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PubMed2006

Nonlinear fingering dynamics of reaction-diffusion acidity fronts: self-similar scaling and influence of differential diffusion.

Nonlinear interactions between chemical reactions and buoyancy-driven Rayleigh-Taylor instability of reaction-diffusion acidity fronts of the chlorite-tetrathionate (CT) reaction are studied theoretically in a vertical Hele-Shaw cell or a porous medium. To do so, we perform a numerical integration of a two-variable reaction-diffusion model of the CT system coupled through an advection term to Darcy's law ruling the evolution of the velocity field of the fluid. The fingering dynamics of these chemical fronts is characterized by the appearance of several fingers at onset. These fingers then undergo coarsening and eventually merge to form one single symmetric finger. We study this asymptotic dynamics as a function of the three dimensionless parameters of the problem, i.e., the Damkohler number Da, the diffusivity ratio delta of the two chemical species, and the Rayleigh number Ra constructed here on the basis of the width L(y) of the system. For moderate values of Ra, the asymptotic single finger is shown to have self-similar scaling properties while above a given value of Ra, which depends on the other values of the parameters, tip splitting comes into play. Increasing the difference of diffusivities of the two chemical species (i.e., increasing delta) leads to more efficient coarsening and smaller asymptotic fingers. Experimental procedures to verify our predictions are proposed.

Journal Article↗

PubMed2000

Levy diffusion in a force field, huber relaxation kinetics, and nonequilibrium thermodynamics: H theorem for enhanced diffusion with Levy white noise

A characteristic functional approach is suggested for Levy diffusion in disordered systems with external force fields. We study the overdamped motion of an ensemble of independent particles and assume that the force acting upon one particle is made up of two additive components: a linear term generated by a harmonic potential and a second term generated by the interaction with the disordered system. The stochastic properties of the second term are evaluated by using Huber's approach to complex relaxation [Phys. Rev. B 31, 6070 (1985)]. We assume that the interaction between a moving particle and the environment can be expressed by the contribution of a large number of relaxation channels, each channel having a very small probability of being open and obeying Poisson statistics. Two types of processes are investigated: (a) Levy diffusion with static disorder for which the fluctuations of the random force are frozen and last forever and (b) diffusion with strong dynamic disorder and independent Levy fluctuations (Levy white noise). In both cases we show that the probability distribution of the position of a diffusing particle tends towards a stationary nonequilibrium form. The characteristic functional of concentration fluctuations is evaluated in both cases by using the theory of random point processes. For large times the fluctuations of the concentration field are stationary and the corresponding probability density functional can be evaluated analytically. In this limit the fluctuations depend on the distribution of the total number of particles but are independent of the initial positions of the particles. We show that the logarithm of the stationary probability functional plays the role of a nonequilibrium thermodynamic potential, which has a structure similar to the Helmholtz free energy in equilibrium thermodynamics: it is made up of the sum of an energetic component, depending on the external mechanical potential, and of an entropic component, depending on the concentration field. We show that the conditions for the existence and stability of the nonequilibrium steady state, which emerges for large times, can be expressed in terms of the stochastic potential. For Levy white noise the average concentration field can be expressed as the solution of a fractional Fokker-Planck equation. We show that the stochastic potential is a Lyapunov function of the fractional Fokker-Planck equation, which ensures that all transient solutions for the average concentration field tend towards a unique stationary form.

Journal Article↗

PubMed2003

Diffusion and anomalous diffusion of light in two-dimensional photonic crystals.

The transport properties of electromagnetic waves in disordered, finite, two-dimensional photonic crystals composed of circular cylinders are considered. Transport parameters such as the transport and scattering mean free paths and the transport velocity are calculated, for the case where the electromagnetic radiation has its electric field along the cylinder axes. The range of the parameters in which the diffusion process can take place is specified. It is shown that the transport velocity upsilon(E) can be as much as 10(8) times less than its free space value, while just outside the cluster upsilon(E) can be 0.3c. The effects of weak and strong disorders on the transport velocity are investigated. Different regimes of the wave transport-ordered propagation, diffusion, and anomalous diffusion-are demonstrated, and it is inferred that Anderson localization is incipient in the latter regime. Exact numerical calculations from the Helmholtz equation are shown to be in good agreement with the diffusion approximation.

Journal Article↗

PubMed2003

Power law diffusion coefficient and anomalous diffusion: analysis of solutions and first passage time.

We investigate one-dimensional equations for the diffusion with a nonconstant diffusion coefficient inside the second derivative and between the derivatives. In particular, we employ the diffusion coefficient D(x) proportional to /x/(-theta)(theta in R) and a quartic potential. These diffusion equations present a rich variety of behaviors associated with different regimes. Results of two approaches are analyzed and compared. We also investigate the mean first passage time of these systems. We show that the system with the coefficient D(x) between the derivatives can produce different behaviors for the mean first passage time in comparison with those obtained by the system with the coefficient inside the derivatives.

Journal Article↗

PubMed2006

Reaction-diffusion fronts in systems with concentration-dependent diffusivities.

We examine properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities. We study two different models of such systems and find that in the limit of a vanishingly small diffusivity of the reaction product, the reaction front dynamics enters a separate universality class, with the front width asymptotically tending to a constant value, and the reaction rate at the reaction front center diminishing with time t as t(-1/2). This behavior can be also observed in systems with nonvanishing (but small) diffusivity of the reaction product at intermediate times.

Journal Article↗

PubMed2003

Diffuse scattering and short-range order in uranium iodine phthalocyanine [U1-xPc(2)]I2-y and the X-ray structure analysis of crystals with diffuse superstructure reflections.

Crystals of uranium iodine phthalocyanine present an example of a disordered commensurate modulated structure of the intergrowth type. The short-range order of both uranium ions and iodine chains [I(3)(-)](n) has been analysed by Reverse Monte Carlo (RMC) simulation of X-ray diffuse scattering. The diffraction pattern of uranium iodine phthalocyanine contains diffuse superstructure reflections. In the routine crystal structure analysis diffuse superstructure reflections may be either omitted or measured and classified along with other Bragg reflections. The crystal structure of uranium iodine phthalocyanine is an example of such ambiguity. The crystal structures of two specimens of [U(1-x)Pc(2)]I(2-y) with slightly different composition have been published in the literature with different space groups and unit cells. We have shown that the structure of both specimens differs only in the degree of short-range order and is isostructural with [YbPc(2)]I(2). We have also shown that while the omission of diffuse reflections results in the average crystal structure, the treatment of these reflections as normal Bragg reflections is incorrect and produces the structure averaged over a limited small range.

Journal Article↗

PubMed1998

[Change of pulmonary diffusing capacity, membrane diffusing capacity and pulmonary capillary blood volume in patients with COPD and connective tissue disease at rest and post-exercise].

OBJECTIVE: Studying the changes of pulmonary diffusing capacity (DL), alveolar capillary membrane diffusing capacity (Dm) and pulmonary capillary blood volume (Vc) in patients with COPD and connective tissue disease (CTD) at rest and post-exercise; evaluating the diagnostic values of DL, Dm and Vc in early stage of pulmonary involvement of CTD. METHOD: Spirometry was performed in the sit position. Several measurements of diffusing capacity of the lung for carbon monoxide (DLCO) were measured by single-breath method at increasing alveolar oxygen tension. The estimations of Dm and Vc were done by the method of Roughton and Forster. RESULT: (1) In COPD group, the values of DL were lower than that of the control group at rest. The decreases were due to the reduction of Dm, but Vc were normal. In CTD group, all the value of DL, Dm and Vc were lower than that of its control group at rest. (2) COPD patients had the higher DL, Dm and Vc after the end of exercise than that of at rest. But the changes of DL Dm and Vc in COPD patients were lower compared with the control group. In contrast to the control group, DL, Dm and Vc did not increase or even decreased after the end of exercise in CTD group. (3) There was no significant differences of DL, Dm and Vc between the 7 CTD patients with normal pulmonary volume and DLCO and the control subjects at rest. But after the end of exercise, DL, Dm and Vc of CTD patients kept unchanging or even decreasing. The difference between CTD patients and its control group was found significant. CONCLUSION: The measurements of post-exercise Dm and Vc are sensitive tests for pulmonary involvement in of CTD patients. The results are abmormal much earlier in subject with minimal dyspnea and roentgenologic change. They are useful tests for early stage CTD.

Aged↗

PubMed2006

Focal lesions of the corticospinal tract demonstrated by diffusion tensor imaging in patients with diffuse axonal injury.

OBJECTIVES: Diffusion tensor imaging (DTI) with fiber tractography (FT) could be useful for exploration of the state of the corticospinal tract (CST) at the subcortical white matter level. The purpose of this study was to demonstrate focal lesions of the CST in patients with diffuse axonal injury (DAI), using DTI with FT. DESIGN: Two patients with DAI and six normal control subjects were recruited to this study. DTI was performed using 1.5-T with a synergy-L Sensitivity Encoding (SENSE) head coil. Fractional anisotropy (FA) and apparent diffusion coefficients (ADC) were measured using a region of interest (ROI) method. FTs were obtained with FA <0.3 and an angle change >45 degrees as termination criteria. RESULTS: On the DTI with FT, the focal lesions, which could not observed using routine brain MRI, were detected in the left brainstem of patient 1 and in the right pons and the left and right medulla of patient 2. The patients showed significantly decreased FA values in the focal lesions compared to normal controls. CONCLUSIONS: DTI with FT demonstrated focal lesions at the brainstem that had not been revealed by conventional brain MRI; these focal lesions explained the weaknesses of the patients. We conclude that DTI with FT may be a useful modality for use in investigating the status of CST in patients with DAI.

Adult↗

PubMed2000

Anisotropic diffusion in kidney: apparent diffusion coefficient measurements for clinical use.

The purpose of this study was to evaluate anisotropy of the kidney by measurements of the apparent diffusion coefficient (ADC) using commercially available magnetic resonance (MR) imaging. Fifty-one consecutive patients underwent diffusion-weighted echoplanar MR imaging of the upper abdomen with five different strengths of motion probing gradients (b = 1.51, 55.3, 36.6, 317, and 932 sec/mm2) applied along the z-axis. Four ADC values for the upper pole and central portion of the kidney were calculated from four different b-value ranges and compared. The ADCs for the kidney calculated in the lower b-value ranges were significantly higher than those in the higher ranges. The ADCs for the upper pole portion were significantly higher than those for the central portion except for one in the highest b-value range. Diffusion in the kidney is anisotropic, probably due to the kidney's radially oriented structures such as renal vessels and tubules.

Anisotropy↗

PubMed2000

Diffusion-weighted EPI of cystic ovarian lesions: evaluation of cystic contents using apparent diffusion coefficients.

Diffusion-weighted echoplanar imaging (EPI) was performed to evaluate the contents of cystic ovarian lesions [33 endometrial cysts, 16 ovarian cysts, 5 serous cystadenomas, 6 mucinous cystadenomas, 13 malignant cystic ovarian tumors, and 3 benign cystic lesions mimicking malignant cystic ovarian tumor (BMMs)]. Apparent diffusion coefficient (ADC) values were calculated for the cystic contents. Many lesions showed unrealistically high ADC greater than water at body temperature (0.00324 mm(2)/sec), especially in lesions more than 12 cm in diameter. The higher ADC values were attributed to the sloshing effect: intermittent compression of large ovarian lesions by abdominal breathing before the breath-hold scan. When limited to lesions with ADC less than 0. 00324 mm(2)/sec, endometrial cysts and malignant cystic ovarian tumors showed lower ADC values than ovarian cysts and serous cystadenomas (P < 0.03). When further limited to lesions less than 12 cm in axial diameter, an additional ADC difference between malignant cystic ovarian BMMs was demonstrated (P < 0.03). Diffusion-weighted EPI showed the possibility that calculated ADC values might be useful in evaluating small to medium cystic ovarian lesions. J. Magn. Reson. Imaging 2000;12:1014-1019.

Adult↗

PubMed2003

Diffusion in compartmental systems. II. Diffusion-weighted measurements of rat brain tissue in vivo and postmortem at very large b-values.

Diffusion-weighted single-voxel (1)H spectroscopic measurements were performed on rat brain tissue in vivo and postmortem. Diffusion weighting was achieved by varying the diffusion time from 23 ms to 1.18 sec via the mixing time in a stimulated echo sequence. A series of constant gradient (cg-) experiments of eight effective gradient strengths q(2)(q(2) = gamma(2)delta(2)g(2)) from 24.2 x 10(3) to 490.2 x 10(3) mm(-2) was performed, resulting in a maximum attenuation factor of b = 580,000 s/mm(2). A fit of three exponential terms was found to be appropriate to represent the attenuation signal over the whole b-range. The behavior of the slowest decaying component can be fully understood in terms of a long time limit of a modified Kärger formalism for a two-compartment system. This allowed estimation of the transmembrane water exchange rate: the intracellular exchange time was determined to be 622 +/- 29 ms and 578 +/- 20 ms in vivo and postmortem, respectively.

Animals↗

PubMed2003

Magnetic resonance measurement of tetramethylammonium diffusion in rat brain: Comparison of magnetic resonance and ionophoresis in vivo diffusion measurements.

Magnetic resonance (MR) and ionophoresis are two experimental methods that provide measurements of molecular diffusion in living tissue. Typical experimental settings yield MR studies that are sensitive to mean molecular displacements of approximately 5 microm, and ionophoresis experiments to displacements of > or =100 microm. An assessment of the correspondence between the methods is hampered by the fact that no common probe molecule has been used. One of the most frequently utilized probe molecules in ionophoresis measurements is the tetramethylammonium (TMA) ion. In the current work the diffusion properties of TMA were studied in rat brain in vivo with localized (1)H MR spectroscopy (MRS). Standard treatment of the MR data yielded a 3.6-fold lower apparent diffusion coefficient (ADC) compared to ionophoresis. To explore the source of this discrepancy, a separate data processing scheme was applied to the MR data to monitor individual elapsed displacement-distance subpopulations of TMA molecules. This analysis revealed a dependence of the ADC estimation on a given subpopulation's elapsed displacement distance. The MR-derived ADC approached the ionophoresis-derived value as the elapsed displacement distance increased to 15 microm. These observations demonstrate that MR and ionophoresis studies provide complementary information, and that ADC estimates obtained from the two techniques are sensitive to different biophysical determinants.

Animals↗

PubMed1994

Magnetic resonance diffusion-weighted imaging: sensitivity and apparent diffusion constant in stroke.

Magnetic resonance diffusion-weighted imaging (MR-DWI) is sensitive to the diffusibility of water and may offer characterization and anatomical localization of stroke leading to early tailored therapeutic intervention. We compared DWI, the apparent diffusion constant (ADC), and autoradiographic cerebral blood flow (CBF) in a model of focal cerebral ischemia in the rat. Sprague-Dawley rats were embolized with a single silicone cylinder injected into the internal carotid artery. Both common carotids were permanently ligated. The animals were anesthetized (isoflurane in O2), and paralyzed (gallamine). MR-DWI were obtained with a GE 4.7 T magnet (TE = 3 s, TR = 80 msec, b = 2393.10(-3) mm2/s, slice thickness 3 mm). DWI and CBF autoradiograms were compared visually. ADC was assessed in various regions, including ischemic cortex and a region homologous to ischemic cortex. Imaging times from stroke onset were 50 +/- 6 min (mean +/- SEM) for DWI, 185 +/- 17 min for a second DWI. CBF was determined at 258 +/- 15 min. The specificity was 100% at both 50 min and 185 min, indicating that there were no false positives; in 3 animals ischemia was not present. However, the sensitivity analysis indicated that early DWI yields some false negatives; at 50 min the sensitivity was 60%. We attribute our result of low early sensitivity to small infarcts in relation to the slice thickness. Later, at 185 min, sensitivity was 100%. The first ADCs were higher than the second ADC values in ischemic cortex. For infarcts larger than the slice thickness, early MR-DWI is highly sensitive for imaging evolving ischemia.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

PubMed2005

Fractional anisotropy and mean diffusivity measurements on normal human brain: comparison between low-and high-resolution diffusion tensor imaging sequences.

Non-invasive in vivo visualization of white matter fiber tracts is currently feasible by means of diffusion tensor imaging (DTI) techniques. DTI-derived metrics, like fractional anisotropy (FA) and mean diffusivity (MD), have the potential to improve tissue characterization. Technical optimization of diffusion tensor sequences, including signal-to-noise ratio and spatial resolution, was performed for 20 normal subjects. High- and low-resolution DTI sequences were applied on all subjects and FA, MD parametric maps were reconstructed for both protocols. Voxel-based statistical analysis revealed regions with significantly different FA and MD values between the two sequences, while the same type of analysis was performed to illustrate regions with significantly different signal-to-noise ratio. In conclusion, optimized DTI sequences may be applied routinely in clinical practice with a standard MR scanner, while accurate quantification of FA and MD may improve lesion characterization.

Adolescent↗

PubMed1980

Ternary diffusion and effective diffusion coefficients in alveolar spaces.

An experimentally verified mathematical model of non-equimolar ternary gas diffusion is applied to simulate the conditions existing in the alveolar spaces. When a fictitious gas film is erected a certain distance away from the alveolar membrane, and when the compositions at the two boundaries of the film are, respectively, the alveolar gas composition and a proportional mixture of inspired gas with the alveolar gas, the resulting fluxes of O2 and CO2 are essentially linearly related to their respective partial pressure gradients. From the slopes of these flux lines, effective diffusion coefficients are obtained. Ramifications of the effective diffusion coefficients approach are discussed.

Animals↗

PubMed1993

Morphometric model for pulmonary diffusing capacity. I. Membrane diffusing capacity.

The pulmonary diffusing capacity is related to the quantitative design characteristics of the pulmonary gas exchanger. The current model for estimating DLO2 from morphometric data breaks the diffusion path for O2 into four steps, three of which represent the membrane part of DLO2. A critique of this model on the basis of newer evidence leads to a modification of the model where the path from the alveolar surface to the erythrocyte membrane is considered as a single step. The structural determinant of this model for DMO2 is the ratio of effective diffusion surface to effective total barrier thickness. The effective surface is formulated as a fraction of the alveolar surface area, the most robust measure of lung design, whereas the effective barrier thickness is the harmonic mean distance--or mean proximity--between alveolar surface and erythrocyte surface. The methods for obtaining the morphometric measurements are discussed. The results show that the new morphometric estimates of DMO2 are 33% lower than those obtained with the old model, resulting in a reduction of the estimates of DLO2 by 10-20%.

Animals↗

PubMed2004

Imaging of postthalamic visual fiber tracts by anisotropic diffusion weighted MRI and diffusion tensor imaging: principles and applications.

Diffusion weighted MRI offers the possibility to study the course of the cerebral white matter tracts. In the present manuscript, the basics, the technique and the limitations of diffusion tensor imaging and anisotropic diffusion weighted MRI are presented and their applications in various neurological and neurosurgical diseases are discussed with special emphasis on the visual system. A special focus is laid on the combination of fiber tract imaging, anatomical imaging and functional MRI for presurgical planning and intraoperative neuronavigation of lesions near the visual system.

Brain Diseases↗

PubMed2006

The placenta in pre-eclampsia and intrauterine growth restriction: studies on exchange surface areas, diffusion distances and villous membrane diffusive conductances.

We test the null hypothesis that the morphometric diffusive conductance of the placental villous membrane does not alter in pregnancies complicated by intrauterine growth restriction (IUGR) or pre-eclampsia (PE). Placentas were collected from cases of normotensive IUGR, pure PE, PE+IUGR and from control pregnancies. Microscopical fields on formalin-fixed, trichrome-stained histological sections were randomly sampled for location and orientation. Using stereological methods, the exchange surface areas of peripheral (terminal and intermediate) villi and their fetal capillaries and the arithmetic and harmonic mean thicknesses of the villous membrane (maternal aspect of trophoblast to luminal aspect of vascular endothelium) were estimated. An index of the variability in thickness of this membrane, and an estimate of its oxygen diffusive conductance, was derived secondarily. Group comparisons were drawn using two-way analysis of variance to identify main effects (of PE or IUGR) and interaction effects (between PE and IUGR). PE did not have significant effects on placental morphology and there were no significant effects of PE or IUGR on membrane thickness or its variability. In contrast, IUGR (with or without PE) was associated with reduced surface areas and this was the principal factor leading to a smaller membrane diffusive conductance in these placentas. When account was taken of fetal mass, specific conductance showed no effects of PE or IUGR despite the mass-specific conductance in pure IUGR placentas appearing to be smaller than that in controls. The decline in total conductances is indicative of perturbations operating at the levels of villous trophoblast and fetal vasculature and these may contribute to fetal hypoxic stress.

Biological Transport↗