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Articles |
From the Department of Medicine and Research Center, Montreal Heart Institute (R.G., R.F.B., E.B.-A., S.N.); the University of Montreal (S.N.); and the Department of Pharmacology and Therapeutics, McGill University (S.N.), Montreal, Quebec, Canada.
Correspondence to Stanley Nattel, MD, Montreal Heart Institute, 5000 Bélanger St East, Montreal, Quebec, Canada H1T 1C8. E-mail nattel{at}icm.umontreal.ca
| Abstract |
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52% at
-40 mV (P<.0001): from -78.7±4.6 pA/pF (P0, n=28
cells) to -37.7±3.0 pA/pF (P42, n=43 cells).
INa was significantly reduced at all
voltages ranging from -65 to -10 mV. Voltage-dependent activation and
inactivation properties, activation kinetics, and recovery from
inactivation were not altered by rapid atrial pacing; however,
inactivation kinetics were slowed. AF duration was related to mean
INa in each dog
(r2=.573, P<.001). We
conclude that rapid atrial activation significantly reduces both
conduction velocity and INa density. Since
INa is a major determinant of conduction
velocity, our data point to INa reduction as
a potentially important mechanism contributing to the substrate for AF
in this model.
Key Words: atrial fibrillation rapid atrial pacing Na+ current conduction velocity
| Introduction |
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Recently, several chronic animal models of AF that are associated with chronic atrial cardiomyopathy and ultrastructural changes resembling those seen in clinical AF have been developed.810 One of these models uses rapid atrial pacing to cause 1:1 atrial activation at 400/min.10 In addition to producing clinically relevant atrial structural changes, this chronic dog model allows for studies of the relationship between time-dependent electrophysiological and underlying ionic changes during the development of AF. Furthermore, these models are relevant to the way in which sustained AF alters atrial properties to promote its own maintenance, a phenomenon known as "the domestication of AF" or "AF begets AF."9
Wijffels et al9 noted that when AF was maintained
electrically in chronically instrumented goats, the
electrophysiological milieu changed
gradually to allow for spontaneous maintenance of AF. ERP
decreased to attain near-minimal values within 24 hours after the onset
of AF induction, whereas changes in spontaneous AF persistence
developed more slowly, stabilizing after
1 week. Morillo et
al10 reported that chronic rapid atrial pacing (400/min) of
dogs for 6 weeks decreased atrial ERP and allowed for the induction of
sustained AF in >80% of the animals. They also noted P-wave
prolongation after 6 weeks of pacing, but they did not assess
conduction velocity directly or study the time course of
electrophysiological changes. We recently
found that chronic atrial tachycardia causes progressive
decreases in atrial ERP, ERP adaptation to rate, and conduction
velocity.11 The time course of changes in conduction
velocity is somewhat slower than that of ERP alterations, appearing to
account for continuing increases in AF susceptibility after ERP changes
had stabilized.
Little information is available regarding the cellular changes underlying the changes in ERP and conduction velocity caused by chronic atrial tachycardia. In a previous study, we presented evidence for ionic remodeling of ICa as the mechanism underlying ERP changes.12 Phase-0 INa is an important determinant of conduction velocity in fast-channel tissues like the atria,13 but INa changes have not been examined in the atrial tachycardia model of AF.
The present study was designed to assess whether changes in INa density occur and whether they are related to changes in conduction velocity and the ability to maintain AF among dogs subjected to atrial pacing at 400/min for periods of up to 6 weeks. Specifically, we wished to determine (1) whether INa is altered by rapid atrial pacing, (2) whether any changes in current density are associated with and/or due to changes in the voltage-dependent properties and recovery kinetics of INa, (3) whether atrial conduction changes are related to INa alterations, and (4) whether changes in AF duration are related to changes in INa.
| Materials and Methods |
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Twenty-four hours was allowed for the lead to stabilize. The pacemaker was then programmed to stimulate the atrium at 400/min (150-ms cycle length) with the use of 0.42-ms square-wave pulses at twice-threshold current. The atrium was continuously stimulated at 400/min for a pacing period of 7 days (P7, n=6) or 42 days (P42, n=5) days. The surface ECG was verified after 24 hours and then weekly to ensure continuous 1:1 atrial capture. Dogs subjected to rapid atrial pacing were compared with sham-operated dogs that were similarly instrumented but maintained without pacemaker activation for periods ranging from 7 to 42 days (P0, n=6). We have previously noted that the properties of sham-operated dogs are stable over a range of observation periods from 1 to 42 days.
Electrophysiological Study
On study days, dogs were reanesthetized with morphine (2
mg/kg SC) and
-chloralose (120 mg/kg IV bolus,
followed by a continuous infusion of 29.25 mg ·
kg-1 h-1) and ventilated with room air
supplemented with oxygen. Respiratory parameters were
adjusted to maintain physiological
arterial blood gases (SaO2 >90%;
pH 7.38 to 7.44). Body temperature was maintained at 37°C with a
circulating-water temperature control system. Polyethylene catheters
were inserted into the left femoral artery and both femoral veins and
kept patent with heparinized saline solution (0.9%). The left femoral
artery catheter was used to measure arterial blood
pressure. The right and left femoral vein catheters were used to infuse
saline and
-chloralose, respectively. A median sternotomy was
performed, and a pericardial cradle was created. Two bipolar
polytetrafluoroethylene-coated
stainless-steel electrodes were inserted into the right atrial
appendage for recording and stimulation. A programmable
stimulator (Digital Cardiovascular Instruments) was
used to deliver 2-ms pulses at twice-threshold current. A P23 1D
transducer (Statham Medical Instruments),
electrophysiological amplifiers (Bloom
Ltd), and a paper recorder (Astromed Model MT-95000) were used to
record arterial blood pressure, six standard surface
ECG leads, a right atrial electrogram, and stimulus artifacts.
Activation Mapping
In order to obtain conduction velocity measurements, one thin
silicone sheet containing 40 bipolar electrodes with 1-mm interpolar
and 6-mm interelectrode distances was sewn into position on the right
atrial epicardial surface, covering the posterior aspect of the atrial
appendage and the free wall. Each signal was filtered (30 to 400 Hz),
digitized with 12-bit resolution and a 1-kHz sampling rate, and
transmitted into a microcomputer (model 286, Compaq Computer). Software
routines were used to amplify, display, and analyze each
electrogram signal as well as to generate activation
maps.14 Each electrogram was analyzed with
computer-determined peak-amplitude criteria and was reviewed manually.
The accuracy of activation time measurements was ±0.5 ms.
Determination of AF Duration and Conduction Velocity
In paced dogs, a surface ECG was first recorded to confirm
maintenance of 1:1 atrial pacing at 400/min. The pacemaker was
then deactivated. In all groups, activation maps for conduction
velocity measurements were obtained after 2 minutes of continuous
pacing applied at the right atrial appendage at a short basic cycle
length (150 ms), close to the cycle length of AF.
After data for conduction velocity measurements were obtained at all cycle lengths, AF was induced with a train of 10-Hz stimuli delivered to the right atrial appendage at four times threshold current and 2-ms duration. AF was defined as a rapid (>450/min) irregular atrial rhythm with varying atrial electrogram morphology. AF was considered sustained if it persisted for >45 minutes and was distinguished from atrial flutter on the basis of the irregularity of atrial electrogram morphology and frequency. In order to estimate the mean duration of AF, AF was induced 10 times if AF duration was <10 minutes. Two AF inductions were performed if episodes lasted between 10 and 45 minutes. If AF lasted for >45 minutes and no briefer episodes occurred, mean AF duration was based on this episode, and no further AF induction was attempted in order to avoid excessive prolongation of the experiment. Episodes of AF lasting >45 minutes were terminated by DC electrical cardioversion delivered with epicardial paddle electrodes. When electrical cardioversion was performed, a 30-minute rest period was allowed before continuing with the experimental protocol.
AF inducibility was assessed by noting the ability of single premature S2 stimuli at a 400-ms basic cycle length to induce the arrhythmia. AF was considered to be inducible in a given dog if AF was induced reproducibly by the S2 at a given coupling interval.
Activation maps were generated off-line after each experiment, and conduction velocity was determined by analyzing activation times at a series of four electrode sites in the direction of longitudinal propagation in the right atrial free wall. The distance of each site from the first of the series of electrodes was plotted against activation time, and conduction velocity was determined from the slope of the best-fit regression line.11,16 Activation maps were reviewed to ensure continuous longitudinal propagation, and only data with a clear linear relation (correlation coefficient, >.99) were accepted for analysis. The same sites were used for conduction velocity measurements for each experiment.
Cell Isolation and Solutions
At the end of the in vivo experimental protocol, the heart was
excised and immersed in Tyrode's solution containing (mmol/L)
NaCl 136, CaCl2 2, KCl 5.4, MgCl 1.0,
NaH2PO4 0.33, HEPES 5, and glucose 10 at room
temperature (pH adjusted to 7.35 with NaOH). Canine atrial myocytes
were isolated by enzymatic dissociation with the use of previously
described methods.15 All solutions used for dissection and
perfusion were equilibrated with 100% O2. The circumflex
coronary artery was cannulated, and the left atrium was
dissected free and perfused with Tyrode's solution at 37°C for 5
minutes until the atrium was clear of blood. All leaking
arterial branches were ligated with prolene thread to
ensure adequate perfusion. The atrium was then perfused at 12 mL/min
with nominally Ca2+-free Tyrode's solution for 20 minutes.
The solution was changed to one containing 110 U/mL
collagenase (type II, Worthington) and 1% bovine serum
albumin (Sigma Chemical Co). Softened tissue from a
well-perfused region was removed with a forceps, gently triturated, and
kept in a storage solution containing (mmol/L) KCl 20,
KH2PO4 10, dextrose 10, L-glutamic
acid 70, ß-hydroxybutyric acid 10, taurine 10, and EGTA 10, along
with 1% albumin (pH adjusted to 7.35 with KOH).
A small aliquot of the solution containing the isolated cells was placed in a 1-mL open perfusion chamber mounted on the stage of an inverted microscope. After 5 minutes to allow for cell adhesion to the chamber, the cells were perfused at 6 mL/min with a solution containing (mmol/L) NaCl 5, CsCl 132.5, MgCl2 1.0, CaCl2 1.0, HEPES 20, and glucose 11 (pH adjusted to 7.35 with CsOH). To provide optimal control of INa, the bath solution was kept at 17°C with the use of a Peltier effect device. The pipette solution used to record INa contained (mmol/L) NaCl 5, CsF 135, HEPES 5, EGTA 10, and Mg2ATP 5 (pH adjusted to 7.2 with CsOH).
Voltage-Clamp Technique
INa was recorded using the whole-cell
configuration of the voltage clamp technique. Only quiescent rod-shaped
cells showing clear cross striations were used. Small cells were
selected for study to facilitate voltage control. Borosilicate glass
microelectrodes (outer diameter, 1.0 mm) had resistances ranging
from 0.8 to 1.5 M
when filled with pipette solution and were
connected to a patch-clamp amplifier (Axopatch-1D, Axon Instruments).
Data were sampled with an A/D converter (Digidata 1200, Axon
Instruments) and stored on the hard disk of a computer for subsequent
analysis. The sampling frequency was 10 kHz for
INa measurements. Recordings were low
passfiltered at 2 to 5 kHz.
Tip potentials were zeroed before formation of the pipette-membrane
seal. Several minutes after seal formation, the membrane was ruptured
by gentle suction to establish the whole-cell configuration. After
rupture of the cell membrane, pipette Rs was electrically
compensated to minimize the capacitive surge on the current
recording and the voltage drop across the clamped membrane.
Rs was calculated by dividing the capacitive time constant,
obtained by fitting the decay of the capacitive transient, by the
calculated membrane capacitance (the time integral of the capacitive
response to a 5-mV hyperpolarizing pulse from a holding potential of
-60 mV, divided by the voltage drop). Cell capacitance averaged
64.3±2.3 pF in 130 cells. Before compensation, Rs averaged
5.1±0.2 M
, and the capacitive time constant was 306.1±14.7 µs.
The mean Rs and capacitive time constant after compensation
averaged 1.4±0.1 M
and 78.3±2.4 µs, respectively. Care was taken
to ensure that the maximum voltage drop across the Rs in
each cell did not exceed 5 mV, and the mean voltage drop averaged
4.2±0.2 mV in 130 cells. Cells for which the series voltage error
exceeded 5 mV were rejected. Overall, under P0 (sham) conditions, 39%
of the cells (18 of 46 cells) had to be discarded because of voltage
control problems, caused mainly by very large current amplitude. Mean
peak current amplitude, voltage drop, and Rs in cells
rejected from the P0 group because of poor voltage control averaged
7969±741 pA, 9.9±1.2 mV, and 1.3±0.4 M
, respectively. In
contrast, because of a decreased peak current
amplitude, fewer P7 and P42 cells were rejected (7 of 66, or 11% of
the cells, for P7; 2 of 45, or 4% of the cells, for P42). Cells with
significant leak currents were rejected. The small residual leak was
subtracted by a linear leakage compensation algorithm.
Statistical Analysis
Statistical comparisons of multiple group means were obtained by
ANOVA. Nonorthogonal decomposition using Dunnett's test for multiple
comparisons with one control was used to study changes due to different
rapid atrial pacing durations.17 Bartlett's test was used
to analyze the homogeneity of variances between sham-operated
and paced groups.18 The Kruskal-Wallis test was used for
nonparametric data with unpaired measures. Linear
regression was used to analyze the relationship between single
dependent and independent variables, whereas stepwise multilinear
regression was used to assess the dependence of a single dependent
variable on multiple potential contributors to its variance. A
nonlinear least-square curve-fitting program (CLAMPFIT in pCLAMP 6.0 or
Sigma Plot) was used to perform curve-fitting procedures. All average
results are expressed as mean±SEM, and a value of P<.05
was considered statistically significant.
| Results |
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Conduction Velocity Changes Produced by Continuous Rapid
Atrial Pacing
In addition to changes in AF duration and inducibility with
premature beats, rapid atrial stimulation decreased conduction
velocity. The Table
indicates the time-dependent changes in atrial
conduction velocity with atrial tachycardia. Conduction
velocity was somewhat decreased after 7 days of tachycardia
and showed larger, statistically significant decreases at 42 days.
INa Changes Caused by Rapid Atrial
Pacing
In order to avoid any contaminating effects of
time-dependent changes in the INa I-V
relationship, all studies were started 20 minutes after membrane
rupture, with protocols performed in the same sequence in all groups of
cells, beginning with the INa density-voltage
relationship, followed immediately by analysis of
voltage-dependent inactivation and, finally, time-dependent recovery
from inactivation. Typical original current tracings from isolated
canine atrial myocytes obtained from P0, P7, and P42 dogs are shown in
Fig 1A
to 1C. The data were obtained with
a holding potential of -140 mV and a series of 5-mV depolarizing steps
(0.1 Hz) to voltages ranging from -80 to -5 mV. Fig 1D
shows mean
INa density-voltage relations for P0 (n=28
cells), P7 (n=59 cells), and P42 (n=43 cells) cells. Maximum current
was noted at -40 mV, and pacing did not alter the form of the
INa density-voltage relation.
INa density was reduced progressively and highly
significantly by rapid atrial pacing. For example, at -40 mV,
INa density averaged -78.7±4.6 pA/pF in P0
cells compared with -57.0±3.4 pA/pF (P<.0001 versus P0)
in P7 cells and -37.7±3.0 pA/pF (P<.0001 versus P0) in
P42 cells. INa was significantly reduced at
voltages ranging from -65 to -10 mV under P42 conditions. As
indicated by the data in the Table
, changes in
INa occurred in consort with changes in
conduction velocity, AF duration, and AF inducibility.
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To evaluate possible mechanisms involved in the pacing-induced
reduction in INa, we studied the
voltage-dependent properties of the current. Fig 1E
shows the voltage
dependence of INa activation, which was
calculated by dividing peak current during depolarizing test pulses by
the driving force, with an estimated reversal potential of 0 mV as
measured by extrapolating the terminal part of the I-V curve to the
voltage-axis intercept. The data were well-fitted by a Boltzmann
relation, with half-maximum activation voltage averaging -52.0±0.3,
-54.6±0.3, and -50.0±0.2 mV under P0 (n=28 cells), P7 (n=59 cells),
and P42 (n=43 cells) conditions, respectively (P=NS versus
P0). The slope factor averaged 6.0±0.2, 6.3±0.3, and 6.0±0.2 mV for
P0, P7, and P42 cells (P=NS versus P0). These results
indicate that changes in INa density are not
associated with or due to changes in the voltage dependence of
INa activation.
A double-pulse protocol was used to assess the voltage dependence of
INa inactivation, as shown in Fig 2
. A 1-s conditioning pulse to voltages
between -140 and -65 mV was followed by a 30-ms test pulse to -40 mV
(holding potential, -140 mV; frequency, 0.1 Hz). The peak current
elicited by the test pulse was normalized to current without a
prepulse. Panels A to C of Fig 2
display typical original current
recordings from atrial myocytes isolated from P0, P7, and P42
dogs. Fig 2D
shows that voltage-dependent inactivation was complete at
-80 mV under paced and nonpaced conditions. The results were
well-fitted by a Boltzmann relation. Rapid pacing did not alter
INa inactivation, with mean values for
half-maximum activation voltage of -101.7±0.1, -101.7±0.3, and
-101.0±0.2 mV in P0 (n=28 cells), P7 (n=59 cells), and P42 (n=43
cells) cells, respectively (P=NS versus P0). The slope
factor averaged 5.8±0.1, 6.2±0.2, and 5.5±0.2 mV under P0, P7, and
P42 conditions (P=NS versus P0).
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The kinetics of INa activation and inactivation
were analyzed by curve fitting to data obtained with the
protocol shown in Fig 1
, inset. Monoexponential
functions provided good fits to the data (Fig 3A
to 3C). The resulting time constants
shown in Fig 3D
and 3E
were voltage dependent. Although the activation
time course was not altered by rapid pacing, inactivation kinetics
slowed progressively in dogs paced for longer periods of time (n=28,
18, and 15 cells for kinetic analysis in P0, P7, and P42 dogs,
respectively).
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As illustrated in Fig 4
, the recovery
kinetics of INa were evaluated with the use of a
train of 40 pulses from a holding potential of -140 to -40 mV (50-ms
pulse duration, 200-ms interstimulus interval), followed by a 30-ms
test pulse to -40 mV at various recovery intervals. The
INa recovery time course was not altered by
rapid atrial pacing. Recovery was well-fitted by a
monoexponential function, with time constants of
7.2±0.4, 7.6±0.5, and 6.3±0.3 ms in 30, 44, and 29 cells from P0,
P7, and P42 dogs, respectively (P=NS for P7 and P42 versus
P0).
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Relation Between INa, Conduction
Velocity, and AF Duration Changes
One of our goals was to determine whether
INa changes were related to alterations in AF
duration. The logarithm of AF duration correlated with mean
INa in individual dogs
(r2=.573, P=.0004). When conduction
velocity and INa were included as covariates in
a stepwise multilinear regression, the logarithm of AF duration was
best predicted by a model including both INa
(P=.0004) and conduction velocity (P=.025).
| Discussion |
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Conduction Velocity Changes Related to AF
In animal models, rapid atrial activation results in progressive
increases in AF duration, with AF increasingly likely to be sustained
after a week of pacing.10,11 Changes in AF duration are
associated with a reduction in ERP and ERP adaptation to rate, changes
often seen in patients with increased atrial vulnerability and a
tendency to exhibit atrial reentrant arrhythmias.19
Similar results have also been obtained in various animal models using
either rapid atrial pacing10,11 or electrically maintained
AF.9,20
In addition to ERP changes, anomalies of intra-atrial conduction have long been known to be associated with clinical AF and are often indicated by P-wave prolongations during sinus rhythm.21 Increased P-wave durations were observed in rapidly paced dogs by Morillo et al10 and more recently by Elvan et al.22 An increased signal-averaged P-wave duration was detected in hyperthyroid patients with paroxysmal AF, with P-wave changes being a good predictor of the induction of AF in these patients.23 Our previous work suggested a role of conduction slowing in contributing to the maintenance of AF in dogs with maintained rapid atrial activation.11 The present study provides further evidence that chronic atrial tachycardia may itself decrease conduction velocity. Conduction slowing reduces the wavelength for reentry and increases the susceptibility to reentrant atrial arrhythmias.24 Therefore, our findings point to a potential role of atrial conduction slowing due to rapid atrial activation in the perpetuation of atrial arrhythmias.
INa Changes Related to AF
INa plays a major role in the upstroke of
the action potential in atrial myocytes and has been found to be an
important determinant of conduction velocity in cardiac
tissue.13 Consistent with the role of
INa in controlling conduction speed, we found
that changes in conduction velocity accompany
INa alterations. INa is
therefore a candidate to underlie the conduction velocity changes
induced by rapid atrial pacing in the chronic dog model.
The present study provides the first direct evidence, to our knowledge, that chronic rapid atrial pacing decreases not only conduction velocity but also INa density. Several biophysical properties of Na+ channels, including the voltage dependence of activation and inactivation, the time course of activation, and the rate of recovery from inactivation, were not altered in rapidly paced dogs. On the other hand, inactivation development slowed in paced animals. These observations differ somewhat from our findings regarding changes in ICa and Ito density in atrial cells from dogs subjected to rapid atrial pacing, which were not associated with any changes in voltage- or time-dependent current properties.12 Kääb et al25 similarly observed that pacing-induced ventricular failure causes a reduction in Ito density without changing other channel properties.25
One of the possible mechanisms underlying INa alterations in dogs subjected to chronic tachycardia may be related to [Ca2+]i changes. Increases in [Ca2+]i can downregulate Na+ channel expression.26 Evidence of cellular Ca2+ overload has been obtained in histological studies of atria subjected to very rapid atrial activation.27 The authors found mitochondrial swelling consistent with cellular Ca2+ overload and a protective effect of verapamil against electrical remodeling.27 It is possible that in response to a transient rise in Na+ entry during AF due to an increased frequency of depolarization, reverse-mode Na+-Ca2+ exchange may promote Ca2+ entry into myocytes, triggering the release of Ca2+ from the sarcoplasmic reticulum,28 thereby generating Ca2+ overload and leading to INa decrease. The decrease in INa density may thus serve an autoregulatory function by reducing total Na+ entry.
INa is not the only determinant of conduction velocity. Changes in intercellular coupling may also be very important. Observations regarding changes in connexin expression in AF are preliminary and conflicting. One group noted reductions in connexin40 expression and no change in connexin43 in goats with chronic AF,20 whereas other investigators found an increase in connexin43 expression in dogs with AF.29 Further information is needed in order for time-dependent changes caused by rapid atrial activation in determinants of atrial conduction, including INa, connexin expression, and intercellular coupling, to be understood completely.
Potential Clinical Relevance
The present study is the first of which we are aware to
evaluate the changes in INa caused by chronic
rapid atrial activation. Our findings are relevant to mechanisms of
altered atrial conduction and P-wave prolongation in clinical
AF.21,23,30 Changes in INa may
participate in the "domestication of AF" by slowing atrial
conduction, whereas decreases in ICa appear also
to contribute by accelerating atrial repolarization and abbreviating
refractoriness.12 Thus, changes in both refractoriness and
conduction appear to be involved in the promotion of AF
maintenance by continuous atrial
tachycardia.11 There is reason to believe that
decreases in both INa and
ICa may be due to Ca2+ overload.
Preventing Ca2+ overload might thus prevent ionic
remodeling and the domestication of AF. Evidence for such an effect on
a short-term basis has recently been
presented.27,31 These considerations point to the
possibility of intervening to prevent the development of the
substrate of AF in-stead of using the present pharmacological
approaches, which target the
electrophysiological properties of the
substrate.
Limitations of Our Findings
In the present study, conduction velocity was measured in the
right atrial free wall, while cells were isolated from the
inferoposterior left atrial region. It is possible that conduction
velocity measurements obtained from the right atrium are different from
those elsewhere in the atria and cannot be related to changes observed
in INa in cells obtained from other portions of
the atria. However, this is unlikely, since conduction velocity
measured in the right atrial free wall is highly correlated with
overall conduction time and conduction velocity in Bachmann's bundle
under similar experimental settings.11
Voltage control can be a problem when studying INa. Great care was therefore taken to minimize voltage drop across the Rs by using small cells and pipettes with low resistance in order to clamp the membrane effectively. Cells that had a >5-mV voltage drop across the Rs were rejected. A significant number of cells obtained under control conditions (P0) had to be discarded because of excessive current amplitude and associated series voltage errors, whereas this was not the case for cells obtained from paced dogs. Since cells with larger currents tend to have larger voltage drops across the Rs, the rejection of cells with large series voltage errors would tend to result in an underestimation of INa in P0 dogs. If anything, this error would have reduced the difference between control and paced dogs and is therefore unlikely to have contributed to the differences we observed in INa between these groups.
| Selected Abbreviations and Acronyms |
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| Acknowledgments |
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Received March 21, 1997; accepted September 5, 1997.
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