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

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.