Nonlinear changes of transmembrane potential during defibrillation shocks: role of Ca(2+) current

Probing field-induced tissue polarization using transillumination fluorescent imaging

Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart, recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock electrodes. There is little consensus as to whether these differences result from deficiencies of experimental techniques, artifacts of tissue damage, or deficiencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensitive dyes and transillumination optical imaging to perform, for the first time that we know of, noninvasive probing of field effects deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold diastolic field stimulation produces activation of deep myocardial layers 2-6 mm away from the cathodal surface, contrary to theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous bidomain model.

Mechanisms of defibrillation

Electrical shock has been the one effective treatment for ventricular fibrillation for several decades. With the advancement of electrical and optical mapping techniques, histology, and computer modeling, the mechanisms responsible for defibrillation are now coming to light. In this review, we discuss recent work that demonstrates the various mechanisms responsible for defibrillation. On the cellular level, membrane depolarization and electroporation affect defibrillation outcome. Cell bundles and collagenous septae are secondary sources and cause virtual electrodes at sites far from shocking electrodes. On the whole-heart level, shock field gradient and critical points determine whether a shock is successful or whether reentry causes initiation and continuation of fibrillation.

Towards predictive modelling of the electrophysiology of the heart

The simulation of cardiac electrical function is an example of a successful integrative multiscale modelling approach that is directly relevant to human disease. Today we stand at the threshold of a new era, in which anatomically detailed, tomographically reconstructed models are being developed that integrate from the ion channel to the electromechanical interactions in the intact heart. Such models hold high promise for interpretation of clinical and physiological measurements, for improving the basic understanding of the mechanisms of dysfunction in disease, such as arrhythmias, myocardial ischaemia and heart failure, and for the development and performance optimization of medical devices. The goal of this article is to present an overview of current state-of-art advances towards predictive computational modelling of the heart as developed recently by the authors of this article. We first outline the methodology for constructing electrophysiological models of the heart. We then provide three examples that demonstrate the use of these models, focusing specifically on the mechanisms for arrhythmogenesis and defibrillation in the heart. These include: (1) uncovering the role of ventricular structure in defibrillation; (2) examining the contribution of Purkinje fibres to the failure of the shock; and (3) using magnetic resonance imaging reconstructed heart models to investigate the re-entrant circuits formed in the presence of an infarct scar.

Membrane time constant during internal defibrillation strength shocks in intact heart: effects of Na+ and Ca2+ channel blockers

INTRODUCTION

We assessed defibrillation strength shock-induced changes of the membrane time constant (tau) and membrane potential (DeltaVm) in intact rabbit hearts after administration of lidocaine, a sodium (Na(+)) channel blocker, or nifedipine, a L-type calcium (Ca(2+)) channel blocker.

METHODS AND RESULTS

We optically mapped anterior, epicardial, electrical activity during monophasic shocks (+/-100, +/-130, +/-160, +/-190, and +/-220 V; 150 microF; 8 ms) applied at 25%, 50%, and 75% of the action potential duration via a shock lead system in Langendorff-perfused hearts. The protocol was run twice for each heart under control and after lidocaine (15 microM, n = 6) or nifedipine (2 microM, n = 6) addition. tau in the virtual electrode area away from the shock lead was approximated with single-exponential fits from a total of 121,125 recordings. The same data set was used to calculate DeltaVm. We found (1) Under all conditions, there is inverse relationship between tau and DeltaVm with respect to changes of shock strength, regardless of shock polarity and phase of application: a stronger shock resulted in a larger DeltaVm, which corresponded to a smaller tau (faster cellular response); (2) Lidocaine did not cause appreciable changes in either tau or DeltaVm versus control, and (3) Nifedipine significantly increased both tau and DeltaVm in the virtual cathode area; in contrast, in the virtual anode area, this effect depended on the phase of shock application.

CONCLUSION

tau and DeltaVm are inversely related. Na(+) channel blocker has minimal impact on either tau or DeltaVm. Ca(2+) blocker caused polarity and phase-dependent significant changes in tau and DeltaVm.

Calculation of optical signal using three-dimensional bidomain/diffusion model reveals distortion of the transmembrane potential

Optical mapping experiments allow investigators to view the effects of electrical currents on the transmembrane potential, V(m), as a shock is applied to the heart. One important consideration is whether the optical signal accurately represents V(m). We have combined the bidomain equations along with the photon diffusion equation to study the excitation and emission of photons during optical mapping of cardiac tissue. Our results show that this bidomain/diffusion model predicts an optical signal that is much smaller than V(m) near a stimulating electrode, a result consistent with experimental observations. Yet, this model, which incorporates the effect of lateral averaging, also reveals an optical signal that overestimates V(m) at distances >1 mm away from the electrode. Although V(m) falls off with distance r from the electrode as exp(-r/lambda)/r, the optical signal decays as a simple exponential, exp(-r/lambda). Moreover, regions of hyperpolarization adjacent to a cathode are emphasized in the optical signal compared to the region of depolarization under the cathode. Imaging methods utilizing optical mapping techniques will need to account for these distortions to accurately reconstruct V(m).

Effect of electroporation on cardiac electrophysiology

Defibrillation shocks are commonly used to terminate life-threatening arrhythmias. According to the excitation theory of defibrillation, such shocks are aimed at depolarizing the membranes of most cardiac cells, resulting in resynchronization of electrical activity in the heart. If shock-induced transmembrane potentials are large enough, they can cause transient tissue damage due to electroporation. In this review, evidence is presented that electroporation of the heart tissue can occur during clinically relevant intensities of the external electrical field and that electroporation can affect the outcome of defibrillation therapy, being both pro- and antiarrhythmic.Here, we present experimental evidence for electroporation in cardiac tissue, which occurs above a threshold of 25 V/cm as evident from propidium iodide uptake, transient diastolic depolarization, and reductions of action potential amplitude and its derivative. These electrophysiological changes can induce tachyarrhythmia, due to conduction block and possibly triggered activity; however, our findings provide the foundation for future design of effective methods to deliver genes and drugs to cardiac tissues, while avoiding possible side effects such as arrhythmia and mechanical stunning.

Evaluating intramural virtual electrodes in the myocardial wedge preparation: simulations of experimental conditions

While defibrillation is the only means for prevention of sudden cardiac death, key aspects of the process, such as the intramural virtual electrodes (VEs), remain controversial. Experimental studies had attempted to assess intramural VEs by using wedge preparations and recording activity from the cut surface; however, applicability of this approach remains unclear. These studies found, surprisingly, that for strong shocks, the entire cut surface was negatively polarized, regardless of boundary conditions. The goal of this study is to examine, by means of bidomain simulations, whether VEs on the cut surface represent a good approximation to VEs in depth of the intact wall. Furthermore, we aim to explore mechanisms that could give rise to negative polarization on the cut surface. A model of wedge preparation was used, in which fiber orientation could be changed, and where the cut surface was subjected to permeable and impermeable boundary conditions. Small-scale mechanisms for polarization were also considered. To determine whether any distortions in the recorded VEs arise from averaging during optical mapping, a model of fluorescent recording was employed. The results indicate that, when an applied field is spatially uniform and impermeable boundary conditions are enforced, regardless of the fiber orientation VEs on the cut surface faithfully represent those intramurally, provided tissue properties are not altered by dissection. Results also demonstrate that VEs are sensitive to the conductive layer thickness above the cut surface. Finally, averaging during fluorescent recordings results in large negative VEs on the cut surface, but these do not arise from small-scale heterogeneities.

Quantification of shock-induced microscopic virtual electrodes assessed by subcellular resolution optical potential mapping in guinea pig papillary muscle

INTRODUCTION

The primary objective of this study was the quantitative description of shock-induced, locally occurring virtual electrodes in natural cardiac tissue.

METHODS AND RESULTS

Multiscale optical potential mapping using 10x, 20x, and 40x magnifying objectives, achieving resolutions of 0.13, 0.065, and 0.033 mm, was performed when applying uniform shocks (+/-10 V/cm, 5 ms) during diastole and action potential plateau. A procedure was developed to identify local potential deviations as depolarizing or hyperpolarizing peaks and to quantify their occurrence and characteristic amplitudes, lateral extents, and dynamics. At shock onset, peaks of either polarity developed significantly faster (tau = 0.92 +/- 0.65 ms, N = 64) than the average bulk polarization (tau = 2.25 +/- 0.96 ms, P < 0.001) and appeared locally fixed, changing their polarity at shock reversal. The mean peak magnitude (21.2 +/- 12 mV) and the amplitude distribution were essentially independent from the magnification. The peak density continuously increased with decreasing peak extent (taken at 70% of the amplitude), reaching a maximum of approximately 3 peaks/mm2 in the range of approximately 30-65 microm. There was no correlation between peak amplitude and size throughout. Potentially exciting peaks were found with a density of 0.04-0.2 peaks/mm2 corresponding to estimated 1-5 peaks/mm3.

CONCLUSIONS

Our results suggest that microscopic inhomogeneities form a substantial substrate for far-field excitation in natural cardiac tissue. Here, we effectively bridged the gap between the extensively studied myocyte cultures and larger heart preparations.

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.

Do Intramural Virtual Electrodes Facilitate Successful Defibrillation? Model-Based Analysis of Experimental Evidence

INTRODUCTION

Recent computer model and experimental studies have suggested that microscopic intramural collagenous planes may facilitate successful defibrillation through the generation of shock-induced virtual electrodes deep within the ventricular wall. Evidence supporting the existence of intramural virtual electrodes has been drawn from several recent studies, which map shock-induced membrane potential (Vm) over the cut transmural surface of dissected segments of porcine left ventricle (LV). The artificially created transmural boundary in these experiments is impermeable to intracellular current. It is not known how this constraint limits the interpretation of these experiments in terms of the shock response of the intact ventricle.

METHODS AND RESULTS

This study uses a realistic 3D computer model of LV myocardium to aid experimental interpretation. The model incorporates a microstructural description of intramural cleavage plane discontinuities measured by confocal microscopy of rat LV. Electrical shocks are applied across the model tissue, with and without introduced transmural boundaries. Shocks of varying strength (4-40 V/cm) are also applied to the model and the response analyzed. Results show that shock-induced Vm changes (deltaVm) on a transmural tissue boundary are significantly different to deltaVm of the intact ventricle, and the extent of difference depends on boundary orientation. However, the presence and qualitative behavior of intramural virtual electrodes is preserved irrespective of boundary placement. The model also confirms experimental observations that most rapid transmural activation occurs for shocks of strength 5-10 V/cm. Two distinct mechanisms suppress virtual electrode propagation, and hence slow tissue activation, outside of this optimal shock strength range.

CONCLUSIONS

This study supports the hypothesis that distributed microscopic intramural virtual electrodes contribute to rapid activation of the ventricular wall during defibrillation.

Defibrillation of the heart: insights into mechanisms from modelling studies

Despite its critical role in restoring cardiac rhythm and thus in saving human life, cardiac defibrillation remains poorly understood. Further mechanistic inquiry is hampered by the inability of presently available experimental techniques to resolve, with sufficient accuracy, electrical behaviour confined to the depth of the ventricles. The objective of this review article is to demonstrate that realistic 3-D simulations of the ventricular defibrillation process in close conjunction with experimental observations are capable of bringing a new level of understanding of the electrical events that ensue from the interaction between fibrillating myocardium and applied shock. The article does this by reviewing the results of two studies, one on vulnerability to electric shocks and another on defibrillation. An overview of the modelling tools used in these studies is also provided.

Cardiac microimpedance measurement in two-dimensional models using multisite interstitial stimulation

We analyzed central interstitial potential differences during multisite stimulation to assess the feasibility of using those recordings to measure cardiac microimpedances in multidimensional preparations. Because interstitial current injected and removed using electrodes with different proximities allows modulation of the portion of current crossing the membrane, we hypothesized that multisite interstitial stimulation would give rise to central interstitial potential differences that depend on intracellular and interstitial microimpedances, allowing measurement of those microimpedances. Simulations of multisite stimulation with fine and wide spacing in two-dimensional models that included dynamic membrane equations for guinea pig ventricular myocytes were performed to generate test data ( partial differentialphio). Isotropic interstitial and intracellular microimpedances were prescribed for one set of simulations, and anisotropic microimpedances with unequal ratios (intracellular to interstitial) along and across fibers were prescribed for another set of simulations. Microimpedance measurements were then obtained by making statistical comparisons between partial differentialphio values and interstitial potential differences from passive bidomain simulations (Deltaphio) in which a wide range of possible microimpedances were considered. Possible microimpedances were selected at 25% increments. After demonstrating the effectiveness of the overall method with microimpedance measurements using one-dimensional test data, we showed microimpedance measurements within 25% of prescribed values in isotropic and anisotropic models. Our findings suggest that development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.

Cell and tissue responses to electric shocks

AIM

Existing models of myocardial membrane kinetics have not been able to reproduce the experimentally-observed negative bias in the asymmetry of transmembrane potential changes (DeltaV(m)) induced by strong electric shocks. The goals of this study are (1) to demonstrate that this negative bias could be reproduced by the addition, to the membrane model, of electroporation and an outward current, I(a), part of the K(+) flow through the L-type Ca(2+)-channel, and (2) to determine how such modifications in the membrane model affect shock-induced break excitation in a 2D preparation.

METHODS AND RESULTS

We conducted simulations of shocks in bidomain fibres and sheets with membrane dynamics represented by the Luo-Rudy dynamic model (LRd'2000), to which electroporation (LRd + EP model) and the outward current, I(a), activated upon strong shock-induced depolarization (aLRd model) was added. Assuming I(a) is a part of K(+) flow through the L-type Ca(2+)-channel enabled us to reproduce both the experimentally observed rectangularly-shaped positive DeltaV(m) and the value of near 2 of the negative-to-positive DeltaV(m) ratio. In the sheet, I(a) not only contributed to the negative bias in DeltaV(m) asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaV(m). Electroporation, in its turn, was responsible for the decrease in cathode-break excitation threshold in the aLRd sheet, compared with the other two cases, as well as for the occurrence of the excitation after the shock-end rather than during the shock.

CONCLUSIONS

The incorporation of electroporation and I(a) in a membrane model ensures match between simulation results and experimental data. The use of the aLRd model results in a lower threshold for shock-induced break excitation.

Electroporation of the heart

Defibrillation shocks are commonly used to terminate life-threatening arrhythmias. According to the excitation theory of defibrillation, such shocks are aimed at depolarizing the membranes of most cardiac cells resulting in resynchronization of electrical activity in the heart. If shock-induced changes in transmembrane potential are large enough, they can cause transient tissue damage due to electroporation. In this review evidence is presented that (a) electroporation of the heart tissue can occur during clinically relevant intensities of the external electrical field, and (b) electroporation can affect the outcome of defibrillation therapy; being both pro- and anti-arrhythmic.

Role of microscopic tissue structure in shock-induced activation assessed by optical mapping in myocyte cultures

INTRODUCTION

Termination of ventricular fibrillation by electric shocks is believed to be due to the direct activation of large tissue mass that may be caused by microscopic virtual electrodes formed at discontinuities in tissue structure. Here, microscopic shock-induced activation was measured optically in myocyte cultures; spatially averaged microscopic Vm measurements were compared with macroscopic measurements from left ventricular (LV) tissue.

METHODS AND RESULTS

Experiments were performed in linear cell strands of different width (approximately 0.1 and 0.8 mm) and isolated porcine LV preparations. Uniform field shocks were applied across strands or LV preparations during diastole and action potential (AP) plateau. Depending on shock strength, three different types of activation were observed in cell strands. Weakest shocks produced "delayed make" activation that started on the cathodal strand side after long latency and rapidly spread to the anodal side. Stronger shocks caused "make" activation with short latency and rapid spread across strands. Strongest shocks caused nonuniform "make-break" activation where the cathodal side was activated with a short latency but activation of the anodal side was delayed until after the shock end due to a large negative shock-induced polarization. Spatial averaging of Vm responses across 0.1-mm (but not 0.8-mm) strands resulted in AP upstrokes and plateau polarizations that closely resembled the Vm responses measured in LV myocardium. The shock strength for the transition between fast and delayed activation in 0.1-mm cell strands and LV myocardium was similar as well.

CONCLUSION

These data provide evidence that microscopic tissue structures with dimensions of approximately hundred microns are responsible for shock-induced activation of ventricular tissue.

Examination of stimulation mechanism and strength-interval curve in cardiac tissue

Understanding the basic mechanisms of excitability through the cardiac cycle is critical to both the development of new implantable cardiac stimulators and improvement of the pacing protocol. Although numerous works have examined excitability in different phases of the cardiac cycle, no systematic experimental research has been conducted to elucidate the correlation among the virtual electrode polarization pattern, stimulation mechanism, and excitability under unipolar cathodal and anodal stimulation. We used a high-resolution imaging system to study the spatial and temporal stimulation patterns in 20 Langendorff-perfused rabbit hearts. The potential-sensitive dye di-4-ANEPPS was utilized to record the electrical activity using epifluorescence. We delivered S1-S2 unipolar point stimuli with durations of 2-20 ms. The anodal S-I curves displayed a more complex shape in comparison with the cathodal curves. The descent from refractoriness for anodal stimulation was extremely steep, and a local minimum was clearly observed. The subsequent ascending limb had either a dome-shaped maximum or was flattened, appearing as a plateau. The cathodal S-I curves were smoother, closer to a hyperbolic shape. The transition of the stimulation mechanism from break to make always coincided with the final descending phase of both anodal and cathodal S-I curves. The transition is attributed to the bidomain properties of cardiac tissue. The effective refractory period was longer when negative stimuli were delivered than for positive stimulation. Our spatial and temporal analyses of the stimulation patterns near refractoriness show always an excitation mechanism mediated by damped wave propagation after S2 termination.

Ionic currents involved in shock-induced nonlinear changes in transmembrane potential responses of single cardiac cells

An exhaustive characterization of how an isolated cardiac cell responds to applied electric fields could serve as an important groundwork for understanding responses of more complex higher order systems. Field stimulation of single cardiac cells during the early plateau of the action potential results in a nonuniform change in transmembrane potential (Vm) across the cell length that is more heavily weighted in the negative direction. These negatively shifted Vm responses are not replicated theoretically using present day membrane models. The goal of this study was to explore the membrane currents involved in the field responses during the plateau by selectively blocking various ion channels. Enzymatically isolated single guinea pig cells were stimulated with uniform field S1-S2 pulses, and the transmembrane potential responses were optically recorded from several sites along the cell length to assess the drug effect. We used nine different pharmacological agents to manipulate the conductance of major cardiac ion channels of which only barium (Ba2+) altered the transmembrane potential responses. At 50 microM Ba2+, which specifically blocks inwardly rectifying current I(K1), the negative shift in Vm responses was accentuated. At 1 mM Ba2+ , which blocks both I(K1) and sustained plateau current I(Kp), the negative shift diminished. However, 1 mM Ba2+ also depolarized the cells, and depressed or completely eliminated the action potential. Based on these results we conclude that I(K1) contributes to field-induced responses during the plateau stimulation by passing a net inward current, which when blocked accentuates the negative shift in the Vm responses. A conclusive role of I(Kp) could not be demonstrated because of confounding changes in membrane potential. However, from our results it remains as the most viable candidate for the elusive current that contributes a net outward current to produce negatively weighted Vm responses during plateau stimulation and warrants further investigation.

Asymmetry in membrane responses to electric shocks: insights from bidomain simulations

Models of myocardial membrane dynamics have not been able to reproduce the experimentally observed negative bias in the asymmetry of transmembrane potential changes (DeltaVm) induced by strong electric shocks delivered during the action potential plateau. The goal of this study is to determine what membrane model modifications can bridge this gap between simulation and experiment. We conducted simulations of shocks in bidomain fibers and sheets with membrane dynamics represented by the LRd'2000 model. We found that in the fiber, the negative bias in DeltaVm asymmetry could not be reproduced by addition of electroporation only, but by further addition of hypothetical outward current, Ia, activated upon strong shock-induced depolarization. Furthermore, the experimentally observed rectangularly shaped positive DeltaVm, negative-to-positive DeltaVm ratio (asymmetry ratio) = approximately 2, electroporation occurring at the anode only, and the increase in positive DeltaVm caused by L-type Ca2+-channel blockade were reproduced in the strand only if Ia was assumed to be a part of K+ flow through the L-type Ca2+-channel. In the sheet, Ia not only contributed to the negative bias in DeltaVm asymmetry at sites polarized by physical and virtual electrodes, but also restricted positive DeltaVm. Inclusion of Ia and electroporation is thus the bridge between experiment and simulation.

Effects of electroporation on optically recorded transmembrane potential responses to high-intensity electrical shocks

The outcome of defibrillation shocks is determined by the nonlinear transmembrane potential (Δ Vm) response induced by a strong external electrical field in cardiac cells. We investigated the contribution of electroporation to Δ Vm transients during high-intensity shocks using optical mapping. Rectangular and ramp stimuli (10–20 ms) of different polarities and intensities were applied to the rabbit heart epicardium during the plateau phase of the action potential (AP). Δ Vm were optically recorded under a custom 6-mm-diameter electrode using a voltage-sensitive dye. A gradual increase of cathodal and well as anodal stimulus strength was associated with 1) saturation and subsequent reduction of Δ Vm; 2) postshock diastolic resting potential (RP) elevation; and 3) postshock AP amplitude (APA) reduction. Weak stimuli induced a monotonic Δ Vm response and did not affect the RP level. Strong shocks produced a nonmonotonic Δ Vm response and caused RP elevation and a reduction of postshock APA. The maximum positive and maximum negative Δ Vm were recorded at 170 ± 20 mA/cm2 for cathodal stimuli and at 240 ± 30 mA/cm2 for anodal stimuli, respectively (means ± SE, n = 8, P = 0.003). RP elevation reached 10% of APA at a stimulus strength of 320 ± 40 mA/cm2 for both polarities. Strong ramp stimuli (20 ms, 600 mA/cm2) induced a nonmonotonic Δ Vm response, reaching the same largest positive and negative values as for rectangular shocks. The transition from monotonic to nonmonotonic morphology correlates with RP elevation and APA reduction, which is consistent with cell membrane electroporation. Strong shocks resulted in propidium iodide uptake, suggesting sarcolemma electroporation. In conclusion, electroporation is a likely explanation of the saturation and nonmonotonic nature of cellular responses reported for strong electric stimuli.

Nonlinear effects in subthreshold virtual electrode polarization

Introduction of the virtual electrode polarization (VEP) theory suggested solutions to several century-old puzzles of heart electrophysiology including explanation of the mechanisms of stimulation and defibrillation. Bidomain theory predicts that VEPs should exist at any stimulus strength. Although the presence of VEPs for strong suprathreshold pulses has been well documented, their existence at subthreshold strengths during diastole remains controversial. We studied cardiac membrane polarization produced by subthreshold stimuli in 1) rabbit ventricular muscle using high-resolution fluorescent imaging with the voltage-sensitive dye pyridinium 4-[2-[6-(dibutylamino)-2-naphthalenyl]-ethenyl]-1-(3-sulfopropyl)hydroxide (di-4-ANEPPS) and 2) an active bidomain model with Luo-Rudy ion channel kinetics. Both in vitro and in numero models show that the common dog-bone-shaped VEP is present at any stimulus strength during both systole and diastole. Diastolic subthreshold VEPs exhibited nonlinear properties that were expressed in time-dependent asymmetric reversal of membrane polarization with respect to stimulus polarity. The bidomain model reveals that this asymmetry is due to nonlinear properties of the inward rectifier potassium current. Our results suggest that active ion channel kinetics modulate the transmembrane polarization pattern that is predicted by the linear bidomain model of cardiac syncytium.

Hyperpolarization and lysophosphatidylcholine induce inward currents and ethidium fluorescence in rabbit ventricular myocytes

Strong electric pulses produce reversible or irreversible membrane breakdown (electroporation). We analysed the permeation properties of minute pores caused by hyperpolarization or lysophosphatidylcholine (LPC) by comparing the amount of charge carried by irregular inward currents (I(hi)) with changes in ethidium bromide (EB) fluorescence in isolated rabbit ventricular myocytes. Forty-second negative pulses from a holding potential of -20 mV induced I(hi) whose conductance increased with hyperpolarization; the mean conductance (G(hi)) was 63.6 +/- 9.9 pS pF(-1) (mean +/- S.E.M., n = 9) at -160 mV. EB fluorescence increased during voltage pulses in parallel with the time integral of I(hi) (Q(hi)), with the magnitude of the increases in nuclear EB fluorescence being 5.3 times greater than in the cytoplasm at -160 mV. Similar hyperpolarization-induced parallel increases in I(hi) and EB fluorescence were also obtained in Na(+)-free, N-methyl-D-glucamine (NMDG) solution. LPC (10 microM) induced large (101.2 +/- 21.2 pS pF(-1), n = 16), rapid (rise times, 1-10 ms) I(hi) with slow relaxation rates at -80 mV that reflected increases in G(hi) to 94.3 +/- 24.8 pS pF(-1) (n = 8) at 6 min. Plots of EB fluorescence vs. Q(hi) were well fitted by a common Hill's equation with a Hill coefficient of 0.97. Taken together, our findings indicate that hyperpolarization and LPC produced pores having the same filter properties for the permeation of small ions, including ethidium(+), and that I(hi) (carried in part by Ca(2+)) generated by membrane breakdown are capable of supplying sufficient ions to evoke abnormal excitation and contraction in cardiac myocytes.

Averaging over depth during optical mapping of unipolar stimulation

Numerical simulations have predicted the distribution of transmembrane potential during electrical stimulation of cardiac tissue. When comparing these predictions to measurements obtained using optical mapping techniques, the optical signal should not be compared to the transmembrane potential calculated at the surface of the tissue, but instead to the transmembrane potential averaged over depth. In this paper, the bidomain model is used to calculate the transmembrane potential in a three-dimensional slab of cardiac tissue, stimulated by a unipolar electrode on the tissue surface. For an optical decay constant of 0.3 mm and an electrode radius of 1 mm, the surface transmembrane potential is more than a factor of three larger than the transmembrane potential averaged over depth. Our results suggest that optical mapping underestimates the surface transmembrane potential during electrical stimulation.

Decomposition of field-induced transmembrane potential responses of single cardiac cells

In this study, we used a multi-site optical mapping system to record field-induced responses of single cells isolated from guinea pig hearts. The cells were stained with voltage sensitive dye di-8-ANEPPS and stimulated with two uniform field (S1-S2) pulses along their longitudinal axes. The first pulse (S1 = 5 ms, <10 V/cm) was applied during rest and elicited an action potential. The second pulse (S2 = 10 ms, 4-50 V/cm) was applied 15 ms after the break of the S1 pulse (during the action potential plateau). The transmembrane potential responses, Vm(F)s, were optically recorded from up to 12 sites along the cell length using a fiber optic based optical mapping system at a resolution of 17 or 25 microm. The field-induced Vm(F)s had a complex spatio-temporal pattern. We show that these responses can be decomposed into simpler components. The first component, termed the differential-mode component (Vmd(F)), is like the response of a passive cell. The second component, termed the common-mode component (Vmc(F)), is identical all along the cell and adds a constant offset to the differential mode response of various sites along the cell length, to produce the total Vm(F) responses of the cell.

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.

Mechanisms of make and break excitation revisited: paradoxical break excitation during diastolic stimulation

Onset and termination of electric stimulation may result in "make" and "break" excitation of the heart tissue. Wikswo et al. (30) explained both types of stimulations by virtual electrode polarization. Make excitation propagates from depolarized regions (virtual cathodes). Break excitation propagates from hyperpolarized regions (virtual anodes). However, these studies were limited to strong stimulus intensities. We examined excitation during weak near-threshold diastolic stimulation. We optically mapped electrical activity from a 4 x 4-mm area of epicardium of Langendorff-perfused rabbit hearts (n = 12) around the pacing electrode in the presence (n = 12) and absence (n = 2) of 15 mM 2,3-butanedione monoxime. Anodal and cathodal 2-ms stimuli of various intensities were applied. We imaged an excitation wavefront with 528-micros resolution. We found that strong stimuli (x5 threshold) result in make excitation, starting from the virtual cathodes. In contrast, near-threshold stimulation resulted in break excitation, originating from the virtual anodes. Characteristic biphasic upstrokes in the virtual cathode area were observed. Break and make excitation represent two extreme cases of near-threshold and far-above-threshold stimulations, respectively. Both mechanisms are likely to contribute during intermediate clinically relevant strengths.