Use, misuse, and abuse of apparent diffusion coefficients

The notion of effective, time-dependent or, equivalently, apparent diffu- sion coefficient (ADC) and its use for characterization of porous media are revisited. It is argued that the dynamic ADC, quantifying the mean-square displacement of spin-bearing particles, should not be confused with its counterpart measured by a pulsed gradient spin echo technique. The former is an intrinsic characteristic of the medium, independ- ent of the applied magnetic field. In contrast, the spin-echo ADC depends on the experi- mental setup (e.g., gradient intensity and temporal profile), raising potential ambiguities in the interpretation of diffusion-weighted measurements, which may be strongly misleading when the Gaussian phase approximation (GPA) does not hold. The oversim- plified use of a single b-value is criticized. Several fitting models beyond the GPA are discussed. 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part A 36A: 24-35, 2010.

[1]  E. Purcell,et al.  Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments , 1954 .

[2]  D. Woessner,et al.  N.M.R. SPIN-ECHO SELF-DIFFUSION MEASUREMENTS ON FLUIDS UNDERGOING RESTRICTED DIFFUSION , 1963 .

[3]  J. E. Tanner,et al.  Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient , 1965 .

[4]  Baldwin Robertson,et al.  Spin-Echo Decay of Spins Diffusing in a Bounded Region , 1966 .

[5]  J. E. Tanner,et al.  Restricted Self‐Diffusion of Protons in Colloidal Systems by the Pulsed‐Gradient, Spin‐Echo Method , 1968 .

[6]  T. R. Kirkpatrick Time dependent transport in a fluid with static traps , 1982 .

[7]  Joseph W. Haus,et al.  Diffusion in regular and disordered lattices , 1987 .

[8]  Joseph Klafter,et al.  Molecular dynamics in restricted geometries , 1989 .

[9]  J. Bouchaud,et al.  Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .

[10]  Dyson,et al.  Transverse spin relaxation in inhomogeneous magnetic fields. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[11]  P. Callaghan,et al.  Diffraction-like effects in NMR diffusion studies of fluids in porous solids , 1991, Nature.

[12]  Sen,et al.  Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: Simple pore geometries. , 1992, Physical review. B, Condensed matter.

[13]  H. Pfeifer Principles of Nuclear Magnetic Resonance Microscopy , 1992 .

[14]  Klaus Schulten,et al.  Edge enhancement by diffusion in microscopic magnetic resonance imaging , 1992 .

[15]  Per Linse,et al.  The NMR Self-Diffusion Method Applied to Restricted Diffusion. Simulation of Echo Attenuation from Molecules in Spheres and between Planes , 1993 .

[16]  J. Ravey,et al.  Diffraction-like Effects Observed in the PGSE Experiment When Applied to a Highly Concentrated Water/Oil Emulsion , 1994 .

[17]  P. Sen,et al.  Decay of nuclear magnetization by bounded diffusion in a constant field gradient , 1994 .

[18]  Karl G. Helmer,et al.  Restricted Diffusion in Sedimentary Rocks. Determination of Surface-Area-to-Volume Ratio and Surface Relaxivity , 1994 .

[19]  Paul T. Callaghan,et al.  Pulsed gradient spin echo nuclear magnetic resonance for molecules diffusing between partially reflecting rectangular barriers , 1994 .

[20]  M. H. Blees,et al.  The Effect of Finite Duration of Gradient Pulses on the Pulsed-Field-Gradient NMR Method for Studying Restricted Diffusion , 1994 .

[21]  Sapoval General formulation of Laplacian transfer across irregular surfaces. , 1994, Physical review letters.

[22]  Neural Networks Used to Interpret Pulsed-Gradient Restricted-Diffusion Data , 1994 .

[23]  T. M. Deswiet Diffusive Edge Enhancement in Imaging , 1995 .

[24]  Karl G. Helmer,et al.  Spin Echoes in a Constant Gradient and in the Presence of Simple Restriction , 1995 .

[25]  Per Linse,et al.  The Validity of the Short-Gradient-Pulse Approximation in NMR Studies of Restricted Diffusion. Simulations of Molecules Diffusing between Planes, in Cylinders and Spheres , 1995 .

[26]  Paul T. Callaghan,et al.  Pulsed-Gradient Spin-Echo NMR for Planar, Cylindrical, and Spherical Pores under Conditions of Wall Relaxation , 1995 .

[27]  Kikuko Hayamizu,et al.  Pulsed-Field-Gradient NMR of Diffusive Transport through a Spherical Interface into an External Medium Containing a Relaxation Agent , 1995 .

[28]  Karl G. Helmer,et al.  Determination of ratio of surface area to pore volume from restricted diffusion in a constant field gradient , 1995 .

[29]  Sen,et al.  Debye-Porod law of diffraction for diffusion in porous media. , 1995, Physical review. B, Condensed matter.

[30]  Bengt Jönsson,et al.  Restricted Diffusion in Cylindrical Geometry , 1995 .

[31]  The Modified Stretched-Exponential Model for Characterization of NMR Relaxation in Porous Media , 1996 .

[32]  Kuchel,et al.  Analytical Solutions and Simulations for Spin-Echo Measurements of Diffusion of Spins in a Sphere with Surface and Bulk Relaxation , 1996, Journal of magnetic resonance. Series B.

[33]  D. Norris,et al.  Biexponential diffusion attenuation in various states of brain tissue: Implications for diffusion‐weighted imaging , 1996, Magnetic resonance in medicine.

[34]  Pabitra N. Sen,et al.  Time dependent diffusion coefficient in a disordered medium , 1996 .

[35]  Eiichi Fukushima,et al.  A Multiple-Narrow-Pulse Approximation for Restricted Diffusion in a Time-Varying Field Gradient , 1996 .

[36]  P W Kuchel,et al.  NMR “diffusion‐diffraction” of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics , 1997, Magnetic resonance in medicine.

[37]  William S. Price,et al.  Pulsed-Field Gradient Nuclear Magnetic Resonance as a Tool for Studying Translational Diffusion. Part 1. Basic Theory , 1997 .

[38]  Callaghan,et al.  A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms , 1997, Journal of magnetic resonance.

[39]  A. T. Watson,et al.  Characterizing porous media with NMR methods , 1997 .

[40]  S. Patz,et al.  Pulsed-field-gradient measurements of time-dependent gas diffusion. , 1998, Journal of magnetic resonance.

[41]  S. Codd,et al.  Generalised calculation of NMR imaging edge effects arising from restricted diffusion in porous media. , 1998, Magnetic resonance imaging.

[42]  William S. Price,et al.  Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: part II. Experimental aspects , 1998 .

[43]  K. Hayamizu,et al.  A model for diffusive transport through a spherical interface probed by pulsed-field gradient NMR. , 1998, Biophysical journal.

[44]  A. Barzykin EXACT SOLUTION OF THE TORREY-BLOCH EQUATION FOR A SPIN ECHO IN RESTRICTED GEOMETRIES , 1998 .

[45]  Callaghan,et al.  Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity. , 1999, Journal of magnetic resonance.

[46]  S. Patz,et al.  Probing porous media with gas diffusion NMR. , 1999, Physical review letters.

[47]  Paul T. Callaghan,et al.  Spatial coherence phenomena arising from translational spin motion in gradient spin echo experiments , 1999 .

[48]  William S. Price,et al.  Pulsed-Field Gradient Nuclear Magnetic Resonance as a Tool for Studying Translational Diffusion. Part 2. Experimental Aspects , 1999 .

[49]  P W Kuchel,et al.  Permeability coefficients from NMR q-space data: models with unevenly spaced semi-permeable parallel membranes. , 1999, Journal of magnetic resonance.

[50]  A. Barzykin,et al.  Theory of spin echo in restricted geometries under a step-wise gradient pulse sequence. , 1999, Journal of magnetic resonance.

[51]  C. Westin,et al.  Multi‐component apparent diffusion coefficients in human brain † , 1999, NMR in biomedicine.

[52]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[53]  Seungoh Ryu,et al.  Determining multiple length scales in rocks , 2000, Nature.

[54]  D. Le Bihan,et al.  Water diffusion compartmentation and anisotropy at high b values in the human brain , 2000, Magnetic resonance in medicine.

[55]  Zielinski,et al.  Relaxation of nuclear magnetization in a nonuniform magnetic field gradient and in a restricted geometry , 2000, Journal of magnetic resonance.

[56]  P. Barrie Characterization of porous media using NMR methods , 2000 .

[57]  Scott Axelrod,et al.  Nuclear magnetic resonance spin echoes for restricted diffusion in an inhomogeneous field: Methods and asymptotic regimes , 2001 .

[58]  The behavior of diffusion eigenmodes in the presence of internal magnetic field in porous media , 2001 .

[59]  S. Arridge,et al.  Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data , 2002, Magnetic resonance in medicine.

[60]  J. Neil,et al.  Evidence that both fast and slow water ADC components arise from intracellular space , 2002, Magnetic resonance in medicine.

[61]  Dmitriy A Yablonskiy,et al.  Effects of restricted diffusion on MR signal formation. , 2002, Journal of magnetic resonance.

[62]  Rainer Kimmich,et al.  Strange kinetics, porous media, and NMR , 2002 .

[63]  Bengt Jönsson,et al.  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. , 2003, Journal of magnetic resonance.

[64]  Yi-Qiao Song Using internal magnetic fields to obtain pore size distributions of porous media , 2003 .

[65]  Pabitra N. Sen,et al.  Time-dependent diffusion coefficient as a probe of the permeability of the pore wall , 2003 .

[66]  J. Hyde,et al.  Characterization of continuously distributed cortical water diffusion rates with a stretched‐exponential model , 2003, Magnetic resonance in medicine.

[67]  John P Mugler,et al.  Functional MRI of the lung using hyperpolarized 3‐helium gas , 2004, Journal of magnetic resonance imaging : JMRI.

[68]  Pabitra N. Sen,et al.  Time-dependent diffusion coefficient as a probe of geometry , 2004 .

[69]  J. Helpern,et al.  Diffusional kurtosis imaging: The quantification of non‐gaussian water diffusion by means of magnetic resonance imaging , 2005, Magnetic resonance in medicine.

[70]  B. Sapoval,et al.  Diffusional screening in real 3D human acini—a theoretical study , 2005, Respiratory Physiology & Neurobiology.

[71]  Roland Bammer,et al.  Limitations of apparent diffusion coefficient‐based models in characterizing non‐gaussian diffusion , 2005, Magnetic resonance in medicine.

[72]  Stephan E Maier,et al.  Biexponential parameterization of diffusion and T2 relaxation decay curves in a rat muscle edema model: Decay curve components and water compartments , 2005, Magnetic resonance in medicine.

[73]  Denis S. Grebenkov,et al.  Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena , 2006, math/0610080.

[74]  D. Yablonskiy,et al.  Hyperpolarized 3He and perfluorocarbon gas diffusion MRI of lungs , 2006 .

[75]  Ray F. Lee,et al.  Diffusional kurtosis imaging in the lung using hyperpolarized 3He , 2006, Magnetic resonance in medicine.

[76]  B. Sapoval,et al.  Mathematical basis for a general theory of Laplacian transport towards irregular interfaces. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[77]  Valerij G Kiselev,et al.  Effect of impermeable boundaries on diffusion-attenuated MR signal. , 2006, Journal of magnetic resonance.

[78]  Nuclear magnetic resonance restricted diffusion between parallel planes in a cosine magnetic field: an exactly solvable model. , 2007, The Journal of chemical physics.

[79]  Kevin R Minard,et al.  3D MRI of non-Gaussian (3)He gas diffusion in the rat lung. , 2007, Journal of magnetic resonance.

[80]  The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application Multiple correlation function approach: rigorous , 2007 .

[81]  B. Sapoval,et al.  Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results. , 2007, Journal of magnetic resonance.

[82]  Valerij G Kiselev,et al.  Is the “biexponential diffusion” biexponential? , 2007, Magnetic resonance in medicine.

[83]  Denis S. Grebenkov,et al.  NMR survey of reflected brownian motion , 2007 .

[84]  T R Brown,et al.  Diffusion‐based MR methods for bone structure and evolution , 2008, Magnetic resonance in medicine.

[85]  Denis S Grebenkov,et al.  Analytical solution for restricted diffusion in circular and spherical layers under inhomogeneous magnetic fields. , 2008, The Journal of chemical physics.

[86]  Denis S. Grebenkov,et al.  Laplacian Eigenfunctions in NMR. I. A Numerical Tool , 2008 .

[87]  M. Conradi,et al.  Multi-exponential signal decay from diffusion in a single compartment. , 2009, Journal of magnetic resonance.

[88]  Y. Song,et al.  Visualization of inhomogeneous local magnetic field gradient due to susceptibility contrast. , 2009, Journal of magnetic resonance.

[89]  E. Hahn,et al.  Spin Echoes , 2011 .