© 1998 American Heart Association, Inc.
Original Contributions |
Spatial Changes in the Transmembrane Potential During Extracellular Electric Stimulation
From the Division of Cardiovascular Disease, Department of Medicine (X.Z., W.M.S., D.R., R.E.I.), Department of Biomedical Engineering (S.B.K., W.M.S., A.E.P., R.E.I.), and Department of Physiology (R.E.I.), University of Alabama at Birmingham, Birmingham, Ala.
Correspondence to Xiaohong Zhou, MD, B140 Volker Hall, Box 201, University of Alabama at Birmingham, Birmingham, AL 35294-0019. E-mail xhz{at}crml.uab.edu
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Abstract—The purpose of this study was to determine the spatial changes in the transmembrane potential caused by extracellular electric field stimulation. The transmembrane potential was recorded in 10 guinea pig papillary muscles in a tissue bath using a double-barrel microelectrode. After 20 S1 stimuli, a 10-ms square wave S2 shock field with a 30-ms S1–S2 coupling interval was given via patch shock electrodes 1 cm on either side of the tissue during the action potential plateau. Two shock strengths (2.1±0.2 and 6.5±0.6 V/cm) were tested with both shock polarities. The recording site was moved across the tissue along fibers with either 200 µm (macroscopic group [n=5], 12 consecutive recording sites over a 2.2-mm tissue length in each muscle) or 20 µm (microscopic group [n=5], 21 consecutive recording sites over a 0.4-mm tissue length in each muscle) between adjacent recording sites. In the macroscopic group, the portion of the tissue toward the anode was hyperpolarized, whereas the portion toward the cathode was depolarized, with 1 zero-potential crossing from hyperpolarization to depolarization present near the center of the tissue. In the microscopic group, only 1 zero-potential crossing was observed in the center region of the tissue, whereas, away from the center, only hyperpolarization was observed toward the anode and depolarization toward the cathode. Although these results are consistent with predictions from field stimulation of continuous representations of myocardial structure, ie, the bidomain and cable equation models, they are not consistent with the prediction of depolarization-hyperpolarization oscillation from representations based on cellular-level resistive discontinuities associated with gap junctions, ie, the sawtooth model.
Key Words: hyperpolarization • defibrillation • simulation
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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To understand the mechanism of ventricular defibrillation, it is important to acquire knowledge of the transmembrane potential changes (
Vm) caused by
the shock in addition to the action potential changes after the shock.
This is because the cellular excitation and alteration in action
potentials that occur after a defibrillation shock are thought to
result from the changes in the transmembrane potential caused by the
shock.1 2 Several studies have been performed to
obtain such information. Some studies used optical recording
techniques to evaluate the Vm caused by the
shock field in either isolated myocytes1 3 4 5 or
perfused hearts.2 6 7 8 9 10 With a few
exceptions,1 3 4 5 11 the optical
recording represents the weighted average of the
Vm changes in many
cells.2 7 9 Recordings of the
transmembrane potential by a double-barrel microelectrode can supply
information about the Vm caused by the shock
from an individual cell within the myocardial
syncytium.12 13
A range of modeling studies completed over the past 15 years suggests
that shock-induced Vm can change markedly over
the length of an individual cell.14 15 16 17 These
studies are based on the hypothesis that highly resistive gap junctions
located at the cell ends create a sawtooth pattern of
depolarization-hyperpolarization
oscillation in the spatial distributions of
Vm. Experimentally, the sawtooth pattern has been
observed during shocks applied to isolated
myocytes,1 with the cell end closest to the
cathode depolarized and the end closest to the anode hyperpolarized.
However, because the gap-junction resistance is considerably less than
the membrane resistance at the end of an isolated myocyte, the
possibility exists that the sawtooth pattern is never established
within the myocardial syncytium or that its magnitude is so small that
it can be neglected. Either possibility might explain the fact that the
sawtooth pattern, while evident in modeling studies assuming resistive
discontinuities of intracellular coupling in both
monodomain14 15 16 and
bidomain17 representations of tissue
structure, has not been observed
experimentally.2 5 For example, a recent study by
Gillis et al5 used optical recording
techniques to record the Vm caused by
electric shocks in individual cells of monolayers and strands of
cultured neonatal rat myocytes. In that study, a local
hyperpolarization and depolarization of the
sawtooth pattern was not observed at the borders between cells when
electric field stimulation was applied across the entire strand of
cells.
We undertook the present study to examine whether the sawtooth
pattern arises in shock-induced Vm in
syncytial tissue. In an attempt to exclude possible contributions of
fiber curvature associated with a bidomain representation of
tissue structure in the shock-induced Vm, we
used isolated guinea pig papillary muscles.
Histological characteristics of this preparation are
well documented; ie, fibers are oriented parallel to one another
through the preparation.18 Using a double-barrel
microelectrode recording technique and fine spatial resolution
that included multiple impalements along the longitudinal axis of the
papillary muscle, we were able to examine whether the sawtooth pattern
arose during shocks of different strengths and polarities.
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Details about the use of the double-barrel microelectrode to record the transmembrane potential before, during, and after a shock from a papillary muscle in a tissue bath have been previously reported.12 13
Tissue Preparation
Ten guinea pig papillary muscles were used. Guinea pigs weighing
approximately 300 g were injected with sodium pentobarbital
(Nembutal, 75 mg in 1.5 mL via the abdomen). The hearts were rapidly
excised through a median sternotomy and immersed in cold Tyrode's
solution. The Tyrode's solution was of the following formula (in
mmol/L): NaCl 129, CaCl2 1.8,
MgCl2 1.1, KCl 4.5,
Na2HPO4 1,
NaHCO3 20, and glucose 11. The left
ventricular anterior papillary muscle, 4.5±0.4 mm
long and 1.5±0.1 mm wide, was removed and pinned on silicon
rubber in the center of a 2x2–cm2 tissue bath.
The base of the papillary muscle faced the right side of the tissue
bath, and the apex faced the left side of the bath (Figure 1
). The tissue was continuously
superfused with Tyrode's solution bubbled with a mixture of 95%
O2 and 5% CO2 (pH 7.35 to
7.40). The solution temperature was maintained in the range of 35 to
36°C. Two mesh patch platinum shock electrodes were placed on
each side of the tissue bath and immersed in the Tyrode's solution to
generate a constant electric field across the tissue bath. In this way,
the shock potential gradient was oriented along the long axis of the
tissue.12 The cardiac tissue was paced at one end
via 2 extracellular (0.2-mm diameter) pacing electrodes with a
stimulator controlled by a Macintosh II computer. Two extracellular
recording electrodes, which were fixed on the silicon rubber,
were just beside the tissue to record the extracellular potentials
generated by the shock. The distance between these 2 extracellular
recording electrodes was about 2 mm, measured with a
dissecting microscope. These 2 extracellular electrodes were aligned so
that the line between them was perpendicular to the mesh shocking
electrodes. This line was assumed to be parallel to the shock potential
gradient. The potential between the two electrodes was recorded
differentially with a data acquisition system.12
The potential gradient generated by the shock was obtained by dividing
the potential difference between the 2 extracellular electrodes
generated by the shock by the distance between them.
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Signal Recordings
To make the double-barrel microelectrode, 2 single glass
capillaries (WPI Glass 1BBL W/FIL 1.0 mm) were glued together,
except in the region where the tips were to be formed, and were pulled
by a horizontal micropipette puller (Industrial Science Associates,
Inc). The capillary tubes were pulled to have an impedance of 
10
M
for both tips when filled with 3 mol/L KCl. The distance
between the 2 microelectrode tips measured under a light microscope was
about 30 µm. The double-barrel microelectrode was mounted on a
motorized micromanipulator (WPI DC3001) that could move in 3 dimensions
with 0.5-µm resolution. Each barrel of the double-barrel
microelectrode was connected to the input of a differential
preamplifier (WPI Duo 773 Dual Microprobe System) with an Ag-AgCl wire.
Capacitor compensation within the preamplifier was used to eliminate
capacitive coupling between the 2 tips when needed. The signals were
recorded differentially as a voltage between the 2 double-barrel
microelectrode tips. After preamplification, the signal was
recorded with DC coupling and a 10-KHz low-pass filter cutoff
frequency using a data acquisition system. Signals were recorded
digitally with 12-bit accuracy at a rate of 8000 samples per second.
The data were stored on VCR tape and optical disk for later computer
analysis.
Experimental Protocol
The 10 guinea pig papillary muscles were divided into 2 groups,
with 5 experiments in each group. Group 1 was studied to determine how
the Vm caused by a shock varied over the
length of the papillary muscle. This was called the macroscopic group.
Group 2 was studied to determine how the Vm
caused by a shock varied over a much shorter length. This was called
the microscopic group. In the macroscopic group, there were 12
consecutive recording sites in each muscle, with 200 µm
between adjacent sites. The total recorded tissue length was
2.2 mm (Figure 1
). In the microscopic group, there were 21
consecutive recording sites in each muscle, with 20 µm
between adjacent sites. The total recorded tissue length was
0.4 mm, a distance that spanned at least 2 recording sites
in the macroscopic group (Figure 1). In each papillary muscle of both
groups, the double-barrel microelectrode was moved from the first
recording site to the last recording site in the same
direction along the longitudinal axis of the papillary muscle. If an
action potential was not obtained at the intended recording
site, the double-barrel microelectrode was moved <3 µm to
the left or right of that recording site to obtain the action
potential recording. The next recording site was still
at the originally intended site. Because of the high spatial resolution
in the microscopic group, the tissue was treated with 10 mmol/L
diacetyl monoxime to eliminate motion of the tissue caused by
contraction.
The total length of the papillary muscle was determined with a
motorized micromanipulator. The total recording length in the
macroscopic group was predetermined to be in the midportion of the
tissue so that the recordings were not performed at either
end of the tissue (Figure 1). The recording sites in the
microscopic group were made within the center 2 mm of the tissue
and so were within the region in which recordings were made for
the macroscopic group. Because the mean length of the tissue was
4.5±0.4 mm long, recordings were usually not made within
1 mm of either end of the tissue. After the recording
location was determined, the double-barrel microelectrode was slowly
lowered into the Tyrode's solution just above the tissue with a
motorized micromanipulator. It was then rotated slightly until the
potential difference between the 2 tips was almost undetectable during
shocks that created a shock field of approximately 6 V/cm, as reported
previously.12 The double-barrel microelectrode
was then lowered into the tissue until an action potential was seen in
the differential recording between the 2 barrels shown on the
monitoring oscilloscope. An S1–S2 stimuli-shock protocol was then
performed as described below. After recording the
Vm caused by the shock at one site, the
double-barrel microelectrode was withdrawn just above the tissue and
moved to the next recording site until recordings were
made from all sites. All recordings from the same papillary
muscle were made from the superficial layer of the tissue and with the
same double-barrel microelectrode.
After 20 S1 stimuli consisting of 2-ms square waves with a 300-ms
S1–S1 pacing interval at twice the diastolic threshold, a
10-ms S2 shock field consisting of a square waveform was applied along
the papillary muscle through the pair of mesh shock electrodes. The
onset of the S2 shock was given with a 30-ms S1–S2 coupling interval
so that it was delivered during the plateau of the 20th S1 action
potential. This S1–S2 interval was chosen to give shocks during the
absolute refractory period so that the Vm
during the shock would not be obscured by a shock-induced action
potential that could occur if the shock were given during the relative
refractory period or diastole. Two shock potential
gradients were created. Each shock potential gradient was given twice,
the second time with the polarity reversed with respect to the first.
The same S1–S2 protocol was given with the microelectrode at each
recording site. The transmembrane potential was recorded
before, during, and after the shock.
Data Analysis
The control transmembrane action potential was defined as the
19th S1-paced action potential during which no shock was delivered. The
test transmembrane action potential was defined as the 20th S1-paced
action potential during which the S2 shock was delivered. The
Vm was defined as the voltage difference
between the membrane potential just before the shock and the membrane
potential just before the end of the shock, ie, the shock-induced
Vm. The Vm was
determined by a computer program as described in a previous
report.12 To obtain Vm,
the control and test transmembrane action potentials were superimposed
by aligning the time of maximum dV/dt of the upstroke of the action
potentials, and the control transmembrane action potential was
subtracted from the test transmembrane action potential to obtain the
true membrane response (ie, the shock-induced
Vm).12 Depolarization of
the membrane potential during a shock was defined as a more positive
membrane potential during the shock than just before the shock, whereas
hyperpolarization was defined as a more negative
membrane potential during than just before the shock.
The paired t test and analysis of variance were used for statistical analysis of the data as presented in Results. A P value <0.05 was considered significant. Data are given as mean±SD.
Computer Simulations
The electric activity within the guinea pig papillary muscles
was modeled using a bidomain representation of tissue structure
based on a standard formulation19 :
 | (1) |
i was the specific intracellular
conductivity, e the specific
interstitial conductivity, Vm the
intracellular potential, 
e the
interstitial potential, and Im
the transmembrane current density. Im was
further specified in terms of membrane sources as follows:
 | (2) |
, we determined
Vm from the following equation:
 | (3) |
, we assumed sealed-end boundary conditions at the
edges of the tissue. The tissue portion of the model measured 4 mm
in length by 50 µm in width. We then determined the
interstitial and extracellular potential distributions from
the transmembrane potential distribution using a rewritten form of
Equation 1:
 | (4) |
to the following:
 | (5) |
A schematic of the model is shown in Figure 1B. All conductivity
parameters for the simulation were selected to approximate
ones used by Roth.19 The full size for the
combined interstitial and extracellular region measured
4 mm in length by 100 µm in width. Sealed-end boundary
conditions were imposed on all edges, and matching conditions to ensure
that the continuity of the interstitial and extracellular
potential distribution20 were imposed at the
interface between the tissue and the bath.
The numerical solution scheme was similar to that reported
previously.21 Ordinary differential equations
defining the gating variables for the individual ionic currents of
Iion in Equation 2 were integrated
numerically in time using an analytic method. We prescribed Luo-Rudy
(LRd)22 23 membrane equations at all
tissue nodes. The parabolic partial differential equation in Equation 3
was discretized in space over those nodes using a 5-point finite
difference stencil. Discretization in time used a semi-implicit
averaging scheme analogous to the Crank-Nicholson method in 1 space
dimension. The resulting matrix for the linear system was sparse. As a
result, efficient solutions for Vm were achieved
with a preconditioned conjugate gradient scheme (DITSOL.PCG from the
Digital Equipment Corp Digital Extended Math Library, dxml).
Integration time steps were dynamically adjusted during the
calculations between minimum (dtmin) and maximum
(dtmax) values to take advantage of slowly
changing characteristics of Vm after the
depolarization wavefront had spread through the model. Adjustment
followed a variation of the method of Rush and
Larsen.24 Equations 4, and 5 were also discretized
in space over the full model using a 5-point finite difference stencil.
Matching conditions at the interface between the tissue and the bath
were embedded in the difference equations. During the parts of each
simulation at which we applied "shocks," we modified the difference
equations for nodes on the left and right edges of the model to fix the
extracellular potentials on each edge. The resulting sparse linear
system for e and o
was solved using the same preconditioned conjugate gradient method as
in solutions for Vm.
To represent the
electrophysiological state within the
papillary muscle preparations, we simulated a train of 10 action
potentials initiated with 200 µA/cm2 strength
transmembrane current pulses of 2.0-ms duration applied at the leftmost
tissue nodes. The S1–S1 interval measured 300 ms. Action potential
waveform shapes and durations were constant after the fourth beat.
Because the bulk solution and the interstitium complicate analytic
determination of the resting space constant
(
),25 26 was determined by transmembrane
current injection to the model. Using the state-variable
descriptions at the end of the action potential train as initial
conditions, a 10-ms, 2 µA/cm2 pulse was applied
to the leftmost tissue nodes. Vm was recorded
at every point, at the end of the stimulus. Vm
values were calculated by subtracting Vrest from
Vm. The distance from the left edge of the
model at which Vm decayed to 37% was taken as
. We followed a similar procedure to determine the space constant
during the action potential plateau (p). Using
state-variable descriptions from the train as initial conditions,
S1 was followed by a subthreshold S2, again measuring 10 ms in duration
and 2 µA/cm2 in strength, at an S1–S2 coupling
interval of 30 ms. Vm values were calculated
by subtracting Vm values determined at the
end of the 10-ms interval during a simulation with no current injection
from Vm values during a simulation with current injection.
Then, p was determined in the same way as .
To measure shock-induced Vm, the boundary
conditions within the simulation were changed 30 ms after S1 stimuli.
Shocks were of variable strengths and 10-ms duration.
Vm values were calculated by subtracting
Vm values determined at the end of the 10-ms
interval during a simulation in which no shock was applied from
Vm values during a simulation with applied shock.
All modeling parameters, including measured values for
and p, are summarized in the
Table. Simulations were executed on a
Digital Equipment Corp AlphaServer 2100 4/233 computer with 4 CPUs and
256 MB of memory. CPU time requirement for a simulation was
approximately 15 minutes.
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Results |
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Vm Caused by Shocks in the Macroscopic
GroupIn the macroscopic group, which had adjacent recording sites spaced 200 µm apart, the portion of the tissue toward the anode was hyperpolarized, whereas the portion toward the cathode was depolarized. There was only 1 zero-potential crossing near the center of the tissue, as shown in Figure 2
. Two
shock strengths, 2.2 V/cm (panel A) and 6.8 V/cm (panel B), with both
shock polarities were applied to the papillary muscle. When the shock
polarity was cathodal on the left side of the tissue and anodal on the
right side of the tissue (upper tracings in each panel), the left side
of the tissue was depolarized and the right side was hyperpolarized
with 1 zero-potential crossing present at the site 100 µm to
the right side of the center of the tissue. Vm
in response to the 6.8-V/cm shock underwent a polarization shift from
54 mV of depolarization to -111 mV of
hyperpolarization (total 165 mV) across the tissue
length of 2.2 mm (upper tracing in panel B).
Vm in response to the 2.2-V/cm shock underwent
a polarization shift from 26 mV of depolarization to -80 mV of
hyperpolarization (total 106 mV) across the tissue
length of 2.2 mm (upper tracing in panel A). When the shock
polarity was reversed with the anode on the left side of the tissue and
the cathode on the right side of the tissue (lower tracing in each
panel), the direction of Vm was also reversed,
with hyperpolarization on the left side of the
tissue and depolarization on the right side of the tissue.
Vm in response to the 6.8 V/cm shock underwent
a polarization shift from -102 mV of
hyperpolarization to 64 mV of depolarization (total
166 mV) across the tissue length of 2.2 mm (lower tracing in panel
B). The magnitude of the Vm over space in
response to the 2.2 V/cm shock underwent a polarization shift from -54
mV of hyperpolarization to 49 mV of depolarization
(total 103 mV) across the tissue length of 2.2 mm (lower tracing
in panel A).
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Results in Figure 2 are consistent with results from the other
4 muscles in the macroscopic group. Figure 3 shows the magnitude of the
Vm caused by the shock over space for all 5
muscles in the macroscopic group. Zero-potential crossings were
observed in the center region of the tissue about 200 µm to the
right side of the center, whereas, away from the region of the
zero-potential crossing, only hyperpolarization in
the portion toward the anode or depolarization toward the cathode was
present. The direction of Vm changed when
the shock polarity was reversed. The gradient of changes in the
magnitude of Vm in response to 6.5±0.6 V/cm
was 166±23 mV/2.2 mm for the shock polarity of L-R+ and 166±34
mV/2.2 mm for the shock polarity of L+R-. The magnitude of the
shock-induced hyperpolarization was significantly
greater than that of depolarization at the same recording sites
when the same shock strength was applied (P<0.05). The
response of the membrane to a shock field of 6.5±0.6 V/cm was greater
than that to a shock field of 2.1±0.2 V/cm at all recording
sites (P<0.05). The ratio of the Vm for 6.5 V/cm to 2.2
V/cm shocks was 1.95±0.56, demonstrating that tripling the shock
strength did not triple the Vm.
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, 
, transmembrane potential changes caused
by reversed shock polarity, L+R-. The solid line represents
results for a shock strength of 2.1±0.2 V/cm, whereas the dashed line
represents results for a shock strength of 6.5±0.6 V/cm. Bars,
1 SD. B, Magnitude of the
Vm Caused by Shocks in the Microscopic
Group
In the microscopic group, the transmembrane potential was
recorded at 21 sites with 20 µm between adjacent sites in
each papillary muscle. The shock strength used in this group was
6.2±0.4 V/cm. Figure 4 shows an example
of the transmembrane potential recordings within a space of
0.4 mm from the central region of 1 papillary muscle. During
cathodal stimulation on the left side of the tissue and anodal
stimulation on the right side of the tissue (upper tracings in Figure 4), the portion of the recorded tissue nearest the cathode was
depolarized, whereas the portion nearest the anode was hyperpolarized.
As in the macroscopic group, there was only 1 zero-potential crossing
present near the recording site, 120 µm to the right
side of the center of the tissue. Changing the shock polarity reversed
the direction of the Vm and moved the
zero-potential crossing near the recording site at 140
µm to the right side of the center of the tissue (lower tracings in
Figure 4). Figure 5 shows another example
of the transmembrane potential recordings within the space of
0.4 mm in the right portion of the tissue starting at the
recording site 600 µm away from the center of the
tissue. One shock polarity caused hyperpolarization
at all recording sites (upper tracings in Figure 5), whereas
the opposite shock polarity caused depolarization at all
recording sites without a zero-potential crossing present
in the space of 0.4 mm (lower tracings in Figure 5).
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Figure 6 shows the changes in the
transmembrane potential caused by the shock over space in the
microscopic group for each of the 5 papillary muscles.
Recordings were made in the central regions in 3 muscles
(labeled -200, -100, and -100 with respect to the center of the
tissue in Figure 6), in the right portion of the tissue in 1 muscle
(labeled 600 with respect to the center of the tissue in Figure 6), and
in the left portion of the tissue in another muscle (label -700 with
respect to the center of the tissue in Figure 6). As shown in Figure 6, no zero-potential crossing was recorded in either the left or right
portion of the tissue. Only 1 zero-potential crossing was recorded
in the central region of the tissue. Changing the shock polarity
reversed the direction of the Vm during the
shock. Although no zero-potential crossing was recorded away from
the central region of the tissue, a jump in the transmembrane potential
of >10 mV between 2 adjacent recording sites was sometimes
observed, raising the possibility of nonuniform intracellular
conductivity between adjacent recording sites.
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Computer Simulations
The computer simulations closely mimicked the experimental
preparation and stimulation protocol. Results from these simulations
are presented in Figure 7. Figure 7A shows the spatial distribution of Vm after
subthreshold stimuli by current injection at the left end of the model.
With all tissue in the model at rest initially, measured 362
µm, which was close to that reported for frog ventricular
myocardium by Chapman and Fry27 at
300 µm but much less than that reported for skinned calf
trabeculae by Weidmann28 at
880 µm. During the action potential plateau, the space
constant was longer than at rest. From Figure 7A, p measured 738 µm as determined by
current injection at a 30-ms S1–S2 coupling interval.
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Shocks applied at an S1–S2 coupling interval of 30 ms during the
action potential plateau affected the spatial distribution of
Vm across the model. Figure 7B shows
Vm for shock strengths of 0.6, 1.5, and 3.0
V/cm. Field strengths were determined by dividing the potential
difference recorded at the ends of the model by the total model
length. As a result, these field strengths were lower than the ones
used in the experiments. Nevertheless, even at low field strengths,
Vm was positive at all model nodes toward the
cathode and negative at all nodes toward the anode. In the central
2 mm of the model (Figure 7C), which was the sampled region
referred to as the macroscopic group in the experiments,
Vm changed by 48 mV (+24 to -24 mV) during
L+R- stimulation and during L-R+ stimulation (-25 to +23 mV) with a
1.5-V/cm shock field strength. Vm was as high
as 5 mV near the center of the model. From Figure 7D, a zone of 0
Vm present for a distance along the tissue
was not even observed at the lowest shock strength of 0.6 V/cm.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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This study demonstrates experimentally in the papillary muscle of the guinea pig that the response to electric field stimulation consists of hyperpolarization in the portion of the tissue facing the anode and depolarization in the portion facing the cathode with 1 zero-potential crossing near the center of the tissue.
Cardiac muscle is a syncytium, the morphology of which is anisotropic
and the electrophysiological properties of
which depend on the cell membrane, cell-to-cell coupling, and the
properties of the extracellular and intracellular volume conductors.
Therefore, the response of simple resistor-capacitor membrane
models, 1-dimensional cable models, and cultured cell strand
preparations to field stimulation may have limited applicability to
defibrillation of the intact ventricles. For example, our previous
studies have indicated that the relationship between the shock
potential gradient and the Vm caused by that
gradient is much more complicated than the relationship predicted by
mathematical models.2 12 13
The present study uses papillary muscles from the left
ventricle, which have a unidirectional fiber orientation. That geometry
simplified the complex relationship between the response of the
membrane during a shock and fiber orientation for this study. Thus, our
results approximate the Vm caused by a shock
in 1-dimensional tissue, which has been the focus in previous
mathematical modeling studies of
defibrillation.14 15 16 29 30 Because our results
are obtained from real cardiac tissue characterized by a multicell
syncytium connected by gap junctions between cells, they should offer
some information, although not all information, about the
Vm caused by extracellular electric field
stimulation in myocardium and, hence, about the mechanism
of defibrillation.
Knisley et al1 found that in a single
isolated ventricular cell with a length of 119±29
µm, the end of the cell that faces the cathode during field
stimulation is depolarized, while the other end facing the anode is
hyperpolarized. A zero-potential crossing is present in the middle
region of the cell separating the regions of depolarization and
hyperpolarization.1 This
phenomenon is referred to as a sawtooth
pattern.14 15 16 According to sawtooth pattern
models, the depolarization-hyperpolarization
oscillation at each cell is established by the
intracellular periodic conductivity caused by high gap-junction
resistance.14 15 16 Because an isolated myocyte has
high resistance at the sealed ends, depolarization at one end of the
cell and hyperpolarization at the other end of the
cell can be established during an electric shock field as observed in
experiments.1 11 But, because a single cell can
also be treated as a 1-dimensional cable, the same phenomenon can be
effectively modeled with the cable equation or with the bidomain
model.17 31 To test whether the sawtooth pattern
exists in multicellular syncytia with gap junctions between cells,
Gillis et al5 used optical recording
techniques to record the Vm caused by a
shock field from a monolayer of cultured cardiac cells. The length of
cell strands in the study by Gillis et al5 was 2
to 3 mm. A local
depolarization-hyperpolarization
oscillation was not observed at the borders between cells
in that study.5 Instead,
hyperpolarization occurred in the portion of the
cell strand nearest the anode and depolarization in the portion nearest
the cathode, similar to the results of our study in the papillary
muscle.
In the macroscopic group of the present study, recordings were made over a total length of 2.2 mm with 200 µm recording resolution in the middle portion of the papillary muscle. The recorded length in the microscopic group was 0.4 mm, with a 20 µm recording resolution in either the central or lateral portion of the papillary muscle. Because the length of a cardiac cell is about 100 µm and the long axis is parallel to the papillary muscle,18 >1 zero-potential crossing should have been recorded in either the middle or lateral portion of the tissue in both the macroscopic and microscopic groups if the sawtooth pattern were present. Yet, only 1 zero-potential crossing was observed in the present study. This implies that either the model of the sawtooth pattern is incorrect or that each sawtooth oscillation occurs over a bundle of cells >2 mm long instead of over a single cell.32
The model study of Plonsey and Barr14 indicated
that the magnitude of the
depolarization-hyperpolarization
oscillation of the sawtooth pattern depends on the
resistance of the gap junctions between cells in addition to the shock
strength. These authors showed that the
depolarization-hyperpolarization
oscillation of the sawtooth pattern is largest when a large
gap-junction resistance is chosen.14 Therefore,
if the resistance in the gap junction of the normal syncytial tissue is
not very large in the real
myocardium,33 34 the sawtooth pattern
may be very small and not observed or may be superimposed on other
membrane responses.15 As shown in Figure 6, the
curves of the Vm caused by the shock were not
very smooth over short distances, and sometimes an obvious voltage
difference between 2 adjacent recording sites was observed.
This finding might be caused by gap junctions. Thus, if a sawtooth
pattern exists, its amplitude may be small and superimposed on a larger
pattern of transmembrane potential changes, as observed in this
study.
The following considerations also suggest that the
depolarization-hyperpolarization
oscillation of the sawtooth pattern is not the primary
mechanism for defibrillation. (1) If the sawtooth pattern exists and
the magnitude of depolarization equals that of
hyperpolarization, the Vm
during a shock should be summed to 0 when a single averaged measurement
of transmembrane potential is made from many cells over a large space.
However, both depolarization and hyperpolarization
have been recorded by using optical recording
techniques.2 6 7 8 (2) Defibrillation efficacy
depends on the shock polarity for some
waveforms,35 suggesting that the response of
ventricular myocardium is not symmetrical as
predicted by the sawtooth pattern. (3) Excitation latency of the
ventricles with field stimulation is much shorter for a depolarizing
shock than for a hyperpolarizing shock of the same
strength,2 and this difference in excitation
latency (10 ms) is much larger than the time required for activation
at one end of a cell to propagate to the other end of the
cell.2 Taken together, these findings suggest a
minimal contribution of gap-junction resistance to successful
defibrillation.
The cable equation model and the bidomain model, which is equivalent to
the cable equation when a 1-dimensional strand is
used,17 both predict that the tissue beneath the
anodal electrode undergoes hyperpolarization while
the tissue beneath the cathodal electrode undergoes depolarization, and
that the magnitude of such exchanges in the transmembrane potential
decreases with distance away from the stimulating
electrode.17 31 36 The computer simulations in
the present study used a bidomain model. Results were
consistent with the prediction of a single zero crossing and
also with the experimental results. Because the simulation included
active ionic channels defined by the LRd membrane
equations,22 it was possible to apply shocks
during the action potential plateau, mimicking the experimental
protocol. Results from this simulation demonstrated that the space
constant during this part of the action potential greatly exceeded the
resting space constant (Figure 7A). Therefore, membrane resistance is
perhaps greater in importance than is axial resistance in predicting
shock-induced Vm. Furthermore, the strong
qualitative fit between the experimentally observed spatial
distribution of Vm and the simulated
Vm from a model with no resistive
discontinuities supports our assertion that the sawtooth pattern plays
a minimal role in defibrillation. Even at low shock strengths, as shown
in Figure 7D, all nodes on the anodal side of the model hyperpolarized
and all nodes on the cathodal side of the model depolarized.
The primary goal of the simulation reported here was to provide an
explanation for the point of zero crossing in shock-induced
Vm that we observed experimentally. As a
result, lower shock strengths were used in the simulation than in the
experiments. Despite this difference, the qualitative fit between the
model and experimental data was strong. However, the simulation did
fail to reproduce (1) an asymmetric Vm
response with greater hyperpolarization than
depolarization at all shock strengths and (2) the relatively sharp
transition in Vm at the zero-crossing point.
Although these differences may simply be a consequence of the lower
field strength used in the simulations, they may also be related to the
membrane equations themselves. The equations are based, primarily, on
data from voltage clamp experiments using isolated cells. As a result,
responses of individual ion channels at the large
dVm/dt associated with shocks may not be
complete, suggesting the need for further study.
The limitations of the present study are the following:
1. Shock potential gradients: The spatial recordings of the transmembrane potential during the shock were obtained with a resolution as fine as 20 µm, whereas the shock potentials were recorded only by a single pair of extracellular recording electrodes in the solution. Therefore, the distribution of the shock potential throughout the tissue, especially the shock potential gradients at each microelectrode recording site, was not known in the present study. However, we speculate that the shock potential distribution is fairly even in the microscopic region, because (1) the shock potential field in the present study was created by 2 large patch shock electrodes across the entire tissue bath and (2) the size of the papillary muscle was much smaller than the size of the shock electrodes and the tissue bath.
2. One- versus 3-dimensional tissue: Although the papillary muscle has
a uniform fiber orientation and the results obtained from the
present study are consistent with those from simulation in
1-dimensional tissue, a 4-mm-long and 1.5-mm-wide papillary muscle
still has a characteristic 3-dimensional structure with respect to
20-µm cell diameters. In addition, the data of the present study
were obtained when the electric field was parallel to the longitudinal
axis of the papillary muscle and hence along the fiber orientation.
Thus, the results are likely to represent a special case with
regard to the direction of the shock field, the structure, and
connective tissue distribution and may be different in more complicated
3-dimensional myocardium, which has a nonuniform fiber
orientation. In addition, lateral gap junctions exist between 2
adjacent cells so that lateral averaging effect may occur to affect a
local Vm caused by a shock. Although a
double-barrel microelectrode records the end result, it may not be
able to elucidate a lateral averaging effect if it exists.
3. Location of the recording sites within the cardiac cells: Although the recording resolution in the present study was 20 µm in the microscopic group, it was not known where the impalements were located, ie, near the end or near the center of a cell, or whether consecutive impalements were made within the same cell or in different cells. Therefore, the results cannot directly elucidate the phenomena occurring within each cell. However, the results of the present study still offer information for evaluation of the mathematical models. Statistically, the total recording length (0.4 mm) in the microscopic group should cover several cells. Therefore, with a resolution of 20 µm between 2 adjacent recording sites, the probability of recording depolarization during a shock should be almost the same as that of recording hyperpolarization with several zero-potential crossings if the sawtooth pattern existed. Yet, we did not observe this pattern.
4. Space constant versus the recording region: When electric stimulation is locally applied to the cardiac tissue, the stimulated region undergoes either depolarization or hyperpolarization or both. The response of the membrane is largest near the stimulating region, and the magnitude of the response decreases with distance, indicating the existence of a space constant that has been shown to be about 1 mm in cardiac tissue.28 The sawtooth pattern has been predicted to be superimposed on the local transmembrane potential changes near the stimulating sources and to become more obvious away from the sources.15 The recordings in the present study were made in the middle region, about 1 mm away from the end of the tissue. This means that the recordings were obtained in the region between 1 and 2 space constants from the sources. Thus, measurements were not made more distant from the electrodes, where the sawtooth pattern may have been more obvious. However, as shown in the Appendix, the depolarization-hyperpolarization oscillation of the sawtooth pattern is not observed in the central region of a 20-mm-long fiber, where the measurements were made far beyond several length constants.
5. Effects of diacetyl monoxime: Diacetyl monoxime has been used in the myocardium to eliminate the effect of motion on the optical recordings. Whereas several studies have documented no significant effects of 10 mmol/L diacetyl monoxime on the electrophysiological properties of cardiac tissue,37 38 other studies have shown an electric uncoupling effect of diacetyl monoxime.39 Although the present study did not investigate the effects of diacetyl monoxime on the cardiac electrophysiological properties, the sawtooth pattern would have been more easily observed if 10 mmol/L diacetyl monoxime had caused electric uncoupling in papillary muscles. Thus, the conclusion of the present study that the sawtooth pattern is small or absent is not influenced by using 10 mmol/L diacetyl monoxime.
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Acknowledgments |
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This work was supported in part by the National Institutes of Health research grants HL-42760 and HL-54024, American Heart Association North Carolina Affiliate Grant NC-93-GS-19, National Science Foundation (under National Young Investigator Award BES-9457212), and a Whitaker Foundation Special Opportunities Award.
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Appendix 1 |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionAppendix 1References |
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The purpose of the study described in this Appendix is to verify that the double-barrel microelectrode can record a change in the local transmembrane potential caused by a discrete, small region of increased intracellular resistance, ie, the sawtooth pattern. Recordings were made from the median giant fiber in the ventral nerve cord of the earthworm. This animal model was chosen because the axons in the median giant fiber are extremely large, so that (1) the location of each tip of the double-barrel microelectrode can be seen with a dissecting microscope to verify that one electrode is within the axon while the other is outside of it, and (2) the intracellular space of a single axon can be interrupted by constricting it at a discrete location with a suture and recording a known distance away from this constriction with a double-barrel microelectrode. The median giant fiber consists of a chain of about 100 median giant axons with electric connections by gap junctions called septa, which have an averaged resistance of 38 K
.40
Materials and Methods
Adult Lumbricus terrestris earthworms
(Carolina Biological Supply, Burlington, NC) were
anesthetized by immersion for 15 minutes in 0.2% (wt/vol)
chlorobutanol (Chloretone). A 20- to 30-mm-long ventral nerve
cord was carefully isolated from the earthworm; pinned, ventral side
down, on a silicon rubber within a chamber 10 mm wide, 40 mm
long, and 8 mm deep; and filled with earthworm saline ([in
mmol/L] NaCl 100, KCl 1.6, CaCl2 1.8, and
NaHCO3 1.2, pH 7.3 to 7.4). The earthworm saline
also contained 50 to 100 µmol/L carbachol to stop contractions
of the ventral nerve cord. Two patch shocking electrodes (8x10
mm) were placed on opposite sides of the chamber so that the shock
field vector was parallel to the longitudinal axis of the ventral nerve
cord (Figure 8). Under the dissecting
microscope with x80 magnification and a view field 2.5 mm in
diameter (Leeds Microscope, Leeds Precision Instruments, Inc),
the median giant fiber was clearly seen with 2 lateral giant fibers on
each side. The median giant axons could be identified approximately by
their branches.40 The median giant fiber was
penetrated by a double-barrel microelectrode with a 100- to 150-µm
intertip distance. Because the diameter of the median giant axons is
approximately 5 times greater than that of myocardial fibers, the
intertip distance was also increased by a factor of 5 to perform a
comparable test of the ability of the double-barrel microelectrode to
record local changes in the transmembrane potential. The
recording technique was the same as that described in Materials
and Methods of the main text. In 2 earthworm experiments, optical
recordings were used to detect the Vm
during a shock simultaneously from 8 sites along a 2-mm
region of median giant fiber stained with di-4-ANEPPS. The diameter of
each laser spot was approximately 40 µm, and the sampling rate
was 8 KHz. The optical recording techniques are the same as
those reported previously.8
The double-barrel microelectrode was slowly lowered into the saline
just above the tissue with a motorized micromanipulator. It was then
rotated slightly until the potential difference between the 2 tips was
almost undetectable on the monitoring oscilloscope during a 10-V shock.
The double-barrel microelectrode was next lowered into the tissue until
an action potential was seen. The transmembrane potential was
recorded from a total of at least 6 sites within a 2-mm region of
the central portion of a median giant fiber (Figure 8). At least 2
recording sites were made within a single median giant axon. A
total of 8 ventral nerve cords were used, 2 in each protocol. In
protocol 1, one end of the 2-mm region was tied by a 0.05-mm silk
thread with the other end open (Figure 8A). In protocol 2, both ends of
the 2-mm region were tied (Figure 8B). In protocol 3 (consisting of
protocol 3a, using double-barrel microelectrode recordings, and
protocol 3b, using optical recordings), both ends of the 2-mm
region were first left open followed by a tie at the center of the 2-mm
region. (Figure 8C and 8D). In the electric recording
experiments, a square wave shock with a 50-ms duration and at a
strength of 1 V below the excitation threshold was applied for all
recordings from all sites. In the optical experiments, a 35-mA
square wave shock of 30-ms duration was applied during all
recordings.
Results and Discussion
The length between 2 adjacent branches, which is approximately
the length of a single axon,40 was
0.79±0.06 mm (n=13), and the width was 0.064±0.01 mm (n=8).
In protocol 1 (Figure 8A), the Vm caused by a
5-V shock decreased with distance from the tied site. The results
demonstrate that the polarization at the tied site of the median giant
fiber caused by an electric shock can be recorded with the
double-barrel microelectrode.
In protocol 2 (Figure 8B), in which a 6-V shock was given, a small
hyperpolarization was recorded near the tied
site facing the anode (tracing a in panel B), and a small
depolarization was recorded near the tied site facing the cathode
(tracing f in panel B). One zero-potential crossing was observed in the
middle region.
In protocol 3 (Figure 8C and 8D), no Vm during
a 4-V shock with electric recordings (tracings a through f in
Figure 8C) or during a 35-mA shock with optical recordings
(tracings a through h in Figure 8D) was observed in the central 2-mm
region. After the center of this 2-mm region was tied (dotted crossing
lines in panels C and D), depolarization was observed to the left of
the tie (tracings L1 and L2 for electric recordings and
tracings a through c for optical recordings), whereas
hyperpolarization was observed to the right
(tracings R1 and R2 for electric recordings and tracings d
through f for optical recordings).
Each protocol was performed twice under the same conditions in 2 different ventral nerve cords. The results were similar for both ventral nerve cords, suggesting that the protocol is repeatable.
Conclusion
The results are consistent with the predictions of
mathematical models of secondary sources created by interruptions of
the intracellular space in a core conductor
model.14 These predictions include (1)
depolarization on the side of the intracellular interruption closer to
the anode and hyperpolarization on the side closer
to the cathode, (2) a decrease in Vm with
distance away from the interruption, and (3) a decrease in
Vm caused by an intercellular interruption
when another intracellular interruption is made nearby. The results
from the earthworm study demonstrate the double-barrel microelectrode
as an effective tool for detecting such changes in transmembrane
potential within a single cell.
Received August 25, 1997; accepted September 1, 1998.
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