On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR
Nuclear magnetic resonance (NMR) diffusion measurements can be used to probe porous structures or biological tissues by means of the random motion of water molecules. The short-time expansion of the diffusion coefficient in powers of t1/2, where t is the diffusion time related to the duration of the...
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2017-11-01
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doaj-e56c347bb08f4bdf80ab5d5a0096cb9a2020-11-25T00:37:15ZengFrontiers Media S.A.Frontiers in Physics2296-424X2017-11-01510.3389/fphy.2017.00056300621On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMRFrederik B. Laun0Kerstin Demberg1Armin M. Nagel2Micheal Uder3Tristan A. Kuder4Institute of Radiology, University Hospital Erlangen, Erlangen, GermanyMedical Physics in Radiology, German Cancer Research Center, Heidelberg, GermanyInstitute of Radiology, University Hospital Erlangen, Erlangen, GermanyInstitute of Radiology, University Hospital Erlangen, Erlangen, GermanyMedical Physics in Radiology, German Cancer Research Center, Heidelberg, GermanyNuclear magnetic resonance (NMR) diffusion measurements can be used to probe porous structures or biological tissues by means of the random motion of water molecules. The short-time expansion of the diffusion coefficient in powers of t1/2, where t is the diffusion time related to the duration of the diffusion-weighting magnetic field gradient profile, is universally connected to structural parameters of the boundaries restricting the diffusive motion. The t1/2-term is proportional to the surface to volume ratio. The t-term is related to permeability and curvature. The short time expansion can be measured with two approaches in NMR-based diffusion experiments: First, by the use of diffusion encodings of short total duration and, second, by application of oscillating gradients of long total duration. For oscillating gradients, the inverse of the oscillation frequency becomes the relevant time scale. The purpose of this manuscript is to show that the oscillating gradient approach is blind to the t-term. On the one hand, this prevents fitting of permeability and curvature measures from this term. On the other hand, the t-term does not bias the determination of the t1/2-term in experiments.http://journal.frontiersin.org/article/10.3389/fphy.2017.00056/fullmagnetic resonance imagingdiffusionshort-time limitsurface-to-volume ratiogradient profileoscillating gradients |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Frederik B. Laun Kerstin Demberg Armin M. Nagel Micheal Uder Tristan A. Kuder |
spellingShingle |
Frederik B. Laun Kerstin Demberg Armin M. Nagel Micheal Uder Tristan A. Kuder On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR Frontiers in Physics magnetic resonance imaging diffusion short-time limit surface-to-volume ratio gradient profile oscillating gradients |
author_facet |
Frederik B. Laun Kerstin Demberg Armin M. Nagel Micheal Uder Tristan A. Kuder |
author_sort |
Frederik B. Laun |
title |
On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR |
title_short |
On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR |
title_full |
On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR |
title_fullStr |
On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR |
title_full_unstemmed |
On the Vanishing of the t-term in the Short-Time Expansion of the Diffusion Coefficient for Oscillating Gradients in Diffusion NMR |
title_sort |
on the vanishing of the t-term in the short-time expansion of the diffusion coefficient for oscillating gradients in diffusion nmr |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Physics |
issn |
2296-424X |
publishDate |
2017-11-01 |
description |
Nuclear magnetic resonance (NMR) diffusion measurements can be used to probe porous structures or biological tissues by means of the random motion of water molecules. The short-time expansion of the diffusion coefficient in powers of t1/2, where t is the diffusion time related to the duration of the diffusion-weighting magnetic field gradient profile, is universally connected to structural parameters of the boundaries restricting the diffusive motion. The t1/2-term is proportional to the surface to volume ratio. The t-term is related to permeability and curvature. The short time expansion can be measured with two approaches in NMR-based diffusion experiments: First, by the use of diffusion encodings of short total duration and, second, by application of oscillating gradients of long total duration. For oscillating gradients, the inverse of the oscillation frequency becomes the relevant time scale. The purpose of this manuscript is to show that the oscillating gradient approach is blind to the t-term. On the one hand, this prevents fitting of permeability and curvature measures from this term. On the other hand, the t-term does not bias the determination of the t1/2-term in experiments. |
topic |
magnetic resonance imaging diffusion short-time limit surface-to-volume ratio gradient profile oscillating gradients |
url |
http://journal.frontiersin.org/article/10.3389/fphy.2017.00056/full |
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