The implementation of the inverse problem solution techniques for epileptic source localization

For the treatment of brain diseases such as epilepsy, determination of the locations of source/s of electrical activity in the brain is highly important. For this purpose, nowadays in addition to several functional imaging systems, which have low temporal resolutions and high spatial resolutions, Electromagnetic Source Imaging (EMSI) methods, which have high temporal resolutions, have been used that employ electromagnetic signals such as Electroencephalography (EEG) or Magnetoencephalography (MEG) measured from the head surface. In EMSI, inverse problem solutions are applied on the computer model of the head from which EEG or MEG measurements are acquired and thus the locations of sources are estimated. In this study, first a four-layer ideal head model was constructed. In this model, EEG electrodes were assumed to be positioned on an 8-cm-radius hemispherical head, and 930 dipole sources were located on the 7-cm-radius hemispherical cortex with a surface-normal orientation. For each dipole source an analytical forward solution was computed. Later, EEG inverse problem algorithms such as minimum norm (MN), weighted minimum norm (WMN), LAURA, and EPIFOCUS were implemented for different number of measurement electrodes. In addition, a similar analysis that included the investigation of the effect of truncated singular value decomposition (tSVD) method was performed with EEG data with signal-to-noise ratios at 10 dB, 20 dB, and 30 dB levels. In addition to the single dipole source localization study, both EPIFICUS and MN inverse problem algorithms were analyzed for double dipole sources. As a result, EPIFOCUS was found to be the best approach for single dipole sources with and without noise. For double source cases the performance of EPIFOCUS decreased to a relatively low level. For single dipole source analysis with noise, when the number of electrodes and noise levels increased source localization performances clearly diminished. The tSVD regularization improved the performance of the inverse algorithms for increased number of measurement electrodes.KEY WORDS: Source localization, EMSI, EEG forward-inverse problem.Advisor: Assist. Prof. Dr. Bülent YILMAZ, Başkent University, Department of Biomedical Engineering