Effect of Na⁺-channel blockade on the three-dimensional substrate of atrial fibrillation in a model of endo-epicardial dissociation and transmural conduction

Abstract

Introduction

Atrial fibrillation (AF) is known to induce significant electrophysiological alterations in atrial myocytes and causes significant structural changes (structural remodelling). Several studies have demonstrated that structural remodelling, including fibrosis, is associated with a decrease in the size of fibrillatory waves, an increase in the electrical activity dissociation between the epicardial layer and the endocardial bundle network, and an increase in the incidence of transmural conduction (‘breakthroughs’, BTs).^1–3

Numerous therapeutic strategies, ranging from pharmaceutical interventions to ablation, have been used in AF treatment. Antiarrhythmic drugs have been an important part of AF therapy for many years.^4–8 Among all antiarrhythmic drugs, sodium (Na⁺)-channel blockers have a long history in AF treatment.^5–10 Recent studies witness an increased interest in Na⁺-channel blockers such as flecainide for AF therapy.^5,9–11 Although several studies have been performed on Na⁺-channel blockers it is not clear how these agents facilitate cardioversion of AF and why they are less effective in advanced stages of AF, as clinical studies have reported.^5,8,10 Three possible mechanisms of cardioversion have been proposed including (i) enlargement of phase singularity (PS) tips, (ii) decreased anchoring of rotors to functional obstacles, and (iii) reduction in number of waves, due to an increase in the excitable gap (EG).¹² While all simulation studies reported a high success rate in AF termination by the application of Na⁺-channel blockers, several experimental studies have revealed a reduction in termination rates after administration of Na⁺-channel blockers in both animal models and patients in later stages of AF.^{5,6,8–10,13} Recently one possible mechanism for this efficacy loss has been proposed by Eckstein.¹³ This study suggested that the three-dimensional substrate of AF conduction, which occurs in the later stages of AF and due to structural remodelling, could have an important effect on sodium channel blockers’ efficacy of AF termination.¹³ In this work, it was demonstrated that flecainide reduced the incidence of BTs and endo-epicardial electrical dissociation significantly.¹³ This aspect, three-dimensional substrate of AF, is missing in all simulation studies performed so far on the effect of sodium channel blockers on AF termination. All those simulations were performed in either a two-dimensional model or two-dimensional sheets of atrial myocytes folded into a three-dimensional shape of human atria. Therefore, in this study, we used a previously developed dual-layer model^14–16 which enabled us to study the effect of three-dimensional substrate on Na⁺-channel blocker efficacy.

In this study, we investigated why a Na⁺-channel blocker is effective in early stages of AF but gradually loses its efficacy in the later stages of AF or, more precisely, with progressive structural remodelling. We hypothesized that the possible explanation for this loss is that structurally remodelled atria represent a higher degree of three-dimensionality in the AF substrate. We addressed this hypothesis by assessing the effect of Na⁺-channel blockade on endo-epicardial electrical activity dissociation (EED), transmural conduction, and AF stability at different degrees of structural remodelling.

Methods

Model

To investigate the effect of Na⁺-channel blockade on AF stability, endo-epicardial dyssynchrony, and BT events during AF, we used a dual-layer computer model (Figure 1A).¹⁴

Figure 1

Dual-layer model of the atrial wall. (A) Model structure with two layers (epi- and endocardium) and transmural connections (grey cylinders). (B) Dissociation of electrical activity between the two layers and transmural conduction resulting in a breakthrough wave (black arrow). (C) Simulation protocol (see Methods section for details). (D) Number of waves per second for a control and Na⁺-channel blockade simulation with 12 connections. The first 1 s represents Step 1 of the simulation protocol. Time points between 2 s and 7 s represent Step 2 of the simulation protocol. Time points between 7s and 13 s represent Steps 3 and 4 of the simulation protocol.

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Electrical coupling between the two layers was implemented by adding an Ohmic conductor between opposing segments at so-called connection points. Each connection point was a circle with a radius of 0.1 cm (see Figure 1A and B).

Simulation protocol

To investigate the effect of Na⁺-channel blocks on EED and transmural conduction at different stages of structural remodelling, the following simulation protocol was applied (see Figure 1C):

1. In one layer, a spiral wave was initiated using an S1–S2 protocol, whereas the other layer was quiescent, as described in a previous study.¹⁴ The simulation was continued for 1 s in order to achieve a stable spiral wave.

2. One second after the start of the simulation, six connection points were added at randomly chosen sites, with the constraint that two connection points were at least 0.15 cm apart. To exclude possible bias resulting from a particular geometry of connection points, eight different geometries with six randomly chosen sites were created. For each of the eight geometries, the simulation of Step 1 was continued for six more seconds. This resulted in eight different simulations that were used as a starting point of the next stages of the simulation.

3. The eight simulations from Step 2 were used and continued for another 6 s, either without changing the connection points or after adding more randomly chosen connection points (at least 0.15 cm apart), so that the total number of connections was 6, 12, 24, 48, or 96. In addition, each simulation from Step 2 was continued as well with 100% connectivity, which means that all opposing segments in the two layers were connected to one another.

4. All simulations at Step 3 were simulated twice, once with the normal sodium conductance (control) and once with 60% sodium channel conductance block. As described above, Steps 2 and 3 were performed eight times such that in total 48 simulation runs were performed in Step 3.

In our model, 6 and 12 connections represented severely remodelled atria; 24 and 48 connections represented moderately remodelled atria, and 96 connections and 100% connectivity represented a healthy atrium.

Analysis

In all 48 simulations of Step 3 the following parameters were analysed as described previously^14,19:

• Number of PSs.

• Number of fibrillation waves (see Figure 1D).

• Atrial fibrillation cycle length (AFCL).

• Temporal EG.

• Degree of endo-epicardial dyssynchrony

• Breakthrough rates (BTRs).

• AF stability.

Results

Figure 2 shows representative examples of AF in control and in the presence of Na⁺-channel block for two different degrees of endo-epicardial connectivity (96 and 12 connections).

Figure 2

Colour-coded membrane potentials of representative simulations with two different numbers of endo-epicardial electrical conn. (A and C) Simulations without Na⁺-channel blockade. (B and D) Simulations with Na⁺-channel blockade. The epicardial layer is shown in the top, the endocardial in the bottom panel. Snapshots are shown for every second of a simulation. Conn., connections.

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In 96 connections simulations—representing a healthy atrium—a large number of BTs occurred immediately after the additional connections were introduced, leading to effective synchronization of the two layers. Complete synchronization of the two layers on average took approximately 250 ms. After synchronization, no BTs were observed, and the AF episode quickly terminated (see Figure 2). In contrast to 96 connections, in simulations with 12 connections BTs occurred throughout the simulation. However, none of those BTs could synchronize two layers.

Atrial fibrillation stability

Atrial fibrillation stability in different degrees of connectivity, with or without Na⁺-channel block, is illustrated in the Kaplan–Meier curves in Figure 3. As shown in this figure, in simulations with a high number of connections (96 connections and 100% connectivity), Na⁺-channel block accelerated AF termination. Upon a progressive reduction in the connectivity between the two layers (48 and 24 connections) Na⁺-channel block gradually lost its efficacy, and AF persistence became comparable with the control simulations. After a stronger reduction (6 and 12 connections) Na⁺-channel block was not only able to facilitate AF termination but also made AF more stable when compared with control simulations.

Figure 3

AF persistence. Kaplan–Meier curves showing atrial fibrillation persistence with and without Na⁺-channel blockade (solid line = control, dashed line = Na⁺-channel blockade) in different sets of simulations with 6, 12, 24, 48, and 96 connections, and 100% connectivity (n = 8 for all different sets of simulations). Star shows significant difference between control and Na⁺-channel blockade groups for different number of connections, P < 0.05. AF, atrial fibrillation.

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Effect of sodium channel blockade on fibrillation patterns

As described above, Na⁺-channel block only decreased AF persistence in simulations with 96 connections and 100% connectivity. To understand this failure of AF termination in simulations with a smaller number of connections, we tried to further assess the mechanisms causing AF termination by computing several electrophysiological parameters in all groups of simulations with or without Na⁺-channel block (Figure 4). As expected and reported in the previous studies,^4,20 presence of Na⁺-channel block increased the AFCL and the EG in all groups of connectivity (Figure 4A and B). The number of waves in both groups was similar, except at high degrees of connectivity, where Na⁺-channel block decreased the number of waves (Figure 4C). Similarly, Na⁺-channel block decreased the number of PSs only for 96 connections and 100% connectivity (Figure 4D). Dyssynchrony was not, or subtly, affected by Na⁺-channel block, and the BTR showed a non-significant trend towards a decrease in the presence of Na⁺-channel block (Figure 4E and F).

Figure 4

Electrophysiological parameters calculated in simulations with (grey) and without Na⁺-channel blockade (red). (A) AFCL. (B) EG. (C) Number of waves. (D) Number of PSs. (E) Electrical activity dyssynchrony between two layers. (F) BTR (per ms). *P < 0.05. AFCL, atrial fibrillation cycle length; BTR, breakthrough rate; EG, excitable gap; PS, phase singularity.

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To further uncover the reasons underlying this efficacy loss, we divided the simulations in two groups, 3D and 2D. The 3D group contained simulations with 6 and 12 connections, and represented severely remodelled atrium. The 2D group contained 96 connections and 100% connectivity simulations, and represented healthy atrium. As expected and mentioned above, in the 3D group we observed a pronounced loss of efficacy of sodium channel blockade, whereas in the 2D group blocking Na⁺-channel effectively terminated AF (see Figure 5).

Figure 5

AF persistence. Kaplan–Meier curve showing atrial fibrillation persistence with and without Na⁺-channel blockade (solid line = control, dashed line = Na⁺-channel blockade) in simulations entitled in 2D and 3D groups (n = 16 for all different sets of simulations). Star shows significant difference between control and Na⁺-channel blockade groups for 2D simulations, *P < 0.05. AF, atrial fibrillation.

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In both groups the presence of Na⁺-channel block also significantly increased both the AFCL and EG when compared with the control (see Figure 6A and B). Atrial fibrillation pattern complexity, quantified as the number of waves and PSs, in the 2D group was significantly lower in the presence of Na⁺-channel block when compared with control. Interestingly, the Na⁺-channel block was unable to decrease AF pattern complexity in the simulations in the 3D group (see Figure 6C and D). Breakthroughs, which are a reflection of three-dimensional substrate of AF, were significantly reduced in the 3D group. This reduction in the number of BTs occurred, while the degree of endo-epicardial dyssynchrony, which was the main cause of BT occurrences, remained unaltered in the presence of Na⁺-channel block. The main argument, which can describe this phenomenon, is a pronounced increase in the number of unsuccessful BTs in all simulations regardless of the number of connections (Figure 7).

Figure 6

Measured electrophysiological parameters in slightly structurally remodelled (2D) and severely structurally remodelled (3D) atrial models in control and in the presence of Na⁺-channel block (Na-block). (A) AFCL. (B) EG. (C) Number of PS. (D) Number of waves. (E) BTR. *P < 0.05. AFCL, atrial fibrillation cycle length; BTR, breakthrough rate; EG, excitable gap; PS, phase singularity; 2D, two dimension; 3D, three dimension.

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Figure 7

Examples of (A) a successful BT and (B) an unsuccessful BT (red circle). (C) The number of unsuccessful BTs in both control and Na⁺-blockade group. *P < 0.05. BT, breakthrough; BTR, breakthrough rate.

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Discussion

Although the effects of Na⁺-channel blockade on AF have been studied extensively, the mechanism of AF termination by Na⁺-channel block and the reason for the loss of its efficacy in structurally remodelled atria are poorly understood. These mechanisms are likely multifactorial, involving depression of excitability and impaired impulse propagation resulting in progressive merging of fibrillation waves in the presence of wide EG or enhanced meandering of rotors leading to collision of wave fronts with anatomical boundaries.^12,21–23

Although simulation studies investigated several mechanisms underlying AF termination in the presence of Na⁺-channel block, the question regarding the loss of efficacy of Na⁺-channel block in later stages of AF is still unanswered. In a goat model of AF, it was demonstrated by Eijsbouts et al.²⁰ that this loss of efficacy was not due to a loss of AFCL or temporal EG prolongation in the presence of the drug. The study by Eckstein suggests that the loss of AF termination rather could be due to the increasingly three-dimensional conduction pattern of AF in later stages of remodelling.

Parameters determining atrial fibrillation stability

In this study, we showed the efficacy loss of Na⁺-channel block in AF termination in different stages of structural remodelling. In all simulations with no structural remodelling (96 connections and 100% connectivity) AF episodes terminated much faster in the presence of Na⁺-channel block. However, in all simulations with severe structural remodelling (6 or 12 connections), Na⁺-channel block was unable to terminate AF. Interestingly, we did not observe significant differences in AF termination rate between control and Na⁺-channel block simulations with severe (6 and 12 connections) and moderate (24 and 48 connections) structural remodelling. Atrial fibrillation termination rate was significantly different in 96 connections and 100% connectivity simulations in the presence of Na⁺-channel block compared with the control simulations. As illustrated in Figures 4 and 6, AFCL and EG were increased in the presence of Na⁺-channel block. These findings agreed with findings reported in previous studies.^12,24 Since this increase was present at all different numbers of connections and in both 2D and 3D groups, it cannot explain the loss of efficacy with structural remodelling in our model. The presence of Na⁺-channel block decreased AF complexity, quantified as the number of waves and PSs, in the 2D group simulations, in which two layers were well coupled and degrees of dyssynchrony were low. Therefore, fibrillation waves could not find opportunities to propagate from one layer to the other. However, Na⁺-channel block was unable to perform the same in the 3D group simulations. In this group the degree of dyssynchrony was higher due to a lower number of connections between two layers, and fibrillation waves could find more opportunities to propagate from one layer to the other. This inability of Na⁺-channel block to reduce AF complexity in simulations of severe remodelling, which has a more three-dimensional character, could be an explanation for the Na⁺-channel blocker efficacy loss at the later stage of AF.

The effect of Na⁺-channel blocker on dyssynchrony and breakthroughs

In the goat atria, Eckstein¹³ showed a decrease in both endo-epicardial dissociation and BTs in the presence of flecainide. In our model, we observed only a slight, insignificant increase in dyssynchrony as a result of Na⁺-channel blockade, regardless of the degree of connectivity. At first glance, a similar degree of dyssynchrony in combination with an increase in EG should increase the number of opportunities for BTs to occur. However, we observed a decrease in BT incidence (see Figure 4F). To investigate possible mechanisms for this reduction, we analysed the number of unsuccessful BTs (Figure 7B). Unsuccessful BT was defined as a BT that did not conduct transmurally despite the presence of local endo-epicardial electrical dyssynchrony. A pronounced increase in the number of unsuccessful BTs as a result of Na⁺-channel block was observed in all sets of connections (Figure 7C). This transmural conduction block due to reduced excitability or a sink/source mismatch could explain the surprisingly low number of BTs in the presence of Na⁺-channel block (given the increase in EG). However, the decline of the BTR in the presence of Na⁺-channel block was obviously not strong enough to allow for sufficient reduction of AF complexity and AF termination.

Limitations

Our dual-layer model should be considered as a proof-of-principle model. This model does not reflect three-dimensional geometry and complex structure of the atrium, fibre orientation arrangement, heterogeneity in ionic membrane currents, and variability in atrial wall thickness. According to this, the effect of myocardial thickness could not be addressed. In this study, a simple pore-block model (a fixed percentage decrease in maximum Na⁺-channel conductance) was used to simulate Na⁺-channel blockade. A more detailed exploration of the impact of state-dependent I_Na block as occurs for all clinically used Class I drugs, with the application of a mathematical formulation of such action, would be of great interest but is beyond the scope of this study. However, the work in this study does demonstrate for the first time that pure reduction of Na⁺ current fails to terminate AF in the presence of severe structural remodelling leading to a three-dimensional substrate for AF.

We also did not consider ectopic focal discharges as a mechanism contributing to AF maintenance in this study. Despite these limitations, we have shown that our model is well suited to investigate the effect of Na⁺-channel blockade on endo-epicardial dissociation, BTs, and AF stability.

Conclusion

Using a simple bilayer model, we have shown that severe structural remodelling, resulting in a small number of connections between the subendocardial and subepicardial layers of the atria, can prevent termination of AF by Na⁺-channel block.

Acknowledgements

The authors acknowledge financial support by the Theo Rossi di Montelera Foundation, the Metis Foundation Sergio Mantegazza, the Fidinam Foundation, and the Horten Foundation to the Center for Computational Medicine in Cardiology.

Funding

This work was supported by grants from the European Union, the ITN NetworkAFibTrainNet, No. 675351; and the ERACoSysMED H2020 ERA-NET Cofound project Systems medicine for diagnosis and stratification of atrial fibrillation to US. This work was also supported by grants from the Swiss National Supercomputing Centre (CSCS) under project ID s668 and s778.

Conflict of interest: none declared.

References