Fast skull conductivity estimation using Boundary Element Method

Inter subject variability of skull conductivity highly constraints the possibility to use EEG (Electro Encephalography) amplitude parameters as a biomarker to compare the amount neural activity between different patients. The same inter subject variability limits the accuracy by which it is possible to localize the current sources underlying EEG using forward models with standardized parameters for the conductivity of brain, skull and skin. To solve this problem, it has been proposed to estimate conductivity parameters in vivo by analyzing the potentials generated by precisely known electric currents, injected into different pairs of EEG electrodes. Here the efficiency of this conductivity parameter estimation problem is analyzed in the context of boundary element method (BEM). The geometries of brain, skull and skin compartments are fixed and given by triangular meshes, whereas the conductivity parameters are varied in order to predict the observed potentials. Using the Woodbury update formula, a method is here proposed to quickly update the BEM matrix, for new combinations of conductivity parameters. In a simulation study, using a BEM model it is shown that that the gain in speed amounts to factor of 20, compared to the direct computations. This gain in speed is achieved without compromising the numerical accuracy. Therefore, we foresee that the proposed algorithm will play an important role in future EEG systems where patient specific head models are constructed in the EEG preparation phase, to enable calibrated EEG and accurate source localization.