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Solving the forward problem of electrical source imaging by applying the reciprocal approach and the finite difference method

Ahi, Sercan Taha
One of the goals of Electroencephalography (EEG) is to correctly localize brain activities by the help of voltage measurements taken on scalp. However, due to computational difficulties of the problem and technological limitations, the accuracy level of the activity localization is not perfect and should be improved. To increase accuracy level of the solution, realistic, i.e. patient dependent, head models should be created. Such head models are created via assigning realistic conductivity values of head tissues onto realistic tissue positions. This study initially focuses on obtaining patient dependent spatial information from T1-weighted Magnetic Resonance (MR) head images. Existing segmentation algorithms are modified according to our needs for classifying eye tissues, white matter, gray matter, cerebrospinal fluid, skull and scalp from volumetric MR head images. Determination of patient dependent conductivity values, on the other hand, is not considered as a part of this study, and isotropic conductivity values anticipated in literature are assigned to each segmented MR-voxel accordingly. Upon completion of the tissue classification, forward problem of EEG is solved using the Finite Difference (FD) method employing a realistic head model. Utilization of the FD method aims to lower computational complexity and to simplify the process of mesh creation for brain, which has a very complex boundary. Accuracy of the employed numerical method is investigated both on Electrical Impedance Tomography (EIT) and EEG forward problems, for which analytical solutions are available. The purpose of EIT forward problem integration into this study is to evaluate reciprocal solution of the EEG forward problem.