spatial distributions, displayed more central foci, less variability in cycle lengths and synchronization of electrical activation for similar spatial patterns, but more variability in those same variables for dissimilar spatial patterns. Compared to their isotropic counterparts, in silico anisotropic monolayers had less central foci and displayed more variability in cycle lengths and synchronization of electrical activation for both similar and dissimilar spatial patterns. The present study established a link between microscopic structure and macroscopic behavior of the biological pacemaker, and may provide crucial information for optimized biological pacemaker therapies.

Implantation of electronic pacemakers is a standard treatment to pathologically slow heart rhythm. Despite improving quality of life, those devices display many shortcomings. Bioengineered tissue pacemakers may be a therapeutic alternative, but associated design methods usually lack control of the way cells with spontaneous activity are scattered throughout the tissue. Our study is the first to use a mathematical model to rigorously define and thoroughly characterize how pacemaker cells scattering at the microscopic level may affect macroscopic behaviors of the bioengineered tissue pacemaker. Automaticity strength (ability of pacemaker cell to drive its non-pacemaker neighbors) and anisotropy (preferential orientation of cell shape) are also implemented and give unparalleled insights on how effects of uncontrollable scattered pacemaker cells may be modulated by available experimental techniques. Our model is a powerful tool to aid in optimized bioengineered pacemaker therapies.

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

Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue.

Percolation as a mechanism to explain atrial fractionated electrograms and reentry in a fibrosis model based on imaging data

BACKGROUND

Complex fractionated atrial electrograms (CFAEs) have long been associated with proarrhythmic alterations in atrial structure or electrophysiology. Structural alterations disrupt and slow smoothly propagating wavefronts, leading to wavebreaks and electrogram (EGM) fractionation, but the exact nature and characteristics for arrhythmia remain unknown. Clinically, in atrial fibrillation (AF) patients, increases in frequency, whether by pacing or fibrillation, increase EGM fractionation and duration, and reentry can occur in relation with the conduction disturbance. Recently, percolation has been proposed as an arrhythmogenic mechanism, but its role in AF has not been investigated.

OBJECTIVE

We sought to determine if percolation can explain reentry formation and EGM behavior observed in AF patients.

METHODS

Computer models of fibrotic tissue with different densities were generated based on late gadolinium-enhanced magnetic resonance images, using pixel intensity as a fibrosis probability to avoid an arbitrary binary threshold. Clinical pacing protocols were followed to induce AF, and EGMs were computed.

RESULTS

Reentry could be elicited, with a biphasic behavior dependent on fibrotic density. CFAEs were recorded above fibrotic regions, and consistent with clinical data, EGM duration and fractionation increased with more rapid pacing.

CONCLUSION

These findings confirm percolation as a potential mechanism to explain AF in humans and give new insights into dynamics underlying conduction distortions and fractionated signals in excitable media, which correlate well with the experimental findings in fibrotic regions. The greater understanding of the different patterns of conduction changes and related EGMs could lead to more individualized and effective approaches to AF ablation therapy.

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 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.

Attractive and repulsive contributions of localized excitability inhomogeneities and elimination of spiral waves in excitable media

The attracting and repelling of spiral waves in a two-dimensional excitable medium in the presence of localized excitability inhomogeneities are studied. The choice of two effects depends on the comparison of excitabilities inside and outside the localized obstacle. We inspect the changes in attracting and repelling behaviors with respect to the size of the obstacle and the initial distance between the center of the spiral core and the obstacle. To understand the occurrence of these phenomena, we investigated the small v-value areas near the tip and the function of the wave velocity as the excitability parameter ε. Considering the attributes of the attractive obstacle, an eliminating scheme of spiral waves is proposed in which the attractive obstacle is rapidly moved at several fixed times. This method can avoid the high-amplitude and high-frequency stimulus in most conventional methods.

Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture

Pacemaker interactions can lead to complex wave dynamics seen in certain types of cardiac arrhythmias. We use experimental and mathematical models of pacemakers in heterogeneous excitable media to investigate how pacemaker interactions can be a mechanism for wave break and reentrant wave dynamics. Embryonic chick ventricular cells are cultured in vitro so as to create a dominant central pacemaker site that entrains other pacemakers in the medium. Exposure of those cultures to a potassium channel blocker, E-4031, leads to emergence of peripheral pacemakers that compete with each other and with the central pacemaker. Waves emitted by faster pacemakers break up over the slower pacemaker to form reentrant waves. Similar dynamics are observed in a modified FitzHugh-Nagumo model of heterogeneous excitable media with two distinct sites of pacemaking. These findings elucidate a mechanism of pacemaker-induced reentry in excitable media.