Accuracy of Dipole Localization with a Spherical Homogeneous Model

Dipole localization methods (DLM\´s) with a spherical, homogeneous, isotropic model were applied to the problem of locating and characterizing simulated dipole sources of the brainstem acoustic evoked response (BAER) in cats. Dipole source parameters considered were chosen to be consistent with measurements of gross potential within the brainstem during the BAER. The steepest ascent method was used to solve the least-squares minimization problem on a set of noiseperturbed surface voltages to obtain parameters of a single assumed dipole source. The magnitudes of errors in dipole postion and in dipole moment vectors were calculated for two surface voltage location sets, two assumed dipole source locations, and a range of surface signal-to-noise ratios. An approximate analytic approach to the simulation results attributed DLM errors to an apparent "noise dipole" calculated as the dipole term in the multipole expansion of the added surface noise. The standard deviation of the "noise dipole" magnitude was directly proportional to the standard deviation of surface noise voltage and inversely proportional to the root of the number of surface voltages. This analytic result was in general agreement with the mean of the dipole moment parameter errors in the simulation study. It was found that recalculation of the surface voltage set from the solution dipole of the simulation problem or from the "noise dipole" of the analytic treatment resulted in an improvement of signal-to-noise ratio at the surface.