Practical Identification of Dipolar Sources in Human Brain

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In various fields of science and engineering, many problems can be considered as inverse problems for partial differential equations. One of such problems is to identify the electrical activity in the human brain from observation data of electric and magnetic fields called ElectroEncephaloGram and Magneto-EncephaloGram. Many researchers assume spherically symmetric conductor model for the human head and dipole model for the electrical activity of human brain. Our problem is to identify locations, moments, and number of dipolar sources in the human brain from observations of electric and magnetic fields outside of the human head.Before this project, we have already proposed two identification methods for a quasi-static case using magnetic observations. In this project, we extend our investigations of such problems. The main results of our project are shown as follows :1. Improvement of our method which is mentioned in our previous research. Without using a-priori information, improved method gives reasonable results with these error estimates.2. By using electric and magnetic observations, we can obtain all components of dipolar sources.3. Extension of governing equation such that Poisson equation is extended to Helmholtz equation or time harmonic Maxwell equation.4. Uniqueness and convergence of numerical solution obtained by Charge Simulation Method.The results are shown in references, and we are preparing two papers at the present time. Further discussions are needed for the analytical and numerical stability of identified results.