SPLINE LAPLACIAN ESTIMATE OF EEG POTENTIALS OVER A REALISTIC MAGNETICRESONANCE-CONSTRUCTED SCALP SURFACE MODEL

This paper presents a realistic Laplacian (RL) estimator based on a te nsorial formulation of the surface Laplacian (SL) that uses the 2-D th in plate spline function to obtain a mathematical description of a rea listic scalp surface. Because of this tensorial formulation, the RL do es not need an orthogonal reference frame placed on the realistic scal p surface. In simulation experiments the RL was estimated with an incr easing number of ''electrodes'' (up to 256) on a mathematical scalp mo del, the analytic Laplacian being used as a reference. Second and thir d order spherical spline Laplacian estimates were examined for compari son. Noise of increasing magnitude and spatial frequency was added to the simulated potential distributions. Movement-related potentials and somatosensory evoked potentials sampled with 128 electrodes were used to estimate the RL on a realistically shaped, MR-constructed model of the subject's scalp surface. The RL was also estimated on a mathemati cal spherical scalp model computed from the real scalp surface. Simula tion experiments showed that the performances of the RL estimator were similar to those of the second and third order spherical spline Lapla cians. Furthermore, the information content of scalp-recorded potentia ls was clearly better when the RL estimator computed the SL of the pot ential on an MR-constructed scalp surface model.