© 1998 American Heart Association, Inc.
Original Contributions |
Purkinje-Muscle Reentry as a Mechanism of Polymorphic Ventricular Arrhythmias in a 3-Dimensional Model of the Ventricles
From the Department of Pharmacology, SUNY Health Science Center at Syracuse, Syracuse, NY.
Correspondence to Omer Berenfeld, Department of Pharmacology, SUNY Health Science Center at Syracuse, 750 E Adams St, Syracuse, NY 13210. E-mail beren{at}sundial.pharm.hscsyr.edu
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Abstract—Multiple electrode mapping of the ventricles during complex tachyarrhythmias has revealed focal subendocardial activation whose mechanism remains unexplained. We hypothesized that reentry involving the Purkinje-muscle junctions (PMJs) may be a mechanism for such focal excitations. We have constructed an anatomically appropriate computerized 3-dimensional model of the mammalian ventricles that includes the Purkinje conduction system and 214 PMJs distributed throughout the endocardium. Isochronal maps during normal excitation, as well as during right or left bundle branch block, resembled experimental measurements and compared well with isochronal maps of propagation in the human heart. Activity observed at both sides of a PMJ in the model showed that propagation from Purkinje fibers to muscle was slower than in the opposite direction. Under these realistic and normal conditions, the evolution of reentrant activity involving muscle and the Purkinje network was simulated. The reentry pattern was independent of the initiation site. It evolved with drifting epicardial breakthroughs and transformed on the endocardium from focal activity to figure-of-8 reentry. In addition, the ECG amplitude undulated during the evolution, and decrease in the cycle period, apparent wavelength, and propagation velocity were observed. Finally, the reentry was terminated if the Purkinje system was disconnected from the muscle before it reached a relative steady state. The simulation results suggest the following: (1) Epicardial breakthroughs and endocardial focal activity may originate at the PMJs. (2) The ECG amplitude may decrease as the reentry stabilizes and the excitation wavelength decreases. (3) The Purkinje system may have a double role in the evolution of reentry: first, it is essential to the reentry at the initial stage; second, it may lead to the establishment of intramyocardial reentry, at which time the Purkinje system becomes irrelevant.
Key Words: ventricular modeling • Purkinje system • polymorphic tachycardia • reentry
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Introduction |
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The use of high-resolution mapping techniques in the study of ventricular excitation, together with numerical analyses based on nonlinear wave propagation theory, have provided important insight into the dynamics of life-threatening ventricular tachyarrhythmias.1 2 3 4 However, many questions remain unanswered. For example, multiple electrode mapping of the ventricles during complex tachyarrhythmias has revealed focal subendocardial activation, the mechanism of which has not been established. It has been suggested that focal activity may arise at the border zone of an ischemic region as a result of injury currents5 or may be the result of pacemaker automaticity.6 Although these hypotheses are feasible, they have, as yet, not been demonstrated to be valid. Injury currents are associated with heterogeneity in action potential properties as well as spatial coupling gradients. Heterogeneity is inherent to the region where the specialized conduction system of Purkinje fibers interacts with the myocardium.7 The His-Purkinje system is characterized by appreciably higher upstroke velocity and intercellular coupling and by longer APD than the myocardial cells. In addition, Purkinje fibers are capable of undergoing spontaneous pacemaker discharges and, under certain conditions, triggered activity. Thus, the presence of Purkinje fibers may be sufficient to establish the required conditions for focal activity.8 9 Alternatively, focal activity at a PMJ may be the result of simple reentry that includes orthodromic propagation from a Purkinje fiber pacemaker site or antidromic propagation from a depolarized muscle site undergoing abnormal automaticity.10
The Purkinje fiber system is a major factor in the synchronization of myocardial activity because of its unique propagation properties and its geometrically widespread distribution, with abundant PMJs over the two ventricular subendocardial surfaces. During normal orthodromic excitation, fast propagation over long fibers, together with wide distribution of PMJs, induces a high degree of correlation between distant regions of the myocardium.11 12 On the other hand, the complex geometry and high degree of heterogeneity in APD of that system compared with the myocardium, as well as the asymmetrical propagation velocity across the PMJs, may decorrelate parts of the system and create dispersion of APD and refractoriness.13 This, in turn, may increase the susceptibility for unidirectional block, which is topologically essential for initiation of reentrant activity. The role of Purkinje-muscle interactions in microreentry is evident,10 14 15 and the involvement of the His-Purkinje system in macroreentry during monomorphic VT has been established.16 However, to our knowledge, the role of these structures in the mechanism of PVT and VF17 remains undefined. The appropriate sites and protocols for clinical induction of VT or VF are still under study. Common endocardial sites used for pacing are the RV apex and the outflow tracts.18 19 Triggering protocols involve a basic driving pulse train (cycle length, 600 to 400 ms) with up to four premature extrastimuli. Morady et al20 reported that when coupling intervals were higher than 180 ms during extrastimulation, monomorphic VTs were induced, whereas below that value, the VTs induced were polymorphic. VF may also be induced in a significant number of patients without obvious heart disease.21 22 In a limited number of subjects, spontaneous PVT, with no structural cardiac disease, was documented.23 24 25 To date, the triggering mechanisms of those PVTs are unknown, and these patients are believed to suffer from some primary electrical disorder. Arnar et al26 recently reported that spontaneous VT during acute ischemia in dogs was initiated often with a focal Purkinje origin. In another recent work, Peeters27 reported that endocardial ectopic impulses were observed during induced PVT in patients with documented spontaneous VF in the absence of structural heart disease. In the present simulations, unidirectional propagation is reproduced by a regionally confined impulse penetration from the Purkinje system into the myocardium, whereas unidirectional block prevents the impulse from spreading into the Purkinje system. We do not explore in the present study the nature of the triggering mechanism but concentrate on the evolution of the simulated activity following such a stimulation.
We have hypothesized that reentry at the PMJ may be an underlying mechanism of focal excitation, seen as endocardial and/or epicardial breakthroughs, during PVT and VF. We further hypothesized that the Purkinje system has a role in determining the overall dynamics of ventricular excitation during such complex arrhythmias. To test these two hypotheses, we have constructed an anatomically appropriate computerized 3-D model of the mammalian ventricles that includes rotational anisotropy and the Purkinje conduction system. Previous modeling studies have considered the atrioventricular conduction system to account for the normal cardiac rhythm or to establish the characteristics of the impulse and its spread.11 12 28 29 30 31 32 33 Other modeling studies, which regard reentry as the mechanism underlying the most dangerous arrhythmias, emphasize cellular properties, such as excitability, refractoriness, APD recovery, and intercellular coupling, but do not account for the conduction system.34 35 In the present study, we have combined the two approaches by incorporating a simulated Purkinje fiber conduction system into an anatomically realistic model of ventricular excitation. The model undergoes reentrant excitation under the appropriate conditions and shows that the Purkinje fiber system plays an important role in it. It is required initially for maintaining reentry across the PMJs, until the system stabilizes into a condition under which the PMJs are no longer essential for arrhythmia maintenance.
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Materials and Methods |
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Model Structure and Incorporation of the Purkinje Conduction System
Extensive anatomic measurements of the canine ventricular structure and muscle fiber organization allowed description of the myocardial units in terms of a 3-D field of geometry and of orientation unit vectors, in an interpolated 60-element structure, formulated in a prolate spheroidal coordinate system.36 Dr A. Panfilov kindly provided us with the translation of these 3-D fields into a cartesian coordinate system of 94x94x94 elements with a 1-mm physical distance between the nodes. On the basis of Panfilov's regular geometry grids and portions of his developed software, we have established the ventricular myocardial structure (Figure 1A
). Pollard
and Barr37 have developed a strategy for the
construction of Purkinje network models that is based on real
microscopic and macroscopic features. While keeping the same anatomic
basis here,38 we have simplified the
electrophysiological considerations of the
Purkinje system structure. We established the Purkinje fibers as an
interconnected chain of nodes on the cartesian coordinate system in
which variability in fiber thickness was achieved by packing fibers
parallel next to each other in a bundle. We assigned a single
macroscopic coupling coefficient to distinguish them from the muscle
nodes and set the geometrical arrangement of the Purkinje nodes to lead
the propagation direction of the action potential in the grid. The
incorporation of the Purkinje system into the ventricular
model involved the following steps (see Figure 1B and 1C): (1) The
borders of the LV and RV endocardial surfaces were identified on the
3-D geometry database by an edge-detection algorithm and sketched on a
2-D bit map. (2) Graphic presentations of the left and
right bundle branches and the Purkinje system were digitized from
anatomic data in the literature38 and were scaled
to fit within border limits of the 2-D surfaces using the main bundle
branches and boundaries as markers. The digital description of the
Purkinje system was then manually manipulated and retouched for scanner
and rescaling errors, as well as for incomplete anatomic data. (3) The
end points of the Purkinje system in each ventricle were labeled to
allow the identification of the PMJs and the connections to the His
bundle (HB in Figure 1B). (4) The 2-D Purkinje digital bit–map
presentations were superimposed on the 3-D structure by
laying it onto the detected endocardial surfaces. (5) The His bundle
and the left and right bundle branches were established and connected
to the left and right conduction system. (6) The 3-D grid was scanned
throughout to bridge over any discontinuity in the Purkinje 1-D
branches that may have resulted from the superposition process. (7)
Normal and bundle branch block sequences of excitation were simulated
to verify the correctness of the overall Purkinje-muscle system
synchronization of the excitation process. In case the sequence was
unrealistic, we reiterated the process from step 2 until the sequence
satisfied experimental isochronal maps.39
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Kinetics
The kinetics of all the units in the model are governed by a set
of piecewise linearized FitzHugh-Nagumo–type equations, which
constitute the reaction-diffusion activity40:
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) is as follows:
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(V
V2)=30 to prolong
their APD. The electrical kinetics adopted do not reproduce the precise
membrane action potential but rather its phenomenological features,
including the spontaneous or suprathreshold excitation, spontaneous
recovery, and absolute and relative refractoriness. To verify the
restitution properties of the model kinetics, we performed measurements
of a steady-state APD in an isolated element subject to varying cycle
lengths. Figure 2A presents the
steady-state APD restitution relations (normalized to
APD0) of an isolated Purkinje unit
(APD0, 274 ms) and a muscle unit
(APD0, 184 ms). It is shown that the APD shortens
as the cycle length shortens. These restitution curves correlate well
(r0.82) with the empirical formulation suggested by
Elharrar and Surawicz41 for dog cardiac Purkinje
fibers and demonstrate that the model kinetics are appropriate to
simulate activity in which the front and the back of the action
potential interact during reentry. It should be realized though that
the incorporation of a given element into a collective structure will
alter its APD characteristics because it will be subject to different
source-sink conditions.42
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The Purkinje-Muscle Junction
In the present study, we assume that the Purkinje fibers
interact with the myocardium only at discrete sites through
passive resistors.43 Figure 1C
illustrates
schematically a Purkinje fiber that is stretched along the myocardial
surface and is electrically uncoupled from the myocardial units except
at its end points. At the Purkinje terminal points in that
illustration, there are 3 intermediate units (green) that are coupled
to the Purkinje fiber (red), on the one hand, and to the
myocardium (white), on the other, and thus constitute the
PMJ. Figure 2B shows a connective diagram of a typical junction: The
intermediate units (J) are shown to be coupled through a single passive
resistance to the Purkinje unit (P) and through several passive
resistors to adjacent myocardial units (M). In the model, however, the
number of intermediate units varied, and only on the average, there
were 3 units at each end point that interacted with the muscle units.
At locations where the orthodromic propagation was blocked, >3
interacting units were assigned, and where the density of Purkinje
terminals was higher than the spatial resolution of the model, the
interacting units were shared by >1 Purkinje terminal. The arrangement
of several interacting units at the Purkinje terminal set up a gradual
transition from a 1-D cable to a 3-D grid and allowed enough
electrotonic currents for orthodromic excitation of the muscle units.
As shown in Figure 2C, recorded activity from both sides of a PMJ
showed that propagation from Purkinje to muscle (orthodromic) was
slower than in the opposite direction (antidromic) and suggested that
the safety factor for propagation was higher for the excitation of the
Purkinje fibers by the
myocardium.14 44 45
Numerical Implementation
The whole model set of units is divided into 3 functional
subsets, each one independently integrated in time explicitly in an
Euler scheme. The largest subset contains 211494 myocardial
units; the second largest subset is that of 4539 Purkinje units; and
the third subset is that of 214 Purkinje terminal units. Interaction
among subsets occurs only at the common boundaries, which are the PMJs.
Each subset of units stores the potential of its own nodes in a designated array that is accessed by the other subsets of units when boundary interaction currents are calculated. The interaction of a given unit with its 18 neighboring units (immediate and second closest neighbors) is obtained by performing the laplacian operator with central finite differences (with no-flux boundary conditions) and with each grid node possessing a local diffusion coupling tensor. The diffusion tensors of all the units are precalculated on the basis of the orientation of the fiber at the particular node35 and stored in a database that, in addition, contains the unit's precalculated vector of the local diffusion gradient. Because of great coupling gradients across the PMJs that may lead to numerical instabilities, the interaction between a myocardial unit and a terminal Purkinje unit is obtained by calculating the transmembrane current as the product of the potential difference between the 2 units and the conductivity, measured as the myocardial longitudinal coupling coefficient.
The distance between the grid nodes in the model is 1 mm, and the
integration time step is 0.0181 ms. The diffusion constant has a value
(in 10-3 m2/s) of 8.287 in
the Purkinje system and 0.331 and 0.058 in the myocardial fibers in the
longitudinal and transverse directions, respectively. On the basis of
these values, the passive and active properties of the model were
calculated for a 1-D chain of 400 nodes that were 1 mm apart from
each other and had the membrane kinetics and corresponding coupling
values. Subthreshold stimulation applied to the middle of the cable
yielded space constants of 1.18, 0.33, and 0.21 mm for the
Purkinje, longitudinal, and transverse muscle couplings, respectively.
In the literature, values reported for the space constant vary from
0.357 mm in rabbit RV papillary muscle46 to
0.88±0.07 mm in sheep and calf ventricular
myocardium.47 The time constants in
those preparations were 2.57 and 4.4±0.55 ms, respectively. The
kinetics used in the present model exhibit a dependency of the rate
of change of potential on the stimulating current even for subthreshold
current levels; therefore, the rate of change was measured for the
upstroke of a solitary propagating action potential. With the above
passive values, the cellular kinetics yield a maximal upstroke rate of
44 V/s (when the action potential amplitude is scaled to 100 mV peak to
peak) for the 3 types of cells modeled, which is about half the average
myocardial rate and an order of magnitude lower than in the Purkinje
fibers.48 49 Nevertheless, the propagation
velocities obtained are 3.48, 0.64, and 0.21 m/s in the 1-D cable with
Purkinje, transverse, and longitudinal muscle couplings, respectively.
The reported values for the wave-front propagation vary considerably:
Whereas Scher and Spach50 have reported average
propagation velocities of 0.4 m/s in the muscle and 1.25 m/s in the
Purkinje system, Ganong51 gives velocities of 1.0
m/s in the muscle and 4.0 m/s in the Purkinje system. Our model values
for the propagation velocities are in accordance with that range of
values. The fact that the characteristic front width measured on the
1-D cable is 2 mm indicates that the characteristic minimal
length of observed activity in the model structure is greater than the
distance between the lattice nodes.
The model was coded in the C language, and the simulations were
executed on Sun Sparc station 10 (model 512). The required central
processing unit time was 
1.5 hours per 10 ms of cardiac activity,
which imposed great limits on our ability to carry out longer or more
detailed simulations. The estimation of the time required for the
simulations as a refinement of the model grid space (h) by a factor n
(n<1) is based on 2 effects. The first is the increase in the number
of model elements by n-3, and the second stems
from the numerical stability requirement that states, in its simplest
form, that the time step (
t) should always satisfy
t
h2/2D (where D is the diffusion constant).
Therefore, reducing h by n implies reducing t by
n2; the total time of computation then increases
by n-2. Combining together the 2 effects results
in the dependence on n-5 of the refinement in n.
Therefore, if n=0.5, then the total computation time would increase by
a factor of 32. Adopting a more detailed membrane kinetics, with a
realistic upstroke rate, would require a mesh constant of 0.2
mm, implying using n=0.2 (since currently we use h=1 mm) and
therefore an increase of computation time by
0.2-5=3125. Presently, it takes 25 days
to complete 4 s of simulation, and such an increase would result
in 25x3125
214 years(!) of computation, which is entirely
impractical. The 3-D excitation process was visualized using the AVS
software package (Advanced Visual Systems Inc), and the software to
visualize 2-D cross sections and projections was custom made.
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Results |
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Normal Sequence of Activation
When the His bundle was excited, the impulse propagated along the Purkinje fibers through the PMJs and then spread throughout the myocardial walls. In Figure 3
, we
present snapshots of the excitation process after the external
stimulation of the His bundle. Excitation spreads rapidly from the His
bundle (red) to the right and left bundle branches and their
subdivisions. The impulse then moves down to the left and right septum
with bifurcations on the left side into the anterior, middle, and
posterior walls. On the right septum, there is a fiber connecting the
septum directly to the papillary muscle location on the RV free wall.
Until 30 ms after stimulation of the His bundle, the propagation is
through the Purkinje fiber system without invading the
myocardium. The snapshots at 29 and 36 ms after onset show
the initiation of the myocardial excitation first in the mid lower left
septal endocardium and then, with some delay, in the apex of the RV
septum and papillary muscle region. Figure 4 illustrates the effect of the Purkinje
system on the excitation sequence in the ventricles. It shows
isochronal maps of vertical and horizontal cross sections of the
model during external excitation of the ventricles in the absence
(Figure 4A) and presence (Figure 4B) of the His-Purkinje system. The
isochronal maps in Figure 4A show that without the Purkinje system,
the excitation front propagates somewhat radially from the point of
stimulation in the most basal portion of the septum (asterisk). It then
spreads along pathways that depend on the anisotropic coupling. In
contrast, Figure 4B demonstrates that the introduction of the Purkinje
system allows almost simultaneous activation at multiple
sites on the endocardial surfaces of both ventricles. In addition, the
general trend of propagation in the myocardium is
transmural, from endocardium to epicardium. Overall, the results in
Figure 4B resemble experimental measurements and compare well with
isochronal maps of propagation in the isolated human
heart.39
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The Calculated ECG During Normal Activation and Bundle Branch
Block
Pseudo precordial and limb-lead ECGs were calculated for the
Purkinje-muscle model by summing up all the transmembrane intercellular
dipoles (P) weighted by the distance (r) from the electrode and its
direction:
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, panel A shows the ECG leads for the
normal activation sequence. Panels B and C show the ECG generated when
we induced right and left bundle branch block, respectively. To obtain
the correct deflection of the T wave in the ECG, the repolarization of
the units was timed in the reverse order of the excitation. This was
achieved by arbitrarily assigning each node with a quadratically
decreasing value of the rate constant at
VV2, from 30 to 0.05, as a function of the
excitation time of that node obtained from a previous simulation.
Qualitatively, the configuration of the individual ECG tracings falls
within the limits expected in the clinic for each particular
condition.52
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Simulation of Reentry
After establishing the anatomic geometrical structure and function
of the discrete elements of the model, we proceeded to study the
interrelations between the Purkinje system and the
myocardium during reentrant activation in the ventricles.
Since the conditions responsible for the initiation of reentrant
activity may be different from the conditions for its
maintenance, one can study these two separately. In the
present study, we ignore the pathophysiological
mechanisms that are responsible for the initiation of reentry (ie, the
triggers) and address the maintenance of reentrant propagation
in the ventricles in general and through the PMJ in particular. To
initiate the arrhythmia, we conveniently apply initial
conditions of an outwardly propagating spherical excitation wave that
is centered at a PMJ in the basal region of the LV free wall. This
corresponds to a local penetration into the myocardium
while the rest of the surrounding PMJs are blocking the orthodromic
propagation. Such conditions may exist, for example, when an early
afterdepolarization is initiated locally at a distal Purkinje fiber
branch.53 54 Because of asymmetry in the
refractory period within that branch (eg, electrotonic interactions at
the PMJ shorten the refractory period in distal Purkinje fibers), the
early afterdepolarization may be unable to propagate retrogradely into
the Purkinje network but successfully invade the neighboring PMJ. As
shown in Figure 6, under such initial conditions, the
wave front propagates radially from the PMJ at the center of the
initial sphere into the muscle mass in all directions. As soon as the
propagating wave front encounters a resting PMJ, it penetrates the
Purkinje system antidromically, travels through it, and also returns
toward the PMJ at the center of the sphere. When the wave arrives at
the center area, the muscle at that PMJ is no longer refractory and
allows orthodromic propagation and a repetition of a generally similar
Purkinje-muscle reentrant pattern. The propagation into the
myocardium is followed by the appearance of an epicardial
breakthrough approximately across the same endocardial location of the
PMJ through which the invasion occurs.
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Figure 7 shows ECG traces of 3.7
s in the reentry episode that resulted from the above initial
conditions. All leads displayed a clear undulating morphology. The
traces are V2, V5, and the
3 VCG component leads (base-apex, left-right, and posterior-anterior),
calculated as the sum of the model dipole moments, at each node. The
undulating behavior consisted of an initial increase in the amplitude
until 1200 ms after the onset of the reentry and, generally after
that, a gradual decrease in that amplitude for 800 ms. Thereafter,
the amplitude remained relatively unchanged for at least 600 ms, until
the simulation was ended deliberately. As illustrated by the spectral
analyses on the right, all the traces show a narrow-banded
power spectrum with a significantly larger contribution of frequencies
at 4.8 Hz. The fact that V5 and
V2 electrodes, which record activity from
opposite sides of the ventricles (note the half-cycle phase difference
between the 2 traces), show an approximate synchronized pattern of
amplitude increase and decrease indicates that the equivalent dipole is
not moving from one electrode to the other. In addition, the
possibility of rotation of that dipole source is excluded by the fact
that amplitude of the VCG components is also generally
synchronized.
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Figure 8A shows a sequence of snapshots
of the epicardial surface on the lateral wall of the LV during the
reentry episode. Several activity sites are seen on that surface, but
let us concentrate on the breakthroughs in the middle and lower
portions of the surface. The data in Figure 8A demonstrate that after
the onset of Purkinje-muscle reentry, the epicardial breakthrough
(shown inside the white circle and indicated by arrows) migrates
gradually from the base of the lateral free wall of the LV to the apex,
where it anchors for at least 6 s (not shown). The change in the
breakthrough location is marked by the appearance of a new breakthrough
in a nearby location and, only then, the disappearance of the old
breakthrough. This could be the result of either an alteration of the
direction of the wave propagation or the creation of new sources by
reentry breakups in the apex region, which take over the ones in the
basal region because of their shorter periods. As demonstrated by the
sequential series of polar projections of the left endocardial
surface shown in Figure 8B, there is a gradual transformation of the
excitation pattern in the free wall: from a breakthrough at the base
(see frame taken at 44 ms) into a figure-of-8 wave
source8 anchored at the mid apex region (see
frame taken at 2238 ms).
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In Figure 9, we display the dynamics of
3-D activity using representative snapshots at 6
instants in time. This provides a clear picture of the relationship
between changes in the mechanism of reentrant activation and the
corresponding changes in the position of epicardial and endocardial
breakthroughs as well as in the ECG during the tachycardia.
Figure 9A shows early activity; at 65 ms, Purkinje-muscle activation
resulted in an endocardial breakthrough (shown as x on the
figure), which, after transmural propagation, gave rise to an
epicardial breakthrough (asterisk) at 130 ms. In Figure 9B, four cycles
later (989 to 1054 ms after onset), activity had drifted downward and
to the left. At this time, 2 simultaneous Purkinje-muscle
activations could be seen as endocardial breakthroughs that
subsequently gave rise to epicardial breakthroughs near the apex of the
LV. The drift in the position of the endocardial breakthroughs ruled
out the possibility that the drift in the epicardial breakthroughs was
caused by a change in the direction of transmural propagation. In fact,
the results presented thus far demonstrated that up until
1450 ms after onset, the mechanism of the tachycardia
was Purkinje-muscle reentry occurring sequentially at varying sites.
Thereafter (Figure 9C and 9D), Purkinje-muscle activation no longer
occurred, but an intramural scroll wave was seen.
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Scroll waves have been demonstrated in previous studies of reentrant VT
using realistic anatomic models of the ventricles in the absence of
Purkinje fibers.3 Scroll-wave properties are
usually characterized by the dynamics of the axis of rotation, the
so-called filament,55 which, in the 2-D plane, is
detected at a point where the wave front and the wave tail
meet.56 To reconstruct the filament in our 3-D
simulations, we calculated the time difference of the binarized
activity of each model element, assigning to the wave front and wave
tail positive and negative values, respectively. The location where
these 2 regions came together formed a series of points considered to
be the filament. In Figure 9C, we present the earliest epicardial
breakthrough (right) that originated from a scroll wave, 7 cycles after
onset (1456 ms). The scroll-wave filament (left) was 15 mm
long, almost linear in shape, but had its 2 curled ends connected to
the endocardial surface. The latter is characteristic of a U-type
filament,55 which is consistent with the
figure-of-8 reentry seen on the endocardial surface in Figure 8B.
As discussed above for Figure 8A, the epicardial breakthroughs
became stationary near the apex of the LV after 1.5 s. In addition,
as shown in Figure 9D, the intramural activity evolved up until 1990
ms (10 cycles) after onset, at which time it had become relatively
stable. The scroll-wave filament seen in Figure 9D had curled such that
one of its ends was located near the center of the endocardium of the
LV free wall. Toward its center, the filament aligned vertically
downward, and then it bent steeply to form an horizontal loop around
the LV apex and climbed upward to reattach its other end to the
endocardium at the bottom of the LV free wall. In spite of its
complicated shape, the filament shown is topologically equivalent to a
U-type filament and is therefore consistent with endocardial
figure-of-8 reentry giving rise to a single epicardial breakthrough.
Analysis at later stages (not shown) demonstrated that the
shape of the filament was not significantly different from that seen at
1990 ms in Figure 9D.
Periodicity, Wavelength, and Propagation Velocity
The ECG amplitude continued to decrease at a time when epicardial
breakthroughs became stationary near the apex of the LV; thus,
breakthrough drift does not explain the mechanism of ECG changes.
Nevertheless, the excitation that propagated from the LV apex toward
the rest of the heart was characterized by a progressive reduction in
wavelength, which could be the source for the ECG amplitude reduction.
Panels A and B of Figure 10 show
snapshots of activity cycles obtained during high and low amplitude of
the ECG, during the episode presented by the ECG in panel C
(lead V5). The cycle length is 197 ms during the
high amplitude and 156 ms during the low amplitude. The general
patterns of propagation seen on the epicardium and outside the
endocardial focal region during these 2 cycles are similar; therefore,
we can compare their wavelengths and the propagation velocity.
Examination of the epicardial projection snapshots shown in Figure 10A and 10B suggests that there is a shortening of the wavelength from
30 to 15 mm and a decrease in speed from 0.28 to 0.18
m/s (along the indicating arrows) during the high and low ECG amplitude
cycles, respectively.
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Essential Role of Purkinje Fibers in Reentry Stabilization
To address the cooperative role of the Purkinje fibers and the
myocardium in the formation of the reentry, we performed
simulations using a model in which the 2 subsets were separated just
before a second cycle was about to begin. At 196 ms after the onset of
the reentry, we disconnected the 2 systems and allowed each to continue
its activation on its own. Figure 11B
shows the ECG traces (lead V5) obtained in that
simulation. It is seen that although the combined
(Purkinje+myocardium) structure maintains a periodic
activity, each of the separated subsystems fails to do so. The activity
ceased in the Purkinje system after 32 ms and in the
myocardium after 351 ms, showing that at this stage of
the reentry, both systems are essential for
maintenance of the activity. If the Purkinje system is removed
at 1011 ms after the onset of the reentry (Figure 11C), then the
activity is eliminated abruptly after 3 cycles (880 ms). In contrast
with the gradual amplitude decrease in the simulation of the combined
(Purkinje+myocardium) structure at this time, the 3 cycles
before termination show relatively constant QRS morphology and
amplitude. This demonstrates that the reentry pathway used the
conduction system and that the existence of the Purkinje system somehow
caused the decrease of the ECG amplitude (discussed below). At this
time, the high amplitude of the ECG is associated with the long
wavelength in the myocardium, which cannot support the
reentry for >880 ms. As shown by the 2 traces in Figure 11D, if the
Purkinje system is disconnected at 1989 ms, at which time the QRS
amplitude begins to achieve a relatively stable low amplitude and an
intramural scroll wave is already present (Figure 9D), then the
reentry is sustained by the myocardium alone. In all 3
cases shown here, at the time of Purkinje-myocardium
disconnection, the reentry is not sustained in the Purkinje system by
itself. However, as demonstrated here, the Purkinje network is
essential only up to a certain point, at which the reentry process
stabilizes in the myocardium. When the trace of the
myocardial reentrant activity (top trace in Figure 11D) is compared
with the combined reentrant trace (Figure 11A), great similarity is
noted. The fact that the existence of the Purkinje system, or lack
thereof, does not affect the myocardial trace indicates the obvious
dominance of the myocardium over the Purkinje system during
that interval.
|
Figure 12A presents the potential
traces from a sample terminal Purkinje fiber and a sample muscle unit
located across the same PMJ. These traces are the result of the
membrane kinetics adopted and, as such, are only a phenomenological
representation of the action potentials. The action potential
traces show that at the beginning of the reentry, the terminal Purkinje
fiber excitation precedes the excitation of the myocardial unit across
the PMJ. Yet, at 2000 ms, the Purkinje excitation becomes almost
simultaneous with its myocardial counterpart. It is also
noted from these traces that the APD of both units is reduced with
time, in agreement with the observation of reduction in the activity
period. To verify the change in the relative times of excitation of the
Purkinje and muscle units across the PMJs, we show in Figure 12B the
time delay between their excitation (measured by the
dV/dtmax at 0.2<V<0.8) at four PMJs located in
the basal region of the LV free wall. It is seen that although in the
four Purkinje units excitation precedes that of their muscle
counterparts at the initial stages of the reentry, after 2000 ms,
the excitation of all of them follows muscle unit activation. Although
only four PMJs are shown here, they provide evidence for an interchange
in the role of source versus sink between the Purkinje fiber and the
muscle unit. The reverse in the order of excitation further supports
the notion that the myocardium dominates the Purkinje
activity at the later stage of the reentry, as was indicated by the
similarity between the ECG traces in simulations with (Figure 11A) and
without (Figure 11D) the Purkinje system.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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Major Findings
A computerized model of the ventricles was developed to study the role of the Purkinje system in the evolution of reentrant arrhythmias. The model consists of a realistically shaped grid of 211494 units corresponding to the ventricular myocardium and 4539 units corresponding to the Purkinje system. The 2 systems interact at 214 individual locations that provide the physiologically observed asymmetrical propagation across the PMJs.14 The kinetics of the various units were of the FitzHugh-Nagumo type with a monodomain anisotropic coupling term. The model structure is adjusted to generate a normal excitation sequence that is consistent with the experimental results of Durrer et al39 in the human heart and to produce a realistic pseudo ECG.52 Reentrant excitation was initiated in the myocardium of the free wall of the LV by unidirectional propagation, and its evolution was traced. The reentry showed a seemingly transient undulating QRS pattern in the ECG and VCG amplitudes, as well as a drift of epicardial and endocardial breakthroughs from the basal left free wall to the apex region of that wall. Although scroll-like activity was seen on the LV endocardial surface after stabilization, no such behavior was seen on the epicardial surface. Maintenance of that reentry was dependent on the coexistence of the myocardium and the Purkinje system at its initial stage, when the ECG amplitude was relatively high. At a later stage, when an intramural scroll wave was established and the arrhythmia stabilized at a relatively low QRS amplitude, the reentry was sustained in the myocardium even without the Purkinje system. The reentry stabilization was accompanied by decreases in the period, the apparent characteristic wavelength, and the propagation velocity. Stabilization was also characterized by a process in which the myocardium gained electrical dominance over the Purkinje system.
Drifting of Breakthroughs and Doppler Shifts
Our results show that drifting of sources of activity in the LV
free wall, reflected as epicardial breakthrough drifting, was
correlated with ECG amplitude changes over several cycles. Recent work
from this laboratory has related the dynamics of spiral wave reentry to
the initiation and maintenance of polymorphic
ventricular arrhythmias. Particularly, changes in
the QRS morphology during the sustained arrhythmia have been
attributed to spiral wave drift on the basis of the Doppler
effect.4 By examining the drift of the epicardial
breakthrough in Figure 8A, we surmised that this effect may have
contributed to the amplitude changes up to 1450 ms, since,
afterward, the breakthrough stabilizes near the apex. To test this
hypothesis, we examined the frequency content of the ECG during the
first 1853 ms of the simulation, which revealed a narrow-banded
spectrum with the highest power at 4.86 Hz. We further estimated
from Figures 8A and 10 that the velocity of drift of the epicardial
breakthrough was 0.034 m/s and that the velocity of the wave front
was 0.25 m/s for that period. Using these values and the
unidimensional Doppler relation, we predicted that the frequency
spectrum should be narrow-banded with dominant frequencies between 4.27
and 5.64 Hz. As shown by the narrow-banded spectra presented in
Figure 7, the Doppler effect explanation seems applicable. However,
it is important to note that the spectrum of a narrower window
(excluding the beginning of the reentry and up to 1450 ms) should be
obtained in order to verify or discard a Doppler shift effect
during the limited interval in which we actually observed a migration
of reentry. The fact that during that window in time the signals
measured at V2 and V5 leads
are relatively similar should not disqualify the applicability of the
Doppler effect, since in the simulations presented here,
these 2 leads are located generally perpendicular to the migration
direction of the reentry.
Mechanisms of Beat-to-Beat ECG Changes
We observed beat-to-beat changes in the ECG amplitude and
periodicity, as well as more or less sudden reduction in the activity
wavelength (Figures 9 and 10) and propagation velocity. We attribute
the reduction in the ECG amplitude to the reduction in the wavelength.
The wavelength shortening may have increased the number of dipole
moments while, at the same time, their relative geometrical
redistribution created conditions in which more dipoles are
self-canceling out their contribution to the ECG. The phenomenon may be
explained as follows: Assume that the front and the tail of an
excitation wave are represented by 2 dipoles that point in
opposite directions. The dipole that is closer to the ECG electrode
lead contributes more to the recorded voltage change than the
distant dipole. On the other hand, the closer these 2 dipoles are to
each other, the more similar their respective contribution to the
potential will be. Because of their opposite orientation, equal
contribution of the 2 dipoles would result in a cancellation. Hence, as
the wavelength in the myocardium shortens, the front and
the tail come closer to each other; thus, the ECG amplitude is reduced.
It is important to note, however, that this simplified illustration
holds only when the relative strength and orientation of the dipoles
are maintained. Indeed, the biphasic potential nature of the membrane
(outside the reentry core region) keeps the relative strength of the 2
dipoles independent of the wavelength. The fact that the pattern of
activity in Figure 10A and 10B remains similar indicates that some
dipoles are likely to remain in their original orientation. It is also
worth noting that the relation between the sources and the calculated
ECG is nonlinear; therefore, the amount of wavelength shortening cannot
be easily used as a predictor for the amount of the ECG amplitude
reduction.
The decrease in the ECG amplitude takes place at times longer than
1000 ms after onset, even while the epicardial breakthrough and the
endocardial wave source of the 2-D map are stable (see Figures 8 through 10). Because no new breakthroughs are seen during that period
of stability, the possibility of a wave breakup as the source for the
wavelength shortening is diminished. It is therefore proposed that
slower propagation velocity and the restitution properties of the
tissue, which respond with adaptation of a shorter APD to the
increasing excitation frequency,57 are
responsible for the shortening of the wavelength throughout the
ventricles and, thus, for the decrease in the ECG amplitude. The
underlying cause of these changes is a short-path short-wavelength
reentry at the apex region. Clearly, the shortening in APD is the
reason for the period decrease in the ECG. With this picture of events
in mind, we can assign to the Purkinje system the role of providing the
ventricles the necessary structure for correlation of distant regions
and for reentry maintenance while the adaptation process
shortens the wavelength below some critical value that allows the
reentry without the Purkinje system.
A different picture would be accounted for by the fact that APD in the
Purkinje system is longer than in the myocardium. This may
introduce phase differences between the Purkinje and myocardial sources
on the endocardial surface that, once the Purkinje is removed (as in
Figure 12), repolarize each other because their phases are not
correlated. As the reentry evolves in the Purkinje+myocardial system,
the APD of the Purkinje fiber is continuously abbreviated by the
dominant myocardium (see Figure 12A), and that occurrence
prevents the Purkinje system from interfering with the myocardial
reentry. It is therefore plausible that different recovery rates of the
Purkinje fibers and the myocardium across the PMJs would
have an effect on the alternation of the source-sink role between the 2
systems. This alternation will have an indirect effect on the
modulation of wavelengths in the myocardium and, thus, on
the ECG amplitude modulation and time of achievement of the critical
wavelength for myocardial reentry.
Role of the Purkinje System
The role of the Purkinje network in the cardiac vulnerability to
fibrillation has been the subject of much controversy. On one hand,
Janse et al5 have reported that in the
ischemic rabbit heart, ectopic beats are generated by
myocardial tissue even when the subendocardium, including the Purkinje
system, has been destroyed, but these beats never degenerate into VF.
On the other hand, Cha et al58 have reported that
prolonged VF in dogs could continue without the Purkinje fibers, but at
a slower rate. Our simulation results indicate that for the structure
and initial conditions imposed here, the Purkinje system is a necessary
requirement for polymorphic tachycardia at some initial
stage but that the excitation pattern evolves into a state in which
Purkinje fibers are not needed for arrhythmia
maintenance. Although our results did not show a deterioration
into irregular arrhythmia, we suggest that the Purkinje fiber
system may have similar roles in the onset and maintenance of
VF as those demonstrated here for polymorphic
tachycardia. In other words, our results indicate that the
role of the Purkinje system may vary according to the reentry patterns.
Indeed, contrary to its essential role in the initialization and
stabilization of the reentry in our simulations, previous simulations
have shown that a reentrant disturbance is reproducible with
the same model but without the Purkinje system if
heterogeneous recovery stimulation protocols are
adopted.3
Limitation of the Study
The model used here imposes certain limitations on the conclusions
drawn from the present study. We consider the major limitation to
be of a methodological nature. Practical computational limitations have
restricted the extent of our exploration of the model sensitivity to
states that may have had physiological or clinical
interest. Therefore, additional simulations were performed in order to
asses the generality of the observed phenomena. A reentry, similar to
the one shown in Figure 6, was initialized near the apex. By applying a
protocol of Purkinje-muscle disconnection similar to the one in Figure 11, we obtained the same qualitative results, indicating that the
conclusions drawn from the present study do not depend on unique
initial conditions. We also produced reentry by triggering antidromic
propagation (myocardium
Purkinje system), as opposed to
the initiation of the reentry in Figure 6, to verify that reentry could
be generated by stimulation leading to propagation in any desired
direction. Nevertheless, the conclusions shown here are associated with
a particular structure and a set of initial conditions, and the results
should be regarded as evidence for the richness of events possible when
the Purkinje system interacts with the myocardium.
From a structural point of view, our model ignores the bidomain nature of the cardiac tissue, the effects of the adjacent volume conductors and the detailed penetration of the Purkinje system into the myocardium. Our spatial resolution is 1 mm, and the bulk of tissue of concern is much larger than the biological cell. Our monodomain approach should be seen therefore as a space-averaging over the electrical properties. The realistic morphology of the calculated ECG indicates that the infinite volume conductor and the monodomain approximations are acceptable for the purpose of extracting the major markers of that signal, such as the relative peak values and the time interval between them. The first 2 limiting factors have also been shown numerically to have an effect on the propagation patterns in a tissue.59 Nevertheless, the main feature of our model is the incorporation of the Purkinje system and the PMJs, whose structure reproduces the realistic propagation behavior. The model units simplified interaction with the adjacent volume conductor is further justified in light of the experimental results of Cha et al58 showing that the replacement of the cavitary blood by air did not alter the endocardial electrical activity during VF. Regarding the penetration of the Purkinje fibers into the myocardium, we believe that the main feature of the PMJs is their asymmetrical safety factor, regardless of their respective location; therefore, the penetration of the distant fibers into the myocardium should not affect our results qualitatively.
We adopted FitzHugh-Nagumo kinetics, which, from the cellular point of view, are clearly an oversimplification of the biological excitation process and have an upstroke rate that is slower than the actual upstroke rate. The slow upstroke is appropriate to obtain a wave-front width of several units across. However, this implies a critical curvature that is lower than the real critical curvature, which may result in a reentry breakup phenomenon. We used an upstroke rate similar to that used by Panfilov and Keener35 to show reentry in an anatomic model of the ventricles. Panfilov and Hogeweg60 studied the effect of the recovery dynamics on 2-D breakups with an upstroke rate slower than the present one. They argued that a 3-D structure may be more prone to breakups.4 This indicates that the type of kinetics used in our simulations was adequate both for reentry in the myocardium alone and for the possible creation of turbulence by wave-front breakups. For the simulation of reentry, the myocardial and Purkinje units were assigned different yet homogeneous APDs for each system, ignoring the intrinsic heterogeneities of the myocardium and Purkinje network that are known to be present across and along the walls61 and at different fibers of the Purkinje system. This approach was adopted to avoid the masking of the interdependence of the 2 systems by an internal complexity. It is worth noting also that in the FitzHugh-Nagumo kinetics the APD can be controlled not only by changing the time constant during the plateau phase of the action potential but also by changing the slope of the middle portion of the linear f(V). Increasing that slope increases APD but, at the same time, increases the upstroke rate and excitability. Although this may be a desirable feature, it affects also the propagation velocity and masks the effects of the passive properties of the tissue in a heterogeneous and uncontrolled manner.
From a numerical standpoint, the limitation of the developed model is that the accuracy of solutions could not be verified by reducing the lattice constant, since the geometry of the PMJ is not scalable; if one reduces the lattice constant, then the effective diffusion constant is increased, and, therefore, the load of the muscle units on the Purkinje terminal is also increased. The PMJs in the model have 2 levels of ramification (P-junction units-M) to account for the increased load due to the transition from a 1-D structure to the 3-D structure of the muscle. This ramification was found to support the orthodromic wave propagation for the particular lattice constant that was selected. The junction structure would need a modification of additional levels of branching, if one increases the load on the terminal in the rescaling process and wants to maintain propagation.
Unanswered Questions
Some of the questions that remain to be investigated in a combined
structure of myocardium and the Purkinje system concern the
detailed description of the reentry evolution in terms of general
concepts of scroll waves. In our simulations, we noticed a drift of the
breakthroughs in the epicardium of the LV free wall, from the basal
region to the apex region, but we did not see a spiral-like reentry
there. Figure 9 shows that the epicardial activity originates at the
endocardial sources. On the endocardium, on the other hand, the pattern
of excitation gradually transformed from expanding breakthrough
sources, indicating Purkinje system invasion, at the initial stages of
the reentry, into a figure-of-8 source (Figures 8 and 9). Therefore,
the endocardial source drift should be attributed to different
mechanisms before and after it is converted from Purkinje invasion to
sustained figure-of-8 activity. The Purkinje-myocardium
invasion drift could be the result of shortest pathway loop drift that
results from the longer APD and higher propagation velocity of the
Purkinje system. The endocardial filament end-points drift, on the
other hand, could be the result of the boundary and the muscle fiber
curvature effects.62 63 The stable activity is
seen to produce a periodic epicardial breakthrough and endocardial
figure-of-8, consistent with a U-type filament (Figures 8 and 9). The intriguing curled filament may correspond to stabilization
along the longitudinal direction of the myocardial fibers. This
hypothesis, however, needs verification, and the dynamics need to be
understood. It is proposed that the mechanism involved in the
initiation of the myocardium-only reentry is the detachment
of the excitation from the endocardial surface as it propagates from
the Purkinje into the myocardium. According to that
proposal, during partial recovery of the membrane due to the high
frequency of excitation, unexcitable obstacles with sharp edges may
destabilize the propagation of the electrical
waves,64 causing the formation of self-sustained
vortices and turbulent cardiac activity. If a detachment of the
excitation indeed occurs, then it is enough to have a single one for
the creation of a U-type filament. The intramural scroll wave would
further dominate the ventricular activity if its period
were smaller than the Purkinje-muscle reentry period.
Conclusions
The above limitations notwithstanding, it is safe to conclude the
following: (1) The simulations suggest that published examples of
subendocardial activity with epicardial breakthroughs observed in
experimental preparations may be the result of reentrant excitation
originating at the PMJs. This reentry provides a mechanism for a
subendocardial focal activity that evolves into epicardial
breakthroughs. (2) A mechanism to decrease the ECG amplitude may be the
stabilization process of the reentry in which the activity wavelength
shortens as the reentry proceeds. (3) A particular initial condition in
our model yields a type of reentrant activity in which the Purkinje
system plays a double role. First, it provides the required structure
for the initial maintenance of the reentry; second, once the
reentry becomes sustained, the Purkinje system allows for drift and the
eventual establishment of intramyocardial reentry. When these
conditions are met, the Purkinje system becomes a bystander, with its
activity being enslaved by the rotating activity in the
myocardium.
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Selected Abbreviations and Acronyms |
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Acknowledgments |
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This study was supported by grant PO1-HL-39707 from the National Heart, Lung, and Blood Institute, National Institutes of Health. Dr Berenfeld is a fellow of the American Heart Association, New York State Affiliate, Inc.
Received July 3, 1997; accepted March 13, 1998.
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