Vol. 277, Issue 1, H351-H362, July 1999
Nonuniform responses of transmembrane potential during
electric field stimulation of single cardiac cells
David Ker-Liang
Cheng,
Leslie
Tung, and
Eric A.
Sobie
Department of Biomedical Engineering, The Johns Hopkins University,
Baltimore, Maryland 21205
 |
ABSTRACT |
The response of cellular transmembrane
potentials (Vm)
to applied electric fields is a critical factor during electrical
pacing, cardioversion, and defibrillation, yet the coupling
relationship of the cellular response to field intensity and polarity
is not well documented. Isolated guinea pig ventricular myocytes were stained with a voltage-sensitive fluorescent dye, di-8-ANEPPS (10 µM). A green helium-neon laser was used to excite the fluorescent dye
with a 15-µm-diameter focused spot, and subcellular
Vm were recorded
optically during field stimulation directed along the long axis of the
cell. The membrane response was measured at the cell end with the use
of a 30-ms S1-S2 coupling interval and a 10-ms S2 pulse with strength
of up to ~500-mV half-cell length potential (field strength × one-half the cell length). The general trends show that
1) the response of
Vm at the cell
end occurs in two stages, the first being very rapid (<1 ms) and the
second much slower in time scale, 2)
the rapid response consists of hyperpolarization when the cell end
faces the anode and depolarization when the cell end faces the cathode,
3) the rapid response varies
nonlinearly with field strengths and polarity, being relatively larger
for the hyperpolarizing responses, and
4) the slower, time-dependent response has a time course that varies in slope with field strength. Furthermore, the linearity of the dye response was confirmed over a
voltage range of 
280 to +140 mV by simultaneous measurements of
optically and electrically recorded
Vm. These
experimental findings could not be reproduced by the updated, Luo-Rudy
dynamic model but could be explained with the addition of two currents that activate outside the physiological range of voltages: a
hypothetical outward current that activates strongly at positive
potentials and a second current that represents electroporation of the
cell membrane.
voltage-sensitive dye; Luo-Rudy model; electroporation; cardiac
electrophysiology; computer model
| |
INTRODUCTION |
ELECTRICAL STIMULATION of cardiac muscle is a common
practice in clinical and academic medicine to pace, cardiovert, or
defibrillate the heart. The mechanisms by which the electric field
stimulus affects the transmembrane potential
(Vm) of cardiac
cells have been investigated theoretically, but experimental evidence
is limited. A detailed study of how an external electric field affects a single cardiac myocyte is an important step toward understanding how
electric fields affect the whole heart.
The cellular response during field stimulation has been explored in
detail in passive spheroidal and cylindrical cell models (2, 9) and,
more specifically, in cardiac cell models with active membranes (6,
12-14, 18, 19, 26). Single cells are predicted to respond to an
external field in two stages. The first stage takes place immediately
after the external field is turned on and consists of a differential
charging of the cell membrane such that the end of the cell facing the
cathode depolarizes and the end facing the anode hyperpolarizes. The
membrane charging is a function of specific membrane capacitance and
series resistance through the intracellular and extracellular spaces
(2, 26) and occurs on a time scale of microseconds. As the cell
membrane attains its reciprocal polarization, ionic channels are gated differentially by the
Vm, resulting in
a highly nonuniform flow of ionic currents into and out of the cell.
The integral of the currents can result in a net flow of charge that
causes the intracellular potential to change (13, 26). This second
stage occurs over a much slower time scale, on the order of many
milliseconds. When field stimuli are applied at rest, the net ionic
current that is activated is inward and results in a net depolarization
of the cell, leading to an action potential if excitation threshold is
exceeded (26).
To monitor these events experimentally, optical indicators of
Vm are necessary
for at least two reasons. First, unlike electrodes, they are free from
electrical stimulus artifacts that may easily arise when currents are
applied to the tissue (21). Second, unlike microelectrodes, they
provide the spatial resolution that is necessary to monitor the
Vm at different
parts of the cell (10, 30). However, optical studies of this type on
single cardiac cells have been few and are not highly detailed.
Experiments by Knisley and co-workers (10, 11) on single rabbit
ventricular myocytes showed that field pulses applied during the action
potential plateau induced depolarization and hyperpolarization at the
cell ends with a magnitude that was roughly correlated to the product of field strength and cell length. Nevertheless, their data were unclear as to the degree of symmetry in the responses, the
time-dependent changes that occurred during the stimulus pulse, and the
quantitative relation between field intensity and response amplitude as
field strength is varied. A preliminary report by Windisch and
co-workers (29) on guinea pig ventricular myocytes showed a symmetrical variation in Vm
along the length of the cell during field stimulation at rest at a
single field strength, although the strength was not reported. The goal
of this study, then, was to use voltage-sensitive dyes to obtain
detailed, quantitative measurements of the subcellular changes in the
Vm of adult
ventricular myocytes induced by electric field stimulation. A second
goal of this study was to compare the measurements thus obtained with
computational models of cells undergoing field stimulation as a test of
the predictive accuracy of the models.
| |
METHODS |
Single-cell isolation and staining procedure.
Guinea pigs (~250 g, Hartley strain) were given an intraperitoneal
injection of 0.3 ml of pentobarbital sodium solution (50 mg/ml, Abbott
Laboratories, Chicago, IL). The heart was removed by a thorocotomy,
quickly mounted on a perfusion setup, and retrograde perfused through
the aorta with Ca2+-free Tyrode
solution for 7 min and then with enzyme solution for 3 min. The
composition of Ca2+-free Tyrode
solution (in mM) was 135 NaCl, 5.4 KCl, 1 MgCl2, 0.33 NaH2PO4,
5 HEPES, and 5 glucose (adjusted to pH 7.4 with NaOH); enzyme solution
was Ca2+-free Tyrode solution with
0.2 mM CaCl2, 0.1 mg/ml protease
(type XIV, 5.5 U/mg; catalog no. P-5147, Sigma Chemical, St. Louis, MO), and 1 mg/ml BSA (catalog no. A-2153, Sigma Chemical). After digestion, the cardiac tissue was cut into small pieces and stirred in
5 ml of enzyme solution for 3 min and filtered with a 70-µm-pore filter. The filtered supernatant with isolated cells was then diluted
by a factor of 5 with Tyrode solution containing 1.8 mM CaCl2. For optical recordings,
cells were stained with the voltage-sensitive dye di-8-ANEPPS (10 µM;
Molecular Probes, Eugene, OR; stored in DMSO stock solution at 10 mM)
for 5 min at room temperature (0.1% DMSO final).
Experimental setup.
A schematic diagram of the experimental system is shown in Fig.
1. The optical path is shown with dashed
lines, and the electrical system with solid lines. Light from the
excitation source, a 543-nm 1.5-mW green He-Ne laser (model 05-LGR-171,
Melles Griot, San Marcos, CA), was gated by a bistable mechanical
shutter (model 846HP, Newport, Irvine, CA) to minimize photobleaching
and phototoxic effects. The laser was turned on for 
20 min before
experiments to allow stabilization of the beam output. The beam was
steered by a two-dimensional galvomotorized mirror (model 6800/CB6580, Cambridge Technologies, Watertown, MA), passed through a 546 ± 7.5-nm interference filter, reflected off a dichroic beam splitter (model DM580, Nikon, Tokyo, Japan), and focused by an objective (Fluor
×40, 1.3 NA, Nikon) onto a cardiac myocyte stained by fluorescent voltage-sensitive dye. The laser beam was expanded by a factor of
f2/f1 with use of two biconvex lenses, L1 (f1 = 75.6 mm, 1-in. diameter) and L2 (f2 = 200 mm, 2-in. diameter), separated by a distance of 275.6 mm, to fill ~80% of the back aperture of the objective. This resulted in a 15-µm spot size in the specimen plane.
L2 was placed 1,533 mm from the back aperture of the objective with use
of a pair of adjustable mirrors, and the galvomotorized mirror was
positioned at the conjugate plane for the back aperture (230 mm from
L2) to keep the center rays orthogonal to the specimen plane and to
prevent light from being blocked by the objective when the laser spot
was moved.
View larger version (33K):
[in this window]
[in a new window]
|
Fig. 1.
Schematic of optical recording system. Shutter-gated beam from a green
He-Ne (Grn HeNe) laser was steered by a 2-dimensional (2-D) scanning
mirror and reflected from a dichroic beam splitter. Reflected beam was
focused by an objective onto a subcellular region (15-µm diameter) of
a cardiac myocyte stained with fluorescent voltage-sensitive dye.
Fluorescent signal was collected through the same objective and passed
through a dichroic and a long-pass filter. Filtered signal was
converted proportionally to an electrical signal through a photodiode
and custom-built preamplifier circuit. A video camera was used to
record size and orientation of cell. Two stimulators were used to
excite the cell. Glass pipettes were pulled with ~10-µm tips to
measure electric field near cell. I-V,
current-voltage; L1 and L2, lenses.
|
|
Fluorescent light collected from the myocyte was then filtered through
a long-pass filter (580 nm, model BA580, Nikon) to further attenuate
residual excitation light. Finally, at the end of the optical path the
fluorescent light was measured with a photodiode (model S2386-5K,
Hamamatsu, Bridgewater, NJ) coupled to a high-gain current-to-voltage
amplifier (model OPA111, Burr-Brown, Tucson, AZ) and a 1-G
feedback
resistor (Eltec Instruments, Daytona Beach, FL). To limit overshoot and
ringing of the amplifier, a small capacitor was formed with a
Teflon-insulated wire-wrap wire and added to the feedback path by
soldering one end to the output lead of the amplifier and wrapping the
other end around the input of the amplifier with insulation intact. The
step response of the amplifier circuit was tested with a fast
light-emitting diode and had a rise time (10-90%) of 0.97 ms.
Baseline fluorescent signals (F) were sampled with a sample-and-hold
circuit and subtracted from the raw fluorescence signal to yield the
Vm-dependent
change in fluorescence (
F). The F was then amplified 10 times and
filtered with a 1-kHz low-pass single-pole filter before digitization
by the computer (Lab NB board, National Instruments, Austin, TX) driven
by LabVIEW software (National Instruments) running on a Macintosh IIci
(Apple Computer, Cupertino, CA).
Control circuits for the experimental system were custom designed to
provide timing signals for the laser shutter, data acquisition system,
sample-and-hold circuit, and stimulus pulses. The laser shutter was
opened for up to 400 ms and timed to begin before the start of the data
acquisition. The sampling interval for the sample-and-hold circuit was
40 ms, and stimulus pulses were 10 ms in duration.
Field stimulation procedure.
Approximately 30 µl of solution containing isolated,
di-8-ANEPPS-stained guinea pig ventricular myocytes were placed into a
field stimulation chamber (Fig.
2A)
containing 1 ml of 1.8 mM Ca2+-containing Tyrode solution at
room temperature. Two stimulators (models SD9 and S44, Grass
Instruments, Quincy, MA) were used to excite the myocytes with locally
uniform electric field in the bath solution through a pair of parallel
platinum wires (0.010-in. diameter) 4.5 mm long and 6.5 mm apart. Small
S1 field stimulus pulses (10-ms-duration rectangular pulse with
magnitude at 10% above diastolic threshold of ~3.6 V/cm) were turned
on from one of the stimulators to pace the cells at 0.2 Hz. An isolated
cardiac cell was located under the microscope using a ×10
objective and then aligned at ×40 with the laser excitation spot
so that the edge of one of the longitudinal ends of the cell lay within
the laser spot (Fig. 2B). Only cells
that lay parallel to the electric field and contracted during
stimulation were selected. After an experiment on a particular cell,
the cells in the chamber were discarded and replaced by a fresh droplet
of cells. Glass field recording pipettes (~10-µm-diameter tip) were
filled with 1.8 mM Ca2+-containing
Tyrode solution and inserted into the bath. The field recording
pipettes were oriented ~300 µm apart parallel to the long axis of
the cell and positioned laterally ~200 µm away from the cell. The
cells and field recording pipettes were viewed with a video camera
(model JE7362, Javelin Electronics, Los Angeles, CA) under
bright-field or Hoffman modulation contrast optics, from which the cell
length and spacing between the pipettes could be determined.
View larger version (55K):
[in this window]
[in a new window]
|
Fig. 2.
Experimental chamber and single cell.
A: schematic of experimental chamber.
Chamber was formed by a rubber gasket overlying a square coverslip,
sandwiched together between 2 aluminum plates. Stimulus electrodes
consisted of 2 parallel 0.010-in.-diameter, 4.5-mm-long platinum wires
separated by a distance of 6.5 mm. Two glass pipettes were filled with
bath solution, and their potential difference was measured with Ag-AgCl
wires to determine the applied field strength.
B: bright spot on single guinea pig
ventricular myocyte is laser-induced di-8-ANEPPS fluorescence of cell
membrane. Transmembrane potential at end of cell could be recorded
during field stimulation by acquiring the fluorescent signal at this
spot with photodiode. Photomicrograph was obtained using Hoffman
modulation contrast optics.
|
|
During each experimental recording, the repetitive pacing stimuli were
turned off. An S1-S2 field stimulation procedure was used to quantify
the electric field-induced hyperpolarization and depolarization at the
ends of the cell. An S1 pulse (10 ms rectangular) from one of the
stimulators was used to elicit an action potential. An S2 pulse (10 ms
rectangular) from the other stimulator was timed to occur during the
action potential plateau 30 ms after the onset of the S1 pulse and was
set at a different amplitude every time. S1 and S2 polarities were
always set to be in the same direction. In this study we define the
stimulus to the cell in terms of the half-cell length potential (HCLP), where HCLP is the product of electric field strength and one-half the
cell length. A negative HCLP indicates a field orientation from the end
(being observed) toward the center of the cell (resulting in
hyperpolarization of the end), and a positive HCLP indicates a field
orientation in the opposite direction (resulting in depolarization of
the end). The reasons for using HCLP are twofold:
1) the HCLP is a normalized quantity
that accounts for variations in cell length (10), and
2) for cells lying in a conductive
bath and oriented along the electric field, the HCLP is the theoretical potential that develops at the end of the cell provided that the cell
exerts only a minor perturbation of the applied field (2, 9, 26). For
long, narrow cells this is a reasonable approximation. With this method
of expressing the field strength, data from cells of different sizes
can be combined and compared. The strength of S2 was varied from
400- to +510-mV HCLP. The change in fluorescence (F) from the
×10 amplifier stage, total fluorescence (F) from the photodiode
preamplifier circuit, voltage from the field recording glass pipette
electrodes, and stimulus current (measured across a 10- resistor in
series with the platinum wire electrodes) were recorded. S1-S2 trials
were repeated on the same cell until the cell was damaged by phototoxic
effects or by field-induced injury caused by very large HCLP. Injured
cells were identified by the onset of spontaneous contractions and in
the extreme case by hypercontraction at the cell end.
In the experiments of this study, the optical response to fields with
varying intensities and polarities was generally recorded at one end of
the cell. The alternative procedure would have been to record responses
sequentially at both ends of the cell for fields with various
intensities but a single polarity. This latter type of experiment was
not routinely performed for the bulk of the study because the accurate
repositioning of the spot was difficult once the experiment was
started, and accessibility to the microscope controls was difficult
because the entire experimental setup was enclosed in a light-tight
box. However, the results of one such experiment are included in this report.
Whole cell clamp.
Additional experiments were conducted to calibrate optically recorded
dye responses against electrically recorded
Vm by using whole
cell voltage clamp with a patch-clamp amplifier (model PC-One, Dagan,
Minneapolis, MN). The bathing solution was changed to one containing a
mixture of channel blockers along with elevated
K+ (in mM): 120 potassium
glutamate, 25 KCl, 1 MgCl2, 1 BaCl2, 10 tetraethylammonium, 5 4-aminopyridine, 0.005 tetrodotoxin, 0.010 nifedipine, 0.5 CdCl2, 0.1 EGTA, 10 HEPES, and 10 glucose (adjusted to pH 7.4 with HCl). A bathing solution of this
composition was used to inactivate as many channels as possible and to
reduce the ionic current across the cell membrane, which at high levels can produce significant errors between the applied command signal and
the true Vm owing
to voltage drops across the resistance of the pipette electrode (30).
The solution in the pipette electrode consisted of (in mM) 110 potassium glutamate, 5 NaCl, 5 MgCl2, 5 MgATP, 10 EGTA, and 5 HEPES (adjusted to pH 7.2 with KOH), resulting in a pipette resistance
on the order of 5-10 M.
After the successful attachment of the pipette electrode to the cell,
the laser shutter was manually turned on. The laser spot was moved onto
the cell close to the tip of the glass pipette and quickly turned off.
The voltage-clamp waveform consisted of a series of rectangular pulse
triplets with test potentials varying over a range of 400 to
+400 mV. Each triplet consisted of an initial 10-ms clamp to 95
mV (near resting potential), a 10-ms clamp to +35 mV (near plateau
potential), and a third 10-ms clamp to the test potential. This triplet
protocol was designed in part to mimic how the membrane potential
changes during S2 field stimulation. Moreover, the clamp potential
always cycled through the same resting and plateau potentials for each
triplet to allow for a two-point calibration with each test pulse. Thus
it was possible to correct for any time-dependent change in the
fluorescence signal owing to photobleaching effects or to motion
artifact over the duration of the entire voltage-clamp series.
Simultaneous optical and electrical recordings were obtained, and F,
F, clamp voltage, and clamp current were recorded.
Computer simulations.
Detailed model studies of field stimulation of cardiac cells having
active membranes have been conducted for stimuli applied during
diastole (14, 26) or during the relative refractory period (6, 12, 14).
However, none of these studies have focused on the spatial and temporal
patterns of the
Vm within the
cell as field strength is varied. Therefore, computer simulations of an
isolated cardiac myocyte in a uniform electric field with various
intensities were conducted for the purposes of comparison with the
experimental data. The reciprocal polarization model for field
stimulation has been described in detail previously (22, 26). Briefly,
the cell was assumed to be a 120-µm-long, 24-µm-wide prolate
spheroid, and the imposed field was assumed to be directed along the
cell's major axis. During the stimulus the extracellular
surface potentials were determined by the applied field, and the
intracellular space was assumed to remain isopotential. The cell
membrane was discretized into 11 patches, and the voltage-dependent ionic currents that developed in each of the patches led to further changes in Vm.
Each membrane patch was assigned the kinetics of the updated Luo-Rudy
dynamic (LRd) model of the guinea pig ventricular cell (16, 32). The
model was implemented in Advanced Continuous Simulation Language
(Mitchell and Gauthier, Concord, MA) on a Silicon Graphics (Mountain
View, CA) POWER Challenge XL minisupercomputer. The nonlinear
differential equations that govern the cellular response were solved
iteratively using a second-order Runge-Kutta-Fehlberg algorithm with a
variable step size of 
10 µs.
| |
RESULTS |
S1-S2 field stimulation.
The Vm estimated
by optical means is denoted in this study as
VFm. The optically
measured action potential amplitude
(APAF) was determined by using
the upstroke phase of the action potential as a calibration signal
equal to 128 mV, the mean value of the action potential amplitude for
isolated adult guinea pig ventricular myocytes (28, 30). Changes in
Vm and
VFm during the field
stimulus are designated
Vm and
VFm, respectively.
An example of VFm during
S1-S2 field stimulation is shown in Fig.
3A. One
end of the cell was monitored for stimulus fields of various
intensities and polarities. Guinea pig ventricular cell lengths were in
the range of 128 ± 23 (SD) µm
(n = 14). The S2 response
consists of a rapid, initial stage that occurs in <1 ms. In this
example, it is clear that for fields of opposite polarity the amplitude
of the field-induced hyperpolarization is larger than the amplitude of
depolarization at a comparable field strength by a factor of 1.54 at an
HCLP of 70 mV and 3.29 at 180 mV (after correction for the slight
differences in intensities for the 2 field polarities). The same
experiment also shows marked differences in maximum upstroke velocity
[(dVFm/dt)max] of the action potentials elicited by the S1 pulses with a strength of
26.8-mV HCLP (Fig. 3A, left). The
(dVFm/dt)max was 23.5% faster for the average of the two hyperpolarizing S1 pulses
than the average of the two depolarizing pulses. This observation is
consistent with the notion that the rapid upstroke of the action potential reflects the change in the average potential of the cell but
can be modulated from one end of the cell to the other by the
reciprocal polarization of the membrane induced by the field stimulus
(30).
View larger version (15K):
[in this window]
[in a new window]
|
Fig. 3.
Field-induced polarization changes. A:
optical transmembrane potentials were measured at the same end of a
single guinea pig ventricular cell before and after reversal of S1 and
S2 field directions. Resulting hyperpolarized and depolarized responses
are shown. S1 intensity was 4.7 V/cm; cell length was 114 µm. S2
field intensities were ~12 and 32 V/cm, and stimulus strength is
expressed as half-cell length potential (HCLP, field intensity × one-half cell length). S1 and S2 polarities were always in the same
direction. Fields with same intensity but opposite polarities cause an
asymmetrical response during action potential plateau. F, fluorescence.
B: parameters used for data analysis.
Action potential amplitude and response to stimulus field were
quantified from the fluorescence signal.
APAF is action potential amplitude
and is always positive. Initial
VFm is amplitude of
S2 response at point of inflection relative to amplitude just before S2
stimulus and is negative for hyperpolarizing responses and positive for
depolarizing responses.
|
|
The field-induced
VFm was analyzed as
shown in Fig. 3B. The initial
amplitude of VFm was
measured as the peak magnitude of
VFm in the depolarizing
direction or as the point of inflection in the hyperpolarizing
direction, with both relative to the value just before the onset of the
S2 pulse. This calculation resulted in an estimate of the field-induced
Vm (in mV) at
the end of the cell. Figure
4A shows
the composite results from eight different cells in which the initial
VFm (at the onset of
the S2 pulse) is plotted against HCLP. Also plotted in Fig. 4A is a dashed line with unity slope,
which represents the
VFm expected for a
cell with a membrane impedance much larger than that of the surrounding
bath and an intracellular volume that is isopotential (26). Just as in
Fig. 3A, the composite results show
that the initial VFm
varies nonlinearly with field intensity and that the
Vm is
overhyperpolarized with one polarity and underdepolarized with the
other at large values of HCLP compared with the straight-line response.
The data are relatively linear over the range of 100- to +50-mV
HCLP and can be fit using a least-squares error with the line
VFm = 2.280 + 0.780 * HCLP
(R = 0.974). In some cells,
VFm was recorded for
both polarities of field stimuli. In those cases the total
VFm (equal to the
difference between the 2 VFm values) was
plotted against the difference between the two HCLPs (sum of their
magnitudes; Fig. 4B). Also plotted
is a dashed line with unity slope that represents the total
VFm expected under
ideal passive conditions (see
DISCUSSION), as in the case for Fig.
4A. The points are close to but
slightly below the line of identity and, with the exception of the
point around +600 mV, can be fit by a straight line:
(VFm)tot = 0.837 * (HCLP+ HCLP
)
(R = 0.997).
View larger version (15K):
[in this window]
[in a new window]
|
Fig. 4.
Field-induced membrane response. A:
initial VFm at cell
end plotted against HCLP during S2 field stimulation. Initial value of
membrane response
VFm (estimated in
mV) was calculated assuming an action potential amplitude of 128 mV.
Plot represents data pooled from 8 myocytes, as indicated by different
symbols (data from Figs. 3A and 5 are
included). Dashed line, line of identity that is expected if cell
membrane were to behave as a passive insulator with impedance much
higher than that of bathing solution.
B: for those cells that were
stimulated by fields of both polarities and with approximately the same
intensity, the difference between
VF+m and
VFm for the
2 polarities HCLP+ and
HCLP, respectively, is
plotted against HCLP+ HCLP. Data from different
cells are indicated by symbol set used in
A.
|
|
The S2 response also consists of a second, slower stage that occurs
over the duration of the S2 pulse. The magnitude and slope of the
slower response are shown in detail in Fig.
5 and vary with the field intensity.
Responses in the depolarizing direction are shown in Fig.
5A from a single cell for HCLPs
ranging from 100 to 510 mV. After the initial depolarization at the
beginning of the pulse,
VFm fell in the
hyperpolarizing direction at an HCLP field intensity of 100 mV,
remained relatively constant at 201 mV, and rose in the depolarizing
direction at 304 mV. At 514 mV,
VFm fell again and
was followed by a postshock depression of the action potential plateau. Responses in the hyperpolarizing direction are shown in Fig.
5B for a different cell for HCLP field
intensities ranging from 81 to 316 mV and were
directionally similar in slope to the depolarizing responses of Fig.
5A.
VFm fell in the
hyperpolarizing direction at an HCLP of 130 mV, remained
relatively constant at 223 mV, and rose in the depolarizing
direction at 316 mV. The 316-mV shock was followed by a
postshock depression of the action potential plateau. Larger
hyperpolarizing responses were difficult to measure owing to injury
effects. During very intense field stimulation (>400-mV
hyperpolarizing HCLP), we observed that cells always hypercontracted at
the hyperpolarized end. If the field direction was then reversed,
hypercontracture was observed at the previously depolarized but now
hyperpolarized end.
View larger version (15K):
[in this window]
[in a new window]
|
Fig. 5.
Field-induced polarization of cell membrane. A 10-ms S1 field pulse was
used to elicit an action potential in a guinea pig ventricular cell.
When S2 field stimuli were applied during the action potential plateau,
the anodal end of the cell hyperpolarized and the cathodal end
depolarized. Polarities of S1 and S2 field stimuli were always in the
same direction. Initial
VFm and time course
of VFm varied with
S2 field strength. A: multiple
recordings from cathodal end of a 156-µm-long single cell.
B: multiple recordings from anodal end
of a 173-µm-long different cell. S2 field strengths, expressed in
units of HCLP, are indicated at right of their respective responses.
|
|
Calibration of di-8-ANEPPS.
To check the linearity of the response of the dye di-8-ANEPPS, we
attempted to record optical and electrical measurements simultaneously
in the same cell. This was very difficult to perform and was successful
in only one attempt. The command potential that was used is shown in
Fig. 6A
and consisted of a series of 33 shock triplets, with each triplet
consisting of three 10-ms pulses in succession. The first pulse was at
90 mV, the second at +35 mV, and the third at a variable
amplitude Vt. The
VFm values from the
first two pulses were used to calibrate the
VFm measured with the
third (test) pulse (Fig. 6B) and
eliminated the need to assume a value for the action potential
amplitude. When VFm was
plotted against
Vt, the data were
fit well by a line having a slope of nearly unity (0.961, R = 0.997) over the range of
280 to +140 mV (Fig. 6C).
View larger version (23K):
[in this window]
[in a new window]
|
Fig. 6.
Simultaneous optical and electrical recordings during voltage clamp. A
whole cell voltage clamp of a guinea pig ventricular cell was used to
calibrate dye di-8-ANEPPS in a guinea pig ventricular myocyte.
A: a chopped rectangular pulse train
was used (top trace), in which a
series of 33 triplets of 10-ms pulses was applied. Each triplet
consisted of a clamp to 90 mV, followed by a clamp to +35 mV,
followed by a clamp to a test potential in the range 440 to +390
mV. B: simultaneously recorded
VFm.
C:
VFm plotted against
test potential
(Vt). A nearly
linear response of dye with slope of 0.961 was obtained for
VFm in the range
280 to +140 mV (R = 0.997).
|
|
Responses at the center of the cell.
To gain additional insight into the nature of the asymmetrical
responses of Fig. 4 and to verify further that the responses were not
an artifact of an asymmetry of the dye response for large polarization
changes, VFm was
recorded at the center position of two cells to determine whether this
site also mirrored the hyperpolarizing behavior seen at the cell ends. Figure 7 shows
VFm in one such
experiment compared with responses in the same cell at each of the two
ends. The VFm values
at the two ends are qualitatively similar to those at one end of a cell
when the field polarity is reversed (Fig.
3A) and show an asymmetry in the
hyperpolarizing direction for the larger responses.
VFm at the center
hyperpolarizes rapidly with time (as indicated by the arrow) and then
continues to decline slowly in the hyperpolarization direction. The
significance of this finding is discussed below. As in Fig.
3A, these data also show that the
upstroke velocity of the action potential varies with the polarization
of the membrane and is 27.8 and 30.0% faster for the center and
hyperpolarized end of the cell, respectively, than for the depolarized
end.
View larger version (12K):
[in this window]
[in a new window]
|
Fig. 7.
Field-induced response at different parts of cell.
VFm was measured at the
center (bold trace) and ends (light traces) of a single guinea pig
ventricular cell. A 10-ms S1 field pulse was used to excite cell, and
then a second 10-ms S2 field pulse was used to elicit field response.
S2 field strength in this experiment was not measured directly but is
estimated to have been ~175 mV HCLP. S1 and S2 polarities were always
set to be in the same direction. Individual traces exhibit small
oscillations that may have resulted from a residual settling of the
mechanical shutter of the excitation light source.
|
|
Cell model simulations.
Computer simulations were performed of an LRd model cell that was field
stimulated with a 5-ms S1 pulse followed by a 10-ms S2 pulse at a
coupling interval of 30 ms with three representative field strengths
(Fig.
8A). The
model not only fails to reproduce the asymmetry of responses in the
hyperpolarizing direction that were observed experimentally (Figs. 5
and 7) but exhibits an asymmetry in the opposite (depolarizing)
direction at all field strengths when measured at the end of the S2
pulse. Moreover, at high field strengths the model fails to reproduce
the depression of the action potential plateau, as was observed
experimentally (Fig. 5), and instead shows a decaying depolarized
response. These discrepancies can be resolved by postulating two
currents that activate outside the physiological voltage range for
which the LRd model was developed: a hypothetical time-independent
outward current
Ia and a current Iep associated
with electroporation of the cell membrane. We refer to the LRd model,
modified by the addition of these two currents, as the LRdm model.
Ia was assumed to have the form (in
µA/µF) ![<IT>I</IT><SUB>a</SUB> = <FENCE><AR><R><C><IT>e</IT><SUP>0.09 (<IT>V</IT><SUB>m</SUB> − 100)</SUP>, <IT>V</IT><SUB>m</SUB> ≤ 160 mV (1a)</C></R><R><C> </C></R><R><C><IT>e</IT><SUP>0.09 ∗ 60</SUP>[0.09 (<IT>V</IT><SUB>m</SUB> − 160) + 1], <IT>V</IT><SUB>m</SUB> > 160 mV (1b)</C></R></AR>:</FENCE>](/content/vol277/issue1/fulltext/H351/img001.gif)
and is plotted in Fig.
8C. The effect of
Ia is to
introduce the hyperpolarizing asymmetry seen in the traces for ±200-mV HCLP in Fig. 8B owing to
activation of this outwardly rectifying current at the depolarized end
of the cell.
View larger version (21K):
[in this window]
[in a new window]
|
Fig. 8.
Computer simulation of transmembrane potential response of cell to
field stimulation. A: responses of
both ends of a Luo-Rudy (LRd) model cell. A 5-ms rectangular S1 pulse
was applied to model, and then a 10-ms S2 pulse was applied in same
direction with an S1-S2 interval of 30 ms. Field intensities were 100-, 200-, and 350-mV HCLP. B: similar
responses of an LRd model cell modified by addition of time-independent
outward current
(Ia) and
electroporation current
(Iep) (LRdm model
cell), as given by Eqs. 1 and 2. These
responses are hyperpolarized compared with corresponding responses in
A. C:
I-V relation of hypothetical ionic
channel with current
Ia.
D: plot of initial field-induced
response of end of cell as a function of field strength (in HCLP)
analogous to Fig. 4A. Dashed line,
passive response (line of identity); ×, responses of unaltered
LRd model cell;  , responses of LRdm model cell.
|
|
To account for the depolarizing (ascending slope)
VFm seen in the
traces for 316- and +304-mV HCLP in Fig. 5, as well as the
postshock depression of the plateau potential observed at 316-
and +514-mV HCLP also in Fig. 5, a second current is proposed. It is
known that when
Vm exceeds
300-400 mV across membrane patches, electroporation of the patch
can occur (25). Recently, an electroporation current
Iep was
formulated by DeBruin and Krassowska (4) to describe the saturation of
Vm that develops at the ends of guinea pig muscle strips that are stimulated by electric
fields
|
(2a)
|
where
the conductance of a single electropore
(gp) is a nonlinear,
instantaneous function of
Vm and the number
of pores per unit area (N) has a
growth rate given by
|
(2b)
|
where
N0 is the
equilibrium density of pores at
Vm = 0 and 
,
, and q are model constants. When
added with its published parameters to our LRd model simulations,
Iep becomes
activated primarily at the hyperpolarized end of the cell during the S2 pulse, which produces the depolarizing
VFm seen in the
traces for ±350-mV HCLP in Fig.
8B. The residual activation of
Iep also results
in a small postshock depression of the plateau potential, consistent
with the experimental observations.
The net effect of
Ia and
Iep on the field
responses at the end of the cell is shown in Fig.
8D for field strengths ranging from
350- to +350-mV HCLP. The dashed line is the line of identity, which is the result expected from purely passive models. Plotted is
Vm measured 1 ms after the onset of the S2 pulse. The curve obtained with the
unmodified LRd model is nearly linear but with a slight upward
concavity. The curve obtained with the LRdm model exhibits a downward
concavity that reproduces the hyperpolarizing asymmetry that was
observed experimentally (Fig. 4A).
| |
DISCUSSION |
This study used voltage-sensitive dyes to document the
electrophysiological responses of single guinea pig ventricular
myocytes to electric field stimulation during the plateau of the action potential. The main findings are as follows:
1) the response of the
Vm at the cell
end to the field occurs in two stages, the first being very rapid (<1
ms) and the second much slower in time scale,
2) the rapid response consists of
hyperpolarization when the cell end faces the anode and depolarization
when the cell end faces the cathode,
3) the rapid response varies
linearly with HCLP field strengths from 100 to +50 mV and
nonlinearly with higher strengths, being larger in magnitude than the
HCLP at the hyperpolarized end and smaller than the HCLP at the
depolarized end, and 4) the slower
response has a time course with a slope that varies with the field
strength. 5) We also found that model simulations of an
idealized cell with updated, Luo-Rudy dynamic properties fail to reveal
the hyperpolarizing asymmetry that was observed experimentally but can
be reconciled with the data by the addition of two membrane currents
that activate outside the physiological voltage range.
Initial Vm induced by an
applied electric field.
During excitation with rectangular field pulses,
VFm undergoes two
characteristic stages of response. The first occurs during the 1st ms
of the onset of the pulse (Fig. 3B),
and the second occurs more slowly, over the full duration of the field pulse.
Concerning the first stage, at HCLP amplitudes between 100 and
+50 mV we observed a linear relation between
VFm and field
strength (Fig. 4A) and symmetrical
changes with field polarity, as expected from theoretical models. For
symmetrically shaped cells stimulated along their long axis by uniform
fields, the cell end should respond linearly with field intensity,
symmetrically in amplitude with field polarity, and symmetrically in
amplitude with respect to the other end (2, 26). Symmetrically shaped cells stimulated by nonuniform fields (14) or arbitrarily shaped cells
stimulated by uniform fields (13) are also expected to have responses
at one end that are linear with field intensity and symmetrical with a
reversal of field polarity, although the two ends of the cell should
respond asymmetrically with respect to one other.
However, contrary to expectations, the relation between
VFm and HCLP has a
slope of slightly <1 (0.78). The value of the slope is influenced by
several competing factors. Because the measurement spot was not truly
at the end of the cell but situated a distance up to a spot radius (7.5 µm) from the end, this would have led to a consistent underestimate
of VFm. The value of
128 mV assumed for the action potential amplitude is a multiplicative
factor for the slope and may have been in error. Finally, the effect of
the cell to perturb the applied field is an additional factor that can
change the slope, although this would have been in the opposite
(increasing) direction and was assumed to be negligible in our analysis.
Higher levels of field intensity (less than 100-mV HCLP or
greater than +50-mV HCLP), which at 50-mV HCLP corresponds to ~8 V/cm
for cells with mean length of 128 µm, resulted in a
VFm at the cell end
that was larger in the hyperpolarizing direction when the field
polarity was reversed (Fig. 3A).
Moreover, the VFm
values at both ends of the cell and at the center of the cell shifted
in the hyperpolarizing direction from the line of identity (Figs. 4 and
7).
Knisley and co-workers (10, 11) also reported asymmetrical
VFm at the opposite
ends of the cell with field stimulation during the action potential
plateau but found the changes to be nonsignificant. Nevertheless, the
field intensities that they used (20 and 40 V/cm or HCLPs of 130 and
260 mV with the assumption that their cells are 130 µm long) should
have placed their experiments well within the nonlinear region that we
measured (Fig. 4). However, several differences exist between the study of Knisley et al. (10) and our study. First, their responses were
averaged over a 25-ms window centered within a 50-ms S2 pulse and would
have included some of what we have termed the slow second-stage response of the membrane. On this basis, we would have expected their
recordings to have been even more asymmetrical than ours, but this was
not the result reported. Another difference is that they measured
changes in potential at the opposite ends of cells with a single
polarity of field, whereas we generally measured the changes in
potential at the same end of the cell with opposite polarities of
field. As noted earlier, measurements at just one end may fail to
reveal asymmetries that might otherwise be seen at the two ends,
particularly for asymmetrical cell shapes or nonlinear fields. Thus the
measurement procedure of Knisley et al. should have favored the
observation of asymmetrical responses, contrary to the reported
findings. A more likely explanation for the differences in the results
is that the recordings of Knisley et al. were much noisier than ours
and may have prevented a finding of statistical significance.
Furthermore, their experiments were conducted on rabbit ventricular
cells rather than guinea pig cells and, hence, may have involved
different amounts or types of ionic currents that might contribute to
the asymmetry (see below). Finally, their S1-S2 coupling interval was
slightly longer (50 vs. 30 ms) and may have affected the degree of
asymmetry, which has been shown to diminish with longer S1-S2 coupling
intervals (7).
Optical mapping studies were conducted by Windisch and co-workers (30,
31) on single guinea pig cardiac cells and showed that
VFm varies spatially
across the cell during field stimulation. In one preliminary experiment
with an unspecified field strength, they reported a spatially linear
relation between polarization amplitude and position along the myocyte in the direction of the applied field (29). Such a relation is not
incompatible with an asymmetrical
VFm at the end of
the cell with a reversal in field polarity, provided that the linear
relation is not symmetrical about the center of the cell. Additional
experiments involving multisite optical mapping of cellular responses
on a subcellular length scale are required to test this hypothesis.
As we reported earlier (27) and also showed in Fig.
8A, simulations based on passive
models or on the active LRd model are unable to explain these
consistent findings of a hyperpolarizing asymmetry. Given that existing
models have been derived primarily from data in the physiological
range, it may not be surprising for discrepancies to appear between
experiment and model, particularly at the higher field intensities. A
possible explanation for the discrepancy is that symmetrical responses
are in fact occurring but are not faithfully recorded owing to the
limited rise time (~1 ms) of our photodetector system. Indeed, the
speed of the first-stage response is expected to be very fast, with a
time constant equal to the product of specific membrane capacitance, a
weighted sum of intracellular and extracellular resistivities, and the
radius of the cell (2, 26). For typical values in cardiac cell
membranes, this time constant is expected to be on the order of microseconds.
If indeed there is a symmetrical response that is being masked, then
over the entire cell there must be a net outward current that rapidly
activates and hyperpolarizes the intracellular potential. Thus the
hyperpolarized end of the cell would become even more hyperpolarized,
the depolarized end less depolarized, and the center hyperpolarized, as
was observed experimentally (Fig. 7). This scenario was tested using a
hypothetical current
Ia that activates
outside the normal physiological voltage range with the instantaneous,
outwardly rectifying current-voltage relation shown in Fig.
8C. The addition of this current to
the LRd model enables much of the experimentally observed behavior to
be reproduced (Fig. 8B). Note that
the very rapid transients predicted by the model at the onset of the S2
pulse would not be observable in the data because of the limited
frequency response of the recording system.
If this explanation is correct, then according to our model simulations
the augmentation of the hyperpolarization at one end of the cell and
reduction of the depolarization at the other should be equal for a
given field intensity. Expressed in another way, the difference between
the Vm values
should equal the difference between the HCLPs, i.e., the extracellular
potential difference from one end of the cell to the other, or the
product of the field strength and the whole cell length. Although we
did not map the responses simultaneously at the two ends of the cell,
if we assume that the cell ends behave symmetrically with respect to
one another, we can combine our data at one end of the cell for HCLPs
with comparable magnitudes but opposite polarity. Our results fall close to the expected relation (Fig.
4B), although they are better fit
with a line having a slope of slightly <1 (0.84). The reasons for the
lower slope may be identical to those discussed earlier regarding the
lower-than-expected slope of the linear region of the relation of Fig.
4A.
Thus a rapidly changing ionic conductance within the 1st ms of
VFm may account for
the nonlinear and asymmetrical behavior of the membrane that is not
otherwise accounted for by present-day theoretical models of cardiac
cells undergoing field stimulation. This mechanism may also contribute
to the asymmetrical VFm values recorded
optically (7, 33) and Vm values
recorded with microelectrodes (34) at the tissue level after reversal
of the field stimulus polarity. Although we have demonstrated that a
current such as
Ia is consistent with the findings of asymmetry, further investigation is necessary to
confirm the existence and nature of this current. Possible candidates
for Ia may
include Cl or
K+ currents, which have negative
reversal potentials and can have outwardly rectifying current-voltage relations.
An alternative explanation for the asymmetry may be that the
voltage-sensitive dye itself responds nonlinearly with
Vm. Experiments were performed to test the linearity of the dye response by using the
voltage-clamp method in conjunction with simultaneous optical recordings. As shown in Fig. 6, we found an excellent correlation between fluorescence intensity of di-8-ANEPPS and
Vm over a range of 280 to +140 mV. Deviation of the data from a linear
relationship outside this range of potentials might be attributed to
the fact that, at the high amplitude potentials, not all ionic currents were blocked. Indeed, the voltage limits of the linear relation are
approximately where we have hypothesized
Ia and
Iep to activate. These currents may not have been eliminated by our mixture of channel
blockers and could have led to a failure of
Vm to be clamped to the command potential by virtue of the voltage drop across the
pipette resistance (30) or of intracellular potential gradients along
the cell length. In other studies, experiments on single frog
ventricular cells also showed a nearly linear relation of VFm to
Vm during the
action potential or during ramp clamps in voltage over a range of
150 to +150 mV (3). With a similar dye (di-4-ANEPPS),
experiments performed on guinea pig ventricular myocytes showed a
linear relation between
VFm and
Vm over a range
of 120 to +40 mV (30). A linear relation between di-4-ANEPPS
fluorescence and
Vm has also been
demonstrated in other cell types (5, 8, 15, 17), over a range as large
as 200 to +200 mV in HeLa cells (17). Regardless of the exact
limits of linearity, the dye does appear to respond linearly with
Vm, at least in
the physiological range of
Vm. Although we were not able to verify the linearity of response over the entire range
of VFm at the cell
end (almost 600 to +150 mV; Fig. 4), the observation of a
hyperpolarizing response at the center of the cell, which does remain
within the physiological voltage range (Fig. 7), further supports the
notion that the asymmetrical responses seen at the cell end with
reversals in field polarity are true physiological changes and not an
artifact of nonlinearities in dye response.
Time course of Vm during
field stimulus.
As the field stimulus strength is increased, the time course of the
slower, second-stage response of
VFm to the field
pulse changes its slope in a consistent manner, regardless of the field
direction or which end of the cell is being observed (Fig. 4). On
theoretical grounds, a nonzero slope reflects a net imbalance of ionic
currents from the different parts of the cell during field stimulation
(13, 26). If the imbalance results in a net outward current, the
isopotential interior of the cell will move in the negative direction.
Because the profile of extracellular potential along the surface of the
cell is essentially unchanged during the field stimulus, the average
Vm of the cell
will become more negative. This is seen with HCLPs on the order of
±100 mV (Fig. 5). Indeed, our model simulations (Fig. 8) indicate
that the net outward current arises because the sum total of ionic current exiting at the depolarized end of the cell exceeds the total
current entering the hyperpolarized end (results not shown).
When the HCLP is raised to approximately ±200 mV, the
VFm responses are
essentially flat in time after the initial rapid response, indicating
that the net sum of ionic currents over the entire cell membrane is
zero. For even greater HCLPs on the order of ±300 mV or more (Fig.
5), VFm diminishes
in hyperpolarization and becomes more positive during the latter part
of the S2 pulse. The upward turn in
VFm measured at the
higher field strengths could not be reproduced by the LRd model in
combination with
Ia and presumably
results from an increase of an inward current and/or a decrease of an outward current. Previous work from our laboratory showed that electroporation of the cell membrane can occur with
Vm in the range
of 300-400 mV (25). When an
Iep
(Eq. 2, a and
b) was added along with
Ia to the LRd
model, the upward turn in
VFm and the
postshock depression of the plateau potential were reproduced at high
field strengths (cf. Figs. 5 and 8), since
Iep acts to drive
Vm toward the
short-circuit potential of 0 mV. Visual observations of cells by
Knisley et al. (11) and by us have demonstrated that spontaneous
contractions and hypercontracture occur first at the hyperpolarized end
as field strength is increased, consistent with the entry of
extracellular Ca2+ there via
electroporation. Although Knisley et al. invoked electroosmosis together with electroporation as a mechanism to explain the asymmetry of Ca2+ entry with shocks given
during the action potential plateau, our findings of a hyperpolarizing
asymmetry in VFm at
the two ends of the cell suggest that electroporation by itself is
consistent with the data, since it would occur first at the hyperpolarized end of the cell. At even higher field strengths, electroporation would be expected to occur at the depolarized end as
well and would explain the downward turn in
VFm now seen at that
end (Fig. 5). Knisley et al. also reported that VFm decays toward
zero potential at both ends of the cell at high field strengths (50 V/cm).
Although an Iep
is consistent with the upward turn in
VFm seen at the
highest field strengths (Fig. 5), it is nonetheless still speculative,
and other possibilities exist. One possibility is that there is a
hyperpolarization-activated inward current
If and
voltage-dependent block of the inward rectifier current
IK1, as described
recently by Ranjan et al. (20). To test this idea, we ran additional
simulations in which these currents were implemented in their published
form together with
Ia in the LRd
model. However, the resulting effect of
If on
VFm was relatively
insignificant (results not shown) and unable to account for our
experimental findings, despite the large magnitude of hyperpolarization
achieved at the cell end. Another possibility is that, at the cell end
undergoing hyperpolarization, large inward currents in the form of
"tail currents," such as these from activated Ca2+ channels, could contribute to
membrane depolarization as well as the contractile asymmetry commented
on earlier. Clearly, further investigation is required to identify the
precise ionic currents underlying the temporal aspects of
Vm during the
field stimulus.
Responses to field stimuli applied at rest.
Although this study focused on the responses of the membrane to field
stimuli of various amplitudes that are applied during the early plateau
of the action potential, our data also reveal the responses to field
stimuli applied during rest. In Fig.
3A the membrane response to the S1
field pulse can be seen at the left side of the traces. The end of the
cell exhibits a rapid change in potential at the onset and cessation of
the S1 stimulus pulse, similar to the response during the plateau to
the S2 pulse. However, the slower second-stage responses exhibit a
pronounced depolarization that reaches threshold followed by a rapid
depolarization and upstroke. From a previous modeling study (26) and as
shown in Fig. 8, such a depolarizing response is expected to occur as a
result of net inward currents arising from the nonlinear conductive properties of the inward rectifier
K+ channel combined with
activation of the Na+ channel. The
same study also predicted that the fast
Na+ current would be larger at the
hyperpolarized than at the depolarized end of the cell. The present
experimental results support this prediction and show the maximum
upstroke velocity to be 23.5-30.0% faster for membrane patches
that are hyperpolarized than for those that are depolarized by the
field stimulus (Figs. 3A and 7). An elegant experimental mapping study by Windisch and co-workers (30)
showed that the upstroke velocity of the action potential varies
linearly with the amplitude of the membrane polarization produced by
the field pulse, being fastest at the hyperpolarized end and slowest at
the depolarized end.
Limitations of the study.
The main drawback of this study is that
VFm values were not
measured simultaneously across the cell owing to the nature of our
recording system (single spot measurements). Hence, several
expectations derived from theoretical models remain unproven. For
example, the potential changes during the slower stage of polarization
are expected to parallel one another in field-stimulated cells (13, 14,
26). This behavior is characteristic not only of single cells but also
of tissue in which virtual sources of opposite polarity may exist in
close proximity to one another, with a separation on the order of a
space constant or less (1, 23, 24). Figure 7 suggests that this
expected behavior does occur in the single cell, although the data were
not obtained simultaneously for the same field stimulus, so that some
changes in the state of the cell might have occurred between
recordings. In experiments on guinea pig myocytes, Windisch et al. (30) recorded potentials from multiple sites simultaneously across the cell
and showed parallel shifts in potential, although measurements were
made only during diastole. Further research is necessary to determine
whether such changes also occur during other phases of the action
potential and for what range of field intensities this behavior exists.
| |
ACKNOWLEDGEMENTS |
We are grateful to Robert Susil for assisting with the development
of the computer simulations and to Matthew Fishler and Vinod Sharma for
comments regarding the manuscript.
| |
FOOTNOTES |
This work was supported by National Heart, Lung, and Blood Institute
Grant HL-48266.
Much of this work was performed as part of a master's dissertation (3)
and was presented in abstract form (27).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: L. Tung, Dept.
of Biomedical Engineering, The Johns Hopkins University, Rm. 703, Traylor Bldg., 720 Rutland Ave., Baltimore, MD 21205 (E-mail:
ltung{at}bme.jhu.edu).
Received 20 July 1998; accepted in final form 9 March 1999.
| |
REFERENCES |
1.
Cartee, L. A.,
and
R. Plonsey.
The effect of cellular discontinuities on the transient subthreshold response of a one-dimensional cardiac model.
IEEE Trans. Biomed. Eng.
39:
260-70,
1992[Medline].
2.
Cartee, L. A.,
and
R. Plonsey.
The transient subthreshold response of spherical and cylindrical cell models to extracellular stimulation.
IEEE Trans. Biomed. Eng.
39:
76-85,
1992[Medline].
3.
Cheng, D.
Optical Measurements of Transmembrane Potential Change During Electrical Field Stimulation of Isolated Cardiac Myocytes (Master's thesis). Baltimore, MD: Johns Hopkins University, 1996.
4.
DeBruin, K. A.,
and
W. Krassowska.
Electroporation and shock-induced transmembrane potential in a cardiac fiber during defibrillation strength shocks.
Ann. Biomed. Eng.
26:
584-596,
1998[Medline].
5.
Ehrenberg, B.,
D. L. Farkas,
E. N. Fluhler,
Z. Lojewska,
and
L. M. Loew.
Membrane potential induced by external electric field pulses can be followed with a potentiometric dye.
Biophys. J.
51:
833-837,
1987[Abstract/Free Full Text]. [Corrigenda. Biophys. J. 52: July 1987, following p. 141.]
6.
Fishler, M. G.,
E. A. Sobie,
N. V. Thakor,
and
L. Tung.
Mechanisms of cardiac cell excitation with premature monophasic and biphasic field stimuli
a model study.
Biophys. J.
70:
1347-1362,
1996[Abstract/Free Full Text].
7.
Gillis, A. M.,
V. G. Fast,
S. Rohr,
and
A. G. Kléber.
Spatial changes in transmembrane potential during extracellular electrical shocks in cultured monolayers of neonatal rat ventricular myocytes.
Circ. Res.
79:
676-690,
1996[Abstract/Free Full Text].
8.
Gross, D.,
L. M. Loew,
and
W. W. Webb.
Optical imaging of cell membrane potential changes induced by applied electric fields.
Biophys. J.
50:
339-348,
1986[Abstract/Free Full Text].
9.
Klee, M.,
and
R. Plonsey.
Stimulation of spheroidal cellsthe role of cell shape.
IEEE Trans. Biomed. Eng.
23:
347-354,
1976[Medline].
10.
Knisley, S. B.,
T. F. Blitchington,
B. C. Hill,
A. O. Grant,
W. M. Smith,
T. C. Pilkington,
and
R. E. Ideker.
Optical measurements of transmembrane potential changes during electric field stimulation of ventricular cells.
Circ. Res.
72:
255-270,
1993[Abstract/Free Full Text].
11.
Knisley, S. B.,
and
A. O. Grant.
Asymmetrical electrically induced injury of rabbit ventricular myocytes.
J. Mol. Cell. Cardiol.
27:
1111-1122,
1995[Medline].
12.
Krassowska, W.,
and
M. S. Kumar.
The role of spatial interactions in creating the dispersion of transmembrane potential by premature electric shocks.
Ann. Biomed. Eng.
25:
949-963,
1997[Medline].
13.
Krassowska, W.,
and
J. C. Neu.
Response of a single cell to an external electric field.
Biophys. J.
66:
1768-1776,
1994[Abstract/Free Full Text].
14.
Leon, L. J.,
and
F. A. Roberge.
A model study of extracellular stimulation of cardiac cells.
IEEE Trans. Biomed. Eng.
40:
1307-1319,
1993[Medline].
15.
Loew, L. M.,
L. B. Cohen,
J. Dix,
E. N. Fluhler,
V. Montana,
G. Salama,
and
J. Y. Wu.
A naphthyl analog of the aminostyryl pyridinium class of potentiometric membrane dyes shows consistent sensitivity in a variety of tissue, cell, and model membrane preparations.
J. Membr. Biol.
130:
1-10,
1992[Medline].
16.
Luo, C.-H.,
and
Y. Rudy.
A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes.
Circ. Res.
74:
1071-1096,
1994[Abstract/Free Full Text].
17.
Montana, V.,
D. L. Farkas,
and
L. M. Loew.
Dual-wavelength ratiometric fluorescence measurements of membrane potential.
Biochemistry
28:
4536-4539,
1989[Medline].
18.
Platzer, D.,
E. Hofer,
and
H. Windisch.
Modeling geometrical aspects in cardiac stimulation and propagation experiments.
Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc.
17:
710-711,
1995.
19.
Quan, W.,
and
T. J. Cohen.
Field stimulation of single cardiac cellthe dependency of membrane excitation threshold on waveform shape and cellular refractoriness.
Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc.
15:
869-870,
1993.
20.
Ranjan, R.,
N. Chiamvimonvat,
N. V. Thakor,
G. F. Tomaselli,
and
E. Marban.
Mechanism of anode break stimulation in the heart.
Biophys. J.
74:
1850-1863,
1998[Abstract/Free Full Text].
21.
Salama, G.
Optical measurements of transmembrane potential in heart.
In: Spectroscopic Membrane Probes, edited by L. Loew. Boca Raton, FL: CRC, 1988, p. 137-199.
22.
Sobie, E. A.,
and
L. Tung.
Post-shock potential gradients and dispersion of repolarization in cells stimulated with monophasic and biphasic waveforms.
J. Cardiovasc. Electrophysiol.
9:
743-756,
1998[Medline].
23.
Susil, R. C.,
E. A. Sobie,
and
L. Tung.
Virtual source separation modulates cardiac tissue response to field stimulation.
Proc. Annu. Int. Conf. IEEE Eng. Med. Biol. Soc.
19:
182-184,
1997.
24.
Susil, R. C.,
E. A. Sobie,
and
L. Tung.
Separation between virtual sources modifies the response of cardiac tissue to field stimulation.
J. Cardiovasc. Electrophysiol.
10:
715-727,
1999[Medline].
25.
Tovar, O.,
and
L. Tung.
Electroporation and recovery of the cardiac cell membrane with rectangular voltage pulses.
Am. J. Physiol.
263 (Heart Circ. Physiol. 32):
H1128-H1136,
1992[Abstract/Free Full Text].
26.
Tung, L.,
and
J. R. Borderies.
Analysis of electric field stimulation of single cardiac muscle cells.
Biophys. J.
63:
371-386,
1992[Abstract/Free Full Text].
27.
Tung, L.,
D. K. Cheng,
R. Susil,
and
E. A. Sobie.
Electrical field excitation of cardiac cellsmatching theory to experiment (Abstract).
Ann. Biomed. Eng.
24:
S-57,
1996
TOP
ABSTRACT
INTRODUCTION
