© 2005 The European Society of Cardiology. Published by Elsevier Ltd. All rights reserved.
Volume conductor effects involved in the genesis of the P wave
aResearch, Vitatron Arnhem, The Netherland; bDepartment of Cardiology CHUV, Lausanne, Switzerland
Manuscript submitted 19 January 2005. Revision received 28 July 2005. Accepted after revision 3 May 2005.
*Corresponding author. Meander 1051, 6825 MJ Arnhem, The Netherlands. Tel.: +31 26 3767292; fax: +31 26 3767666. E-mail address: peter.van.dam{at}vitatron.com (P.M.van Dam).
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Abstract |
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AIM: To assess the effect of inhomogeneities in the conductivity of different tissues, such as blood and lung tissue, on the body surface potentials generated by atrial electrical activity.
METHODS: A 64-lead ECG from a healthy subject was recorded. The subject's geometries of torso, lungs, heart, and blood cavities were derived by magnetic resonance imaging. These geometries were used to construct a numerical volume conductor model. The boundary element method was applied to simulate the potentials on the surface of the thorax generated by the atria. The equivalent double layer served as the source description during depolarization. Recorded body surface potentials were used as a check on the simulations. Subsequently, the conductivities in the model were varied to determine their influence on P wave morphology and amplitude.
RESULTS: The model with realistic conductivity values for blood and lungs produced potentials that closely matched the measured ones (correlation 98%). The subsequent variation of conductivity of blood and lungs revealed a major influence on P wave morphology and amplitude: a mean reduction in amplitude by 42%, with pronounced inter-lead differences.
CONCLUSION: The inhomogeneities of lungs and atrial blood cavities need to be incorporated in volume conductor models linking atrial electric activity to body surface potentials.
Key Words: atria, volume conduction effects, P waves, atrial Brody factors
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Introduction |
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The current clinical interest in the electrical activity of the atria, in particular related to atrial fibrillation and atrial flutter, raises the question of how much of the involved complexity is retained in the electrocardiographic signals (ECG) observed on the surface of the thorax. Studies on the generators representing the ventricular electrical activity and its expression on the thorax have demonstrated the need for the inclusion of volume conductor effects while interpreting the ECG [1]
. Far less attention has so far been given to these effects on the atrial signals. This paper focuses on the volume conduction effects involved in the genesis of atrial signals as observed on the thorax.
Volume conductor effects govern the fanning out of the electric currents throughout the thorax that generate the electric potential differences, observed clinically as the surface ECG. As a consequence, observed potentials resulting from the actual currents generated by the myocytes are blurred images of these currents. De-blurring the potentials can reveal the electrical activity of the heart itself, which enables the detection of pathologies [2].
The methods for de-blurring the potentials on the thorax, resulting in images of the electrical activity of the heart itself, require an accurate description of the involved volume conductor effects. These entail the position and orientation of the heart, the geometry of the thorax, the location of the electrodes on the thorax, and the parts of the thorax where the electrical conductivity differ substantially from that of the surrounding tissue.
This study is based on recorded body surface potentials and geometries derived from magnetic resonance imaging (MRI). From these data, a boundary element model of the thorax was constructed, which was used in the stimulation of body surface potentials originating from the equivalent double layer source model of atrial electrical activity. The objectives of this work are to explore how the major inhomogeneities in the body affect the P wave morphology and amplitude.
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Methods |
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Data acquisition
ECGs
Body surface potentials (BSPs) were recorded from a healthy 22-year-old human male by using the Nijmegen 64-lead system [3]
. This system has the standard-12 ECG leads as a subset. The potentials were recorded with an AC coupled amplifier (high-pass filter at 0.05 Hz) and sampled at 1000 sps. The BSPs were recorded during breath-hold, to mimic the conditions during the subsequent MRI recording session. MR-markers, 1.5 cm long, were fixed to the thorax at the electrode positions. The BSPs were recorded beforehand, to avoid a possible effect of the magnetic field inside the MRI equipment on the electric potentials. These potentials served as a set of reference potentials simulated for this study.
Geometry
MR-imaging was performed at the UMC Utrecht, on a Phillips Gyroscan Intera 1.5 Tesla MRI machine. All images were recorded during breath-hold at half expiration. The body was scanned, with slice thickness of 6 mm and slice distance of 8 mm, from neck to navel.
The heart was scanned in 31 slices, from its apex to the top of the aortic arch. Both the slice distance and slice thickness were 6 mm for the complete heart. For every slice, the complete heart cycle was sampled at 15 ms intervals, starting at the R-peak as observed in a lead near V2. The subject's heart rate varied between 80 and 85 bpm. In all, 50 images per heartbeat for each slice were recorded.
Data processing
Volume conductor model
MRI images were used to extract the geometry of the heart, lungs and torso, as well as the atrial and ventricular blood cavities. These constitute the major required compartments of an electric volume conductor.
All geometries were reconstructed by using custom-built software (MRIgeom). This software enables the user to draw contours on the MRI images, either manually or by a regional growing algorithm. The reconstruction of the geometry of torso and lungs is rather straightforward. First, all contours were drawn, allowing the software to triangulate the surfaces described by these contours. From this initial geometry a numerical torso was distilled, specified by 300 vertices (Fig. 1). The left and right lungs have 259 and 293 vertices, respectively.
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For the heart and cavities, 50 subsequent time frames were recorded, from which the corresponding geometry was documented. For the present study we used the heart geometry recorded at 165 ms before the peak of the R wave, i.e., at the start of the atrial excitation. The atrial geometry reconstructed at this moment in time had 664 vertices. The blood filled cavities of the ventricles are in direct contact with those of the atria, and have a volume that is of the same order of magnitude as those of the atria. Hence, they could be expected to have a direct influence on the volume conduction effects. Therefore, both left and right atrial and ventricular cavities were also incorporated in the volume conductor model. Additionally, major parts included were the vena cava and the aorta up to the aortic arch. The numbers of vertices for left and right cavities were 864 and 636, respectively.
The MR-markers were clearly visible on the recorded MR-images, which allowed us to determine the exact position of each individual electrode on the body surface.
Conductivity values
As a reference for the current analysis, the fully inhomogeneous thorax model was used, incorporating both the deviated conductivities of lungs and blood cavities. The conductivities assigned to the individual compartments were: thorax and atrial muscle: 0.2 S/m, lungs: 0.04 S/m and blood cavities: 0.6 S/m. While testing the influence of the conductivities of lungs and cavities, these values were switched between the indicated ones and those of the thorax.
The transfer between the current sources representing the myocardial cells and the resulting potentials were computed by means of the boundary element method. The potential generated at lead l by source element n is denoted by element al,n of the so-called transfer matrix A. Individual transfer matrices were computed for all of the different combinations of conductivity values studied.
Processing recorded P waves
During the ECG recording the subject's heart rate varied between 80 and 85 bpm, i.e., the same as during the MRI measurements. One representative beat of these recordings was selected as our reference beat. First, a linear baseline correction was applied between a point at the onset of the P wave of the selected beat and the one of the subsequent beat. These points were identified from the RMS(t) curve, the curve describing the root-mean-square value of all recorded 64 leads as a function of time. The same curve was used to identify onset QRS. The duration of the PQ interval identified in this way was 165 ms. The potential reference used was the mean of all the 64 signals, the so-called zero-mean reference.
The RMS(t) curve during the final 45 ms of this interval, the interval starting at what is usually considered to be the end of the P wave and onset QRS, clearly showed non-zero values (Fig. 2). These reflect the repolarization of the atria, a process that in fact starts directly following the onset of the P wave [4]. Since this study was restricted to the depolarization of the atria, the first 125 ms interval of the PQ interval was selected for the subsequent analysis, to which a separate baseline correction was applied between t = 1 ms and t = 125 ms. In this way a crude elimination of the contribution of atrial repolarization currents to the observed potentials was effected.
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Simulating P waves
For the study of volume conductor effects on body surface potentials a specification of the electric current sources that generate these potentials is needed.
Source description
The model of the current generator used was the equivalent double layer, a source distributed over the surface bounding all atrial myocytes. The time course of the local source strength was taken to be proportional to the transmembrane potentials of the neighbouring myocytes. This source model has a direct link with electrophysiology and has previously been shown to be very effective in the simulation of the potentials during depolarization and repolarization of the ventricles [5,6].
When just studying depolarization in healthy myocardium, the time course of the local source strength may be modelled by a jump of a fixed magnitude of 40 mV at the moment of local depolarization, 
n, for node (vertex) n of the surface bounding all atrial myocytes. The strength of any source element at node n at time instant t can be denoted as Sn(t) = S(t – n). For discrete time steps the entire source may be denoted by a matrix S, the columns of which represent the instantaneous strengths of the source elements:
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Timing of the excitation wave
The timing of local depolarization of the subject's atrial surface was not available from invasive measurements. Instead, the timing was derived by solving the associated inverse problem. The basic principles of this procedure are the same as those developed for the ventricles [5,6]. The results of a clinical validation of the application of such methods to atrial activation were recently shown to be very promising [7].
The inverse procedure may be characterized as a non-linear parameter estimation problem, the parameters being the timing of local activation at the nodes (vertices) specifying the atrial surface. Such procedures require an initial estimate of the solution, on which the quality of the final solution critically depends.
In this study we used a new approach to determine the initial excitation sequence, inspired by the known electrophysiology of the atrium. In a previous study [8] the excitation wave initiated at the sinus node location and propagating at a constant speed was found to agree well with clinical data [9,10] as well as with detailed models of ion kinetics [11,12]. Based on an assumed uniform propagation velocity, activation patterns were created for each of the individual nodes representing the atrial surface. When starting from node m the timing at any node n was taken to be n = dm,n/v, with v the (uniform) propagation velocity of the wave front and dm,n the distance between both nodes. This distance was taken to be that of the shortest route while traveling through the myocardium, found by means of the shortest path algorithm [8,13]. For all N = 664 nodes constituting the atrial surface, this resulted in a set of N different maps of atrial activation. From this set, the initial estimate was selected as the one yielding the smallest difference between the resulting simulated BSPs and the measured ones.
Forward computation
From the source descriptions S specified above and for each of the transfer matrices A related to individual conductivity values, matrices of the body surface potentials 
of the P waves at the leads considered at time instants at 1 ms interval were computed from the matrix multiplication:
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Results |
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Geometry
The geometries of the major compartments involved are shown in Fig. 1. The atrial wall volume was 45 ml, left and right atrial blood cavities were 40 ml and 83 ml, respectively. The larger size of the right atrial blood cavity relates to the fact that the inferior vena cava is partially included in the atrial geometry. The mean atrial wall thickness is 3.6 ± 1.7 mm with median wall thickness 3.2 mm.
Timing of the excitation wave
The new procedure for finding the initial estimate identified a node in the area near the superior vena cava, at the end of the terminal crest, as the optimal focus for the uniformly propagating wave (0.9 m/s). This area is consistent with the known location of the sinus node [9,10]. The subsequent application of this initial estimate to the inverse procedure resulted in the activation pattern shown in Fig. 3. While showing only minor changes in the pattern compared with the initial estimate, this sequence resulted in a close correlation between simulated and measured BSPs. For this solution, the duration of the complete excitation was 114 ms. During the first 35 ms only a minor part of the surface was activated. Subsequently the left and right atria were activated more or less synchronously. This solution was judged to have sufficient realism to serve for the objective of the present study.
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Simulated potentials
The model incorporating the inhomogeneities of lungs and cavities was judged to reflect most faithfully the complexity of the volume conduction inside the thorax. This was based on the results of similar studies of the signals arising from the ventricles [14]
. The relative mean square difference, rd, between the simulated and measured signals, computed over all of the 125 time instances and all of the 64 leads' signals involved, was 0.196. This corresponds to a correlation coefficient of greater than 98%. For the pre-cordial standard leads, V1–V6, the correspondence between measured and simulated data was close. For the extremity leads VR and VL the correspondence was less good, as is illustrated in Fig. 4. This set of simulated potentials was taken as the reference while studying the effect of the different conductivity values of the compartments.
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Discussion |
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The study focused on the possible effects of the inhomogeneities of lungs and blood inside the atrial cavities on P wave morphology and amplitude. It was inspired by the dominance and significance of such effects on BSPs arising during ventricular activity, as documented in several reports, e.g., [2,
14,15].
Table 1 shows that the higher conductivity of the blood cavities has a major influence on P wave morphology (Fig. 5), both far field (VL, VR and VF) and near field (V2). This effect is commonly referred to as the Brody effect. The amplitude always reduces (mean reduction about 42%), in agreement with the fact that the wave front is mainly tangential. However, note that these factors are non-uniform over the individual 64 leads. Moreover, clear waveform changes are observed, seemingly indicating that the reduction varies with time. However, as explained for the ventricles [16], this relates to the fact that the total expression of the effect also depends on the instantaneous position of the wave fronts. The magnitude of the influence of the higher conductivity of blood in the atrial cavities is much greater than that reported for the ventricles using a similar type of analysis [14]. This may be attributed to the smaller thickness of the atrial wall. The effect of the lung found in that study was of the same order as found for the P waves in the present study. Although this effect is smaller than that of the cavities it cannot be ignored, in particular if the forward modelling is used in solving the associated inverse problem [17].
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Study limitations
Other types of inhomogeneities, e.g. those related to subcutaneous fat, and the anisotropy of the conductivity of muscle fibres were not considered in this study. However, previous studies have shown that their effects on BSPs are smaller than the effect of the deviating lung conductivity [15]
. In our simulation we used a rigid geometry based on the MRI images recorded 165 ms before the R-top, thus the motion of the atria is discarded. Although the total volume of the heart during the cardiac cycle stays relatively constant [18], the motion of the atrial wall is considerable. The volume changes between the start of the P wave and R-peak are about 25–35%. Due to the fact that the right atrium and especially the right atrial appendage are located near the body surface, any change in their shape may affect the potentials on the body surface. The effect of this movement on BSPs is a topic of our current research. |
Conclusion |
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This study shows that the inclusion of the inhomogeneities of lungs and cavities may lead to a very high correspondence (correlation higher than 98%) between measured and simulated atrial ECGs. The inclusion of these inhomogeneities in models linking atrial electric activity to the body surface potentials is essential. From the inhomogeneities tested, lungs and blood cavities, the blood cavities play a major role in the determination of P wave morphology and amplitude.
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Acknowledgements |
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The authors acknowledge with gratitude the support of Dr. Event-Jan Vonken (Image Sciences Institute, University Hospital Utrecht), who recorded the MRI images, and Dr. Rudi Hoekema (Experimental Cardiology, Radboud University Nijmegen), who recorded the body surface potentials. We thank the editors of this issue for their constructive comments on the manuscript.
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References |
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