Obtaining T1-T2 distribution functions from 1-dimensional T1 and T2 measurements: The pseudo 2-D relaxation modelShow others and affiliations
2016 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 269, p. 186-195Article in journal (Refereed) Published
Abstract [en]
We present the pseudo 2-D relaxation model (P2DRM), a method to estimate multidimensional probability distributions of material parameters from independent 1-D measurements. We illustrate its use on 1-D T1 and T2 relaxation measurements of saturated rock and evaluate it on both simulated and experimental T1-T2 correlation measurement data sets. Results were in excellent agreement with the actual, known 2-D distribution in the case of the simulated data set. In both the simulated and experimental case, the functional relationships between T1 and T2 were in good agreement with the T1-T2 correlation maps from the 2-D inverse Laplace transform of the full 2-D data sets. When a 1-D CPMG experiment is combined with a rapid T1 measurement, the P2DRM provides a double-shot method for obtaining a T1-T2 relationship, with significantly decreased experimental time in comparison to the full T1-T2 correlation measurement.
Place, publisher, year, edition, pages
2016. Vol. 269, p. 186-195
Keywords [en]
Heterogeneity, Inverse Laplace transform, Inverse-gamma distribution, Lognormal distribution, Multidimensional distribution function, Porous media, Relaxation correlation, T1, T2, Distribution functions, Inverse problems, Inverse transforms, Laplace transforms, Porous materials, Inverse gamma distribution, Log-normal distribution, Multidimensional distributions, Relaxation correlations, T
1, T
2, Probability distributions
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:ri:diva-27636DOI: 10.1016/j.jmr.2016.06.009Scopus ID: 2-s2.0-84975855895OAI: oai:DiVA.org:ri-27636DiVA, id: diva2:1059546
Note
References: Kleinberg, R.L., Kenyon, W.E., Mitra, P.P., Mechanism of NMR relaxation of fluids in rock (1994) J. Magn. Reson., Ser. A, 108, pp. 206-214; Bloch, F., Nuclear relaxation in gases by surface catalysis (1951) Phys. Rev., 83, pp. 1062-1063; Brownstein, K.R., Tarr, C.E., Importance of classical diffusion in NMR-studies of water in biological cells (1979) Phys. Rev. A, 19, pp. 2446-2453; Song, Y.Q., Venkataramanan, L., Hürlimann, M.D., Flaum, M., Frulla, P., Straley, C., T1–T2 correlation spectra obtained using a fast two-dimensional laplace inversion (2002) J. Magn. Reson., 154, pp. 261-268; Hürlimann, M.D., Venkataramanan, L., Quantitative measurement of two-dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields (2002) J. Magn. Reson., 157, pp. 31-42; Callaghan, P.T., Arns, C.H., Galvosas, P., Hunter, M.W., Qiao, Y., Washburn, K.E., Recent fourier and laplace perspectives for multidimensional NMR in porous media (2007) Magn. Reson. Imaging, 25, pp. 441-444; Mitchell, J., Gladden, L.F., Chandrasekera, T.C., Fordham, E.J., Low-field permanent magnets for industrial process and quality control (2014) Prog. Nucl. Magn. Reson. Spectrosc., 76, pp. 1-60; Hürlimann, M.D., Well Logging (2007) eMagRes, , John Wiley & Sons, Ltd; Röding, M., Bradley, S.J., Williamson, N.H., Dewi, M.R., Nann, T., Nydén, M., The power of heterogeneity: parameter relationships from distributions (2016) PLoS ONE, 11, p. e0155718; Edzes, H.T., An analysis of the use of pulse multiplets in the single scan determination of spin-lattice relaxation rates (1975) J. Magn. Reson., 17, pp. 301-313; Hürlimann, M.D., Encoding of diffusion and T1 in the CPMG echo shape: single-shot D and T1 measurements in grossly inhomogeneous fields (2007) J. Magn. Reson., 184, pp. 114-129; Loening, N.M., Thrippleton, M.J., Keeler, J., Griffin, R.G., Single-scan longitudinal relaxation measurements in high-resolution NMR spectroscopy (2003) J. Magn. Reson., 164, pp. 321-328; Chandrasekera, T.C., Mitchell, J., Fordham, E.J., Gladden, L.F., Johns, M.L., Rapid encoding of T1 with spectral resolution in n-dimensional relaxation correlations (2008) J. Magn. Reson., 194, pp. 156-161; Weber, D., Mitchell, J., McGregor, J., Gladden, L.F., Comparing strengths of surface interactions for reactants and solvents in porous catalysts using two-dimensional NMR relaxation correlations (2009) J. Phys. Chem. C, 113, pp. 6610-6615; Mitchell, J., Broche, L.M., Chandrasekera, T.C., Lurie, D.J., Gladden, L.F., Exploring surface interactions in catalysts using low-field nuclear magnetic resonance (2013) J. Phys. Chem. C, 117, pp. 17699-17706; McDonald, P., Korb, J.-P., Mitchell, J., Monteilhet, L., Surface relaxation and chemical exchange in hydrating cement pastes: a two-dimensional NMR relaxation study (2005) Phys. Rev. E, 72, p. 011409; Casieri, C., De Luca, F., Nodari, L., Russo, U., Terenzi, C., Detection of magnetic environments in porous media by low-field 2D NMR relaxometry (2010) Chem. Phys. Lett., 496, pp. 223-226; Ahola, S., Telkki, V.V., Ultrafast two-dimensional NMR relaxometry for investigating molecular processes in real time (2014) ChemPhysChem, 15, pp. 1687-1692; King, J.N., Lee, V.J., Ahola, S., Telkki, V.V., Meldrum, T., Ultrafast multidimensional laplace NMR using a single-sided magnet (2016) Angew. Chem. Int. Ed., 55, pp. 5040-5043; Mitchell, J., Hürlimann, M., Fordham, E., A rapid measurement of T1/T2: the DECPMG sequence (2009) J. Magn. Reson., 200, pp. 198-206; Carr, H.Y., Purcell, E.M., Effects of diffusion on free precession in nuclear magnetic resonance experiments (1954) Phys. Rev., 94, pp. 630-638; Meiboom, S., Gill, D., Modified spin-echo method for measuring nuclear relaxation times (1958) Rev. Sci. Instrum., 29, pp. 688-691; Callaghan, P.T., Translational Dynamics and Magnetic Resonance (2011), Oxford University Press IncFredholm, I., Sur une classe d’équations fonctionnelles (1903) Acta Math., 27, pp. 365-390; Vold, R.L., Waugh, J.S., Klein, M.P., Phelps, D.E., Measurement of spin relaxation in complex systems (1968) J. Chem. Phys., 48, p. 3831; English, A.E., Whittall, K.P., Joy, M.L.G., Henkelman, R.M., Quantitative two-dimensional time correlation relaxometry (1991) Magnet. Reson. Med., 22, pp. 425-434; Whittall, K.P., MacKay, A.L., Quantitative interpretation of NMR relaxation data (1989) J. Magn. Reson., 84, pp. 134-152; Röding, M., Williamson, N.H., Nydén, M., Gamma convolution models for self-diffusion coefficient distributions in PGSE NMR (2015) J. Magn. Reson., 261, pp. 6-10; Venkataramanan, L., Song, Y.Q., Hürlimann, M.D., Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions (2002) IEEE Trans. Signal. Process., 50, pp. 1017-1026; Provencher, S.W., A constrained regularization method for inverting data represented by linear algebraic or integral equations (1982) Comput. Phys. Commun., 27, pp. 213-227; Provencher, S.W., CONTIN: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations (1982) Comput. Phys. Commun., 27, pp. 229-242; Borgia, G., Brown, R., Fantazzini, P., Uniform-penalty inversion of multiexponential decay data (1998) J. Magn. Reson., 132, pp. 65-77; Borgia, G., Brown, R., Fantazzini, P., Uniform-penalty inversion of multiexponential decay data: II. Data spacing, T2 data, systematic data errors, and diagnostics (2000) J. Magn. Reson., 147, pp. 273-285; Röding, M., Bernin, D., Jonasson, J., Särkkä, A., Topgaard, D., Rudemo, M., Nydén, B.M., The gamma distribution model for pulsed-field gradient NMR studies of molecular-weight distributions of polymers (2012) J. Magn. Reson., 222, pp. 105-111; Håkansson, B., Nydén, M., Söderman, O., The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments (2000) Colloid. Polym. Sci., 278, pp. 399-405; Layton, K.J., Morelande, M., Wright, D., Farrell, P.M., Moran, B., Johnston, L.A., Modelling and estimation of multicomponent T2 distributions (2013) IEEE Trans. Med. Imaging, 32, pp. 1423-1434; Williamson, N.H., Nydén, M., Röding, M., The lognormal and gamma distribution models for estimating molecular weight distributions of polymers using PGSE NMR (2016) J. Magn. Reson., 267, pp. 54-62; Arns, C.H., A comparison of pore size distributions derived by NMR and X-ray-CT techniques (2004) Phys. A, 339, pp. 159-165; Marschall, D., Method for correlating NMR relaxometry and mercury injection data (1995) Society of Core Analysts Conference, p. 12; Kleinberg, R.L., Horsfield, M.A., Transverse relaxation processes in porous sedimentary rock (1990) J. Magn. Reson., 88, pp. 9-19; Schoenfelder, W., Gläser, H.-R., Mitreiter, I., Stallmach, F., Two-dimensional NMR relaxometry study of pore space characteristics of carbonate rocks from a Permian aquifer (2008) J. Appl. Geophys., 65, pp. 21-29; Mitchell, J., Fordham, E.J., Contributed review: nuclear magnetic resonance core analysis at 0.3 T (2014) Rev. Sci. Instrum., 85, p. 111502; Haber-Pohlmeier, S., Stapf, S., Van Dusschoten, D., Pohlmeier, A., Relaxation in a natural soil: comparison of relaxometric imaging, T1-T2 correlation and fast-field cycling NMR (2010) Open Magnet. Reson. J., 3, pp. 57-62; Jaeger, F., Shchegolikhina, A., Van As, H., Schaumann, G.E., Proton NMR relaxometry as a useful tool to evaluate swelling processes in peat soils (2010) Open Magnet. Reson. J., 3, pp. 27-45; McDonald, P.J., Mitchell, J., Mulheron, M., Aptaker, P.S., Korb, J.-P., Monteilhet, L., Two-dimensional correlation relaxometry studies of cement pastes performed using a new one-sided NMR magnet (2007) Cem. Concr. Res., 37, pp. 303-309; Casieri, C., Terenzi, C., De Luca, F., Two-dimensional longitudinal and transverse relaxation time correlation as a low-resolution nuclear magnetic resonance characterization of ancient ceramics (2009) J. Appl. Phys., 105, p. 034901; Peemoeller, H., Shenoy, R.K., Pintar, M.M., Two-dimensional nmr time evolution correlation spectroscopy in wet lysozyme (1969) J. Magn. Reson., 45 (1981), pp. 193-204; Kleinberg, R.L., Farooqui, S.A., Horsfield, M.A., T1/T2 ratio and frequency dependence of NMR relaxation in porous sedimentary rocks (1993) J. Colloid Interface Sci., 158, pp. 195-198; Limpert, E., Stahel, W.A., Abbt, M., Log-normal distributions across the sciences: keys and clues (2001) Bioscience, 51, pp. 341-352; Lindquist, W.B., Venkatarangan, A., Dunsmuir, J., Wong, T.F., Pore and throat size distributions measured from synchrotron X‐ray tomographic images of Fontainebleau sandstones (2000) J. Geophys. Res.: Solid Earth, 105, pp. 21509-21527; Chunyan, J., Shunli, H., Shusheng, G., Wei, X., Huaxun, L., Yuhai, Z., The characteristics of lognormal distribution of pore and throat size of a low permeability core (2013) Pet. Sci. Technol., 31, pp. 856-865; McCall, K.R., Johnson, D.L., Guyer, R.A., Magnetization evolution in connected pore systems (1991) Phys. Rev. B, 44, pp. 7344-7355; Wong, P.Z., Lucatorto, T., De Graef, M., Methods of the Physics of Porous Media (1999), Academic PressSong, Y.Q., Venkataramanan, L., Burcaw, L., Determining the resolution of Laplace inversion spectrum (2005) J. Chem. Phys., 122, p. 104104; Alper, J.S., Gelb, R.I., Standard errors and confidence intervals in nonlinear regression: comparison of Monte Carlo and parametric statistics (1990) J. Phys. Chem., 94, pp. 4747-4751; Godefroy, S., Callaghan, P.T., 2D relaxation/diffusion correlations in porous media (2003) Magn. Reson. Imaging, 21, pp. 381-383
2016-12-222016-12-212023-05-25Bibliographically approved