# NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution

## Abstract

We introduce a nuclear magnetic resonance method for quantifying the shape of axially symmetric microscopic diffusion tensors in terms of a new diffusion anisotropy metric, D{sub Δ}, which has unique values for oblate, spherical, and prolate tensor shapes. The pulse sequence includes a series of equal-amplitude magnetic field gradient pulse pairs, the directions of which are tailored to give an axially symmetric diffusion-encoding tensor b with variable anisotropy b{sub Δ}. Averaging of data acquired for a range of orientations of the symmetry axis of the tensor b renders the method insensitive to the orientation distribution function of the microscopic diffusion tensors. Proof-of-principle experiments are performed on water in polydomain lyotropic liquid crystals with geometries that give rise to microscopic diffusion tensors with oblate, spherical, and prolate shapes. The method could be useful for characterizing the geometry of fluid-filled compartments in porous solids, soft matter, and biological tissues.

- Authors:

- Division of Physical Chemistry, Department of Chemistry, Lund University, Lund (Sweden)
- CR Development AB, Lund (Sweden)
- Lund University Bioimaging Center, Lund University, Lund (Sweden)
- Department of Radiology, BWH, Harvard Medical School, Boston, Massachusetts MA 02215 (United States)
- (Sweden)

- Publication Date:

- OSTI Identifier:
- 22415499

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 10; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ANISOTROPY; AXIAL SYMMETRY; DIFFUSION; DISTRIBUTION FUNCTIONS; LIQUID CRYSTALS; MAGNETIC FIELDS; NUCLEAR MAGNETIC RESONANCE; ORIENTATION; POROUS MATERIALS; SOLIDS; SPHERICAL CONFIGURATION; TENSORS

### Citation Formats

```
Eriksson, Stefanie, Topgaard, Daniel, E-mail: daniel.topgaard@fkem1.lu.se, Lasič, Samo, Nilsson, Markus, Westin, Carl-Fredrik, and Department of Biomedical Engineering, Medical Informatics, Linköping University, Linköping.
```*NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution*. United States: N. p., 2015.
Web. doi:10.1063/1.4913502.

```
Eriksson, Stefanie, Topgaard, Daniel, E-mail: daniel.topgaard@fkem1.lu.se, Lasič, Samo, Nilsson, Markus, Westin, Carl-Fredrik, & Department of Biomedical Engineering, Medical Informatics, Linköping University, Linköping.
```*NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution*. United States. doi:10.1063/1.4913502.

```
Eriksson, Stefanie, Topgaard, Daniel, E-mail: daniel.topgaard@fkem1.lu.se, Lasič, Samo, Nilsson, Markus, Westin, Carl-Fredrik, and Department of Biomedical Engineering, Medical Informatics, Linköping University, Linköping. Sat .
"NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution". United States.
doi:10.1063/1.4913502.
```

```
@article{osti_22415499,
```

title = {NMR diffusion-encoding with axial symmetry and variable anisotropy: Distinguishing between prolate and oblate microscopic diffusion tensors with unknown orientation distribution},

author = {Eriksson, Stefanie and Topgaard, Daniel, E-mail: daniel.topgaard@fkem1.lu.se and Lasič, Samo and Nilsson, Markus and Westin, Carl-Fredrik and Department of Biomedical Engineering, Medical Informatics, Linköping University, Linköping},

abstractNote = {We introduce a nuclear magnetic resonance method for quantifying the shape of axially symmetric microscopic diffusion tensors in terms of a new diffusion anisotropy metric, D{sub Δ}, which has unique values for oblate, spherical, and prolate tensor shapes. The pulse sequence includes a series of equal-amplitude magnetic field gradient pulse pairs, the directions of which are tailored to give an axially symmetric diffusion-encoding tensor b with variable anisotropy b{sub Δ}. Averaging of data acquired for a range of orientations of the symmetry axis of the tensor b renders the method insensitive to the orientation distribution function of the microscopic diffusion tensors. Proof-of-principle experiments are performed on water in polydomain lyotropic liquid crystals with geometries that give rise to microscopic diffusion tensors with oblate, spherical, and prolate shapes. The method could be useful for characterizing the geometry of fluid-filled compartments in porous solids, soft matter, and biological tissues.},

doi = {10.1063/1.4913502},

journal = {Journal of Chemical Physics},

number = 10,

volume = 142,

place = {United States},

year = {Sat Mar 14 00:00:00 EDT 2015},

month = {Sat Mar 14 00:00:00 EDT 2015}

}