Time-dependent Apparent Diffusion Coefficient Research Articles

Time-dependent diffusion MRI as a probe of microstructural changes in a mouse model of Duchenne muscular dystrophy.

Dystrophic muscles show a high variability of fibre sizes and altered sarcolemmal integrity, which are typically assessed by histology. Time-dependent diffusion MRI is sensitive to tissue microstructure and its investigation through age-related changes in dystrophic and healthy muscles may help the understanding of the onset and progression of Duchenne muscular dystrophy (DMD). We investigated the capability of time-dependent diffusion MRI to quantify age and disease-related changes in hind-limb muscle microstructure between dystrophic (mdx) and wild-type (WT) mice of three age groups (7.5, 22 and 44 weeks). Diffusion time-dependent apparent diffusion coefficients (ADCs) of the gastrocnemius and tibialis anterior muscles were determined versus age and diffusion-gradient orientation at six diffusion times (Δ; range: 25-350 ms). Mean muscle ADCs were compared between groups and ages, and correlated with T2 , using Student's t test, one-way analysis of variance and Pearson correlation, respectively. Muscle fibre sizes and sarcolemmal integrity were evaluated by histology and compared with diffusion measurements. Hind-limb muscle ADC showed characteristic restricted diffusion behaviour in both mdx and WT animals with decreasing ADC values at longer Δ. Significant differences in ADC were observed at long Δ values (≥ 250 ms; p < 0.05, comparison between groups; p < 0.01, comparison between ages) with ADC increased by 5-15% in dystrophic muscles, indicative of reduced diffusion restriction. No significant correlation was found between T2 and ADC. Additionally, muscle fibre size distributions showed higher variability and lower mean fibre size in mdx than WT animals (p < 0.001). The extensive Evans Blue Dye uptake shown in dystrophic muscles revealed substantial sarcolemmal damage, suggesting diffusion measurements as more consistent with altered permeability rather than changes in muscle fibre sizes. This study shows the potential of diffusion MRI to non-invasively discriminate between dystrophic and healthy muscles with enhanced sensitivity when using long Δ.

SpinDoctor: A MATLAB toolbox for diffusion MRI simulation

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation. Under the assumption of negligible water exchange between compartments, the time-dependent apparent diffusion coefficient can be directly computed from the solution of a diffusion equation subject to a time-dependent Neumann boundary condition.This paper describes a publicly available MATLAB toolbox called SpinDoctor that can be used 1) to solve the Bloch-Torrey partial differential equation in order to simulate the diffusion magnetic resonance imaging signal; 2) to solve a diffusion partial differential equation to obtain directly the apparent diffusion coefficient; 3) to compare the simulated apparent diffusion coefficient with a short-time approximation formula.The partial differential equations are solved by P1 finite elements combined with built-in MATLAB routines for solving ordinary differential equations. The finite element mesh generation is performed using an external package called Tetgen.SpinDoctor provides built-in options of including 1) spherical cells with a nucleus; 2) cylindrical cells with a myelin layer; 3) an extra-cellular space enclosed either a) in a box or b) in a tight wrapping around the cells; 4) deformation of canonical cells by bending and twisting; 5) permeable membranes; Built-in diffusion-encoding pulse sequences include the Pulsed Gradient Spin Echo and the Oscillating Gradient Spin Echo.We describe in detail how to use the SpinDoctor toolbox. We validate SpinDoctor simulations using reference signals computed by the Matrix Formalism method. We compare the accuracy and computational time of SpinDoctor simulations with Monte-Carlo simulations and show significant speed-up of SpinDoctor over Monte-Carlo simulations in complex geometries. We also illustrate several extensions of SpinDoctor functionalities, including the incorporation of T2 relaxation, the simulation of non-standard diffusion-encoding sequences, as well as the use of externally generated geometrical meshes.

Presence of time-dependent diffusion in the brachial plexus.

This work describes the development of a method to measure the variation of apparent diffusion coefficient (ADC) with diffusion time (Δ) in the brachial plexus, as a potential method of probing microstructure. Diffusion-weighted MRI with body signal suppression was used to highlight the nerves from surrounding tissues, and sequence parameters were optimized for sensitivity to change with diffusion time. A porous media-restricted diffusion model based on the Latour-Mitra equation was fitted to the diffusion time-dependent ADC data from the brachial plexus nerves and cord. The ADC was observed to reduce at long diffusion times, confirming that diffusion was restricted in the nerves and cord in healthy subjects. T2 of the nerves was measured to be 80 ± 5 ms, the diffusion coefficient was found to vary from (1.5 ± 0.1) × 10-3 mm2 /s at a diffusion time of 18.3 ms to (1.0 ± 0.2) × 10-3 mm2 /s at a diffusion time of 81.3 ms. A novel method of probing restricted diffusion in the brachial plexus was developed. Resulting parameters were comparable with values obtained previously on biological systems. Magn Reson Med 79:789-795, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Symmetry of the gradient profile as second experimental dimension in the short-time expansion of the apparent diffusion coefficient as measured with NMR diffusometry

The time-dependent apparent diffusion coefficient as measured by pulsed gradient NMR can be used to estimate parameters of porous structures including the surface-to-volume ratio and the mean curvature of pores. In this work, the short-time diffusion limit and in particular the influence of the temporal profile of diffusion gradients on the expansion as proposed by Mitra et al. (1993) is investigated. It is shown that flow-compensated waveforms, i.e. those whose first moment is zero, are blind to the term linear in observation time, which is the term that is proportional to mean curvature and surface permeability. A gradient waveform that smoothly interpolates between flow-compensated and bipolar waveform is proposed and the degree of flow-compensation is used as a second experimental dimension. This two-dimensional ansatz is shown to yield an improved precision when characterizing the confining domain. This technique is demonstrated with simulations and in experiments performed with cylindrical capillaries of 100μm radius.

Time dependent models of apparent diffusion coefficient and surface chloride for chloride transport in fly ash concrete

This paper presents a Fick-based chloride transport model, which is mathematically consistent with time dependent apparent diffusion coefficient and surface chloride for fly ash concrete. In the paper, the inconsistency in a simple close-formed solution used to predict chloride penetration through fly ash concrete in a previous study of other researchers is pointed out. The inconsistency can be seen by comparing chloride profiles calculated by the simple close-formed solution to those calculated by a finite difference program. The inconsistency is caused by the use of simplified diffusion coefficient and mathematically incompatible surface chloride models. To avoid the inconsistency, a chloride transport model is developed in this study. In developing the model, regression analysis to fit coefficients of the developed model is compared to the regression analysis results obtained from the experiment of the researchers. In the experiment of the researchers, the effect of water to binder ratio and the amount of fly ash replacement in concrete is considered. Furthermore, the chloride transport calculated from the developed model is validated by comparing to other experimental results. Finally, the sensitivity analysis of the model coefficients and some remarks on the developed model are presented.

Effect of W/B to the Time Dependent Chloride Diffusion in Concrete with GGBS

This paper studied the influence of water to binder ratio to time dependent diffusion coefficients in concrete exposed to marine environments. And a refined diffusion model which considered the time dependent apparent diffusion coefficients and time dependent surface chloride concentration was established. It was found that both apparent diffusion coefficients and surface chloride concentration are time dependent and both are significantly influenced by water to binder ratio. Apparent diffusion decrease with time while surface chloride concentration increase with time. but water to binder ratio has similar influence to the constant of time dependent diffusion coefficients and the parameter of time dependent surface chloride concentration.

Gastrointestinal Stromal Tumors Treated with Imatinib Mesylate: Apparent Diffusion Coefficient in the Evaluation of Therapy Response in Patients

To prospectively investigate the use of the apparent diffusion coefficient (ADC) as an early response indicator in patients with gastrointestinal stromal tumors (GISTs) treated with imatinib mesylate. This study was approved by the institutional review board and written informed consent was obtained from all patients. Diffusion-weighted magnetic resonance (MR) imaging was performed in 32 patients with GISTs before and 1, 4, and 12 weeks after treatment with a tyrosine kinase inhibitor, imatinib mesylate. The measurable lesions were classified as having responded well or poorly according to size alterations at clinical evaluation following the first round of treatment (3 months). A linear mixed-effects model was applied to analyze changes in the ADCs of tumors during treatment and to compare the variation and slopes of the time-dependent ADC curves between the good- and poor-response groups. There were 56 lesions in the good-response group and 35 in the poor-response group. An early (1 week after therapy) noticeable and statistically significant (P < .001) increase in the ADC was observed in the good-response group (median ADC increase, 44.8%) but not in the poor-response group (median ADC increase, 1.5%). The time-dependent ADC variation was significantly different between the good- and poor-response groups, with a sharper median ADC increase displayed in the former (week 1: 44.8% vs 1.5%; week 4: 80.4% vs 7.8%; week 12: 89.6% vs 16.7%; F = 25.78, P < .001). The largest difference in the weekly percentage increase in ADC between the good- and poor-response groups was observed at 1 week after therapy (week 0-1: 44.8% vs 1.5%; week 1-4: 7.0% vs 2.8%; week 4-12: 1.6% vs 0.7%). The pretherapy mean ADC (± standard deviation) of lesions in the good-response group (1.06 [×10(-3) mm(2)/sec] ± 0.27) was significantly lower than that in the poor-response group (1.24 [×10(-3) mm(2)/sec] ± 0.32) (F = 8.34, P = .005). Comparatively low pretherapy ADC and marked ADC increase at 1 week after therapy is associated with good response to imatinib mesylate in patients with GISTs.

Diffusive motions in liquid medium-chain n-alkanes as seen by quasielastic time-of-flight neutron spectroscopy

Different diffusive motions in liquid C(32)H(66) on a picosecond time scale could be disentangled by resolution resolved quasielastic time-of-flight neutron spectroscopy (QENS). It is demonstrated that at all observation times, the dominating motion causes a Q(2) proportionality of the QENS signal, which indicates a Fickian diffusion mechanism. The observed motions can be characterized by an observation time dependent apparent diffusion coefficient D(a)(t(o)), which is up to one order of magnitude larger than the molecular self-diffusion coefficient D(s). By comparison with molecular dynamics simulations, the identified motions are attributed to displacements of hydrogen atoms reflecting not only global but also local molecular trajectories. Despite the rodlike shape of the molecules, the center of mass diffusion was found to be essentially isotropic. A coherent picture of the diffusional processes ranging from the fast tumbling of CH(2) groups to the slow long range molecular diffusion is presented.

Simulation and experimental verification of the diffusion in an anisotropic fiber phantom

Diffusion weighted magnetic resonance imaging enables the visualization of fibrous tissues such as brain white matter. The validation of this non-invasive technique requires phantoms with a well-known structure and diffusion behavior. This paper presents anisotropic diffusion phantoms consisting of parallel fibers. The diffusion properties of the fiber phantoms are measured using diffusion weighted magnetic resonance imaging and bulk NMR measurements. To enable quantitative evaluation of the measurements, the diffusion in the interstitial space between fibers is modeled using Monte Carlo simulations of random walkers. The time-dependent apparent diffusion coefficient and kurtosis, quantifying the deviation from a Gaussian diffusion profile, are simulated in 3D geometries of parallel fibers with varying packing geometries and packing densities. The simulated diffusion coefficients are compared to the theory of diffusion in porous media, showing a good agreement. Based on the correspondence between simulations and experimental measurements, the fiber phantoms are shown to be useful for the quantitative validation of diffusion imaging on clinical MRI-scanners.

Application of porous-media theory to the investigation of water ADC changes in rabbit Achilles tendon caused by tensile loading

The water apparent diffusion coefficient (ADC) in rabbit Achilles tendon is anisotropic, diffusion-time dependent, and changes as a function of tensile load. Water ADC changes of tendon under mechanical load are thought to be due to the extrusion of water from the more restricted tendon core to a relatively unrestricted bulk phase at the periphery (rim) of the tendon. Tensile loading may influence water ADC values by changing the spatial separation of restricting barriers (e.g., increasing the tendon fibril packing density). To explore this issue, we have applied porous-media theory to the investigation of water ADC changes in rabbit Achilles tendon under two different mechanical loading conditions (a baseline condition with a minimal tensile stress and a second in which the tensile stress was approximately 1 MPa). Diffusion sensitivity was applied in directions parallel and perpendicular to the long axis of the tendon. The short diffusion-time behavior of the resulting time-dependent ADC curves was used to indirectly infer information regarding the average surface area to volume ratio of the space available for molecular diffusion. From these values, we estimated a 40% reduction in volume available for diffusion in the perpendicular direction after tensile loading, but only a 10% reduction in the parallel direction. These differences are consistent with the known geometry of the tendon microstructure and suggest an increase in fibril packing density upon loading. The long diffusion-time behavior of the time-dependent ADC curves was used to indirectly infer the tortuosity of the diffusion pathways through the interstitial space. The tortuosity in the direction perpendicular to the tendon long axis was approximately 2.5 times greater than that in the parallel direction. Stimulated-echo measurement of the ADC values at longer diffusion times resulted in T 1 spin editing of water with shorter T 1 values (and correspondingly lower ADC values). The resulting increase in water ADC with increasing diffusion time was attributed to multiple components arising from the (overlapping) distribution of T 1 values in the core and rim regions of the tendon.

Correlation time and diffusion coefficient imaging: application to a granular flow system.

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = <u(t)u(t + tau)>, expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = <u(2)>e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = <u(2)>tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature <u(2)> was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.

Study of diffusion phenomenon using an experimental magnetic resonance system (SIS 200/400) for small animals--reliability and apparent diffusion coefficient of normal animals

We have developed a magnetic resonance (MR) spin echo method to obtain diffusion weighted imaging using motion probing gradient (MPG) pulses in orthogonal direction before and after a 180 degree pulse. Phantom models containing water, acetone, cupric sulfate and agar, and normal brains of Wistar rats and puppies were examined. MRI was performed using a SISCO SIS 200/400 MRI/MRS experimental system for small animals (4.7 tesla, 400 mm bore). The apparent diffusion coefficient (ADC) values, given in mm2/sec, were 2.19 +/- 0.02 x 10(-3) in water, 4.51 +/- 0.18 x 10(-3) in acetone, and the ADC of water was independent on longitudinal (T1) or transverse (T2) relaxation time. Time-dependent ADC changes were not demonstrated, however position-dependent ADC changes were significant. It is therefore important to set the sample at the same position for repeated MRI studies and for the evaluation of the time course of experimental studies. Mean ADC values of rat brains were 0.65 x 10(-3) for cortex, 0.69 x 10(-3) for caudate-putamen, 0.69 x 10(-3) (perpendicular to axon) for corpus callosum, 1.11 x 10(-3) (parallel to axon) for optic nerve, and 1.38 x 10(-3) (parallel to axon) for trigeminal nerve. Those of puppies were 1.14-1.42 x 10(-3) for gray matter, 1.17 (parallel to axon) and 0.89 (perpendicular to axon) x 10(-3) for white matter, 1.66 (parallel to axon) and 0.57 (perpendicular to axon) x 10(-3) for internal capsule, and 0.91-0.95 x 10(-3) for thalamus. On the in vivo ADC maps, white matter tracts successfully showed anisotropic diffusion. This technique has promising implications for the evaluation of the time course of cerebral damage and degenerative changes.

Hydrated calcium aluminates

This paper presents a Fick-based chloride transport model, which is mathematically consistent with time dependent apparent diffusion coefficient and surface chloride for fly ash concrete. In the paper, the inconsistency in a simple close-formed solution used to predict chloride penetration through fly ash concrete in a previous study of other researchers is pointed out. The inconsistency can be seen by comparing chloride profiles calculated by the simple close-formed solution to those calculated by a finite difference program. The inconsistency is caused by the use of simplified diffusion coefficient and mathematically incompatible surface chloride models. To avoid the inconsistency, a chloride transport model is developed in this study. In developing the model, regression analysis to fit coefficients of the developed model is compared to the regression analysis results obtained from the experiment of the researchers. In the experiment of the researchers, the effect of water to binder ratio and the amount of fly ash replacement in concrete is considered. Furthermore, the chloride transport calculated from the developed model is validated by comparing to other experimental results. Finally, the sensitivity analysis of the model coefficients and some remarks on the developed model are presented.