A Fast Method for Forward Computation of Multiple-shell Spherical Head Models

Using a combination of 3 suitably located dipoles in a homogeneous sphere, the scalp potential due to a dipole source in a 4-shell spherical head model can be approximated with a high degree of precision and a more than 30-fold increase in computing speed. Magnitudes and locations of the 3 equivalent dipoles can be fitted in a homogeneous sphere to data generated from a source at one location in a 4-shell head model. The resulting parameters are used to compute scalp potentials for sources at other locations and orientations. Residual variance measures showed close agreement between the new approximation and a standard 4-shell computation method. Further tests of the method used scalp data from 500 randomly selected pairs of sources generated by the standard 4-shell computation and fitted using, for forward computations, the new approximation and the single-shell Ary-corrected head model. Errors with the new approximation were marginally larger than with the standard computation, but sources were located within 0.5 mm and 0.6 degrees of the original position in 99% of the fits. 99% error limits for the Ary model were up to 18 mm and 25 degrees and depended on the head model parameters.