NMR imaging and structure measurements using the long-range dipolar field in liquids

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 4, 2002, Pages 10-

  Ramanathan, Chandrasekhar ^a   Bowtell, Richard W ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION FUNCTIONS; LIQUID DIPOLAR FIELDS; MEIJER TRANSFORM; MODULATED MAGNETIZATION;

CORRELATION METHODS; FOURIER TRANSFORMS; MAGNETIC FIELD EFFECTS; MAGNETIC FLUIDS; MAGNETIZATION; MODULATION; NUCLEAR MAGNETIC RESONANCE; QUANTUM THEORY; STRUCTURE (COMPOSITION);

MAGNETIC RESONANCE IMAGING;

ARTICLE;

EID: 37649030290     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.041201     Document Type: Article

References (28)

1. P. Mansfield and P.K. Grannell, J. Phys. C 6, 422 (1973).
2. P. Mansfield and P.K. Grannel, Phys. Rev. B 12, 3618 (1975).
3. D.G. Cory and A.N. Garroway, Magn. Reson. Med. 14, 435 (1990).
4. P.T. Callaghan, A. Coy, D. MacGowan, K.J. Packer, and F.O. Zelaya, Nature (London) 351, 467 (1991).
5. G.A. Barral, L. Frydman, and G.C. Chingas, Science 255, 714 (1992).
6. A. Vlassenbroek, J. Jeener, and P. Broekaert, J. Mang. Reson. A 118, 234 (1996).
7. G. Deville, M. Bernier, and J.M. Delrieux, Phys. Rev. B 19, 5666 (1979).
8. D. Einzel, G. Eska, Y. Hirayoshi, T. Kopp, and P. Wölfle, Phys. Rev. Lett. 53, 2312 (1984).
9. R.W. Bowtell, R.M. Bowley, and P. Glover, J. Magn. Reson. (1969-1992) 88, 643 (1990).
10. H.T. Edzes, J. Magn. Reson. (1969-1992) 86, 293 (1990).
11. W.S. Warren, W. Richter, A.S. Andreotti, and B.T. Farmer III, Science 262, 2005 (1993).
12. W. Richter, S. Lee, W.S. Warren, and Q. He, Science 267, 654 (1995).
13. R.W. Bowtell and P. Robyr, Phys. Rev. Lett. 76, 4971 (1996).
14. P. Robyr and R.W. Bowtell, J. Chem. Phys. 106, 467 (1997).
15. R.W. Bowtell, S. Gutteridge, and C. Ramanathan, J. Magn. Reson. 150, 147 (2001).
16. S.M. Brown, P.N. Sen, and D.G. Cory, J. Chem. Phys. 116, 295 (2002).
17. S.M. Brown, P.N. Sen, and D.G. Cory, J. Magn. Reson. 154, 154 (2002).
18. P. Robyr and R.W. Bowtell, J. Chem. Phys. 107, 702 (1997).
19. We can analyze the experiment in the long time regime by integrating the magnetization over the entire sample, expanding the exponential in Eq. (19) as a Taylor series and applying Parseval’s relations to get (Formula presented)where (Formula presented)(Formula presented) is given in Eq. (17) above and (Formula presented) represents a convolution. Since (Formula presented) is of the form of (Formula presented) (Formula presented) will contain terms ranging from (Formula presented) to (Formula presented) Thus for a gradient of magnitude (Formula presented) the first nonzero term on the right-hand side of the above equation is (Formula presented)
20. V.A. Ditkin and A.P. Prudnikov, Integral Transforms and Operational Calculus (Pergamon Press, Oxford, 1965), English edition.
21. S. Stapf, K.J. Packer, S. Békri, and P.M. Adler, Phys. Fluids 12, 566 (2000).
22. P.D. Majors and A. Caprihan, J. Magn. Reson. (1969-1992) 94, 225 (1991).
23. Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover Publications, New York, 1972).
24. H. Bateman, Tables of Integral Transforms – Volumes I and II (McGraw-Hill, New York, 1954).
25. The Meijer transform is closely related to the Laplace transform, and reduces to it (apart from a scaling factor) for the special in which (Formula presented) 24.
26. S. Gutteridge, C. Ramanathan, and R.W. Bowtell, Magn. Reson. Med. 47, 871 (2002).
27. R.W. Bowtell, G.D. Brown, P.M. Glover, M. McJury, and P. Mansfield, Philos. Trans. R. Soc. London, Ser. A 333, 457 (1990).
28. M. Holz, S.R. Heil, and A. Sacco, Phys. Chem. Chem. Phys. 2, 4740 (2000).