TY - JOUR
T1 - Theory of FID NMR signal dephasing induced by mesoscopic magnetic field inhomogeneities in biological systems
AU - Sukstanskii, Alexander L.
AU - Yablonskiy, Dmitriy A.
N1 - Funding Information:
The authors are grateful to Professors Joseph J. H. Ackerman and Mark S. Conradi for helpful discussions. This work is supported in part by the WU McDonnell Center for Higher Brain Function and NIH Grant R24 CA83060.
PY - 2001
Y1 - 2001
N2 - 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, si, 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, se, is always characterized by Gaussian time dependence, se ∼ exp[- ζk(t/tc)2], with ζ being a volume fraction occupied by the objects, tc 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 se is always "quasispherical"-linear exponential in time, se ∼ exp(-ζCt/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 (ζC/tc).
AB - 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, si, 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, se, is always characterized by Gaussian time dependence, se ∼ exp[- ζk(t/tc)2], with ζ being a volume fraction occupied by the objects, tc 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 se is always "quasispherical"-linear exponential in time, se ∼ exp(-ζCt/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 (ζC/tc).
UR - http://www.scopus.com/inward/record.url?scp=0035744058&partnerID=8YFLogxK
U2 - 10.1006/jmre.2001.2363
DO - 10.1006/jmre.2001.2363
M3 - Article
C2 - 11444944
AN - SCOPUS:0035744058
SN - 1090-7807
VL - 151
SP - 107
EP - 117
JO - Journal of Magnetic Resonance
JF - Journal of Magnetic Resonance
IS - 1
ER -