Aggarwal, M.: Restricted diffusion and spectral content of the gradient waveforms, in: Advanced Diffusion Encoding Methods in MRI, edited by: Topgaard, D., Royal Society of Chemistry, Cambridge, UK, 103–122, https://doi.org/10.1039/9781788019910-00103, 2020.
Basser, P. J., Mattiello, J., and Le Bihan, D.: Estimation of the effective self-diffusion
tensor from the NMR spin echo, J. Magn. Reson. B, 103, 247–254, https://doi.org/10.1006/jmrb.1994.1037, 1994.
Boito, D., Yolcu, C., and Özarslan, E.: Multidimensional diffusion MRI methods with confined subdomains, Front. Phys., 10, 830274, https://doi.org/10.3389/fphy.2022.830274, 2022.
Callaghan, P. T.: Translational dynamics & magnetic resonance. Oxford University Press, Oxford, https://doi.org/10.1093/acprof:oso/9780199556984.001.0001, 2011.
Callaghan, P. T. and Söderman, O.: Examination of the lamellar phase of Aerosol OT
water using pulsed field gradient nuclear magnetic resonance, J. Phys. Chem., 87, 1737–1744, https://doi.org/10.1021/j100233a019, 1983.
Callaghan, P. T. and Stepišnik, J.: Frequency-domain analysis of spin motion using modulated-gradient NMR, J. Magn. Reson. A, 117, 118–122, https://doi.org/10.1006/jmra.1995.9959, 1995.
Carr, H. Y. and Purcell, E. M.: Effects of diffusion on free precession in nuclear magnetic resonance experiments, Phys. Rev., 94, 630–638, https://doi.org/10.1103/PhysRev.94.630, 1954.
Daimiel Naranjo, I., Reymbaut, A., Brynolfsson, P., Lo Gullo, R., Bryskhe, K., Topgaard, D., Giri, D. D., Reiner, J. S., Thakur, S., and Pinker-Domenig, K.: Multidimensional diffusion magnetic resonance imaging for characterization of tissue microstructure in breast cancer patients: A prospective pilot study, Cancers, 13, 1606, https://doi.org/10.3390/cancers13071606, 2021.
de Swiet, T. M. and Mitra, P. P.: Possible systematic errors in single-shot measurements of the trace of the diffusion tensor, J. Magn. Reson. B, 111, 15–22, https://doi.org/10.1006/jmrb.1996.0055, 1996.
Eriksson, S., Lasič, S., Nilsson, M., Westin, C.-F., and Topgaard, D.: NMR diffusion encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution, J. Chem. Phys., 142, 104201, https://doi.org/10.1063/1.4913502, 2015.
Eriksson, S., Lasič, S., and Topgaard, D.: Isotropic diffusion weighting by magic-angle spinning of the
q-vector in PGSE NMR, J. Magn. Reson., 226, 13–18, https://doi.org/10.1016/j.jmr.2012.10.015, 2013.
Frydman, L., Chingas, G. C., Lee, Y. K., Grandinetti, P. J., Eastman, M. A., Barrall, G. A., and Pines, A.: Variable-angle correlation spectroscopy in solid-state nuclear magnetic resonance, J. Chem. Phys., 97, 4800–4808, https://doi.org/10.1063/1.463860, 1992.
Haeberlen, U.: High resolution NMR in solids, Selective averaging, Academic Press, New York, https://doi.org/10.1016/B978-0-12-025561-0.X5001-1, 1976.
Hahn, E. L.: Spin echoes, Phys. Rev., 80, 580–594, https://doi.org/10.1103/PhysRev.80.580, 1950.
Hennel, F., Michael, E. S., and Pruessmann, K. P.: Improved gradient waveforms for oscillating gradient spin-echo (OGSE) diffusion tensor imaging, NMR Biomed., 34, e4434, https://doi.org/10.1002/nbm.4434, 2021.
Kärger, J.: Zur Bestimmung der Diffusion in einem Zweibereichsystem mit Hilfe von gepulsten Feldgradienten, Ann. Phys., 479, 1–4, https://doi.org/10.1002/andp.19694790102, 1969.
Kindlmann, G.: Superquadric tensor glyphs, in: Proceedings IEEE TVCG/EG Symposium on Visualization, edited by: Deussen, O., Hansen, C., Keim, D. A., and Saupe, D., Eurographics Association Aire-la-Ville, Switzerland, 147–154, https://doi.org/10.2312/VisSym/VisSym04/147-154, 2004.
Kingsley, P. B.: Introduction to diffusion tensor imaging mathematics: Part II. Anisotropy, diffusion-weighting factors, and gradient encoding schemes, Conc. Magn. Reson. A, 28, 123–154, https://doi.org/10.1002/cmr.a.20049, 2006.
Lasič, S., Åslund, I., and Topgaard, D.: Spectral characterization of diffusion with chemical shift resolution: Highly concentrated water-in-oil emulsion, J. Magn. Reson., 199, 166–172, https://doi.org/10.1016/j.jmr.2009.04.014, 2009.
Lasič, S., Szczepankiewicz, F., Eriksson, S., Nilsson, M., and Topgaard, D.: Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the
q-vector, Front. Phys., 2, 11, https://doi.org/10.3389/fphy.2014.00011, 2014.
Le Bihan, D., Breton, E., Lallemand, D., Grenier, P., Cabanis, E., and Laval-Jeantet, M.: MR imaging of intravoxel incoherent motions – application to diffusion and perfusion in neurological disorders, Radiology, 161, 401–407, https://doi.org/10.1148/radiology.161.2.3763909, 1986.
Lundell, H. and Lasič, S.: Diffusion encoding with general gradient waveforms, in: Advanced Diffusion Encoding Methods in MRI, edited by: Topgaard, D., Royal Society of Chemistry, Cambridge, UK, 12–67, https://doi.org/10.1039/9781788019910-00012, 2020.
Lundell, H., Sønderby, C. K., and Dyrby, T. B.: Diffusion weighted imaging with circularly polarized oscillating gradients, Magn. Reson. Med., 73, 1171–1176, https://doi.org/10.1002/mrm.25211, 2015.
Lundell, H., Nilsson, M., Dyrby, T. B., Parker, G. J. M., Cristinacce, P. L. H., Zhou, F. L., Topgaard, D., and Lasič, S.: Multidimensional diffusion MRI with spectrally modulated gradients reveals unprecedented microstructural detail, Sci. Rep., 9, 9026, https://doi.org/10.1038/s41598-019-45235-7, 2019.
Malmborg, C., Sjöbeck, M., Brockstedt, S., Englund, E., Söderman, O., and Topgaard, D.: Mapping the intracellular fraction of water by varying the gradient pulse length in
q-space diffusion MRI, J. Magn. Reson., 180, 280–285, https://doi.org/10.1016/j.jmr.2006.03.005, 2006.
Mills, R.: Self-diffusion in normal and heavy water in the range 1–45
∘, J. Phys. Chem., 77, 685–688, https://doi.org/10.1021/j100624a025, 1973.
Mori, S. and van Zijl, P. C. M.: Diffusion weighting by the trace of the diffusion tensor within a single scan, Magn. Reson. Med., 33, 41–52, https://doi.org/10.1002/mrm.1910330107, 1995.
Narvaez, O., Yon, M., Jiang, H., Bernin, D., Forssell-Aronsson, E., Sierra, A., and Topgaard, D.: Model-free approach to the interpretation of restricted and anisotropic self-diffusion in magnetic resonance of biological tissues, arXiv:2111.07827, https://doi.org/10.48550/arXiv.2111.07827, 2021.
Narvaez, O., Svenningsson, L., Yon, M., Sierra, A., and Topgaard, D.: Massively multidimensional diffusion-relaxation correlation MRI, Front. Phys., 9, 793966, https://doi.org/10.3389/fphy.2021.793966, 2022.
Neuman, C. H.: Spin echo of spins diffusing in a bounded medium, J. Chem. Phys., 60, 4508–4511, https://doi.org/10.1063/1.1680931, 1974.
Nielsen, J. S., Dyrby, T. B., and Lundell, H.: Magnetic resonance temporal diffusion tensor spectroscopy of disordered anisotropic tissue, Sci. Rep., 8, 2930, https://doi.org/10.1038/s41598-018-19475-y, 2018.
Nilsson, M., Szczepankiewicz, F., Lampinen, B., Ahlgren, A., de Almeida Martins, J. P., Lasič, S., Westin, C.-F., and Topgaard, D.: An open-source framework for analysis of multidimensional diffusion MRI data implemented in MATLAB, Proc. Intl. Soc. Mag. Reson. Med., 26, 5355, 2018.
Parsons, E. C., Does, M. D., and Gore, J. C.: Modified oscillating gradient pulses for direct sampling of the diffusion spectrum suitable for imaging sequences, Magn. Reson. Imaging, 21, 279–285, https://doi.org/10.1016/s0730-725x(03)00155-3, 2003.
Persson, N.-O., Fontell, K., Lindman, B., and Tiddy, G. J. T.: Mesophase structure studies by deuteron magnetic resonance observations for the sodium octanoate-decanol-water system, J. Colloid Interface Sci., 53, 461–466, https://doi.org/10.1016/0021-9797(75)90063-6, 1975.
Price, W. S.: NMR studies of translational motion, Cambridge University Press, Cambridge, https://doi.org/10.1017/CBO9780511770487, 2009.
Reymbaut, A.: Diffusion anisotropy and tensor-valued encoding, in: Advanced Diffusion Encoding Methods in MRI, edited by: Topgaard, D., Royal Society of Chemistry, Cambridge, UK, 68–102, https://doi.org/10.1039/9781788019910-00068, 2020.
Reymbaut, A., Zheng, Y., Li, S., Sun, W., Xu, H., Daimiel Naranjo, I., Thakur, S., Pinker-Domenig, K., Rajan, S., Vanugopal, V. K., Mahajan, V., Mahajan, H., Critchley, J., Durighel, G., Sughrue, M., Bryskhe, K., and Topgaard, D.: Clinical research with advanced diffusion encoding methods in MRI, in: Advanced Diffusion Encoding Methods in MRI, edited by: Topgaard, D., Royal Society of Chemistry, Cambridge, UK, 406–429, https://doi.org/10.1039/9781788019910-00406, 2020.
Samoson, A., Lippmaa, E., and Pines, A.: High resolution solid-state NMR: Averaging of second-order effect
s by means of a double-rotor, Mol. Phys., 65, 1013–1018, https://doi.org/10.1080/00268978800101571, 1998.
Sjölund, J., Szczepankiewicz, F., Nilsson, M., Topgaard, D., Westin, C.-F., and Knutsson, H.: Constrained optimization of gradient waveforms for generalized diffusion encoding, J. Magn. Reson., 261, 157–168, https://doi.org/10.1016/j.jmr.2015.10.012, 2015.
Stejskal, E. O. and Tanner, J. E.: Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient, J. Chem. Phys., 42, 288–292, https://doi.org/10.1063/1.1695690, 1965.
Stepišnik, J.: Analysis of NMR self-diffusion measurements by a density matrix calculation, Physica B, 104, 305–364, https://doi.org/10.1016/0378-4363(81)90182-0, 1981.
Stepišnik, J.: Time-dependent self-diffusion by NMR spin-echo, Physica B, 183, 343–350, https://doi.org/10.1016/0921-4526(93)90124-O, 1993.
Stepišnik, J.: Validity limits of Gaussian approximation in cumulant expansion for diffusion attenuation of spin echo, Physica B, 270, 110–117, https://doi.org/10.1016/S0921-4526(99)00160-X, 1999.
Stepišnik, J. and Callaghan, P. T.: The long time tail of molecular velocity correlation in a confined fluid: observation by modulated gradient spin-echo NMR, Physica B, 292, 296–301, https://doi.org/10.1016/S0921-4526(00)00469-5, 2000.
Szczepankiewicz, F., Westin, C. F., and Nilsson, M.: Maxwell-compensated design of asymmetric gradient waveforms for tensor-valued diffusion encoding, Magn. Reson. Med., 82, 1424–1437, https://doi.org/10.1002/mrm.27828, 2019.
Tanner, J. E.: Self diffusion of water in frog muscle, Biophys. J., 28, 107–116, https://doi.org/10.1016/S0006-3495(79)85162-0, 1979.
Topgaard, D.: Isotropic diffusion weighting in PGSE NMR: Numerical optimization of the
q-MAS PGSE sequence, Micropor. Mesopor. Mat., 178, 60–63, https://doi.org/10.1016/j.micromeso.2013.03.009, 2013.
Topgaard, D.: Director orientations in lyotropic liquid crystals: Diffusion MRI mapping of the Saupe order tensor, Phys. Chem. Chem. Phys., 18, 8545–8553, https://doi.org/10.1039/c5cp07251d, 2016.
Topgaard, D.: Multidimensional diffusion MRI, J. Magn. Reson., 275, 98–113, https://doi.org/10.1016/j.jmr.2016.12.007, 2017.
Topgaard, D.: Multiple dimensions for random walks, J. Magn. Reson., 306, 150–154, https://doi.org/10.1016/j.jmr.2019.07.024, 2019a.
Topgaard, D.: Diffusion tensor distribution imaging, NMR Biomed., 32, e4066, https://doi.org/10.1002/nbm.4066, 2019b.
Topgaard, D.: Multidimensional diffusion MRI, Github [code and data set],
https://github.com/daniel-topgaard/md-dmri-data (last access: 1 October 2022), 2021.
Wadsö, L., Anderberg, A., Åslund, I., and Söderman, O.: An improved method to validate the relative humidity generation in sorption balances, Eur. J. Pharm. Biopharm., 72, 99–104, https://doi.org/10.1016/j.ejpb.2008.10.013, 2009.
Woessner, D. E.: N. M. R. spin-echo self-diffusion measurements on fluids undergoing restricted diffusion, J. Phys. Chem., 67, 1365–1367, https://doi.org/10.1021/j100800a509, 1963.
Xu, J., Jiang, X., Devan, S. P., Arlinghaus, L. R., McKinley, E. T., Xie, J., Zu, Z., Wang, Q., Chakravarthy, A. B., Wang, Y., and Gore, J. C.: MRI-cytometry: Mapping nonparametric cell size distributions using diffusion MRI, Magn. Reson. Med., 85, 748–761, https://doi.org/10.1002/mrm.28454, 2021.
Yang, G. and McNab, J. A.: Eddy current nulled constrained optimization of isotropic diffusion encoding gradient waveforms, Magn. Reson. Med., 81, 1818–1832, https://doi.org/10.1002/mrm.27539, 2019.
Yolcu, C., Memic, M., Simsek, K., Westin, C. F., and Özarslan, E.: NMR signal for particles diffusing under potentials: From path integrals and numerical methods to a model of diffusion anisotropy, Phys. Rev. E, 93, 052602, https://doi.org/10.1103/PhysRevE.93.052602, 2016.
