Accuracy and limitations of magnetic field measurement for validation of current density distribution using MRI

There is increasing interest in accurately measuring bioelectric currents inside the human body. Practical problems exist relating to the placement of electrodes on the body as well as with the resolution and accuracy of the measurements. A number of researchers are investigating magnetic resonance imaging (MRI) as a noninvasive means to measure at a high resolution the magnetic field generated by a conductor, and, by Maxwell's equations, extract the current distribution. This paper explores the limitations inherent to using MRI to study current distributions, in particular when applied at microscopic resolutions. A modeling program based on quasi-static electromagnetics and Bloch equation simulation has been developed and parameter relationships have been extracted in order to guide the measurement procedure past two fundamental issues: signal averaging in a voxel due to an inhomogeneous field close to a conductor and the need to remain close to the conductor in order to resolve multiple current elements. Simple formulas regarding the error of the signal observed, the voxel size used, and the distance of the voxel from the conductor have been established and design curves have been extracted for future use in this developing area.