High accessory pathway conductivity blocks antegrade conduction in Wolff‐Parkinson‐White syndrome: A simulation study

Abstract Background Wolff‐Parkinson‐White (WPW) syndrome is characterized by an anomalous accessory pathway (AP) that connects the atrium and ventricles, which can cause abnormal myocardial excitation and cardiac arrhythmias. The morphological and electrophysiological details of the AP remain unclear. The size and conductivity of the AP may affect conduction and WPW syndrome symptoms. Methods To clarify this issue, we performed computer simulations of antegrade AP conduction using a simplified wall model. We focused on the bundle size of the AP and myocardial electrical conductivity during antegrade conduction (from the atrium to the ventricle). Results We found that a thick AP and high ventricular conductivity promoted antegrade conduction, whereas a thin AP is unable to deliver the transmembrane current required for electric conduction. High ventricular conductivity amplifies transmembrane current. These findings suggest the involvement of a source‐sink mechanism. Furthermore, we found that high AP conductivity blocked antegrade conduction. As AP conductivity increased, sustained outward transmembrane currents were observed. This finding suggests the involvement of an electrotonic effect. Conclusions The findings of our theoretical simulation suggest that AP size, ventricular conductivity, and AP conductivity affect antegrade conduction through different mechanisms. Our findings provide new insights into the morphological and electrophysiological details of the AP.


| INTRODUC TI ON
Accessory pathways (APs) are microscopic anomalous muscular bundles that connect the atrial and ventricular myocardium, bypassing the normal conduction system. APs can cause abnormal excitation of the myocardium leading to cardiac arrhythmias. 1 APs are present in patients with Wolff-Parkinson-White (WPW) syndrome. 2 Clinically, WPW syndrome is classified according to the location of the APs, as established by electrocardiographic (ECG) and electrophysiological tests. 3,4 Recently, radiofrequency AP catheter ablation has been used to treat WPW syndrome with good results. 5,6 However, the morphological and electrophysiological details of APs remain unclear. Few studies have investigated the morphological and electrophysiological characteristics of APs. 7,8 Wei et al 9 reproduced the ECG characteristics of WPW in a computer simulation.
Recently, we successfully visualized APs using three-dimensional (3D) reconstruction images of histological sections. 10 It is widely accepted that a narrow AP poorly sustains electrical conduction. 11 Myocardial electrical conductivity affects the stability of excitation propagation. Preliminary computer simulations of AP conduction were performed using a simplified 3D wall model to investigate the effects of the morphological and electrophysiological properties of AP on conduction. We focused on the effects of AP bundle size and myocardial electrical conductivity on antegrade (from atrium to ventricle) AP conduction. A preliminary version of this work has been reported. 12

| ME THODS
We constructed a 3D model consisting of a simplified atrial wall, ventricular wall, and myocardial bundle representing an AP ( Figure 1A,B). The atrial model combined two walls 20 × 15 × 1.05 and 20 × 10 × 1.05 mm in dimension. The ventricular wall dimensions were 20 × 25 × 7.05 mm. Although the left ventricular free wall thickness is usually approximately 10 mm, the thickness was set to 7.05 mm in our model because the myocardium near the mitral valve is generally thin. The myocardial bundle models (AP models), which included various bundle sizes, were integrated with the atrial and ventricular models. We constructed five models using various bundle sizes (Table 1).
To investigate AP conduction in detail, we configured recording sites near the junction of the AP (P AP ) and ventricular wall (P V , Figure 1C) to record membrane potential and current during the simulation experiments.
The membrane kinetics of the simulated atrial myocardium and AP were produced using Courtemanche-Ramirez-Nattel mathematical equation. 13 The membrane kinetics of the simulated ventricular myocardium were produced using O'Hara-Rudy model equation 14 with modification of the conductance of the sodium channel current. The electrophysiological models were Hodgkin-Huxley type differential equation, 15 which were configured based on the experimentally measured responses of various ion channel/exchange/ pump currents. Furthermore, the models incorporated intracellular calcium dynamics and extracellular/intracellular ion concentrations.
The wet experiments validated whole-cell responses such as stimulus frequency dependence of the action potential duration (APD) as well as early afterdepolarizations (EAD) and APD alternans.  To simulate the propagation of a cardiac action potential, cardiac tissue is usually modeled as a two-phase ohmic medium (one phase representing the intracellular space and the other representing the extracellular space) with the two phases linked by a network of resistors and capacitors. 16 Monodomain equation 17 were used as governing equations in our 3D model. The no-flux Neumann boundary condition was applied to the tissue border. We configured six levels of isotropic intercellular conductivity, ranging from 0.17 to 1.36 mS/cm. Previous studies have shown that conduction velocity can be achieved within a physiological range at these conductivity levels. 12,18,19 To simulate excitation conduction from the atrium to the ventricle via the AP, 10 pacing stimuli (2-ms duration and 2,000 pA amplitude) were delivered to the top of the atrial wall at a cycle length of 1,000 ms After the last pacing stimulus, we measured membrane potentials and transmembrane currents at the P AP and P V recording sites.
The simulation program was written in C++ with OpenMP for parallel processing. We used the forward Euler numerical integration method to solve the ordinary differential equations numerically. In all the simulations, the spatial resolution per unit was set to 0.150 mm in all directions, and the time step was set to 0.005 ms

| A thick AP triggers antegrade conduction
First, we set the isotropic intercellular conductance to 0.17 mS/ cm in the atrial and ventricular walls and the AP. Under constant intercellular conductance, the excitation propagation ran from the atria to the AP, but not from the AP to the ventricle in model C ( Figure 2A,B). Moreover, no action potentials were generated at the P AP and P V recording sites ( Figure 2C). In contrast, in model D, in which the AP was thicker, excitation propagation ran from the atria to the ventricle via the AP ( Figure 2D,E), and normal action potentials were recorded at P AP and P V ( Figure 2F). AP thickness had an effect on membrane potential ( Figure 3). No action potentials were generated in models A-C, in which the APs were thinner. In contrast, the action potentials were normal in models D and E with thicker simulated APs.
Furthermore, AP bundle size had an effect on the transmembrane current (Figure 4). The transmembrane currents recorded at P V were larger in models D and E than in models A-C. Moreover, the peak time was slightly earlier in model E than in model D.
These findings suggest that a thick AP triggered antegrade conduction. In other words, a small bundle blocked conduction.

| Ventricular conductivity promotes antegrade conduction
In model C, where the intercellular conductivity was 0.17 mS/cm, excitatory propagation from the AP to the ventricle was blocked

| AP conductivity prevents antegrade conduction
When the intercellular conductivity was 0.17 mS/cm in model D, excitation propagation ran from the atria to the ventricle via the AP ( Figure 2). In contrast, high AP conductivity (g AP = 0.79 and 1.36 mS/ cm) blocked conduction from the AP to the ventricle.
As AP conductivity increased, complete action potentials were not formed, suggesting that AP conductivity blocked antegrade conduction.

| D ISCUSS I ON
We investigated the effects of AP bundle size and intercellular con-

| Effects of AP bundle size and ventricular conductivity on antegrade conduction
We investigated whether antegrade conduction from the atrium to the ventricle passed through an AP. Antegrade conduction was blocked when the AP bundle was small but occurred when the bundle was large. When we increased ventricular conductivity in a small AP bundle, antegrade conduction occurred. Both AP bundle size and ventricular conductivity had marked effect on the peak inward transmembrane current. These findings can be explained by a source-sink relationship. 11,20 Spector 21 described the electric propagation in terms of the source of the depolarizing current and the tissue (sink) to be depolarized.In our study, the AP bundle provided a smaller source than the sink of the larger ventricular tissue sink to which it was connected.
Therefore, the source-sink balance was asymmetrical. A small AP would be unable to supply the current required for electric conduction.
As the AP bundle size increased, the total amount of transmembrane current at the junction of the AP and ventricular wall increased. As ventricular conductivity increased, the transmembrane current density at the junction of the AP and ventricular wall increased. From the perspective of source-sink balance, both increased the "source". Our findings clarified the roles of AP bundle size and ventricular conductivity in antegrade AP conduction.

| Effect of AP conductivity on antegrade conduction
Antegrade conduction was observed in model D. However, when AP conductivity was increased, antegrade conduction was blocked.
Differences in AP conductivity did not affect the peak membrane potential or inward transmembrane current. In contrast, sustained outward transmembrane currents were recorded when antegrade conduction was blocked, suggesting an electrotonic effect. 22 Myocardial tissues interact with each other electrically. The extent of such interactions depends on the membrane potential difference and intercellular conductivity. As AP conductivity increases, the electrotonic current rises in both the waveback area and the wavefront. These findings indicate that the sustained outward current prevented formation of the action potential waveform despite having sufficient current for excitation propagation. From the sourcesink balance perspective, increased AP conductivity provided a larger sink via an increase in the outward transmembrane current. 21 These findings clarify the effect of AP conductivity on antegrade AP conduction.  APs, such as the Kent bundle, are congenital in nature; however, symptomatic WPW in patients with normal hearts is age dependent. 29 We found that reduced AP conductivity triggered anterograde conduction. In general, myocardial conductivity decreases with age. Our simulation findings suggest that an agerelated reduction in AP conductivity leads to the onset of WPW syndrome, which may be suppressed by using drug treatment to alter AP conductivity.

| Study limitations
We did not consider ion channel conductance in our atrial wall, ventricular wall, or AP models. Furthermore, we used the Courtemanche-Ramirez-Nattel model 13 to reproduce the membrane kinetics of the AP; however, the model was developed to reproduce human atrial action potentials. Few studies have investigated the electrophysiological properties of ion channel conductance in APs. Ion channel conductance is thought to influence the excitability and refractoriness of AP conduction.
Furthermore, we did not explore retrograde conduction.
Gallagher et al 1 and Tonkin et al 27 showed that the AP refractory period was markedly different in anterograde and retrograde con- duction. An AP with a short effective refractory period is associated with a high risk of sudden cardiac death in patients with WPW syndrome. 29,30 We focused on the AP bundle size and myocardial conductivity, and thus, did not investigate the refractory period of the AP during atrial fibrillation.
We used a simplified 3D wall model and did not investigate the effects of AP shape or length, heterogeneity, or anisotropy. The electrophysiological properties and shape at the junction of the AP and ventricular wall may affect AP conduction.

| CON CLUS IONS
The findings of our theoretical simulation suggest that AP size, ventricular conductivity, and AP conductivity affect antegrade conduction through different mechanisms. We offer new insights into the morphological and electrophysiological details of the AP.

ACK N OWLED G EM ENT
This study was supported by JSPS KAKENHI grant numbers JP 20K12605, 20K07232, 17K01366, and 16K09431.

D I SCLOS U R E S
Authors declare no Conflict of Interests for this article.