Analytical Theory of Susceptibility Induced NMR Signal Dephasing in a Cerebrovascular Network

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.