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Themed Issue Papers |
1 Department of Biomedical Engineering, Tulane University, New Orleans, USA
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(Received 25 September 2005;
accepted after revision 22 December 2005; first published online 9 February 2006)
Corresponding author N. Trayanova: Department of Biomedical Engineering, 500 Lindy Boggs Center, Suite 500, Tulane University, New Orleans, LA 70118, USA. Email: nataliat{at}tulane.edu (alternative Email: nataliat{at}cox.net)
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Introduction |
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Recent developments in the understanding of defibrillation mechanisms
Arrhythmia induction and defibrillation. The mechanisms of cardiac defibrillation have been strongly linked to cardiac vulnerability to electric shocks. A large body of research has demonstrated that an electric shock can induce ventricular arrhythmias if it is given during the ‘vulnerable window’ within the normal cardiac cycle (Wiggers, 1930). Furthermore, shocks that result in induction of arrhythmia are bound by a minimum and a maximum strength, termed the lower and upper limits of vulnerability (LLV and ULV; Fabiato et al. 1967). Fabiato et al. (1967) were the first to suggest that the mechanisms of induction and termination of ventricular fibrillation (VF) may be similar. This suggestion is now supported by the correlation between ULV and defibrillation threshold (DFT; Chen et al. 1986). For a defibrillation shock to succeed, it must extinguish existing VF activations throughout the myocardium (or in a critical mass of it), as well as not initiate new fibrillatory wavefronts. Extinguishing existing VF activations is not sufficient; the shock may still reinitiate VF by the same mechanism as it induces VF if applied during the vulnerable window. Therefore, understanding cardiac vulnerability to electric shocks is a route to understanding defibrillation and arrhythmogenesis by failed shocks. In this light, the present article reviews both defibrillation and vulnerability studies. Finally, this article follows in the footsteps of numerous electrical and optical mapping studies of VF induction and defibrillation; it focuses on the mechanisms that govern the responses to the shock in the normal isolated heart preparation as a necessary step in solving the riddles of clinical defibrillation in diseased hearts.
Recent findings: virtual electrode polarization and the resulting post-shock behaviour. Over a decade ago, bidomain simulations (Sepulveda et al. 1989) followed by optical mapping studies (Knisley et al. 1994; Wikswo et al. 1995) demonstrated that the membrane response in the vicinity of a strong unipolar stimulus involved simultaneous occurrence of positive (depolarizing) and negative (hyperpolarizing) effects in close proximity. This finding of ‘virtual electrodes’ was in stark contrast with the established view that tissue responses should only be depolarizing (hyperpolarizing) if the stimulus was cathodal (anodal) (Hodgkin & Rushton, 1946). Since then, virtual electrode polarization (VEP) has been documented in experiments and simulations involving field stimulation with various electrode configurations (Efimov et al. 1998, 2000c; Knisley et al. 1999). Detailed analysis of VEP aetiology demonstrated that both applied field (Sobie et al. 1997; Knisley et al. 1999) and tissue structure (Trayanova & Skouibine, 1998; Knisley et al. 1999; Trayanova, 2001) are major determinants of the shape, location, polarity and intensity of the shock-induced polarization (Trayanova et al. 1998b; Trayanova, 1999; Hooks et al. 2002; Rodriguez & Trayanova, 2003; Rodriguez et al. 2005).
The cellular response to shock-induced VEP depends on the strength and polarity of the shock, as well as on the electrophysiological state of the cell at the time of shock delivery. Positive VEP can result in regenerative depolarization in regions where tissue is at or near diastole; such activation is termed ‘make’ because it takes place at the onset (make) of the shock. Furthermore, action potential duration can be either extended (by positive VEP) or shortened (by negative VEP) to a degree that depends on VEP magnitude and shock timing (Efimov et al. 2000b). Finally, strong negative VEP can completely abolish (de-excite) the action potential (i.e. regenerative repolarization), thus creating post-shock excitable gaps in the virtual anode regions. The close proximity of a de-excited region and a virtual cathode has been shown, in both modelling studies (Roth, 1995) and optical mapping experiments (Wikswo et al. 1995), to result in an excitation at shock end (termed ‘break’ excitation, i.e. at the break of the shock). The virtual cathode serves as an electrical stimulus eliciting a regenerative depolarization and a propagating wave in the newly created excitable gap. Break activations arise at the borders between oppositely polarized regions provided that the transmembrane potential gradient across the border spans the threshold for regenerative depolarization (Cheng et al. 1999a). A shock succeeds in extinguishing fibrillatory wavefronts and not initiating new re-entry if make/break excitations manage to traverse the shock-induced excitable gaps before the rest of the myocardium recovers from shock-induced depolarization (Efimov et al. 2000b; Skouibine et al. 2000a; Rodriguez et al. 2005). Thus, latency in the onset of these excitations, their propagation velocity through the excitable gaps, and shock-induced extension of refractoriness in the depolarized areas determine how quickly post-shock activity subsides following successful shocks (Cheng et al. 1999a; Skouibine et al. 2000a; Trayanova et al. 2002b).
Vulnerability to electric shocks and defibrillation failure can also stem from the shock-induced VEP. Make excitation can result in the formation of a new re-entry via the critical point mechanism (Winfree, 1987), where a phase singularity is formed at the intersection of a critical level of shock-induced depolarization and a critical level of recovery of a preshock wave. The onset of a break excitation is also associated with the formation of a (VEP-induced) phase singularity (Efimov et al. 1998); it forms at a point along the boundary between shock-induced depolarization and de-excitation (Efimov et al. 2000c) and is independent of the preshock state of the myocardium. If these phase singularities survive, allowing a spiraling wavefront to develop, the shock results in the (re)initiation of re-entrant arrhythmia.
The continued search for answers. The majority of the findings above were reported in isolated rabbit heart studies; activity in these experiments was mapped optically over an epicardial area typically limited to the vicinity of the electrodes. In studies by Knisley's group (Knisley et al. 1994, 1999), a window of 6 x 6 mm was scanned; Kwaku & Dillon (1996) scanned 100 sites over 30% of the rabbit anterior epicardium. Publications by Efimov et al. (1998, 2000a,c) documented behaviour within a 16 x 16 mm window that occupied about half of the anterior epicardium of the rabbit ventricles over the right ventricle (RV) catheter; the observed break excitations originated at the border of regions of opposite-in-sign strong polarization that occurred above the shock electrode. Thus, the global effect of the shock, as well as the post-shock activity that ensued from it, could not be observed in these studies. Dual CCD camera simultaneous anterior and posterior recordings allowed Gray and coworkers (Evans et al. 2002; Trayanova et al. 2003) to map the effect of the shock over the majority of the epicardium in Langendorff-perfused rabbit heart preparations. Records of epicardial activity revealed that the aetiology of post-shock excitation is more complex than previously believed. For instance, post-shock activations were shown to originate away from (Evans et al. 2002), rather than in the vicinity of (Efimov et al. 1998), the shock catheter. In the study by Evans et al. (2002), global epicardial activity following shocks of the same strength but reversed polarity was radically different from activity observed, under similar conditions, in the vicinity of the catheter (Efimov et al. 2000c). This indicates that anatomical features and geometrical asymmetries in the heart could significantly affect global post-shock propagation.
Mapping the entire epicardial surface of the ventricles, a course that most recent developments in optical mapping have taken, will not, however, reveal the global 3-D activity that follows the shock. Activations could propagate intramurally, without a signature on the epicardial surface (Winfree, 1988). While reports disagree on the depth of penetration of the optical signal, it is clear that the spatiotemporal characteristics of activity in the depths of the myocardium cannot presently be resolved; efforts to achieve this, although promising, remain at a nascent stage (Hooks et al. 2001; Byars et al. 2003). The problem is particularly aggravated in post-shock arrhythmogenesis, since there is a dramatic difference between the magnitude and pattern of shock-induced VEP in the surface layers and in the depth of the myocardium. As determined by simulation studies (Trayanova et al. 1998b; Entcheva et al. 1999), these differences emanate from the different mechanisms that govern surface polarization and polarization in the tissue bulk. Such differences in VEP could result in different electrophysiological behaviour on the surfaces and in the depth. Thus, it is feasible that midmyocardial post-shock activity could remain confined to the depth of the ventricular wall and detached from surface post-shock behaviour for significant stretches of time.
From this brief review, it is apparent that, despite numerous advancements in understanding the mechanisms of shock-induced arrhythmogenesis and defibrillation, the global 3-D post-shock behaviour in the ventricles remains largely unknown. Contributions of ventricular anatomical features to VEP and post-shock propagation patterns have never been quantified. Most importantly, the characteristics of post-shock electrical activity in the depth of the myocardium cannot be presently be resolved. Below we present recent results from our laboratory demonstrating how these questions can be answered using a realistic computer model of defibrillation in close conjunction with experimental studies.
Multiscale modelling of defibrillation
This section provides an overview of the modelling tools used in our recent studies of defibrillation. Over the last several years, our laboratory has developed a 3-D finite-element bidomain model of the rabbit ventricles for use in defibrillation studies. The model has been described in detail in our recent publications (Trayanova et al. 2002a, 2004; Trayanova & Eason, 2002; Aguel et al. 2003; Rodriguez et al. 2005). Here we briefly outline its major components.
Description of myocardial geometry and fibre architecture. Our 3-D model of anatomically based rabbit ventricular geometry and fibre orientation used the University of California San Diego geometrical model of the rabbit ventricles (Vetter & McCulloch, 1998). The original geometry was defined in prolate spheroidal coordinates which we translated into Cartesian coordinates. We used MSC Patran (MSC Software Corporation, Santa Ana, CA, USA) to generate the computational grids. The surfaces and the ‘solids’ of the mesh were created with Patran functions. Additional ‘solids’ were generated to represent the ventricular cavities and the perfusing bath; the conductivity of these regions was assigned the value of blood. Using Patran, surfaces and solids were meshed to create unstructured triangular and tetrahedral meshes, respectively, with an average element edge length of 300–500 µm in the tissue and 1 mm in the cavities and the perfusing bath. Once the entire mesh was complete, files containing node coordinates, elemental connectivity, and the original finite element to which each tetrahedral element in the new mesh belongs were generated. This information was then used to determine, with the combination of two multidimensional root-finding algorithms, fibre orientation at the centroid of each tetrahedron. Local material properties were assigned to each element using the fibre orientations. Figure 1 illustrates the 3-D geometry and fibre orientation in the rabbit ventricles as determined by this algorithm.
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Numerical solutions for the bidomain equations employed the semi-implicit finite element method (Eason & Trayanova, 2002; Aguel et al. 2003; Rodriguez et al. 2005).
Representation of ionic currents and membrane electroporation.
Our group has assembled a library of membrane models, including versions of Beeler-Reuter (BR; Beeler & Reuter, 1977) and Luo Rudy (LR1 and LRd) models and their recent modifications (Luo & Rudy, 1991, 1994; Faber & Rudy, 2000), all of which have been employed in some aspect of our computational electrophysiology research. Figure 2 shows fibrillation in the rabbit ventricular model induced by a train of 12 rapid pacing stimuli; the membrane model is LR1 with steep restitution properties. For defibrillation studies, all membrane models were further modified to ensure stability during the shock (Skouibine et al. 2000b) when a dramatic change in transmembrane potential takes place. It is important to understand, however, that defibrillation shocks induce complex changes in transmembrane potential, some of which have been consistently observed in experiments but never reproduced by membrane models, mostly because membrane models were developed for the study of action potential conduction and arrhythmogenesis and not defibrillation. These observed phenomena are as follows. First, strong shocks applied during action potential plateau in isolated guinea-pig papillary muscle (Zhou et al. 1995), cultured neonatal rat myocyte strands (Fast et al. 2000), and isolated guinea-pig myocytes (Cheng et al. 1999b) induce asymmetrical changes in transmembrane potential (Vm) with the negative transmembrane potential change (
Vm) being larger than the positive change, i.e. Vm– > Vm+. Second, with increase in shock strength, Vm magnitude does not increase proportionally but instead saturates (Zhou et al. 1995; Fast et al. 2000). Third, for large shock strengths, Vm– exhibits non-monotonic behaviour with an initial rapid increase and then a decrease (Cheng et al. 1999b; Fast et al. 2000). None of the presrent membrane models reproduces these responses to strong shocks. Since the purpose of creating the rabbit ventricular model of defibrillation is to unravel the mechanisms of post-shock behaviour observed experimentally, we needed first to make sure that the membrane model we use reproduced the behaviour described above. This necessitated membrane model modifications.
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Vm asymmetry could not be reproduced by the natural addition of electroporation (model LRd + EP), the latter documented always to take place following strong shocks (Al Khadra et al. 2000). Only when we incorporated the outward current activated upon strong shock-induced depolarization (Ia), first suggested by Cheng et al. (1999b), did we achieve a match between simulation and experiment (Fig. 3), provided we assumed that Ia was part of the K+ flow through the L-type Ca+ channel (the model was termed aLRd model). With the use of the new aLRd model we were able to reproduce the experimentally observed rectangularly shaped positive Vm transient: negative-to-positive Vm ratio of near 2 (Cheek et al. 2000; Fast et al. 2000); stronger electroporation at the anode (Cheek & Fast, 2004); and dependence of Vm magnitude on field strength (compare Fig. 3 to Cheek et al. 2000; Fast et al. 2000). Being equipped with a membrane model, such as the aLRd, that can accurately reproduce the membrane responses to shocks (Ashihara & Trayanova, 2004) was essential to our ability to simulate tissue and organ behaviour observed experimentally, and thus to provide insight about behaviour in the depth of the tissue that cannot be assessed by the presently available experimental techniques.
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In this section, we present two studies, one on cardiac vulnerability to electric shocks (Rodriguez et al. 2005) and another on defibrillation (Trayanova et al. 2004), that illustrate the capabilities of the model and address questions raised in the beginning of this article regarding the role of ventricular anatomy in these processes.
Arrhythmogenesis following shocks administered to an isolated, paced rabbit heart. The goal of this study was to investigate the role of ventricular anatomy, specifically the geometrical differences between LV and RV in vulnerability to electric shocks. Since spatial non-uniformity of the applied electric field has been implicated in generating shock-induced polarization in addition to polarization stemming from tissue geometry and fibrous structure (Trayanova et al. 1998a; Trayanova & Skouibine, 1998; Skouibine et al. 1999; Trayanova, 1999; Lindblom et al. 2000, 2001) and is therefore a factor in shock outcome, a uniform applied field (as delivered by large external plate electrodes) was used. In this case, reversal of shock polarity acts only to change the direction of the current flow through the ventricular chambers. This allowed us to examine, for the same magnitude and configuration of the applied field, how differences between LV and RV chamber anatomy result in differences in shock-induced transmembrane potential changes and post-shock electrical activity, and thus in shock outcome. Of particular importance is knowledge regarding the location of the main post-shock excitable area formed typically by de-excitation of previously refractory myocardium (Efimov et al. 2000a; Trayanova et al. 2002a; Hillebrenner et al. 2003, 2004) in a large portion of the ventricular volume. Post-shock wavefront propagation through it is characterized by long uninterrupted pathways (Trayanova et al. 1999; Rodriguez & Trayanova, 2003) allowing for the recovery of the surrounding myocardium. Therefore, the main post-shock excitable area is directly responsible for the global electrical behaviour of the ventricles following the shock and ultimately, for shock outcome. To permit full elucidation of the role of ventricular anatomy in shock-induced vulnerability, this study used a combination of optical mapping experiments and 3-D computer simulations.
In simulations and experiments, the ventricles were paced at the apex. To ensure uniform applied field, in both approaches the shocks were delivered via two large planar electrodes located at the vertical walls of the perfusion chamber (Fig. 4, left panel). Consistent with the goal of the study, examining the change in cardiac vulnerability upon reversal of field direction necessitated the use of monophasic shocks in both simulations and experiments (8 ms duration truncated exponential waveforms of 65% tilt). The shocks were applied over a range of coupling intervals (CIs, measured with respect to the last pacing stimulus). The applied electric field was referred to as RV when the electrode near the RV was used as the cathode and the one near the LV was the earth electrode. The opposite electrode orientation was referred to as LV. Shock strength (SS) referred to the leading edge value of the electric field between the electrodes. Vulnerability areas (VAs), i.e. areas on a 2-D grid that encompass episodes of re-entry induction for various SSs and CIs, were determined for both field directions in simulations and in experiments. For each field direction, the ULV was estimated as the highest shock strength that induced sustained arrhythmia. The vulnerable window was estimated to be the interval in time between the lowest and the highest CI at which a sustained arrhythmia was induced.
Figure 6A demonstrates that the probability of arrhythmia induction is distributed differently over SSs and CIs for the two field directions. In order to combine data from different experiments, SS and CI were represented as deviations from the ULV and the longest CI in the vulnerable window (CImax), respectively. In the experiment (Fig. 6A, top panel), for RV shocks, a probability of arrhythmia induction greater than 0.2 (i.e. occurring in at least 2 rabbits) was documented for a wide range of CIs (CI–CImax from 0 to 80 ms) and for SSs ranging from 0 to 6 V cm–1 SS–ULV. For LV shocks, a probability of arrhythmia induction larger than 0.2 was found to concentrate within a much narrower CI range (CI–CImax from 0 to 40 ms). In addition, in all hearts examined, ULV occurred at CImax for LV shocks, and over a range of CIs for RV shocks (mean ULV values in the experiment were 12.2 ± 1.6 and 11 ± 2.1 V cm–1 for RV and LV shocks, respectively). The bottom panel of Fig. 6A presents VAs for both field directions as obtained from the rabbit ventricular model. For RV shocks (ULV = 9.6 V cm–1), consistent with the experimental data, VA extends over a broad CI range, from 0 to 60 ms CI–CImax and for SS ranging from 0 to 6.4 V cm–1 SS–ULV. In addition, as in the experiment, it has a somewhat rectangular shape. Reversing field direction (ULV = 12.7 V cm–1) alters VA shape in a manner similar to experimental data: the majority of arrhythmias are induced at long CIs, from 0 to 20 ms CI–CImax, and ULV is reached at CImax. Furthermore, in simulations as in experiments, only shocks of strength less than 8 V cm–1 induce arrhythmia when applied at short CIs (CI–CImax less than 20 ms).
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The difference in the 3-D shock-end transmembrane distributions between the two cases is examined in Fig. 7 for episodes inside and outside the VA. For RV shocks (Fig. 7, left panel), one observes that increasing SS by 6.4 V cm–1 from below to above the ULV for the same CI, i.e. moving vertically across the VA border (compare episode b to episode a), results in an increase in the areas strongly depolarized by the shock; the trend remains the same when CI is increased (compare episodes c and d). Furthermore, the simulation results in the left panel of Fig. 7 demonstrate that for this orientation of the applied field, regardless of SS or CI, the main post-shock excitable area is always within the LV wall (deep blue areas). The shock-end negative polarization in the RV is a thin stripe in a thin wall; the RV is thus not a major structure for post-shock propagation. For instance, in case b, by the time the wavefronts propagate through the LV excitable area, the rest of the myocardium recovers, allowing re-entry to be established. Two rotors are induced, one anticlockwise and one clockwise, on the anterior and posterior sides of the ventricles, respectively, with a common pathway in the apex (Fig. 8, top panel). The same re-entrant pattern was observed in the experiment as documented by the activation map shown in the top panel of Fig. 8. This behaviour is similar for every CI in the VA, hence the nearly rectangular shape of the VA for RV shocks.
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The combination of optical mapping experiments and 3-D computer simulation studies creates, as demonstrated by the present study, a unique opportunity to explore cardiac electrical behaviour following a defibrillation shock. The simulations provide information regarding behaviour in the depth of the ventricular walls (including the septum) unachievable by any imaging technique thus far. This study revealed that ventricular anatomy plays a major role in shock-induced electrical behaviour, and thus in the outcome of a defibrillation shock. The difference in the thickness of the ventricular walls is ultimately manifested as a preferential location of the post-shock excitable area. In addition, the location of this area determines the types of post-shock re-entrant circuits. The findings of the study are directly applicable to external defibrillation with monophasic shocks. They are also very relevant to implantable cardioverter defibrillator (ICD) electrode configurations and biphasic waveforms. In these more complex cases, a main post-shock excitable area(s) will still be developed within the 3-D volume of the tissue; it will be at least partly determined by cardiac anatomy. Identifying the location of the main post-shock excitable area could be very important for improving clinical defibrillation efficacy, since its eradication can be specifically targeted by auxiliary small magnitude shocks, resulting in a dramatic decrease in defibrillation threshold.
Spatiotemporal organization of 3-D electrical activity following defibrillation. Understanding the complex spatiotemporal dynamics of post-shock activity in the heart could be aided by the tools of non-linear dynamics (Gray et al. 1998; Larson et al. 2003). Instead of the evolution of transmembrane potential distribution in the myocardium, these tools analyse the dynamics of the phase singularities, which represent the organizing centres of re-entrant activity. Applying this approach to the post-shock activity in the 3-D volume of the rabbit model ventricles allows examination of the evolution and behaviour of the transmural post-shock filaments, the 3-D strings of phase singularities. This avenue provides a new opportunity to clarify the interaction of the shock with the preshock phase singularities that underlie VF, to evaluate how the shock itself creates phase singularity filaments, and to examine the behaviour of these filaments for failed and successful shocks. The present study provides insight into some of these issues. Specifically, it aims: (1) to establish a relationship between spatiotemporal post-shock filament dynamics, particularly the change in filament shape and location within the ventricles, and shock outcome; and (2) to relate the complexity of the preshock state (phase of VF) to shock efficacy.
Figure 9 presents three instances of post-shock activity following a successful defibrillation shock delivered to the fibrillating ventricles shown in Fig. 2. The shock was of strength 154.12 mA and was given at a shock timing of 1300 ms after VF initiation. This figure shows posterior and apical (from apex to base) semi-transparent views of both transmembrane potential and filament distributions. The 1310 ms panels depict the virtual electrode polarization at the end of the 9 ms shock and the high number of scroll-wave filaments induced by the shock. By 1320 ms, propagating wavefronts have begun to invade de-excited tissue (blue areas), and the number of filaments present has decreased owing to filament annihilation and aggregation in the limited volume of the ventricles. By 1330 ms, the number of filaments has significantly decreased. All defibrillation episodes, both successful and failed, produced post-shock behaviour similar to the one portrayed in Fig. 9 over the same post-shock time interval.
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Figure 11 examines the type of the filaments and their location in the ventricles. Three timings following the shock, 30, 100 and 300 ms, are presented for each location. The individual histograms depict the number of filaments of each type (I, O, U or transitional) as a function of shock strength. Since half of the shocks are successful, the number of filaments in these cases is zero at 300 ms in all three major parts of the ventricles; it is also already zero at 100 ms at some locations in the ventricles. The weakest shock strength does not produce filaments in the LV.
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The majority of type O filaments (vortex rings), the most unstable filaments, are formed early after the shock. In Fig. 11, their number is the largest at t= 30 ms. Early septal activity appears dominated by vortex rings (in addition to transitional types). The initial number of O filaments (see t= 30 ms) is also the smallest in the RV. While some vortex rings are found in the later stages of ventricular activity, they seem to appear only in the LV and the septum, which are the thicker walls. One further observes that early after the end of the shock, type I filaments are found only in the RV (see histograms at t= 30 ms). However, regardless of location, type I is the dominant filament type in the activity sustained for more than 200 ms following the shock; as the histograms at t= 300 ms indicate, every failed shock is characterized with the formation of type I filaments in the three major parts of the ventricles. Finally, type U filaments are the main filament type in the LV during the first 100 ms after the shock. They are also a major player in the early RV activity.
Figure 11 also reveals that for successful shocks, the post-shock filament activity in the time interval 100–200 ms (right before all filaments disappear) is located only in the LV; the majority of these filaments are type U. Thus, in the case of successful shocks, the activity in the septum and the RV is extinguished earlier, with re-entry lingering only in the LV before the final annihilation of the remaining filaments. In fact, most of these remaining LV filaments are located on the epicardial surface of the LV. For failed shocks, the histograms demonstrate that the activity during this time interval is characterized by a lower overall number of filaments. This is consistent with the (nearly) flat stretch of the curves shown in Fig. 10.
In conclusion, the presented simulations of defibrillation in the rabbit ventricular model reveal that the number of shock-induced scroll-wave filaments is the largest at the end of the shock and rapidly decreases in the first 100 ms following shock delivery. For all successful shocks, the filaments disappear completely within 250 ms of post-shock activity. For all failed shocks, the number of filaments increases again after 200–250 ms of post-shock activity. One of the most significant findings in this paper is that, in the case of shock success, the activity is maintained only in the LV, while in the RV and the septum the filaments vanish earlier. Thus, for successful shocks, re-entry in fact takes place only in the LV, while transient ‘seeds’ of re-entry that do not develop into full-blown circuits appear at all three major parts of the ventricles. Finally, the results reveal that the transitions between the various types of filaments are most frequent at the early stages of post-shock activity. Type I is the dominant filament type of the activity sustained for more than 200 ms after the shock, particularly in the RV.
Limitations and future directions
While the presented studies demonstrate an excellent match between simulation and experiment in terms of the pattern of VEP and shock-induced propagation, there remains a discrepancy between the values of simulated and measured VEP. The reason for this is that the optically recorded signal is distorted by photon scattering in the myocardium. In order to achieve a match between simulation and experiment in terms of shock-induced transmembrane potential values, the formation of optical signals based on transmembrane potential maps in the rabbit ventricles needs to be modelled. We have recently developed the first stage of such a model, and it is our hope that with the use of this model we can achieve in the future a more meaningful comparison between simulation results and experimental data. An important further step in this direction is to obtain a rabbit ventricular cell model that is based on experimental data for the membrane response to strong shocks, rather than relaying on ad hoc adjustments of ionic models to represent defibrillation.
The 3-D model of defibrillation in the rabbit ventricles presented here is homogeneous, i.e. it does not incorporate microscale heterogeneities present in the myocardium; these might have significant effects on VEP, particularly under the conditions of fibrosis. Furthermore, the defibrillation mechanisms presented here might be altered in the diseased heart, where ischaemia and infarction are bound to modify the substrate for arrhythmigenesis following defibrillation shocks.
Concluding remarks
The two example studies included in this review article, one on vulnerability to electric shocks and one on defibrillation, clearly demonstrate the power of realistic modelling in revealing electrical behaviour hidden within the cardiac wall. When matched to experimental observations of behaviour during and after the shock over the cardiac surfaces, realistic whole-organ simulations become invaluable in elucidating the mechanisms of ventricular defibrillation. Insights into vulnerability and defibrillation such as those presented here are unachievable with experimental methodology alone owing to its present lack of ability to provide, with sufficient resolution, information about the 3-D electrical activity in the heart following defibrillation shocks.
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