INSTITUTE OF PHYSICS PUBLISHING Physiol. Meas. 26 (2005) 911–923
PHYSIOLOGICAL MEASUREMENT
doi:10.1088/0967-3334/26/6/003
Quantification of synchronization during atrial fibrillation by Shannon entropy: validation in patients and computer model of atrial arrhythmias Michela Mas`e1, Luca Faes1, Renzo Antolini1, Marco Scaglione2 and Flavia Ravelli1 1 2
Department of Physics, University of Trento, via Sommarive, 14, I-38050 Povo, Trento, Italy Division of Cardiology, Civil Hospital Asti, via Botallo, 4, 14100 Asti, Italy
E-mail:
[email protected]
Received 16 May 2005, accepted for publication 4 August 2005 Published 23 September 2005 Online at stacks.iop.org/PM/26/911 Abstract Atrial fibrillation (AF), a cardiac arrhythmia classically described as completely desynchronized, is now known to show a certain amount of synchronized electrical activity. In the present work a new method for quantifying the level of synchronization of the electrical activity recorded in pairs of atrial sites during atrial fibrillation is presented. A synchronization index (Sy) was defined by quantifying the degree of complexity of the distribution of the time delays between sites by Shannon entropy estimation. The capability of Sy to discriminate different AF types in patients was assessed on a database of 60 pairs of endocardial recordings from a multipolar basket catheter. The analysis showed a progressive and significant decrease of Sy with increasing AF complexity classes as defined by Wells (AF type I Sy = 0.73 ± 0.07, type II Sy = 0.56 ± 0.07, type III Sy = 0.36 ± 0.04, p < 0.001). The extension of Sy calculation to the whole right atrium showed the existence of spatial heterogeneities in the synchronization level. Moreover, experiments simulated by a computer model of atrial arrhythmias showed that propagation patterns with different complexity could be the basis of different synchronization levels found in patients. In conclusion the quantification of synchronization by Shannon entropy estimation of time delay dispersion may facilitate the identification of different propagation patterns associated with AF, thus enhancing our understanding of AF mechanisms and helping in its treatment. Keywords: atrial fibrillation, signal processing, computer simulation, arrhythmia (mechanisms), electrophysiology
0967-3334/05/060911+13$30.00 © 2005 IOP Publishing Ltd Printed in the UK
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1. Introduction Atrial fibrillation (AF) is a common cardiac disorder, affecting up to 10% of individuals more than 70 years of age (Halperin et al 1988). During the arrhythmia the electrical activity of the atria is highly disorganized (Allessie et al 1985) and any coherent mechanical contraction is lost. Therefore AF has been classically defined as a random and completely disorganized arrhythmia. However, more recently experimental observations (Jalife 2003) and signal processing methods (Botteron and Smith 1995, Sih et al 1999, Everett et al 2001) have shown AF to exhibit certain features that suggest an underlying order in its activation pattern. Up to now the underlying structure of AF has been mainly addressed by studying endocardial recordings in terms of ‘organization’ (Everett et al 2001, Jalife 2003, Faes et al 2002). By contrast the degree of ‘synchronization’ of the local activation process during AF has not been extensively analysed. The measure of the synchronization in atrial activation may aid in diagnosis of the electropathological substrate of AF. Measuring synchronization requires that the activity at one site be compared to the activity at another site. While absolute temporal behaviour is still important, these measures emphasize the relative temporal behaviour between two sites and thus are more informative with regard to the dynamics of propagation. Synchronization in wave propagation is generally interpreted as the propagation of the same wavefront through different regions. Thus it is a straightforward concept during normal sinus rhythm or atrial tachycardia, since in both cases two regions are successively depolarized by the same, stable wave, resulting in almost constant activation time delays between the regions. In contrast during AF synchronization can be transient and have limited extent in time and space. In fact during the arrhythmia many factors may act as desynchronizing conditions. The spatial dispersion of electrophysiological properties, such as conduction velocity and refractory periods, may influence the stability of the propagation path, leading to changes in propagation direction and/or velocity and to wave fragmentation. Thus, during AF, regions can be activated by the same unstable wave or by different waves, resulting in an increased variability of the activation time delays between the regions. Different algorithms have been proposed previously to measure properties somehow related to synchronization. Botteron and Smith (1995) estimated the cross correlation of closely spaced bipolar endocardial recordings and demonstrated that AF is spatially correlated, with the degree of correlation decaying monotonically with distance. Sih et al (1999) observed short-time, transient, linear relationships between atrial signals on canine atria by means of adaptive filters. Lovett et al (1997) found the emergence of a structured time–frequency topography and an increased spectral coherence during AF, concomitant with the conversion to normal sinus rhythm. All these measures gave evidence to the existence of transient instances of synchronized electrical activity during AF. However, in the majority of cases the measured parameters, obtained by signal processing tools applied to the whole signal, could hardly be related to the underlying propagation patterns of the arrhythmia. In this study a different perspective is applied, which focuses on the temporal information in the activation process rather than on the characteristics of the electrograms. We introduce a new method of evaluating the synchronization of the atrial electrical activity during AF, based on a quantitative characterization of the distribution of the time delays between coupled activation time series in two sites. Since time delays can be regarded as a descriptor of the electrophysiological properties of atrial tissue, our measure is directly related to the dynamics of propagation. Our index of synchronization is based on the rationale that, if two atrial sites are repeatedly affected by the passage of the same stable activation wave (i.e. are synchronized), the consecutive time delays between coupled activations should have a structured and narrow distribution. On the other hand, when sites are activated by the same unstable wave and/or by
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Figure 1. Quantification of synchronization of fibrillation signals recorded by a basket catheter in the right atrium. (a) Fluoroscopic appearance (LAO) of the multielectrode basket catheter. (b) Couple of endocardial signals recorded during atrial fibrillation from adjacent bipoles of the catheter. Point sequences represent the estimated activation times for each signal. Arrows indicate coupled activation times. On the right, construction of the time delay histogram and calculation of the synchronization index Sy.
different wavelets, the values of the delays should present higher variability and complexity. Different degrees of complexity in the time delay distribution were quantitatively characterized by Shannon entropy, while the significance assessment of the measurement was obtained by a comparison with surrogate data obtained from the original series. The index was applied to endocardial signals in patients with AF and validated in a computer model of atrial arrhythmias. Specifically, we set out to determine whether AF classes of increasing complexity could be distinguished in terms of patients’ synchronization indexes and what could be inferred from time delay distributions about their underlying propagation pattern. The latter task was performed by comparing the results in patients with data obtained by simulated experiments. 2. Methods 2.1. Data collection The algorithm was applied to bipolar electrograms obtained from a multielectrode basket catheter (Constellation catheter, EP Technologies, Boston Scientific) in the right atrium of 13 patients with idiopathic AF. The basket (figure 1(a)) was composed of 64 electrodes mounted on eight flexible splines, each carrying eight electrodes equally spaced (4 mm apart). By expansion, the splines were positioned in contact with the endocardial surface. Thirtytwo bipolar intracardiac recordings were acquired by coupling adjacent pairs of electrodes. The position of each electrode was monitored by two orthogonal x-ray images. Bipolar electrograms and the surface lead II were simultaneously recorded (CardioLab System, 30–500 Hz (Prucka Engineering, Inc.)) and digitized at a 1 kHz sampling rate and 12 bit precision. If AF was not spontaneously present, it was induced with atrial extrastimuli or atrial bursts. To assess the possibility of distinguishing different AF types in terms of synchronization, a data set was composed of 60 pairs of AF signals, recorded by adjacent electrodes and equally distributed between type I (AF1), type II (AF2) and type III (AF3). Couple of adjacent strips were chosen and classified by an expert cardiologist exclusively on the basis of their morphology (Well’s visual scoring criteria) and no attention was given to the position of the recording sites in the right atrium at this stage of the analysis. According to Well’s criteria,
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type I was characterized by discrete, beat-to-beat, atrial electrogram complexes of variable morphology and cycle length separated by an isoelectric baseline free of perturbation; type II was similar to type I, but the baseline was not isoelectric and presented various perturbations; in type III discrete intervals and isoelectric segments were no longer detectable (Wells et al 1978). The analysed period was randomly chosen, excluding the first and last minute of AF. Moreover, as a reference case of highly synchronized activity, ten couples of bipolar endocardial signals recorded in patients with atrial flutter (AFl) were analysed. 2.2. Quantification of synchronization by Shannon entropy estimation The quantification of the level of synchronization of the electrical activity between couples of atrial sites was related to a Shannon entropy measurement of the distribution of the time delays (figure 1). Atrial activation times were estimated from bipolar recordings by measuring the barycenter of local activation waves, defined as the time that divides into two equal parts the local area of the modulus of the signal (Sandrini et al 2002, Faes et al 2002). Activation time series were obtained for both sites and coupled by associating each activation in one series with the closest activation in the other. A time delay for each couple was then defined as the absolute value of the difference between the two activation times. Histograms were constructed by quantization of N time delays in time intervals with fixed size (bin size). To quantitatively describe the properties of the time delay distribution we introduced a measure of Shannon entropy (SE). As a functional of probability density, SE is related to distribution parameters and is widely used as a measure of dispersion and structure complexity of a series. By using entropy no specific distribution needs to be assumed (Shannon 1948). SE is formally defined as the average value of logarithms of the probability density function: SE = −
M
p(i) ln p(i)
(2.1)
i=1
where M is the number of discrete values the considered variable can assume and p(i) is the probability of assuming the ith value. In our study the discrete variable was the quantized time delay, and SE estimates were obtained from N observations by the Miller–Meadow estimator SEˆ (Schurmann 2004): SEˆ = −
m i=1
ˆ ln p(i) ˆ + p(i)
m−1 2N
(2.2)
ˆ where the discrete probabilities p(i) are replaced by the maximum likelihood estimates p(i) (i.e. the frequency of occurrence of the ith realization in the ensemble of N observations), and m is the number of bins with non-zero probability. The second term in the formula is introduced to reduce the systematic underestimation of SE due to the replacement of p(i) by ˆ p(i) and is obtained by taking the first order of Taylor expansion around the probability p(i) to the ln-function. To relate the dispersion of the time delays with the strength of synchronization in the activation process, a synchronization index Sy was defined as follows: SEˆ . (2.3) ln N The index Sy ranges from 0, when the spreading of the delays is maximal (i.e. when all delays lie in different bins), to 1, when a δ-function like probability distribution is found (i.e. all time delays lie in a single bin). As the maximal dispersion condition is rarely satisfied Sy = 1 −
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even by independent series (i.e. there is a non-null probability of finding at least two delays in the same bin), a case-by-case assessment of significance for Sy values was performed by surrogate data analysis to ensure a correct interpretation of the obtained zero level of synchronization (see section 2.3 for details). Assessment of the optimal parameters for the calculation of Sy was performed by studying the variation of the index by increasing the series length N from 5 to 250 activations, step 1, and the bin size from 1 to 100 ms, step 1 ms. The parameters which best discriminated different atrial rhythms resulted N = 50 and bin size = 6 ms (see section 3.1). For these parameter values, the correction introduced by the use of Miller–Meadow estimator SEˆ in place of the maximum likelihood estimator was ∼0%, 3.1%, 4.1%, 5.3%, which resulted in a correction of Sy of ∼0%, 1.1%, 3.1%, 8.3% for AFl, AF1, AF2, AF3 respectively. The bias and the variance of the estimator SEˆ were empirically evaluated by creating simulated time series originating from a pseudo-random generator, which reproduced frequency distributions typical of the analysed classes of signals (Gaussian deviates with low variance (m = 4) for AF1, Gaussian deviates with high variance (m = 10) for AF2 and uniform deviates (m = 16) for AF3). For the used ensemble length (N = 50) and bin size (6 ms), these values resulted 0.002, 0.004, 0.014 for bias and 0.008, 0.009, 0.004 for variance in AF1, AF2 and AF3 respectively. 2.3. Statistics and surrogate data analysis All data were expressed as a mean value ± SD. The Kruskal–Wallis test was performed to explore differences among the four Sy distributions. In addition the Wilcoxon–Mann–Whitney test was used to identify differences between couples of groups. A statistical test based on surrogate data analysis (Schreiber et al 2000) was performed on a case-by-case basis to differentiate significant Sy values from background coupling values (i.e. originating from independent series) and thus to assess a correct level of significance to the values of Sy obtained. For each pair of activation time series, a set of surrogate pairs (35 surrogate series from each original series) was obtained by randomly permuting the order of the activation time intervals. A significant coupling (p < 0.05) was recognized when the Sy value for the original series was higher than the 95th percentile of Sy distribution from surrogate data. 3. Results 3.1. Discrimination of AF types in terms of synchronization To evaluate the capability of the synchronization index to distinguish different types of AF, the index was applied on atrial fibrillation signals of increasing complexity classes (Well’s classification) recorded in patients. The representative example reported in figure 2 shows that different types of AF produced different shapes of time delay histograms and thus different values of Sy. In type I AF the time delays presented an evident peak with a small spread of values, resulting in a high value of the index (Sy = 0.76). In type II the spread of the delays increased, the distribution did not present any prevalent peak and the index Sy dropped to 0.57. Finally in type III the distribution of the delays became highly spread, resulting in a much smaller value of Sy = 0.40. The Sy index was calculated as a function of the number of activations in the series (figure 3, left) and of the bin size (figure 3, right) for the four classes of signals. The four
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Figure 2. Strips of atrial bipolar electrograms (top) recorded in patients during AF of increasing Well’s types and corresponding time delay distributions (bottom). Point sequences under each signal represent the estimated activation times in the signals. Signals belonging to different classes produce different shapes of the time delay histogram, with increasing dispersion of the delays and decreasing Sy values from type I to type III AF.
Figure 3. Dependence of the index Sy on the number of activations N (left) and on the width of the bins (bin size) for atrial flutter (AFl) and atrial fibrillation of type I (AF1), type II (AF2) and type III (AF3).
distributions of Sy were significantly different for 10 N 235 (p < 0.001, Kruskall–Wallis and Wilcoxon–Mann–Whitney). Varying the width of the histogram bins, the four classes were significantly different for bin size 20 (p < 0.001, Kruskall–Wallis and Wilcoxon– Mann–Whitney). Moreover, for bin size 6 ms the algorithm returned Sy = 1 for all atrial flutter recordings. Within the range of statistically significant values, statistical significance was maximal for N = 50 and bin size = 6 ms, indicating these values as optimal parameters for discriminating among various degrees of synchronization. Results of the analysis for N = 50 and bin size = 6 ms are summarized in figure 4. Maximum synchronization (Sy = 1) was found for atrial flutter, while Sy index progressively and significantly (p < 0.001) decreased with increasing AF complexity classes (AF1: Sy = 0.73 ± 0.07; AF2: Sy = 0.56 ± 0.07; AF3: Sy = 0.36 ± 0.04). According to surrogate data analysis, for atrial flutter, type I and type II AF all the values of the index Sy differed significantly from their surrogate counterparts (p < 0.01 for atrial flutter and type I, p < 0.05 for type II). By contrast in type III the coupling was significant (p < 0.05) only in the 65% of the pairs of signals, while in the remaining 35% the activation time series could not be distinguished from independent series.
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Figure 4. Means (white bars) and standard deviations (whiskers) of the index Sy for atrial flutter (AFl) and atrial fibrillation of type I (AF1), type II (AF2) and type III (AF3). The mean values are obtained by average over 20 couples of signals. Grey bars indicate the Sy mean values obtained from surrogate counterparts. The Sy values arising from different kinds of arrhythmias decrease significantly (p < 0.001, Wilcoxon–Mann–Whitney test) from atrial flutter to atrial fibrillation of increasing complexity classes. Atrial flutter presents null standard deviation.
Figure 5. Spatial distribution of synchronization during paroxysmal fibrillation. On the left, mapping of the index Sy and representation on a scheme of the open right atrium with the position of the basket bipolar recordings on the endocardial wall (grey points). The eight splines of the basket catheter were respectively positioned on the anterior, posterior and free lateral walls, on the septum and on intermediate positions. On the right, selected bipolar electrograms from recording sites ‘a’, ‘b’, ‘c’, ‘d’. The Sy values were calculated on 50 time delays for all pairs of adjacent electrodes and represented by colour-coded arrows. Green arrows indicate high synchronization levels and red arrows low synchronization levels.
3.2. Spatial distribution of synchronization and dependence on electrode distance The possibility of spatially extending calculation of the Sy index to the whole atrial surface, thereby enhancing capability of detecting spatial differences in synchronization levels, is shown in figure 5, where Sy is simultaneously measured for all the pairs of adjacent bipoles of the basket catheter. Results are displayed as colour-coded arrows, with green arrows indicating high synchronization levels and red arrows low synchronization levels. The analysis showed that AF synchronization was spatially distributed. Large zones of synchronized activity
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Figure 6. Dependence of Sy on the distance between recording sites. Sy was calculated for each of the three interelectrode distances along each basket spline. See the text for details.
(green arrows) were found in the antero-lateral and lateral walls of the right atrium and between the electrodes in the upper part of the atrium (first row of electrodes). By contrast the posterior and septal regions showed a prevalent desynchronized behaviour (red arrows), except for the presence of restricted areas (isolated couples of electrodes) of synchronized activity. The dependence of the Sy index on the electrode distance for each spline of the basket is shown in figure 6. The index was calculated between all bipole couples along the same spline. Available measures at each of the three possible distances (8, 16, 24 mm) were then averaged. Sy decreased as the interbipole distance increased. On average, Sy decreased from 0.55 ± 0.12 to 0.43 ± 0.09 with increasing bipole distance from 8 mm to 24 mm (p < 0.05). However, different splines showed different levels of synchronization and different extent and timing of the decrease. While the lateral and anterolateral walls showed high values of Sy which decreased with increasing distance, other splines such as the anterior wall presented low values for all distances. 4. Validation of the Sy index by simulation 4.1. Cellular automaton model To study the relationship between synchronization indexes during AF and the underlying electrophysiological pattern, a cellular automaton (CA) model of atrial arrhythmias was used. The model consisted of a two-dimensional lattice of 100 × 100 cells with a Moore neighbourhood of radius 1. Each cell at time (t) is assigned an excitability state Eij (t), where the subscript refers to the cell coordinates. The excitability state is bounded between 0 Eij (t) 1. Eij (t) = 1 represents the quiescent state. Eij (t) = 0 represents the excited state. If a cell becomes excited at time texc its state evolves in time as follows: Ei,j (t) = 0 texc t texc + ARPi,j (4.1) Ei,j (t) = 1 − exp[−(t − texc − ARPi,j )/RRPi,j ] t texc + ARPi,j where ARPi,j and RRPi,j are parameters defined for each cell and represent respectively the absolute and relative refractory periods. Eij (t) determines both the state of excitation for a cell and the time required for the transmission of excitation between neighbouring cells. Supposing the cell (i, j ) becomes excited at time texc , transmission of excitation towards neighbouring cells (i + 0, ±1 j + 0, ±1) may occur, provided that such cells satisfy E(i+0,±1j +0,±1) (texc ) Th, where Th is a constant
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pre-assigned threshold value. In this case, the excitation is transmitted after a delay τ , which is defined according to the formula τ = Li,j /E(i+0,±1j +0,±1) (texc )
(4.2)
where Li,j is a parameter defined for each cell and represents the minimal propagation delay. The delay is minimal for cells in the quiescent state (E(i+0,±1j +0,±1) )(texc ) = 1), but increases for cells in the recovery state (Th E(i+0,±1j +0,±1) (texc ) < 1), thus reproducing the slow conduction of premature impulses. To carry out simulations the model requires as inputs the assignment of the parameters ARP, RRP and L for each cell, and the timing and location of external stimulation. In the present study, the model was used to simulate atrial fibrillation. The fragmentation of wavefronts leading to fibrillatory conduction was obtained by delivering extrastimuli in a lattice with a non-homogeneous distribution of refractory periods. Five areas with different properties were defined in the lattice and ARP values were normally distributed within each area according to the following mean and standard deviations: 35 ± 1, 40 ± 1, 40 ± 3, 45 ± 2, 50 ± 3. The other parameters were set constant, namely RRP = 20, L = 1. The stimulation site was chosen at the border of the previously defined areas and the timing of extrastimuli was set to 50 time steps, on a basic cycle length of 100 time steps. To display the propagation of activation waves, colour-coded excitability maps in which different colours represented distinct excitability states were introduced. To calculate simulated time delay distributions, the activation time series of selected paired cells were compiled during each simulation. 4.2. Simulation results To understand which electrophysiological patterns may affect time delay distributions and the level of synchronization, atrial fibrillation (figure 7) was simulated by the CA model. The simulated arrhythmia was characterized by the simultaneous presence of independent and wandering waves, which gave rise to collisions and breaking-up (figure 7(a)). Different zones of the lattice presented different patterns of propagation. Couples of recording sites at fixed distances were located in these zones to characterize different patterns in terms of synchronization. The upper part of the lattice (zoom in figure 7(b)) was characterized by a highly complex activity, due to the simultaneous presence of several waves, which collided, changed their directions and gave rise to new wavelets. This complex activation pattern resulted in a highly spread distribution of the time delays without prevalent peaks and was characterized by very low values of synchronization (Sy = 0.26). In contrast, the lower region of the lattice (zoom in figure 7(c)) presented a more regular activity, characterized by a periodic figure-of-eight pattern (Jalife 2003). In particular, snapshots showed both the collision of the two parts of the re-entry and the subsequent generation of a single wave, which propagated in partially excitable tissue. Both situations presented less dispersed histograms and values of Sy higher than the upper part of the lattice, reflecting a less complex activation pattern. However, the time delays measured in the collision region (recording sites C-D) presented a higher dispersion and thus a lower synchronization (Sy = 0.49) than in the single wave area, where a synchronization index of 0.85 was found (recording sites E-F). The simulation allowed the study of the dependence of Sy on the distance between recording sites, for different propagation patterns. Figure 8 displays the values of Sy as a function of the distance (2D Euclidean distance) calculated between a fixed reference cell and 100 cells, randomly chosen in the lattice. Two different reference points were considered: one located in the area displayed in figure 7(c), which showed a periodic single wave pattern
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(a)
(b)
(c)
0 0
Figure 7. Simulation of atrial fibrillation and determination of synchronization indexes. Successive snapshots of excitation maps for the whole lattice (a) show the presence of different propagation patterns in the lattice: a complex pattern in the left upper corner and a figure-of-eight pattern in the right lower corner. In panels (b) and (c) zooms of the areas enclosed by lines at three successive times are shown together with the time delay distributions obtained for selected pairs of sites. In panel (b) recording sites are positioned in the complex propagation area, while in panel (c) two couples of recording sites are positioned in the figure-of-eight region in two different positions, respectively, on wave collision and on single wave area. See the text for details. (Excitability map colour-scale: red = firing state; orange, yellow = absolute refractory state; green, cyan, blue = relative refractory states; white = quiescent state; black = barriers.) Arrows indicate the direction of propagation of wavefronts. Letters (A-B, C-D, E-F) printed in excitability maps represent recording positions.
and the other located in the area displayed in figure 7(b), which showed a multiple wavelet activation pattern. In the first case, Sy showed a high level of synchronization that decreased with an increase in the distance (figure 8, left panel). Specifically, Sy shortened from 0.90 ± 0.06 to 0.64 ± 0.06 with an increase in the distance from 8.5 ± 3.2 to 24.3 ± 3.8 (p < 0.001) and then to 0.26 ± 0.04 when an average distance of 63.5 ± 4.2 (p < 0.001) was reached. For larger distances, Sy did not change significantly. These changes in Sy with the distance were associated with spatial variations in the activation pattern. The first slight decrease from high levels of synchronization appeared when the electrode was moved inside the area of single wave activation, while the second progressive decrease of Sy appeared when the recording site approached the area with two wave patterns. When the moving electrode invaded the multiple wavelet complex area Sy reached constant minimum values. In contrast, when the reference point was located in the complex activated area, the Sy values were very low (0.29 ± 0.01) and were not affected by changes in the distance between recording points (figure 8, right panel).
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Figure 8. Dependence of Sy on the distance between recording sites in AF simulation. The Sy values are calculated between a reference cell and 100 cells, randomly chosen in the lattice and labelled by their distance from the reference point. Reference cells were chosen respectively from areas with highly regular (left panel) and highly irregular (right panel) activity. See the text for details.
5. Discussion This work presented a new method to quantify the level of synchronization during AF based on a Shannon entropy measure of the dispersion of the time delays. The major findings of the study can be summarized as follows: (1) in patients different types of AF could be distinguished on the basis of a Shannon entropy measure, (2) synchronization was spatially distributed in the right atrium and presented a monotonic decrease when the distance between recording sites was increased, (3) different values of synchronization found in patients were linked to different underlying electrophysiological patterns. Our method analyses the temporal information carried by activation time series. This allows attention to be focused on the activation process, with consequent reduction of computational cost, given a consistent estimation of activation time series from signals. In the present work signals were recorded by bipolar configuration of the electrodes, which allowed a reduction of noise with respect to unipolar configuration. Nevertheless, while unipolar electrograms have a well-defined relationship with the upstroke of the action potential, which is generally accepted as a fiducial point for marking local activation, activation times determined from bipolar electrograms carry some degree of inaccuracy depending on the inter-electrode distance. To avoid biased estimates of local activation times, which may lead to overestimates of time delay variability, this study applied a morphology-based method to obtain activation time series. As the algorithm accounted for the whole shape of the activation wave, it allowed consistent estimations of activation time even in the presence of highly fragmented electrograms (Sandrini et al 2002, Pieper et al 1993). In this study time delay distributions were quantitatively characterized by Shannon entropy. Shannon entropy is conceptually different from measures of variability (as variance) that quantify the magnitude of deviation from a mean value, since it quantifies the intrinsic unpredictability of an event series. Specifically, in our study, the measurement of the time delay series predictability aimed to quantify the stability of activation patterns. In addiction to Shannon entropy, other parameters could be calculated to show specific features of time delay distributions and to provide a more complete characterization of the complexity of activation. Nevertheless, the calculation of a single index can be easily extended to the whole atrial surface to obtain spatial information. The example of spatial mapping shown in this study raises the issue of spatial heterogeneities in the pattern of activation and thus clarifies the importance of performing such spatial extension. Results obtained were consistent with mapping studies in patients during paroxysmal AF (Gaita et al 2001), which observed regular activity in the lateral wall and prevalently disorganized activity in the septum. Spatial differences in the
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synchronization index may be due to the heterogeneous anatomical structure of the right atrium as well as to spatial differences in its electrophysiological properties (Gaita et al 2001). However, these aspects need to be explored in greater detail in a further study. In the present work attention was paid to assessing the electrophysiological meaning of the synchronization measure proposed and providing an interpretation of the results obtained in patient by means of simulations. The use of a time domain definition of synchronization allowed the coupling of our synchronization index with a cellular automaton model of propagation. Although simplified, cellular automaton models are suitable, low-computational cost tools to reproduce the macroscopic properties of activation propagation in cardiac muscle (Abildskov 1994). In the present model the possibility of setting heterogeneities in the distribution of refractory periods and conduction properties allowed the simulation of atrial fibrillation patterns, providing simulated activation time series and time delay distributions. The simulation showed that our index was sensitive to the number of wavelets present in the recording area and discriminated different underlying propagation patterns. The comparison of patient and simulation data allowed us to infer the propagation pattern underlying the different shapes of time delay distribution observed in patients. The distributions of the time delays in type I AF, characterized by a single peak with small dispersion of the values and a high synchronization index, were likely to be produced by the presence of a single wave propagating in refractory tissue. Type III AF signals showed distributions with no prevalent peaks and highly dispersed values, which were obtained in simulations for recording sites activated by multiple and unstable wave propagation. Finally, the distributions obtained in type II AF, with no prevalent peaks, as in type III AF, but less dispersed, could be attributed to the presence of a limited number of wavelets in the recording area. These findings were consistent with the classification of AF introduced by Konings et al (1994), who used high density mapping in patients to distinguish different classes of AF on the basis of their underlying propagation patterns. Comparison with simulations can also clarify the dependence of the synchronization index on the recording site distance. The monotonic decrease of Sy observed in patients for increasing distances was consistent with the study of Botteron and Smith (1995), which showed an exponential decrease in the correlation between the activities of sites at increasing distances during paroxysmal AF. The extent of the decrease differed among splines, which could be attributed to spatial variations in the activation pattern during AF. In simulations deriving from our study a decrease of the index for increasing distance, as observed in the lateral and anterolateral wall of patients, was obtained for sites belonging to single-wave or two-wave area. Differentially stronger decreases were obtained when one of the recording electrodes entered the area of complex propagation patterns. Finally, constant, low values of the index such as those found in the anterior wall were obtained in simulations for recording sites in areas of multiple wavelet propagation. 6. Clinical and physiological implications A technique for measurement of synchronization that can be related to the underlying mechanisms of AF and is spatially extendible may have both basic and clinical applications. At a basic research level, the spatial and temporal measure of synchronization may help to improve our understanding of the mechanisms of AF by aiding in the recognition of specific patterns of wavelet interaction and their correlation with the functional and structural characteristics of the atria. A measure of synchronization may also have implications in advancing new strategies for the treatment of AF, such as ablation therapy and electric cardioversion. In fact, the spatial mapping of synchronization may guide definition of the optimal ablative pathways
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by selecting targeting areas on the basis of the local level of synchronization. Moreover, as the synchronization of the atrial electrical activity during AF by atrial pacing seems to reduce the atrial defibrillation threshold (Villani et al 2002), quantification of changes in synchronization levels during AF could help in the choice of the optimal timing for defibrillation. References Abildskov J A 1994 Additions to the wavelet hypothesis of cardiac fibrillation J. Cardiovasc. Electrophysiol. 5 553–9 Allessie M A, Lammers W J E P, Bonke F I M and Hollen J 1985 Experimental evaluation of Moe’s multiple wavelets hypothesis of atrial fibrillation Cardiac Electrophysiology and Arrhythmias ed D P Zipes and J Jalife (Orlando: Grune and Stratton) 265–75 Botteron G W and Smith J M 1995 A technique for measurement of the extent of spatial organization of atrial activation during atrial fibrillation in the intact human heart IEEE Trans. Biomed. Eng. 42 579–86 Everett T H, Kok L C, Vaughn R H, Moorman J R and Haines D E 2001 Frequency domain algorithm for quantifying atrial fibrillation organization to increase defibrillation efficacy IEEE Trans. Biomed. Eng. 48 969–78 Faes L, Nollo G, Antolini R, Gaita F and Ravelli F 2002 A method for quantifying atrial fibrillation organization based on wave morphology similarity IEEE Trans. Biomed. Eng. 49 1504–13 Gaita F et al 2001 Different patterns of atrial activation in idiopathic atrial fibrillation: simultaneous multisite atrial mapping in patients with paroxysmal and chronic atrial fibrillation J. Am. Coll. Cardiol. 37 534–41 Halperin J L and Hart R G 1988 Atrial fibrillation and stroke: new ideas, persisting dilemmas Stroke 19 937–41 Jalife J 2003 Rotors and spiral waves in atrial fibrillation J. Cardiovasc. Electrophysiol. 14 776–80 Konings K T, Kirchhof C J, Smeets J R, Wellens H J, Penn O C and Allessie M A 1994 High-density mapping of electrically induced atrial fibrillation in humans Circulation 89 1665–80 Lovett E G and Ropella K M 1997 Time-frequency coherence analysis of atrial fibrillation termination during procainamide administration Ann. Biomed. Eng. 25 975–84 Pieper C F, Blue R and Pacifico A 1993 Simultaneously collected monopolar and discrete bipolar electrograms: comparison of activation time detection algorithms PACE 16 426–33 Sandrini L, Faes L, Ravelli F, Antolini R and Nollo G 2002 Morphology-based measurement of activation time in human atrial fibrillation Comp. Cardiol. 29 593–6 Schreiber T and Schmitz A 2000 Surrogate time series Physica D 142 346–82 Schurmann T 2004 Bias analysis in entropy estimation J. Phys. A: Math. Gen. 37 L295–L301 Shannon C E 1948 A mathematical theory of communication Bell System Tech. J. 379–423 Sih H J, Zipes D P, Berbari E J and Olgin J E 1999 A high-temporal resolution algorithm for quantifying organization during atrial fibrillation IEEE Trans. Biomed. Eng. 46 440–50 Villani G Q, Nollo G, Ravelli F, Piepoli M and Capucci A 2002 Capture of atrial fibrillation reduces the atrial defibrillation threshold PACE 25 1159–65 Wells J L Jr, Karp R B, Kouchoukos N T, MacLean W A, James T N and Waldo A L 1978 Characterization of atrial fibrillation in man: studies following open heart surgery PACE 1 426–38
