On the transverse relaxation rate enhancement induced by diffusion of spins through inhomogeneous fields

The design of magnetic particles as a magnetic resonance contrast agent will rely on the prediction of their ability to induce transverse relaxation among the surrounding protons. There exists several divergent predictions of the contribution of these agents to 1/T2. This article points out a problem, commonly overlooked, in the development of expressions for the relaxation enhancement which has led some workers to the derivation of results inappropriate for large magnetic particles. The size of the magnetic inhomogeneity created by the particle precludes the averaging of the interaction over a single proton unless it experiences an average field in the time tau between pulses. Computer simulations following the trajectories of diffusing water molecules in inhomogeneous fields are shown to be the correct approach to dealing with large inhomogeneities.