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Bioelectric source analysis in the human brain from scalpelectroencephalography (EEG) signals is sensitive to the conductivity of thedifferent head tissues. Conductivity values are subject dependent, sonon-invasive methods for conductivity estimation are necessary to fine tune theEEG models. To do so, the EEG forward problem solution (so-called lead fieldmatrix) must be computed for a large number of conductivity configurations.Computing one lead field requires a matrix inversion which is computationallyintensive for realistic head models. Thus, the required time for computing alarge number of lead fields can become impractical. In this work, we propose toapproximate the lead field matrix for a set of conductivity configurations,using the exact solution only for a small set of basis points in theconductivity space. Our approach accelerates the computing time, whilecontrolling the approximation error. Our method is tested for brain and skullconductivity estimation , with simulated and measured EEG data, correspondingto evoked somato-sensory potentials. This test demonstrates that the usedapproximation does not introduce any bias and runs significantly faster than ifexact lead field were to be computed.

Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation