(Circulation. 2001;103:1017.)
© 2001 American Heart Association, Inc.
Basic Science Reports |
Dynamic Relationship of Cycle Length to Reentrant Circuit Geometry and to the Slow Conduction Zone During Ventricular Tachycardia
From the Departments of Pharmacology and Biomedical Engineering, College of Physicians and Surgeons, Columbia University, New York, NY.
Correspondence to Edward J. Ciaccio, PhD, Department of Pharmacology, PH7W, Columbia University, 630 W 168th St, New York, NY 10032. E-mail ciaccio{at}columbia.edu
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Abstract |
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Background—Knowledge of cycle-to-cycle changes in isthmus geometry is of potential importance for radiofrequency catheter ablation to stop reentrant ventricular tachycardia. It was hypothesized that isthmus geometry often undergoes continuous evolution throughout reentry and that cycle-length variability measurements could be used to segment reentry into distinct phases and to predict changes in isthmus geometry.
Methods and Results—A canine infarct model of reentrant ventricular tachycardia in the epicardial border zone with a figure 8 pattern of conduction was used for analysis (25 monomorphic reentry episodes, 20 experiments). Tachycardias were segmented, on the basis of cycle-length variations, into 2 to 3 distinct phases corresponding to onset, maintenance, and spontaneous termination, when it occurred (6/25 episodes). Trends of linear cycle-length change occurred throughout the maintenance phase in all tachycardias. For each trend, quantitative geometric parameters of the isthmus were measured, and the following linear relationships were established. During a trend, the slow conduction zone activation interval and tachycardia cycle length increased, while isthmus length decreased. When isthmus length decreased, isthmus width decreased at its narrowed portion. Larger decreases in isthmus length corresponded to higher rates of linear cycle-length prolongation. Also, greater cycle-length variability tended to prolong tachycardia.
Conclusions—Cycle-length alterations occur throughout reentry in this canine model and are predictive of isthmus geometry changes. Because similar reentry dynamics, which affect catheter ablation efficacy, have been observed clinically, estimation of changes in geometry during electrophysiological study may help target ablation sites.
Key Words: catheter ablation • dynamics • electrophysiology • mapping • reentry
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Introduction |
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Radiofrequency catheter ablation of the left ventricular endocardium is an important therapy to stop ventricular tachycardia caused by a reentrant circuit.1 The energy imparted by the radiofrequency current creates an endocardial lesion that is designed to interrupt conduction of the activating wave front to terminate reentry. A target site to ablate is the slow conduction zone1 (SCZ) located at the narrowed portion of the protected isthmus in the circuit, because it is there that the activating wave front is most constrained by arcs of block, so that theoretically, a small lesion is sufficient to stop conduction.2 Hence, knowledge of isthmus geometry is important for successful ablation therapy. During radiofrequency therapy, however, the geometric properties of the reentry circuit are usually incompletely known,1 3 and it is often necessary to create multiple lesions because the position, size, or shape of the initial ablation lesion is not adequate to completely stop conduction.2 The creation of lesions that are unsuccessful at stopping reentry increases the likelihood of patient morbidity.1 In some cases, lesion creation may also cause formation of other potential reentry paths, whereby initiation of other reentrant circuit morphologies becomes possible.1
The reentry pathway can possess dynamic properties (ie, cycle-to-cycle changes in geometry and/or conduction velocity) that may account for some of the difficulties associated with unsuccessful ablation therapy.3 When reentry is dynamic, characteristics of the protected isthmus can vary such that the best possible lesion dimensions to prevent recurrence may depend on all changes that can occur during the course of tachycardia. The presence of dynamic properties during reentry includes large cycle-length variations after onset4 5 and before spontaneous termination,6 7 linear changes in cycle length in both clinical8 and experimental9 cases, and changes in isthmus geometry.10 Given these findings, it was hypothesized that isthmus geometry often undergoes continuous evolution throughout reentry and that measurements of cycle-length variability can be used to segment reentry into onset, maintenance, and spontaneous termination phases and to predict changes in isthmus geometry. Such information is of potential importance in catheter ablation therapy, when it is desirable to know the precise geometry of the isthmus during reentry and to predict any dynamic changes that might occur.
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Methods |
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Cycle-Length Measurements
Myocardial infarcts were created by ligation of the left anterior descending coronary artery of canine hearts.11 Data from monomorphic reentrant ventricular tachycardias, induced by premature stimulation 4 to 5 days after ligation of the left anterior descending coronary artery, were used for creation of activation maps and measurement of cycle length and isthmus geometry parameters. Twenty-five reentry episodes with a figure 8 pattern of conduction were studied (20 canine experiments). Tachycardia cycle length was measured as the R-R interval of the ECG. Figure 1A
shows a graph of cycle length versus cycle number
from onset (cycle 1) to spontaneous termination (cycle 49) for a
selected reentry episode. Large changes in cycle length follow onset
and precede termination, whereas during most of the reentry episode,
cycle length tends to prolong gradually with small cycle-length
oscillations. The sequence of cycle-length alterations in
Figure 1A was characteristic of many reentry episodes and
was used to segment tachycardias into distinct phases. First, the range
in cycle length (maximum to minimum) was computed over a 5-cycle
sliding window as a gauge of localized cycle-length variability. The
window was then shifted by 1 cardiac cycle and the range recomputed
over the new 5-cycle interval. This measurement, termed the moving
average of the range in cycle length (MARC), was repeated with each
shift of the sliding window by 1 cardiac cycle from onset to
termination of tachycardia. The 5-cycle MARC window length was a
compromise between too short a window (the range parameter becomes less
meaningful) and too long a window (lowered time
resolution).
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For each tachycardia episode, MARC magnitude was graphed
versus cycle number at the start of the window
(Figure 1B
). MARC was used to segment all tachycardias into 2
to 3 distinct phases. At onset, called phase I, MARC tended to be large
(ie, large changes in cycle length occurred over the 5-cycle window).
After a few cardiac cycles, cycle length tended to stabilize, and MARC
decreased. The phase I/II boundary was considered to occur when MARC
ceased to decrease rapidly. It was computed mathematically as the
starting time of that MARC sliding window after tachycardia onset
(Figure 1B, left hatched bar), for which the second
derivative of MARC was at a maximum
(Figure 1B, inset trace). During phase II, MARC tended to be
relatively small (ie, small changes in cycle length occurred over a
5-cycle window). The phase II/III boundary (if present) was considered
to be the point when MARC began to increase rapidly. It was computed
mathematically as the ending time of that MARC sliding window before
spontaneous termination of tachycardia
(Figure 1B, right hatched bar), for which the second
derivative of MARC was again at a maximum
(Figure 1B, inset trace). During phase III, when present as
in
Figure 1, MARC was often large (ie, large changes in cycle
length occurred). In tachycardias terminated by electrical stimulation,
the cycle before commencement of stimulation was arbitrarily taken as
the last cardiac cycle in phase II.
Several statistical measurements were computed with respect to tachycardia phase. For phase I, II, and III (when present), the number of cardiac cycles, mean cycle length, and mean value of MARC during the phase were determined. Additionally, during phase II, discrete linear trends of cycle-length change, defined as having a minimum duration of 25 cycles, were discerned by eye. The following cycle-length measurements were computed for each of the 34 linear cycle-length trends that occurred during phase II in 25 reentry episodes: (1) average MARC, (2) rate of cycle-length change (slope of the linear regression line), and (3) coefficient of determination (r2 value).
Isthmus Geometric Parameters
Activation maps were then constructed by
automatically marking activation times of electrogram signals using
electrogram slope and peak criteria and printing the times for all
sites on a computerized map
grid.11 In these maps, arcs
of block separated sites in which activation differed by >40 ms and
where wave fronts on opposite sides of the arcs moved in different
directions.11 The arcs were
drawn with a cubic spline interpolation program (PSI-Plot version 4,
PSI) that is based on a polynomial equation that minimizes the
straight-line distance to a set of boundary points. In all activation
maps, for consistency, the boundary points designating the position of
each arc of block were positioned manually at equal distances between
bordering recording sites. Although the actual spacing between sites
was 4 to 5 mm, the spline interpolation function generates a curved
line that was superimposed on the computerized grid with 0.1-mm
precision.
Figure 2A and 2B
show, respectively, for a selected reentry episode, activation maps
from the starting and ending cycle of the phase II interval. During
phase II in this reentry episode, there was a single linear trend in
cycle-length change. In each map, the isthmus is bounded by 2
superimposed arcs of block (thick curvy black lines). The scale with
respect to the epicardial surface, determined from the multielectrode
array dimensions, is shown (1 cm reference). Several geometric
measurements were computed from the starting and ending maps: (1) the
isthmus width at its narrowest point (dotted line); (2) average of the
lengths of each arc of block from one end to the other (dashed lines),
which was the estimated isthmus length; and (3) the activation interval
from proximal to distal SCZ edge, determined from the end cycle
(Figure 2B). SCZ edges were arbitrarily defined as bordering
the longest contiguous segment of the isthmus, during the end cycle,
where conduction velocity was at least 25% slower than elsewhere in
the isthmus. The difference in the time of activation at proximal and
distal sites was taken as the SCZ activation interval. The same sites
were then used to compute the SCZ activation interval at the start of
phase II
(Figure 2A). According to the geometric parameters shown in
Figure 2, during phase II, SCZ activation interval and cycle
length increased nearly in concordance (14 and 15 ms, respectively),
and both isthmus length and narrowed width decreased.
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The above-described measurements were made for each reentry episode, and the measurements for all episodes were then pooled. Each pooled statistical and geometric variable was separately treated as the dependent variable, and best subsets regression (SigmaStat version 2.0, Jandel Scientific) was used to determine significant correlation (P<0.001) when all other variables were treated as independent variables.
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Results |
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Dynamic Changes During Reentry
Graphs of cycle-length change from onset to termination of reentry for 9 episodes are shown in Figure 3
. In all panels, the gray scale denotes phase (I,
black; II, gray; III, white). Solid vertical lines denote phase
boundaries, and when present, dashed lines delineate distinct phase II
linear trends. During phase I, dramatic changes in shape and location
of the reentry path caused large cycle-length oscillations to occur.
During phase II, cycle length tended to prolong slowly and linearly
(all panels), with 2 distinct trends of linear cycle-length change
occurring in some episodes
(Figure 3E through 3I). Overall, 34 phase II trends of
cycle-length change occurred in 25 reentry episodes (31 positive, 3
negative, mean 0.11 ms/cycle with mean
r2=0.81).
Trend-to-trend transitions were observed from activation maps to be
precipitated by breakthrough across portions of the arcs of
block.
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In some episodes, small, quasi-periodic oscillations of 1 to
5 ms in cycle length were present during phase II
(Figure 3A through 3E), whereas in other episodes, which
tended to be of longer duration, large cycle-length alternans of >5 ms
occurred
(Figure 3F through 3I). Large alternans was observed from
activation maps to be caused by alternation in circuit path length due
to an area that was alternately refractory to activation. During
alternans, when cycle length gradually prolonged, greater time for
recovery of excitability caused the refractory surface to diminish in
size on successive cardiac cycles so that path-length differences, and
therefore alternans magnitude, decreased
(Figure 3F, 3G, and 3I).
On the other hand, when cycle-length prolongation was of small
magnitude (or nonexistent), recovery of excitability did not improve,
and alternans did not markedly diminish
(Figure 3H). Reentry terminated spontaneously in 6 of 25
episodes, and MARC increased before spontaneous termination (ie, phase
III occurred) in 4 of 6, including
Figure 3A and 3B.
Figure 4 shows examples of shifts in the arcs of block
bounding the isthmus that occurred from start (solid lines) to end
(dashed lines) of phase II for 9 reentry episodes. In almost every
case, each arc of block shifted inward, particularly near the narrowest
isthmus width, and the shape of the isthmus changed. For 2 episodes,
shown in
Figure 4G and 4I,
block lines were initially short, and only slight narrowing occurred.
Alterations in arcs of block caused a narrowing of the isthmus for all
episodes shown, a general shortening of the isthmus in some episodes
(Figure 4A through
4E),
and occasionally, reinforced block lines at the narrowest point of the
isthmus
(Figure 4, A, B, D, and F).
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Geometric variables of the 34 phase II trends with
significant linear correlation
(P<0.001) are presented in
Figure 5. Shown are the relationships between changes in
cycle length versus SCZ activation interval
(Figure 5A), SCZ activation interval versus isthmus length
(Figure 5B), narrowed isthmus width versus isthmus length
(Figure 5C), and isthmus length versus rate of cycle-length
prolongation
(Figure 5D). The regression equation describing the
relationship between the variables is given in each panel. The
relationships can be summarized as follows. During a phase II trend,
the SCZ activation interval and the cycle length tended to increase,
whereas isthmus length tended to decrease. When isthmus length
decreases, narrowed isthmus width also tends to decrease, and larger
decreases in isthmus length tend to correspond to higher rates of
cycle-length prolongation. Overall, for the 34 linear trends of
cycle-length change during phase II that occurred in 25 reentry
episodes, cycle length and SCZ activation interval increased by a mean
14.2 and 14.8 ms, respectively, and isthmus width and length decreased
by a mean of 2.1 and 6.3 mm, respectively. There was also a significant
linear correlation between the 25 phase II intervals themselves: phase
II duration tended to prolong (by 30.6 cycles) as variability increased
(per millisecond increase in MARC)
(r2=0.431).
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Summary Statistics
Table 1 gives the mean cycle-length statistics of
the phases. Phases I and III were of short duration (mean 8.6 and 4.8
cycles, respectively) and high cycle-length variability (average MARC
of 29.4 and 17.3 ms, respectively). Phase II was of longer duration
(mean 144.9 cycles) and much lower cycle-length variability (average
MARC 3.0 ms). Cycle length was often prolonged during tachycardia (mean
increase 7.3 ms from phase I to II and 22.6 ms from phase II to III).
Significant correlation of variables between phases
(P<0.001) is shown in
Table 2. Mean cycle lengths of phases I and II were
linearly related. In addition, cycle-length variability during phase II
(MARC) and duration of phase III (number of cardiac cycles) were both
linearly related to duration of phase
I.
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Discussion |
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Reentry Dynamic Patterns
During phase I, peaks of cycle-length oscillation, which damped within a few cycles, sometimes occurred (Figure 3
, A, C, D, and E); such peaks have also been
observed in clinical studies at onset of
reentry5 and after a step
change in rate during
pacing,12 as well as in
canine atria when premature stimuli reset
reentry.6 The dramatic
changes in shape and location of the reentry path observed during
cycles after onset may have caused this oscillatory behavior, due to
incomplete recovery of excitability and diminished conduction velocity
after cycles with shorter diastolic
intervals.6 Similar decreases
in cycle-length variability after onset, as are evident in
Figure 3, have been observed in human ventricular
tachycardias.4 Cycle-length
alternans caused by refractoriness to activation
(Figure 3F through 3I) can be precipitated by a critical
shortening of the diastolic
interval.13 Similar
conduction alternans, with changes in return tracts, have been observed
during human ventricular
tachycardia3 14
and in canine atrial
reentry.6 In 2 of 6 episodes
that terminated spontaneously, breakthrough of the activating wave
front across a broad segment of an arc of block resulted in its arrival
at the SCZ before recovery of excitability, causing block. MARC did not
increase significantly during these episodes. However in 4 of 6
episodes, cycle length increased exponentially before termination,
producing a large increase in MARC (including the episodes shown in
Figure 3A and 3B). In general, large cycle-length changes
before spontaneous termination of reentry are infrequent in this canine
infarct model,15 although
they are prevalent in ventricular reentry occurring in
humans7 and in canine atrial
tissue.6
Relationship of Dynamic Phases I
Through III During Reentry
Phases I, II, and III (when it occurred) were
associated, respectively, with onset, maintenance, and spontaneous
termination of reentry. Despite these distinctive dynamic processes,
cycle length still tended to prolong from onset to termination
(Table 1). All 3 of the pairs of variables with highly
significant correlation between phases involved phase I
(Table 2). The results shown in
Tables 1 and 2 suggest that there is a range to the pattern
of dynamic activity occurring during tachycardia and that this pattern
might be predictable from onset. At one extreme, reentry processes are
relatively devoid of instability, so that onset and spontaneous
termination are short (few cycles during phases I and III), with
quiescent conduction pattern during the maintenance phase (small
average MARC during phase II), which would tend to increase the
distinction between phase boundaries
(Table 2). At the other extreme, because of instabilities in
reentry processes, onset and spontaneous termination are long
(large number of cycles during phase I and III) with
fluctuating conduction pattern during the maintenance phase (large
average MARC during phase II)
(Table 2). The phase boundaries are then less distinct.
Greater instabilities, in terms of larger average MARC during phase II,
tended to prolong phase II (see Results), increasing the duration of
the entire reentry episode. A theoretical treatment of ranges in
patterns of reentry from stable to irregular suggests that the pattern
depends in part on the relationship of circuit path length to cellular
excitability,16 which vary,
respectively, according to reentrant circuit morphology and substrate
properties.
Isthmus Constriction Versus SCZ
Conduction Velocity
In 34 phase II trends, the relationship between
narrowed isthmus width and conduction time through the SCZ followed an
approximately 1/x law; that is, when isthmus width at its narrowest
point is x, SCZ activation interval is proportional to 1/x. The
manifestation in terms of cycle length was that as isthmus width
constricted, cycle length prolonged linearly at first
(Figure 3, A through I, phase II), followed by an
approximately exponential increase and block in some episodes
(Figure 3 A and B, phase III). A 1/x relationship has also
been described theoretically for the case of activation through a
narrow channel bounded by parallel block
lines.17 When path width was
decreased in the range of 15 to 5 mm, conduction velocity decreased
linearly; when path width decreased below 5 mm, conduction velocity
decreased exponentially and approached zero at 
1.2
mm.17 Limited electrode
spatial resolution precluded investigation of the precise relationship
at x<4 mm for the data presented herein. However, in such cases, the
SCZ activation interval tended to be long (>75 ms), and reentry often
terminated spontaneously on a subsequent cycle, either because of
greatly diminished conduction velocity or complete block, so that a
sinus escape beat captured conduction of the
heart.
Proposed Mechanism of Phase II
Cycle-Length Change
Decreasing conduction velocity, and sometimes
block, occurs when an area of narrowed path width, or stricture, in the
circuit is followed by an abrupt, 2D geometric expansion, because less
current is available for
activation.17 18
This phenomena is caused by electrical impedance mismatch at the
transition site and a change in wave-front curvature beyond the
transition.18 19
It suggests a mechanism for constriction of the narrowed isthmus
observed during phase II of tachycardia
(Figures 4 and 5). During wave-front traversal through the
narrowed SCZ stricture to the outward expansion of the isthmus, the
current available for activation ahead of the activating wave front
decreases, and conduction slows there. An inward current gradient
immediately develops along the arcs of block at the exit of the
stricture, causing a slight inward shift of the functional block lines
there. During successive cardiac cycles, wave-front velocity in the SCZ
decelerates, and available current for activation diminishes further
via feedback as block lines continue to shift inward (constrict) at the
narrowed isthmus width. The rate of deceleration and constriction
depend on the funicular quality of isthmus shape. More nearly parallel
bounding arcs of block would result in more current available for
activation, a current gradient across the arcs of block more nearly in
equilibrium, and therefore a lower constriction rate (or no
constriction). In contrast, arcs of block that are more narrowed along
a portion (ie, more funicular shaped) would result in less current
available for activation at the exit of the stricture, causing an
increased magnitude of inward current gradient along the block lines,
faster inward constriction, and more rapid wave-front deceleration. As
cycle length prolonged, increased time available for recovery of
excitability on subsequent cycles would cause shortening of the arcs of
block at their ends, where refractoriness to conduction is least. Were
breakthrough across an arc of block on a particular cardiac cycle to be
suitably large and well placed, such that the relationship between
shape and surface area of the stricture and its distal expansion
drastically changed, then the rate of linear cycle-length prolongation
would also significantly change (ie, this event would delineate a
boundary between differing phase II trends of cycle-length
change).
The phase II data support the suggested mechanism of cycle-length change. Cycle length was generally prolonged, and distinct trends of differing linear cycle-length change were delineated by cardiac cycles with significant breakthrough across the arcs of block. During 3 of 34 phase II trends, cycle-length decrease occurred while the narrowed isthmus expanded slightly and SCZ activation interval decreased concomitantly. However, in these episodes, complex block lines external to the isthmus were present, which may have contributed to a possible reversal in the direction of the current gradient across the arcs of block.
Limitations and Future
Directions
During cycle-length calculations, an alteration in the
window length for MARC computation may shift the precise location of
phase I-II and II-III boundaries; therefore, the boundaries are only
approximate. Isthmus arcs of block were localized by spline
interpolation to 0.1 mm, which was beyond the 4- to 5-mm resolution of
the multielectrode array but consistent from one activation map to the
next. Any inaccuracy in placement of the arcs of block may have served
to decrease significance of correlation between variables; higher
electrode spatial resolution may reveal other geometric variables with
significant correlation. The simple measurements used to gauge isthmus
length and narrowed width from the arcs of block are not indicative of
subtle variations in isthmus geometry. For improved representation,
more sophisticated geometric measurements might be useful; however,
complexity of analysis would increase. Because similar cycle-length
changes as those described herein can occur during reentrant
ventricular tachycardia in
humans,8 it might be possible
to correlate cycle-length changes to geometric alterations that have
been observed in clinical cases of
reentry.3 At present,
however, it is unknown how the properties of functional circuits might
apply to the dynamics of the SCZ of ventricular tachycardia circuits in
humans, where the isthmus may more frequently be bounded by anatomic
arcs of block.1 Use of an
anatomic model of reentry in canine hearts might better serve to
describe the dynamics of some reentry episodes in humans.
The results presented herein categorize dynamic changes in isthmus geometry, which may be a cause of unsuccessful ablation therapy.3 At present, it is unknown how infarct border zone areas that are only transiently part of the reentry isthmus affect catheter ablation. The relationship of changes in isthmus geometry to targeted ablation sites under both experimental and clinical conditions is a subject of future study, as is the correlation of absolute isthmus measurements (such as absolute length, width, and location) to cycle length.
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Acknowledgments |
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Supported by an Established Investigator Award from the American Heart Association, a Whitaker Foundation Research Award, and grants R37 HL31393 and HL30557 from the National Heart, Lung, and Blood Institute, National Institutes of Health. The author would like to thank Dr Andrew L. Wit, Dr Melvin M. Scheinman, and Dr James Coromilas for their participation in some of the experiments and for their discussion of this manuscript.
Received June 16, 2000; revision received August 25, 2000; accepted August 31, 2000.
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