Performances of surface Laplacian estimators: A study of simulated and real scalp potential distributions

Abstract

This paper presents a study of the performance of various local and spherical spline methods currently in use for the surface Laplacian (SL) estimate of scalp potential distributions. The SL was estimated from simulated instantaneous event-related scalp potentials generated over a three-shell spherical head model. Laplacian estimators used planar and spherical scalp models. Noise of increasing magnitude and spatial frequency was added to the potential distributions in order to simulate noise presumed to contaminate scalp-recorded event-related potentials. A comparison of noise effects on various Laplacian estimates was made for increasing number of "electrode" positions in variants of the 10-20 system. Furthermore, to evaluate the error due to the use of unrealistic scalp models, the matching between SL estimates of human scalp-recorded movement-related potentials computed on spherical and realistically-shaped MRI-constructed models of the scalp was examined. With all methods the error of the SL estimate increased proportionally with the magnitude and spatial frequency of noise. Increased number of "electrodes" up to 256 significantly reduced the error (p < 0.05). In general, the best SL estimates were computed by second and third order splines including lambda correction, the performances of the second order spline being better with more than 64 "electrodes". Compared with spline Laplacians, the best local methods provided nearly equal estimates with low spatial sampling (19 and 28 "electrodes"), as well as high spatial frequency noise. The error of the SL estimate due to unrealistic scalp model was significant, and it augmented with increased spatial sampling from 64 to 128 electrodes.

Sub-second “temporal attention” modulates alpha rhythms. A high-resolution EEG study

“…However, the present surface Laplacian estimates should be interpreted with caution. Surface Laplacian maxima could not overlie cortical sources of EEG potentials, due to the influence of tangentially oriented cortical generators [1,2]. As a consequence of the intrinsic limitations in spatial resolution, we investigated attentional effects as revealed by alpha ERD/ERS over large cortical regions of interest such as prefrontal (frontal), sensorimotor (central), and posterior parietal (parietal) areas of the two hemispheres.…”

“…Individual ERD/ERS data sets were then interpolated by a spline function [1], in order to obtain ERD/ERS data sets at theoretical 54 electrode sites of augmented 10 -20 system. These electrodes were disposed over a 3-D ''quasirealistic'' head model (i.e., approximating each ''realistic'' individual head model).…”

Human cortical EEG rhythms during long-term episodic memory task. A high-resolution EEG study of the HERA model

“…As a limitation, the cortical sources of the ERD/ERS must be inferred with caution based on the topographical mapping. Indeed, surface Laplacian maxima could not precisely overlie the corresponding cortical sources due to the influence of tangentially oriented generators (Babiloni et al, 1995(Babiloni et al, , 1996. Here, we accounted for such a limitation considering relatively wide frontal and parietal regions of interest to model the activity of underlying prefrontal and posterior parietal areas.…”

“…A spline interpolating function (Babiloni et al, 1995) determined individual ERD/ERS values at theoretical 46 sites of augmented 10-20 system. These electrodes were displaced over a 3-D head model approximating each ''realistic'' individual head model.…”

The surface Laplacian technique in EEG: Theory and methods

“…Another observation is that the columns of S λ sum to 1 (whereas the columns of L λ sum to 0), implying that the transformation (47) preserves the reference potential. In practice, the search for λ is constrained to a finite interval which typically spans several decades on a log scale (Babiloni et al, 1995). In order to facilitate interpretation and comparisons across studies, instead of thinking in terms of λ it is convenient to think in terms of a parameter DF λ that has more practical meaning.…”