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

1.我们开发了一种“具有极平移的等效多极矩方法（EMMM-PT）”。该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“体素模型的快速多极表面电荷模拟方法（FMM-SCM-V）”。该方法采用了众所周知的高效的0(N)求解器FMM，使我们能够基于MR图像处理由几亿到几亿体素组成的高分辨率人体模型。分类了脑磁图线圈信号幅值的数值计算方法。其中一条路径为“等效电流偶极子→边界势→Geselowitz公式磁通”，另一条路径为“交流线圈电流→感应电场-伊顿互易定理磁通”。EMMM-PT数值分析证明了这两种方法在多媒体组织模型中的可识别性。通过比较FMM-SCM-V和EMMM-PT在七球头部模型灰质区域的数值结果，对FMM-SCM-V的精度进行了评价。在体素尺寸为0.34mm的情况下，电场误差向量的标准差约为0.81%（以灰质区域最大电场归一化）。在本例中，体素数为106,575,801体素，表面元素数为4,936,874个元素，计算时间为59分39秒。fMRI-MEG综合方法是利用“异常应用最小二乘”和“线性约束自适应波束形成器”，基于由Sarvas方程计算的引线场矩阵。研究发现，后者的非自适应版本与前者等效，并且两种方法在时空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.