Using weighted linear spatial decomposition to investigate brain activity through a set of ®xed current dipoles Christopher J. James a, b, * , Katsuhiro Kobayashi a, c , Jean Gotman a a Department of Neurology and Neurosurgery, Montreal Neurological Institute, McGill University, Montreal, Quebec, Canada b Neural Computing Research Group, Aston University, Birmingham, UK c Department of Child Neurology, Okayama University Medical School, Okayama 700-8558, Japan Accepted 29 November 1999 Abstract Objectives: We developed a method with the aim of decorrelating scalp EEG based on a set of spatial constraints. Methods: We assume that the scalp EEG can be modelled by a small number of current dipoles of ®xed location and orientation, placed at regions of interest. The algorithm is based on weighted linear spatial decomposition in order to obtain a weighted solution to the inverse problem. An EEG data matrix is ®rst weighted in favour of a single dipole in the set. The dipole moment is then calculated from the weighted EEG by the pseudo-inverse method. This is repeated for each dipole. Results: Six seizures were processed from 4 patients using the standard least-squares solution and our weighted version. The average cross-correlation between channels was calculated for each case. The ®rst method resulted in a mean drop in cross-correlation of 16.5% from that of the scalp. Our method resulted in a reduction of 34.5%. Conclusions: Our method gives a more spatially decorrelated signal in regions of interest (although it is not intended as an accurate localization tool). Subsequent analysis is more robust and less likely to be dependent on speci®c recording montages. This is more than could be obtained using a standard least-squares solution using the same model. q 2000 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Current dipole modelling; Spherical head model; Weighted linear spatial decomposition; Remontaging scalp EEG 1. Introduction Through the analysis of the electroencephalogram it is possible to develop many powerful techniques to analyze brain function. Of particular interest to many researchers is the localization of brain function. However, estimating the location and distribution of current sources within the brain using recorded scalp EEG requires the solution of an inverse problem. Due to the nature of the problem, there is no unique solution to this inverse, i.e. the problem is ill posed (Helmholtz, 1853). This means that different source con®gurations can lead to the same measured scalp poten- tials. Even increasing the number of scalp measurements will not lead to determining a unique solution. The technique of modelling the activity of a group of neurons in the cortex with a current source is not new (Bishop, 1949; Sholl, 1956; Braitenburg, 1978). Whether the head is modelled as a conductive sphere, or whether a realistically shaped conductive head model is constructed, the potentials measured at the scalp surface of both models due to such a current source can be readily calculated using standard electrostatic theory (Nunez and Katznelson, 1981). This forms the so-called forward solution. In general, such current sources can be modelled as discrete current dipoles, consisting of a few dipoles in a localized brain region, or a multiple source solution spread out over larger regions of the brain. However, the assumptions required about model order in equivalent current dipole models is a major dif®culty when attempting to solve the inverse problem (Snyder, 1991). In epilepsy monitoring, scalp EEG recordings can contain 30 or 40 EEG channels. Rather than analyzing each channel independently it would be bene®cial if we could integrate the multi-channel information meaningfully. This would have multiple bene®ts but most importantly it would allow us to (1) obtain a representation that is relatively independent of speci®c montage, as long as electrodes cover all regions, (2) decrease the number of channels that need to be processed (this is desirable because the level of correlation between channels is high with a normal montage), and (3) obtain a region-speci®c representation, Clinical Neurophysiology 111 (2000) 773±780 CLINPH 99086 1388-2457/00/$ - see front matter q 2000 Elsevier Science Ireland Ltd. All rights reserved. PII: S1388-2457(99)00316-8 www.elsevier.com/locate/clinph * Corresponding author. Neural Computing Research Group, Aston University, Aston Triangle, Birmingham B4 7ET, UK. Tel.: 144-121- 359-3611 ext 4652; fax: 144-121-333-4586. E-mail address: jamescj@aston.ac.uk (C.J. James)