Line Stimulation Parallel to Myofibers Enhances Regional Uniformity of Transmembrane Voltage Changes in Rabbit Hearts
Abstract The sign of transmembrane voltage (Vm) change (ΔVm) in the heart during unipolar point stimulation is nonuniform, which introduces dispersion of states of Vm-dependent ion channels that depends on fiber orientation. We hypothesized that line stimulation parallel to cardiac fibers increases regional uniformity of the ΔVm sign. To test this, we evaluated electrode current distribution and ΔVm produced by unipolar line stimulation in isolated rabbit hearts. The Vm-sensitive fluorescent dye, di-4-ANEPPS, and a laser scanner provided ΔVm measurements at 63 spots in an 8×8-mm epicardial region. Line stimulation was tested at specific angles with respect to the fiber direction. Current peaks occurred at electrode ends. For electrodes parallel to fibers (0°), epicardium in regions beyond the ends exhibited a nonuniform ΔVm sign, whereas epicardium between the ends exhibited a uniform ΔVm sign that was essentially negative (hyperpolarized) during anodal pulses and positive (depolarized) during cathodal pulses. The ΔVm sign between the ends became less uniform when the stimulation angle was increased relative to the long axis of the fibers. At 90°, the ΔVm sign between the ends was nonuniform and was frequently opposite, near versus away from the electrode. Spatial distributions of ΔVm during line stimulation were qualitatively predictable from anisotropic effects of point stimulation provided that combined effects of points along the electrode and points with higher current near ends were considered. For biphasic line stimulation, ΔVm during the second phase was weakly correlated with the temporal sum of effects of phases given individually, indicating limited ability of summation to predict ΔVm. Thus, uniformity of the ΔVm sign during stimulation is enhanced in the region between the ends of a line electrode parallel to fibers. This may lessen arrhythmogenic dispersion of Vm-dependent ion channel states in the region.
The transmembrane voltage (Vm) change produced by and during a stimulation pulse (ΔVm) is thought to be responsible for changes in states of Vm-dependent membrane ion channels that lead to excitation or repolarization. The distribution of ΔVm is difficult to measure with conventional microelectrode techniques because of interference from the stimulation electric field and inability to record at many locations simultaneously. Vm-sensitive dye fluorescence techniques have been used to measure ΔVm optically, which has overcome the problem of electrical interference and has allowed measurements at many locations.1 2 3 4 5 6 7 Recent measurements have shown that ΔVm at sites a few millimeters away from a unipolar point stimulation electrode in anisotropic myocardium is nonuniform and contains a prominent ΔVm sign reversal on the axis parallel to myocardial fibers but not on the axis perpendicular to the fibers. Thus, regions that have ΔVms of opposite signs occur away from the electrode on perpendicular axes. These effects were not predicted by one-dimensional cable theory8 9 but were predicted by more recent two- and three-dimensional theory of myocardium, assuming realistic anisotropic resistivities in the intracellular and extracellular spaces.10 11 The ΔVm during point stimulation introduces different Vm-dependent Na+ channel excitation states on perpendicular axes at a given time after the onset of stimulation given in diastole. For example, early excitation occurs in a “dogbone-shaped” virtual cathode region perpendicular to fibers for cathodal stimulation and in two virtual cathode regions away from the electrode in the direction parallel to fibers for anodal stimulation.6 7 12 The ΔVm may also contribute to the induction of cardiac arrhythmias when the stimulation is given in the vulnerable period. Saypol and Roth,13 using a mathematical bidomain model of the myocardium, have demonstrated that depolarization (positive ΔVm) of the tissue under a point cathodal electrode and away from the electrode in the direction perpendicular to the fibers and hyperpolarization (negative ΔVm) in the direction parallel to the fibers modify the refractory period differently in the two directions, resulting in unidirectional block and stable reentry.13 This suggests that the nonuniform ΔVm produced by point stimulation may not be advantageous during pacing or antiarrhythmic electrical stimulation.
The present study focuses on whether a line electrode having a specific orientation with respect to myocardial fibers can influence the uniformity of the ΔVm sign in a region of the heart. Effects of line stimulation on ΔVm may be predicted by considering the line electrode to be a set of point electrodes that together produce the sum of the various ΔVms produced by each point electrode. One consideration is that the ΔVm produced by each point should depend on the amount of current emanating from the point. Theoretical studies have shown that flat circular-shaped disk electrodes produce a larger current density near the edges of the disk compared with areas near the disk center.14 15 Since the geometry of a line electrode is different from that of a point electrode or disk, stimulation current emanating from a line electrode may have a different distribution from that of a point electrode or across the area of a disk. Another consideration is that the ΔVm should depend on orientation of the line electrode with respect to the myocardial fibers. For a line electrode oriented parallel to fibers, tissue on either side of the electrode is located away from points in the electrode in the direction perpendicular to fibers, ie, the direction in which the sign of ΔVm does not reverse. Such stimulation may enhance uniformity of the ΔVm sign in the region between electrode ends, ie, on either side of the electrode.
In the present study, computer simulations and measurements were performed to determine the distribution of current delivered by line stimulation electrodes. Also, ΔVm during line stimulation parallel or at other angles with respect to the fibers was examined in regions between line electrode ends and beyond ends.
Materials and Methods
Hearts from 13 New Zealand White rabbits were arterially perfused as described previously.7 The perfusate contained (mmol/L) NaCl 129, KCl 4.5, CaCl2 1.8, MgCl2 1.1, NaHCO3 26, Na2HPO4 1, and glucose 11, along with 0.04 g/L bovine serum albumin bubbled with 95% O2/5% CO2 at a pH of 7.3 to 7.4, an aortic pressure of 60 to 80 cm H2O, and a temperature measured in the right ventricular cavity of 35°C to 37°C. Diacetyl monoxime was added at a concentration of 20 mmol/L to lessen motion effects in optical recordings.16
Hearts were stained with 400 to 800 mL of perfusate containing 0.5 mg di-4-ANEPPS (Molecular Probes, Inc) dissolved in 1 mL ethanol. Fluorescence signals that followed ΔVm were measured with a laser scanner system using an argon laser with a wavelength of 514 nm. Acousto-optic deflectors steered the beam to scan 63 laser spots having diameters of 100 μm in an 8×8-mm region of the ventricular epicardium. The intensity of laser light, measured with a light power meter and probe (models 815 and 818-ST, Newport), was 271±64 mW to the acousto-optic deflectors and 13±8 mW to the heart during recording. This corresponded to a density of light at each laser spot on the heart of ≈128 W/cm2 that was time-shared among the spots. Fluorescence emitted from the heart passed through a 590-nm long-pass filter and onto a photomultiplier tube having a wide-band current-to-voltage amplifier. The scanner system provided fluorescence recordings with a sampling rate of 1 kHz for each laser spot.7 17
ΔVm Produced by Unipolar Line Stimulation
Continuous line stimulation electrodes (Fig 1⇓) were fabricated from a 0.25-mm-diameter Ag wire and a glass microscope slide. The glass introduced optical losses of 8.4% of laser light and 8.9% of fluorescence. A single electrode or two orthogonal electrodes with insulation between them at their contact point were cemented to the glass near the ends with insulating epoxy. The wire segment between cemented regions provided continuous linear electrodes ≈13 mm long. When two electrodes were used, the stimulation pulse was switched to either electrode.
Intermittent line stimulation electrodes (Fig 1⇑) were fabricated from 25 insulated 0.25-mm-diameter Ag wires that were cemented to form a ribbon. Two coplanar glass microscope slides were cemented edge to edge on either side of the ribbon. The plane containing the ribbon was perpendicular to the plane containing the glass. The ribbon was tilted 40° in its plane to help prevent blockage of the laser light. While being viewed under a dissection microscope, wire ends were cut even with the glass to produce a 10-mm line of terminals having an average terminal width of 0.23 mm, terminal length of 0.3 mm, and interterminal insulation space of 0.12 mm.
Electrodes were positioned in the center of a rotatable ring that was held by a stationary bearing. Electrodes gently contacted the anterior epicardium of the left ventricle in eight hearts and right ventricle in five hearts. Contact with the epicardium was verified visually and confirmed by current measurements with intermittent line electrodes. Contact pressure was lower than perfusion pressure to avoid occlusion of epicardial vessels. Electrodes could be rotated without noticeably displacing the heart or the electrode center. The stimulation return electrode was a 2-cm2 Ag/AgCl coil or a titanium mesh electrode mounted on a flexible arm on the posterior epicardium.
The grid of laser spots was rotated to each desired angle by using a computer program that calculated spot coordinates for the acousto-optic deflectors.18 For each new angle, the glass was rotated so that electrodes were parallel to two sides of the grid, crossed the center of the grid, and did not block laser light for any spots. In four hearts for which several angles were tested, the first angle was chosen so that an electrode was slightly clockwise from the perpendicular to the expected fiber direction, based on previous measurements of the fiber direction on the rabbit anterior left ventricle.4 18 19 Trials were performed with grid angles that changed in 10° increments rotating in the counterclockwise direction. In two hearts in which a single continuous line electrode was used, angles were varied over a range of 130° to ensure that electrode orientations approximately parallel and perpendicular to the fiber direction were tested. In two hearts in which two orthogonal continuous line electrodes were used, the range of grid angles was reduced to 100°.
In all hearts, fiber direction was determined histologically with 5-μm serial sections parallel to the epicardial surface.7 In 12 hearts, fiber direction was also determined by measuring the fast axis of propagation produced by cathodal point stimulation in diastole at 1.5 times threshold strength.
In each test of line stimulation, the heart was paced with an epicardial bipolar electrode located away from the recording region in the direction toward the left side of the heart using a strength of ≈2 times diastolic threshold, a duration of 5 milliseconds, and an interval of 250 milliseconds. Four pacing stimuli were given, and then a 5- to 10-millisecond unipolar monophasic or biphasic line stimulation pulse of 24 to 250 mA and either polarity was given during the plateau of a previously induced action potential. Thus, action potential phase-zero depolarization existed just before the line stimulation, allowing measurement of the ΔVm as a percentage of the phase-zero depolarization amplitude at each spot, and the ΔVm during line stimulation was not obscured by new phase-zero depolarization.2 Preliminary experiments in which stimulation timing was varied as much as 40 milliseconds indicated that the ΔVm sign change away from the electrode in the direction parallel to fibers was not sensitive to the precise time within the first half of the action potential when the stimulation was given.
Current Distribution on Line Electrodes
Video recordings of continuous line electrodes during stimulation were obtained to determine whether spatial differences in the change in the electrode reflectance relative to the reflectance before the stimulation indicated nonuniform current density at the electrode surface. Reflectance, ie, the fraction of the total radiant flux incident upon the electrode that was reflected, was used as an index of the accumulation of the AgCl on the exposed wire. We considered that electrode reflectance will change when current-induced AgCl formation or electrolysis occurs at the surface and that under some conditions these changes are monotonically related to current density at the surface. A glass slide containing an electrode was inverted and placed on an externally blackened 50-mL beaker filled with 0.9% NaCl or the perfusion solution. A chlorided Ag coil return electrode was normally located in the bottom of the beaker. A circular lamp (model FC8T9-CW, General Electric), magnifying lens, and camera (model CG684, General Electric) were positioned above the beaker to illuminate the electrode and image the light reflected from it. Timing of stimulation pulses was indicated by a light-emitting diode connected to the stimulation timer and placed in the field of view. Phototransistors (model 276-145A, Tandy) connected to custom circuits that produced voltages inversely related to light intensity and having identical responses to a given change in intensity were positioned on the video monitor at the ends and center of the electrode and at the light-emitting diode. Signals were low pass–filtered and recorded on a digitizing oscilloscope (model Norland 3001A, High-Techniques). Slight baseline oscillations introduced by interference were numerically subtracted.
Current distribution on intermittent line electrodes was measured by placing a 10-Ω resistor in series with each terminal. The value of the resistors was sufficiently low such that voltages across the resistors during stimulation were only ≈0.3% of the applied voltage. Voltages across resistors were measured with an isolated differential amplifier (model AD210, Analog Devices) and a digitizing oscilloscope. Measurements for all terminals were performed sequentially, and then the first measurement was repeated to verify reproducibility.
The ΔVm at each spot was determined as the difference in fluorescence averages from a 7-millisecond time window just before the line stimulation pulse to a 3-millisecond time window during the pulse minus the difference in fluorescence averages at the same times relative to the action potential phase-zero depolarization in a preceding action potential that did not receive line stimulation. For monophasic pulses, the time window during the pulse was the last 3 milliseconds preceding the millisecond that contained the break of the pulse. For biphasic pulses, the time window during each phase was the last 3-milliseconds preceding the millisecond that contained the break of the phase. Each ΔVm was normalized to the amplitude of the action potential phase-zero depolarization (action potential amplitude) from the same recording.2 Measurements from unsmoothed recordings were performed by a computer program and visually with action potentials that received the line stimulation pulse overlaid with the previous action potential, for which ink of a different color was used. Reproducibility of visual measurements was verified by different individuals and by comparison with computer measurements. Measurements for trials in which the stimulation strength was zero resulted in negligible ΔVm, indicating that measurements were not affected by baseline shifts due to photobleaching. Contours of ΔVm were generated by Surfer (Golden Software).7 20
A uniformity index of the ΔVm sign was defined as the number of spots at which a positive ΔVm was found minus the number at which a negative ΔVm was found, divided by the total number of spots at which a ΔVm was found. A ΔVm was found when the magnitude of ΔVm was ≥5% of the action potential amplitude. The sign of this uniformity index thus represents the dominant sign of ΔVm; the maximum and minimum magnitudes of the uniformity index that are possible are 1 and 0.
Two-tailed paired t tests were used to determine statistical significance of differences in (1) current for terminals at electrode ends versus the average current for all terminals, (2) ΔVm when one return electrode was used versus that when another return electrode was used, (3) fiber direction determined with serial sections versus that determined with the fast axis of propagation, and (4) slopes, intercepts, and coefficients of correlation from linear regressions of ΔVm produced by biphasic stimulation with the sum of ΔVm produced by the phases for the measurements corresponding to the first phase versus those corresponding to the second phase. The differences in slopes and intercepts were also evaluated using nonparametric two-tailed sign tests.
The null hypothesis that positive ΔVm and negative ΔVm were equally probable was tested with nonparametric two-tailed sign tests.21 When the sign of ΔVm is sufficiently uniform (ie, of those spots that undergo ΔVm, a sufficiently large number undergo positive [negative] ΔVm), the null hypothesis will be rejected. When the sign of ΔVm is not uniform (ie, of those spots that undergo ΔVm, the number that undergo positive ΔVm is not sufficiently different from the number that undergo negative ΔVm), the null hypothesis will not be rejected. Values of P<.05 were considered significant.
Computer Simulation of Current on a Line Electrode
The distribution of current on a line electrode in a conductive medium was evaluated by the finite-element method using an electrostatics solver (Algor) and a personal computer (model P4D-66, Gateway 2000). Laplace’s equation was solved subject to the conditions that the potential on the surface contacting the electrode was 10 or 100 V and that the potential on the perimeter of the conductive medium was zero. The conductive medium was modeled as a 100×100-cm sheet with resistivity of either 100 or 1000 Ω/cm based on a thickness of 1 cm. A 1-cm line electrode was located in the center. A 3.6×3.6-cm central region that contained the electrode was modeled as 8100 elements with sizes of 0.4×0.4 mm. The surrounding region that did not contain the electrode was modeled as 200 elements with sizes of 10×4.82 cm above and below the central region and 50 elements with sizes of 9.64×0.72 cm on either side of the central region. A simulation in which the surrounding region that did not contain the electrode was modeled as just four large elements indicated that the currents at each of the nodes along the line electrode were not sensitive to this change in element sizes. Also, changes in the resistivity of the conductive medium or the potential on the surface contacting the electrode did not alter any of the fractions of current of the nodes (current at a node divided by total current at all nodes).
Nonuniform Current Distribution on a Line Electrode
Fig 1⇑ (bottom panel) shows the current distribution at the line electrode surface in the finite-element model. Currents through 25 element faces with lengths of 0.4 mm in contact with the line electrode are shown as fractions of the total current. Current through element faces at electrode ends was 151% larger than current at faces near the electrode center. When the finite-element size was increased to 0.6 mm to test whether a coarser grid produces a smaller peak as proposed by Wiley and Webster15 (not shown), the rise in current at electrode ends decreased to 113%.
Changes in Electrode Reflectance
Nonuniformity of current density at the surface of continuous line electrodes in a saline bath was determined from changes in electrode reflectance by comparing reflectance during the stimulation pulse to reflectance before the pulse. Changes in reflectance, and not absolute reflectance, were measured. We considered that regions where current density is greatest should undergo the greatest decrease in reflectance because of the AgCl formation at the electrode surface during anodal stimulation. Also, reactions other than AgCl production may occur at the electrode surface and may produce their own effects on reflectance. To determine limits within which AgCl reactions may occur, pulse duration and polarity were varied. When the first pulse from a new Ag electrode was a 10-mA cathodal pulse with a duration of 1 second, macroscopic bubbles occurred during the pulse. When a 10-mA anodal pulse was applied with a duration of ≈8 seconds, a light blue color and bubbles occurred, which increased the reflectance, possibly because of reflection of light at the surfaces of bubbles. Neither bubbles nor blue color was observed under the conditions that (1) the first pulse was anodal, (2) the polarity of subsequent pulses of equal current strength and duration alternated, and (3) pulses did not exceed a duration of ≈2 to 4 seconds for a strength of 10 mA. Under these conditions, an anodal pulse decreased electrode reflectance, and a later cathodal pulse increased electrode reflectance. These reflectance changes were reproducible when such pulse pairs of equal strength and duration were repeated, which was verified for up to 50 repetitions in one electrode. Thus, under the three conditions stated above, decreased reflectance during anodal stimulation corresponded to generation of AgCl, and increased reflectance during later cathodal stimulation corresponded to electrolysis of the AgCl. It is possible that instead of electrolysis of the AgCl, microscopic bubbles increased reflectance of the surface during the cathodal pulse in each pair. However, it was found that the introduction of an extra cathodal pulse after the normal cathodal pulse in a pair produced macroscopic bubbles similar to those produced by giving a cathodal pulse first to a new Ag electrode. Also, if electrolysis of the AgCl did not occur during the cathodal pulses, AgCl produced during the later anodal pulses would be expected to accumulate, producing a cumulative decrease in reflectance. The repetitions of pulse pairs did not produce a cumulative decrease in reflectance after the first four pulses.
Fig 2⇓ shows an example of changes in reflectance of a line electrode that correspond to anodally induced AgCl production and cathodally induced AgCl electrolysis. The upper trace for each polarity shows the onset (downward deflection) and termination (upward deflection) of the pulse. The other traces show changes in reflectance at the ends and center of the electrode. Upward deflections represent decreases in reflectance of the electrode. The anodal pulse decreased reflectance mostly at electrode ends. The cathodal pulse increased reflectance mostly at electrode ends, again indicating higher current density at ends.
In experiments in which stimulation strength was increased to produce macroscopic bubbles, the bubbles occurred sooner at electrode ends than at centers. This further indicated higher current density at the ends.
Current Measurements In Vitro
Current distribution on intermittent line electrodes was determined by measuring current through each terminal of the electrode. All 25 of the terminals were connected through their respective current-sensing resistors to a common node that was connected to a single constant-current source having a return electrode in the beaker as shown in Fig 3⇓. At any given time, the voltages on all terminals with respect to the return electrode were identical to within <0.3%. Fig 3⇓ shows that current near electrode ends (0 or 10 mm) was larger than current between ends. Results were similar for different return electrode locations. Fig 4⇓ shows that similar rises in current near electrode ends occurred for different total current strengths.
Current Measurements in Hearts
Intermittent line electrodes were positioned on the epicardium of four rabbit hearts to determine the current distribution produced by line stimulation. The top panel of Fig 5⇓ shows the fraction of current that passed through each terminal. For anodal stimulation, current through terminals at electrode ends, ie, 0 and 10 mm, was 10.4±6.9 mA, whereas average current for all terminals was 5.7±2.6 mA (P=.032 for current at ends versus average current, n=8 hearts×ends). For cathodal stimulation, current through terminals at electrode ends was −11.8±7.4 mA, whereas average current for all terminals was −5.7±2.7 mA (P=.012 for current at ends versus average current, n=8 hearts×ends).
The impact of changing the return electrode location on current distribution was evaluated in two hearts by switching between different return electrodes. Two 1.25-cm2 mesh return electrodes were positioned on the posterior epicardium ≈0.7 cm apart at their nearest edges and 2.7 cm apart at their farthest edges. The bottom panel of Fig 5⇑ shows that the current distributions were practically identical when the return lead was connected to one of the return electrodes compared with when the lead was connected to the other return electrode.
ΔVm Produced by Line Stimulation
Line Stimulation Parallel or Perpendicular to Fibers
Fig 6⇓ shows fluorescence recordings of ΔVm produced by stimulation with a continuous line electrode parallel to fibers in a rabbit heart. Recordings from 63 laser spots on the left anterior epicardium show the action potential phase-zero depolarization produced by pacing on the lateral left ventricular epicardium and the effect of line stimulation given 80 milliseconds after pacing. The recording in the upper right corner of each panel shows timings of the pacing and line stimulation pulses. The fluorescence recordings have been inverted so that upward deflections correspond to positive ΔVm and downward deflections correspond to negative ΔVm.
Anodal line stimulation produced ΔVm having a magnitude ≥5% of the action potential amplitude at 59 of the 63 recording spots. Of these 59 spots, the ΔVm was negative at 100% and positive at 0%. Negative ΔVm occurred at spots <1 mm from the stimulation electrode and at spots as far as 3 to 4 mm from the electrode. A region existed near the center of the line electrode where a small ΔVm occurred.
Cathodal stimulation was tested after reversing the line stimulation leads without changing electrode locations, laser spot locations, or stimulation strength. The cathodal stimulation produced ΔVm having a magnitude ≥5% of the action potential amplitude at 52 of the 63 recording spots. Of these 52 spots, the ΔVm was negative at 2% and positive at 98%. A region of small ΔVm existed near the center of the line electrode in which distinct negative ΔVm occurred (eg, recording at row 5, column 5).
Fig 7⇓ shows measurements and contours of ΔVm during the stimulation described in Fig 6⇑. Contour lines are shown for ΔVm of −60% to −10% of the pacing-induced action potential amplitude for anodal stimulation and −10% to 50% for cathodal stimulation in increments of 10%. Magnitudes of ΔVm on either side of the line electrode remained approximately constant or increased with distance (central region) for the first few millimeters away from the electrode. Magnitudes of ΔVm began to decrease in tissue 3 mm from the electrode (corner regions). The ΔVms having the largest magnitudes in the recording region occurred during anodal stimulation, had a negative sign, and were located near electrode ends. For both anodal and cathodal stimulation, a region near the center of the electrode had a negligible ΔVm.
Figs 8⇓ and 9⇓ show effects of stimulation from a continuous line electrode oriented perpendicular to the fibers on Vm-sensitive fluorescence. Stimulation strength and laser spot locations were the same as those in the two preceding figures. Anodal stimulation produced negative ΔVm at all 16 recording spots 0.5 mm from the line stimulation electrode. Some spots farther away from the electrode underwent positive ΔVm. Of the 31 recording spots in the leftmost two columns and the rightmost two columns, 22 underwent positive ΔVm.
Cathodal stimulation shown in Fig 8⇑ produced positive ΔVm at all 16 recording spots 0.5 mm from the line stimulation electrode. Many spots farther away from the line electrode underwent negative ΔVm. Of the 31 recording spots in the leftmost two columns and the rightmost two columns, 22 underwent negative ΔVm.
Fig 9⇑ shows measurements and contours of ΔVm during the line stimulation described in Fig 8⇑. Contour lines are shown for ΔVm of −50% to 30% of the pacing-induced action potential amplitude for anodal stimulation and −30% to 50% for cathodal stimulation in increments of 10%. The patterns of ΔVm were similar for anodal stimulation compared with cathodal stimulation. Four distinct extrema (maxima for anodal stimulation and minima for cathodal stimulation) occurred near corners of the recording region. A valley (anodal stimulation) or ridge (cathodal stimulation) projected along the long axis of the fibers from the center of the electrode. The ΔVm in some regions away from the line electrode had a sign that was the opposite of the sign in the region near the electrode. The ΔVms were negligible at some spots 4 mm to the left or right of the center of the line electrode.
Stimulation with a line electrode parallel to fibers was tested on the left ventricle in six hearts and right ventricle in three hearts. No qualitative differences in results for right versus left ventricular stimulation sites were found. Of the 144 recording spots near (ie, ≈0.5 mm and on either side of) an anodal electrode, 7 spots underwent positive ΔVm and 121 spots underwent negative ΔVm (P<.0001). Of the 279 recording spots far from (ie, in the four columns ≈3 to 4 mm from and on either side of) an anodal electrode, 20 underwent positive ΔVm and 219 underwent negative ΔVm (P<.0001). For cathodal stimulation parallel to fibers, of the 144 recording spots near a cathodal electrode, 82 spots underwent positive ΔVm and 35 spots underwent negative ΔVm (P<.0001). Of the 279 recording spots far from a cathodal electrode, 211 underwent positive ΔVm and 25 underwent negative ΔVm (P<.0001). (In each of the above comparisons, the null hypothesis that occurrences of positive or negative ΔVm were equally probable was rejected.)
Stimulation with a line electrode perpendicular to fibers in the hearts produced the following results. Of the 144 recording spots near an anodal electrode, 30 spots underwent positive ΔVm and 97 spots underwent negative ΔVm (P<.0001). Of the 279 recording spots far from an anodal electrode, 216 underwent positive ΔVm and 28 underwent negative ΔVm (P<.0001). For cathodal stimulation perpendicular to fibers, of the 144 recording spots near a cathodal electrode, 48 spots underwent positive ΔVm and 78 spots underwent negative ΔVm (P=.014). Of the 279 recording spots far from a cathodal electrode, 9 underwent positive ΔVm and 251 underwent negative ΔVm (P<.0001). (In each of the above comparisons, the null hypothesis that occurrences of positive or negative ΔVm were equally probable was rejected.)
Stimulation at Intermediate Angles Relative to Fibers
Fig 10⇓ shows results for a continuous line electrode oriented at various angles with respect to fibers. The numbers of laser spots, out of a total of 63 for each angle tested, that underwent positive ΔVm, negative ΔVm, and no observed ΔVm (ie, a change of <5% of the action potential amplitude) are shown. For electrode orientations parallel to fibers (eg, 0°), many spots underwent ΔVm of one sign, whereas only a few spots underwent ΔVm of the other sign, indicating that the sign of the ΔVm was essentially uniform. There were ≈10 spots in which no ΔVm was observed. The sign of ΔVm remained uniform for a range of electrode orientations having a width of 30° to 40°.
The ΔVm sign was nonuniform for electrode orientations over a range of angles nonparallel to fibers. When the electrode was perpendicular to fibers (90° in Fig 10⇑), 25 to 30 spots underwent ΔVm of one sign, a similar number of spots underwent ΔVm of the opposite sign, and ≈10 spots had no observed ΔVm.
Regions Beyond Electrode Ends
The results above show that uniformity of the ΔVm sign in epicardium between ends of a line electrode increases when the electrode is parallel to fibers. The uniformity in epicardium beyond ends may be different from that between ends. To test this, ΔVm on right or left ventricular epicardium was measured beyond and between electrode ends in six hearts. A 3-mm line electrode that allowed fluorescence recordings between ends of the electrode and up to 3 mm beyond the ends was used. Current distribution measured on a 3-mm line electrode in vitro showed that the current emanated from the entire length of the electrode and that current peaks occurred at ends. Finite-element models of 3- and 10-mm line electrodes indicated that the distribution of the current that emanated from the electrodes was approximately the same for the two electrode lengths. For example, the current emanating from the two ends that occupy a total of 40% of the length of the 3-mm line electrode was 48.4% of the total electrode current. The remaining 51.6% of the total electrode current emanated from the 60% portion of the electrode not at the ends. For the 10-mm electrode, current emanating from the two ends that occupy a total of 40% of the length of the electrode was 52.6% of the total electrode current. The remaining 47.4% of the total electrode current emanated from the 60% portion of the electrode not at the ends.
Again, the results obtained with fluorescence recordings showed no qualitative differences for right versus left ventricular stimulation sites. Fig 11⇓ shows an example of ΔVm measurements during stimulation with a 3-mm electrode in one heart. When the electrode was oriented parallel to the fibers, ΔVm in the epicardium on either side of the electrode (ie, in the vertical rows of spots perpendicular to the electrode and between electrode ends) had an essentially negative sign during anodal stimulation and positive sign during cathodal stimulation. Epicardium beyond electrode ends (ie, in the vertical rows of spots near the left or right side of the recording region) underwent ΔVm of either sign. When the electrode was oriented perpendicular to the fibers, ΔVm in the epicardium on either side of the electrode (ie, in the horizontal rows of spots perpendicular to the electrode and between electrode ends) had a negative sign near the electrode and a positive sign away from the electrode during anodal stimulation and a negative sign away from the electrode during cathodal stimulation. Epicardium beyond electrode ends (ie, in the horizontal rows of spots near the top or bottom of the recording region) underwent ΔVm of either sign.
Uniformity of the ΔVm sign in regions between and beyond electrode ends was evaluated by calculating a uniformity index of the ΔVm sign (see “Materials and Methods”) for each of eight rows of recording spots perpendicular to the electrode. Fig 12⇓ shows the uniformity index of the ΔVm sign for the rows in the combination of all six hearts. The electrode location corresponded to 3 to 6 mm on the abscissa, so that the three leftmost values in each curve represent rows beyond the left end of the electrode, the next three values represent rows between electrode ends, and the two rightmost values represent rows beyond the right end of the electrode. For each row, the null hypothesis that occurrences of positive or negative ΔVm are equally probable (ie, the ΔVm sign is nonuniform) was tested. In each of these tests, ΔVm was found at 29±6 spots. The null hypothesis will be rejected at P<.05 (ie, the ΔVm sign is not nonuniform) when 8 or fewer of the 29 spots undergo ΔVm of a particular sign. This corresponds to a uniformity index of the ΔVm sign having a magnitude >0.45. Rejection indicated that the probability that a ΔVm has a positive sign was different from .5 and the probability that it has a negative sign was different from .5.
When the electrode was parallel to fibers, P values for each of rows 1 through 8 were .1109, .3899, .0015, <.0001, <.0001, <.0001, .0869, and .3989 for anodal stimulation and .0136, .1856, .1213, .0004, <.0001, .0007, .1421, and .2261 for cathodal stimulation. Rejection of the null hypothesis was found in the rows between ends. The dominant sign of ΔVm was negative for anodal stimulation and positive for cathodal stimulation. The ΔVm sign was not uniform (ie, no rejection of the null hypothesis) in most rows beyond ends of the electrode oriented parallel to fibers. In row 1 at 0 mm on the abscissa, which corresponds to ≈3 mm beyond the left end of the electrode, magnitudes of the uniformity index of ΔVm sign increased for both stimulation polarities, and the dominant sign of ΔVm became positive for anodal stimulation and negative for cathodal stimulation.
When the electrode was oriented perpendicular to fibers, the null hypothesis was rejected for only two of the rows between ends for cathodal stimulation and was not rejected for any of the rows between ends for anodal stimulation, indicating a nonuniform ΔVm sign. The P values for each of rows 1 through 8 were .0290, .0278, .1125, .3989, .2431, .3989, .2630, and .2553 for anodal stimulation and .0527, .1438, .3989, .1763, .0169, .0450, .3433, and .3899 for cathodal stimulation. Beyond the left end of the electrode oriented perpendicular to fibers (eg, row 1 at 0 mm on the abscissa), the ΔVm sign was not nonuniform for anodal stimulation (null hypothesis rejected), and the dominant sign was negative for anodal stimulation and positive for cathodal stimulation.
Absence of Effect of a Change in Return Electrode Location on ΔVm
Whether ΔVm on the anterior epicardium depends on the return electrode location on the posterior epicardium was studied in three hearts with intermittent line electrodes on the anterior left or right ventricular epicardium. Either of two return electrodes was used as described (see “Current Measurements in Hearts”). The ΔVm for all laser spots and either line stimulation polarity was not significantly affected by changing the return electrode location (P=.885 for ΔVm with one return electrode versus the other return electrode, n=378 spots×hearts×polarities). When just the spots on either side of and farthest from the line electrode were included in the statistical test, still no significant effect of changing the return electrode location was found (P=.65, n=90).
Temporal Summation of Effects of Biphasic Line Stimulation
The hypothesis that temporal summation of ΔVm during phases given individually predicts the ΔVm during biphasic stimulation was tested on left or right ventricles of four hearts. In a total of 12 tests, the segmented line electrode was parallel to fibers in 5 and perpendicular in 7; the first phase was anodal and the second phase was cathodal in 7, and the first phase was cathodal and the second phase was anodal in 5. For each test, the following line stimulation trials were performed: a 5-millisecond monophasic pulse of one polarity (ie, first phase given individually), a 5-millisecond monophasic pulse of the other polarity given at a 5-millisecond larger delay than that of the first trial (ie, second phase given individually), and a 10-millisecond biphasic pulse consisting of a 5-millisecond phase identical to that of the first trial followed by a 5-millisecond phase identical to that of the second trial. The ΔVms at times that correspond to each of the phases were measured for all trials. Measurements that correspond to the first phase were used as the control. Control linear regressions were performed for the sum of ΔVms corresponding to the first phase for the trials in which phases were given individually versus ΔVms corresponding to the first phase for the trial in which biphasic stimulation was given. Linear regressions were also performed for the sum of ΔVms corresponding to the second phase for the trials in which phases were given individually versus ΔVms corresponding to the second phase for the trial in which biphasic stimulation was given. If the hypothesis is correct, these regressions will give results similar to that of controls. Slopes, intercepts, and coefficients of correlation from the latter regressions were compared with these values from the controls. For all linear regressions, ΔVm produced by the biphasic stimulation was the dependent variable (ie, ordinate), and the sum of ΔVm produced by individual phases was the independent variable (ie, abscissa).
For the linear regressions that correspond to control, the slope, intercept, and coefficient of correlation were 0.88±0.16, −4.6±5.3% of the action potential amplitude, and .83±.10, respectively. For the linear regressions that correspond to the second phase, the regression slope, intercept, and coefficient of correlation were 0.52±0.14, 5.2±5.0% of the action potential amplitude, and .63±.12 (P<.002 as determined by two-tailed t tests, P=.0005 for slopes and P=.0063 for intercepts as determined by nonparametric sign tests, second phase versus control, n=12 pairs of regressions).
The fiber orientation was determined from serial sections of blocks of tissue cut from the regions where the recording and stimulation were performed (see “Materials and Methods”). In eight left ventricles, the fibers were oriented parallel to a line drawn from the left lateroapical region of the heart to the right laterobasal region of the heart at an approximate angle of 27±15° relative to the equatorial plane of the heart. In five right ventricles, the fibers were oriented parallel to a line that was at an approximate angle of 1±17° relative to the equatorial plane of the heart. In eight left ventricles and four right ventricles, the fast axis of propagation in the regions where recording and stimulation were performed was not different from the fiber direction determined with serial sections (P=.18, n=12 ventricles).
Current Distribution on Line Electrodes
Current peaks occurred at electrode ends in our finite-element model (Fig 1⇑), continuous line electrodes (Fig 2⇑), and intermittent line electrodes (Figs 3 through 5⇑⇑⇑). Although previously published models or measurements of current distribution on a line electrode were not found, previous models of a disk electrode or segmented electrode indicate that peaks occur at the edge of a disk electrode and at ends of segments.14 22 The maximum current density at a peak (eg, precisely at the electrode edge) depends on finite-element size (Reference 1414 and the present results) and should depend on microscopic details of the edge.15 Our measurements of current distribution on the electrode in hearts indicate that elevated current did not exist just at the ends but extended several millimeters along the electrode from the ends and that current existed in the central region of the electrode (Fig 5⇑).
Figs 7⇑ and 9⇑ show qualitatively similar patterns of ΔVm during anodal stimulation versus cathodal stimulation. These results are consistent with our finding that current distribution on the electrode is similar for anodal versus cathodal stimulation (Figs 2 through 5⇑⇑⇑⇑). Also, the results suggest that for a given orientation of the line electrode with respect to the fibers, the current pathways in the myocardium during anodal stimulation may have similarities compared with the pathways during cathodal stimulation.
Current distributions and ΔVm were practically unaffected by switching between return electrodes in different locations in a beaker or as far as 2.7 cm apart at their farthest edges on the heart (eg, Figs 3⇑ and 5⇑). This indicates that even with the changes in return electrode location, the line stimulation on the anterior epicardium remained essentially unipolar. Also, since the distances between switched return electrodes exceeded variations in the return electrode location among hearts, the results indicate that the variations did not influence our measurements of current distributions or ΔVm.
We found that current distributions did not depend on the applied current strength. This is consistent with the results of Kim et al,14 in which magnitudes of current were scaled in proportion to applied current strength (Fig 4⇑).
ΔVm Produced by Line Stimulation
The present study shows that line stimulation produces ΔVm having an approximately uniform sign when the electrode is oriented parallel to the myocardial fibers and a nonuniform sign when the electrode is perpendicular or at some intermediate angles to the fibers. The results can be qualitatively predicted by the hypothesis that summation of the ΔVm produced by each point within a line electrode determines the two-dimensional pattern of ΔVm produced on the surface of the myocardium by the whole electrode. Studies have shown that stimulation of anisotropic myocardium with a single point electrode produces reversal of the sign of ΔVm at regions away from the electrode in the direction parallel to fibers (eg, upper left or lower right of each map in Fig 4⇑ of Reference 77 ).4 5 6 7 23 For a line electrode oriented perpendicular to fibers, summation of the ΔVm produced by points in the line would result in regions of reversal of the sign of ΔVm away from the line electrode in the direction parallel to fibers. Such regions occurred in the rabbit hearts on either side of the electrode (eg, Figs 8⇑ and 9⇑). This is consistent with previous experiments in which a set of discrete point electrodes arranged in a line perpendicular to fibers produced a region of reversed polarization away from the electrodes in the direction parallel to fibers.4
The summation hypothesis also predicts the enhanced uniformity of the ΔVm sign produced by a line-stimulation electrode oriented parallel to fibers. Stimulation of anisotropic myocardium with a single-point electrode produces no prominent reversal of the sign of ΔVm at sites away from the electrode in the direction perpendicular to fibers.5 6 7 Summation of ΔVm produced by point electrodes in a line parallel to fibers would result in no reversal of the sign of ΔVm away from the electrode in the direction perpendicular to fibers. This agrees with the results (eg, Figs 6⇑ and 7⇑).
The findings that magnitudes of ΔVm are small at spots near the center of the line electrode oriented parallel to fibers (Fig 7⇑) and at spots away from and on either side of the center of the line electrode perpendicular to the fibers (Fig 9⇑) are also consistent with the summation hypothesis. The current density at the line electrode surface is not constant but is greater near electrode ends. Summation of the various ΔVms produced by points in the line still occurs; however, the ΔVm contribution from points near electrode ends is larger than that from points between ends. For a cathodal line electrode oriented parallel to fibers, regions of myocardium between electrode ends receive positive contributions to ΔVm from local electrode points. The positive contributions are canceled by sign-reversed contributions to ΔVm from points near electrode ends (since regions between ends are away from ends in the direction parallel to fibers). Such contributions to ΔVm from electrode ends agree with the finding that the current was elevated near the ends.
For a cathodal line electrode oriented perpendicular to fibers, regions between electrode ends receive positive contributions to ΔVm from points near electrode ends (since regions between ends are away from ends in the direction perpendicular to fibers). Summation of this ΔVm with the positive contribution to ΔVm from local electrode points produces a large positive ΔVm between electrode ends, as seen in Fig 9⇑. The negligible ΔVm in regions away from and on either side of the center of the line electrode (Fig 9⇑) is also consistent with the summation hypothesis and enhanced current density at electrode ends. Cathodal point stimulation produces a dogbone-shaped region of positive ΔVm extending perpendicular to fibers.6 7 The wide parts of dogbones produced by points near the electrode ends in Fig 9⇑ will extend away from and to either side of the center of the electrode and contribute a positive ΔVm there. Because of enhanced current density at points near the electrode ends, contributions of the dogbones at sites away from and to either side of the center of the electrode are large enough to cancel contributions of negative ΔVms from electrode points between the ends. Large current density at points near the electrode ends is further evident from the fact that cathodal stimulation produced negative ΔVms in the four corners of the map (Fig 9⇑), in agreement with the negative ΔVm that occurs away from cathodal electrodes in the direction parallel to fibers.4 5 6 7 23
ΔVm Beyond Electrode Ends
The ΔVm beyond the ends of line electrodes differs markedly from that between the ends (Figs 11⇑ and 12⇑). Whereas epicardium between the ends of an electrode oriented parallel to fibers undergoes ΔVm having one sign, epicardium beyond the ends undergoes ΔVm of either sign. In epicardium as far as 3 mm beyond the ends, the sign becomes more uniform and is the opposite of the sign in epicardium between the ends. For an electrode perpendicular to fibers, the epicardium beyond the ends undergoes ΔVm of increasingly uniform sign at large distances. These results are consistent with the ΔVm sign produced by point stimulation6 7 but with the pattern of ΔVm elongated in the direction of the line electrode.
The largest contribution to ΔVm in regions beyond the ends may be from the nearest electrode end. Considering the hypothetical case in which all of the contribution comes from the nearest electrode end, the ΔVm should be that of point stimulation. Then, reversal of sign of ΔVm would occur beyond the end of an electrode oriented parallel to fibers, and no reversal would occur beyond the end of the line electrode oriented perpendicular to fibers. This agrees with the ΔVm sign at many spots beyond electrode ends in Fig 11⇑. This is consistent with the summation in which (1) a high weighting is given to the ΔVm contributions produced beyond the end by electrode points that are near the end (because current density for the points is large), (2) ΔVm contributions produced beyond the end by electrode points that are not near the end are small (because the distance from the points to the region beyond the ends is large), and (3) no ΔVm contributions are produced beyond the end by any points that are beyond the end (because such points are not in the electrode). Differences in ΔVm beyond the ends of a line electrode compared with the corresponding regions away from a point electrode in the direction parallel or perpendicular to fibers (eg, quadrants in Fig 4⇑ of Reference 77 ) may indicate contributions of points in the line electrode that are not at electrode ends.
Temporal Summation of ΔVm During Biphasic Line Stimulation
The small slope of linear regressions for the second phase of the biphasic stimulation indicated that variation in ΔVm among laser spots produced by biphasic stimulation was smaller than the variation in the sum of ΔVm produced by individual phases. Also, the small coefficient of correlation for the second phase indicated that variation in the sum of ΔVm produced by individual phases did not fully account for variation in the sum of ΔVm produced by the biphasic stimulation. A full account will probably need to incorporate known enhancement of nonlinear membrane processes by biphasic stimulation (eg, recovery of inactivated Na+ channels, where the membrane is hyperpolarized during the first phase and then these channels are reexcited during the second phase).24 25
The main finding is that uniformity of the ΔVm sign in the epicardium on either side of the electrode is enhanced by use of a line stimulation electrode oriented parallel to fibers. This was observed in epicardium that underwent positive ΔVm during cathodal stimulation and negative ΔVm during anodal stimulation. One can speculate that therapeutic or diagnostic stimulation with a line electrode positioned in a specific orientation with respect to fibers could be advantageous by providing better control of the spatial distribution of responses to the stimulation. Responses of membrane ion channels involved in excitation and action potential repolarization depend on Vm. A line stimulation electrode parallel to fibers may produce ion channel responses that are more homogeneous than the responses produced by a point stimulation electrode. This may increase the ability of electrical stimulation to regionally block reentrant activation fronts. Such block is thought to be a mechanism of defibrillation.26 27 28 Also, electrical induction of arrhythmias may depend on regions of opposite ΔVm,13 suggesting that orientation of a line electrode parallel to fibers may prevent arrhythmia induction in the part of the heart where the sign of ΔVm is uniform. Since regions exist beyond electrode ends where the ΔVm sign is markedly less uniform, induction may not be prevented there. If true, an advantage may be gained with a long electrode that follows the orientation of the fibers and for which regions beyond ends are a small fraction of the total region influenced by the electrode, an electrode having ends located in unexcitable regions such as near large vessels, or a continual electrode that has no ends. Finally, the finding that the distribution of ΔVm produced by a line electrode can be qualitatively predicted from summation of the effects of point electrodes in a line suggests that distributions of ΔVm produced by electrodes having other shapes may also be predicted by summing the effects of point electrodes in that shape as long as differences in current density in different parts of the electrode are taken into account.
This study was supported by National Institutes of Health grant HL-52003 and American Heart Association, Alabama Affiliate, Inc, Grant-in Aid 950032. Dr Knisley has a consulting agreement with Guidant Corp, St Paul, Minnesota. The authors are grateful to Liesl M. Fox for performing some of the statistical analysis.
Reprint requests to Stephen B. Knisley, PhD, The University of Alabama at Birmingham, B122 Volker Hall, 1670 University Blvd, Birmingham, AL 35294-0019.
- Received January 14, 1997.
- Accepted May 13, 1997.
- © 1997 American Heart Association, Inc.
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