Different Basal Eeg, Meg Is Numerical Solution For Comparison

EEG(Electroencephalography) and MEG(Magnetoenphalography) are two kinds of medicine imaging technologies for investigating neuronal activity in the living human brain. They have been widely used in diagnosis with epilepsy and Parkinsons diseases for harmless and noninvasive. EEG and MEG have high temporal resolutions, so they can reflect the real-time situation of the working brain. The EEG(MEG) forward problem computes the scalp potentials(external magnetic field ) from the current sources in the brain. The EEG(MEG) inverse problem localizes the current sources in brain from measuring the scalp potentials(external magnetic field), they are the basic methods to research the functional working in brain. Because the localization of current source needs a large number of EEG/MEG forward problems calculation, it is important to compute the EEG/MEG forward problem efficiently. The main methods which solve the EEG/MEG forward problem are Boundary Element Method(BEM), Lead Field Approach(LFA) and Finite Element Method(FEM). The BEM is widely used because it can reduce both the dimensionality and the number of unknowns.In most previous work, the direct Boundary Element Method is used. But this method has the defect of low computing efficiency, high degree of freedom and the inflexibility of computer programs. The constant or linear basis functions are often applied in BEM.The comparison of computational accuracy between constant basis and linear function basis was made.But their computational efficiency is not shown. In this paper, we develop the computing formulation of Least Square of Point(PLS) based on weighted residual BEM which has advantages of high computing efficiency, low degree of freedom and the flexibility of computer programs comparing with the general methods such as BEM, LFA, FEM. We conduct simulations in central spherical head model by using Point Least Squares.We compute the scalp potentials and external magnetic fields for different dipole source parameters in three kinds of basis functions, constant basis, bilinear basis and trigonometric basis, respectively,aiming at comparing the performances of potentials and magnetic fields for different dipole parameters and studying the effects of the different kinds of basis functions on the computational efficiency and accuracy of the EEG/MEG forward solution.The results show that the performances of potentials are similar but the magnitude and location of the peak value of potentials are significantly different.The trigonometric basis function is the best among three kinds of basis functions in computational efficiency and accuracy.This paper is organized as follows. In chapter 1, we make a simple introduction of the research history of EEG/MEG, the electrophysiology basis, the measuring principle and the medicine imaging technologies. In chapter 2, we induce the quasistatic approximation of the Maxwells equation and Biot-Savart law. We also show the field equation of EEG/MEG forward problem and the head model which we used in this paper. In chapter 3, we establish the formula of EEG/MEG forward problem by using base on the Point Least Squares(PLS) of BEM based on Weighted Residuals. In chapter 4, we perform the numerical simulations in the different kinds of basis functions (constant basis, bilinear basis, trigonometric basis), analyze the simulation results and sum up the effects of different orientation, location of dipole source and the different basis functions on the forward EEG/MEG problems.