The goal of this study is to investigate the mechanisms responsible for the increase in the upper limit of vulnerability (ULV; highest shock strength that induces arrhythmia) following the increase in pacing rate. To accomplish this goal, the study employs a three-dimensional bidomain finite element model of a slice through the canine ventricles. The preparation was paced eight times at a basic cycle length (BCL) of either 80 or 150 ms followed by delivery of shocks of various strengths and timings. Our results demonstrate that the shock strength, which induced an arrhythmia 50% of the time, increased 20% for the faster pacing compared to the slower pacing. Analysis of the mechanisms underlying the increased vulnerability revealed that delayed post-shock activations originating in the tissue depths appear as breakthrough activations on the surfaces of the preparation following an isoelectric window (IW). However, the IW duration was consistently shorter in the faster-paced preparation. Consequently, breakthrough activations appeared on the surfaces of this preparation earlier, when the tissue was less recovered, resulting in higher probability of unidirectional block and reentry. This explains why shocks of the same strength were more likely to result in arrhythmia induction when delivered to a preparation that was rapidly paced.
Over a decade ago, the programming of an implantable cardioverter defibrillator (ICD) required multiple episodes of ventricular fibrillation (VF) induction to determine the minimum shock strength needed to terminate VF, the defibrillation threshold (DFT; Singer et al. 1991). However, a large body of subsequent research has demonstrated that defibrillation and VF induction with an electric shock delivered to a heart in sinus rhythm are driven by the same mechanisms (Chen et al. 1986a,b, 1991; Malkin et al. 1995; Malkin & Hoffmeister 2000). A relationship between the DFT and the highest shock strength that will induce VF even if given during the vulnerable window, the upper limit of vulnerability (ULV), has been shown to exist in both animals and humans (Chen et al. 1986c, 1993; Shibata et al. 1988a,b; Malkin et al. 1997; Wang et al. 2001). Determining the ULV is a much safer process for a patient undergoing ICD implantation; knowing the ULV, one can approximate the DFT. Therefore, utilization of ULV in programming the implantable device in the clinical setting is becoming more common (Green et al. 2003). In order for the ULV to consistently be used as an approximation of the DFT, conditions that affect the DFT must also affect the ULV in a similar manner. Huang et al. (1997) found that reversal of electrode polarity and changes in waveform duration produced almost identical changes in both the ULV and DFT. It has been demonstrated that when an ICD is programmed at the ULV plus 5J, the success rate for first-shock defibrillation (99%) is much higher than that for programming at the DFT plus 9 or 10J (75 and 85%; Swerdlow et al. 1997).
Nonetheless, when determining the ULV, the heart is beating normally, and its electrophysiological state does not mimic that during VF; its activation rate, action potential duration and number of simultaneous wavefronts present in the heart are substantially different. Rapid pacing of the heart brings its electrophysiological state closer to VF since it produces a larger number of activation wavefronts with shorter action potential duration. Therefore, it has been debated whether a ULV measurement under rapid pacing conditions would yield a better approximation of DFT. To test this hypothesis, Malkin et al. (1995, 2000) measured the ULV of a rapidly paced canine heart and compared it to the ULV of a heart paced at a normal rate. The studies found that the ULV increased as pacing rate increased, yielding a better approximation of DFT. However, the mechanisms underlying this elevation in ULV are not well understood, hampering further optimization of the process of DFT estimation. The goal of the present study is to use computer simulations of arrhythmia induction with electric shocks to determine whether an increased number of simultaneously propagating wavefronts associated with increased pacing rate results in an increase in the ULV, and if so, what are the responsible mechanisms.
(a) Model description
The Auckland model of canine ventricular anatomy and fibre orientation (Nielsen et al. 1991) was used in this simulation study. The ventricles were placed in a box representing the perfusing bath. Two planes 4 mm apart were passed through the ventricles and the bath to isolate a slice through both ventricles. The slice, including cardiac tissue and surrounding conductive media (perfusing bath and a portion of the blood cavities), measured 85×75×4 mm.
The electrical properties of the myocardium in the slice were described by the bidomain equations, while the potentials in the perfusing bath and blood cavities were governed by Laplace's equation. The coupled system of equations is as follows:
Here ϕi, ϕe and ϕb are the intracellular, extracellular and blood cavity (perfusing bath) potentials, respectively; Vm is the transmembrane potential; βsv is the membrane surface area to tissue volume ratio (m−1); Cm is the membrane specific capacitance (F m−2); Istim is the current per unit volume injected at the anode (A m−3); Iion is the ionic current density as represented by the membrane model; and i and e are the conductivity tensors in the intra- and extracellular domains (S m−1). The conductivity tensors account for the fibre architecture and unequal anisotropy ratios of myocardial tissue with values as in Trayanova et al. (2002).
The boundary conditions associated with the bidomain model require that the intracellular current density normal to the tissue boundary be zero, and that the extracellular current density and potential be continuous with the surrounding volume conductor. Thus, at the tissue–bath and tissue–blood interfaces the following equations apply:where b is the bath (blood) conductivity and is the identity tensor. The top and bottom surfaces of the slice were assumed to be insulated as if pressed between glass plates. In this manner, virtual electrode polarization induced by the shock on the cut surfaces of the slice is representative of shock-induced behaviour on any surface in the normal heart (Trayanova & Eason 2002).
Membrane dynamics were described by the Drouhard & Roberge (1987) modification of the Beeler & Reuter (1977) model. The model was additionally adjusted to add stability for high-strength defibrillation shocks (Skouibine et al. 1999, 2000a). Consistent with the goal of the study, the action potential duration of the solitary action potential was additionally shortened to 100 ms to ensure that several simultaneous pre-shock wavefronts can fit on the thin slice; this approach has been widely used in previous computational studies (Gray 2002; Fenton et al. 2002). Finally, electroporation was also included in the model (Krassowska 1995) because of its effects on cardiac electrical activity both during and after shocks.
Details regarding the computational mesh and the numerical solution can be found in Trayanova et al. (2002).
(b) Shock protocol
The largest number of simultaneous propagating wavefronts in the slice was elicited by pacing at a basic cycle length (BCL) of 80 ms; this was the shortest BCL that resulted in 1 : 1 capture in our simulations. To create a pre-shock state that consisted of a smaller number of simultaneous propagating wavefronts, the BCL was increased to 150 ms; the nearly twice as large BCL chosen here was consistent with the difference in pacing rates used in the study by Malkin et al. (1995). Eight pacing transmembrane stimuli were given to the volume of tissue within the black lines in figure 1, top leftmost panel, at the two BCLs; this ensured a steady-state propagation pattern. The steady-state action potential durations were measured as 70 and 81 ms for the two BCLs (figure 1).
After the eighth pacing stimulus, a monophasic square-wave shock of duration 5 ms and variable strength was delivered at one of eight shock timings corresponding to 12.5, 25, 37.5, 50, 62.5, 75, 87.5 and 100% BCL. Figure 1 depicts pre-shock transmembrane potential distributions on the surface of the slice for four shock timings and for both BCLs; these distributions are identical on both cut surfaces and throughout the volume of the slice. Small numbers next to each transmembrane potential map indicate the number of simultaneous propagating wavefronts in the slice at that instant of time; it is clear that a BCL of 80 ms is always associated with a larger number of simultaneous wavefronts than a BCL of 150 ms.
All shocks were delivered through the electrode configuration shown in the top leftmost panel of figure 1, where the cathode (red) was located posteriorly within the cavity of the right ventricle and the anode (blue) was placed in the bath to the left of the left ventricle. This electrode configuration was chosen since it is commonly used in experimental studies of defibrillation (Efimov et al. 1998). The shock duration of 5 ms was based on the fact that a square monophasic shock of this duration has energy comparable to the 8 ms truncated exponential form used in clinical practice. To find the ULV, shocks were administered in increments of 100 mA within the range of 300–1000 mA for a total of seven shock strengths, each delivered to eight pre-shock transmembrane potential distributions for each pacing rate (a total of 112 simulations). The lower boundary of this shock strength range was above the lower limit of vulnerability (Hillebrenner et al. 2004), i.e. the lowest shock strength that results in arrhythmia induction when given during the vulnerable window. This ensured that the shock protocol would yield a ULV value.
(c) Data processing
From the simulation results, a vulnerability curve was constructed for each pre-shock BCL. Vulnerability curves represent the probability of sustained arrhythmia not being induced by the shock, plotted as a function of shock strength. For each shock strength, probability of non-induction of sustained arrhythmia was calculated from the outcome of the eight shock delivery episodes corresponding to the eight shock timings. An arrhythmia was considered sustained if more than two reentrant beats took place following the immediate post-shock activations (Rodriguez et al. 2004). The discrete vulnerability curves for the two pre-shock BCL cases were then best-fitted, with the help of the statistical package R (The R Foundation for Statistical Computing), using a generalized linear model with a probit link function. From the vulnerability curves, the shock strength which resulted in 50% probability of non-induction, termed the ULV50, was assessed for both cases. The p-value, representing the significance of the change in ULV due to the change in pacing rate, was derived from a z-test. The test evaluated ULV magnitude relative to its standard error and was computed using the R package.
The heterogeneity of transmembrane potential distribution on a slice surface was assessed by the uniformity index (UI) calculated as ((P−N)/(P+N)), where P and N denote the total number of nodes on the surface that were above and below the excitation threshold, respectively. The threshold for the modified Beeler–Reuter model was −52.26 mV (Drouhard & Roberge 1987).
The isoelectric window (IW) was defined as the period of time between shock end and the time of appearance on the surface of the slice of the earliest breakthrough activation that followed the immediate break excitations. The IW is an important factor often directly responsible for shock outcome (Chen et al. 1986a; Chattipakorn et al. 2000a, 2001; Wang et al. 2001) and was assessed in all simulations. A Student unpaired t-test was used to determine the statistical significance of differences in IW durations for post-shock episodes corresponding to the two different pre-shock BCLs as well as for shocks that did and did not induce a sustained arrhythmia. A value of p≤0.05 was considered significant. Where appropriate, all values are expressed as mean±s.d. unless otherwise noted.
(a) Vulnerability curves
Vulnerability curves for shocks delivered to the preparations paced at the two different BCLs are shown in figure 2. Actual data points for the two cases are marked by different symbols. The curves show that the probability of non-induction increases with shock strength. In addition, the shorter BCL vulnerability curve is shifted significantly to the right of the longer BCL curve (p≤0.05, z=2.359). The ULV50 value, as calculated from the fitted curves, increases from 595 mA for the longer BCL to 715 mA for the shorter BCL, a 20% increase.
(b) Post-shock behaviour
To understand the mechanisms responsible for the change in ULV associated with the increase in pacing rate, post-shock events in the slice were examined for all simulations. As an example, the outcomes of a 600 mA shock delivered at 62.5% BCL to the faster- and the slower-paced preparations are compared in figure 3. The figure presents the transmembrane potential distributions on the top and bottom surfaces of the slice (as if the surfaces were optically mapped) at shock end (t=0 ms panels) and for several instances over a 200 ms post-shock interval. The transmembrane potential distributions at shock end are nearly identical in both cases. The shock induces positive and negative polarization on the surfaces of the slice, such that the sign of the polarization on the top surface is reversed from that on the bottom surface. After shock withdrawal, excitable areas newly formed by the shock (blue) are quickly traversed by immediate break excitations (t=30 ms panels). Overall, the faster-paced preparation recovers more quickly from the effect of the shock (less red colour in the left t=40 ms panels). Numerous patches of excitable tissue (blue) appear at that time on the surfaces of the faster-paced preparation, while the surfaces of the slower-paced preparation remain predominantly refractory.
As tissue continues to recover, activations, marked by arrows, are observed in both the slower- and faster-paced preparations, in the 40 and 50 ms panels, respectively (see arrows). In figure 3, a total of three post-shock activations are observed on the bottom surface and another one on the top surface of the faster-paced preparation, while only one appears on each surface of the slower-paced preparation. In the case of shorter pre-shock BCL, a sustained arrhythmia is established with activity maintained by two stable spiral waves, while for the longer BCL, the wavefronts resulting from the focal activation and an unstable spiral wave traverse the tissue in opposite directions and collide, terminating all activity. In this example, shocks of the same magnitude and % BCL shock timing yield different outcomes for the two preparations. In both cases, however, the delayed post-shock activations play a major role in the outcome of the shock.
To determine what causes the appearance of delayed global post-shock activations, the transmembrane potential distributions in the tissue depth were examined for all episodes. Figure 4 depicts the shock-end transmembrane potential distribution in the tissue depth for the cases presented in figure 3. The figure demonstrates that the shock induces much stronger polarization on the surfaces than in the depth of the tissue; this is consistent with results from previous studies (Meunier et al. 2002; Hillebrenner et al. 2004). The large surface polarization causes the surfaces to experience immediate post-shock activations, which renders them refractory for a significant post-shock interval (see figure 3, t=30 ms panels). In contrast, in the depth, there are numerous regions with intermediate values of transmembrane potential (green), and the gradients between regions of shock-induced depolarization and de-excitation are much smaller. As shown previously (Skouibine et al. 2000b), this causes a latency in the onset of the post-shock activations that originate in the tissue depth. Therefore, these post-shock activations are formed and linger in the depth; they make a breakthrough on the surfaces of the slice when the surfaces recover, setting the stage for reentry (figure 3). One also notices that in the faster-paced preparation, the transmembrane potential distribution in the depth is more heterogeneous, indicating that it is more likely that a post-shock activation will arise in this case. Indeed, in figure 3, more breakthrough activations are observed in the faster-paced as compared to the slower-paced preparation.
(c) Comparison of isoelectric window durations for the two pacing rates
The post-shock activations that originate in the sub-surface layers of the tissue make a breakthrough on the surfaces as soon as they find an excitable pathway. The time of earliest appearance of a breakthrough activation on a surface of the slice determines the IW duration, as defined in §2. The duration of the IW associated with the first breakthrough activation in figure 3 is 35 and 42 ms, for the shorter and longer BCL, respectively. Isoelectric window duration for all simulations is presented in figure 5 as a function of shock strength for the two BCLs (panel a) and for shocks that did and did not induce a sustained arrhythmia (panel b). A point on the graph in figure 5 for a given shock strength represents the average IW duration across all shock timings.
As figure 5a demonstrates, following shocks administered to the faster-paced preparation, the average IW duration for each shock strength is 22% shorter when compared to the slower-paced preparation (p≤0.05; mean±s.e.m. 31.21±2.10 versus 38.07±1.47 ms, respectively). This difference is the largest for the 600 mA shock strength, which is approximately the ULV50 for 150 ms BCL. In figure 5b, IW durations associated with shocks that did not result in arrhythmia induction despite the emergence of delayed post-shock activations (black trace) and those that did induce an arrhythmia as a result of delayed post-shock activations (grey trace) are compared. The figure reveals that, regardless of shock strength, shocks that induce arrhythmias have a 31% shorter IW duration than those that do not induce arrhythmias (p≤0.05; mean±s.e.m. 29.24±0.956 versus 38.21±0.538 ms, respectively).
As illustrated in figure 5a, the IW for the faster-paced preparation is shorter than that for the slower-paced preparation for all shock strengths (and thus more likely to result in arrhythmia, as per figure 5b). In order for the delayed post-shock activations to appear earlier on the top and bottom surfaces of the faster-paced preparation, these surfaces must repolarize more rapidly to allow the activations from the tissue depth to find their way to the surfaces. In §3d we examine whether indeed there is a difference in the rate of surface recovery for the faster- and slower-paced preparations.
(d) Comparison of surface post-shock recovery for the two pacing rates
Post-shock recovery of the surfaces was assessed by calculating the UI as a function of time. Figure 6 presents an example of surface recovery and the way it was quantified for the case of a 600 mA shock delivered at 62.5% BCL. A UI value of 1 indicates that every node on the surface of the preparation is above threshold, while a value of −1 represents a scenario where every surface node is below threshold. A value of 0 indicates that the same number of nodes are above and below threshold.
As figure 6 illustrates, UI is approximately 1 when the surfaces of both preparations are almost completely refractory following the surface break excitations that take place immediately after shock withdrawal; this is also illustrated with surface transmembrane potential maps at 20 ms post-shock. Soon thereafter, both preparations begin to repolarize and the UI decreases towards 0. The faster-paced preparation repolarizes more quickly and its UI curve crosses the zero line 14 ms earlier than that of the slower-paced preparation, as indicated by the green arrow. In the 58 ms panels, the faster-paced preparation has almost recovered (UI is below zero), with three breakthrough activations just beginning to propagate on the surface, while the slower-paced preparation still has a large percentage of refractory nodes (green) and a UI value above zero.
If an activation appears on a surface earlier following the shock, then the likelihood of this activation encountering patches of refractory tissue and unidirectional block, and thus initiating reentry, is larger since the tissue has not had time to return to rest everywhere. This explains why the faster-paced preparation is more likely, for the same shock strength and % BCL timing, to develop a post-shock arrhythmia. Furthermore, analysing the results of the simulations, we uncovered an effect that additionally exacerbated arrhythmogenesis in the faster-paced preparation.
(e) Comparison of tissue excitability at shock end for the two pacing rates
Figure 7a depicts the percentage of all excitable nodes (nodes with transmembrane potential below threshold) at shock end as a function of shock strength for the 62.5% BCL shock timing. In this example, as in all other cases examined, the slower-paced preparation (black trace) has a higher level of excitability at shock end for all shock strengths. The number of excitable nodes in figure 7a is further broken down in figure 7b into nodes between rest and threshold (top) and hyperpolarized nodes (bottom). As this figure demonstrates, although the faster-paced preparation yields more excitable nodes between rest and threshold, the slower-paced preparation has a much larger percentage of hyperpolarized nodes. This suggests that the propagation of the immediate break excitations in the slower-paced preparation will be through hyperpolarized areas, where propagation velocity is higher, as demonstrated by previous research (Skouibine et al. 2000b). The faster the break excitations traverse the shock-end excitable gaps (mostly on the surfaces), the more uniform the transmembrane potential distribution on these surfaces is tens of milliseconds after shock withdrawal. Therefore, in addition to appearing on the surfaces of the slice earlier, the breakthrough activations in the faster-paced preparation will also appear on a surface of a relatively more heterogeneous transmembrane potential distribution; the latter compounds the arrhythmogenic effect associated with faster pacing.
The present study uses a realistic computational model of a slice of the canine ventricles to characterize the increase in ULV associated with the increase in pacing rate (increased number of simultaneous pre-shock wavefronts) and to provide insight into the mechanisms responsible for this behaviour. Defibrillation-strength shocks were delivered to a faster- and a slower-paced preparation in an attempt to induce a stable arrhythmia. Vulnerability curves were constructed from the outcome of these shock episodes, from which the ULV50 value was determined. The ULV50 for the faster-paced preparation was found to be significantly higher (20%) than that of the slower-paced preparation. Mechanistic enquiry into this increase in vulnerability revealed that delayed breakthrough activations were responsible for arrhythmia initiation. In the faster-paced preparation, these activations appeared on the surfaces of the slices earlier and were more likely to result in unidirectional block and reentry.
The study of Malkin et al. (1995) compared the ULV of a canine heart in normal rhythm to the ULV of a rapidly paced heart. It was found that the ULV50 increased by an average of 31%, from 333±72.8 to 437±111 V, as BCL decreased from an average of 350 to 181 ms (48%). Malkin & Hoffmeister (2000) further extended their study of rapid pacing in the canine heart to the point of haemodynamic collapse, and subsequently measured the ULV. The authors found that rapid pacing raised the ULV50 from 397±70.6 to 507±62.9 V, a 28% increase. An older study by Chen et al. (1991) found a similar trend; however, it reported that the increase in ULV50 was not statistically significant. Our results regarding the ULV values are consistent with the results of Malkin et al. (1995) and Malkin & Hoffmeister (2000); we found that ULV50 increased from 595 to 719 mA with the increase in pacing rate, a 20% change. Our results are particularly encouraging given the fact that our preparation is only a slice of the heart rather then the organ itself, and that our action potential duration is significantly shortened. This indicates that the phenomena we observed and the mechanisms we uncovered could be general and not largely dependent on the shape of the preparation and action potential duration.
As the present study found, an increase in pacing rate, which results in an increase in the number of pre-shock wavefronts, causes a shift in the vulnerability curve toward higher shock strengths. This is consistent with the results of Hillebrenner et al. (2004) who, using the same preparation and (solitary) action potential duration as in this study, investigated the increase in DFT50 (50% dose for defibrillation, i.e. the shock strength that succeeded in terminating the arrhythmia in 50% of the cases) with the increase in the number of pre-shock functional reentrant waves. The study constructed defibrillation dose–response curves, representing the probability of arrhythmia termination as a function of shock strength, which are analogous to our vulnerability dose–response curves; DFT50 values were determined from these curves in a manner similar to what was done in the present study. As in our study, the defibrillation dose–response curve shifted towards the higher shock strengths with the increase in the number of pre-shock reentrant waves. The DFT50 was found to increase by 14% when the number of pre-shock reentrant waves changed from one to six. Clearly, results from both studies indicate that the number of simultaneous pre-shock wavefronts, regardless of whether reentrant or not, is an important determinant of shock outcome, particularly where the 50% probability of success is concerned. As demonstrated previously by Efimov et al. (1998) and Eason & Trayanova (2002), this is much less so when the 90% probability is considered (DFT90 and ULV90).
The present study also demonstrated that there are differences in shock-induced polarization at the surfaces of the preparation and in the depth. As predicted previously (Trayanova et al. 1998; Entcheva et al. 1999), the surfaces experience much higher levels of positive and negative polarization due to current redistribution at the surface layers of myocardium. Owing to the lower gradients between regions of positive and negative polarization in the depth of the tissue, activations arise there with a delay. Our study demonstrates that these activations could be a major mechanism behind the existence of the IW and delayed breakthroughs, as observed in numerous electrical and optical mapping studies (Shibata et al. 1988a,b; Chattipakorn et al. 2000b, 2003; Wang et al. 2001; Evans & Gray 2004).
In the simulations analysed in this study, IW duration varies in the range from 26 to 32 ms for shocks that successfully induce an arrhythmia and from 35 to 39 ms for those that fail. Shocks delivered to the slower-paced preparation are associated with, on average, 22% longer IW durations than those given to the faster-paced preparation. Since longer IW duration is correlated with higher probability of non-induction (due to the breakthrough wavefront encountering decreased dispersion of post-shock refractoriness on the surface, as explained in §3), the shorter duration of the IW for shocks administered to the faster-paced preparation is an indicator of these shocks' higher probability of arrhythmia induction. The IW durations determined here are consistent with experimental findings. Shibata et al. (1988a), in a vulnerability study using canine hearts found IWs ranging from 80±17 to 10±0 ms while varying shock timing. Owing to the artefact from the shock and experimental limitations, 10 ms was the earliest time at which a post-shock activation could be observed. Similarly, Wang et al. (2001) observed an IW of 66 ms following a shock of strength near the ULV that induced an arrhythmia in swine hearts. Chattipakorn et al. (2000a) measured an IW of 51±23 ms for shocks that did induce and 68±78 ms for shocks that did not induce an arrhythmia. As already explained in the paper by Hillebrenner et al. (2004), adjusting these values for action potential duration and thickness of the preparation brings them close to the IW durations reported in the present study.
The limitations associated with this study include the choice of the myocardial preparation and ionic model (action potential duration). Limitations in the ionic model have been discussed in a previous publication of ours (Skouibine et al. 2000a,b). Other limitations have been discussed in previous publications by Meunier et al. (2002) and by Eason & Trayanova (2002), which used similar preparations. Although only one shock electrode configuration was used in this study, Hillebrenner et al. (2003) found that alternative electrode configurations are expected to affect the value of the ULV but not the underlying mechanisms. Clearly, the most significant limitation of the present model is that, due to computational limitations, it is impossible to represent the canine heart in its entirety, and we have to resort to a thin slice of myocardium. As a result, following the shock, large virtual electrode polarization is induced on the top and bottom cut surfaces of the slice. Such effect is, however, not far removed from reality: one can think of effects on the endo- and epicardial surfaces following the shock. During the shock, large virtual electrode polarization is formed on the surfaces of the ventricular walls; similar to the effect shown here, this polarization is of reverse sign on the endo- and epicardial surfaces (Efimov et al. 2000; Trayanova et al. 2002). Furthermore, epicardial breakthrough is often recorded (following an IW) after the strong shock-induced polarization subsides on the epicardium (Wang et al. 2001); the present paper offers a possible explanation of the origins of this epicardial breakthrough and the mechanisms that underlie the duration of the IW associated with it. Thus, while the model does not fully and accurately represent reality, it is nonetheless pertinent to vulnerability and defibrillation, and can be used in the study of its mechanisms. The present study, we hope, will provide useful information regarding the mechanisms that could underlie the increase in vulnerability accompanying rapid pacing in animal and human hearts.
This study investigates the mechanisms responsible for the increase in the ULV following the increase in pre-shock pacing rate (increased number of simultaneous pre-shock wavefronts). The results of the simulations demonstrate that ULV50 increased by 20% when pacing rate was increased from 80 to 150 ms BCL. Analysis of the mechanisms responsible for this increase in vulnerability revealed that for both pacing rates, following the shock, delayed post-shock activations originate in the depths of the tissue and appear as breakthrough activations on the cut surfaces of the preparation following an IW. However, IW duration was consistently shorter in the faster-paced preparation. As a consequence, the breakthrough activations appeared on the surfaces earlier in the faster-paced preparation. There they encountered non-uniform refractoriness, resulting in higher probability of unidirectional block and reentry. This explains why shocks of the same near-ULV50 strength were more arrhythmogenic when delivered to a preparation that was rapidly paced.
This work was supported by NIH grants HL063195 and HL074283, and the Integrative Biology project (EPSRC, ref no: GR/S72023/01). The authors gratefully acknowledge the contributions of Dr Michelle Lacey, Dr James Eason, Dr Felipe Aguel, Craig A. Campbell and Robert C. Blake III.
One contribution of 15 to a Theme Issue ‘Biomathematical modelling II’.
- © 2006 The Royal Society