Systematic in-silico evaluation of fibrosis effects on re-entrant wave dynamics in atrial tissue

Abstract

Despite the key role of fibrosis in atrial fibrillation (AF), the effects of different spatial distributions and textures of fibrosis on wave propagation mechanisms in AF are not fully understood. To clarify these aspects, we performed a systematic computational study to assess fibrosis effects on the characteristics and stability of re-entrant waves in electrically-remodelled atrial tissues. A stochastic algorithm, which generated fibrotic distributions with controlled overall amount, average size, and orientation of fibrosis elements, was implemented on a monolayer spheric atrial model. 245 simulations were run at changing fibrosis parameters. The emerging propagation patterns were quantified in terms of rate, regularity, and coupling by frequency-domain analysis of correspondent synthetic bipolar electrograms. At the increase of fibrosis amount, the rate of reentrant waves significantly decreased and higher levels of regularity and coupling were observed (p < 0.0001). Higher spatial variability and pattern stochasticity over repetitions was observed for larger amount of fibrosis, especially in the presence of patchy and compact fibrosis. Overall, propagation slowing and organization led to higher stability of re-entrant waves. These results strengthen the evidence that the amount and spatial distribution of fibrosis concur in dictating re-entry dynamics in remodeled tissue and represent key factors in AF maintenance.

Figure 1

Scheme of the systematic computer simulation approach. (a) Stochastic generation of fibrotic patterns. On the left, sphere with fibrotic pattern (in purple). On the right, magnification of the mesh and highlight of the candidate node and neighbor nodes considered in the process of node attribution to fibrotic regions. See text for details. (b) Simulation protocol composed by an induction window under high-frequency pacing, and an observation window with propagation pattern free evolution. (c) Generation and frequency-domain analysis of synthetic bipolar electrograms (sEGMs: s1, s2) and computation of power spectra and magnitude squared-coherence (MSC) to extract rate, organization, and coupling information.

Figure 2

Generation of fibrosis patterns. (a) Exemplary fibrotic patterns (in purple) obtained setting the stochastic algorithm parameters D, p_th, and α to the indicated values. From left to right: very-low density fibrosis, low-medium density fibrosis, high density diffuse fibrosis, high density compact fibrosis, high density patchy fibrosis. (b) Distribution of the weighted mean size (expressed in terms of mesh nodes) of fibrosis elements from the stochastic realizations used in the simulation, displayed as a function of the size parameter p_th, for different fibrosis densities (indicated in different colors). Black dots and whiskers indicate average values and standard deviation over simulation subgroups, while small colored dots correspond to single simulation outcomes.

Figure 3

Exemplary propagation patterns emerging for different geometrical features of fibrosis. Subsequent snapshots of action potential maps are indicated in color code. Spiral wave meandering and break-up in the presence of very-low (a) and medium–low densities of fibrosis (b). Stable spiral wave without break-up at high-density diffuse fibrosis (c). Spiral wave fragmentation in the presence of a high-density of compact fibrosis (d). Wave canalization in the presence of a high-density of patchy fibrosis (e).

Figure 4

Quantification of propagation patterns properties in the frequency-domain. For each propagation pattern (rows, corresponding to patterns in Fig. 3), a snapshot of the activation pattern is shown together with dominant frequency (DF), regularity index (RI), and coupling (Cxy) maps (displayed from left to right). Meandering spiral waves (a, b) present the highest rate, and the lowest regularity and coupling. Stable spiral waves (c) present the slowest rate and the highest regularity and coupling. Wave fragmentation (d) is associated with an intermediate rate, and low regularity and coupling. Wave canalization is characterized by intermediate rate and low regularity, with higher coupling along splines than lines.

Figure 5

Voltage amplitude of synthetic electrograms for different fibrosis amounts and sizes. Average values (P2P, left panel) and spatial variability values (P2P_std, right panel) of electrogram voltage amplitude are displayed as a function of fibrosis overall amount (density, D) and color-coded according to fibrosis size parameter (p_th). Black dots and whiskers indicate mean values and standard deviations over simulation subgroups, while small colored dots correspond to single simulation outcomes. Only simulations obtained for diffuse and compact fibrosis (α = 0) are shown. The increase of fibrosis density determined a decrease in voltage amplitude and increase in voltage amplitude spatial variability.

Figure 6

Frequency-domain properties of synthetic electrograms for different fibrosis amounts and sizes. Average values (top panels) and spatial variability values (std, bottom panels) of rate (DF and DF_std), regularity (RI and RI_std) and coupling (Cxy and Cxy_std) are shown as a function of fibrosis overall amount (density, D) and color-coded according to fibrosis size parameter (p_th). Black dots and whiskers indicate mean values and standard deviations over simulation subgroups, while small colored dots correspond to single simulation outcomes. Only simulations obtained for diffuse and compact fibrosis (α = 0) are considered. The increase of fibrosis amount determines slowing and organization of wave propagation, with an overall decrease of DF and DF_std and increase in RI, Cxy, and Cxy_std, albeit with an increased stochasticity of simulation outcomes.

Figure 7

Effects of fibrosis texture on coupling asymmetry of synthetic electrograms. Coupling asymmetry index (DCxy), quantified as the ratio between line-wise and spline-wise coupling values, is compared in diffuse/compact (unoriented) versus stringy/patchy (oriented) fibrotic elements for D = 30% fibrosis density. Black dots and whiskers indicate mean values and standard deviations over the simulation subgroups, while small dots correspond to single simulation outcomes and are color-coded according to fibrosis size parameter (p_th). Oriented fibrosis determined a prevalent coupling of electrical activity along splines than lines, resulting in asymmetry values lower than one with respect to compact fibrosis where asymmetry values were higher than one.

Figure 8

Stability of propagation patterns for different fibrosis amounts and sizes. The number of episodes persisting over the whole observation window is indicated as a function of fibrosis amount (density, D) and for different fibrosis sizes (p_th parameter, in color). Only simulations obtained for diffuse and compact fibrosis (α = 0) are considered. Fibrosis had a stabilizing effect on propagation patterns, with the number of stable patterns increasing at the increase of fibrosis density.