© 1997 American Heart Association, Inc.
Articles |
Line Stimulation Parallel to Myofibers Enhances Regional Uniformity of Transmembrane Voltage Changes in Rabbit Hearts
From the Department of Biomedical Engineering and the Division of Cardiovascular Disease of the School of Medicine, The University of Alabama, Birmingham.
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Abstract The sign of transmembrane voltage (Vm) change (
Vm) 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 Vm sign. To
test this, we evaluated electrode current distribution and
Vm produced by unipolar line stimulation in isolated
rabbit hearts. The Vm-sensitive fluorescent dye,
di-4-ANEPPS, and a laser scanner provided Vm
measurements at 63 spots in an 8x8-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 Vm sign, whereas epicardium
between the ends exhibited a uniform Vm sign that was
essentially negative (hyperpolarized) during anodal pulses and positive
(depolarized) during cathodal pulses. The Vm sign
between the ends became less uniform when the stimulation angle was
increased relative to the long axis of the fibers. At 90°, the
Vm sign between the ends was nonuniform and was
frequently opposite, near versus away from the electrode. Spatial
distributions of Vm 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, Vm during the second phase was weakly
correlated with the temporal sum of effects of phases given
individually, indicating limited ability of summation to predict
Vm. Thus, uniformity of the Vm 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.
Key Words: transmembrane potential • fluorescent dye • electrical stimulation
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Introduction |
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The transmembrane voltage (Vm) change produced by and during a stimulation pulse (
Vm) is thought to be responsible for
changes in states of Vm-dependent membrane ion channels
that lead to excitation or repolarization. The distribution of
Vm 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
Vm 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
Vm at sites a few millimeters away from a unipolar point
stimulation electrode in anisotropic myocardium is
nonuniform and contains a prominent Vm sign reversal on
the axis parallel to myocardial fibers but not on the axis
perpendicular to the fibers. Thus, regions that have Vms
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 Vm 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 Vm 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
Vm) of the tissue under a point cathodal electrode and
away from the electrode in the direction perpendicular to the fibers
and hyperpolarization (negative Vm)
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
Vm 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 Vm sign in a region of the heart.
Effects of line stimulation on Vm may be predicted by
considering the line electrode to be a set of point electrodes that
together produce the sum of the various Vms produced by
each point electrode. One consideration is that the Vm
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 Vm 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 Vm does not reverse. Such
stimulation may enhance uniformity of the Vm 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, Vm during line stimulation
parallel or at other angles with respect to the fibers was examined in
regions between line electrode ends and beyond ends.
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Experimental Preparation
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
Fluorescence Recordings
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 Vm
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 8x8-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
Vm 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.
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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 Vm as
a percentage of the phase-zero depolarization amplitude at each spot,
and the Vm 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 Vm 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-
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.
Data Analysis
The Vm 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 Vm 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 Vm, indicating that
measurements were not affected by baseline shifts due to
photobleaching. Contours of Vm were generated by Surfer
(Golden Software).7 20
A uniformity index of the Vm sign was defined as the
number of spots at which a positive Vm was found minus
the number at which a negative Vm was found, divided by
the total number of spots at which a Vm was found. A
Vm was found when the magnitude of Vm was
5% of the action potential amplitude. The sign of this uniformity
index thus represents the dominant sign of Vm;
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)
Vm 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 Vm produced by
biphasic stimulation with the sum of Vm 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 Vm and negative
Vm were equally probable was tested with
nonparametric two-tailed sign tests.21 When
the sign of Vm is sufficiently uniform (ie, of those
spots that undergo Vm, a sufficiently large number
undergo positive [negative] Vm), the null hypothesis
will be rejected. When the sign of Vm is not uniform
(ie, of those spots that undergo Vm, the number that
undergo positive Vm is not sufficiently different from
the number that undergo negative Vm), 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
100x100-cm sheet with resistivity of either 100 or 1000 /cm based
on a thickness of 1 cm. A 1-cm line electrode was located in the
center. A 3.6x3.6-cm central region that contained the electrode
was modeled as 8100 elements with sizes of 0.4x0.4 mm. The
surrounding region that did not contain the electrode was modeled
as 200 elements with sizes of 10x4.82 cm above and below the central
region and 50 elements with sizes of 9.64x0.72 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).
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Results |
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Nonuniform Current Distribution on a Line Electrode
Finite-Element Model
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.
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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.
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) or cathodal (
) current.
Terminals near the electrode ends had larger current than terminals
between the ends.
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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 heartsxends). 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 heartsxends).
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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.
Vm Produced by Line Stimulation
Line Stimulation Parallel or Perpendicular to Fibers
Fig 6 shows fluorescence
recordings of Vm 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 Vm and downward deflections
correspond to negative Vm.
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Anodal line stimulation produced Vm having a magnitude
5% of the action potential amplitude at 59 of the 63
recording spots. Of these 59 spots, the Vm was
negative at 100% and positive at 0%. Negative Vm
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 Vm
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
Vm having a magnitude 5% of the action potential
amplitude at 52 of the 63 recording spots. Of these 52 spots,
the Vm was negative at 2% and positive at 98%. A
region of small Vm existed near the center of the line
electrode in which distinct negative Vm occurred (eg,
recording at row 5, column 5).
Fig 7 shows measurements and contours of
Vm during the stimulation described in Fig 6. Contour
lines are shown for Vm 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 Vm 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 Vm began to decrease in tissue 3 mm
from the electrode (corner regions). The Vms 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 Vm.
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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 Vm at all
16 recording spots 0.5 mm from the line stimulation
electrode. Some spots farther away from the electrode underwent
positive Vm. Of the 31 recording spots in the
leftmost two columns and the rightmost two columns, 22 underwent
positive Vm.
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Cathodal stimulation shown in Fig 8 produced positive Vm
at all 16 recording spots 0.5 mm from the line stimulation
electrode. Many spots farther away from the line electrode underwent
negative Vm. Of the 31 recording spots in the
leftmost two columns and the rightmost two columns, 22 underwent
negative Vm.
Fig 9 shows measurements and contours of Vm during the
line stimulation described in Fig 8. Contour lines are shown for
Vm 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
Vm 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 Vm 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 Vms 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 Vm and
121 spots underwent negative Vm (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 Vm and 219 underwent negative
Vm (P<.0001). For cathodal stimulation
parallel to fibers, of the 144 recording spots near a cathodal
electrode, 82 spots underwent positive Vm and 35 spots
underwent negative Vm (P<.0001). Of the 279
recording spots far from a cathodal electrode, 211 underwent
positive Vm and 25 underwent negative Vm
(P<.0001). (In each of the above comparisons, the null
hypothesis that occurrences of positive or negative Vm
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 Vm and
97 spots underwent negative Vm (P<.0001). Of
the 279 recording spots far from an anodal electrode, 216
underwent positive Vm and 28 underwent negative
Vm (P<.0001). For cathodal stimulation
perpendicular to fibers, of the 144 recording spots near a
cathodal electrode, 48 spots underwent positive Vm and
78 spots underwent negative Vm (P=.014). Of
the 279 recording spots far from a cathodal electrode, 9
underwent positive Vm and 251 underwent negative
Vm (P<.0001). (In each of the above
comparisons, the null hypothesis that occurrences of positive or
negative Vm 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 Vm, negative
Vm, and no observed Vm (ie, a change of
<5% of the action potential amplitude) are shown. For electrode
orientations parallel to fibers (eg, 0°), many spots underwent
Vm of one sign, whereas only a few spots underwent
Vm of the other sign, indicating that the sign of the
Vm was essentially uniform. There were 10 spots in
which no Vm was observed. The sign of Vm
remained uniform for a range of electrode orientations having a width
of 30° to 40°.
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),
negative
The Vm 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
Vm of one sign, a similar number of spots underwent
Vm of the opposite sign, and 10 spots had no observed
Vm.
Regions Beyond Electrode Ends
The results above show that uniformity of the Vm
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,
Vm 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
Vm measurements during stimulation with a 3-mm electrode
in one heart. When the electrode was oriented parallel to the fibers,
Vm 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
Vm of either sign. When the electrode was oriented
perpendicular to the fibers, Vm 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 Vm of either
sign.
|
Uniformity of the Vm sign in regions between and
beyond electrode ends was evaluated by calculating a uniformity index
of the Vm 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 Vm 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 Vm are equally probable (ie, the
Vm sign is nonuniform) was tested. In each of these
tests, Vm was found at 29±6 spots. The null hypothesis
will be rejected at P<.05 (ie, the Vm sign
is not nonuniform) when 8 or fewer of the 29 spots undergo
Vm of a particular sign. This corresponds to a
uniformity index of the Vm sign having a magnitude
>0.45. Rejection indicated that the probability that a
Vm 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 Vm was negative for
anodal stimulation and positive for cathodal stimulation. The
Vm 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 Vm sign increased for both
stimulation polarities, and the dominant sign of Vm
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 Vm
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 Vm 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
Vm
Whether Vm 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 Vm for all laser spots and either line
stimulation polarity was not significantly affected by changing the
return electrode location (P=.885 for Vm with
one return electrode versus the other return electrode, n=378
spotsxheartsxpolarities). 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 Vm during
phases given individually predicts the Vm 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 Vms 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 Vms corresponding to the
first phase for the trials in which phases were given individually
versus Vms corresponding to the first phase for the
trial in which biphasic stimulation was given. Linear regressions were
also performed for the sum of Vms corresponding to the
second phase for the trials in which phases were given individually
versus Vms 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, Vm produced by the biphasic
stimulation was the dependent variable (ie, ordinate), and the sum
of Vm 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).
Fiber Orientation
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).
|
Discussion |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
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 Vm
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 Vm 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
Vm.
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).
Vm Produced by Line Stimulation
The present study shows that line stimulation produces
Vm 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 Vm
produced by each point within a line electrode determines the
two-dimensional pattern of Vm 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 Vm 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 Vm produced by points in the
line would result in regions of reversal of the sign of
Vm 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
Vm 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 Vm at sites away from
the electrode in the direction perpendicular to fibers.5 6 7
Summation of Vm produced by point electrodes in a line
parallel to fibers would result in no reversal of the sign of
Vm 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 Vm 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 Vms produced by
points in the line still occurs; however, the Vm
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 Vm from local
electrode points. The positive contributions are canceled by
sign-reversed contributions to Vm from points near
electrode ends (since regions between ends are away from ends in the
direction parallel to fibers). Such contributions to Vm
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
Vm from points near electrode ends (since regions
between ends are away from ends in the direction perpendicular to
fibers). Summation of this Vm with the positive
contribution to Vm from local electrode points produces
a large positive Vm between electrode ends, as seen in
Fig 9. The negligible Vm 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 Vm 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 Vm 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 Vms
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 Vms in the four corners of
the map (Fig 9), in agreement with the negative Vm that
occurs away from cathodal electrodes in the direction parallel to
fibers.4 5 6 7 23
Vm Beyond Electrode Ends
The Vm 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 Vm having one sign, epicardium beyond the ends
undergoes Vm 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
Vm of increasingly uniform sign at large distances.
These results are consistent with the Vm sign
produced by point stimulation6 7 but with the pattern of
Vm elongated in the direction of the line electrode.
The largest contribution to Vm 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 Vm should be that of point
stimulation. Then, reversal of sign of Vm 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 Vm 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
Vm contributions produced beyond the end by electrode
points that are near the end (because current density for the points is
large), (2) Vm 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 Vm contributions are produced beyond the end by
any points that are beyond the end (because such points are not in the
electrode). Differences in Vm 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 Vm During Biphasic Line
Stimulation
The small slope of linear regressions for the second phase of the
biphasic stimulation indicated that variation in Vm
among laser spots produced by biphasic stimulation was smaller than the
variation in the sum of Vm produced by individual
phases. Also, the small coefficient of correlation for the second phase
indicated that variation in the sum of Vm produced by
individual phases did not fully account for variation in the sum of
Vm 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
Conclusion
The main finding is that uniformity of the Vm 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 Vm during
cathodal stimulation and negative Vm 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
Vm,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 Vm is
uniform. Since regions exist beyond electrode ends where the
Vm 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
Vm produced by a line electrode can be qualitatively
predicted from summation of the effects of point electrodes in a line
suggests that distributions of Vm 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.
|
Acknowledgments |
|---|
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.
|
Footnotes |
|---|
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.
|
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