Prevalence of endoepicardial asynchrony and breakthrough patterns in a bilayer computational model of heterogeneous endoepicardial dissociation in the left atrium

Fig 1. Construction of the atrial model. (A) Fiber orientation in the epicardium (top) and in the endocardium (bottom) from which longitudinal cables were generated. (B) Action potentials simulated using the two membrane models during paced rhythm at 200 bpm. (C) Illustration of a transmural cross-section of the cable model showing the epi- and endocardial layers and the transmural cables with nz = 4. The color (blue/gray) of the nodes corresponds to those of the patterns below. (D) Examples of random realizations of endoepicardial coupling patterns with increasing length scale. The number of connected regions is indicated below each pattern. The number of transmural cables is, however, the same in all patterns.

Fig 2. Examples of membrane potential maps during sinus rhythm (A) and atrial fibrillation (B-G) in arrhythmogenic substrates with increasing levels of endoepicardial dissociation. Membrane potential maps in the epicardium (blue color map) and in the endocardium (pink color map) were blended with transparency on each atrial surface to highlight the delay between the activation of the two layers. Arrows indicate direction of propagation. Yellow stars are referred to in the text. The Workman model was used in all panels except panels E and G. In panels F and G, the contours of the connected regions as shown in Fig 1 are outlined in black. Parameter sets encoded as a quadruple (nz, #connected regions, σz, fibrosis density) were as follows: Panel A, from left to right: (4, 1.2k, 0.4, 30%), (6, 536, 0.2, 30%), (10, 301, 0.2, 20%), (10, 1.2k, 0.2, 30%); Panel B: (2, 6.5k, 0.4, 20%), (4, 1.2k, 0.4, 30%), (2, 301, 0.4, 20%), (2, 191, 0.4, 20%); Panel C: (4, 536, 0.3, 30%), (6, 536, 0.2, 30%), (10, 191, 0.2, 30%); Panel D: (10, 50, 0.2, 30%); Panel E: (4, 6.5k, 0.3, 30%), (10, 1.2k, 0.3, 20%), (6, 536, 0.3, 30%), (6, 27, 0.2, 20%); Panel F: (10, 191, 0.4, 30%), (4, 27, 0.2, 30%), (6, 50, 0.2,…

Fig 3. Occurrence of self-termination in simulated episodes of atrial fibrillation (AF), represented by Kaplan-Meier estimates of the survival curve with its confidence intervals displayed as light shaded regions. (A) The simulations with the Kim model were divided into two subgroups depending on the number of intermediate nodes nz being smaller or larger than 6. The hazard ratio between the two subgroups was 0.74 (confidence interval: 0.61 to 0.90) as obtained by Cox regression (p<0.005). The simulations using the Workman model are displayed as a single group. (B) Survival curves for the Kim model divided into two subgroups where the mode of the endoepicardial delay distribution is smaller or larger than 3 ms. (C) Survival curves for the Kim model with two subgroups formed using a threshold on the breakthrough rate (BTR). Note that in panels B and C, a minimum AF duration is needed to estimate the quantities, so the sample size is smaller than in panel A.

Fig 4. Two examples of transmural reentries. Membrane potential maps are color-coded as in Fig 2. Endocardial breakthroughs are indicated as a pink star and epicardial breakthroughs as a purple star. Parameter sets encoded as a quadruple (nz, #connected regions, σz, fibrosis density) were as follows. Panel A: (2, 50, 0.3, 30%); Panel B: (2, 27, 0.4, 30%).

Fig 5. Examples of distributions of endoepicardial delays during sinus rhythm (SR) and atrial fibrillation (AF). Positive delay means that the endocardium is activated earlier. The distribution over all sites is shown in light gray. Mean and standard deviation of the delay is written next to each distribution. The Gaussian kernel-density estimate of the distribution over the sites in the connected (respectively disconnected) regions is displayed as solid (resp. dashed) curve. (A) uniform endoepicardial coupling (48k connected regions) without fibrosis, nz = 2, σz = 0.3 mS/cm; (B) same as A, but with only 536 connected regions; (C) uniform coupling with 20% fibrosis, nz = 4, σz = 0.4 mS/cm; (D) same as C, but with nz = 8; (E) same as C, but with 30% fibrosis; (F) same C, but with σz = 0.2 mS/cm; (G) same as C, but with 191 connected regions; (H) same as G, but with nz = 8.

Fig 6. Measured and predicted mode of the endoepicardial delay distribution based on the regression formula. The membrane model is color coded. (A) Delays during sinus rhythm. Error bars indicate the standard deviation over 5 statistical realizations of the substrate. (B) Delays during atrial fibrillation. Error bars indicate the standard deviation over 5 fibrillatory initial conditions. (C) Measured model of the delay distribution in sinus rhythm vs atrial fibrillation.

Fig 7. Lifespan and location of breakthroughs. (A) Scatter plot of life span vs maximum area for all breakthroughs in all simulations. Membrane model is color coded. The limits of the y-axis correspond to the minimum observable area (2 × 2 mm) and the total left atrium area. The diagonal gray line has a slope of 2 in logarithmic scale. (B) Survival curves of breakthroughs in sinus rhythm and atrial fibrillation, indicating their life span. The number of breakthroughs included is indicated in parentheses. (C) Map of breakthrough density averaged over all simulations during fibrillation. Density is color coded from 0 (white) to 1.5 breakthroughs per computational node (orange) after spatial filtering with a length scale of 2 mm.

Fig 8. Incidence and prevalence of breakthroughs. Incidence (A) and prevalence (B) of breakthroughs during atrial fibrillation (AF) as a function of the level of endoepicardial dissociation heterogeneity (number of endoepicardial connections, as shown in Fig 1D), for epicardial fibrosis density from 10% (left) to 30% (right), and for both membrane models (color coded). Boxplots show the statistics over AF episodes with different values of nz and σz of with different initial conditions. Small gray circles indicate outliers.

Fig 9. Correlation of the incidence of breakthrough during sinus rhythm (SR) and atrial fibrillation (AF) for both membrane model (color coded). Error bars indicate standard deviation over 5 statistical realizations of the substrate (SR) or 5 fibrillatory initial conditions (AF).

Fig 10. Ranges of breakthrough rates reported in clinical (orange) and experimental studies (red), compared to our simulations (blue). Mean ± standard deviation (unless stated otherwise) is shown in log scale. When needed, breakthroughs per cycle were calculated from breakthroughs per second using the mean cycle length. The mapping area used for normalization (if not indicated in the original paper) was estimated as the number of electrodes multiplied by the interelectrode distance squared. Notes: (a) recomputed from individual data [21]; (b) mapping area was calculated based on 90 electrodes [18]; (c) focal activations were excluded from breakthroughs [17]; (d) baseline data before drug injection [49]; (e) median ± half of interquartile range [50]; (f) median and quartiles [51]; (g) statistics computed from all histograms using a mean cycle length of 854 ms and 128 electrodes [22]; (h) based on repetitive nonrandom breakthroughs [52] and a mapping area of 92.85 cm2; (i) based on the percentages of breakthrough patterns [20]; (j) all data for each number of connected regions, Kim and Workman models combined. AF: atrial fibrillation; SR: sinus rhythm; RA: right atrium; LA: left atrium.