High Speed Electric and Magnetic Field calculation Algorithm for fMRI-MEG Integrative Analysis of Neural Activity

1.提出了一种“极平移等效多极矩方法(EMMM-PT)”。这种方法使我们能够数值计算多球模型中拉普拉斯方程所描述的精确解。我们还开发了一种用于体素模型的快速多极表面电荷模拟方法(FMM-SCM-V)。该方法采用了著名的高效0(N)求解器FMM，使我们能够处理基于磁共振图像的由几个到几亿个体素组成的高分辨率人体模型。2.对脑磁线圈信号幅度的数值计算方法进行了分类。其中一条途径是用Geselowitz公式追踪边界上的等效电流偶极→势→磁通量，另一条途径是用伊顿互易定理追踪交流线圈电流→感应电场-磁通量。通过EMMM-PT的数值分析，验证了这两种方法在多媒体组织模型中的识别性。3.通过比较FMM-SCM-V和EMMM-PT在七球头模型灰质区的计算结果，对FMM-SCM-V的精度进行了评估。在体素尺寸为0.34 mm的情况下，电场误差向量的标准偏差约为0.81%(以灰质区域的最大场归一化)。在这种情况下，体素的数量、表面元素的数量和计算时间是106,575,801体素，4,936,874个元素，59分钟。FMRI-MEG综合方法是基于由Sarvas方程计算出的引导场矩阵，利用“反常应用的最小二乘法”和“线性约束自适应波束形成器”来实现的。研究发现，后者的非自适应版本等同于前者，并且这两种方法在空间和时间分辨率特性上各有优缺点。

1.We have developed an 'equivalent multipole moment method with polar translations (EMMM-PT)'. This method enables us to numerically calculate exact solution described by Laplace's equation in multi spheres model. We also have developed a 'fast-multipole surface-charge-simulation method for voxel models (FMM-SCM-V)'. This method adopts the FMM that is well known as an efficient 0(N) solver, and it enables us to treat high-resolution human model composed of several to hundred million voxels based on MR images.2.Numerical calculation procedures for magnitude of MEG coil signal are classified. One way traces 'Equivalent current dipole→Potential on boundary→Magnetic flux by Geselowitz formula', the other traces 'AC coil current→Induced electric field-Magnetic flux by Eaton's reciprocity theorem'. Analyses by EMMM-PT numerically proved the identification of these two ways in multi-media tissue models.3.The accuracy of FMM-SCM-V is estimated by comparing the numerical results by FMM-SCM-V and EMMM-PT in the grey matter region of a seven spheres head model. The standard deviation of error vector of the electric field is about 0.81% (normalized by the maximum field in the grey matter region) in the case of 0.34mm voxel size. In this case, the number of voxels, the number of surface elements, and calculation time are 106,575,801 voxels, 4,936,874 elements, 59 min. 39 sec., respectively.4.fMRI-MEG Integrative method is performed by utilizing 'an anomalously applied least squares' and 'linearly-constrained adaptive beamformer' based on the lead field matrix calculated by the Sarvas equation. It has been found that a non-adaptive version of the latter is equivalent to the former, and the both methods have advantages and disadvantages in the spatial and temporal resolution properties.