Stimulus-induced critical point. Mechanism for electrical initiation of reentry in normal canine myocardium

Cathodal stimulation in the recovery phase of a propagating planar wave in the rabbit heart reveals four stimulation mechanisms

The stimulation of cardiac tissue in the recovery phase has significant importance in relation to reentry induction. In the theoretical experiment proposed by Winfree, termed the 'pinwheel' experiment, a point stimulus (S2) is applied in the wake of a freely propagating planar wave (S1). Reentry induced from this S1-S2 pinwheel protocol has been observed experimentally in heart preparations. However, in these experiments, which focused on activation outcomes, only mapping of extracellular voltages has been conducted. The lack of transmembrane potential (Vm) distribution data makes it impossible to analyse the underlying stimulation mechanisms which precede the reentry induction. In this work we sought to elucidate the stimulation mechanisms throughout the heart cycle using the pinwheel protocol. We examined the cardiac tissue responses during and immediately after cathodal stimulation in the refractory wake of a propagating planar wave. The voltage-sensitive dye di-4-ANEPPS was utilized to measure Vm directly from quasi two-dimensional preparations of cryoablated Langendorff-perfused rabbit hearts. Four stimulation mechanisms were observed that depended on the Vm magnitude during S2 cathodal stimulation. Make stimulation always occurred during diastolic stimulation. When stimulation was at the beginning of the relative refractory period (RRP), transitional make-break stimulation was detected. During the RRP the excitation was due to the break mechanism. While approaching the effective refractory period (ERP), the tissue response is characterized by a damped wave mediated response. These four stimulation mechanisms were observed in all hearts whether the S1 planar wave propagation was parallel or perpendicular to the fibre direction. This study is the first examination of Vm and the stimulation mechanisms throughout the cardiac cycle using the pinwheel protocol, and the results have implications in the development and improvement of pacing protocols for artificial cardiostimulators.

Intracellular calcium and vulnerability to fibrillation and defibrillation in Langendorff-perfused rabbit ventricles

BACKGROUND

The role of intracellular calcium (Ca(i)) in defibrillation and vulnerability is unclear.

METHODS AND RESULTS

We simultaneously mapped epicardial membrane potential and Ca(i) during shock on T-wave episodes (n=104) and attempted defibrillation episodes (n=173) in 17 Langendorff-perfused rabbit ventricles. Unsuccessful and type B successful defibrillation shocks were followed by heterogeneous distribution of Ca(i), including regions of low Ca(i) surrounded by elevated Ca(i) ("Ca(i) sinkholes") 31+/-12 ms after shock. The first postshock activation then originated from the Ca(i) sinkhole 53+/-14 ms after the shock. No sinkholes were present in type A successful defibrillation. A Ca(i) sinkhole also was present 39+/-32 ms after a shock on T that induced ventricular fibrillation, followed 22+/-15 ms later by propagated wave fronts that arose from the same site. This wave propagated to form a spiral wave and initiated ventricular fibrillation. Thapsigargin and ryanodine significantly decreased the upper limit of vulnerability and defibrillation threshold. We studied an additional 7 rabbits after left ventricular endocardial cryoablation, resulting in a thin layer of surviving epicardium. Ca(i) sinkholes occurred 31+/-12 ms after the shock, followed in 19+/-7 ms by first postshock activation in 63 episodes of unsuccessful defibrillation. At the Ca(i) sinkhole, the rise of Ca(i) preceded the rise of epicardial membrane potential in 5 episodes.

CONCLUSIONS

There is a heterogeneous postshock distribution of Ca(i). The first postshock activation always occurs from a Ca(i) sinkhole. The Ca(i) prefluorescence at the first postshock early site suggests that reverse excitation-contraction coupling might be responsible for the initiation of postshock activations that lead to ventricular fibrillation.

Dispersion of repolarization and refractoriness are determinants of arrhythmia phenotype in transgenic mice with long QT

Enhanced dispersion of repolarization (DR) and refractoriness may be a unifying mechanism central to arrhythmia genesis in the long QT (LQT) syndrome. The role of DR in promoting arrhythmias was investigated in several strains of molecularly engineered mice: (a) Kv4.2 dominant negative transgenic (Kv4.2DN) that lacks the fast component of the transient outward current, I(to,f), have action potential (AP) and QT prolongation, but no spontaneous arrhythmias, (b) Kv1.4 targeted mice (Kv1.4-/-) that lack the slow component of I(to) (I(to,s)), have no QT prolongation and no spontaneous arrhythmias, and (c) double transgenic (Kv4.2DN x Kv1.4-/-) mice that lack both I(to,f) and I(to,s), have AP and QT prolongation, and spontaneous ventricular tachyarrhythmias. Hearts were perfused, stained with di-4-ANEPPS and optically mapped. Activation patterns and conduction velocities were similar between the strains but AP duration at 75% recovery (APD75) was longer in Kv4.2DN (28.0 +/- 2.5 ms, P < 0.01, n = 6), Kv1.4-/- (28.4 +/- 0.4 ms, P < 0.01, n = 5) and Kv4.2DN x Kv1.4-/- (34.3 +/- 2.6 ms, P < 0.01, n = 6) mice than controls (20.3 +/- 1.0 ms, n = 5). Dispersion of refractoriness between apex and base was markedly reduced in Kv4.2DN (0.3 +/- 0.5 ms, n = 6, P < 0.05) but enhanced in Kv1.4-/- (14.2 +/- 2.0 ms, n = 5, P < 0.05) and Kv4.2DN x Kv1.4(-/-) (15.0 +/- 3 ms, n = 5, P < 0.5) mice compared with controls (10 +/- 2 ms, n = 5). A premature pulse elicited ventricular tachycardia (VT) in Kv1.4-/- (n = 4/5) and Kv4.2DN x Kv1.4-/- hearts (n = 5/5) but not Kv4.2DN hearts (n = 0/6). Voltage-clamp recordings showed that I(to,f) was 30% greater in myocytes from the apex than base which may account for the absence of DR in Kv4.2DN mice. Thus, dispersion of repolarization (DR) appears to be an important determinant of arrhythmia vulnerability.

Role of intramural virtual electrodes in shock-induced activation of left ventricle: Optical measurements from the intact epicardial surface

BACKGROUND

According to one hypothesized mechanism of defibrillation, shocks directly excite the bulk of ventricular myocardium in the excitable state due to intramural virtual electrodes; however, this hypothesis has not been examined in intact myocardium.

OBJECTIVES

The purpose of this study was examine the role of intramural virtual electrodes in shock-induced activation of intact left ventricular (LV) tissue.

METHODS

Twelve isolated porcine LV preparations were stained with a transmembrane potential (V(m))-sensitive dye by two methods: (1) surface staining and (2) global staining via coronary perfusion. Shocks (E approximately 0.8-48 V/cm, duration = 10 ms) were applied across the wall from epicardium to endocardium during diastole via transparent electrodes. Shock-induced V(m) responses were measured optically from the intact epicardial surface after surface staining and global staining.

RESULTS

Surface-staining recordings demonstrated different V(m) responses to cathodal and anodal shocks. Whereas cathodal shocks caused depolarization and rapid activation of the epicardial surface, anodal shocks induced hyperpolarization and delayed surface activation. In contrast, global-staining V(m) responses to cathodal and anodal shocks were qualitatively similar. Both responses were characterized by activation with small latency and rapid propagation. Weak shocks of both polarities induced monotonic action potential upstrokes; stronger shocks induced nonmonotonic upstrokes with two rising phases at shock onset and end. Such features of global-staining V(m) responses as make activation of the epicardium by anodal shocks and the nonmonotonic action potential upstrokes can be explained by the presence of subepicardial intramural virtual electrodes.

CONCLUSION

These data suggest that shocks induce intramural virtual electrodes that directly excite LV tissue and account for the shape of optical V(m) responses recorded from the epicardial surface.

The effect of the fiber curvature gradient on break excitation in cardiac tissue

BACKGROUND

Break excitation has been hypothesized as a mechanism for the initiation of reentry in cardiac tissue. One way break excitation can occur is by virtual electrodes formed due to a curving fiber geometry. In this article, we are concerned with the relationship between the peak gradient of fiber curvature and the threshold for break stimulation and the initiation of reentry.

METHODS

We calculate the maximum gradient of fiber curvature for different scales of fiber geometry in a constant tissue size (20x20 mm), and also examine the mechanisms by which reentry initiation fails.

RESULTS

For small peak gradients, reentry fails because break excitation does not occur. For larger peak gradients, reentry fails because break excitation fails to develop into full-scale reentry. For strong stimuli above the upper limit of vulnerability, reentry fails because the break excitation propagates through the hyperpolarized region and then encounters refractory tissue, causing the wave front to die.

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles

Unidirectional conduction block of premature extrasystoles can lead to initiation of cardiac reentry, causing lethal arrhythmias including ventricular fibrillation. Multiple extrasystoles are often more effective at inducing unidirectional conduction block and reentry than a single extrasystole. Since the substrate for conduction block is spatial dispersion of refractoriness, in this study we investigate how the first extrasystole modulates this dispersion to influence the "vulnerable window" for conduction block by subsequent extrasystoles, particularly in relation to action potential duration restitution and conduction velocity restitution properties. Using a kinematic model to represent wavefront-waveback interactions and simulations with the Luo-Rudy model in a one-dimensional cable of cardiac cells, we show that in homogeneous tissue, a premature extrasystole can create a large dispersion of refractoriness leading to conduction block of a subsequent extrasystole. In heterogeneous tissue, however, a premature extrasystole can either reduce or enhance the dispersion of refractoriness depending on its propagation direction with respect to the previous beat. With multiple extrasystoles at random coupling intervals, vulnerability to conduction block is proportional to their number. In general, steep action potential duration restitution and broad conduction velocity restitution promote dispersion of refractoriness in response to multiple extrasystoles, and thus enhance vulnerability to conduction block. These restitution properties also promote spatially discordant alternans, a setting which is particularly prone to conduction block. The equivalent dispersion of refractoriness created dynamically in homogeneous tissue by spatially discordant alternans is more likely to cause conduction block than a comparable degree of preexisting dispersion in heterogeneous tissue.

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 1: single extrasystoles

Spatial dispersion of refractoriness, which is amplified by genetic diseases, drugs, and electrical and structural remodeling during heart disease, is recognized as a major factor increasing the risk of lethal arrhythmias and sudden cardiac death. Dispersion forms the substrate for unidirectional conduction block, which is required for the initiation of reentry by extrasystoles or rapid pacing. In this study, we examine theoretically and numerically how preexisting gradients in refractoriness control the vulnerable window for unidirectional conduction block by a single premature extrasystole. Using a kinematic model to represent wavefront-waveback interactions, we first analytically derived the relationship (under simplified conditions) between the vulnerable window and various electrophysiological parameters such as action potential duration gradients, refractoriness barriers, conduction velocity restitution, etc. We then compared these findings to numerical simulations using the kinematic model or the Luo-Rudy action potential model in a one-dimensional cable of cardiac cells. The results from all three methods agreed well. We show that a critical gradient in action potential duration for conduction block can be analytically derived, and once this critical gradient is exceeded, the vulnerable window increases proportionately with the refractory barrier and is modulated by conduction velocity restitution and gap junctional conductance. Moreover, the critical gradient for conduction block is higher for an extrasystole traveling in the opposite direction from the sinus beat than for one traveling in the same direction (e.g., an epicardial extrasystole versus an endocardial extrasystole).

Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: a computational study

Background

Regional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood.

Methods

We simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution.

Results

Wavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms).

Conclusion

Regional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve.

Effect of plunge electrodes in active cardiac tissue with curving fibers

OBJECTIVES

Our goal is to determine if plunge electrodes change how the heart responds to electrical stimulation.

BACKGROUND

Several experiments designed to study the induction of a rotor in cardiac tissue have used plunge electrodes to measure the transmural potential. It is our hypothesis that these electrodes may have affected the electrical response of the tissue to a shock.

METHODS

We previously have shown that a single plunge electrode in two-dimensional, passive cardiac tissue induces a significant transmembrane potential when stimulated by a large shock. In this study, we expand our simulation to include an array of nine electrodes in active tissue with curving fibers. We compare the thresholds for rotor induction in tissue with and without electrodes by initiating a planar S1 wavefront and then stimulating the tissue at different intervals with a uniform S2 electric field perpendicular to S1. In tissue without plunge electrodes, virtual electrode polarization due to the curving fibers is generally widespread over the entire tissue, whereas polarization tends to be localized around the electrodes in tissue including them.

RESULTS

Our results show that at some S1-S2 intervals, the presence of plunge electrodes can result in reentry when it otherwise would not be possible. For other S1-S2 intervals, such as during the vulnerable period when the reentry threshold is at a minimum, the induction of reentry is unaffected by the presence of plunge electrodes.

CONCLUSIONS

Plunge electrodes can play an important role during the stimulation of cardiac tissue, but this is highly dependent on the chosen S1-S2 interval.

Modeling wave propagation in realistic heart geometries using the phase-field method

We present a novel algorithm for modeling electrical wave propagation in anatomical models of the heart. The algorithm uses a phase-field approach that represents the boundaries between the heart muscle and the surrounding medium as a spatially diffuse interface of finite thickness. The chief advantage of this method is to automatically handle the boundary conditions of the voltage in complex geometries without the need to track the location of these boundaries explicitly. The algorithm is shown to converge accurately in nontrivial test geometries with no-flux (zero normal current) boundary conditions as the width of the diffuse interface becomes small compared to the width of the cardiac action potential wavefront. Moreover, the method is illustrated for anatomically realistic models of isolated rabbit and canine ventricles as well as human atria.

Of circles and spirals: Bridging the gap between the leading circle and spiral wave concepts of cardiac reentry

The “leading circle model” was the first detailed attempt at understanding the mechanisms of functional reentry, and remains a widely-used notion in cardiac electrophysiology. The “spiral wave” concept was developed more recently as a result of modern theoretical analysis and is the basis for consideration of reentry mechanisms in present biophysical theory. The goal of this paper is to present these models in a way that is comprehensible to both the biophysical and electrophysiology communities, with the idea of helping clinical and experimental electrophysiologists to understand better the spiral wave concept and of helping biophysicists to understand why the leading circle concept is so attractive and widely used by electrophysiologists. To this end, the main properties of the leading circle and spiral wave models of reentry are presented. Their basic assumptions and determinants are discussed and the predictions of the two concepts with respect to pharmacological responses of arrhythmias are reviewed. A major difference between them lies in the predicted responses to Na+-channel blockade, for which the spiral wave paradigm appears more closely to correspond to the results of clinical and experimental observations. The basis of this difference is explored in the context of the fundamental properties of the models.

Refractory Gradient is Responsible for the Increase in Ventricular Vulnerability Under Sodium Channel Blockade

BACKGROUND

Previous studies have shown that sodium channel (I(Na)) blockade increases ventricular vulnerability; however, there were differences in the degree of the increase. Because the vulnerable window (VW) is altered by the type of preshock refractory gradient (RG), the hypothesis was that the differences in the arrhythmogenesis of I(Na) blockade result from the different types of preshock RG employed.

METHODS AND RESULTS

Simulations of regio(Na)l electric shock following constant pacing stimuli in 2-dimensional bidomain myocardial sheets under I(Na) blockade were conducted using 3 types of preshock RG: longitudinally tilted (LRG), transversely tilted (TRG), and non-tilted RG (NRG). The increase in the degree of I(Na) blockade almost linearly decreased the conduction velocity. The action potential duration in the LRG and TRG cases was non-linearly shortened with the increase in INa blockade because of electrotonic influences, whereas in the case of NRG it was slightly prolonged. In both LRG and TRG cases, the VW for reentry induction by electric shock was considerably widened by the INa blockade; however, this was not the case for NRG in which the VW was rather narrowed by the INa blockade.

CONCLUSION

The type of preshock RG alters the degree of the increase in ventricular vulnerability under INa blockade.

Electrophysiological mechanisms of ventricular fibrillation induction

Ventricular fibrillation (VF) is known as a main responsible cause of sudden cardiac death which claims thousands of lives each year. Although the mechanism of VF induction has been investigated for over a century, its definite mechanism is still unclear. In the past few decades, the development of new advance technologies has helped investigators to understand how the strong stimulus or the shock induces VF. New hypotheses have been proposed to explain the mechanism of VF induction. This article reviews most commonly proposed hypotheses that are believed to be the mechanism of VF induction.

Molecular mechanisms and global dynamics of fibrillation: an integrative approach to the underlying basis of vortex-like reentry

Art Winfree's scientific legacy has been particularly important to our laboratory whose major goal is to understand the mechanisms of ventricular fibrillation (VF). Here, we take an integrative approach to review recent studies on the manner in which nonlinear electrical waves organize to result in VF. We describe the contribution of specific potassium channel proteins and of the myocardial fiber structure to such organization. The discussion centers on data derived from a model of stable VF in the Langendorff-perfused guinea pig heart that demonstrates distinct patterns of organization in the left (LV) and right (RV) ventricles. Analysis of optical mapping data reveals that VF excitation frequencies are distributed throughout the ventricles in clearly demarcated domains. The highest frequency domains are found on the anterior wall of the LV at a location where sustained reentrant activity is present. The optical data suggest that a high frequency rotor that remains stationary in the LV is the mechanism that sustains VF in this model. Computer simulations predict that the inward rectifying potassium current (IK1) is an essential determinant of rotor stability and frequency, and patch-clamp results strongly suggest that the outward component of IK1 of cells in the LV is significantly larger than in the RV. Additional computer simulations and analytical procedures predict that the filaments of the reentrant activity (scroll waves) adopt a non-random configuration depending on fiber organization within the ventricular wall. Using the minimal principle we have concluded that filaments align with the trajectory of least resistance (i.e. the geodesic) between their endpoints. Overall, the data discussed have opened new and potentially exciting avenues of research on the possible role played by inward rectifier channels in the mechanism of VF, as well as the organization of its reentrant sources in three-dimensional cardiac muscle. Such an integrative approach may lead us toward an understanding of the molecular and structural basis of VF and hopefully to new preventative approaches.

Dynamics of virtual electrode-induced scroll-wave reentry in a 3D bidomain model

Functional reentry in the heart can be caused by a wave front of excitation rotating around its edge. Previous simulations on the basis of monodomain cable equations predicted the existence of self-sustained, vortex-like wave fronts (scroll waves) rotating around a filament in three dimensions. In our simulations, we used the more accurate bidomain model with modified Beeler-Reuter ionic kinetics to study the dynamics of scroll-wave filaments in a 16 x 8 x 1.5-mm slab of ventricular tissue with straight fibers. Wave fronts were identified as the areas with inward current. Their edges represented the filaments. Both transmural and intramural reentries with I- and U-shaped filaments, respectively, were obtained by the S1-S2 point stimulation protocol through the virtual electrode-induced phase singularity mechanism. The filaments meandered along elongated trajectories and tended to attach to the tissue boundaries exposed to air (no current flow) rather than to the bath (zero extracellular potential). They completely detached from electroporated (zero transmembrane potential) boundaries. In our simulations, the presence of the bath led to generation of only U-shaped filaments, which survived for the 1.5-mm-thick slab but not for the slabs of 0.5- or 3-mm thicknesses. Thus boundary conditions may be another determinant of the type and dynamics of reentry.

Activation sequences following failed atrial defibrillation

OBJECTIVES

The purposes of this study were to examine the first activations following atrial defibrillation shocks to help understand how and where atrial fibrillation (AF) relapsed following failed shocks and to assess the difference in postshock activation between failed and successful shocks.

BACKGROUND

While many studies have investigated the mechanism of ventricular defibrillation, much less is known about the mechanisms of AF.

METHODS

Sustained AF was induced electrically after pericardial infusion of methylcholine in 10 sheep. Biphasic subthreshold shocks were delivered to three configurations: right atrium to distal coronary sinus (RA-CS), sequential shocks with RA-CS as the first pathway followed by proximal CS to superior vena cava as the second pathway (Sequential), and right ventricle to superior vena cava plus can (V-triad). In eight sheep, global atrial mapping was performed with 504 electrodes spaced 3 to 4 mm apart.

RESULTS

Earliest postshock activations mostly arose from the left atrium for V-triad but arose from either atrium for RA-CS and Sequential. Preshock AF cycle lengths were significantly shorter at the earliest activation sites than at seven of eight other sites globally distributed over both atria. In all type B successful episodes in which one or more rapid activations occurred after the shock and in 50 of the 72 failed episodes analyzed, activation fronts spread away from the earliest site in a focal pattern, and discrete nonfragmented activation complexes were present in the first derivatives of the electrograms. In the other 22 failed episodes, earliest activation fronts spread in a nonfocal pattern, and earliest postshock electrogram derivatives were fractionated. To better interpret the activation pattern in the fragmented regions, a 504 electrode plaque with 1.5-mm electrode spacing was placed on the right atrial appendage in two additional sheep. In 11 of 108 failed episodes, earliest postshock activation appeared inside the plaque and spread in a focal pattern with nonfragmented electrogram derivatives in 10 episodes and in a reentrant pattern with fragmented electrogram derivatives in the other.

CONCLUSIONS

(1) The electrode configuration influenced the location of earliest postshock activation. (2) Earliest postshock activation occurred where the preshock AF cycle length was short. (3) Earliest activations following all type B successful and most failed episodes were not fragmented and spread in a focal pattern. (4) The region of earliest postshock activation in the failed episodes without a focal postshock activation pattern exhibited regions of fragmented electrogram derivatives that may represent conduction block and possibly reentry.

Examination of optical depth effects on fluorescence imaging of cardiac propagation

Optical mapping with voltage-sensitive dyes provides a high-resolution technique to observe cardiac electrodynamic behavior. Although most studies assume that the fluorescent signal is emitted from the surface layer of cells, the effects of signal attenuation with depth on signal interpretation are still unclear. This simulation study examines the effects of a depth-weighted signal on epicardial activation patterns and filament localization. We simulated filament behavior using a detailed cardiac model, and compared the signal obtained from the top (epicardial) layer of the spatial domain with the calculated weighted signal. General observations included a prolongation of the action upstroke duration, early upstroke initiation, and reduction in signal amplitude in the weighted signal. A shallow filament was found to produce a dual-humped action potential morphology consistent with previously reported observations. Simulated scroll wave breakup exhibited effects such as the false appearance of graded potentials, apparent supramaximal conduction velocities, and a spatially blurred signal with the local amplitude dependent upon the immediate subepicardial activity; the combination of these effects produced a corresponding change in the accuracy of filament localization. Our results indicate that the depth-dependent optical signal has significant consequences on the interpretation of epicardial activation dynamics.

Basic mechanisms of cardiac impulse propagation and associated arrhythmias

Propagation of excitation in the heart involves action potential (AP) generation by cardiac cells and its propagation in the multicellular tissue. AP conduction is the outcome of complex interactions between cellular electrical activity, electrical cell-to-cell communication, and the cardiac tissue structure. As shown in this review, strong interactions occur among these determinants of electrical impulse propagation. A special form of conduction that underlies many cardiac arrhythmias involves circulating excitation. In this situation, the curvature of the propagating excitation wavefront and the interaction of the wavefront with the repolarization tail of the preceding wave are additional important determinants of impulse propagation. This review attempts to synthesize results from computer simulations and experimental preparations to define mechanisms and biophysical principles that govern normal and abnormal conduction in the heart.

Spatiotemporal correlation between phase singularities and wavebreaks during ventricular fibrillation

Phase Singularity and Wavebreak.

INTRODUCTION

Phase maps and the detection of phase singularities (PSs) have become a well-developed method for characterizing the organization of ventricular fibrillation (VF). How precisely PS colocalizes with wavebreak (WB) during VF, however, is unknown.

METHODS AND RESULTS

We performed optical mapping of 27 episodes of VF in nine Langendorff-perfused rabbit hearts. A WB is a point where the activation wavefront and the repolarization waveback meet. A PS is a site where its phase is ambiguous and its neighboring pixels exhibit a continuous phase progression from -pi to +pi. The correlation coefficient between the number of WBs and PSs was 0.78 +/- 0.09 for each heart and 0.81 for all VF episodes (P < 0.001), indicating a significant temporal correlation. We then superimposed the WBs and PSs for every 100 frames of each episode. These maps showed a high degree of spatial colocalization. To quantify spatial colocalization, the spatial shifts between the cumulative maps of WBs and PSs in corresponding frames were calculated by automatic alignment to obtain maximum overlap between these two maps. The spatial shifts were 0.04 +/- 0.31 mm on the x-axis and 0.06 +/- 0.27 mm on the y-axis over a 20 x 20 mm2 mapped field, indicating highly significant spatial correlation.

CONCLUSION

Phase mapping provides a convenient and robust approach to quantitatively describe wave propagation and organization during VF. The close spatiotemporal correlation between PSs and WBs establishes that PSs are a valid alternate representation of WB during VF and further validated the use of phase mapping in the study of VF dynamics.

Optical mapping of transmural activation induced by electrical shocks in isolated left ventricular wall wedge preparations

INTRODUCTION

It is believed that electrical shocks interrupt fibrillation by directly stimulating the bulk of ventricular myocardium in excitable states, but how shocks activate intramural tissue layers is not known. In this study, Vm responses and transmural activation patterns induced by shocks during diastole were measured in isolated coronary perfused preparations of porcine left ventricle.

METHODS AND RESULTS

Rectangular shocks (duration = 10 ms; field strength, E = 1-44 V/cm) were applied across preparations (thickness = 14.9 +/- 2.5 mm, n = 9) via large mesh electrodes during diastole or action potential (AP) plateau. Vm responses at the transmural surface were measured using optical mapping technique (resolution = 1.2 mm). Depending on shock strength, three types of Vm responses were observed. (1) Weak shocks (E approximately 1-4 V/cm) applied in diastole induced APs with simple monophasic upstrokes. The latency and time of transmural activation (TTA) rapidly decreased with increasing shock strength. Earliest activation occurred predominantly at the cathodal side of preparations in the areas that exhibited maximal DeltaVm during AP plateau. (2) Intermediate shocks (E approximately 4-23 V/cm) induced monophasic and biphasic upstrokes that were paralleled with predominantly negative plateau DeltaVm. Activation was initiated at multiple transmural sites and rapidly spread across the myocardial wall (TTA = 0.6 +/- 0.2 ms). (3) Very strong shocks (E approximately 23-44 V/cm) could cause triphasic upstrokes, likely reflecting occurrence of membrane electroporation, and delayed activation (TTA = 6.7 +/- 3.8 ms) at sites of largest negative plateau DeltaVm.

CONCLUSION

Shocks applied during diastole cause direct and rapid (within 1 ms) activation of ventricular bulk over a wide range of shock strengths, supporting the excitatory hypothesis of defibrillation. Very strong shocks can cause multiphasic Vm responses and delayed activation.

Evolution of activation patterns during long-duration ventricular fibrillation in dogs

Although resuscitation for sudden cardiac arrest attempts are frequently not instituted for several minutes after the onset of ventricular fibrillation (VF), previous mapping studies have examined only the first 40 s of VF or have involved isolated perfused hearts that did not become ischemic during VF. We applied quantitative pattern analysis to mapping data throughout the first 10 min of VF acquired from a 21 x 24 unipolar electrode array located on the ventricular epicardium of six open-chest dogs. The following twelve descriptors were continuously quantified: 1) number of wavefronts, 2) incidence of reentry, 3) wavefront propagation velocity, 4) incidence of breakthrough/focus, 5) incidence of block, 6) mean area activated by the wavefronts, 7) wavefront fractionations, 8) wavefront collisions, 9) multiplicity index, 10) repeatability, 11) negative peak rate of voltage change, and 12) peak frequency of activation. Cluster analysis of these descriptors divided VF into five stages (stages i-v). The values of most descriptors (except block and breakthrough incidence) increased during stage i (1-11 s after VF induction) and maintained high values with rapid dynamic fluctuations during stage ii (12-62 s). Descriptors changed quickly to values indicating greater organization during stage iii (63-86 s), decreased steadily during stage iv (87-310 s), and approached zero during stage v (311-600 s). There was a high incidence of reentry just before, during, and after stage iii. In conclusion, during the first 10 min, VF can be divided into five stages according to the evolution of electrophysiological characteristics. All of the parameters show a rapid deterioration during VF, except for a temporary reversal approximately 1 min after induction when activation briefly became more organized. Thus a quantitative description of activation does not uniformly decrease as VF progresses, but undergo rapid changes and exhibit a brief interval of increased organization after approximately 1 min of VF. Further studies are warranted to determine whether these changes, particularly the increased organization of stage iii, have clinical consequences, such as an alteration in defibrillation efficacy.

Filament behavior in a computational model of ventricular fibrillation in the canine heart

The aim of this paper was to quantify the behavior of filaments in a computational model of re-entrant ventricular fibrillation. We simulated cardiac activation in an anisotropic monodomain with excitation described by the Fenton-Karma model with Beeler-Reuter restitution, and geometry by the Auckland canine ventricle. We initiated re-entry in the left and right ventricular free walls, as well as the septum. The number of filaments increased during the first 1.5 s before reaching a plateau with a mean value of about 36 in each simulation. Most re-entrant filaments were between 10 and 20 mm long. The proportion of filaments touching the epicardial surface was 65%, but most of these were visible for much less than one period of re-entry. This paper shows that useful information about filament dynamics can be gleaned from models of fibrillation in complex geometries, and suggests that the interplay of filament creation and destruction may offer a target for antifibrillatory therapy.

Effects of lidocaine on shock-induced vulnerability

INTRODUCTION

Lidocaine is known to increase the defibrillation threshold (DFT) of monophasic shocks (MS) and have no effect on DFT of biphasic shocks (BS). The aim of this study was to enhance our understanding of the mechanisms of vulnerability and defibrillation through the investigation of this difference.

METHODS AND RESULTS

We studied the effect of 15 microM lidocaine on shock-induced vulnerability using fluorescent imaging of Langendorff-perfused rabbit hearts. Vulnerability was assessed as vulnerable window with shock strengths of 15 to 150 V and vulnerable period (VP) with shock delivery phase of 0% to 100% of action potential duration (% APD). With MS, lidocaine caused a significant increase in both the upper limit of vulnerability (ULV, 71 +/- 17 V vs 120 +/- 1.5 V, P < 0.01) and upper limit of VP (91 +/- 8.0% APD vs 110 +/- 4.2% APD, P < 0.01). With BS, lidocaine had no effect on ULV (40 +/- 3.4 V vs 45 +/- 4.5 V) and did not increase the upper limit of VP (78 +/- 8.9% APD vs 96 +/- 12% APD, P < 0.01). Lidocaine caused reduction of the conduction velocity during pacing (0.58 +/- 0.08 m/s vs 0.44 +/- 0.05 m/s, P < 0.01), shock-induced break excitation (0.82 +/- 0.17 m/s vs 0.30 +/- 0.07 m/s, P < 0.01), and postshock reentry (0.34 +/- 0.07 m/s vs 0.19 +/- 0.08 m/s, P < 0.01). Lidocaine had no effect on shock-induced virtual electrode polarization.

CONCLUSION

Lidocaine increased MS ULV due to slowing of shock-induced break-excitation wavefronts, which resulted in enhanced probability of survival of virtual electrode induced phase singularity. Lidocaine had no effect on BS ULV because no break excitation was induced by BS. Reduction of conduction velocity by lidocaine resulted in increased dispersion of repolarization and led to upper limit of VP increase for both MS and BS.

Toward an understanding of the molecular mechanisms of ventricular fibrillation

A major goal of basic research in cardiac electrophysiology is to understand the mechanisms responsible for ventricular fibrillation (VF). Here we review recent experimental and numerical results, from the ion channel to the organ level, which might lead to a better understanding of the cellular and molecular mechanisms of VF. The discussion centers on data derived from a model of stable VF in the Langendorff-perfused guinea pig heart that demonstrate distinct patterns of organization in the left (LV) and right (RV) ventricles. Analysis of optical mapping data reveals that VF excitation frequencies are distributed throughout the ventricles in clearly demarcated domains. The highest frequency domains are usually found on the anterior wall of the LV, demonstrating that a high frequency reentrant source (a rotor) that remains stationary in the LV is the mechanism that sustains VF in this model. Computer simulations predict that the inward rectifying potassium current (IK1) is an essential determinant of rotor stability and rotation frequency, and patch-clamp results strongly suggest that the outward component of the background current (presumably IK1) of cells in the LV is significantly larger in the LV than in the RV. These data have opened a new and potentially exciting avenue of research on the possible role played by inward rectifier channels in the mechanism of VF and may lead us toward an understanding of its molecular basis and hopefully lead to new preventative approaches.

Shock-Induced Epicardial and Endocardial Virtual Electrodes Leading to Ventricular Fibrillation via Reentry, Graded Responses, and Transmural Activation

INTRODUCTION

The mechanism of ventricular fibrillation (VF) induction by T wave shocks has been attributed to reentry, propagated graded responses (PGR), and triggered activity. The limitation of recording transmembrane potential (V(m)) from only a single surface has hampered efforts to elucidate the relative role of these phenomena and their relationship to shock-induced virtual electrodes.

METHODS AND RESULTS

V(m) patterns from epicardial and endocardial surfaces of isolated sheep right ventricles were recorded with two CCD cameras for monophasic (M) and biphasic (B) shocks delivered at various coupling intervals (CI) from a unipolar mesh electrode on the epicardium. VF was induced via (1) the formation of reentry following make or break excitation; (2) propagated graded responses during apparent isoelectric window; and (3) breakthrough activation patterns coincident with endocardial-to-epicardial gradients in V(m). M shocks depolarized both surfaces at long CIs and polarized epicardial and endocardial surfaces oppositely at short CIs. At intermediate CIs, postshock V(m) patterns could lead to reentry on one surface or endocardial-to-epicardial gradients resulting in breakthrough. B induced VF less than M for short and intermediate CIs due to more homogeneous end-shock V(m) patterns. However, at long CIs these homogeneous patterns resulted in more VF induction because B left the tissue closer to the V(m) threshold for propagation.

CONCLUSION

Postshock activity occurred either immediately via epicardial or endocardial reentry, or after a delay caused by transmural propagation or propagated graded responses. These findings could explain the isoelectric window and focal activation patterns observed on the epicardium following VF induction shocks.

Nonlinear changes of transmembrane potential during electrical shocks: role of membrane electroporation

Defibrillation shocks induce nonlinear changes of transmembrane potential (DeltaVm) that determine the outcome of defibrillation. As shown earlier, strong shocks applied during action potential plateau cause nonmonotonic negative DeltaVm, where an initial hyperpolarization is followed by Vm shift to a more positive level. The biphasic negative DeltaVm can be attributable to (1) an inward ionic current or (2) membrane electroporation. These hypotheses were tested in cell cultures by measuring the effects of ionic channel blockers on DeltaVm and measuring uptake of membrane-impermeable dye. Experiments were performed in cell strands (width approximately 0.8 mm) produced using a technique of patterned cell growth. Uniform-field shocks were applied during the action potential plateau, and DeltaVm was measured by optical mapping. Shock-induced negative DeltaVm exhibited a biphasic shape starting at a shock strength of approximately 15 V/cm when estimated peak DeltaV-m was approximately -180 mV; positive DeltaVm remained monophasic. Application of a series of shocks with a strength of 23+/-1 V/cm resulted in uptake of membrane-impermeable dye propidium iodide. Dye uptake was restricted to the anodal side of strands with the largest negative DeltaVm, indicating the occurrence of membrane electroporation at these locations. The occurrence of biphasic negative DeltaVm was also paralleled with after-shock elevation of diastolic Vm. Inhibition of I(f) and I(K1) currents that are active at large negative potentials by CsCl and BaCl2, respectively, did not affect DeltaVm, indicating that these currents were not responsible for biphasic DeltaVm. These results provide evidence that the biphasic shape of DeltaVm at sites of shock-induced hyperpolarization is caused by membrane electroporation.

Upper limit of vulnerability in a defibrillation model of the rabbit ventricles

The goal of this modeling study is to investigate the mechanisms responsible for the upper and lower limits of vulnerability (ULV and LLV) to re-entry induced by electric shocks within the three-dimensional volume of the heart. We use a geometrically accurate rabbit ventricular model with realistic fiber architecture that also includes the blood in the cavities and a perfusing bath. The shocks are delivered over a range of strengths and coupling intervals via two large mesh electrodes located at the vertical boundaries of the perfusing bath. Our results demonstrate that shock-induced virtual electrode polarization (VEP) in the midmyocardium is weaker and more complex than VEP on the surfaces, where only 2 areas, one of positive and one of negative polarization, are induced. Transmural views of the ventricles show that, in all cases, tissue in the LV free wall and in the septum is deexcited by the shock providing an excitable path for wavefront propagation. Conversely, the RV free wall myocardium is depolarized after the end of the shock. The evolution of postshock electrical activity in the RV free wall plays a critical role in determining the outcome of the shock. In all cases, a wavefront starts in the apex at the site of largest transmembrane voltage gradient between oppositely polarized areas. For shocks of strength above the LLV, the postshock refractoriness of the RV free wall produces the unidirectional block necessary for reentry induction. If shock strength is below the ULV, the RV free wall recovers in time to provide the reentrant pathway. In contrast, for shocks of strength above the ULV, the postshock excitable gap in the LV free wall and in the septum is depolarized before the RV free wall recovers. Therefore, both ventricles are refractory and reentry is not induced

Effect of sotalol and acute ventricular dilatation on action potential duration and dispersion of repolarization after defibrillation shocks

Ventricular dilatation shortens action potential duration and increases the defibrillation threshold, whereas sotalol prolongs action potential duration and may decrease the defibrillation threshold. Whether these action potential changes remain after defibrillation shocks, and how they relate to defibrillation success, is not known. In this study, eight monophasic action potentials were recorded simultaneously during electrical defibrillation (shock strength: 20%-200% of the defibrillation threshold) in 16 normal and acutely dilated isolated rabbit hearts at baseline and after addition of sotalol (2 x 10-5 M). Post-shock action potential duration (PS-APD) and dispersion of PS-APD [Disp(PS-APD)] of monophasic action potentials were analyzed after 322 defibrillation shocks at different repolarization levels and related to defibrillation success. Acute ventricular dilatation shortened PS-APD, whereas sotalol prolonged PS-APD. Successful defibrillation was associated with lower Disp(PS-APD) at all repolarization levels in the normal and dilated heart at baseline and with sotalol (mean difference: 33%-46%, all P < 0.005). Minimal PS-APD was longer (mean difference: 5%-11%), while maximal PS-APD was shorter (mean difference: 2%-16%) after successful defibrillation shocks than after failing defibrillation shocks. Therefore, sotalol prolongs action potential duration after defibrillation shocks. Synchronization of repolarization, caused by both prolongation of short PS-APD and shortening of long PS-APD, is associated with successful defibrillation in the normal, acutely dilated, and sotalol-treated heart.

Amiodarone-induced postrepolarization refractoriness suppresses induction of ventricular fibrillation

It is still incompletely understood why amiodarone is such a potent antiarrhythmic drug. We hypothesized that chronic amiodarone treatment produces postrepolarization refractoriness (PRR) without conduction slowing and that PRR modifies the induction of ventricular arrhythmias. In this study, the hearts of 15 amiodarone-pretreated (50 mg/kg p.o. for 6 weeks) rabbits and 13 controls were isolated and eight monophasic action potentials were simultaneously recorded from the epicardium and endocardium of both ventricles. Steady-state action potential duration (APD), conduction times, refractory periods, and dispersion of action potential durations were determined during programmed stimulation and during 50-Hz burst stimuli, and related to arrhythmia inducibility. Amiodarone prolonged APD by 12 to 15 ms at pacing cycle lengths of 300 to 600 ms (p < 0.05) but did not significantly increase conduction times or dispersion of APD. Amiodarone prolonged refractoriness more than action potential duration, resulting in PRR (refractory period - APD at 90% repolarization, 14 +/- 10 ms, p < 0.05 versus controls). PRR curtailed the initial sloped part of the APD restitution curve by 20%. During burst stimulation, pronounced amiodarone-induced PRR (40 +/- 15 ms, p < 0.05 versus controls) reduced the inducibility of ventricular arrhythmias (p < 0.05 versus controls). Furthermore, in 35% of bursts only monomorphic ventricular tachycardias and no longer ventricular fibrillation were inducible in amiodarone-treated hearts (p < 0.05 versus controls). Chronic amiodarone treatment prevents ventricular tachycardias by inducing PRR without much conduction slowing, thereby curtailing the initial part of APD restitution. PRR without conduction slowing is a desirable feature of drugs designed to prevent ventricular arrhythmias.

A novel approach to identifying antiarrhythmic drug targets

Sudden cardiac death, secondary to ventricular fibrillation (VF), remains the leading cause of death in the USA. Recent experimental and theoretical studies suggest that VF could be caused by spiral wave re-entry. The initiation and subsequent break-up of spiral waves has been linked to electrical alternans, a phenomenon produced in cardiac tissue that has a steeply sloped restitution relation. Agents that reduce the slope of the restitution relation have been shown to suppress alternans and, presumably by that mechanism, terminate VF. These results suggest that electrical restitution could be a promising new target for antiarrhythmic therapies.

Calcium-dependent arrhythmias in transgenic mice with heart failure

Transgenic mice overexpressing the inflammatory cytokine tumor necrosis factor (TNF)-alpha (TNF-alpha mice) in the heart develop a progressive heart failure syndrome characterized by biventricular dilatation, decreased ejection fraction, atrial and ventricular arrhythmias on ambulatory telemetry monitoring, and decreased survival compared with nontransgenic littermates. Programmed stimulation in vitro with single extra beats elicits reentrant ventricular arrhythmias in TNF-alpha (n = 12 of 13 hearts) but not in control hearts. We performed optical mapping of voltage and Ca(2+) in isolated perfused ventricles of TNF-alpha mice to study the mechanisms that lead to the initiation and maintenance of the arrhythmias. When compared with controls, hearts from TNF-alpha mice have prolonged of action potential durations (action potential duration at 90% repolarization: 23 +/- 2 ms, n = 7, vs. 18 +/- 1 ms, n = 5; P < 0.05), no increased dispersion of refractoriness between apex and base, elevated diastolic and depressed systolic [Ca(2+)], and prolonged Ca(2+) transients (72 +/- 6 ms, n = 10, vs. 54 +/- 5 ms, n = 8; P < 0.01). Premature beats have diminished action potential amplitudes and conduct in a slow, heterogeneous manner. Lowering extracellular [Ca(2+)] normalizes conduction and prevents inducible arrhythmias. Thus both action potential prolongation and abnormal Ca(2+) handling may contribute to the initiation of reentrant arrhythmias in this heart failure model by mechanisms distinct from enhanced dispersion of refractoriness or triggered activity.

Effect of regional differences in cardiac cellular electrophysiology on the stability of ventricular arrhythmias: a computational study

Re-entry is an important mechanism of cardiac arrhythmias. During re-entry a wave of electrical activation repeatedly propagates into recovered tissue, rotating around a rod-like filament. Breakdown of a single re-entrant wave into multiple waves is believed to underlie the transition from ventricular tachycardia to ventricular fibrillation. Several mechanisms of breakup have been identified including the effect of anisotropic conduction in the ventricular wall. Cells in the inner and outer layers of the ventricular wall have different action potential durations (APD), and support re-entrant waves with different periods. The aim of this study was to use a computational approach to study twisting and breakdown in a transmural re-entrant wave spanning these regions, and examine the relative role of this effect and anisotropic conduction. We used a simplified model of action potential conduction in the ventricular wall that we modified so that it supported stable re-entry in an anisotropic model with uniform APD. We first examined the effect of regional differences on breakdown in an isotropic model with transmural differences in APD, and found that twisting of the re-entrant filament resulted in buckling and breakdown during the second cycle of re-entry. We found that breakdown was amplified in the anisotropic model, resulting in complex activation in the region of longest APD. This study shows that regional differences in cardiac electrophysiology are a potentially important mechanism for destabilizing re-entry and may act synergistically with other mechanisms to mediate the transition from ventricular tachycardia to ventricular fibrillation.

Three-dimensional mapping of earliest activation after near-threshold ventricular defibrillation shocks

INTRODUCTION

Following shocks with a 50% defibrillation success (DFT50) delivered from electrodes at the right ventricular (RV) apex and superior vena cava (SVC), the earliest epicardial postshock activation always appears focally in the left ventricular (LV) apex for both successful and failed shocks. Because the heart is a three-dimensional (3D) structure, questions remain whether this activation truly arises from a focus or the focal pattern represents epicardial breakthrough resulting from intramural reentry. To answer these questions, 3D electrical mapping was performed.

METHODS AND RESULTS

In six pigs, 60 to 84 epoxy fiberglass needles (0.7-mm-diameter), each containing six electrodes 2 mm apart, were inserted into the LV with 3- to 5-mm spacing around the apex and 5- to 10-mm spacing near the base. Ten DFT50 shocks (RV-->SVC, biphasic, 6/4 msec) were delivered after 10 seconds of fibrillation in each animal. The first five activations after each shock were mapped. Of 60 DFT50 shocks, 31 were successful, of which the first postshock cycle was a sinus beat in 13. In the other 18 successful shock episodes, the first postshock activation was detected 63 +/- 16 msec after the shock, which was not significantly different from the 58 +/- 23 msec postshock interval for the 29 failed shock episodes. In these 47 successful and failed shock episodes, the earliest postshock activation always arose focally from the LV apex. Its origin was in the subepicardium in 76% +/- 17%, midmyocardium in 16% +/- 12%, and subendocardium in 8% +/- 6% of cases.

CONCLUSION

Following near-DFT50 shocks, the first postshock cycles did not arise by macroreentry. Instead, they originated from a true focus or microreentry, most commonly near the epicardium.

Use of topological charge to determine filament location and dynamics in a numerical model of scroll wave activity

The unique time course of an excitable element in cardiac tissue can be represented as the phase of its trajectory in state space. A phase singularity is defined as a spatial point where the surrounding phase values changes by a total of 2 pi, thereby forming the organizing center for a reentrant excitatory wave, a phenomenon which occurs in cardiac fibrillation. In this paper, we describe a methodology to detect the singular filament in numeric simulations of three-dimensional (3-D) scroll waves by using the concept of topological charge. Here, we use simple two-variable models of cardiac activity to construct the state space, generate the phase field, and calculate the topological charge as a summation of 3-D convolution operations. We illustrate the usage of the algorithm on the basic dynamics of vortex ring filament behavior as well as the more complex spatiotemporal behavior observed in fibrillation. We also compare the motion of filament wavetips as determined by the phase field produced by two-variable state space and single-variable, time-delay embedded state space. Finally, we examine the state spaces produced by a more complex three-variable model. We conclude that the use of state-space analysis, along with the unique properties of topological charge, allows for a novel means of filament localization.

Artifacts, assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart

Insidious experimental artifacts and invalid theoretical assumptions complicate the comparison of numerical predictions and observed data. Such difficulties are particularly troublesome when studying electrical stimulation of the heart. During unipolar stimulation of cardiac tissue, the artifacts include nonlinearity of membrane dyes, optical signals blocked by the stimulating electrode, averaging of optical signals with depth, lateral averaging of optical signals, limitations of the current source, and the use of excitation-contraction uncouplers. The assumptions involve electroporation, membrane models, electrode size, the perfusing bath, incorrect model parameters, the applicability of a continuum model, and tissue damage. Comparisons of theory and experiment during far-field stimulation are limited by many of these same factors, plus artifacts from plunge and epicardial recording electrodes and assumptions about the fiber angle at an insulating boundary. These pitfalls must be overcome in order to understand quantitatively how the heart responds to an electrical stimulus. (c) 2002 American Institute of Physics.

Shock-induced arrhythmogenesis in the myocardium

The focus of this article is the investigation of the electrical behavior of the normal myocardium following the delivery of high-strength defibrillation shocks. To achieve its goal, the study employs a complex three-dimensional defibrillation model of a slice of the canine heart characterized with realistic geometry and fiber architecture. Defibrillation shocks of various strengths and electrode configurations are delivered to the model preparation in which a sustained ventricular tachycardia is induced. Instead of analyzing the post-shock electrical events as progressions of transmembrane potential maps, the study examines the evolution of the postshock phase singularities (PSs) which represent the organizing centers of reentry. The simulation results demonstrate that the shock induces numerous PSs the majority of which vanish before the reentrant wavefronts associated with them complete half of a single rotation. Failed shocks are characterized with one or more PSs that survive the initial period of PS annihilation to establish a new postshock arrhythmia. The increase in shock strength results in an overall decrease of the number of PSs that survive over 200 ms after the end of the shock; however, the exact behavior of the PSs is strongly dependent on the shock electrode configuration. (c) 2002 American Institute of Physics.

Modified ionic models of cardiac tissue for efficient large scale computations

Recirculation of excitation, or re-entry, is one of the most important mechanisms of life-threatening cardiac arrhythmias and fibrillation. Modelling these phenomena requires large scale computations in two and three-dimensional slabs of cardiac tissue. Because of computational constraints, most of the studies use simplified (non-ionic) models of cardiac tissue, which are electrophysiologically less accurate than the detailed ionic models. In this paper, we propose a method to modify ionic models of cardiac tissue into an intermediate class of models, which are almost as efficient for computations as simplified models, and retain most of the properties of the original ionic models, such as the shape of the action potential, the restitution of action potential duration and of the conduction velocity, as well as unchanged description of most of the ionic currents.

A computationally efficient electrophysiological model of human ventricular cells

Recent experimental and theoretical results have stressed the importance of modeling studies of reentrant arrhythmias in cardiac tissue and at the whole heart level. We introduce a six-variable model obtained by a reformulation of the Priebe-Beuckelmann model of a single human ventricular cell. The reformulated model is 4.9 times faster for numerical computations and it is more stable than the original model. It retains the action potential shape at various frequencies, restitution of action potential duration, and restitution of conduction velocity. We were able to reproduce the main properties of epicardial, endocardial, and M cells by modifying selected ionic currents. We performed a simulation study of spiral wave behavior in a two-dimensional sheet of human ventricular tissue and showed that spiral waves have a frequency of 3.3 Hz and a linear core of approximately 50-mm diameter that rotates with an average frequency of 0.62 rad/s. Simulation results agreed with experimental data. In conclusion, the proposed model is suitable for efficient and accurate studies of reentrant phenomena in human ventricular tissue.

The pinwheel experiment re-revisited

Virtual electrode induced phase singularity hypothesis explains the origin of cardiac arrhythmias caused by artificial electrical induction of rotors, i.e. vortex-like self-sustained sources of activity. This mechanism is thought to underlie both stimulus-induced arrhythmias and shock defibrillation therapy. In this paper, we extend this hypothesis to three dimensions using the bidomain model of cardiac tissue. We predict that virtual electrode polarization can produce three topologically distinct types of rotors anchored to: (1) transmural I-shaped scroll wave filaments; (2) near-surface U-shaped scroll wave filaments; and (3) intramural O-shaped scroll wave filaments.

The role of approximate entropy in predicting ventricular defibrillation threshold

BACKGROUND

The role of myocardial tissue mass on ventricular defibrillation threshold (DFT) is unclear. We hypothesized that changes in tissue mass modulate DFT by changing ventricular fibrillation (VF) wavefront regularity (entropy).

METHODS AND RESULTS

The right ventricles (RV) of seven farm pigs were isolated, superfused and perfused through the right coronary artery with oxygenated Tyrode's solution at 37 degrees C. The epicardial surface was stained with the voltage sensitive dye, di-4-ANEPPS, and activation wavefront numbers (AWN) during VF were determined from the optical maps using a CCD camera (96 x 96 pixels over a 3.5 x 3.5 cm area). The RV mass was progressively reduced by sequential cutting of 1 to 2 g of tissue (approximately 12 cuts in total) distal to the perfusion site. After each cut, VF was reinduced, optical maps obtained, and the 50% probability of successful DFT(50) determined using an up-down algorithm. After each cut, the approximate entropy (ApEn) was also computed using 5 seconds of VF data obtained with a bipolar electrode and a pseudo-electrocardiogram. Tissue mass reduction of up to one third of the RV mass (ie, from 48.4 +/- 4.25 g to 34 +/- 4.7 g) caused little or no change in the DFT, ApEn or AWN. However, further progressive reduction of the RV mass near the critical mass of VF resulted in a significant (P < 0.05) progressive decrease in all three measured parameters. DFT energy was reduced by 27% (1.47 +/- 0.34 J vs. 1.02 +/- 0.14 J). There was a significant (P < 0.01) correlation between the DFT and ApEn, which significantly further increased (P < 0.001) near the critical mass. In a separate series of 6 isolated RVs, the ApEn correlated well with the Kolmogorov-Sinai (K-S) entropy, the standard method of calculating entropy.

CONCLUSION

Tissue mass reduction significantly reduces DFT when the mass reduction increases VF wavefront regularity.

Modelling induction of a rotor in cardiac muscle by perpendicular electric shocks

A strong, properly timed shock applied perpendicularly to a propagating wavefront causes a rotor in the canine myocardium. Experimental data indicate that the induction of this rotor relies on the shock exciting tissue away from the electrodes. The computational study reproduced such direct excitation in a two-dimensional model of a 2.7 x 3 cm sheet of cardiac muscle. The model used experimentally measured extracellular potentials to represent 100 and 150 V shocks delivered through extracellular electrodes. The shock-induced transmembrane potential was computed according to two mechanisms, the activating function and the unit-bundle sawtooth potential. The overall process leading to initiation of a rotor was the same in model and experiment. For the 100 V shock, the directly excited region extended 2.26 cm away from the electrode; the centre of the rotor ('critical point') was 1.28 cm away, where the electric field Ecr was 4.54 Vcm(-1). Increasing the shock strength to 150 V moved the critical point 1.02 cm further and decreased Ecr by 0.39 Vcm(-1). The results are comparable with experimental data. The model suggests that the unit-bundle sawtooth is responsible for the creation of the directly excited region, and the activating function is behind the dependence of Ecr on shock strength.

The effect of plunge electrodes during electrical stimulation of cardiac tissue

The mechanism for far-field stimulation of cardiac tissue is not known, although many hypotheses have been suggested. This paper explores a new hypothesis: the insulated plunge electrodes used in experiments to map the extracellular potential may affect the transmembrane potential when an electric field is applied to cardiac tissue. Our calculation simulates a 10-mm-diameter sheet of passive tissue with a circular insulated plunge electrode in the middle of it, ranging in diameter from 0.05 to 2 mm. We calculate the transmembrane potential induced by a 500-V/m electric field. Our results show that a transmembrane potential is induced around the electrode in alternating areas of depolarization and hyperpolarization. If the electric field is oriented parallel to the myocardial fibers, the maximum transmembrane potential is 89 mV. A layer of fluid around the electrode increases the transmembrane potential. We conclude that plunge electrodes may introduce artifacts during experiments designed to study the response of the heart to strong electric shocks.