Simulation studies of biomagnetic computed tomography.
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.