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A deterministic analytical model which describes the time course of NMR signal relaxation in media where the magnetic field is perturbed by stochastic low-density inclusions having one-dimensional extent is developed. Both static and diffusion dephasing mechanisms are included. The model is applied to a simulation of a living tissue where the inclusions are identified with blood microvessels. This application is a ground for quantitation of signal changes during brain activation measured by functional magnetic resonance imaging. The results are consistent with previous Monte Carlo simulations.
Kiselev et al. (Mon,) studied this question.