Dr. Epstein is presently a professor in the Mathematics department at the University of Pennsylvania. He proposes to spend a year visiting the magnetic resonance research group in the Radiology Department of the Hospital of the University of Pennsylvania, where Dr. Felix Wehrli has agreed to be his host. While there he will study topics related to magnetic resonance imaging and gain hands on experience with imaging apparatus. His study will be directed toward determining the practical feasibility of magnetic resonance imaging using an inhomogeneous background field and non-linear gradient fields. The initial part of this problem involves the analysis of certain special solutions of Maxwell's equations. The next step is to study the practical invertibility of a class of integral transforms which are perturbations of the standard Fourier transform. Hopefully this will lead up to designs for magnets whose fields, though inhomogeneous, can still be used for magnetic resonance imaging. The ultimate goal is to build a working prototype. If inhomogeneous field imaging should prove feasible it could reduce the cost of the imaging apparatus and increase the flexibility and applicability of this technology. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).
