The role of dynamic instabilities in the initiation of reentry in diseased (remodeled) hearts remains poorly explored. Using computer simulations, we studied the effects of altered Na+ channel and cell coupling properties on the vulnerable window (VW) for reentry in simulated two-dimensional cardiac tissue with and without dynamic instabilities. We related the VW for reentry to effects on conduction velocity, action potential duration (APD), effective refractory period dispersion and restitution, and concordant and discordant APD alternans. We found the following: 1) reduced Na+ current density and slowed recovery promoted postrepolarization refractoriness and enhanced concordant and discordant APD alternans, which increased the VW for reentry; 2) uniformly reduced cell coupling had little effect on cellular electrophysiological properties and the VW for reentry. However, randomly reduced cell coupling combined with decoupling promoted APD dispersion and alternans, which also increased the VW for reentry; 3) the combination of decreased Na+ channel conductance, slowed Na+ channel recovery, and cellular uncoupling synergistically increased the VW for reentry; and 4) the VW for reentry was greater when APD restitution slope was steep than when it was flat. In summary, altered Na+ channel and cellular coupling properties increase vulnerability to reentrant arrhythmias. In remodeled hearts with altered Na+ channel properties and cellular uncoupling, dynamic instabilities arising from electrical restitution exert important influences on the VW for reentry.
- vulnerable window
- action potential duration alternans
- computer simulation
in the normal heart, dynamic instability has been shown to have an important influence on the propensity for wavebreak during reentry (20, 26, 39). Dynamic instability is caused by factors such as restitution of the action potential duration (APD) or effective refractory period (ERP) (27, 29), restitution of conduction velocity (CV) (26, 41), intracellular calcium cycling (3), and other factors (8). Although dynamic instability in normal hearts promotes wavebreak during reentry, it is not well characterized as to whether it also increases vulnerability to the induction of reentry (the clinically relevant goal for therapeutic intervention). Moreover, the role of dynamic instabilities on cardiac vulnerability to reentry in diseased (remodeled) hearts received less attention. In diseased hearts, preexisting electroanatomic tissue heterogeneity is amplified considerably, which by itself increases vulnerability to reentrant arrhythmias. For example, in hearts with myocardial infarctions, electrical and structural remodeling in the epicardial border zone (EBZ) causes regional slowing of conduction, reduced excitability, and prolonged ERP compared with adjacent noninfarcted tissue. This increased dispersion of electrophysiological properties is known to enhance vulnerability to arrhythmias (12, 40, 42, 43). It is unclear whether dynamic instability has important additional influences on arrhythmia inducibility in this setting. Computer simulations in a one-dimensional (1-D) cable by Starmer et al. (34, 35) showed that reduced Na+ channel density or slowed recovery simulating electrical remodeling increased the vulnerable window (VW) for unidirectional conduction block. In addition, computer simulations investigating abnormal cell coupling on unidirectional block in 1-D cables (14, 31, 38) and conduction in two-dimensional (2-D) tissue (6, 7, 19, 32) have demonstrated that abnormal coupling promotes unidirectional conduction block and irregular conduction. However, susceptibility to unidirectional conduction block in a 1-D cable is not equivalent to vulnerability to reentry in 2-D or three-dimensional (3-D) tissue, because, in addition to unidirectional conduction block, induction of reentry requires an alternate conduction pathway of adequate spatial dimension. Finally, whereas both Na+ channel and gap junction remodeling cause slow conduction, their relative importance to reentry vulnerability has not been systematically examined.
The extent to which dynamic instability influences vulnerability to arrhythmias in the diseased heart is important because it has been proposed that decreasing dynamic instability pharmacologically by modifying electrical restitution might be an effective antifibrillatory strategy (39). This strategy would have limited usefulness if it only prevented wave break during reentry without suppressing arrhythmia inducibility in remodeled hearts.
In this study, we begin to address this important issue by examining the effects of globally or regionally altered Na+ channel function and cell coupling on the VW for reentry in simulated 2-D tissue. We used phase I of the Luo-Rudy action potential model (LR1) ventricular action potential model, because its level of dynamic instability can be readily controlled by alteration of the APD restitution slope (17). In contrast, the factors controlling dynamic wave instability in later generation models, which incorporate detailed formulations of intracellular Ca2+ cycling, are more complex and not as well understood. Using the LR1 action potential model with either steep or flat APD restitution curves, we first analyzed the effects of altered Na+ channel and cell coupling properties on CV, APD, and ERP dispersion and restitution. Next, we characterized the effects on APD alternans, an established predictor of arrhythmia susceptibility (30). Finally, we examined the effects on the VW for reentry induced by both premature extrastimuli and rapid pacing.
- Control action potential model with steep APD restitution (Fig. 1)
- Control action potential model with flat APD restitution (Fig. 1)
- Abnormal zone
- Membrane capacitance
- Diffusion constant in the x-direction
- Diffusion constant in the y-direction
- Diffusion constant between the (i, j)th cell and the (i + 1, j)th cell
- Diffusion constant between the (i, j)th cell and the (i, j +1)th cell
- Average diffusion constant in the x-direction
- Average diffusion constant in the y-direction
- Ḡ Na
- Maximum conductance of the Na+ channel
- Ḡ K
- Maximum conductance of the time-dependent K+ channel
- Ḡ si
- Maximum conductance of the slow inward current or the L-type Ca2+ channel
- The total ionic current
- Na+ current
- Interpulse interval
- Slow inactivation gate of Na+ channel
- Normal zone
- Pacing cycle length
- Surface-to-volume ratio
- Transmembrane potential of (i, j)th cell in the tissue
- Factor by which the j gate is slowed
- Parameter determining the coupling strength in the x-direction
- Parameter determining the coupling strength in the y-direction
- Resistivity in the x-direction
- Resistivity in the y-direction
- Standard deviation of APD in the tissue
- Time constant of the activation gate of the L-type Ca2+ channel
- Time constant of the inactivation gate of the L-type Ca2+ channel
- Time constant of the slow recovery gate of the Na+ channel
Differential equations. We simulated the following set of differential equations (1) where Vij is the membrane potential of the (i,j)th cell and Cm = 1 μF/cm2. is the local diffusion constant in the longitudinal direction between the (i+1,j)th cell and the (i,j)th cell; ) is that in the transverse direction between the (i,j+1)th cell and the (i,j)th cell; and are the corresponding resistivities, and Sv = 2,500 cm–1. For normal tissue, we assumed that the resistivities were uniform and set them as and , which gives rise to diffusion constants of and corresponds to a 3:1 longitudinal-to-transverse CV ratio in the continuum limit. Δx is the length and Δy is the width of a myocyte. The ratio of length to width measured in isolated canine ventricular myocytes is ∼6:1 (124 ± 24 μm in length and 21 ± 6 μm in width) but because of the irregular shape and connections between cells, the actual length-to-width ratio is 3.4:1 (10, 21). Therefore, we used Δx = 125 μm and Δy = 35 μm in this study, which has a length-to-width ratio of 3.6:1. Iion, the current density, was generated using the LR1 model (17) with modifications.
Action potential models. We used two action potential models for normal (control) tissue, as shown in Fig. 1, A and B, as APsteep and APflat, respectively. In all cases, we used ḠNa = 16 mS/cm2 and extracellular [K+] = 5.4 mM, and other changes as detailed in Fig. 1. CV was ∼0.49 m/s in the longitudinal direction and ∼0.165 m/s in the transverse direction, agreeing with experiments (21, 33).
Modeling the Na+ channel abnormalities. To simulate altered Na+ channel function, we reduced ḠNa to reduce current density and increased the time constant τj of the j gate to slow recovery from inactivation as follows (2) where and are the corresponding values in the normal tissue.
Modeling cell coupling abnormalities. Under control conditions, cells were uniformly coupled with diffusion constants and . We reduced coupling strength in two ways: uniform reduction and randomly distributed reduction. For uniform reduction, the coupling strength was decreased as (3) where δx and δy are two parameters representing the percentage of reduction from control. For random cell coupling reduction, we assumed that the coupling strength from cell to cell varied randomly, with some cells disconnected from their neighbors. The diffusion constants were modeled as (4) and where and are random numbers uniformly distributed in [0,1]. γx and γy are two parameters representing the strength of reduction from control. The average diffusion in the x-direction and y-direction was (5) and (6) respectively. In this case, when γx < 1 and γy < 1, a cell is connected to its all four neighbors though the coupling strength varies randomly. However, when γx > 1 or γy > 1, a cell may be disconnected with one or more of its four neighbors. According to Eq. 4, the probability that a coupling between two neighboring cells is lost is px = (γx – 1)/γx in the x-direction or py = (γy – 1)/γy in the y-direction. For example, for γx = 1.25, 1/5 of the couplings between two neighboring cells in the x-direction are lost and for γx = 1.5, 1/3 of the couplings are lost. Because a cell has four couplings, the probability that a cell does not lose any of its four connections is (1 – px)2(1 – py)2, and thus the probability that a cell loses coupling to one or more of its four neighbors is Pdecoupling = 1 – (1 – px)2(1 – py)2. Therefore, when γx = γy = 1.25, we have Pdecoupling = 0.59, i.e., ∼60% of cells are either partially or completely decoupled from its four neighbors, of which only 0.16% () of the cells are completely decoupled from its four neighbors. When γx = γy = 1.5, ∼80% of the cells are either partially or completely decoupled from its four neighbors, of which only 1.2% of the cells are completely decoupled from its four neighbors.
Tissue models. We simulated three tissue models: 1) uniform cell coupling throughout the tissue, 2) random cell-to-cell coupling differences throughout the tissue, and 3) a heterogeneous tissue model with an AZ in the center as shown in Fig. 1C. The black area represents the AZ, the white area is the NZ, and the gray area is a transitional zone (TZ), in which all parameters change linearly from AZ to NZ.
Pacing protocol and measurements. Two pacing sites were used (S1 and S2 in Fig. 1C). The stimulus strength was 30 μA/cm2 (∼1.5× threshold) with a 2-ms duration applied over a 0.125 cm in the 1-D (S1) cable or a 0.125 × 0.07-cm area in the 2-D tissue (S2). For homogeneous tissue, S1 was applied at the bottom left corner unless otherwise specified. For the heterogeneous tissue, S1 was located at the bottom left corner and the S2 site was located at x = 1.5 cm and y = 0.7 cm. S1-S2 pacing was used to measure APD restitution by the extrastimulus method in a 1-D cable. APD was defined as the duration for which V > –72 mV during an action potential, and diastolic interval (DI) was defined as the duration for which V < –72 mV.
Numerical simulation. We integrated Eq. 1 using our advanced method (25) with a time step varying adaptively from 0.01 to 0.1 ms, with no-flux boundary conditions. For a tissue consisting of 500 × 1,000 cells, a 6-s simulation used 50 h of central processing unit time running on a 500 MHz DEC Alpha workstation with 500 MB RAM. Most of the simulations were carried out in the Beowulf cluster at University of California-Los Angeles Academic Technology Services.
Effects of altered Na+ channel properties on CV, APD, and ERP. Figure 2 shows the electrophysiological effects of reducing INa density and slowing its recovery from inactivation. Using the same protocol as in animal experiments by Pu and Boyden (23), we simulated INa recovery by slowing the j gate of the LR1 model. Figure 2A shows normalized peak INa versus IPI in a single cell and compared with the experimental measurements by Pu and Boyden (23). To quantitatively simulate the experimental measurements, we had to slow the j gate by a factor of 3 (β = 3) for the normal cells and a factor of 12 (β = 12) for cells from the EBZ. Because the experiments by Pu and Boyden (23) were carried out at room temperature while LR1 model was formulated for 37°C, we used the original Na+ channel kinetics of the LR1 model to represent normal cells and slowed the j gate by a certain factor to model the Na+ channel kinetics slowing for the remodeled cells at 37°C. Figure 2B shows the effects of slowing INa recovery on CV restitution, showing that slowing the recovery of INa broadened the range of DI over which CV varied in the CV restitution curve. This change in CV restitution was also observed in the EBZ in animal experiments and was much more prominent in the presence of the class I antiarrhythmic drugs flecainide or lidocaine (28, 46).
Using these alterations, we next studied the effects of reduced INa density and slowed recovery on postrepolarization refractoriness. In Fig. 2C (using APsteep with steep APD restitution) and Fig. 2D (using APflat with flat APD restitution), we show contour plots of ERP as a function of the maximum Na+ channel conductance (ḠNa or α) and the slowing factor for the j gate (β). ERP was measured in a 1-D cable with S1 PCL of 400 ms. At this PCL, APD is ∼190 ms for APsteep and 180 ms for APflat. Changing ḠNa (e.g., from 16 to 4) and slowing the j gate (e.g., changing β from 1 to 10) had little effect on APD at this PCL. However, either reducing INa density or slowing its recovery prolonged ERP, but if both occurred simultaneously, they caused substantial postrepolarization refractoriness, as indicated by the crowding of contour lines in Fig. 2, C and D. For example, for APsteep under PCL = 400 ms, at control case, APD is 190 ms and ERP is 200 ms. When α = 0.5 and β = 5, APD at PCL = 400 ms is still ∼190 ms, but the ERP increases to 230 ms. Prolongation of ERP and postrepolarization refractoriness did not depend on APD restitution steepness except that the ERP was ∼10 ms longer for APsteep (Fig. 2C) than for APflat (Fig. 2D). The effects of Na+ channel on ERP can be generally understood as follows: a longer recovery time is needed for INa to reach the threshold if its density is reduced or recovery is slowed, as was illustrated in detail by Cabo and Boyden (1) in their modeling study.
Because most of the INa effects occur during the upstroke of the action potential, alterations in Na+ channel properties have a big impact on conduction. Do they affect APD and APD restitution? In Fig. 2E, we show that for APsteep, either reducing INa density or slowing its recovery had little effect on baseline APD, but together they further steepened APD restitution over a wider range of DIs. In other words, the prolongation of ERP by Na+ channel remodeling shifts the APD restitution curve toward larger DIs, thus making the slope of APD restitution curve greater than for the control case at the same DI. However, for APflat, alternations of the Na+ channel had much smaller effects on APD restitution (Fig. 2F), with APD restitution curves before and after reducing the Na+ conductance reduced by 50% and slowing the j gate fivefold remaining virtually superimposable.
Effects of cell coupling on CV, APD, and ERP. Figure 3 illustrates how altered gap junction conductance affects the CV of a planar wave (induced at one end and traveling in the x-direction) in 2-D tissue. When cell coupling along the x-axis (Dx) was reduced uniformly (Fig. 3A), CV of the planar wave decreased. Because of the discretized nature of the system, CV fell more rapidly than predicted from the continuum limit (, solid line in Fig. 3A). Similar to the uniform coupling case (solid line in Fig. 3B), when the cell coupling strength was reduced randomly along the x-axis (Fig. 3B), CV also decreased (symbols in Fig. 3B) in proportion to the decrease in average coupling strength Dx. However, when cells were uncoupled along the x-axis (i.e., γx > 1 in Eq. 4), CV fell more rapidly. The decrease in CV was even faster if cell uncoupling also occurred in the y-direction. Figure 3, C and D, compares voltage snapshots with randomly reduced conductance and either no uncoupling (γx = γy = 0.95 in Eq. 4) or with 80% of the cells partially decoupled (γx = γy = 1.5 in Eq. 4; see methods). In the former case (Fig. 3C), the wavefront remained almost synchronized, although some cells were only coupled by 5% of the normal coupling strength. In the latter case, however, the wavefront became very irregular, similar to the optical mapping results in atrial tissue partially uncoupled with heptanol (18). Despite the marked slowing of CV with random cell uncoupling, CV restitution properties remained similar to the case without uncoupling.
In addition to its effects on wavefront propagation, random cell uncoupling also affected repolarization. As shown in Fig. 4A for 2-D tissue paced at a PCL of 500 ms, there was no significant degree of APD dispersion when coupling was reduced yet all cells remained connected, albeit some very weakly by as little as 5% of normal conductance (the γx = γy = 0.95 case). However, when 80% of the cells were partially decoupled (the γx = γy = 1.5 case), APD dispersion increased markedly (Fig. 4B) and became further potentiated when PCL was decreased from 500 to 250 ms (Fig. 4C). Figure 4D shows standard deviation σ for APD versus γx and γy. When either γx < 1 or γy < 1, σ was always small, and only when both γx > 1 and γy > 1, σ increased to large values, for which cell uncoupling in both direction occurred. When both γx and γy were very large, no conduction was possible (white area in Fig. 4D).
Figure 4E summarizes the effects of PCL on average APD and σ. For reduced coupling without frank uncoupling (the γx = γy = 0.95 case), σ was always small and did not increase at short PCL. However, when 80% of the cells were partially decoupled (the γx = γy = 1.5 case), σ was significantly larger at long PCL and increased dramatically at short PCL. Thus, compared with reducing gap junction conductance alone, uncoupling of cells had a much more potent effect at promoting dispersion of refractoriness.
The effects of cell uncoupling on APD dispersion were also promoted by steeper APD restitution slope, as expected because greater changes in CV promotes greater dispersion in DI, which in turn promote greater APD dispersion if restitution is steep. Figure 4F shows σ versus PCL for the two cases in which APD restitution was either flat or steep.
Effects of Na+ channel and cell coupling alterations on APD alternans. APD alternans is an important predictor of increased arrhthymia risk (30). Because the slope of APD restitution curve is shallow for APflat, no APD alternans occurred at any pacing rate whether Na+ channel was altered or not. For APsteep, however, decreasing INa density and slowing its recovery made the APD restitution curve steeper at longer DIs, so that APD alternans occurred at slower pacing rates. We first studied this in a 1-D homogeneous cable with rapid pacing. Figure 5A shows a contour plot of the critical PCL below which APD alternans occurs (PCLc) as a function of the maximum Na+ channel conductance (α) and slowing factor of the j gate (β). Either blocking INa or slowing its recovery increases PCLc.
A prediction of our previous study (26) is that broadening CV restitution (i.e., increasing the range of DIs over which CV varies) should promote discordant alternans. Figure 5, B1–B4, shows APD distribution along the cable for two sequential beats at different α and β values and PCLs. Slowing the INa recovery promoted a greater degree of discordant alternans (Fig. 5B3), whereas reducing the INa density did not (Fig. 5B2).
To extend these findings to 2-D tissue, we next studied the effects of Na+ channel alterations on APD alternans in the heterogeneous tissue model shown in Fig. 1. Figure 5, C–E, shows that when INa recovery was slowed by a factor of 5 in the AZ, while leaving INa density normal, concordant alternans occurred in the AZ at PCL = 240 ms and became discordant at PCL = 220 ms (Fig. 5C). In contrast, when INa density in the AZ was reduced by 50% without slowing INa recovery, alternans in the AZ began at the same PCL = 240 ms, but remained concordant even at PCL = 200 ms (Fig. 5D). Even when INa density was reduced by 65%, alternans remained concordant at PCL = 200 ms, although alternans in the AZ began at PCL = 300 ms. In contrast, with both INa density reduced by 50% and recovery slowed by five times, alternans in the AZ occurred at a much longer PCL (Fig. 5E).
Because cell uncoupling influences APD, it may also affect APD alternans. Figure 6, A and B, shows APD distribution in space for two sequential beats in 2-D tissue with 60% of the cells partially decoupled (γx = γy = 1.25) and uniform coupling with a 60% reduction in diffusion (so that the average diffusion constants are the same in both cases) during pacing at PCL = 190 ms. There was a larger amplitude and shorter wavelength of APD alternans for random coupling. When 80% of the cells were partially decoupled (γx = γy = 1.5), discordant APD alternans now occurred at a longer PCL of 240 ms and had a patchy distribution, with some areas showing no alternans and some discordant APD alternans (Fig. 6C). In uniform coupling of 67% reduction, however, no APD alternans occurred at the same PCL (Fig. 6D). Thus random uncoupling promoted both the onset of a patchy distribution of discordant APD alternans at a longer PCL and also increased the amplitude of alternans.
Because gap junction remodeling in the postinfarct setting is regional, we also studied the effects of regional alterations in cell coupling on APD alternans in simulated 2-D tissue using the heterogeneous tissue model shown in Fig. 1C. For random coupling with 80% of the cells partially decoupled (γx = γy = 1.5) in the AZ, patchy discordant APD alternans occurred in the AZ (Fig. 6E) at PCL-230 ms. If coupling in the AZ was uniform, however, discordant APD alternans could be induced at similar PCL, but only if the conductance was reduced to a substantially greater extent than the average conductance value with random uncoupling. Figure 6F shows an example with the conductance Dx decreased by 90% [i.e., δx = δy = 0.9 in Eq. 3] in the AZ. APD alternans began at PCL = 220 ms (see bar 10 in Fig. 8A) and was discordant.
Induction of reentry by rapid pacing in electrically uniform tissue. We first investigated induction of reentry by rapid pacing in an electrically uniform tissue, i.e., only cell coupling inhomogeneities exist in the tissue and the coupling strength is randomly set as in Eq. 4 through the whole tissue. For APsteep, reentry could not be induced in completely homogeneous tissue, although concordant APD alternans occurred at PCL <200 ms. With randomly decreased coupling strength between cells, reentry was also not inducible as long as all cells remained somewhat coupled (i.e., the γx = γy = 0.95 case). Figure 7A shows the voltage snapshots for PCL = 180 ms in this case, illustrating APD alternans but no reentry. The last pacing beat was applied at t = 1,620 ms (third panel in Fig. 7A); 300 ms later (t = 1,960 ms), the last wave in the tissue marched off the tissue (last panel in Fig. 7A). When 80% of the cells partially decoupled (the γx = γy = 1.5 case), however, reentry could be induced over the range of PCL from 190 to 220 ms. One example (PCL = 210 ms) is shown in Fig. 7B, illustrating that reentry was induced and broke up spontaneously into multiple wavelets.
In contrast, for APflat, reentry was much more difficult to induce. For the case with 80% of the cells partially decoupled (γx = γy = 1.5), reentry was not inducible up to PCL as fast as 190 ms (Fig. 7C). At PCL = 180 ms, however, reentry was induced (Fig. 7D). Because the cycle length of reentry was longer than 180 ms, no further wavebreaks occurred and reentry finally formed a stable pattern (compare the last two panels in Fig. 7D). For pacing faster than 180 ms, 2:1 block occurred at the pacing site. Thus, even in very heterogeneous tissue with a significant degree of cell uncoupling, APD restitution remained a significant determinant of vulnerability.
Induction of reentry by rapid pacing in inhomogeneous tissue. We used the rapid pacing protocol described by Yashima et al. (45) to induce reentry by pacing tissue at least for 16 beats in the inhomogeneous tissue shown in Fig. 1C. For each PCL, we recorded APD at every cell in the tissue for the last four beats to analyze APD alternans. We used the voltage snapshots after stopping pacing to analyze whether reentry occurred or not. If a single spiral wave or multiple spiral waves occurred in the tissue, reentry was induced by this protocol. Figure 8A summarizes the occurrence of APD alternans and induction of reentrant arrhythmias for various conditions.
Induction of reentry with Na+ channel altered in AZ. The first seven bars in Fig. 8A are for APsteep and altered Na+ properties in AZ. If INa recovery was slowed five times in the AZ without altering INa density, alternans occurred at PCL <250 ms, reentry was inducible at PCLs between 190 and 160 ms, and 2:1 block occurred at pacing site for PCL <160 ms. If INa density was reduced by 50% in the AZ without slowing INa recovery, APD alternans also occurred for PCL <250 ms. However, the VW during which reentry was induced was barely visible. When INa density was reduced by 65%, alternans began at PCL <300 ms, but the VW was similar. In both cases, the APD alternans that developed in the AZ was almost always concordant, as shown in Fig. 3. If both INa recovery was slowed (by five times) and INa density halved in the AZ, alternans occurred for PCL <280 ms, and reentry was induced for PCL between 220 and 160 ms. Figure 8B shows voltage snapshots at PCL = 190 ms, showing figure-of-eight reentry leading to multiple wavelets resembling VF. This induction of reentry scenario is very similar to that in the postinfarct canine model described by Yashima et al. (45). In that study, APD alternans occurred first in the EBZ (analogous to the AZ in our simulation), leading to a figure-of-eight reentry at faster pacing rates and finally multiple wavelets VF.
Reentry was less inducible for the APflat case. Compared with the same Na+ channel alterations in the AZ for APsteep shown in Fig. 8A, reentry could only be induced in one case, when Na+ channel conductance was reduced by 50% and the j gate slowed five times (bar 9 in Fig. 8A). However, the VW was much smaller than for the APsteep case. Reentry was also induced via figure-of-eight patterns as shown in Fig. 8C. At faster pacing rates, conduction block occurred in the AZ, but did not induce reentry because the two broken waves self healed (Fig. 8D).
Induction of reentry with altered cell coupling in AZ. When cell coupling in the AZ was uniformly reduced by <50%, alternans occurred at the same critical PCL as in the control case, but no reentry was induced. If coupling was severely decreased (e.g., by 90%), alternans occurred at PCL <220 ms, and a very narrow VW for reentry appeared. Because it has been hypothesized (5, 21, 44) that the difference in anisotropic ratio between the border zone and the normal tissue may facilitate reentry, we also reduced the coupling strength differentially in longitudinal and transverse directions to create a different anisotropic ratio (6:1) in the AZ compared with the NZ (3:1). Alternans started at a slightly longer PCL, but the VW remained barely visible (bar 11 in Fig. 8A). If the coupling reduction in the AZ was randomly distributed, but without cell uncoupling (the γx = γy = 0.95 case), alternans occurred at the same PCL as in the control case and again reentry could not be induced (bar 12 in Fig. 8A). With 60% of the cells partially decoupled (the γx = γy = 1.25 case), APD alternans occurred at slightly longer PCL but reentry still did not occur (bar 13 in Fig. 8A). With 80% of the cells partially decoupled (the γx = γy = 1.5 case), however, alternans occurred at PCL <260 ms and reentry was induced at PCL <220 ms (bar 14 in Fig. 8A). Figure 8E shows voltage snapshots at PCL = 200 ms illustrating the induction of reentry. Reentry was not the typical figure-of-eight pattern. For APflat, reentry could not be induced for any of the coupling changes in the AZ described above.
Induction of reentry with altered INa and cell coupling in AZ. In the postinfarct heart, both gap junction remodeling and altered Na+ channel properties contribute to conduction abnormalities. To study how these factors interact, we examined their combined effects. When Na+ channel conductance was reduced by 50% in the AZ, it was difficult to induce reentry with normal cell coupling (bar 4 in Fig. 8A). Conversely, when 60% of the cells in the AZ were partially decoupled (the γx = γy = 1.25 case), reentry was also not inducible if Na+ channel properties were normal (bar 14 in Fig. 8A). However, the combination of altered Na+ channel conductance and abnormal cell coupling caused APD alternans to appear at PCL = 270 ms, and reentry was now induced over a wide range of PCLs (bar 15 in Fig. 8A). In contrast to reducing Na+ channel conductance, slowing Na+ channel recovery by a factor of 5 created a large vulnerable window for reentry even when cell coupling was normal in the AZ (bar 2 in Fig. 8A). In this case, 60% of the cells partially decoupled in the AZ (γx = γy = 1.25) only slightly increased the windows for alternans and induction of reentry (bar 16 in Fig. 8A). With both Na+ channel conductance reduced by 50% and its recovery slowed fivefold in the AZ, and 60% of the cells partially decoupled (γx = γy = 1.25 in the AZ) caused APD alternans and induction of reentry to occur at much longer PCL (bar 17 in Fig. 8A). However, the vulnerable window was actually narrower because under these extremely low excitability conditions, unidirectional conduction block in the AZ failed to induce reentry due to the re-fusing (healing) of the broken waves beyond the site of block.
Induction of reentry by premature extrastimulus. With the S1 rapid pacing protocol, we paced the tissue until reentry and fibrillation were induced. Alternatively, we investigated induction of reentry by a single premature beat (S2) delivered at a distant site after an S1 pacing train, analogous to the clinical situation of premature ventricular beats during sinus rhythm. Figure 9A summarizes the VW for different cases of Na+ channel and cell coupling alterations in AZ. Comparing to the results of rapid pacing-inducing reentry shown in Fig. 8A, a premature extrastimulus has less ability to induce reentry. In other words, reentry cannot be induced by S2 but can be induced by rapid pacing in a number of the cases. For example, reentry could be induced in a large window by rapid pacing in the case of slowed INa recovery in the AZ but could not be induced by S2; reentry could be induced by rapid pacing in the case of 80% decoupling in the AZ but could not be induced by S2. The reason is simply because APD alternans causes more heterogeneities (and thus the ERP dispersion) in the tissue, making the tissue vulnerable to reentry.
We also systematically studied the relation between the VW and the ERP difference (ΔERP) between the AZ and NZ, as shown in Fig. 9B (for APsteep) and Fig. 9C (for APflat). When ΔERP reached a critical value (which depended on the location of S2), unidirectional conduction block occurred and induced reentry. The VW progressively widened as ΔERP increased. However, when ΔERP was very large, the VW then decreased, despite unidirectional conduction block occurring over a very large window of S1/S2 intervals. In this case, unidirectional conduction block failed to induce reentry because the broken waves healed behind the AZ. This conclusion is different from that of the 1-D cable studies (34, 35), in which once unidirectional block occurred, it was considered to be in the VW. The critical value of ΔERP was smaller and the VW was larger for APsteep than for APflat (compare Fig. 9, B with C).
We investigated the effects of Na+ channel remodeling, gap junction remodeling, and APD restitution slope on vulnerability to reentry using computer simulations of 2-D cardiac tissue. There are several major findings. First, reducing Na+ channel conductance or slowing its recovery prolongs ERP, alters APD restitution, reduces CV, and broadens CV restitution. ERP is synergistically prolonged if both Na+ channel conductance is reduced and recovery is slowed, leading to postrepolarization refractoriness. Second, both alterations cause APD alternans to occur at longer PCLs, but slowing recovery specifically promotes discordant APD alternans. Third, in heterogeneous tissue, VW for reentry is larger with slowed Na+ channel recovery than for reduced conductance and larger for steep APD restitution than for shallow APD restitution. VW increases first as the ERP difference between the AZ and the NZ increases, but becomes smaller if the ERP difference is very large. Fourth, a uniform or a random decrease in gap junction conductance has little effect on cellular electrophysiological properties and VW. Sudden gradients in coupling strength or anisotropy ratio in heterogeneous tissue promote APD alternans, but have only small effects on the VW for reentry. Fifth, although reduced cell coupling has minor effects on vulnerability to reentry, randomly distributed uncoupling of cells markedly enhances CV dispersion, APD dispersion, and APD alternans, all of which increase the VW for reentry. Sixth, the combination of altered Na+ channel properties and cell uncoupling are synergistic at increasing the VW for reentry. Under these conditions, however, the VW for unidirectional conduction block does not always correspond to an increased VW for reentry, especially for low excitability conditions (Figs. 8 and 9). Finally, in either globally or regionally heterogeneous tissue with random cell uncoupling and/or altered Na+ channel properties, APD restitution slope has a major influence on the VW for reentry. Taken together, our results show that decreasing dynamic wave instability by flattening APD restitution slope powerfully suppresses inducibility of reentry even in structurally and electrophysiologically heterogeneous (remodeled) tissue. This suggests that flattening APD restitution slope (39) or targeting other measures that decrease dynamic wave instability, such as cardiac memory (8, 9) or intracellular Ca2+ cycling (3), may be viable therapeutic approaches for reducing the risk of lethal ventricular arrhythmias in humans with ischemic heart disease.
Implications for arrhythmogenesis in ischemia and infarction. Electrical and structural remodeling occur in ischemia and infraction, and remodeling of Na+ channels and cell-to-cell coupling contributes importantly to slowed conduction, lowered excitability, and prolonged ERP in the EBZ (11, 21, 22). In either acute or subacute phase of ischemia, the APD is shorter in the EBZ than in normal tissue, but ERP is longer in the EBZ, by as much as 100 ms (36), requiring >100 ms of postrepolarization refractoriness. Our modeling shows that this requires the combination of both reduced Na+ channel conductance and slowing of recovery (Fig. 2). Experimental observations have shown both properties are substantially altered in the infarcted heart and by Na+ channel blocking drugs (15, 23, 24, 28, 46).
Abnormal cell coupling is considered to be an important factor promoting cardiac arrhythmias (13, 21, 37) and has been proposed as a potential antiarrhythmic target. The present study shows that reduced cell coupling has a minor effect on induction to reentry, but randomly distributed cell uncoupling powerfully enhances the VW for reentry in the presence of steep APD restitution. Moreover, when altered Na+ channel properties and cell uncoupling occur simultaneously, the probability of inducing reentry is synergistically enhanced.
Implications for anti- and proarrhythmic effects of class I antiarrhythmic drugs. In the postmyocardial infarction setting, Na+ channel blockade with class I antiarrhythmic drugs further reduces INa density and slows Na+ channel recovery in a heterogeneous manner (24, 28, 46), with effects being much greater in the EBZ than in normal tissue. According to our simulations, this is predicted to markedly increase the ERP difference between the EBZ zone and the normal tissue in the acute or subacute phase of ischemia. This can serve to either increase or decrease the VW, according to simulations shown in Fig. 9, B and C. This dual effect was observed in experiments by Yin et al. (46). Therefore, class I drugs can be either antiarrhythmic or proarrhythmic. Experiments by Yin et al. (46) showed that lidocaine had antiarrhythmic effects because of the prolongation of ERP in the EBZ, but proarrhythmic effects related to increased conduction delay, while other studies (4, 28) found that flecainide was proarrhythmic. In contrast, in healed myocardial infraction, Na+ channel properties in the EBZ are nearly normal. By depressing Na+ channel conductance and slowing recovery, however, class I drugs may still increase the ERP difference between EBZ and NZ, steepen APD restitution, and promote APD alternans, thus making reentry more likely to break up into multiple wavelets. This may be an important factor linking these drugs to increased clinical incidence of lethal arrhythmias in the postinfarct setting (2).
Limitations. We modeled abnormal cell coupling as either a uniform reduction or a random cell-by-cell reduction. However, spatial scale of cell coupling abnormalities in diseased hearts may be different, and could have different consequences for arrhythmogenesis not recognized in the present study. For example, we used an arbitrarily selected oval defect to model regional heterogeneity, whereas regional heterogeneities in infarcted hearts are highly variable in size and shape. Also, we used a random model in which the contiguous span of abnormally coupled cells within the NZ or AZ tends to be small, although differences between the NZ and AZ were large. If intermediate-sized regions of reduced coupling within the NZ or AZ were used, the VW for reentry might have changed. We did not include regional dispersion of APD, ERP or their restitution properties arising from other currents besides INa. This additional source of electrophysiological dispersion is likely to have further effects, especially when cells are weakly coupled, even uniformly. Also, our simulations were performed in 2-D tissue, and we cannot exclude the possibility that additional factors may impact arrhythmogensis in 3-D tissue. We used five-point coupling in the tissue model, in which a cell only has four neighboring cells. In real tissue, however, there are an estimated 11 neighbors for a cell in normal tissue and 6.5 neighbors in healed infarction (10, 16, 21). We used a cell action potential model without intracellular Ca2+ dynamics, which may also contribute to dynamic wave instability, and did not consider other factors influencing dynamic instability, such as short-term cardiac memory or diffusive currents. Thus our findings may be specific to dynamic instability generated by steep APD restitution slope and may not generally apply to other factors generating dynamic instability. However, the advantage of the LR1 model is that its level of dynamic instability, unlike to later generation models, is easily controlled by adjusting the APD restitution slope, a feature that allowed us to effectively test our hypotheses. In addition, we did not model other aspects of structural or electrical remodeling, such as heterogeneous sympathetic innervation, K+ or Ca2+ channel remodeling, or altered intracellular Ca2+ dynamics, which are also likely to have important consequences on arrhythmogenesis in intact diseased hearts. Despite these limitations, however, these simulations are the first attempt to systematically examine the interaction between tissue heterogeneity and dynamic instability on inducibility of reentrant ventricular arrhythmias and provide a first step toward rigorously analyzing how structural and electrical remodeling impact vulnerability to reentrant arrhythmias in diseased ventricles.
This study was supported by American Heart Association (AHA) Scientist Development Grant 0131017N, National Institutes of Health Specialized Center of Research in Sudden Cardiac Death Grant P50HL-52319, AHA Western States Affiliates Grant-in-Aid 0255937Y, UC-TRDRP, 11RT-0058, and the Laubisch and Kawata Endowments.
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- Copyright © 2004 by the American Physiological Society