Modeling the interaction between propagating cardiac waves and monophasic and biphasic field stimuli: the importance of the induced spatial excitatory response

Cardiac resynchronization therapy and phase resetting of the sinoatrial node: a conjecture

Congestive heart failure is a severe chronic disease often associated with disorders that alter the mechanisms of excitation-contraction coupling that may result in an asynchronous left ventricular motion which may further impair the ability of the failing heart to eject blood. In recent years a therapeutic approach to resynchronize the ventricles (cardiac resynchronization therapy, CRT) has been performed through the use of a pacemaker device able to provide atrial-based biventricular stimulation. Atrial lead senses the spontaneous occurrence of cells depolarization and sends the information to the generator which, in turn, after a settled delay [atrioventricular (AV) delay], sends electrical impulses to both ventricles to stimulate their synchronous contraction. Recent studies performed on heart rate behavior of chronically implanted patients at different epochs after implantation have shown that CRT can lead to sustained overall improvement of heart function with a reduction in morbidity and mortality. At this moment, however, there are no studies about CRT effects on spontaneous heart activity of chronically implanted patients. We performed an experimental study in which the electrocardiographic signal of five subjects under chronic CRT was recorded during the activity of the pacemaker programmed at different AV delays and under spontaneous cardiac activity after pacemaker deactivation. The different behavior of heart rate variability during pacemaker activity and after pacemaker deactivation suggested the hypothesis of a phase resetting mechanism induced by the pacemaker stimulus on the sinoatrial (SA) node, a phenomenon already known in literature for aggregate of cardiac cells, but still unexplored in vivo. The constraints imposed by the nature of our study (in vivo tests) made it impossible to plan an experiment to prove our hypothesis directly. We therefore considered the best attainable result would be to prove the accordance of our data to the conjecture through the use of models and physical considerations. We first used the data of literature on far-field effects of cardiac defibrillators to prove that the pacemaker impulses delivered to the two ventricles were able to induce modifications in membrane voltage at the level of the SA node. To simulate a phase resetting mechanism of the SA node, we used a Van der Pol modified model to allow the possibility of changing the refractory period and the firing frequency of the cells separately. With appropriate parameters of the model we reproduced phase response curves that can account for our experimental data. Furthermore, the simulated curves closely resemble the functional form proposed in literature for perturbed aggregate of cardiac cells. Despite the small sample of subjects investigated and the limited number of ECG recordings at different AV delays, we think we have proved the plausibility of the proposed conjecture.

Field stimulation of cardiac fibers with random spatial structure

Polarization of individual cells ("sawtooth") has been proposed as a mechanism for field stimulation and defibrillation. To date, the modeling work has concentrated on the myocardium with periodic spatial structure; this paper investigates potentials arising in cardiac fibers with random spatial structure. Ten different random fibers consisting of cells with varying length (l(c) = 100 +/- 50 microm), diameter (d(c) = 20 +/- 10 microm), thickness of extracellular space (t(e) = 1.18 +/- 0.59 microm), and junctional resistance (R(j) = 2 +/- 1 M(omega)) are studied. Simulations demonstrate that randomizing spatial structure introduces to the field-induced potential (V(m)) a randomly varying baseline, which arises due to polarization of groups of cells. This polarization appears primarily in response to randomizing t(e); R(j), l(c), and d(c) have less influence. The maximum V(m) increases from 3.5 mV in a periodic fiber to 20.5+/-4.7 mV in random fibers (1 V/cm field applied for 5 ms). Field stimulation threshold E(th) decreases from 6.9 to 1.59 +/- 0.43 V/cm, which is within the range of experimental measurements. Thresholds for normal and reversed field polarities are statistically equivalent: 1.59 +/- 0.43 versus 1.44 +/- 0.41 V/cm (p value = 0.453). Thus, V(m) arising due to random structure of the myocardium may play an important role in field stimulation and defibrillation.

A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium

Presented here is an efficient algorithm for solving the bidomain equations describing myocardial tissue with active membrane kinetics. An analysis of the accuracy shows advantages of this numerical technique over other simple and therefore popular approaches. The modular structure of the algorithm provides the critical flexibility needed in simulation studies: fiber orientation and membrane kinetics can be easily modified. The computational tool described here is designed specifically to simulate cardiac defibrillation, i. e., to allow modeling of strong electric shocks applied to the myocardium extracellularly. Accordingly, the algorithm presented also incorporates modifications of the membrane model to handle the high transmembrane voltages created in the immediate vicinity of the defibrillation electrodes.

Virtual electrodes and deexcitation: new insights into fibrillation induction and defibrillation

Previous models of fibrillation induction and defibrillation stressed the contribution of depolarization during the response of the heart to a shock. This article reviews recent evidence suggesting that comprehending the role of negative polarization (hyperpolarization) also is crucial for understanding the response to a shock. Negative polarization can "deexcite" cardiac cells, creating regions of excitable tissue through which wavefronts can propagate. These wavefronts can result in new reentrant circuits, inducing fibrillation or causing defibrillation to fail. In addition, deexcitation can lead to rapid propagation through newly excitable regions, resulting in the elimination of excitable gaps soon after the shock and causing defibrillation to succeed.

Factors governing mechanical stimulation in frog hearts

Because stretch-induced activation may be important in generating clinically relevant arrhythmias in the heart, we delineated the ability of different types of stretches to activate ventricular tissue. Geometrically simple sheets of frog (Rana catesbeiana) ventricular tissue were mounted to allow stretches to be applied perpendicular to one edge. Every heart could be activated by a stretch pulse (n = 25), and several parameters were varied to determine their effects on mechanical activation threshold. At shorter coupling intervals, a larger stretch was needed to excite the tissue, and activation-recovery intervals were shorter, similar to previously published electrically probed strength-interval and restitution relations. Additionally, the tissue became easier to activate as the speed of the stretch increased from 0.09 to 2.6% length/ms. The increment in stretch needed for activation decreased as the baseline stretch increased from 0 to 6% length. Thus we show that mechanical activation is similar to electrical activation and that increasing uniquely mechanical parameters such as the speed of the applied stretch or baseline level of stretch can decrease the mechanical activation threshold.

The biphasic mystery: why a biphasic shock is more effective than a monophasic shock for defibrillation

We demonstrate that a biphasic shock is more effective than a monophasic shock at eliminating reentrant electrical activity in an ionic model of cardiac ventricular electrical activity. This effectiveness results from early hyperpolarization that enhances the recovery of sodium inactivation, thereby enabling earlier activation of recovering cells. The effect can be seen easily in a model of a single cell and also in a cable model with a ring of excitable cells. Finally, we demonstrate the phenomenon in a two-dimensional model of cardiac tissue.

Separation between virtual sources modifies the response of cardiac tissue to field stimulation

INTRODUCTION

While it is now understood that the tissue geometry and the electric field distribution are important in generating virtual electrodes, the effects of interaction between a collection of electrodes have not been examined. To develop a basis for understanding such interactions, we have studied a single pair of oppositely polarized virtual sources. Although such oppositely polarized pairs of virtual electrodes can be generated by a variety of field distributions and tissue geometries, we examine one simple system that incorporates the salient features of source interaction.

METHODS AND RESULTS

Our model system is a homogeneous tissue strip stimulated by a uniform extracellular field. To clarify virtual source interaction, we show that field stimulated tissue can be equivalently polarized by a set of intracellular current sources with magnitude and distribution defined by the generalized activating function. In our model system, an intracellular current source is produced at one edge of the tissue and an intracellular current sink at the other. Therefore, the tissue length acts to modulate the overlap, or interaction, between the polarizations arising from each source. To quantify the effects of source interaction, the chronaxie and rheobase values of the strength-duration relation were determined for source separations varying between 1.0 cm and 100 microm (active membrane dynamics were modeled with the Luo-Rudy phase I formulation). At all separations >3.0 mm, the chronaxie was constant at 3.09 msec and the rheobase was 0.38 V/cm. Under 0.2 mm, the chronaxie decreased to 0.55 msec while the rheobase increased linearly with the inverse of source separation. The dependence of these parameters on separation primarily reflects passive electrotonic interactions between the two virtual electrodes. However, the exact values are strongly dependent upon active tissue properties-largely the inward rectifier potassium channel and activation of the sodium current.

CONCLUSION

Tissue excitation in response to field stimulation is strongly modulated by the proximity of, and therefore the interaction between, oppositely polarized virtual electrode sources.

Effects of electroporation on the transmembrane potential distribution in a two-dimensional bidomain model of cardiac tissue

INTRODUCTION

Defibrillation shocks, when delivered through internal electrodes, establish transmembrane potentials (Vm) large enough to electroporate the membrane of cardiac cells. The effects of such shocks on the transmembrane potential distribution are investigated in a two-dimensional rectangular sheet of cardiac muscle modeled as a bidomain with unequal anisotropy ratios.

METHODS AND RESULTS

The membrane is represented by a capacitance Cm, a leakage conductance g(l) and a variable electroporation conductance G, whose rate of growth depends exponentially on the square of Vm. The stimulating current Io, 0.05-20 A/m, is delivered through a pair of electrodes placed 2 cm apart for stimulation along fibers and 1 cm apart for stimulation across fibers. Computer simulations reveal three categories of response to Io: (1) Weak Io, below 0.2 A/m, cause essentially no electroporation, and Vm increases proportionally to Io. (2) Strong Io, between 0.2 and 2.5 A/m, electroporate tissue under the physical electrode. Vm is no longer proportional to Io; in the electroporated region, the growth of Vm is halted and in the region of reversed polarity (virtual electrode), the growth of Vm is accelerated. (3) Very strong Io, above 2.5 A/m, electroporate tissue under the physical and the virtual electrodes. The growth of Vm in all electroporated regions is halted, and a further increase of Io increases both the extent of the electroporated regions and the electroporation conductance G.

CONCLUSION

These results indicate that electroporation of the cardiac membrane plays an important role in the distribution of Vm induced by defibrillation strength shocks.

Spatiotemporal effects of syncytial heterogeneities on cardiac far-field excitations during monophasic and biphasic shocks

INTRODUCTION

It has recently been postulated that syncytial (anatomic) heterogeneities inherent within cardiac tissue might represent a significant mechanism underlying field-induced polarization of the bulk myocardium. This simulation study examines and characterizes the spatiotemporal excitatory dynamics associated with this newly hypothesized mechanism.

METHODS AND RESULTS

Two-dimensional regions of syncytially heterogeneous cardiac tissue were simulated with active membrane kinetics. Heterogeneities were manifested via random spatial variations of intracellular volume fractions over multiple length scales. Excitation thresholds were determined for uniform rectangular monophasic (M) and symmetric biphasic (B) far-field stimuli, from which strength-duration and strength-interval relationships were constructed. For regions measuring 5.4 x 5.4 mm, baseline diastolic thresholds for longitudinal (L) and transverse (T) shocks of 5-msec total duration averaged (in V/cm, n = 10) M-L = 2.87+/-0.26, M-T = 6.71+/-0.83, B-L = 3.22+/-0.25, and B-T = 7.93+/-0.51. These thresholds decreased by 15% to 25% when the region sizes were increased to 10.8 x 10.8 mm. Strength-duration relationships correlated strongly with the Weiss-Lapicque hyperbolic relationship, with rheobases and chronaxies of 2.33 V/cm and 1.15 msec for M-L stimuli, and 2.28 V/cm and 2.04 msec for B-L stimuli. Strength-interval relationships for M-L and B-L stimuli decreased monotonically with increasing coupling intervals, with similar minimum coupling intervals at absolute refractoriness. However, the B-L thresholds were substantially less sensitive to changes in coupling intervals than their M-L counterparts.

CONCLUSION

This study provides strong additional support for and understanding of the syncytial heterogeneity hypothesis and its manifested properties. Furthermore, these results predict that syncytial heterogeneities of even modest proportions could represent a significant mechanism contributing to the far-field excitation process.

Postshock potential gradients and dispersion of repolarization in cells stimulated with monophasic and biphasic waveforms

INTRODUCTION

Even though the clinical advantage of biphasic defibrillation waveforms is well documented, the mechanisms that underlie this greater efficacy remain incompletely understood. It is established, though, that the response of relatively refractory cells to the shock is important in determining defibrillation success or failure. We used two computer models of an isolated ventricular cell to test the hypothesis that biphasic stimuli cause a more uniform response than the equivalent monophasic shocks, decreasing the likelihood that fibrillation will be reinduced.

METHODS AND RESULTS

Models of reciprocally polarized and uniformly polarized cells were used. Rapid pacing and elevated [K]o were simulated, and either 10-msec rectangular monophasic or 5-msec/5-msec symmetric biphasic stimuli were delivered in the relative refractory period. The effects of stimulus intensity and coupling interval on response duration and postshock transmembrane potential (Vm) were quantified for each waveform. With reciprocal polarization, biphasic stimuli caused a more uniform response than monophasic stimuli, resulting in fewer large gradients of Vm (only for shock strengths < or = 1.25x threshold vs < or = 2.125x threshold) and a smaller dispersion of repolarization (1611 msec2 vs 1835 msec2). The reverse was observed with uniform polarization: monophasic pulses caused a more uniform response than did biphasic stimuli.

CONCLUSION

These results show that the response of relatively refractory cardiac cells to biphasic stimuli is less dependent on the coupling interval and stimulus strength than the response to monophasic stimuli under conditions of reciprocal polarization. Because this may lead to fewer and smaller spatial gradients in Vm, these data support the hypothesis that biphasic defibrillation waveforms will be less likely to reinduce fibrillation. Further, published experimental results correlate to a greater degree with conditions of reciprocal polarization than of uniform polarization, providing indirect evidence that interactions between depolarized and hyperpolarized regions play a role in determining the effects of defibrillation shocks on cardiac tissue.

Disparate effects of biphasic and monophasic shocks on postshock refractory period dispersion

The magnitude by which a defibrillation shock extends the refractory period immediately postshock (refractory period extension, RPE) does not explain why biphasic shocks defibrillate with greater efficacy than monophasic shocks. It may be that spatial heterogeneity of RPE is a more important regulator of defibrillation efficacy. We measured RPE in 15 pentobarbital-anesthetized swine using 400-V biphasic and monophasic shocks of equal pulse duration at three discrete myocardial sites. Spatial heterogeneity of RPE was calculated as the difference between the maximum and minimum values of the three recording sites. Monophasic shocks produced greater magnitude of RPE than biphasic shocks at all sites tested (82 +/- 6 to 99 +/- 13 and 64 +/- 6 to 68 +/- 5 ms, respectively; P < 0.05). However, RPE dispersion was significantly less with biphasic shocks versus monophasic shocks (29 +/- 4 and 48 +/- 7 ms, respectively; P < 0.05). This suggests that one potential mechanism by which biphasic shocks defibrillate with greater efficacy is limiting postshock spatial heterogeneity of refractoriness. Thus these data support our hypothesis that RPE heterogeneity is a more likely predictor of defibrillation efficacy than magnitude of RPE.

Progressive depolarization: a unified hypothesis for defibrillation and fibrillation induction by shocks

Experimental studies of defibrillation have burgeoned since the introduction of the upper limit of vulnerability (ULV) hypothesis for defibrillation. Much of this progress is due to the valuable work carried out in pursuit of this hypothesis. The ULV hypothesis presented a unified electrophysiologic scheme for linking the processes of defibrillation and shock-induced fibrillation. In addition to its scientific ramifications, this work also raised the possibility of simpler and safer means for clinical defibrillation threshold testing. Recent results from an optical mapping study of defibrillation suggest, however, that the experimental data supporting the ULV hypothesis could instead be interpreted in a manner consistent with traditional views of defibrillation such as the critical mass hypothesis. This review will describe the evidence calling for such a reinterpretation. In one regard the ULV hypothesis superseded the critical mass hypothesis by linking the defibrillation and shock-induced fibrillation processes. Therefore, this review also will discuss the rationale for developing a new defibrillation hypothesis. This new hypothesis, progressive depolarization, uses traditional defibrillation concepts to cover the same ground as the ULV hypothesis in mechanistically unifying defibrillation and shock-induced fibrillation. It does so in a manner consistent with experimental data supporting the ULV hypothesis but which also takes advantage of what has been learned from optical studies of defibrillation. This review will briefly describe how this new hypothesis relates to other contemporary viewpoints and related experimental results.

Syncytial heterogeneity as a mechanism underlying cardiac far-field stimulation during defibrillation-level shocks

INTRODUCTION

The mechanisms by which a defibrillation shock directly stimulates regions of cardiac tissue distal to the stimulus electrodes ("far-field" stimulation) are still not well understood. Existing hypotheses have proposed that intercellular discontinuities and/or fiber curvatures induce the requisite membrane polarizations. This article hypothesizes a third potential mechanism: one based on the existence and influences of syncytial (anatomic) heterogeneities inherent throughout the bulk myocardium itself.

METHODS AND RESULTS

We simulated the effects of such heterogeneities in a model of a two-dimensional region of passive cardiac tissue subjected to uniform 1 V/cm longitudinal or transverse field stimuli. Heterogeneities were manifested via random spatial variations of intracellular volume fractions (fi) over multiple length scales, with mean fi of 80% and standard deviation of fi (sigma[fi]) ranging from 0% to 10%. During field stimulation, many interspersed and variously shaped and sized islands of hyperpolarization and depolarization developed across the tissue, with their locations and extents correlated to the spatial gradients of the underlying heterogeneities. Increases in sigma(fi) correspondingly increased the shock-induced magnitudes of resulting membrane polarizations. The ratio of maximal polarizations for equivalent longitudinal and transverse shocks approximated 2:1 across all sigma(fi) tested. At sigma(fi) = 5%, these maximal induced polarizations were 17.4 +/- 2.4 mV and 8.18 +/- 1.5 mV, respectively. Assuming an excitation threshold of 25 mV, these data suggest corresponding diastolic thresholds of 1.47 +/- 0.20 V/cm and 3.14 +/- 0.50 V/cm, respectively.

CONCLUSION

This study predicts that syncytial heterogeneities inherent within cardiac tissue could represent a significant-and heretofore unappreciated-mechanism underlying field-induced polarizations throughout the bulk myocardium.

A generalized activating function for predicting virtual electrodes in cardiac tissue

To fully understand the mechanisms of defibrillation, it is critical to know how a given electrical stimulus causes membrane polarizations in cardiac tissue. We have extended the concept of the activating function, originally used to describe neuronal stimulation, to derive a new expression that identifies the sources that drive changes in transmembrane potential. Source terms, or virtual electrodes, consist of either second derivatives of extracellular potential weighted by intracellular conductivity or extracellular potential gradients weighted by derivatives of intracellular conductivity. The full response of passive tissue can be considered, in simple cases, to be a convolution of this "generalized activating function" with the impulse response of the tissue. Computer simulations of a two-dimensional sheet of passive myocardium under steady-state conditions demonstrate that this source term is useful for estimating the effects of applied electrical stimuli. The generalized activating function predicts oppositely polarized regions of tissue when unequally anisotropic tissue is point stimulated and a monopolar response when a point stimulus is applied to isotropic tissue. In the bulk of the myocardium, this new expression is helpful for understanding mechanisms by which virtual electrodes can be produced, such as the hypothetical "sawtooth" pattern of polarization, as well as polarization owing to regions of depressed conductivity, missing cells or clefts, changes in fiber diameter, or fiber curvature. In comparing solutions obtained with an assumed extracellular potential distribution to those with fully coupled intra- and extracellular domains, we find that the former provides a reliable estimate of the total solution. Thus the generalized activating function that we have derived provides a useful way of understanding virtual electrode effects in cardiac tissue.

Membrane refractoriness and excitation induced in cardiac fibers by monophasic and biphasic shocks

INTRODUCTION

This modeling study examines the effect of low-intensity monophasic and biphasic waveforms on the response of a refractory cardiac fiber to the defibrillation shock.

METHODS AND RESULTS

Two cardiac fiber representations are considered in this study: a continuous fiber and a discrete fiber that incorporates gap junctions. Each fiber is undergoing a propagating action potential. Shocks of various strengths and coupling intervals are delivered extracellularly at fiber ends during the relative refractory period. In a continuous fiber, monophasic shock strengths of three times the diastolic threshold either elicit no response or, for coupling intervals above 380 msec, reinitiate propagation. In contrast, biphasic shocks of same strength are capable of terminating the existing wavefronts by either invoking a nonpropagating response (coupling intervals 370 to 382 msec) that prolongs the refractory period or inducing wavefront collision (coupling intervals above 400 msec). The fiber response is similar for other shock strengths and when cellular discontinuity is accounted for. Thus, for a refractory fiber, biphasic shocks have only a small "vulnerable" window of coupling intervals over which propagation is reinitiated.

CONCLUSION

At short coupling intervals, a significant extension of refractoriness is generated at regions where the biphasic shock induced hyperpolarization followed by depolarization. At large coupling intervals, the enhanced efficacy of biphasic shocks is associated with their ability to induce wavefront collision, thus decreasing the probability of reinitiating fibrillation. Overall, the defibrillation shock affects the tissue through the induced large-scale hyperpolarization and depolarization, and not through the small-scale transmembrane potential oscillations at cell ends.