Studies of diffusion in random fields produced by variations in susceptibility

Abstract

The effects of diffusion of nuclear spins on the echo amplitudes in a multiple echo sequence are analyzed in a medium containing random distributions of susceptibility variations. It is predicted from theory that the apparent transverse relaxation rate is directly proportional to the variance of the distribution of the magnetic field gradients in a heterogeneous region. This dependence has been confirmed by computer simulation of diffusion in a randomly varying array of gradient fields. A physical model has been developed by considering the magnetostatic superposition of the field perturbations arising from many microspherical deposits, and a relationship derived between the number density, composition and size of the particles, and the variance of the resultant gradient field distribution. The Bloch equations are solved numerically for spins diffusing in random arrangements of such particles for multiple echo sequences of RF pulses, and the rate of loss of coherent transverse magnetization due to diffusion effects is calculated. The precise dependence of the apparent T2 on the statistics of the field arrangement has been demonstrated. The relevance of these calculations to a variety of problems, including the design and behavior of superparamagnetic and ferromagnetic contrast materials, and to the effects of susceptibility variations arising from metal deposits or air-tissue interfaces in NMR imaging is discussed.