  Inter subject variability of the electrical conductivity of brain, skull and
skin strongly limits the accuracy by which current sources underlying
electro-encephalography (EEG) can be localized in the brain. This inter subject
variability also constrains the possibility to use EEG amplitude parameters as
a biomarker to compare the amount of neural activity between different
patients. To overcome this problem, one may estimate conductivity parameters in
vivo by analyzing the potentials generated by known electric currents, injected
into different pairs of EEG electrodes. At present, routine application of this
approach is hampered by the computational complexity of the conductivity
estimation problem. Here we analyze the efficiency of this conductivity
parameter estimation problem in the context of boundary element method (BEM).
We assume geometries of brain, skull and skin compartments are fixed triangular
meshes whereas conductivity parameters are treated as unknowns. We show that a
Woodbury update algorithm can be used to obtain a fast conductivity update
scheme for both the single and double layer BEM formalism. This algorithm
yields a speed gain up to a factor of 20 when compared to the direct
computations, apart from at most 50% of additional computation time in the
initialization phase of the algorithm. We also derive novel analytically closed
expressions for the efficient and accurate computation of BEM matrix elements.
Finally, we discuss which further steps are needed to equip future EEG systems
with software devices that enable subject tailored head models for calibrated
EEG and accurate source localization, on a routine basis.
