17.1 MOVING DIPOLE
We have noted that the source associated with cardiac activation is a double layer, which lies at the activation surface. This double layer can be approximated by a single resultant dipole. As the activation front in the ventricular wall progresses, the dipole which is at the center of gravity of the cover that closes the cup-like activation front, also moves. Consequently, the location of the equivalent electric dipole of the heart tracks this movement. However, if there is more than one simultaneous activation wave, this movement will be a complex function of the movement of the individual resultant dipoles. When one is trying to develop an improved model for the cardiac electric generator, the moving dipole is a logical target of interest.
17.2 MULTIPLE DIPOLE
The first suggestion for a multiple dipole model of the heart was made by E. J. Fischmann and M. R. Barber (1963). Based on this idea Ronald Selvester constructed a computer model consisting of 20 dipoles (Selvester, Collier, and Pearson, 1965). In this first model the effect of the thorax boundary and internal inhomogeneities were omitted. Selvester later constructed another model in which these effects were included (Selvester et al., 1966; see Figure 17.1).
R. M. Arthur conducted experiments to evaluate the moving dipole (Arthur et al., 1971). In these experiments he used a finite homogeneous model for the torso. It appeared that the path of the moving electric center of the cardiac activation is within the heart border throughout the cardiac cycle, in the atria during the P-wave and in the ventricles during the QRS- and T-waves.
Additional insight into the moving dipole model was gained through more recent work by Pierre Savard and colleagues (Savard et al., 1980). These investigators used an animal model so that the computed trajectory could be compared with actual intramural cardiac data. They obtained their best results when there was only a single confined activation surface, a result that is not unexpected. For this reason, some recent investigators have been examining a two moving dipole model.
J. H. Holt and his colleagues formulated a model consisting of 12 dipoles, whose locations and directions in the myocardium were fixed (Holt et al., 1969a). To evaluate these dipoles, he recorded ECG signals from an 126-electrode array on the surface of the thorax. The number of the electrodes was intentionally selected to be an order of magnitude larger than the number of variables in the multiple-dipole model. This step provided an opportunity to improve accuracy based on the redundancy, and could compensate for missing signals and for the presence of noise (Lynn et al., 1967)..
Fig. 17.1 Multiple-dipole model of Selvester.
(17.1)
(17.2)
(17.3)
where FN = false negatives FP = false positives TN = true negatives TP = true positives The investigation of Holt, based on the multiple dipole model, gave remarkably good results (Holt et al., 1969b,c). In the diagnosis of hypertrophy the diagnostic performance was about 90%. However, for the diagnosis of myocardial infarction the Holt et al. method gave a diagnostic performance of about 80%. Thus, in spite of being much more sophisticated, it did not achieve better results than the simpler conventional approaches.
Table 17.1 summarizes the volume source and volume conductor models used as the basis for various ECG systems and ECG research. It would be natural to select the most accurate model for the volume source as well as for the volume conductor when trying to solve the inverse problem most accurately. Hence the choice of modeling approaches should be located on the right side and on one of the lowest rows in Table 17.1.
In Section 7.5.4, it was noted that any model should have good correspondence with the physiological preparation it represents, to have clinical importance. Application of this principle would lead to the choice of the multiple dipole model, since it simulates each region of the myocardium.
The components of the multipole model are orthogonal and can be shown to have a unique solution; however, it is difficult to conceptualize the physiological meaning of this solution. On the other hand, one can show that the evaluation of a multiple dipole model beyond three or four dipoles becomes very sensitive to noise and errors in geometry. The problem is ill-defined. Furthermore, the interpretation of an inverse dipole in terms of underlying cellular behavior is unclear and probably also not unique. Fundamentally, the inverse problem in regard to intramural sources is not unique; this is, in a nutshell, the underlying problem of the inverse solution in ECG. For this reason, it is evident that the single dipole model remains central in clinical electrocardiology.
In recent years a number of sophisticated mathematical techniques have been applied to the inverse problem in electrocardiography. These now concentrate data from lead systems composed of large numbers of electrodes (100-200). In addition, the goal, rather than a search for intramural information, is limited to a determination of epicardial surface potentials. In principle, these are uniquely determined by the body surface potentials, and they additionally provide enhanced regional information. The various approaches utilize different ways to stabilize what is an ill-conditioned problem (involving inversion of ill-conditioned matrices). Such methods depend on a priori physiological constraints such as the outward propagation of activity or the spectral properties and the amplitude of the noise, smoothness of potential distributions, or smoothness of their gradients/Laplacians.
The reader is referred to three publications that review and summarize the current status of inverse electrocardiography, namely Pilkington and Plonsey (1982), Gulrajani (1988; 1989), and Rudy and Messinger-Rapport (1988).
