Multidimensional encoding of restricted and anisotropic diffusion by double rotation of the q-vector
- Physical Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden
- Physical Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden
Abstract. Diffusion NMR and MRI methods building on the classic pulsed gradient spin echo sequence are sensitive to many aspects of translational motion, including time/frequency-dependence (“restriction”), anisotropy, and flow, which leads to ambiguities when interpreting experimental data from complex heterogeneous materials such as living biological tissues. Higher specificity to restriction or anisotropy can be obtained with, respectively, oscillating gradient or tensor-valued encoding which nevertheless both have some sensitivity to the property not being of direct interest. Here we propose a simple scheme derived from the “double rotation” technique in solid-state NMR to generate a family of modulated gradient waveforms allowing for comprehensive exploration of the two-dimensional frequency-anisotropy space and convenient investigation of both restricted and anisotropic diffusion with a single multidimensional acquisition protocol. The method is demonstrated by measuring multicomponent isotropic Gaussian diffusion in simple liquids, anisotropic Gaussian diffusion in a polydomain lyotropic liquid crystal, and restricted diffusion in a yeast cell sediment.
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Hong Jiang et al.
Status: closed (peer review stopped)
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CC1: 'Comment on mr-2022-16', Tom Barbara, 17 Oct 2022
This paper is interesting and I want to read it carefully. I have a comment right away however and that is the poor clarity of the : colon operator which actually and more simply is just the trace of the product of two matrices. In addition, referencing Kingsley for the" low down" on this notation is not very helpful. It is not actually defined clearly and is only presented in passing as equation 64 of that paper. If one works this out then that equation is the trace of the product of two symmetric matrices. Now this colon notion is sort of popular and if the authors want to use it they should define it in their paper right off. It is not that difficult!
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RC1: 'Comment on mr-2022-16', Tom Barbara, 08 Nov 2022
I am experiencing something of a conudrum with the theory of this paper. Please see the supplemental pdf for more details.
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RC2: 'Reply on RC1', Tom Barbara, 09 Nov 2022
Daniel cleared up my confusion by pointing out that all the gradients (imaging, diffusion, crusher, and slice selection) are included in the integral of Equation 4. That of course is not rank one. However, I believe that my confusion is shared by many, even though they are involved in diffuion studies in MRI and NMR, so having some language to make it clear from the outset is very much worth the effort. Indeed many of the references to the past literature merely repeat the stylized notation and so a reader new to the field cannot get the essential point very easily unless they know exactly where to look. I feel it is also important to include a diagram of the pulse sequence with all the gradients that are believed to contribute to this "sum over all gradients".
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RC3: 'Reply on RC2', Tom Barbara, 15 Nov 2022
I forgot to mention that a very nice paper (also suggested by Daniel) is Mattiello,Basser and LeBihan, journal of magnetic resonance A108, 131 (1994). In that paper one can see that because of the discontinuous nature of the gradient time evolution, the integral breaks up into a finite sum of terms and the construction of the b matrix will contain rank one contributions from each term and each of the pairwise cross terms.
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RC3: 'Reply on RC2', Tom Barbara, 15 Nov 2022
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RC2: 'Reply on RC1', Tom Barbara, 09 Nov 2022
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RC4: 'Comment on mr-2022-16', Anonymous Referee #2, 01 Jan 2023
The comment was uploaded in the form of a supplement: https://mr.copernicus.org/preprints/mr-2022-16/mr-2022-16-RC4-supplement.pdf
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RC5: 'Reply on RC4', Tom Barbara, 03 Jan 2023
I was relieved to see that the second reviewer agreed with mine that the theory could use some clairification and I agree with the terminology used to point to the "paper chase" syndrome. I have experienced it many times. Supplementary information is a great idea and I would be happy to see it, but I want to emphasize that even a brief mention of the reality behand the stylized notation along with a citation to an accurate reference that gives further explaination, will go a long way in making readers happy and able to champion an effort as "a great paper". I do have coworkers who do work in the area of diffusion and I do talk to them (and my name often gets on some publication as a result) and very often I hear "well I could not understand that paper".
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RC5: 'Reply on RC4', Tom Barbara, 03 Jan 2023
Status: closed (peer review stopped)
-
CC1: 'Comment on mr-2022-16', Tom Barbara, 17 Oct 2022
This paper is interesting and I want to read it carefully. I have a comment right away however and that is the poor clarity of the : colon operator which actually and more simply is just the trace of the product of two matrices. In addition, referencing Kingsley for the" low down" on this notation is not very helpful. It is not actually defined clearly and is only presented in passing as equation 64 of that paper. If one works this out then that equation is the trace of the product of two symmetric matrices. Now this colon notion is sort of popular and if the authors want to use it they should define it in their paper right off. It is not that difficult!
-
RC1: 'Comment on mr-2022-16', Tom Barbara, 08 Nov 2022
I am experiencing something of a conudrum with the theory of this paper. Please see the supplemental pdf for more details.
-
RC2: 'Reply on RC1', Tom Barbara, 09 Nov 2022
Daniel cleared up my confusion by pointing out that all the gradients (imaging, diffusion, crusher, and slice selection) are included in the integral of Equation 4. That of course is not rank one. However, I believe that my confusion is shared by many, even though they are involved in diffuion studies in MRI and NMR, so having some language to make it clear from the outset is very much worth the effort. Indeed many of the references to the past literature merely repeat the stylized notation and so a reader new to the field cannot get the essential point very easily unless they know exactly where to look. I feel it is also important to include a diagram of the pulse sequence with all the gradients that are believed to contribute to this "sum over all gradients".
-
RC3: 'Reply on RC2', Tom Barbara, 15 Nov 2022
I forgot to mention that a very nice paper (also suggested by Daniel) is Mattiello,Basser and LeBihan, journal of magnetic resonance A108, 131 (1994). In that paper one can see that because of the discontinuous nature of the gradient time evolution, the integral breaks up into a finite sum of terms and the construction of the b matrix will contain rank one contributions from each term and each of the pairwise cross terms.
-
RC3: 'Reply on RC2', Tom Barbara, 15 Nov 2022
-
RC2: 'Reply on RC1', Tom Barbara, 09 Nov 2022
-
RC4: 'Comment on mr-2022-16', Anonymous Referee #2, 01 Jan 2023
The comment was uploaded in the form of a supplement: https://mr.copernicus.org/preprints/mr-2022-16/mr-2022-16-RC4-supplement.pdf
-
RC5: 'Reply on RC4', Tom Barbara, 03 Jan 2023
I was relieved to see that the second reviewer agreed with mine that the theory could use some clairification and I agree with the terminology used to point to the "paper chase" syndrome. I have experienced it many times. Supplementary information is a great idea and I would be happy to see it, but I want to emphasize that even a brief mention of the reality behand the stylized notation along with a citation to an accurate reference that gives further explaination, will go a long way in making readers happy and able to champion an effort as "a great paper". I do have coworkers who do work in the area of diffusion and I do talk to them (and my name often gets on some publication as a result) and very often I hear "well I could not understand that paper".
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RC5: 'Reply on RC4', Tom Barbara, 03 Jan 2023
Hong Jiang et al.
Hong Jiang et al.
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