Ramon C, Meyer M G, Nelson A C, Spelman F A, Lamping J
Center for Bioengineering, University of Washington, Seattle 98195.
IEEE Trans Biomed Eng. 1993 Apr;40(4):317-22. doi: 10.1109/10.222323.
The reconstruction of planar and three-dimensional current distributions from measured biomagnetic signals is a new field of research, known as biomagnetic computed tomography. This noninvasive imaging technique promises to provide precise, millimeter-sized resolution images of the electrical currents in tissues or organs. We performed simulation studies on phantom models of electrical sources. As a first step towards the development of an imaging algorithm, we addressed a simplified problem to identify the shape and direction of current flow in a planar surface. The problem was formulated by identifying a space in which the image was to be reconstructed. The space was segmented into a grid. Each grid space represented a current element. The magnetic field at a sampling point due to the current elements was computed using the Biot-Savart law. Since there were many more current elements than sample points, the problem was undetermined and had an uncountable number of solutions. The projection theorem was used to define an analytic solution for the magnitude and orientation of the current elements in the grid space. The solution required the inversion of large matrices in double precision. Such arrays were preprocessed on a mainframe computer, which permitted them to be rendered on any workstation. The accuracy of the image was determined by comparing it with the known location of the sources. Our results show that shape of the filamentary current flow can be imaged with our techniques. The resolution of images based on the sampling of the field, number of voxels in the reconstruction space, and noise is also analyzed.
从测量的生物磁信号重建平面和三维电流分布是一个新的研究领域，称为生物磁计算机断层扫描。这种非侵入性成像技术有望提供组织或器官中电流的精确、毫米级分辨率图像。我们对电源的体模模型进行了模拟研究。作为开发成像算法的第一步，我们解决了一个简化问题，即识别平面表面上电流的形状和方向。该问题通过确定要重建图像的空间来表述。该空间被分割成网格。每个网格空间代表一个电流元。使用毕奥 - 萨伐尔定律计算电流元在采样点处产生的磁场。由于电流元的数量比采样点多得多，该问题是不确定的，并且有无数个解。投影定理用于定义网格空间中电流元大小和方向的解析解。该解需要对双精度大矩阵求逆。此类数组在大型计算机上进行预处理，从而可以在任何工作站上呈现。通过将图像与源的已知位置进行比较来确定图像的准确性。我们的结果表明，丝状电流的形状可以用我们的技术成像。还分析了基于场采样、重建空间中的体素数量和噪声的图像分辨率。
