Barnes Derek N, George John S, Ng Kwong T
Klipsch School of Electrical and Computer Engineering, New Mexico State University, MSC 3-O, Las Cruces, NM 88003, USA.
Med Biol Eng Comput. 2008 Sep;46(9):901-10. doi: 10.1007/s11517-008-0344-9. Epub 2008 May 14.
Currently the resolution of the head models used in electroencephalography (EEG) studies is limited by the speed of the forward solver. Here, we present a parallel finite difference technique that can reduce the solution time of the governing Poisson equation for a head model. Multiple processors are used to work on the problem simultaneously in order to speed up the solution and provide the memory for solving large problems. The original computational domain is divided into multiple rectangular partitions. Each partition is then assigned to a processor, which is responsible for all the computations and inter-processor communication associated with the nodes in that particular partition. Since the forward solution time is mainly spent on solving the associated matrix equation, it is desirable to find the optimum matrix solver. A detailed comparison of various iterative solvers was performed for both isotropic and anisotropic realistic head models constructed from MRI images. The conjugate gradient (CG) method preconditioned with an advanced geometric multigrid technique was found to provide the best overall performance. For an anisotropic model with 256 x 128 x 256 cells, this technique provides a speedup of 508 on 32 processors over the serial CG solution, with a speedup of 20.1 and 25.3 through multigrid preconditioning and parallelization, respectively.
目前，脑电图（EEG）研究中使用的头部模型的分辨率受到正向求解器速度的限制。在此，我们提出一种并行有限差分技术，该技术可以减少头部模型控制泊松方程的求解时间。使用多个处理器同时处理该问题，以加快求解速度并为解决大型问题提供内存。原始计算域被划分为多个矩形分区。然后将每个分区分配给一个处理器，该处理器负责与该特定分区中的节点相关的所有计算和处理器间通信。由于正向求解时间主要花在求解相关矩阵方程上，因此希望找到最佳矩阵求解器。针对从MRI图像构建的各向同性和各向异性真实头部模型，对各种迭代求解器进行了详细比较。结果发现，采用先进几何多重网格技术预处理的共轭梯度（CG）方法具有最佳的整体性能。对于一个具有256×128×256个单元的各向异性模型，该技术在32个处理器上比串行CG解的加速比为508，通过多重网格预处理和并行化的加速比分别为20.1和25.3。
