Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Alveolar echinococcosis of the liver: Diffusion-weighted MRI findings and potential role in lesion characterisation

PURPOSE: To report the diffusion-weighted MRI findings in alveolar echinococcosis (AE) of the liver and evaluate the potential role of apparent diffusion coefficients (ADCs) in the characterisation of lesions. MATERIALS AND METHODS: We retrospectively included 22 patients with 63 AE liver lesions (≥1cm), examined with 3-T liver MRI, including a free-breathing diffusion-weighted single-shot echo-planar imaging sequence (b-values=50, 300 and 600s/mm(2)). Two radiologists jointly assessed the following lesion features: size, location, presence of cystic and/or solid components (according to Kodama's classification system), relative contrast enhancement, and calcifications (on CT). The ADCtotal, ADCmin and ADCmax were measured in each lesion and the surrounding liver parenchyma. RESULTS: Three type 1, 19 type 2, 17 type 3, three type 4 and 21 type 5 lesions were identified. The mean (±SD) ADCtotal, ADCmin and ADCmax for all lesions were 1.73±0.50, 0.76±0.38 and 2.63±0.76×10(-3)mm(2)/s, respectively. The mean ADCtotal for type 1, type 2, type 3, type 4 and type 5 lesions were 1.97±1.01, 1.76±0.53, 1.73±0.41, 1.15±0.42 and 1.76±0.44×10(-3)mm(2)/s, respectively. No significant differences were found between the five lesion types, except for type 4 (p=0.0363). There was a significant correlation between the presence of a solid component and low ADCmin (r=0.39, p=0.0016), whereas an inverse correlation was found between the relative contrast enhancement and ADCtotal (r=-0.34, p=0.0072). CONCLUSION: The ADCs of AE lesions are relatively low compared to other cystic liver lesions, which may help in the differential diagnosis. Although ADCs are of little use to distinguish between the five lesion types, their low value reflects the underlying solid component.

Diffusion-weighted MR imaging of the spine at 3-T: feasibility, optimization of b-value and utility to differentiate benign from pathological vertebral compression fractures

Purpose: To evaluate the feasibility, determine the optimal b-value, and assess the utility of 3-T diffusion-weighted MR imaging (DWI) of the spine in differentiating benign from pathologic vertebral compression fractures.Methods and Materials: Twenty patients with 38 vertebral compression fractures (24 benign, 14 pathologic) and 20 controls (total: 23 men, 17 women, mean age 56.2years) were included from December 2010 to May 2011 in this IRB-approved prospective study. MR imaging of the spine was performed on a 3-T unit with T1-w, fat-suppressed T2-w, gadolinium-enhanced fat-suppressed T1-w and zoomed-EPI (2D RF excitation pulse combined with reduced field-of-view single-shot echo-planar readout) diffusion-w (b-values: 0, 300, 500 and 700s/mm2) sequences. Two radiologists independently assessed zoomed-EPI image quality in random order using a 4-point scale: 1=excellent to 4=poor. They subsequently measured apparent diffusion coefficients (ADCs) in normal vertebral bodies and compression fractures, in consensus.Results: Lower b-values correlated with better image quality scores, with significant differences between b=300 (mean±SD=2.6±0.8), b=500 (3.0±0.7) and b=700 (3.6±0.6) (all p<0.001). Mean ADCs of normal vertebral bodies (n=162) were 0.23, 0.17 and 0.11×10-3mm2/s with b=300, 500 and 700s/mm2, respectively. In contrast, mean ADCs were 0.89, 0.70 and 0.59×10-3mm2/s for benign vertebral compression fractures and 0.79, 0.66 and 0.51×10-3mm2/s for pathologic fractures with b=300, 500 and 700s/mm2, respectively. No significant difference was found between ADCs of benign and pathologic fractures.Conclusion: 3-T DWI of the spine is feasible and lower b-values (300s/mm2) are recommended. However, our preliminary results show no advantage of DWI in differentiating benign from pathologic vertebral compression fractures.

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.

Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T.

PURPOSE: To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. MATERIALS AND METHODS: The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (Di ± standard deviations) and their fractions (fi ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. RESULTS: The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D1 = 1.35 ± 0.03 × 10(-3) mm(2)/s; f1 = 72.7 ± 0.9 %), a fast (D2 = 26.50 ± 2.49 × 10(-3) mm(2)/s; f2 = 13.7 ± 0.6 %) and a very fast (D3 = 404.00 ± 43.7 × 10(-3) mm(2)/s; f3 = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm(2) CONCLUSION: The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm(2) range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. KEY POINTS: ? For normal liver, tri-exponential IVIM model might be superior to bi-exponential ? A very fast compartment (D = 404.00 ± 43.7 × 10 (-3)  mm (2) /s; f = 13.5 ± 0.8 %) is determined from the tri-exponential model ? The compartment contributes to the IVIM signal only for b ≤ 15 s/mm (2.)

A DGT Technique for Plutonium Bioavailability Measurements.

The toxicity of heavy metals in natural waters is strongly dependent on the local chemical environment. Assessing the bioavailability of radionuclides predicts the toxic effects to aquatic biota. The technique of diffusive gradients in thin films (DGT) is largely exploited for bioavailability measurements of trace metals in waters. However, it has not been applied for plutonium speciation measurements yet. This study investigates the use of DGT technique for plutonium bioavailability measurements in chemically different environments. We used a diffusion cell to determine the diffusion coefficients (D) of plutonium in polyacrylamide (PAM) gel and found D in the range of 2.06-2.29 × 10(-6) cm(2) s(-1). It ranged between 1.10 and 2.03 × 10(-6) cm(2) s(-1) in the presence of fulvic acid and in natural waters with low DOM. In the presence of 20 ppm of humic acid of an organic-rich soil, plutonium diffusion was hindered by a factor of 5, with a diffusion coefficient of 0.50 × 10(-6) cm(2) s(-1). We also tested commercially available DGT devices with Chelex resin for plutonium bioavailability measurements in laboratory conditions and the diffusion coefficients agreed with those from the diffusion cell experiments. These findings show that the DGT methodology can be used to investigate the bioaccumulation of the labile plutonium fraction in aquatic biota.

Fluorescence imaging reveals the nuclear behavior of peroxisome proliferator-activated receptor/retinoid X receptor heterodimers in the absence and presence of ligand.

In a global approach combining fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), and fluorescence resonance energy transfer (FRET), we address the behavior in living cells of the peroxisome proliferator-activated receptors (PPARs), a family of nuclear receptors involved in lipid and glucose metabolism, inflammation control, and wound healing. We first demonstrate that unlike several other nuclear receptors, PPARs do not form speckles upon ligand activation. The subnuclear structures that may be observed under some experimental conditions result from overexpression of the protein and our immunolabeling experiments suggest that these structures are subjected to degradation by the proteasome. Interestingly and in contrast to a general assumption, PPARs readily heterodimerize with retinoid X receptor (RXR) in the absence of ligand in living cells. PPAR diffusion coefficients indicate that all the receptors are engaged in complexes of very high molecular masses and/or interact with relatively immobile nuclear components. PPARs are not immobilized by ligand binding. However, they exhibit a ligand-induced reduction of mobility, probably due to enhanced interactions with cofactors and/or chromatin. Our study draws attention to the limitations and pitfalls of fluorescent chimera imaging and demonstrates the usefulness of the combination of FCS, FRAP, and FRET to assess the behavior of nuclear receptors and their mode of action in living cells.

Alveolar echinococcosis of the liver: diffusionweighted MR imaging findings

Purpose: To report the diffusion-weighted MR imaging (DWI) findings in hepatic alveolar echinococcosis (AE). To evaluate the usefulness of apparent diffusion coefficients (ADCs) for differentiating the 5 types of AE lesions (as reported by Kodama, Radiology, 2003).Methods and Materials: We retrospectively included 17 patients (10 women, mean age 64.3years) with 48 AE liver lesions (>1cm2) that had been investigated by 3-Tesla MR imaging between March 2008 and August 2011 performing our standard protocol including DWI (b-values: 0, 300 and 600s/mm2). In consensus, two radiologists assessed lesion characteristics such as diameter, cystic and/or fibrotic components including Kodama classification, signal intensity, contrast enhancement, calcifications (on CT), and measured the ADC of each lesion. AE was confirmed by serology, biopsy and/or surgery in all patients.Results: Seventeen lesions of Kodama type 1, 10 of type 2, 19 of type 3, 1 of type 4 and 1 of type 5 were found. Mean(±SD) ADC of all AE lesions was 1.75±0.45 ×10-3mm2/s. Mean(±SD) ADCs of Kodama type 1, 2, 3, 4 and 5 lesions were 1.74±0.55, 1.71±0.49, 1.82±0.36, 1.46±0 and 1.43±0 ×10-3mm2/s, respectively. No significant difference was noted between the different Kodama types (p=0.89). Presence of fibrotic (p=0.24) and/or calcified (p=0.90) components, or contrast enhancement (p=0.84) of AE lesions were not correlated with significant differences in ADCs.Conclusion: ADCs of AE lesions are relatively low compared to other cystic liver lesions, which is helpful in suggesting the diagnosis. However, ADCs were not found to be useful for differentiating Kodama types of AE lesions.

Detecting and measuring deprivation in primary care: development, reliability and validity of a self-reported questionnaire: the DiPCare-Q.

OBJECTIVES: Advances in biopsychosocial science have underlined the importance of taking social history and life course perspective into consideration in primary care. For both clinical and research purposes, this study aims to develop and validate a standardised instrument measuring both material and social deprivation at an individual level. METHODS: We identified relevant potential questions regarding deprivation using a systematic review, structured interviews, focus group interviews and a think-aloud approach. Item response theory analysis was then used to reduce the length of the 38-item questionnaire and derive the deprivation in primary care questionnaire (DiPCare-Q) index using data obtained from a random sample of 200 patients during their planned visits to an ambulatory general internal medicine clinic. Patients completed the questionnaire a second time over the phone 3 days later to enable us to assess reliability. Content validity of the DiPCare-Q was then assessed by 17 general practitioners. Psychometric properties and validity of the final instrument were investigated in a second set of patients. The DiPCare-Q was administered to a random sample of 1898 patients attending one of 47 different private primary care practices in western Switzerland along with questions on subjective social status, education, source of income, welfare status and subjective poverty. RESULTS: Deprivation was defined in three distinct dimensions: material (eight items), social (five items) and health deprivation (three items). Item consistency was high in both the derivation (Kuder-Richardson Formula 20 (KR20) =0.827) and the validation set (KR20 =0.778). The DiPCare-Q index was reliable (interclass correlation coefficients=0.847) and was correlated to subjective social status (r(s)=-0.539). CONCLUSION: The DiPCare-Q is a rapid, reliable and validated instrument that may prove useful for measuring both material and social deprivation in primary care.

Imagerie de diffusion (DWI) dans la caractérisation de l'échinococcose alvéolaire hépatique.

Objectifs: Etudier l'utilité de DWI dans l'échinococcose alveolaire (EA) hépatique. Matériels et méthodes: Dix-sept patients (10 hommes, âge moyen 64.3) avec 55 lésions hépatiques ont été examinés par IRM. La sémiologie des lésions a été étudiée après classification selon Kodama. Les coefficients apparent de diffusion (ADCmax, ADCmin, ADCtot) ont été mesurés. Résultats: Trois lésions de Kodama de type 1, 13 de type 2, 15 de type 3, 3 de type 4, et 21 de type 5. L'ADCtot des lésions mesurait 1.23±0.18 x 10-3 mm2/s. L'ADCtot de Kodama type 1, 2, 3, 4 et 5 mesuraient 1.97±0.27, 1.66±0.13, 1.73±0.12, 1.15±0.27 et 1.76±0.10 x 10-3 mm2/s, respectivement. Il n'y avait pas de différence significative de l'ADCtot entre les types (p=0.25) hormis le type 4 qui représente une lésion solide (p=0.035). Conclusion: Les valeurs d'ADC des lésions d'EA ne se révèlent pas utiles pour différencier les différents types selon Kodama, hormis pour le type 4 ce qui suggère la présence d'une composante solide. Celles-ci sont relativement basses comparées à d'autres lésions kystiques hépatiques, ce qui peut aider à suggérer le diagnostic.

Interobserver and intraobserver variability of the apparent diffusion coefficient in treated malignant hepatic lesions on a 3.0T machine: measurements in the whole lesion versus in the area with the most restricted diffusion.

PURPOSE: To assess the inter/intraobserver variability of apparent diffusion coefficient (ADC) measurements in treated hepatic lesions and to compare ADC measurements in the whole lesion and in the area with the most restricted diffusion (MRDA). MATERIALS AND METHODS: Twenty-five patients with treated malignant liver lesions were examined on a 3.0T machine. After agreeing on the best ADC image, two readers independently measured the ADC values in the whole lesion and in the MRDA. These measurements were repeated 1 month later. The Bland-Altman method, Spearman correlation coefficients, and the Wilcoxon signed-rank test were used to evaluate the measurements. RESULTS: Interobserver variability for ADC measurements in the whole lesion and in the MRDA was 0.17 x 10(-3) mm(2)/s [-0.17, +0.17] and 0.43 x 10(-3) mm(2)/s [-0.45, +0.41], respectively. Intraobserver limits of agreement could be as low as [-0.10, +0.12] 10(-3) mm(2)/s and [-0.20, +0.33] 10(-3) mm(2)/s for measurements in the whole lesion and in the MRDA, respectively. CONCLUSION: A limited variability in ADC measurements does exist, and it should be considered when interpreting ADC values of hepatic malignancies. This is especially true for the measurements of the minimal ADC.

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.

Melanoma patients respond to a cytotoxic T lymphocyte-defined self-peptide with diverse and nonoverlapping T-cell receptor repertoires.

HLA-A2+ melanoma patients develop naturally a strong CD8+ T cell response to a self-peptide derived from Melan-A. Here, we have used HLA-A2/peptide tetramers to isolate Melan-A-specific T cells from tumor-infiltrated lymph nodes of two HLA-A2+ melanoma patients and analyzed their TCR beta chain V segment and complementarity determining region 3 length and sequence. We found a broad diversity in Melan-A-specific immune T-cell receptor (TCR) repertoires in terms of both TCR beta chain variable gene segment usage and clonal composition. In addition, immune TCR repertoires selected in the patients were not overlapping. In contrast to previously characterized CD8+ T-cell responses to viral infections, this study provides evidence against usage of highly restricted TCR repertoire in the natural response to a self-differentiation tumor antigen.