A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion

An epidemic model is formulated by a reactionâeuro"diffusion system where the spatial pattern formation is driven by cross-diffusion. The reaction terms describe the local dynamics of susceptible and infected species, whereas the diffusion terms account for the spatial distribution dynamics. For both self-diffusion and cross-diffusion, nonlinear constitutive assumptions are suggested. To simulate the pattern formation two finite volume formulations are proposed, which employ a conservative and a non-conservative discretization, respectively. An efficient simulation is obtained by a fully adaptive multiresolution strategy. Numerical examples illustrate the impact of the cross-diffusion on the pattern formation.

Thalamic connectivity in patients with essential tremor treated with MR imaging-guided focused ultrasound: in vivo fiber tracking by using diffusion-tensor MR imaging.

PURPOSE: To use diffusion-tensor (DT) magnetic resonance (MR) imaging in patients with essential tremor who were treated with transcranial MR imaging-guided focused ultrasound lesion inducement to identify the structural connectivity of the ventralis intermedius nucleus of the thalamus and determine how DT imaging changes correlated with tremor changes after lesion inducement. MATERIALS AND METHODS: With institutional review board approval, and with prospective informed consent, 15 patients with medication-refractory essential tremor were enrolled in a HIPAA-compliant pilot study and were treated with transcranial MR imaging-guided focused ultrasound surgery targeting the ventralis intermedius nucleus of the thalamus contralateral to their dominant hand. Fourteen patients were ultimately included. DT MR imaging studies at 3.0 T were performed preoperatively and 24 hours, 1 week, 1 month, and 3 months after the procedure. Fractional anisotropy (FA) maps were calculated from the DT imaging data sets for all time points in all patients. Voxels where FA consistently decreased over time were identified, and FA change in these voxels was correlated with clinical changes in tremor over the same period by using Pearson correlation. RESULTS: Ipsilateral brain structures that showed prespecified negative correlation values of FA over time of -0.5 or less included the pre- and postcentral subcortical white matter in the hand knob area; the region of the corticospinal tract in the centrum semiovale, in the posterior limb of the internal capsule, and in the cerebral peduncle; the thalamus; the region of the red nucleus; the location of the central tegmental tract; and the region of the inferior olive. The contralateral middle cerebellar peduncle and bilateral portions of the superior vermis also showed persistent decrease in FA over time. There was strong correlation between decrease in FA and clinical improvement in hand tremor 3 months after lesion inducement (P < .001). CONCLUSION: DT MR imaging after MR imaging-guided focused ultrasound thalamotomy depicts changes in specific brain structures. The magnitude of the DT imaging changes after thalamic lesion inducement correlates with the degree of clinical improvement in essential tremor.

Double-tagged fluorescent bacterial bioreporter for the study of polycyclic aromatic hydrocarbon diffusion and bioavailability.

Bacterial degradation of polycyclic aromatic hydrocarbons (PAHs), ubiquitous contaminants from oil and coal, is typically limited by poor accessibility of the contaminant to the bacteria. In order to measure PAH availability in complex systems, we designed a number of diffusion-based assays with a double-tagged bacterial reporter strain Burkholderia sartisoli RP037-mChe. The reporter strain is capable of mineralizing phenanthrene (PHE) and induces the expression of enhanced green fluorescent protein (eGFP) as a function of the PAH flux to the cell. At the same time, it produces a second autofluorescent protein (mCherry) in constitutive manner. Quantitative epifluorescence imaging was deployed in order to record reporter signals as a function of PAH availability. The reporter strain expressed eGFP proportionally to dosages of naphthalene or PHE in batch liquid cultures. To detect PAH diffusion from solid materials the reporter cells were embedded in 2 cm-sized agarose gel patches, and fluorescence was recorded over time for both markers as a function of distance to the PAH source. eGFP fluorescence gradients measured on known amounts of naphthalene or PHE served as calibration for quantifying PAH availability from contaminated soils. To detect reporter gene expression at even smaller diffusion distances, we mixed and immobilized cells with contaminated soils in an agarose gel. eGFP fluorescence measurements confirmed gel patch diffusion results that exposure to 2-3 mg lampblack soil gave four times higher expression than to material contaminated with 10 or 1 (mg PHE) g(-1).

Le problème de l'interdépendance dans la comparaison des politiques publiques infranationales : une méta-analyse des mécanismes de diffusion

Un des problèmes majeurs de la méthode comparative, et notamment de la comparaison entre politiques publiques infranationales, est le fait que les phénomènes à comparer, au lieu de consister en unités analytiques indépendantes les unes des autres, sont au contraire susceptibles de s'influencer mutuellement. Cette contribution aborde la problématique de l'interdépendance, avec une attention particulière aux différences entre politiques publiques internationales et infranationales. Elle synthétisera et discutera les apports des travaux empiriques sur la diffusion, à travers une métaanalyse des « conditions nécessaires » pour les différents mécanismes de diffusion des politiques publiques. Dans ce but, elle analysera, un échantillon de la littérature scientifique avec la technique des ensembles flous, et illustré à l'aide d'exemples concrets.

High b-value diffusion-weighted imaging: A sensitive method to reveal white matter differences in schizophrenia.

Over the last 10 years, diffusion-weighted imaging (DWI) has become an important tool to investigate white matter (WM) anomalies in schizophrenia. Despite technological improvement and the exponential use of this technique, discrepancies remain and little is known about optimal parameters to apply for diffusion weighting during image acquisition. Specifically, high b-value diffusion-weighted imaging known to be more sensitive to slow diffusion is not widely used, even though subtle myelin alterations as thought to happen in schizophrenia are likely to affect slow-diffusing protons. Schizophrenia patients and healthy controls were scanned with a high b-value (4000s/mm(2)) protocol. Apparent diffusion coefficient (ADC) measures turned out to be very sensitive in detecting differences between schizophrenia patients and healthy volunteers even in a relatively small sample. We speculate that this is related to the sensitivity of high b-value imaging to the slow-diffusing compartment believed to reflect mainly the intra-axonal and myelin bound water pool. We also compared these results to a low b-value imaging experiment performed on the same population in the same scanning session. Even though the acquisition protocols are not strictly comparable, we noticed important differences in sensitivities in the favor of high b-value imaging, warranting further exploration.

l0-deconvolution for compressive diffusion MRI

Diffusion MRI is a well established imaging modality providing a powerful way to non-invasively probe the structure of the white matter. Despite the potential of the technique, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a wide variety of methods have been proposed to shorten acquisition times. [...] We here review a recent work where we propose to further exploit the versatility of compressed sensing and convex optimization with the aim to characterize the fiber orientation distribution sparsity more optimally. We re-formulate the spherical deconvolution problem as a constrained l0 minimization.

Diffusion tensor imaging shows structural remodeling of stroke mirror region: results from a pilot study.

Background: The role of the non-injured hemisphere in stroke recovery is poorly understood. In this pilot study, we sought to explore the presence of structural changes detectable by diffusion tensor imaging (DTI) in the contralesional hemispheres of patients who recovered well from ischemic stroke. Methods: We analyzed serial DTI data from 16 stroke patients who had moderate initial neurological deficits (NIHSS scores 3-12) and good functional outcome at 3-6 months (NIHSS score 0 or modified Rankin Score ≤1). We segmented the brain tissue in gray and white matter (GM and WM) and measured the apparent diffusion coefficient (ADC) and fractional anisotropy in the infarct, in the contralesional infarct mirror region as well as in concentrically expanding regions around them. Results: We found that GM and WM ADC significantly increased in the infarct region (p < 0.01) from acute to chronic time points, whereas in the infarct mirror region, GM and WM ADC increased (p < 0.01) and WM fractional anisotropy decreased (p < 0.05). No significant changes were detected in other regions. Conclusion: DTI-based metrics are sensitive to regional structural changes in the contralesional hemisphere during stroke recovery. Prospective studies in larger cohorts with varying levels of recovery are needed to confirm our findings.

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.

Test-retest reliability of thermal quantitative sensory testing on two sites within the L5 dermatome of the lumbar spine and lower extremity.

INTRODUCTION: Quantitative sensory testing (QST) is widely used in human research to investigate the integrity of the sensory function in patients with pain of neuropathic origin, or other causes such as low back pain. Reliability of QST has been evaluated on both sides of the face, hands and feet as well as on the trunk (Th3-L3). In order to apply these tests on other body-parts such as the lower lumbar spine, it is important first to establish reliability on healthy individuals. The aim of this study was to investigate intra-rater reliability of thermal QST in healthy adults, on two sites within the L5 dermatome of the lumbar spine and lower extremity. METHODS: Test-retest reliability of thermal QST was determined at the L5-level of the lumbar spine and in the same dermatome on the lower extremity in 30 healthy persons under 40 years of age. Results were analyzed using descriptive statistics and intraclass correlation coefficient (ICC). Values were compared to normative data, using Z-transformation. RESULTS: Mean intraindividual differences were small for cold and warm detection thresholds but larger for pain thresholds. ICC values showed excellent reliability for warm detection and heat pain threshold, good-to-excellent reliability for cold pain threshold and fair-to-excellent reliability for cold detection threshold. ICC had large ranges of confidence interval (95%). CONCLUSION: In healthy adults, thermal QST on the lumbar spine and lower extremity demonstrated fair-to-excellent test-retest reliability.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.