Why is only type 1 electrocardiogram diagnostic of Brugada Syndrome? Mechanistic insights from computer modeling

Abstract

Background.

Three types of characteristic ST-segment elevation are associated with Brugada syndrome (BrS) but only type 1 is diagnostic. Why only type 1 electrocardiogram (ECG) is diagnostic remains unanswered.

Methods.

Computer simulations were carried out in single cells, one-dimensional cables, and two-dimensional tissues to investigate the effects of the peak and late components of the transient outward potassium current (I_to), sodium current (I_Na), and L-type calcium current (I_Ca,L) as well as other potassium currents on the genesis of ECG morphologies and phase 2 reentry (P2R).

Results.

Although a sufficiently large peak I_to was required to result in the type 1 ECG pattern and P2R, increasing the late component of I_to converted type 1 ECG to type 2 ECG and suppressed P2R. Increasing the peak I_to promoted spiral wave breakup, potentiating the transition from tachycardia to fibrillation, but increasing the late I_to prevented spiral wave breakup by flattening the action potential duration restitution and preventing P2R. A sufficiently large I_Ca,L conductance was needed for P2R to occur, but once above the critical conductance, blocking I_Ca,L promoted P2R. However, selectively blocking the window and late components of I_Ca,L suppressed P2R, countering the effect of the late I_to. Blocking either the peak or late components of I_Na promoted P2R, with the late I_Na blockade having the larger effect. As expected, increasing other potassium currents potentiated P2R, with I_K-ATP exhibiting a larger effect than I_Kr and I_Ks.

Conclusions.

The peak I_to promotes type 1 ECG and P2R, whereas the late I_to converts type 1 ECG to type 2 ECG and suppresses P2R. Blocking the peak I_Ca,L and either the peak or the late I_Na promotes P2R whereas blocking the window and late I_Ca,L suppresses P2R. These results provide important insights into the mechanisms of arrhythmogenesis and potential therapeutic targets for treatment of BrS.

Graphical Abstract

Introduction

Brugada syndrome (BrS) is an inherited heart disease characterized by J-point and ST-segment elevation in surface ECG and associated with a high risk of sudden cardiac death ^1–4. As described in current consensus statements ^5–7, there are three types of characteristic ECGs associated with BrS (see Fig.I in Data Supplement). Type 1 is characterized by coved ST-segment elevation >2 mm in leads V1-V3 with a negative T-wave, type 2 by a saddleback ST-segment elevation >2 mm, and type 3 with either coved or saddleback ST-segment ST elevation <1 mm. In all three types of ECGs, the J-point is elevated. However, only type 1 is diagnostic of BrS ^5–7. Patients exhibiting type 2 or type 3 ECGs can sometimes be converted to type 1 by provocative drugs such Na⁺ channel blockers, but still have very low risk of arrhythmias ^{7, 8}.

The cellular mechanisms of coved and saddleback ECGs have been linked to the spike-and-dome action potential (AP) morphology caused by the transient outward K⁺ current (I_to) by Antzelevitch and coworkers ⁹, who also showed that the spike-and-dome AP morphology promotes phase 2 reentry (P2R) initiating ventricular fibrillation ^10–12. However, why only type 1 ECGs are diagnostic of BrS and confer a high risk of sudden cardiac death remains unanswered. In this study, we used computer models to investigate the mechanisms underlying the three characteristic ECG morphologies and their links to arrhythmogenesis. We carried out simulations in single cells, one-dimensional (1D) cables, and two-dimensional (2D) tissues to investigate the effects of the peak and late components of I_to, the L-type calcium current (I_Ca,L) and the sodium current (I_Na). We also investigated the effects of other K⁺ currents, i.e., the rapid (I_Kr) and slow (I_Ks) components of the delayed rectifier K⁺ current, and the ATP-sensitive K⁺ current (I_K-ATP). We show that while a sufficiently large peak I_to is required to initiate phase 2 reentry (P2R), increasing the late component of I_to converts type 1 ECG to type 2 ECG and suppresses P2R. Increasing the peak I_to promotes spiral wave breakup, but increasing the late I_to prevents spiral wave breakup by flattening the AP duration (APD) restitution and preventing focal excitations. For I_Ca,L, a sufficiently large peak conductance is required for P2R, but above a critical conductance, further increases in I_Ca,L suppress P2R. Moreover, increasing the window and late I_Ca,L promotes P2R by countering the P2R-suppressing effect of the late I_to. For I_Na, blocking either the peak or the late component promotes P2R, with the late I_Na blockade exhibiting the larger effect. Increasing other K⁺ currents, such as I_Ks, I_Kr or I_K-ATP, can promote P2R, with I_K-ATP exhibiting the largest effect. Men are more susceptible to P2R, mainly because men have a larger I_to and a smaller I_Ca,L than women. For the same reason, P2R is more likely to occur at nighttime than daytime. The implications for arrhythmogenesis and therapies of BrS are discussed.

Methods

The data that support the findings of this study are available from the corresponding author upon reasonable request. No institutional review board approval was necessary since only simulations were performed.

1D cable and 2D tissue model.

We carried out single cell, 1D cable, and 2D tissue simulations. For the 1D cable model, the governing equation for voltage (V) is:

$$\frac{\partial V}{\partial t}=-\frac{I_{ion}+I_{sti}}{C_m}+D_x\frac{{\partial }^{2}V}{\partial x^2}$$ (1)

where C_m is the capacitance and I_ion is the total ionic current density described by the 1994 Luo and Rudy model ¹³. I_sti is the stimulus current density of a 0.5 ms pulse with a −80 μA/cm². D_x is the diffusion constant representing the gap junction coupling strength.

The governing equation for voltage in the 2D tissue model is:

$$\frac{\partial V}{\partial t}=-\frac{I_{ion}+I_{sti}}{C_m}+D_x\frac{{\partial }^{2}V}{\partial x^2}+D_y\frac{{\partial }^{2}V}{\partial y^2}$$ (2)

We also performed 1D cable and 2D tissue simulations using the 2004 ten Tusscher et al human ventricular AP model ¹⁴ and the results are shown in Figs.V–X and Movies II–IV in Data Supplement. The parameter settings for heterogeneities, calculation of pseudo-ECG, and the numerical methods are also presented as supplemental methods in Data Supplement. Unless stated specifically, the parameters were the same as in the original cell models.

I_to model.

For either the 1994 Luo and Rudy model or the 2004 ten Tusscher et al model, we used (or substituted the I_to in the ten Tusscher et al model with) the I_to formulation by Dumaine et al ¹⁵:

$$I_{to}=G_{to}{z}^{3}y{e}^{\frac{V}{100}}(V-E_K)$$ (3)

where G_to is the maximum conductance, z is the activation gating variable, and y is the inactivation gating variable. To vary the late component of I_to, we altered the steady-state inactivation as

$$y_{\mathrm{\infty },new}=\gamma +(1-\gamma )y_{\mathrm{\infty }}$$ (4)

where γ controls the strength of the late I_to and increasing γ increases the late component.

Results

Late I_to coverts type 1 ECG to type 2 ECG and prevents P2R

We first carried out 2D tissue simulations to demonstrate the effects of late I_to on ECG morphology and the occurrence of P2R. We altered the late I_to in the model by changing γ as described in Eq.4. Fig.1A shows the time-space plots of voltage and the corresponding pseudo-ECGs for different maximum I_to conductance (G_to) for γ = 0. When G_to=0, the T-wave was upright since the APD was shorter in the epicardium. As G_to was increased, the J-point and the ST-segment became elevated, and the T-wave amplitude became smaller and then negative. When G_to was large still, the ST-segment then became coved (type 1) and spontaneous PVCs began to occur. As G_to was increased even further, the APD shortened on the epicardial side and the ST-segment became highly elevated, but spontaneous PVCs disappeared. The coved ECGs were also promoted by blocking I_Na or I_Ca,L when G_to was large enough (see Fig.II in Data Supplement). For γ = 0.1 (Fig.1B), both the J-point and ST-segment become elevated with a saddleback ST-segment (type 2) as G_to was increased, but no PVCs occurred for any G_to values.

Figure 1. Effects of late I_to on ST-segment properties and P2R.

Simulations were carried out in a 2D tissue model with an endocardial-to-epicardial I_to gradient. A. Time-space plots of V and ECGs for different levels of G_to (in unit mS/cm²) when γ = 0. The arrow in the 2^nd panel points to the elevated J-point. The asterisk in the 5^th panel indicates the P2R/PVC. B. Same as A but when γ = 0.1. C. Wave dynamics in the same 2D tissue as for A but with an I_to heterogeneity in the longitudinal direction. Shown are voltage snapshots at different time points. Arrows indicate propagating wavefronts. A wave elicited from two stimulus sites (t=10 ms) propagated from the endocardium to epicardium (t=100 ms). Due to the early repolarization in the lower-right quadrant, a P2R occurred (t=210 ms, marked by *), propagated toward the tissue boundary (t=240 ms) and disappeared. The repolarization pattern remained heterogeneous (t=300 ms) and a new P2R occurred (t=350 ms) that propagated as a spiral wave reentry (t=400 ms) before wandering off the tissue boundary (t=450 ms). New P2Rs (*) also occurred in snapshots at t=450, 550, and 650 ms. Due to the tissue size, the last P2R shown in t=650 ms was not able to survive, and the tissue became quiescent before the next pacing beat. See Movie I in Data Supplement for the detailed wave dynamics. Tissue size was 7.68 cm × 1.92 cm.

In simulated 2D tissue with an endo-epi gradient in I_to density, PVCs occurred, but reentry was never observed. However, when a longitudinal gradient in I_to density was also introduced, spontaneous PVCs began to initiate reentry. Fig.1C shows voltage snapshots at different time points illustrating the spontaneous formation of reentry in the 2D tissue model with both transmural and longitudinal heterogeneities (see Movie I in Data Supplement for the entire episode). Note that after the first episode of P2R, repolarization heterogeneities became very dynamic, resulting in additional P2R episodes at different locations in the tissue. Depending on the tissue size and degree of heterogeneity, P2R could manifest as a single PVC or induce non-sustained and sustained arrhythmias.

To provide a systematic analysis of the effects I_to on P2R, we carried out simulations in a 1D cable in which all other ionic currents were uniform except I_to. G_to in one half (the “endocardial” side) of the cable was zero and the other half (the “epicardial” side) was non-zero, as illustrated in the inset of Fig.2D. The cable was paced from the “endocardial” side. In the 1D cable, only PVCs were observed, which, for simplicity, we also call P2Rs. Fig.2A shows the P2R region versus G_to and γ from the 1D cable simulations obtained by scanning G_to and γ with small increments. At γ = 0, P2R occurred for G_to between 1.59 and 1.85 mS/cm² (see the middle panel in Fig.2B for an example of time-space plot of voltage for P2R). When G_to was smaller than 1.59 mS/cm², the spike-and-dome AP morphology occurred in the epicardial side of the cable (see the lower panel in Fig.2B) with a later repolarization. When G_to was larger than 1.85 mS/cm², the AP became a spike on the epicardial side with very early repolarization (see the upper panel in Fig.2B). In this case, the tissue was very heterogeneous. Although the G_to threshold for P2R (the boundary between “Spike & Dome” and “P2R”) decreased as γ increased, the P2R region shrank quickly, and no P2R occurred when γ > 0.06. This agrees with the observation in Fig.1 that increasing the late I_to converts type 1 ECG to type 2 ECG and suppresses P2R.

Figure 2. Effects of I_to properties on P2R.

1D cable simulations with a single pacing beat from the endocardium. The cable is uniform except that I_to is heterogeneous as indicated in the inset of panel D. The gray region is the P2R region. The region marked by “Spike & Dome” is the region where the AP is normal or exhibits a spike-and-dome morphology in the endocardial side (see the lower panel in B). The region marked by “Spike” is the region where the AP in the epicardial side becomes a spike with a very abbreviated APD (see the upper panel in B). The boundary between the “Spike & Dome” region to the “P2R” region is the threshold for P2R as indicated in C. A. P2R region versus G_to and γ. γ (Eq.4) controls the level of incomplete inactivation of the steady state as indicated in the inset. B. Space and time plots of V from the parameter locations marked in A. Asterisk indicates the PVC. C. P2R region versus G_to and the voltage shift (V_shift) of the steady-state inactivation curve (y_∞) as indicated in the inset. V_shift>0 means a right shift and vice versa. D. P2R region versus G_to and the inactivation time constant τ_y. α (τ_y) is the fold change of τ_y.

We also investigated the effects of window I_to and inactivation time constant on P2R. Fig.2C shows the P2R region versus G_to and the voltage shift (V_shift) of the steady-state inactivation curve (y_∞). Increasing the window I_to (shifting the curve rightward, V_shift>0) shrank the G_to range for P2R. However, this also caused P2R to occur at a lower G_to. Slowing inactivation suppressed the G_to range for P2R but also lowered the G_to threshold. Note that increasing the window I_to or slowing I_to inactivation exhibited a much larger effect on lowering the G_to threshold for P2R than increasing γ. This is because shifting y_∞ or slowing inactivation increased the late component of I_to, which tended to suppress P2R, but also increased the amplitude of I_to, which lowered the G_to threshold for P2R. Therefore, it is unclear if a strategy of altering window I_to or its inactivation time constant would promote or suppress P2R.

In Fig.2, the simulations were performed for a fixed initial condition with a single pacing beat. To investigate how continuous pacing and late I_to affect P2R, we paced the cable with two other pacing protocols: periodic pacing and random pacing (Fig.3). Fig.3A shows the P2R region and percent of the beats exhibiting PVCs versus G_to and pacing cycle length (PCL) for γ = 0, γ = 0.02, and γ = 0.05. The P2R region (G_to range) decreased as PCL was increased or as γ was increased. Moreover, the percentage of the beats exhibiting PVCs increased with PCL but decreased sharply with γ. Note that although the cable was paced periodically, not all beats exhibited PVCs due to the complex dynamics (see a time-space plot of voltage for an example in Fig.III in Data Supplement). In the simulations in Fig.3A, we only paced 200 beats for each combination of G_to and PCL. To obtain more accurate statistics on PVC rates, we paced 2000 beats for a fixed PCL (1500 ms) and different G_to for the three γ values. We calculated the percentage of the beats exhibiting a PVC and plotted it against G_to in Fig.3B for the three γ values. For γ = 0, the highest PVC rate was 60%. When γ = 0.02, the highest PVC rate was less than 10% and decreased to less than 1% for γ = 0.05. We did not observe any PVCs for γ > 0.07 for the 2000 pacing beats. We also used a random pacing protocol in which we randomly picked the PCLs in the interval from 500 ms to 1500 ms, and paced for 2000 beats for each chosen G_to. Fig.3C shows the percentage of the beats exhibiting PVCs against G_to for the three γ values. The PVC rates became lower but the G_to ranges were wider than for the periodic pacing. We did not observe any PVCs when used γ=0.05 or larger.

Figure 3. Dependence of P2R on heart rate and late I_to.

1D cable simulations with periodic or random pacing from the endocardium. A. Percentage of beats exhibiting PVCs versus G_to and PCL under periodic pacing for γ = 0, γ = 0.02, and γ = 0.05. 200 pacing beats were applied for each combination of G_to and PCL. Color scale indicates the percentage of PVC beats. B. Histograms showing percentage of PVC beats versus G_to for γ = 0, γ = 0.02, and γ = 0.05 under periodic pacing with PCL=1500 ms. 2000 pacing beats were applied for each G_to. C. Same as B but for the random pacing protocol with random PCLs uniformly drawn from the interval between 500 ms and 1500 ms.

Note that although P2R occurred over a wider G_to range for the periodic and random pacing protocols (Fig.3) than those for the single-beat pacing (Fig.2A), the likelihood of P2R occurrence decreased sharply with γ in all three pacing protocols, and the threshold γ values for complete suppression of P2R were similar.

Late I_to stabilizes spiral wave reentry

In a previous study ¹⁶, we showed that I_to could destabilize spiral wave reentry, causing spiral wave breakup. Here we show that the late I_to stabilizes reentry and can prevent the spiral wave breakup caused by the peak I_to. Fig.4A shows voltage snapshots for four G_to values with γ = 0. When G_to was small, the spiral wave was stable. When G_to was in the intermediate range, spiral wave breakup occurred. When G_to was large, the spiral wave became stable again. The mechanisms that I_to promotes spiral wave instabilities have been investigated in our previous study ¹⁶. Fig.4B shows voltage snapshots for the same G_to values with γ = 0.2, and the spiral waves were all stable. In Fig.4C, we show the spiral wave cycle length (CL) versus γ for the two G_to values (1.5 and 3.2 mS/cm²) that gave rise to spiral wave breakup in Fig.4A, showing that increasing γ stabilized the spiral wave reentry, i.e., the CL became less variable and finally constant as γ was large enough.

Figure 4. Effects of late I_to on reentry stability in 2D homogeneous tissue.

A. Voltage snapshots for different G_to (in unit mS/cm²) for γ = 0. B. Same as A but for γ = 0.15. C. Cycle length (CL) of reentry versus γ for G_to=1.5 mS/cm² and 3.2 mS/cm². Since the tissue is homogeneous, reentry cannot occur spontaneous, and thus it was induced using the traditional cross-field protocol.

Mechanistic insights from cellular dynamics caused by late I_to

To better understand the effects of late I_to on the ECG morphology, P2R generation, and reentry stability, we carried out single-cell simulations to investigate the effects of the late I_to on APD, APD restitution, and APD dynamics. Fig.5A shows APD versus G_to for three γ values. For γ = 0, as G_to was increased from zero, APD increased slowly at first and then rapidly to a maximum before a sudden and discontinuous shortening (an all-or-none response). As γ was increased, the spike-and-dome morphology was attenuated, the APD lengthening was less prominent, and the sudden shortening was attenuated. When γ was large enough, the APD exhibited a continuous and graded response to G_to. Figs.5 B and C show APD restitution curves for different G_to for γ = 0 and γ = 0.2, respectively. For γ = 0 (Fig.5B), if G_to was small, we observed a regular monotonic APD restitution curve. For larger G_to, APD first increased with DI but then shortened suddenly and discontinuously at a certain DI, resulting in non-monotonic restitution curves. For γ = 0.2 (Fig.5C), APD increased with DI, similar to the regular monotonic APD restitution curve but became less steep with larger G_to. To show how G_to and γ affect the cellular APD dynamics, we paced the cell periodically. Fig.5D is a bifurcation diagram showing APD versus G_to for γ = 0. APD was regular for either small G_to or large G_to, but for the intermediate G_to, complex APD dynamics, such as alternans, high periodic and non-periodic behaviors occurred (see the example shown in Fig.5E). Increasing γ stabilized the APD dynamics (Fig.5F). I_to-promoted complex APD dynamics have been demonstrated previously in experiments and simulations ^17–21.

Figure 5. Effects of late I_to on cellular properties.

A. APD versus G_to for three different γ values as marked. Inset shows the APs from the peaks of the three curves. B. S1S2 APD restitution for γ = 0 and different G_to as marked. C. S1S2 APD restitution for γ = 0.2 and different G_to as marked. D. APD versus G_to for γ = 0 under periodic pacing with PCL=500 ms. 200 consecutive APDs are plotted for each G_to. E. APD versus beat # for G_to=1.425 mS/cm² from a simulation in D. F. APD versus γ for G_to=1.25 mS/cm² under periodic pacing with PCL=500 ms. G-I. S1S2 APD restitution curves measured in experiments by Aiba et al ²² for control (G), the ones exhibiting VF (H), and the ones exhibiting VT (I). Panels G-I were modified from Aiba et al with permission.

The single-cell simulation results shown in Figs.5A–F provided the following mechanistic insights:

1. When the late I_to was small (e.g., the γ = 0 case in Fig.5A), APD increased with G_to but then suddenly shortened due to the sudden loss of the dome. Lengthening APD in the epicardial side resulted in a later repolarization, causing the positive T-wave to become negative and thus giving rise to the coved ST-segment. The sudden shortening of APD resulted in a large repolarization gradient, which together with a prominent spike-and-dome morphology resulted in P2R (see Fig.1A or Fig.2B). When the late I_to was large (e.g., the γ = 0.2 case in Fig.5A), APD decreased as G_to was increased, and APD remained shorter on the epicardial side than the endocardial side, which elevated both the ST-segment and the T-wave, resulting in the saddleback ST-segment.

2. In an experimental study, Aiba et al ²² showed different APD restitution properties under control conditions (Fig.5G), BrS with VF (Fig.5H), and BrS with VT (Fig.5I). The APD restitution curve under control conditions was a regular monotonic curve, which corresponded to the curves in the model for small G_to (Figs.5 B and C). For the BrS VF case, the APD restitution became a non-monotonic curve, in which APD first increased to a maximum and then decreased quickly as DI was increased. A similar restitution behavior was also observed experimentally in canine ventricular epicardial myocytes ¹⁷. This property agrees well with the APD restitution property in the model for small γ and large G_to (see Fig.5B). As shown in our simulations (Fig.4), spiral wave breakup occurred for small γ and large G_to. This agrees with the experimental observation that the non-monotonic APD restitution is associated with VF. For the BrS VT case, the APD restitution curve was flattened, which agrees with the APD restitution curves of the model when γ was large (Fig.5C). As shown in our simulations (Fig.4), increasing γ stabilized spiral waves. This agrees with the experimental observation that flatted APD restitution is associated with VT rather than VF. Therefore, our simulations agree with the experimental observations, providing mechanistic links between the late I_to, APD restitution, and VT and VF in BrS.

Effects of I_Ca,L and I_Na on P2R

As shown above, the peak and late I_to exhibited opposite effects on the genesis of P2R and reentry stability. Since I_Ca,L and I_Na also play important roles in arrhythmogenesis in BrS (by adjusting the background conditions upon which I_to operates), we investigated whether the different components of these two currents exhibit different effects on the genesis of P2R.

Fig.6 shows the effects of the different I_Ca,L components on the genesis of P2R. Fig.6A plots the P2R region versus P_Ca and G_to. P_Ca is the parameter describing the maximum conductance of I_Ca,L. For P2R to occur, a minimum P_Ca was needed. As P_Ca was increased, the G_to range for P2R increased, but at the same time, the G_to threshold for P2R became higher. Therefore, under the right conditions in which P_Ca was high, P2R could be promoted by reducing P_Ca. Fig.6B shows the P2R region versus γ and P_Ca, illustrating that although increasing γ lowered the P_Ca threshold (i.e., P2R occurs at a larger P_Ca), it quickly suppressed the P_Ca range for P2R. Removing the late component of I_Ca,L by removing the incomplete steady-state inactivation from the original formulation (see Fig.6F) resulted in a smaller P_Ca range of P2R (Fig.6C), indicating that P2R was potentiated by the late I_Ca,L. Increasing the window I_Ca,L (by shifting the steady-state inactivation curve rightward) raised the G_to threshold slowly but quickly increased the G_to range of P2R (Fig.6D). To show how the window I_Ca,L interacts with late I_to, we show in Fig.6E the P2R region versus γ and the voltage shift (V_shift) of the steady-state inactivation curve, showing that as γ was increased, the V_shift range for P2R remained roughly the same. This indicates that the effects of late I_to could be countered by the window I_Ca,L. The effects of late I_to could also be countered by the late I_Ca,L (see Fig.IV in Data Supplement). This is different from Fig.2A, Figs.6 B and C, in which the P2R regions shrank quickly with γ. The results in Fig.6 show that blocking the peak I_Ca,L may promote P2R by bringing the system closer to the threshold, but blocking the window and late I_Ca,L can effectively suppress P2R by reducing the size of the P2R region.

Figure 6. Effects of I_Ca,L on P2R.

Simulations were carried out in a 1D cable as for Fig.2. A. P2R versus P_Ca and G_to for γ = 0. P_Ca is a parameter proportional to the maximum conductance of I_Ca,L. B. P2R region versus γ and P_Ca for G_to=1.75 mS/cm². C. Same as B but after removing the late component of I_Ca,L. This was done by removing the elevated part of the original f_∞ in the high voltage range as indicated in panel F. D. Effects of window I_Ca,L on P2R, simulated by shifting f_∞ as indicated in panel F. Shown is the P2R region versus V_shift and G_to. E. P2R region versus γ and V_shift. G_to=1.75 mS/cm². F. Alterations of f_∞. Solid black curve is the original f_∞. Dashed red curve is the one after the late component removed, corresponding the change from panel B to panel C. Dashed blue curves indicate the right or left shift from the dashed red curve used in D and E. V_shift>0 for the right shift and V_shift<0 for the left shift.

Fig.7 illustrates the effects of the peak and late I_Na on the genesis of P2R. We added the formulation of late I_Na from Hund Rudy²³ into the model. Fig.7A is a plot of the P2R region versus G_Na and G_to, showing that changing G_Na had a small effect on both the G_to threshold and the G_to range for P2R. For certain G_to values (e.g., G_to=1.5 mS/cm²), reducing G_Na could promote P2R, indicating that blocking I_Na potentiates P2R. Fig.7B is a plot of the P2R region versus G_Na and P_Ca, showing that reducing G_Na slightly elevated the P_Ca threshold but had little effect on the P_Ca range for P2R. Fig.7C plots the P2R region versus the maximum conductance of late I_Na (G_NaL) and G_to, showing that increasing G_NaL had a small effect on the G_to range for P2R but raised the G_to threshold for P2R. Fig.7D plots the P2R region versus γ and G_NaL, showing that increasing γ raised the G_NaL threshold for P2R slightly, but the G_NaL range for P2R shrank quickly. Thus, unlike the window I_Ca,L, the effects of the late I_Na are not countered by the effects of the late I_to component but rather by the effects of the peak I_to (Fig.7C).

Figure 7. Effects of I_Na on P2R.

Simulations were carried out in a 1D cable as for Fig.2. A. P2R region versus G_Na and G_to. B. P2R region versus G_Na and P_Ca. G_to=1.75 mS/cm². C. P2R region versus G_NaL and G_to. D. P2R region versus γ and G_NaL. In A and B, G_NaL=0.

Effects of sex difference and circadian rhythm on P2R

The vast majority of BrS patients are male (91.3%) ²⁴ with arrhythmia risk being higher after midnight ^25–28, possibly because current densities differ in male and female hearts and exhibit different responses to sex hormones ^29–34 and circadian rhythm ^35–37. To investigate the effects on P2R, we carried out additional 1D cable simulations. We set the female-to-male ratios of the maximum conductance of the ionic currents (See Table I in Data Supplement) based on previous studies^{30, 33}. The K⁺ currents are smaller and I_Ca,L is larger in female than in male. Fig.8A shows the P2R regions versus fold change of the maximum conductance of I_Ca,L and I_to for male (blue) and female (red). The P2R region was much smaller for female than for male, and started at a lower fold change of I_Ca,L and a higher fold change of I_to. Therefore, a much larger increase in I_to and/or a much larger reduction in I_Ca,L is required to produce P2R in females, agreeing with the clinical profile of BrS occurring predominantly in men. Fig.8B plots the P2R regions for male and female versus the fold changes of I_Ca,L and I_Ks, showing that increasing G_Ks exhibited a very small effect on promoting P2R. It has been shown that I_Ca,L is reduced during nighttime ^{35, 36} while I_to is increased during nighttime ³⁷ (as indicated by the arrow from sun to moon in Fig.8A). In addition, β-adrenergic activity, which elevates both I_Ca,L and I_Ks, is higher during daytime than nighttime and thus both I_Ca,L and I_Ks are smaller during nighttime than daytime (as indicated by the arrow from sun to moon in Fig.8B). Therefore, our simulations indicate that P2R is more likely to occur during nighttime than daytime, agreeing with the clinical observation. Figs.8 C and D show two sets of additional simulations for the effects of I_Kr and I_K-ATP on P2R. The mathematical model of I_K-ATP was taken from Shaw and Rudy ³⁸. Increasing G_Kr or G_K-ATP caused P2R to occur at a larger P_Ca, indicating that increasing I_Kr or I_K-ATP promotes P2R. Note that for the three K⁺ currents (Figs.8 B–D), I_K-ATP exhibits the largest effect on promoting P2R and I_Ks the smallest effect, which is more prominent in the ten Tusscher et al human model (see Fig.X in Data Supplement).

Figure 8. Effects of sex difference and circadian rhythm on P2R.

Simulations were done in the 1D cable as for Fig.2 except that the maximum conductances of ionic currents were different for female and male. The control parameters for male were the same as for Fig.2. The female-to-male ratios of the maximum conductance were shown in Table I in Data Supplement. α is the fold change of the maximum conductance from the control values. For example, α(P_Ca) implies the P_Ca value is α-fold of the control P_Ca for either female or male. Similar to Fig.6A, the “Spike & Dome” region is in the right and the “Spike” region is in left of the P2R region for all the panels in this figure. A. P2R regions for male and female versus α(P_Ca) and α(G_to). B. P2R regions for male and female versus α(P_Ca) and α(G_Ks). C. P2R regions for male and female versus α(P_Ca) and α(G_Kr). D. P2R regions for male and female versus α(P_Ca) and G_K-ATP. Since there was no I_K-ATP in control, G_K-ATP instead of α(G_K-ATP) was used in this panel. α(G_to)=4 was used for B-D. Note that the P2R region in D is more tilted to the right than those in B and C, indicating that I_K-ATP exhibits a larger effect in changing the I_Ca,L threshold for P2R and thus a larger effect on promoting P2R. In the ten Tusscher human model, we observed an even more tilted P2R region which also expanded as G_K-ATP increased (see Fig.XD in Data Supplement).

Discussion

Three types of characteristic ECGs are associated with BrS, but only type 1 is diagnostic. In this study, we carried out computer simulations to investigate the effects of different components of I_to, I_Ca,L, and I_Na, as well as other K⁺ currents, on the genesis of P2R and the stability of reentry in BrS. Our major findings are that the late I_to component suppresses the spike-and-dome morphology and shortens APD, converting type 1 ECG to type 2 ECG and preventing P2R. The peak I_to promotes spiral wave breakup, promoting VF, but the late I_to stabilizes reentry, converting VF to VT. Blocking the peak I_Ca,L potentiates P2R but blocking the window or the late I_Ca,L suppresses P2R. Bocking the peak or the late I_Na promotes P2R with the late I_Na exhibiting a larger effect. Increasing other K⁺ currents, such as I_Ks, I_Kr or I_K-ATP, can promote P2R, with I_K-ATP exhibiting the largest effect. Men is more susceptible to P2R, mainly due to that men have a larger I_to and a smaller I_Ca,L than women. For the same reason, P2R is more likely to occur at nighttime than daytime. We performed the same simulations using the ten Tusscher et al human ventricular AP model ¹⁴ and obtained almost the same results (see Figs.V–X in Data Supplement), indicating that the findings are not likely model dependent. The mechanistic insights from our computer simulation results and the implications for arrhythmogenesis and potential therapies for BrS are discussed below.

Ionic mechanisms of ECG morphology and links to P2R

The AP configurations giving rise to coved and saddleback ECG were first proposed by Antzelevitch ⁹, and our simulations agree with their interpretation. An additional insight from our simulations is the contribution of the late I_to component to the ECG characteristics. Combined with the insight from our simulations into the role of late I_to in the genesis of P2R, we link the ECG characteristics with the genesis of P2R. More specifically, when I_to is large with a small late component, the spike-and-dome AP morphology is prominent and a coved ST-segment (type 1) occurs (e.g., the case with G_to=1.5 in Fig.1A). When I_to and its late component are both small, a type 3 ECG occurs (e.g., the cases with G_to=0.5 and 1 in Fig.1A). When the late component is large, the AP dome is attenuated and a saddleback ST-segment (type 2) occurs (e.g., the cases with G_to=0.5 and 1 in Fig.1B). Since a large I_to is needed for P2R, the I_to giving rise to type 3 ECG is still far away from the threshold for P2R. For the I_to giving rise to type 2 ECG, its late component maybe too strong to allow P2R to occur. Note that when the overall I_to is very large with or without the late component, APD becomes very short in the epicardium (the “Spike” regions in Figs. 2, 6, and 7), resulting in a highly elevated ST-segment (e.g., the large G_to cases in Figs. 1 A and B). The effects of the late I_to can be countered by the window or the late I_Ca,L.

Roles of late I_to on P2R formation and stability

Unlike the traditional mechanisms of reentry formation in which a PVC and a vulnerable heterogeneous tissue substrate may arise from independent processes ³⁹, the PVC and heterogeneous tissue substrate in P2R arise from the same dynamical process. Mechanisms of P2R have been investigated in computer simulation studies ^{40, 41}. In a recent study ⁴², we analyzed the dynamical mechanisms of P2R genesis and showed that the occurrence of P2R is determined by two factors: 1) the transition from the spike-and-dome AP morphology to the spike AP morphology in the single cell; and 2) the spatial instability caused by the repolarization heterogeneity in tissue. The former determines the parameter threshold and the later determines the size (or the parameter range) of the P2R region. For example, for γ = 0, the spike-and-dome to spike transition in the single cell occurs at G_to=1.59 mS/cm² (Fig.5A) while the G_to threshold for P2R in the cable is also 1.59 mS/cm² (Fig.2A). Increasing γ reduces the G_to for the spike-and-dome to spike transition (Fig.5A), agreeing with increasing γ decreasing the threshold for P2R (Fig.2A). Even for γ = 0, P2R occurs in a range of G_to above the threshold, and when I_to is too strong, P2R is suppressed due to suppression of the spatial instability ⁴². As shown in Fig.2A, the late I_to exhibits a strong effect on suppressing the spatial instability, i.e., the P2R region is reduced quickly as γ increases. In the diagrams shown in Figs.2, 6, and 7, the parameter threshold is the boundary between the “Spike & Dome” and “P2R” and the gray region is the parameter range for P2R. As shown in these figures, different ionic currents or their different components exhibit different effects on the threshold for P2R and the size of the P2R region.

Besides suppressing the genesis of P2R, late I_to can also prevent spiral wave breakup. We showed in a previous study ¹⁶ that I_to could promote spiral wave breakup by steepening the APD restitution curves. Besides the steep APD restitution-induced breakup, we also observed P2Rs resulting from the complex wave dynamics, giving rise to a mixture of spontaneous firings (P2Rs) and spiral wave reentry (see Fig.VII and Movies III and IV in Data Supplement). Since late I_to flattens APD restitution and suppresses P2R, it stabilizes spiral wave reentry, preventing the occurrence of VF. This provides an ionic mechanism for the association of VT and VF to the different APD restitution properties observed in the experiments by Aiba et al ²².

The late component of I_to can be caused by incomplete inactivation or slow inactivation. As shown in Fig.2D, speeding up inactivation enlarges the region but elevates the G_to threshold for P2R. Therefore, whether a drug that speeds up inactivation is anti- or pro-arrhythmic depends on the relative effects on the peak and the late components. For example, experimental studies showed that acacetin caused a faster inactivation and greatly reduced the amplitude of I_to ⁴³, which effectively prevented P2R ⁴⁴. On the other hand, the ability of ajmaline and flecainide to promote type 1 ECG and P2R has been attributed to their effects on blocking I_Na. However, it is also shown that they may reduce I_to by speeding up inactivation ^45–47. Reducing peak I_to might oppose their effect on suppressing P2R, but reducing the late component due to fast inactivation might promote type 1 ECG and P2R. Therefore, whether a drug speeding up I_to inactivation promotes or suppresses P2R may depend on its differential effects on reducing the peak and the late components of I_to.

Implications to arrhythmogenesis and therapies for BrS

As discussed above, the occurrence of P2R is determined by the parameter threshold and the parameter range, and different ionic currents and their different components affect these properties differently. So far 23 BrS mutations have been identified ⁴⁸ causing either a loss of function of I_Na or I_Ca,L, or a gain of function of I_to or I_K-ATP. Our simulation results show that P2R is promoted by reduction of I_Na (Fig.7) or I_Ca,L (Fig.6), or increase of I_to (Fig.2) or I_K-ATP (Fig.8), agreeing in general with the clinical consequences of the BrS mutations. In addition, our simulations offer the following insights into the genesis and prevention of arrhythmias for BrS:

1. I_to amplitude needs to be large enough but not too large for P2R to occur, i.e., there is a range of optimal I_to strength for P2R (Fig.2). The P2R region becomes smaller as the late component increases and then completely disappears. Prior to the P2R region (i.e., in “Spike & Dome” region), the ST-segment is coved. Beyond the P2R region (i.e., in the “Spike” region), particularly for large late I_to, the ST-segment becomes saddleback. Therefore, to suppress P2R using I_to as a target, one can either block the I_to amplitude or enhance its late component. However, a drug preferentially blocking the late component may convert a type 2 ECG to a type 1 ECG and promote P2R.

2. As for I_Ca,L (Fig.6), when I_to is strong, reducing the maximum conductance of I_Ca,L promotes P2R, in agreement with the general knowledge of the effects of I_Ca,L on P2R and arrhythmogenesis in BrS. Interestingly, blocking the window or the late components of I_Ca,L does not promote P2R, but instead suppress P2R, providing a novel therapeutic target for BrS.

3. As for I_Na (Fig.7), blocking either the peak or the late component can promote P2R, with the late component being more sensitive. While increasing late I_Na can suppress P2R, however, it is well-known that increasing late I_Na can also promote long QT associated arrhythmias.

Note that in real hearts, I_to is not the only transient outward current. Other transient outward currents can exhibit similar effects as I_to to influence the genesis of P2R. For example, the Ca²⁺-activated small conductance K⁺ current is a transient outward current ^{49, 50} known to promote J-wave syndrome and P2R ^51–53. The Ca²⁺-activated chloride current is also a spiky transient outward current ^{54, 55} that may potentiate P2R. On the other hand, the late components of these currents are likely to have the same effects as those of late I_to. These currents may contribute to the ECG morphologies and P2R genesis in the real heart.

Limitations

Several limitations should be mentioned. Pseudo-ECGs were calculated in 2D tissue and a whole-heart simulation may result in more realistic ECG morphologies ⁵⁶. We mainly simulated the endo-epi heterogeneity in I_to conductance. P2R can occur due to the I_to heterogeneities in the epicardium, or due to transmural or base-to-apex heterogeneities of other ionic currents. It also hypothesized that regional slow conduction in the right ventricle due to fibrosis can also result in coved ECG morphology ⁵⁷, and may provide an alternative or synergistic mechanism promoting reentrant arrhythmias in BrS (the so-called depolarization hypothesis ⁵⁸), which is a subject for investigation in future simulation studies.

Conclusions

While the peak I_to promotes the type 1 ECG morphology and P2R in BrS, the late component can convert type 1 to type 2 ECG and suppress P2R. The late I_to can also stabilize spiral wave reentry, converting VF to VT. Therefore, blocking the peak I_to is antiarrhythmic but blocking the late component can be proarrhythmic in patients with BrS. Our simulations also show that blocking either the peak or the late I_Na can be proarrhythmic. Blocking the peak I_Ca,L is also proarrhythmic, whereas blocking the window or the late I_Ca,L components are antiarrhythmic. These observations may provide valuable insights for guiding the development of novel therapeutic targets for prevention of arrhythmias in BrS.

What is known?

• Three types of characteristic ECGs are associated with Brugada syndrome, only type 1 (coved ST-segment) is diagnostic.

• Phase 2 reentry induced by Ito is a candidate mechanism of arrhythmias in Brugada syndrome.

What the study adds?

• Computer simulations provide mechanistic insights into why only type 1 is diagnostic, showing that the peak Ito promotes type 1 ECG and phase 2 reentry, but the late component of Ito converts coved ECG into saddleback (type 2) ECG and suppresses phase 2 reentry.

• Besides the well-known fact that blocking an inward current or enhancing an outward current promotes phase 2 reentry, blocking the window and late calcium current suppresses phase 2 reentry.

Non-standard Abbreviations and Acronyms

1D

1-dimensional

2D

2-dimensional

AP

action potential

APD

action potential duration

BrS

Brugada syndrome

CL

cycle length

DI

diastolic interval

ECG

electrocardiogram

PVC

premature ventricular complex

PCL

pacing cycle length

P2R

phase 2 reentry

VT

ventricular tachycardia

VF

ventricular fibrillation

Na⁺

sodium ion

Ca²⁺

calcium ion

K⁺

potassium ion

I_to

transient outward potassium current

I_Ca,L

L-type calcium current

I_Kr

rapid component of the delayed rectifier potassium current

I_Ks

slow component of the delayed rectifier potassium current

I_Na

sodium current

I_K-ATP

ATP-sensitive potassium current

I_NaL

late sodium current

G_to

maximum conductance of I_to

P_Ca

maximum conductance of I_Ca,L

G_Na

maximum conductance of I_Na

G_NaL

maximum conductance of I_NaL

G_Kr

maximum conductance of I_Kr

G_Ks

maximum conductance of I_Ks

G_K-ATP

maximum conductance of I_K-ATP

γ

parameter controlling strength of late I_to