Identification of Dipoles in Bioengineering

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An important problem in bioengineering is to identify the activity of human brain from observation data of magnetic fields called Magneto Encephalo Gram. Many researchers assume spherically symmetric conductor model for the human head and dipole model for the activity of human brain. Our problem is to identify locations, moments, and number of dipoles in human brain from observations of magnetic induction outside of human head.Before this project, we have already proposed the following two methods.Method 1: Local search method based on weighted integrals for the two-dimensional caseMethod 2: Global search method based on an extension of observations to the interior of three-dimensional domainIn this project, we extend Method 1 to three-dimensional problem, and give error estimates of identified results. However, Method 1 needs a priori information of locations, moments, and number of dipoles. Method 2 is applicable without any a priori information of dipoles. We construct a new method combining Method 1 and Method 2. Our proposed method gives reasonable identification results with practical error estimation.At the present time, we are preparing a paper with respect to the proposed identification method. Further discussions are needed for the error caused by numerical integrations and noisy observations, and also needed for the arrangement of observation points