The Complete Inversion Formulation For EEG and MEG

Researchers: Thanasis Fokas, Parham Hashemzadeh

The medical significance of Electroencephalography (EEG), and Magneto-Electroencephalography is well established. EEG and MEG are considered two of the most important imaging techniques for real time brain imaging. In order to generate images of the brain activation using either EEG or MEG, it is necessary to analyse certain mathematical inverse problems. Indeed, the neuronal current (the so called primary current) creates an electric potential which in EEG is measured on the scalp, as well as a magnetic field which in MEG is measured outside the head. The associated inverse problems for EEG and MEG involve the estimation of the neuronal current from the knowledge of the above electric potential and magnetic field, respectively.

We have recently derived the complete inversion model for both EEG and MEG imaging. The key findings in these model are that the time-series data (electric potential and the magnetic field) are only affected by the values of the relevant unknown components of the neuronal current (to be estimated) on the boundary of the cerebrum. This in turn implies that this problem is severely ill-posed. We have already submitted a paper to the IEEE Transactions on Biomedical Engineering with the title \EEG for current with two dimensional support”, see Dassios et al (submitted). Furthermore, with regards to our recent finding, we are in the process of submitting this crucial finding to the relevant journal as well presenting it at various conferences, workshops and meetings.

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