(Circulation. 1996;93:1845-1859.)
© 1996 American Heart Association, Inc.
Articles |
Cycle Length Dynamics and Spatial Stability at the Onset of Postinfarction Monomorphic Ventricular Tachycardias Induced in Patients and Canine Preparations
Presented in part at the 16th Annual Scientific Sessions of the North American Society of Pacing and Electrophysiology, Boston, Mass, May 5, 1995, and published in abstract form (Pacing Clin Electrophysiol. 1995;18:899).
From the Research Centre, Hôpital du Sacré-Coeur de Montréal, the Departments of Pharmacology and Surgery, and the Institut de Génie Biomédical, Faculty of Medicine, Université de Montréal, Montréal, Québec, Canada.
Correspondence to René Cardinal, PhD, Centre de Recherche, Hôpital du Sacré-Coeur de Montréal, 5400 Gouin Blvd W, Montréal, Québec, Canada H4J 1C5.
 |
Abstract |
|---|
 Top Abstract IntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
Background The aim of this study was to determine whether cycle length (CL) variations at the onset of monomorphic ventricular tachycardias follow distinctive patterns.
Methods and Results We retrospectively analyzed 59
monomorphic ventricular tachycardias induced in 40
patients in whom intraoperative mapping was performed with 63
epicardial and 64 endocardial electrograms recorded
simultaneously. Activation times and CL were determined at
each electrode site over several beats (36±10 beats, mean±SD)
starting with the first after programmed stimulation. In the majority
of the tachycardias, CL variations were accounted for by
fitting to an exponential function:
CL=CLs+Ae-b/
,
where CLs is the stable CL, b is beat number, is the
time constant (in beat number), and A is the magnitude of CL
relaxation. A decelerating trend (with reference to rate) (negative A)
accounted for 21 tachycardias, an accelerating trend in rate
(positive A) accounted for 12 tachycardias, and 4 others
displayed a double dynamic behavior, with an initial acceleration
followed by a decelerating trend in rate. Among the
ventricular tachycardias that were not fitted to
exponential models, 12 showed a constant trend and 10 others showed
irregular CL fluctuations. The monomorphic character of the
tachycardias was established by principal-component
analysis, which also indicated that CL dynamics associated with
the accelerating and decelerating trends may be related to shortening
or prolongation of activation times, respectively, occurring in equal
proportion at all recording sites. In canine preparations in
which reentry circuits could be mapped with high resolution, CL showed
an accelerating trend in rate when circus movement of excitation
occurred around a transmural scar in muscle generating unipolar
electrograms with relatively high
-dV/dtmax, and a decelerating trend in
rate occurred when functional reentry occurred in muscle generating
unipolar electrograms with depressed
-dV/dtmax.
Conclusions Beat-to-beat CL variations may occur at the onset of sustained monomorphic ventricular tachycardia as a result of uniform acceleration or deceleration of activation times while the overall activation pattern remains constant. The associated initial trends in the rate of sustained monomorphic ventricular tachycardia follow typical patterns that might provide "signatures" corresponding to reentry substrates with distinctive functional properties.
Key Words: tachycardia • reentry • myocardial infarction
|
Introduction |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
Cycle length variations occur in the initial beats of sustained monomorphic ventricular tachycardias induced by programmed stimulation in patients with coronary artery disease and prior myocardial infarction.1 2 It is not known, however, whether such cycle length variations and the associated trends in rate follow distinctive temporal patterns and whether they may occur independently of changes in the activation sequence. Induction of a sustained monomorphic ventricular tachycardia by programmed stimulation (S1, S2 through S4) may be regarded as a transition from a relatively slow rate (sinus rhythm and basic train of S1 pulses) to a relatively faster rate (ventricular tachycardia). Since postinfarction ventricular tachycardias are thought to be caused by reentry,3 the transition from a slow to a fast rate may call into play the rate-dependent conduction and repolarization properties of muscle fibers involved in the reentry circuit, causing beat-to-beat variations in the tachycardia cycle length in the initial beats before the properties of the muscle have settled and a steady state is achieved. Accordingly, Volosin et al1 reported that cycle length variations decreased significantly over time, being greatest in the first 10 to 30 beats after induction by programmed stimulation.
In response to transition from a slow to a fast rhythm, the time course of changes in action potential duration shows an initial abrupt shortening over the first few beats, which is followed by more progressive shortening over the next few minutes.4 5 If reentry occurred around a fixed obstacle (either anatomic or pathological) and the length of the circuit were small enough for the action potential upstroke to encroach on the repolarization phase of the preceding action potential, the rate of tachycardia might accelerate initially, as the action potential duration shortened and the head of the reentrant impulse withdrew from the refractory tail in the wake of the preceding impulse. In contrast, an initial phase showing a decelerating trend in the tachycardia rate might occur if the reentry circuit (whether or not it occurred around a fixed obstacle) involved tissue displaying rate-dependent depression of action potential upstroke and conduction velocity, as shown to occur in ischemically damaged ventricular muscle of canine preparations of myocardial infarction.6 Third, the dynamic behavior of the tachycardia might be flat (constant cycle length) if the length of the circuit were long enough for complete recovery to occur between action potentials or if the tachycardia rate were slow enough for rate-dependent properties to remain latent. Thus, at least three patterns of dynamic behavior may be expected to occur in the early beats of reentrant ventricular tachycardias: (1) an accelerating trend in rate (ie, decreasing tachycardia cycle length), (2) a decelerating trend in rate (ie, increasing cycle length), and (3) a constant trend.
We retrospectively studied series of many beats at the onset of 59 monomorphic tachycardias induced in 40 patients undergoing map-directed surgery for ventricular tachycardia. The activation times determined at each of 127 epicardial and endocardial sites were subjected to principal-component analysis7 to establish the stability of their activation sequences while cycle length variations occurred. Cycle lengths were computed in successive beats, and a quantitative description of their dynamics was sought by fitting to exponential functions.
The hypothesis that the functional properties of the tissue involved in reentry might bear a specific dynamic "signature" shaping the initial course of the tachycardia cycle length was investigated in canine preparations of myocardial infarction,3 8 9 in which reentrant activity can be recorded with a degree of spatial resolution higher than can be achieved during intraoperative studies.3 10 11
|
Methods |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
Intraoperative Mapping in Patients
Surgical treatment of refractory ventricular tachycardias associated with myocardial infarction is conducted at our institution under the guidance of intraoperative mapping.10 12 Mapping data were analyzed retrospectively from a group of 40 patients (35 men and 5 women) 36 to 76 years old (57±10 years, mean±SD) who were operated on 1 to 216 months after myocardial infarction (70±61 months). Twenty-five patients had an anterior infarction, and 15 had an inferior infarction. The primary indications for surgery were refractory ventricular tachycardias in 25 patients and other complications of coronary artery disease in 15. Coronary artery bypass graft surgery was performed in 29 patients (one to three grafts). Before surgical treatment, one to four antiarrhythmic drugs were tried in all patients (2.1±1.1 drugs). Treatment with class 1 drugs or sotalol was interrupted at least 5 half-lives before surgery. Amiodarone was interrupted at least 3 weeks before surgery in the 8 patients reported here in whom this drug was used. In the operating room, sustained monomorphic ventricular tachycardias were induced by programmed stimulation consisting of eight basic bipolar stimuli (S1-S1=400 to 600 ms) followed by single (S2) (2 tachycardias), double (S2, S3) (17 tachycardias), or triple (S2, S3, S4) (25 tachycardias) premature stimuli delivered at progressively shorter S1-S2, S2-S3, or S3-S4 intervals. Eleven tachycardias were induced by burst pacing. Details regarding the induction of 4 tachycardias were unavailable. When only polymorphic ventricular tachycardias were induced during surgery, procainamide was injected intravenously at a relatively low dose of 500 mg to facilitate the induction of sustained monomorphic tachycardia, a well-known practice in intraoperative studies.13 14 This was done in 8 of the patients reported here (10 tachycardias) and will be given special consideration in the "Results" and "Discussion" sections. ECG leads I, II, III, and V6 were monitored on a VR-16 (Honeywell) analog recorder. Correspondence between monomorphic ventricular tachycardias induced during surgery and those occurring spontaneously (emergency room ECG, when available) or induced during preoperative investigation in the electrophysiology laboratory was established on the basis of the ECG morphology. Under normothermic cardiopulmonary bypass, 63 right and left ventricular unipolar electrograms were recorded with an epicardial sock electrode array and 64 unipolar electrograms were recorded from the left ventricular endocardial surface with an inflatable balloon electrode array introduced in the intact left ventricle from the left atrium.10 Anatomic landmarks indicating the course of the left anterior descending and posterior descending coronary arteries and the location of visible scar tissue were provided by the surgeon. The mapping system used a micro-VAX host computer (Digital Equipment Corp) and custom-made software (CARDIOMAP, Institut de Génie Biomédical, Ecole Polytechnique et Université de Montréal). Signals were amplified by programmable-gain analog amplifiers with a 0.05- to 200-Hz bandwidth, sampled at 500 to 1000 Hz, and converted to a 12-bit digital format. It has been standard practice to store files containing up to 26 seconds of continuous data, which included responses to programmed stimulation and several subsequent beats of monomorphic ventricular tachycardia. This report is based on the retrospective analysis of files from a database that was systematically collected in all patients undergoing arrhythmia surgery.
Experimental Procedures in Canine Preparations of Myocardial
Infarction
Anesthetized dogs were subjected to left thoracotomy and
occlusion of the left anterior descending coronary artery to
induce infarction of the anterior left ventricular wall.
The dogs recovered for 3 days with postoperative care, after which time
they were anesthetized and their hearts exposed via bilateral
thoracotomy.9 15 Among 32 canine 3-day-old infarct
preparations that were used recently to conduct electropharmacological
studies (as reported separately16 ), sustained monomorphic
ventricular tachycardias were induced in the
drug-free (control) state in 12 preparations and were
analyzed for the present study. The tachycardias
were induced by programmed stimulation consisting of 8 basic stimuli
(S1) followed by single (S2: 5
tachycardias), double (S2,
S3: 6 tachycardias), or 4 (S2,
S3, S4, S5: 1
tachycardia) extrastimuli. Unipolar electrograms were
recorded with reference to Wilson's central terminal by use of the
256-channel computerized system described above and silicone plaque
electrode arrays carrying 127 or 192 unipolar recording
contacts with 4.5- and 2.7-mm interelectrode spacing, respectively (see
below, Fig 7
). The procedures were done in accordance with the
guidelines of the Canadian Council for Animal Care and monitored by an
Institutional Animal Care Committee.
|
Time Course of Mean Cycle Length
Files retrieved from the disk were transferred to an Iris-4D
computer (Silicon Graphics, Inc). Since activation times were detected
at 127 to 191 sites for 27 to 81 tachycardia beats (requiring
several thousand detections), we used an automatic method (see
"Appendix A") based on the principle that, in unipolar
electrograms, activation occurs at the point of maximum negative slope
(-dV/dtmax).17 18
Automatic detections could be displayed and edited, ie, moved or
deleted manually, since in electrograms recorded from infarcted
tissue, QS cavity potentials can display relatively high
-dV/dtmax values overtaking rs deflections,
which indicate true activation of surviving muscle.17 19
Cycle lengths CLb,e from beat b to the next (b+1)
were calculated from activation times at each individual electrode site
e as
 | (1) |
 | (2) |
 | (3) |
 | (4) |
is the exponential time constant, and 
b
expresses the deviation of CLb from the exponential trend.
Least-squares estimates of the
parameters20 were obtained by the minimization
procedure of a commercial mathematical package (Matlab, MathWorks Inc).
The interbeat cycle length SD 
CL was defined as
 | (5) |
Interelectrode Cycle Length Variations
In the previous section, mean cycle lengths CLb were
fitted to an exponential model. To take into account interelectrode
cycle length variations, the quantity Dbe was defined:
 | (6) |
the expression of
Tbe derived from Equation 6 and using Equation 3,
CLbe can then be reexpressed as
 | (7) |
Db,e for a subset of electrodes e) or
(2) uniform acceleration or deceleration of all activation times while
the overall activation sequence remains constant (uniform scaling). In
uniform scaling, there is a reference activation sequence
V={Vi, i=1, ne}, where
ne is the number of electrode sites, for which the
activation time at each electrode site in a beat can be expressed
as
 | (8) |
becomes
 | (9) |
 |
Spatial Stability of Ventricular Activation
Sequences
For each beat of a ventricular tachycardia,
an isochronal map can be constructed from activation times at all
electrode sites, providing a spatial representation of the
activation sequence. Even when the ventricular
tachycardia is designated as "monomorphic," some degree
of variability in the activation sequence may occur between beats.
Therefore, principal-component analysis7 (see
"Appendix B") was used to define a reference activation sequence
V1={V1,i, i=1,
ne} from which the activation sequence of any beat b can
be expressed as Db={Dbe, e=1,
ne}=wb V1. When more than one
principal component is needed, a set of reference activation sequences
Vc={Vce, e=1,
ne} is defined from which the activation sequence of any
beat b can be expressed as Db=
wcb Vc, where wcb is the
scaling factor associated with Vc in the
reconstruction of beat b. The concordance between the activation times
in the vector Db of any selected beat b and those in each
principal component Vc was estimated with a standard
correlation coefficient (r). The set of reference maps
generated by principal-component analysis is ranked in
order of importance, ie, decreasing percent contribution to the total
intrabeat variance (see "Appendix B"). By analogy (albeit an
imperfect one) to vector analysis, principal-component
analysis may be regarded as providing a set of base vectors
(ie, the activation sequence corresponding to each principal component)
that can be used to generate, by weighted summation, the particular
activation sequence of any individual beat of the tachycardia
under consideration. The analogy breaks down, however, because contrary
to the i,j,k vector base of the
three-dimensional vector space, there is no universal set of
principal components applicable to all ventricular
tachycardias but only a set of specific principal components
that need to be determined for each ventricular
tachycardia. Thus, principal-component analysis was
used to investigate to what extent beat-to-beat changes in
activation might be related to uniform scaling (weights) of a single
activation sequence (primary component only) or to modifications of the
primary activation sequence with contributions from secondary,
tertiary, etc, components. The advantage of principal-component
analysis for the purpose of this study is to provide separate
descriptions of the intrabeat variance (activation sequences, see
"Appendix B") and interbeat variance (cycle length), thereby
enabling us to investigate the spatial stability of activation
sequences along with the dynamic behaviors of the
tachycardias.
Statistical Comparisons
Stable cycle lengths (CLs), time constants (),
and amplitudes of relaxation (A) were compared between groups by
standard ANOVA and Student's t test (Statistical Package
for Social Sciences, SPSS Inc). The effects of programmed stimulation
and intraoperative procainamide injection, when it was used,
were investigated by Pearson's 
2 test.
|
Results |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
Most of the monomorphic ventricular tachycardias induced in patients displayed monotonic trends of either the decelerating, accelerating, or constant type (with reference to rate) after their induction by programmed stimulation.
Decelerating Trend in Rate
Fig 1 illustrates a monomorphic
ventricular tachycardia in which the cycle length
increased from an initial value of 266 ms toward a value of 274 ms,
where it stabilized. Fitting mean cycle length values to an exponential
model (see above, "Methods," Equation 4) yielded a time constant
of 10.0 beats and a relaxation (negative A) of 7.7 ms from the
initial to the steady-state value. The exponential increase in
cycle length (ie, decelerating rate) accounted for 89% of the
interbeat SD of cycle length values (CL; see
"Methods," Equation 5), and therefore, there was little departure
(b) of the data from the exponential model (Fig 1B). The
activation sequence was highly correlated with a single component (Fig 1C) that accounted for virtually all (99.93%) of the intrabeat
variability summed over the entire series of beats
(t2; see below, "Appendix B," Equation 14). With the appropriate scaling, the primary component accounted for
the exponential increase in cycle length, and therefore the weight
presented a similar exponential trend (Fig 1D).
|
The isochronal maps shown in Fig 2A were not
generated by conventional analysis of activation times in a
single beat but rather corresponded to the primary principal component
(Fig 2A). These maps suggest that the tachycardia was caused by
reentry in subepicardial muscle surviving in the region of infarction.
The association between delayed activation in the anterior wall and
tachycardia was supported by the fact that the
tachycardia was interrupted when pressure (surgeon's finger)
was applied in the area in which delayed activation occurred (Fig 2B:
192 ms). This tachycardia could be repeatedly induced and
terminated by either pressure (two trials) or reversible cooling
(application of the cryosurgical probe at 0°C for a few seconds).
After cryoablation (-65°C for 2 minutes) in this area, the
tachycardia was no longer inducible. The portion of the cycle
over which activations were detected at the subepicardial and
subendocardial levels (active) encompassed most of the
tachycardia cycle length, the portion of the cycle length
during which activations failed to be detected being termed
"silent" (Fig 2C and 2D). The progressive relaxation in the
tachycardia cycle length corresponded to a trend developing in
the "active" portion of the cycle (Fig 2D).
|
Accelerating Trend in Rate
In another patient, who had been resuscitated from cardiac arrest
after spontaneous occurrence of a fast ventricular
tachycardia, it was possible to induce, during surgery, a fast
monomorphic ventricular tachycardia of the type
designated as ventricular flutter.21 The
dynamic course of the cycle length (Fig 3A) showed an
exponential decrease ( of 5.6 beats and relaxation of 22.6 ms).
However, the exponential model explained only 49% of cycle length SD
(CL, see "Methods," Equation 5) because of
marked cycle length fluctuations superimposed on the exponential trend
in the earliest 10 beats of the tachycardia (Fig 3B). The
correlation between the activation sequences of individual beats and
the first principal component was lower in the first 3 beats (first
beat: .849) but increased to .94 in the fourth and fluctuated between
.94 and .98 thereafter (Fig 3C), and this component accounted for 92%
of the total intrabeat variability
(t2, see "Appendix B," Equation 14). Therefore, a second principal component contributed to the
activation sequences of the early beats (correlation of .39, .37, and
.32 with the activation sequences of beats 1 through 3), but its
contribution fell rapidly thereafter (Fig 3C). Weights are scaling
factors through which, by multiplication, the activation sequence of
each beat can be derived from the first principal component, but they
are also reduced in beats that are better represented by
including contributions from a second component (Fig 3D).
|
The activation sequence corresponding to the first (primary) principal
component of the tachycardia illustrated in Fig 3 shows that
the earliest detected activity occurred epicardially at the apical
margin of an inferobasal scar, from which it propagated to the rest of
the ventricles (Fig 4A). The endocardial breakthrough
occurred 12 ms later. The second component (Fig 4B) described a
modulation, in the first few beats, of a pattern that was set primarily
by the first component. In contrast to the first, the second component
did not represent a distinct activation sequence, since, even
when its contribution was maximum (first few beats), it accounted for
<15% of the variability (ie, information on activation sequence)
contained in these beats. When it contributed positively (positive
weight) to a given beat, the second component indicated the regions in
which propagation was either accelerated (negative numbers) or slowed
(positive numbers) in relation to the main activation pattern described
by component 1.
|
Although activation times were detected throughout the
tachycardia cycle length (since it was equal to the active
phase beyond beat 10, see Fig 4C and 4D), the isochronal maps shown
in Fig 4A suggest that critical portions of the reentry circuit were
missed in areas in which bridging activity from one beat to the next
occurred. Moreover, in the initial beats, the portion of the cycle
length accounted for by actual detections (active) displayed an
increasing course, whereas the accelerating trend (decreasing cycle
length) was entirely localized in the silent phase. This situation is
representative of most activation maps, in which the
critical part of the reentry circuit, governing the dynamic behavior of
the tachycardia cycle length, occurred outside the
recording field (thereby excluding parallelism between the
dynamic behavior of the tachycardia and weights of the first or
any other principal component).
Constant Cycle Length
In the ventricular tachycardia displaying the
longest cycle length (464 ms) among those that were analyzed
for this study, the time course of the cycle length (Fig 5A) was found to be represented by a flat
curve (constant). The activation sequence also was stable, as shown by
an almost perfect correlation with a single principal component that
accounted for most (99.7%) of the intrabeat variance (Fig 5B through
5D).
|
Summary of Ventricular Tachycardias Induced
in Patients
Among the 59 monomorphic ventricular
tachycardias induced in 40 patients, a decelerating trend in
rate of the type illustrated in Fig 1 was the most frequently
encountered trend, accounting for 21 tachycardias (Table 1A). An accelerating trend similar to that illustrated
in Fig 3 occurred in 12 tachycardias (Table 1B). On the whole,
the decelerating trends developed over a more progressive time course
than the accelerating trends, which tended to be more abrupt, as
reflected by longer time constants in the former than in the latter
(Student's t=2.7, 31 df, P<.05).
There were significant differences in the cycle length at steady state
(CLs) between the types of trend (ANOVA: 5 types;
F=6.03; 4 and 54 df; P<.0003). In
particular, CLs of the tachycardias displaying an
accelerating trend was shorter than that of tachycardias with a
decelerating trend (P<.001) or, for that matter, any other
of the other dynamic patterns.
|
Four tachycardias displayed a double trend, as illustrated in
Fig 6A. An accelerating trend was manifest in the first
3 or 4 beats and was followed by a slower decelerating trend. Such
double trends were fitted by use of a model consisting of a sum of two
exponential terms (instead of a single one as used to fit monotonic
trends), and a relaxation amplitude (A) and time constant () were
calculated for each (Table 1C, double trend: fast and slow).
|
In 6 tachycardias there was an abrupt reduction in the first
cycle length, which was followed by an exponential increase. Since it
was statistically meaningless to fit a double exponential (thereby
adding two parameters, A and ) on account of a single
beat, these beats were rejected and these 6 tachycardias were
included in the group of tachycardias displaying a decelerating
trend in rate (Table 1A). Conversely, 2 tachycardias showed an
abrupt increase in the first cycle length, which was followed by an
exponential decrease. For the same reason, these beats were disregarded
and the 2 tachycardias were included with those displaying an
accelerating trend in rate (Table 1B).
In the three groups of monomorphic ventricular
tachycardias in which exponential models were used to fit the
time course of cycle length, the percentage of the interbeat SD
explained by the model varied, being as low as 10% in some
tachycardias. In these cases, organized fluctuations consisting
of alternans (period 2) or higher-order periodicity (periods 3
through 6) were superimposed onto the accelerating or decelerating
trend, thereby increasing the interbeat cycle length variability
unaccounted for by the exponential model. Fig 6B illustrates such a
case, in which alternans was superimposed on a decelerating trend,
which accounted for only 10% of the interbeat SD.
Among the monomorphic ventricular tachycardias that
were not fitted to exponential models (Table 1D and 1E), 12 showed a
constant trend (with various degrees of superimposed organized
fluctuations) and in 10 others, beat-to-beat cycle length
variations were too irregular to be described either as being constant
or with any other simple model (Fig 6C).
In 36 of the 59 tachycardias, their morphology was set from the very first beat after programmed stimulation. The first beat was rejected in 9 tachycardias on the basis of a different morphology (correlation coefficient <.849), the first 2 beats were rejected in 9 tachycardias, the first 3 beats in 4 tachycardias, and the first 4 beats in 1 tachycardia, for a total of 43 rejected beats (of a total of 2137 beats analyzed). The primary component accounts for most of the total intrabeat variance in each ventricular tachycardia. Once the beats with correlation coefficients <.849 had been rejected, the first principal components were found to account for 90% or more of the intrabeat variance (mean, 98%). In all instances, the second components represented <2% of the total intrabeat variance, and on this basis, they were not considered in the analysis.
No statistically significant association was found between the
incidence of each type of dynamic behavior and the mode of induction of
the tachycardias (S2, S3,
S4, or burst) as assessed by cross-table
analysis (5 typesx4 modalities; 2=9.3,
12 df). In general, the observed and predicted incidences
corresponded very well. Although it did not reach statistical
significance, the only detectable tendency concerned a lower incidence
of the decelerating trend in rate among the 11 tachycardias
that were induced by burst pacing (the incidence was only 1, whereas 4
would have been expected on the basis of the class distribution), which
was compensated by a relatively higher incidence of the decelerating
trend among the tachycardias induced by triple extrastimuli (9
were predicted, whereas 12 occurred). Ten sustained monomorphic
tachycardias were induced after injection of 500 mg
procainamide. These 10 tachycardias were distributed
among the groups showing decelerating (5), accelerating (2), and
irregular (3) trends in proportions of 5/21, 2/12, and 3/10,
respectively. The distribution of tachycardias induced after
procainamide injection among the types of dynamic behaviors was
not significantly different from that of tachycardias induced
without procainamide injection (5 typesx2 modalities;
2=5.17, 4 df, P>.25).
Within the accelerating and decelerating types, the
tachycardias induced after procainamide injection
displayed amplitudes of relaxation (A), time constant (), and
steady-state cycle length (CLs) values that were not
statistically different from those of tachycardias induced
without procainamide (ANOVA: 2 typesx2 modalities;
P>.1). Therefore, all tachycardias are
presented together in the Table.
Canine Preparations of Myocardial Infarction
Fig 7A and 7B illustrates 2 sustained monomorphic
ventricular tachycardias (induced in different
preparations) in which reentrant activity displaying distinctive
anatomic and functional characteristics could be mapped completely with
a relatively high-resolution plaque electrode applied to the
anterior wall of the left ventricle. In one of the
tachycardias, the isochronal map (Fig 7A: upper map,
corresponding to the primary principal component) suggested that circus
movement of excitation occurred around a pathological obstacle (gray
area in the center) where, at postmortem examination, tissue necrosis
was seen to extend transmurally. Circus movement of excitation occurred
in areas in which the most rapid downward deflections of unipolar
electrograms displayed relatively high
-dV/dtmax (
1.0 mV/ms along most of the
reentrant pathway) (Fig 7A: lower map, primary principal component). In
the other preparation, the isochronal map (Fig 7B: upper map)
displayed a double-loop reentrant pattern in which functional
dissociation occurred in the central part of the ischemically
injured region where unipolar electrograms displayed depressed
-dV/dtmax values (<1.0 mV/ms) (Fig 7B: lower
map).
In addition to their distinct configurations and functional properties,
the two sustained monomorphic ventricular
tachycardias displayed different dynamic behaviors at their
onset. Fig 8A shows that the cycle length of the
tachycardia illustrated in Fig 7A decreased toward a minimum
value, at which it stabilized at a CLs of 201 ms. Fitting
mean cycle length values to an exponential model yielded a time
constant of 7.1 beats and a relaxation (A) of 19 ms from the
initial to the steady-state value. At the scale of the
tachycardia cycle length, the term b expressing
the distance between the postulated model and the data (Fig 8B) showed
initial damped oscillations, which became negligible beyond
beat 10. The activation sequences of individual beats correlated very
highly with the sequence corresponding to the principal component (Fig 8C). Scaling of the primary component by the weighting factor (Fig 8D)
accounted for both the exponential trend and superimposed damped
oscillations.
|
The dynamic behavior of the ventricular tachycardia
illustrated in Fig 7B displayed an exponential increase in cycle length
(to a CLs of 252 ms) during the early 87 beats, as shown in
Fig 9A. Relaxation occurred with a magnitude A of
-15 ms and according to a time constant of 43 beats. Thus, in
addition to the fact that relaxation occurred in the opposite
direction, it was less marked (lower magnitude) and slower (higher )
in this tachycardia than in the one analyzed in Figs 7A and 8. There was marked deviation from the exponential trend in the
beats indicated by asterisks, and b was greater in these
beats (Fig 9B). Fig 9C shows that there was a very high correlation
between the activation sequence of the primary component (shown in Fig 7B: upper map) and the activation sequences of individual beats.
Scaling of the primary component with the weighting factor shown in Fig 9D accounted for the exponential trend as well as the abrupt
fluctuations in cycle length (Fig 9A), indicating that the exponential
trend was related to homogeneous deceleration and the
abrupt fluctuations were related to homogeneous
acceleration of the activation process at all recording
sites.
|
A decelerating trend in rate similar to that reported in Fig 9 occurred
in 7 of 12 sustained monomorphic ventricular
tachycardias and displayed a steady-state cycle length
(CLs) of 194±34 ms, a magnitude of the initial relaxation
(A) of -11.9±6.0 ms, and a time constant () of 18.6±17.1 (in
beat number). An accelerating trend in rate was observed in only one
preparation other than the one illustrated in Fig 8, with the
parameters CLs=138 ms, A=14.9 ms, and =1.1
beat. The three remaining tachycardias were irregular and could
not be classified as displaying either a decelerating, an accelerating,
or a constant trend.
|
Discussion |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
This study confirms the occurrence of spontaneous cycle length variations at the onset of reentrant monomorphic ventricular tachycardias1 2 and provides mathematical approaches to answer the two following questions: Do cycle length variations occurring at the onset of the tachycardias follow distinctive dynamic patterns? How spatially stable is the activation sequence of a "monomorphic" ventricular tachycardia during cycle length variations? A major finding was that most (49/59) of the tachycardias induced in patients displayed at their onset a distinctive trend with reference to rate, which either decelerated, accelerated, showed a double trend, or remained constant. The remaining tachycardias displayed irregular cycle length dynamics that could not be fitted with such simple exponential or linear trends. Organized fluctuations consisting of alternans or higher-order 3 through 6 periodicities were superimposed onto the accelerating, decelerating, or constant trends and may have been related to fluctuations of the action potential duration and diastolic interval in consecutive beats, thereby modulating the action potential upstroke and conduction velocity in the reentry circuit.22 23
Spatial Stability of Activation Sequences
The accelerating and decelerating trends in rate occurring during
the initial beats of the ventricular tachycardias
might be related to rate-dependent repolarization or conduction
characteristics (see below) on condition that the sequence of
excitation in the substrate sustaining the tachycardia remain
stable. Otherwise, it is possible that the changes in
tachycardia cycle length might be caused by "remodeling"
of the reentry circuit. Recording from the reentry circuit with
relatively high resolution in canine preparations strongly suggests
that the sequence of excitation remained constant for all beats
throughout the period of cycle length relaxation, as indicated by a
single principal component correlating highly with all individual
beats. Although the resolution provided by the recording arrays
used in patients was more limited and only a few, if any, of the
electrograms were recorded directly from the reentry circuit, it
was found that a single principal component accounted for all beats in
series of 14 to 81 beats (r=.98, on average). In the
clinical tachycardias, stability of the reentry circuit
configuration is inferred on the basis of the stability of the overall
ventricular activation process determined from epicardial
and left ventricular endocardial recordings. In a
minority of the tachycardias, 1 to 4 beats were rejected on the
basis of a difference in morphology when the correlation coefficient
was <.849. In the present state of principal-component
analysis, there is no statistical criterion to establish the
number of significant components when (1) the dimensionality of the
vectors is high (in this case, number of electrode sites) in relation
to the number of replicates (number of beats) and (2) the structure of
correlation is complex, since variations in the activation vectors of
individual beats (interelectrode) may impact on the activation vectors
of others (interbeat). The .849 cutoff emerged empirically when we
considered the conditions under which inclusion of a second component
produced a physiologically meaningful
modification of the activation sequence corresponding to the first
component in order to account for individual beats (Figs 3 and 4).
Thus, the data suggest that, at the onset of the
tachycardias, cycle length variations may occur while the
reentrant activation pattern remains constant.
Moreover, it was found that the accelerating and decelerating dynamic
behaviors could be related to scaling (ie, acceleration or
deceleration) of local activation times while the overall activation
pattern remained constant. The accelerating (Fig 8) and decelerating
(Figs 1 and 9) rate trends corresponded to shortening and prolongation
of activation times, respectively, occurring in equal proportion at all
recording sites, as determined by weights multiplying the
primary component and governing the degree of shortening or
prolongation of activation times in any given beat. When the dynamic
course of the weight of the primary component (Fig 3D) did not parallel
the course of the cycle length (Fig 3A), the trend would be related to
the dynamic behavior of activation in areas located outside the
recording field (silent portion) (as Fig 4D indicates it to be
the case in this tachycardia) or to the scaling of a second
component. In the majority of cases, the monomorphic character of
tachycardias selected on the basis of their ECG features was
confirmed by principal-component analysis of epicardial and
endocardial activation times. Preliminary analysis of
polymorphic tachycardias (not reported here) indicates that
at least two principal components are necessary to represent
such tachycardias.24
Relationship Between Tachycardia Onset Dynamics and the
Functional Properties of the Underlying Reentry Circuits: A
Hypothesis
Data obtained in canine preparations in which reentry could be
mapped with relatively high resolution support the hypothesis that
cycle length variations occurring at the onset of monomorphic
ventricular tachycardias might provide information
regarding the functional properties of the underlying reentry circuits.
An accelerating rate trend occurred in the tachycardia
associated with circus movement in muscle generating unipolar
electrograms with relatively high -dV/dtmax
(reflecting fairly good action potential upstroke characteristics).
Normal action potentials typically show parallel changes in duration
and refractory period, whereas action potentials with depressed
upstrokes may show refractory period prolongation while duration
shortens in response to an abrupt increase in beating rate. Thus, we
postulate that accelerating-onset dynamics may be related to
withdrawal of the head of the reentrant impulse from the refractory
tail of the preceding action potential as the action potential duration
shortens. The relatively short cycle lengths of clinical
tachycardias showing an accelerating rate trend (mean, 223 ms)
are consistent with this hypothesis. The cycle lengths of
tachycardias showing constant cycle length dynamics were longer
(mean, 297 ms), suggesting that the reentry circuit might have been
long enough for complete recovery to occur between action potentials.
We have not yet encountered constant cycle length dynamics in canine
preparations, in which the length of the circuits may be too short.
A decelerating trend in rate was the dynamic behavior that occurred most frequently in the canine preparations (7/12) and among the clinical tachycardias (25/59). Cycle lengths were longer (mean, 319 ms) in clinical tachycardias showing decelerating onset dynamics than in the other types. In the canine preparation illustrating the substrate of a tachycardia with decelerating-onset dynamics, functional reentry occurred in muscle generating unipolar electrograms with depressed -dV/dtmax. The clinical tachycardia showing a similarly decelerating rate trend appeared to be caused by reentry in subepicardial muscle generating middiastolic unipolar deflections with low -dV/dtmax. It is postulated that this type of onset dynamics may be associated with rate-dependent slowing of conduction velocity in the reentry circuit.6 One possibility is that cellular excitability and its course of recovery may be altered (active generator properties of the cell membrane) as a result of depolarization, depression of the Na+-dependent action potential upstroke, and delayed reactivation kinetics of the Na+ channel, which are known to occur in 3-day-old infarct canine preparations.25 Another possibility is that the primary cause of slow conduction would be impairment of cell coupling (passive electrical properties of muscle) either at a microscopic level with abnormalities in intercellular gap junctions26 or at a more macroscopic level, with physical separation of surviving myocytes by fibrotic tissue, which is typical of healed myocardial infarction.27 Action potentials with apparently normal configuration have occasionally been recorded from tissue thought to be involved in tachycardia generation28 ; conversely, it is also possible to record action potentials displaying depressed upstrokes from human arrhythmogenic ventricular tissues excised at surgery.29 The analysis of electrograms recorded in patients is complicated by the signal-attenuating effect of overlying scar tissue.30 Which muscle fiber properties may be associated with rate-dependent depression of conduction in patients remains unclear; it is possible that alterations in both their passive electrical and active generator properties contribute to conduction disturbances.
Study Limitations
Although we are postulating that the tachycardia onset
dynamics may be determined largely by the functional properties of the
reentry substrate, it would be reasonable to think that they might also
be influenced by programmed stimulation as well as the low dose of
procainamide used in 8 patients to facilitate monomorphic
tachycardia induction. However, no statistically significant
association emerged between the type of dynamic behavior (eg,
decelerating, accelerating) and the mode of induction of the
tachycardias (S2, S3,
S4, or burst) or the use of procainamide to
facilitate induction. Lack of a demonstration of an effect of
programmed stimulation may be the consequence of the fact that a
relatively small number of tachycardias (information was
available in 55) was tested against their distribution into four
classes of stimulation modalities (S2,
S3, S4, or burst) in the
cross-table analysis. Interestingly, the only detectable
tendency concerned a lower incidence of the decelerating trend in rate
among the 11 tachycardias that were induced by burst pacing,
since this stimulation modality uses a greater number of stimuli
delivered at a fast rate. Intraoperative mapping was performed at least
5 half-lives after therapy was interrupted with a class 1
antiarrhythmic drug or sotalol (except for the injection of a single
dose of procainamide during surgery in 8 patients, as discussed
above). Eight patients received amiodarone, which was
discontinued at least 3 weeks before surgery. In patients in whom
amiodarone was discontinued only 1 week before surgery (not
included in this study), the cycle lengths of the tachycardias
induced during surgery were longer.
It would be inappropriate, from the analysis of a limited number of cases, to claim any definitive statement regarding the dynamic behavior of monomorphic ventricular tachycardias associated with myocardial infarction. However, the clinical tachycardias reported here represent the entire set of data collected with the computerized system currently in use and therefore available for analysis. The ventricular tachycardias analyzed in this study are deemed to be clinically relevant because, in most cases, their morphologies correlated with those of tachycardias occurring spontaneously or induced before surgery in the electrophysiology laboratory.
Conclusions
Analysis of the onset dynamics of a given monomorphic
ventricular tachycardia could be used to gain
further information on the functional properties of the underlying
reentry circuit. Since the temporal analysis could be made from
a single ECG lead, it may be an interesting noninvasive method to
acquire such information. Further studies are needed to explore its
usefulness for the selection of antiarrhythmic drugs and
antitachycardia pacemaker parameters.
|
|
Acknowledgments |
|---|
This work was supported by the Medical Research Council of Canada (grant PG11190). The authors wish to express their appreciation to Suzan Senechal and Diane Abastado for their excellent secretarial assistance.
|
Appendix A |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
Determination of Activation Times
Once an interval has been selected for analysis in the 26-second computer file, the first time derivative (dV/dt) of the unipolar electrogram recorded is computed at each recording site by a three-point approximation method. Local activation occurs when the amplitude of the dV/dt reaches a negative extremum. However, secondary deflections may be generated by noise or nonlocal events.31 The algorithm aims at determining, for all electrograms in a protracted episode, a series of peak -dV/dt that can be distinguished from such secondary deflections on the basis of their amplitude. Threshold values are sought beyond which the dV/dt extrema are considered to indicate local activations, as illustrated in Fig 10
. The vertical lines drawn in Fig 10A indicate,
on a 1-second segment of the dV/dt signal, all negative extrema. Their
values are plotted on the abscissa of a cumulative histogram (B), which
shows that there is an interval between high and low dV/dt values
during which the rate at which extrema are cumulated is lower, thus
defining a plateau. After a refractory period (60 ms) was imposed, the
number of extrema was reduced (C) and the corresponding cumulative
histogram (D) showed a clear plateau. The detection threshold was set
at the point corresponding to midplateau, yielding a single activation
time per beat. A similar procedure is repeated for each
electrogram. In a second step, a histogram of the number of activations selected for each channel is constructed. Outlier channels are those in which the number of activations does not correspond to the mode of the histogram (±1, to account for the arbitrary limits of the time window). For the outliers, the second plateau of their dV/dt histogram is used as threshold if it moves the number of detections closer to the global mode of the number of detections.
|
Appendix B |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
Principal-Component Analysis
By the notation introduced in Equation 5
("Methods"),
Db,e is the activation time of channel e
(e=1,Ne) in beat b (b=1,Nb) expressed as a
difference from the mean activation time for each beat. The set of
activation times at each electrode site is a vector
De=[D1e, · · ·,
DNbe] of dimension Nb. The vectors for all
electrode sites are collected as the rows of a matrix D:
 | (10) |
 | (11) |
k,Vk, k=1,
Nb). The associated Ne-dimension vectors
Mk=D Vk are also
orthogonal and give a basis to reexpress all the activation sequences
as
 | (12) |
 |
 | (13) |
t2 is the sum over all beats of
b2, which is the variance of
activation times at all sites with reference to the mean activation
time in each beat:
 | (14) |
k represents the portion of the total
variance t2 that is explained by
Mk. The 's can be used to rank the
Mk in order of importance, and a cutting point
can be defined beyond which the components are ignored. Each
Mk can also be represented as an
isochronal map. For each beat, the portion of
b2 explained by a given principal component
is equal to the square of the correlation between the component and the
activation sequence of the beat. Received July 19, 1995; revision received November 2, 1995; accepted November 5, 1995.
|
References |
|---|
|
TopAbstractIntroductionMethodsResultsDiscussionAppendix AAppendix BReferences |
|---|
1. Volosin KJ, Beauregard LAM, Fabiszewski R, Mattingly H, Waxman HL. Spontaneous changes in ventricular tachycardia cycle length. J Am Coll Cardiol. 1991;17:409-414. [Abstract]
2. Fromer M, Cardinal R, Pagé P, Nadeau R, Shenasa M. Variation in cycle length of induced ventricular tachycardia episodes in humans: incidence and electrophysiologic mechanisms. In: Shenasa M, Borggrefe M, Breithardt G, eds. Cardiac Mapping. Mount Kisco, NY: Futura Publishing Co Inc; 1993:507-514.
3. Wit AL, Janse MJ. The Ventricular Arrhythmias of Ischemia and Infarction: Electrophysiological Mechanisms. Mount Kisco, NY: Futura Publishing Co Inc; 1993:454-540.
4. Franz MR, Swerdlow CD, Liem LB, Schaefer J. Cycle length dependence of human action potential duration in vivo: effects of single extrastimuli, sudden sustained rate acceleration and deceleration, and different steady-state frequencies. J Clin Invest. 1988;82:972-979.
5. Kanaan N, Jenkins J, Childs K, Ge YZ, Kadish AA. Monophasic action potential duration during programmed electrical stimulation. Pacing Clin Electrophysiol. 1991;14:1049-1059. [Medline] [Order article via Infotrieve]
6. Hope RR, Scherlag BJ, Lazzara R. Excitation of ischemic myocardium: altered properties of conduction, refractoriness and excitability. Am Heart J. 1980;99:753-765. [Medline] [Order article via Infotrieve]
7. Morrison DF. Multivariate Statistical Methods. New York, NY: McGraw-Hill Inc; 1990:312-351.
8.
Mehra R, Zeiler RH, Gough WB, El-Sherif N.
Reentrant ventricular arrhythmias in the late
myocardial infarction period, 9: electrophysiologic-anatomic
correlation of reentrant circuits.
Circulation. 1983;67:11-24.
9.
Cardinal R, Vermeulen M, Shenasa M, Roberge F,
Pagé P, Hélie F, Savard P. Anisotropic conduction
and functional dissociation of ischemic tissue during reentrant
ventricular tachycardia in canine myocardial
infarction. Circulation. 1988;77:1162-1176.
10.
Kaltenbrunner W, Cardinal R, Dubuc M, Shenasa M, Nadeau
R, Tremblay G, Vermeulen M, Savard P, Pagé PL. Epicardial
and endocardial mapping of ventricular tachycardia
in patients with myocardial infarction: is the origin of the
tachycardia always subendocardially localized?
Circulation. 1991;84:1058-1071.
11. Downar E, Kimber S, Harris L, Mickleborough LL, Sevaptsidis E, Masse S, Chen TCK, Genga A. Endocardial mapping of ventricular tachycardia in the intact human heart, II: evidence for multiuse reentry in a functional sheet of surviving myocardium. J Am Coll Cardiol. 1992;20:869-878. [Abstract]
12. Pagé PL, Cardinal R, Shenasa M, Kaltenbrunner W, Cossette R, Nadeau R. Surgical treatment of ventricular tachycardia: regional cryoablation guided by computerized epicardial and endocardial mapping. Circulation. 1989;80(suppl I):I-124-I-134.
13. Buxton AE, Waxman HL, Marchlinski FE, Josephson ME. Electropharmacology of nonsustained ventricular tachycardia: effects of class I antiarrhythmic agents, verapamil and propranolol. Am J Cardiol. 1984;53:738-744. [Medline] [Order article via Infotrieve]
14. Josephson ME. Clinical Cardiac Electrophysiology: Techniques and Interpretations. Malvern, Pa: Lea & Febiger; 1993:787.
15.
Cardinal R, Savard P, Carson DL, Perry JB, Pagé
P. Mapping of ventricular tachycardia
induced by programmed stimulation in canine preparations of myocardial
infarction. Circulation. 1984;70:136-148.
16. Hélie F, Cossette J, Vermeulen M, Cardinal R. Differential effects of lignocaine and hypercalcaemia on anisotropic conduction and reentry in the ischaemically damaged canine ventricle. Cardiovasc Res. 1995;29:359-372. [Medline] [Order article via Infotrieve]
17. Durrer D, van Lier AAW, Buller J. Epicardial and intramural excitation in chronic myocardial infarction. Am Heart J. 1964;68:765-776. [Medline] [Order article via Infotrieve]
18. Ideker RE, Smith WM, Blanchard SM, Reiser SL, Simpson EV, Wolf PD, Daniely ND. The assumptions of isochronal cardiac mapping. Pacing Clin Electrophysiol. 1989;12:456-478. [Medline] [Order article via Infotrieve]
19. Blanchard SM, Damiano RJ, Asano T, Smith WM, Ideker RE, Lowe JE. The effects of distant cardiac electrical events on local activation in unipolar epicardial electrograms. IEEE Trans Biomed Eng. 1987;BMD-34:539-546.
20. Bates DM, Watts DG. Nonlinear Regression Analysis and its Applications. New York, NY: John Wiley & Sons; 1988:32-67.
21. Silber EN, Katz LN. Heart Disease. New York, NY: Macmillan Publishing Co Inc; 1975:339-340.
22. Chialvo DR, Jalife J. On the non-linear equilibrium of the heart: locking behavior and chaos in Purkinje fibers. In: Zipes DP, Jalife J, eds. Cardiac Electrophysiology: From Cell to Bedside. Philadelphia, Pa: WB Saunders Co; 1990:201-214.
23. Vinet A, Roberge FA. The dynamics of sustained reentry in a ring model of cardiac tissue. Ann Biomed Eng. 1994;22:568-591. [Medline] [Order article via Infotrieve]
24. Cardinal R, Vinet A, LeFranc P, Hélie F, Pagé P. Beat-to-beat stability of spatial activation patterns during monomorphic and polymorphic ventricular tachycardias induced in human myocardial infarction. Circulation. 1995;92(suppl I):I-335. Abstract.
25.
Ursell PC, Gardner PI, Albala A, Fenoglio JJ Jr, Wit
AL. Structural and
electrophysiological changes in the
epicardial border zone of canine myocardial infarcts during infarct
healing. Circ Res. 1985;56:436-451.
26. Luke RA, Saffitz JE. Remodeling of ventricular conduction pathways in healed canine infarct border zones. J Clin Invest. 1991;87:1594-1602.
27.
Gardner PI, Ursell PC, Fenoglio JJ Jr, Wit AL.
Electrophysiologic and anatomic basis of fractionated electrograms
recorded from healed myocardial infarcts.
Circulation. 1985;72:596-611.
28.
De Bakker JMT, van Capelle FJL, Janse MJ, Wilde AAM,
Coronel R, Becker AE, Dingemans KP, van Hemel NM, Hauer RNW.
Reentry as a cause of ventricular tachycardia in
patients with chronic ischemic heart disease:
electrophysiologic and anatomic correlation.
Circulation. 1988;77:589-606.
29. Moore EN, Spear JF, Horowitz LN, Josephson ME. Electrophysiological mechanisms causing ventricular tachyarrhythmias. In: Sandoe E, Julian DG, Bell JW, eds. Management of Ventricular Tachycardia: Role of Mexiletine. Amsterdam, Netherlands: Excerpta Medica; 1978:3-15.
30.
Miller JA, Tyson GS, Hargrove WC, Vassallo JA,
Rosenthal ME, Josephson ME. Effect of subendocardial resection
on sinus rhythm endocardial electrogram abnormalities.
Circulation. 1995;91:2385-2391.
31. Biermann M, Shenasa M, Borggrefe M, Hindricks G, Haverkamp W, Breithardt G. The interpretation of cardiac electrograms. In: Shenasa M, Borggrefe M, Breithardt G, eds. Cardiac Mapping. Mount Kisco, NY: Futura Publishing Co Inc; 1993:11-34.
32.
Lux RL, Evans AK, Burgess MJ, Wyatt RF, Abildskov
JA. Redundancy reduction for improved display and
analysis of body surface potential maps.
Circ Res. 1981;49:186-196.
33. Sirovich L, Everson R. Management and analysis of large scientific datasets. Int J Supercomp Appl. 1992;6:50-68.
This article has been cited by other articles:
 |
|
 |
|
  R. Cardinal, G. Rousseau, C. Bouchard, M. Vermeulen, J.-G. Latour, and P. L. Page Myocardial electrical alteration in canine preparations with combined chronic rapid pacing and progressive coronary artery occlusion Am J Physiol Heart Circ Physiol, April 1, 2004; 286(4): H1496 - H1506. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
S. Iravanian, Y. Nabutovsky, C.-R. Kong, S. Saha, N. Bursac, and L. Tung Functional reentry in cultured monolayers of neonatal rat cardiac cells Am J Physiol Heart Circ Physiol, June 5, 2003; 285(1): H449 - H456. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 E. J. Ciaccio Dynamic Relationship of Cycle Length to Reentrant Circuit Geometry and to the Slow Conduction Zone During Ventricular Tachycardia Circulation, February 20, 2001; 103(7): 1017 - 1024. [Abstract] [Full Text] [PDF]
|
|
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||