Quantification of pore size distribution using diffusion NMR: Experimental design and physical insights

Journal of Chemical Physics

Volumn 140, Issue 16, 2014, Pages

  Katz, Yaniv ^a   Nevo, Uri ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; INVERSE PROBLEMS; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; OPTIMAL SYSTEMS; OPTIMIZATION; PORE SIZE; POROUS MATERIALS;

EXPERIMENTAL PARAMETERS; MICROSTRUCTURAL INFORMATION; MULTIPLE CORRELATION; OPTIMAL DESIGN METHODS; OPTIMIZATION FRAMEWORK; OPTIMIZATION METHOD; PULSED FIELD GRADIENTS; RESTRICTED DIFFUSION;

DIFFUSION;

DIFFUSION; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; PHYSICAL CHEMISTRY; POROSITY; PROCEDURES;

DIFFUSION; MAGNETIC RESONANCE SPECTROSCOPY; PHYSICOCHEMICAL PHENOMENA; POROSITY;

EID: 84899853374     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4871193     Document Type: Article

References (72)

1. Y. Assaf and Y. Cohen, NMR Biomed. 12, 335 (1999). 10.1002/(SICI)1099- 1492(199910)12:6<335::AID-NBM581>3.0.CO;2-A
2. J. F. Kuntz, G. Trausch, P. Palmas, P. Mutzenhardt, and D. Canet, J. Chem. Phys. 126, 134904 (2007). 10.1063/1.2713379
3. X. Wang and Q. Ni, J. Orthop. Res. 21, 312 (2003). 10.1016/S0736-0266(02) 00157-2
4. R. Kleinberg, W. Kenyon, and P. Mitra, J. Magn. Reson. 108, 206 (1994). 10.1006/jmra.1994.1112
5. J. C. Gore, A. W. Anderson, M. D. Does, D. F. Gochberg, J. M. Joers, R. P. Kennan, E. C. Parsons, and M. Schachter, Magn. Reson. Imaging 19, 295 (2001). 10.1016/S0730-725X(01)00239-9
6. E. O. Stejskal and J. E. Tanner, J. Chem. Phys. 42, 288 (1965). 10.1063/1.1695690
7. P. Callaghan, J. Magn. Reson., Ser. A 113, 53 (1995). 10.1006/jmra.1995.1055
8. D. G. Cory, A. N. Garroway, and J. B. Miller, Polym. Prepr. 31, 149 (1990).
9. P. P. Mitra, Phys. Rev. B 51, 15074 (1995). 10.1103/PhysRevB.51.15074
10. D. Benjamini, Y. Katz, and U. Nevo, J. Chem. Phys. 137, 224201 (2012). 10.1063/1.4769792
11. D. Benjamini and U. Nevo, J. Magn. Reson. 230, 198 (2013). 10.1016/j.jmr.2013.03.001
12. N. Shemesh, E. Özarslan, T. Adiri, P. J. Basser, and Y. Cohen, J. Chem. Phys. 133, 044705 (2010). 10.1063/1.3454131
13. E. Özarslan, J. Magn. Reson. 199, 56 (2009). 10.1016/j.jmr.2009.04. 002
14. K. Packer and C. Rees, J. Colloid Interface Sci. 40, 206 (1972). 10.1016/0021-9797(72)90010-0
15. J. S. Murday, J. Chem. Phys. 48, 4938 (1968). 10.1063/1.1668160
16. K. R. Brownstein and C. E. Tarr, Phys. Rev. A 19, 2446 (1979). 10.1103/PhysRevA.19.2446
17. S. Davies and K. J. Packer, J. Appl. Phys. 67, 3163 (1990). 10.1063/1.345395
18. Y. Assaf, T. Blumenfeld-Katzir, Y. Yovel, and P. J. Basser, Magn. Reson. Med. 59, 1347 (2008). 10.1002/mrm.21577
19. K. Hollingsworth and M. Johns, J. Colloid Interface Sci. 258, 383 (2003). 10.1016/S0021-9797(02)00131-5
20. E. Özarslan, N. Shemesh, C. G. Koay, Y. Cohen, and P. J. Basser, New J. Phys. 13, 015010 (2011). 10.1088/1367-2630/13/1/015010
21. R. Deriche and J. Treilhard, SPIE Med. Imaging 8314, 83140L (2012). 10.1117/12.910673
22. H. T. Banks, K. Holm, and F. Kappel, Inverse Probl. 27, 075002 (2011). 10.1088/0266-5611/27/7/075002
23. S. Skare, M. Hedehus, M. E. Moseley, and T. Q. Li, J. Magn. Reson. 147, 340 (2000). 10.1006/jmre.2000.2209
24. C. G. Koay, E. Ozarslan, K. M. Johnson, and M. E. Meyerand, Med. Phys. 39, 2499 (2012). 10.1118/1.3700166
25. L. W. Kuo, J. H. Chen, V. J. Wedeen, and W.-Y. I. Tseng, NeuroImage 41, 7 (2008). 10.1016/j.neuroimage.2008.02.016
26. D. C. Alexander, J. Magn. Med. 60, 439 (2008). 10.1002/mrm.21646
27. L. Marielba Rojas, Regularization of Large Scale Ill-Conditioned Least Square Problems (Center for Research on Parallel Computation, Rice University 1996).
28. D. Rachkovskij and E. Revunova, Cybern. Sys. Anal. 48, 621 (2012). 10.1007/s10559-012-9443-6
29. X. Ge and J. Wu, Int. J. Geosci. 03, 14 (2012). 10.4236/ijg.2012.31002
30. G. M. Davies and N. A. Seaton, Langmuir 15, 6263 (1999). 10.1021/la990160s
31. F. Pukelsheim, Optimal Design of Experiments (Society for Industrial and Applied Mathematic, 2006).
32. W. K. Wong, Comput. Stat. Data Anal. 18, 441 (1994). 10.1016/0167- 9473(94)90161-9
33. A. Bardow, Comput. Chem. Eng. 32, 115 (2008). 10.1016/j.compchemeng.2007. 05.004
34. D. Simon, Evolutionary Optimization Algorithms (Wiley, 2013), pp. 21-23.
35. S. Yang, Y. Jiang, and T. Nguyen, IMA J. Manage. Math. 24, 451 (2013). 10.1093/imaman/dps021
36. D. S. Grebenkov, Concepts Magn. Reson., Part A 32A, 277 (2008). 10.1002/cmr.a.20117
37. A. V. Barzykin, J. Magn. Reson. 139, 342 (1999). 10.1006/jmre.1999.1778
38. D. S. Grebenkov, Rev. Mod. Phys. 79, 1077 (2007). 10.1103/RevModPhys.79. 1077
39. F. B. Laun, J. Chem. Phys. 137, 044704 (2012). 10.1063/1.4736849
40. H. Torrey, Phys. Rev. 104, 563 (1956). 10.1103/PhysRev.104.563
41. F. B. Laun, T. A. Kuder, A. Wetscherek, B. Stieltjes, and W. Semmler, Phys. Rev. E 86, 021906 (2012). 10.1103/PhysRevE.86.021906
42. E. Özarslan, N. Shemesh, and P. J. Basser, J. Chem. Phys. 130, 104702 (2009). 10.1063/1.3082078
43. D. S. Grebenkov, J. Chem. Phys. 128, 134702 (2008). 10.1063/1.2841367
44. L. Ambrosone, A. Ceglie, G. Colafemmina, and G. Palazzo, J. Chem. Phys. 110, 797 (1999). 10.1063/1.478047
45. K. G. Hollingsworth, A. J. Sederman, C. Buckley, L. F. Gladden, and M. L. Johns, J. Colloid Interface Sci. 274, 244 (2004). 10.1016/j.jcis.2004.02.074
46. A. Curtis, Geophys. J. Int. 136, 637 (1999). 10.1046/j.1365-246x.1999. 00749.x
47. D. D. Joshi, Linear Estimation and Design of Experiments (South Asia Books, 1990), p. 12.
48. J. E. Gentle, Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer, 2007), p. 439.
49. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (Society for Industrial and Applied Mathematics, 1987).
50. Y. Wang, X. Li, Z. Nashed, F. Zhao, H. Yang, Y. Guan, and H. Zhang, Remote Sens. Environ. 111, 36 (2007). 10.1016/j.rse.2007.03.007
51. J. Demmel, Numer. Math. 51, 251 (1987). 10.1007/BF01400115
52. A. Das and D. Kempe, in Proceedings of the 40th Annual ACM Symposium on Theory of Computing (ACM, New York, 2008), p. 45.
53. X. Wu and V. Kumar, The Top Ten Algorithms in Data Mining (Chapman and Hall/CRC, 2009), pp. 22-30.
54. S. H. Cha, Int. J. Math. Models Methods Appl. Sci. 1, 300 (2007).
55. S. Peled and D. Cory, J. Magn. Med. 42, 911 (1999). 10.1002/(SICI)1522- 2594(199911)42:5<911::AID-MRM11>3.0.CO;2-J
56. E. Özarslan and P. J. Basser, J. Magn. Reson. 188, 285 (2007). 10.1016/j.jmr.2007.08.002
57. G. P. Quinn and M. J. Keough, Experimental Design and Data Analysis for Biologists (Cambridge University Press, 2002), pp. 74-77.
58. B. Hofmann, Regularization for Applied Inverse and Ill-Posed Problems: A Numerical Approach (Vieweg+Teubner Verlag, 1986), pp. 29-37.
59. P. T. Callaghan, Translational Dynamics and Magnetic Resonance: Principles of Pulsed Gradient Spin Echo NMR (Oxford University Press, 2011).
60. E. Özarslan and P. J. Basser, J. Chem. Phys. 128, 154511 (2008). 10.1063/1.2905765
61. B. Ghadirian, A. M. Torres, N. N. Yadav, and W. S. Price, J. Chem. Phys. 138, 094202 (2013). 10.1063/1.4793525
62. N. Shemesh, E. Özarslan, P. J. Basser, and Y. Cohen, J. Chem. Phys. 132, 034703 (2010). 10.1063/1.3285299
63. S. N. Jespersen, NMR Biomed. 25, 813 (2012). 10.1002/nbm.1808
64. L. Venkataramanan, Y.-q. Song, and M. D. Hürlimann, IEEE Trans. Signal Process. 50, 1017 (2002). 10.1109/78.995059
65. R. C. O. Sebastião, C. N. Pacheco, J. P. Braga, and D. Piló-Veloso, J. Magn. Reson. 182, 22 (2006). 10.1016/j.jmr.2006.06.005
66. I. Drobnjak, B. Siow, and D. C. Alexander, J. Magn. Reson. 206, 41 (2010). 10.1016/j.jmr.2010.05.017
67. L. Van der Weerd, M. M. A. E. Claessens, C. Efdé, and H. Van As, Plant, Cell Environ. 25, 1539 (2002). 10.1046/j.1365-3040.2002.00934.x
68. Y. Seo, A. Takamata, T. Ogino, H. Morita, S. Nakamura, and M. Murakami, J. Physiol. 545, 217 (2002). 10.1113/jphysiol.2002.027227
69. R. Wang, T. Pavlin, M. S. Rosen, R. W. Mair, D. G. Cory, and R. L. Walsworth, Magn. Reson. Imaging 23, 329 (2005). 10.1016/j.mri.2004.11.044
70. S. Fichele, M. N. J. Paley, N. Woodhouse, P. D. Griffiths, E. J. R. van Beek, and J. M. Wild, J. Magn. Reson. 167, 1 (2004). 10.1016/j.jmr.2003.10.019
71. D. S. Grebenkov, G. Guillot, and B. Sapoval, J. Magn. Reson. 184, 143 (2007). 10.1016/j.jmr.2006.09.026
72. G. B. Folland, Fourier Analysis and Its Applications (American Mathematical Society, 2009), p. 133.