Lew S, Wolters C H, Dierkes T, Röer C, Macleod R S
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA.
Appl Numer Math. 2009 Aug;59(8):1970-1988. doi: 10.1016/j.apnum.2009.02.006.
Accuracy and run-time play an important role in medical diagnostics and research as well as in the field of neuroscience. In Electroencephalography (EEG) source reconstruction, a current distribution in the human brain is reconstructed noninvasively from measured potentials at the head surface (the EEG inverse problem). Numerical modeling techniques are used to simulate head surface potentials for dipolar current sources in the human cortex, the so-called EEG forward problem.In this paper, the efficiency of algebraic multigrid (AMG), incomplete Cholesky (IC) and Jacobi preconditioners for the conjugate gradient (CG) method are compared for iteratively solving the finite element (FE) method based EEG forward problem. The interplay of the three solvers with a full subtraction approach and two direct potential approaches, the Venant and the partial integration method for the treatment of the dipole singularity is examined. The examination is performed in a four-compartment sphere model with anisotropic skull layer, where quasi-analytical solutions allow for an exact quantification of computational speed versus numerical error. Specifically-tuned constrained Delaunay tetrahedralization (CDT) FE meshes lead to high accuracies for both the full subtraction and the direct potential approaches. Best accuracies are achieved by the full subtraction approach if the homogeneity condition is fulfilled. It is shown that the AMG-CG achieves an order of magnitude higher computational speed than the CG with the standard preconditioners with an increasing gain factor when decreasing mesh size. Our results should broaden the application of accurate and fast high-resolution FE volume conductor modeling in source analysis routine.
准确性和运行时间在医学诊断与研究以及神经科学领域中都起着重要作用。在脑电图（EEG）源重建中，人脑内的电流分布是根据头部表面测量到的电位进行非侵入性重建的（EEG逆问题）。数值建模技术用于模拟人类皮层中偶极电流源的头部表面电位，即所谓的EEG正问题。本文比较了代数多重网格（AMG）、不完全Cholesky（IC）和雅可比预处理器用于共轭梯度（CG）法迭代求解基于有限元（FE）法的EEG正问题的效率。研究了这三种求解器与全减法方法以及两种直接电位方法（用于处理偶极奇点的韦南特方法和部分积分方法）之间的相互作用。该研究在具有各向异性颅骨层的四室球体模型中进行，其中准解析解允许精确量化计算速度与数值误差。经过特殊调整的约束Delaunay四面体化（CDT）有限元网格在全减法和直接电位方法中都能实现高精度。如果满足均匀性条件，全减法方法可实现最佳精度。结果表明，随着网格尺寸减小，AMG - CG比使用标准预处理器的CG计算速度提高了一个数量级，且增益因子不断增加。我们的结果应能拓宽精确快速的高分辨率有限元容积导体建模在源分析日常工作中的应用。
