Insidious errors in dipole localization parameters at a single time-point due to model misspecification of number of shells

Abstract

Insidi3us errors (unexpected and difficult-to-detect under usual conditions) were found using a single time-point dipole localization method, when two dipoles were simultaneously active and there was misspecification of the number of shells (usually intended to mimic the conductivity differences of the brain, skull, and scalp). The errors involved all dipole parameters (i.e., location, orientation, and magnitude). Potentials at 65 “electrode” locations on the surface of a 3-shell sphere were computed for dipoles of known location, orientation, and magnitude. These “maps” were then used to compute the best-least-squares-fit of the surface potentials based upon dipole parameters in a 1-shell sphere when either one or two dipoles were active. The dipole parameters were often significantly different when computed with two equal-magnitude dipoles active, compared with only one dipole, with location errors of 0–36 mm, orientation errors of 0–63°, and magnitude errors of 2–98%. When the two dipole magnitudes were not the same, the errors in the computed dipole parameters were even larger. All these errors occurred when the LSE (least-square-error) was small and at or near minimum. Moreover, location errors increased as LSE decreased over iterations. These errors generally occur because the fitted dipole parameters under different potential maps do not obey the superposition law when there is shell model misspecification, which is also the reason that presently used “correction” methods cannot satisfactorily remove these errors from the analyses. This problem must be dealt with when analyzing evoked response “maps” from simultaneously active generators, if correspondence to anatomy and physiology is desired.