Range Of Diffusion Times Research Articles

Time-dependent diffusion tensor imaging and diffusion modeling of age-related differences in the medial gastrocnemius and feasibility study of correlations to histopathology.

Implement STEAM-DTI to model time-dependent diffusion eigenvalues using the random permeable barrier model (RPBM) to study age-related differences in the medial gastrocnemius (MG) muscle. Validate diffusion model-extracted fiber diameter for histological assessment. Diffusion imaging at different diffusion times (Δ) was performed on seven young and six senior participants. Time-dependent diffusion eigenvalues (λ2 (t), λ3 (t), and D⊥ (t); average of λ2 (t) and λ3 (t)) were fit to the RPBM to extract tissue microstructure parameters. Biopsy of the MG tissue for histological assessment was performed on a subset of participants (four young, six senior). λ3 (t) was significantly higher in the senior cohort for the range of diffusion times. RPBM fits to λ2 (t) yielded fiber diameters in agreement to those from histology for both cohorts. The senior cohort had lower values of volume fraction of membranes, ζ, in fits to λ2 (t), λ3 (t), and D⊥ (t) (significant for fit to λ3 (t)). Fits of fiber diameter from RPBM to that from histology had the highest correlation for the fit to λ2 (t). The age-related patterns in λ2 (t) and λ3 (t) could tentatively be explained from RPBM fits; these patterns may potentially arise from a decrease in fiber asymmetry and an increase in permeability with age.

Diffusion time dependency of extracellular diffusion.

To quantify the variations of the power-law dependences on diffusion time t or gradient frequency of extracellular water diffusion measured by diffusion MRI (dMRI). Model cellular systems containing only extracellular water were used to investigate the dependence of , the extracellular diffusion coefficient. Computer simulations used a randomly packed tissue model with realistic intracellular volume fractions and cell sizes. DMRI measurements were performed on samples consisting of liposomes containing heavy water(D2 O, deuterium oxide) dispersed in regular water (H2 O). was obtained over a broad range (∼1-1000 ms) and then fit power-law equations and . Both simulated and experimental results suggest that no single power-law adequately describes the behavior of over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limited ranges; for example, is valid only for short times, whereas or is valid only for long times but cannot describe other ranges simultaneously. For the specific range of 5-70 ms used in typical human dMRI measurements, matches the data well empirically. The optimal power-law fit of extracellular diffusion varies with diffusion time. The dependency obtained at short or long limits cannot be applied to typical dMRI measurements in human cancer or liver. It is essential to determine the appropriate diffusion time range when modeling extracellular diffusion in dMRI-based quantitative microstructural imaging.

Time-dependent diffusivity and kurtosis in phantoms and patients with head and neck cancer.

To assess the reliability of measuring diffusivity, diffusional kurtosis, and cellular-interstitial water exchange time with long diffusion times (100-800 ms) using stimulated-echo DWI. Time-dependent diffusion MRI was tested on two well-established diffusion phantoms and in 5 patients with head and neck cancer. Measurements were conducted using an in-house diffusion-weighted STEAM-EPI pulse sequence with multiple diffusion times at a fixed TE on three scanners. We used the weighted linear least-squares fit method to estimate time-dependent diffusivity, , and diffusional kurtosis, . Additionally, the Kärger model was used to estimate cellular-interstitial water exchange time ( ) from . Diffusivity measured by time-dependent STEAM-EPI measurements and commercial SE-EPI showed comparable results with R2 above 0.98 and overall 5.4± 3.0% deviation across diffusion times. Diffusional kurtosis phantom data showed expected patterns: constant and = 0 for negative controls and slow varying and for samples made of nanoscopic vesicles. Time-dependent diffusion MRI in patients with head and neck cancer found that the Kärger model could be considered valid in 72% ± 23% of the voxels in the metastatic lymph nodes. The median cellular-interstitial water exchange time estimated for lesions was between 58.5 ms and 70.6ms. Based on two well-established diffusion phantoms, we found that time-dependent diffusion MRI measurements can provide stable diffusion and kurtosis values over a wide range of diffusion times and across multiple MRI systems. Moreover, estimation of cellular-interstitial water exchange time can be achieved using the Kärger model for the metastatic lymph nodes in patients with head and neck cancer.

Unusual surface microstructural evolution of Nd–Ce–Fe–B sintered magnets by (Nd, Pr)Hx grain boundary diffusion

Usually the grain boundary diffusion process (GBDP) provides a facile approach toward high-coercivity Nd–Fe–B magnets by modulating the surface microstructure, i.e. constructing nonferromagnetic grain boundary layers and forming magnetically hardening shells of 2:14:1 main phase. However, by applying (Nd, Pr)H x GBDP to the 25 wt% Ce-substituted Nd–Ce–Fe–B sintered magnet, it is surprisingly discovered the ultimate coercivity below 12.4 kOe over a wide range of diffusion times. The low coercivity increment level of 1.5 kOe after an optimal 10 h diffusion is restrained by the unusual surface layer, i.e. an apparent Ce segregation at the surface region to form REFe 2 (RE = rare earth) intergranular phase at both triple junctions and grain boundaries, rather than the expected Nd/Pr-rich enrichment at the RE 2 Fe 14 B/RE-rich interface or at the GBs. Prolonging diffusion time from 6 to 20 h exacerbates the formation of REFe 2 phase and witnesses a more pronounced surface layer with a limited diffusion depth of ~80 μm, which is much lower than the reported GBDP Nd–Fe–B (millimeters) or Nd–La–Ce–Fe–B (hundreds of micrometers). The limited diffusion depth may be correlated to the blocked diffusion channel by the massive REFe 2 intergranular phase that replaces the conventional RE-rich phase. Above findings demonstrate that the characteristic REFe 2 phase highly affects the surface microstructural evolution of GBDP Nd–Ce–Fe–B magnet, and highlight future work toward sophisticated engineering of REFe 2 phase. • (Nd, Pr)H x GBDP yields unusual surface microstructure evolution of Nd–Ce–Fe–B sintered magnets. • REFe 2 TJ and GB phase forms preferentially at the diffusion surface. • Massive Ce segregates at surface region, rather than the expected Nd/Pr-rich intergranular phase. • Long-time diffusion of 20 h still restrains the diffusion depth to be below 100 μm. • The coercivity increment level of 1.5 kOe is much lower than other reported GBDP magnets.

Clinically feasible diffusion MRI in muscle: Time dependence and initial findings in Duchenne muscular dystrophy.

To characterize the diffusion time-dependence in muscle in healthy adult volunteers, boys with Duchenne's muscular dystrophy (DMD), and age-matched controls in a clinically feasible acquisition time for pediatric applications. Diffusion data were acquired using a pulsed gradient stimulated echo diffusion preparation at 5 different diffusion times (70, 130, 190, 250, and 330 ms), at 4 different b-values (0, 200, 400, 600, and 800 s/mm2 ) and 6 directions (orthogonal x, y, and z and diagonal xy, xz, and yz) and processed to obtain standard diffusion indices (mean diffusivity [MD] and fractional anisotropy [FA]) at each diffusion time. Time-dependent diffusion was seen in muscle in healthy adult volunteers, boys with DMD, and age-matched controls. Boys with DMD showed reduced MD and increased FA values in comparison to age matched controls across a range of diffusion times. A diffusion time of Δ = 190 ms had the largest effect size. These results could be used to optimize diffusion imaging in this disease further and imply that these diffusion indices may become an important biomarker in monitoring progression in DMD in the future.

Diffusion in Sephadex Gel Structures: Time Dependency Revealed by Multi-Sequence Acquisition over a Broad Diffusion Time Range.

It has been increasingly reported that in biological tissues diffusion-weighted MRI signal attenuation deviates from mono-exponential decay, especially at high b-values. A number of diffusion models have been proposed to characterize this non-Gaussian diffusion behavior. One of these models is the continuous-time random-walk (CTRW) model, which introduces two new parameters: a fractional order time derivative α and a fractional order spatial derivative β. These new parameters have been linked to intravoxel diffusion heterogeneities in time and space, respectively, and are believed to depend on diffusion times. Studies on this time dependency are limited, largely because the diffusion time cannot vary over a board range in a conventional spin-echo echo-planar imaging sequence due to the accompanying T2 decays. In this study, we investigated the time-dependency of the CTRW model in Sephadex gel phantoms across a broad diffusion time range by employing oscillating-gradient spin-echo, pulsed-gradient spin-echo, and pulsed-gradient stimulated echo sequences. We also performed Monte Carlo simulations to help understand our experimental results. It was observed that the diffusion process fell into the Gaussian regime at extremely short diffusion times whereas it exhibited a strong time dependency in the CTRW parameters at longer diffusion times.

Water and Ion Dynamics in Confined Media: A Multi-Scale Study of the Clay/Water Interface

This review details a large panel of experimental studies (Inelastic Neutron Scattering, Quasi-Elastic Neutron Scattering, Nuclear Magnetic Resonance relaxometry, Pulsed-Gradient Spin-Echo attenuation, Nuclear Magnetic Resonance Imaging, macroscopic diffusion experiments) used recently to probe, over a large distribution of characteristic times (from pico-second up to days), the dynamical properties of water molecules and neutralizing cations diffusing within clay/water interfacial media. The purpose of this review is not to describe these various experimental methods in detail but, rather, to investigate the specific dynamical information obtained by each of them concerning these clay/water interfacial media. In addition, this review also illustrates the various numerical methods (quantum Density Functional Theory, classical Molecular Dynamics, Brownian Dynamics, macroscopic differential equations) used to interpret these various experimental data by analyzing the corresponding multi-scale dynamical processes. The purpose of this multi-scale study is to perform a bottom-up analysis of the dynamical properties of confined ions and water molecules, by using complementary experimental and numerical studies covering a broad range of diffusion times (between pico-seconds up to days) and corresponding diffusion lengths (between Angstroms and centimeters). In the context of such a bottom-up approach, the numerical modeling of the dynamical properties of the diffusing probes is based on experimental or numerical investigations performed on a smaller scale, thus avoiding the use of empirical or fitted parameters.

Finite element simulations of hyperpolarized gas DWI in micro-CT meshes of acinar airways: validating the cylinder and stretched exponential models of lung microstructural length scales.

This work assesses the accuracy of the stretched exponential (SEM) and cylinder models of lung microstructural length scales that can be derived from hyperpolarized gas DWI. This was achieved by simulating 3 He and 129 Xe DWI signals within two micro-CT-derived realistic acinar airspace meshes that represent healthy and idiopathic pulmonary fibrosis lungs. The healthy and idiopathic pulmonary fibrosis acinar airway meshes were derived from segmentations of 3D micro-CT images of excised human lungs and meshed for finite element simulations of the Bloch-Torrey equations. 3 He and 129 Xe multiple b value DWI experiments across a range of diffusion times (3 He Δ = 1.6 ms; 129 Xe Δ = 5 to 20 ms) were simulated in each mesh. Global SEM mean diffusive length scale and cylinder model mean chord length value was derived from each finite element simulation and compared against each mesh's mean linear intercept length, calculated from intercept length measurements within micro-CT segmentation masks. The SEM-derived mean diffusive length scale was within ±10% of the mean linear intercept length for simulations with both 3 He (Δ = 1.6 ms) and 129 Xe (Δ = 7 to 13 ms) in the healthy mesh, and with 129 Xe (Δ = 13 to 20 ms) for the idiopathic pulmonary fibrosis mesh, whereas for the cylinder model-derived mean chord length the closest agreement with mean linear intercept length (11.7% and 22.6% difference) was at 129 Xe Δ = 20 ms for both healthy and IPF meshes, respectively. This work validates the use of the SEM for accurate estimation of acinar dimensions and indicates that the SEM is relatively robust across a range of experimental conditions and acinar length scales.

MRI-cytometry: Mapping nonparametric cell size distributions using diffusion MRI.

This report introduces and validates a new diffusion MRI-based method, termed MRI-cytometry, which can noninvasively map intravoxel, nonparametric cell size distributions in tissues. MRI was used to acquire diffusion MRI signals with a range of diffusion times and gradient factors, and a model was fit to these data to derive estimates of cell size distributions. We implemented a 2-step fitting method to avoid noise-induced artificial peaks and provide reliable estimates of tumor cell size distributions. Computer simulations in silico, experimental measurements on cultured cells in vitro, and animal xenografts in vivo were used to validate the accuracy and precision of the method. Tumors in 7 patients with breast cancer were also imaged and analyzed using this MRI-cytometry approach on a clinical 3 Tesla MRI scanner. Simulations and experimental results confirm that MRI-cytometry can reliably map intravoxel, nonparametric cell size distributions and has the potential to discriminate smaller and larger cells. The application in breast cancer patients demonstrates the feasibility of direct translation of MRI-cytometry to clinical applications. The proposed MRI-cytometry method can characterize nonparametric cell size distributions in human tumors, which potentially provides a practical imaging approach to derive specific histopathological information on biological tissues.

Twice-refocused stimulated echo diffusion imaging: Measuring diffusion time dependence at constant T1 weighting.

Diffusion times longer than 50 ms are typically probed with stimulated-echo sequences. Varying the diffusion time in stimulated-echo sequences affects the T1 weighting of subcompartments, complicating the analysis of diffusion time dependence. Although inversion recovery preparation could be used to change the T1 weighting, it cannot ensure equal T1 weighting at arbitrary mixing times. In this article, a sequence that ensures constant T1 weighting over a wide range of diffusion times is presented. The proposed sequence features 2 independent longitudinal storage periods: TM1 and TM2 . Diffusion encoding is performed during TM1 , effectively coupling the diffusion time and TM1 . Equal T1 weighting at arbitrary diffusion times is realized by keeping the total mixing time TM1 + TM2 constant. The sequence was compared with conventional stimulated-echo measurements of diffusion in a 2-compartment phantom consisting of distilled water and paraffinum perliquidum. Additionally, in vivo DTI of the brain was carried out for 8 healthy volunteers with diffusion times ranging from 50 to 500 ms. Diffusion time dependence of the axial and radial diffusivity was detected in the brain. Both sequences resulted in almost identical diffusivities in white matter. In regions containing partial volumes of gray and white matter, a dependency on T1 weighting was observed. In accordance with previous studies, little variance of T1 values appeared to be present in healthy white matter. However, this is likely different in diseased tissue.Here, the proposed sequence can be effective in differentiating between diffusion time dependence and T1 weighting effects.

Global sensitivity analysis of skeletal muscle dMRI metrics: Effects of microstructural and pulse parameters.

Estimating microstructural parameters of skeletal muscle from diffusion MRI (dMRI) signal requires understanding the relative importance of both microstructural and dMRI sequence parameters on the signal. This study seeks to determine the sensitivity of dMRI signal to variations in microstructural and dMRI sequence parameters, as well as assess the effect of noise on sensitivity. Using a cylindrical myocyte model of skeletal muscle, numerical solutions of the Bloch-Torrey equation were used to calculate global sensitivity indices of dMRI metrics (FA, RD, MD, , , ) for wide ranges of microstructural and dMRI sequence parameters. The microstructural parameters were: myocyte diameter, volume fraction, membrane permeability, intra- and extracellular diffusion coefficients, and intra- and extracellular times. Two separate pulse sequences were examined, a PGSE and a generalized diffusion-weighted sequence that accommodates a larger range of diffusion times. The effect of noise and signal averaging on the sensitivity of the dMRI metrics was examined by adding synthetic noise to the simulated signal. Among the examined parameters, the intracellular diffusion coefficient has the strongest effect, and myocyte diameter is more influential than permeability for FA and RD. The sensitivity indices do not vary significantly between the two pulse sequences. Also, noise strongly affects the sensitivity of the dMRI signal to microstructural variations. With the identification of key microstructural features that affect dMRI measurements, the reported sensitivity results can help interpret dMRI measurements of skeletal muscle in terms of the underlying microstructure and further develop parsimonious dMRI models of skeletal muscle.

Quantitative temporal diffusion spectroscopy as an early imaging biomarker of radiation therapeutic response in gliomas: A preclinical proof of concept

PurposeThis study aims to test the ability of quantitative temporal diffusion spectroscopy (qTDS) to assess cellular changes associated with radiation-induced cell death in a rat glioma model. Methods and MaterialsTumor response to a single fraction of 20 Gy of x-ray radiation was investigated in a rat glioma (9L) model. Tumor response was monitored longitudinally at postinoculation days 21, 23, and 25, using a specific implementation of qTDS with acronym IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion), as well as conventional diffusion and high-resolution anatomic imaging. IMPULSED method combines diffusion-weighted signals acquired over a range of diffusion times that are then analyzed and interpreted using a theoretical model of water diffusion in tissues, which generates parametric maps depicting cellular and subcellular structural information on a voxel-wise basis. Results from different metrics were compared statistically. ResultsA single dose of 20 Gy x-ray radiation significantly prolonged survival of 9L-bearing rats. The mean cell sizes of irradiated tumors decreased (P < .005) after radiation treatment, which we associate with cell shrinkage and the formation of small cellular bodies during apoptosis and necrosis. A combination of IMPULSED-derived parameters (mean cell size d and extracellular structural parameter βex) separated 90% of irradiated tumors from the nonirradiated cases at post inoculation day 23, whereas a combination of tumor growth and conventional apparent diffusion coefficient did not differentiate irradiated tumors from nonirradiated tumors. ConclusionsThis proof-of-concept study demonstrates the IMPULSED method to be a new method for deriving quantitative microstructural parameters in a preclinical tumor model. The method provides unique information based on the diffusion time dependency of diffusion magnetic resonance imaging, which cannot be obtained by conventional diffusion weighted imaging methods, and the results have a close correlation with primary biologic markers of treatment efficacy, such as cell death and survival.

Brain Metabolite Diffusion from Ultra-Short to Ultra-Long Time Scales: What Do We Learn, Where Should We Go?

In vivo diffusion-weighted MR spectroscopy (DW-MRS) allows measuring diffusion properties of brain metabolites. Unlike water, most metabolites are confined within cells. Hence, their diffusion is expected to purely reflect intracellular properties, opening unique possibilities to use metabolites as specific probes to explore cellular organization and structure. However, interpretation and modeling of DW-MRS, and more generally of intracellular diffusion, remains difficult. In this perspective paper, we will focus on the study of the time-dependency of brain metabolite apparent diffusion coefficient (ADC). We will see how measuring ADC over several orders of magnitude of diffusion times, from less than 1 ms to more than 1 s, allows clarifying our understanding of brain metabolite diffusion, by firmly establishing that metabolites are neither massively transported by active mechanisms nor massively confined in subcellular compartments or cell bodies. Metabolites appear to be instead diffusing in long fibers typical of neurons and glial cells such as astrocytes. Furthermore, we will evoke modeling of ADC time-dependency to evaluate the effect of, and possibly quantify, some structural parameters at various spatial scales, departing from a simple model of hollow cylinders and introducing additional complexity, either short-ranged (such as dendritic spines) or long-ranged (such as cellular fibers ramification). Finally, we will discuss the experimental feasibility and expected benefits of extending the range of diffusion times toward even shorter and longer values.

Diffusion time dependence of microstructural parameters in fixed spinal cord

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.

Choice of reference measurements affects quantification of long diffusion time behaviour using stimulated echoes.

PurposeTo demonstrate how reference data affect the quantification of the apparent diffusion coefficient (ADC) in long diffusion time measurements with diffusion‐weighted stimulated echo acquisition mode (DW‐STEAM) measurements, and to present a modification to avoid contribution from crusher gradients in DW‐STEAM.MethodsFor DW‐STEAM, reference measurements at long diffusion times have significant b 0 value, because b = 0 cannot be achieved in practice as a result of the need for signal spoiling. Two strategies for acquiring reference data over a range of diffusion times were considered: constant diffusion weighting (fixed‐b 0) and constant gradient area (fixed‐q 0). Fixed‐b 0 and fixed‐q 0 were compared using signal calculations for systems with one and two diffusion coefficients, and experimentally using data from postmortem human corpus callosum samples.ResultsCalculations of biexponential diffusion decay show that the ADC is underestimated for reference images with b > 0, which can induce an apparent time‐dependence for fixed‐q 0. Restricted systems were also found to be affected. Experimentally, the exaggeration of the diffusion time–dependent effect under fixed‐q 0 versus fixed‐b 0 was in a range predicted theoretically, accounting for 62% (longitudinal) and 35% (radial) of the time dependence observed in white matter.ConclusionsVariation in the b‐value of reference measurements in DW‐STEAM can induce artificial diffusion time dependence in ADC, even in the absence of restriction. Magn Reson Med 79:952–959, 2018. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Diffusion in hierarchical systems: A simulation study in models of healthy and diseased muscle tissue

PurposeTo investigate the sensitivity of diffusion‐MR signal to microstructural change in muscle tissue associated with pathology, and recommend optimal acquisition parameters.MethodsWe employ Monte‐Carlo simulation of diffusing spins in hierarchical tissue to generate synthetic diffusion‐weighted signal curves over a wide range of scan parameters. Curves are analyzed using entropy—a measure of curve complexity. Entropy change between a baseline and various microstructural scenarios is investigated. We find acquisitions that optimize entropy difference in each scenario.ResultsPermeability changes have a large effect on the diffusion‐weighted signal curve. Muscle fiber atrophy is also important, although differentiating between mechanisms is challenging. Several acquisitions over a range of diffusion times is optimal for imaging microstructural change in muscle tissue. Sensitivity to permeability is optimized for high gradient strengths, but sensitivity to other scenarios is optimal at other values.ConclusionsThe diffusion‐attenuated signal is sensitive to the microstructural changes, but the changes are subtle. Taking full advantage of the changes to the overall curve requires a set of acquisitions over a range of diffusion times. Permeability causes the largest changes, but even the very subtle changes associated with fiber radius distribution change the curves more than noise alone. Magn Reson Med 78:1187–1198, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made.

In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

A Macroscopic Model for the Diffusion MRI Signal Accounting for Time-Dependent Diffusivity

Diffusion magnetic resonance imaging (dMRI) encodes water displacement due to diffusion and is a powerful tool for obtaining information on the tissue microstructure. An important quantity measured in dMRI in each voxel is the apparent diffusion coefficient ($ADC$), and it is well established from imaging experiments that, in the brain, in vivo, the $ADC$ is dependent on the measured diffusion time. To aid in the understanding and interpretation of the $ADC$, using homogenization techniques, we derived a new asymptotic model for the dMRI signal from the Bloch--Torrey equation governing the water proton magnetization under the influence of diffusion-encoding magnetic gradient pulses. Our new model was obtained using a particular choice of scaling for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. The $ADC$ of the resulting model is dependent on the diffusion time. We numerically validated this model for a wide range of diffusion times for two-dimensional geometrical configurations.

Quantification of cell size using temporal diffusion spectroscopy.

A new approach has been developed to quantify cell sizes and intracellular volume fractions using temporal diffusion spectroscopy with diffusion-weighted acquisitions. Temporal diffusion spectra may be used to characterize tissue microstructure by measuring the effects of restrictions over a range of diffusion times. Oscillating gradients have been used previously to probe variations on cellular and subcellular scales, but their ability to accurately measure cell sizes larger than 10 μm is limited. By combining measurements made using oscillating gradient spin echo (OGSE) and a conventional pulsed gradient spin echo (PGSE) acquisition with a single, relatively long diffusion time, we can accurately quantify cell sizes and intracellular volume fractions. Based on a two compartment model (incorporating intra- and extracellular spaces), accurate estimates of cell sizes and intracellular volume fractions were obtained in vitro for (i) different cell types with sizes ranging from 10 to 20 μm, (ii) different cell densities, and (iii) before and after anticancer treatment. Hybrid OGSE-PGSE acquisitions sample a larger region of temporal diffusion spectra and can accurately quantify cell sizes over a wide range. Moreover, the maximum gradient strength used was lower than 15 G/cm, suggesting that this approach is translatable to practical MR imaging.

Diffusion and Trapping of Single Particles in Pores with Combined Pressure and Dynamic Voltage

In this article we report resistive-pulse experiments with polystyrene particles whose transport through pores is controlled by modulating the driving voltage during the process of translocation. Balancing electric and hydrostatic forces acting on the particles allowed us to observe a random walk of single particles in a pore for tens of seconds and to quantify their diffusion coefficient using two methods. The first approach is based on the mean square displacement and requires passage of multiple particles for a range of diffusion times. The diffusion coefficient of individual particles was determined based on the variance of their local diffusion velocities. The developed methods for measuring the diffusion coefficient in pores are applicable to particles of different sizes, do not require fluorescence labeling, and are entirely based on ion current recordings. In addition, application of a modulating voltage signal together with rising edge triggers enabled transporting the same particle back and forth in the pore without letting the particle leave the pore.