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

Abstract

A theory of the NMR signal dephasing due to the presence of tissue-specific magnetic field inhomogeneities is developed for a two-compartment model. Randomly distributed magnetized objects of finite size embedded in a given media are modeled by ellipsoids of revolution (prolate and oblate spheroids). The model can be applied for describing blood vessels in a tissue, red blood cells in the blood, marrow within trabecular bones, etc. The time dependence of the dephasing function connected with the spins inside of the objects, s(i), is shown to be expressed by Fresnel functions and creates a powder-type signal in the frequency domain. The short-time regime of the dephasing function for spins outside the objects, s(e), is always characterized by Gaussian time dependence, s(e) approximately exp[-zeta(k)(t/tc)2], with zeta being a volume fraction occupied by the objects, t(c) being a characteristic dephasing time, and the coefficient k depending on the ellipsoid's shape through the aspect ratio of its axes (a/c). The long-time asymptotic behavior of s(e) is always "quasispherical"-linear exponential in time, s(e) approximately exp(-zetaCt/tc), with the same "spherical" decay rate for any 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/tc).