[en] Evaluating and understanding the performances of magnetic colloids as contrast agents for MRI requires a theory describing their magnetic interactions with water protons. The field dependence of the proton longitudinal relaxation rate (nuclear magnetic relaxation dispersion profiles) in aqueous colloidal suspensions of superparamagnetic particles is based on the so-called Curie relaxation, which essentially accounts for the high field part of the NMRD profiles (B0>0.02 T). The low-field part of the NMRD profiles can only be explained by the crystal's internal anisotropy energy, a concept which clarifies the important difference between superpara- and paramagnetic compounds: the anisotropy energy modifies both the electronic precession frequencies and the thermodynamic probability of occupation of the crystal magnetic states. Our theory clearly explains why a low-field dispersion exists for suspensions of small size crystals, and why it does not for large crystals' suspensions. This important effect is due to the Boltzmann factors depending on the anisotropy energy, which is itself proportional to the particle volume.
Disciplines :
Radiology, nuclear medicine & imaging Chemistry Physics
Y. Ayant, E. Belorizky, J. Alizon, and J. Gallice, J. Phys. A 36, 991 (1975).
J. H. Freed, J. Chem. Phys. 68, 4034 (1978).
M. Guerun, J. Magn. Reson. 19, 538 (1975).
L. Banci, I. Bertini, and C. Luchinat, Nuclear and Electron Relaxation (VCH. Weinheim, 1991).
P.-O. Westlund, J. Chem. Phys. 108, 4945 (1998).
W. C. Elmore, Phys. Rev. 54, 1092 (1938).
C. P. Bean and J. D. Livingston, J. Appl. Phys. 30, 120 (1959).
L. Néel, Ann. Geophys. (C.N.R.S.) 5, 99 (1949).
W. F. Brown, Phys. Rev. 130, 1677 (1963).
J.-L. Dormann, Rev. Phys. Appl. 16, 275 (1981).
A. Roch, Ph.D. thesis, University of Mons-Hainaut, 1994.
A. Roch, P. Gillis, and R. N. Muller, Proceeding of the 3rd Annual Meeting of the Society of Magnetic Resonance, 1995, p. 1094.
A. Roch and R. N. Muller, Proceedings of the 11th Annual Meeting of the Society of Magnetic Resonance in Medicine, Works in Progress, 1992. p. 1447.
S. H. Koenig and K. Kellar. Magn. Reson. Med. 34, 227 (1995).
A. E. Berkowitz, J. A. Lahut, I. S. Jacobs, L. M. Levinson, and D. W. Forester, Phys. Rev. Lett. 34, 594 (1975).
S. Linderoth, P. V. Hendriksen, F. Bødker, S. Wells, K. Davies, S. W. Charles, and S. Mørup, J. Appl. Phys. 75, 6583 (1994).
C. Kittel, Phys. Rev. 73, 155 (1948).
C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1996).
J. L. Garcia-Palacios and F. J. Lazaro, Phys. Rev. B 55, 1006 (1997).
D. A. Dimitrov and G. M. Wysin, Phys. Rev. B 54, 9237 (1997).
B. Lax and K. J. Button, Microwave Ferrites and Ferrimagnetics (McGraw-Hill, New York, 1962).
A. Abragam, The Principles of Nuclear Magnetism (Clarendon, Oxford, 1961).
The coefficients appearing in the expressions of the relaxation rates, respectively multiplying the Curie term and the fluctuating ones, cannot be those originally given by Gueron (Ref. 3), who was interested in a zero-field limit, the magnetization being then proportional to the external field. The values used in Ref. 14, extrapolated from Gueron, are also erroneous. Correct values for these coefficients, obtained thanks to an exact evaluation of (S2Z), are calculated elsewhere [P. Gillis, A. Roch, and R. A. Brooks, J. Magn. Reson. (in press)].
A. Roch, P. Gillis, A. Ouakssim, and R. N. Muller, J. Magn. Magn. Mater, (in press).