Mechanisms of Myocardial Capture and Temporal Excitable Gap During Spiral Wave Reentry in a Bidomain Model
Background— Recent studies have demonstrated that regional capture during cardiac fibrillation is associated with an elevated capture threshold. It is typically assumed that the temporal excitable gap (capture window) during fibrillation reflects the size of the spatial excitable gap (excitable tissue between fibrillation waves). Because capture threshold is high, virtual electrode polarization is expected to be involved in the process. However, little is known about the underlying mechanisms of myocardial capture during fibrillation.
Methods and Results— To clarify these issues, we conducted altogether 3168 simulations of single spiral wave capture in a bidomain sheet. Unipolar stimuli of strengths 4, 8, 16, and 24 mA and 2-ms duration were delivered at 99 locations in the sheet. We found that cathode-break rather than cathode-make excitation was the dominant mechanism of myocardial capture. When the stimulation site was located diagonally with respect to the core (upper left or lower right if the spiral wave rotates counterclockwise), the cathode-break excitation easily invaded the spatial excitable gap and resulted in a successful capture as a result of the formation of virtual anodes in the direction of the myocardial fibers. Thus, the spatial distribution of the temporal excitable gap did not reflect the spatial excitable gap.
Conclusions— The areas exhibiting wide temporal excitable gaps were areas in which the cathode-break excitation wave fronts easily invaded the spatial excitable gap via the virtual anodes. This study provides mechanistic insight into myocardial capture.
Received March 13, 2003; de novo received May 9, 2003; accepted December 2, 2003.
A number of mapping studies have demonstrated regional capture in dogs,1,2 goats,3,4 and humans5,6 during atrial fibrillation as well as in ventricular fibrillation,7,8 thus indicating the presence of an excitable gap (EG). It is typically assumed that the temporal EG (capture window) during cardiac fibrillation reflects the size of the spatial EG (excitable tissue between fibrillation waves); thus, measurement of the temporal EG is considered important for evaluating pharmacological cardioversion.3,9 During atrial fibrillation, the capture threshold is generally high, ≈5 times the diastolic pacing threshold1,2,4; during ventricular fibrillation, it ranges from 5 to 10 times the pacing threshold.7,8
However, little is known about the underlying mechanisms of myocardial capture during fibrillation. Because capture threshold is several times higher than the diastolic threshold, “cloverleaf” virtual electrode polarization (VEP)10,11 (a virtual cathode of dog-bone shape accompanied by 2 oval virtual anodes located near the virtual cathode) induced by a point stimulation could be involved in the process. If formation of VEP indeed takes place, then it is unclear to what degree the temporal EG reflects the spatial EG.
It also remains unknown why the value of the capture threshold during fibrillation is high despite the existence of a spatial EG. It is possible that cathode-break rather than cathode-make excitation12–14 after the VEP contributes as a mechanism of myocardial capture. Indeed, the cathode-break excitation threshold is typically several times higher than the cathode-make diastolic threshold not only in diastole but also during the relative refractory period.12,14–16 The aim of the present study is to address these issues in computer simulations of myocardial capture.
As shown in Figure 1, the model consisted of a homogeneous and anisotropic bidomain myocardial sheet 3.75×1.5 cm (100 000 discrete myocardial units). Two grounding electrodes (shaded bars) were located vertically at the left and right borders of the sheet. Fibers in the sheet were oriented horizontally. The equations, the tissue conductivity values, and the boundary conditions for the bidomain model were the same as in a previous study.14 Membrane kinetics were represented by the LR-A model, a modified version17 of the Luo-Rudy-1 model.18 In addition, to obtain a stationary single spiral wave (SW), we incorporated further modifications of ion channel conductance as suggested by Qu et al.19 Mathematical stability and validation of this model have been addressed elsewhere.17
Stationary Single SW Reentry as a Model of Fibrillation
As a model of cardiac fibrillation, a stationary single SW was initiated by an S1–S2 cross-field protocol. The onset of S1 was at time zero. The SW rotated counterclockwise around a horizontally elongated core (Figure 1, top) with a period of 48 ms. In the present study, we defined the core as the area circumscribed by the SW tip trajectory (in a manner described previously20) and defined the spatial EG as the area in which the transmembrane potential was <−75 mV (refer to the areas colored in blue in Figure 1).
During the SW reentry, a cathodal current stimulus of 2-ms duration was delivered extracellularly via a unipolar electrode. The locations of the stimulating electrode are indicated by the grid of 99 black dots in the top panel of Figure 1. The surface area of the stimulating electrode was 8.1×10−3 cm2. The stimulus strengths were chosen as 4, 8, 16, and 24 mA, because in a preliminary study (not shown), we found that the capture threshold far from the SW core was ≈5 mA. The reentrant cycle of the SW (beginning at 516 ms) was divided into 8 equal intervals, and the stimulus was delivered at the beginning of each interval (8 timings). With 99 stimulation sites, 4 values of stimulus strengths, and 8 stimulus timings, 3168 stimulation episodes were analyzed in this study.
In this study, “capture ratio” was defined as the ratio of the number of successful capture attempts to the total number (8) of stimulation episodes during a single cycle of the SW reentry; thus, it reflects the ratio of the temporal EG to the SW cycle length. For example, with 3 capture episodes, the capture ratio is 3/8=37.5%. The capture ratio was calculated at each electrode position, and maps of its spatial distribution in the sheet were constructed. To monitor capture and for comparison with previous experimental results,3,4,9 we also calculated electrograms at various locations on the sheet.
The basic numerical approach (methods for integration and solving the linear system) has been described elsewhere.21 The spatial discretization step was 0.0075 cm in all directions, and the time discretization step was varied adaptively in the range of 0.00125 to 0.01 ms, depending on the rate of transmembrane potential change. The method for calculating electrograms has also been described previously.20
Stimulus-Induced Transmembrane Potential Maps
Figure 1 shows the transmembrane potential maps in the myocardial sheet just before the onset and immediately after the end of a cathodal 16-mA stimulus (516 and 518 ms, respectively) delivered through a unipolar electrode (black open square in the 518-ms panel). On stimulation, the characteristic VEP10,11 was observed in the vicinity of the unipolar electrode. In addition, the areas in the sheet near the grounding electrodes were hyperpolarized.
Examples of myocardial capture and noncapture by a single cathodal stimulus are presented in Figure 2. To better view the transmembrane potential maps around the stimulation site, the panels in this figure are clipped out from the original maps along the red dotted lines shown in the top panel of Figure 1. The top row of panels (518 ms) in Figure 2 presents maps at the end of 2-ms stimuli of strengths 16 mA (Figure 2, A through D) and 4 mA (Figure 2E). The stimulation sites are indicated by the black open squares. Figure 2, A and B, present typical examples of “capture,” and Figure 2, C through E, illustrate “noncapture.” Electrograms recorded by a bipolar electrode (2 unipolar electrodes arranged vertically at a distance of 0.09 cm) located at the stimulation site and by a neighboring unipolar electrode at a location marked by x in the 518-ms panel are shown at the bottom of each column.
In the case of capture, as shown in Figure 2A (stimulation site 2A in Figure 1), the cathode-break excitation wave front (marked with * in the 522-ms panel) propagated through the virtual anode on the right and resulted in a new SW reentry (arrows in 522- to 562-ms panels). In another case of capture, as shown in Figure 2B (stimulation site 2B in Figure 1), the cathode-break excitation wave fronts (* in 522-ms panel) propagated through the virtual anodes on both sides and resulted in a figure-of-eight reentry (arrows in 522- to 562-ms panels). In both capture examples, the electrograms exhibited morphology consistent with experimental recordings.3,4,9 It is interesting to note that all capture episodes in the present study were based on cathode-break rather than cathode-make excitation.
In the case of noncapture, as shown in Figure 2C (stimulation site 2C in Figure 1), the stimulus was delivered during the refractory period (518-ms panel), and despite initial propagation of the cathode-break excitations through the virtual anodes, it failed to excite the sheet (522- to 562-ms panels). In another example of noncapture, as shown in Figure 2D (stimulation site 2D in Figure 1), the cathode-break excitation wave fronts were blocked by the passage of the SW through the site of stimulation (522- to 562-ms panels). In Figure 2E (stimulation site 2B in Figure 1), the events are similar to those in Figure 2D even though the stimulation site was the same as in Figure 2B. The electrograms in the latter 3 cases are consistent with those of noncapture as obtained in experiments.3,4,9
Capture Ratio Maps
The capture ratio maps in Figure 3 reflect the spatial distribution of the temporal EG during SW reentry for different stimulus strengths. The black ellipse in each panel represents the SW core. The size of each panel corresponds to the rectangle outlined with black dotted lines in the top panel of Figure 1.
When a comparatively weak 4-mA stimulus was used, the capture ratio far from the core was 0% (colored black), and the high–capture ratio area (colored white and yellow) was limited within the elliptical core. It is interesting to note that the low–capture ratio area (colored red) was distributed diagonally in the sheet (top left to bottom right).
Conversely, after the 8-mA stimulus, the area far from the core was captured (mostly red color). As in the 4-mA stimulus case, the area within the core was characterized by a high capture ratio. However, it is noteworthy that the high capture ratio was also observed in some of the areas diagonally adjacent to (open thick black arrows) and those on the left and right of (solid thin black arrows) the core. When higher-strength stimuli (16 and 24 mA) were used, the trend toward diagonal distribution outside the core became well pronounced, as shown in the third and fourth panels of Figure 3.
Effect of Stimulus Strength on Myocardial Capture
Examples demonstrating the effect of stimulus strength on myocardial capture are presented in Figure 4. The 2-ms stimuli (open black squares in the 518-ms panels) of strengths 8, 16, and 24 mA were delivered at 516 ms. Similar to previous figures, each panel refers to the rectangle outlined with the white dotted lines in the top panel of Figure 1.
As shown in Figure 4A, when the stimulation site (4A in Figure 1) was to the left of and above the SW core, the 8- and 16-mA stimuli did not capture the myocardium, but the stronger 24-mA stimulus did (* in the 530-ms panel of Figure 4A). This is because of the enlargement of the virtual anode, which provided an escape pathway for the break excitation.
In Figure 4B, the stimulation site (4B in Figure 1) was just below the one in the preceding case. Here, both the 16- and 24-mA stimuli captured (* in the 530-ms panels of Figure 4B). Because the right virtual anode was formed in a closer proximity to the spatial EG than the one in Figure 4A, the cathode-break excitation wave front easily escaped into the spatial EG, resulting in myocardial capture.
In contrast, as shown in Figure 4C, when the stimulation site (4C in Figure 1) was to the left of and below the core, no stimuli could capture, even though the proximity of the stimulation site to the core was the same as the one in Figure 4B. This area was refractory and far from the spatial EG of the counterclockwise-rotating SW.
Stimulus Within the SW Core
Figure 5 presents snapshots of the transmembrane potential distribution around the SW core within the area outlined by the solid white lines in the top panel of Figure 1. Because of electrotonic influences, the transmembrane potential at the core center (approximately −55 mV) was less negative than that of the peripheral spatial EG; therefore, the core was not fully excitable in this case. Indeed, no excitation wave front induced by a stimulus outside the core could invade the core in all simulation episodes (not shown), except when the virtual anode hyperpolarized the core (eg, Figure 2A). However, the 4-mA stimulus in Figure 5 was associated with a high capture ratio within the core, whereas the same-strength stimulus did not capture the peripheral area, as seen in Figure 3. To elucidate this discrepancy, we examined in detail the stimulus-induced wave dynamics around the core.
When the 4-mA stimulus was delivered at the core center at 516 ms in Figure 5, VEP formed (518-ms panel). A cathode-break excitation ensued (* in the 522-ms panel) and propagated through the right virtual anode (arrow in the 522-ms panel). Thus, the cathode-break excitation wave front escaped into the spatial EG on the outside of the core (see arrow in the 530-ms panel). Therefore, in this example, the stimulus delivered inside the core falls within the temporal EG; however, the core itself is not part of the spatial EG. We examined the wave dynamics further after the same-strength stimuli applied within the core for the 7 remaining timings. We found that the cathode-break excitation wave front escaped into the spatial EG regardless of the SW reentrant phase (not shown) because the spatial EG was always adjacent to the edge of the core.
Cathode-Break Excitation as a Mechanism of Capture During SW Reentry
To the best of our knowledge, the present study is the first to focus on the VEP effect as a mechanism of capture during SW reentry. We have demonstrated that cathode-break rather than cathode-make excitation is the dominant mechanism of myocardial capture (Figures 2, 4, and 5⇑⇑). In a capture experiment, Newton et al8 observed that the activation away from the stimulation site did not have an elliptical shape; they attributed this to the dispersion in refractoriness and activation times during fibrillation. However, the myocardial capture in this case might have involved cathode-break excitation, because 2 wave fronts propagating in opposite directions were shown in their report.8
Why Is the Capture Threshold Higher Than the Diastolic Threshold?
As shown in Figure 3, the capture threshold far from the SW core was >4 mA. This threshold was much higher than the diastolic threshold (0.5 mA). We found that 2 factors were responsible for the high capture threshold.
The first factor was the virtual anode size. The comparison between panels in Figure 4 demonstrated that a large virtual anode resulting from the high-strength stimulus presented itself as an escape pathway for the cathode-break excitation, thus leading to successful capture. This factor contributed to the capture mechanism primarily when the stimulus was delivered to refractory tissue.
The second factor was the conduction velocity of the cathode-break excitation wave fronts. Stimulation sites in Figure 2, B and E, were the same; they were both outside the refractory area. However, the cathode-break excitation after the 4-mA stimulus did not capture (Figure 2E), whereas those after the 16-mA stimulus captured (Figure 2B). This was because of the slower conduction velocity of the cathode-break excitation wave fronts resulting from the weaker stimulus (4 mA),22,23 which allowed the SW arriving at the stimulation site to catch up with and engulf the excitations. This factor contributed to the capture mechanism primarily when the stimulus was delivered to recovered tissue.
Distribution of the Temporal EG Does Not Reflect the Spatial EG
For a stationary single SW reentry, if the spatial distribution of the temporal EG is to reflect the spatial EG during a single cycle of the SW, the highly captured area in the capture ratio maps must be distributed elliptically around the core. This is because the action potential duration around the SW tip is reduced (EG is widened) as a result of the electrotonic influences exerted by the core.24,25 However, this is not the case in the present study. We found that the high capture ratio distribution was not elliptical (Figure 3). Of the 2 virtual anodes formed in the direction of the fibers during the stimulus, at least 1 recovered the regional excitability of the SW arm. Hence, when the stimulation site was located diagonally with respect to the core (upper left or lower right in the case of counterclockwise SW rotation), the cathode-break excitation wave front easily invaded the spatial EG present above or below the core, resulting in a successful capture (Figure 4). In other words, the areas exhibiting wide temporal EGs (ie, high capture ratio) were areas in which the cathode-break excitation wave fronts easily invaded the spatial EG via the virtual anodes.
As shown in the present study, the temporal EG may be modified by electrode configuration and fiber orientation. We believe that the temporal EG measurement is still a useful tool for evaluating pharmacological cardioversion because the change in the temporal EG can indirectly reflect the change in the spatial EG size,3,9 provided that the SW direction of rotation is the same and the SW core position does not change significantly. However, it should be noted that the spatial distribution of the temporal EG does not directly reflect the spatial EG.
The limitations associated with the use of the LR-A model have been discussed in a previous article.17 Here, we did not take into account the effects of the complex 3D tissue structure with intricate fiber orientation and tissue heterogeneity, the surrounding tissue bath, etc. Furthermore, we did not consider other configurations of the stimulating and grounding electrodes, which strongly affect the VEP.
In the present study, the capture threshold (5 mA) was 10 times the diastolic threshold (0.5 mA), which is near the top of the capture threshold range in experiments.7,8 Here, the capture threshold was associated with cathode-break excitations only. This might be because we used a stationary SW with relatively small spatial EG. SW meandering and/or breakup can lower the capture threshold because of spatial EG widening or movement of the core, which has a lower threshold than the noncore area. Thus, it is possible that cathode-make excitation might contribute as an additional mechanism of capture.
To achieve a stationary SW, we implemented a short action potential duration (≈50 ms for a planar wave and ≈36 ms in the SW arm) with a short cycle length of SW reentry (48 ms). However, the action potential duration in the present study is still longer than that in the canine right atrium during acetylcholine infusion.26 In addition, although we showed that the SW core was refractory, core refractoriness may differ greatly with core size and meandering pattern.19,25
Further computer simulations and experimental studies are needed to elucidate the exact capture mechanisms during cardiac fibrillation. Despite its limitations, the present study is a step toward mechanistic insight into myocardial capture.
This study was supported by Department of Energy grant DE-FG02-01ER63119, National Institutes of Health grants HL-063196 and HL-067322 (to Dr Trayanova), and Grants-in-Aid (14580843 and 14780658) for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.
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