MEG Study, EEG Forward Problem Of Numerical Simulation And Its Inverse Problem

At present, EEG (Electroencephalography)and MEG (Magnetoenphalography)have become important technical means in investigation of the brain function andclinical diagnosis. They have significant research value to the location of dipole. In theinverse problem of EEG/MEG, a lot calculation of forward problem is indispensable.Seeking the scalp potentials V from position and direction of neural current sourcesin the brain is called the EEG forward problem. Distribution of known neural currentsources to look for external magnetic field B is called the MEG forward problem.Conversely, reconstructing neural current sources from distribution of eachmeasurement data scalp potentials V and external magnetic field B are EEG inverseproblem and MEG inverse problem.We know that the human body tissues such as muscle and brain magneticmedium will produce weak current, while the changeable electric field with time candevelop biological magnetic field from the knowledge of brain electrical physiological.The scalp potentials V and external magnetic field B can be measured by EEG/MEG,respectively. In order to establish and analyze the accuracy of measuring data of EEG/MEG, we study the spherical geometry model and use the BEM of weightedresiduals (collocation method) to establish the fast and effective algorithm for theEEG/MEG forward problem simply. We see that this kind of head model can get theanalytic solutions mathematically. It is helpful to precision test for various numericalmethod, as well as the research value and application background. At the same time,the simulation results show that the computational efficiency and accuracy of thismethod comparing with the boundary element method, finite difference method orthe finite element method are obviously improved.This paper is divided into five chapters. In chapter1, we make a simpleintroduction of the research progress about EEG/MEG, measurement equipment andseveral neuron imaging technologies. In chapter2, we induce the field equations ofEEG/MEG forward problem under the condition of quasi static Maxwell equations.We also show the dipole source model and head model which we used to solve the forward problem and inverse problem in this paper. In chapter3, we use BEMWeighted Residual (collocation method) to establish the simple fast and effectivealgorithm about EEG/MEG forward problem. In chapter4, on the one hand, we usefour kinds of basis functions and perform the numerical simulation for EEG/MEGforward problem. We compare and analyze the scalp potentials V and externalmagnetic field B with the change of different the dipole source positions. Numericalresults describe that the change of dipole parameters have effect on the solutions ofEEG/MEG forward problem. On the other hand, we compare the simulation resultsof the scalp potentials with the analytical solution. Numerical results show BEM ofWeighted Residuals method is reliable and efficiency. In chapter5, we study theinverse problem of current source localization in non-spherical model. The resultsshow that under the constraints some of the model condition, it is possible to solveof determining the source current distribution uniquely.