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1 Department of Medicine and 2 Department of Surgery, Montreal Heart Institute and University of Montreal, Montreal, Quebec, Canada H1T 1C8
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ABSTRACT |
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Limited information is available about transmural heterogeneity in cardiac electrophysiology in man. The present study was designed to evaluate heterogeneity of cardiac action potential (AP), transient outward K+ current (Ito1) and inwardly rectifying K+ current (IK1) in human right ventricle. AP and membrane currents were recorded using whole cell current- and voltage-clamp techniques in myocytes isolated from subepicardial, midmyocardial, and subendocardial layers of the right ventricle of explanted failing human hearts. AP morphology differed among the regional cell types. AP duration (APD) at 0.5-2 Hz was longer in midmyocardial cells (M cells) than in subepicardial and subendocardial cells. At room temperature, observed Ito1, on step to +60 mV, was significantly greater in subepicardial (6.9 ± 0.8 pA/pF) and M cells (6.0 ± 1.1 pA/pF) than in subendocardial cells (2.2 ± 0.7 pA/pF, P < 0.01). Slower recovery of Ito1 was observed in subendocardial cells. The half-inactivation voltage of Ito1 was more negative in subendocardial cells than in M and subepicardial cells. At 36°C, the density of Ito1 increased, the time-dependent inactivation and reactivation accelerated, and the frequency-dependent reduction attenuated in all regional cell types. No significant difference was observed in IK1 density among the regional cell types. The results indicate that M cells in humans, as in canines, show the greatest APD and that a gradient of Ito1 density is present in the transmural ventricular wall. Therefore, the human right ventricle shows significant transmural heterogeneity in AP morphology and Ito1 properties.
electrophysiology; ionic channels
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INTRODUCTION |
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TRANSMURAL HETEROGENEITY in cardiac electrophysiology has been demonstrated in several species (5, 8, 13, 15, 35) and is considered to be an important factor for understanding electrical properties of hearts and arrhythmic mechanisms (3, 4). Transmural electrical differences were first demonstrated by the recording of transmembrane action potentials in ventricular tissues (3, 5, 15, 28). The studies (4, 5, 38) have provided the evidence for three functionally different cell types in the canine ventricular wall with a distinct electrophysiological profile. These cell types include endocardial cells, epicardial cells, and a subpopulation of midmyocardial layer cells (M cells) in the deep subepicardial layer. The M cells have action potential durations (APD) longer than and electrophysiological features intermediate between those of myocardial and conducting cells (4, 5, 38), with pharmacological responsiveness different from that of either epicardial or endocardial cells (9, 10, 29, 33). The differences in action potential characteristics are mainly due to different intrinsic electrophysiological properties (9, 10, 29, 33, 38). It has been shown that a 4-aminopyridine-sensitive transient outward K+ current (Ito1) contributes to the difference in early phase of the action potential in the ventricular wall (5, 28, 31), whereas the lower density in the slow component of delayed rectifier K+ current (IKs) has been thought to be related to longer APD in M cells (17, 30).
The differences in action potential morphology and Ito1 were described in subepicardial and subendocardial cells isolated from the left ventricle of human hearts (6, 34, 41). M cells were not studied with regard to properties of the action potential and Ito1 in these reports. Drouin et al. (10) reported that heterogeneity in the action potential and M cells were present in the human left ventricle, and the M cell shows features similar to those in the canine ventricle, namely longer APD and greater maximal rate of the increase in action potential upstroke (10). However, whether transmural heterogeneity in the action potential and Ito1 properties is present in the human right ventricle is unknown.
The purposes of the present study were to evaluate 1) transmural heterogeneity in action potentials, Ito1, and inwardly rectifying K+ current (IK1), and 2) temperature dependence of Ito1 in density and kinetics in right ventricular myocytes isolated from subepicardial, midmyocardial, and subendocardial layers of explanted human hearts.
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MATERIALS AND METHODS |
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Myocyte preparation. Right ventricular tissues from explanted hearts were obtained at the time of heart transplantation in patients. The ventricular cells were isolated using a procedure described previously (26). Briefly, all hearts were initially placed in cold (4°C) oxygenated Krebs solution and then transferred to cardioplegic solution for dissection and coronary artery cannulation. A portion of the free transmural wall of the right ventricle (~20 × 40 mm) was removed along with the coronary artery branch irrigating it, with dissection and arterial cannulation completed within 30 min of excision of the heart. The free wall was perfused with oxygenated, nominally Ca2+-free Tyrode solution for 20-30 min, and the solution was then changed to one containing 200-300 U/ml collagenase (CLS II, Worthington Biochemical, Freehold, NJ) for 60-100 min. Regional myocytes were separated from the digested tissue. Subendocardial and subepicardial cells were taken from the endocardial and epicardial surfaces (<1 mm thick), whereas M cells were dissociated from the midmyocardial layer. The cells were placed in a high-K+ storage solution (see Solutions) and gently triturated with a Pasteur pipette. Isolated myocytes were kept in the medium at least 1 h (at room temperature) before use.
Cells used in the present study were from seven hearts. The underlying heart disease was congestive cardiomyopathy in five cases and heart failure due to aortic valve disease in two cases. Subsequent examination of the right ventricle by a cardiac pathologist revealed it to be microscopically normal in four cases, to show minor extramyocardial abnormalities consisting of fatty infiltration in one case and subendocardial fibrosis in another, and to show cellular hypertrophy in the final case. A small aliquot of the solution containing the isolated cells was placed in an open perfusion chamber (1 ml) mounted on the stage of an inverted microscope. Myocytes were allowed to adhere to the bottom of the dish for 5-10 min and were then superfused at 2-3 ml/min with Tyrode solution. Only quiescent, rod-shaped cells showing clear cross-striations were used.Solutions.
The Tyrode solution contained (in mmol/l) 136 NaCl, 5.4 KCl, 1 MgCl2, 2 CaCl2, 0.33 NaH2PO4,
10 glucose, and 10 HEPES, with pH adjusted to 7.4 with NaOH. The
high-K+ storage medium contained
(in mmol/l) 20 KCl, 10 KH2PO4,
10 glucose, 70 K-glutamate, 10
-hydroxybutyric acid, 10 taurine, 5 EGTA, and 10 mannitol as well as 0.1% albumin, with pH adjusted to 7.2 with KOH. The pipette solution contained (in mmol/l) 20 KCl, 110 K-aspartate, 1 MgCl2, 10 HEPES, 5 EGTA (0.05 for the recording of action potentials), 0.1 GTP, 5 Na2-phosphocreatine, and 5 Mg2-ATP, with pH adjusted to 7.2 with KOH. For
Ito1
determination, BaCl2 (0.5 mmol/l)
was used to inhibit
IK1, and
CdCl2 (0.2 mmol/l) was used to
block Ca2+ current
(ICa).
Ca2+-dependent transient outward
Cl
current
(ICl,Ca or
Ito2) was
inhibited by 5 mmol/l EGTA in the pipette solution and by the addition
of Cd2+ to the external solution.
The experiments were conducted at 36°C and/or room
temperature (specified).
Data acquisition and analysis.
The whole cell patch-clamp technique was used. Borosilicate glass
electrodes (1.0-mm OD) were pulled with a Brown-Flaming puller (model
P-87) and had tip resistances of 2-3 M
when filled with pipette
solution. The tip potentials were compensated before the pipette
touched the cell. A gigaseal (>10 G
) was obtained, and the cell
membrane was ruptured by gentle suction to establish the whole cell
configuration. Data were acquired with the use of an Axopatch 200A
and/or 200B amplifier (Axon Instruments, Foster City, CA).
Command pulses were generated by a 12-bit digital-to-analog converter
controlled by pCLAMP software (Axon Instruments). Recordings of the
action potential and the current were low-pass filtered at 2 kHz and
stored on the hard disk of an IBM-compatible computer.
60 mV (in the presence of 0.5 mmol/l BaCl2)
divided by 5 mV. The series resistance (Rs) was
electrically compensated to minimize the duration of the capacitive
transient. Rs
along the clamp circuit was estimated by dividing the time constant
obtained by fitting the decay of the capacitive transient by the cell
membrane capacitance. Before Rs compensation,
decay of the capacitance was expressed by a single exponential with a
time constant of 1,107 ± 108 µs and an
Rs of 6.7 ± 0.5 M
. After compensation, the values were reduced to 336 ± 23 µs and 2.1 ± 0.3 M
, respectively.
Action potentials were recorded in current-clamp mode. Recorded resting
potentials were corrected for liquid junction potentials. To calculate
the junction potential, pipettes filled with solution were immersed
into a solution identical to the pipette solution and subsequently
immersed into the bath solution used for action potential recording.
The potential difference recorded was the junction potential of the
pipette. The average junction potential (10.5 ± 0.3 mV) of 14 pipettes was subtracted from the resting membrane potential.
The temperature coefficient
(Q10) (20) for
Ito1 density was
calculated by using the equation
Q10 = 1 + 10(A2
A1)/[A1 (T2
T1)], where
A1 and
A2 are
Ito1 density at
different temperatures T1 and
T2, whereas
Q10 for
Ito1 inactivation
and reactivation time constants was calculated with the equation
Q10 = exp
{[10/(T2
T1)] ln
(
1/
2)},
where
1 and
2 are the time constants
obtained at T1 and
T2, respectively.
Nonlinear curve-fitting programs [Clampfit in pCLAMP 6 (Axon
Instruments) or SigmaPlot (Jandel Scientific, Rafael, CA)] was used to perform curve-fitting procedures. Results are presented as
means ± SE. Paired and unpaired Student's
t-tests were used as appropriate to
evaluate the statistical significance of differences between two group
means, and ANOVA was used for multiple groups. Values of
P < 0.05 were considered to indicate
statistical significance.
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RESULTS |
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Cell capacitance. The average membrane capacitance of human right ventricular myocytes was 162 ± 12 pF in subepicardial cells (n = 41), 167 ± 16 pF in midmyocardial cells (n = 58), and 158 ± 14 pF in subendocardial cells (n = 57). No significant difference was observed in membrane capacitance among the regional cell types. The currents described below as the current density (pA/pF) were obtained relative to individual cell capacitance for control of variation in cell size.
Transmural heterogeneity in action potentials.
Action potentials were determined with a train of 15 depolarization
current pulses (2-ms duration) with frequencies of 0.5, 1, and 2 Hz
(60-s interval between trains) in current-clamp mode. Figure
1 shows typical action potentials recorded
from subepicardial, midmyocardial, and subendocardial cells at the 15th
pulse. The subepicardial cells exhibited a large phase 1 spike,
followed by a notch of the action potential similar to that previously reported in canine ventricles and that is considered to be related to
the inactivation of
Ito1 (4, 5, 31).
The midmyocardial cells displayed longer APD (426 ± 29 ms, at 1 Hz)
than subepicardial (298 ± 17 ms) and subendocardial cells (281 ± 27 ms) and a large phase 1 magnitude, but not a notch of the
action potential. Subendocardial cells did not show an apparent phase 1 spike or a notch of the action potential. No significant difference was
observed in the resting potential among the regional cell types:
82 ± 2 mV for subepicardial cells
(n = 21);
83 ± 3 mV for
midmyocardial cells (n = 31); and
81 ± 3 mV for subendocardial cells (n = 20).
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Inwardly rectifying
K+ current.
The transmembrane current was determined using 300-ms steps from a
holding potential of
40 mV to between
120 and
20
mV in increments of 10 mV (Fig.
3B,
inset) every 2 s. Figure 3,
A and
B, displays representative recordings
from a subepicardial cell in the absence and presence of 0.5 mmol/l
Ba2+. The membrane current was
fully suppressed by the addition of Ba2+ to the superfusion solution,
indicating that the current elicited by the voltage protocol shown is
IK1. The peak and
steady-state currents of
IK1 were measured
from zero current to the current peak and steady-state level at the end
of the voltage steps. Figure 3C shows
current-voltage (I-V) relationships
of the average values of
IK1 density
(between
100 and
20 mV). Steady-state
IK1 densities at
90 and
50 mV were
10 ± 1.7 and 1.5 ± 0.3 pA/pF for subepicardial cells (n = 16),
8.3 ± 0.8 and 1.8 ± 0.3 pA/pF for midmyocardial cells (n = 23), and
8.2 ± 0.7 and 1.8 ± 0.4 pA/pF for subendocardial cells
(n = 19). No significant difference in
IK1 density was
observed in inward (at
90 mV) and outward (at
50 mV)
components among the regional cell types
[P = not significant
(NS)].
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Heterogeneity in density of Ito1.
Because temperature may significantly affect the amplitude and kinetics
of membrane currents (1, 20, 27),
Ito1 was determined at room temperature and at 36°C with a 30-ms step to
40 mV, followed by 300-ms depolarizing steps between
30
and +60 mV in increments of 10 mV every 10 s from a holding potential of
80 mV (Fig.
4C,
inset). To directly analyze the
effect of temperature, we studied
Ito1 at room
temperature (23°C) and then repeated the measurements at 36°C
in the same cells to determine the temperature dependence of changes in
Ito1 amplitude
and kinetics in all regional cell types.
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Voltage-dependent inactivation and activation of
Ito1.
The voltage dependence of
Ito1 inactivation
was determined at room temperature and 36°C with 1,000-ms
conditioning potentials between
90 and +30 mV in increments of
10 mV every 10 s, and then
Ito1 was recorded
during a 300-ms test pulse to +50 mV. Figure 5A shows
the protocol and representative recordings (at room temperature) used
to assess Ito1
inactivation. The inactivation variable (denoted as
B
, see Ref.
36) was determined by normalizing
Ito1 at a given
prepulse potential with the maximum
Ito1 at
90
mV prepulse. Figure 5B shows the
results obtained from the analyses of voltage-dependent inactivation of
Ito1 in
subepicardial, midmyocardial, and subendocardial cells at room
temperature. Mean values are represented by the symbols, and the curves
are best-fit Boltzmann functions. As Table
1 shows, the half-inactivation voltage
(V0.5) was more
negative in subendocardial cells than in subepicardial and
midmyocardial cells (P < 0.05), and
the average slope factor was similar among the regional cell types.
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21.2 ± 1.1,
25.1 ± 1.3, and
32.9 ± 1.5 mV, and the average slope factor was 7.3 ± 0.4, 7.4 ± 0.5, and
8.0 ± 0.5 mV, in subepicardial, midmyocardial, and subendocardial
cells, respectively (P = NS vs.
results at room temperature).
The voltage dependence of
Ito1 activation
was determined by calculating an activation variable (denoted as
A
, see Ref. 36) with data from Fig. 4, c (measured
reversal potential about
68 mV, data not shown). The results are
displayed in Fig. 5B. Normalized mean
data at room temperature are represented by the symbols, and the curves
are Boltzmann fits. No difference in
V0.5 and slope
factor was observed among regional cell types (Table 1). The
V0.5 and slope
factor for Ito1
activation were not changed by increasing bath temperature, and similar
values were obtained at 36°C.
Time-dependent inactivation of Ito1. The time dependence of Ito1 inactivation was studied with 300-ms depolarizing pulses in regional cell types at both room temperature and 36°C. The time-dependent inactivation of Ito1 was reported to be a single exponential in human ventricular myocytes (21, 34, 41). However, we found that Ito1 tracings from +30 to +60 mV were not well fitted by a monoexponential equation in most of the cells studied at room temperature, and at 36°C, Ito1 tracings were only best fitted by a biexponential equation. Therefore, we applied the biexponential equation to fit Ito1 tracings to evaluate the temperature-dependent inactivation of Ito1.
Figure 6A shows typical recordings obtained from a midmyocardial cell during a 300-ms voltage step to +40 mV. The raw data were best fitted by a biexponential function with the time constants
1 and
2: 16.5 and 57.2 ms at room
temperature, and 8.1 and 32.5 ms at 36°C. The time-dependent
inactivation of
Ito1 was faster at 36°C than at room temperature, and
Q10 was 1.72 for
1 and 1.54 for
2 in this cell. Figure
6B displays the average values of
Ito1 inactivation
time constants at room temperature and 36°C in the regional cell
types. No significant regional and voltage-dependent differences were
observed in time constants of
Ito1
inactivation. However, both
1
and
2 were much smaller at
36°C (P < 0.01), indicating that
the time-dependent inactivation of
Ito1 is
substantially accelerated by the increase of bath temperature.
Inactivation time constants of
Ito1 at +60 mV
and their Q10 values are shown in
Table 2.
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80 mV were delivered every 10 s, with varying
P1-P2
intervals. The current during P2
relative to the current during P1
was determined as a function of the
P1-P2
reactivation interval. Curves in Fig. 7B show nonlinear curve fits to
averaged data in subepicardial, midmyocardial, and subendocardial cells
at room temperature and 36°C.
Ito1 was not
completely recovered during the interval observed. Curves at both room
temperature and 36°C were well fitted by a biexponential function.
As Table 3 shows, the reactivation time constants
1 and
2 of
Ito1 were larger
in subendocardial cells than in subepicardial and midmyocardial cells
(P < 0.01), indicating slower recovery of
Ito1 from
inactivation. At 36°C,
1
and
2 were smaller in all
regional cells (P < 0.01). The
results indicate that an increase in bath temperature accelerates
Ito1
reactivation. Q10 values for
1 and
2 were similar in
subendocardial, midmyocardial, and subepicardial cells
(P = NS among the regional cell
types).
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Frequency-dependent reduction of Ito1. Because Ito1 reactivation showed significant time dependence, frequency-dependent reduction of Ito1 might be expected at physiologically relevant frequencies. Changes are shown in Ito1 with repeated pulsing at 0.1, 0.5, 1, 2, and 3 Hz by a 15-pulse train (60-s interval between trains) (Fig. 8B, inset) at room temperature and 36°C in the same regional cells (Fig. 8, A and B, respectively). Steady-state current (at 15th pulse) was normalized to values at 1st pulse at each frequency. Compared with that at 0.1 Hz, significant Ito1 frequency-dependent reduction was observed at room temperature from 0.5 to 3 Hz in subendocardial (n = 7) cells and from 1 to 3 Hz in midmyocardial (n = 7) and subepicardial (n = 8) cells. Ito1 significantly decreased at 1 Hz to 80 ± 8, 90 ± 2, and 96 ± 2% in subendocardial, midmyocardial, and subepicardial cells, respectively (P < 0.05 or P < 0.01). The frequency-dependent reduction of Ito1 was greatly attenuated by the increase of bath temperature (to 36°C; Fig. 8B, P < 0.05 or P < 0.01 vs. results at room temperature), and Ito1 reduced at 1 Hz to only 90 ± 10, 99 ± 1, and 99.5 ± 1% in subendocardial (P < 0.01), midmyocardial (P = NS), and subepicardial cells (P = NS), respectively.
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DISCUSSION |
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In the present study, we demonstrated that 1) transmural heterogeneity of the action potential morphology exists in the human right ventricle, 2) a gradient of Ito1 density and differences in Ito1 kinetics are present in cells isolated from the transmural right ventricular wall, and 3) the density and time-dependent kinetics of Ito1 are significantly altered by increasing the bath temperature from room temperature to 36°C.
Comparison with previously published studies of action potential morphology and Ito1 in human ventricular cells. Two groups have previously described the differences of action potential shape (34) and/or Ito1 (6, 34, 41) in human ventricular subepicardial and subendocardial cells. Our study differs from these in that we characterized the action potential and Ito1 in cells from three regional zones, the subendocardium, midmyocardium, and subepicardium of the human right ventricle. We provided evidence that heterogeneity in action potential morphology and a gradient of Ito1 were present in myocytes isolated from the right ventricle of explanted human hearts. M cells in the human right ventricle showed longer APD. Drouin et al. (10) have recently reported evidence for the presence of M cells in human left ventricles. The M cell in the human left ventricle showed characteristics similar to those in canine ventricles (4, 5, 38), namely longer APD and greater maximal rate of rise of upstroke of the action potential. However, a notch of the action potential was not clear in the M cell of the human left ventricle (10), which is consistent with our observations in the right ventricle. We and Drouin et al. (10) found that APD is still longer in M cells than in epicardial and endocardial cells at physiological heart rates. We did not find a significant difference in IK1 among the three regional cell types.
In most of the studies on Ito1 in human ventricles, experiments have been conducted at room temperature. We (27) and others (1, 20) have found that the density and kinetics of membrane currents are dependent on bath temperature. Therefore, we determined temperature dependence of Ito1 density and kinetics and then evaluated Q10. By increasing the bath temperature to 36°C, the density of Ito1 was increased. The time-dependent inactivation and reactivation were substantially accelerated, and the frequency-dependent inactivation was attenuated in all regional cell types. However, the voltage-dependent inactivation and activation of Ito1 were not affected by the change of bath temperature. Information about Q10 values for Ito1 is not available to compare with the present study. Q10 values (1.3-1.37) for Ito1 amplitude were smaller than those of other currents (ICa, IK1, and IK, see Refs. 1, 20). The densities (at +60 mV) of Ito1 in the present study were 2.2 ± 0.7, 6.0 ± 1.1, and 6.9 ± 0.8 pA/pF in subendocardial, midmyocardial, and subepicardial cells, respectively, at room temperature. The data from our observation in subepicardial and subendocardial cells are close to those reported by Wettwer et al. (41). They reported that the densities of Ito1 were 2.3 ± 0.3 pA/pF (at +60 mV) for subendocardial cells and 7.9 ± 0.7 pA/pF for subepicardial cells in human normal left ventricles. However, a higher density of Ito1 in subepicardial cells was reported by Näbauer et al. (34) that is probably due to different experimental conditions and/or tissue types. Our observation is consistent with previous reports (34, 41) that Ito1 recovery is slower in subendocardial cells than in subepicardial cells.Significance of our studies for electrophysiology of human heart. The present study provides evidence that the heterogeneity of the action potential and Ito1 exists in the transmural wall of the human right ventricle. The action potential morphology in M cells is similar to that recorded by Drouin et al. (10) in the human left ventricular tissue. Similarly, M cells have been reported in the subendocardium in the anterior wall and septum and in the deep subepicardium in the posterolateral walls of canine hearts (4, 5, 39), which has been considered to be related to the generation of the electrocardiogram U wave (4). The findings from the present study further support the hypothesis that M cells contribute importantly to the manifestation of the U wave or highly bifurcated T waves on the clinical electrocardiogram (4, 10, 23).
The present study has demonstrated that the phase 1 variation of the action potential is associated with the gradient of Ito1 in cells from the transmural ventricular wall. Ito1 shows less frequency-dependent reduction at 36°C. The property is similar to that of Ito1 in human atrial myocytes (2, 14), suggesting that Ito1 plays an important role in action potential repolarization of the human myocardium at normal heart rates. It has been shown that Ito1 plays an important role in the mammalian myocardium (5, 7, 8, 15, 16, 28, 41). Liu et al. (31) have recently demonstrated that the distinguished electrical behavior and pharmacological responses are related to the transmural heterogeneity of Ito1 in the canine ventricle. The greater density of Ito1 was found to contribute to the high sensitivity of epicardial myocardium to electrical depression during ischemia (33). Several antiarrhythmic agents (11, 19, 22) and Ca2+ antagonists (18, 24) have been reported to block Ito1. It has been reported that Ito1 might be modulated by adrenergic stimulation (12), atrionatriuretic factor (25), metabolic inhibitor, and oxidant stress (35). Also, the density of Ito1 might be altered by pathological conditions, including cardiac hypertrophy (40) or failure (32) and hyperthyroidism (37). All of the above would have immediate clinical implications, because the gradient of Ito1 is present in the transmural ventricular wall of human hearts.Potential limitations. We studied right ventricular cells from patients with severe left ventricular failure. Although the cells used in the present study were from right ventricles that were assessed by expert pathological microscopic examination to have relatively mild or no changes, and the characteristics of action potentials of our cells were similar to those previously reported by Drouin et al. (10) in the normal human left ventricular tissue, we cannot exclude the possibility that our results were influenced by a relatively mild change in cardiac tissue, such as fatty infiltration, subendocardial fibrosis, or cellular hypertrophy.
In conclusion, this study demonstrates that M cells are present in the right ventricle in humans and that a gradient of Ito1 exists in cells across the human right ventricular wall from the endocardium to the epicardium. Ito1 in subendocardial cells is smaller, inactivates more negatively, and recovers more slowly than in midmyocardial and subepicardial cells. Therefore, the human heart shows significant transmural heterogeneity in the action potential and Ito1 properties, which points to an important clinical relevance in human cardiac electrophysiology.| |
ACKNOWLEDGEMENTS |
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We thank Dr. Alvin Shrier for review, constructive suggestions, and discussion concerning the manuscript; Dr. Tack Ki Leung for expert pathological examination of explanted human hearts; and Haiying Sun for data analysis and technical support.
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FOOTNOTES |
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The study was supported by the Quebec Heart Foundation and Fonds de la Recherche en Santé du Québec (FRSQ). G.-R. Li was a research scholar of FRSQ.
Address for reprint requests: G.-R. Li, Research Center, Montreal Heart Institute, 5000 Belanger St. East, Montreal, Quebec, Canada H1T 1C8.
Received 15 December 1997; accepted in final form 20 April 1998.
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