A Novel Approach to Propagation Pattern Analysis in Intracardiac

Atrial Fibrillation Signals

ULRIKE RICHTER,1 LUCA FAES,2 ALESSANDRO CRISTOFORETTI,2 MICHELA MASE,2 FLAVIA RAVELLI,2

MARTIN STRIDH,1 and LEIF SORNMO1

1Department of Electrical and Information Technology, and Center for Integrative Electrocardiology (CIEL), Lund University,Box 118, 221 00 Lund, Sweden; and 2Department of Physics and BioTech, University of Trento, Trento, Italy

(Received 7 May 2010; accepted 13 August 2010)

Associate Editor Nathalie Virag oversaw the review of this article.

Abstract—The purpose of this study is to investigate prop-agation patterns in intracardiac signals recorded during atrialfibrillation (AF) using an approach based on partial directedcoherence (PDC), which evaluates directional couplingbetween multiple signals in the frequency domain. ThePDC is evaluated at the dominant frequency of AF signalsand tested for significance using a surrogate data procedurespecifically designed to assess causality. For significantlycoupled sites, the approach allows also to estimate the delayin propagation. The methods potential is illustrated with twosimulation scenarios based on a detailed ionic model of thehuman atrial myocyte as well as with real data recordings,selected to present typical propagation mechanisms andrecording situations in atrial tachyarrhythmias. In bothsimulation scenarios the significant PDCs correctly reflectthe direction of coupling and thus the propagation betweenall recording sites. In the real data recordings, clear propa-gation patterns are identified which agree with previousclinical observations. Thus, the results illustrate the ability ofthe novel approach to identify propagation patterns fromintracardiac signals during AF, which can provide importantinformation about the underlying AF mechanisms, poten-tially improving the planning and outcome of arrhythmiaablation.

Keywords—Multivariate autoregressive modeling, Partial

directed coherence, Granger causality, Electrograms, Map-

ping, Frequency analysis, Simulation, Atrial arrhythmias.

INTRODUCTION

The mechanisms leading to the induction and per-petuation of atrial fibrillation (AF), which is the mostcommon arrhythmia in clinical practice, are still the

subject of extensive research. The complex electricalpattern observed during AF has been explained withmultiple wavelets that propagate along varying routesthroughout the atria.22 More recently, available datahas also supported a ‘‘focal’’ mechanism, according towhich drivers or foci, mainly located in the pulmonaryveins, trigger and sustain the propagation of the elec-trical activity in the atria.1,2,19 These observations haveled to increased interest in methods that analyze theatrial activity at multiple intracardiac sites, e.g., for thepurpose of guiding the ablation catheter to the atrialsites at which the arrhythmia originates or which rep-resent arrhythmia substrates. One approach to suchguidance is to identify and ablate atrial sites withcomplex fractionated atrial electrograms.24 Anotherapproach is based on the identification of dominantfrequency (DF) sites.33 Despite a large number of fol-low-up studies, recent publications show that suchapproaches are still controversial,12,27 and thereforefurther studies are needed to better understand themechanisms of AF.

With the advancement of catheter technology,catheters that cover major parts of the atria and allowfor simultaneous recording of a large number of elec-trograms have become available. This advancementmakes it possible to perform spatiotemporal analysisof the mechanisms during AF, e.g., in order to char-acterize the propagation patterns of the electricalactivity. The challenge of such analysis is to determinethe interrelationship among all signals. In contrast,most approaches involve either individual signals orpairs of signals to quantify the electrical activity interms of ‘‘organization.’’ In the time domain, theproposed organization measures are often related tosignal morphology or activation times.6,29 Theapproach of coupling activation times in adjacent pairs

Address correspondence to Ulrike Richter, Department of Elec-

trical and Information Technology, and Center for Integrative

Electrocardiology (CIEL), Lund University, Box 118, 221 00 Lund,

Sweden. Electronic mail: urr@eit.lth.se

Annals of Biomedical Engineering (� 2010)

DOI: 10.1007/s10439-010-0146-8

� 2010 Biomedical Engineering Society

of signals6 has recently been extended to more thantwo signals such that activation wavefronts can bedetected.30 While this may identify certain propagationpatterns, a disadvantage of the method is its depen-dence on activation detection which becomes increas-ingly difficult with decreasing AF organization. Also,coupling of activations cannot be established in certaincases. These issues may be solved using frequencydomain methods not requiring activation detection,such as the coherence function, which has been used toquantify AF organization based on pairs of electro-grams.36 While the coherence function can differentiatebetween non-fibrillatory rhythms, such as sinus rhythmand atrial flutter, and fibrillatory rhythms, i.e., AF,two major disadvantages have become apparent. First,the coherence function cannot identify the direction ofcoupling between the signals, i.e., the direction inwhich the electrical activity propagates. Second, thecoherence function is only defined for pairs of signals.Thus, when more than two simultaneously recordedsignals are to be analyzed, the coherence function iseither calculated for all possible combinations of pairsof signals, or one particular signal has to be chosen as areference on which the results strongly depend. Amethod that overcomes these disadvantages is there-fore highly desirable.

Even though frequency domain methods quantify-ing the directional coupling among multiple signalshave not been tested in AF studies, they have beendeveloped in other fields, especially for the analysis ofbrain signals.3,5,15 The methods are based on the fit ofa multivariate autoregressive (MVAR) model to mul-tichannel recordings, characterizing causal couplingbetween multiple signals. The spectral representationof the MVAR process can be employed to derivefunctions reflecting the causal coupling in the fre-quency domain, an example being the partial directedcoherence (PDC) function which is obtained fromdecomposing the partial coherence.3,5

In the present study, we propose the PDC for theanalysis of the propagation of the electrical activitywithin the atria during AF. In order to make themethod suitable for intracardiac signals, a prepro-cessing procedure is performed before MVAR modelfitting. The proposed approach for propagation pat-tern analysis offers several advantages compared toexisting methods: First, it quantifies the directionalcoupling and identifies the underlying propagationpattern between the recording sites by employing amultivariate approach that simultaneously evaluatesall signals. Second, the method can handle anincreasing number of recorded signals and does notrequire any knowledge on the relative positioning ofthe recording sites. These aspects are of special interest

during electrophysiological studies performed, e.g., inconnection to ablation procedures, where it is desirableto map larger parts of the atria in order to identifyfrom which direction the electrical activity originates.Yet another advantage of the method is that the timedelays between different recording sites can be esti-mated. Finally, the frequency domain implementationavoids certain difficulties that come with atrial activa-tion detection.

The potential of the method will be illustrated withtwo simulation scenarios, modeling various propaga-tion mechanisms in play during atrial tachyarrhythmiasuch as atrial flutter and AF, and real data recordingsof atrial flutter and AF, acquired with either one- ortwo-dimensional catheters.

METHODS

Preprocessing

The preprocessing consists of bandpass filtering(finite impulse response (FIR), 40–250 Hz, order 40,Kaiser window), rectification, and lowpass filtering(FIR, 0–20 Hz, order 40, Kaiser window).8 After thefiltering, the sampling rate is decimated to 100 Hz, andthe mean is subtracted from each electrogram.

In the time domain, the preprocessing results insignals with an amplitude proportional to the high-frequency components (40–250 Hz), which correspondto the rapid changes in amplitude characteristics ofthe activations. In the frequency domain, the pre-processing results in spectra with a pronounced fun-damental frequency.25 Figure 1 illustrates how thepreprocessing emphasizes the rhythm in the signals asopposed to signal morphology by displaying fivesimultaneously recorded bipolar electrograms fromthe right atrium (RA) during AF both before andafter preprocessing.

Multivariate Autoregressive Modeling

Each set of N simultaneous observations xðnÞ ¼½x1ðnÞ . . . xNðnÞ�T obtained from different sites in theatria, is assumed to be represented by an MVARmodel of order m

xðnÞ ¼Xm

k¼1Akxðn� kÞ þ wðnÞ; ð1Þ

where each Ak is an N 9 N matrix comprising the ARcoefficients aij(k),i; j ¼ 1; . . . ;N; and wðnÞ ¼ ½w1ðnÞ . . .wNðnÞ�T is a multivariate white noise processcharacterized by the diagonal covariance matrix Rw; in

RICHTER et al.

which each diagonal element rjj2 defines the variance of

wj(n).The PDC from xj(n) to xi(n) can be derived from

factorization of the partial coherence function,3,5 andis given by

pijðfÞ ¼1rii

�AijðfÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNk¼1

1r2kk

j �AkjðfÞj2q ; ð2Þ

where �AijðfÞ is an element of the matrix �AðfÞ; which isbased on the Fourier transform (FT) of the MVARprocess in Eq. (1),

�AðfÞ ¼ IN�N �Xm

k¼1Ake

�|2pfk; ð3Þ

where I is the unity matrix. The definition in Eq. (2) isthat of the generalized PDC,5 being especially useful inthe case of widely different variances rjj

2. The denom-inator of the PDC serves as a normalization withrespect to the source, i.e., xj(n), such that

XN

i¼1jpijðfÞj2 ¼ 1 ð4Þ

and

0 � jpijðfÞj2 � 1: ð5Þ

Given this normalization, the value of the magnitude-squared PDC |pij(f)|

2 from j to i represents the strengthof the direct coupling from xj(n) to xi(n) at frequency f,viewed in relation to the direct coupling strength ofxj(n) to all other signals xk(n), k „ i, at that frequency.For reasons of convenience, the magnitude-squaredPDC |pij(f)|

2 is referred to as PDC in the following.During AF, the PDC is of special interest in

an interval centered around the DF of the source xj(n),here assumed to represent the mean atrial fibrillatorycycle length at the corresponding recording site. Thus,the integrated PDC is defined by Wilke et al.38

P2ij ¼

1

2Df

Zf0þDf

f0�Df

jpijðfÞj2df; ð6Þ

where f0 is the DF, corresponding to the highest peakin the 3–12 Hz range of the auto-spectrum of xj(n),denoted by Sjj(f), and Df is a parameter determiningthe width of the integration interval. The integral isnormalized such that, similar to the PDC, it rangesfrom 0 to 1, and thus represents the average couplingfrom xj(n) to xi(n) in the frequency range of interest. Incase no obvious DF can be identified in signal xj(n), thecorresponding P2

ij is set to zero for all i. The auto-spectra Sjj(f) are the diagonal elements in the powerspectral density matrix of the MVAR process, definedas

SðfÞ ¼ �A�1ðfÞRwð�A�1ðfÞÞH: ð7Þ

The time delay from xj(n) to xi(n), denoted Dij; can beestimated from the phase spectrum /ij(f) of the corre-sponding cross-spectral density,23

SijðfÞ ¼ jSijðfÞje|/ijðfÞ; ð8Þ

which is obtained from Eq. (7). The delay Dij is equalto that value of d which maximizes the integral, i.e.,

Dij ¼ argmaxd

Zf0þDf

f0�Df

CijðfÞ1�CijðfÞ

cos ½/ijðfÞ � 2pfd�df; ð9Þ

where Cij(f) is the magnitude-squared coherence spec-trum defined as

CijðfÞ ¼jSijðfÞj2

SiiðfÞSjjðfÞ: ð10Þ

The estimator in Eq. (9) evaluates the weighted good-ness-of-fit of a line with slope d to the phase spectrumover the frequency range of interest. The delay esti-mation is only computed when the corresponding

0 1 2 3 4 5

H19/20

H17/18

H15/16

H13/14

H11/12

Time (s)

0 1 2 3 4 5

H19/20

H17/18

H15/16

H13/14

H11/12

Time (s)

(a) (b)

FIGURE 1. Preprocessing of five simultaneously recorded bipolar electrograms from the RA during AF. The amplitude scale is inarbitrary units. (a) Original electrograms. (b) Preprocessed electrograms.

Propagation Patterns in Intracardiac AF Signals

integrated PDC is significant, see Section ‘‘SurrogateData Testing.’’

Model Identification and Selection

The AR coefficient matrices Ak are estimated usingthe least-squares (LS) method, and the optimal modelorder m is determined by the Bayesian informationcriterion (BIC).35 The best model order was searchedfor in the range 1–15. The model order is chosen asthat value of m for which the minimum is reached, or,in case the BIC does not reach a minimum, an addi-tional model selection criterion is defined where thatvalue of m is chosen for which the successive differencein BIC is smaller than 5% of the largest successivedifference.

Surrogate Data Testing

The significance of the PDC |pij(f)|2 is assessed

separately for each coupling by means of a statisticalapproach based on surrogate data testing.14 Themethod of surrogate data relies on computing theindex of interest, i.e., the PDC |pij(f)|

2, both on theoriginal time series x(n) and on a set of surrogate time

series yðlÞðnÞ ¼ ½yðlÞ1 ðnÞ . . . yðlÞN ðnÞ�

T; l ¼ 1; . . . ;M: The

latter time series lacks by construction the investigatedproperty, i.e., there is no direct causal coupling fromyj(l)(n) to yi

(l)(n). A statistical test is then applied tocompare the values of the index of interest for theoriginal series and for the set of surrogate series. Theindex is assumed to be significant if the original valuelies above a certain percentile of the distribution ofvalues obtained from the surrogates.

In detail, it is assumed that an MVAR model hasbeen fitted to x(n), resulting in estimates of Ak,k ¼ 1; . . . ;m; and Rw: To test the significance of thePDC, e.g., from xj(n) to xi(n), the M surrogatesy(l)(n) are computed by repeatedly applying the fol-lowing procedure (the surrogate index l is omittedhereafter for simplicity). First, a new set of signals �xðnÞis computed using N independent noise realizations

ð� N ð0;RwÞÞ as input to the MVAR model defined by�Ak ¼ Ak; with �aijðkÞ ¼ 0; k ¼ 1; . . . ;m; implying that

there is no direct coupling from �xjðnÞ to �xiðnÞ: After

calculating the FT of x(n) and �xðnÞ; i.e., XiðfÞ ¼jXiðfÞje|ffXiðfÞ and �XiðfÞ ¼ j �XiðfÞje|ff �XiðfÞ; respectively,i ¼ 1; . . . ;N; the FT of y(n) is defined as YiðfÞ ¼jXiðfÞje|ff �XiðfÞ; such that the absolute values of the FT ofy(n) are identical to those of x(n) at each frequency,while the phase is altered such that there is no directcoupling from yj(n) to yi(n) at any frequency. Finally,the surrogate series y(n) is obtained by computing theinverse FT of Yi(f), i ¼ 1; . . . ;N:

The significance threshold j~pijðfÞj2 is then, at eachfrequency, defined as the 95th percentile of the PDCscalculated from the M surrogates, i.e., |pij(f)|

2 of theoriginal signals is considered to be significant(p< 0.05), if it exceeds j~pijðfÞj2: Similarly, the inte-grated PDC is calculated for each surrogate series, andthe 95th percentile defines the significance threshold~P2ij : a significant direct coupling is said to exist from

xj(n) toward xi(n) if P2ij>

~P2ij:

DATABASE

The database comprises simulated electrogramsfrom two different simulation scenarios as well aselectrograms from patients with atrial flutter andAF recorded with either one- or two-dimensionalcatheters.

Simulation Model

Computer simulations were performed employingthe Courtemanche–Ramirez–Nattel (CRN) ionicmodel11 in a monodomain formulation. The model,which has been specifically developed for the humanatrial action potential, computes the cell transmem-brane potential V by the reaction–diffusion equation

@V

@t¼ r �DrV� Iion

Cmþ IstCm

; ð11Þ

where Iion is the total ionic current, Ist is an externalstimulus current, Cm is the membrane capacitance, andD is the diffusion tensor. The total ionic current Iionconsists of 12 separate contributions, which representthe ionic and pump currents and include reticularcalcium handling. A detailed description of thecurrents and their representation can be found inCourtemanche et al.11

The ionic model was implemented on a simplifiedanatomy, represented by a monolayer sphere with adiameter of 6 cm. The sphere was discretized into a tri-angularmesh comprising approximately 125,000 nodes,which resulted in a spatial resolution of about 300 lm:The diffusion tensor D was considered uniform andisotropic. The partial differential equations of the CRNmodel were solved by employing the forward non-standard Rush–Larsen integration scheme31 for thereaction part, while a finite volume method for anirregular mesh,39 integrated with a standard forwardEuler scheme, was used for the diffusion part. Theintegration time step was fixed to 0.1 ms, which wassufficiently small to guarantee the stability of bothintegration schemes.

Simulated bipolar electrograms corresponding to dif-ferent simulation patterns were obtained by applying

RICHTER et al.

the current source approximation.21 Specifically, theextracellular potential at spatial position y was com-puted according to

uðyÞ ¼XNk

k¼1

Ikmjjyk � yjjXk; ð12Þ

where the sum is extended to all the Nk nodes of themesh, Im

k is the transmembrane current per unit area atnode k, yk is the position of node k, and Xk is the areacorresponding to node k. In order to obtain bipolarelectrograms, electrode pairs with an intra-electrodedistance of 2 mm were placed at a distance of 0.5 mmfrom the surface of the sphere. Bipolar electrogramswere computed as the difference between the extra-cellular signals recorded at the corresponding electrodepair. For each simulation pattern, 5-s signals wereobtained with a sampling rate of 1 kHz and used forfurther validation of the method.

Simulation of Atrial Tachyarrhythmias

The first scenario is a simulation of atrial flutter,modeled as a reentry around an anatomical obstaclewith a diameter of 1.3 cm. The diffusion coefficient wasset to 0.3 cm2/s. In order to induce reentrant activity, asingle electrical impulse was delivered in proximity tothe anatomical obstacle, while a temporary unidirec-tional conduction block was present. The subsequent

removal of the block allowed the establishment of aself-sustained activation of the tissue. As shown inFig. 2(a), the reentrant wave activated first the tissue atrecording site S1, and subsequently passed by record-ing sites S2–S5. The corresponding signals, obtainedafter stabilization of the reentrant activity, are dis-played in Fig. 2(b).

The second scenario is a simulation of AF, mim-icking multiple wavelet propagation in the presence ofa regularly firing ectopic focus. Sustained AF wascreated starting from a configuration with two func-tional spiral reentries, which were initiated by a singleelectrical impulse delivered adjacent to a temporaryline of block. Subsequently, the currents of the ionicmodel Ito, ICa,L, IKur, and IKr (see Courtemancheet al.11 for definitions) were modified according toJacquemet et al.21 in order to obtain a restitution curvewhich caused repeated spiral breakups and the for-mation of a multiple wavelet pattern. After 10 s ofsustained AF, a point source firing with a period of275 ms became active at the upper pole of the sphere.The diffusion coefficient was 0.2 cm2/s throughout theentire scenario. As shown in Fig. 2(c), the result is aregular propagation in proximity to the focus (site S1),which progressively deteriorates when entering thearea dominated by the multiple wavelet behavior(lower part of the sphere). The simulated signals wereobtained after the point source became active and aredisplayed in Fig. 2(d).

0 1 2 3 4 5

S5

S4

S3

S2

S1

Time (s)

0 1 2 3 4 5

S5

S4

S3

S2

S1

Time (s)

(a) (b)

(c) (d)

FIGURE 2. Illustration of the simulation scenarios: (a, c) snapshots of the membrane voltage with the electrode positions indi-cated (snapshots are 120 ms apart) for the simulation of an anatomical reentry and the simulation of AF, respectively. (b, d) Theelectrograms corresponding to the simulation of an anatomical reentry and the simulation of AF, respectively. See text for furtherdetails.

Propagation Patterns in Intracardiac AF Signals

Electrograms from Patients with Atrial Arrhythmias

The first case is a recording from a patient withatypical left atrial flutter. Atrial bipolar electrogramswere recorded with a decapolar catheter in the coro-nary sinus (CS). Five-second electrograms corre-sponding to the equally spaced bipolar electrodesCS1/2, CS5/6, CS9/10, and CS13/14 from distal-to-proximal CS were extracted for analysis, see Fig. 3. Inthe following, the electrograms from CS1/2 to CS13/14are indexed by i ¼ 1; . . . ; 4:

Two other cases comprise AF signals acquired withdifferent mapping modalities, i.e., by a linear or abasket catheter, respectively. In the first patient withpersistent AF, electrograms were recorded using a dualdecapolar catheter (Cordis Webster Deflectable Halo)placed in the RA, with bipolar electrodes recording theatrial activity from the low lateral (H1/H2) to theseptal wall (H19/20). H13/H14 recorded atrial activityin approximately the high septal wall. Five-second

electrograms corresponding to the five bipoles H11/12to H19/20 in the septal wall, in the following indexedby i ¼ 1; . . . ; 5: were chosen for further analysis, seeFig. 1(a).

In the second patient with paroxysmal AF, theelectrophysiological study was performed with amultielectrode basket catheter (Constellation catheter,EP Technologies, Boston Scientific) in the RA. Thebasket catheter consisted of eight splines, each car-rying eight equally spaced electrodes (4 mm inter-electrode distance). Thirty-two bipolar intracardiacelectrograms were acquired by coupling adjacentpairs of electrodes (CardioLab System, 30–500 Hz[Prucka Engineering, Inc.]). In this patient, six elec-trodes had to be excluded because of poor signal tonoise quality. From the recording of the remaining 26electrodes, 5 s were chosen for analysis. A schematicrepresentation of the recording positions and theoriginal electrograms, illustrating varying degrees of

0 1 2 3 4 5

CS13/14

CS9/10

CS5/6

CS1/2

Time (s)

0 1 2 3 4 5

CS13/14

CS9/10

CS5/6

CS1/2

Time (s)

(a) (b)

FIGURE 3. Electrograms from a patient with atrial flutter. (a) Original electrograms. (b) Preprocessed electrograms.

Superior vena cava

Fossa ovalis

Tricuspid valve

Sinocoronaric ostium

Inferior vena cava

Auricula

Tricuspid valve

Crista terminalis

Anterior Antero- lateral Lateral

Postero- lateral

Posterior Postero- septal

Septal

Antero- septal

Anterior

111

222

333

444

1

2

3

4

5

55

5

6 66

6

7777

888

8

1

2

3

4

GH AB CD EF

GH

GH

AB

AB

CD

CD

EF

EF

0 1 2 3 4 5EF7EF6EF5EF4EF3EF2EF1CD8CD6CD5CD4CD2CD1AB8AB7AB6AB5AB4AB3AB2AB1GH8GH6GH5GH3GH1

Time (s)

(a) (b)

FIGURE 4. (a) Schematic representation of the open RA with the position of the bipolar recording sites on the intracardiac wall.The eight splines of the basket catheter were positioned on the anterior, lateral, posterior, and septal walls, as well as onintermediate positions. (b) Original electrograms.

RICHTER et al.

signal organization, are shown in Fig. 4(a) and (b),respectively.

All electrograms were digitized at a sampling rate of1 kHz.

RESULTS

The results were obtained for fD set to 0.5 Hz,cf. Eqs. (6) and (9), and the number of surrogatesy(n) was chosen to M = 100.

Simulation Scenarios

Simulation of a Reentry Around an Anatomical Obstacle

The results from the MVAR analysis (p = 5) arepresented in Fig. 5. The estimated auto-spectra of thesignals are displayed on the diagonal, exhibiting a clearharmonic pattern for all signals. Off-diagonal, thePDCs are shown together with their correspondingsignificance thresholds. The direct coupling of, e.g., thesignal recorded at site S1 toward the other signals isreflected by |pi1(f)|

2, i> 1, displayed in the first col-umn. A significant direct coupling from S1 is onlyidentified toward S2, as only |p21(f)|

2 exceeds its sig-nificance threshold. As a consequence of the stablepropagation pattern and the high signal organization,

a significant coupling can in fact be observed across theentire frequency range. Of specific interest is |p21(f)|

2 atthose frequencies for which S11(f) has the highestpower, i.e., the highlighted frequency range around theDF. The integrated PDC over this frequency range,P2

21; yields 0.82. In terms of propagation, theseobservations lead to the conclusion that there is anactivation wavefront propagating from S1 to S2. Incase the wavefront propagates further to any otherrecording site, this should be reflected by |pi2(f)|

2. Infact, only |p32(f)|

2 exceeds its significance thresholdðP2

32 ¼ 0:61Þ; indicating that the activation wavefrontpropagates from S2 to S3. The PDCs |p43(f)|

2 and|p54(f)|

2 exceed their significance thresholds for thefrequency range of interest, and thus it can be con-cluded that the activation wavefront propagates fromS3 to S4 to S5. The corresponding integrated PDCsP2

43 and P254 equal 0.82 and 0.66, respectively.

The delays D21;D32;D43; and D54 are equal to 27, 51,52, and 50 ms, respectively. For this particular casewith well-organized propagation, the delays can alsobe estimated by detecting the activations in all elec-trograms and coupling the closest activations fromadjacent recording sites.6 The delays, taken as thetime difference within these activation pairs, yield28 ± 4 ms (mean ± SD), 51 ± 5 ms, 54 ± 5 ms, and50 ± 3 ms, and thus D21;D32;D43; and D54 are within± 1 SD of these values.

0

1

S1

0

1

S2

0

1

S3

0

1

S4

0

1

S5

S1 S2 S3 S4 S5

FIGURE 5. MVAR analysis applied to simulated reentry signals. On the diagonal: the auto-spectra of the signals for f 2 [0, 25] Hz.Off-diagonal: the PDCs jjjjpij (f )jjjj2 (solid line) and the corresponding significance thresholds jjjj~pij (f )jjjj2 (dashed line) for f 2 [0, 25] Hz.The area beneath jjjjpij (f )jjjj2; f 22 [f0---Df ; f0 + Df ], has been highlighted when P2

ij is significant.

Propagation Patterns in Intracardiac AF Signals

Simulation of AF

Figure 6 shows the results of the MVAR analysis(p = 5) applied to the simulation of AF. Compared tothe previous case, the auto-spectra exhibit a less pro-nounced but still discernible harmonic pattern. Fromthe PDCs, a significant direct coupling can be observedfrom S1 fi S2 fi S3 fi S4. Furthermore, no sig-nificant direct coupling is present toward recording siteS5. It can thus be concluded that there is an activationwavefront which is passing by S1, S2, S3, and S4, butwhich is not propagating further toward S5. Thisreflects well the propagation of the activation wave-front starting at the point source as well as the morechaotic propagation on the lower half of the sphere,which results in the absence of significant direct cou-pling from or toward S5. The decreasing values ofP2

21;P232; and P2

43; being equal to 0.59, 0.31, and 0.15,respectively, indicate the decreasing relevance of theactivation wavefront for the atrial activity at S1–S4.The delays D21;D32; and D43 are estimated to 51, 48,and 56 ms, respectively.

Recordings of Patients with Atrial Tachyarrhythmias

Atrial Flutter Data

The results of the MVAR analysis (p = 5) showthat the auto-spectra are characterized by harmonicpatterns with decreasing power toward higher fre-quencies, see Fig. 7. The significant integrated PDCs

indicate a distal-to-proximal propagation of the elec-trical activity along the catheter and reflect, because ofthe anatomic position of the CS, the sequential acti-vation of the left atrium by the reentrant wavefront. Indetail, the integrated PDCs corresponding to the directcoupling from CS1/2 toward CS5/6, CS5/6 towardCS9/10, and CS9/10 toward CS13/14 yield 0.82, 0.28,and 0.31, respectively. The corresponding delays Dij

yield 29, 31, and 38 ms, respectively, which suggests apropagation along the catheter. Similar to the simu-lation of reentry, the delays estimated from the de-tected activation times can be used for validation.These delays yield 26 ± 3 ms, 31 ± 2 ms, and 40± 7 ms.

AF Data: Linear Catheter Recording

The results from the MVAR analysis (p = 4) areshown in Fig. 8, where it can be seen that the auto-spectra are characterized by a dominant peak and adecreasing power toward higher frequencies. The sig-nificant integrated PDCs indicate an activation wave-front propagating from an inner electrode of thecatheter (H13/14) to the remaining electrodes at bothsides. Specifically, in the high septal RA a propagationfrom H13/14 to both H11/12 ðP2

12 ¼ 0:29Þ and H15/16ðP2

32 ¼ 0:31Þ can be identified. From H15/16, theactivation wavefront is propagating further towardH17/18 ðP2

43 ¼ 0:49Þ and H19/H20 ðP254 ¼ 0:33Þ: The

delay from H13/14 toward H11/12 and H15/16 is

0

1

S1

0

1

S2

0

1

S3

0

1

S4

0

1

S5

S1 S2 S3 S4 S5

FIGURE 6. MVAR analysis applied to simulated AF signals, see Fig. 5 for details.

RICHTER et al.

estimated to be 25 and 19 ms, respectively. Further-more, the delays from H15/16 toward H17/18 andfurther toward H19/20 are estimated to be 5 and10 ms, respectively. The large variation in propagationdelay indicates that the wavefront is probably notpropagating exactly along the catheter.

AF Data: Two-Dimensional Catheter Recording

MVAR analysis (p = 4) was performed on all 26available electrograms. In order to simplify the inter-pretation, the significance thresholds ~P2

ij are redefinedto the 99th percentile, such that significance is givenwith p £ 0.01. In this way, 4.5% of the theoreticallypossible directed coupling paths between the recordingsites are found to be significant; P2

ij ranges from 0.07 to0.30 (0.15 ± 0.06). The propagation pattern is illus-trated by the directed graph in Fig. 9(a). The analysisevidences an activation wavefront propagating fromthe high septal region toward the lateral and septalwalls in craniocaudal direction. In more detail, thelarger values of P2

ij indicate an impulse from the LAentering the RA in the high septal region, nearby CD5and EF1, from where the propagation divides into twowavefronts. One wavefront propagates along thesuperior RA toward the high lateral wall (AB1), whichis subsequently activated in craniocaudal direction.The second wavefront propagates along the superiorRA toward the high anterior wall (GH1), as well asfrom the mid antero-septal to the anterior wall, wherethe two wavefronts meet again (GH3). A similar

directed graph illustrates the corresponding propaga-tion delays in Fig. 9(b), ranging from 2 to 87 ms (24± 19 ms).

DISCUSSION

A novel approach to the analysis of atrial propa-gation patterns is proposed and evaluated on simu-lated as well as real data, representing typicalpropagation mechanisms and recording situations.While the MVAR frequency domain description hasbeen considered in brain signal analysis, see, e.g.,Baccala and co-workers3,5, Franaszczuk et al.,15

several modifications have been made here to improveperformance for intracardiac signal analysis. While thespectra of the electrograms mainly reflect signal mor-phology, the preprocessing emphasizes the rhythm,which results in spectra characterized by a pronouncedfundamental frequency corresponding to the DF. As aresult, not only are lower MVAR model orders neededto describe the signals, but also the interpretation ofthe PDC is simplified. Specifically, the evaluation ofthe PDCs from intracardiac AF signals can berestricted to the frequency range of interest centeredaround the DF, as implemented in Eq. (6). In fact, thePDC integrated within this frequency range reflects thestrength of coupling between the rhythmic activities atthe two considered atrial sites. Significant PDC valuesoutside this range, though being expected when the

0

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FIGURE 7. MVAR analysis applied to atrial flutter data, see Fig. 5 for details.

Propagation Patterns in Intracardiac AF Signals

analyzed signals exhibit harmonic patterns in the fre-quency domain, are of little physiological interest andcan thus be excluded from further analysis. Anotheradvancement in the present article is the application ofa recently proposed surrogate data approach,14 whichis especially well-suited for the PDC as it preserves thecausal coupling in all directions but the direction underevaluation. Furthermore, the frequency domain rep-resentation of the MVAR model is also employed toestimate the delays along directions with significant

coupling, facilitating the estimation of propagationdelays. The delays are usually not of interest in brainsignal analysis, whereas they provide interestinginsights on AF propagation patterns through theestimation of atrial conduction times.

The PDC belongs to a class of causality measureswhich are frequency domain representations ofGranger causality.17 According to this concept, there isGranger causality from signal xj(n) to signal xi(n) ifknowledge about past values of xj(n) improves the

0

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FIGURE 8. MVAR analysis applied to AF data recorded with a linear catheter, see Fig. 5 for details.

Anterior Antero- lateral Lateral

Postero- lateral

Posterior Postero- septal

Septal

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Anterior

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GH AB CD EF

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(a) (b)

FIGURE 9. MVAR analysis applied to AF data recorded with a two-dimensional catheter. Illustration of the results for 26 simul-taneously recorded electrograms from the RA. (a) A directed graph representing the significant integrated PDCs Pij (p � 0:01). Thewidth of the arrows is related to the size of the corresponding Pij : (b) A directed graph in which the width of the arrows is related tothe size of the corresponding delay Dij .

RICHTER et al.

prediction of xi(n). MVAR modeling has become themost common tool to identify Granger causality, andfrom the definition in Eq. (1), it can be seen thatGranger causality from xj(n) to xi(n) is reflected bycertain aij(k) being different from zero. Measures suchas the PDC represent this concept in the frequencydomain: Eq. (2) shows that the absence of Grangercausality from xj(n) to xi(n) results in a PDC which iszero for all frequencies. The link between causality inthe time and frequency domain makes the PDC apowerful tool as direct coupling from xj(n) to xi(n) canbe evaluated at a specific frequency. In the literaturethere are also other, widely used frequency domainmeasures similar to the PDC, such as the DirectedCoherence (DC).4 In contrast to the PDC, the DCquantifies the presence of both direct and indirectcoupling, which results from the fact that DC andPDC are defined as factors in the decomposition of theordinary coherence and the partial coherence, respec-tively.3 This leads to different fields of application forthe two measures: while the PDC is especially suitablefor tracking the path of the direct information flow, theDC is advantageous when the main interest is toidentify the source of the information flow. In thepresent article, the analysis of propagation patterns ofthe electrical activity has been prioritized over sourceidentification.

The present study aims at demonstrating thepotential of the method for analysis of atrial arrhyth-mia mechanisms. For this purpose, two scenarios havebeen simulated using the CNR model, which hasproved to be particularly useful for the simulation ofhuman atrial arrhythmias and the reproduction ofrealistic electrograms.21 The results showed that thePDC well reflected the known simulated patterns,thereby validating the use of the evaluated approach inthe analysis of atrial electrograms. This is an importantresult, as MVAR modeling assumes that the signal isstationary over the analyzed time window and thatonly linear coupling is present, while the propagationduring AF can change over time and the coupling isknown to be both linear and non-linear, see, e.g., Censiet al. 9 During the simulation of AF with an ectopicfocus, the propagation on the lower part of the spherewas disorganized, thus resulting in signals in whichnon-linear and non-stationary features are likely to bepredominant. However, the results showed that theabsence of a stable and coherent rhythm is reflected bya low or non-significant PDC, while the couplings onthe upper part of the sphere, where the propagationwas more organized, could still be correctly identified.

Regarding the values of the PDC, it is important toconsider the normalization in Eq. (4), which states thatthe sum of the PDCs from one signal to all other sig-nals must be 1 at all frequencies. This normalization

implies that the PDC can have large values even atfrequencies at which the power of the source signal islow, see, e.g., Fig. 5. However, a large value at a fre-quency at which the power spectrum is low is actuallyof little relevance. Thus, when interpreting the PDC, itis important to consider both the significance thresh-olds and the power spectra. The latter has been takencare of by interpreting the PDC at the DF, which, afterthe preprocessing, almost always has the largest power.While a pronounced DF is not a prerequisite forfinding a significant causal coupling, it reflects thepresence of a pronounced rhythm in the correspondingtime signal, and thus a propagation as well as a sig-nificant causal coupling leading toward or away fromthe corresponding recording site becomes more likely.On the other hand, two sites having different rhythms,reflected by different DFs, or a site with a less pro-nounced rhythm, reflected by a less pronounced DF,are more likely to have low PDCs, indicating theabsence of propagation. The behavior of the method insuch rare cases as a 2:1 conduction block, during whichthere is a regular propagation between two sitesthough the corresponding DFs differ by a factor oftwo, would be highly interesting to investigate.

In a recent study13, Elvan et al. found that the DFduring AF correlates poorly with AF cycle length, andtherefore recommended time domain analysis of theelectrogram. While their results would call in questionthe present approach, being inherently frequencydomain in nature, certain aspects of the study by Elvanet al. have been the subject for discussion, includingtheir algorithms used for noise rejection, preprocessingand the determination of DF.7,28 In another recentstudy, Grzeda et al.18 found that frequency domainanalysis was more robust than time domain analysis indetecting the average local activation rate.

The method was evaluated on both atrial flutter andfibrillation electrograms, recorded with different map-ping modalities. The evaluation of the propagationpattern during atrial flutter evidenced the typicalsequential activation found during reentrant activity.The propagation patterns evidenced during AF pro-vided more detailed information about the underlyingmechanisms of the arrhythmia. In both cases, the siteof earliest activation within the recording area wasfound to be in the high septal RA, suggesting atrialimpulses entering the RA from the left atrium throughthe Bachmans bundle region. This agrees with the roleof the LA as a driver of AF as well as with previousfindings about RA breakthrough sites.32,40 Moreover,RA activation observed in paroxysmal AF, involvingthe earliest activation of the upper septal region and asubsequent cranio-caudal spreading in both the lateraland septal RA, is in agreement with previous clinicalobservations.26,32,40 Interestingly, this specific RA

Propagation Patterns in Intracardiac AF Signals

activation pattern has been associated to the presenceof a focal source in the right upper pulmonary veins.26

These results further emphasize the potential of themethod in extracting information about the underlyingpropagation pattern, which has substantial valueduring electrophysiological studies, especially whenperformed in connection to ablation procedures.Nevertheless, additional validation is required beforeintroducing the approach into clinical practice. Infuture studies, it would thus be of interest to furtherevaluate the method on a larger database recordedduring atrial arrhythmia, which ideally should alsocomprise recordings from the left atrium. The com-putational time of the algorithm is compatible withpractical utilization in electrophysiology; the most timeconsuming part being the significance test, which maytake several minutes. However, optimization and uti-lization of simpler algorithms, such as phase random-ization14 or theoretical significance levels,34 should beinvestigated.

In the example of paroxysmal AF recorded with abasket catheter weaker direct couplings over longerdistances are also observed, e.g., from AB1 to EF7.From a physiological point of view, such couplings areless likely. Methodologically, they can arise from thefact that LS estimation tends to overfit the MVARmodel when the number of unknown MVAR coeffi-cients, N2p, exceeds the sample size.37 A possibility toimprove the estimation of the MVAR coefficients andthe corresponding propagation delays in such a case isto consider estimation methods that encourage sparsityby putting constraints, such as the L1-norm, on the LSestimation.37 In addition, sparse estimation methodscan be motivated by the observation that connectivityduring AF may be viewed as a priori sparse, as it iswell-known that coupling between the recording sitesduring AF decreases with increasing distance. Cur-rently, we are investigating approaches to sparseMVAR model estimation, as well as the possibility toincorporate information about the distance betweenthe recording sites into the estimation, to improve themethod when a larger number of signals is involved.

In the present study, the analysis is performed over5-s time windows, thus revealing propagation patternswhich are stable over a larger number of activationwavefronts. This is in contrast to methods relying onactivation detection, which, provided that AF organi-zation is sufficiently high, facilitate the detection andcharacterization of individual activation wavefronts.In order to improve time resolution and track temporalvariations in the propagation pattern, the time windowshould be shortened, and the MVAR model coeffi-cients estimated adaptively.38 Furthermore, the analy-sis could be improved by a modeling approach which isable to capture linear as well as non-linear coupling.

Tests performed in the present study to check theassumption that the MVAR model is generated by amultivariate white noise process revealed that, in somecases, minor correlation between the residuals exists.However, multivariate approaches to non-linearGranger causality have never been performed in AFsignal analysis. So far, the concept of non-linearGranger causality has only been addressed briefly rel-ative AF, employing a bivariate measure20; bivariatesignal analysis is a common restriction of mostapproaches to non-linear causality.10,16 Another dis-advantage is that non-linear Granger causality has atime domain representation only, thus missing thebenefits of a frequency domain representation whichcan be evaluated for a specific frequency range such asthe DF. Nevertheless, a multivariate approach to non-linear causality could allow further exploration of thenature of the mechanisms underlying propagationpatterns during atrial arrhythmias.

CONCLUSIONS

In the present article, a novel approach has beenintroduced to the characterization of atrial propaga-tion patterns during atrial tachyarrhythmias. Themethod can identify the underlying propagationmechanisms and serve as a support for the electro-physiologist when locating ablation sites. Moreover,the possibility of quantifying the propagation patternin terms of direction and strength of the coupling aswell as the propagation delay can be applied to effi-ciently evaluate such patterns in existing databases.

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