An analytic method to determine the effect of source modeling errors on the apparent location and direction of biological sources

Evoked potentials (EPs) and electroencephalograms (EEGs) can be used to determine the location, the direction, and strength of electrical brain activity. For this purpose mathematical models are used which describe regions in the head with different conductivity. In most models, the sources are described by mathematical (current) point dipoles. However, EPs and EEGs are generated with more extensive cortical areas. In this study an analytic method is described to calculate the effect of source extension on the potential distribution measured at the scalp and also on the difference between the location of the extended source and the location of the equivalent point dipole. General formulas are derived which express in spherical harmonics the potential distribution that results from a circularly symmetric extended source. It is shown that for sources that obey specific symmetries the influence of source extension on the potential distribution is a fourth-order effect in the distance between electrode and the origin (the middle point of the head), and a second-order effect in the extension. It is also shown that for such sources the error in localization (i.e., the distance between the position of the equivalent dipole and the center of the extended source) is zero when Geselowitz’s method IEEE Trans. Biomed. Eng. BME-12, 164 (1965) is used. Because in volume conductor models the relation between source and potential is given by Poisson’s equation, it is suggested by the authors that the results of the present study may be extended to applications in other fields of physics as well.