Analytical model of susceptibility‐induced MR signal dephasing: Effect of diffusion in a microvascular network

A deterministic analytical model that describes the time course of magnetic resonance signal relaxation due to magnetic field inhomogeneity induced by a vascular network is developed. Both static and diffusion dephasing are taken into account. The contribution of the diffusion dephasing is calculated for relatively large vessels (R > 10μm) or short measurement times when the diffusion length is smaller than the vessel radius. The signal is found to possess the following features: a) an initial deviation from the monoexponential relaxation which is more pronounced for the imaginary part of the signal; b) a deviation from monoexponential relaxation at short echo times for the spin‐echo (SE) signal measured as a function of the echo time; c) the echo maximum of the SE signal shifted from the nominal echo time to a shorter time; and d) a diffusion effect much stronger for the SE than for the free induction decay experiment. The model presented agrees within its validity domain with a known Monte Carlo simulation. Magn Reson Med 41:499–509, 1999. © 1999 Wiley‐Liss, Inc.

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