Research On The Positive And Negative Problems Of EEG And MEG Under Ellipsoidal Brain Model And Its Numerical Simulation

As the medical imaging technology has been developing swiftly,the brain science research has come to the frontier of the world.EEG and MEG are two important technology of medical imaging for studying neural physiology processes in the human working brain.They both have advantages of much higher temporal resolution and non-invasive measurement,which is the future trend of development in imaging technology.In this paper we study the mathematical problems in EEG and MEG,that is,EEG/MEG forward problem and inverse problem.The forward problems of EEG/MEG respectively computes the scalp potentials and external magnetic fields from the given current source.And the inverse problems of EEG /MEG determine the current source from the measurement of scalp potentials and external magnetic fields,respectively.Here we present the integral formula of EEG/MEG field based on the quasi-static approximation of the Maxwell’ s equations.We approximate the human head using rotation ellipsoid and general ellipsoid.We choose two source models : current dipole source and distributive current source.Firstly,we derive the analytical formulae for potential and magnetic field in current dipole source model by combining EEG and MEG,by which we could uniquely determine the inner dipole source from external measurement of potentials and magnetic fields.For the distributive current source we obtained the analytic relationship between magnetic potential and current by decomposing the primary neural current in sphere coordinate system in rotation ellipsoid head model.Hence we see that using non-spherical head model can obtain much more information of tangential current source than using sphere head model from the measurement of external magnetic.Based on decomposition of algebra in ellipsoidal coordinate system,we present the matrix form of MEG kernels in general ellipsoid head model.This formulation decouples not only the dipole moment and the observation point,but also the source location and the observation point,which can reduce the complexity of solving solution and benefits to the solution of inverse problem.At last,we perform the numerical simulations in two kinds of ellipsoid head models,so that the laws of change of external magnetic field versus the parameters of dipole are investigated.This article are divided into the four parts:Chapter1: Introduction Chapter2: The basic theory and head model of electrical magnetic activity in the brain Chapter3: The analytic relationship between the magnetic field and primary current in different ellipsoid head models Chapter4: The simulation of MEG and conclusion...