[en] Chemical exchange (CE) theory is compared with two theories of T2-shortening caused by microscopic magnetic centers: inner- and outer-sphere relaxation theory (long-echo limit) and mean gradient diffusion theory (short-echo limit). The CE equation is shown to be identical to these theories in the respective limits, and appropriate parameter relationships are derived for spherical particles. The theories are then compared with computer simulations of spherical particles and with a recent general theory, with good agreement in the asymptotic regions. The CE model also reproduces the essential relaxation characteristics in the intermediate range. Finally, good agreement of a CE model with simulations for magnetized cylinders is also demonstrated. The discussion is limited to weakly-magnetized particles such that the maximum phase shift during an echo interval is less than one radian, permitting the use of the Luz-Meiboom CE equation.
Disciplines :
Radiology, nuclear medicine & imaging Biochemistry, biophysics & molecular biology
Author, co-author :
Brooks, R. A.
Moiny, Francis ; Université de Mons > Faculté Polytechnique > Physique Générale
1 Jensen JH, Chandra R. NMR relaxation in tissues with weak magnetic inhomogeneities. Magn Reson Med 2000 ; 44: 144–156.
2 Gueron M. Nuclear relaxation in macromolecules by paramagnetic ions: a novel mechanism. J Magn Reson 1975 ; 19: 58–66.
3 Roch A, Muller RN. Longitudinal relaxation of water protons in colloidal suspensions of superparamagnetic crystals. In: Proc 11th Annual Meeting SMRM, Works in Progress; 1992: 1447.
4 Gillis P, Roch A, Brooks RA. Corrected equations for susceptibility‐induced T2‐shortening. J Magn Reson 1999 ; 137: 402–407.
5 Carr HY, Purcell EM. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys Rev 1954 ; 94: 630–638.
6 Majumdar S, Gore JC. Studies of diffusion in random fields produced by variations in susceptibility. J Magn Reson 1988 ; 78: 41–55.
7 Hardy P, Henkelman RM. On the transverse relaxation rate enhancement induced by diffusion of spins through inhomogeneous fields. Magn Reson Med 1991 ; 17: 348–356.
8 Luz Z, Meiboom S. Nuclear magnetic resonance study of the protolysis of trimethylammonium ion in aqueous solution—order of the reaction with respect to solvent. J Chem Phys 1963 ; 39: 366–370.
9 Allerhand A, Gutowsky HS. Spin‐echo NMR studies of chemical exchange. I. Some general aspects. J Chem Phys 1964 ; 41: 2115–2126.
10 Thulborn KR, Waterton JC, Matthews PM, Radda GK. Oxygenation dependence of the transverse relaxation time of water protons in whole blood at high field. Biochim Biophys Acta 1982 ; 714: 265–270.
11 Gillis P, Peto S, Moiny F, Mispelter J, Cuenod C‐A. Proton transverse nuclear magnetic relaxation in oxidized blood: a numerical approach. Magn Reson Med 1995 ; 33: 93–100.
12 Ye FQ, Allen PS. Relaxation enhancement of the transverse magnetization of water protons in paramagnetic suspensions of red blood cells. Magn Reson Med 1995 ; 34: 713–720.
13 Brooks RA, Vymazal J, Bulte JWM, Baumgarner CD, Tran V. Comparison of T 2 relaxation in blood, brain and ferritin. J Magn Reson Imaging 1995 ; 4: 446–450.
14 Gillis P, Koenig SH. Transverse relaxation of solvent protons induced by magnetized spheres: application to ferritin, erythrocytes, and magnetite. Magn Reson Med 1987 ; 5: 323–345.
15 Ayant Y, Belorizky E, Alizon J, Gallice J. Calcul des densités spectrales résultant d'un mouvement aléatoire de translation en relaxation par interaction dipolaire magnétique dans les liquides. J Phys 1975 ; 36: 991–1004.
16 Kiselev VG, Posse S. Analytical theory of susceptibility induced NMR signal dephasing in a cerebrovascular network. Phys Rev Lett 1998 ; 81: 5696–5699.
17 Kiselev VG, Posse S. Analytical model of susceptibility‐induced MR signal dephasing: effect of diffusion in a microvascular network. Magn Reson Med 1999 ; 41: 499–509.
18 Kennan RP, Zhong J, Gore JC. Intravascular susceptibility contrast mechanisms in tissues. Magn Reson Med 1994 ; 31: 9–21.
19 Boxerman JL, Hamberg LM, Rosen BR, Weisskoff RM. MR contrast due to intravascular magnetic susceptibility perturbations. Magn Reson Med 1995 ; 34: 555–566.
20 Moiny F. Relaxation magnétique nucléaire par diffusion en champ inhomogène. Ph.D. thesis, Université de Mons‐Hainaut; 1994.
21 Moiny F, Gillis P, Roch A, Muller RN. Transverse relaxation of super‐paramagnetic contrast agents: a numerical analysis. In: Proc 11th Annual Meeting SMRM, Works in Progress; 1992: 1431.
22 Muller RN, Gillis P, Moiny F, Roch A. Transverse relaxivity of particulate MRI contrast media: from theories to experiments. Magn Reson Med 1991 ; 22: 178–182.
23 Brown RJS. Distribution of fields from randomly placed dipoles: free‐precession signal decay as result of magnetic grains. Phys Rev 1961 ; 121: 1379–1382.
24 Yablonskiy DA, Haacke EM. Theory of NMR signal behavior in magnetically inhomogeneous tissues: the static dephasing regime. Magn Reson Med 1994 ; 32: 749–763.