Download Pacemaker interactions induce reentrant wave dynamics

Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture
Bartomiej Borek, T. K. Shajahan, James Gabriels, Alex Hodge, Leon Glass, and Alvin Shrier
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 22, 033132 (2012); doi: 10.1063/1.4747709
View online: http://dx.doi.org/10.1063/1.4747709
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CHAOS 22, 033132 (2012)
Pacemaker interactions induce reentrant wave dynamics in engineered
cardiac culture
Bartłomiej Borek, T. K. Shajahan, James Gabriels, Alex Hodge, Leon Glass,
and Alvin Shriera)
Department of Physiology, McGill University, 3655 Promenade Sir William Osler, Montreal,
Quebec H3G 1Y6, Canada
(Received 11 June 2012; accepted 9 August 2012; published online 27 August 2012)
Pacemaker interactions can lead to complex wave dynamics seen in certain types of cardiac
arrhythmias. We use experimental and mathematical models of pacemakers in heterogeneous
excitable media to investigate how pacemaker interactions can be a mechanism for wave break and
reentrant wave dynamics. Embryonic chick ventricular cells are cultured in vitro so as to create a
dominant central pacemaker site that entrains other pacemakers in the medium. Exposure of those
cultures to a potassium channel blocker, E-4031, leads to emergence of peripheral pacemakers that
compete with each other and with the central pacemaker. Waves emitted by faster pacemakers
break up over the slower pacemaker to form reentrant waves. Similar dynamics are observed in a
modified FitzHugh-Nagumo model of heterogeneous excitable media with two distinct sites of
pacemaking. These findings elucidate a mechanism of pacemaker-induced reentry in excitable
C 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4747709]
media. V
Excitable media, such as the heart, nerves, and some
chemical reactions support propagating waves of activity.
Following a wave, there is a refractory period in which
the media cannot be excited. Collision of two waves leads
to annihilation of the waves. Two dimensional excitable
media support a variety of wave patterns including target
waves emanating from a pacemaker and spiral waves.
Since spiral waves underlie some serious cardiac arrhythmias, we are interested in understanding how these waves
originate. Using both an experimental system composed
of cells from embryonic chick heart and a mathematical
model of cardiac tissue, we show that spiral waves can
arise from the interaction of waves from two pacemakers.
This observation may help in the understanding of the
initiation of cardiac arrhythmias.
I. INTRODUCTION
The heart rate in birds and mammals is set by a small
region located in the right atrium of the heart called the sinus
node. Waves emanating from the sinus node propagate
through the rest of the heart leading to cardiac contraction
and the pumping of blood throughout the body. These normal circumstances can become unstable leading to a variety
of abnormal cardiac rhythms. In some instances, these
arrhythmias may be associated with serious impairment of
heart function or even death.1
Reentrant arrhythmias are the most dangerous class of
abnormal cardiac rhythms. In reentrant arrhythmias, the
rhythm is not set by the sinus node but by a circulating wave
of excitation that typically has a faster frequency than the
sinus rhythm.1 Further, in reentrant arrhythmias, the pattern
of contraction of the heart is abnormal and this impairs the
a)
[email protected].
1054-1500/2012/22(3)/033132/7/$30.00
pumping action of the heart. In some situations, the reentrant
wave circulates on a well defined anatomical pathway,1
whereas in other circumstances, there are spiral or scroll
waves.2,3 A major challenge in cardiology is to predict which
patients are most likely to develop a spontaneous transition
to a reentrant arrhythmia.4,5
A variety of mechanisms lead to the initiation of reentrant
waves in both experimental and theoretical models. These
mechanisms include stimuli delivered during a short time interval (called the vulnerable period) following the excitation;6–8
instabilities in propagation during rapid excitation frequencies
leading to fluctuations in excitation properties and eventual
formation of reentrant waves;9–13 blocked propagation by large
inexcitable heterogeneities in cardiac tissue;14–16 and blocked
propagation due to small but dispersed heterogeneities leading
to wave break.17–21
Experimental studies in intact cardiac tissue2,3,22–24 and
cardiac tissue culture11,13,17,18,24–32 represent important
approaches to study both the properties of reentrant waves and
the mechanisms that lead to their initiation. While others have
used electrical stimulation to induce reentrant waves,11,30 we
have focused on the induction of reentry that occurs as a function of cell density and the addition of drugs that modify ion
channels.17,18,25 In particular, addition of drugs that block a
specific potassium channel (hERG), such as E-4031, induces
complex rhythms in cultured heart cell aggregates33 and intact
hearts.22,34–36 These experimental studies have been complemented by extensive theoretical analyzes using both simplified
models such as cellular automata,17,18,25 and FitzHughNagumo type equations,19–21,25,37,38,43,45,48,49 or more realistic
models, such as the Luo-Rudy model,14,39–41 based on ionic
mechanisms.
In the current work, we describe the induction of reentrant waves in tissue culture. In Sec. II, we describe a method
that we have developed to engineer tissue culture with a
dominant pacemaker region. In Sec. III, we describe the
22, 033132-1
C 2012 American Institute of Physics
V
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Borek et al.
rhythms that arise following addition of a drug, E-4031, that
blocks potassium ion channels found in the heart cells. The
resulting dynamics can be simple with the fastest pacemaker
entraining other pacemakers. However, we also observe
more complex rhythms in which there is initiation of reentrant waves followed by interaction between the reentrant
waves and the original pacemaker. In Sec. IV, we develop a
simplified FitzHugh-Nagumo type model to analyze these
mechanisms. We show that the range of 1:1 entrainment
between two pacemakers depends on the relative frequencies
and sizes of the pacemakers. We also illustrate complex
rhythms that arise as a consequence of the interactions
between induced reentrant rhythms and the original pacemakers. We discuss the results in Sec. V.
II. EXPERIMENTAL METHODS
A. Engineering dominant pacemaker in cultures of
embryonic chick ventricular cells
Hearts were harvested from white Leghorn chicken
embryos after incubation for 7–8 days at 37 C. Tissue was
excised from the apical region of the ventricle and single
cells were isolated using a multiple-cycle dissociation procedure using trypsin.17,42
The dissociated cells were first centrifuged, then suspended in culture medium 818a, and finally plated in 32 mm
diameter CellBindTM-coated dishes (GIBCO). To produce a
dominant central pacemaker, the cells were plated in two
stages. First, we constructed a small central inner disk by
pipetting cells with a density of qi ¼ 3 104 cells=cm2
inside a small glass ring of diameter di ¼ 2 mm in the center
of the dish. The cultures were then incubated in medium
818a at 37 C in 5%CO2 for 6 h. Following this, a larger disk
of diameter do ¼ 9 mm was plated on top of the small disk
with a density of qo ¼ 104 cells=cm2 , and the cells were reinserted into the incubator.
After 48 h, cultures were loaded with Calcium Green-1
(Invitrogen) fluorescent dye (10 lg) that was dissolved in
10 ml Hank’s solution containing 25ll of 2% Pluronic acid
in dimethylsulfoxide (Invitrogen). After 25 min of loading,
the cultures were washed three times and then transferred
into a chamber for imaging which was supplied with humidified air (0:1%CO2 ) and maintained at 3561 C.
Chaos 22, 033132 (2012)
polating the light intensity time series. The interbeat intervals
were found by subtracting two contiguous crossing times.
III. EXPERIMENTAL RESULTS
Figure 1 shows a typical recording of spontaneous pacemaker activity found in the engineered cultures. The central
mound rhythmically emits waves that propagate outward and
entrain all other pacemakers in the medium. These rhythms
were persistent over several minutes and had interbeat intervals ranging between 0:9160:03 s and 2:156 0:03 s in
different dishes.
Because of the important role of potassium channels in
normal and pathophysiological cardiac activity,44 we studied
the effects of the potassium channel blocker E-4031. Addition
of E-4031 to heart cell aggregates leads to a speeding up of the
rhythm, often following a sequence of complex bifurcations.33
In other cardiac preparations, E-4031 can lead to a decreased
incidence of reentrant waves as a consequence of increased
refractoriness34–36 or an increased incidence of reentrant waves
as a consequence of induction of early afterdepolarizations.22
Addition of 0:75 lME-4031 (Sigma-Aldrich) to dishes
with a dominant central pacemaker rapidly induced pacemakers at the outer perimeter of the culture dish. These side
pacemakers had a faster frequency than the central pacemaker.
Figure 2 shows an example in which the central pacemaker
with period 1:4 s is entrained by an emergent side pacemaker, whose period is 0:6 s.
In four cases more than one side pacemaker emerged,
resulting in a complex sequence of switching between
B. Imaging and analysis of calcium waves
Calcium waves were detected using a custom-built macroscopic fluorescence imaging system43 with a field of view
of 1 cm2 . This system provides excitation centered at 500 nm
and monitors emission at 545 nm. Images were acquired using
the Cardio-CCD camera (Redshirt Imaging) with CARDIOPLEX
software (Redshirt). In this study, the spatial resolution was
0:15 lm2 (80 80 pixels) and the time resolution was 25 ms
(40 Hz sampling). The raw data were exported to MATLAB
(Mathworks Inc.) for spatial averaging (bins of 2 2 pixels)
and band-pass filtered using a third-order Butterworth filter.
All maps of calcium waves are 1 cm2 .
To compute crossing times and interbeat intervals (IBIs),
an excitation detection threshold was manually set. The
activation crossing time at each pixel was calculated by inter-
FIG. 1. (a) Periodic target waves in cardiac tissue culture with a central
pacemaker imaged with a calcium sensitive fluorescent dye. (b) Time series
showing the fluorescence activation (arbitrary units) and the corresponding
IBI recorded at pixel x in the central pacemaker, shown in the first panel of
(a) (enhanced online) [URL: http://dx.doi.org/10.1063/1.4747709.1].
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Borek et al.
FIG. 2. Dynamics in cardiac culture following addition of E-4031. (a) Activation maps show a wave emitted from a central pacemaker followed by the
emergence of a side pacemaker whose wave resets the central pacemaker.
(b) Time series showing the fluorescence activation (arbitrary units) and the
corresponding IBI recorded at pixel x in the central pacemaker (enhanced
online) [URL: http://dx.doi.org/10.1063/1.4747709.2].
pacemaker foci. Figures 3(a)–3(e) give a representative
sequence of dynamics. Waves emitted from a pacemaker on the
left edge of the culture initially entrain the culture. At
t 12:25 s, the wave generated by the side pacemaker breaks
up over the central pacemaker Fig. 3(b), leading to the establishment of reentrant double armed spiral waves that reenter back
into the central pacemaker, Figs. 3(c) and 3(d). The timing of
interbeat intervals at the side pacemaker (x1 ), central pacemaker
(x2 ), and site behind the central pacemaker (x3 ) are summarized
in Fig. 3(e).
IV. THEORETICAL MODEL
A. FitzHugh-Nagumo model of pacemakers in
excitable media
Previous studies have analyzed the effects of a stimulus
on a pacemaker in one45,46 and two47 dimensional excitable
media modeled by modified FitzHugh-Nagumo equations. A
critically timed stimulus delivered to a pacemaker in a one
dimensional system induced a family of reflected waves.46
The experimental results in Fig. 3 suggest that we should
observe the initiation of reentrant spiral waves from the
interaction of pacemakers embedded in a two dimensional
excitable medium.
We adopt the FitzHugh-Nagumo equations to model
cardiac activity by adding terms that control the duration of
various phases of the cycle. These have the form
Chaos 22, 033132 (2012)
FIG. 3. Induction of reentrant waves following addition of E-4031. (a)
Waves from a pacemaker on the left hand side of the figure entrain the central pacemaker; (b) waves from the side pacemaker break around the central
pacemaker; (c) reentrant wave are established and (d) evolve into a pair of
stably rotating reentrant waves. (e) Summary of interbeat intervals recorded
at three locations in the medium (marked x1 ; x2 ; x3 in the first panel of (a)
(enhanced online) [URL: http://dx.doi.org/10.1063/1.4747709.3].
2
@v 1
@ v @2v
¼ ðv v3 =3 wÞ þ IP þ D
þ
@t e
@x2 @y2
@w
wh wL
;
¼ eðv þ b cwÞ
þ
w
L
1 þ e4v
@t
(1)
where v and w are the activation and inhibition variables.
The coupling strength D ¼ 0:2 cm2 =s is used to obtain excitable dynamics with propagation velocity ( 13 cm=s). The
parameters ¼ 0:6, b ¼ 0:7, wH ¼ wL ¼ 0:1 s1 , IP ¼ 0 s1
are selected to obtain an excitable medium that supports rotating spiral waves. Pacemaking sites are defined as a central disk
with a radius of 0.175 mm and a peripheral half-disk of radius
0.1 mm at the center-left edge of the medium. A pacemaker
current IP ¼ 1 s1 is added to these sites and wL is varied to
control the rate of pacemaking.
The system was integrated using forward Euler discretization with Dt ¼ 0:5 ls on a 200 200 grid with Dx ¼ 50 lm.
To simulate the irregularity of wave propagation seen in experiments, small obstacles were randomly distributed throughout
the media as described in Shajahan et al.21 These obstacles,
termed breaks, are defined by cells with no-flux conditions,
dv
dt ¼ 0. To generate the random spatial distribution of breaks, a
probability of being a heterogeneity, PH , is chosen for every
cell in the discretized lattice. This generates a mean proportion
of cells marked as a heterogeneity averaged over all possible
distributions, h/i PH . The proportion of breaks in the simulations is / ¼ 0:1 unless otherwise stated.
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Chaos 22, 033132 (2012)
The parameter wL controls the intrinsic period of oscillation in the pacemaker regions. The dynamics of model equations with respect to wL can be understood from the state space
trajectory of Eq. (1), shown as the blue line in Figure 4(a).
This periodic trajectory is separated into four phases. Phase 1
represents the action potential upstroke. Phase 2 is the plateau,
and phase 3 represents repolarization. The parameter wL controls the rate of the trajectory along phase 4, which is the pacemaker phase. The total period of an oscillation is
T ¼ T0 þ T4 ðwL Þ;
where T0 is the time spent in the first three branches, and T4
is the time spent in the fourth branch. On branch 4, the trajectory moves along the v-nullcline, where dv
dt ¼ 0 or
v ¼ vðwÞ. The time spent in this branch is
ð
1 wmin
dw
h
¼
;
T4 ¼
wL wmax ðVL ðwÞ þ b cwÞ wL
where h is a constant. Hence, the period of oscillation can be
written as a function of wL as
h
;
wL
T ¼ T0 þ
(2)
where T0 ¼ 0:391 s and h ¼ 0:0460 from numerical integration of Eq. (2). Although Eq. (2) is derived for an isolated
cell, it also gives a good estimate (within 10%) of the pacemaking period when the pacemaker is embedded in the excitable medium.
B. Entrainment and reentry resulting from two
pacemakers in excitable medium
To study the dynamics resulting from the interaction
between side and central pacemakers, a central pacemaker
with intrinsic period TCP ¼ 1:55 s is incorporated into the
medium and the rate of the side pacemaker and the diameter
of the central pacemaker are varied. For the current set of
parameters, Eq. (1), the shortest period that supports 1:1 conduction in the medium is about 0.61 s.
The range of 1:1 entrainment of the central pacemaker
by the side pacemaker depends both on the diameter of the
central pacemaker and the density of break heterogeneities,
Fig. 5. As the diameter of the central pacemaker becomes
larger, the medium is more susceptible to wave break and
the initiation of spiral waves. Near the limits of 1:1 entrainment, the excited region of the wave narrows as the wave
propagates through the relatively refractory region of the
central pacemaker. If the amplitude of the excitation wave
through the central pacemaker wave is below threshold, then
propagation will fail and the wave will break. In larger
pacemakers, the increased distance between broken waves
facilitates retrograde invasion into the pacemaker through
the isthmus between the broken waves.
Further, during 1:1 propagation, the excitation in the
excitable medium surrounding the pacemaker forms a continuous band with the excitation in the pacemaker. Thus, it is
not simply the properties of the pacemaker that leads to the
breakup but the properties of the surrounding medium. This
is demonstrated in two ways. First, the presence of heterogeneities in the excitable medium makes the medium more susceptible to the formation of reentry, Fig. 5. Further, we have
carried out computations (not shown) in which we studied
wave break in a one dimensional model with a central pacemaker. For the same parameters used in Fig. 5, wave block
occurred in the one dimensional model, whereas 1:1 entrainment was found in the two dimensional model.
At values of the intrinsic period of the side pacemaker,
TSP , that are shorter than the 1:1 entrainment limit, there is
an initiation of reentrant spiral waves, which in turn continue
0.72
a)
b)
4
2
0.7
1
2
v
0.5
0
−2
0
v
1
[s]
−1
0
−2
0
2
1:1
0.68
SP
w
1
3
1
2
time [s]
T
1.5
0.66
c)
T (s)
1.5
1
0.5
reentry
0.64
0.62
2.5
3
3.5
4
4.5
5
5.5
6
central pacemaker diameter [mm]
0.06
0.09
w
0.12
0.15
L
FIG. 4. Single cell dynamics of a pacemaker in Eq. (1). (a) Phase plane trajectory (solid line) and nullclines (dotted-dashed lines). (b) Examples of
activations when wL ¼ 0:16 s1 (solid line) and when wL ¼ 0:04 s1 (dashed
line). (c) The period of oscillation as a function of wL in the simulations
(circles) and in Eq. (2) (solid line).
FIG. 5. The boundary of the region for 1:1 entrainment between side and
central pacemakers as a function of the pacemaker diameter and the intrinsic
period of the side pacemaker, TSP . The solid line represents homogeneous
medium and the dashed line represents a medium with 10% break heterogeneities with 5 spatial distributions for each pacemaker diameter. The 1:1
entrainment is in the upper left hand region and reentrant waves are in the
lower right hand region.
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Borek et al.
Chaos 22, 033132 (2012)
FIG. 6. Wave break and regular reentry in the model. We plot activation
maps of v. (a) The side pacemaker, activated at 6 s, entrains the central pacemaker; (b) the side pacemaker wave breaks around the central pacemaker
site; (c) a pair of reentrant waves remain following the removal of the side
pacemaker at 26 s; (d) reentrant pattern at long times; and (e) a summary of
interbeat intervals during the transition from side pacemaker to reentrant
waves at three locations in the medium (marked x1 ; x2 ; x3 in the first panel
of (a)) (enhanced online) [URL: http://dx.doi.org/10.1063/1.4747709.4].
FIG. 7. Wave break and complex reentry in the model. We plot activation
maps of v. (a) The side pacemaker, activated at 6 s, entrains the central pacemaker; (b) the side pacemaker wave breaks around the central pacemaker
site; (c) the coexistence of the side pacemaker and reentrant waves; (d) eventual reentrant pattern; and (e) a summary of interbeat intervals during transition from side pacemaker to reentrant waves at three locations in the
medium (marked x1 ; x2 ; x3 , in the first panel of (a)) (enhanced online)
[URL: http://dx.doi.org/10.1063/1.4747709.5].
interacting with the pacemakers leading to complex spatiotemporal patterns of activation. In order to study this in
the simplest possible manner, following initiation of the
reentrant waves, we set the pacemaker current of the side
pacemaker to 0, Fig. 6. There is an initiation of two counterrotating spirals similar to what is observed experimentally,
Fig. 3(c). In the experiment and in the simulation, there
appears to be an evolution of the dynamics. In the experiment, the positions of the counterrotating spirals migrate
from a symmetry line at around 3 o’clock to a symmetry line
around 6 o’clock. In the model, the counterrotating spirals
are initiated from a symmetry plane at around 3 o’clock, but
there are subtle changes over the course of several rotations,
leading eventually to a single rotating spiral wave. Recall
that in the model, there are random break heterogeneities.
When these are eliminated, the counter-rotating spirals maintain the initial symmetry around 3 o’clock.
When the initial pacemaker is maintained after the initiation of the reentry, complex spatiotemporal patterns arise
from the interaction of the pacemakers and the spiral waves,
Fig. 7. In particular, the side pacemaker can be shielded
from the reentrant rhythm leading to two different regions
that have different predominant frequencies.
reentrant rhythms. These results have implications for physiological studies of pacemaking and reentry and also pose
interesting theoretical problems.
The current work presents a new experimental model
where interactions between pacemakers give rise to reentrant
waves. One of the classic mechanisms for the initiation of
reentry is the initiation of an activation in the refractory tail of
a propagating pulse.7 In contrast, the spontaneous initiation of
spiral waves here arises as a consequence of wave break over
a refractory pacemaker. In this regard, the blockage of excitation by the pacemaker, evident in Figs. 3, 6, and 7, appears
similar to the blockage of activation caused by refractory tissue.14,39,40 Similarly, complex patterns of activity, pacemaking, and refractoriness leading to spiral waves have been
found recently in theoretical models of cardiac tissue containing ion channels sensitive to mechanical deformation.48,49
The presence break heterogeneities in the excitable medium were not critical to reentry formation but allowed for
reentry at lower side pacemaker periods (Fig. 5). This is consistent with previous computational results showing that
increasing the proportion of randomly-distributed break heterogeneities induced wave break and reentry at lower pacing
periods.20
Earlier work has studied the interactions of multiple spiral waves or spiral waves generated by a pacemaker.
Although such problems arise in a search for better ways to
annihilate and thereby control reentrant cardiac rhythms,30,50
they are also relevant to understanding waves spontaneously
V. DISCUSSION
In this study, we used a novel engineered tissue culture
model to demonstrate that pacemaker interactions can spawn
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Borek et al.
generated in aggregating slime molds51 and the BelousovZhabotinsky chemical reaction.52 Although the fastest frequency
will generally entrain the slower frequencies,1,30,50,51,53–56 Xie
et al.37 observed that heterogeneity of the excitable medium in a
theoretical model can allow for the coexistence of two spiral
waves with distinct periods. Similarly, we have observed the
coexistence of a pacemaker with one frequency, and a reentrant
spiral with a different frequency is possible when they are
shielded from each other by the central pacemaker (Fig. 7).
These results contribute to earlier experimental studies of paced
reentrant waves,30,57 but further investigations are required to
understand the varied dynamics that arise even from very simple
configurations like a central pacemaker and a reentrant wave.
The engineered culture promoted the presence of a dominant pacemaker in the central plating region where the tissue
culture was thickest. This observation is consistent with previous work in which the addition of heart cell aggregates to
monolayer cultures created thickened regions that tended to
become the dominant pacemaker sites.58 Although the mechanism for these observations is not known, one possibility is
that the regions of greater thickness and cell density express
different ion channels and transporters. Heart cell aggregates
tend to have action potentials with a rapid tetrodotoxin sensitive upstroke phase that reflects significant sodium current.59
In contrast, monolayers are relatively insensitive to tetrodotoxin60 and the conduction velocity of the excitation wave is
far slower than that observed in excitable tissue possessing sodium channels.17 Thus, our preparation generates pacemakers
in a slowly conducting medium and provides a powerful
method to analyze the interaction of pacemakers in excitable
medium. In view of the interest in the growth of cardiac tissue
for medical purposes,61,62 insights concerning spontaneous
pacemaker induction and interaction in vitro are of practical
significance.
In these experiments, pharmacological blockade of one
specific potassium channel (hERG) and its associated repolarization current (IKr ) using E-4031 induces pacemakers in the
tissue culture. This effect has not been reported previously in
cardiac tissues treated with E-4031.22,34–36,63 However, in
embryonic chick ventricular aggregates E-4031 causes an
increase in the beat rate33,64 due to shortening of the pacemaker phase.64 Assuming a similar effect in the monolayers,
it is unclear why the effect of blocking of IKr on pacemaking
activity should be most pronounced at the edge of the culture
where the secondary pacemaker sites always emerged. This
observation reflects the interactions between cell density, cell
communication, and the induction of ion channels and is a
direction for future research.
In conclusion, we have investigated conditions leading
to wave breakup and the formation of reentrant waves in heterogeneous excitable media with two sites of pacemaking.
Experimental induction of faster pacemakers in the engineered cardiac tissue causes wave break and reentry around
the slower pacemaker site. Similar observations were made
in the FitzHugh-Nagumo model. These results underscore
the observation that excitable media with multiple pacemakers and/or spiral reentrant waves can support a variety of
complex patterns of activity. Finally, since the intact heart
often has multiple potential pacemaking sites, it may not be
Chaos 22, 033132 (2012)
surprising that reentrant waves can be sometimes generated,
but rather that this does not happen more often.
ACKNOWLEDGMENTS
We thank Michael Guevara for numerous insightful discussions. We are grateful for financial support by CIHR,
NSERC, MITACS, and the Heart and Stroke Foundation of
Quebec.
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