The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem--a simulation study

In this paper we propose a new method, using the principles of electrical impedance tomography (EIT), to correct for the systematic errors in the inverse problem (IP) of electroencephalography (EEG) that arise from the wrong specification of the electrical conductivities of the head compartments. By injecting known currents into pairs of electrodes and measuring the resulting potential differences recorded from the other electrodes, the equivalent conductivities of brain (sigma3), skull (sigma2) and scalp (sigma1) can be estimated. Since the geometry of the head is assumed to be known, the electrical conductivities remain as the only unknown parameters to be estimated. These conductivities can then be used in the inverse problem of EEG. The simulations performed in this study, using a three-layer sphere to model the head, prove the feasibility of the method, theoretically. Even in the presence of simulated noise with a value of signal-to-noise ratio (SNR) equal to 10, estimations of the electrical conductivities within 5% of the true values were obtained. Simulations showed the existence of a strong relation between errors in the skull thickness and the EIT estimated conductivities. If the skull thickness is wrongly specified, for example overestimated by a factor of two, the conductivity determined by EIT is also overestimated by a factor of two. Simulations showed that this compensation effect also works in the inverse problem of EEG. Application of the proposed method reduces systematic errors in the dipole localization, up to an amount of 1 cm. However it proved to be ineffective to decrease the dipole strength error.