F. Babiloni et al., SPLINE LAPLACIAN ESTIMATE OF EEG POTENTIALS OVER A REALISTIC MAGNETICRESONANCE-CONSTRUCTED SCALP SURFACE MODEL, Electroencephalography and clinical neurophysiology, 98(4), 1996, pp. 363-373
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.