Abstract
Water diffusion is generally anisotropic in porous media, giving the opportunity to access the microstructure of a substance. Two-dimensional (2D) Diffusion-Diffusion COrrelation SpectroscopY (DDCOSY), which is one kind of multi-dimensional diffusometry (MUD) techniques, was introduced to reveal microscopic anisotropy by tracing molecular displacements in orthogonal spatial directions. As DDCOSY is most applicable to substances with long transverse relaxation times, a short version of DDCOSY (i.e. sDDCOSY) was proposed with two diffusion gradient pairs applied simultaneously. With the increased interest in applying the MUD techniques in more complex media, it should be noted that the non-zero off-diagonal diffusion coefficients may lead to ambiguous correlation results in macroscopically anisotropy systems. In this work, we investigate the behavior of off-diagonal diffusion coefficients and suppress their influences on final correlation maps by altering one pulsed-field-gradient (PFG) direction. Results from Monte-Carlo simulations in a three-dimensional confining domain with a bundle of capillaries orientated by a certain degree verified the correction. Further experiments on different capillary networks demonstrate the ability of the proposed approach to unveil sample microstructure. The proposed sDDCOSY approach allows for applying MUD techniques for both microscopic and macroscopic anisotropic systems, with potentials to combine with imaging encodings.
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References
Callaghan, P.T., Komlosh, M.E.: Locally anisotropic motion in a macroscopically isotropic system: displacement correlations measured using double pulsed gradient spin-echo NMR. Magn. Reson. Chem. 40(13), S15–S19 (2002)
Callaghan, P.T., Furó, I.: Diffusion-diffusion correlation and exchange as a signature for local order and dynamics. J. Chem. Phys. 120(8), 4032–4038 (2004)
Song, Y.Q., Zielinski, L., Ryu, S.: Two-dimensional NMR of diffusion systems. Phys. Rev. Lett. 100(24), 248002 (2008)
Bernin, D., Topgaard, D.: NMR diffusion and relaxation correlation methods: new insights in heterogeneous materials. Current Opin. Colloid Interface Sci. 18(3), 166–172 (2013)
Paulsen, J.L., Song, Y.Q.: Two-dimensional diffusion time correlation experiment using a single direction gradient. J. Magn. Reson. 244, 6–11 (2014)
Komlosh, M.E., Özarslan, E., Lizak, M., Horkayne-Szakaly, I., Freidlin, R.Z., Horkay, F., Basser, P.J.: Mapping average axon diameters in porcine spinal cord white matter and rat corpus callosum using d-PFG MRI. Neuroimage 78, 210–216 (2013)
Komlosh, M.E., Benjamini, D., Hutchinson, E.B., King, S., Haber, M., Avram, A.V., Holtzclaw, L.A., Desai, A., Pierpaoli, C., Basser, P.J.: Using double pulsed-field gradient MRI to study tissue microstructure in traumatic brain injury (TBI). Microporous Mesoporous Mater. (2017)
Qiao, Y., Galvosas, P., Callaghan, P.T.: Diffusion correlation NMR spectroscopic study of anisotropic diffusion of water in plant tissues. Biophys. J. 89(4), 2899–2905 (2005)
Zong, F., Ancelet, L.R., Hermans, I.F., Galvosas, P.: Determining mean fractional anisotropy using DDCOSY: preliminary results in biological tissues. Magn. Reson. Chem. 55(5), 498–507 (2017)
Spindler, N.: Diffusion and flow investigations in natural porous media by nuclear magnetic resonance. Schriften des Forschungszentrums Jülich (2011)
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. IEEE Trans. Signal Process. 50(5), 1017–1026 (2002)
Zong, F., Spindler, N., Ancelet, L.R., Hermans, I.F., Galvosas, P.: Local and global anisotropy-recent re-implementation of 2D ILT diffusion methods. Microporous Mesoporous Mater. 269, 71–74 (2018)
Callaghan, P.T., Eccles, C.D., Xia, Y.: NMR microscopy of dynamic displacements: \(k\)-space and \(q\)-space imaging. J. Phys. E 21(8), 820–822 (1988)
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. J. Magn. Reson. 154(2), 261–268 (2002)
Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. V. H. Winson Sons (1977)
Fieremans, E., De Deene, Y., Delputte, S., Ozdemir, M.S., D’Asseler, Y., Vlassenbroeck, J., Deblaere, K., Achten, E., Lemahieu, I.: Simulation and experimental verification of the diffusion in an anisotropic fiber phantom. J. Magn. Reson. 190(2), 189–199 (2008)
Carr, H.Y., Purcell, E.M.: Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94, 630–638 (1954)
Meiboom, S., Gill, D.: Modified spin-echo method for measuring nuclear relaxation times. Review in Scientific Instrument. 29(8), 688 (1958)
de Graaf, R.A., Brown, P.B., McIntyre, S., Nixon, T.W., Behar, K.L., Rothman, D.L.: High magnetic field water and metabolite proton \(t_1\) and \(t_2\) relaxation in rat brain in vivo. Magn. Reson. Med. 56(2), 386–394 (2006)
Benjamini, D., Basser, P.J.: Use of marginal distributions constrained optimization (MADCO) for accelerated 2D MRI relaxometry and diffusometry. J. Magne. Reson. 271, 40–45 (2016)
Acknowledgments
This work was supported by the New Zealand Ministry of Business, Innovation, and Employment (Grant E1990) and the Chinese National Major Scientific Equipment R&D Project (Grant ZDYZ2010-2).
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Zong, F., Zhuo, Y., Spindler, N., Liu, H., Galvosas, P. (2020). Diffusion Anisotropy Identification by Short Diffusion-Diffusion Correlation Spectroscopy. In: Bonet-Carne, E., Hutter, J., Palombo, M., Pizzolato, M., Sepehrband, F., Zhang, F. (eds) Computational Diffusion MRI. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-030-52893-5_5
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