Temporal scaling characteristics of diffusion as a new MRI contrast: Findings in rat hippocampus

NeuroImage

Volumn 60, Issue 2, 2012, Pages 1380-1393

  Özarslan, Evren ^a,b   Shepherd, Timothy M ^c   Koay, Cheng Guan ^d   Blackband, Stephen J ^e,f   Basser, Peter J ^a  

^a EUNICE KENNEDY SHRIVER NATIONAL INSTITUTE OF CHILD HEALTH AND HUMAN DEVELOPMENT   (United States)

^b UNIFORMED SERVICES UNIVERSITY OF THE HEALTH SCIENCES   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITY OF WISCONSIN SCHOOL OF MEDICINE AND PUBLIC HEALTH   (United States)

^e UNIVERSITY OF FLORIDA COLLEGE OF MEDICINE   (United States)

^f FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Anisotropy; Anomalous diffusion; Diffusion time; DWI; Fractal; Noise floor; Power law; Q Space; Rician; Scaling; SHORE

Indexed keywords

ACCURACY; ANIMAL TISSUE; ANISOTROPY; ARTICLE; CONTROLLED STUDY; DIFFUSION WEIGHTED IMAGING; HIPPOCAMPUS; MATHEMATICAL PARAMETERS; MICROSCOPY; NONHUMAN; PRIORITY JOURNAL; REPRODUCIBILITY; TEMPORAL SCALING;

ANIMALS; ANISOTROPY; DIFFUSION MAGNETIC RESONANCE IMAGING; HIPPOCAMPUS; RATS; TIME FACTORS;

EID: 84856851435     PISSN: 10538119     EISSN: 10959572     Source Type: Journal    
DOI: 10.1016/j.neuroimage.2012.01.105     Document Type: Article

References (76)

1. Alexander S., Orbach R. Density of states on fractals: "fractons". J. Phys. Lett. Paris 1982, 43(17):L-625-L-631.
2. Banavar J.R., Lipsicas M., Willemsen J.F. Determination of the random-walk dimension of fractals by means of NMR. Phys. Rev. B 1985, 32(9):6066.
3. Basser P.J., Mattiello J., LeBihan D. MR diffusion tensor spectroscopy and imaging. Biophys. J. 1994, 66(1):259-267.
4. Basser P.J., Pierpaoli C. Microstructural and physiological features of tissues elucidated by quantitative diffusion tensor MRI. J. Magn. Reson. B 1996, 111(3):209-219.
5. Bennett K.M., Schmainda K.M., Bennett(Tong) R., Rowe D.B., Lu H., Hyde J.S. Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magn. Reson. Med. 2003, 50(4):727-734.
6. Blinnikov S., Moessner R. Expansions for nearly Gaussian distributions. Astron. Astrophys. Suppl. Ser. 1998, 130:193-205.
7. Candés E.J., Romberg J.K., Tao T. Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 2006, 59:1207-1223.
8. Caserta F., Stanley H.E., Eldred W., Daccord G., Hausman R., Nittmann J. Physical mechanisms underlying neurite outgrowth: a quantitative analysis of neuronal shape. Phys. Rev. Lett. 1990, 64(1):95-98.
9. Cheng K.H. Quantitation of non-Einstein diffusion behavior of water in biological tissues by proton MR diffusion imaging: synthetic image calculations. Magn. Reson. Imaging 1993, 11(4):569-583.
10. Condamin S., Bénichou O., Tejedor V., Voituriez R., Klafter J. First-passage times in complex scale-invariant media. Nature 2007, 450(7166):77-80. (URL). http://dx.doi.org/10.1038/nature06201.
11. Cory D.G., Garroway A.N. Measurement of translational displacement probabilities by NMR: an indicator of compartmentation. Magn. Reson. Med. 1990, 14(3):435-444.
12. Damion R.A., Packer K.J. Predictions for pulsed-field-gradient NMR experiments of diffusion in fractal spaces. Proc. R. Soc. Lond. A 1997, 453:205-211.
13. de Carvalho Rangel C., Hygino Cruz L.C., Takayassu T.C., Gasparetto E.L., Domingues R.C. Diffusion MR imaging in central nervous system. Magn. Reson. Imaging Clin. N. Am. 2011, 19(1):23-53. (URL). http://dx.doi.org/10.1016/j.mric.2010.10.006.
14. Donoho D.L. Compressed sensing. IEEE Trans. Inf. Theory 2006, 52:1289-1306.
15. Gao Q., Srinivasan G., Magin R.L., Zhou X.J. Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: analysis using fractional order calculus. J. Magn. Reson. Imaging 2011, 33(5):1177-1183. (URL). http://dx.doi.org/10.1002/jmri.22522.
16. Gefen Y., Aharony A., Alexander S. Anomalous diffusion on percolating clusters. Phys. Rev. Lett. 1983, 50(1):77-80.
17. Ghosh A., Özarslan E., Deriche R. Challenges in reconstructing the propagator via a cumulant expansion of the one-dimensional q-space MR signal. Proc. Intl. Soc. Mag. Reson. Med. 2010, Vol. 18.
18. Gradshteyn I.S., Ryzhik I.M. Table of Integrals, Series, and Products 2000, Academic Press, London. 6th ed.
19. Grebenkov D.S. Subdiffusion in a bounded domain with a partially absorbing-reflecting boundary. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2010, 81(2 Pt 1):021128.
20. Hall M.G., Barrick T.R. From diffusion-weighted MRI to anomalous diffusion imaging. Magn. Reson. Med. 2008, 59(3):447-455. (URL). http://dx.doi.org/10.1002/mrm.21453.
21. Havlin S., ben Avraham D. Diffusion in disordered media. Adv. Phys. 2002, 51(1):187-292.
22. Jian B., Vemuri B.C., Özarslan E., Carney P.R., Mareci T.H. A novel tensor distribution model for the diffusion-weighted MR signal. Neuroimage 2007, 37(1):164-176. (URL). http://dx.doi.org/10.1016/j.neuroimage.2007.03.074.
23. Jug G. Theory of NMR field-gradient spectroscopy for anomalous diffusion in fractal networks. Chem. Phys. Lett. 1986, 131(1,2):94-97.
24. Kärger J., Pfeifer H., Heink W. Principles and applications of self-diffusion measurements by nuclear magnetic resonance. Advances in Magnetic Resonance 1988, 1-89. Academic Press, London. J.S. Waugh (Ed.).
25. Kim S., Chi-Fishman G., Barnett A.S., Pierpaoli C. Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart. Magn. Reson. Med. 2005, 54(6):1387-1396. (URL). http://dx.doi.org/10.1002/mrm.20676.
26. Kiselev V.G., Hahn K.R., Auer D.P. Is the brain cortex a fractal?. Neuroimage 2003, 20(3):1765-1774.
27. Klemm A., Metzler R., Kimmich R. Diffusion on random-site percolation clusters: theory and NMR microscopy experiments with model objects. Phys. Rev. E 2002, 65(2):021112.
28. Koay C.G., Basser P.J. Analytically exact correction scheme for signal extraction from noisy magnitude MR signals. J. Magn. Reson. 2006, 179(2):317-322. (URL). http://dx.doi.org/10.1016/j.jmr.2006.01.016.
29. Koay C.G., Özarslan E., Basser P.J. A signal transformational framework for breaking the noise floor and its applications in MRI. J. Magn. Reson. 2009, 197(2):108-119. URL. http://dx.doi.org/10.1016/j.jmr.2008.11.015.
30. Koay C.G., Özarslan E., Pierpaoli C. Probabilistic identification and estimation of noise (PIESNO): a self-consistent approach and its applications in MRI. J. Magn. Reson. 2009, 199(1):94-103. URL. http://dx.doi.org/10.1016/j.jmr.2009.03.005.
31. Kohlrausch R. Über das Dellmann'sche Elektrometer. Ann. Phys. 1847, 72:393-405.
32. Köpf M., Corinth C., Haferkamp O., Nonnenmacher T.F. Anomalous diffusion of water in biological tissues. Biophys. J. 1996, 70:2950-2958.
33. Köpf M., Metzler R., Haferkamp O., Nonnenmacher T.F. NMR studies of anomalous diffusion in biological tissues: experimental observation of Lévy stable processes. Fractals in Biology and Medicine 1998, Vol. 2:354-364. Birkhäuser, Basel.
34. Kveder M., Lahajnar G., Blinc R., Zupancic I. Non-Brownian water self-diffusion in lung tissue. Magn. Reson. Med. 1988, 6(2):194-198.
35. Langlands T.A.M., Henry B.I. Fractional chemotaxis diffusion equations. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2010, 81(5 Pt 1):051102.
36. Latour L.L., Svoboda K., Mitra P.P., Sotak C.H. Time-dependent diffusion of water in a biological model system. Proc. Natl. Acad. Sci. 1994, 91:1229-1233.
37. Lichtman J.W., Denk W. The big and the small: challenges of imaging the brain's circuits. Science 2011, 334(6056):618-623. (Nov), (URL). http://dx.doi.org/10.1126/science.1209168.
38. Liu C.L., Bammer R., Moseley M.E. Generalized diffusion tensor imaging (GDTI): a method for characterizing and imaging diffusion anisotropy caused by non-Gaussian diffusion. Isr. J. Chem. 2003, 43(1-2):145-154.
39. Magin R.L., Abdullah O., Baleanu D., Zhou X.J. Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation. J. Magn. Reson. 2008, 190(2):255-270. (URL). http://dx.doi.org/10.1016/j.jmr.2007.11.007.
40. Mandelbrot B.B. The Fractal Geometry of Nature 1982, Freeman, San Francisco.
41. Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 2000, 339:1-77.
42. Mulkern R.V., Gudbjartsson H., Westin C.F., Zengingönül H.P., Gartner W., Guttmann C.R., Robertson R.L., Kyriakos W., Schwartz R., Holtzman D., Jolesz F.A., Maier S.E. Multi-component apparent diffusion coefficients in human brain. NMR Biomed. 1999, 12(1):51-62.
43. Müller H.P., Kimmich R., Weis J. NMR flow velocity mapping in random percolation model objects: evidence for a power-law dependence of the volume-averaged velocity on the probe-volume radius. Phys. Rev. E 1996, 54(5):5278-5285.
44. O'Shaughnessy B., Procaccia I. Analytical solutions for diffusion on fractal objects. Phys. Rev. Lett. 1985, 54:455-458.
45. Özarslan E. Compartment shape anisotropy (CSA) revealed by double pulsed field gradient MR. J. Magn. Reson. 2009, 199(1):56-67. (URL). http://dx.doi.org/10.1016/j.jmr.2009.04.002.
46. Özarslan E., Basser P.J. MR diffusion-"diffraction" phenomenon in multi-pulse-field-gradient experiments. J. Magn. Reson. 2007, 188(2):285-294. URL. http://dx.doi.org/10.1016/j.jmr.2007.08.002.
47. Özarslan E., Vemuri B.C., Mareci T.H. Generalized scalar measures for diffusion MRI using trace, variance, and entropy. Magn. Reson. Med. 2005, 53(4):866-876. (URL). http://dx.doi.org/10.1002/mrm.20411.
48. Özarslan E., Basser P.J., Shepherd T.M., Thelwall P.E., Vemuri B.C., Blackband S.J. Characterization of anomalous diffusion from MR signal may be a new probe to tissue microstructure. Conf. Proc. IEEE Eng. Med. Biol. Soc. 2006, 1:2256-2259. URL. http://dx.doi.org/10.1109/IEMBS.2006.259651.
49. Özarslan E., Basser P.J., Shepherd T.M., Thelwall P.E., Vemuri B.C., Blackband S.J. Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal. J. Magn. Reson. 2006, 183(2):315-323. (URL). http://dx.doi.org/10.1016/j.jmr.2006.08.009.
50. Özarslan E., Basser P.J., Vemuri B.C., Shepherd T.M., Thelwall P.E., Blackband S.J. Observation of anomalous diffusion in excised tissue using the diffusion time dependence of the MR signal. 47th Experimental Nuclear Magnetic Resonance Conference 2006.
51. Özarslan E., Koay C.G., Basser P.J. Simple harmonic oscillator based estimation and reconstruction for one-dimensional q-space MR. Proc. Intl. Soc. Mag. Reson. Med. 2008, Vol. 16:35.
52. Özarslan E., Nevo U., Basser P.J. Anisotropy induced by macroscopic boundaries: surface-normal mapping using diffusion-weighted imaging. Biophys. J. 2008, 94(7):2809-2818. (URL). http://dx.doi.org/10.1529/biophysj.107.124081.
53. Özarslan E., Koay C.G., Basser P.J. Remarks on q-space MR propagator in partially restricted, axially-symmetric, and isotropic environments. Magn. Reson. Imaging 2009, 27(6):834-844. (URL). http://dx.doi.org/10.1016/j.mri.2009.01.005.
54. Özarslan E., Shemesh N., Koay C.G., Cohen Y., Basser P.J. Nuclear magnetic resonance characterization of general compartment size distributions. New J. Phys. 2011, 13:015010.
55. Pajevic S., Pierpaoli C. Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain. Magn. Reson. Med. 1999, 42(3):526-540.
56. Palombo M., Gabrielli A., Santis S.D., Cametti C., Ruocco G., Capuani S. Spatio-temporal anomalous diffusion in heterogeneous media by nuclear magnetic resonance. J. Chem. Phys. 2011, 135(3):034504. (URL). http://dx.doi.org/10.1063/1.3610367.
57. Pfeuffer J., Flögel U., Dreher W., Leibfritz D. Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of 1H NMR measurements on perfused glial cells. NMR Biomed. 1998, 11(1):19-31.
58. Rigaut J.P. An empirical formulation relating boundary lengths to resolution in specimens showing 'non-ideally fractal' dimensions. J. Microsc. 1984, 133:41-54.
59. Rigaut J.P., Schoëvaërt-Brossault D., Downs A.M., Landini G. Asymptotic fractals. Fractals in Biology and Medicine 1998, Vol. 2. Birkhäuser, Basel.
60. Ruppert D., Wand M.P., Carroll R.J. Semiparametric Regression 2003, Cambridge University Press.
61. Sanabria H., Kubota Y., Waxham M.N. Multiple diffusion mechanisms due to nanostructuring in crowded environments. Biophys. J. 2007, 92(1):313-322. (URL). http://dx.doi.org/10.1529/biophysj.106.090498.
62. Santis S.D., Gabrielli A., Bozzali M., Maraviglia B., Macaluso E., Capuani S. Anisotropic anomalous diffusion assessed in the human brain by scalar invariant indices. Magn. Reson. Med. 2011, 65(4):1043-1052. (URL). http://dx.doi.org/10.1002/mrm.22689.
63. Saxton M.J. A biological interpretation of transient anomalous subdiffusion. I. Qualitative model. Biophys. J. 2007, 92(4):1178-1191. (URL). http://dx.doi.org/10.1529/biophysj.106.092619.
64. Sen P.N. Time-dependent diffusion coefficient as a probe of geometry. Concepts Magn. Reson. A 2004, 23A(1):1-21.
65. Sen P.N., Hürlimann M.D., de Swiet T.M. Debye-Porod law of diffraction for diffusion in porous media. Phys. Rev. B 1995, 51(1):601-604.
66. Shepherd T.M., Özarslan E., King M.A., Mareci T.H., Blackband S.J. Structural insights from high-resolution diffusion tensor imaging and tractography of the isolated rat hippocampus. Neuroimage 2006, 32(4):1499-1509. (URL). http://dx.doi.org/10.1016/j.neuroimage.2006.04.210.
67. Shepherd T.M., Özarslan E., Yachnis A.T., King M.A., Blackband S.J. Diffusion tensor microscopy indicates the cytoarchitectural basis for diffusion anisotropy in the human hippocampus. AJNR Am. J. Neuroradiol. 2007, 28(5):958-964.
68. Smith T.G., Marks W.B., Lange G.D., Sheriff W.H., Neale E.A. A fractal analysis of cell images. J. Neurosci. Methods 1989, 27(2):173-180.
69. Stallmach F., Vogt C., Kärger J., Helbig K., Jacobs F. Fractal geometry of surface areas of sand grains probed by pulsed field gradient NMR. Phys. Rev. Lett. 2002, 88(10):105505.
70. Stanley H.E., Meakin P. Multifractal phenomena in physics and chemistry. Nature 1988, 335:405-409.
71. Torrey H.C. Bloch equations with diffusion terms. Phys. Rev. 1956, 104(3):563-565.
72. Wahba G. Spline Models for Observational Data 1990, SIAM, Philadelphia.
73. Widom A., Chen H.J. Fractal Brownian motion and nuclear spin echoes. J. Phys. A 1995, 28:1243-1247.
74. Zavada T., Südland N., Kimmich R., Nonnenmacher T.F. Propagator representation of anomalous diffusion: the orientational structure factor formalism in NMR. Phys. Rev. E 1999, 60(2):1292-1298.
75. Zhou X.J., Gao Q., Abdullah O., Magin R.L. Studies of anomalous diffusion in the human brain using fractional order calculus. Magn. Reson. Med. 2010, 63(3):562-569. (URL). http://dx.doi.org/10.1002/mrm.22285.
76. Zupančič I. Effect of the background gradients on PGSE NMR diffusion measurements. Solid State Commun. 1988, 65(3):199-200.