NUMERICAL-CALCULATION OF THE POTENTIAL DISTRIBUTION DUE TO DIPOLE SOURCES IN A SPHERICAL MODEL OF THE HEAD

A three-dimensional spherical model of the head was investigated numer ically. The model consists of four conductive layers representing the scalp, the skull, the cerebrospinal fluid, and the cortex with a dipol e current source. The potential created by the dipole was calculated u sing quasistatic formulation and a linear medium. The volume conductio n equation was discretized by the finite volume method to ensure the c onservation of fluxes and efficient solution method. The large set of algebraic equations for the electric potential was solved iteratively by the successive over relaxation method. The new formulation of the v olume conduction problem was validated by comparing the numerical resu lts with two analytical solutions. The first test-case considers a hom ogeneous spherical model with a dipole in the center. The potential on the outer surface, as well as within the volume conductor, was calcul ated and very good agreement was obtained with the analytical solution . In the second test-case, the scalp potential due to a radially orien ted eccentric dipole in a four concentric spheres model was compared w ith an analytic solution, It was found that a grid of 90 x 90 x 90 vol ume elements yielded accurate results on the scalp surface with errors on the order of 1%. The present numerical model can be extended to ge neral cases with any volume conductor shape or with any distribution o r orientation of the current dipoles. Compared to other numerical meth ods, this approach offers enhanced accuracy for given computational re sources (both in CPU time and memory), The gain might be more than one order of magnitude, allowing simulation with considerably larger mesh es. (C) 1994 Academic Press, Inc.