Spatial dynamics of atrial activity assessed by the vectorcardiogram: from sinus rhythm to atrial fibrillation
1 Ecole Polytechique Federale de Lausanne (EPFL), Signal Processing Institute, STI-ITS-LTS1, Station 11, CH 1015, Lausanne, Switzerland; 2 Computational Electrophysiology Lab, Duke University, Durham NC, USA; 3 Department of Cardiology, Centre Hospitalier Universitaire Vaudois (CHUV), Lausanne, Switzerland; 4 CardioMet, Centre Hospitalier Universitaire Vaudois (CHUV), Lausanne, Switzerland
* Corresponding author. Tel: +41 21 693 69 33; fax: +41 21 693 76 00. E-mail address: mathieu.lemay{at}epfl.ch
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Abstract |
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Aim: This study aims at developing methods for extracting spatiotemporal information about the electric activity of the atria from electrocardiographic signals, in particular during atrial fibrillation.
Methods: A biophysical model of the atria and a volume conductor model of the thorax were used to simulate the atrial electrical activity as expressed on the atrial surface as well as on the thorax surface. In all, 22 different types of atrial electric activity were generated, 20 of which related to atrial fibrillation (AF). The spatiotemporal behaviour of the ‘true’ equivalent dipole expression of these activities was documented as well as those of their estimation based on body surface potentials, the vectorcardiogram. Measures were developed for describing the spatial complexity of atrial signals as observed in the ‘atrial’ vectorcardiogram.
Results: Coherence between time course of the vectorcardiogram and the electrical atrial activity of the simulated sinus rhythm and typical atrial flutter has been observed. Identification of the local extremes of the distribution of instantaneous vector orientations revealed the location of stable and single atrial activity sources. Moreover, the spatial complexity of the vectorcardiogram can be quantified in a very natural way by the proposed features and their visualization.
Conclusions: The proposed analysis extracts spatial information that has hitherto remained unnoticed in non-invasive studies on atrial fibrillation (AF).
Key Words: VCG, AF, ECG, Substrates, Discrimination, Spatiotemporal
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Introduction |
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The 12-lead electrocardiogram (ECG) is currently the standard non-invasive tool used in the diagnosis of atrial fibrillation (AF). So far, the complexity of the electrical atrial activity (AA) during AF has mainly been assessed through the analysis of its frequency spectrum or of their time-frequency analysis (spectrogram) of the ECG signals.1
,2 An improved diagnosis of atrial ECG signals, in particular during AF, could result from the extraction of information derived from the spatial dynamics of the signals. Recent signal-analytical advances have created the possibility of observing the expression of electrical AA by means of ECG signals that previously were largely obscured by the signal components stemming from electrical ventricular activity.3 The current study aims at exploring the potential of such ‘clean’ atrial ECG signals. The spatiotemporal behaviour of the electrical activity during AF precludes in all likelihood the characterization of its complexity by means of an inverse procedure. This holds true in particular if the available ECG data are restricted to those of the standard 12-lead ECG, the data that are usually the only ones available in the clinical setting.
One of the methods used for the interpretation of the time course of the potentials observed on the body surface is the vectorcardiogram (VCG). The VCG provides a global representation of the electrical cardiac activity, the time course of the vector orientation and magnitude in 3D space. The atrial VCG is an estimate of the so-called equivalent dipole (ED), a current source that summarizes all of the instantaneously ongoing electric activity of the atria. In model studies involving realistic source descriptions, the ED can be computed with great accuracy, and may be taken as the gold standard for testing the potential of the VCG.4
In this study, the expression of the spatial complexity of the different AA dynamics as observable in the VCG was analysed. A biophysical model of the dynamics of AA was used to generate electrophysiologically realistic source descriptions during sinus rhythm (SR), atrial flutter (AFL), and episodes of AF resulting from different substrates. The EDs as well as the VCGs resulting from these sources were computed.5 This allowed us to compare the quality of the VCG for characterizing AA dynamics with that of the gold standard, the ED.
In addition to documenting the basic differences in the VCG signals corresponding to different types of AA, the paper introduces some methods for extracting a sparse set of features that can be extracted from the VCG. These are aimed at being used in the classification of different types of AA.
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Methods |
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Simulating atrial activity
A three-dimensional, thick-walled, biophysical model of the atria that simulates the propagation of the electrical impulse was developed based on magnetic resonance (MR) images.5
,6 The resulting atrial geometry is shown in Figure 1 A. The major anatomical details indicated are those of the valves and connections to the major vessels, at which no propagation takes place. The electrical propagation of the cardiac impulse was simulated using a reaction–diffusion system (monodomain formulation) comprising a total of 800 000 units based on a detailed ionic model of the cell membrane kinetics, formulated by Courtemanche et al.7
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Besides a normal SR, an episode of typical AFL and 20 episodes of AF were simulated. The AF episodes differ by their substrates and procedures for initiating AF. The substrate for AF consisted of patchy heterogeneities in the action potential duration (APD_90) implemented by setting the local membrane properties.8
,9 An example of the distribution of these intrinsic APD_90 values is shown in Figure 1 B. AF was induced by a cross-shock protocol or by rapid pacing in either of eight different locations, as shown in Figure 1 C. Specifications of the various conditions setting up the 22 different types of AA are listed in Table 1. In the sequel, these types are labelled as nos. 1, 2, etc.
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The electrical activity of the entire ensemble of 800 000 units was represented by the equivalent double layer (EDL) specified at the closed surface bounding the myocardium.6
,8 This double layer expresses the electric activity within the atrial myocardium by a sheet of electric current dipoles located on the surface bounding the atria (endocardium and epicardium: 1297 nodes), the local strength of which is proportional to the time course of the local membrane potential, Vm(t).
Simulating potentials
The expression of the electrical potential field generated by the atrial sources demands the specification of a volume into which the electric currents flow, thus setting observable potential differences. In this study, the effect of the heterogeneity in the electric conductivity of the tissues surrounding the atrial myocardium was computed by means of the boundary element method. This was applied to a compartmental torso model derived from MR images, which includes atria, ventricles, and lungs.8 Body surface potential maps of AA were computed over the entire torso. The potentials at locations of the nine ECG electrodes of the standard 12-lead system were selected to simulate ECG signals. Figure 1 D displays the torso geometry (left anterior 20° view), also derived from MR images, as well as the positions of the nine electrodes contributing to the information content of the standard 12-lead ECG.
The equivalent dipole
The ED 
represents, to a first-order approximation, the spatial distribution throughout the myocardium of the time course of the currents generated at the membranes of all cardiac myocytes. Based on the EDL, the time courses of its three strength components in 3D space, DEx(t), DEy(t), and DEz(t), are equal to the integral (summation) over the atrial surface Sa of Vm(t)
, the local EDL strengths at the elements 
of Sa. Note that 
have the nature of a vector in 3D space, directed along the local surface normal of Sa. The integration reads
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| (1) |
The proportionality symbol 
is used since 
, the electric conductivity of the medium scaling the result, is not shown. The integral in Eq. (1) was computed numerically, the elementary surface elements being the elements of a triangular mesh describing Sa.
The VCG dipole
In any clinical application, neither the atrial surface Sa, nor the EDL source strength is available. An accurate estimate of 
, denoted here as 
, can be computed from the full potential field on the 
(t) on the body surface as
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| (2) |
This expression is known as the Gabor–Nelson equation.10 Its evaluation requires a full specification of the potential field on the body surface, as well as of the geometry of the body surface, data that are not readily available.
When relying on clinical ECG data, the VCG, denoted here as 
, is an even cruder estimate of 
. Classically, it is derived from the linear combination of the potentials at seven locations on the thorax as proposed by Frank.11 Alternative schemes for the estimation of 
from the potentials observed on a limited number of electrodes have been described in the literature. In essence, all these estimates are of the type
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| (3) |
ECG(l, t) observed at l = 1,..., L electrodes on the thorax. A version of matrix T that uses the potentials observed at the nine electrodes of the standard 12-lead ECG system, dedicated to the analysis of atrial signals, has recently been proposed.4 This is the one used in the results shown in this paper.
Displaying vector data
The evolution in space and time of vector data can be displayed in different ways. In this paper, the following methods are applied:
- method one: the display of the trajectory of the projection of the vector on three (2D) planes (horizontal, frontal, and left sagittal),
- method two: the display of the vector magnitude [m(t)] and its three components [x(t), y(t), and z(t)], and
- method three: the display of the trajectory of the normalized vector (the vector magnitude) on a unit sphere, similar to the method proposed by Dower.12
For method three, the origin of a unit sphere was placed at the centre of gravity of the atrial tissue. To facilitate the interpretation of the orientation of the sphere and the link between vector direction and atrial geometry, the contours of the major atrial details (valves and vessel connections) were also projected on the unit sphere (Figure 1 E). Examples of the three different types of displays of the VCG during SR (one complete cardiac cycle; duration 512 ms) are presented in Figure 2.
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When followed over some longer periods, most AF trajectories could not be interpreted easily. In such situations, an alternative method was used. The projections of the subsequent samples in time were left unconnected, resulting in a scatter plot of the vector directions on the sphere (Figures 3 and 4).
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Analysis methods: feature extraction
The analysis and ultimate quantification of the spatiotemporal information on AF as derived from the vector data will ultimately require the identification of relevant features. A first attempt at the identification of useful features was carried out in this study. These were tested in their application in order to distinguish the 22 different types of AA for which both the true dipole1
and its crude estimate3 became available by means of the model-based simulations (Results section, Figure 8).
The spatial distribution of the dipole orientations observed in the VCG was estimated by using an un-normalized kernel approach.13 This estimates the distribution from the sum of Gaussian functions (kernels) centred on the sample locations of the dipole on the unit sphere.
The following features were used to characterize the complexity of the spatial distribution, extracted from the normalized VCGs. For each of the signal segments studied, the second-order raw moment matrix C of the three components of a dipole d(t) was computed as:
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| (4) |
1 
2 3 0, of this matrix C of size 3 x 3, were tested as features. Because the trace of the integrand in Eq. (4) is 1, we have 1 + 2 + 3 = 1.
This approach is related to the analysis of bidirectional data by parametric statistical modelling.14 As an illustration, Figure 3 shows three different (extreme) types of scatter plots and their values. The robustness of the values with respect to the perturbing elements (nine electrode limitations, ventricular artefacts, etc.) has been studied previously.15 The results indicated that the first two eigenvalues 1 and 2 yield a robust measure of spatial complexity of the VCG during AF.
The ternary (triangle) plot was used to display the values in 2D. In a ternary plot, the proportions of the three variables must add up to a constant, in our case 1 + 2 + 3 = 1. Thus, there are only two degrees of freedom involved in plotting a sample point (1, 2, and 3). To this end, the variables 1, 2, and 3 were converted into 
1, 2, and 3, where 1 = 1 – 2, 2 = 2(2 – 3) and 3 = 33 (Figure 4).
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Results |
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Results on simulated atrial activity
Modifications of the substrates and of the AF initiating procedures created different dynamics such as rapid pacing,16
micro-reentries,17 mother-rotor,18 etc. The documentation of the simulated dynamics is presented in Table 1 and Figure 5. Table 1 relates each simulated AA with its specific dynamics and displays the available duration of the different simulations (the fifth and sixth columns, respectively). Figure 5 displays the transmembrane potential distribution map of 12 different simulated AAs and their different dynamics denoted by white spots and arrows. These 12 simulated AAs represent the different types of dynamics observed among all 22 simulations.
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In order to illustrate the potential of spatiotemporal information on AA provided by the VCG, Figure 6 displays the loop derived from the normalized 12-lead VCG for the simulated SR (simulation no. 1).19
In addition, it displays the time course of the vector for selected episodes of typical AFL (no. 2) and AFs (nos. 7 and 15, respectively). Note that the trajectory of the VCG of typical AFL is correlated with its counter-clockwise macro-reentry direction and it is opposite to the trajectory during SR.
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As mentioned previously, the VCG derived from the 12-lead ECG is an estimate of the dipole derived from the complete body surface potential field which is, itself, an estimate of the ED. Figure 7 displays an example of the time course differences between the true dipole and the one derived from the 12-lead ECG for simulation no. 2 (typical AFL). The three different types of displays are used.
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Results on spatial distribution analysis
The spatial information contained in the normalized 12-lead VCG is displayed in Figure 8. It shows the VCG spatial distributions of the same simulated AAs as shown in Figure 5. The observations based on the presence of VCG distribution clusters have suggested a separation of the simulated data into three groups. Group one (n = 14) includes the simulated AAs in which the dipole distributions were coherent with the AA dynamics, i.e. a distribution cluster was located close to the AA source location for the AAs with stable dynamics (simulation nos. 1, 2, 3, 7, 13, and 22), or the dipole distribution was uniform (
1 < 0.17) for the AFs with complex dynamics (simulation nos. 8, 15, 16, 17, 18, 19, 20, and 21). For instance, the VCG distribution in Figure 8 that represents the simulation no. 1 is characterized by a dipole cluster at the sinoatrial (SA) node location, which corresponds to the SA node pacing in SR. The VCG distribution that represents the simulation no. 13 is characterized by a dipole cluster at the left appendage location, which corresponds to a focal AF induced by burst pacing on the left appendage. Group two (n = 3) includes the AFs with multiple AF sources in which a dipole cluster was located close to the one of the multiple AF source locations (simulation nos. 9, 10, and 11). In Figure 8, the simulation no. 9 that corresponds to AF with two mother-rotors (one around the lower right PV and one between the PVs) displays a dipole cluster near the lower right PV but no cluster is present between the PVs. Group three (n = 5) includes the AFs in which no dipole cluster was located close to the AA source location (simulation nos. 4, 5, 6, 10, and 14). These observations were also tested on the ED. The use of the gold standard dipole had a small impact on the dipole cluster locations and produced the same groups as for the 12-lead VCGs.
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Figure 9 shows the results on the ternary plot for the simulation of SR (star), for the simulation of typical AFL (cross), and for the 20 simulations of AF (circles). Simulated AFs with specific electrical propagation such as micro-reentries, broad and multiple wavelets (nos. 5, 13, and 19, respectively) are indicated. The white noise simulation is also indicated by a black dot. Note its position halfway between the uniform distribution and the distribution along a great circle.
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Discussion |
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Several studies have already been dedicated to the investigation of different types of AF from electrogram20
or surface ECG recordings.2,21 These works have focused mainly on the prediction of AF termination (paroxysmal vs. persistent), the efficacy of drugs, and the discrimination of AF types I, II, and III (Wells' criteria). Time-frequency and information theory tools were mostly used. We have investigated how accurate the global representation of the electrical AA is as obtainable from an atrial VCG derived from the 12-lead ECG signals. This global representation of the electrical AA is well reflected in the results during SR and the typical AFL as observed by either of the display methods used. During SR, the VCG during depolarization points in the frontal-downward direction, pointing away from the SA node. During repolarization, the vector predominantly points in the opposite direction. The typical AFL VCG displays complete loops that correspond to the counter-clockwise orientation of the AFL macro-reentry; its trajectory passes between the coronary sinus and the MV areas projected on the unit sphere. The well-documented SR VCG trajectory is more complex than the AFL VCG trajectory. This is due to the regularity and completeness of the AFL macro-reentry cycle in opposition to the activity that follows the pacing of the SA node in SR. During AF, the VCG trajectory is even more complex and the presence of a preferential circuit is hardly observable.
The difference between the time course of the true dipole and the VCG derived from the nine electrodes of the 12-lead ECG on the unit sphere for the simulation no. 2 (typical AFL) demonstrates the effect using a limited set of electrodes. As observed by Jacquemet et al., 15 it expresses the difficulty in estimating the z component (front-back axis). By comparing the different AFL dipole results, even if the 12-lead VCG is not identical to the true dipole, the general trajectory is similar. The direction of the VCG still corresponds to the counter-clockwise orientation.
The observation of the atrial VCG spatial distributions was our first attempt to identify relevant differences between the 20 different types of AF. Identification of the distribution peaks, i.e. regions of the unit sphere most frequently visited by the dipole over time, have revealed the location of stable and single AF sources such as micro-reentries, mother-rotor or focal (AF) in most of the simulated AFs. The absence of such peaks exposed that the AF dynamic was complex (multiple AF sources or no identifiable source at all). This was clearly reflected in the simulated AF signals. The simulated SR and the simulated AFL confirmed these observations. Their distributions also revealed peaks in the location of the SA node (SR) or between the MV and the coronary sinus (typical AFL macro-reentry circuit).
As illustrated, the VCG spatial complexity can be visualized in a very natural and synthetic way by the proposed features. Any AA dynamics can be represented as a point inside a triangle, the corners of which correspond to archetypal dynamics (focal AA, AA that evolves around a fixed circuit and complex disorganized AA). The simulated SR has enabled us to validate one of the three extreme distributions, the modal one (bottom left of the triangle). The simulated typical AFL is closer to the bottom right corner. The parameters for the simulated SR (AFL, respectively) were 1 = 0.86, 2 = 0.13, and 3 = 0.01 (1 = 0.72, 2 = 0.26, and 3 = 0.02, respectively). This is consistent with the fact that AFL has a stable dynamic, slightly more complex than that of SR and characterized by a fixed circuit. The two VCGs for simulation nos. 5 (stable micro-reentries) and 19 (multiple wavelet reentries) differ by the complexity of their dynamics as visible in Figure 6 and on the triangle in Figure 9. The AF episodes were characterized by 1 = 0.65, 2 = 0.23, and 3 = 0.12 for AF simulation no. 5 and 1 = 0.42, 2 = 0.31, and 3 = 0.27 for AF simulation no. 19. This reflects the fact that the average wavelength of the depolarization waves is shorter in AF simulation no. 19 (7.3 cm) vs. AF simulation no. 5 (9.4 cm), leaving enough space for more wavelets and reentries.
Limitations
As mentioned by Mardia,14 the major problem of the 12-lead VCG is related to the difficulty in estimating the z component (front-back axis) of the ED from the signals observed on just nine electrodes. This limitation for characterizing the AA dynamic is visible on the ternary plot. White noise simulation should be close to the uniform distribution and we did indeed observe this with the ED-based results. The results of the characterization using the values applied to the 20 AF variants form a cluster located between the uniform distribution and the distribution along a great circle. The variation in the spatial complexity analysis results obtained from the ED was higher and closer to the uniform distribution. The use of an optimized lead system dedicated to the extraction of an atrial VCG4 significantly improved the estimation of the ED.
The examples we show in this report indicate that the relationship between the VCG spatial distribution cluster and the AA source location is not always feasible, in particular when multiple AA sources are present.
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Conclusion |
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Based on the simulations, the atrial VCG seems to be a promising, useful tool for summarizing the spatio-temporal complexity of electrical AA. Even in a limited electrode set context such as the standard 12-lead ECG, the ED is still well estimated by the VCG in terms of trajectory and global distribution. The proposed analysis, based on the VCG, extracts spatial information that is generally lacking in typical non-invasive AF studies. It permits the estimation and localization of a stable and single AA source. The analysis also synthesizes the spatial complexity of the AA dynamics and may procure information on the average wavelength. Further studies will investigate other features that include VCG temporal information (trajectory) and investigate clinical results based on the proposed features in respect to different AF types (paroxysmal, persistent, permanent, etc.) and different AA source locations.
Conflict of interest: none declared.
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The study was made possible by grants from the Swiss National Science Foundation (SNSF, no 205320–113445).
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