(Circulation. 1996;93:168-177.)
© 1996 American Heart Association, Inc.
Articles |
Regional Differences in Current Density and Rate-Dependent Properties of the Transient Outward Current in Subepicardial and Subendocardial Myocytes of Human Left Ventricle
Presented in part at the 66th Scientific Sessions of the American Heart Association, Atlanta, Ga, November 8-11, 1993, and published in abstract form in Circulation (1993;88[suppl I]:I-89).
From the Departments of Medicine I (M.N., G.S.) and Cardiovascular Surgery (P.Ü.), University of Munich, and the Department of Medicine III, University of Cologne (D.J.B.), Cologne, Germany.
Correspondence to Dr Michael Näbauer, Medizinische Klinik I, Klinikum Großhadern, 81377 Munich, Germany.
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Abstract |
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Background Recordings of outward currents in human ventricular myocytes revealed the presence of a large calcium-insensitive transient outward current. This current has been suggested to contribute significantly to regional electrophysiological heterogeneity in myocardial cells and tissue of several animal species and to cause electrical gradients across the ventricular wall.
Methods and Results The patch-clamp technique was used to record action potentials and outward currents in myocytes enzymatically isolated from thin subepicardial and subendocardial layers of human nonfailing and failing left ventricle. In all subepicardial cells studied, a calcium-insensitive transient outward current (Ito1) could be recorded with large density (10.6±1.08 pA/pF at 40 mV), whereas current density of Ito1 in subendocardial cells was fourfold smaller (2.63±0.31 pA/pF, P<.0001, nonfailing myocardium). In failing hearts, the density of Ito1 was significantly smaller in subepicardial cells (7.81±0.53 pA/pF, P=.012) but not different in subendocardial myocytes (2.01±0.23 pA/pF, P=.25). Rate-dependent reduction of peak Ito1 at a 2-Hz depolarization rate was minimal in subepicardial cells (to 92.3±1.9%), whereas peak Ito1 in subendocardial myocytes was almost suppressed at 2 Hz (reduction to 13.2±2.1%, P<.0001). The different rate-dependent reduction of the transient outward current was due to a much slower time course of recovery from inactivation in subendocardial cells. Kinetic data, including action potentials recorded at 35°C, allow assessment of the role of the transient outward current for electrical activity and transmural voltage gradients in human left ventricle.
Conclusions Marked regional differences in density and rate-dependent properties of the transient outward current exist in subendocardial and subepicardial layers in human left ventricular myocardium, causing transmural electrical gradients that are important for normal and pathological electrical behavior of the human heart. The difference in recovery rates of the transient outward current is a distinguishing feature between subepicardial and subendocardial myocytes.
Key Words: action potentials • electrophysiology • heart failure • ventricles
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Introduction |
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TopAbstractIntroductionMethods Results Discussion References |
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Electrical heterogeneity within the ventricular myocardium of the mammalian heart has been described in several animal species and is considered to be an important factor for the electrical properties of the heart.1 2 3 4 5 Regional electrical differences within different layers of the working myocardium were first recognized by use of action potential recordings in syncytial preparations.6 The similarity of action potential characteristics of syncytial preparations and isolated myocytes of identical regions of the myocardium has led to the conclusion that regional differences in electrical behavior are due to a large part to different intrinsic properties of the myocytes.1 The ionic basis for these intrinsic electrophysiological differences, however, is largely unknown. Recent data indicate that different densities of a 4-aminopyridine–sensitive, calcium-independent transient outward current (Ito1) contributes significantly to regional electrical heterogeneity within the left ventricular wall1 6 because current densities several times larger in subepicardial than in subendocardial myocytes have been found in dog, cat, and, to a lesser degree, rabbit left ventricle.4 7 8 In canine left ventricle, where regional electrical differences have been studied most extensively, the difference in density of the transient outward current was approximately fivefold and found to be closely related to differences in electrical behavior of subepicardial and subendocardial tissue and myocytes with respect to frequency-dependent action potential changes, pharmacological sensitivity, and response to extracellular ion changes or ischemia.1 9 10 11
Although the exact roles of the transient outward current for action potential duration and processes of excitation-contraction coupling are complex12 and remain to be clarified, the transient outward current clearly exerts a significant effect on the height of the early plateau, thus influencing activation of other plateau currents that control repolarization. Furthermore, there is increasing evidence that the transient outward current may play an important role as mediator of neurohumoral influences on electrical properties of the myocytes.13 14 15
We previously reported the presence of a large calcium-independent transient outward current in myocardial cells isolated from central parts of the left ventricular wall of the human heart.16 17 18 Action potential recordings from other layers of the left ventricular wall indicated marked differences in the size of the notch of the early plateau (phase 1), strongly suggesting regional heterogeneity of the transient outward current in the human heart.1 17 19 Differences in current density of Ito1 in human myocardium were described recently for myocytes isolated from the epicardial and endocardial third of the left ventricular wall, but only a small difference in Ito1 density (1.54-fold) was found for nonfailing myocardium.20 In the present study, tissue sampling has been restricted to the subendocardial and subepicardial layers (up to 1-mm depth) of the left ventricular anterior wall. The data indicate not only an approximately fourfold larger Ito1 in subepicardial cells but also a much slower time course of recovery from inactivation in subendocardial cells, a feature distinguishing them from the very fast recovery in subepicardial cells. In addition, kinetic data at 35°C are presented to allow assessment of the role of Ito1 for electrical heterogeneity of the left ventricular wall.
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Methods |
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Patients
Cells were prepared from 6 undiseased donor hearts (mean age, 41.6 years; range, 16 to 51 years) that were not transplanted for technical reasons and from 11 hearts of patients with end-stage heart failure caused by dilated cardiomyopathy (mean, 41.4 years; range, 17 to 62 years; 3 women; cardiac index, 2.21±0.19 L·min-1·m-2; ejection fraction, 23.6±2.2%). All patients with dilated cardiomyopathy received digoxin and diuretics and were under vasodilator therapy. No catecholamines, ß-adrenoceptor blocking drugs, calcium antagonists, or antiarrhythmic agents were given 48 hours before the operation. Informed consent was obtained before organ explantation. The protocol was approved by the Ethical Review Board of the University of Munich.
Cell Isolation
The isolation procedure was described in
detail
previously.21 A segment of the myocardium
approximately midway between the apex and base of the left
ventricular anterior wall was excised, together with an
arterial branch of the left anterior descending
coronary artery. This wall segment was then perfused through
this arterial branch: 30 minutes with a nominally
Ca2+-free modified Tyrode's solution ([mmol/L]
NaCl 138,
KCl 4, MgCl2 1, glucose 10, NaH2PO4
0.33, and HEPES 10; pH 7.3 was adjusted with NaOH at 37°C), followed
by 40 minutes with the same solution with added collagenase
(type II, 70 mg/50 mL, Worthington Biochemical Corp) and protease (type
XIV, 6 mg/50 mL, Sigma Chemical Co). Finally, the enzyme was washed out
for 15 minutes with modified Tyrode's solution that contained 200
µmol/L Ca2+. After this enzymatic digestion, the tissue
still had its anatomic structure, so that identified regions of the
myocardial wall could be sampled. Subepicardial and subendocardial
myocytes were obtained by removing a thin layer (maximal thickness,
1 mm) from the subepicardial and subendocardial surface with a
scalpel. On the basis of a thickness of the left
ventricular wall in this area of 8 to 11 mm, the layers
used correspond to 1/10th of the left ventricular wall.
The distance of the two layers can be estimated to be between 7 and 10
mm. The tissue slices were cleared of myocytes of other regions
sticking to the outer surfaces by washing with Tyrode's solution and
then processed separately. After the tissue was cut into small pieces
with scissors, the myocytes were disaggregated by mechanical agitation
and, after filtration through a nylon mesh, stored at room temperature
in Tyrode's solution containing 2.0 mmol/L Ca2+.
Living cell yield was 5% to 8%. Only cells with clear cross
striations without spontaneous contraction or significant granulation
were selected for experiments. When field stimulated, these myocytes
contracted as confirmed visually.
Solutions
For action potential recordings, cells were
superfused
at 35°C with a modified Tyrode's solution containing (mmol/L) NaCl
138, KCl 4, CaCl2 2.0, NaH2PO4
0.33, MgCl2 1, glucose 10, and HEPES 10; pH was adjusted to
7.3 with NaOH. For voltage-clamp experiments, 10 µmol/L
tetrodotoxin was routinely added to reduce the fast sodium current
(INa), facilitate voltage control, and minimize
interference of current measurements by INa.22
In addition, a 100-ms prepulse to -60 mV from a holding potential
of -80 mV was used to partially inactivate
INa. To further minimize interference of INa
with current readings, quantitative measurements of Ito1
were made close to the reversal potential of INa at 40 mV.
The slow inward calcium current (ICa), which would
interfere with measurements of Ito1 and might
activate calcium-dependent
currents,23 24 25 was
blocked by addition of CdCl2 (0.3 mmol/L) to the
extracellular solution, in line with our earlier studies and work by
others.16 17 26 27 Although
CdCl2 has been
shown to cause a shift of inactivation and activation
parameters of the transient outward current in the
depolarizing direction,28 the alternative use of high
concentrations of organic calcium channel blockers would similarly have
been complicated by their effects on the density and kinetics of
Ito1.29 30 Experimental conditions in
voltage-clamp experiments were chosen to minimize
calcium-activated outward currents by inclusion of EGTA to
buffer [Ca2+]i and omission of
Na+ from the intracellular solution to inhibit calcium
influx through Na-Ca exchange and block of ICa by external
Cd2+. Voltage-clamp experiments were performed at room
temperature (21°C to 23°C). Under these recording
conditions, no evidence for a contribution of chloride currents to the
transient or pedestral outward current was found in previous
studies.16 When recordings of kinetic
parameters of Ito1 were made at 35°C, they
are explicitly identified in the "Results" section. Fresh
4-aminopyridine was dissolved right before use in
Tyrode's solution.
For current recordings, cells were dialyzed internally for at least 2 minutes with the patch electrode with (mmol/L) potassium aspartate 120, KCl 10, MgCl2 2, HEPES 10, EGTA 5, and MgATP 2; pH was adjusted to 7.2 with KOH. After this time, contraction on depolarization had ceased even in the absence of external Cd2+. For action potential recordings, an identical internal solution was used, supplemented by 5 mmol/L NaCl.
Recording Techniques
Experiments were carried out by standard
single microelectrode
whole-cell patch-clamp recording
techniques31 with an Axopatch 200 A amplifier (Axon
Instruments). Microelectrodes were pulled from borosilicate glass and
had resistances of 2.0 to 3.0 M
. Series resistance was compensated
as much as possible (30% to 80%). Analog filtering of current
recordings was at 3 kHz. Currents were digitized at 2 to 10 kHz
(unless stated otherwise) and stored for off-line analysis.
Action potentials were recorded in current clamp mode. Cell
capacitance was calculated by applying 5-mV steps from a holding
potential of -80 mV in the hyperpolarizing direction and
integrating the current required to charge the membrane when stepping
back to -80 mV. No significant time-dependent currents were
observed at this voltage. The temperature of the superfusing solution
was measured with an NiCr-Ni microsensor.
Data Analysis
Fits to Boltzmann distribution and exponential
kinetics were
obtained by nonlinear least-squares techniques; goodness of fit for
single exponential current decay was judged by visual inspection and
2 testing as previously described.16
With the results (mean±SEM), the number of cells used is given,
followed by a slash and the number of hearts from which the cells were
derived. The Mann-Whitney nonparametric test was used for
statistical evaluation, and values of P<.05 were considered
significant.
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Results |
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Action potentials recorded in current clamp mode from subepicardial and subendocardial myocytes revealed a prominent notch in all cells of subepicardial origin. Action potential duration tended to be shorter in subepicardial cells (subepicardial, 424±20.9 ms, n=7/5; subendocardial, 486.2±32.6 ms, n=7/3; P=NS); resting membrane potential was similar in both groups (subepicardial, -79.5±0.48 mV; subendocardial, -78.8±1.38 mV; P=NS). The plateau of the action potential was consistently lower in subepicardial than in subendocardial cells (subepicardial: maximum plateau voltage after the notch at phase 1, 23.7±3.1 mV, n=7/5; subendocardial: voltage during plateau phase at dV2/dt2=0, ie, the transition from early repolarization to final repolarization, 36.0±3.06 mV, n=7/3; P<.05; see Fig 1
, as well as Figs 8
and 9).
The notch in subepicardial cells, measured as the difference between
the minimum of the notch and the plateau voltage, was 8.61±1.6 mV
(n=7/5).
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For assessment of the density of Ito1 in subepicardial and
subendocardial myocytes, current-voltage relations for the
transient outward current were obtained by applying depolarizing pulses
to voltages from -30 to 80 mV. To allow adequate recovery from
inactivation, the pulse frequency was set to 1 per 20 seconds. In five
subendocardial cells, no significant increase in Ito1 was
observed when the holding time at -80 mV was prolonged from 20 to
90 seconds (at 20 seconds, the value was 96.3% of the value at 90
seconds), indicating that recovery was essentially complete after 20
seconds. Ito1 was measured as the difference in current
between the peak of the transient outward current and the maintained
current component at the end of the depolarizing clamp pulse. Current
densities in myocytes from nonfailing hearts, calculated by dividing
the transient outward current by the capacitance of the myocyte, are
given as current-voltage relations of Ito1 in
subepicardial and subendocardial cells in Fig 2.
Densities of Ito1 were strikingly different in
subepicardial and subendocardial cells, being about four times larger
in cells of subepicardial origin (difference between peak current and
maintained current at the end of the pulse to 40 mV at room
temperature: subepicardial, 10.6±1.08 pA/pF, n=12/5;
subendocardial,
2.63±0.31 pA/pF, n=22/5; P<.0001; nonfailing hearts;
Table 1). Membrane capacitance of the myocytes was not
different in the two groups (subepicardial, 184.5±20.5 pF;
subendocardial, 174.2±16.9 pF; P=NS). In the same
cells,
the maintained, late component of the outward current was similar in
subepicardial and subendocardial cells (at 40 mV and room temperature:
subepicardial, 2.14±0.58 pA/pF; subendocardial, 1.49±0.17 pA/pF;
P=NS). In myocytes derived from failing hearts, the density
of Ito1 (difference between the peak and maintained
currents at the end of the pulse to 40 mV) was significantly smaller in
subepicardial cells (7.81±0.53 pA/pF, n=20/5;
P=.012) but
not different in subendocardial myocytes (2.01±0.23 pA/pF,
n=14/4;
P=.25; see Table 1).
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n=12 cells from 5 hearts, mean±SEM) and subendocardial myocytes
(B,
, n=22/5). Holding potential was -80 mV, and a 100-ms
prepulse to -60 mV was applied before the membrane voltage was
stepped from -30 to 80 mV for 500 ms. Ito1 was
measured as the difference between absolute peak current of
Ito1 and maintained current at the end of the clamp pulse.
Pulse rate, 1 per 20 seconds; room temperature.
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Steady state inactivation parameters of Ito1
were obtained with a double-pulse protocol with 1-second prepulses
to voltages from -60 to 40 mV from a holding potential of
-80 mV as previously described.16 Peak currents at
the test pulse to 60 mV were normalized to the maximal transient
outward current elicited by the test pulse and fitted individually for
each cell by a single Boltzmann distribution, resulting in a slightly
more negative V1/2 in subendocardial cells
(V1/2, -17.6±1.02 mV; slope factor, 8.9±0.92
mV, n=10/4) compared with subepicardial cells (V1/2,
-9.5±0.38 mV, P=.0012; slope factor,
5.1±0.44 mV,
P=.0054; n=8/3). Activation of the transient outward
current
was observed first around 0 mV in both subepicardial and subendocardial
cells with a similar current-voltage relation in cells of both
origins. Activation parameters of Ito1
(calculated by assuming a linear open channel conductance and a
reversal potential of -58 mV16 ) were not different
in subepicardial (V1/2, 29.1±1.2 mV; slope
factor, -12.9±1.1 mV; n=12/5) and subendocardial myocytes
(V1/2, 32.0±1.11 mV, P=NS; slope factor,
-14.9±0.81 mV, P=NS; n=22/5). In myocytes
from
failing hearts, activation parameters in subepicardial
(V1/2, 25.7±1.5 mV; slope factor, -13.4±0.74
mV; n=14/4) and subendocardial cells (V1/2,
31.6±1.61 mV; slope factor, -15.0±1.1 mV; n=11/4)
were not
different from the corresponding values in nonfailing
myocardium (Fig 3). It should be noted that
the V1/2 -values are expected to shift to more positive
potentials because of the use of the divalent ion Cd2+ to
block ICa.28 Determination of potassium
selectivity from tail currents was not successful owing to the small
size of decaying tails in endocardial cells that could not be measured
reliably. In both subepicardial and subendocardial cells,
Ito1 was sensitive to 4-aminopyridine with
almost complete block of the transient outward current at 3 mmol/L
4-aminopyridine (depolarization to 40 mV for 300 ms at
0.1 Hz). The nature of the small maintained outward current component
remains to be clarified. The insensitivity of this current component to
4-aminopyridine in human ventricular
myocytes16 suggests that it is not due to the ultrarapid
delayed rectifier current described recently.32 However,
the complex state-dependent blocking properties of
4-aminopyridine with respect to
Ito133 may obscure a contribution of this
current to the observed late maintained outward current.16
An IK-delayed rectifier current would not be expected to
contribute significant outward currents at room temperature.
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The time course of inactivation of the transient outward current, which
has been shown to be largely independent of voltage in human myocytes
and myocytes of several other
species,16 24 28 was not
different in subepicardial and subendocardial myocytes (Fig 4
and Table 2). To allow estimation of
the time-dependent influence of Ito1 on action
potential configuration at physiological
temperatures, inactivation kinetics were studied at 35°C.
Determination at physiological temperatures is
especially important because the kinetic properties of the transient
outward current are known to be highly temperature
dependent.34 The results indicate that inactivation is
speeded up by a factor of six at 35°C compared with room temperature
(data summarized in the legend to Fig 4).
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For analysis of frequency-dependent properties of the
transient outward current, depolarizing steps to 40 mV were given for
250 ms from a holding potential of -80 mV at frequencies up to 2
Hz. When comparing the fifth pulse in a train of pulses at 2 Hz to the
first pulse given after a 30-second rest at -80 mV, only a small
reduction of peak transient outward current was observed in
subepicardial cells (to 92.3±1.9%, n=16/4), whereas
Ito1
was almost completely suppressed in subendocardial cells (reduction to
13.2±2.1%, n=15/4, P<.0001; Fig 5).
Rate-dependent reduction of Ito1 was not different in
myocytes isolated from failing myocardium (subepicardial,
90.8±1.9%, n=6/3, P=.36; subendocardial,
10.1±2.3%,
n=6/3, P=.39).
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This different rate-dependent reduction of Ito1
suggested differences in recovery from inactivation in cells of
subepicardial and subendocardial origin, prompting the study of
restitution of Ito1. At room temperature (21°C to
23°C), recovery of the transient outward current from inactivation
was very fast in subepicardial cells (time constant of main component,
46.1 ms), similar to what has been observed in myocytes derived from
central parts of the left ventricular
myocardium.16 In contrast, recovery from
inactivation in subendocardial cells was slow, with only half of the
current available after 1800 ms (Fig 6). To obtain
time parameters of recovery kinetics, nonlinear fitting was
performed with biexponential functions, based on earlier observations
in myocytes of human myocardium and several other species
that two exponentials usually were required to adequately fit the
recovery kinetics of
Ito1.12 14 16 35 36
The
resulting values, summarized in Table 2
, indicated that >90%
of the
recovery of Ito1 in subepicardial cells follows a fast time
course, whereas about 90% of the recovery follows a slow time course
in subendocardial myocytes. To allow assessment of availability of
Ito1 during the cardiac cycle at
physiological temperatures, recovery
parameters were determined at 35°C. The differences in
speed of recovery of subepicardial and subendocardial myocytes were
similar at 35°C (Fig 7). However, the recovery
processes of the major components in subepicardial cells (fast
component) and subendocardial cells (slow component) were faster by
factors of >5 and 3.7, respectively, at 35°C compared with at room
temperature (Table 2). A comparison of the time constants of
the small
components did not appear to be useful because of the large errors
expected for the values obtained from fitting.
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Frequency-dependent changes of the action potential in
subepicardial and subendocardial myocytes, suggested to be influenced
by differences in Ito1,12 were
evaluated in current clamp mode at 35°C. Stimulation (at 150% of
threshold) and recording of intracellular potentials was
through the patch electrode. Increasing the stimulation frequency from
1 per 30 seconds to 2 per 1 second caused the action potential to
shorten in both subepicardial and subendocardial myocytes, with a
slight increase of the early plateau voltage (Fig 8).
The depth of the notch at phase 1 did not change significantly in the
train of pulses (n=12/3; Fig 8). In endocardial cells, a
notch at phase
1 of the action potential could not be detected, even when the interval
between depolarizations was made long enough to allow essentially
complete recovery of Ito1 from inactivation (30
seconds).
In the dog, restitution of phase 1 of the action potential (which is
considered to be related to Ito1 density3 ) was
found to be biphasic, with reduced availability of Ito1
during early recovery of the action potential
plateau.1 3 9 In dog heart subepicardium,
some important
pathophysiological phenomena, such as
supernormal conduction1 or phase 2 reentry,9
may be linked in part to delayed reactivation of Ito1. In
contrast, the fast reactivation time course of Ito1 in
human subepicardial cells suggests rapid restitution of the phase 1
action potential notch and plateau characteristics. Therefore,
restitution of action potential characteristics was studied in human
subepicardial and subendocardial myocytes. The data (Fig 9)
indicate that the notch at phase 1 of the action
potential reappeared rapidly in subepicardial cells, with no
significant changes in the depth of the notch at phase 1 in action
potentials elicited after >20 ms of repolarization. This is
consistent with the rapid time course of recovery of
Ito1 in subepicardial cells (time constant 
=7.86 ms at
35°C; Fig 7). In subendocardial cells, where the notch at
phase 1 was
absent, restitution of the final shape of the action potential
proceeded with an equally fast time course. It should be noted that
experimental conditions were selected to preferentially study
Ito1, so other ionic currents possibly important for
physiological modulation of the action potential
height, shape, and duration may have been reduced or eliminated,
especially Ca2+-activated currents.
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Discussion |
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TopAbstractIntroductionMethods Results Discussion References |
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This report characterizes regional densities and properties of Ito1 in human ventricular myocytes. The results indicate large differences in density of Ito1 in subepicardial and subendocardial layers of the left ventricular wall of the human heart. Detailed experimental evidence is provided to show that rate-dependent properties of Ito1 are distinctly different in subepicardial and subendocardial layers of human left ventricle. Action potential recordings were performed for assessment of the role of Ito1 for transmural voltage gradients and frequency dependence of the action potential configuration. However, limitations caused by the experimental conditions favoring dissection of Ito1 (use of dialyzing pipettes with alteration of the intracellular constituents and, most importantly, suppression of Ca2+ transients by EGTA) must be considered when the action potential data are extrapolated to physiological conditions.
Differences in Action Potential Characteristics
The
characteristic difference in action potential shape between
subepicardial and subendocardial cells was the presence of a notch at
phase 1 of the action potential in myocytes of subepicardial origin
(Figs 1, 8, and 9). A similar
difference was noted previously in
dog,4 cat,5 rat,7 and
rabbit8 left ventricular myocytes in which
this notch could also be related to the presence of a prominent
transient outward current in cells of subepicardial origin.
Furthermore, action potential duration tended to be shorter and the
voltage level of the plateau to be lower in subepicardial cells, the
latter reflecting the early repolarizing effect of the transient
outward current. Because the rapid inactivation kinetics of the
transient outward current at physiological
temperatures ( <10 ms at 40 mV; Fig 4) make a direct
contribution
of the transient outward current to the final phase of repolarization
(ie, after 300 ms) very unlikely, the transient outward current
probably exerts its influence on action potential duration indirectly
by setting the voltage of the early plateau
phase.1 12
Current Density of Ito1
For nonfailing myocardium,
current density of the
Ito1 was larger by a factor of about four in myocytes of
subepicardial compared with subendocardial origin. This difference and
the absolute densities of Ito1 in subepicardial and
subendocardial myocytes were in a similar range as the values reported
for dog left ventricular wall at comparable voltages
(subepicardial, 29.0±13.7 pA/pF; subendocardial, 5.59±3.19 pA/pF
at
70 mV8 ). It should be noted that the myocytes used in this
study were derived from a very similar area of the left
ventricular wall. In feline myocytes, current densities
three to four times larger (102±47.7 pA/pF at 80 mV) were reported in
subepicardial myocytes, whereas the current density in subendocardial
cells was similar (3.3±3.3 pA/pF).7 In contrast, the
difference reported for rabbit left ventricle was markedly smaller and
significant only at very positive potentials.4 In a recent
study in human ventricular myocytes from segments spanning
approximately one third of the epicardial and endocardial wall, current
densities were smaller for cells of subepicardial but similar for
subendocardial origin, possibly related to the differences in cell
origin and experimental conditions, including the use of
2,3-butanedione monoxime for myocardial
preservation.20
Frequency-Dependent Properties
Despite the
electrophysiological
similarities in subepicardial and subendocardial myocytes,
Ito1 in subepicardial and subendocardial myocytes is
clearly distinguished by the time course of recovery from inactivation.
When overall recovery from inactivation of Ito1 is
assessed, only about 35 ms (at room temperature) was required for
half-maximal recovery of Ito1 compared with 1800 ms
in subendocardial cells. When a biexponential function is fit to the
time course of recovery from inactivation, >90% of the recovery from
inactivation followed a fast time course in epicardial cells but a very
slow time course in subendocardial cells (Figs 6 and
7 and Table 2).
Biphasic recovery of whole-cell transient outward current from
inactivation was observed previously in myocytes derived from central
parts of the left ventricular wall16 and
atrial myocytes36 of the human heart and several animal
species.12 14 35 In addition, a wide
range of recovery
rates has been reported for the transient outward current in
ventricular myocytes of different animal species, with fast
recovery in rat37 but relatively slow kinetics in dog or
rabbit.35 36 38 This indicates a large
variability of this
parameter in different species and illustrates the
difficulties in extrapolating data from animal to human myocardial
tissue.
Because the current densities given in Fig 2
were measured at a low
pulse rate selected to allow essentially complete recovery of
Ito1 from inactivation (1 per 20 seconds), the transmural
difference in current density of Ito1 will become even
larger with increasing frequency owing to incomplete recovery of
Ito1 in subendocardial cells. In subepicardial cells, on
the other hand, Ito1 will contribute with nearly its
maximal density to repolarization, largely independent of frequency at
physiological heart rates. This very fast recovery
of Ito1 in subepicardial myocytes resembles findings in
human atrial myocytes, where Ito1 was also found to be
essentially rate independent at physiological heart
rates.36
Although Ito1 is small in subendocardial myocytes, it may nevertheless contribute to repolarization of the early plateau phase because even small currents can have a significant effect on the balance of currents during the plateau of the action potential. With about half of Ito1 available within 500 ms at 35°C, a significant frequency-dependent variability of Ito1 is expected in the subendocardial layer within the physiological range of heart rates. Furthermore, although the current densities reported here are from the two extreme surfaces of the left ventricular myocardium, the change in current densities from subepicardial to subendocardial is most likely a continuous process, with increasing density of the fast recovering transient outward current and decreasing density of the slowly recovering subtype from subendocardial to subepicardial layers, involving regions with transitional electrophysiological characteristics, as suggested from action potential recordings in dog left ventricle.39 This is also supported by previous data from central parts of the left ventricular wall,16 in which Ito1 current densities and the fraction of current recovering at a fast rate had values between those of subepicardial and subendocardial cells found in this study.
A recent study on
Ito120 in human myocytes
also presented support for our previous report of a slow
recovery process in subendocardial myocytes,40 even though
the results were from limited data in a few cells derived from the
endocardial one third of the myocardial wall. However, recovery was
still found to be relatively fast, reaching 50% of its final value
within 100 ms (compared with 10% in this study; Fig 6). In
addition, some analyzed cells apparently displayed a biphasic
decay of the outward current with a second slow phase of current decay
(Fig 9 in Reference 20). This is atypical for
Ito116 34 and suggests the presence of
additional unidentified current components that may have contributed to
apparently nonrecovering current components as
proposed.20
Influence of Underlying Pathology
Several studies have
indicated that the density of the transient
outward current may be subjected to alterations in cardiac
hypertrophy41 or failure,17
during ischemia,42 after myocardial
infarction,43 or under the influence of an altered thyroid
state.44 In a previous study in myocytes derived from
central parts of the left ventricular wall,
Ito1 was significantly reduced (by 37%) in myocytes
derived from failing compared with nonfailing
myocardium.17 A similar finding has now been
made for myocytes in the subepicardial layer: Ito1 density
was 26.4% smaller for cells from failing myocardium.
Current density of Ito1 in myocytes from the subendocardial
layer was not different for failing and nonfailing hearts. These
findings differ from those of Wettwer et al,20 who
reported a decrease in current density of Ito1 in
subendocardial but not subepicardial cells in heart failure. However,
tissue sampling was not as strictly defined in their study in that no
specific ventricular site was selected and a thick wall
segment was included to obtain "subepicardial" and
"subendocardial" myocytes (up to 1/3 of the thickness of the wall
on each side). This allows a large variability of the origin of the
myocytes (data in dog left ventricle indicate that important density
changes of Ito1 may occur in as little as 1/10th of the
thickness of the myocardial wall45 ), which might have
significantly influenced the results, especially because the data for
subepicardial cells of nonfailing myocardium were obtained
from only two hearts. It also may have contributed to the small current
density in nonfailing subepicardial cells (6.8±0.4 pA/pF at 60 mV)
compared with our data (15.6±1.7 pA/pF at 60 mV) and their previous
value in nonselected left ventricular cells of nonfailing
myocardium (8.7±1.0 pA/pF at 60 mV37 ). This,
together with the very small difference of Ito1 in
subepicardial to subendocardial cells in nonfailing
myocardium (1.54-fold; this study, 4-fold; dog left
ventricle, 5.2-fold at 70 mV8 ) and the relatively fast
recovery in their subendocardial cell preparation (50% within 100
ms), suggests that the inner and outer 1/3 of the human left
ventricular wall may not closely reflect the properties of
thin subepicardial and subendocardial layers. Precautions against
regional influences of tissue sampling are especially warranted for the
subendocardial layer because the small size of Ito1 and the
rapid increase of Ito1 toward the deeper subendocardium
render data on current densities from this layer very sensitive to the
contaminating influence of cells from deeper layers.
Implications for Electrophysiology of Human Heart
The large
gradient in current density of the transient outward
current in myocytes from subendocardial to subepicardial layers
suggests the presence of a pronounced electrical
heterogeneity in the left ventricular wall
of the human heart. The relevance of the measurements in isolated
myocytes for myocardial tissue is strengthened by the similarity of the
findings in isolated canine tissue and myocytes obtained from identical
myocardial regions8 and by action potential
recordings in human subepicardial tissue that also indicated
the presence of a transient outward current.46
The importance of the transient outward current for heterogeneity of electrical behavior and pharmacological responses of myocardium was demonstrated recently in dog heart.1 In tissue and myocytes of canine left ventricular wall, differences in action potential characteristics, rate dependence of action potential restitution, and sensitivity to extracellular ion changes (potassium and Ca2+) were shown to be closely related to the different densities of Ito1.9 Furthermore, the high density of the transient outward current was found to contribute significantly to the increased sensitivity of epicardial myocardium to electrical depression during ischemia.11 Because the transient outward current appears to be present in similar densities and gradients in subepicardial and subendocardial layers of the human left ventricular wall as in the dog, some findings may be applicable to the human heart under similar conditions. However, the rapid recovery of Ito1 in human subepicardial cells should be remembered when phenomena possibly related to reduced early availability of Ito1 in dog, such as supernormal conduction1 or phase 2 reentry, are considered.9
In addition, drugs blocking Ito1 will differentially influence electrophysiological properties in subepicardial and subendocardial myocytes. This has been studied for 4-aminopyridine, considered to be a relatively selective blocker of the transient outward current, which exerts markedly different effects in subepicardial compared with subendocardial cells in canine left ventricle on action potential duration, rate-dependent effects, ischemia-induced electrical depression, and other electrical phenomena considered to be related to Ito1.1 Different densities of Ito1 also may cause differential sensitivity to reduction of inward currents conducting at a similar time during the action potential, such as block of the sodium channel. For flecainide, this has been implicated to promote electrical heterogeneity and dispersion of repolarization as possible mechanisms of proarrhythmic effects.1 10 47 Because several antiarrhythmic drugs, including quinidine,48 propafenone, flecainide,49 50 tedisamil,51 and the antidepressant imipramine,52 have recently been shown to block Ito1 in possibly therapeutically relevant concentrations, the density gradient of Ito1 may have immediate clinical implications in that these compounds might differentially affect electrical properties of subepicardial and subendocardial myocardium.
In conclusion, a large gradient in density- and rate-dependent properties of the transient outward current exists in different layers of the left ventricular wall of the human heart causing a pronounced electrophysiological heterogeneity. Ito1 appears to be reduced in heart failure in subepicardial myocytes, similar to what has been found in central layers of human left ventricle. Even though other currents might also exhibit regional variability within the left ventricular wall, the large difference in density and properties suggests that the transient outward current is of primary importance for the regional heterogeneity of electrophysiological properties of the myocytes and the electrical behavior of the myocardium in human left ventricular wall.
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Acknowledgments |
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This research was supported by a grant of the Deutsche Forschungsgemeinschaft.
Received December 7, 1994; revision received August 1, 1995; accepted August 14, 1995.
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References |
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N. Decher, A. S. Barth, T. Gonzalez, K. Steinmeyer, and M. C. Sanguinetti Novel KChIP2 isoforms increase functional diversity of transient outward potassium currents J. Physiol., June 15, 2004; 557(3): 761 - 772. [Abstract] [Full Text] [PDF]
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S. P. Patel, R. Parai, R. Parai, and D. L. Campbell Regulation of Kv4.3 voltage-dependent gating kinetics by KChIP2 isoforms J. Physiol., May 15, 2004; 557(1): 19 - 41. [Abstract] [Full Text] [PDF]
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C. E Conrath, R. Wilders, R. Coronel, J. M.T de Bakker, P. Taggart, J. R de Groot, and T. Opthof Intercellular coupling through gap junctions masks M cells in the human heart Cardiovasc Res, May 1, 2004; 62(2): 407 - 414. [Abstract] [Full Text] [PDF]
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K. H. W. J. ten Tusscher, D. Noble, P. J. Noble, and A. V. Panfilov A model for human ventricular tissue Am J Physiol Heart Circ Physiol, April 1, 2004; 286(4): H1573 - H1589. [Abstract] [Full Text] [PDF]
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J. Tamargo, R. Caballero, R. Gomez, C. Valenzuela, and E. Delpon Pharmacology of cardiac potassium channels Cardiovasc Res, April 1, 2004; 62(1): 9 - 33. [Abstract] [Full Text] [PDF]
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M. Fernandez-Velasco, N. Goren, G. Benito, J. Blanco-Rivero, L. Bosca, and C. Delgado Regional distribution of hyperpolarization-activated current (If) and hyperpolarization-activated cyclic nucleotide-gated channel mRNA expression in ventricular cells from control and hypertrophied rat hearts J. Physiol., December 1, 2003; 553(2): 395 - 405. [Abstract] [Full Text] [PDF]
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B. Rosati, F. Grau, S. Rodriguez, H. Li, J. M Nerbonne, and D. McKinnon Concordant expression of KChIP2 mRNA, protein and transient outward current throughout the canine ventricle J. Physiol., May 1, 2003; 548(3): 815 - 822. [Abstract] [Full Text] [PDF]
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H.-S. Wang and I. S Cohen Calcium channel heterogeneity in canine left ventricular myocytes J. Physiol., March 15, 2003; 547(3): 825 - 833. [Abstract] [Full Text] [PDF]
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H. L Tan, C. R Bezzina, J. P.P Smits, A. O Verkerk, and A. A.M Wilde Genetic control of sodium channel function Cardiovasc Res, March 15, 2003; 57(4): 961 - 973. [Abstract] [Full Text] [PDF]
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R. Sah, R. J Ramirez, G. Y Oudit, D. Gidrewicz, M. G Trivieri, C. Zobel, and P. H Backx Regulation of cardiac excitation-contraction coupling by action potential repolarization: role of the transient outward potassium current (Ito) J. Physiol., January 1, 2003; 546(1): 5 - 18. [Abstract] [Full Text] [PDF]
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W. Han, L. Zhang, G. Schram, and S. Nattel Properties of potassium currents in Purkinje cells of failing human hearts Am J Physiol Heart Circ Physiol, December 1, 2002; 283(6): H2495 - H2503. [Abstract] [Full Text] [PDF]
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G.-R. Li, C.-P. Lau, A. Ducharme, J.-C. Tardif, and S. Nattel Transmural action potential and ionic current remodeling in ventricles of failing canine hearts Am J Physiol Heart Circ Physiol, September 1, 2002; 283(3): H1031 - H1041. [Abstract] [Full Text] [PDF]
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R. Kaprielian, R. Sah, T. Nguyen, A. D. Wickenden, and P. H. Backx Myocardial infarction in rat eliminates regional heterogeneity of AP profiles, Ito K+ currents, and [Ca2+]i transients Am J Physiol Heart Circ Physiol, September 1, 2002; 283(3): H1157 - H1168. [Abstract] [Full Text] [PDF]
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Y. Xu, P. H. Dong, Z. Zhang, G. U. Ahmmed, and N. Chiamvimonvat Presence of a calcium-activated chloride current in mouse ventricular myocytes Am J Physiol Heart Circ Physiol, July 1, 2002; 283(1): H302 - H314. [Abstract] [Full Text] [PDF]
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W. Guo, H. Li, F. Aimond, D. C. Johns, K. J. Rhodes, J. S. Trimmer, and J. M. Nerbonne Role of Heteromultimers in the Generation of Myocardial Transient Outward K+ Currents Circ. Res., March 22, 2002; 90(5): 586 - 593. [Abstract] [Full Text] [PDF]
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S. P Patel, D. L Campbell, M. J Morales, and H. C Strauss Heterogeneous expression of KChIP2 isoforms in the ferret heart J. Physiol., March 15, 2002; 539(3): 649 - 656. [Abstract] [Full Text] [PDF]
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S. S. Po, R. C. Wu, G. J. Juang, W. Kong, and G. F. Tomaselli Mechanism of alpha -adrenergic regulation of expressed hKv4.3 currents Am J Physiol Heart Circ Physiol, December 1, 2001; 281(6): H2518 - H2527. [Abstract] [Full Text] [PDF]
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B Huang, D Qin, and N El-Sherif Spatial alterations of Kv channels expression and K+ currents in post-MI remodeled rat heart Cardiovasc Res, November 1, 2001; 52(2): 246 - 254. [Abstract] [Full Text] [PDF]
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N. Decher, O. Uyguner, C. R Scherer, B. Karaman, M. Yuksel-Apak, A. E Busch, K. Steinmeyer, and B. Wollnik hKChIP2 is a functional modifier of hKv4.3 potassium channels: Cloning and expression of a short hKChIP2 splice variant Cardiovasc Res, November 1, 2001; 52(2): 255 - 264. [Abstract] [Full Text] [PDF]
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B. Rosati, Z. Pan, S. Lypen, H.-S. Wang, I. Cohen, J. E Dixon, and D. McKinnon Regulation of KChIP2 potassium channel {beta} subunit gene expression underlies the gradient of transient outward current in canine and human ventricle J. Physiol., May 15, 2001; 533(1): 119 - 125. [Abstract] [Full Text] [PDF]
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R. Sah, R. J Ramirez, R. Kaprielian, and P. H Backx Alterations in action potential profile enhance excitation-contraction coupling in rat cardiac myocytes J. Physiol., May 15, 2001; 533(1): 201 - 214. [Abstract] [Full Text] [PDF]
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D. J. Huelsing, A. E. Pollard, and K. W. Spitzer Transient outward current modulates discontinuous conduction in rabbit ventricular cell pairs Cardiovasc Res, March 1, 2001; 49(4): 779 - 789. [Abstract] [Full Text] [PDF]
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T. Volk, T. H.-D. Nguyen, J.-H. Schultz, J. Faulhaber, and H. Ehmke Regional alterations of repolarizing K+ currents among the left ventricular free wall of rats with ascending aortic stenosis J. Physiol., February 1, 2001; 530(3): 443 - 455. [Abstract] [Full Text] [PDF]
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C. R Bezzina, M. B Rook, and A. A.M Wilde Cardiac sodium channel and inherited arrhythmia syndromes Cardiovasc Res, February 1, 2001; 49(2): 257 - 271. [Full Text] [PDF]
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J. L. Greenstein, R. Wu, S. Po, G. F. Tomaselli, and R. L. Winslow Role of the Calcium-Independent Transient Outward Current Ito1 in Shaping Action Potential Morphology and Duration Circ. Res., November 24, 2000; 87(11): 1026 - 1033. [Abstract] [Full Text] [PDF]
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H.-G. Shin, J. V. Barnett, P. Chang, S. Reddy, D. C. Drinkwater, R. N. Pierson, R. G. Wiley, and K. T. Murray Molecular heterogeneity of protein kinase C expression in human ventricle Cardiovasc Res, November 1, 2000; 48(2): 285 - 299. [Abstract] [Full Text] [PDF]
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K. R. Sipido, P. G. A. Volders, S. H. M. de Groot, F. Verdonck, F. Van de Werf, H. J. J. Wellens, and M. A. Vos Enhanced Ca2+ Release and Na/Ca Exchange Activity in Hypertrophied Canine Ventricular Myocytes : Potential Link Between Contractile Adaptation and Arrhythmogenesis Circulation, October 24, 2000; 102(17): 2137 - 2144. [Abstract] [Full Text] [PDF]
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W. Guo, H. Li, B. London, and J. M. Nerbonne Functional Consequences of Elimination of Ito, f and Ito, s : Early Afterdepolarizations, Atrioventricular Block, and Ventricular Arrhythmias in Mice Lacking Kv1.4 and Expressing a Dominant-Negative Kv4 {alpha} Subunit Circ. Res., July 7, 2000; 87(1): 73 - 79. [Abstract] [Full Text] [PDF]
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J. M Nerbonne Molecular basis of functional voltage-gated K+ channel diversity in the mammalian myocardium J. Physiol., June 1, 2000; 525(2): 285 - 298. [Abstract] [Full Text] [PDF]
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H. Yu, J. Gao, H. Wang, R. Wymore, S. Steinberg, D. McKinnon, M. R. Rosen, and I. S. Cohen Effects of the Renin-Angiotensin System on the Current Ito in Epicardial and Endocardial Ventricular Myocytes From the Canine Heart Circ. Res., May 26, 2000; 86(10): 1062 - 1068. [Abstract] [Full Text] [PDF]
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A. D. Wickenden, R. Kaprielian, X.-M. You, and P. H. Backx The thyroid hormone analog DITPA restores Ito in rats after myocardial infarction Am J Physiol Heart Circ Physiol, April 1, 2000; 278(4): H1105 - H1116. [Abstract] [Full Text] [PDF]
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T. Stankovicova, M. Szilard, I De Scheerder, and K. R Sipido M cells and transmural heterogeneity of action potential configuration in myocytes from the left ventricular wall of the pig heart Cardiovasc Res, March 1, 2000; 45(4): 952 - 960. [Abstract] [Full Text] [PDF]
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M.A. McIntosh, S.M. Cobbe, and G.L. Smith Heterogeneous changes in action potential and intracellular Ca2+ in left ventricular myocyte sub-types from rabbits with heart failure Cardiovasc Res, January 14, 2000; 45(2): 397 - 409. [Abstract] [Full Text] [PDF]
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J. R. Hume, D. Duan, M. L. Collier, J. Yamazaki, and B. Horowitz Anion Transport in Heart Physiol Rev, January 1, 2000; 80(1): 31 - 81. [Abstract] [Full Text] [PDF]
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W. Guo, H. Xu, B. London, and J. M Nerbonne Molecular basis of transient outward K+ current diversity in mouse ventricular myocytes J. Physiol., December 15, 1999; 521(3): 587 - 599. [Abstract] [Full Text] [PDF]
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R. Dumaine, J. A. Towbin, P. Brugada, M. Vatta, D. V. Nesterenko, V. V. Nesterenko, J. Brugada, R. Brugada, and C. Antzelevitch Ionic Mechanisms Responsible for the Electrocardiographic Phenotype of the Brugada Syndrome Are Temperature Dependent Circ. Res., October 29, 1999; 85(9): 803 - 809. [Abstract] [Full Text] [PDF]
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K. R. Wong, A. E. O. Trezise, S. Bryant, G. Hart, and J. I. Vandenberg Molecular and functional distributions of chloride conductances in rabbit ventricle Am J Physiol Heart Circ Physiol, October 1, 1999; 277(4): H1403 - H1409. [Abstract] [Full Text] [PDF]
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J.-A. Yao, M. Jiang, J.-S. Fan, Y.-Y. Zhou, and G.-N. Tseng Heterogeneous changes in K currents in rat ventricles three days after myocardial infarction Cardiovasc Res, October 1, 1999; 44(1): 132 - 145. [Abstract] [Full Text] [PDF]
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Y. A. Kuryshev, G. M. Brittenham, H. Fujioka, P. Kannan, C.-C. Shieh, S. A. Cohen, and A. M. Brown Decreased Sodium and Increased Transient Outward Potassium Currents in Iron-Loaded Cardiac Myocytes : Implications for the Arrhythmogenesis of Human Siderotic Heart Disease Circulation, August 10, 1999; 100(6): 675 - 683. [Abstract] [Full Text] [PDF]
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P. Schaffer, B. Pelzmann, E. Bernhart, P. Lang, H. Machler, B. Rigler, and B. Koidl Repolarizing currents in ventricular myocytes from young patients with tetralogy of Fallot Cardiovasc Res, August 1, 1999; 43(2): 332 - 343. [Abstract] [Full Text] [PDF]
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E. Carmeliet Cardiac Ionic Currents and Acute Ischemia: From Channels to Arrhythmias Physiol Rev, July 1, 1999; 79(3): 917 - 1017. [Abstract] [Full Text] [PDF]
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A. C.G. van Ginneken and M. W. Veldkamp Implications of inhomogeneous distribution of IKS and IKr channels in ventricle with respect to effects of class III agents and beta-agonists Cardiovasc Res, July 1, 1999; 43(1): 20 - 22. [Full Text] [PDF]
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J. Cheng, K. Kamiya, W. Liu, Y. Tsuji, J. Toyama, and I. Kodama Heterogeneous distribution of the two components of delayed rectifier K+ current: a potential mechanism of the proarrhythmic effects of methanesulfonanilideclass III agents Cardiovasc Res, July 1, 1999; 43(1): 135 - 147. [Abstract] [Full Text] [PDF]
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J van der Velden, L.J Klein, M van der Bijl, M.A.J.M Huybregts, W Stooker, J Witkop, L Eijsman, C.A Visser, F.C Visser, and G.J.M Stienen Isometric tension development and its calcium sensitivity in skinned myocyte-sized preparations from different regions of the human heart Cardiovasc Res, June 1, 1999; 42(3): 706 - 719. [Abstract] [Full Text] [PDF]
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A. D. Wickenden, T. J. Jegla, R. Kaprielian, and P. H. Backx Regional contributions of Kv1.4, Kv4.2, and Kv4.3 to transient outward K+ current in rat ventricle Am J Physiol Heart Circ Physiol, May 1, 1999; 276(5): H1599 - H1607. [Abstract] [Full Text] [PDF]
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G. F. Tomaselli and E. Marban Electrophysiological remodeling in hypertrophy and heart failure Cardiovasc Res, May 1, 1999; 42(2): 270 - 283. [Full Text] [PDF]
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D. M. Roden and S. Kupershmidt From genes to channels: normal mechanisms Cardiovasc Res, May 1, 1999; 42(2): 318 - 326. [Abstract] [Full Text] [PDF]
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D. J Snyders Structure and function of cardiac potassium channels Cardiovasc Res, May 1, 1999; 42(2): 377 - 390. [Abstract] [Full Text] [PDF]
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S. M Bryant, S.J. Shipsey, and G. Hart Normal regional distribution of membrane current density in rat left ventricle is altered in catecholamine-induced hypertrophy Cardiovasc Res, May 1, 1999; 42(2): 391 - 401. [Abstract] [Full Text] [PDF]
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F. Aimond, J. L Alvarez, J.-M. Rauzier, P. Lorente, and G. Vassort Ionic basis of ventricular arrhythmias in remodeled rat heart during long-term myocardial infarction Cardiovasc Res, May 1, 1999; 42(2): 402 - 415. [Abstract] [Full Text] [PDF]
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U. C. Hoppe, D. C. Johns, E. Marban, and B. O'Rourke Manipulation of Cellular Excitability by Cell Fusion : Effects of Rapid Introduction of Transient Outward K+ Current on the Guinea Pig Action Potential Circ. Res., April 30, 1999; 84(8): 964 - 972. [Abstract] [Full Text] [PDF]
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R. L. Winslow, J. Rice, S. Jafri, E. Marban, and B. O'Rourke Mechanisms of Altered Excitation-Contraction Coupling in Canine Tachycardia-Induced Heart Failure, II : Model Studies Circ. Res., March 19, 1999; 84(5): 571 - 586. [Abstract] [Full Text] [PDF]
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S. M. Bryant, X. Wan, S.J. Shipsey, and G. Hart Regional differences in the delayed rectifier current (IKr and IKs) contribute to the differences in action potential duration in basal left ventricular myocytes in guinea-pig Cardiovasc Res, November 1, 1998; 40(2): 322 - 331. [Abstract] [Full Text] [PDF]
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L. Priebe and D. J. Beuckelmann Simulation Study of Cellular Electric Properties in Heart Failure Circ. Res., June 15, 1998; 82(11): 1206 - 1223. [Abstract] [Full Text] [PDF]
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