电偶极子源定位问题的研究

Study on the localization of the electric dipole sources

首先得到了封闭形式的电偶极子处于任意位置时电场分布的公式,它是一个线性变换,称其变换矩阵为传递矩阵.并给出了传递矩阵的具体表达式和许多有用的性质,得到了传递矩阵的逆矩阵,导出了利用电场分布来确定单个或者多个偶极子源位置矢量和电偶极矩矢量的公式.对单个偶极子源的计算表明,如果测得两点的电场分布相同,就可以确定偶极子处于它们连线的中点上.

The research of dipole source localization has great significance in both clinical research and applications. For example, the EEG recording from the scalp is widely used for the localization of sources of electrical activity in the brain. This paper presents a closed formula that describes the electric field of dipoles at arbitrary position, which is a linear transformer called the transfer matrix.The expression of transfer matrix and its many useful characteristics are given, which can be used for the analysis of the electrical fields of dipoles.This paper also presents the closed formula for determining the location and magnitude of single dipole or multi-dipoles according to its electrical field distribution.A calculation result for a single dipole shows that the dipole will be located at the midpoint of a line segment if there are equivalent fields at its two ends.