Mechanism of point-defect diffusion in a two-dimensional colloidal crystal

The dynamics and mechanism of migration of a vacancy point defect in a two-dimensional (2D) colloidal crystal are studied using numerical simulations. We find that the migration of a vacancy is always realized by topology switching between its different configurations. From the temperature dependence of the topology switch frequencies, we obtain the activation energies for possible topology transitions associated with the vacancy diffusion in the 2D crystal. (C) 2011 American Institute of Physics. [doi:10.1063/1.3615287]

Water diffusion in hydroxyethyl methacrylate (HEMA)-based hydrogels formed by gamma-radiolysis

Polymer hydrogels based upon methacrylates are used extensively in the pharmaceutical industry, particularly as controlled release drug delivery systems. These materials are generally prepared by chemically initiated polymerization, but this can lead to the presence of unwanted initiator fragments in the polymer matrix. In the present work, initiation of polymerization by gamma-irradiation of hydroxyethyl methacrylate, with and without added crosslinkers, has been investigated, and the diffusion coefficients for water in the resulting polymers have been measured through mass uptake by the polymers. The diffusion of water in poly(hydroxyethyl methacrylate) at 310 K was found to be Fickian, with a diffusion coefficient of 1.96 +/- 0.1 x 10(11) m(2) s(-1) and an equilibrium water content of 58%, NMR imaging analyses confirmed the adherance to a Fickian model of the diffusion of water into polymer cylinders. The incorporation of small amounts (0.2-0.5 wt%) of added ethyleneglycol-dimethacrylate-based crosslinkers was found to have only a small effect on the diffusion coefficient and the equilibrium water content for the copolymers. (C) 1999 Society of Chemical Industry.

Refining the perfusion-diffusion mismatch hypothesis

Background and Purpose-The Echoplanar Imaging Thrombolysis Evaluation Trial ( EPITHET) tests the hypothesis that perfusion-weighted imaging (PWI)-diffusion-weighted imaging (DWI) mismatch predicts the response to thrombolysis. There is no accepted standardized definition of PWI-DWI mismatch. We compared common mismatch definitions in the initial 40 EPITHET patients. Methods-Raw perfusion images were used to generate maps of time to peak (TTP), mean transit time (MTT), time to peak of the impulse response (Tmax) and first moment transit time (FMT). DWI, apparent diffusion coefficient ( ADC), and PWI volumes were measured with planimetric and thresholding techniques. Correlations between mismatch volume (PWIvol-DWIvol) and DWI expansion (T2(Day) (90-vol)-DWIAcute-vol) were also assessed. Results-Mean age was 68 +/- 11, time to MRI 4.5 +/- 0.7 hours, and median National Institutes of Health Stroke Scale (NIHSS) score 11 (range 4 to 23). Tmax and MTT hypoperfusion volumes were significantly lower than those calculated with TTP and FMT maps (P < 0.001). Mismatch >= 20% was observed in 89% (Tmax) to 92% (TTP/FMT/MTT) of patients. Application of a +4s ( relative to the contralateral hemisphere) PWI threshold reduced the frequency of positive mismatch volumes (TTP 73%/FMT 68%/Tmax 54%/MTT 43%). Mismatch was not significantly different when assessed with ADC maps. Mismatch volume, calculated with all parameters and thresholds, was not significantly correlated with DWI expansion. In contrast, reperfusion was correlated inversely with infarct growth (R= -0.51; P = 0.009). Conclusions-Deconvolution and application of PWI thresholds provide more conservative estimates of tissue at risk and decrease the frequency of mismatch accordingly. The precise definition may not be critical; however, because reperfusion alters tissue fate irrespective of mismatch.

The states, diffusion, and concentration distribution of water in radiation-formed PVA/PVP hydrogels

Hydrogels with various compositions of polyvinyl alcohol (PVA) and poly(1-vinyl-2-pyrrolidinone) (PVP) were prepared by irradiating mixtures of PVA and PVP in aqueous solutions with gamma-rays from Co-60 sources at room temperature. The states of water in the hydrogels were characterized using DSC and NMR T-2 relaxation measurements and the kinetics of water diffusion in the hydrogels were studied by sorption experiments and NMR imaging. The DSC endothermic peaks in the temperature range -10 to +10 degrees C implied that there are at least two kinds of freezable water present in the matrix. The difference between the total water content and the freezable water content was refer-red to as bound water, which is not freezable. The weight fraction of water at which only nonfreezable water is present in a hydrogel with F-VP = 0.19 has been estimated to be g(H2O)/g(Polymer) = 0.375. From water sorption experiments, it was demonstrated that the early stage of the diffusion of water into the hydrogels was Fickian. A curve-fit of the early-stage experimental data to the Fickian model allowed determination of the water diffusion coefficient, which was found to lie between 1.5 x 10(-11) m(2) s(-1) and 4.5 x 10(-11) m(2) s(-1), depending on the polymer composition, the cross-link density, and the temperature. It was also found that the energy barrier for diffusion of water molecules into PVA/PVP hydrogels was approximate to 24 kJ mol(-1). Additionally, the diffusion coefficients determined from NMR imaging of the volumetric swelling of the gels agreed well with the results obtained by the mass sorption method.

Acute Toxic Leukoencephalopathy: Potential for Reversibility Clinically and on MRI With Diffusion-Weighted and FLAIR Imaging

OBJECTIVE. Toxic leukoencephalopathy may present acutely or subacutely with symmetrically reduced diffusion in the periventricular and supraventricular white matter, hereafter referred to as periventricular white matter. This entity may reverse both on imaging and clinically. However, a gathering together of the heterogeneous causes of this disorder as seen on MRI with diffusion-weighted imaging (DWI) and an analysis of their likelihood to reverse has not yet been performed. Our goals were to gather causes of acute or subacute toxic leukoencephalopathy that can present with reduced diffusion of periventricular white matter in order to promote recognition of this entity, to evaluate whether DWI with apparent diffusion coefficient (ADC) values can predict the extent of chronic FLAIR abnormality ( imaging reversibility), and to evaluate whether DWI can predict the clinical outcome ( clinical reversibility). MATERIALS AND METHODS. Two neuroradiologists retrospectively reviewed the MRI examinations of 39 patients with acute symptoms and reduced diffusion of periventricular white matter. The reviewers then scored the extent of abnormality on DWI and FLAIR. ADC ratios of affected white matter versus the unaffected periventricular white matter were obtained. Each patient`s clinical records were reviewed to determine the cause and clinical outcome. Histology findings were available in three patients. Correlations were calculated between the initial MRI markers and both the clinical course and the follow-up extent on FLAIR using Spearman`s correlation coefficient. RESULTS. Of the initial 39 patients, seven were excluded because of a nontoxic cause (hypoxic-ischemic encephalopathy [HIE] or congenital genetic disorders) or because of technical errors. In the remaining 32 patients, no correlation was noted between any of the initial MRI markers (percentage of ADC reduction, DWI extent, or FLAIR extent) with the clinical outcome. Three patients had histologic correlation. However, moderate correlation was seen between the extent of abnormality on initial FLAIR and the extent on follow-up FLAIR (r = 0.441, p = 0.047). Of the 13 patients who underwent repeat MRI at 21 days or longer, the reduced diffusion resolved in all but one. Significant differences were noted between ADC values in affected white matter versus unaffected periventricular white matter on initial (p < 0.0001) but not on follow-up MRI (p = 0.13), and in affected white matter on initial versus follow-up (p = 0.0014) in those individuals who underwent repeat imaging on the same magnet (n = 9), confirming resolution of the DWI abnormalities. CONCLUSION. Acute toxic leukoencephalopathy with reduced diffusion may be clinically reversible and radiologically reversible on DWI, and may also be reversible, but to a lesser degree, on FLAIR MRI. None of the imaging markers measured in this study appears to correlate with clinical outcome, which underscores the necessity for prompt recognition of this entity. Alerting the clinician to this potentially reversible syndrome can facilitate treatment and removal of the offending agent in the early stages.

Measurements of neutral atom diffusion and electron-ion recombination by laser enhanced ionisation and planar laser induced fluorescence in an air-acetylene flame

The spatial and temporal evolution of a depleted atomic distribution created by laser enhanced ionisation (LEI) was employed to determine both a diffusion coefficient for sodium (Na) and an electron (e(-)) and sodium ion recombination rate coefficient in an analytical air-C2H2 flame. A depleted distribution of neutral sodium atoms was produced in a flame by ionising approximately 80% of the irradiated sodium atoms in a well defined region using a two step LEI excitation scheme. Following depletion by ionisation, planar laser induced fluorescence (PLIF) images of the depleted region recorded the diffusion and decay of the depleted Na distribution for different depletion-probe delays. From measurements of the diffused width of the distribution, an accurate diffusion coefficient D = (1.19 +/- 0.03) x 10(-3) m(2) s(-1) for Na was determined in teh burnt gases of the flame. Measurements of the integrated fluorescence intensity in the depleted region for different depletion-probe delays were related to an increase in atomic sodium concentration caused by electron-ion recombination. At high concentrations (greater than or equal to 50 mu g ml(-1)), where the electron and ion concentrations in the depleted region were assumed equal, a recombination rate coefficient of 4.2 x 10(-9) cm(3) s(-1) was calculated. (C) 1997 Elsevier Science B.V.

Nmr imaging of the diffusion of water into poly(tetrahydrofurfuryl methacrylate-co-hydroxyethyl methacrylate)

0Nuclear magnetic resonance (n.m.r.) imaging was used to study the ingress of water into poly(tetrahydrofurfuryl methacrylate-co-hydroxyethyl methacrylate). The study offers strong evidence that the diffusion is Fickian in nature. The diffusion coefficient, D, obtained by fitting the underlying diffusion profile, attainable from the images, according to the equation for Fickian diffusion, is 1.5 x 10(-11) m(2) s(-1), which is in good correlation with the value of 2.1 x 10(-11) m(2) s(-1), obtained from mass uptake measurements. Additionally, from the T-2-weighted images, Superimposed features observed in addition to the underlying Fickian diffusion profiles were shown to have a longer spin-spin relaxation time, T-2. This Suggests the presence of two types of water within the polymer matrix; a less mobile phase of absorbed water that is interacting strongly with the polymer matrix and a more mobile phase of absorbed water residing within the cracks observed in the environmental scanning electron micrograph. (C) 1997 Elsevier Science Ltd.

Diffusion characteristics of ethylene glycol in skeletal muscle

Part of the optical clearing study in biological tissues concerns the determination of the diffusion characteristics of water and optical clearing agents in the subject tissue. Such information is sufficient to characterize the time dependence of the optical clearing mechanisms—tissue dehydration and refractive index (RI) matching. We have used a simple method based on collimated optical transmittance measurements made from muscle samples under treatment with aqueous solutions containing different concentrations of ethylene glycol (EG), to determine the diffusion time values of water and EG in skeletal muscle. By representing the estimated mean diffusion time values from each treatment as a function of agent concentration in solution, we could identify the real diffusion times for water and agent. These values allowed for the calculation of the correspondent diffusion coefficients for those fluids. With these results, we have demonstrated that the dehydration mechanism is the one that dominates optical clearing in the first minute of treatment, while the RI matching takes over the optical clearing operations after that and remains for a longer time of treatment up to about 10 min, as we could see for EG and thin tissue samples of 0.5 mm.

The characteristic time of glucose diffusion measured for muscle tissue at optical clearing

The study of agent diffusion in biological tissues is very important to understand and characterize the optical clearing effects and mechanisms involved: tissue dehydration and refractive index matching. From measurements made to study the optical clearing, it is obvious that light scattering is reduced and that the optical properties of the tissue are controlled in the process. On the other hand, optical measurements do not allow direct determination of the diffusion properties of the agent in the tissue and some calculations are necessary to estimate those properties. This fact is imposed by the occurrence of two fluxes at optical clearing: water typically directed out of and agent directed into the tissue. When the water content in the immersion solution is approximately the same as the free water content of the tissue, a balance is established for water and the agent flux dominates. To prove this concept experimentally, we have measured the collimated transmittance of skeletal muscle samples under treatment with aqueous solutions containing different concentrations of glucose. After estimating the mean diffusion time values for each of the treatments we have represented those values as a function of glucose concentration in solution. Such a representation presents a maximum diffusion time for a water content in solution equal to the tissue free water content. Such a maximum represents the real diffusion time of glucose in the muscle and with this value we could calculate the corresponding diffusion coefficient.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Diffusion-weighted magnetic resonance imaging in metastatic gastrointestinal stromal tumor (GIST): a pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT.

BACKGROUND: Diffusion-weighted magnetic resonance imaging (MRI) is increasingly being used for assessing the treatment succes in oncology, but the real clinical value needs to evaluated by comparison with other, already established, metabolic imaging techniques. PURPOSE: To prospectively evaluate the clinical potential of diffusion-weighted MRI with apparent diffusion coefficient (ADC) mapping for gastrointestinal stromal tumor (GIST) response to targeted therapy compared with 18F-fluorodeoxyglucose positron emission tomography/computed tomography (18F-FDG PET/CT). MATERIAL AND METHODS: Eight patients (mean age, 56 ± 11 years) known to have metastatic GIST underwent 18F-FDG PET/CT and MRI (T1Gd, DWI [b = 50,300,600], ADC mapping) simultaneously, before and after change in targeted therapy. MR and PET/CT examinations were first analyzed blindly. Second, PET/CT images were co-registered with T1Gd-MR images for lesion detection. Only 18F-FDG avid lesions were considered. Maximum standardized uptake value (SUVmax) and the corresponding minimum ADCmin were measured for the six largest lesions per patient, if any, on baseline and follow-up examinations. The relationship between changes in SUVmax and ADCmin was analyzed (Spearman's correlation). RESULTS: Twenty-four metastases (12 hepatic, 12 extra-hepatic) were compared on PET/CT and MR images. SUVmax decreased from 7.7 ± 8.1 g/mL to 5.5 ± 5.4 g/mL (P = 0.20), while ADCmin increased from 1.2 ± 0.3 × 10(-3)mm(2)/s to 1.5 ± 0.3 × 10(-3)mm(2)/s (P = 0.0002). There was a significant association between changes in SUVmax and ADCmin (rho = - 0.62, P = 0.0014), but not between changes in lesions size (P = 0.40). CONCLUSION: Changes in ADCmin correlated with the response of 18F-FDG avid GIST to targeted therapy. Thus, diffusion-weighted MRI may represent a radiation-free alternative for follow-up treatment for metastatic GIST patients.

Assessment of liver tumor response by high-field (3T) MRI after radiofrequency ablation: Short- and mid-term evolution of diffusion parameters within the ablation zone.

PURPOSE: To compare the apparent diffusion coefficient (ADC) values of malignant liver lesions on diffusion-weighted MRI (DWI) before and after successful radiofrequency ablation (RF ablation). MATERIALS AND METHODS: Thirty-two patients with 43 malignant liver lesions (23/20: metastases/hepatocellular carcinomas (HCC)) underwent liver MRI (3.0T) before (<1month) and after RF ablation (at 1, 3 and 6months) using T2-, gadolinium-enhanced T1- and DWI-weighted MR sequences. Jointly, two radiologists prospectively measured ADCs for each lesion by means of two different regions of interest (ROIs), first including the whole lesion and secondly the area with the visibly most restricted diffusion (MRDA) on ADC map. Changes of ADCs were evaluated with ANOVA and Dunnett tests. RESULTS: Thirty-one patients were successfully treated, while one patient was excluded due to focal recurrence. In metastases (n=22), the ADC in the whole lesion and in MRDA showed an up-and-down evolution. In HCC (n=20), the evolution of ADC was more complex, but with significantly higher values (p=0.013) at 1 and 6months after RF ablation. CONCLUSION: The ADC values of malignant liver lesions successfully treated by RF ablation show a predictable evolution and may help radiologists to monitor tumor response after treatment.

Speed of reaction-diffusion fronts in spatially heterogeneous media

The front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis, the geometric approach of Hamilton-Jacobi dynamics, and the local speed approach. Exact and perturbed expressions for the front speed are obtained in the limit of large times. For linear and fractal heterogeneities, the analytic results have been compared with numerical results exhibiting a good agreement. Finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

Diffusion-weighted MRI in metastatic gastrointestinal tumors (GIST): A pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT

Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumor (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT. Methods and materials: Five patients (3W/2M, aged 56 ± 13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analyzed blindly, then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analyzed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analyzed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2 ± 7.7 g/mL to 5.9 ± 5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

Diffusion-weighted MRI in metastatic gastrointestinal tumours (GIST): a pilot study on the assessment of treatment response in comparison with 18 F-FDG PET/CT

Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumour (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT Methods and Materials: Five patients (3 W/2M, aged 56±13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analysed blindly and then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analysed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analysed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2±7.7 g/mL to 5.9±5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.