利用有限差分法计算真实头模型脑电正问题

脑电研究领域的两个关键问题是脑电正问题和脑电逆问题,脑电正问题是脑电逆问题的基础.由于复杂、非规则真实头模型中的脑电正问题不存在解析解,因此脑电源分析依赖于正问题数值算法的精度和效率.文章首先详细推导了有限差分算法求解三维各向同性脑电正问题的数学模型,然后在三层同心球模型上通过与解析解比较验证了该算法的精度和效率,最后将该算法应用于真实头模型.仿真结果表明,有限差分法可以有效地处理任意形状几何体的电位场分布问题,是模拟计算真实头模型中脑电正问题的有力工具.

Solving the EEG Forward Problems in a Realistic Geometry Head Model by means of the Finite Difference Method

There are two important problems in the field of Electroencephalogram (EEG): EEG forward problem and inverse problem. The EEG forward problem is an important component of the EEG inverse problem. In realistic geometry head models, EEG source analysis depends on the accuracy and the efficiency of the numerical method chosen for solving the Forward Problem, as there is no analytical solution for realistic geometry models. In this paper, a finite difference method (FDM) has been implemented to solve the 3-dimensional isotropic EEG forward problem. Then, the effects of dipole eccentricity, spacing of finite difference elements and number of grid nodes on the solution accuracy and efficiency are discussed by comparing the FDM numerical solutions with the analytic solutions on a three-concentric-sphere model. Finally, the FDM has been applied to a realistic-shaped head model to solve the EEG forward problem. The present computer simulation results suggest that FDM is convenient to solve the potential distribution in irregular shaped objects, and provides an effective tool for the EEG forward problem in realistic geometry head models.