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中国物理学会期刊

分层球形导体中任意位置直流电流元产生电位的解析解

CSTR: 32037.14.aps.54.1950

Analytical solution of electric potential produced by a direct current point sou rce located in a multilayered spherical volume conductor

CSTR: 32037.14.aps.54.1950
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  • 建立了任意层球形导体头模型.从泊松方程出发,利用电磁边界条件求解了分层球形导体中由任意位置直流电流元产生电位的一般解析解,并且给出了一种以矩阵形式表示的快速求解电位表达式中相关系数的方法.以表示头皮、颅骨、脑脊液和脑的四层球导体模型为例,对解析解进行了计算.结果表明,此解在除源点外的全域内收敛,且比仅用球谐函数展开形式的电位收敛快,计算量明显降低.给出了等位线图和流线图,表明低电导率对电位分布和电流流向的影响不可忽视.还给出了球表面电位分布特征,这有利于脑电逆问题的研究以及对脑电位测量结果的解释.

     

    A general analytical solution is derived for an electric potential produced by a direct current point source located at any position in a multilayered spher ical volume conductor. Starting from Poisson's equation, the electric potential whose coefficients are rapidly got in the form of matrix expressions is obtained according to the boundary conditions. Simulation for a four-layered spherical volume conductor denoting the scalp, skull, cerebrospinal fluid and brain tissue proves that electric potential in this paper converges more rapidly in the whol e region than that expressed only in spherical harmonics expansion form, and ite rative times decrease. Electric potential contour and current streamline figur es show that it is important to consider the effect of the low conductivity of s kull on electric potential and current flow. The distribution of electric potent ial on the surface of sphere is discussed, which will be useful in electroenceph alography inverse problems, and also in analyzing and interpreting the electric potential measurement.

     

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