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The Wavelength of the Cardiac Impulse and
Reentrant Arrhythmias in Isolated Rabbit Atrium
The Role of Heart Rate, Autonomic Transmitters, Temperature, and
Potassium
Joep L.R.M. Smeets, Maurits A. Allessie, Wim J.E.P. Lammers, Felix I.M. Bonke, and
Jan Hollen
From the Department of Physiology, Biomedical Center, University of Limburg, Maastricht, The Netherlands
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SUMMARY. We measured the wavelength of the cardiac impulse, defined as the distance traveled
by the depolarization wave during the functional refractory period, in isolated narrow strips of
rabbit atrium. During control, wavelength was 42 mm during pacing with 2 Hz, and was 28 mm
at the maximum pacing rate; early premature beats had a wavelength as short as 23 mm.
Administration of carbamylcholine (4 X 10"7 g/ml) shortened the wavelength to 21 mm during 2
Hz, 18 mm at the maximum pacing rate V^,^ and 16 mm during an early premature impulse,
respectively. The effects of epinephrine (6 X 1CT7 M) were strongly rate dependent. At slow heart
rates, epinephrine clearly prolonged the wavelength (58 mm), whereas, during maximum pacing,
wavelength remained unchanged (28 mm). Hypokalemia (2 ITIM) decreased the length of the
impulse at all stimulation frequencies. Moderate hyperkalemia (5.6 and 7.0 DIM) did not modify
wavelength because refractoriness and conduction velocity were affected proportionally. Above
7.0 ITIM potasssium, the wavelength became progressively prolonged because of the development
of post-repolarization refractoriness. Cooling to 27°C resulted in a slight lengthening of the
impulse. At lower temperatures, however, wavelength prolonged significantly because of a
relatively strong prolongation of the refractory period. In separate experiments in 15 X 20 mm
segments of atrium, reentrant tachyarrhythmias were induced and the circuit size compared with
the wavelength. The size of intraatrial circuits was similar to the magnitude of the measured
wavelength during maximum pacing. Carbamylcholine and hypokalemia, both of which shorten
the impulse length, also clearly decreased the size of reentrant circuits. Cooling to 27°C, which
affects both refractoriness and conduction velocity, only slightly prolonged the wavelength;
accordingly, the size of reentrant circuits at 27°C was only slightly longer than at 37°C. These
experiments emphasize the importance of the wavelength of the cardiac impulse in relation to
the occurrence of inrramyocardial reentry. (Circ Res 58: 96-108, 1986)
IN the last decade it has become increasingly clear
that relatively small reentrant circuits within either
atrial or ventricular myocardium may be important
mechanisms of atrial and ventricular tachyarrhythmias (Allessie et al., 1973, 1976, 1977a, 1977b, 1984,
1985; De Bakker et al., 1979; Boineau et al., 1980;
Janse et al., 1980; Wit et al., 1982; El-Sherif et al.,
1982; Boyden et al., 1983; Okumura et al., 1984).
From these studies it also became clear that the
properties of intramyocardial reentry are different
from circus movement in a fixed anatomic pathway.
Good examples of macro-reentrant loops are circus
movement tachycardia incorporating an accessory
pathway in patients with the WPW syndrome (Wellens, 1978) and some cases of atrial flutter (Lewis et
al., 1920; Rosenblueth and Garcia Ramos, 1947;
Disertori et al., 1983; Frame et al., 1983). The stability of this kind of arrhythmia is determined by
the fact that the anatomical circuit is longer than the
wavelength of the electrical impulse, leaving an
excitable gap between head and tail of the circulating wave (Mines, 1913; Lewis et al., 1925; Rosenblueth and Garcia Ramos, 1947; Waldo et al., 1977;
Wellens, 1978). In contrast, inrramyocardial reentry
without the involvement of a gross anatomic obstacle is determined by the electrophysiclogical and
ultrastructural properties of the myocardium. Because of the absence of a central anatomic obstacle,
the circulating impulse will travel along the shortest
possible circuitous route, resulting in a tight fit between the crest of the depolarization wave and its
own relative refractory tail. The dimension of such
'leading circle' reentry, instead of being anatomically defined, is equal to the wavelength or 'electrical length' of the circulating excitation wave (Allessie et al., 1977a).
The significance of the wavelength for circus
movement in the heart is implicit in the early model
of reentry put forward by Mines in 1913 and has
been explicitly discussed by Lewis (1925). The wave-
Smeets et al. /Wavelength and Reentrant Arrhythmias
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length of the cardiac impulse is defined as the distance traveled by the depolarization wave during
the time the tissue restores its excitability sufficiently
to propagate another impulse (wavelength = conduction velocity X functional refractory period). This
implies that conditions which shorten the refractory
period or depress conduction will result in a shorter
wavelength. Under such conditions, reentrant circuits of smaller dimensions may become possible.
On the other hand, interventions which prolong
refractoriness or improve conduction will prolong
the length of the excitation wave, and only circuits
of larger size can exist.
We consider the wavelength of the cardiac impulse of utmost importance for both the induction
and perpetuation of tachyarrhythmias based on
leading circle reentry. Prerequisites for the initiation
of circus movement are: (1) the creation of an arc of
unidirectional conduction block, (2) conduction
around the area of block, and (3) reexcitation of the
tissue proximal to the site of conduction block
(Mines, 1913). It seems that these requisites are more
easily fulfilled when the wavelength of the impulse
is short. Then, already small areas of conduction
block may serve as pivoting points for reentry (Allessie et al., 1977). Given a certain degree of inhomogeneity of the myocardium, the chances for the
occurrence of small patches of block seem higher
than the creation of a single long arc of conduction
block. Normally, the length of the excitation wave
protects the heart against Lntramyocardial microreentry. However under conditions which shorten
the wavelength, this protection may become less
effective, and the occurrence of small areas of block
may lead to inrramyocardial reentry and fibrillation
(Moe et al., 1962; Allessie et al., 1985).
In this study, we present a simple biological model
to measure directly the length of the excitation wave
in atrial muscle. The influences of heart rate, premature beats, autonomic transmitters, extracellular
potassium, and changes in temperature are studied
and compared with the indudbility and dimensions
of intraatrial reentry. Direct measurement of the
cardiac excitation wave is a simple method, which
expresses the minimal size of an inrramyocardial
circuit and may be used as an indicator for the risk
of leading circle reentry. Since many antiarrhythmic
drugs affect both refractory period and conduction
velocity, measurement of the wavelength which
combines both parameters may help to evaluate and
improve our understanding of the mechanisms of
action of antiarrhythmic drugs.
Methods
Young New Zealand rabbits of both sexes weighing
between 1.5 and 2.0 kg were killed with a single blow to
the head. The thorax was opened by a mid-sternal incision, and the heart was rapidly excised and transferred to
a tissue bath where further dissection was performed.
After separation of the atria from the ventricles, a strip of
atrial tissue was cut from the roof of the left atrium. The
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left atrial strip, showing no spontaneous activity, was
about 20 mm long and 2-3 mm wide. The thickness of
the preparation varied from site to site but never exceeded
0.5 mm. The strip of left atrial myocardium was placed in
a tissue bath (content 50 ml) and superfused at a rate of
100 ml/min. The perfusion solution had the following
composition (ITIM): NaCl, 130; KG, 4.5; CaCl^ 2.2; MgClj,
0.6; NaHCO3, 24.2; NaH2PO4, 1.2; glucose, 11; and sucrose, 13. The solution was saturated with a mixture of
95% O2 and 5% CO2; pH was 7.35 ± 0.05, and temperature was kept at 37°C unless stated otherwise.
A programmable stimulator was used to deliver constant current pulses (duration 1-2 msec, strength 2-4 times
diastolic threshold) through two platinum plates ( 2 x 4
mm) embracing one end of the preparation. The distance
between the two stimulating electrodes was such that the
preparation could move freely between the two plates.
Field stimulation was preferred above point stimulation
because, in this way, a shorter coupling interval of premature beats and a higher maximum pacing rate could be
achieved. In addition, the variability between different
experiments was less. To check whether neurotransmittors
were released during field stimulation, we measured the
effects of a train of strong stimuli applied during the
absolute refractory period. This had no effect on either
the refractory period or the conduction velocity. Also, the
administration of atropine (10~6 M) did not affect the
measurements. Impulse propagation along the strip of
atrial myocardium was monitored with a multiple-recording electrode, consisting of a row of Teflon-coated silver
wires (diameter 0.3 mm) at an interelectrode distance of 2
mm. Unipolar elecrrograms were recorded, with a large
silver plate in the tissue bath as indifferent electrode. After
amplification (bandwidth 5-400 Hz), the elecrrograms
were displayed simultaneously on an eight-channel oscilloscope (Tektronix 1503N). Conduction velocity along the
strip of atrial myocardium was measured between the first
and last electrode on the preparation. The most rapid
negative deflection of the electrogram was taken as moment of activation at the recording site. For a reliable
measurement of the conduction velocity, it is essential to
measure the activation time between two recording sites,
rather than using the time difference between the stimulus
artefact and a single electrogram. With the latter technique, the latency between the application of an external
stimulus and the start of a propagating wavefront is
included in the measurement. This may lead to serious
underestimation of the conduction velocity. Another reason why one should not use the stimulus artefact is that,
because the latency is dependent on the stimulus strength,
the measured conduction velocity varies with the amount
of current used for stimulation. These problems can easily
be avoided by measuring between two recording electrodes. To ascertain that variations in latency and actual
origin of the activation wave could not influence our
measurements, we positioned the proximal recording electrode at a distance at least 3 mm from the stimulating
electrodes.
The wavelength of a cardiac impulse is defined as the
distance traveled by the impulse during the time the
myocardium restores its excitability to such an extent that
a second wave can propagate again. It is determined by
the product of conduction velocity and functional refractory period (FRP). To measure the length of the excitation
wave, the following stimulation protocols were used. For
determination of the wavelength of a regular rhythm, the
preparation was paced at a chosen basic rate, and after
Circulation Research/Vo/. 58, No. 1, January 1986
98
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every 20th basic stimulus, a premature stimulus was introduced at progressively shorter coupling intervals in steps
of 1-5 msec. The functional refractory period of the regular rhythm was defined as the shortest possible interval
between the last basic beat and the premature beat (shortest A,-A2 interval at the electrode closest to the site of
stimulation) which was conducted all along the atrial strip.
Conduction block of premature impulses usually occurred
at the stimulation site. The average conduction velocity
along the strip of atrial myocardium during the chosen
regular rhythm was calculated from the conduction time
and the distance between the first and last recording
electrodes along the bundle. The wavelength of premature
beats can be measured in a similar manner. The only
difference is that now two successive premature stimuli
must be given after every 20th basic impulse. The basic
rate and the degree of prematurity of the first premature
impulse are kept constant, while the coupling interval of
the second premature stimulus is progressively shortened
to determine the functional refractory period of the premature impulse. To measure the wavelength during maximum pacing (FnuO/ the basic cycle length was gradually
shortened until conduction block occurred somewhere
along the atrial bundle. The shortest possible pacing interval (interval FnuO was defined as the pacing interval at
which every impulse is conducted all along the strip of
atrial myocardium during at least 400-500 consecutive
beats. The wavelength at Fnux can be simply calculated
from the shortest pacing interval and the conduction
velocity during Fm^. In a minority of preparations, a slight
alternation in conduction velocity (±5%) was observed at
the highest driving rate. In that case, the average conduction velocity was used for the calculation of the wavelength.
For mapping studies, we used the isolated roof of the
left atrium (measuring about 15 X 20 mm) and a multiplexing system allowing simultaneous registration of 192
signals. Details of the mapping system have been given
elsewhere (Allessie et al., 1984). The multiple mapping
electrode consisted of a regular matrix of 192 Tefloncoated silver wires (diameter 0.3 mm) with an interelectrode distance of 1.4 mm. This "brush" of recording electrodes was gently positioned on the endocardial surface
of the left atrium.
Results
The Effects of Rate and Rhythm on the Length
of the Excitation Wave
The effects of different pacing rates and premature beats were studied in 30 left atrial preparations.
In Figure 1, the effects of heart rate on the functional
refractory period, conduction velocity, and wavelength of the atrial impulse are shown. The atrium
was paced with frequencies ranging from 2 Hz
(interval 500 msec) up to the maximum pacing rate.
The shortest possible pacing interval in this tissue
was 75 msec (±9.6). At pacing intervals between
200 and 500 msec, both refractory period and impulse conduction showed only minor changes, and
the length of the excitation wave was constant.
There was a slight decrease in refractory period if
the pacing interval was prolonged from 200-500
msec. It is likely that this shortening of refractoriness
at low pacing rates is particular for the rabbit, since
REF. PER.
80
60
COND. VEL.
60
40
WAVE LENGTH
mm
40
20
100
200
300
400
500
PACING INTERVAL (ms)
FIGURE 1. The effects of incremental pacing on the wavelength of
regularly driven impulses. The mean values (n = 30) and standard
deviation of the refractory period, conduction velocity, and wavelength are plotted as a function of the pacing interval.
it is absent in most other mammals and has also
been found in rabbit ventricular myocardium (Gibbs
and Johnson, 1961). At pacing rates above 5 Hz, the
length of the excitation wave becomes clearly affected. If the pacing interval is gradually shortened
from 200 msec to the shortest possible pacing interval, a progressive shortening of the wavelength up
to 40% is seen. This clear rate-dependent shortening
of the wavelength is caused both by a shortening of
the refractory period and a slowing of conduction at
high heart rates.
The effects of single premature beats on refractoriness, conduction velocity, and wavelength are
shown in Figure 2. On the abscissa, the degree of
prematurity is expressed relative to the functional
refractory period during a basic pacing rate of 2 Hz
(the shortest A,-A2 interval is taken as zero). Late
and moderately early premature beats do not differ
in their wavelength from regular impulses (refractory period and conduction velocity are unaltered).
Only closely coupled premature beats show a markedly shortened wavelength, the length of the excitation wave of the earliest premature beat (FRP)
being 23 mm compared to 40 mm of a late extrasystole. This shortening of the wavelength of early
premature impulses by about 40% is caused mainly
by a depression of conduction velocity from 55-33
cm/sec. A slight shortening of the refractory period
from 68-61 msec further adds to this effect. It is of
interest that, although the amount of shortening of
the wavelength by rapid pacing is similar to the
shortening brought about by single early premature
beats, the range of coupling intervals in which this
shortening occurs is different. During single premature beats, the wavelength is abruptly shortened
Smeets et al./Wavelength and Reentrant Arrhythmias
REF.
PER.
COND. VEL.
cm
/sec
WAVE LENGTH
mm
40
20
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0
+100 +200 +300 +400
FRP
COUPLING INTERVAL
(ms)
FIGURE 2. The xuavclength of premature beats. The mean values (n
= 7) and standard deviation of refractory period, conduction velocity,
and the wavelength of premature beats are plotted against the degree
of prematurity. The shortest possible A^-A? interval [functional refractory period (FRP)] is taken as zero; the degree of prematurity of
all other extrasi/stoles is related to the FRP. Late premature beats
have the same wavelength as the underlying basic rhythm. Only at
very early premature beats, in a narrow zone of 40 msec after the
FRP, docs a sudden and pronounced shortening of the wavelength
occur. The short length of early premature beats is caused mainly by
their reduced speed of propagation.
in a narrow zone of only 40 msec directly after the
functional refractory period. During rapid pacing,
the shortening of the wavelength occurs more gradually over a range of about 125 msec (pacing intervals between 75 and 200 msec). In some experiWAVE LENGTH
mm
50
40
REGULAR
30
EPB+20 ms
-
+10
"
- +5
EARLIEST
PREMATURE
BEAT
20
10
PACING
0
RHYTHM
100
INTERVAL
300
ms
500
FICURE 3. The wavelength of a regular rhythm (top thick curve), the
earliest premature beat (lower thick curve), and premature beats
elicited 5, 10, and 20 msec after the functional refractory period, are
plotted at different pacing rates. All impulses of both regular and
premature beats become shortened if the pacing rate exceeds 5 Hz
(interval 200 msec). Note that the wavelength of the earliest premature
beat during maximum pacing is only one-third of the impulse length
during sloiv heart rale.
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ments, a more elaborate stimulation protocol was
applied in which the wavelength of premature beats
of varying prematurity were measured at different
basic pacing rates. In this way, we could directly
compare the respective effects of pacing rate and
prematurity. Figure 3 gives the data of such an
experiment. The top thick curve shows the changes
in wavelength during regular pacing at different
cycle lengths. The lower thick curve gives the wavelength of the earliest possible premature beat elicited
at those pacing rates. The thinner curves represent
the wavelength at different basic pacing rates of
premature beats induced respectively 5, 10, and 20
msec after the functional refractory period. From
this family of curves, it is clear that an increase in
pacing rate above 5 Hz always resulted in a shortening of the length of the excitation wave. This is
true for the regular rhythm itself, the earliest premature beat, and for premature beats coming later
in the cycle. At all pacing rates, the length of the
earliest premature impulse is about half the wavelength of the regular rhythm. Premature beats arise
slightly later in the cardiac cycle (5, 10, and 20 msec
after the FRP) and have intermediate values.
The Effects of Carbamylcholine
The effects of carbamylcholine (4 X 10~7 g/ml) on
the atrial impulse were studied in 13 preparations.
After a 1-hour control period in which all measured
variables were constant, carbamylcholine was added
to the perfusate, and the wavelength during slow
pacing (2 Hz), the earliest premature impulse, and
the highest pacing rate were measured. During
wash-out, all variables quickly returned to control
values. The effects of carbamylcholine on refractory
period, conduction velocity, and wavelength are
given in Table 1. As expected, the refractory period
was markedly shortened by carbamylcholine. During pacing with 2 Hz, the FRP decreased from 7038 msec, refractoriness of the earliest possible premature beat shortened from 66-37 msec, whereas
the shortest possible pacing interval changed from
80-54 msec. The conduction velocity was not affected by carbamylcholine, with the exception of the
earliest premature impulse, which propagated somewhat faster during carbamylcholine administration
(42 vs. 35 cm/sec). These changes in refractory
period and conduction velocity resulted in a shortening of the length of the excitation wave of 48%
during slow pacing, 33% during rapid pacing, and
30% during an early premature beat. This shortening
of the wavelength was found at a wide range of
pacing rates. This is illustrated in Figure 4 in which
the wavelength during regular pacing and the earliest premature beat are plotted at different pacing
intervals. Under the influence of carbamylcholine,
both curves shift downward and to the left. For
early premature beats, the effect of carbamylcholine
is the same at all different pacing rates, as can be
seen from the parallel shift of the carbamylcholine
Circulation Research/Vo/. 58, No. 1, January 1986
100
TABLE I
The Effects of Carbamylcholine
Refractory period
(msec)
Control
Carbamylcholine
70 ± 1 1.0 38 ± 6.7*
Slow regular rhythm
(2 Hz)
Earliest premature beat
Shortest pacing interval
66 ± 9.8
80 ± 8.1
37 ± 6.4*
54 ± 6.0
Conduction velocity
(cm/sec)
Wavelength (mm)
Control
Carbamylcholine
Control
Carbamylcholine
60 ± 11.6
57 ± 11.0
41 ± 8.4
21 ±4.4*
35 ±8.6
33±6.1
42 ± 7.8*
34 ±6.1
23 ± 5.8
27 ±5.1
16 ± 5.0*
18 ± 3.0*
71 = 1 3 .
* P< 0.001.
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curve compared to control. However, during regular
pacing, the shortening of the wavelength by
carbamylcholine is most marked during slow heart
rates. At higher pacing rates (interval shorter than
200 msec), when the wavelength is already signifiREGULAR RHYTHM
WAVE LENGTH
mm
•
50
•
Control
4C
30
A
20
CCh
10
PACING
100
INTERVAL
300
ms
500
WAVE LENGTH
mm
50
PREMATURE BEAT
40
30
•
•
•
Control
4
4
A CCh
20
A
10
PACING
100
300
INTERVAL
ms
500
FIGURE 4. The effect of carbamylcholine (CCIi) (4 x 10~7 g/ml) on the
wavelength of a regular rhythm and premature impulses in a single
representative experiment. On the abscissa, the interval of the bask
pacing rate is plotted. In the top panel, the wavelength of a regular
rhythm is given, whereas the bottom panel shows the wavelength of
the earliest possible premature beat at different basic pacing cycles.
Control values are plotted as filled circles; CCh values are indicated
with triangles. Carbamylcholine shortens the wavelength of a regular
rhythm at all pacing intervals. However, this effect is stronger at
sloioer heart rates. The wavelength of the earliest premature beat is
equally shortened by carbamylcholine at all pacing rates.
cantly shortened by the rapid rhythm itself, there
still is additional shortening by carbamylcholine, but
less than during slow heart rates.
The Effects of Epinephrine
The action of epinephrine (6 X 10"7 M) was studied
in 12 atrial preparations. Table 2 summarizes the
effects on refractory period, conduction velocity,
and wavelength during regular pacing and premature stimulation. During slow regular pacing (2 Hz),
epinephrine prolonged the refractory period from
66-98 msec; refractoriness of early premature beats
increased from 62-93 msec. In contrast, the shortest
possible pacing interval increased only slightly (from
80-87 msec). Epinephrine had no significant effect
on the conduction velocity in the atrium, nor during
slow pacing, rapid pacing or the induction of premature beats. These changes in refractoriness and
conduction by epinephrine resulted in a prolongation of the wavelength from 38-58 mm (53%) during slow heart rates and a lengthening of premature
impulses from 20-29 mm (45%). At the highest
possible pacing rate, however, the wavelength was
not significantly altered by epinephrine (27 compared to 28 mm). Thus, the effect of epinephrine on
the wavelength of the atrial impulse seems to be
strongly rate dependent. In Figure 5, this rate dependency is further investigated by measuring the
wavelength during pacing at different basic cycles.
hi the top panel, the wavelength of regular impulses
is plotted as a function of the pacing cycle; the
bottom panel gives the wavelength of the earliest
premature beats elicited during different heart rates.
At pacing cycles between 500 and 300 msec, epinephrine clearly prolonged the wavelength of both
basic and premature impulses. However, at heart
rates with cycle lengths shorter than 300 msec, the
prolongation of the atrial impulses by epinephrine
gradually diminished. At the highest possible pacing
rate, epinephrine exerted almost no effect on the
wavelength of impulses in the atrium.
The Effects of Extracellular Potassium
Changes in extracellular potassium concentration
strongly affect the vulnerability of the heart to various arrhythmias (Surawicz, 1980). In particular,
Smeets et al./Wavelength and Reentrant Arrhythmias
101
TABLE 2
The Effects of Epinephrine
Refractory period
(msec)
Control
Slow regular rhythm 66 ± 8 . 1
(2 Hz)
Earliest premature
62 ± 7.4
beat
Shortest pacing in80 ± 8.3
terval
Epinephrine
Conduction velocity
(cm/sec)
Wavelength
Control
Epinephrine
Control
Epinephrine
98 ± 9.9*
56 ± 1 0 . 4
58 ± 1 0 . 9
38 ± 8.3
58 ± 1 5 . 8 *
93 ± 1 3 . 3 *
33 ±.9.7
31 ± 9 . 1
20 ± 6.6
87 ± 1 2 . 4
34 ± 5.9
32 ± 5.2
27 ± 6 . 1
29 ± 8 . 4 *
28 ± 5.4
n = 12.
* P < 0.001.
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intraatrial reentry is shown to be facilitated by low
potassium (Lammers et al., 1981). In the present
study, we investigated whether the increased incidence of reentrant arrhythmias during hypokalemia
REGULAR RHYTHM
WAVE LENGTH
mm
A
70
A Epinephrine
60
50
Control
40
30
20
10
PACING
100
INTERVAL
300
WAVE LENGTH
mm
ms
500
PREMATURE BEAT
50
A Epinephrine
40
A
A
30
•
•
• Control
20
10
PACING
100
300
INTERVAL
ms
500
FIGURE 5. The effect of epinephrine (6 x 10~7 M) on the wavelength
of a regular rhythm (top panel) and premature impulses (bottom panel)
in a representative experiment. The interval of the pacing rate is
plotted on the abscissa. Control measurements are plotted as filled
circles; epinephrine values are plotted as triangles. Epinephrine
causes a prolongation of the wavelength of both a regular rhythm
and premature beats. This effect is strongly rate dependent. At shorter
pacing intervals, the effect of epinephrine diminishes and has completely disappeared at the highest pacing rate.
might be related to changes in the length of the
excitation wave. In 13 experiments, the potassium
concentration of the perfusate was varied stepwise
between 2 and 9 HIM. The heart was allowed to
equilibrate at each potassium level for at least 1
hour. In Table 3, the effects of different extracellular
potassium concentrations on refractoriness, conduction velocity, and wavelength are summarized. Lowering extracellular K+ (2 ITIM) clearly shortened the
refractory period, whereas, at high potassium levels
(7 or 9 ITIM), refractoriness was prolonged. This was
true during slow heart rate, as well as during maximum pacing. During slow pacing (2 Hz), propagation of the atrial impulse was optimal at physiological K+ concentrations (4.5 and 5.6 ITIM); both at
lower and higher concentrations, conduction became depressed. The maximum heart rate was highest at a potassium concentration of 2 mM. Increasing
the extracellular potassium level resulted in a progressive decrease.of the highest possible pacing rate.
At 9 mM K+, the shortest possible pacing interval
was as long as 235 msec. In contrast with what we
found during slow pacing, hypokalemia did not
depress conduction during rapid pacing. At 2 ITIM
K+, the conduction velocity during ¥nax was not
different from the propagation of rapid impulses at
4.5 or 5.6 ITIM K+. As a result of these changes,
hypokalemia markedly shortened the wavelength of
the impulse during slow heart rate (40%), whereas,
during fast rhythms, the wavelength is shortened
only moderately (17% during Fma*). Elevation of
extracellular potassium to 7 mm did not affect the
length of the impulse, but severe hyperkalemia (9
mm) prolonged the wavelength as much as 59%.
The Effects of Temperature
Since hypothermia clearly affects the vulnerability
of the heart to various arrhythmias (Holland and
Klein, 1958; Covino and Damato, 1962; Nielsen and
Owman, 1968), it is of interest to know the influence
of changes in temperature on the length of the
excitation wave. It is well known that cooling prolongs the refractory period and depresses conduction of the cardiac impulse. However, because the
effects on refractoriness and conduction velocity are
opposite, it is difficult, if not impossible, to predict
102
Circulation Research/Vo/. 58, No. 1, January 1986
TABLE 3
The Effects of Extracellular Potassium
Potassium
Slow regular
rhythm (2 Hz)
Karliesi premature
beat
Shortest pacing inlerval
2.0 HIM
4.5 HIM
Rcfr period
50 ± 7.0*
70 ± 10.0
C o n d velocity
Wavelength
Refr period
52 ± 9.2*
25 ± 6.6*
39 ± 8.7*
60 ±10.1
42 ± 9 . 1
60 ± 7.4
5.6 HIM
7.0 HIM
9.0 HIM
76 ± 10.3*
6 2 ± 7.0 5 1 + 8 . 3 *
39 ± 7.7
Cond velociiy 34 ± 5.7
Wavelength
14 ± 5 . 4 *
Interval Hnux 66 ± 1 3 . 4 *
38 ± 7.5
23 ± 6.4
78 ± 7.6
86 ± 9.5 97 ± 10.3*
Cond velociiy 37 ± 6.3
Wavelength
24 ± 4.3*
37 ± 6 . 1
29 ± 4.4
35 ± 4.5 30 ± 3.9*
29 ± 4.4 29 ± 4.8
33 ±10.2*
235
31.9*
21 ± 5.0*
46 ± 9.9*
Refr = refractory: cond = conduction.
* I' < 0.001 (4.5'niM K+ = control).
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how the wavelength of the impulse will be modified
without simultaneous measurement of both electrophysiological properties. We studied the wavelength
at several temperatures in 13 experiments; only the
wavelength during maximum pacing (Fmav) was
measured. Temperature was varied in steps of 2°
between 38°C and 26°C in all experiments; in two
experiments the temperature was further lowered to
23°C and 21°C. In Figure 6, the average values of
the minimum pacing interval, the conduction velocity at Fm,lx/ and the wavelength during maximum
pacing are plotted for different temperatures. It is
clear that changes in temperature have pronounced
effects on both conduction velocity and the maximum pacing rate. Cooling the heart from 37°C to
27°C almost doubled the shortest possible pacing
interval (prolongation of interval Fmax from 86-167
msec). The speed of propagation at ¥max was decreased from 34-21 cm/sec. Since the length of the
excitation wave is determined by the balance between refractoriness and conduction velocity, this
resulted in only a moderate lengthening of the atrial
impulse from 28 mm at 37°C, to 33 mm at 27°C.
Further cooling caused a steeper prolongation of the
wavelength, because below 27°C the prolongation
of the shortest possible pacing interval clearly outweighs the concomitant depression in conduction
velocity. Thus, lowering temperature from 37°C to
27°C resulted in a strong reduction of the maximum
pacing frequency, whereas the wavelength of the
impulses is only slightly affected. Only when the
temperature falls below 27°C, is there prolongation
of the wavelength until complete inexcitability occurs.
Wavelength and the Size of Intramyocardial
Circuits
To test our hypothesis that the size of intramyocardial circuits is governed by the wavelength
of the cardiac impulse, we mapped reentrant circuits
in the same type of tissue in which the wavelength
was measured. For these mapping experiments (n =
5), instead of a narrow strip of left atrial muscle, a
15 X 20 mm sheet cut from the roof of the left
atrium was used. Figure 7 shows the effects of
carbamylcholine on rate and dimensions of an intraatrial circuit. During a long-lasting episode of
regular reentrant rhythm, evoked by a critically timed premature beat, carbamylcholine was added to
the perfusate. This resulted in an immediate gradual
shortening of the cycle length of the arrhythmia
from 90-60 msec (middle panel, Fig. 7). At the
bottom of this figure, activation maps of the rapid
reentrant rhythm are shown before and after the
administration of carbamylcholine. During control
(left map), the impulse circulated in a clockwise
direction with a revolution time of 90 msec. From
the length of the central arc of functional conduction
block (indicated by a thick line), the size of the
intraatrial circuit can be estimated to be about 30
mm. Under the influence of carbamylcholine, the
revolution time of the circulating impulse shortened
to 60 msec (right map). This acceleration of the
reentrant rhythm was not brought about by an
increase in speed of conduction, but by a shortening
of the circular pathway. As can clearly be seen by
comparing both maps, the central arc of block has
considerably "shrunken* and now is no longer than
5 mm. Obviously, because of the shortening of the
refractory period by carbamylcholine, the impulse
was able to short-cut part of the circuit, resulting in
an intramyocardial circuit as small as 17 mm.
Intraatrial reentry during low potassium was
mapped in four experiments. At normal potassium
levels, it is difficult to induce reentry within the
atrium. However, when the potassium level is lowered, runs of rapid repetitive activity can be induced
easily by the induction of a single early premature
beat. In Figure 8, two experiments are shown in
which runs of 10 and 20 rapid repetitive responses
were induced by a single premature stimulus. In
panel A, the maps of the second and fifth cycle are
103
Smeets el a\. /Wavelength and Reentrant Arrhythmias
320
MINIMUM
PACING 280
INTERVAL"
ms
240
CARBAMYL
CHOLINE
10
6
G/ML
CYCLE 140 i
LENGTH
200
160
120
80 L
40
COND.
VELOCITY 30
cm
/sec
20
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10
10 mm
40
WAVE LENGTH
30
20 *-
TEMPERATURE
15
20
25
30
35
401
FIGURE 6. The influence of temperature on the shortest possible
pacing interval (top panel), the conduction velocity (middle panel),
and the wavelength during maximum pacing (lower panel). Lowering
temperature from 37°C to 27°C caused a marked prolongation of the
minimum pacing interval from 86-167 msec. At the same time,
conduction velocity decreased from 34-27 cm/sec. Since prolongation
of refractory period and depression of conduction velocity have opposite effects on the wavelength, the effect of cooling on the wavelength was limited. Lowering the control temperature by 10 degrees
resulted in only a slight lengthening of the activation wave from 2833 mm. If the heart is further cooled below 27°C, the minimum
pacing interval becomes greatly prolonged, leading to a marked
prolongation of the wavelength at very low temperature.
reconstructed. They show intraatrial reentry with a
cycle length of 50 msec and a circular pathway of
about 15 mm. It is also interesting to see that the
position of the vortex is shifted from the upper right
corner of the atrium during the second cycle to a
mid-lower position during the fifth cycle of the
tachyarrhythmia. In panel B, two beats of a longer
period of rapid repetitive responses are shown. In
this case, two separate areas of block were present.
The reentrant circuit had a "figure 8" configuration,
where two wavefronts circulated around two arcs of
block, one in a clockwise and the other in a counterclockwise direction. However these two circulating
impulses cannot be regarded as two independent
circuits, since the isthmus between the two zones of
FIGURE 7. The effects of administration of carbamykholine (lCT6 g/
ml) on cycle length (middle panel) and dimension of intraatrial reentry
(lower panel). Carbamykholine caused a dramatic acceleration of the
already very fast reentrant rhythm; the cycle length decreased from
90-60 msec. The two maps at the bottom show the spread of excitation
before and after the administration of carbamykholine. Both maps
arc reconstructed from multiple unipolar electrograms recorded 1.4
mm apart. Using such high spatial resolution, it was not necessary
to calculate isochrones by interpolation. As shown by the maps, the
rapid rhythm is based on a clockivise circulating wavefront. The solid
line in the center of the vortex represents the central arc of block
where the impulse turns around. Comparing the two maps, it is
evident that, under the influence of carbamykholine, the reentrant
loop has become considerably smaller. We estimate the perimeter of
the intraatrial circuit, before and after carbamykholine, to be 30 and
3 7 mm.
block served as a common reentrant pathway for
both circulating wavefronts. At one side of the isthmus (the "entrance' of the common pathway), the
two wavefronts coalesced. At the other end (the
"exit" of the isthmus) the impulse diverged again in
a clockwise and a counter-clockwise rotating wave.
In this example, also, the position of the vortices
changed between the first and the 12th cycle. In
addition, the direction in which the common wavefront travels through the isthmus between the two
arcs of block is reversed. In the map of the first
cycle, the common wave propagates through the
isthmus from left to right, whereas, during the 12th
beat, the isthmus is traversed in a right-to-left direction. The size of the two circuits during the first
reentrant beat can be estimated to be 15-16 mm.
During the 12th beat, the circuits seem a little larger,
and measure 17 and 21 mm, respectively. These
mapping studies seem to confirm that the shortening
of the refractory period caused by low potassium
leads to reentrant rhythms which are faster than
104
Circulation Research/Vo/. 58, No. 1, January 1986
CYCLE
180 -\
29° C
LENGTH
140
SECOND CYCLE
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FIRST
CYCLE
FIFTH CYCLE
TWELFTH
CYCLE
10 mm
159
10 mm
FIGURE 8. Two examples of paroxysms of rapid repetitive reentry in
isolated pieces of rabbit atrium induced by a single early premature
beat. The extracellular potassium concentration was loiuered to 2 nm
In panel A, the second and fifth cycles of a short run of reentrant
activity are mapped. A small reentrant loop with a circular pathway
of about 15 mm around a 5-mm central arc of block (thick solid line)
is seen. The functional and dynamic nature of this kind of intramyocardial reentry is illustrated by the dear shift in position of the
vortex between the second and fifth cycle of the arrhythmia. In panel
B, another example of a longer run of reentrant activity in low K* is
shown. In this case, two arcs of conduction block were present, and
the reentrant activity had a "figure of 8" configuration. Again, the
position of the reentrant activity is not fixed, but "wanders" around
the myocardium. Circuit size varies between 15 and 21 mm.
normal and are based on intramyocardial circuits
which are smaller in size because of the concomitant
shortening of the wavelength of the impulse.
The effects of cooling on intraatrial reentry was
studied in three preparations. At 37°C, a long-lasting reentrant arrhythmia was induced in the isolated
left atrium by the induction of early premature beats
and continuous administration of carbarnylcholine
(1CT7 M). When the cycle length of the circus movement had become constant, the temperature of the
perfusate was gradually lowered until the intraatrial
circuit was interrupted. Figure 9 is an example. At
37°C/ the impulse was found to circulate in a clockwise direction with a cycle length of 98 msec. The
S-shaped thick line in the center of the vortex indicates the arc of functional conduction block around
which the impulse circulates; the size of this intraa-
FIGURE 9. The effects of temperature on intramyocardial reentry.
During a long-lasting episode of intraatrial reentry, the temperature
of the perfusion solution was dropped from 37°C to 29°C In response
to this cooling, the cycle length of the arrhythmia prolonged from 98159 msec. From the activation maps it can be seen that the rapid
rhythm is caused by a single clockwise circulating wavefrotit around
an S-shaped area of conduction block. Cooling has a quantitatively
different effect on the cycle length and the size of the reentrant circuit.
The revolution time of the circulating impulse is prolonged by 60%
(from 98-159 msec), whereas the length of the reentrant pathway has
increased by only J5% (from 27-31 mm). In the bottom panels, four
electrograms were selected to show the pathway of the circulating
impulse around the upper pivoting point. The exact position of the
four electrograms is indicated on the maps.
trial loop can be estimated to be about 27 mm. A
gradual decrease of the temperature to 29°C resulted
in a progressive increase of the revolution time from
98-159 msec. It is noteworthy that despite this
strong reduction in rate, the reentrant rhythm remained regular and did not terminate. The number
of isochrones increased and are closer together, indicating that the speed of propagation has slowed
down uniformally along the circuitous pathway. The
central S-shaped arc of functional block is somewhat
enlarged, resulting in some increase in size of the
circuit from 27 to about 31 mm. In the lower panels
of Figure 9, four electrograms (A-D) have been
selected to illustrate the pathway around the upper
pivoting point of the circuit. At 37°C, the impulse
turned around the upper end of the S-shaped central
arc of block propagating along a straight line from
site A to D. At 29°C, the pivoting point has clearly
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Smeets et al. /Wavelength and Reentrant Arrhythmias
105
moved upward. Instead of traveling directly from
site A to D, the impulse now reaches site D after
making a detour along the upper part of the preparation (note the shift in position of the intervening
electrograms B and C).
Moderate cooling strongly reduced both the maximum rate of pacing and the cycle length of intraatrial reentry. At the same time, the length of the
excitation wave and the size of a leading circuit are
only slightly prolonged. At temperatures below
27°C, the wavelength is markedly prolonged and
intraatrial circuits are interrupted.
Again these temperature experiments show a
good agreement between: (1) the maximum pacing
frequency (F^*) and the rate of intraatrial reentry,
and (2) the wavelength of the impulse and the
dimensions of intramyocardial circuits.
a strong reduction of the length of the excitation
wave under the influence of carbamylcholine. During slow rhythm, this drug shortened the impulse
from 41-21 mm. Induction of premature beats further reduced the wavelength up to 16 mm. During
regular pacing at the highest possible frequency, the
wavelength was 18 mm. Mapping of intraatrial reentry confirmed that the length of the circuit was
similar to the wavelength of the impulse as measured during maximum pacing. During carbamylcholine administration, circuits as small as 15-20 mm
were identified. Not only do circuits of this size
easily fit in the available tissue mass, but the reduction in wavelength also strongly facilitates the initiation of circus movement. For the successful induction of reentry, an area of unidirectional conduction
block of at least half the wavelength is a condition
'sine qua non.' It is obvious that the chances to
fulfill this criterion are higher when the required
area of conduction block is smaller. For the isolated
left atrium of the rabbit, the critical wavelength for
easy induction of intramyocardial reentry is in the
order of 20 mm.
In the intact canine heart, and also in man, atrial
fibrillation induced by programmed stimulation in
healthy individuals usually terminates spontaneously within seconds or minutes. However, during vagal stimulation or administration of acetylcholine, fibrillation becomes self-sustained and spontaneous reversion to sinus rhythm no longer occurs
(Burn et al., 1955; Allessie et al., 1985). The data
presented in this study strongly suggest that the
fibrillatory action of parasympathetic transmitters is
based on an overall shortening of the wavelength
in the atria. Because of the smaller dimensions of
intraatrial circuits, more circulating wavelets can be
present simultaneously in the available cardiac tissue mass (Moe, 1962; Allessie et al., 1985). During
rapid pacing, carbamylcholine shortened the wavelength of the impulse about 30%, suggesting that
this amount of shortening is sufficient to prevent
resumption of sinus rhythm and may be responsible
for perpetuation of atrial fibrillation. On the other
hand, this value gives a clue that drugs which prolong the activation wave about 30% may be effective
in preventing paroxysms of atrial fibrillation.
The role of the sympathetic nervous system in the
initiation and perpetuation of intraatrial reentry is
uncertain. Clinical evidence that catecholamines
play a role in the occurrence of paroxysmal atrial
fibrillation is scarce (Coumel et al., 1982). In animal studies, the effects of administration of
(nor)epinephrine on the electrophysiological prop
differ from species to species (Webb and Hollander,
1956; Hoffman and Cranefield, 1960). Reentry
within segments of isolated left atrium of the rabbit
is not affected by the addition of epinephrine to the
tissue bath; the only effect observed was a very
slight prolongation in cycle length of the reentrant
rhythm (Allessie et al., 1977). In the present studies,
Discussion
We propose to use the wavelength of the cardiac
impulse as an index for the vulnerability of the heart
to fibrillation. Together with the mass of cardiac
tissue and the degree of inhomogeneity of conduction properties, the length of the excitation wave
seems a key factor in the inducibility and stability
of fibrillation. In this study, we developed a simple
in vitro model in which the wavelength can be
directly measured under a wide variety of circumstances. The wavelength of the atrial impulse as
found in this model was compared with the actual
dimensions of intraatrial reentry determined by high
resolution mapping in a small sheet of the same
tissue. A number of important physiological variables were investigated, including cardiac rate and
rhythm, autonomic nervous transmitters, extracellular potassium, and changes in temperature. Under
all those different conditions, there was good agreement between the length of the excitation wave and
the size of intra-myocardial circuits.
Autonomic Transmitters
Under normal conditions, the wavelength of the
impulse in the isolated rabbit atrium is longer than
4 cm. Compared to the small size of a rabbit heart,
it is unlikely that a circuit of that size can exist.
However, during rapid heart rate or the occurrence
of early premature beats, the wavelength is considerably shortened to about 2.5 cm. Normally, this
wavelength is still long enough to protect the rabbit
atrium against initiation of intraatrial reentry, and
in only a minority of cases can short runs of rapid
repetitive activity be induced in the isolated left
atrium of the rabbit by programmed stimulation
alone. In contrast, atrial fibrillation and intraatrial
reentry can easily be induced in combination with
vagal stimulation or the administration of acetylcholine (Burn et al., 1955; Allessie et al., 1977, 1984,
1985). Also, in man, paroxysms of atrial fibrillation
may be related to a high parasympathetic tone (Coumel et al., 1978). In the present study, we measured
106
we found that epinephrine prolonged the refractory
period and the wavelength only at slow driving
rates. At higher heart rates, this effect disappears
and no effect of epinephrine on refractoriness or
conduction was found when the atrium was paced
at its maximum driving rate. From these measurements, one might expect that, because of prolongation of the refractory period and the wavelength of
premature beats, the induction of intraatrial circuits
is less likely when epinephrine is present. However,
perpetuation of intraatrial reentry, once established,
seems to be unaffected by adrenergjc compounds.
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Potassium
During low potassium, intraatrial reentry can be
readily induced, but is generally self-terminating
(Lammers et al., 1981). One of the interesting findings of the present study is that during hypokalemia
(2 ITIM), the wavelength of early premature beats is
markedly shortened (by 40%), whereas, during
rapid pacing, the impulse is only slightly shorter
than normal. This observation offers a good explanation for the arrhythmogenic profile of low potassium. The easy induction of rapid repetitive responses by a single premature beat fits with the
extremely short wavelength of premature impulses.
The self-terminating character of the arrhythmias is
based on the gradual prolongation of the length of
the rapid impulses leading to a gradual increase of
circuit size and, finally, to interruption of the circulating impulse.
Increased extracellular potassium depresses conduction and prolongs refractoriness in cardiac tissue.
When the potassium level is moderately elevated
(up to 7 ITIM), these two electrophysiological properties are affected to the same extent. Since they
exert opposite effects on the wavelength of the
impulse (slow conduction shortens the wavelength,
whereas prolonged refractoriness lengthens it), the
length of the excitation wave was not altered by
moderate hyperkalemia. However, at extracellular
potassium levels exceeding 7 ITIM, the time course of
recovery of excitability becomes more affected than
the speed of conduction. As a result, the length of
the cardiac impulse is dramatically prolonged at
severe hyperkalemia. This may well be the underlying mechanism of the long-known defibrillatory
action of potassium infusion (Wiggers, 1953). To
terminate atrial or ventricular fibrillation, it is not
necessary that potassium be raised to such a high
level that cardiac conduction is completely blocked.
Fibrillation can be stopped with the myocardium
still able to conduct normal impulses (Grumbach et
al., 1954). At about 10 ITIM [K]O, prolongation of the
wavelength of the fibrillatory impulses may be expected to be sufficient to terminate the fibrillatory
process.
Cooling and Arrhythmias
The concept that the rate of intramyocardial
reenty is similar to the maximum pacing rate and
Circulation Research/VoJ. 58, No. 1, January 1986
that its size is equal to the wavelength of the impulse
was tested further by changing the temperature of
the heart. Cooling exerted different quantitative effects on the maximum pacing rate and the length of
the impulse, the maximum pacing rate being more
sensitive to temperature changes than the wavelength (Qio = 1.94 and 1.17, respectively). Intraatrial
reentry showed the same behavior. The rate of a
reentrant rhythm slowed down markedly when the
atrium was cooled. At the same time, the circuit
length increased only slightly until—at very low
temperatures—the circulating impulse was blocked
and the reentrant rhythm suddenly terminated. This
observation is in agreement with the studies of
Holland and Klein (1958) who found that isolated
but intact rabbit atria did not fibrillate at temperatures below 24°C. In man, also, temperature plays
an important role in the occurrence of cardiac arrhythmias. In patients in whom, during normothermia, ventricular tachycardia can be readily induced by programmed electrical stimulation, it is
much more difficult, or even impossible, to produce
ventricular tachycardia during intraoperative mapping performed under hypothermia (Josephson and
Wellens, 1984). If these tachycardias are based on
reentry within a relatively small diseased part of the
ventricles, the prolongation of the wavelength by
cooling might have disturbed the delicate balance
between the functional size of the circuit and the
available mass of diseased tissue, resulting in disappearance of the arrhythmia.
Inhomogeneity and Anisotropy
By stressing the significance of the wavelength of
the impulse in reentrant arrhythmias, we do not
mean to say that other factors are not involved. It is
quite well understood that structural inhomogeneities or local differences in electrophysiological or
ultrastructural properties might be equally important. The relative importance of wavelength and
inhomogeneity may well differ from case to case;
some arrhythmias are caused by too short a wavelength, whereas other arrhythmias predominantly
arise on the basis of overtly increased inhomogeneity. In addition, we want to emphasize that anisotropy of the heart may also play an important role.
Conduction velocity in the myocardium is dependent on the direction of propagation relative to the
fiber orientation (Spach et al., 1982). Therefore, even
at the same site, the wavelength of the impulse may
vary, depending on the direction of the propagating
wavefront. When a bundle of muscle fibers is activated by an impulse running parallel to the long
fiber axis, the wavelength will be long, whereas,
when the same bundle is activated perpendicular to
the fiber direction, the wavelength will be shorter.
Since the strips of atrial muscle used in our studies
did not consist of a single bundle of parallel fibers
(like the crista terminalis or Bachmann's bundle),
the measured wavelength of the atrial impulse
should be considered as some intermediate value
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Smeets el al. /Wavelength and Reentrant Arrhythmias
107
between a maximum wavelength for parallel conduction and a minimum wavelength for an impulse
propagating perpendicular to the fiber orientation.
So far, it has been difficult to quantify the degree
of spatial inhomogeneity and anisotropy, which together determine the propagation of the impulse.
Before wavelength and heterogeneity can be used
together as indices for the vulnerability to fibrillation, we need a method to quantify the spatial
dispersion in the ability of atrial or ventricular myocardium to propagate an impulse, and to determine
the role of anisotropy in the occurrence and stability
of intramyocardial reentry.
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These investigations were supported in part by the Foundation for
Medical Research FUNGO (Grant 13-22-76).
Address for reprints: Maurits A. Allessie, M.D., Department of
Physiology, Biomedical Center, University ofLimburg, P.O. Box 616,
6200 MD Maastricht, The Netherlands.
Received February 20, 1985; accepted for publication September
26, 1985.
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INDEX TERMS: Arrhythmias • Wavelength • Reentry • Atrial
flutter • Atrial fibrillation
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The wavelength of the cardiac impulse and reentrant arrhythmias in isolated rabbit atrium.
The role of heart rate, autonomic transmitters, temperature, and potassium.
J L Smeets, M A Allessie, W J Lammers, F I Bonke and J Hollen
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Circ Res. 1986;58:96-108
doi: 10.1161/01.RES.58.1.96
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Copyright © 1986 American Heart Association, Inc. All rights reserved.
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