Identification of Dipoles in Bioengineering

生物工程中的一个重要问题是如何从磁场观测数据中识别人脑的活动，即脑磁图。许多研究人员假设人类头部为球对称导体模型，人脑活动为偶极子模型。我们的问题是通过观察人脑外的磁感应来确定人脑中偶极子的位置、时刻和数量。在这个项目之前，我们已经提出了以下两种方法。方法1：基于加权积分的二维局部搜索方法方法2：基于将观测值扩展到三维域内部的全局搜索方法在本项目中，我们将方法1扩展到三维问题，并对识别结果进行误差估计。然而，方法1需要先验的位置、矩和偶极子数量的信息。方法2适用于没有任何先验偶极子信息的情况。我们结合方法1和方法2构造了一个新的方法。在实际误差估计的基础上，给出了合理的辨识结果。目前，我们正在就提出的识别方法编写一份文件。数值积分和噪声观测引起的误差，以及观测点的布置都需要进一步讨论

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