68 resultados para Non-constant coefficient diffusion equations

em Université de Lausanne, Switzerland


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Wear of polyethylene is associated with aseptic loosening of orthopaedic implants and has been observed in hip and knee prostheses and anatomical implants for the shoulder. The reversed shoulder prostheses have not been assessed as yet. We investigated the volumetric polyethylene wear of the reversed and anatomical Aequalis shoulder prostheses using a mathematical musculoskeletal model. Movement and joint stability were achieved by EMG-controlled activation of the muscles. A non-constant wear factor was considered. Simulated activities of daily living were estimated from in vivo recorded data. After one year of use, the volumetric wear was 8.4 mm(3) for the anatomical prosthesis, but 44.6 mm(3) for the reversed version. For the anatomical prosthesis the predictions for contact pressure and wear were consistent with biomechanical and clinical data. The abrasive wear of the polyethylene in reversed prostheses should not be underestimated, and further analysis, both experimental and clinical, is required.

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The present study analyses the spatial pattern of quaternary gravitational slope deformations (GSD) and historical/present-day instabilities (HPI) inventoried in the Swiss Rhone Valley. The main objective is to test if these events are clustered (spatial attraction) or randomly distributed (spatial independency). Moreover, analogies with the cluster behaviour of earthquakes inventoried in the same area were examined. The Ripley's K-function was applied to measure and test for randomness. This indicator allows describing the spatial pattern of a point process at increasing distance values. To account for the non-constant intensity of the geological phenomena, a modification of the K-function for inhomogeneous point processes was adopted. The specific goal is to explore the spatial attraction (i.e. cluster behaviour) among landslide events and between gravitational slope deformations and earthquakes. To discover if the two classes of instabilities (GSD and HPI) are spatially independently distributed, the cross K-function was computed. The results show that all the geological events under study are spatially clustered at a well-defined distance range. GSD and HPI show a similar pattern distribution with clusters in the range 0.75?9 km. The cross K-function reveals an attraction between the two classes of instabilities in the range 0?4 km confirming that HPI are more prone to occur within large-scale slope deformations. The K-function computed for GSD and earthquakes indicates that both present a cluster tendency in the range 0?10 km, suggesting that earthquakes could represent a potential predisposing factor which could influence the GSD distribution.

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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.

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Messages à retenir: Connaître le principe physique de l'imagerie de diffusion (DWI) à l'IRM adaptée à l'exploration des tumeurs du foie.Savoir la bonne technique d'acquisition des séquences pour évaluer la diffusion du parenchyme hépatique ainsi que des lésions focales intra -hépatiques les plusfréquentes.Apprendre l'utilité de la DWI pour évaluer le succès d'un traitement médical oncologique ou interventionnel .Discuter les avantages et les pièges liés à la DWI hépatique susceptibles d'influencer l'interprétation des tumeurs hépatiques. Résumé: Le principe d'imagerie de diffusion (DWI) à l'IRM repose sur la mobilité des molécules d'eau dans les différents tissus. Ce «mouvement Brownien» dépend de lacellularité tissulaire , des membranes cellulaires intactes et de la vascularisation . L'augmentation de ces paramètres précités résulte en une restriction de ladiffusion moléculaire, caractérisée par un hypersignal, puis quantifié par le calcul d'un coefficient apparent de diffusion (ADC). Basée sur des séquenceséchoplanaires pondérées en T2, la technique d'acquisition est rapide et non-invasive, donc souvent intégrée à l'IRM hépatique de routine. La DWI s'est révéléetrès sensible pour la détection de tumeurs hépatiques, même à un diamètre infracentimétrique. Néanmoins, sans être très spécifique, elle ne donne pas d'information certaine sur le caractère bénin ou malin, et elle doit être interprétée avec les autres séquences d'IRM et dans le contexte clinique donné. L'informationdiagnostique résultant de la DWI est morphologique et fonctionnelle, ce qui permet d'évaluer le succès de traitements oncologiques, notamment en absence dechangement de taille ou persistance de prise de contraste des lésions hépatiques. Très sensibles aux mouvements respiratoires, la DWI hépatique peut êtreaccompagnée d'artéfacts, qui influencent le calcul de l'ADC dont la valeur dépend de la machine IRM utilisée.

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Objectifs : Le coefficient de diffusion apparente (ADC) est utilisé pour le suivi des lésions hépatiques malignes traitées. Cependant, l'ADC est généralement mesuré dans la lésion entière, alors que cela devrait être réalisé dans la zone la plus restreinte (ZLPR), cette dernière représentant potentiellement du résidu tumoral. Notre objectif était d'évaluer la variabilité inter/intraobservateur de l'ADC dans la tumeur entière et dans la ZLPR. Matériels et méthodes : Quarante patients traités par chimioembolisation ou radiofréquence ont été évalués. Après consensus, deux lecteurs ont indépendamment mesuré l'ADC de la lésion entière et de la ZLPR. Les mêmes mesures ont été répétées deux semaines plus tard. Le test de Spearman et la méthode de Bland-Altman ont été utilisées. Résultats : La corrélation interobservateur de l'ADC dans la lésion entière et dans la ZLPR était de 0,962 et de 0,884. La corrélation intraobservateur était de 0,992 et de 0,979, respectivement. Les limites de variabilité interobservateur (mm2/sec*10 - 3) étaient entre -0,25/+0,28 dans la lésion entière et entre -0,51/+0,46 dans la ZLPR. Les limites de variabilité intraobservateur étaient respectivement : -0,25/+0,24 et -0,43/+0,47. Conclusion : La corrélation inter/intraobservateur dans les mesures d'ADC est bonne. Toutefois, une variabilité limitée existe et doit être considérée lors de l'interprétation des valeurs d'ADC des tumeurs hépatiques.

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Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumor (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT. Methods and materials: Five patients (3W/2M, aged 56 ± 13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analyzed blindly, then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analyzed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analyzed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2 ± 7.7 g/mL to 5.9 ± 5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

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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.

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Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumour (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT Methods and Materials: Five patients (3 W/2M, aged 56±13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analysed blindly and then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analysed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analysed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2±7.7 g/mL to 5.9±5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

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Purpose: To evaluate the short- and mid-term evolutions of the apparent diffusion coefficient of lesions treated with RF, in order to determine if the ADC can be used as a marker of tumour response. Methods and Materials: Twenty patients were treated for a liver malignancy with RF and were examined on a 1.5 T/3.0 T machine with T2, gadolinium-enhanced T1 and diffusion sequences: before treatment (< 1 month), just after treatment (< 1 month) and midterm (3-6 months). The ADC was measured in the whole lesion and in the area with the most restricted diffusion (MRDA). The ROI size was also measured on the diffusion map. The Pearson/ANOVA tests were used. Results: All patients were successfully treated with complete disappearance of CE. The lesional size on T2 showed a negative evolution in time (p < 0.002). The ADC in the whole lesion showed a bell-shaped evolution (increasing just after RF, then decreasing, p = 0.02). The ROI size on the diffusion map followed a similar course (p = 0.01). For the MRDA, such evolutions were also found, but they were not significant. There was a negative correlation between CE and the ADC (p < 0.02) and between the lesional size on T2 and ADC (p = 0.03) in the whole lesion. There were also positive correlations between the ROI size and ADC (p = 0.0008) and between CE and the size on T2 (p = 0.0002). The ADC in MRDA showed some non-significant correlations with other variables. Conclusion: The lesions successfully treated with RF have a clear and predictable evolution in terms of T2 size, CE and ADC.

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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.

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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.

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Introduction: Growth is a central process in paediatrics. Weight and height evaluation are therefore routine exams for every child but in some situation, particularly inflammatory bowel disease (IBD), a wider evaluation of nutritional status needs to be performed. The assessment of body composition is essential in order to maintain acceptable growth using the following techniques: Dual-energy X-ray absorptiometry (DEXA), bio-impedance-analysis (BIA) and anthropometric measurements (skinfold thickness skin), the latter being most easily available and most cost effective. Objectives: To assess the accuracy of skinfold equations in estimating percentage body fat (%BF) in children with inflammatory bowel disease (IBD), compared with assessment of body fat dual energy X-ray absorptiometry (DEXA). Methods: Twenty-one patients (11 females, 10 males; mean age: 14.3 years, range 12 - 16 years) with IBD (Crohn's disease n = 15, ulcerative colitis n = 6)). Estimated%BF was computed using 6 established equations based on the triceps, biceps, subscapular and suprailiac skinfolds (Deurenberg, Weststrate, Slaughter, Durnin & Rahaman, Johnston, Brook) and compared to DEXA. Concordance analysis was performed using Lin's concordance correlation and the Bland-Altman limits of agreement method. Results: Durnin & Rahaman's equation shows a higher Lin's concordance coefficient with a small difference amongst raw values for skinfolds and DEXA compared to the other equations. Correlation coefficient between mean and difference is close to zero with a non-significant Bradley-Blackwood test. Conclusion: Body composition in paediatric IBD patients using the Durnin & Rahaman skinfold-equation adequately reflects values obtained by DEXA.

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Purpose: The increase of apparent diffusion coefficient (ADC) in treated hepatic malignancies compared to pre-therapeutic values has been interpreted as treatment success; however, the variability of ADC measurements remains unknown. Furthermore, ADC has been usually measured in the whole lesion, while measurements should be probably centered on the area with the most restricted diffusion (MRDA) as it represents potential tumoral residue. Our objective was to compare the inter/intraobserver variability of ADC measurements in the whole lesion and in MRDA. Material and methods: Forty patients previously treated with chemoembolization or radiofrequency were evaluated (20 on 1.5T and 20 on 3.0T). After consensual agreement on the best ADC image, two readers measured the ADC values using separate regions of interest that included the whole lesion and the whole MRDA without exceeding their borders. The same measurements were repeated two weeks later. Spearman test and the Bland-Altman method were used. Results: Interobserver correlation in ADC measurements in the whole lesion and MRDA was as follows: 0.962 and 0.884. Intraobserver correlation was, respectively, 0.992 and 0.979. Interobserver limits of variability (mm2/sec*10-3) were between -0.25/+0.28 in the whole lesion and between -0.51/+0.46 in MRDA. Intraobserver limits of variability were, respectively: -0.25/+0.24 and -0.43/+0.47. Conclusion: We observed a good inter/intraobserver correlation in ADC measurements. Nevertheless, a limited variability does exist, and it should be considered when interpreting ADC values of hepatic malignancies.