Encoding of anisotropic diffusion with tetrahedral gradients: A general mathematical diffusion formalism and experimental results

Magnetic Resonance in Medicine

Volumn 35, Issue 3, 1996, Pages 399-412

  Conturo, Thomas E ^a   McKinstry, Robert C ^a   Akbudak, Erbil ^a   Robinson, Bruce H ^b  

^a WASHINGTON UNIVERSITY SCHOOL OF MEDICINE   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

anisotropy; diffusion; MRI; muscle

Indexed keywords

ANISOTROPY; MAGNETIC RESONANCE IMAGING; MUSCLE; PARAMETER ESTIMATION; SENSITIVITY ANALYSIS; SIGNAL ENCODING; SIGNAL TO NOISE RATIO; TENSORS;

ANISOTROPIC DIFFUSION; DIFFUSION ANALYSIS; DIFFUSION GRADIENTS; DIFFUSION MEASUREMENTS; MATHEMATICAL FORMALISM; ORIENTATION ANGLES; ORIENTATION INDEPENDENCES; ROTATIONAL INVARIANTS;

DIFFUSION;

ARTICLE; IMAGE PROCESSING; IMAGE RECONSTRUCTION; MATHEMATICAL ANALYSIS; NUCLEAR MAGNETIC RESONANCE IMAGING; SIGNAL NOISE RATIO; SIGNAL PROCESSING;

EID: 0030033487     PISSN: 07403194     EISSN: None     Source Type: Journal    
DOI: 10.1002/mrm.1910350319     Document Type: Article

References (35)

1. G. E. Wesbey, M. E. Moseley, R. L. Ehman, Translational molecular self-diffusion in magnetic resonance imaging. II. Measurement of the self-diffusion coefficient. Invest. Radiol. 19, 491-498 (1984).
2. M. E. Moseley, J. Kucharczyk, J. Mintorovitch, Y. Cohen, J. Kuchanewicz, N. Derugin, H. Asgari, D. Norman, Diffusion-weighted MR imaging of acute stroke: correlation with T2-weighted and magnetic susceptibility-enhanced MR imaging in cats. Am. J. Neuroradiol. 11, 423-429 (1990).
3. M. E. Moseley, Y. Cohen, J. Mintorovitch, L. Chileuitt, H. Shimuzu, J. Kucharczyk, M. F. Wendland, P. R. Weinstein, Early detection of regional cerebral ischemia in cats: comparison of diffusion- and T2-vveighted MRI and spectroscopy. Magn. Reson Med. 14, 330-346 (1990).
4. M. E. Moseley, Y. Cohen, J. Kucharczyk, J. Mintorovitch, H. S. Asgari, M. E. Wendland, J. Tsuruda, D. Norman, Diffusion weighted MRI of anisotropic water diffusion in cat central nervous system. Radiology 176, 439-445 (1990).
5. R. Turner, D. Le Bihan, J. Maier, R. Vavrek, L. K. Hedges, J. Pekar, Echo-planar imaging of intravoxel incoherent motion. Radiology 177, 407-414 (1990).
6. T. E. Conturo, B. H. Robinson, Optimizing the signal-tonoise ratio in velocity imaging: the tetrahedral gradient method, in "Proc., SMRM, 10th Annual Meeting, San Francisco, 1991," p. 813.
7. V. Gulani, Y. Yang, J. S. Shimony, S. Chandra, P. C. Lauterbur, Determination of orientation and diffusion anisotropy of parallel fibers using four diffusion measurements, in "Proc., SMR, 2nd Meeting, San Francisco, 1994," p. 1040.
8. G. Liu, P. vanGelderen, C. T. W. Moonen, Single-shot diffusion MRI on a conventional clinical instrument, in "Proc., SMR. 2nd Meeting, San Francisco, 1994," p. 1034.
9. E. O. Stejskal, J. E. Tanner. Spin diffusion measurements: spin echoes in the presence of a time dependent field gradient. J. Chem. Phys. 42, 288-292 (1965).
10. D. Le Bihan, E. Breton, D. Lallemand, P. Grenier, E. Cabanis, M. Laval-Jeantet. MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. Radiology 161, 401-407 (1986).
11. R. C. McKinstry, "Ultrafast NMR imaging of brain water mobility." Thesis, Massachusetts Institute of Technology, 1991.
12. R. C. McKinstry, R. M. Weisskoff, J. W. Belliveau, J. M. Vevea, J. B. Moore, K. W. Kwong, E. F. Halpern, B. R. Rosen, Ultrafast MR imaging of water mobility: animal models of altered cerebral perfusion. J. Magn. Reson. Imaging 2, 377-384 (1992).
13. D. Chien, R. B. Buxton, K. K. Kwong, T. J. Brady, B. R. Rosen, MR diffusion imaging of the human brain. J. Comput. Assist. Tomogr. 14, 514-520 (1990).
14. J. J. Neil, J. J. H. Ackerman, Detection of pseudodiffusion in rat brain following blood substitution with perfluorocarbon. J. Magn. Reson. 97, 194 (1992).
15. T. L. Chenevert, J. A. Brunberg, J. G. Pipe, Anisotropic diffusion in human white matter: demonstration with MR techniques in vivo. Radiology 177, 401-405 (1990).
16. M. Doran, J. V. Hajnal, N. VanBruggen, M. D. King, I. R. Young, and G. M. Bydder. Normal and abnormal white matter tracts shown by MR imaging using directional diffusion weighted sequences. J Comput. Assist. Tomogr. 14, 865-873 (1990).
17. G. G. Cleveland, D. C. Chang, C. F. Hazlewood. Nuclear magnetic resonance measurement of skeletal muscle. Anisotropy of the diffusion coefficient of the intracellular water. Biophys. J. 16, 1043-1053 (1976).
18. P. J. Basser, J. Mattiello, D. Le Bihan. MR diffusion tensor spectroscopy and imaging. Biophys. J. 66, 259-267 (1994).
19. P. J. Basser, J. Mattiello, D. Le Bihan, Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. Ser. B 103, 247-254 (1994).
20. S. Mori, P. C. M. van Zijl. Diffusion weighting by the trace of the diffusion tensor within a single scan. Magn. Reson. Med. 33, 41-52 (1995).
21. E. O. Stejskal. Use of spin echoes in a pulsed magnetic-fieid gradient to study anisotropic, restricted diffusion and flow. J. Chem. Phys. 43, 3597-3603 (1965).
22. P. van Gelderen, H. M. de Vleeschouwer, D. DesPres, I. Pekar, P. C. M. van Zijl, C. T. W. Moonen, Water diffusion and acute stroke. Magn. Reson. Med. 31, 154-163 (1994).
23. L. Garrido, V. J. Wedeen, K. K. Kwong, U. M. Spencer, H. L. Kantor, Anisotropv of water diffusion in the myocardium of the rat. Circ. Res. 74, 789-793 (1994).
24. H. C. Torrey, Bloch equation with diffusion terms. Phys. Rev. 104, 563 (1956).
25. C. P. Slichter, Diffusion in an inhomogeneous magnetic field (Appendix G), in "Principles of Magnetic Resonance," pp. 597-600, Springer-Verlag. Berlin, 1990.
26. J. Crank, "The Mathematics of Diffusion," p. 6. Clarendon Press. Oxford, 1975.
27. P. Douek, R. Turner, J. Pekar, N. Patronas, D. Le Bihan, MR color mapping of myelin fiber orientation. J. Comput. Assist. Tomogr. 15, 923-929 (1991).
28. D. Le Bihan, Molecular diffusion nuclear magnetic resonance imaging. Magn. Reson. Q. 7, 1-30 (1991).
29. J. Mattiello, P. J. Basser, D. Le Bihan, Analytical expressions for the b matrix in MR diffusion imaging and spectroscopy. J. Magn. Reson. 108, 131-141 (1994).
30. J. Freed, Anisotropic rotational diffusion and electron spin resonance linewidths. J. Chem. Phys. 41, 2077-2083 (1964).
31. J. Mathews, R. L. Walker, "Mathematical Methods of Physics," p. 145, Benjamin/Cummings, Menlo Park, CA, 1964.
32. J. H. Zar, "Biostatistical analysis." p. 81. Prentice Hall. Englewood Cliffs, NJ, 1984.
33. P. J. Basser, J. Mattiello, D. Le Bihan, Anisotropic diffusion: MR diffusion tensor imaging, in "Diffusion and perfusion magnetic resonance imaging: Applications to functional MRI" (D. Le Bihan, Ed.), pp. 140-149. Raven Press, New York, 1995.
34. R. Cherry. Methods Enzymol. 54, 47-61 (1978).
35. J. H. Simpson, H. Y. Carr. Diffusion and nuclear spin relaxation in water. Phys. Rev. 111, 1201-1202 (1958).