Reentry and Ectopic Pacemakers Emerge in a Three-Dimensional Model for a Slab of Cardiac Tissue with Diffuse Microfibrosis near the Percolation Threshold

Abstract

Arrhythmias in cardiac tissue are generally associated with irregular electrical wave propagation in the heart. Cardiac tissue is formed by a discrete cell network, which is often heterogeneous. Recently, it was shown in simulations of two-dimensional (2D) discrete models of cardiac tissue that a wave crossing a fibrotic, heterogeneous region may produce reentry and transient or persistent ectopic activity provided the fraction of conducting connections is just above the percolation threshold. Here, we investigate the occurrence of these phenomena in three-dimensions by simulations of a discrete model representing a thin slab of cardiac tissue. This is motivated (i) by the necessity to study the relevance and properties of the percolation-related mechanism for the emergence of microreentries in three dimensions and (ii) by the fact that atrial tissue is quite thin in comparison with ventricular tissue. Here, we simplify the model by neglecting details of tissue anatomy, e. g. geometries of atria or ventricles and the anisotropy in the conductivity. Hence, our modeling study is confined to the investigation of the effect of the tissue thickness as well as to the comparison of the dynamics of electrical excitation in a 2D layer with the one in a 3D slab. Our results indicate a strong and non-trivial effect of the thickness even for thin tissue slabs on the probability of microreentries and ectopic beat generation. The strong correlation of the occurrence of microreentry with the percolation threshold reported earlier in 2D layers persists in 3D slabs. Finally, a qualitative agreement of 3D simulated electrograms in the fibrotic region with the experimentally observed complex fractional atrial electrograms (CFAE) as well as strong difference between simulated electrograms in 2D and 3D were found for the cases where reentry and ectopic activity were triggered by the micro-fibrotic region.

Microscopic Isthmuses and Fibrosis Within the Border Zone of Infarcted Hearts Promote Calcium-Mediated Ectopy and Conduction Block

“…This topological metric is a mathematical concept related to percolation theory, which describes the process of a moving substance passing through a medium with random structure. Although, quantitatively the critical FIB BZ values in this work differ from the percolation threshold [32], qualitatively our results showing that the FIB BZ threshold increases with tissue dimensionality are in line with the findings of Alonso et al [32]. However, wavefronts in their work were initiated by pacing the tissue rather than by stochastic firing of errant cells.…”

“…The authors concluded that fibroblasts placed exclusively between the sides of myocytes had a major effect on PVC formation since they separate cells, turning a 2D tissue into a stack of longitudinal 1D fibers [13]. Fibrosis in all models employed in our study was modelled by randomly removing myocytes from the BZ [32]. Increased levels of fibrosis in the infarct BZ FIB BZ gave rise to complex arrangements between cells resembling 1D strands or 2D clusters.…”

“…Fibrosis in all geometrical models was modeled by including synthetic patterns of non-conducting tissue in the BZ [31][32][33] (see Figure 2B). Fibrosis patterns were generated by randomly transforming some of the BZ myocytes in fibrosis, i.e., nonconducting material.…”

“…Moreover, this threshold increased from FIB BZ = 60% in 2D sheet to FIB BZ = 90% in the 3D BiV model. Interestingly, recent studies have suggested a strong correlation between arrhythmogenesis and the percolation threshold [31][32][33]. This topological metric is a mathematical concept related to percolation theory, which describes the process of a moving substance passing through a medium with random structure.…”

Perlin Noise Generation of Physiologically Realistic Patterns of Fibrosis

“…Non-invasive imaging techniques remain unable to fully characterise the nature of fibrosis in the lung [8] and particularly the heart [9], resulting in a reliance upon ex vivo studies [10,11]. This has motivated in silico investigations, seeking to explain both the creation of different fibrotic patternings [12] and in the case of cardiac fibrosis, its pro-arrhythmic consequences [13,14,15,16,17]. Although some in silico investigations have directly used invasively-collected data of cardiac fibrosis localisation to study the electrophysiological impacts of realistic patterns of affliction [10,18,19,20], the reliance on this limited data has meant that the effects of variability in these patterns remains very poorly understood.…”