Spline generated surface Laplacian estimates for improving spatial resolution in electroencephalography
Description
Methods to estimate the surface Laplacian from scalp potentials are developed for improving spatial resolution in electroencephalography. This dissertation addresses two issues involved with estimating the surface Laplacian: (1) head geometry models; and (2) interpolation of the surface potential distribution. Theoretical and human data were used to validate the methods developed The surface Laplacian is defined as the second spatial derivative of the scalp potential, a direct measure of the radial current density flowing from the brain through the skull to the scalp. Previous research has shown the surface Laplacian to be a better estimator of underlying brain electrical activity. However, no apparent comprehensive research had been performed to develop and validate optimal methods for estimating the surface Laplacian, 'optimal' being defined in the practical sense as suitable interpolation methods based on present knowledge of head geometry and volume conduction properties Quantitative measurements of the upper surface of the human head show an ellipsoid surface to be an excellent geometric model of the head. RMS errors and maximum residuals between the digitized head and best fit ellipsoid are below the standard scalp electrode size of one cm. A three-variable natural cubic spline was found to be the apparent best means of obtaining an accurate estimate of the scalp surface potential. Other interpolation methods and splines have inherent characteristics which can result in unrealistic functions, or are limited to one surface geometry. The surface Laplacian estimate has been derived for the sphere and ellipsoid for the case of three-variable spline interpolation The algorithms were validated with the three-concentric sphere model of the head and two types of evoked potential tests, somatosensory and auditory evoked response (cognitive) potentials. The spline generated surface Laplacian topographic maps of theoretical data provided better spatial resolution than potential based maps. Topographic maps of human data were consistently repeatable between trials and subjects. The results agree with published literature and, additionally, suggest new regions of brain electrical activity not previously cited in the published literature. The results suggest that the surface Laplacian methods developed here provide accurate estimates of brain electrical activity