The Computation Of EEG/MEG Forward Problem In The Ellipsoidal Head Model

EEG (electroencephalography) and MEG (magnetoencephalography) are two important brainimaging techniques that are used in researches of brain function and clinical diagnosis. Comparedwith other imaging, such as MRI, PET ect., EEG/MEG have the advantages of high temporal res-olutions and noninvasiveness, which can trail physiological changes at the speed of the order of10ms and can be used to study the dynamics of human brain function. EEG/MEG are interdisci-plinary research area between biomedicine engineering, superconducting technique, mathematics,physics, computer science and so on, which is divided as theory, instruments and applications.In order to quantitatively study their measurement data, theoretically, we have to deal withbioelectromagnetics inverse problem,that is, estimate the neuronal current source in the brain byexternal measurements of electric potentials and magnetic fields. Therefore, mathematical model,method and numerical computation is indispensable.In EEG/MEG study, electric dipole are commonly used as an approximation of neuronal cur-rent source in a small area. In this paper, under the assumption of quasi-static Maxwell Equations,we use dipole source model to study the computation of EEG/MEG forward problem which isessential to the inverse problem of dipole source localization. EEG/MEG forward problems arerespectively to compute the scalp potential and external magnetic field with given current source.The accurate localization of dipole source depends on the head model and mathematical methodwe used. Spherical head models are widely applied in the previous work. However, some studieshave shown that the use of the spherical approximation to head shape has some key drawbacksin the research of dipole source localization. The nonspherical head models are in needed inbiomedicine community. Recently, some progress has been made. The realistic head shape mod-els which are numerically constructed based on the image of MRI come into use. But the excessivecomputing made it impractical to inverse problem and this model makes theoretical analysis incon-venient. In this paper, we use analytic ellipsoidal geometry as an approximation of human head.The numerical methods for computing EEG/MEG forward solutions are formed based on BEM.Numerical simulations are implemented for three oriented dipole located on x-axis, y-axis and z-axis, respectively in ellipsoidal head model and sphere head model. We compared the simulationresults in these two head models and analyzed the forward solution versus dipole parameters. Thewhole paper is divided into four parts as follows:Chapter 1. IntroductionChapter 2. Basic theoryChapter 3. The method of computing EEG/MEGforward problem Chapter 4. Numerical simulationsIn Chapter 1.,we introduce the research history, instrumentation and physiological basis ofEEG/MEG techniques. In Chapter 2., under the assumption of quasi-static Maxwell equations,EEG and MEG field equations are given. In Chapter 3., The computing formulations based onBEM are respectively constructed for EEG and MEG forward problems. In Chapter 4., we imple-ment numerical simulations and test our method in ellipsoidal head model and sphere head model.In different cases of three directed dipole located on x-axis, y-axis and z-axis, we compare andanalyze the maps of potentials and magnetic fields versus dipole parameters.