The effects of diffusion through locally inhomogeneous magnetic fields on transverse nuclear spin relaxation in heterogeneous systems. Proton transverse relaxation in striated muscle tissue

Abstract

The effect on transverse nuclear spin relaxation of diffusion of molecules through magnetic field-gradients arising from heterogeneity of the magnetic susceptibility of the system are discussed. Similarities of these effects with the effects of spatially restricted diffusion in the presence of applied field-gradients and the motional narrowing of NMR lines are pointed out. An expression is deduced for the contribution of diffusion through internal inhomogeneous fields to the attenuation of a spin echo. The result is obtained from Robertson's approximate theory for the effect of restricted diffusion between plane parallel barriers and involves Δω, the width of the inhomogeneously broadened NMR absorption line and ξ the time taken for a spin to diffuse a distance of the order of the lattice constant for the structure of the system. The application of the result to striated muscle shows that diffusion through internal field-gradients is a negligible contribution to the transverse relaxation of the water protons.