Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

Journal of Magnetic Resonance

Volumn 210, Issue 2, 2011, Pages 184-191

  Magin, Richard L ^a   Li, Weiguo ^a   Pilar Velasco, M ^b   Trujillo, Juan ^c   Reiter, David A ^d   Morgenstern, Ashley ^d   Spencer, Richard G ^d  

^a University of Illinois at Chicago   (United States)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^c UNIVERSIDAD DE LA LAGUNA   (Spain)

^d NATIONAL INSTITUTE ON AGING   (United States)

Author keywords

Cartilage; Extracellular matrix; Fractional calculus; Magnetic resonance imaging; T1 relaxation; T2 relaxation

Indexed keywords

ANOMALOUS BEHAVIOR; AQUEOUS ENVIRONMENT; BI-EXPONENTIAL MODELS; BIOLOGICAL TISSUES; BLOCH EQUATION; CHONDROITIN SULFATES; CURVE-FIT; EXPONENTIAL RELAXATION; EXTRACELLULAR MATRIX; FRACTIONAL CALCULUS; HETEROGENEOUS MATERIALS; HOMOGENEOUS FORMS; MATRIX; MATRIX COMPONENTS; MICRO-STRUCTURAL; MULTI-EXPONENTIAL DECAY; NMR RELAXATION; RELAXATION MODELS; SIGNAL TO NOISE; STRETCHED EXPONENTIAL FUNCTIONS; T1 RELAXATION; T2 RELAXATION; TYPE I COLLAGEN; VISCOELASTIC RELAXATION;

COLLAGEN; CURVE FITTING; DIELECTRIC MATERIALS; EXPONENTIAL FUNCTIONS; GELS; MAGNETIC RESONANCE IMAGING; NUCLEAR MAGNETIC RESONANCE; RELAXATION PROCESSES; RESONANCE; SIGNAL TO NOISE RATIO; TISSUE;

CARTILAGE;

CHONDROITIN SULFATE;

ALGORITHM; ANIMAL; ARTICLE; CARTILAGE; CATTLE; CHEMISTRY; EXTRACELLULAR MATRIX; METHODOLOGY; NOSE SEPTUM; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; RAT; SHARK; STAINING;

ALGORITHMS; ANIMALS; CARTILAGE; CATTLE; CHONDROITIN SULFATES; EXTRACELLULAR MATRIX; MAGNETIC RESONANCE SPECTROSCOPY; NASAL SEPTUM; RATS; SHARKS; STAINING AND LABELING;

BOVINAE;

EID: 79955925037     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2011.03.006     Document Type: Article

References (48)

1. A. Abragam Principles of Nuclear Magnetism 2002 Oxford University Press New York
2. E.M. Haacke, R.W. Brown, M.R. Thompson, and R. Venkatesan Magnetic Resonance Imaging: Physical Principles and Sequence Design 1999 John Wiley and Sons New York
3. E.D. Becker High Resolution NMR: Theory and Chemical Applications third ed. 2000 Academic Press San Diego
4. P.T. Callaghan Principles of Magnetic Resonance Microscopy 1991 Oxford University Press Oxford
5. R. Lenk Brownian Motion and Spin Relaxation 1977 Elsevier Amsterdam
6. R. Kimmich Strange kinetics, porous media, and NMR Chem. Phys. 284 2002 253 285
7. A.E. Sitnitsky, G.G. Pimenov, and A.V. Anisimov Spin-lattice NMR relaxation by anomalous translational diffusion J. Magn. Reson. 172 2005 48 55
8. K.B. Oldham, and J. Spanier The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order 1974 Academic Press New York
9. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives: Theory and Applications 1993 Gordon and Breach Switzerland
10. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Application of Fractional Differential Equations 2006 Elsevier Amsterdam
11. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific Singapore
12. B.J. West, M. Bolgona, and P. Grigolini Physics of Fractal Operators 2003 Springer-Verlag New York
13. R.L. Magin Fractional Calculus in Bioengineering 2006 Begell House Connecticut
14. D.A. Reiter, P.C. Lin, K.W. Fishbein, and R.G. Spencer Multicomponent T2 relaxation analysis in cartilage Magn. Reson. Med. 61 2009 803 809
15. P.C. Lin, D.A. Reiter, and R.G. Spencer Classification of degraded cartilage through multi-parametric MRI analysis J. Magn. Reson. 201 2009 61 71
16. M. Berberan-Santos, E.N. Bodunov, and B. Valeur Luminescence decays with underlying distributions of rate constants: General properties and selected cases M.N. Berberan-Santos, Fluorescence of Supermolecules, Polymers, and Nanosystems 2008 Springer Berlin 67 103
17. R.S. Lakes Viscoelastic Solids 1998 CRC Press Boca Raton
18. Y.C. Fung Biomechanics: Mechanical Properties of Living Tissues second ed. 1993 Springer New York
19. Z.P. Liang, and P.C. Lauterbur Principles of Magnetic Resonance Imaging: A Signal Processing Perspective 2000 IEEE Press New York
20. M.A. Bernstein, K.F. King, and X.J. Zhou Handbook of MRI Pulse Sequences 2004 Elsevier Academic Press Burlington
21. M.T. Vlaardingerbroek, and J.A. den Boer Magnetic Resonance Imaging second ed. 1999 Springer- Verlag Berlin
22. R.L. Magin, O. Abdullah, D. Baleanu, and X.J. Zhou Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation J. Magn. Reson. 190 2008 255 270
23. R.L. Magin, X. Feng, and D. Baleanu Fractional calculus in NMR Magn. Reson. Eng. 34 2009 16 23
24. I. Podlubny Fractional Differential Equations 1999 Academic Press New York
25. R. Freeman A Handbook of Nuclear Magnetic Resonance 1988 Wiley New York
26. K. Diethelm, N.J. Ford, A.D. Freed, and Y.F. Luchko Algorithms for the fractional calculus: a selection of numerical methods Comput. Meth. Appl. Mech. Eng. 194 2005 743 777
27. X.J. Zhou, Q. Gao, O. Abdullah, and R.L. Magin Studies of anomalous diffusion in the human brain using fractional order calculus Magn. Reson. Med. 63 2010 562 569
28. N.M. Menezes, M.L. Gray, J.R. Hartke, and D. Burstein T-2 and T1, MRI in articular cartilage systems Magn. Reson. Med. 51 2004 503 509 (Pubitemid 38298663)
29. D.S. Grebenkov Use, misuse, and abuse of apparent diffusion coefficients Conc. Magn. Reson. 36A 2009 24 35
30. 2 relaxation mapping in subjects with intervertebral disc degeneration and clinical symptoms Magn. Reson. Med. 63 2010 1193 1200
31. 2 Magn Reson. Imag. 23 2006 547 553
32. R.M. Mazo, Brownian Motion: Fluctuations, Dynamics, and Applications 2002 Oxford University Press Oxford
33. K.D. Whittall, and A.L. MacKay Quantitative interpretation of NMR relaxation data J. Magn. Reson. 84 1989 134 152
34. K. Diethelm The Analysis of Fractional Differential Equations 2010 Springer NewYork
35. A. Carpinteri, and F. Mainardi Fractals and Fractional Calculus in Continuum Mechanics CISM Courses and Lectures No. 378 1997 Springer-Wien New York
36. R. Kopelman Fractal reaction kinetics Science 241 1988 1620 1626
37. J. Garnier, and K. Soina Effective fractional acoustic wave equations in one-dimensional random multiscale media J. Acoust. Soc. Am. 127 2010 62 72
38. S. Holm, and R. Sinkus A unifying fractional wave equation for compressional and shear waves J. Acoust. Soc. Am. 127 2010 542 548
39. W.G. Gloeckle, and T.F. Nonnenmacher Fractional integral operators and Fox functions in the theory of viscoelasticity Macromolecules 24 1991 6426 6434
40. R. Metzler, W. Schick, H.-G. Kilian, and T.F. Nonnenmacher Relaxation in filled polymers: a fractional calculus approach J. Chem. Phys. 103 1995 7180 7186
41. R. Kimmich NMR Tomography, Diffusion, Relaxometry 1997 Springer Berlin pp. 183-187
42. J.R. Banavar, M. Lipsicas, and J.F. Willemsen Determination of the random-walk dimension of fractals by means of NMR Phys. Rev. B 32 1985 5575 6112
43. G. Jug Theory of NMR field-gradient spectroscopy for anomalous diffusion in fractal networks Chem. Phys. Lett. 131 1986 94 97
44. J. Kärger, and G. Vojta On the use of NMR pulsed field-gradient spectroscopy for the study of anomalous diffusion in fractal networks Chem. Phys. Lett. 141 1987 411 413
45. J. Kärger, H. Pfeifer, and G. Vojta Time correlation during anomalous diffusion in fractal systems and signal attenuation in NMR field-gradient spectroscopy Phys. Rev. A 37 1988 4514 4517
46. A. Widom, and H.J. Chen Fractal Brownian motion and nuclear spin echoes J. Phys. A 28 1995 1243 1247
47. R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Repts. 339 2000 1 77
48. R. Metzler, and J. Klafter The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics J. Phys. A: Math. Gen. 37 2004 R161 R208