Theory of FID NMR signal dephasing induced by mesoscopic magnetic field inhomogeneities in biological systems

A theory of the NMR signal dephasing due to the presence of tissue-specific magnetic field inhomogeneities is developed for a two-compartment model. R andomly distributed magnetized objects of finite size embedded in a given m edia are modeled by ellipsoids of revolution (prolate and oblate spheroids) . The model can be applied for describing blood vessels in a tissue, red bl ood cells in the blood, marrow within trabecular bones, etc. The time depen dence of the dephasing function connected with the spins inside of the obje cts, s(i), is shown to be expressed by Fresnel functions and creates a powd er-type signal in the frequency domain. The short-time regime of the dephas ing function for spins outside the objects, s(e), is always characterized b y Gaussian time dependence, s(e) similar to exp[ - zetak(t/t(c))(2)], with zeta being a volume fraction occupied by the objects, t(c) being a characte ristic dephasing time, and the coefficient k depending on the ellipsoid's s hape through the aspect ratio of its axes (a/c), The long-time asymptotic b ehavior of s(e) is always "quasispherical"-linear exponential in time, s(e) similar to exp(-zeta Ct/t(c)), with the same "spherical" decay rate for an y ellipsoidal shape. For long prolate spheroids (a/c) << 1, there exists an intermediate characteristic regime with a linear exponential time behavior and an aspect-ratio-dependent decay rate smaller than (zetaC/t(c)). (C) 20 01 Academic Press.