INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

NORMAL CARDIAC FUNCTION DEPENDS on a high degree of synchronization between myocytes that results from cell-to-cell electrotonic coupling. Communication between neighboring myocytes is mediated by cardiac gap junctions that are composed of connexin proteins through which electrotonic current flows (4). Because cell-to-cell coupling plays a critical role in propagation, repolarization, and arrhythmias (12), a measurement of cell-to-cell coupling in the intact ventricle is important for understanding arrhythmia mechanisms in the whole heart. Cell-to-cell coupling was previously assessed indirectly by immunohistochemical analysis of gap junction protein expression (25, 26, 30). However, these studies provided information regarding gap junction density and distribution but not function. Direct measurements of gap junctional conductance made between isolated cell pairs revealed the kinetics and conductance of gap junction channels and their regulation by pharmacological agents, temperature, phosphorylating conditions, and intracellular pH (22, 34, 39). However, in the intact heart, each myocyte is electrically coupled to ~10 neighbors (11); hence, measurements performed in isolated cell pairs only partially reflect important electrotonic interactions present in intact preparations. Moreover, changes in cell-to-cell coupling could not be related to fiber structure, propagation, or arrhythmias. Assessment of cell-to-cell coupling in multicellular tissues was attempted by measuring overall tissue resistivity in papillary muscle (14) and the canine wedge preparation (40). However, to satisfy linear cable theory, calculations of tissue resistivity from extracellular voltages required uniform flow of current such that the preparation was assumed to be one-dimensional, precluding assessment of resistivity in the intact ventricle.

On the basis of predictions from cable theory, Weidmann (35) and Woodbury and Crill (38) hypothesized that the cardiac space constant () could be determined in isolated, multicellular preparations from the decay in space of transmembrane potential responses (V_m) to subthreshold (ST) stimuli (ST-V_m). These investigators measured values of  ranging between 0.2 mm and 2.0 mm; thereby revealing a relatively long distance over which electrotonic current decayed relative to the myocyte dimensions. However, these studies required tedious, sequential measurements of V_m by multiple intracellular microelectrode impalements, which is not feasible in the intact beating heart.

The advent of voltage-sensitive dye techniques led to the exciting possibility of recording V_m free of stimulus artifacts from hundreds of sites across the intact heart. This feature was widely applied to the investigation of V_m during relatively large defibrillatory shocks (6, 15, 17). However, the distribution of V_m during ST electrical stimuli is more difficult to investigate because it requires a high density of recording sites within a relatively small distance (<2 mm) and a high degree of sensitivity to relatively small changes in V_m. Therefore, we developed a high-resolution optical action potential mapping system capable of measuring V_m with sufficient fidelity to calculate  from the decay of ST-V_m in space, yielding a functional index of cell-to-cell coupling in the intact guinea pig heart. This report establishes the feasibility of measuring  in the intact heart and indicates a strong dependency of  on fiber orientation and pharmacological alterations of gap junction conductance.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Experimental preparation. As described in detail elsewhere (8, 9, 19), adult guinea pigs (n = 20) were anesthetized with pentobarbital sodium (30 mg/kg ip), and perfused as Langendorff preparations with oxygenated (95% O₂-5% CO₂) Tyrode solution at 35 ± 1°C containing (in mmol/l) 130 NaCl, 1.2 MgSO₄, 4.75 KCl, 5.0 dextrose, and 1.25 CaCl₂ (pH 7.40). The right atrium was removed to avoid competitive stimulation from the sinoatrial node. Hearts were stained with the voltage-sensitive dye, di-4-ANEPPS (15 µmol/l) for 10 min, and then positioned in a chamber such that the mapping field was centered over a 5.8 × 5.8 mm region of left ventricular epicardium, 5 mm from the left anterior descending coronary artery, midway between apex and base (Fig. 1A). The epicardial surface of the left ventricle was stimulated with the use of a 70-µm diameter Teflon-coated (except at the tip) silver unipolar electrode placed in the center of the mapping region, with a reference electrode in the perfusate-filled chamber (Fig. 1A). Gentle pressure was applied to the posterior surface of the heart with a movable piston to stabilize the mapped surface against the imaging window of the chamber (9, 24). This also minimized current shunting by eliminating the layer of conductive Tyrode solution between the heart and the imaging window. To ensure that the same cells contributed to fluorescence at each recording pixel throughout the entire experiment, contraction was eliminated with 15 mmol/l of diacetyl monoxime. Although diacetyl monoxime can potentially affect ionic currents (3, 18, 21, 33), this was not a major concern because this study focused on passive and not active membrane properties, and because control measurements were made in every experiment. Cardiac rhythm and stimulus capture were monitored via three silver disk electrodes fixed to the chamber in positions corresponding to electrocardiogram limb leads I, II, and III (8). Although experiments were typically completed within 1 to 2 h, these preparations remained stable for over 4 h of perfusion.

View larger version (36K): [in this window] [in a new window]   Fig. 1.   Experimental preparation and protocol. A: preparation indicating the region (5.8 × 5.8 mm) from which optical measurements of transmembrane potential responses (Vm) were taken (see box). Stimulating electrode was placed in the center of the mapping region. B: experimental protocol for the stimulus waveform (STIM), electrocardiogram (ECG), and optical potentials recorded from sites 0 to 2 mm away from the stimulating electrode. Unlike subthreshold (ST) stimuli, stimuli delivered above threshold were associated with QRS complexes and T waves on the ECG and action potentials in all three sites. ST stimulus was associated with ST-Vm responses at sites a, b, and c. RV, right ventricle; LV, left ventricle; LAD, left anterior descending coronary artery; and DT, diastolic threshold.

High-resolution optical mapping. An optical mapping system was designed with the capability of recording low-level membrane responses from 256 sites in close proximity to the electrode with sufficient fidelity to determine . Because in preliminary experiments we found that excitation spectra of di-4-ANEPPS bound to myocytes peaked at ~500 nm, fluorescence was excited using a 270-W tungsten light source filtered at 500 ± 25 nm. This enhanced fluorescence signals sixfold compared with standard interference filters used previously (7, 9, 19). Fluoresced light was collected using a tandem lens imaging system consisting of a pair of single-lens-reflex photographic lenses (35 mm, f/1.4, and 105 mm, f/2; Nikon), focused at infinity and placed with the bayonet mounts facing outwards. The heart was placed in the focal plane of the objective lens, and a 16 × 16 element photodiode array (model C4675-102, Hammamatsu) was placed at the focal plane of the detector lens. For tandem-lens imaging, magnification, which is determined by the ratio of focal lengths of detector to objective lens (28), was ×3 using this configuration. Fluoresced light exiting the detector lens was filtered (>610 nm) and focused onto the photodiode array. Previously, we (20) found that tandem lens imaging at high magnifications substantially enhanced signal intensity (by over ×3) compared with standard single-lens optics. A current from each photodiode underwent current-to-voltage conversion, amplification (×200), band-pass filtering (0.1-1,000 Hz), multiplexing, and digitization (2,000 samples/s per channel) with 12-bit precision. This configuration allowed us to record V_m with spatial, temporal, and voltage resolutions of 365 µm, 0.5 ms, and 1.0 mV, respectively. Under these circumstances, ST-V_m responses were detected above background noise levels an average of 2.5 and 4.8 mm from the electrode in the transverse and longitudinal directions, respectively.

Experimental protocol. Cathodal ST square wave current pulses were applied to the left ventricular epicardium (see Fig. 1A), whereas ST-V_m was measured from 256 sites surrounding the stimulating electrode. In preliminary experiments, we found that the ST-V_m response at each recording site required ~15 ms to reach steady state. Therefore, it was desirable to use relatively long stimulus pulse widths (~20 ms). However, the diastolic pacing threshold associated with such long pulse widths was <0.1 mA, making delivery of ST stimuli technically difficult. Hence, pacing threshold was increased to ~1.5 mA (at a pulse width of 20 ms) by raising extracellular potassium concentration ([K⁺]_o) to 8 mmol/l. Figure 1B illustrates the pacing protocol used in these experiments. Following a 20-beat steady-state stimulus drive train (400 ms, BCL) delivered at ~1.2× diastolic threshold, the current strength was instantaneously reduced to ~0.8× diastolic threshold, producing ST-V_m that failed to propagate an action potential (Fig. 1B). ST-V_m at each recording site was measured as the maximum change in V_m occurring during the application of ST current relative to resting membrane potential, and was normalized with respect to the amplitude of the baseline action potential at each site. This procedure allowed comparison of V_m between recording sites, as described previously (24). We ensured the reproducibility of ST-V_m responses by repeating stimulus trains in every experiment.

Measurement of . In one-dimensional cable theory, V_m caused by unipolar stimulation from a point source decays exponentially with distance from the site of stimulation. The  of the decay reflects the combined influences of membrane (R_m), intracellular (R_i), and extracellular (R_o) resistances as
where  is the ratio of membrane surface to tissue volume (27). In the heart, R_i reflects the sum of gap junctional and cytoplasmic resistances. Because membrane and cytoplasmic resistances are relatively constant in space (i.e., between cells) and over time throughout diastole (i.e., in the absence of an action potential), a change in  indicates a change in cell-to-cell electrotonic interactions of which gap junctional and extracellular resistances are major determinants. In this study, the decay of ST-V_m along each of multiple linear paths directed away from the site of ST stimulation was fit to a monoexponential for each path.  along any given path was defined as the normalized rate of decay of ST-V_m in that direction.

Measurement of conduction velocity. Conduction velocity (CV) was also measured along multiple linear propagation paths from the site of stimulation. Velocity vectors, which represent the magnitude and direction of CV at each recording site, were calculated by fitting the depolarization time measured at each site to a parabolic surface, and were assigned the gradient of that surface as the velocity vector (2). CV along each direction of propagation was calculated by averaging velocity vectors in that direction. Contour maps were used to depict the spread of activation. Measurements of CV were made along multiple angles with respect to the fast axis of propagation. Girouard et al. (9) found that the fast axis of epicardial propagation corresponds with the longitudinal fiber axis in the guinea pig epicardium.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Optically recorded subthreshold membrane responses. V_m resulting from stimuli delivered above and below diastolic threshold are compared in Fig. 2. In this example, recordings are shown from equally spaced sites (a-d in Fig. 2) at increasing distances from the stimulus electrode. ST-V_m (Fig 2, left) was characterized by depolarizing and repolarizing phases that exactly followed the timing of the stimulus waveform. Both phases followed exponentials having similar time constants (9.2 ± 0.7 ms for depolarization and 9.7 ± 0.8 ms for repolarization, P = 0.18) that were not affected by the distance of the cell from the site of stimulation (9.1 ± 0.7 ms for proximal cells and 9.2 ± 0.8 ms for distal cells, P = 0.26). In contrast to the time-course of ST-V_m responses, the amplitude of ST-V_m varied considerably in space, decaying with increasing distances from the site of stimulation (sites a-d). Several clear distinctions between action potentials and ST-V_m are illustrated in Fig. 2. First, because they arise from regenerative active ionic processes, action potentials did not decay in amplitude at sites distal to the electrode. Second, action potential repolarization far outlasted the stimulus pulse, whereas the onset of ST-V_m repolarization coincided exactly with the stimulus pulse due to its passive membrane nature. Third, action potential depolarization, plateau, and repolarization were generated by active ionic currents, giving the action potential its distinctive shape; whereas ST-V_m had a symmetric morphology, typical of the charging and discharging of a resistive-capacitive network, which characterizes passive properties of myocytes. Fourth, whereas action potential depolarization was associated with step delays when the impulse propagated from one site to the next (Fig. 2, sites a-d), ST-V_m depolarization and repolarization were essentially simultaneous at all sites.

View larger version (9K): [in this window] [in a new window]   Fig. 2.   Optical recording Vm induced by a stimulus above (right) and below (left) diastolic threshold from 4 sites 0 to 1.5 mm away from the electrode (sites a-d, respectively). Top, a schematic representation of the stimulus pulse in both cases illustrating time course and relative amplitude.

Follows tissue anisotropy. Figure 3 illustrates the effect of tissue anisotropy on the decay of ST-V_m across the epicardial surface from a representative experiment. ST-V_m recorded from sites along the longitudinal and transverse fiber axes are shown in Fig. 3A. Whereas ST-V_m decayed away from the site of stimulation in both directions, the decay was faster transverse compared with longitudinal to cardiac fibers. The isopotential map (Fig. 3B) shows that the distribution of ST-V_m was anisotropic, and closely followed fiber orientation (Fig. 3B, dotted lines). Consequently,  was longer longitudinal compared with transverse to cardiac fibers (Fig. 3C). Similar results were seen in all eight experiments (Table 1), where  was significantly (P < 0.001) shorter (by ~50%) in the transverse compared with longitudinal directions.

View larger version (13K): [in this window] [in a new window]   Fig. 3.   Cardiac space constant () follows tissue anisotropy. A: ST-Vm shown for sites 0-2.5 mm from the stimulating electrode along the longitudinal (Long) and transverse (Trans) axes of propagation. B: distribution of ST-Vm surrounding the site of ST stimulation shown as isopotential plot. C: decay of ST-Vm in space plotted along and transverse to fiber orientation.  was calculated from the exponential decay constant in each direction. Trans is ~50% of Long reflecting directional differences in intercellular coupling.

ST-V_m does not exhibit dogbone effect. Previously, adjacent regions of opposite V_m polarizations were described during unipolar shock (>5× diastolic threshold) stimulation of the heart (16, 23, 37). For example, regions of hyperpolarization (virtual anodes) developed parallel to cardiac fibers during cathodal shocks resulting in a nonuniform distribution of depolarization around the stimulating electrode (i.e., dogbone effect), which was attributed to unequal anisotropy ratios of the intra- and extracellular domains (i.e., bidomain model) (32). In the present study, a cathodal ST stimulus resulted in depolarizing only ST-V_m that decayed monotonically in space without apparent hyperpolarizations or dogbone effect (Fig. 3). However, our results are consistent with earlier findings regarding the myocardial response to strong unipolar stimuli. As shown in Fig. 4A, a shock (20× diastolic threshold) delivered during the plateau of an action potential, was associated with both depolarizations (red) and hyperpolarizations (blue). The distinct presence of depolarizations under the electrode and hyperpolarizations in adjacent regions along the longitudinal fiber axis (dashed line in Fig. 4A) supports earlier findings (16, 23, 37) regarding the unique bidomain characteristics of myocardium (i.e., dogbone effect).

View larger version (31K): [in this window] [in a new window]   Fig. 4.   Differential effect of ST vs. suprathreshold stimuli on ST-Vm. A: distribution of Vm on the guinea pig epicardium during application of a shock reveal a "dogbone" effect with adjacent regions of depolarized (red) and hyperpolarized (blue) myocardium. B: bidomain simulation illustrating differences in Vm associated with shocks and ST stimuli. Inset: whereas shocks were associated with depolarizations near and hyperpolarizations distal to the electrode, ST stimuli-induced hyperpolarizations were present but very small. Bidomain calculations were performed using the methods described in Ref. 29, except that the surface-to-volume ratio was increased by a factor of 10 to better match the calculated Vm distribution to the experiment, and the electrode size was 200 µm long and 160 µm in diameter.

Relationship between CV and . Because cell excitability is constant throughout the mapped epicardial surface, differences in CV relative to fiber orientation can only be explained by directional differences in intercellular coupling. Therefore, if  is a measure of axial resistivity, one would expect a direct relationship between CV and , which, according to theory, is linear (35). The relationship between CV and  was examined in a subset of experiments (n = 4), where both parameters were measured along four angles (0°, 30°, 45°, and 90°) with respect to the longitudinal fiber axis. Figure 5 illustrates that indeed the relationship between CV and  was linear. Also, this relationship was qualitatively and quantitatively similar in every experiment (Fig. 5), indicating that  was a reflection of absolute intercellular resistance. The slope of this relationship indicates the extent to which a change in  affects CV in the intact heart.

View larger version (19K): [in this window] [in a new window]   Fig. 5.   Linear relationship between conduction velocity and  from 4 experiments, where both parameters were measured at 4 angles (0°, 30°, 45°, and 90°) with respect to the fast axis of propagation. A similar relationship between conduction velocity and  was observed in all experiments.

Heptanol reduces . Figure 6 illustrates the effect of the uncoupling agent heptanol from a representative experiment. Heptanol caused a profound reduction in CV (by 60%) relative to control, which was paralleled by a marked (~50%) reduction in  measured along the longitudinal direction (Fig. 6, top). The effect of heptanol on CV and  was reversible, because both parameters recovered progressively during heptanol washout. The effect of heptanol on  is summarized for all experiments in Fig. 7. Heptanol produced consistent attenuation of ST-V_m, resulting in significant (P < 0.001) shortening of  (0.7 ± 0.1 mm) compared with control (1.5 ± 0.1 mm). Heptanol produced a comparable (~50%) reduction in CV (from 22 to 12 cm/s) and  (from 0.8 to 0.4 mm) when measured along the transverse direction (not shown in Fig. 7). Therefore, the anisotropy of CV and  was maintained during perfusion with heptanol.

View larger version (45K): [in this window] [in a new window]   Fig. 6.   Effect of heptanol (H) on conduction (C) velocity and  in a representative experiment. H reduced both C velocity, as indicated by crowding of isochrones, and  by ~50%. Exponential fits describing the decay of ST-Vm as a function of distance were associated with r2 values of 0.98-0.99. Both C and  recovered toward baseline during 10 and 20 min of H washout (WO).

View larger version (16K): [in this window] [in a new window]   Fig. 7.   Summary data illustrating effect of heptanol on ST-Vm in 4 experiments. Heptanol accelerated decay of ST-Vm, and therefore shortened . Exponential fits describing the decay of ST-Vm as a function of distance were associated with r2 of 0.99 (Control) and 0.98 (Heptanol).

Flecainide does not reduce . Figure 8 illustrates the effect of sodium channel blockade with flecainide on CV and  from a representative experiment. While perfusion with flecainide reduced CV by 40%, it had essentially no effect on  measured along the longitudinal (1.4 ± 0.2 mm before and 1.5 ± 0.1 mm after flecainide) and transverse (0.8 ± 0.2 mm before and 0.9 ± 0.2 mm after flecainide) fiber axis. Therefore, despite a significant reduction in CV caused by reducing excitability,  was not affected, reaffirming that  was an index of passive, not active electrical properties.

View larger version (27K): [in this window] [in a new window]   Fig. 8.   Effect of flecainide on  (top) and conduction velocity (bottom) is shown. Although conduction velocity was significantly slowed with flecainide, no significant effect on  was detected. Exponential fits describing the decay of ST-Vm as a function of distance was associated with r2 values of 0.99 (Control) and 0.98 (Flecainide).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Electrical coupling between cells plays a critical role in propagation, repolarization, and arrhythmias. Therefore, the measurement of cell-to-cell coupling in the intact heart is important for understanding arrhythmia mechanisms such as reentry, which are inherently dependent on cell-to-cell interactions. This study establishes the feasibility of measuring  as an index of cell-to-cell coupling in the intact heart and indicates that  is strongly influenced by fiber structure and pharmacological interventions that alter cell-to-cell coupling.

Optically recorded subthreshold membrane responses. Previously, optical mapping was used extensively to measure changes in V_m during propagation (i.e., action potentials) (1, 8, 31) or defibrillatory shocks (5, 6, 10, 15, 23). In this report, we establish the feasibility of measuring small V_m changes produced by ST stimuli in the intact heart. Optical mapping was well suited for this purpose because it allowed the simultaneous measurement of V_m at 256 sites in very close proximity to the stimulus electrode, and because optical signals were free of electrical artifacts produced by the stimulus. The characteristics of optically recorded ST-V_m supported involvement of passive but not active membrane properties because 1) the amplitudes of ST-V_m were substantially smaller than those of action potentials, not reaching levels required for sodium channel activation (see Fig. 2), 2) ST-V_m consisted of depolarizing and repolarizing phases which coincided exactly with the stimulus pulse, and 3) the exponential time constants () of both phases were equal (9.4 ms) and, based on the theory of passive resistive-capacitive membranes, predicted a diastolic membrane resistance (R_m = /C_m = 9.4 ms/1 µF/cm² = 9.4 k/cm²) in the range of those measured previously (5-20 k/cm²) (13, 35, 36). These observations support the absence of nonlinear, voltage, and/or time-dependent ionic contributions to ST-V_m.

Measurement of . Several lines of evidence indicate that optical measurements of  reflected cell-to-cell coupling in the intact guinea pig heart. Values of  in the guinea pig ventricle were similar to those measured previously in Purkinje (1.9 mm) and trabecular (1.0 mm) preparations (35, 36). Moreover, as expected,  closely followed tissue anisotropy, being largest longitudinal and smallest transverse to cardiac fibers.  was also linearly related to CV, as predicted by linear cable theory, providing further evidence that it is an index of axial resistivity. Finally,  was reduced by intercellular uncoupling pharmacologically, but unaffected by depressing excitability suggesting selective sensitivity to factors that influence passive and not active membrane properties.

Limitations. Optical mapping is well suited for measuring V_m on the epicardial surface of intact hearts. However, V_m could not be measured from deep layers of myocardium, and hence the contribution of these layers to the complex three-dimensional nature of cellular coupling could not be investigated using this technique. More importantly, fiber direction is known to change across the ventricular wall, thereby affecting cell-to-cell coupling in that direction. Moreover, in this study, no major structural discontinuities, such as those introduced by fibrotic lesions near the border zone of an infarction were present. The presence of such discontinuities may influence the measurement of ST-V_m (and hence ) by violating continuous cable theory. Furthermore, our measurement of  is sensitive to both intra- and extracellular resistivities, and our data does not allow the distinction between the two. Optical measurements may underestimate maximal V_m due to spatial averaging over a single pixel and with depth into the tissue. This is expected to mostly affect the measurement of V_m in very close proximity to the stimulus electrode, where the greatest amount of variation in V_m is expected. However, in this study, we found that V_m in very close proximity to the electrode were ~30 mV. Greater depolarizations would be expected to stimulate active ionic currents and hence not constitute a ST response. Finally, in three-dimensional myocardium, ST-V_m is not expected to have a purely exponential decay with distance from the stimulating electrode. The analytical solution for V_m by using the bidomain model with equal anisotropy ratios indicate that the fall off in three dimensions is approximately described by exp(r/)/r, where r is the scaled distance from the electrode (27). However, our data indicate that the decay of V_m was well described by a single exponential.