Use, misuse, and abuse of apparent diffusion coefficients

Concepts in Magnetic Resonance Part A: Bridging Education and Research

Volumn 36, Issue 1, 2010, Pages 24-35

  Grebenkov, Denis S ^a  

^a LABORATOIRE DE PHYSIQUE DE LA MATIÈRE CONDENSÉE   (France)

Author keywords

ADC; Diffusion weighted imaging; Geometry; NMR; PGSE; Restricted diffusion

Indexed keywords

EID: 77952070298     PISSN: 15466086     EISSN: 15525023     Source Type: Journal    
DOI: 10.1002/cmr.a.20152     Document Type: Article

References (88)

1. Klafter J, Drake JM. 1989. Molecular Dynamics in Restricted Geometries. New York: John Wiley and Sons.
2. Grebenkov DS. 2007. NMR survey of reflected brownian motion. Rev Mod Phys 79:1077-1137.
3. Bouchaud JP, Georges A. 1990. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys Rep 195:127-293.
4. Metzler R, Klafter J. 2000. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 339:1-77.
5. Kimmich R. 2002. Strange kinetics, porous media, and NMR. Chem Phys 284:253-285.
6. Haus JW, Kehr KW. 1987. Diffusion in regular and disordered lattices. Phys Rep 150:263-406.
7. Sen PN. 2004. Time-dependent diffusion coefficient as a probe of geometry. Conc Magn Reson A 23:1- 21.
8. Callaghan PT. 1991. Principles of Nuclear Magnetic Resonance Microscopy. Oxford: Clarendon Press.
9. Hahn EL. 1950. Spin echoes. Phys Rev 80:580-594.
10. Carr HY, Purcell EM. 1954. Effects of diffusion on free precession in NMR experiments. Phys Rev 94: 630-638.
11. Stejskal EO, Tanner JE. 1965. Spin diffusion measurements: spin echoes in the presence of a timedependent field gradient. J Chem Phys 42:288-292.
12. Tanner JE, Stejskal EO. 1968. Restricted self-diffusion of protons in colloidal systems by the pulsedgradient, spin-echo method. J Chem Phys 49:1768- 1777.
13. Price WS. 1997. Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 1. Basic theory. Conc Magn Reson 9: 299-336.
14. Price WS. 1998. Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: Part 2. Experimental aspects. Conc Magn Reson 10:197-237.
15. Callaghan PT, Codd SL, Seymour JD. 1999. Spatial coherence phenomena arising from translational spin motion in gradient spin echo experiments. Conc Magn Reson 11:181-202.
16. Woessner DE. 1963. NMR spin-echo self-diffusion measurements on fluids undergoing restricted diffusion. J Phys Chem 67:1365-1367.
17. Watson AT, Chang CTP. 1997. Characterizing porous media with NMR methods. Prog Nucl Magn Reson Spectrosc 31:343-386.
18. Barrie PJ. 2000. Characterization of porous media using NMR methods. Annu Rep NMR Spectrosc 41: 265-316.
19. van Beek EJR, Wild JM, Kauczor HU, Schreiber W, Mugler JP, de Lange EE. 2004. Functional MRI of the lung using hyperpolarized 3-helium gas. J Magn Reson Imag 20:540-554.
20. Conradi MS, Saam B, Yablonskiy DA, Woods JC. 2006. Hyperpolarized 3He and perfluorocarbon gas diffusion MRI of lungs. Prog Nucl Magn Reson Spectr 48:63-83.
21. Hürlimann MD, Helmer KG, Latour LL, Sotak CH. 1994. Restricted diffusion in sedimentary rocks. Determination of surface-area-to-volume ratio and surface relaxivity. J Magn Reson A 111:169-178.
22. Song YQ, Ryu S, Sen PN. 2000. Determining multiple length scales in rocks. Nature (London) 406:178- 181.
23. Helmer KG, Hürlimann MD, de Swiet TM, Sen PN, Sotak CH. 1995. Determination of ratio of surface area to pore volume from restricted diffusion in a constant field gradient. J Magn Reson A 115:257- 259.
24. Kirkpatrick TR. 1982. Time dependent transport in a fluid with static traps. J Chem Phys 76:4255-4259.
25. de Swiet TM, Sen PN. 1996. Time dependent diffusion coefficient in a disordered medium. J Chem Phys 104:206-209.
26. Balinov B, Jönsson B, Linse P, Söderman O. 1993. The NMR self-diffusion method applied to restricted diffusion. Simulation of echo attenuation from molecules in spheres and between planes. J Magn Reson A 104:17-25.
27. Blees MH. 1994. The effect of finite duration of gradient pulses on the pulsed-field-gradient NMR method for studying restricted diffusion. J Magn Reson A 109:203-209.
28. Lennon AJ, Kuchel PW. 1994. Neural networks used to interpret pulsed-gradient restricted-diffusion data. J Magn Reson A 107:229-235.
29. Coy A, Callaghan PT. 1994. Pulsed gradient spin echo nuclear magnetic resonance for molecules diffusing between partially reflecting rectangular barriers. J Chem Phys 101:4599-4609.
30. Linse P, Söderman O. 1995. The validity of the short-gradient-pulse approximation in NMR studies of restricted diffusion. Simulations of molecules diffusing between planes, in cylinders and spheres. J Magn Reson A 116:77-86.
31. Kuchel PW, Lennon AJ, Durrant C. 1996. Analytical solutions and simulations for spin-echo measurements of diffusion of spins in a sphere with surface and bulk relaxation. J Magn Reson B 112:1-17.
32. Hagslätt H, Jönsson B, Nydén M,Söderman O. 2003. Predictions of pulsed field gradient NMR echo-decays for molecules diffusing in various restrictive geometries. Simulations of diffusion propagators based on a finite element method. J Magn Reson 161:138-147.
33. Robertson B. 1966. Spin-echo decay of spins diffusing in a bounded region. Phys Rev 151:273-277.
34. Callaghan PT, Coy A, MacGowan D, Packer KJ, Zelaya FO. 1991. Diffraction-like effects in NMR diffusion studies of fluids in porous solids. Nature (London) 351:467-469.
35. Balinov B, Söderman O, Ravey J-C. 1994. Diffraction-like effects observed in the PGSE experiment when applied to a highly concentrated water-oil emulsion. J Phys Chem 98:393-395.
36. Kuchel PW, Coy A, Stilbs P. 1997. NMR "diffusion- diffraction" of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics. Magn Reson Med 37:637-643.
37. Stoller SD, Happer W, Dyson FJ. 1991. Transverse spin relaxation in inhomogeneous magnetic fields. Phys Rev A 44:7459-7477.
38. de Swiet TM, Sen PN. 1994. Decay of nuclear magnetization by bounded diffusion in a constant field gradient. J Chem Phys 100:5597-5604.
39. Hürlimann MD, Helmer KG, de Swiet TM, Sen PN, Sotak CH. 1995. Spin echoes in a constant gradient and in the presence of simple restriction. J Magn Reson A 113:260-264.
40. Alexander DC, Barker GJ, Arridge SR. 2002. Detection and modeling of non-Gaussian apparent diffusion coefficient profiles in human brain data. Magn Reson Med 48:331-340.
41. Jensen JH, Helpern JA, Ramani A, Lu H, Kaczynski K. 2005. Diffusional Kurtosis imaging: the quantification of non-Gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 53:1432-1440.
42. Liu C, Bammer R, Moseley ME. 2005. Limitations of apparent diffusion coefficient-based models in characterizing non-Gaussian diffusion. Magn Reson Med 54:419-428.
43. Trampel R, Jensen JH, Lee RF, Kamenetskiy I, McGuinness G, Johnson G. 2006. Diffusional Kurtosis imaging in the lung using hyperpolarized 3He. Magn Reson Med 56:733-737.
44. Jacob RE, Laicher G, Minard KR. 2007. 3D MRI of non-Gaussian 3He gas diffusion in the rat lung. J Magn Reson 188:357-366.
45. Kiselev VG, Il'yasov KA. 2007. Is the "biexponential diffusion" biexponential? Magn Reson Med 57:464- 469.
46. Grebenkov DS, Guillot G, Sapoval B. 2007. Restricted diffusion in a model acinar labyrinth by NMR. Theoretical and numerical results. J Magn Reson 184:143-156.
47. Grebenkov DS. 2008. Laplacian Eigenfunctions in NMR. I. A numerical Tool. Conc Magn Reson A 32: 277-301.
48. Mair RW, Cory DG, Peled S, Tseng CH, Patz S, Walsworth RL. 1998. Pulsed-field-gradient measurements of time-dependent gas diffusion. J Magn Reson 135:478-486.
49. Mair RW, Wong GP, Hoffmann D, Hürlimann MD, Patz S, Schwartz LM, et al. 1999. Probing porous media with gas diffusion NMR. Phys Rev Lett 83: 3324-3327.
50. Axelrod S, Sen PN. 2001. Nuclear magnetic resonance spin echoes for restricted diffusion in an inhomogeneous field: methods and asymptotic regimes. J Chem Phys 114:6878-6895.
51. Grebenkov DS. 2007. NMR restricted diffusion between parallel planes in a cosine magnetic field: an exactly solvable model. J Chem Phys 126:104706-1- 15.
52. Lisitza NV, Song Y-Q. 2001. The behavior of diffusion eigenmodes in the presence of internal magnetic field in porous media. J Chem Phys 114:9120-9124.
53. Sigmund EE, Cho H, Chen P, Byrnes S, Song Y-Q, Guo XE, et al. 2008. Diffusion-based MR methods for bone structure and evolution. Magn Reson Med 59:28-39.
54. Cho H, Ryu S, Ackerman JL, Song Y-Q. 2009. Visualization of inhomogeneous local magnetic field gradient due to susceptibility contrast. J Magn Reson 198:88-93.
55. Zielinski LJ, Sen PN. 2000. Relaxation of nuclear magnetization in a nonuniform magnetic field gradient and in a restricted geometry. J Magn Reson 147: 95-103.
56. Pütz B, Barsky D, Schulten K. 1992. Edge enhancement by diffusion in microscopic MRI. J Magn Reson 97:27-53.
57. de Swiet TM. 1995. Diffusive edge enhancement in imaging. J Magn Reson B 109:12-18.
58. Song YQ. 2003. Using internal magnetic fields to obtain pore size distributions of porous media. Conc Magn Reson A 18:97-110.
59. Mitra PP, Sen PN. 1992. Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: simple pore geometries. Phys Rev B 45: 143-156.
60. Grebenkov DS. 2007. Multiple correlation function approach: rigorous results for simple geometries. Diff Fundam 5:1-34.
61. Grebenkov DS. 2008. Analytical solution for restricted diffusion in circular and spherical layers in inhomogeneous magnetic fields. J Chem Phys 128: 134702-1-14.
62. Codd SL, Callaghan PT. 1999. Spin echo analysis of restricted diffusion under generalized gradient waveforms: planar, cylindrical and spherical pores with wall relaxivity. J Magn Reson 137:358-372.
63. Sapoval B. 1994. General formulation of Laplacian transfer across irregular surfaces. Phys Rev Lett 73: 3314-3317.
64. Felici M, Filoche M, Straus C, Similowski T, Sapoval B. 2005. Diffusional screening in real 3D human acini: a theoretical study. Resp Physiol Neurobiol 145:279-293.
65. Grebenkov DS, Filoche M, Sapoval B. 2006. Mathematical basis for a general theory of laplacian transport towards irregular interfaces. Phys Rev E 73: 021103.
66. Grebenkov DS. 2006. Partially reflected brownian motion: a stochastic approach to transport phenomena. In: Velle LR ed. Focus on Probability Theory. Hauppauge. Nova Science Publishers. pp. 135-169.
67. Kuchel PW, Durrant CJ. 1999. Permeability coefficients from NMR q-space data: models with unevenly spaced semi-permeable parallel membranes. J Magn Reson 139:258-272.
68. Sen PN. 2003. Time-dependent diffusion coefficient as a probe of permeability of the pore wall. J Chem Phys 119:9871-9876.
69. Barzykin AV, Hayamizu K, Price WS, Tachiya M. 1995. Pulsed-field-gradient NMR of diffusive transport through a spherical interface into an external medium containing a relaxation agent. J Magn Reson A 114:39-46.
70. Price WS, Barzykin AV, Hayamizu K, Tachiya M. 1998. A model for diffusive transport through a spherical interface probed by pulsed-field gradient NMR. Biophys J 74:2259-2271.
71. Caprihan A, Wang LZ, Fukushima E. 1996. A multiple-narrow-pulse approximation for restricted diffusion in a time-varying field gradient. J Magn Reson A 118:94-102.
72. Callaghan PT. 1997. A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms. J Magn Reson 129: 74-84.
73. Callaghan PT, Codd SL. 1998. Generalized calculation of NMR imaging Edge effects arising from restricted diffusion in porous media. Magn Reson Imag 16:471-478.
74. Sukstanskii AL, Yablonskiy DA. 2002. Effects of restricted diffusion on MR signal formation. J Magn Reson 157:92-105.
75. Barzykin AV. 1998. Exact solution of the TorreyBloch equation for a spin echo in restricted geometries. Phys Rev B 58:14171-14174.
76. Barzykin AV. 1999. Theory of spin echo in restricted geometries under a step-wise gradient pulse sequence. J Magn Reson 139:342-353.
77. Niendorf T, Dijkhuizen RM, Norris DG, van Lookeren Campagne M, Nicolay K. 1996. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn Reson Med 36:847-857.
78. Mulkern RV, Gudbjartsson H, Westin CF, Zengingonul HP, Gartner W, Guttmann CR, et al. 1999. Multicomponent apparent diffusion coefficients in human brain. NMR Biomed 12:51-62.
79. Clark CA, Le Bihan D. 2000. Water diffusion compartmentation and anisotropy at high b values in the human brain. Magn Reson Med 44:852-859.
80. Sehy JV, Ackerman JJH, Neil JJ. 2002. Evidence that both fast and slow water ADC components arise from intracellular space. Magn Reson Med 48: 765-770.
81. Ababneh Z, Beloeil H, Berde CB, Gambarota G, Maier SE, Mulkern RV. 2005. Biexponential parameterization of diffusion and T2 relaxation decay curves in a rat muscle edema model: decay curve components and water compartments. Magn Reson Med 54: 524-531.
82. Milne ML, Conradi MS. 2009. Multi-exponential signal decay from diffusion in a single compartment. J Magn Reson 197:87-90.
83. Callaghan PT. 1995. Pulsed gradient spin echo NMR for planar, cylindrical and spherical pores under conditions of wall relaxation. J Magn Reson A 113:53- 59.
84. Söderman O, Jönsson B. 1995. Restricted diffusion in cylindrical geometry. J Magn Reson A 117:94-97.
85. Sen PN, Hürlimann MD, de Swiet TM. 1995. DebyePorod law of diffraction for diffusion in porous media. Phys Rev B 51:601-604.
86. Frohlich AF, Ostergaard L, Kiselev VG. 2006. Effect of impermeable boundaries on diffusion-attenuated MR signal. J Magn Reson 179:223-233.
87. Bennett KM, Schmainda KM, Bennett R, Rowe DB, Lu H, Hyde JS. 2003. Characterization of continuously distributed cortical water diffusion fates with a stretched-exponential model. Magn Reson Med 50: 727-734.
88. Peyron M, Pierens GK, Lucas AJ, Hall LD, Stewart RC. 1996. The modified stretched-exponential model for characterization of NMR relaxation in porous media. J Magn Reson A 118:214-220