© 1999 American Heart Association, Inc.
Original Contribution |
Incidence, Evolution, and Spatial Distribution of Functional Reentry During Ventricular Fibrillation in Pigs
From the Departments of Biomedical Engineering (J.M.R., W.M.S., R.E.I.) and Medicine (J.M.R., J.H., W.M.S., R.E.I.), University of Alabama at Birmingham, Birmingham, Ala.
Correspondence to Jack M. Rogers, PhD, University of Alabama at Birmingham, 1670 University Blvd, Volker Hall, B140, Birmingham AL, 35294. E-mail jmr{at}crml.uab.edu
 |
Abstract |
|---|
 Top Abstract IntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
Abstract—Functional reentry has been hypothesized to be an underlying mechanism of ventricular fibrillation (VF); however, its contribution to activation patterns during fully developed VF is unclear. We applied new quantitative pattern analysis techniques to mapping data acquired from a 21x24 unipolar electrode array (2-mm spacing) located on the ventricular epicardium of 7 open-chest, unsupported pigs. Data epochs 4 seconds long beginning 1, 10, 20, 30, and 40 seconds after electrical induction were analyzed. Reentrant circuits were automatically identified and quantified. We found that 2.3% of activation pathways could unambiguously be classified as reentrant. From scaling analysis, an additional 28% of the pathways may also have been reentrant. Reentry was short-lived with 1.5±1.5 (mean±SD) complete cycles per circuit. The fraction of reentrant pathways, number of cycles per circuit, cycle duration, and area and perimeter of the cores all increased significantly as VF progressed. Core drift speed decreased significantly. Neither the orientation of the cores nor the direction of drift was well predicted by the epicardial fiber orientation (r2=0.108 and 0.138, respectively, by linear regression). Reentrant circuits were clustered in regions of the epicardium. We conclude the following: (1) Epicardial reentry is relatively uncommon and short-lived during VF, suggesting either that sustained reentry is transmural or that mechanisms governing sustained reentry are relatively unimportant to the dynamics of VF. (2) Reentrant circuits become more common, larger, and longer-lived as VF progresses, which may explain a recently observed increase in VF organization during the first minute of VF. (3) The conditions necessary to induce and sustain reentry are distributed nonuniformly.
Key Words: functional reentry • activation pattern • wavetip • wavefront isolation • graph theory
|
Introduction |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
Functional reentry occurs when some event breaks an activation wave, placing the excitation wavefront in contact with its own refractory tail.1 In such a situation, the wavefront pivots around the wavebreak, circling about its tail.1 If uninterrupted, this pattern becomes a sustained, high-frequency source of wavefronts. Functional reentry has often been hypothesized as an underlying mechanism of ventricular fibrillation (VF).2 3 4 5 6 Although it has been clearly demonstrated at the onset of electrically induced VF,7 8 9 the contribution of functional reentry to activation patterns as VF progresses is less clear.
Our laboratory has recently developed a new series of computational
methods for quantifying activation patterns observed in high-resolution
epicardial mapping data.10 These methods are based on
wavefront isolation, in which the individual activation wavefronts
making up a VF episode are isolated from one another, allowing the
episode to be quantified in terms of the statistical properties of the
wavefronts and their interactions. The methods are automatic, allowing
large VF mapping datasets to be objectively analyzed. In the
present study, we extended these methods and applied them to
mapping data acquired from an electrode array covering 
20% of the
epicardium. VF was studied in normal, healthy, in situ porcine
hearts.
These new methods allow us to address, in a quantitative manner, several specific issues relating to the role of reentry in the mechanisms of VF. (1) Recently, many investigators have reported the presence of reentry during developed VF in normal, healthy hearts.2 11 12 13 However, the incidence of reentry, ie, the number wavefronts that are reentrant compared with the number that are not, has never been reported. We compute this parameter, which is critical in determining the importance of reentry during VF. (2) Several studies have shown that after losing organization in the transition from Wiggers' stage I to stage II, VF recovers organization in the remainder of the first minute.14 15 16 We recently reported that this reorganization is characterized by a gradual growth of spatial patterns and proposed that this growth is due to an increase in the size of the area circumscribed by reentrant wavefronts.15 In the present study, we test this hypothesis. (3) The orientation of cardiac muscle fibers is an important determinant of propagation patterns. We therefore test the hypothesis that the orientation and drift direction of reentrant wavefronts correlates with epicardial fiber orientation. (4) VF is widely believed to be perpetuated by a nonuniform dispersion of refractoriness.17 If this is true, we would expect reentry to occur in preferential locations. We therefore test whether reentry is uniformly distributed during VF.
|
Materials and Methods |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
The use of experimental animals in the present study was approved by the Institutional Animal Care and Use Committee at the University of Alabama at Birmingham. All studies were performed in accordance with the guidelines established in the Position Statement of the American Heart Association on Research Animal Use adopted by the American Heart Association on November 11, 1984.
Animal Preparation
Seven 32- to 43-kg pigs (Snyder Farms, Cullman, Ala) were
studied; the hearts weighed 159±38 g. Detailed methods of animal
preparation and instrumentation were described in our previous
study.15 The data analyzed in the present
study include data from the previous work. Briefly, the animals were
anesthetized with sodium pentobarbital, intubated, and
ventilated with a mixture of room air and oxygen. The heart was exposed
through a median sternotomy and instrumented with a 504-electrode
(21x24) plaque sutured to the anterior lateral right
ventricular and medial left ventricular
epicardium. The electrodes were 1-mm-diameter silver spheres with 2-mm
spacing (on centers) in each direction. This spatial resolution has
been shown to be appropriate for mapping VF.18 The plaque
covered 20.16 cm2, which is 20% of the
epicardial surface. The ground reference for the unipolar
recordings was attached to the right leg. Two stainless steel
wires were sutured to the lateral left ventricle at least 2 cm from the
plaque for use as bipolar pacing electrodes. A mesh electrode was
sutured to the left ventricular apex, and a catheter
electrode was inserted into the superior vena cava for use as rescue
defibrillation electrodes.
Data Acquisition
The 504 plaque electrodes were connected to a 528-channel
mapping system.19 The unipolar electrograms were
bandpass-filtered from 0.5 to 500 Hz, sampled at 2 kHz, and
recorded to videotape with 14-bit resolution. Data were
recorded continuously during S1–S2 stimulation and VF. From this
datastream, permanent records 4 to 5 seconds in duration beginning
0, 10, 20, 30, and 40 seconds after induction were saved.
VF was induced using the programmed pacing protocol described previously.15 Cardiac perfusion was not maintained during VF. Six VF episodes were induced in each animal. A rescue biphasic shock at the minimum reliable defibrillation strength (typically 400 to 500 V) was delivered 45 seconds after each induction. A minimum of 15 minutes was allowed to elapse before VF induction was again attempted. On completion of the protocol, the pig was killed by electrically induced VF. The location of the recording plaque was marked, and the heart was excised, weighed, and fixed in 10% formalin.
Determination of Epicardial Fiber Orientation
In 6 hearts, the heart wall under the plaque was cut out and the
epicardium was dissected away using forceps. Under a dissecting
microscope, suture material was inserted in the myocardium
in alignment with the fibers at 16 sites (4x4 grid). The tissue
was then placed under a video camera connected to an image processing
system (Universal Imaging Corp). The fiber orientation at the 16
gridpoints, the coordinates of the gridpoints, and the coordinates of
the 4 corners of the array were acquired. The fiber orientation at any
point was determined from linear interpolation of these data.
Quantitative Analysis of VF Activation Patterns
In each episode, 4-second epochs of VF mapping data beginning 1,
10, 20, 30, and 40 seconds after induction were extracted from the
permanent recordings and transferred to a
high-performance workstation (Silicon Graphics Inc) for
analysis. Four to six episodes in each animal were successfully
recorded and transferred. In total, 179 VF epochs (716 seconds) of
VF were analyzed. To verify the integrity of the data before
quantitative analysis, the activation patterns were visualized
using animated maps of the first temporal derivatives of the 504
unipolar electrograms.
Wavefront Isolation
The basis for the analysis is the decomposition of the
overall activation pattern into its constitutive units. This
decomposition is described in detail elsewhere.10 Briefly,
all 504 electrograms were differentiated using a 5-point digital
filter. The discrete samples of the differentiated signals (one for
each electrode every 0.5 ms) were stored in a 3-dimensional array, 2 of
the dimensions corresponding to the dimensions of the plaque and the
third to time. As in our previous studies,10 15 Active
samples were defined as those for which dV/dt<-0.5
V/s.
Individual wavefronts in the pattern were identified and isolated by
grouping together active samples that were adjacent in space and time.
A specially developed spatiotemporal filter that allows small
discontinuities in wavefronts was then applied.10 15 In
this decomposition of the overall activation pattern, wavefronts, by
definition, end after interaction with other wavefronts. For example,
when 2 or more wavefronts collide and coalesce, the original wavefronts
end at the time of the collision, and a new wavefront results.
Conversely, when a wavefront fractionates into 2 or more parts, the
original wavefront terminates, and 2 or more new wavefronts result. In
this context, the timing of the wavefronts and their interactions can
be summarized as a wavefront graph. Here, the word "graph"
describes a mathematical construct built of line segments, or edges,
connected at nodes. In a wavefront graph, each edge represents
a wavefront. The horizontal coordinates of the 2 endpoints locate the
wavefront in time. The nodes of the graph represent
fractionations and collisions, which we collectively call contacts,
because in the wavefront graph representation, wavefronts
touch at these times. An example of a wavefront graph derived
from 0.5 second of VF is shown in Figure 1
.
|
Because of the frequent contact events during VF, wavefronts typically
have short durations, on the order of tens of milliseconds. However, if
a wavefront terminates with a contact, the propagating activity
associated with the wavefront does not end; it continues with the
contact's resultant wavefront(s). Tracing such a stream of propagating
activity from its appearance on the array through a series of
wavefronts and contacts to its disappearance might seem a more
intuitive definition of a "wavefront." However, because of the
branching nature of the wavefront graphs (eg, Figure 1
), any
particular wavefront might be part of many such streams that connect
the appearance of activity with its disappearance. To contend with this
ambiguity, we introduce a higher level of structure apparent in the
wavefront graphs: families of wavefronts interrelated by contact events
form subgraphs that are disconnected from the remainder of the graph.
In graph theoretical terminology, these subgraphs are called
"components," and algorithms exist for automatically identifying
them.20 Each component contains one or more routes, each
of which is a set of one or more wavefronts that together connect the
appearance of a stream of activity with its disappearance. In Figure 1, there are 6 components, one of which is outlined by a dashed
box. A single route through this component is shown by the large
arrows. In the present study, we will use the number of components
in a VF episode as a measure of the number of propagating
"units."
Initial Reentry Detection
After constructing the wavefront graph and identifying its
components for a VF episode, we identified which components were
reentrant with a 2-step method. In the first step, all routes through a
component were processed in turn. For each route, we counted the number
of electrodes that were activated by the wavefronts in the
route. Next, we counted the number of activations associated with the
route. We defined an activation as dV/dt at an electrode
crossing the activation threshold at least 40 ms after any previous
activation at that electrode. The 40-ms cutoff was chosen to be
slightly shorter than the shortest refractory period observed during VF
by Cha et al.7 For nonreentrant routes, the ratio of the
number of activations to the number of electrodes activated was
1.0, indicating that no electrodes were activated more than
once by the same route. Following Bollacker et al,21 we
defined potentially reentrant routes as those for which this ratio was
at least 1.1. Wavefront graph components were considered potentially
reentrant if they contained at least one reentrant route. If a
component had multiple reentrant routes, only the route with the
largest ratio was used in the analyses that follow.
Reentry Confirmation and the Wavetip Path
Confirmation of the presence of reentry and our subsequent
analyses use the concept of the wavetip, ie, the broken end of
a reentrant wave. The path traced out by the wavetip defines many of
the wave's interesting dynamic properties. In the event that the
wavetip path follows a fixed course from cycle to cycle, the region
enclosed by the path, which is excitable but not excited by the wave,
is known as the "core."1 In computer modeling studies
of functionally reentrant waves, the wavetip is typically defined as
the crossing point of the contours of 2 variables, one determining
the state of excitation and the other the state of
recovery.22 In experimental preparations of cardiac
tissue, the latter variable is generally not available, and so the
wavetip path has been estimated by inspection of isochronal contour
maps,23 analyzing frame stack plots of optically
recorded transmembrane potential data,6 24 manually
locating the wavetip in animated displays of activation times picked
from electrical mapping data,2 or by identifying phase
singularities.12
We devised a new method for accurately and automatically finding the
wavetip path associated with a reentrant wavefront graph component. We
define the wavetip path as the shortest possible path connecting active
samples in each timestep of a reentrant component. Only active samples
on the outer layer of the wavefronts in the component (ie, active
samples that have at least one nonactive neighbor) may lie on the
wavetip path. This idea is illustrated in Figure 2A. Each block represents an
active sample in a counterclockwise reentrant component. Each gray
level represents a different timestep (note that only 4
timesteps of the entire reentrant component are shown). The shortest
path running through a sample in each timestep is indicated by the
circles and clearly tracks the pivoting end of the wave. Note that the
hatched sample in the second timestep of Figure 2A is not on the
outer layer of the component and hence cannot be on the wavetip
path.
|
A network optimization algorithm was used to find wavetip paths
(Figure 2B and 2C). First, a directed graph was constructed in
which a node represented every eligible active sample in
the most-reentrant route (ie, the route with the largest ratio of
activations to activated electrodes) through the wavefront
graph component. The edges of this graph connected each active sample
with all of the active samples in the succeeding timestep. Each edge
was then weighted with the distance between the electrodes associated
with the active samples connected by the edge. The graph therefore
defined all possible paths that contain one active sample in each
timestep. The length of any path was simply the sum of the weights of
the edges along the path. A hypothetical wavefront containing 6 active
samples in 3 timesteps is illustrated in Figure 2B. The graph
and associated edge weights constructed from this wavefront are shown
in Figure 2C.
The shortest path through such a graph is our desired wavetip path. To find it, we used a well-known algorithm from graph theory, Dijkstra's shortest path algorithm.25 Given a starting node, Dijkstra's algorithm finds the shortest path to the remaining nodes in the graph. We therefore ran the algorithm for each active sample in the first timestep, each time setting the active sample as the start node. The shortest path from a start node to an active sample in the last timestep, which also crossed itself at least once, was taken as the wavetip path. If none of the paths crossed themselves, then the component was deemed nonreentrant.
If there are multiple paths with the same length, then Dijkstra's algorithm selects as the shortest the one that contains the fewest active samples. If there is still a tie, then the algorithm selects the first such it encounters. This order is dictated by the internal numbering of the active samples and so is effectively arbitrary.
Figure 2D illustrates an example of a wavetip path computed by
this method. Each snapshot shows the active samples associated with a
single reentrant component during VF (all other active samples were
removed from the figure for clarity). The black sample in each frame is
the current location of the wavetip, and the fine black line traces its
path. This particular component completed one full cycle.
It is well-known that double potentials are often found adjacent to lines of block, the first deflection registering local activation and the second an electrotonic response to a wavefront on the opposite side of the line of block.26 If a wavetip were to follow a U-shaped course around a line of block, yet fail to reenter, the second deflection of a double potential could be misinterpreted as a second local activation, thus causing a complete reentrant circuit to be incorrectly registered. Our algorithms minimize this possibility in 2 ways. First, we require at least 10% of electrodes to be reactivated before reentry is recognized, and second, reentry is not confirmed unless the wavetip path crosses itself. These conditions help prevent sporadic activations incorrectly registered on the "wrong" side of a line of block from being interpreted as the completion of reentry.
Wavetip Path Loops
We next analyzed each wavetip path to identify closed
loops. Figure 3A shows an example. We
will refer to these loops as cycles, because for a stationary reentrant
circuit, each such loop corresponds to a single traversal of the
circuit. The cycle identification process began by searching pairs of
segments in the wavetip path for intersections. When intersections were
found, the involved segments were split, if necessary, so that the
intersections only occurred at segment endpoints. This operation was
implemented with an efficient line-sweep algorithm.27
Because of finite spatial and temporal resolution and the relatively
slow speed of the wavetip, the wavetip was often located at the same
electrode site for several timesteps. Thus, the time required to
traverse a segment of the wavetip path was often greater than the
timestep (0.5 ms). If a segment was split at an intersection, the
durations of the 2 new segments were fractions of the original duration
in proportion to their spatial length.
|
Next, the wavetip path was traversed, one segment at a time, keeping
track of which segment endpoints had been visited. When an endpoint was
visited for the second time, the segments intervening the first and
second visits were identified as members of a cycle (dashed line in
Figure 3A). An ambiguity arises for reentrant circuits with more
than one cycle. Consider the wavetip path in Figure 3B. There
are clearly 2 cycles, yet because the wavetip does not follow a
repeating course, it is not immediately obvious where each cycle begins
and ends. To contend with this ambiguity, we allow cycles to nest, that
is, an inner cycle (eg, the bold line in Figure 3B) can begin
and end after an outer cycle (eg, the dashed line in Figure 3B)
has begun, but before it has ended. Unlimited levels of nesting are
allowed. This definition always yields measurable cycles, even for
complex wavetip paths with multiple overlapping cycles of differing
sizes.
Core Excitability
To determine whether reentry was functional or anatomical, we
identified the electrodes that were encircled by each cycle and checked
to see if they were ever activated either in the same VF
dataset or in other datasets from the same animal. Unactivated
electrodes would suggest an anatomical obstacle in the interior of the
circuit.
Cycle Quantification
Once the segments of the cycles were identified, the perimeters
and durations of the cycles were calculated by summing the lengths and
durations of their segments. Segments belonging to nested cycles were
not included in the sums for the corresponding outer cycles. The areas
and centroids of the cycles were computed as well.
We computed cycle orientation and aspect ratio by forming an inertia
tensor:
 |
is
indicated by the L-shaped symbol. The centroid is at the angle of the
"L." The arms of the "L" are 33% of the respective principal
lengths. The aspect ratio of this cycle is 1.51.
Drift Velocity
If a wavetip path completed 2 or more cycles, we estimated the
average drift velocity of the core by plotting the x- and
y-coordinates of the cycle centroids against the average of
the cycle's starting and ending times. Straight lines were fitted to
these data by least-squares. The slopes of these 2 lines gave the
average x- and y- drift velocity components from
which average drift speed and direction were computed.
|
Results |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
In the 179 VF epochs analyzed, there were a total of 19 441 components. Of these, 448 (2.3%) were reentrant. In the 448 reentrant circuits, there were a total of 681 complete cycles (1.5±1.5 cycles per circuit). Very few circuits had more than 1 or 2 cycles, but one had 18 (Figure 4
). We measured the
duration, area, perimeter, and aspect ratio of each cycle, and for
components with multiple cycles, the average core drift speed, and the
fraction of time the wavetip spent between closed cycles relative to
time spent in cycles. Values are presented as mean±SD for
these parameters in the
Table.
|
|
In 651 of the cycles, all of the electrodes in the core region were activated at least once by other wavefronts in the same dataset. In the remaining 30 cycles, the 1 or 2 core electrodes that were unactivated in the same dataset were activated in other datasets recorded from the same animal. This indicates that the core regions were excitable and that all reentry was functional, although some circuits may have been anchored to heterogeneities too small to be detected with our spatial resolution (2 mm).
We tested the dependence on time of 7 parameters: the
fraction of components that were reentrant, the number of cycles per
reentrant circuit, the duration of the cycles, the area of the cycles,
the perimeter of the cycles, the aspect ratio of the cycles, and the
drift speed of the core. Because the distribution of some of these
parameters was markedly nonnormal, we used the
nonparametric Kruskal-Wallis H statistic to test
for a time effect.29 The fraction of reentrant
components, number of cycles, and area, perimeter, and duration of
cycles all increased significantly between 1 and 40 seconds after
induction (Figure 5A through 5E). Aspect
ratio did not change (Figure 5F), and drift speed decreased
(Figure 5G).
|
To determine if the reentrant cycles were aligned with the epicardial
fibers, in 6 of the hearts, we estimated the fiber orientation at the
centroid of each cycle. The orientation of the principal axis of the
cycles was poorly predicted by the corresponding epicardial fiber
orientation (Figure 6). The coefficient
of determination (r2 value) for a
simple linear regression was 0.108, indicating that only 10% of the
variance in cycle orientation was accounted for by a linear fit to
fiber orientation. Because the orientation of the cycles becomes
arbitrary as the aspect ratio approaches 1, we repeated the linear
regression using (aspect ratio-1) to weight each observation. The
strength of the linear association in this analysis did not
change.
|
We also sought a linear relationship between the direction of core
drift and fiber orientation. In 6 hearts, we found a reentry center for
each reentrant circuit by averaging the cycle centroids. We then
determined the fiber orientation at these sites. If necessary, the
direction of drift was reversed so that the difference in orientation
was always less than 90°. The relationship between the 2
variables was weak, with r2=0.138
by simple linear regression (Figure 7).
|
To determine if reentry occurs in preferred locations, we plotted the
spatial locations of the reentry centers found above for each heart
individually and for all 7 hearts together (Figure 8). In each heart, the reentry centers
tended to cluster in specific regions (Figure 8A through 8G),
although these regions did not appear to be consistent from
heart to heart (Figure 8H). To rigorously test if the reentry
centers differed from a uniform random distribution, we implemented a
2-dimensional Kolmogorov-Smirnov (KS) goodness-of-fit
test.30 This test determines, within specified confidence
bounds, whether a sample of points was drawn from a uniform probability
density function. Given that reentry centers were unlikely to fall near
the boundary of the array, because of the finite radius of the cycles,
to avoid biasing the KS test, we computed the mean of all principal
axis lengths (both major and minor) and offset the KS analysis
window by half of this length (5.2 mm) from all boundaries. The
resulting window is shown by the dashed box in Figure 8H. In all
8 cases, the distribution of reentry centers differed significantly
(P<0.05) from a uniform random distribution. The
correlation coefficient of the distribution of all reentry centers
(Figure 8H) is -0.21 (P<0.0001).
|
|
Discussion |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
Major Findings
The major findings of the present study are as follows. (1) Complete reentrant circuits are present on the epicardium during VF but are relatively uncommon and most persist for only 1 or 2 cycles. (2) The characteristics of the reentrant circuits change with time, with the circuits becoming more common, larger, longer-lived, and more slowly drifting as VF progresses. (3) The epicardial fiber orientation is only weakly correlated with the principal axes of the reentrant pathways and the direction in which the centers of the reentrant pathways drift. (4) The reentrant pathways are not uniformly distributed spatially; rather, they tend to cluster in specific regions that vary from heart to heart.
These findings were established using a new series of quantitative methods for analyzing cardiac mapping databased on graph theory and computational geometry. Because these methods are automatic and objective, the results are unaffected by observer bias or interobserver variability. The results can be affected by user-specified parameters; however, the sensitivity of the methods to these parameters has been characterized,10 and appropriate values were chosen and consistently applied.
Limitations
Duration and Spacing of Data Epochs
In our previous study,15 we analyzed data
epochs of 0.5 second in duration. This choice was dictated by our use
of the "multiplicity" parameter for quantifying
organization.16 The analyses used in the
present study have no such upper limit on epoch duration; thus,
dividing each VF episode into contiguous epochs would have been
appropriate. However, because of technical limitations of the data
archival system, the data epochs we could transfer to a computer for
analysis were limited to 4 to 5 seconds. We therefore chose 4
seconds as the length of our analysis window. This temporal
sampling—4 seconds of every 10—should not have affected our results
because (1) 4 seconds is much longer than the durations of the
reentrant circuits we found, almost all of which were well under 1
second (the longest-lived outlier persisted for about 2 seconds); and
(2) our previous studies indicate that no additional trends in VF
patterns are revealed by temporal resolution finer than 10
seconds.10 15 16
Mapping Limitations
Many of the limitations of the present study are common to
extracellular electrical mapping studies from epicardial arrays. (1)
The array covered only 20% of the epicardium, and so complete
activation pathways could not be determined. As we discuss in the
following section, this must be considered in our estimate for the
incidence of reentry. It may also have biased our estimate of the
number of cycles per reentrant circuit, because the cycle count of a
nonstationary circuit near the edge of the array will be erroneously
low if the circuit drifts out of the mapped region. However, this is
unlikely to have significantly affected our results, because so few
circuits had multiple cycles (Table) and the drift rate for
circuits that did was relatively slow (4 mm per cycle). In
addition, because data were recorded only from the anterior right
ventricle and a small portion of the left ventricle, activation
patterns in other regions of the heart could have been markedly
different. (2) Because mapping was confined to the surface of the
heart, intramural reentry could not be detected. The statistical
properties of reentry could have been different if, for example, the
mapping plane cut through the heart wall. (3) Our spatial resolution
was 2 mm, which is in the upper range of that recommended by Bayly
et al.18 Finer details of the reentrant cycles may have
emerged with greater electrode density. (4) We only analyzed
data up to 44 seconds after induction. Subsequent changes in activation
patterns were not studied.
Figure-of-Eight Reentry
Components arising from figure-of-eight reentry have 2 counter
rotating wavetip paths. However, because our wavetip tracking method
finds only the single shortest wavetip path for each reentrant
component, these components could not be identified as such. Thus, if a
component had 2 wavetips, only the parameters of the
shortest wavetip path were included in our results. Assuming that the 2
wavetips in a figure-of-eight pattern behave similarly (eg, have
similar cycle area and duration), this should not have affected our
results. In particular, our results relating to the incidence of
reentry are not affected, because they are based on counting reentrant
components (ie, the complex of wavefronts associated with the paired
wavetips) not the wavetips themselves.
Activation Rate and Cycle Duration
In the present study, overall activation rates, as estimated
from the reciprocal of the cycle durations shown in Figure 5C, are faster than the average activation rates estimated in our previous
publication.15 We attribute this difference primarily to 2
factors. (1) When reentry is nonstationary, as it was in the
present study, the duration of closed cycles underestimates the
period of the repeating pattern, which should include the duration of a
closed cycle plus the interval until the beginning of the next closed
cycle. We found that in wavetip paths with multiple cycles, time
between cycles was 17% of cycle duration (Table). Wavetip paths
with a single cycle typically include a significant interval exclusive
of the closed cycle as well (eg, Figure 3A). Therefore, as a
rough estimate, activation rate at a reentrant site should be corrected
upward by 17%. (2) The activation rates in the earlier study were
computed using data from the entire mapped region, including regions
where block was occurring, and the local rate was therefore slower.
However, estimating overall activation rate from sites of reentry
biases the computation to specific regions and times where activation
is probably at its fastest and therefore overestimates the overall
activation rate.
In Figure 5C, it is apparent that a few of the cycle durations
are quite short—shorter, in fact, than the 40-ms refractory period we
used to detect potentially reentrant components. We attribute these
short cycles (16 of 681) to failure of our algorithms to screen out
false reentry due to double potentials (see Materials and Methods).
Although the effect is minor, these short cycles also bias the overall
activation rate upward.
Contribution of Reentry to VF Activation Patterns
In the present study, the contribution of reentry to the
overall activation pattern was quantified by the percentage of
wavefront graph components that completed at least one reentrant cycle
(2.3%; of all datasets, 448 of 19 441 components). This is a lower
bound; many of the nonreentrant components may in fact have been due to
reentrant circuits whose wavetip path was either partially or totally
out of the mapped region. Using a scaling argument, we can estimate an
upper bound for the percentage of epicardial wavefronts that were due
to reentry. Because of the finite size of the reentrant cycles, the
area sampled for reentrant circuits is not the total mapped region but
is rather the area obtained by offsetting all 4 boundaries by half of
the mean principal length of the cycles. This region (shown by the
dotted line in the lower right panel of Figure 8) has an area of
1188 mm2 and covers 12% of the
epicardium (assuming a total epicardial area of 10 000
mm2). Assuming a spatially uniform distribution
of reentrant pathways, we therefore estimate that there were a total of
448/0.1188=3771 reentrant pathways, of which 3771-448=3323 were not
located in our mapped region. Assuming further that these 3323 circuits
each persisted for 1.5 cycles, and that each cycle emitted a wave that
propagated into the mapped region, we estimate that 4985 of the
observed components were due to reentrant circuits not fully contained
within the mapped region. Thus, as many as (4985+448)/19 441=27.9% of
the observed components may have been due to epicardial reentry. This
estimate is an upper bound, because it is unlikely that all wavefronts
generated anywhere on the heart could propagate into the mapped region.
Thus, the true percentage of reentrant wavefront graph components is
likely to lie between 2.3% and 27.9%.
There are 3 possible classifications for the nonreentrant components. (1) They may have been due to reentry that did not complete a full cycle. (2) They may have been due to intramural reentry. Reentry of this type cannot be detected from epicardial recordings: when a wavefront emanating from an intramural reentrant source reaches the epicardium, it spreads away in all directions and cannot be distinguished from a wavefront generated by a nonreentrant source. (3) They may have been truly nonreentrant. A wave of the third type must either extend all the way across the recording array or close on itself in an expanding ring. If it does not, then a wavebreak exists, and the wave is therefore functionally reentrant (ie, type 1 above).1 24 31 Gray et al12 recently reported that for every wavebreak (phase singularity in their terminology) that completed at least one full circuit, there were four that did not. This estimate implies that a large percentage—perhaps all—of wavefront graph components not identified as reentrant were in fact due to reentry of type 1 above.
Temporal Changes in Reentry Characteristics
In our previous study,15 we found that the size of
spatial patterns increased between 10 and 40 seconds after induction.
Based on the theory of excitable media,31 we proposed that
this change was due to growth in the size of reentrant circuits
secondary to diminishing excitability and lengthening refractory
periods due to metabolic changes caused by early
ischemia in the unsupported fibrillating hearts. Our
present data strongly support this hypothesis: between 1 and 40
seconds after induction, cycle duration, area, and perimeter increased
(Figure 5C through 5E). During this same period, the stability
of reentry appeared to increase, with reentrant wavefront graph
components becoming more common and persisting for more cycles (Figure 5A and 5B). The apparent increase in reentry incidence may have
been secondary to the increase in persistence; ie, as the duration of
the reentrant components increased, more components completed their
first cycle and could therefore be identified as reentrant. We did not
observe any changes consistent with the loss of organization
usually reported for the first few seconds of VF.15 This
was probably because our first data epoch began too late (1 second
after induction) and was too long (4 seconds) to resolve these early
changes.
Cycle Aspect Ratio and Orientation
The aspect ratio of the reentrant cycles did not change with time
(Figure 5F), suggesting that aspect ratio was determined by some
structural characteristic of the heart, such as fiber orientation, that
does not vary with time. However, a correlation analysis to
determine how well the orientation of the cycles was predicted by the
epicardial fiber orientation found a weak relationship (Figure 6) with only 10% of the variance in cycle orientation
accounted for by the epicardial fiber orientation. This finding was
surprising, because previous studies have reported that reentrant cores
align well with the fiber orientation.2 24 One explanation
for this is that cycle orientation is determined by fiber orientation,
but that the fiber orientations at all depths through the
ventricular wall contribute, not just the epicardial
orientation. Thus, reentrant circuits in the 2-dimensional preparation
used by Pertsov et al24 would be expected to align more
closely with the epicardial fibers. In the study by Lee et
al,2 only two thirds of reentrant circuits were reported
to align with fibers, and in these, the 2 angles were not quantified.
Thus, more detailed analysis may have yielded results similar
to ours.
Core Drift Speed
Movement of the reentrant core has been observed both in
experimental preparations and in models32 and has been
attributed to an interplay between the excitability and refractory
period of homogeneous tissue (ie, meander),32
gradients in electrophysiological
properties,32 or gradients in fiber
orientation.33 In the present study, we found that the
drift speed decreased as VF progressed (Figure 5G), and
furthermore, that the direction of drift correlated only weakly with
epicardial fiber orientation
(r2=0.138), which is
consistent with previous reports.24 34 35
These data suggest that core movement was due to either meander or
functional gradients that diminished as VF progressed.
Spatial Distribution of Reentry
The centers of the reentrant circuits were not uniformly
distributed over the mapped region; rather, in each heart, there were
specific regions in which reentry tended to cluster (Figure 8A
through 8G). This departure from a uniform random distribution was
statistically significant. When the reentry centers from all hearts
were plotted together, the distribution was still significantly
nonuniform, although the clustering was less striking (Figure 8H). Some of the variation from heart to heart may have resulted
from small changes in the location of the electrode array. The
correlation coefficient of the overall distribution was -0.21,
indicating that reentry was most likely to be observed along a line
roughly perpendicular to the left anterior descending coronary
artery. These data indicate that there were specific structural or
functional heterogeneities that either made reentrant wavebreaks more
likely to form in particular locations, or stabilized existing
wavebreaks, making them more likely to complete a full cycle. A
structural feature that may be involved is the attachment of papillary
muscles to the bulk myocardium. Such sites have been
implicated in the formation and stabilization of
reentry.36
Implications for Mechanisms of VF
The results from our present and previous
studies15 indicate that although wavebreaks may be very
common during reentry, the associated wavefronts complete a full cycle
relatively infrequently, and circuits completing more than 2 cycles are
even less common (Figure 4). There are 2 possible
interpretations of this finding. (1) If persistent reentrant circuits
drive VF, then they are either transmural or located in another region
of the heart. (2) Phenomena governing the initiation and termination of
reentry play a larger role in the dynamics of VF in in situ hearts than
phenomena, such as rapid drift,6 that involve the behavior
of persistent reentrant circuits.
There are 2 broad classes of theory that address the dynamics of wavefronts during VF. The classical model relies on an underlying patchy heterogeneity of recovery properties.17 When a wavefront propagates over a region with delayed recovery, part of the wavefront may block, creating one or more wavebreaks. Uniformly decreasing excitability and lengthening mean refractory periods in such a medium make block more likely to occur and should therefore lead to a more complex and highly fractionated activation pattern.37 More recent proposals hold that the proliferation of wavefronts during VF occurs when reentrant wavefronts break up into multiple child reentrant wavefronts. One proposed mechanism for this phenomenon is spiral breakup, which is caused by oscillatory instabilities that occur when the slope of the tissue's action potential duration restitution curve exceeds 1.0.38 39 40 41 Other proposed mechanisms involve the development of bends in the central filament of 3-dimensional reentrant vortices. When these bends contact the tissue's boundaries, they are annihilated, effectively cutting the filament in two.42 Most of these newer mechanisms share the property that decreasing the excitability of the medium stabilizes reentrant circuits and retards their proliferation,40 42 although one proposed mechanism makes the opposite prediction.43 Thus, our finding that reentry stabilizes as fibrillation proceeds and the tissue becomes depressed through ischemia provides experimental support for the notion that VF is maintained by the dynamic proliferation of reentrant wavefronts.
On the other hand, the classic nonuniform dispersion of refractoriness hypothesis predicts that reentry should occur at preferred sites, whereas the newer mechanisms do not depend on patchy failure and therefore predict a uniform distribution of reentry. Thus, our finding that reentry is nonuniformly distributed would seem to contradict our conclusion of the previous paragraph. The two findings may be reconciled by considering that spiral breakup has been reported to occur only in specific tissue property ranges.5 Thus, spiral breakup may be responsible for wavebreak formation, but the conditions in which it occurs may be nonuniformly distributed. Likewise, the filament instability model relies on filament bends coming into contact with the heart's boundaries. The complex shape of the heart is likely to predispose this event to occur at specific locations.
|
Acknowledgments |
|---|
This work was supported in part by grants from the National Institutes of Health (HL-28429 and HL-33637), the Whitaker Foundation, and the American Heart Association (9820030SE).
Received August 31, 1998; accepted February 12, 1999.
|
References |
|---|
|
TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
|---|
1. Davidenko JM, Salomonsz R, Pertsov AM, Baxter WT, Jalife J. Effects of pacing on stationary reentrant activity. Theoretical and experimental study. Circ Res. 1995;77:1166–1179.
2.
Lee JJ, Kamjoo K, Hough D, Hwang C, Fan W, Fishbein
MC, Bonometti C, Ikeda T, Karagueuzian HS, Chen PS. Reentrant wave
fronts in Wiggers' stage II ventricular fibrillation.
Characteristics and mechanisms of termination and spontaneous
regeneration. Circ Res. 1996;78:660–675.
3.
Winfree AT. Electrical turbulence in three-dimensional
heart muscle. Science. 1994;266:1003–1006.
4. Winfree AT. Mechanisms of cardiac fibrillation. Science. 1995;270:1224–1225.
5. Panfilov AV, Hogeweg P. Mechanisms of cardiac fibrillation. Science. 1995;270:1223–1224.
6.
Gray R, Jalife J, Panfilov A, Baxter W, Cabo C,
Davidenko J, Pertsov A. Mechanisms of cardiac fibrillation.
Science. 1995;270:1222–1223.
7.
Cha Y, Birgersdotter-Green U, Wolf P, Peters B, Chen
P. The mechanism of termination of reentrant activity in
ventricular fibrillation. Circ Res. 1994;74:495–506.
8.
Chen P-S, Wolf PD, Dixon EG, Danieley ND, Frazier DW,
Smith WM, Ideker RE. Mechanism of ventricular vulnerability
to single premature stimuli in open-chest dogs. Circ Res. 1988;62:1191–1209.
9. Frazier D, Wolf P, Wharton J, Tang A, Smith W, Ideker R. Stimulus-induced critical point. Mechanism for electrical initiation of reentry in normal canine myocardium. J Clin Invest. 1989;83:1039–1052.
10. Rogers JM, Usui M, KenKnight BH, Ideker RE, Smith WM. A quantitative framework for analyzing epicardial activation patterns during ventricular fibrillation. Ann Biomed Eng. 1997;25:749–760.[Medline] [Order article via Infotrieve]
11. Hillsley RE, Bollacker KD, Simpson EV, Rollins DL, Yarger MD, Wolf PD, Smith WM, Ideker RE. Alteration of ventricular fibrillation by propranolol and isoproterenol detected by epicardial mapping with 506 electrodes. J Cardiovasc Electrophysiol. 1995;6:471–485.[Medline] [Order article via Infotrieve]
12. Gray RA, Pertsov AM, Jalife J. Spatial and temporal organization during cardiac fibrillation. Nature. 1998;392:75–78.[Medline] [Order article via Infotrieve]
13. Witkowski FX, Leon LJ, Penkoske PA, Giles WR, Spano ML, Ditto WL, Winfree AT. Spatiotemporal evolution of ventricular fibrillation. Nature. 1998;392:78–82.[Medline] [Order article via Infotrieve]
14. Bayly PV, Johnson EE, Wolf PD, Greenside HS, Smith WM, Ideker RE. A quantitative measurement of spatial order in ventricular fibrillation. J Cardiovasc Electrophysiol. 1993;4:533–546.[Medline] [Order article via Infotrieve]
15. Huang J, Rogers JM, KenKnight BH, Rollins DL, Smith WM, Ideker RE. Evolution of the organization of epicardial activation patterns during ventricular fibrillation. J Cardiovasc Electrophysiol. 1998;9:1291–1304.[Medline] [Order article via Infotrieve]
16. Rogers JM, Usui M, KenKnight BH, Ideker RE, Smith WM. The number of recurrent wavefront morphologies: a method for quantifying the complexity of epicardial activation patterns. Ann Biomed Eng. 1997;25:761–768.[Medline] [Order article via Infotrieve]
17. Moe GK, Reinboldt WC, Abildskov JA. A computer model of atrial fibrillation. Am Heart J. 1964;67:200–220.[Medline] [Order article via Infotrieve]
18. Bayly PV, Johnson EE, Idriss SF, Ideker RE, Smith WM. Efficient electrode spacing for examining spatial organization during ventricular fibrillation. IEEE Trans Biomed Eng. 1993;40:1060–1066.[Medline] [Order article via Infotrieve]
19. Wolf PD, Rollins DE, Simpson EV, Smith WM, Ideker RE. A 528 channel system for the acquisition and display of defibrillation and electrocardiographic potentials. In: Murray M, Arzbaecher R, eds. Computers in Cardiology. London, England: IEEE Computer Society Press; 1993:125–128.
20. Mehlhorn K. Data Structures and Algorithms. Berlin, Germany: Springer-Verlag; 1984.
21. Bollacker KD, Simpson EV, Hillsley RE, Blanchard SM, Gerstle RJ, Walcott GP, Callihan RL, King MC, Smith WM, Ideker RE. An automated technique for identification and analysis of activation fronts in a two-dimensional electrogram array. Comput Biomed Res. 1994;27:229–244.[Medline] [Order article via Infotrieve]
22. Barkley D, Kness M, Tuckerman LS. Spiral-wave dynamics in a simple model of excitable media: the transition from simple to compound rotation. Phys Rev A. 1990;42:2489–2492.[Medline] [Order article via Infotrieve]
23. Fast VG, Pertsov AM. Drift of a vortex in the myocardium. Biophysics. 1990;35:489–494.
24.
Pertsov AM, Davidenko JM, Salomonsz R, Baxter WT,
Jalife J. Spiral waves of excitation underlie reentrant activity in
isolated cardiac muscle. Circ Res. 1993;72:631–650.
25. Dijkstra EW. A note on two problems in connection with graphs. Numerische Mathematik. 1959;1:269–271.
26.
Olshansky B, Moreira D, Waldo AL. Characterization of
double potentials during ventricular
tachycardia. Studies during transient entrainment.
Circulation. 1993;87:373–381.
27. Bentley JL, Ottmann TA. Algorithms for reporting and counting geometric intersections. IEEE Trans Comput. 1979;C-28:643–647.
28. Ginsberg JH. Advanced Engineering Mechanics. 2nd ed. Cambridge, England: Cambridge University Press; 1995.
29. Norusis MJ. SPSS 6.1 Base System User's Guide. Chicago, Ill: SPSS; 1994. -
30. Fasano G, Franceschini A. A multidimensional version of the Kolmogorov-Smirnov test. Mon Notices Royal Astronom Soc. 1987;225:155–170.
31. Zykov VS. Simulation of Wave Processes in Excitable Media. New York, NY: Manchester University Press; 1987.
32.
Fast VG, Kleber AG. Role of wavefront curvature in
propagation of cardiac impulse. Cardiovasc Res. 1997;33:258–271.
33. Rogers JM, McCulloch AD. Nonuniform muscle fiber orientation causes spiral wave drift in a finite element model of cardiac action potential propagation. J Cardiovasc Electrophysiol. 1994;5:496–509.[Medline] [Order article via Infotrieve]
34. Davidenko JM, Pertsov AV, Salomonsz R, Baxter W, Jalife J. Stationary and drifting spiral waves of excitation in isolated cardiac muscle. Nature. 1992;355:349–351.[Medline] [Order article via Infotrieve]
35. Gray RA, Jalife J. Self-organized drifting spiral waves as a mechanism for ventricular fibrillation. Circulation. 1996;94:I-48. Abstract.
36. Kim YH, Masaaki Y, Wu TJ, Valderrabano M, Doshi R, Karaguezian HS, Chen PS. Role of papillary muscle in the generation and maintenance of reentry during ventricular tachycardia and fibrillation. PACE Pacing Clin Electrophysiol. 1998;21:982. Abstract.
37.
Smith JM, Cohen RJ. Simple finite-element model
accounts for a wide range of cardiac dysrhythmias. Proc Natl Acad
Sci U S A. 1984;81:233–237.
38. Courtemanche M. Complex spiral wave dynamics in a spatially distributed ionic model of cardiac electrical activity. Chaos. 1996;6:579–600.[Medline] [Order article via Infotrieve]
39. Karma A. Spiral breakup in model equations of action potential propagation in cardiac tissue. Phys Rev Lett. 1993;71:1103–1106.[Medline] [Order article via Infotrieve]
40. Panfilov A, Hogeweg P. Spiral breakup in a modified FitzHugh-Nagumo model. Phys Lett A. 1993;176:295–299.
41.
Gerhardt M, Schuster H, Tyson JJ. A cellular automaton
model of excitable media including curvature and dispersion.
Science. 1990;247:1563–1566.
42. Fenton F, Karma A. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. Chaos. 1998;8:20–47.[Medline] [Order article via Infotrieve]
43. Biktashev VN, Holden AV, Zhang H. Tension of organizing filaments of scroll waves. Philos Trans R Soc London A. 1994;347:611–630.
This article has been cited by other articles:
 |
|
 |
|
  R. H. Keldermann, K. H. W. J. ten Tusscher, M. P. Nash, C. P. Bradley, R. Hren, P. Taggart, and A. V. Panfilov A computational study of mother rotor VF in the human ventricles Am J Physiol Heart Circ Physiol, February 1, 2009; 296(2): H370 - H379. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 N. A. Trayanova The Long and the Short of Long and Short Duration Ventricular Fibrillation Circ. Res., May 23, 2008; 102(10): 1151 - 1152. [Full Text] [PDF]
|
|
|
|
|
|
L. Li, Q. Jin, J. Huang, K.-A. Cheng, and R. E. Ideker Intramural Foci During Long Duration Fibrillation in the Pig Ventricle Circ. Res., May 23, 2008; 102(10): 1256 - 1264. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
R. H. Keldermann, K. H. W. J. ten Tusscher, M. P. Nash, R. Hren, P. Taggart, and A. V. Panfilov Effect of heterogeneous APD restitution on VF organization in a model of the human ventricles Am J Physiol Heart Circ Physiol, February 1, 2008; 294(2): H764 - H774. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. H.W.J. Ten Tusscher, R. Hren, and A. V. Panfilov Organization of Ventricular Fibrillation in the Human Heart Circ. Res., June 22, 2007; 100(12): e87 - e101. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Masse, E. Downar, V. Chauhan, E. Sevaptsidis, and K. Nanthakumar Ventricular fibrillation in myopathic human hearts: mechanistic insights from in vivo global endocardial and epicardial mapping Am J Physiol Heart Circ Physiol, June 1, 2007; 292(6): H2589 - H2597. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. W. Kay, G. P. Walcott, J. D. Gladden, S. B. Melnick, and J. M. Rogers Lifetimes of epicardial rotors in panoramic optical maps of fibrillating swine ventricles Am J Physiol Heart Circ Physiol, October 1, 2006; 291(4): H1935 - H1941. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 J. P. Daubert, W. Zareba, W. J. Hall, C. Schuger, A. Corsello, A. R. Leon, M. L. Andrews, S. McNitt, D. T. Huang, A. J. Moss, et al. Predictive Value of Ventricular Arrhythmia Inducibility for Subsequent Ventricular Tachycardia or Ventricular Fibrillation in Multicenter Automatic Defibrillator Implantation Trial (MADIT) II Patients J. Am. Coll. Cardiol., January 3, 2006; 47(1): 98 - 107. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 S. P. Thomas, A. Thiagalingam, E. Wallace, P. Kovoor, and D. L. Ross Organization of Myocardial Activation During Ventricular Fibrillation After Myocardial Infarction: Evidence for Sustained High-Frequency Sources Circulation, July 12, 2005; 112(2): 157 - 163. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. Taneja, G. Horvath, D. K. Racker, D. Johnson, J. Goldberger, and A. Kadish Is there a correlation between ventricular fibrillation cycle length and electrophysiological and anatomic properties of the canine left ventricle? Am J Physiol Heart Circ Physiol, August 1, 2004; 287(2): H823 - H832. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Huang, J. M. Rogers, C. R. Killingsworth, K. P. Singh, W. M. Smith, and R. E. Ideker Evolution of activation patterns during long-duration ventricular fibrillation in dogs Am J Physiol Heart Circ Physiol, March 1, 2004; 286(3): H1193 - H1200. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
P.-S. Chen, T.-J. Wu, C.-T. Ting, H. S. Karagueuzian, A. Garfinkel, S.-F. Lin, and J. N. Weiss A Tale of Two Fibrillations Circulation, November 11, 2003; 108(19): 2298 - 2303. [Full Text] [PDF]
|
|
|
|
|
|
M. Valderrabano, P.-S. Chen, and S.-F. Lin Spatial Distribution of Phase Singularities in Ventricular Fibrillation Circulation, July 22, 2003; 108(3): 354 - 359. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
R. C. Saumarez, L. Chojnowska, R. Derksen, M. Pytkowski, M. Sterlinski, C. L.-H. Huang, N. Sadoul, R. N.W. Hauer, W. Ruzyllo, and A. A. Grace Sudden Death in Noncoronary Heart Disease Is Associated With Delayed Paced Ventricular Activation Circulation, May 27, 2003; 107(20): 2595 - 2600. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
H. Qin, M. W. Kay, N. Chattipakorn, D. T. Redden, R. E. Ideker, and J. M. Rogers Effects of heart isolation, voltage-sensitive dye, and electromechanical uncoupling agents on ventricular fibrillation Am J Physiol Heart Circ Physiol, May 1, 2003; 284(5): H1818 - H1826. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. M. Rogers, J. Huang, S. B. Melnick, and R. E. Ideker Sustained Reentry in the Left Ventricle of Fibrillating Pig Hearts Circ. Res., March 21, 2003; 92(5): 539 - 545. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
K. Nanthakumar, J. Huang, J. M. Rogers, P. L. Johnson, J. C. Newton, G. P. Walcott, R. K. Justice, D. L. Rollins, W. M. Smith, and R. E. Ideker Regional Differences in Ventricular Fibrillation in the Open-Chest Porcine Left Ventricle Circ. Res., October 18, 2002; 91(8): 733 - 740. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T.-J. Wu, S.-F. Lin, J. N. Weiss, C.-T. Ting, and P.-S. Chen Two Types of Ventricular Fibrillation in Isolated Rabbit Hearts: Importance of Excitability and Action Potential Duration Restitution Circulation, October 1, 2002; 106(14): 1859 - 1866. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
B.-R. Choi, W. Nho, T. Liu, and G. Salama Life Span of Ventricular Fibrillation Frequencies Circ. Res., August 23, 2002; 91(4): 339 - 345. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Huang, J. L. Skinner, J. M. Rogers, W. M. Smith, W. L. Holman, and R. E. Ideker The effects of acute and chronic amiodarone on activation patterns and defibrillation threshold during ventricular fibrillation in dogs J. Am. Coll. Cardiol., July 17, 2002; 40(2): 375 - 383. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Valderrabano, J. Yang, C. Omichi, J. Kil, S. T. Lamp, Z. Qu, S.-F. Lin, H. S. Karagueuzian, A. Garfinkel, P.-S. Chen, et al. Frequency Analysis of Ventricular Fibrillation in Swine Ventricles Circ. Res., February 8, 2002; 90(2): 213 - 222. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M.-H. Lee, S.-F. Lin, T. Ohara, C. Omichi, Y. Okuyama, E. Chudin, A. Garfinkel, J. N. Weiss, H. S. Karagueuzian, and P.-S. Chen Effects of diacetyl monoxime and cytochalasin D on ventricular fibrillation in swine right ventricles Am J Physiol Heart Circ Physiol, June 1, 2001; 280(6): H2689 - H2696. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. S. Spach Mechanisms of the Dynamics of Reentry in a Fibrillating Myocardium : Developing a Genes-to-Rotors Paradigm Circ. Res., April 27, 2001; 88(8): 753 - 755. [Full Text] [PDF]
|
|
|
|
|
|
B.-R. Choi, T. Liu, and G. Salama The Distribution of Refractory Periods Influences the Dynamics of Ventricular Fibrillation Circ. Res., March 16, 2001; 88 (5): e49 - e58. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Huang, J. M. Rogers, C. R. Killingsworth, G. P. Walcott, B. H. KenKnight, W. M. Smith, and R. E. Ideker Improvement of Defibrillation Efficacy and Quantification of Activation Patterns During Ventricular Fibrillation in a Canine Heart Failure Model Circulation, March 13, 2001; 103(10): 1473 - 1478. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 J. Chen, R. Mandapati, O. Berenfeld, A. C Skanes, R. A Gray, and J. Jalife Dynamics of wavelets and their role in atrial fibrillation in the isolated sheep heart Cardiovasc Res, November 1, 2000; 48(2): 220 - 232. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
T. J. Hund, N. F. Otani, and Y. Rudy Dynamics of action potential head-tail interaction during reentry in cardiac tissue: ionic mechanisms Am J Physiol Heart Circ Physiol, October 1, 2000; 279(4): H1869 - H1879. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. M. Rogers and R. E. Ideker Fibrillating Myocardium : Rabbit Warren or Beehive? Circ. Res., March 3, 2000; 86(4): 369 - 370. [Full Text] [PDF]
|
|
|
|
|
|
J. Chen, R. Mandapati, O. Berenfeld, A. C. Skanes, and J. Jalife High-Frequency Periodic Sources Underlie Ventricular Fibrillation in the Isolated Rabbit Heart Circ. Res., January 7, 2000; 86(1): 86 - 93. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Valderrabano, J. Yang, C. Omichi, J. Kil, S. T. Lamp, Z. Qu, S.-F. Lin, H. S. Karagueuzian, A. Garfinkel, P.-S. Chen, et al. Frequency Analysis of Ventricular Fibrillation in Swine Ventricles Circ. Res., February 8, 2002; 90(2): 213 - 222. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. Valderrabano, M.-H. Lee, T. Ohara, A. C. Lai, M. C. Fishbein, S.-F. Lin, H. S. Karagueuzian, and P.-S. Chen Dynamics of Intramural and Transmural Reentry During Ventricular Fibrillation in Isolated Swine Ventricles Circ. Res., April 27, 2001; 88(8): 839 - 848. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
F. H. Samie, O. Berenfeld, J. Anumonwo, S. F. Mironov, S. Udassi, J. Beaumont, S. Taffet, A. M. Pertsov, and J. Jalife Rectification of the Background Potassium Current: A Determinant of Rotor Dynamics in Ventricular Fibrillation Circ. Res., December 7, 2001; 89(12): 1216 - 1223. [Abstract] [Full Text] [PDF]
|
|
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||