© 1999 American Heart Association, Inc.
Original Contribution |
Reentry and Fibrillation in the Mouse Heart
A Challenge to the Critical Mass Hypothesis
From the State University of New York Health Science Center at Syracuse, NY.
Correspondence to José Jalife, MD, Department of Pharmacology, SUNY Health Science Center, 766 Irving Ave, Syracuse, NY 13210. E-mail jalifej{at}vax.cs.hscsyr.edu
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Abstract |
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Abstract—The idea that fibrillation is only possible in hearts exceeding a critical size was introduced by W. Garrey >80 years ago and has since been generally accepted. In ventricular tissue, this critical size was originally estimated to be 400 mm2. Recent estimates suggest that the critical size required for sustained reentry is
100
to 200 mm2, whereas 6 times this area is required for
ventricular fibrillation. According to these estimates,
fibrillation is not possible in the mouse heart, where the
ventricular surface area is 100 mm2. To
test whether sustained ventricular fibrillation could be
induced in such an area, we used a high-speed video imaging system and
a voltage-sensitive dye to quantify electrical activity on the
epicardial surface of the Langendorff-perfused adult mouse heart. In 6
hearts, measurements during ventricular pacing at a basic
cycle length (BCL) of 120 ms yielded maximum and minimum conduction
velocities (CVmax and CVmin) of 0.63±0.04 and
0.38±0.02 mm/ms, respectively. At a BCL of 80 ms,
CVmax and CVmin changed to 0.55±0.03 and
0.34±0.02 mm/ms. Action potential durations (APDs), measured at
70% repolarization at those pacing frequencies were found to be
44.5±2.9 and 40.4±2.6 ms, respectively. The wavelengths (CVxAPD)
were calculated to be 28.6±3.4 mm in the CVmax
direction and 16.8±1.5 mm in the CVmin direction at
BCL 120 ms. Wavelengths were significantly reduced
(P<0.05) at BCL 80 ms (CVmax,
22.2±1.8 mm; CVmin, 13.7±0.9 mm). In 5 hearts,
stationary vortex-like reentry organized by single rotors (4 of 5
hearts) or by pairs of rotors (1 of 5 hearts) was induced by burst
pacing. In the ECG, the activity manifested as sustained monomorphic
tachycardia. Detailed analysis showed that the
local CVs were reduced in the vicinity of the rotor center, which
allowed the reentry to take place within a smaller area than was
calculated from wavelength measurements during pacing. In 4 of 7
hearts, burst pacing resulted in a polymorphic ECG pattern
indistinguishable from ventricular fibrillation. These data
challenge the critical mass hypothesis by demonstrating that
ventricular tissue with an area as small as 100
mm2 is capable of undergoing sustained fibrillatory
activity.
Key Words: rotor • vortex-like reentry • curvature • wavelength • conduction velocity
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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The concept that reentry and fibrillation are only possible in hearts exceeding a "critical mass" was introduced >80 years ago and is presently widely accepted.1 2 3 4 Garrey1 originally observed a direct relationship between the size of a piece of cardiac tissue and its ability to sustain fibrillatory activity. He noted that if he cut the tissue into progressively smaller pieces he could achieve a size at which fibrillation would stop. On the basis of his results, he concluded that the minimum size of cardiac tissue required for fibrillation was
400 mm2.
More recent studies support Garrey's findings.3 4 5 6
For example, Winfree5 calculated the critical size
required for sustained reentry to be 100 to 200
mm2. Such an estimate was based on the assumption
that the mechanism of ventricular fibrillation (VF)
involves rotors (vortex-like reentry). Winfree also predicted that VF
requires substantially more tissue. His estimates suggested that the
minimum size required for sustained fibrillation was 6 times the
diameter of a rotor. This approximation was based on the ability of the
center of rotation of a vortex wave to drift at high speed
throughout the ventricles. On the basis of such estimates, VF requires
a volume of 6x6x1 cm, which corresponds to 12 g of cardiac
tissue. Accordingly, sustained fibrillation should not be possible in
the mouse heart of which the ventricular area is
100 mm2 and the total mass is 200
mg.
Theoretical7 8 and experimental studies9 have suggested that meandering or drifting rotors should result in complex electrocardiographic (ECG) patterns. Recently, video imaging experiments by Gray et al10 have shown that polymorphic ventricular tachycardia may result from a single rotor that drifts throughout the ventricles, as recorded from the epicardial surface of the rabbit heart. When the drift speed was >30% of the wavefront speed, the ECG was indistinguishable from VF.11 12 These data suggest that the critical size required for fibrillation may not be significantly larger than that required for reentry. Other data have also suggested that reentry may be possible in much smaller pieces of cardiac tissue9 13 14 15 than those predicted by the critical mass hypothesis.
Our aim here was to carefully examine the predictions of the critical mass hypothesis and the basis for those predictions. In this regard, our first objective was to determine whether arrhythmias are possible in the ventricles of the adult mouse heart of which the ventricular surface area is <100 mm2. According to the critical mass hypothesis, the wavelength is relevant for predicting the ability to initiate and maintain reentry in cardiac tissue. Using high-speed video imaging and voltage-sensitive dyes, we have characterized the electrophysiology of the normal adult mouse heart. This included measurements of epicardial longitudinal and transverse conduction velocities (CVs), mean action potential duration (APD), APD frequency dependence, and wavelength of the tissue. Our second objective was to use these measurements to determine whether there is indeed a predictive relationship between the wavelength during regular epicardial pacing and the ability to sustain arrhythmias. Our data demonstrate for the first time that the normal Langendorff-perfused mouse heart is capable of sustaining rotors and VF.
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Materials and Methods |
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Langendorff-Perfused Mouse Heart
All animal care protocols conformed to institutional and NIH guidelines. Adult C57 mice were heparinized (0.5 U/g IP) and then anesthetized with a mixture of ketamine (100 µg/g) and acepromazine (0.5 µg/g). The hearts were quickly removed through a thoracotomy and rinsed in a Tyrode's solution containing (in mmol/L) NaCl 130, NaHCO3 24, NaH2PO4 1.2, MgCl2 1.0, glucose 5.6, KCl 4.0, and CaCl2 1.8, equilibrated with a 95% O2, 5% CO2 gas mixture. Hearts were then rapidly cannulated and perfused in a retrograde fashion via an aortic cannula with warm (37°C to 39°C) oxygenated Tyrode's solution (2 to 3 mL/min). Once connected to the Langendorff perfusion system, hearts were placed in a custom-built perfusion chamber. Warm oxygenated Tyrode's solution was also superfused; this ensured that no temperature gradients were present between the endocardium and the epicardium. The solution in the chamber was used as a volume conductor for recording ECGs. The front of the chamber is glass, which allows for the hearts to be stabilized against and imaged. To ensure that the hearts were in sinus rhythm and contracting forcefully and rhythmically, they were allowed to equilibrate for 20 minutes in the perfusion apparatus, while a horizontal ECG was recorded. Thereafter, a 5-minute bolus perfusion of the fluorescent voltage-sensitive dye di-4-ANEPPS (1.5 µg; Molecular Probes) was started. Fluorescence associated with the electrical activity was recorded in the absence of mechanical artifacts by continuously perfusing diacetyl monoxime (DAM, 15 mmol/L). In 2 hearts, DAM was not perfused. In these hearts, optical mapping was not analyzed because of motion artifacts, and only the ECGs were monitored.
High-Resolution Mapping of the Mouse Heart
The video imaging used was similar to that described by Gray et
al.10 Briefly, light from a tungsten-halogen lamp was
collected and passed through an interference filter (520±40 nm) and a
heat filter. The excitation light source was directed toward the
epicardial surface of the heart. The emitted light was collected and
passed through an emission filter (645±65 nm) and projected onto a
charge-coupled device video camera (Cohu). Video images of the
epicardial surface were acquired with an analog-to-digital frame
grabber (Epix) at a rate of 240 frames per second. To reveal the
signal, the background fluorescence was subtracted from each
frame. Signals were further improved using low-pass spatial filtering
techniques.
To increase the temporal resolution of the video recordings, we implemented a synchronous acquisition system,16 whereby the first frame acquired by the camera was synchronized with each stimulus delivered to the tissue; ie, each stimulus occurred precisely when the camera started acquiring a frame. Later, offline, 6 to 10 of these activations were ensemble averaged17 to reveal a sequence of frames that the camera acquired at 0 ms, 4 ms, etc, from the instant of stimulus delivery. Immediately after the above acquisition, the camera was again synchronized with a delay of 1 ms from the time of stimulus. An ensemble average of these activations revealed a sequence of frames that the camera recorded at 1 ms, 5 ms, etc, from the instant of stimulus delivery. Thus, each frame of this sequence is offset from the corresponding frame of the previous sequence by 1 ms. Similarly, sequences were obtained with the camera delayed 2 and 3 ms from the time of the stimulus. All 4 sequences were obtained within a single episode of steady-state pacing, and the total acquisition procedure lasted 4 seconds. The frames from all 4 sequences were then interleaved (0, 1, 2, 3, 4, 5 ms, etc), to reveal an activation sequence with a 1-ms resolution. Acquisition with this system was limited to signals that were regular. The electronics were tested using the camera to record defined sweeps of an oscilloscope beam. In another study, we have carefully evaluated the CVs (see below) measured with this technique and have determined that this approach yields measurements that are statistically indistinguishable from those obtained with a faster camera (DALSA, CA-D1 1484 frames per second) running in a nontriggered acquisition mode.18 CV measurements were obtained by averaging local conduction vectors as described by Morley et al.18 Briefly, an activation time (defined as the time a given pixel reached 50% of the maximal fluorescent amplitude) was determined for each pixel. Local conduction vectors were calculated for each pixel on the basis of the activation times of the surrounding pixels. The conduction vectors were used to establish both the direction and speed of conduction for every point on the heart and to determine maximum and minimum CVs (CVmax and CVmin).
Stimulation Protocol
Bipolar pacing electrodes were placed on the epicardium near the
center of the anterior left ventricle. Preparations were paced at basic
cycle lengths (BCLs) of 80 and 120 ms. The left ventricle was paced
using pulses equivalent to 1.5x threshold amplitude at each BCL with a
duration of 2 ms. The BCLs were set at random, and 1.5 minutes was
allowed at each BCL before changing to a new BCL. Arrhythmias
were induced using a burst-pacing stimulation protocol. Short bursts
(20 stimuli) were applied at critical pacing frequencies, which were
determined by scanning a range of cycle lengths shorter than the 1:1
capture cycle length. It was our experience that induction of
arrhythmias in the mouse heart was variable and dependent
on many factors, including the electrode position, stimulus strength,
and pacing frequency. In all cases, this pacing protocol was repeated
many times while the above variables were changed before an
arrhythmia was successfully induced. Typically, the source of
any sustained arrhythmia was located outside the field of view
of the camera. Thus, the camera was repositioned to record the
source of the arrhythmia.
Pseudo-ECGs
The fluorescent signals from pixels in the left and
right halves of each frame were summed, and the difference between the
2 halves was calculated. The pseudo-ECG,19 ie, the time
series of these differences, was used to summarize the optical data
from a recording.
Electrocardiograms
ECG leads I, II, and III were recorded sequentially from
lightly anesthetized animals (avertin, 0.015 to 0.017 mL/g body
weight, IP). Horizontal ECG recordings were obtained
continuously from the Langendorff-perfused heart using electrode leads
immersed in the tissue bath and flanking the heart.10 11 12
Signals were amplified and filtered with a differential amplifier
(World Precision Instruments, Inc) and displayed on an oscilloscope.
Signals were digitized at 2471 Hz and stored for offline
analysis.
Signal Processing
Standard signal processing techniques were used to study the
spectral content of VF. Spectral analysis was performed using
the fast Fourier transform (FFT).20
Determination of Stability of Reentrant Activity During
Monomorphic Tachycardias
Optical records that were obtained during
arrhythmias associated with monomorphic volume–conducted ECGs
were signal averaged to confirm the stability of reentrant processes.
Fluorescent signals were averaged17 at the peak
frequency obtained from the FFT of the volume-conducted electrogram.
Enhancement of the signal-to-noise ratio in these movies
indicated the stability of the activation pattern during the total
acquisition period.
Statistical Analysis
When appropriate, statistical analysis was carried out
with the Excel software package. Values are reported as mean±SEM for a
given measurement. ANOVA (with post hoc Student t test) was
performed on the wavelength data, and regression and correlation
analysis were used to determine the relation between CV and
radial distance. Differences were considered significant when
P<0.05.
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Results |
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ECG of the Normal Mouse Heart
A 3-lead ECG from an anesthetized mouse in sinus rhythm is presented in Figure 1A
. The
spontaneous cycle length was 113 ms, corresponding to a heart rate
of 531 bpm. In Figure 1B, the horizontal ECG of the
Langendorff-perfused heart (same animal as in Figure 1A) shows a
similar but somewhat slower rhythm (390 bpm) than that obtained from
the surface ECG. Surface ECG data obtained from 10 lightly
anesthetized male mice are summarized in the
Table. Surface ECG intervals and heart
rates measured here are similar to those previously reported for the
normal anesthetized mouse.21
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Sequence of Activation During Epicardial Pacing
Color isochrone maps obtained during point bipolar stimulation
near the base of the anterior left ventricle at BCLs of 120 and 80 ms
are shown in Figure 2. In each case, the
pattern of optical action potentials recorded from any position of
the stained preparation (not shown) was nearly identical, confirming a
high signal-to-noise ratio. Figure 2A shows data at a BCL of 120
ms. The color map reveals an anisotropic excitation wavefront moving
away from the stimulating electrode (black shadow) toward the apex and
base, to excite the entire anterior epicardial wall in <13 ms. In
Figure 2B, stimulation at a BCL of 80 ms yielded a similar but
somewhat slower activation sequence. The respective vector maps are
shown in Figure 2C and 2D. The vertical arrow in the
lower left corner of Figure 2D marks a magnitude of 1.0
mm/ms. For clarity, only a few of the calculated vectors are drawn.
Note the vectors emanating from the site of stimulation in an
anisotropic fashion, permitting identification and quantitative
analysis of CVmax and
CVmin.
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CV, APD, and Wavelength
Measurements of CVmax,
CVmin, and mean APD at 70% repolarization
(APD70) were made to estimate the wavelength in
the longitudinal and transverse direction of the fibers. As in other
species, CV in the normal mouse heart was dependent on stimulation
cycle length, as well as fiber orientation. At a BCL of 120 ms,
CVmax was 0.63±0.04 mm/ms, and
CVmin was 0.38±0.02 mm/ms (n=6). At a BCL
of 80 ms, CVmax decreased to
0.55±0.03 mm/ms, whereas CVmin went down to
0.34±0.02 mm/ms (n=6).
Optical measurements of APD are presented in Figure 3. In Figure 3A, the
fluorescent image of a heart is shown together with action
potentials (inset) recorded by all pixels in a demarcated
1.1x1.1-mm square on the anterior epicardial surface. The heart was
paced at a constant BCL of 120 ms. In Figure 3B, we present
mean values of APD70 (n=6) at constant BCLs of
120 ms (APD70, 44.5±2.9 ms) and 80 ms
(APD70, 40.4±2.6 ms). The bar graph in Figure 3C shows the calculated wavelengths
(CVmaxxAPD70 and
CVminxAPD70) at these
BCLs. It is clear that, regardless of the BCL or epicardial fiber
direction, the wavelength was much larger than the long axis of the
heart (7 mm).
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Arrhythmias in the Normal Mouse Heart
In 7 of 7 separate hearts (5 perfused with DAM and mapped, and 2
not perfused with DAM and not mapped), burst pacing near the apex of
the left ventricle induced sustained monomorphic
tachycardias. We defined a sustained arrhythmic episode as
one that lasted >30 seconds. In 4 of the 5 hearts that were mapped,
sustained vortex-like reentry occurring around a single organizing
center (core) was observed. In Figure 4A, we present the color isochrone map of a single counterclockwise
rotation of a stationary vortex induced by burst pacing. The wavefront
rotated with a period of 72 ms. In Figure 4B we show the
pseudoelectrogram obtained from the optical data (upper trace) and the
horizontal volume–conducted ECG (lower trace); the FFTs of these
records are in Figure 4C. The FFTs of both the electrogram
and the pseudoelectrogram show single narrow peaks at nearly identical
frequencies that are consistent with the observed rotation
period. This suggests that the rotor that gives rise to the periodicity
in the pseudoelectrogram is also responsible for the periodic frequency
of the volume-conducted electrogram. In one heart, 2 counterrotating
vortices (figure-of-8 reentry) were recorded during sustained
monomorphic tachycardia. Figure 5 shows an isochrone map of this
episode. The black areas indicate pixel locations near the centers of
rotation, where activation times could not be clearly identified. These
data demonstrate that the mouse heart is capable of sustaining at least
2 stable reentrant sources.
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In Figure 6, we present the
analysis of the velocity vector field obtained from the
clockwise rotation (arrow) of a stationary vortex with a period of 68
ms. In the pseudo-ECG, vortex-like activity manifested as a stable
episode of monomorphic ventricular
tachycardia. In Figure 6B, the vector map
shows the spatial variation of the CV vectors displayed over the entire
cycle. The direction of the propagation vectors was normal to the
rotating wavefront, and the speed of propagation increased radially
from the core. This is displayed quantitatively in Figure 6C. A
sector was identified in the vector map, the tip of which was located
at the center of the core. The local velocities within this sector are
plotted against the radial distance. The regression line shows a
significant positive correlation
(r2=0.342, P<0.05). As a
control, Figure 6D shows an isochrone map obtained from the
same heart during stimulation at a constant BCL of 120 ms, soon after
the termination of the tachycardia. As shown also in the
vector map (Figure 6E), the excitation wavefront moved downward
at a faster velocity than during reentry. The vectors within the same
sector as that in Figure 6B show conduction in approximately the
same direction. As shown in Figure 6F, in this case, there was
no correlation (r2=0.0007, NS) between
the velocity within the sector and the distance from the center of the
anterior ventricular surface, which suggests that the
spatial distribution of CVs observed during reentry (Figure 6A
through 6C) was associated with the reentrant process itself.
Overall, the results are in agreement with the theory of wave
propagation in excitable media,6 9 14 which suggests
that during vortex-like reentry, the local curvature of the wavefront
increases toward the core and imposes a slowing of CV.
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In 4 of 7 experiments, including both hearts in which DAM was not
perfused, burst pacing of the left ventricle induced more complex
arrhythmias. Simultaneously recorded
electrograms of these episodes resembled VF. Figure 7A shows color isochrone maps of
activity recorded during an episode of VF. The 2 maps show a
wavefront on the epicardial surface that changes origin and direction.
This aperiodic activity continued throughout the optical record. In
Figure 7B, the horizontal ECG recorded during this episode
shows complex ventricular activity indistinguishable from
VF. In Figure 7C, the FFT of the horizontal ECG shows a
narrow-banded spectrum consistent with VF.22
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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The results presented in this study demonstrate for the first time that ventricular tissue with an area as small as 100 mm2 is capable of undergoing sustained reentrant activity and VF. The results are unexpected in the sense that it is difficult to conceive the occurrence of fibrillation or even sustained reentry in an excitable medium of which the wavelength (
10
to 30 mm) is larger than the length of the medium, particularly a
medium in which APD shows little or no frequency dependence. One
possible explanation for this phenomenon may be found in recent
computer simulations13 that indicate that the core around
which a vortex rotates may exert a strong repolarizing influence on the
surrounding tissues. Under such conditions, APDs of the cells near the
core are shorter than APDs of cells in the periphery of the vortex.
Such a repolarizing influence of the core is evident in the fact that
the average APD of the whole preparation was shorter during reentrant
activity than during external stimulation at a rate identical to that
generated by the reentry. Thus, the results further demonstrate that
the wavelength during periodic stimulation is a poor predictor of the
conditions needed for maintenance of reentry in the mouse
heart.
Electrophysiological Characteristics
We have measured the ECG parameters during sinus
rhythm in the anesthetized mouse. Our results are in good
agreement with those previously reported by other
authors.21 23 24 25 In this study, we have used a technique
for optically measuring conduction and repolarization characteristics
in the Langendorff-perfused mouse heart at 37°C.
Parameters of ventricular conduction, including
CV and APD, have been described in several small
mammals.26 27 28 The ratio of longitudinal to transverse CVs
in murine myocardium is similar to those reported for other
species.29 30
Critical Mass
For >80 years since Garrey's1 experiments, there
has been a general belief that cardiac tissue smaller than a certain
critical mass cannot support fibrillatory activity. This concept has
been applied not only to comparisons between heart tissue of different
sizes from the same species, but also to hearts of different species.
In ventricular tissue, this critical size was originally
estimated by Garrey1 to be 4 cm2. By
contrast, recent data have suggested that reentry is possible in
smaller pieces of cardiac tissue.9 13 14 15 West and
Landa31 reported in 1962 that sustained arrhythmic
activity was detected in fragments of rabbit atrial tissue larger than
30 mg in size, with an estimated area >30
mm2. However, they did not map a reentrant
circuit.
In their paper supporting the leading circle hypothesis, Allessie et
al32 were able to induce a rotor in the rabbit
atrium (1000 mm2 in area). The diameter
of the leading circle was estimated at 6 to 8 mm, suggesting that
an area of 30 to 50 mm2 (which we now term
the core) is not sufficient to sustain a rotor. As Allessie et
al32 note, the leading circle must not only supply
centrifugal wavefronts, but it must also provide current to
nonsustained centripetal waves. Thus, from the calculations of Allessie
et al,32 it is not easy to determine the minimum tissue
area that is required to sustain a rotor.
Although the concept of Allessie et al32 was a vast improvement over Mines'33 original idea of anatomical reentry, it has required radical reworking into the spiral wave paradigm to account for an excitable gap and the effects of wavefront curvature. It is therefore a pleasant surprise that the calculations of Allessie et al,32 which are based on a different model using data from heterogeneous atrial tissue, are not in conflict with our observations.
This is the first demonstration and mapping of sustained reentry in an
area of tissue that is <100 mm2. Spach et
al34 and Spach and Josephson35 demonstrated
nonsustained microscopic reentry in highly anisotropic tissue with an
area <10 mm2. This required very slow
propagation velocities (0.028 m/s), which were similar to the
velocities measured near the center of the rotor in our study (Figure 6
). However, in the case of the data of Spach et
al,34 a fully regenerative wavefront must have been
present very close to the rotor center, and hence, the distance
dependence of velocity demonstrated in this study (Figure 6)
cannot be derived from their interpretation. A circuit so anchored
would also not be expected to drift or give rise to the polymorphic
activity we saw in some hearts.
An estimate of the critical mass required for fibrillation has recently
been made by Winfree5 6 7 who used a "rule of thumb" to
suggest that the rotor size in two dimensions is equal to the diffusion
distance during 1 rotor period, and the diameter d of the
rotor can be given by
d=(2Dt)1/2, where
D is the diffusion coefficient and t is the rotor
period. Average estimates of D found in the literature range
from 0.5 to 2.0 cm2/s. Using these values and the
rotation period of the reentrant activity found in the mouse heart
(70 ms), we come to a range for d of 0.53 to 1.0 cm. This
estimate falls within the long axis of the mouse ventricle of 0.6 cm.
As such, it is not entirely unexpected to find a stable rotor in a
mouse heart with a ventricular surface area of 1
cm2.
VF has been defined as turbulent cardiac excitation. In this regard,
Winfree5 gives the thickness threshold as 1 rotor diameter
corrected for anisotropy, and an adequate area to allow for the
"slithering" of the rotor as at least 6 times the size of the rotor
in each surface dimension. With these assumptions and some general
approximations, he arrives at a ventricular critical volume
of 12 cm3 (mass of 12 g) for fibrillation. The
caveat is that if rotor size is species dependent, the critical mass
must be calculated for that respective species. This leads to a
paradox, as our observations demonstrate that fibrillation is possible
in the mouse heart. We were unable to directly identify the source of
fibrillatory activity; thus, we cannot exclude multiple reentrant
sources. However, given that we observed only a single wavefront in any
frame during the fibrillatory episodes, our observations are
consistent with previous results10 11 12 showing
that a single drifting rotor can give rise to a polymorphic ECG
compatible with VF. On the basis of these results, it is reasonable to
postulate that an area just larger than that required for reentry could
support fibrillation.
Limitations of the Study
In this study, we have addressed two questions regarding the
induction and maintenance of arrhythmias. First, are
arrhythmias possible in the adult mouse heart of which the
ventricular surface area is <100
mm2? Second, what is the relationship between
wavelength during regular epicardial pacing and the ability to sustain
arrhythmias? The observation of ventricular
arrhythmias in Langendorff-perfused mouse hearts, both in the
absence and in the presence of the electromechanical uncoupler DAM,
answers the first question conclusively. However, because the
measurements of APD and CVs were done only in the presence of DAM,
which has been shown to affect APD in other species,36 37
we cannot be certain whether this agent altered wavelength in these
mouse experiments. Therefore, the quantitative accuracy of the estimate
of the relationship between wavelength and heart size remains somewhat
uncertain. Nevertheless, in the presence of DAM, we have shown that the
size of cardiac tissue that is required to sustain rotors and
fibrillation need not exceed the wavelength measured during regular
pacing. Clearly, the critical mass hypothesis needs revision.
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Acknowledgments |
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This work was supported in part by Grant P01-HL39707 from the National Heart, Lung, and Blood Institute, NIH. Faramarz H. Samie was a Medical Student Fellow of the Howard Hughes Medical Institute.
Received October 7, 1998; accepted May 4, 1999.
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