## Abstract

The genesis of complex ventricular rhythms during atrial tachyarrhythmias in humans is not fully understood. To clarify the dynamics of atrioventricular (AV) conduction in response to a regular high-rate atrial activation, 29 episodes of spontaneous or pacing-induced atrial flutter (AFL), covering a wide range of atrial rates (cycle lengths from 145 to 270 ms), were analyzed in 10 patients. AV patterns were identified by applying firing sequence and surrogate data analysis to atrial and ventricular activation series, whereas modular simulation with a difference-equation AV node model was used to correlate the patterns with specific nodal properties. AV node response at high atrial rate was characterized by *1*) AV patterns of decreasing conduction ratios at the shortening of atrial cycle length (from 236.3 ± 32.4 to 172.6 ± 17.8 ms) according to a Farey sequence ordering (conduction ratio from 0.34 ± 0.12 to 0.23 ± 0.06; *P* < 0.01); *2*) the appearance of high-order alternating Wenckebach rhythms, such as 6:2, 10:2, and 12:2, associated with ventricular interval oscillations of large amplitude (407.7 ± 150.4 ms); and *3*) the deterioration of pattern stability at advanced levels of block, with the percentage of stable patterns decreasing from 64.3 ± 35.2% to 28.3 ± 34.5% (*P* < 0.01). Simulations suggested these patterns to originate from the combined effect of nodal recovery, dual pathway physiology, and concealed conduction. These results indicate that intrinsic nodal properties may account for the wide spectrum of AV block patterns occurring during regular atrial tachyarrhythmias. The characterization of AV nodal function during different AFL forms constitutes an intermediate step toward the understanding of complex ventricular rhythms during atrial fibrillation.

- atrioventricular conduction
- atrial arrhythmias
- nonlinear dynamics
- atrioventricular modeling
- atrial fibrillation

the atrioventricular (AV) node is the area of specialized tissue that electrically connects the upper and lower chambers of the heart. During normal sinus rhythm, it assures the correct delay between atrial and ventricular activations, optimizing the pumping function of the heart. During atrial arrhythmias, such as atrial flutter (AFL) and atrial fibrillation (AF), the AV node crucially filters the high-frequency atrial activity, protecting the ventricles against life-threatening ventricular tachyarrhythmias.

Experimental and clinical studies have shown that peculiar functional and structural properties underlie the filtering action of the node and confer it a unique sensitivity to changes in atrial rate (3, 4, 19, 25, 33). Specific premature stimulation protocols at different basic rates have revealed a rate and time-dependent response of the AV node to atrial rate variations. Specifically, nodal response is characterized by conduction delay and eventually dropped beats at higher prematurity, which can be ascribed to kinetically distinct functional properties, such as recovery, facilitation, and fatigue (4, 38, 46, 48). AV node response at high atrial rates is significantly affected by concealed conduction of blocked beats (13, 27, 29, 37), which partially activate the node increasing the refractory period and conduction time of the next beats. Additional complexity in AV conduction arises from the so-called dual-pathway AV node electrophysiology, the functional, and perhaps anatomical, dissociation of the node in two parallel pathways (15, 33, 36, 51, 53). The dissociation determines two different and electrophysiologically distinct wavefronts propagating in tandem from the atria to the His bundle, which may give rise to phasic summation and annihilation of atrial inputs (33).

Although there is evidence that specific nodal properties generate the AV node response under controlled stimulation protocols, the nodal determinants of complex AV patterns, observed in humans during spontaneous arrhythmic conditions, are still poorly understood.

By combining data analysis and computer modeling this article aims to *1*) quantify the dynamical response of the AV node at spontaneous high atrial rates in patients with different atrial flutter (AFL) episodes; *2*) clarify the contribution of specific nodal properties to the observed dynamics. The electrophysiological features of atrial flutter make it a suitable clinical model to investigate nodal dynamics in the high-frequency range. Atrial flutter is a highly regular atrial tachycardia (26, 43), characterized by a high atrial rate >240 beats/min (14), which determines some degree of AV block. Pacing-induced transitions between atrial flutter rhythms are commonly observed during electrophysiological investigations (14, 50) and may accelerate AFL to rates >340 beats/min (14). In this article, the fast regular atrial activation during AFL was used as a stable AV node input to test nodal response at high atrial rates, where conditions of AV block occur. As well, spontaneous or pacing-induced transitions between AFL episodes were used to extend the range of tested atrial frequencies and reveal the dynamics of AV response at changing atrial rate. AV patterns and nodal response curves were determined by application of firing sequence (17) and surrogate data analysis (45) to atrial and ventricular activation time series. The potential nodal determinants of AV dynamics were investigated by modular simulations with a difference-equation model of the AV node, which included recovery, dual pathway physiology, and concealed conduction properties.

## MATERIALS AND METHODS

### Electrophysiological Data

A retrospective analysis was applied to data recorded in previous studies (43), which investigated the effects of rapid pacing on atrial flutter in humans. The study population comprised 10 patients with spontaneous episodes of atrial flutter (age, 70.2 ± 5.6 years; 2 females), whose demography and arrhythmia characteristics are reported in Table 1. In all cases antiarrhythmic treatment had been suspended at least five half-lives before the study, except for one patient (patient 4), who was treated with amiodarone. During the electrophysiological study, a bipolar catheter was advanced into the esophagus for atrial electrogram recording (band-width, 30 to 500 Hz) and stimulation. After 10 min of basic recording, patients underwent bursts of rapid atrial pacing (repeated 5–10 s trains of stimulation at 5–10 Hz), which induced transitions toward more rapid forms of the arrhythmia (see Table 1). Ventricular activity was recorded from a surface ECG. All signals were recorded simultaneously on a FM magnetic tape (TEAC XR-510) for offline analysis. The study was performed in accordance with the principles outlined in the Declaration of Helsinki and approved by the Hospital Ethics Board. All patients gave written informed consent.

### Data Analysis

#### Activation time series extraction.

Signals were digitized at 1 kHz on a personal computer for interval measurement and analysis. A computer program was developed to automatically identify atrial electrogram complexes from the esophageal lead and QRS complexes from the surface ECG. Atrial electrograms were preprocessed and filtered to automatically detect atrial depolarizations, and atrial activation times were set at the time of maximal, positive slope of the signal (32). Ventricular activation times were measured from the ECG by identifying the time of QRS maxima/minima, depending on the surface lead analyzed. Activation time series were visually checked and manually corrected if necessary. Atrial (AA) and ventricular (VV) cycle lengths were measured as intervals between consecutive atrial and ventricular activation times, respectively, and the mean AA-to-VV ratio was used as average index of AV conduction.

#### Firing sequence analysis for the construction of CR curves.

The dynamical response of the AV node to atrial rate changes was determined in each patient by application of firing sequence and surrogate data analysis to atrial and ventricular activation time series. Firing sequence analysis has been previously introduced to characterize the unstable dynamics of a periodically driven oscillator in the presence of noise (17). The method was here applied to cardiac series, modeling the heart as a system of interacting oscillators (20), where the atrium represented the autonomous and the ventricle the forced oscillator. As exemplified in Fig. 1, the firing sequence (fourth row) is a sequence of non-negative integers, which gives the number of firing times of the atrial oscillator (A) in consecutive cycles of the ventricular oscillator (V, third row). Repeated units in the firing sequence are assumed to indicate the presence of coupling conditions between the two oscillators. In the displayed case, the repeating unit 3 in the first part of the sequence indicates a *n:m* coupling of 3:1 (i.e., *n* = 3 atrial beats in m = 1 ventricular cycle) with conduction ratio CR = m/*n* = 1/3 (i.e., fraction of conducted beats, bottom row), whereas the repeating unit 23 in the second part corresponds to a 5:2 AV coupling with CR = 2/5.

In each patient the firing sequence was automatically computed from atrial and ventricular time series and analyzed for the detection of n:m coupling patterns up to order m = 4. To identify even short instances of coupled activity, coupling conditions were detected starting from three repetitions of the repeating unit. Significant coupling conditions were then distinguished from background coupling performing a case-by-case test based on surrogate data analysis (45). Specifically, for each detected repeated sequence, the probability of obtaining the same (or longer) sequence was computed from 1,000 surrogate series, generated by a random permutation of the order of the elements of the patient complete firing sequence. A pattern was considered significant if the probability of obtaining it from random series was <0.05. Finally, the dynamical response of the AV node in each patient was reconstructed in terms of CR curves, which displayed the conduction ratio m/n of each significant n:m pattern as a function of the average atrial cycle lengths at which it was observed.

### Statistical Analysis

Data are expressed as means ± SD or range. Pairwise comparisons between interval parameters obtained at the slowest and fastest AFL rate were performed by Mann-Whitney test. A *P* value <0.05 was considered statistically significant.

### Computer Simulations

To clarify the specific role of different nodal properties in the determination of AV coupling patterns, modular simulations were run with a difference-equation model of the AV node. The model iteratively generated ventricular beat series (V) at given atrial input sequences (A). It included intrinsic properties of AV conduction, such as the slow recovery of excitability, dual pathway physiology, and concealed conduction of blocked beats. These were modeled according to previously proposed schemes (12, 31, 46) and progressively added to the basic recovery model.

#### Recovery properties.

Nodal recovery was modeled assuming an exponential decrease of the conduction time *AV*_{i+1} at the increase of the recovery time *VA*_{i} (time interval from the preceding conducted beat *V*_{i}), i.e., *AV*_{i+1} = α + β·*e* ^{−VAi/τ} if *VA*_{i} > θ (*Eq. 1*), where *α* is the minimum conduction time corresponding to propagation in a fully recovered tissue, *β* and *τ* are positive constants, and *θ* is the refractory period (46). For recovery times *VA*_{i} shorter than the nodal refractory period *θ*, the beat was blocked. The recovery time *VA*_{i} of each atrial beat was recursively obtained from previous conduction times and cycle lengths as

(*Eq. 2*), where atrial intervals *AA*_{j} are numbered from the last conducted beat, *k* is the first beat for which the recovery time exceeds the refractory period, and *AV*_{i} is the previous conduction time.

#### Concealed conduction effects.

Concealed beats with different levels of penetration in the node were assumed to stochastically lengthen the refractory period *θ* of the node (31). Specifically, *θ* was defined as the sum of a basic refractory period *θ*_{0} and a normally distributed concealed conduction term, Δ_{j}, produced by each nonconducted beat *A*_{j}, i.e.,

*θ* = *θ*_{0} + Δ_{j} = *θ*_{0} + Ω_{j}Δ_{std} + Δ_{m} (*Eq. 3*), where Ω_{j} is a normally distributed random number with mean zero and standard deviation 1, and *θ*_{0}, Δ_{std}, and Δ_{m} are positive constants.

#### Dual pathway physiology.

The presence of dual pathway physiology was described with a simplified version of the model (12). Specifically, the two pathways were assembled in a simple Y-shaped structure, starting in the atrium and converging into a final common pathway reaching the bundle of His. The conductions through the fast (FP) and slow (SP) pathways were defined according to Eqs. 1–3, with constants fitted for each pathway (i.e., longer conduction times and shorter refractoriness for the SP, shorter conduction times and longer refractoriness for the FP). Unlike in Ref. 12, constant recovery properties (i.e., parameters *β* and *τ*) were assumed for each pathway. The approximation was consistent with the smaller effect of fatigue and facilitation at the levels of AV block observed during AFL (48) (see paragraph *Additional factors modulating AV conduction* in discussion). Two different conduction times AV were computed for each atrial beat, and the dominant pathway was decided by the model as the nonrefractory pathway, which provided the shortest conduction time (12). After complete block of the AV node, the conduction pattern of the subsequent beats was affected by concealed conduction in the pathway, as quantified by Eq. 3.

#### Modular simulations.

Output ventricular activation series and corresponding conduction ratios were generated for atrial cycle lengths from 100 to 400 ms (time step, 0.05 ms) by using a single pathway model in absence of concealed conduction (M1), and a dual pathway model in the absence (M2) and presence (M3) of concealed conduction. The parameters of the models were set to approximately the midpoint of their physiological ranges, consistently with previous clinical and modeling studies on the human AV node (15, 18, 31, 51). Specifically, we set α = 250 ms, β = 500 ms, τ = 100 ms, θ_{0} = θ = 340 ms for model M1; α_{FP} = 100 ms, θ_{0FP} = θ_{FP} = 450 ms, α_{SP} = 360 ms, θ_{0SP} = θ_{SP} = 300 ms, β_{FP} = β_{SP} =500 ms, τ_{FP} = τ_{SP} = 100 ms for model M2; and previous parameters plus Δ_{mFP} = Δ_{mSP} = 50 ms, 10 < Δ_{stdFP} = Δ_{stdSP} < 30 for model M3. Because of the stochastic term in M3, AV response curves for this model were obtained as an average over 20 trials. In addition to CR curves, simulated time series, mimicking the qualitative features of transitions observed in patients, were calculated. Parameters (α, θ) for patient-specific simulations were searched in the range 0 ≤ α ≤ 400 ms and 0 ≤ θ ≤ 750 ms, and set to the values, which maximized the similarity between the occurrence of observed and simulated *n:m* patterns.

## RESULTS

### Transitions Between Different AFL Rhythms

As shown in Table 1, transitions between a total of 29 (13 spontaneous and 16 pacing induced) AFL episodes were analyzed in the overall population of patients. In all patients high-frequency pacing was effective to induce transitions between the basic AFL and a more rapid form (rate >285 beats/min) of the arrhythmia. In four patients (patients 4, 6, 7, and 10) pacing of the induced rapid AFL generated a third AFL episode, characterized by a further increase in atrial rate. In two patients (patients 2 and 4) spontaneous transitions were observed between the induced rapid AFL episodes and the basic AFL form. Finally, in one patient (patient 1) the rapid AFL form spontaneously reverted to sinus rhythm.

The mean atrial and ventricular cycle lengths and corresponding AA-to-VV ratios for the slowest and fastest AFL form observed in each patient are displayed in Fig. 2. Significant changes in AFL cycle length were observed in all patients, with the mean AA interval decreasing from 236.3 ± 32.4 ms to 172.6 ± 17.8 ms (*P* < 0.01). The decrease in atrial cycle length produced different responses at the ventricular level, resulting in a nonsignificant increase of *VV* intervals from 756.3 ± 243.0 to 772.0 ± 151.4 ms. In contrast the AV response showed augmented levels of AV block in all patients during rapid forms, with the mean AA-to-*VV* ratio significantly decreasing from 0.34 ± 0.12 to 0.23 ± 0.06 (*P* < 0.01) at the increase of the atrial rate.

### Structure of AV Coupling Patterns at Changing Atrial Rates

Firing sequence analysis was applied to the atrial and ventricular activation time series to identify transient instances of AV coupling and to characterize the structure of AV patterns at changing atrial cycle length. Examples of induced and spontaneous transitions between different atrial rhythms and their effects on AV conduction are displayed in Fig. 3 for representative patient 1. The patient showed a basic AFL cycle length of 238.1 ± 2.4 ms, which resulted in a stable 2:1 conduction pattern (CR = 0.5). Rapid stimulation induced a transition to a rapid AFL form (AA = 156.6 ± 4.3 ms), which led to a higher level of AV block (4:1 pattern with CR = 0.25). During the rapid episode the cycle length underwent a tiny spontaneous prolongation, which involved subsequent transitions from 4:1 to 7:2 (at AA = 160.1 ± 2.9 ms) to 10:3 (at AA = 161.5 ± 5.2 ms). Finally, the patient spontaneously reverted to sinus rhythm and 1:1 conduction. The ordering of the conduction patterns at changing atrial rates is shown in the reconstructed AV response curve, which shows a progressive decrease of the conduction ratios at increasing atrial rate, as well as the appearance of repeating patterns in which there are two or three ventricular beats in the repeating unit. Similar patterns were observed in other patients. Specifically, a 7:2 pattern was observed in proximity of a 3:1 pattern in patient 8, whereas 5:2 and 8:3 patterns were observed between 2:1 and 3:1 patterns in patients 2, 7, and 9.

### Appearance of Alternating Rhythms

Atrial rate changes revealed the presence of alternating conduction patterns, characterized by the alternation of *n:1* and *(n+2):1* conduction, which are clinically classified as alternating Wenckebach patterns (type A) (18). An example of alternating pattern is reported in Fig. 4 for patient 3. Although the patient displayed a dominant 4:1 conduction at basic AFL rates (AA = 193.1 ± 4.3 ms), a 10:2 conduction rhythm was observed during the rapid AFL form (AA = 169.9 ± 3.4 ms). The 10:2 pattern was produced from alternation between 4:1 and 6:1 conduction and resulted in large changes of the ventricular intervals, which oscillated between 996 ms and 709 ms. Alternating Wenckebach rhythms (type A), associated with large ventricular interval oscillations (average interval variation of 407.7 ± 150.4 ms), were observed in a total of four patients. In addition to the 10:2 pattern, a 6:2 pattern was observed in patients 4 and 9, whereas a 12:2 pattern was found in patient 10.

### Pattern Instability at Advanced Levels of AV Block

The comparison between AV patterns at different AFL rates showed the stability of coupling patterns to decrease at shorter atrial cycle lengths. This behavior is exemplified by patient 5 in Fig. 5, which shows the appearance of unstable AV patterns with advanced level of block, associated with complex ventricular rhythms. The patient displayed a stable 4:1 conduction rhythm at the basic atrial cycle length of 180.7 ± 7.4 ms. After transition to a faster AFL form (AA = 160.2 ± 6.8 ms), the stability of AV patterns deteriorated, and just a few significant (in gray) coupling epochs were observed, characterized by advanced levels of block (5:1 and 7:1) and short duration (7.1 s and 4.3 s, respectively).

The instability of AV coupling patterns at increasing atrial rate and levels of block was confirmed in the overall population of patients. On average, the percentage of significantly coupled atrial beats decreased from 64.3 ± 35.2% at the slowest AFL rate to 28.3 ± 34.5% at the fastest rate (*P* < 0.01), without significant changes in the variability of atrial cycle length (SD_{AA} = 5.1 ± 3.5 ms vs. 7.0 ± 3.4 ms for slow and fast AFL; *P* = not significant).

### Simulation Results

The role played by different AV properties in the determination of AV pattern structure is evidenced in Fig. 6, which displays simulated CR curves generated by the basic single pathway recovery model (M1), and by the dual pathway model in absence (M2) and presence (M3) of concealed conduction effects. Simulated activation series, generated by the three models, and reproducing the specific transitions observed in patients are displayed in Fig. 7.

The mathematical model of AV conduction via a single pathway, described by a monotonically decreasing recovery curve (M1, Fig. 6, *left*), shows a striking ordering of conduction rhythms as the atrial cycle length is changed. The structure of the mathematically predicted CR curve presents progressively decreasing conduction ratios *m/n* at the shortening of the atrial cycle length, which can be appropriately described by a mathematical concept called the Farey sequence (1). The Farey sequence of order *n* is all fractions between 0 and 1 in increasing order whose denominator is ≤*n.* For example the Farey sequence of order 5 between 1/5 and 1 is: 1/5, ¼, 1/3, 2/5, ½, 3/5, 2/3, ¾, 4/5, 1. At increasing orders of the Farey sequence further rhythms are predicted by concatenation of neighbor rhythms. Specifically, if *m/n* and *M/N* are neighbors in the Farey series, the first term, which appears between them when the order of the series is increased, is *(m+M)/(n+N)* (21). However, higher order Farey series occupy narrower regions of the curve, which makes the observation of higher order AV patterns rarer. AV patterns predicted by the Farey sequence are consistent with the transitions observed in patients at changing atrial rates, as exemplified by the similarity between the simulated series in Fig. 7*A* and patient data in Fig. 3. Indeed, a (4+3):(1:1) or 7:2 rhythm is predicted for intermediate frequencies between those of 4:1 and 3:1 patterns, and a (7+3):(2:1) or 10:3 rhythm between the 7:2 and 3:1 rhythms. Similarly, a 5:2 rhythm concatenates 2:1 and 3:1 rhythms, as well as an 8:3 rhythm appears for frequency between those that give the 3:1 and 5:2 rhythms.

A basic property of the Farey sequence is that *n* and *m* have no common divisors, thus the ordering of conduction patterns given by the single pathway recovery model does not predict the existence of alternating Wenckebach patterns (type A)*,* such as the 6:2 and 10:2 rhythms. Alternating rhythms may instead appear assuming a dual pathway physiology (M2; Figs. 6 and 7, *middle*). In the dual pathway model, the impulse can propagate through the sole fast (mostly at longer cycle lengths) or slow pathway (mostly at shorter cycle lengths), but propagation can also involve both pathways. An alternating propagation, determined by the complementary electrophysiological properties of the two pathways, can give rise to higher-order couplings, such as 6:2, 8:2 (Fig. 6), and 10:2 pattern (Fig. 7*B*, corresponding to patient data in Fig. 4). For instance, the 10:2 pattern is the combination of a 4:1 conduction in the SP and a 6:1 conduction in the FP. Specifically, 4:1 conduction can occur in the SP through its shorter refractoriness but involves a longer conduction time. This shortens recovery and prevents propagation in both pathways for the next five beats. Thanks to the longer pause, the next (sixth) beat can propagate through the recovered FP, resulting in 6:1 conduction. Fast conduction in the FP allows again propagation in the SP after three blocked beats (4:1), repeating the cycle.

The instability of coupling patterns observed at higher levels of AV block can be explained by including concealed conduction effects in the dual pathway model (M3; Figs. 6 and 7, *right*). Concealed conduction smoothes CR curves, with a progressive loss of staircase steps at increasing values of the concealed conduction parameter Δ_{std}. The disappearance of CR curve steps determines a higher instability of the patterns, since the length of each step corresponds to the set of atrial cycle lengths for which the pattern is observed. This is exemplified in Fig. 7*C*, which qualitatively reproduces the instability of patterns at advanced levels of block (5:1 and 6:1) observed in patient 5 (Fig. 5). Although concealed conduction is present at all AFL rates, its effects are more severe at higher atrial rates and advanced levels of block, since these zones of the CR curves have narrower steps and thus are intrinsically more prone to instability.

## DISCUSSION

In the present study, the dynamics of AV conduction at high atrial rates were analyzed during induced or spontaneous transformations between different atrial flutter rhythms. A quantitative description of AV response was provided in terms of CR curves, whereas integration of data analysis and computer modeling suggested the role of intrinsic nodal properties in the generation of AV patterns. The main results of the study can be summarized as follows. First, the AV node response at high-atrial rates displays coupling patterns of decreasing conduction ratio *m/n* at shorter atrial cycle length, according to a Farey sequence ordering. Second, alternating Wenckebach rhythms, such as 6:2, 10:2, and 12:2 patterns, may appear at specific atrial rates and involve large variations of ventricular cycle length (amplitude of 407.7 ± 150.4 ms). Third, the stability of AV patterns is affected by atrial rate, with a consistent decrease in the number of significantly coupled patterns at advanced levels of AV block. Finally, as shown by computer simulations, the dynamical features of complex AV patterns during regular atrial tachyarrhythmias may be explained by the combined effects of nodal recovery, dual pathway physiology, and concealed conduction.

### Quantification of AV Response at High Atrial Rates

AV node response at high atrial rates was dynamically characterized by processing atrial and ventricular time series from AFL patients, by firing sequence and surrogate data analysis.

#### The atrial flutter model.

Previous studies (7, 8) have suggested atrial flutter as a suitable model to investigate AV node response in the high-frequency range. Indeed the spontaneous short atrial cycle length of the arrhythmia allows exploration of AV conduction dynamics where conditions of AV block occur. On the other hand, AFL regularity, i.e., atrial cycle length with small (<20 ms) (14), nonrandom (32, 43, 44) oscillations, allows us to better determine the nodal contribution to ventricular response than during AF. Indeed, during AF the irregular atrial activation and variable spatial pattern of AV node engagement significantly contribute to the irregular ventricular output. Atrial flutter series were previously used to show spontaneous progression, regression, and alternations in AV block at almost fixed atrial cycle length during long-term ECG monitoring in AFL patients (6–8). In contrast, this article focuses on short-term variations of AV conduction at changing atrial rate, analyzing spontaneous or pacing-induced transformations between AFL rhythms in the same patient. In particular, the pacing-induced 27% reduction of atrial cycle length in our patients led to a 32% reduction in conduction ratio. In addition, the small and progressive variations of atrial cycle length during spontaneous returns from rapid to basic AFL forms revealed the subtle structure of AV node transitions in the proximity of dominant *n:1* conduction patterns.

#### Firing sequence and surrogate data analysis.

Consistent with previous stimulation studies (46, 48), nodal conduction properties were quantified with a black-box approach, characterizing nodal output as a function of nodal input by CR curves. However, response curves were reconstructed in this article under spontaneous arrhythmic conditions. This was possible through the combination of firing sequence analysis with a surrogate data approach. Firing sequence analysis integrated in a single time series the information on both atrial and ventricular activations, which are necessary for unambiguous characterization of nodal properties (9, 11, 23, 55). The reliability of the method to detect transient but significant instances of coupled activity was guaranteed by the use of surrogate data. The combined approach led to the identification of short-term transitions between *n:m* patterns at changing atrial cycle length, as well as to an objective exclusion of background coupling epochs from further nodal characterization.

### AV Conduction Patterns and Nodal Properties

By combining data analysis and modular computer modeling, we identified the main features of AV conduction during atrial tachyarrhythmias and indicated their potential nodal determinants.

#### AV patterns ordering and recovery properties.

In all AFL patients we observed a progressive decrease of the conduction ratios at increasing atrial rates, and more specifically a Farey sequence ordering of the transitions, which could be predicted by assuming a monotonically decreasing recovery curve (21). This is consistent with several studies (18, 21, 28, 35, 46), which have used the atrioventricular recovery curve as a unified framework for understanding a broad range of AV block rhythms induced by atrial pacing. In particular, Shrier et al. (46) provided the first systematic quantitative test of the hypothesis that iteration of the clinically measured AV nodal recovery curve alone would predict Wenckebach periodicity in humans during brief periods of rapid atrial pacing involving low levels of AV conduction block (CR ≥ 0.5). The results obtained in the present work extend the validity of recovery model predictions to the high-frequency range, providing evidence for the relevant role of recovery properties in the determination of AV rhythms in humans during spontaneous high atrial rates and advanced levels of AV conduction block.

#### Alternating Wenckebach rhythms and dual pathway physiology.

Firing sequence analysis disclosed the existence of alternating Wenckebach rhythms, such as 6:2, 10:2, and 12:2, which could not be predicted from the AV nodal recovery curve. Alternating Wenckebach rhythms have been previously observed during pacing or spontaneous rhythms (2, 6, 8, 47, 52) and initially explained in the framework of a discrete multilevel block due to transverse (horizontal) nodal dissociation. In agreement with more recent studies (5, 22, 30, 54), we showed that alternating Wenckeback rhythms could be generated by alternating propagation of the impulse in the dual pathways. The alternate propagation originates from the complementary electrophysiological properties of the two pathways, which lead to a shift of conduction from fast to slow pathway as recovery time decreases. In addition to alternating Wenckebach rhythms of type A, simulations showed that dual propagation could participate to the generation of other alternating rhythms, such as 5:2 and 7:2 patterns. This is in agreement with previous experimental and simulation studies in the rabbit heart, where His electrogram alternance demonstrated the involvement of both slow and fast pathway propagation in the generation of Wenckebach periodicity (12, 54). Our results provide further evidence of the intimate connection between dual pathway and rate-dependent properties in the generation of conduction patterns at high atrial rates (3, 5, 54).

#### Pattern instability and concealed conduction.

The comparison of AV patterns at slow and fast atrial rates showed the deterioration of pattern stability and the appearance of complex ventricular rhythms at higher atrial rates. The presence of irregular ventricular activation during AFL conditions has been observed in previous studies (2, 24). The results of computer simulation in this article indicated concealed conduction as a potential underlying mechanisms. Repeated concealment at varying depth of nodal penetration of blocked beats has been suggested to contribute, together with the complex atrial activity, to the irregularity of ventricular intervals during atrial fibrillation (13, 34, 37). Our simulation results showed that concealed conduction per se could lead to irregular ventricular rhythms, even in presence of periodic atrial inputs. More specifically, computer simulations suggested that higher instability of ventricular rhythm at shorter atrial cycle lengths could originate from the combination of concealed conduction effects and nodal recovery properties. Indeed, the zones of the CR curve corresponding to higher order Farey series and advanced levels of block are stable for a limited set of atrial cycle lengths, so that even small changes in refractory period (and thus in recovery time) due to concealed beats, may lead to blocked beats and thus to a higher instability of conduction patterns. However, in patients with rapid AFL, a small additional contribution to AV pattern instability might also derive from a higher irregularity of the atrial inputs to the node in these instable AFL forms (14).

#### Additional factors modulating AV conduction.

Our results suggest that AV coupling patterns at high atrial rates are largely determined by nodal recovery, dual pathway physiology, and concealed conduction effects. Other intrinsic and extrinsic mechanisms may, however, contribute to AV nodal conduction. Previous stimulation studies have shown AV rate-dependent response to be modulated by facilitation and fatigue (4, 10, 38, 48). Changes in autonomic tone also have been shown to exert dromotropic effects on nodal conduction and to modulate concealed conduction (39–42, 49). Because the impact of fatigue and facilitation decreases at increasing levels of block (i.e., passing from 1:1 to 2:1 conduction) (48), their effect should be limited in condition of atrial flutter, where a consistent number of beats is blocked (CR ≤ 0.5). On the other hand, changes in autonomic balance resulting from rapid pacing and/or increases in AFL rate may have partially contributed to the increased variability of ventricular intervals and pattern instability observed at high atrial rates.

### Clinical Implications

Recent studies have clearly stated the importance of “rate control” as an effective strategy for the treatment of atrial flutter and atrial fibrillation (16), especially in the acute setting. Through a better understanding of AV node functioning at high atrial rates, the new methodological framework introduced in this work may supply indications for the development of efficacious rate control approaches. In particular, atrial flutter may provide an ideal intermediate model for the comprehension of nodal response in AF, since it gives access to the high-frequency range typical of AF, without the complexity of the fibrillatory activation process. On the other hand, the firing sequence/surrogate data approach may find application for the reconstruction of AV response curves under spontaneous AF conditions in the clinical setting. Finally, computer modeling may favor the identification of the nodal determinants of AV conduction during atrial tachyarrhythmias, thus indicating potential targets of pharmacological and/or ablative rate control approaches.

### Study Limitations

To prove the actual involvement of nodal properties in the generation of AV response, nodal properties should be directly measured in each patient by ad hoc stimulation protocols, and then used to predict nodal response at high rates. Due to the retrospective nature of the study, nodal properties were not measured in our patients. Nevertheless, indirect evidence on the relation between specific nodal properties and AV patterns was provided by the agreement between simulated and observed patient-specific transitions. Moreover, the recording of atrial activity was performed at a single site through a transaesophageal catheter, which did not allow a direct evaluation of the atrial input to the AV node. Further atrial mapping studies may help to clarify the spatio-temporal pattern of AV node engagement during atrial tachyarrhythmias and its effects on nodal conduction.

### Conclusions

This article points out the presence of complex AV dynamics in patients during regular atrial tachyarrhythmias and suggests intrinsic nodal properties as the underling mechanism. The characterization of AV nodal function during different types of atrial flutter, extending from typical to rapid AFL forms, constitutes an intermediate step towards the understanding of complex ventricular rhythms during atrial fibrillation.

## GRANTS

M. Masè is recipient of a fellowship supported by Fondazione Cassa di Risparmio di Trento e Rovereto.

## DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

## AUTHOR CONTRIBUTIONS

M.D. and F.R. performed experiments; M.M. and L.G. analyzed data; M.M., L.G., and F.R. interpreted results of experiments; M.M. prepared figures; M.M. and F.R. drafted manuscript; M.M., L.G., and F.R. edited and revised manuscript; M.M., M.D., and F.R. conception and design of research; all authors approved final version of manuscript.

## ACKNOWLEDGMENTS

L. Glass thanks the Natural Sciences and Engineering Research Council (Canada) for support.

- Copyright © 2012 the American Physiological Society