Cardiovascular Research Laboratory, Departments of Medicine
(Cardiology), Physiology, and Physiological Science, University of
California, Los Angeles, California 90095
Spiral wave
breakup is a proposed mechanism underlying the transition from
ventricular tachycardia to fibrillation. We examined the importance of
the restitution of action potential duration (APD) and of conduction
velocity (CV) to the stability of spiral wave reentry in a
two-dimensional sheet of simulated cardiac tissue. The Luo-Rudy
ventricular action potential model was modified to eliminate its
restitution properties, which are caused by deactivation or recovery
from inactivation of K+,
Ca2+, and
Na+ currents
(IK,
ICa, and
INa,
respectively). In this model, we find that
1) restitution of
ICa and
INa are the main
determinants of the steepness of APD restitution;
2) for promoting spiral breakup, the
range of diastolic intervals over which the APD restitution slope is
steep is more important than the maximum steepness;
3) CV restitution promotes spiral
wave breakup independently of APD restitution; and
4) "defibrillation" of
multiple spiral wave reentry is most effectively achieved by combining
an antifibrillatory intervention based on altering restitution with an
antitachycardia intervention. These findings suggest a novel paradigm
for developing effective antiarrhythmic drugs.
fibrillation; antiarrhythmic drugs; chemical defibrillation; ventricular tachycardia
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INTRODUCTION |
SPIRAL WAVES as the substrate
of reentrant arrhythmias were first predicted theoretically (23, 47)
and were later observed in several cardiac preparations (4, 9).
Simulations have shown that, depending on the underlying
electrophysiological properties, spiral waves can be stationary,
meander, or spontaneously break up into a fibrillation-like state. The
factors controlling spiral wave stability may be very relevant to
clinical arrhythmias. It is well known that ventricular fibrillation
(VF) develops in stages, with the first stage corresponding to
polymorphic or monomorphic ventricular tachycardia (VT) lasting from
several to many beats (29, 46). In electrically induced VF in the
canine heart, activation mapping studies showed that VF typically
begins as two reentrant wave fronts in a figure eight (4), which can be
terminated by appropriately timed premature stimuli delivered during
the "protective zone" (1, 19). After two to five rotations, however, the initial wave fronts break up into multiple wave fronts, and the ability of a single extrastimulus to terminate fibrillation is
lost. These observations suggest that the initiation of fibrillation corresponds to the generation of one or two reentrant wave fronts, which subsequently break up to produce the multiple reentrant wave
fronts that characterize fully developed fibrillation. Consequently, understanding the electrophysiological mechanisms that control the
stability of spiral wave reentry may provide useful insights for
defining the desirable properties of antifibrillatory drugs.
The restitution properties of the cardiac action potential duration
(APD) and conduction velocity (CV) were shown to be important determinants of the stability of reentrant arrhythmias in general (6,
7, 13, 21, 36). Restitution is the property that, as the diastolic
interval of a premature beat varies, the APD and CV of that beat also
vary, typically decreasing with decreasing diastolic interval. When the
restitution curve relating APD to the preceding diastolic interval has
a steep slope (>1), reentry around an anatomic obstacle becomes
subject to complex oscillations in cycle length (CL) and APD, both in
experimental preparations (11, 13) and in computer simulations (7, 36).
In simulations in two-dimensional (2-D) sheets of cardiac tissue,
restitution characteristics were also shown to be important
determinants of spiral wave stability, influencing whether a single
spiral wave remains stationary, meanders, or breaks up into multiple
reentrant wave fronts resembling cardiac fibrillation (6, 21). However, the effects of steepness of restitution properties on spiral wave stability are not straightforward. For example, Karma (21) found that
with increasing steepness of APD restitution, spiral wave reentry
became progressively unstable, leading to breakup in a 2-D sheet based
on a simplified two-variable model of the cardiac action potential. In
contrast, Courtemanche (6) found that speeding the kinetics of
Isi (slow inward
current) in the Beeler-Reuter action potential model increased the
maximum slope of APD restitution but prevented spiral wave
breakup. The relative importance to spiral wave stability
of the maximum slope of APD restitution, the range of diastolic
intervals over which the slope is steep, and the interaction with CV
restitution are therefore not entirely clear. It is also not clear to
what extent APD restitution properties of an isolated cardiac cell are
predictive of the tissue restitution properties relevant to spiral wave
stability, because diffusive (axial) currents in addition to membrane
ionic currents were shown to alter APD restitution properties (26).
The goal of this study was to further clarify the role of cardiac
restitution properties in spiral wave stability, in a context that
could be potentially extrapolated to and tested in experimental studies. The major determinants of APD and CV restitution at the cellular level are the restitution kinetics of inward and outward currents. We used phase 1 of the Luo-Rudy model of the
ventricular action potential (LR1) (27), which formulates the
most important cardiac ionic currents in detail, to show how the
restitution properties of the major ionic currents contribute to APD
and CV restitution properties and to examine the extent to which
single-cell restitution properties predict spiral wave behavior in a
2-D sheet of simulated cardiac tissue. Our findings show that
single-cell restitution properties are generally, but not always,
predictive of spiral wave stability. Furthermore, these findings
clarify that the range of diastolic intervals for which the slope of
APD restitution is steep, rather than the maximum value of the slope, is the critical determinant of spiral wave breakup. These results provide a template for predicting how the restitution properties of individual K+,
Ca2+, and
Na+ currents, as can be measured
experimentally using appropriate voltage-clamp protocols, could
be altered to influence APD and CV restitution, and hence, spiral wave
stability. Assuming that cardiac restitution properties turn out to be
important in the stability of clinical arrhythmias, this suggests a
potentially useful strategy for evaluating the antifibrillatory
potential of antiarrhythmic drugs by considering their effects on ionic current restitution properties as well as their traditional
antitachycardia properties.
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METHODS |
Mathematical Modeling
Model of electrical wave propagation.
The most widely used equation simulating electrical wave propagation in
cardiac tissue is a cable equation that considers cardiac tissue as a
continuous system (ignoring the microscopic cell structure)
|
(1)
|
where
Cm is membrane
capacitance, Iion
is the sum of ionic currents, V is
voltage, t is time, 
is
resistivity, subscripts x and
y indicate transverse and longitudinal
directions, and Sv is the
surface-to-volume ratio. In Eq. 1, we use the formulation of
Iion
(µA · cm
2)
described in the LR1 model (27), in which
|
(2)
|
where
ICa is our
notation for
"Isi" in
LR1; IK1 is the time-independent K+
current, IKp the plateau K+ current,
and Ib the background current. The gating variables of the individual ionic currents are described by ordinary differential equations, e.g., for the m gate in
Eq. 6
|
(3)
|
where
m
= m(V)
and 
m = m(V)
are both functions of voltage. We simulated a square sheet of cardiac
tissue with "no-flux" boundary conditions, i.e.
where
L is the length of the side of the
square. In Eq. 1, we fixed
Cm at 1 µF/cm2,
Sv at 2,000 cm1, and
x = y = 0.5 k
· cm (8) to produce a planar wave CV
of 0.57 m/s, which is physiological for cardiac muscle.
The LR1 model, developed for guinea pig ventricular muscle, has an APD
of ~360 ms, longer than the APD of guinea pig or human ventricle at
37°C, which is ~200 ms. To shorten the APD, we decreased the
maximum conductance of
ICa
(
Ca)
from 0.09 to 0.07 mS/cm2 and
increased the maximum conductance of the time-dependent
K+ current
(K)
from 0.282 to 0.705 mS/cm2.
Extracellular K+ concentration was
5.4 mM. With these changes, the resting APD for 90% repolarization is
~200 ms. The maximum slope of APD restitution (~2.5), as well as
the range of diastolic intervals over which the slope exceeded 1 (30 ms), was also close to the range of values we have measured
experimentally in isolated rabbit ventricular myocytes at 35°C
(16). We use this parameter setting as our control case.
Measurement of APD and CV restitution.
To measure APD restitution in the single-cell LR1 model, we used an
S1-S2 stimulus protocol. At a basic pacing CL (S1-S1) of 1,000 ms, S2
was applied after a variable diastolic interval. The stimulus strengths
of S1 and S2 were fixed at two times threshold [stimulation
current (Isti) = 
40 µA/cm2], with
a pulse duration of 1.2 ms. APD was defined using a
threshold voltage of 72 mV, in which
V < 72 mV is defined as the
diastolic interval and V > 72
mV is considered the action potential. (72 mV is near the
voltage at which the action potential is 90% repolarized.)
Tissue APD and CV restitution can be measured in the tissue by
periodically pacing one side of the tissue to initiate rectilinear wave
trains. Because there are no voltage gradients producing diffusive
current flow perpendicularly to a rectilinear wave, this is equivalent
to a wave propagating in a one-dimensional cable of cells. To reduce
computational time, we therefore measured tissue APD and CV restitution
in a cable of cells containing the LR1 cell model (or one of its
various modifications described in Altering APD and CV
restitution). The cable was paced at one end, and CV was measured at a point in the middle of the cable. By
progressively increasing the pacing rate we changed the diastolic interval at that point, and thus tissue APD and CV restitution was obtained.
Altering APD and CV restitution.
Ion channel dynamics in the LR1 model uses a Hodgkin-Huxley
formulation modeled by differential equations expressing a relaxation process to a steady-state value. Both the time course of relaxation and
final steady-state variables are functions of voltage. The relaxation
properties of K+,
Ca2+ and
Na+ currents
(IK,
ICa, and
INa,
respectively) determine their restitution properties. The restitutions
of ionic currents are major determinants of APD and CV restitution (27,
39). To eliminate the effects of the current restitution on APD
restitution, we modified their properties in the following manner. The
first requirement was that the elimination of restitution of these
currents have no effect on the fully rested APD (i.e., at diastolic
intervals >1,000 ms). Therefore, we formulated the gating variables
of IK,
ICa, and
INa as functions
of voltage during a fully rested action potential. We then used the
resulting set of gating variables corresponding to each ionic current
for calculating action potentials at all (shorter) diastolic intervals.
Because these functions were now solely voltage dependent, the effect
of restitution of the currents on APD restitution was eliminated (Figs.
1 and 2). In
the voltage-clamp mode, as might be used experimentally for assessing
drug effects, this is equivalent to making the current insensitive to
variations in diastolic interval (Fig. 1). This method, although
phenomenological, was much more practical than attempting to modify the
rate constants of a given ionic current individually, because
of the marked interdependencies between different currents during
the action potential.
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Fig. 1.
Experimental voltage-clamp protocol illustrating effects of eliminating
restitution of various ionic currents in LR1 model, as might be used
experimentally to define properties of antiarrhythmic drugs on ionic
current restitution. A: simulated
voltage-clamp protocol for measuring restitution of
K+,
Ca2+, and
Na+ currents
(IK,
ICa, and
INa,
respectively). After pacing at 1,000-ms cycle length, a steady-state
action potential is followed after a variable diastolic interval (DI)
by a 100-ms voltage-clamp pulse to 0 mV.
B: superimposed traces of
IK
(left),
ICa
(middle), and
INa
(right) during successive
voltage-clamp pulses after variable DI ranging from 5 to 200 ms, as
labeled. Under control conditions
(IK , ICa, and
INa;
top
panels), restitution of various
ionic currents is evident as diastolic interval was prolonged from 5 to
200 ms and was completely eliminated by modifications made to the LR1
model (I'K,
I'Ca, and
I'Na;
bottom
panels).
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Fig. 2.
Effects of eliminating restitution of various ionic currents in
single-cell LR1 model on action potential duration (APD) restitution
(A), slope of APD restitution
[ APD/DI; B;
inset in middle
panel compares slope of APD restitution in single cell
and in 1-dimensional cable of cells (tissue) for NaR case], and
conduction velocity (CV) restitution
(C). Control curves for unmodified
LR1 model are indicated by dashed line for comparison. KR,
CaR, and NaR indicate elimination of restitution of
IK,
ICa, and
INa,
respectively. NaR* refers to special case in which part of
INa restitution
was eliminated without altering CV restitution.
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Specifically, for the K+ current
in the LR1 model, we modified
IK, the only
K+ current with time-dependent
relaxation properties, by recording it during the resting action
potential and tabulating its value as a function of voltage as a
data file for use in the simulation. This modification had no
significant effect on CV restitution, which is determined solely by
INa (Fig.
2C).
To eliminate restitution of the
Ca2+ current, we changed
ICa from
|
(4)
|
to
|
(5)
|
where
and
Fd f(V) = 0 during the upstroke of the action potential.
ECa is the Ca2+ reversal potential;
d and f are gating variables. With this
substitution, the explicit time dependence of all of the gating
variables regulating ICa was
eliminated, thereby eliminating the influence of
ICa restitution on APD restitution (Fig. 2, A and
B). This modification also had no
significant effect on CV restitution (Fig.
2C).
For the Na+ current, we changed
INa from
|
(6)
|
to
|
(7)
|
where
during
the upstroke of action potential, otherwise
Fmh(V) = 0; m, h, and j are gating variables. Here we
clamped the j gate, i.e.,
j = 1.
Because INa is a
critical determinant of CV restitution, this modification (NaR)
markedly flattened the CV restitution curve (Fig.
2C). We therefore also modified
INa in another
way, to eliminate the effects of
INa restitution
on APD restitution without affecting CV restitution (NaR*)
|
(8)
|
where
Fmh(V)
is the same as in Eq. 7. Note that the
explicit time dependence of the gating variable
j was not eliminated, to prevent the
rate of increase of the action potential
(
max), and hence CV restitution, from being affected by the alteration of
INa.
Although the restitution of peak
I'Na was not
significantly altered, preserving normal CV restitution (Fig. 2C, NaR*), the restitution of
total charge carried by
I'Na was eliminated
(Fig. 3).
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Fig. 3.
Special case (NaR*) in which restitution of
INa was
eliminated without significantly altering CV restitution. Restitution
of peak
(INa,peak;
A) was similar to control case
(dashed line), ensuring normal CV restitution, but restitution of total
charge QNa
carried by INa
(B) during APD restitution was
nearly eliminated. Effects on APD restitution, slope of APD
restitution, and CV restitution are shown in Fig. 2 (labeled
NaR*).
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In summary, these modifications to the LR1 model permitted APD
restitution to be changed (Fig. 2A)
without affecting the fully rested APD, and, if desired, without
affecting CV restitution (Fig. 2C).
Although we did not consider in this study intermediate cases of
altered restitution properties, this approach also allows APD
restitution to be changed continuously by substituting the ionic
current (IK,
ICa, or
INa) in
Eq. 2 with
I
x, where
|
(9)
|
I'x
(I'K,
I'Ca, or
I'Na) is the
modified current, and 
is a weight: by varying from 0 to 1, the
restitution of the corresponding ionic current can be continuously
varied to any desired extent.
Chemical defibrillation.
To introduce changes in the restitution properties of ionic currents to
simulate an acute pharmacological intervention after spiral wave
reentry had already been initiated, we used Eq. 9. Starting at t = t0, increases
from 0 to 1 by
![&ggr; = 1 − exp [−(<IT>t</IT> − <IT>t</IT><SUB>0</SUB>)/&tgr;] for <IT>t</IT> ≥ <IT>t</IT><SUB>0</SUB>](/content/vol276/issue1/fulltext/H269/img016.gif)
|
(10)
|
is the time constant for the rate at which the drug effect on the ionic
current takes effect. We also simulated traditional antiarrhythmic drug
effects (classes I, III, and IV) by blocking the relevant ionic
current, i.e., reducing the maximum conductance of
INa,
ICa, or
IK by 20%
![<OVL><IT>G</IT></OVL><SUB><IT>x</IT></SUB>′ = <OVL><IT>G</IT></OVL><SUB><IT>x</IT></SUB> {0.8 + 0.2 exp [−(<IT>t</IT> − <IT>t</IT><SUB>0</SUB>)/&tgr;]} for <IT>t</IT> ≥ <IT>t</IT><SUB>0</SUB>](/content/vol276/issue1/fulltext/H269/img017.gif)
|
(11)
|
where
x = Na, Ca, or K. To minimize boundary
effects (i.e., to avoid spiral waves extinguishing at the tissue
edges), periodic boundary conditions were used instead of no-flux
boundary condition in the "defibrillation" simulations. All
simulations were started with the same fibrillatory-like state at
t0.
Computer Simulation
Numerical simulation of cardiac conduction in tissue requires large
spatial arrays with many cells (because of the space and time constants
inherent in the dynamics) and small time steps (because of the steep
rate of rise of the cardiac action potential, e.g,
max 
400 mV/ms in LR1). Because the conventional forward Euler method to
integrate Eq. 1 is computationally
tedious and costly, we developed a new integration method to speed
computation without losing accuracy. Specifically, using the well-known
operator-splitting method (40), we split Eq. 1 into an ordinary differential equation (ODE) and a
partial differential equation (PDE) and then integrated them separately
and alternately. We used an alternating direction implicit (ADI) method
(35) to integrate the PDE, a time-adaptive second-order Runge-Kutta
method [minimum time step
(tmin) 
0.02 ms and maximum time step
(tmax 0.2 ms)] to integrate the ODEs, and the method of Rush and Larsen
(37) to integrate the ODEs for the gating variables like
Eq. 3. The integration
time step of the PDE was set to
tmax.
Simulations were carried out in a 9 cm × 9 cm tissue divided into
400 × 400 elements. For the integration of the single cell and
the one-dimensional cable of cardiac cells, we used fourth-order
Runge-Kutta and finite-difference methods. Simulations were carried out
on a 266-MHz DEC Alpha work station. We tested the accuracy of our
numerical method in a cable of cells by changing both the time step and
the space step (x). We set parameters as in the control case and fixed
tmax = 0.2 ms. Table 1 shows APD and CV for
tmin = 0.01 ms
and tmin = 0.02 ms, for a x from 0.01 to 0.03 cm. There was a 5-6% change in CV and a <0.2% change in APD
when we increased x from 0.01 to
0.0225 cm. There was an ~1% change in CV when
tmin was
increased from 0.01 to 0.02 ms. We also compared the accuracy and the
speed of our method to the conventional Euler method (Qu and Garfinkel,
unpublished observations), with similar results.
| |
RESULTS |
Effects of Eliminating Ionic Current Restitution on APD and CV
Restitution
Figure 1, A and
B, shows the effects of eliminating
the restitution of
IK,
ICa, or
INa on the
typical currents elicited by a voltage clamp pulse in the LR1 model of
a single ventricular cell, as might be observed during an experimental
drug testing protocol in an isolated ventricular myocyte. Figure 2
shows the effects on APD restitution. None of the modifications changed the APD of the fully rested cell, but they had very different effects
on APD restitution. Particularly important is the effect on the slope
of APD restitution, which is illustrated in Fig. 2B.
Eliminating IK
restitution (i.e., making
IK deactivation
an instantaneous function with respect to membrane voltage) increased the slope of the APD restitution curve at both short and moderate diastolic intervals (Fig. 2, A
and B). CV restitution was
unaffected (Fig. 2C).
Eliminating ICa
restitution (i.e., making recovery from inactivation instantaneous with
respect to membrane voltage) markedly decreased the slope of the APD
restitution curve at moderate diastolic intervals (25-100 ms), but
not at short (<25 ms) or long (>100 ms) diastolic intervals. At
short diastolic intervals, a region remained in which the APD
restitution slope was steeper than in the control case. This steep
region is the effect of
INa restitution on maximum voltage
(Vmax), as
noted below, which determines the extent to which
ICa is activated
through its voltage dependence and hence has a large effect on APD. CV
restitution was not significantly affected (Fig.
2C).
Eliminating INa
restitution decreased the slope of the APD restitution curve to <1 at
short diastolic intervals (<50 ms) but had little effect at
intermediate to long diastolic intervals (>50 ms). However, the slope
of APD restitution was now <1 everywhere, although it approached very
close to 1 (reaching 0.92) at intermediate diastolic intervals. Our
analysis showed that the effect on APD restitution did not directly
result from the contribution of
INa to the
plateau currents, which is negligible in the LR1 model. Rather,
INa determines
the Vmax reached
during the action potential upstroke. The value of
Vmax in turn
strongly determines the extent to which
ICa is activated,
by virtue of its intrinsic voltage dependence. Thus, when
INa restitution
is eliminated,
Vmax is less
depressed so that
ICa is more fully
activated at short diastolic intervals, and APD is thereby preserved.
Eliminating INa
restitution also virtually eliminated CV restitution (Fig.
2C). For the special case in which
INa restitution
on APD was eliminated without altering CV restitution (NaR*; see
METHODS), the effect on APD
restitution was nearly equivalent (Fig.
2C).
In summary, eliminating restitution of the three currents individually
affected both the maximum value of the slope of APD restitution and the
range over which the slope exceeded 1. Without IK restitution,
the range was widened; without
ICa restitution, the range was decreased; without
INa restitution
the slope was <1 everywhere, but just barely so for moderate
diastolic intervals. In the case in which
INa restitution
was eliminated without altering CV restitution (NaR*), however,
the slope also approached 1 at very short diastolic intervals. To
produce an APD restitution curve with slope well below 1 everywhere, it
was necessary to eliminate restitution of both
ICa and
INa (Fig. 2,
A and
B).
Effects of Eliminating Ionic Current Restitution on
Spiral Wave Stability
Reentrant spiral waves were initiated in the 2-D tissue model by two
successive perpendicular rectilinear wave fronts (34). Figure
4A shows
the result for the LR1 model with normal ionic current restitution
properties. After initiation, the spiral wave went through several
rotations before breaking up spontaneously into multiple meandering
wave fronts, simulating the transition from VT to VF. Breakup was
preceded by oscillations in the wavelength (product of APD and CV) in
time and space along the arm of the spiral wave, which increased in
amplitude until the wavelength at one point became too short to
propagate. The resulting break in the arm of the spiral wave led to the
formation of two new daughter spiral waves. Eventually, additional
spiral waves were created by the same process, and the activation
pattern took on a highly irregular appearance of multiple meandering
wave fronts. Existing spiral waves were also annihilated as they ran
into borders or fused with other spirals, so that the number of wave
fronts changed continually. The resulting local activation patterns
were highly irregular, as shown by the time series of diastolic
interval, APD, and CL (Fig. 4B)
obtained by monitoring intracellular potential at a fixed site in the
tissue (Fig. 4C).
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Fig. 4.
A: spiral wave breakup in a 9 cm × 9 cm sheet of cardiac tissue containing 400 × 400 elements, under control conditions. Time
(t) after initiation of a single
spiral wave by perpendicular wave fronts is indicated in each panel.
Voltages are indicated by gray scale, in which white represents peak
(Vmax) of
action potential and black represents resting voltage.
B: local records of APD, DI, and
beat-to-beat interval (CL) at a fixed site in tissue.
C: intracellular membrane potential
(V) during time interval from 0 to 5 s at same site.
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Eliminating restitution of either
IK or
INa did not
prevent spiral wave breakup (Fig. 5,
A and
C) or the highly irregular fluctuations in intracellular potential and beat-to-beat intervals (Fig. 6, A and
C). In contrast, eliminating
restitution of
ICa did prevent
spiral wave breakup (Fig. 5B). The
spiral wave was not stationary but meandered chaotically, as
illustrated by the trajectory of the spiral wave tip in Fig.
5B and in the record of intracellular
potential and beat-to-beat intervals recorded at a fixed site in the
tissue in Fig.
6B.
Although dominated by the quasiperiodic motion, the fine structure of
the meander was chaotic (unpublished observations).
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Fig. 5.
Spiral waves in a sheet of simulated tissue after elimination of
restitution of various ionic currents.
A-C: KR, CaR, and
NaR, respectively. D: special
case (NaR*) in which
INa restitution
was eliminated without affecting CV restitution.
E: combined CaR and
NaR*. Spiral waves are all shown 2 s after their initiation;
trajectory of the spiral tip after 1-s transient is shown below for
cases in which initial spiral wave did not break up.
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Fig. 6.
Local records of APD ( ), DI ( ), CL ( ), and
V during time interval from 0 to 5 s
after initiation of spiral wave reentry, for corresponding cases shown
in Fig. 5. Data were taken at same fixed site in tissue. See Fig. 5
legend for further details.
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In contrast to the modifications to
IK and
ICa, the
modifications to
INa affected CV
restitution as well as APD restitution (Fig. 2). The changes in CV
restitution appeared to play an important role in spiral wave
stability. When spiral wave breakup was prevented by eliminating
ICa restitution
(Fig. 5B), the additional
elimination of
INa restitution
restored spiral wave breakup (data not shown but similar to the effect
of INa
elimination alone shown in Fig. 5C).
To further delineate the role of changes in APD versus CV restitution
in causing spiral wave breakup in this case, we modified INa so that its
effects on APD restitution were retained but CV restitution was
unaffected (see METHODS). In this
case, spiral wave breakup was completely prevented (Fig.
5D), and the degree of meander was
even less prominent (although still quasiperiodic and
mildly chaotic) than when restitution of
ICa was
eliminated (Fig. 6D).
These results illustrate that both CV and APD restitution play
important roles in spiral wave stability. Spiral wave breakup was
promoted either by flattening the slope of CV restitution (Figs.
2C and
5C) or by increasing the slope of
APD restitution (to >1) over a wide range of diastolic intervals
(Figs. 2A and 5A). In the latter case, it was the
range over which the slope was steep (>1) rather than the maximum
steepness of APD restitution that was critical: for the case in
which ICa
restitution was eliminated, the maximum value of the slope actually
increased at very short diastolic intervals (Fig.
2B), yet spiral wave breakup was
prevented because of the shallow slope (<1) over the remaining wide
range of diastolic intervals (Fig.
5B).
In all of the above cases in which
IK,
ICa or
INa restitution
was modified individually, a region of steep slope (closely approaching
or exceeding 1) in the single-cell APD restitution curve remained. To
make the slope shallow (much less than 1) everywhere required
eliminating restitution of both
ICa and
INa. In this case
(using the modified
INa that did not
alter CV restitution), spiral wave breakup was also prevented. Although
a small degree of quasiperiodic meander of the spiral wave remained
(Figs. 5E and
6E), the quasiperiodic meander was
no longer chaotic, representing a qualitative change (i.e., a
bifurcation point) in the behavior of the spiral wave (unpublished observations).
These results show that by appropriately modifying restitution
properties of cardiac ionic currents, it is possible to suppress both
wavelength and CL oscillations to make reentrant spiral waves more
stable, preventing, in a model, the transition from VT to the VF-like state.
Effects of Blocking Ionic Currents on Spiral Wave Stability
Elimination of restitution of ionic currents is easily achieved in a
computer model, but pharmacological tools to achieve the same effects
on ionic currents in real cardiac tissue are not necessarily available.
Therefore, it is useful to consider how less selectively targeted
pharmacological interventions affect APD and CV restitution and spiral
wave stability. For example, because
ICa relaxation is
the major factor regulating the steep region of APD restitution in the
LR1 model, simply reducing the absolute magnitude of
ICa, without
specifically modifying its relaxation properties (a class IV
antiarrhythmic drug effect), might be predicted to lessen the steepness
of APD restitution. This is because the variation in
ICa magnitude
with diastolic interval will be smaller relative to other ionic
currents during the plateau and have a lesser effect on APD. To test
this strategy, we examined individually the effects of decreasing the
magnitudes of IK,
ICa, and
INa by 50%
(analogous to class III, IV, and I antiarrhythmic drug effects,
respectively) without otherwise affecting their relaxation or other
kinetic properties. Figure 7,
A-C, shows the effects on the APD
and CV restitution curves. Reducing
IK by 50% (i.e.,
by decreasing
K
from 0.705 to 0.3525 mS/cm2)
increased the steepness of APD restitution over a broad range (Fig. 7,
A and
B) by preferentially prolonging APD
at long diastolic intervals and did not affect CV restitution (Fig.
7C). The initiated spiral wave still
broke up (Fig. 7F), consistent with
the increased steepness of the APD restitution over a wide range of
diastolic intervals. Reducing
ICa by 50%
(i.e., by decreasing
Ca in Eq. 6 from 0.07 to 0.035 mS/cm2) decreased the range of
diastolic intervals over which APD restitution was steep by reducing
the steepness at moderate to long diastolic intervals (>25 ms),
shortened APD at long diastolic intervals (Fig. 7,
A and
B), and had no effect on the
steepness of CV restitution (Fig.
7C). Blocking
ICa prevented
spiral wave breakup, producing a single chaotically meandering spiral
wave (Fig. 7E). Reducing INa by 50%
(i.e., by decreasing
Na
in Eq. 4 from 23 to 11.5 mS/cm2) also decreased the range
of diastolic intervals over which APD restitution was steep by reducing
the steepness of APD restitution slightly at short to moderate
diastolic intervals (<100 ms) but had no effect on APD at long
diastolic intervals. It also decreased the magnitude and
slope of CV restitution. Similar to the situation in which restitution
of INa was
selectively eliminated, the effects on CV restitution on promoting
spiral wave instability outweighed its stabilizing effects on APD
restitution, so that spiral breakup still occurred (Fig.
7D).
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Fig. 7.
Effects of blocking amplitude of
INa,
ICa, or
IK by 50% on
restitution properties and spiral wave stability.
A: APD restitution.
B: slope of APD restitution.
C: CV restitution.
D-F: patterns of spiral wave
reentry with 50% block of
INa
(D),
ICa
(E), and
IK
(F). Data in
D-F are shown 2 s after
initiation of spiral wave reentry. The tip trajectory of the spiral
wave in E is shown below its snapshot.
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With the caveat that no use-dependent properties were incorporated in
these simulations, these results suggest that pharmacological agents
that block ICa
(class IV drugs) were more effective at stabilizing spiral wave reentry
than IK or
INa blockers
(class III or I drugs) in this model.
Chemical Defibrillation
An important question is whether altering APD and CV restitution after
the VF-like state is established can restore periodic behavior and
convert VF to VT. To test this idea, we initiated a spiral wave with
the LR1 model and allowed the VF-like state to develop. After 2 s, we
then used Eqs. 9-11 with a of
1 s to introduce the modified
IK,
ICa, or
INa in which
restitution was eliminated, either alone or in combination with class
I, III, or IV antiarrhythmic drug effects. When either
IK or
INa restitution was eliminated, the fibrillation-like state persisted for a variety of
different initial conditions (Fig. 8,
A and
C). When
ICa restitution was eliminated, the multiple and variable number of wave fronts coalesced into several meandering spiral waves, whose number
remained constant (Fig. 8B). We
simulated class I, III, or IV antiarrhythmic drug effects by reducing
the magnitude of
INa,
IK, or
ICa,
respectively, by 20%, without altering their kinetic properties. None
of these interventions changed the qualitative behavior of the
fibrillation-like state (Fig. 8,
D-F), either alone or in
combination with the additional elimination of
INa or
IK restitution
(data not shown). However, when a class III antiarrhythmic drug
intervention (but not class I or IV interventions) was combined with
elimination of
ICa restitution, all wave fronts were extinguished after several rotations, as they
encountered refractory tissue from a wave back (Fig. 8,
G-I). Thus, this combined
"antifibrillatory" plus "antitachycardia" intervention was
successful at "defibrillating" the tissue to a quiescent (but
excitable) state.
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Fig. 8.
Chemical defibrillation. With control LR1 model, a spiral wave was
initiated and by 2 s had broken up into multiple reentrant wave fronts.
At this time, one of the following simulated drug interventions was
introduced. A-C: KR,
CaR, and NaR, respectively.
D-F: class III, IV, and I
antiarrhythmic drug action, respectively, simulated by reducing
amplitude of IK,
ICa, or
INa by 20%.
G-I: combination of CaR and class
III, IV, or I antiarrhythmic drug action. Only combination of CaR and
class III antiarrhythmic drug action
(G) was successful at defibrillating
tissue to a quiescent state. Left
tracings show local records of intracellular membrane
potential at fixed site in tissue; right
panels show spatial activation patterns 6 s after drug
was administered.
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DISCUSSION |
A number of studies have investigated spiral wave meander and breakup
in 2-D and three-dimensional (3-D) simulations (8, 33) and in tissue
experiments (9, 17, 34). However, only Karma's (21) and
Courtemanche's (6) 2-D simulations explicitly addressed the role of
restitution in these phenomena. We extended these investigations by
examining directly the effects of restitution properties of the major
currents on APD and CV restitution as well as on spiral wave behavior,
providing a guide for pharmacological manipulations that can be tested
experimentally. Although our method of eliminating the restitution of
individual ionic currents was phenomenologically based, it nevertheless
readily permits an explicit description of how the altered current
would behave during a typical voltage-clamp protocol used in an
experimental drug screening protocol applied to an isolated cardiac
myocyte (Fig. 1). Importantly, the approach can be refined as more
complete descriptions of the cardiac action potential (in ventricular
as well as atrial tissues) are developed.
Although a number of important limitations must be considered (see
Limitations), the major conclusions
arising from these simulations are that in this model
1) the restitution properties of
INa and
ICa are the main
determinants of the steep portions of the APD restitution curve,
whereas IK
restitution plays a lesser role; 2)
steep APD restitution promotes spiral wave meander and breakup
[for the latter, the range of diastolic intervals over which the
slope of APD restitution is steep (>1) is more important than the
maximum steepness]; 3)
eliminating restitution of
ICa is more
effective than eliminating
INa or
IK restitution
for preventing spiral wave breakup in this model;
4) eliminating
INa restitution, which flattens CV restitution, promotes spiral wave breakup
independently of APD restitution; and
5) among nine interventions tested
in this model, "defibrillation" of multiple spiral wave reentry
required combining an antifibrillatory intervention based on altering
restitution properties (to convert VF to VT) with an antitachycardia
intervention (to eliminate VT) based on blocking an ionic conductance
(particularly a class III antiarrhythmic drug effect).
Cellular determinants of APD and CV restitution.
In the LR1 single-cell model, restitution of
INa and
ICa is the major
determinant of the steep portions of the APD restitution curve (Fig.
2). This is consistent with experimental findings in intact cardiac
tissue that INa
and ICa blockers
in general reduce the slope of APD restitution (5, 41), because
reducing the magnitude of the current decreases its influence on APD
restitution independently of any direct effect on APD restitution
properties per se, as illustrated by our simulations with the LR1 model
in Fig. 7. Eliminating restitution of
IK in the LR1
model also changed the steepness of the APD restitution curve, but in
the opposite, i.e., steeper, direction (Fig. 2), also consistent with
experimental observations (24, 25). This effect has usually been
attributed to the reverse use dependence property of these drugs (18), i.e., preferential current block at long diastolic intervals, which
would increase the slope of APD restitution. However, the results from
the LR1 model suggest another explanation, namely that APD restitution
at short diastolic intervals is dominated by restitution of
INa and
ICa, whereas
IK restitution
only assumes importance at longer diastolic intervals.
In contrast to the multiple factors influencing APD restitution, CV
restitution in normally polarized tissue as simulated in this study is
primarily determined by recovery from inactivation of
INa. Consistent
with these results, use-dependent
Na+-current blockers such as
lidocaine were shown experimentally to reduce the slope of CV
restitution (11). However, in depolarized or partially uncoupled tissue
in which INa is
largely inactivated and CV depends on
ICa to support
the action potential upstroke (such as in the setting of
ischemia),
ICa and
IK relaxation
processes would assume greater importance (39).
Mechanism by which restitution properties destabilize spiral wave
reentry.
The mechanism by which a steep restitution curve causes instabilities
was appreciated previously in studies investigating responses of
myocardium to pacing (31, 42, 44) and in reentry around an anatomic
obstacle (7, 11, 13, 36). We believe that the same basic mechanism,
diagrammed in Fig. 9, also applies to
spiral wave reentry in 2-D. Figure 9A
illustrates an APD restitution curve with slope <1. For a stationary
spiral wave with constant CL as defined by the equality CL = APD diastolic interval, the CL can be represented on the
restitution graph by a line with a slope of 1 (dashed line). A
stationary spiral wave will have an APD and diastolic interval
corresponding to the intersection of the dashed line and the APD
restitution curve. If a perturbation (e.g., a premature stimulus) is
applied to shorten the diastolic interval to the point labeled
a, the next APD will fall on the restitution curve at point b,
producing the next diastolic interval at point
c, etc. With iteration, the slope <1 ensures that the APD and diastolic interval converge back to the stable equilibrium at
the intersection point. In contrast, if the slope of the APD restitution curve is >1, as shown in Fig.
9B, the small perturbation in
diastolic interval is unstable and becomes amplified on iteration, eventually reaching a diastolic interval shorter than the refractory period. This results in a wave break along the spiral wave arm, initiating spiral wave breakup. This contrasts to reentry in a ring (7,
11, 13, 36), in which wave break simply terminates the arrhythmia.
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Fig. 9.
Schematic diagram illustrating effects of APD and CV restitution on
stability of spiral wave reentry. A:
slope of APD restitution curve is <1, and no CV restitution is
present. B: slope of APD restitution
curve is >1, and no CV restitution is present.
C: slope of APD restitution curve is
>1, and CV restitution is present. See text for detailed
explanation.
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The role of CV restitution in this process is illustrated in Fig.
9C. CV restitution, when engaged at
short diastolic intervals, slows the CL of spiral reentry, so that
during successive iterations after an initial perturbation of the
diastolic interval, the dashed line representing the CL shifts in an
oscillating manner. When the dashed CL line shifts to the right during
successive rotations of the spiral wave, the oscillations in APD and
diastolic interval are further amplified, effectively further
steepening the slope of the APD restitution curve. For the phase in
which it shifts to the left, APD restitution slope is effectively
decreased. The frequency at which these phases oscillate is identical
to the low-frequency oscillation of the CL of the spiral wave (e.g., Fig. 6, B,
D, and
E).
For spiral wave breakup in our model, the range of diastolic intervals
over which APD restitution is steep (>1) was more important than the
maximum value of the APD restitution slope. We hypothesize the
following explanation based on a theoretical analysis of spiral wave
stability (unpublished observation). We have found that the excitable
gap near the tip of the spiral wave is very narrow, functionally
equivalent to a very short diastolic interval. Moving out from the tip
along the spiral arm, the excitable gap progressively increases,
equivalent to a longer diastolic interval. Thus, if the APD restitution
slope is steep only at very short diastolic intervals, only the spiral
tip will be subject to unstable oscillations (as illustrated in Fig.
9B), thereby causing the tip to
meander. However, spiral breakup will not occur, because the spiral arm is subject to longer diastolic intervals, at which the slope of APD
restitution is <1. Therefore, oscillations in APD and diastolic interval along the spiral arm will be damped (as in Fig.
9A) and wave break will not occur.
In contrast, when the range of diastolic intervals over which the slope
is >1 extends to a wide enough range to include the longer diastolic
intervals experienced by the spiral arm, oscillations in APD and
diastolic interval along the spiral arm also become amplified, leading
to wave break distant from the spiral tip, i.e., spiral breakup. This
mechanism readily accounts for the apparent discrepancy between
Karma's (21) and Courtemanche's (6) observations. In Karma's
simplified two-variable cardiac model, the parameter changes that
increased the maximum slope of APD restitution always concurrently
increased the range of diastolic intervals over which the slope was
steep, resulting in a positive correlation between increasing steepness
of restitution and the extent of meander and breakup. In contrast, in
Courtemanche's study (6), spiral breakup was prevented when the
maximum slope of APD restitution increased (by speeding
Isi kinetics in
the Beeler-Reuter model). Careful inspection of his APD restitution curves (Fig. 11 in Ref. 6), however, reveals that when
Isi kinetics were
more rapid, the average slope of APD restitution had decreased over the
majority of (longer) diastolic intervals. On the basis of our similar
findings (compare Fig. 6, B and
D), we believe that increased
maximum slope at very short diastolic intervals promoted meander of the
spiral tip, but the shallower slope at longer diastolic intervals
prevented spiral breakup.
This mechanism also provides an explanation for the effects of altered
CV restitution on spiral wave behavior when
INa restitution was eliminated. In this case, an important consequence of flattening CV
restitution is to shorten the effective diastolic intervals experienced
along the arm of the spiral wave, because incomplete recovery of
INa no longer
slows the activation wave front when it approaches the repolarization
wave back of the previous excitation. Thus, in contrast to the
situation with normal CV restitution, the spiral arm as well as the
spiral tip is subject to functionally very short diastolic intervals. A
steep APD restitution slope at these short diastolic intervals
therefore causes unstable oscillations in APD and diastolic interval at
both locations, resulting in meander of the spiral tip and wave break
along the spiral arm. Consistent with this explanation, when
INa restitution
was eliminated without affecting CV restitution, the APD restitution
slope was nearly identical (and even steeper at very short diastolic
intervals), yet only meander of the spiral tip was observed and spiral
wave breakup along the spiral arm did not occur (Figs.
5D and
6D).
Limitations.
In this study, we have described the effects of altered ionic current
restitution on spiral wave stability as being mediated through APD and
CV restitution. However, it could be argued that the effects on spiral
wave stability are directly caused by altered ionic current
restitution, and that the effects on APD and CV restitution are
epiphenomena. We do not believe this to be the case, for several
reasons. First, insofar as we have been able to determine, there is
complete agreement between the effects of ionic current modifications
on APD and CV restitution with their effects on spiral wave stability.
For example, increasing the steepness of APD restitution by eliminating
IK restitution, by decreasing IK
(without altering its restitution properties), and by increasing
ICa (also without
altering its restitution) all had the same effect of increasing the
slope of APD restitution, and all destabilized spiral wave reentry.
Second, a similar relationship between APD restitution steepness and
spiral wave breakup was previously established in other cardiac models
in which individual ionic currents are either not specifically
formulated or are formulated differently, such as Karma's two-variable
model (21) or the Beeler-Reuter model (6). The common link to spiral
wave stability with our study is APD restitution steepness, rather than
alterations to restitution properties of specific ionic currents.
Third, there is a clear dynamic mechanism to explain how APD
restitution steepness causes destabilization of spiral wave reentry
(Fig. 9), whereas the same is not true for relating ionic current
restitution properties to spiral wave stability (except through their
effects on APD and CV restitution).
In addition, several important caveats must be recognized in evaluating
the physiological relevance of these simulations to arrhythmias in the
real heart. These caveats primarily relate to two issues, the
completeness and physiological accuracy of the cellular action
potential model and the validity of extrapolating findings in a
simulated homogeneous 2-D sheet of cardiac tissue to real cardiac
tissue, which is 3-D, anisotropic, and both anatomically and
electrophysiologically heterogeneous.
Limitations of the LR1 model include unphysiologically slow kinetics of
ICa, the
incomplete description of individual time-dependent K+ currents [the rapid
K+ current
(IKr), the slow
K+ current
(IKs), and the
transient outward current
(Ito)],
and the lack of detailed intracellular
Ca2+ dynamics. We also found it
necessary to make adjustments to the LR1 model to shorten the APD to a
physiologically realistic value, which simulated the features of our
experimentally measured ventricular APD restitution curves (16). The
limitation on computational speed was one important consideration in
using the LR1 model rather than a more detailed model such as the phase
3 formulation of the Luo-Rudy model (LR3) (28, 48), which is less
tractable from a computational standpoint. However, we recently
confirmed that eliminating ionic current restitution in these more
detailed models has effects on APD and CV restitution qualitatively
similar to that in the LR1 model. For example, eliminating restitution of the various IK
components in the LR3 model
(IKr and
IKs) results in
increasing the range, and steepness of APD restitution is steep (>1),
similar to the LR1 model (unpublished observations). The potential
effects of Ito
relaxation were not studied, because Ito has not been
formulated in these models.
Intracellular Ca2+ dynamics also
may have important effects on cardiac restitution properties (38). The
increase in intracellular Ca2+
during excitation affects a variety of ionic currents influencing APD,
including ICa
(through Ca2+-induced
inactivation), the
Na+/Ca2+
exchange current, and
Ca2+-activated nonselective cation
and Cl currents (45). At
short diastolic intervals, Ca2+
release from the sarcoplasmic reticulum decreases and may influence APD
less prominently than at long diastolic intervals (27). Pretreatment of
cardiac tissue with agents that inhibit
Ca2+ release by the sarcoplasmic
reticulum has been reported to affect APD restitution (38), although in
isolated rabbit ventricular myocytes studied at 35°C, we found that
eliminating the intracellular Ca2+
transient had little effect on the steepness of APD restitution (16).
Because the goal of the present study was to examine the effects of
eliminating ionic current restitution on APD and CV restitution
properties, there was an important practical reason for using an action
potential model that did not incorporate detailed intracellular
Ca2+ dynamics. Specifically, this
avoided the confounding effects of intracellular
Ca2+ dynamics on ionic current
restitution (especially
ICa), which would have made it impossible to predict the properties of the altered
currents under voltage-clamp conditions relevant to drug screening
protocols. With more advanced cardiac models incorporating intracellular Ca2+ dynamics,
however, it will be possible in future studies to evaluate the
influence of intracellular Ca2+
dynamics on restitution and spiral wave behavior.
In this study, we assessed the steepness of APD restitution using an
S1-S2 stimulation protocol applied to a single simulated cardiac cell.
Several factors make it difficult to relate the restitution properties
of the single cardiac cell quantitatively to the restitution properties
during spiral wave reentry. First, the memory feature (32) of APD means
that there is no unique relationship between APD and the previous
diastolic interval, even at the single-cell level. Because the history
of previous excitation is important, it remains to be determined what
is the most accurate method for assessing restitution with a pacing
protocol, to accurately reflect restitution properties occurring during spiral wave reentry. Second, restitution in a single cell differs from
restitution in coupled cells in cardiac tissue, because diffusive (axial) currents between adjacent cells become important, especially at
short diastolic intervals (26). In 2-D and 3-D tissue, the curvature of
the wave front further modulates density of diffusive currents, thereby
influencing APD and CV in a complex curvature-dependent manner. In
reality, the slope >1 criterion as a measure predicting spiral wave
stability really refers to the restitution properties during spiral
wave reentry and not to the restitution properties of the single cell.
An example of a discrepancy between single-cell and tissue APD
restitution properties was encountered in the example in which
restitution of
INa was
eliminated (NaR). Although the maximal slope of APD restitution
in the single cell approached very close to 1 (Fig. 2,
middle), it did not actually exceed
1 anywhere. If the mechanism of spiral wave instability illustrated in
Fig. 9 is correct, the failure of the APD restitution slope to exceed 1 should have prevented spiral wave breakup by dampening oscillations in
APD and diastolic interval along the spiral wave arm. This paradox was
resolved, however, when we examined APD restitution for the NaR
case in a one-dimensional cable of cardiac cells. In contrast to the
single cell, the slope of APD restitution in the ring did exceed 1 at
short diastolic intervals (Fig. 2B, inset in middle panel).
This example illustrates that in cases in which the slope of APD
restitution approaches close to 1 in the single-cell model, tissue
measurements of APD restitution may be required to predict spiral wave
stability. Nevertheless, despite this "gray zone," our study
suggests that interventions that markedly alter the steepness of the
single-cell APD restitution slope to values considerably less than or
greater than 1 remain highly accurate for predicting the spiral wave
behavior. This is an important point for potential drug screening
experiments to predict antifibrillatory efficacy from restitution measurements.
The second major caveat is that our simulations were based on a
homogeneous, isotropically conducting 2-D medium in which the cell
model had a steep (slope > 1) APD restitution curve. We have not yet
studied how anisotropy, electrophysiological heterogeneity, and
anatomic obstacles affect the validity of these conclusions or whether
conclusions about spiral wave behavior in 2-D have direct relevance to
scroll wave behavior in 3-D tissue. For example, Fenton and Karma (12)
recently found in 3-D simulations using a simplified cardiac model that
the rotation of fiber orientation from endocardium to epicardium may
induce breakup of reentrant scroll waves by inducing filament twist.
Also, some investigators have questioned whether APD restitution
properties during spiral wave reentry in the real heart are
sufficiently steep to produce breakup at all, although there are many
examples in the literature in which APD restitution has been found to
have a slope >1 (~50% in our survey of the literature), in both
animal (2, 10, 44) and human (14, 30) studies. The ability to
extrapolate our simulation results to fibrillation in real cardiac
tissue will require this issue to be further clarified by experimental studies. It has also been hypothesized that cardiac fibrillation in 2-D
models may be irrelevant to real cardiac fibrillation, which has been
postulated to require 3-D tissue to develop under physiological
conditions. However, this hypothesis appears to be at odds with the
experimental documentation of sustained fibrillation in relatively thin
cardiac preparations, such as the full-thickness (5-9 mm) porcine
right ventricle (22), thin (2-4 mm) right ventricular sheets in
the presence of drugs that shorten action potential duration (15), and
the thin-walled atria (20).
With respect to the issue of heterogeneity, it is well established that
tissue heterogeneity promotes the initiation of functional reentry.
However, this does not necessarily imply that once spiral wave reentry
has been initiated, tissue heterogeneity continues to have a
destabilizing effect. In both experimental and clinical settings,
monomorphic VT compatible with a stationary spiral wave reentry is
virtually never seen in normal hearts, only in diseased hearts in which
heterogeneity caused by an infarct or other process has occurred. In
contrast, in healthy (less heterogeneous) hearts, functional reentry
compatible with unstable spiral wave reentry is more difficult to
induce but can invariably be initiated with a sufficiently aggressive
stimulation protocol. Once initiated in the healthy heart, however,
this type of functional reentry is never stable if sustained and always
degenerates to VF through a mechanism consistent with spiral breakup
(4, 19). Also, both theoretical and experimental studies documented
that spiral wave stability can be enhanced by tissue heterogeneities,
which tend to anchor the cores of spiral waves by creating local
source-sink mismatches (34). From a therapeutic standpoint, tissue
heterogeneity is a very difficult target, whereas cardiac restitution
properties should be predictably alterable by pharmacological
interventions. Therefore, if it can be demonstrated that spiral wave
stability is primarily controlled by cellular restitution
characteristics, the hope for developing effective antifibrillatory
drug therapy is indeed promising.
Clinical implications for antifibrillatory drug therapy.
If the hypothesis is correct that cardiac fibrillation arises from a
single or double reentrant wave front that subsequently breaks up into
multiple reentrant wave fronts, then understanding the factors
controlling the stability of reentrant wave fronts in cardiac tissue is
critical for developing effective antifibrillatory therapy. To the
extent that spiral wave reentry in simulated cardiac tissue provides a
realistic model for fibrillation, our study suggests that drugs that
alter APD and CV restitution by modulating ionic current restitution
properties may markedly influence the tendency for spiral waves to
break up and cause a fibrillation-like state. The traditional
classification of antiarrhythmic drugs is based on their effects on
APD, CV, and individual ionic currents and was devised largely to
characterize their antitachycardic effects, because tachycardia is much
better understood than fibrillation. Our results provide a preliminary
framework for understanding how these drugs, through their effects on
APD and CV restitution, may affect the tendency to fibrillation. Our
modeling (Fig. 8) suggests that an ideal antiarrhythmic drug should
have both antitachycardic and antifibrillatory efficacy. Subject to the
various caveats discussed above, we suggest that a drug or drug
combination that flattens APD but not CV restitution, in addition to an
antitachycardic action, would have the ideal profile. Drugs with a
favorable antitachycardia profile, but an unfavorable antifibrillation
profile, could potentially contribute to proarrhythmic effects. An
example might be class III antiarrhythmic drugs with reverse use
de
Top
Abstract
Introduction
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