PERTURBATIVE ANALYTICAL SOLUTIONS OF THE ELECTRIC FORWARD PROBLEM FOR REALISTIC VOLUME CONDUCTORS
PERTURBATIVE ANALYTICAL SOLUTIONS OF THE ELECTRIC FORWARD PROBLEM FOR REALISTIC VOLUME CONDUCTORS
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DOI：
10.1063/1.1337089
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发表时间：
1999-08
影响因子：
3.2
通讯作者：
G. Nolte;G. Curio
中科院分区：
文献类型：
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作者：
G. Nolte;G. Curio
实际体积导体中偶极子电流所产生的磁场不能精确计算。在这里，我们根据脑磁图中体积导体（即头部）与球形近似的偏差很小这一事实推导出近似解析解。我们提出了一种显式积分形式，它允许计算磁场的n阶泰勒展开相对于n−1阶电问题的相应解的偏差。特别是，对于磁性问题的一阶解，只需要众所周知的球形体积导体的电解。用一系列球面谐波对这一积分进行计算，得到了一种计算外磁场的快速算法，该算法很好地逼近了实际大小的光滑体导体变形的真实场。因为磁场的近似值是完全无旋度的，所以它同样是……
The magnetic field induced by a current dipole situated in a realistic volume conductor cannot be computed exactly. Here, we derive approximate analytical solutions based on the fact that in magnetoencephalography the deviation of the volume conductor (i.e., the head) from a spherical approximation is small. We present an explicit integral form which allows to calculate the nth order Taylor expansion of the magnetic field with respect to this deviation from the corresponding solution of the electric problem of order n−1. Especially, for a first order solution of the magnetic problem only the well-known electric solution for a spherical volume conductor is needed. The evaluation of this integral by a series of spherical harmonics results in a fast algorithm for the computation of the external magnetic field which is an excellent approximation of the true field for smooth volume conductor deformations of realistic magnitude. Since the approximation of the magnetic field is exactly curl-free it is equally go...