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.

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.

Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Detection of scalar gravitational waves with a hollow spherical antenna

We study the response and cross sections for the absorption of GW energy generated in a Jordan-Brans-Dicke theory by a resonant mass detector shaped as a hollow sphere. As a source of the GW we take a binary system in the Newtonian approximation. For masses of the stars of the order of the solar mass, the emitted GW sweeps a range of frequencies which include the first resonant mode of the detector.

Giant acceleration of free diffusion by use of titled periodic potentials

The effective diffusion coefficient for the overdamped Brownian motion in a tilted periodic potential is calculated in closed analytical form. Universality classes and scaling properties for weak thermal noise are identified near the threshold tilt where deterministic running solutions set in. In this regime the diffusion may be greatly enhanced, as compared to free thermal diffusion with, for a realistic experimental setup, an enhancement of up to 14 orders of magnitude.

First-passage-time noninteger moments for some diffusion and dichotomous processes

We calculate noninteger moments ¿tq¿ of first passage time to trapping, at both ends of an interval (0,L), for some diffusion and dichotomous processes. We find the critical behavior of ¿tq¿, as a function of q, for free processes. We also show that the addition of a potential can destroy criticality.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.