© 2005 The European Society of Cardiology. Published by Elsevier Ltd. All rights reserved.
Genesis of the P wave: Atrial signals as generated by the equivalent double layer source model
aDepartment of Cardiology, Centre Hospitalier Universitaire Vaudois (CHUV) Lausanne, CH, Switzerland; bEcole Polytechnique Fédérale de Lausanne (EPFL), Signal Processing Institute Lausanne, CH, Switzerland
Manuscript submitted 2 February 2005. Accepted after revision 3 May 2005.
*Corresponding author. Ecole Polytechnique Fédérale de Lausanne (EPFL), Signal Processing Institute, 1015 Lausanne, CH, Switzerland. Tel.: +41 21 693 2708; fax: +41 21 693 7600. E-mail address: adriaan.vanoosterom{at}epfl.ch (A.van Oosterom)
 |
Abstract |
|---|
 Top Abstract IntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
AIM: To assess the effectiveness of the equivalent surface source model in the simulation of atrial signals as observed in ECG leads.
METHODS: P waves were extracted from 64-lead ECGs recorded in healthy subjects. The geometries of torso, lungs, heart, and blood cavities of a healthy subject, derived from magnetic resonance imaging, were used to position a detailed, thick-walled 3D model of the atria consisting of a set of 800,000 units representing the activity of all atrial myocytes. The ion-kinetics of the units was based on the formulation of Courtemanche et al. The simulated transmembrane potentials following a normal sinus beat, as well as those during atrial fibrillation, were projected on the 1297 nodes of the surface encapsulating all atrial myocytes (endocardium and epicardium). The transmembrane potentials at these nodes formed the source strengths of the elements of the equivalent generator, which were used to compute body surface potentials.
RESULTS: After invoking slight adaptations of the timing of depolarization of the transmembrane potentials, the simulated signals during the P wave closely corresponded to recorded ones. The correspondence during the entire PR interval improved markedly after the inclusion of early repolarization effects in the interval between the end of the P wave and onset of QRS. This demanded a shortening of the mean action potential duration generated by the Courtemanche model. The simulated ECGs related to atrial fibrillation demonstrated the characteristic features of those clinically observed.
CONCLUSIONS: The equivalent double layer is a useful source model for the genesis of atrial signals observed on the thorax. The interval from the end of the P wave to onset of QRS is not iso-electric. The Courtemanche model of the ion-kinetics of atrial cells needs to be adapted when applied to represent the activity of healthy, ‘common’ atrial myocytes.
Key Words: atria, equivalent double layer source, P waves, atrial fibrillation, PQ segment
|
Introduction |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
Historically, the analysis of the atrial electrical signals that are observed on the thorax has been mainly restricted to the documentation of the timing of the P waves in the standard 12-lead electrocardiograms (ECGs), their amplitude and polarity. More recently, the clinical interest in the electrical activity of the atria during atrial fibrillation (AF) and atrial flutter has prompted the question of how much of the involved complexity might be gleaned from the electrocardiographic signals observed on the thorax.
As in the case of ventricular electrical activity, two major, different tools are available for answering this question. The first is the statistically based analysis, supported by various signal analytical methods for the identification and extraction of relevant features. The second is the biophysical modelling of the genesis of the signals, inspired by the electrophysiology of the involved processes. This paper addresses the second approach. In particular, the feasibility and usefulness of the source description in the form of the recently proposed equivalent double layer (EDL) are investigated. The EDL model has proved to be very effective in linking ventricular electrical activity to body surface potentials [1–
3]. The use of this source model in an inverse computation of the depolarization sequence of the atria (activation time imaging) has recently been shown to yield accurate estimates of the stimulus site [4]. Here, the potential of the EDL is tested by its application to describe atrial electrical activity during depolarization as well as repolarization.
The EDL model is first of all tested for its potential to simulate normal P waves. Next, in an application, its properties are demonstrated by linking the complex atrial electric activity during AF to the signals that this activity generates on the thorax. The discussion concentrates on the source description. The handling of the volume conductor effects is treated in an accompanying paper [5].
|
Theory |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
The true sources of the electrical potentials lie in the biochemical processes in the membranes of the myocytes. They have the nature of electric current sources [6]
. The large number of cells (109) involved prohibits their use as a practical source model. Instead, one has to rely on simpler descriptions of the electric source, the so-called equivalent generators. The electric current dipole is the best known example. It forms the basis of vectorcardiography. However, its interpretation in terms of the underlying processes is generally not straightforward, if not impossible. The EDL model discussed in this paper has superior properties in this respect [1–4]. |
The EDL source model |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
The equivalent surface source model expresses the entire electrical activity within the myocardium by means of a double layer source situated on the closed surface Sh bounding the myocardium. During the depolarization phase, while assigning a constant, uniform source strength to the depolarized parts of Sh, this source model is equivalent to the classic uniform double layer. The basis for the extension to the repolarization phase is as follows. The electric source specification at locations
throughout the myocardium is the divergence of the gradients of the local transmembrane potential (TMP), more precisely 
[6] with 
i the electric conductivity of the intracellular domain. The resulting potential distribution at position 
outside the active source region, 
is found by the addition (volume integration) of the contributions of all source elements:
 | (1) |
e the external electric conductivity, vol referring the entire myocardium, and R the distance from source location to observation point By the application of Gauss' divergence theorem to Eq. (1) it can be shown that(2)
 | (2) |
pointing from surface element 
(directed along the local surface normal) to observation point [7]. Note that the volume integration is replaced by an integration over the surface Sh bounding all myocytes. The term 
is the solid angle subtended by at
Although the assumptions involved in converting Eq. (1) to Eq. (2) may not always entirely hold true [7,8], the application to represent the cardiac sources of ventricular myocytes throughout the entire cardiac cycle i.e., during depolarization and repolarization, has proved to be a very useful approximation [2,3]. In its numerical application, for any position on Sh, the time course of the local source strength is assigned to be proportional to the transmembrane potential, Vm(t), of the cells closest to Sh.
|
Simulating transmembrane potentials |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
As indicated in the previous subsection, the local source strength of the EDL requires the time course of the TMPs of the myocytes in the vicinity to be assessed. However, no set of TMPs, recorded with adequate spatial resolution on both epicardium and endocardium is currently available. Instead, in this study, we used TMPs that were simulated by a biophysical model, implemented on a digital computer. The monolayer variant of the model used has previously been shown to follow closely the electrical behaviour of the atria as known from invasive electrophysiology [9,
10]. |
Methods |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
Data acquisition
Normal ECGs
Body surface potentials were recorded in a healthy 38-year-old human male using the Nijmegen 64-lead system [11]. This system has the standard 12-leads as a subset. The potentials were recorded with an AC coupled amplifier (high-pass filter at 0.05 Hz), sampled at 500 sps with 1 µV resolution and subsequently stored. Markers were attached to the thorax at the locations of the electrodes in order to specify their positions in a subsequent magnetic resonance imaging (MRI) recording of the geometry required for the handling of the volume conductor effects [1–3,5]. The subjects' data have been validated and used in several previous studies related to the modelling of QRST wave forms [12]. The P waves contained in these ECG signals served as reference data for the P wave in the present study. The quality of the recorded P waves was assessed by comparing them with those available from a large database.
Geometry of the thorax
In one of the early applications of MR-imaging to ECG modelling [1], the healthy subject's thorax was scanned at the Research Department of Philips Medical Systems, Best, The Netherlands. In all, 28 cross sections were produced, at 1.5 cm intervals. All images were recorded in the same phase of the cardiac cycle.
Atrial geometry
The geometry of the atria of a healthy male was recorded by MRI techniques. The raw data were furnished by Ryan Lahm, Josée Morisette and Arthur Stillman (Medtronic Inc., Minneapolis, MN, USA).
|
Data processing |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
Geometry of the thorax
MRI images of the thorax were used to extract the geometry of the heart, lungs and torso, as well as the ventricular cavities. These constitute the major prerequisites for modelling the electric volume conductor effects inside the thorax [1–
3,5]. The MR-markers were clearly visible on the recorded MR-images, which facilitated the inclusion of the exact positions of the electrodes in the grid representing the body surface.
Atrial geometry
From the MRI images of the atria, a numerical, triangulated 3D monolayer was extracted, represented by 100,000 points in space [9]. The layer included the major orifices where myocytes are absent: the entries of the two venae cavae and those of the four pulmonary veins, the orifices of the mitral valve and tricuspid valve, the fossa ovalis and coronary sinus. Based on this geometry, a thick-wall variant was constructed, in which the distances between the nodes on the endocardium and those nearby on the epicardium were in the range of 1–2 mm. This closed 3D surface is topologically equivalent to an 8th order doughnut. Its surface is specified by 2622 small triangular elements, the 1297 vertices (nodes) of which served as the location of the EDL source elements. In the sequel, this surface is referred to as Sa. Its position inside the thorax was established by linking up its mitral and tricuspid valve orifices with those of the ventricles.
In addition to this basic structure, sections were added, modelling the fast-conducting system. The crista terminalis, the pectinate muscles and the Bachmann's bundle were included. Their structure and their location were chosen in order to reproduce the main anatomical features of Harrild and Henriquez' atrial model [13].
Processing recorded P waves
Within a 10-s interval of the recorded data of the healthy subject, showing stable baselines in all leads, a spline-based baseline correction was carried out, pivoted at the onsets of the P waves. These points were identified from the RMS(t) curve, the curve describing the instantaneous root-mean-square values of all 64 recorded signals. The data were re-sampled at 1 ms intervals by means of spline interpolation. The contribution of instrumental noise and muscle tremor was reduced by the application of a low-pass moving average filter over 20 samples (zero at 50 Hz). The potential reference used was the mean of all the 64 signals.
The PR interval of a single representative beat, representing the data from onset P to onset QRS, was selected for this study. The data were stored in a matrix 
(size: 64 × 190). Within this interval, the actual P wave lasted 125 ms and was followed by a relatively flat signal episode, denoted here as the PQ segment, lasting about 65 ms.
An analysis of the body surface potential maps during this segment revealed a pattern that was very similar to the pattern at the timing of the apex of the RMS(t) curve, albeit with reversed polarity and a lower magnitude of the individual potential values. This phenomenon was also observed in a selection of 125 body surface potential maps of healthy subjects recorded during previous studies [12]. It was interpreted as reflecting the repolarization of the atria, a process that in fact starts directly following the onset of the P wave [14].
|
Forward computation |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
The computation of the body surface potentials generated by atrial electrical activity requires the specification of the electric sources as well as that of the volume conductor that governs the transfer from source elements to the potentials in the observation points.
Source description
The closed surface Sa formed the basis for the geometry of source description. The TMPs at the 1297 nodes of Sa were copied from the nearest ones in a collection of 800,000 encapsulated units (space distance 300 µm) representing the electric activity of all atrial myocytes. The formulation of the ion-kinetics of the units was the one described by Courtemanche et al. [15]. The interaction between the units was treated in the mono-domain approximation. The tissue resistivity was set to 50 
cm in the fast-conducting system (80 cm in the pectinate muscles), 500 cm (slower conduction) in the inter-atrial connection at the fossa ovalis and 140 cm everywhere else, resulting in a conduction velocity of 80 cm/s in the bulk of the tissue, and 105–135 cm/s in the fast-conducting bundles. Normal propagation was initiated by a stimulus applied at the location of the sino-atrial node [16].
To assess the signals generated on the thorax during a complex rhythm, an episode of AF was simulated in a uniform tissue with a conduction velocity reduced to 70 cm/s. In order to create a substrate for AF, patchy heterogeneities (spatial scale: 2 cm) in the action potential duration APD90 (measured at 90% repolarization) were introduced by modifying the local membrane properties, leading to an APD90 distribution of 195 ± 15 ms (range 150–230 ms) during normal rhythm [20]. Sustained AF was induced by burst pacing in the appendage of the left atrium.
The equivalent double layer was modelled by 1297 double layer elements, small segments of Sa around the nodes specifying its geometry. This source may be represented by a matrix S, whose element Sn,t is the strength of source element n at time instant t.
Transfer matrix
From the available geometry data, a numerical, triangulated thorax was distilled, specified by 300 vertices on its surface. The positions of the 64 ECG electrodes as documented in the MRI session formed a subset of these vertices. An electric conductivity of 0.2 S/m was assigned to this compartment. Similarly, the surfaces bounding the left and right lungs were triangulated, each specified by 116 vertices, conductivity value: 0.04 S/m. The cavities of the left atrium and the left ventricle were combined, as were those of the right atrium and the right ventricle. This resulted in two regions specified by 422 and 428 nodes, respectively, to which a conductivity value of 0.6 S/m was assigned.
The transfer between the elements of the EDL current source and all 300 nodes on the body surface were computed by means of the boundary element method [1]. The algorithm used was formulated with special attention paid to the fact that the location of the nodes describing the endocardial source elements coincides with those of the boundary elements of the atrial cavities. The matrix A expresses the involved transfer. Its element a
,n is the potential generated at lead by (unit strength) source element n.
Computation of body surface potentials
From the source description S and transfer matrix A described above, body surface potentials at the leads considered, at time instants at 1 ms interval, were computed from the matrix multiplication: = AS.
Inclusion of atrial repolarization
The measured potential distribution on the thorax during the PQ segment showed a stable pattern, which was almost identical to that during the apex of the P wave, but for a reversed polarity. The potential distribution of the simulated potentials showed a similar pattern, which was amplified at the height of the simulated atrial T wave. This led us to study the possible involvement of atrial repolarization effects during this interval. To this end, an analytical expression for the representation of the wave form of the TMPs was developed, which allowed us to specify the durations of the individual TMPs by a single parameter, while keeping their shape close to those based on the ion-kinetics. This facilitated the use of a dedicated inverse procedure, similar to the one previously developed for treating ventricular repolarization [2].
Difference measure
The measure used to express the correspondence between simulated and observed data is the relative residual difference (rd). This is the square root of the ratio of the sum of the squared differences (all leads, all time instances) divided by the sum of all squared observations.
|
Results |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
Simulated TMPs
The inspection of the simulated TMPs revealed wave forms that were consistent with those previously described in the Courtemanche model. Fig. 1 shows some of the computed 800,000 signals. The timing of the maximum upstroke velocity was taken as a marker of the local depolarization time (
n for node n) and that of the maximum down-slope as a marker of the local repolarization time 
n and their difference, 
n as a marker for the local action activation recovery interval (n = ARIn = n – n). When compared with the frequently used APD90 marker, the ARI has a more direct link to the timing of apex T in ECGs and electrograms [2,17]. For the TMPs assigned to the 1297 nodes of Sa, the main statistics of these markers are listed in Table 1. The spatial distribution of their depolarization times, n, on Sa, is depicted in Fig. 2. This activation map is comparable with the one reported from experimental data [18] and other anatomical models [13]. The small range of ARI values caused the pattern of the timing of repolarization to be very similar.
|
|
|
P waves in body surface potentials
The body surface potentials at six precordial leads overlying the atria, generated by the simulated TMPs are shown (in red) in the left panel of Fig. 3. The recorded potentials during the PQ interval are shown in blue. Note that the onset of QRS can be seen at the end of this 200 ms interval. During the P wave itself (the first 125 ms) the simulated wave forms bear some resemblance to the measured ones. However, the rd value (all 64 leads; first 190 ms) was 1.06, which was judged as insufficient. It was hypothesized that this might be due to the fact that the atrial geometry was not the one of the (healthy) subject studied. Previous experience in solving the related inverse problem for the ventricles [1,
2] indicated that the correspondence between measured and simulated P waves might improve by using the depolarization times of the simulated TMPs as initial estimates in solving the inverse problem of computing the depolarization times from observed body surface potentials. The application of this initial estimate to a variant of the available inverse procedure, adapted to treating the atria, was tested. First, the method was applied to the first 125 ms only. Without the inclusion of any regularization, this procedure rapidly converged to a solution that was very close to the initial estimate (mean difference: 0.029 ms; SD: 1.5 ms; max(abs(difference)): 7.5 ms). For this interval, the rd value was 0.40, when computed over the first 190 ms it was 0.67. The body surface potentials of six leads, based on the adapted depolarization times while using the TMP wave forms and their durations as in the first test (Fig. 3 left panel) are shown in the right panel of the same figure. The correspondence between the measured and the simulated data clearly improved, but the signals during the PQ segment remained poorly represented.
|
Effect of including atrial repolarization
From an inspection of all 64 measured and simulated signals it became clear that an improved representation of the PQ segment could be expected from a global reduction in the durations of all TMPs. As shown in the previous study on ventricular repolarization, this reduction has as its main effect the shifting of apex T to the left [2]
. This expectation was tested by scanning the rd resulting from different shifts. The optimum value was found to be 90 ms, which produced a reduction in the rd value from 0.67 to 0.52. The results, for just the six leads shown in Fig. 3, are depicted in the left panel of Fig. 4.
|
Next an application of the inverse procedure to the entire PR interval was carried out. The subsequent iterations of the optimization procedure were applied alternately to the timing of depolarization (dep) and repolarization (rep). A severe spatial regularization was included (during the repolarization steps only) in order to constrain the width of the range of the ARIs. For this solution, the rd value was 0.41. The range of the ARI values was 73–130 ms (mean: 99 ms, SD: 12.5 ms).
Simulated AF signals in the standard leads
The TMPs during simulated AF (see Methods) were applied to the (same) forward transfer matrix A. No further tuning was carried out. Examples of the type of resulting ECGs are presented in Fig. 5. Also shown are some of the TMPs involved. The ones selected were those that were closest to the positions of the electrodes used in the standard 12-lead system. The AF signals at the corresponding nearest ECG electrodes are shown alongside. Note that their amplitude scales differ by a factor of 1000. Also note that the extremity leads signals are shown unaugmented, making them equivalent to the other precordial, so-called, unipolar leads.
|
|
Discussion |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
The application of the EDL as a source model for the atrial electrical activity was tested. In combination with a detailed numerical representation of the thick-walled atria, and a realistic numerical representation of the volume conduction effects, it closely reproduced the P wave morphology observed in recorded ECGs during sinus rhythm (Fig. 3). The wave forms simulated for the 12-lead ECG during AF agreed in all respects with the nature of such signals observed in a clinical study.
The scrutiny on the PQ segment suggested a clear involvement of atrial repolarization. During this segment a relatively stable pattern of the potential distribution was observed, based on the recorded 64 lead data. The fact that its pattern showed a reversed polarity when compared with the distribution during apex P supported this idea. An inverse procedure was applied, aiming to corroborate the hypothesis of the involvement of repolarization. Its application to the entire PR interval, dedicated to filling in the contribution of repolarization currents, was carried out with great caution. After all, the major part of such contributions was (might be) hidden in the QRS complex. The application of the inverse procedure to the tuning of the timing of depolarization (Fig. 3), when restricted to the 125 ms long P wave interval, resulted in a highly stable solution, without the application of any constraint. This was also the case during the subsequent application to the entire PR interval, which left the timing of depolarization unaltered.
In contrast, the application of the inverse method to the treatment of the entire PR interval demanded the inclusion of a severe spatial regularization. Without it, the map of the final solution for the repolarization times displayed a highly irregular, physiologically unrealistic pattern. The nature of the inverse method, a parameter estimation procedure, is such that a small residual difference between the observed and the simulated results is no guarantee of the correctness of the solution, in particular when the number of parameters involved is large (here: 1297 n values and 1297 n values).
The rd values listed in this paper could have easily been made much smaller, however, only at the expense of the realism of the underlying solutions. The final values shown are about twice as large as those achieved in earlier work on ventricular depolarization and repolarization [1,2]. We attribute this to the fact that the integrity of the geometric data involved was sub-optimal: the atrial geometry used was not the subject's .
With due awareness of the limitations of the present study, we feel that its results indicate a clear involvement of atrial repolarization during the PQ segment. The relatively large reduction in the ARI values (and, hence, of APD90) compared with those listed in Table 1, which were needed to obtain a good correspondence between simulated and recorded potentials during the PQ segment, suggest that the durations of the action potentials generated by the Courtemanche kinetics may be too long for representing the electrical activity of the atrial myocytes. Based on the difference of about 100 ms between ARI and APD90 observed from Table 1, the mean value of the APD90 values used for the simulations shown in the right panel of Fig. 4, is 199 ms (range 173–230), which is considerably less than the 309 ms for the Courtemanche model (lower row, Table 1), but higher than the 150 ms estimated from Fig. 1 of the report by Gelband et al. [14]. In early simulations of the P wave in the vector-cardiogram this APD90 value produced an excellent correspondence between recorded and simulated VCGs [19]. On the other hand, inter-individual differences may also play a role. This topic deserves further attention.
The much larger width of the range of the repolarization times as resulting from the optimization procedure, may have real significance, suggesting, e.g. a much larger inhomogeneity than currently introduced in the atrial model. However, for the present, we attribute it to the fact that in the recorded ECGs the major part of the atrial T wave coincided with the depolarization of the ventricles (QRS).
|
Conclusion |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
The results of this work show that the EDL is a suitable source model for the description of atrial signals, both during sinus rhythm and AF. The application of this model to the PQ segment indicates the involvement of the repolarization currents during this segment. Moreover, the mean APD90 values resulting from the application of the Courtemanche kinetics of atrial units may need to be reduced by 100 ms. The source model and the computed transfer will be used for the identification of features in ECG signals recorded during AF.
|
References |
|---|
|
TopAbstractIntroductionTheoryThe EDL source modelSimulating transmembrane...MethodsData processingForward computationResultsDiscussionConclusionReferences |
|---|
[1] Huiskamp GJM and van Oosterom A. The depolarization sequence of the human heart surface computed from measured body surface potentials. IEEE Trans Biomed Eng 1988; BME-35: 1047–1058.[CrossRef][Medline]
[2] van Oosterom A. Genesis of the T wave as based on an equivalent surface source model. J Electrocardiol 2001; 34: 217–227.[CrossRef][Web of Science][Medline]
[3] van Oosterom A and Oostendorp TF. ECGSIM an interactive tool for simulating QRST wave forms. Heart 2004; 90: 165–168.
[4] Modre R, Tilg B, Fisher G, Hanser F, Messnarz B, Seger M, et al. Atrial noninvasive activation mapping of paced rhythm data. J Cardiovasc Electrophysiol 2003; 14: 712–719.[Web of Science][Medline]
[5] van Dam P and van Oosterom A. Volume conduction effects involved in the genesis of the P wave. Europace 2005; 7:Suppl. 2 S30–S38.
[6] Plonsey R. An extension of the solid angle potential formulation for an active cell. Biophysical J 1965; 5: 663–667.[Medline]
[7] Geselowitz DB. On the theory of the electrocardiogram. Proc IEEE 1989; 77: 857–876.[CrossRef]
[8] Geselowitz DB. Description of cardiac sources in anisotropic cardiac muscle. Application of bidomain model. J Electrocardiol 1992; 25S: 65–67.[Medline]
[9] Virag N, Jacquemet V, Henriquez CS, et al. Study of atrial arrhythmias in a computer model based on MR images of human atria. Chaos 2002; 12: 754–763.[CrossRef][Web of Science][Medline]
[10] Jacquemet V, Virag N, Ihara Z, et al. Study of unipolar electrogram morphology in a computer model of atrial fibrillation. J Cardiovasc Electrophysiol 2003; 14: S172–S179.[CrossRef][Web of Science][Medline]
[11] Heringa A, Uijen GJH, van Dam RT. A 64-channel system for body surface potential mapping. In Antalôzcy Z and Préda I (Eds.). Electrocardiology 1982; Budapest, Hungary Academia Kiado pp. 297–301.
[12] Hoekema R, Uijen GJH, van Oosterom A. The number of independent signals in body surface maps. Methods Inf Med 1999; 38: 119–124.[Medline]
[13] Harrild D and Henriquez C. A computer model of normal conduction in the human atria. Circ Res 2000; 87: E25–E36.[Web of Science][Medline]
[14] Gelband H, Bush HL, Rosen MR, Myerburg RJ, Hoffman BF. Electrophysiologic properties of isolate preparations of human atrial myocardium. Circ Res 1972; 30: 293–300.
[15] Courtemanche M, Ramirez R, Nattel S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am J Physiol 1998; 275: H301–H321.[Web of Science][Medline]
[16] Schuessler RB, Boineau JP, Bromberg BI. Origin of the sinus impulse. J Cardiovasc Electrophysiol 1996; 7: 263–274.[Web of Science][Medline]
[17] Haws CW and Lux RL. Correlation between in vivo transmembrane action potential durations and activation recovery intervals from electrograms. Circulation 1990; 81: 281–288.
[18] Cox JL, Canavan TE, Schuessler RB, et al. The surgical treatment of atrial fibrillation. II. Intraoperative electrophysiologic mapping and description of the electrophysiologic basis of atrial flutter and fibrillation. J Thorac Cardiovasc Surg 1991; 101: 406–426.[Abstract]
[19] Macchi E. Digital-computer simulation of the atrial excitation in man. PhD thesis 1973; Halifax Dalhausie University.
[20] Jacquemet V, Virag N, Kappenberger L. Wavelength and vulnerability to atrial fibrillation: insights from a computer model of human atria. Europace 2005; 7:Suppl. 2 S83–S92.
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  M. Lemay, J.-M. Vesin, V. Jacquemet, A. Forclaz, L. Kappenberger, and A. van Oosterom Spatial dynamics of atrial activity assessed by the vectorcardiogram: from sinus rhythm to atrial fibrillation Europace, November 1, 2007; 9(suppl_6): vi109 - vi118. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||