An Inverse Source Problem for Maxwell's Equations in Magnetoencephalography
An Inverse Source Problem for Maxwell's Equations in Magnetoencephalography
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DOI：
10.1137/s0036139900373927
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
G. Bao;H. Ammari;J. L. Fleming
中科院分区：
文献类型：
--
作者：
G. Bao;H. Ammari;J. L. Fleming
考虑在确定活体人脑中癫痫灶的位置时出现的麦克斯韦方程的逆源问题。人脑被建模为异质介质，其中电容率、磁导率和电导率都可以是函数。电流偶极子用于模拟癫痫。在这种情况下，反源问题是确定从边界测量的领域的电流偶极子。本文介绍了一种新的求解反问题的计算方法。该方法是基于低频渐近分析的麦克斯韦方程。我们的方法是建设性的，并具有良好的收敛性。该方法的关键步骤是构造特殊的测试函数。反问题的唯一性和稳定性结果也建立。该方法和结果有望在脑磁图中得到应用。
Consider an inverse source problem for Maxwell's equations which arises in determining locations of epileptic foci in the living human brain. The human brain is modeled as a heterogeneous medium, where the electric permittivity, magnetic permeability, and conductivity may all be functions. A current dipole is used to model the epilepsy. The inverse source problem in this context is to determine the current dipole from boundary measurements of the fields. In this paper, a new computational method is introduced for solving the inverse problem. The method is based on a low-frequency asymptotic analysis of Maxwell's equations. Our method is constructive and has good convergence properties. A crucial step of the method is to construct special test functions. Uniqueness and stability results for the inverse problem are also established. The method and results are expected to find applications particularly in magnetoencephalography.