International Journal of Bioelectromagnetism Vol. 4, No. 2, pp. 347348, 2002. 
www.ijbem.org 
VARIABILITY OF SIMULATED ECG AUTOCORRELATION MAPS WITH ELECTRODE PLACEMENT
A.D. Corlan^{1}, R. Corlan^{2}, L. De Ambroggi^{3}
Abstract: Theoretically, under certain assumptions, correlation coefficients between ECG potentials at different instants on the same electrodes would not depend on the electrode system. We simulated ventricles surrounded by various 192lead spherical electrode systems in a homogenous unbounded volume conductor. Autocorrelation maps of the simulated ECG on each lead system were obtained with the same activation and repolarization. Differences between the autocorrelation maps were compared using the correlation coefficient, which was ≧0.937 if only rotation and shifting of the electrodes were involved and reached 0.895 for a system with electrodes at a few millimeters from the epicardium. In conclusion, autocorrelation maps, and thus indices computed from them such as the similarity index, can be considered to reflect only features of the ECG sources in the myocardium if recorded on electrodes systems which are not too close to the epicardium.
Figure 1. Anatomic model and electrodes on a spherical system around the model. The radius of the spherical system is 60mm in this model. The legend shows the directions of the rotations of the electrode system named 'rot' and 'roll'. INTRODUCTIONPotentials recorded in a purely resistive conductor, like the thorax [1], on a lead system with sufficient electrodes covering all directions of space can be converted into potentials recorded on another such lead system through a linear transform. Assuming that the matrix used for the transformation admits an inverse, the correlation coefficient between potentials at two different instants on one of the lead systems should equal the correlation coefficient computed between potentials at the same instants on another lead system. Thus, the set of correlation coefficients computed between every pair of instants during the cardiac cycle should be essentially identical irrespective of the lead system used. This symmetrical square matrix can be displayed as a maplike graphic [2] with the same time interval on both x and y. We call this graphic ``autocorrelation map''. Our purpose was to find out the extent to which the autocorrelation map obtained from a realistic disposition of ECG sources is invariant to the placement of a spherical 192 electrode lead system. METHODSWe used an anatomically realistic model of both ventricles (figure 1) with 27000 simulation elements in six concentrical layers mapped on ellipsoid surfaces. Intracavitary diameter of the left ventricle was 40mm, wall thickness was 9mm for the left ventricle and 4mm for the right ventricle. A Purkinje system was represented on the endocardium. A simplified reactiondiffusion model was used to obtain the activation sequence. Action potential shape was taken from [3] for each layer, the same shape being used for both left and right ventricles. The ventricles were paced in the middle of the left septal endocardium, on the anterior endocardium of the left ventricle and on the anterior endocardium of the right ventricle. A 3D color activation map was constructed and the conduction parameters were adjusted until activation was visually similar to that described in [4]. The ventricles were placed in a sphere of 192 electrodes. The volume conductor was considered to be homogenous and isotropic. The simulated ECGs on the electrodes were computed at every 5ms using the MillerGesselowitz method [5] with 576 regions of the myocardium. Three series of simulations were run: with displacements of the ventricles inside the spherical system, with rotations of the spherical system and with variations of the radius of the spherical system. From each simulated ECG we computed an autocorrelation map. One map was taken as reference (figure 2) and the correlation coefficient between it and each of the others was calculated.
Figure 2. Simulated autocorrelation map in the reference recording. Time is on both x and y, representing the same cardiac cycle. Each point on the map represents, by the intensity of grey, the correlation coefficient between instantaneous potentials at the instants represented by the coordinates of the point. RESULTS
The correlation coefficients between the reference
autocorrelation map and other maps are shown in table I. When the
electrode sphere radius was 50mm, the minimal distance between an
electrode and a simulation element was 2.8mm.
TABLE I
DISCUSSIONAs different lead placements resulted in very similar autocorrelation maps, these may be considered to be influenced only by phenomena taking place in the myocardium and not by the volume conductor around the heart. With 192 electrodes this assumption is no longer valid if the electrode system is closer than 5mm to the epicardium. Consequently, indices which are computed only on the basis of autocorrelation maps, such as the similarity index [6] which is obtained by singular value decomposition of the correlation matrix of the repolarization map or such as the deviation indices [7], as computed from the body surface, should reflect only properties of the ECG source and not of the thorax, at least when refering to the interindividual variability of the human thorax. Autocorrelation maps may also find a use in comparing results from computer models involving only the simulation of the myocardium and not of the thorax with autocorrelation maps from body surface ECG maps. A limitation of the autocorrelation map is that it does not contain all information from the ECG sourcefor example it ignores the general amplitude. REFERENCES[1] R. Gulrajani R, F.A. Roberge, G.E. Mailloux, ``The Forward Problem of Electrocardiography.'' in P.W. Macfarlane, T.D. Veitch Lawrie eds, Comprehensive Electrocardiology: Theory and practice in health and disease, Pergamon Press, Oxford, 1989, p 202. [2] J.A. Abildskov, M.J. Burgess, R.L. Lux, R. Wyatt, M. Vincent, ``The expression of normal ventricular repolarization in the body surface distribution of T potentials,'' Circulation, vol. 54, pp. 901906, 1986. [3] D.W. Liu, G.A. Gintant, C. Antzelevitch, ``Ionic bases for electrophysiological distinctions among epicardial, midmyocardial and endocardial myocytes from the free wall of the canine left ventricle,'' Circ Res vol. 72, pp. 671687, 1993. [4] D. Durrer, ``Electrical aspects of human cardiac activity: A clinicalphysiological approach to excitation and stimulation,'' Cardiovasc Res vol. 2, 1968. [5] W.T. Miller, D.B. Gesselowitz, ``Simulation studies of the electrocardiogram. I. The normal heart,'' Circ Res, pp. 301315, 1978 [6] L. De Ambroggi, E. Aime, C. Ceriotti, M. Rovida, S. Negroni, ``Mapping of ventricular repolarization potentials in patients with arrhythmogenic right ventricular dysplasia: principal component analysis of the STT waves,'' Circulation, vol. 96, pp. 43144318, 1997. [7] A.D. Corlan, L.De Ambroggi, ``New quantitative methods of ventricular repolarization analysis in patients with left ventricular hypertrophy,'' Ital Heart J, vol. 1, pp. 542548, 2000.
