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Anomalous diffusion, solutions, and first passage time: Influence of diffusion coefficient.

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the usual diffusion equation. We consider a space- and time-dependent diffusion coefficient and the presence of absorbing boundaries. We obtain analytical results for the probability distribution and the first passage time distribution for finite and semi-infinite intervals. In addition, we compare our results for the first passage time distribution with the one obtained by the usual diffusion equation with constant diffusion coefficient.

Journal Article↗

Concentration-dependent diffusivity and anomalous diffusion: a magnetic resonance imaging study of water ingress in porous zeolite.

Magnetic resonance imaging is employed to study water ingress in fine zeolite powders compacted by high pressure. The experimental conditions are chosen such that the applicability of Boltzmann's transformation of the one-dimensional diffusion equation is approximately satisfied. The measured moisture profiles indicate subdiffusive behavior with a spatiotemporal scaling variable eta=x/t(gamma/2) (0<gamma<1). A time-fractional diffusion equation model of anomalous diffusion is adopted to analyze the data, and an expression that yields the moisture dependence of the generalized diffusivity is derived and applied to our measured profiles. In spite of the differences between systems exhibiting different values of gamma a striking similarity in the moisture dependence of the diffusivity is apparent. This suggests that the model addresses the underlying physical processes involved in water transport.

Journal Article↗

Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps then the long time asymptotic limit has a standard linear reaction kinetics term but a fractional order temporal derivative operating on a nonstandard diffusion term. Results from the above two models are compared with a phenomenological model with standard linear reaction kinetics and a fractional order temporal derivative operating on a standard diffusion term. We have also developed further extensions of the CTRW model to include more general reaction dynamics.

Journal Article↗

General solution of the diffusion equation with a nonlocal diffusive term and a linear force term.

We obtain a formal solution for a large class of diffusion equations with a spatial kernel dependence in the diffusive term. The presence of this kernel represents a nonlocal dependence of the diffusive process and, by a suitable choice, it has the spatial fractional diffusion equations as a particular case. We also consider the presence of a linear external force and source terms. In addition, we show that a rich class of anomalous diffusion, e.g., the Lévy superdiffusion, can be obtained by an appropriated choice of kernel.

Journal Article↗

Acute diffuse and total alopecia of the female scalp. A new subtype of diffuse alopecia areata that has a favorable prognosis.

BACKGROUND: Although alopecia areata (AA) usually starts with focal lesions of hair loss and then presents several different clinical forms, AA may begin as diffuse hair loss. We examined 9 female patients who presented with acute, diffuse and total hair loss of the scalp and took a similar clinical course with a favorable prognosis. OBJECTIVE: To categorize such cases as a new subgroup of diffuse alopecia. METHODS: We studied 9 patients who showed acute, diffuse and total hair loss of the scalp within 1 month after their first visit to our hospital by comparing their clinical course, laboratory tests and histopathological findings with those of common, patchy AA, alopecia totalis or alopecia universalis. RESULTS: None of the patients had a background of systemic diseases or telogen effluvium. All the patients were female, and 8 of the 9 cases recovered cosmetically acceptable hair growth within 6 months regardless of steroid administration. The histology of he lesions was indistinguishable from that of AA except for a remarkable eosinophilic infiltrate. CONCLUSIONS: These cases can be categorized as a new subtype of inflammatory noncicatricial alopecia that is characterized by a marked female predominance, tissue eosinophilia and uniquely short clinical course. We suggest to name it 'acute diffuse and total alopecia of the female scalp (ADTAFS)'.

Acute Disease↗

Effect of input diffusivity in an axisymmetric mass diffusivity model for liquid metals with an applied magnetic field.

Depending on the magnitude of the diffusivity, convective contamination may result in erroneous measurement of mass diffusivity even in microgravity. The effect of natural or buoyant convection is numerically investigated for liquid germanium with an axisymmetric model using two different magnetic field strengths and four heat transfer conditions. Since the reported input diffusivity value may vary due to inaccuracies in measurements, an order of magnitude lower and higher input diffusivity from the base value of D0 = 2 x 10(-4) cm2/sec was used to evaluate the behavior of liquid germanium in the presence of a magnetic field. From the numerical results, the temperature nonuniformity and the flow velocities in the liquid vary according to the input diffusivity (i.e., an order of magnitude lower and higher than the base cases). The heat transfer pattern is important in achieving a larger temperature nonuniformity in the liquid during the experiments. A stronger magnetic field can tolerate a higher temperature nonuniformity as expected.

Journal Article↗

Simultaneous diffuse sclerosis variant of papillary thyroid carcinoma and diffuse toxic hyperplasia (Graves' disease).

Diffuse sclerosis variant of papillary thyroid carcinoma (DSVPTC) is an unusual malignant neoplasm that typically permeates the entire gland resulting in diffuse thyroid enlargement. In the absence of a dominant nodule, DSVPTC can be histologically deceiving because of exuberant inflammation and the scattered distribution of the microscopic tumor islands. The difficulty in diagnosing this tumor is compounded by its rarity and unusual clinical and histologic features. Herein, we describe a unique case of DSVPTC that was clinically masked by a co-existing second diffuse thyroid process--Graves' disease (GD). A subtotal thyroidectomy was performed in a 27-yr-old Caucasian female who presented with symmetrical diffuse thyromegaly with neck compressive symptoms, thyrotoxicosis, and biochemical signs of GD. Histologic examination of the thyroid gland unexpectedly revealed extensive involvement by DSVPTC in addition to the diffuse hyperplastic non-malignant thyroid follicles. This report illustrates the histologic features as well as the diagnostic challenge encountered in a rare simultaneous occurrence of DSVPTC and GD.

Adult↗

Systemic lupus erythematosus presenting with diffuse low density lesions in the cerebral white matter on computed axial tomography scans: its implication in the pathogenesis of diffuse central nervous system lupus.

We describe a patient with systemic lupus erythematosus (SLE) with severe organic brain syndrome, who showed diffuse low density areas in the cerebral white matter on computed axial tomography (CAT) scans. A 43-year-old woman with SLE showed disturbances in various intellectual functions, followed by the development of consciousness disturbances and urinary incontinence. CAT scans, single photon emission computed tomography (SPECT) and cerebrospinal fluid (CSF) interleukin 6 (IL-6) were serially examined during the clinical course before and after treatment with high doses of prednisolone. CSF IL-6 activity paralleled the central nervous system (CNS) disease activity most consistently. By contrast, the diffuse low density areas in cerebral white matter on CAT scans as well as the decreased blood flow in the cerebral cortices on SPECT persisted long after the improvement of the CNS manifestations. Magnetic resonance imaging (MRI) scans also revealed the diffuse areas of increased signal intensity in the subcortical white matter on T2 weighted images. The diffuse lesions in the cerebral white matter are considered to reflect the edema as well as other irreversible changes that have resulted from the disturbed cerebral circulation presumably due to the diffuse microangiopathies in the cerebral cortices and not to be necessarily correlated with the CNS disease activities. Moreover, it is suggested that the inflammatory process evidenced by the elevation of CSF cytokines in addition to the disturbed circulation in the cerebral cortices might play an important role in the pathogenesis of CNS lupus in our patient.

Adult↗

The cone synapses of DB1 diffuse, DB6 diffuse and invaginating midget, bipolar cells of a primate retina.

The distribution of synapses between cones and two types of diffuse cone bipolar cell in a rhesus monkey retina is described. The dendrites of representative Golgi-stained cells of each of the diffuse cone bipolar cell types DB1 and DB6 were serially sectioned for EM examination. Bipolar cells of the DB1 type have axons terminating in the outer half of the inner plexiform layer. The dendrites of the cell examined were postsynaptic to seven cones at 71 basal synapses; in addition, they had two ribbon synapses with one cone, and one with another. A DB6 type of bipolar cell has axons ending in the inner half of the inner plexiform layer. The dendrites of the cell examined received input from seven cones at 30 ribbon synapses; in addition there were 13 basal junctions distributed between five of the seven cones contacted. Two invaginating midget bipolar cells were found to be postsynaptic at 25 and 26 ribbon synapses of cone pedicles containing 44 and 40 ribbons respectively. These results combined with our previously published work, show that the position and number of synapses is characteristic for each category of cell. Those bipolar cells (flat) making basal synapses have more sites of synaptic contact with the cones than those bipolar cells (invaginating) with predominantly ribbon synaptic input. Over 95% of the cone junctions of the three types of diffuse bipolar cell, DB1, DB2 and DB3, are basal; and their axons always end in the a- (Off-) layer of the inner plexiform layer. All three types of diffuse invaginating cone bipolar cell, DB4, DB5 & DB6, have axons terminating in the b- (On-) layer of the inner plexiform layer; their dendrites are predominantly postsynaptic as central elements invaginating at the cone triads. However, unlike invaginating midget bipolar cells, whose dendrites are exclusively postsynaptic at ribbon synapses, between 10% (DB5) and 40% (DB4 and DB6) of the cone input to diffuse invaginating bipolar cells is through basal junctions. These data are discussed in the context of recent work on the synapses between foveal cones and their bipolar cells.

Animals↗

Prediction of recovery from a post-traumatic coma state by diffusion-weighted imaging (DWI) in patients with diffuse axonal injury.

INTRODUCTION: To determine whether diffusion-weighted magnetic resonance (MR) imaging findings combined with initial clinical factors indicate the depth of shearing lesions in the brain structure and therefore relate to coma duration in diffuse axonal injury (DAI). METHODS: A total of 74 adult patients (48 male and 26 female) with DAI were examined with conventional MR imaging and diffusion-weighted MR imaging between 2 hours and 20 days after injury. Apparent diffusion coefficient (ADC) maps were obtained and the mean ADC values of each region of interest (ROI) were measured using MRI console software. The involvement of the brainstem, deep gray matter, and corpus callosum was determined for each sequence separately as well as for the combination of all sequences. The correlations between MR imaging findings indicating the presence of apparent brain injury combined with initial clinical factors were determined. RESULTS: Clinical characteristics, such as initial score on the Glasgow coma scale (GCS), age and number of all lesions, and ADC scores were predictive of the duration of coma. CONCLUSION: It was possible to predict post-traumatic coma duration in DAI from cerebral MR imaging findings combined with clinical prognostic factors in the acute to subacute stage after head injury. Age, ADC scores, GCS score and number of lesions were highly significant in predicting coma duration. The technique presented here might provide a tool for in vivo detection of DAI to allow the prediction of the coma duration during the early stages in patients with traumatic brain injury.

Accidents, Traffic↗

Diffusion-weighted imaging for the evaluation of diffuse axonal injury in closed head injury.

PURPOSE: The purpose of this work was to compare diffusion-weighted imaging (DWI) with conventional MRI in the detection of shearing injuries in acute closed head injuries. METHOD: Twenty-five patients (19 male, 6 female) were examined within 48 h of trauma. Conventional MRI included T2-weighted fast spin echo, fluid-attenuated inversion recovery (FLAIR), and T2*-weighted gradient echo sequences. Full tensor DWI with calculation of apparent diffusion coefficient (ADC) maps was also performed. Lesions were identified and compared on all sequences. RESULTS: Four hundred twenty-seven lesions were counted by the combined use of all sequences. DWI identified 70 lesions not seen on conventional MRI. DWI identified 310 shearing injuries, followed by T2/FLAIR (n = 248) and T2* (n = 202). The majority of DWI-positive lesions showed decreased diffusion (65%). CONCLUSION: DWI is valuable in closed head injury because it identifies additional shearing injuries not visible on T2/FLAIR or T2* sequences. Furthermore, DWI/ADC maps differentiate between lesions with decreased or increased diffusion. DWI is less sensitive than T2* imaging for detecting hemorrhagic lesions.

Adolescent↗

Diffusion tensor imaging as potential biomarker of white matter injury in diffuse axonal injury.

BACKGROUND AND PURPOSE: Multiple biomarkers are used to quantify the severity of traumatic brain injury (TBI) and to predict outcome. Few are satisfactory. CT and conventional MR imaging underestimate injury and correlate poorly with outcome. New MR imaging techniques, including diffusion tensor imaging (DTI), can provide information about brain ultrastructure by quantifying isotropic and anisotropic water diffusion. Our objective was to determine if changes in anisotropic diffusion in TBI correlate with acute Glasgow coma scale (GCS) and/or Rankin scores at discharge. METHODS: Twenty patients (15 male, five Female; mean age, 31 years) were evaluated. Apparent diffusion coefficients (ADCs) and fractional anisotropy (FA) values were measured at multiple locations and correlated with clinical scores. Results were compared with those of 15 healthy control subjects. RESULTS: ADC values were significantly reduced within the splenium (Delta18%, P =.001). FA values were significantly reduced in the internal capsule (Delta14%; P <.001) and splenium (Delta16%; P =.002). FA values were significantly correlated with GCS (r = 0.65-0.74; P <.001) and Rankin (r = 0.68-0.71; P <.001) scores for the internal capsule and splenium. The correlation between FA and clinical markers was better than for the corresponding ADC values. No correlation was found between ADC of the internal capsule and GCS/Rankin scores. CONCLUSION: DTI reveals changes in the white matter that are correlated with both acute GCS and Rankin scores at discharge. DTI may be a valuable biomarker for the severity of tissue injury and a predictor for outcome.

Adult↗

High-resolution diffusion imaging with DIFRAD-FSE (diffusion-weighted radial acquisition of data with fast spin-echo) MRI.

A novel MRI method, DIFRAD-FSE (diffusion-weighted radial acquisition of data with fast spin-echo), is demonstrated that enables rapid, high-resolution multi-shot diffusion-weighted MRI without significant artifacts due to motion. Following a diffusion-weighting spin-echo preparation period, multiple radial lines of Fourier data are acquired using spin-echo refocusing. Images can be reconstructed from the radial data set using a magnitude-only filtered back-projection reconstruction algorithm that removes phase errors due to motion. Results from human brain imaging demonstrate the ability of DIFRAD-FSE to acquire multiple radial lines of Fourier data each TR period without significant artifacts due to relaxation and to produce high-resolution diffusion-weighted MRI images without significant artifacts from motion.

Algorithms↗

Rapid isotropic diffusion mapping without susceptibility artifacts: whole brain studies using diffusion-weighted single-shot STEAM MR imaging.

A subsecond magnetic resonance imaging (MRI) technique for isotropic diffusion mapping is described which, in contrast to echo-planar imaging (EPI), is insensitive to resonance offsets, i.e., tissue susceptibility differences, magnetic field inhomogeneities, and chemical shifts. It combines a diffusion-weighted (DW) spin-echo preparation period and a high-speed stimulated echo acquisition mode (STEAM) MRI sequence and yields single-shot images within measuring times of 559 msec (80 echoes). Here, diffusion encoding involved one scan without DW, three DW scans with b = 490 sec mm(-2), and three DW scans with b = 1000 sec mm(-2) (orthogonal gradient orientations). An automated on-line evaluation resulted in isotropic DW images as well as ADC maps (trace of the diffusion tensor). Experiments at 2.0 T covered the brain of healthy subjects in 20 contiguous sections of 6 mm thickness and 2.0 x 2.0 mm(2) in-plane resolution within a total measuring time of 78 sec. High-resolution studies at 1.0 x 1.0 mm(2) (interpolated from 2.0 x 1.0 mm(2) acquisitions) were obtained within 5 min 13 sec using four averages. In comparison with EPI, DW single-shot STEAM MRI exhibits only about half the SNR, but completely avoids regional signal losses, high intensity artifacts, and geometric distortions.

Adult↗

Reproducibility and dependence on diffusion weighting of line scan diffusion in the lumbar intervertebral discs.

PURPOSE: To investigate the dependence of line scan diffusion imaging (LSDI) in the lumbar vertebral discs on diffusion weighting, fat suppression (FS), and postprocessing noise correction. MATERIALS AND METHODS: Eleven normal volunteers were scanned using 4 b-value and 12 b-value LSDI protocols, with and without FS. Three repeated four b-value scans were performed for evaluation of the reproducibility of apparent diffusion coefficient (ADC) values calculated with mono- and biexponential decay models. Two-point ADC analysis for 12 b-value scans was performed with and without noise correction to evaluate the ADC dependence on diffusion weighting. Correlations between different ADC calculation and acquisition methods were evaluated. RESULTS: Monoexponential ADC measures had a coefficient of variation (CV) under 3%, while use of a constrained biexponential increased the CV to 6% to 9%. Strong dependence on b-value was seen from chemically shifted marrow fat signal and noise. These systematic variations in ADC were eliminated using noise correction and FS. ADC values from 4 and 12 b-value FS scans correlated strongly (R2 = 0.91), while biexponentially derived ADC values correlated moderately well with the FS ADC (R2 = 0.51). CONCLUSION: LSDI gives reproducible ADC measurements in the lumbar discs, largely independent of b-value and signal-to-noise ratio (SNR) when used with noise correction and FS.

Adult↗

Correction of eddy-current distortions in diffusion tensor images using the known directions and strengths of diffusion gradients.

PURPOSE: To correct eddy-current artifacts in diffusion tensor (DT) images without the need to obtain auxiliary scans for the sole purpose of correction. MATERIALS AND METHODS: DT images are susceptible to distortions caused by eddy currents induced by large diffusion gradients. We propose a new postacquisition correction algorithm that does not require any auxiliary reference scans. It also avoids the problematic procedure of cross-correlating images with significantly different contrasts. A linear model is used to describe the dependence of distortion parameters (translation, scaling, and shear) on the diffusion gradients. The model is solved numerically to provide an individual correction for every diffusion-weighted (DW) image. RESULTS: The assumptions of the linear model were successfully verified in a series of experiments on a silicon oil phantom. The correction obtained for this phantom was compared with correction obtained by a previously published method. The algorithm was then shown to markedly reduce eddy-current distortions in DT images from human subjects. CONCLUSION: The proposed algorithm can accurately correct eddy-current artifacts in DT images. Its principal advantages are that only images with comparable signals and contrasts are cross-correlated, and no additional scans are required.

Algorithms↗

High-resolution diffusion-weighted 3D MRI, using diffusion-weighted driven-equilibrium (DW-DE) and multishot segmented 3D-SSFP without navigator echoes.

In this work we report on the development of a novel technique for high-resolution diffusion-weighted (DW) MRI based upon 3D steady-state free precession (3D-SSFP). First the 3D-SSFP acquisition was segmented (each segment consisting of a series of RF pulses and gradient-recalled echoes), and then DW-driven equilibrium (DE) was inserted between each segment. The in-plane imaging matrix was typically 256 x 192 or 256 x 160, which resulted in high-resolution DW images. The DW-DE segmented SSFP signal was contaminated by the non-DW magnetization, which recovered and contributed signal during the readout train (T(1) contamination). Center-out slice encoding was used to place the greatest diffusion weighting at the center of k-space. A numerical simulation and supporting experiments were performed to evaluate the relationship of the transverse magnetization to imaging parameters, such as the b-value, echo-train length (ETL), echo-train (group) repetition time (TR(g)), and RF excitation TR (Delta t). Both the numerical simulation and the experiments suggested that the effect of T(1) contamination would be reduced with a longer TR(g), smaller b-value, shorter ETL, and center-out slice phase encoding. Phase errors caused by microscopic motions during the diffusion gradients were converted into amplitude errors by the tip-up pulse at the end of the diffusion-weighting segment. As a result, small bulk motions, such as CSF pulsation, did not cause motion-related ghosting artifacts, which would be typical in images from other multishot DWI techniques. This technique can be used for high-resolution DWI of nonbrain anatomies.

Artifacts↗

Deconvolution of compartmental water diffusion coefficients in yeast-cell suspensions using combined T(1) and diffusion measurements.

An NMR method is presented for measuring compartment-specific water diffusion coefficient (D) values. It uses relaxography, employing an extracellular contrast reagent (CR) to distinguish intracellular (IC) and extracellular (EC) (1)H(2)O signals by differences in their respective longitudinal (T(1)) relaxation times. A diffusion-weighted inversion-recovery spin-echo (DW-IRSE) pulse sequence was used to acquire IR data sets with systematically and independently varying inversion time (TI) and diffusion-attenuation gradient amplitude (g) values. Implementation of the DW-IRSE technique was demonstrated and validated using yeast cells suspended in 3 mM Gd-DTPA(2-) with a wet/dry mass ratio of 3.25:1.0. Two-dimensional (2D) NMR data were acquired at 2.0 T and analyzed using numerical inverse Laplace transformation (2D- and sequential 1D-ILT) and sequential exponential fitting to yield T(1) and water D values. All three methods gave substantial agreement. Exponential fitting, deemed the most accurate and time efficient, yielded T(1):D (relative contribution) values of 304 ms:0.023x10(-5) cm(2)/s (47%) and 65 ms:1.24x10(-5) cm(2)/s (53%) for the IC and EC components, respectively. The compartment-specific D values derived from direct biexponential fitting of diffusion-attenuation data were also in good agreement. Extension of the DW-IRSE method to in vivo models should provide valuable insights into compartment-specific water D changes in response to injury or disease. (c) 2002 Elsevier Science (USA).

Contrast Media↗