Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Heavy metals in soils and plants in mango orchards in Petrolina, Pernambuco, Brazil

The monitoring of heavy metal concentrations in areas under intensive agriculture is essential for the agricultural sustainability and food safety. This paper evaluates the total contents of heavy metals in soils and mango trees in orchards of different ages (6, 7, 8, 9, 10, 11, 14, 16, 17, 19, and 26 years) in Petrolina, Pernambuco, Brazil. Soil samples were taken from the layers 0-20 cm and 20-40 cm, and mango leaves were collected in the growth stage. Areas of native vegetation (Caatinga) adjacent to the cultivated areas were used for comparison. The total concentrations of heavy metals (Cu, Cr, Fe, Zn, Mn, Ni, and Pb) were determined in soils and leaves. In general, mango cultivation led to Cu and Zn accumulation in the soil surface and to a reduction in the contents of Ni, Pb, Mn, and Fe in surface and subsurface. Since contamination by Cu, Zn, and Cr was detected, these areas must be monitored to prevent negative environmental impacts. For instance, the presence of Cr in mango tree leaves indicates the need to investigate the source of the element in these orchards. The management strategies of the different companies led to deficiency or excess of some metals in the evaluated areas. However, the Fe and Mn levels were adequate for the mineral nutrition of mango in all areas.

Modelization of surface diffusion of a molecular dimer

A simple model for a dimer molecular diffusion on a crystalline surface, as a function of temperature, is presented. The dimer is formed by two particles coupled by a quadratic potential. The dimer diffusion is modeled by an overdamped Langevin equation in the presence of a two-dimensional periodic potential. Numerical simulation¿s results exhibit some dynamical properties observed, for example, in Si2 diffusion on a silicon [100] surface. They can be used to predict the value of the effective friction parameter. Comparison between our model and experimental measurements is presented.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

RNA interference against aquaporin-4 decreases the apparent diffusion coefficient in the normal brain

Aim: Diffusion weighted magnetic resonance imaging (MRI) is now widely used in human brain diagnosis.1 To date molecular mechanisms underlying changes in Apparent Diffusion Coefficient (ADC) signals remain poorly understood. AQP4, localized to astrocytes, is one of the most highly expressed cerebral AQPs.2 AQP4 is involved in water movement within the cell membrane of cultured astrocytes.3 We hypothesize that AQP4 contributes to water diffusion and underlying ADC values in normal brain. Methods: We used an RNA interference (RNAi) protocol in vivo, to acutely knockdown expression of AQP4 in rat brain and to determine whether this was associated with changes in brain ADC values using MRI protocols as previously described.4 RNAi was performed using specific small interference RNA (siRNA) against AQP4 (siAQP4) and a non-targeted-siRNA (siGLO) as a control. The specificity and efficiency of the siAQP4 were first tested in vitro in astrocyte and hippocampal slice cultures. In vivo, siRNAs were injected into the rat cortex 3d prior to MRI acquisition and AQP4 was assessed by western blot (n=4) and immunohistochemistry (n=6). Histology was performed on adjacent slices. Results: siAQP4 application on primary astrocyte cultures induced a 76% decrease in AQP4 expression after 4 days. In hippocampal slice cultures; we also found a significant decrease in AQP4 expression in astrocytes after siAQP4. In vivo, injection of non-targeted siRNA (siGLO) tagged with CY3 allowed us to show that GFAP positive cells (astrocytes) were positively stained with CY3-siGLO, showing efficient transfection. Western blot and immunohistochemical analysis showed that siAQP4 induced a ~30% decrease in AQP4 expression without modification of tissue properties or cell death. After siAQP4 treatment, a significant decrease in ADC values (~50%) were observed without altered of T2 values. Conclusions: Together these results suggest that AQP4 reduces water diffusion through the astrocytic plasma membrane and decreases ADC values. Our findings demonstrate for the first time that astrocytic AQP4 contributes significantly to brain water diffusion and ADC values in normal brain. These results open new avenues to interpretation of ADC values under normal physiological conditions and in acute and chronic brain injuries.

Interpretation of primary care physicians' attitude regarding rotavirus immunisation using diffusion of innovation theories.

To evaluate primary care physicians' attitude towards implementation of rotavirus (RV) immunisation into the Swiss immunisation schedule, an eight-question internet-based questionnaire was sent to the 3799 subscribers of InfoVac, a nationwide web-based expert network on immunisation issues, which reaches >95% of paediatricians and smaller proportions of other primary care physicians. Five demographic variables were also inquired. Descriptive statistics and multivariate analyses for the main outcome "acceptance of routine RV immunisation" and other variables were performed. Diffusion of innovation theory was used for data assessment. Nine-hundred seventy-seven questionnaires were returned (26%). Fifty percent of participants were paediatricians. Routine RV immunisation was supported by 146 participants (15%; so called early adopters), dismissed by 620 (64%), leaving 211 (21%) undecided. However, when asked whether they would recommend RV vaccination to parents if it were officially recommended by the federal authorities and reimbursed, 467 (48.5%; so called early majority) agreed to recommend RV immunisation. Multivariate analysis revealed that physicians who would immunise their own child (OR: 5.1; 95% CI: 4.1-6.3), hospital-based physicians (OR: 1.6; 95% CI: 1.1-2.3) and physicians from the French (OR: 1.6; 95% CI: 1.2-2.3) and Italian speaking areas of Switzerland (OR: 2.5; 95% CI: 1.1-5.8) were more likely to support RV immunisation. Diffusion of innovation theory predicts a >80% implementation if approximately 50% of a given population support an innovation. Introduction of RV immunisation in Switzerland is likely to be successful, if (i) the federal authorities issue an official recommendation and (ii) costs are covered by basic health care insurance.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

A multi-center study: intra-scan and inter-scan variability of diffusion spectrum imaging.

The objective of this study was to investigate whether it is possible to pool together diffusion spectrum imaging data from four different scanners, located at three different sites. Two of the scanners had identical configuration whereas two did not. To measure the variability, we extracted three scalar maps (ADC, FA and GFA) from the DSI and utilized a region and a tract-based analysis. Additionally, a phantom study was performed to rule out some potential factors arising from the scanner performance in case some systematic bias occurred in the subject study. This work was split into three experiments: intra-scanner reproducibility, reproducibility with twin-scanner settings and reproducibility with other configurations. Overall for the intra-scanner and twin-scanner experiments, the region-based analysis coefficient of variation (CV) was in a range of 1%-4.2% and below 3% for almost every bundle for the tract-based analysis. The uncinate fasciculus showed the worst reproducibility, especially for FA and GFA values (CV 3.7-6%). For the GFA and FA maps, an ICC value of 0.7 and above is observed in almost all the regions/tracts. Looking at the last experiment, it was found that there is a very high similarity of the outcomes from the two scanners with identical setting. However, this was not the case for the two other imagers. Given the fact that the overall variation in our study is low for the imagers with identical settings, our findings support the feasibility of cross-site pooling of DSI data from identical scanners.

Uptake of heavy metals by plants from airborne deposition and polluted soils

Selostus: Kasvien raskasmetallien otto ilmasta ja saastuneesta maasta

Perfusion and diffusion MRI of glioblastoma progression in a four-year prospective temozolomide clinical trial

RESUME BUT Cette étude a été menée sur le suivi de patients traités pour un glioblastome nouvellement diagnostiqué. Son objectif a été de déterminer l'impact des séquences de perfusion et de diffusion en imagerie par résonance magnétique (IRM). Un intérêt particulier a été porté au potentiel de ces nouvelles techniques d'imagerie dans l'anticipation de la progression de la maladie. En effet, l'intervalle de temps libre de progression est une mesure alternative de pronostic fréquemment utilisée. MATERIEL ET METHODE L'étude a porté sur 41 patients participant à un essai clinique de phase II de traitement par temozolomide. Leur suivi radiologique a comporté un examen IRM dans les 21 à 28 jours après radiochimiothérapie et tous les 2 mois par la suite. L'évaluation des images s'est faite sur la base de l'évaluation de l'effet de masse ainsi que de la mesure de la taille de la lésion sur les images suivantes : T1 avec produit de contraste, T2, diffusion, perfusion. Afin de déterminer la date de progression de la maladie, les critères classiques de variation de taille adjoints aux critères cliniques habituels ont été utilisés. RESULAT 311 examens IRM ont été revus. Au moment de la progression (32 patients), une régression multivariée selon Cox a permis de déterminer deux paramètres de survie : diamètre maximal en T1 (p>0.02) et variation de taille en T2 (p<0.05). L'impact de la perfusion et de la diffusion n'a pas été démontré de manière statistiquement significative. CONCLUSION Les techniques de perfusion et de diffusion ne peuvent pas être utilisées pour anticiper la progression tumorale. Alors que la prise de décision au niveau thérapeutique est critique au moment de la progression de la maladie, l'IRM classique en T1 et en T2 reste la méthode d'imagerie de choix. De manière plus spécifique, une prise de contraste en T1 supérieure à 3 cm dans son plus grand diamètre associée à un hypersignal T2 en augmentation forment un marqueur de mauvais pronostic.

Comparison of digestion methods to determine heavy metals in fertilizers

The lack of a standard method to regulate heavy metal determination in Brazilian fertilizers and the subsequent use of several digestion methods have produced variations in the results, hampering interpretation. Thus, the aim of this study was to compare the effectiveness of three digestion methods for determination of metals such as Cd, Ni, Pb, and Cr in fertilizers. Samples of 45 fertilizers marketed in northeastern Brazil were used. A fertilizer sample with heavy metal contents certified by the US National Institute of Standards and Technology (NIST) was used as control. The following fertilizers were tested: rock phosphate; organo-mineral fertilizer with rock phosphate; single superphosphate; triple superphosphate; mixed N-P-K fertilizer; and fertilizer with micronutrients. The substances were digested according to the method recommended by the Ministry for Agriculture, Livestock and Supply of Brazil (MAPA) and by the two methods 3051A and 3052 of the United States Environmental Protection Agency (USEPA). By the USEPA method 3052, higher portions of the less soluble metals such as Ni and Pb were recovered, indicating that the conventional digestion methods for fertilizers underestimate the total amount of these elements. The results of the USEPA method 3051A were very similar to those of the method currently used in Brazil (Brasil, 2006). The latter is preferable, in view of the lower cost requirement for acids, a shorter digestion period and greater reproducibility.