INTRODUCTION

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RECENT INVESTIGATION OF ELECTRICAL stimulation of the heart revealed an important role of tissue heterogeneity in the generation and propagation of muscle excitation. One of the important intrinsic forms of the heterogeneity consists of inequality of anisotropic properties of the extracellular and intracellular spaces of the cardiac syncytium. This inequality was first theoretically described within the framework of the bidomain model (9, 18, 29), which represents cardiac tissue as two interpenetrating extra- and intracellular domains with different conductivities along and across the direction of the fibers, which are coupled via membrane resistance. Using the bidomain model, Sepulveda et al. (26) predicted the existence of adjacent areas of hyperpolarization and depolarization during unipolar stimulation of the tissue. These areas were termed virtual electrode polarizations (VEPs). For a point-size cathodal stimulus, the transmembrane potential (V_m) distribution pattern had a central depolarized virtual cathode (VC) region with a characteristic dog-bone shape and two elongated hyperpolarized virtual anode (VA) regions on the sides that were parallel to the direction of the fibers. In the linear bidomain model, for the opposite polarity of the stimulus, the VEP pattern was symmetrically reversed.

The dog-bone VEP pattern induced by point stimulation was experimentally confirmed using electrode mapping (31) and optical imaging (12, 19, 30). This virtual electrode phenomenon resulted in the formulation of a unified theory of stimulation and suggested solutions to the old puzzles of break-excitation and anodal stimulation (24, 30). The concept of activating function generalized VEP theory to electric fields of any geometrical configuration (27). In particular, strong electric shocks applied during defibrillation also induce areas of adjacent positive and negative polarization, which can be considered VEPs (8). This concept allowed the explanation of shock-induced arrhythmias and defibrillation failure via virtual electrode-induced phase singularities (7, 15, 16).

Despite the impressive success of VEP theory in a wide range of investigations, the very existence of VEPs remains controversial as it pertains to subthreshold stimulation (STS) (1). Measurements of subthreshold VEPs represent a significant experimental challenge (1). Nevertheless, STS plays a crucial role in the generation and propagation of electric pulses. STS of Purkinje fibers was shown to interrupt ventricular tachycardia by synchronization of ventricular excitation (25). Preconditioning by STS inhibited the excitability of Purkinje fibers, which is in contrast to the facilitation of muscle cell fiber excitability (6). Finally, STS is used in the assessment of tissue coupling (1, 2, 14, 22).

Using optical imaging and the active bidomain model, we sought to determine the existence and dynamics of VEPs during unipolar STS.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Experimental preparation, optical mapping setup, and protocol. This study conformed to the guidelines of the American Heart Association. The experiments were performed in vitro on hearts obtained from New Zealand White rabbits (n = 4). In two additional experiments, guinea pig hearts (n = 2) were used to check for possible interspecies differences. The hearts were placed onto a Langendorff apparatus where they were retrogradely perfused with oxygenated modified Tyrode solution as previously described (21). Motion artifacts in optical recordings were suppressed by 15 mM 2,3-butanedione monoxime (BDM). The voltage-sensitive dye pyridinium 4-{2- [6-(dibutylamino)-2-naphthalenyl]-ethenyl}-1-(3-sulfopropyl)- hydroxide (di-4-ANEPPS; 0.5 µM; Molecular Probes; Eugene, OR) was added to the circulating solution within 5 min. Hearts were stained for 40 min before the recordings were started.

The optical mapping setup used for acquisition of the optical signals was described previously (20, 21). Briefly, the light produced by a 250-W quartz-tungsten-halogen DC-powered light source passed through a 520 ± 45-nm excitation filter, was reflected by a 585-nm dichroic mirror, and passed through a 50-mm lens before it illuminated a rabbit heart. The fluorescence emitted from the heart was collected by the same lens, passed through the dichroic mirror, and filtered by a long-pass filter (>610 nm). The light was then detected by a l6 × 16 photodiode array (C4675; Hamamatsu).

For each subthreshold test, stimulus V_m traces (ST-V_m) were recorded from 256 channels of the photodiode array focused on the 5 × 5-mm window around the tip of the test-stimulus electrode. Sampling was performed at a rate of 2,900 frames/s. Therefore, we had a space resolution of 312 µm and a time resolution of 0.3 ms.

For improvement of the signal-to-noise ratio, we averaged 10 consecutive recordings for each stimulus polarity kept at the same duration and current strength. Averaging resulted in a threefold improvement in the signal-to-noise ratios. V_m maps and ST-V_m traces were constructed from these averaged data.

Calibration was performed as previously described (5). Briefly, we assumed resting potential to be 85 mV and action potential amplitude to be 100 mV.

To reach steady state, the heart was paced with 20 basic pulses (with a cycle length of 350 ms) using a bipolar electrode at the base of the left ventricle far from the field of view. After the basic drive, a test-current stimulus was applied from a unipolar electrode (0.12-mm platinum-iridium-Teflon-coated wire) that was positioned in the middle of a 5 × 5-mm field of view at the anterior wall of the left ventricle. The test stimulus was delivered at a coupling interval of 300 ms from a constant-current source (A385; WPI; Sarasota, FL). An ECG was recorded to verify suprathreshold and subthreshold pacing. After determination of the diastolic pacing thresholds for cathodal and anodal pulses, only subthreshold test stimuli were applied. The subthreshold amplitude was kept at 0.1 mA less than the cathodal threshold, and the duration was 20-60 ms. The polarity of the stimuli was reversed each time to ensure a correct comparison between anodal and cathodal stimulations. Basic pacing stimulus strength was adjusted to twice the diastolic threshold of excitation.

Numerical models. We guided our experiments with computer simulations based on the two-dimensional active bidomain model with Luo-Rudy phase I ion channel kinetics (17). For the cases of passive bidomain simulations, the transmembrane current was described by Ohm's law. The two-dimensional slice of cardiac tissue was assumed to have straight fibers and constant intracellular and extracellular conductivities along and across the direction of the fibers. The parameters for the cardiac tissue were the same as those used by Roth (24). The boundaries were sealed for the intracellular space and grounded (zero potential) for the extracellular space. Different-polarity STSs of 0.8 × threshold strength and 60 ms duration were applied from a point-size source to the center of a 2 × 2-cm square domain. The space steps in the directions both across and along the fibers were chosen to be 0.1 mm, which was less than half of the smallest space constant. The time step was 10 µs. To solve for the extracellular potential, the fast Fourier transform method (28) was employed at each step as the most robust and the fastest for our case. Repeating the simulations for the twice-smaller space and time steps confirmed the stability and accuracy of our calculations to <0.001 mV. All calculations were performed on a Pentium 800 MHz personal computer. The results were obtained in terms of V_m values and ionic currents and were plotted and analyzed with MATLAB software (MathWorks; Natick, MA).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

ST-V_m distribution exhibits classical dog-bone-shaped pattern. Pacing thresholds determined in our experiments ranged from 0.15 to 0.60 mA for cathodal stimulation and from +0.85 to +1.76 mA for anodal stimulation. A representative example of optical maps of the V_m recorded at different times (2, 4, and 10 ms) during 20-ms cathodal and anodal STS is shown in Fig. 1. Even for subthreshold stimuli, the VEP pattern is dynamic. Small VEPs are created around the electrode tip almost instantaneously (faster than our temporal resolution) after the application of the stimulus, and the pattern then rapidly spreads out with a simultaneous increase in magnitude of both depolarization and hyperpolarization. The most pronounced VEP pattern is observed at ~4 ms (13), which is determined by the time constant for the passive cardiac tissue resistor-capacitor network. Later VEPs continue to grow slowly; in the case of the cathodal stimulus, this occurs by spreading of the two regions of hyperpolarization, and in the case of the anodal stimulus, it occurs by spreading of the two regions of depolarization. In both cases, the maximum polarization at these two regions diminishes, which makes it more challenging to detect the characteristic VEP pattern at times >10 ms after the onset of the stimulus.

View larger version (57K): [in this window] [in a new window]   Fig. 1.   Experimental virtual electrode polarizations (VEPs) at different times during subthreshold stimulation (STS). Optically recorded and averaged maps of transmembrane potentials (Vm) were obtained from a 5 × 5-mm area of anterior epicardium of rabbit heart for unipolar subthreshold current anodal and cathodal stimuli (±0.5 mA, 20 ms). Sepulveda's dog-bone pattern of VEPs for anodal (A) and cathodal (B) stimuli grows in size with time and becomes asymmetric; central depolarized area for cathodal stimulus at 10 ms is larger than the corresponding hyperpolarized area for anodal stimulus. Vm varies from 90 mV (in blue) to 80 mV (in red); 85 mV (in white) represents the resting state.

Resting tissue at diastole cannot be considered totally passive. A remarkable asymmetry exists in the VEPs for anodal and cathodal stimuli at 10 ms in Fig. 1. First, the central hyperpolarized area for the anodal pulse is substantially smaller than the corresponding depolarized area for the cathodal pulse. The distance from the electrode tip to the closest point with no deviation from the resting potential (white area) is 0.7 mm in the first case, whereas in the second case it is 1.4 mm, which is twice as large. The average ratio of these distances for cathodal vs. anodal stimuli obtained from all animals (n = 4) was 1.9 ± 0.3. Second, VC areas for the anodal stimulus have a maximum depolarization of +1.9 mV and therefore, in absolute terms, are 2.1 times more pronounced than the VA areas for the cathodal stimulus, where the maximum hyperpolarization is only 0.9 mV. The average ratio (n = 4) of the maximum polarizations of the side virtual electrodes for anodal vs. cathodal stimulation was 2.3 ± 0.2.

View larger version (27K): [in this window] [in a new window]   Fig. 2.   VEPs at different times during STS obtained from active two-dimensional bidomain simulations with Luo-Rudy ion channel kinetics. Images for anodal (A) and cathodal (B) stimuli (±60 µA/cm, 20 ms) show the growth of the VEP with time as well as the slight asymmetry of the VEP with respect to the stimulus polarity. Vm variations are within the range of ±1 mV; 84.5 mV represents the resting state (in white).

View larger version (19K): [in this window] [in a new window]   Fig. 3.   Simulated VEP and subthreshold stimulation induced by Vm (ST-Vm) for the passive bidomain model. A: VEP patterns for cathodal and anodal stimuli of the same amplitude at 2 ms after the stimulus application. B: time courses of the Vm changes from the two points of virtual cathode (VC; in red) and virtual anode (VA; in blue) indicated by boxed areas in A. For the passive model, the VEP at any time is reversed with the reversal of the stimulus polarity.

View larger version (31K): [in this window] [in a new window]   Fig. 4.   Experimental VEP and ST-Vm. A: optical maps of VEP patterns for cathodal and anodal stimuli of the same amplitude at 2 ms after the stimulus application. An example of an optical recording of Vm is also shown (bottom). B: time courses of the Vm changes from the two points of VC (in red) and VA (in blue) indicated by boxed area in A. VEP patterns are asymmetric with respect to reversal of the stimulus polarity, with a larger area of depolarization for the cathodal stimulus compared with the corresponding area of hyperpolarization for the anodal stimulus. A slight negative trend in the resting potential is due to slow residual repolarization from the previous beat.

View larger version (19K): [in this window] [in a new window]   Fig. 5.   Simulated VEPs and ST-Vm for active bidomain model. A: VEP patterns are illustrated for cathodal and anodal stimuli of the same amplitude at 2 ms after the stimulus application. B: time courses of the Vm changes from the two points of VC (in red) and VA (in blue) indicated by boxed area in A. VEP patterns are asymmetric with respect to reversal of the stimulus polarity, with larger area of depolarization for the cathodal stimulus compared to the corresponding area of hyperpolarization for the anodal stimulus. These results are in agreement with experimental recordings shown Fig. 4.

Nonlinearity in inward rectifier current causes dog-bone-shaped asymmetry. We analyzed the contributions of different ionic currents into the formation of the ST-V_m traces at the two sites of interest. Figure 6A shows the time course of the changes of the major currents during stimulation. This image illustrates that the total transmembrane current is affected primarily by the inward rectifier potassium current (I_K1), which is known to be responsible for the maintenance of the resting potential. According to our simulations, for cathodal STS, due to rather small deviations of V_m from the resting value, the I_K1 plays the major role for almost the entire central depolarized dog-bone-shaped region with perhaps the nonsignificant exception of a tiny area around the tip of the electrode. This observation excludes a possible explanation of the asymmetry as being created by the influence of the undeveloped excitation in the case of cathodal stimulation.

View larger version (19K): [in this window] [in a new window]   Fig. 6.   Ionic currents and inward rectifier potassium current (IK1) conductivities during STS. Changes in major currents (left) are shown at the two points of VC (in red) and VA (in blue) during cathodal (A) and anodal (B) STS. IK1 is the primary current in both cases and behaves asymmetrically with respect to the reversal of the stimulus polarity. Time courses of IK1 conductivity (GK1; right) are provided at the same two points of VA (in red) and VA (in blue) (indicated by boxed areas) and the site of the stimulation (in black). GK1 changes unequally for cathodal vs. anodal STS.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Conditions for detection of VEP patterns. Advances in voltage-sensitive dye techniques have enabled us to detect VEP patterns on the surface of the heart during stimulation. However, in most of the reported results, the stimuli have been either very strong (suprathreshold) or they have been applied during the plateau phase of the action potential. In the first case, stronger shocks produce higher VEP magnitudes and therefore require less voltage resolution. If a strong shock is delivered during diastole, the resulting VEP pattern becomes overlapped by excitation within several milliseconds, thus preventing one from observing possible VEP dynamics at later times. We show here that for STS, the VEP pattern is most pronounced at 4-5 ms from the moment of the stimulus application, which is the time that is comparable with the resistance-capacitance time of the tissue. Then, because of charge diffusion, the pattern slowly becomes less spatially concentrated with the diminishing of the V_m differences. The STS VEP is asymmetrical with respect to the polarity of the stimulus. We explained the modulation of the VEP pattern by the nonlinear influence of the transmembrane currents, primarily the I_K1. These facts should be taken into consideration when one is trying to experimentally obtain the ST-V_m distribution as well as in attempts to make certain conclusions regarding the tissue properties, for instance, such as intracellular conductance (1), from the STS data.

View larger version (32K): [in this window] [in a new window]   Fig. 7.   VEP for weak cathodal stimulus applied during plateau phase of the action potential: experiment and active bidomain simulation. A: optical maps of VEP at 10 ms of the 0.5-mA, 15-ms stimulus that was applied at a 50-ms coupling interval. B: same VEP obtained from active bidomain simulations is shown. For the same stimulus strength, the resulting VEP for plateau-phase stimulation was larger compared to the stimulation at resting state (see Fig. 1). Vm values are shown as deviations from normal action potential values.

Nonlinearity of V_m response to electric shock. The V_m response to external shock plays a critical role in pacing, defibrillation, and cardioversion. It is generally a function of the strength of the external field, the time of its application, its polarity, and possibly other factors. Many studies investigating the effect of stimulus polarity on V_m changes (V_m) have appeared recently. In experiments on cardiac cell strands, Cheek et al. (3) demonstrated that negative V_m values for a strong anodal stimulus applied during the plateau phase are bigger than positive V_m values for the same-strength cathodal shocks. This asymmetry was attributed to nonlinearity in Ca²⁺ channel kinetics. Similar results have been obtained from microelectrode recordings of guinea pig papillary muscle plateau-phase V_m values (33) and from isolated ventricular myocytes (4). The main idea of these studies consists of emphasizing the crucial role of active ion channel properties in generation of the V_m response to electric stimulation.

Limitations. An optical mapping setup collects averaged fluorescence not only from the surface of the epicardium, but also from a thin layer beneath that surface (10, 11). Therefore, without knowing the exact three-dimensional pattern of the V_m distribution, it is hard to make conclusions about the reasons for the observed asymmetry in response to stimuli of different polarities. Aside from that, the experimental part of our study was accomplished with the excitation-contraction uncoupler BDM, which is known to affect ionic channel properties. Nevertheless, we believe that the results of our computer simulations, which show good qualitative agreement with experimentally observed ST-V_m patterns, alleviate these limitations.