Dynamic Relationship of Cycle Length to Reentrant Circuit Geometry and to the Slow Conduction Zone During Ventricular Tachycardia
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.
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.
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).
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.
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.
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.
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).
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).
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.
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.
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.
- Copyright © 2001 by American Heart Association
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