Numerical Simulation Of EEG Positive Problem Of Two Dipole Sources And Research On MEG Inverse Problem

With the development of medical imaging technology, brain science research and diag-nosis of clinical have been entering the new era during the recent three decades. As two complementary medical imaging technologies, Electroencephalography (EEG) and Magne-toencephalography (MEG), with its high resolution and non-invasive features, which are in line with trend of the development of brain medical diagnosis technology, have become the important research areas which attract lots of the multidisciplinary researchers from all over the worldThis paper studies the mathematical problems in EEG/MEG imaging techniques, namely the forward problem and inverse problem. The inverse problem of EEG, MEG needs a great number of numerical simulations of the forward problem. So the numerical calculation of the forward EEG/MEG problem has a great guiding significance to the in-verse problem.In this article, firstly, we deduce the integral equations of the fields of EEG and MEG based on the quasi steady state of Maxwell’s equations, and establish the numerical form of calculating scalp electric potential for a single current dipole source. Secondly, we de-velop the approximate analytic expression of the scalp electric potential in the view of two current dipoles.Thirdly, we carry out the numerical simulations for a single electric dipole source and t-wo electric dipole sources in the sphere model. In the case of simulations for one current source, we get the potential maps versus the position parameter of electrodes for different dipole locations, which shows that the performances of the potential maps are similar cor-responding to different electric dipole location, but potential peak values are different. For the two dipole sources, we simulate potentials in the following three cases:1)Under the condition of each fixed source parameters, we respectively investigate potential versus the rotation angle on the same latitude, and versus the elevation on the same meridian. The results show that:Corresponding to different lines of latitude and longitude, the potential performance are similar. The potential values are in difference. But the elevation angle has certain effect on the potential. This means that there is a difference in the potentials between the upper hemisphere and lower hemisphere.2) Under the condition of fixed elec-trode position parameters, the rotation angle and elevation angle, respectively, we calculate the potential versus another electrode position parameter for each source parameters. The results showed that:the maps are similar and potential peak values change regularly corre-sponding to the same source parameters.3)We compare scalp potential with the potential at infinity under the same fixed parameters. The results showed that:Corresponding to each of the fixed parameters, these two kinds of potentials are subject to the similar rules.At last, we derive an approximate analytic form of the outside magnetic field for the ellipsoid model and dipole source model, which simplifying the numerical solution of the MEG inverse problem by decomposing the parameters of dipole moment, dipole position and sensor position.