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 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

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 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

Temperature and concentration calibration of aqueous polyvinylpyrrolidone (PVP) solutions for isotropic diffusion MRI phantoms

<div><p>To use the “apparent diffusion coefficient” (<i>D</i>_app) as a quantitative imaging parameter, well-suited test fluids are essential. In this study, the previously proposed aqueous solutions of polyvinylpyrrolidone (PVP) were examined and temperature calibrations were obtained. For example, at a temperature of 20°C, <i>D</i>_app ranged from 1.594 (95% CI: 1.593, 1.595) μm²/ms to 0.3326 (95% CI: 0. 3304, 0.3348) μm²/ms for PVP-concentrations ranging from 10% (w/w) to 50% (w/w) using K30 polymer lengths. The temperature dependence of <i>D</i>_app was found to be so strong that a negligence seems not advisable. The temperature dependence is descriptively modelled by an exponential function exp(<i>c</i>₂ (<i>T</i> − 20°<i>C</i>)) and the determined <i>c</i>₂ values are reported, which can be used for temperature calibration. For example, we find the value 0.02952 K^-1 for 30% (w/w) PVP-concentration and K30 polymer length. In general, aqueous PVP solutions were found to be suitable to produce easily applicable and reliable <i>D</i>_app-phantoms.</p></div

(double column): Images of the used phantom.

<p>a,b,c) High resolution images. d,e,f) Low resolution images. a,d) Signal images without diffusion weighting, i.e. with <i>b</i> = 0 s/mm². b,e) Signal image with <i>b</i> = 700 s/mm². Signal images are min-max normalized. c,f) <i>D</i>_app-maps of the phantom in units of μm²/ms. Cross sections of the volumes of interest are marked in blue in a and d.</p

(single column): Temperature calibration coefficient <i>c</i>₂ in dependence of PVP concentration for K30 and K90.

<p>Error bars denote 95% confidence intervals. The straight lines represent linear fits with weights inversely proportional to the width of the 95% confidence interval.</p

Recommended temperature calibration coefficient <i>c</i>₂ in K^-1.

<p>Recommended temperature calibration coefficient <i>c</i>₂ in K^-1.</p

Fit parameters describing the dependency of <i>D</i>_app on the temperature (see Eq (2)) for K90.

<p>95% confidence intervals are stated in brackets.</p