An efficient algorithm for computing multishell spherical volume conductor models in EEG dipole source localization

Computationally localizing electrical current sources of the electroencephalographic signal requires a volume conductor model which relates theoretical scalp potentials to the dipolar source located within the modeled brain, The commonly used multishell spherical model provides this source-potential relationship using a sum of infinite series whose computation is difficult, This paper provides a closed-form approximation to this sum based on an optimal fitting to the weights of the Legendre polynomials, The second-order (third-order) approximation algorithm, implemented by a provided C-routine; requires only 100 (140) floating point operations to compute a single scalp potential in response to an arbitrary current dipole located within a four-shell spherical volume conductor model. This cost of computation represents only 6.3% (8.9%) of that required by the direct method, The relative mean square error, measured by using 20 000 random dipoles distributed within the modeled brain, is only 0.29% (0.066%).