Error models in hydrogeology applications

Notre consommation en eau souterraine, en particulier comme eau potable ou pour l'irrigation, a considérablement augmenté au cours des années. De nombreux problèmes font alors leur apparition, allant de la prospection de nouvelles ressources à la remédiation des aquifères pollués. Indépendamment du problème hydrogéologique considéré, le principal défi reste la caractérisation des propriétés du sous-sol. Une approche stochastique est alors nécessaire afin de représenter cette incertitude en considérant de multiples scénarios géologiques et en générant un grand nombre de réalisations géostatistiques. Nous rencontrons alors la principale limitation de ces approches qui est le coût de calcul dû à la simulation des processus d'écoulements complexes pour chacune de ces réalisations. Dans la première partie de la thèse, ce problème est investigué dans le contexte de propagation de l'incertitude, oú un ensemble de réalisations est identifié comme représentant les propriétés du sous-sol. Afin de propager cette incertitude à la quantité d'intérêt tout en limitant le coût de calcul, les méthodes actuelles font appel à des modèles d'écoulement approximés. Cela permet l'identification d'un sous-ensemble de réalisations représentant la variabilité de l'ensemble initial. Le modèle complexe d'écoulement est alors évalué uniquement pour ce sousensemble, et, sur la base de ces réponses complexes, l'inférence est faite. Notre objectif est d'améliorer la performance de cette approche en utilisant toute l'information à disposition. Pour cela, le sous-ensemble de réponses approximées et exactes est utilisé afin de construire un modèle d'erreur, qui sert ensuite à corriger le reste des réponses approximées et prédire la réponse du modèle complexe. Cette méthode permet de maximiser l'utilisation de l'information à disposition sans augmentation perceptible du temps de calcul. La propagation de l'incertitude est alors plus précise et plus robuste. La stratégie explorée dans le premier chapitre consiste à apprendre d'un sous-ensemble de réalisations la relation entre les modèles d'écoulement approximé et complexe. Dans la seconde partie de la thèse, cette méthodologie est formalisée mathématiquement en introduisant un modèle de régression entre les réponses fonctionnelles. Comme ce problème est mal posé, il est nécessaire d'en réduire la dimensionnalité. Dans cette optique, l'innovation du travail présenté provient de l'utilisation de l'analyse en composantes principales fonctionnelles (ACPF), qui non seulement effectue la réduction de dimensionnalités tout en maximisant l'information retenue, mais permet aussi de diagnostiquer la qualité du modèle d'erreur dans cet espace fonctionnel. La méthodologie proposée est appliquée à un problème de pollution par une phase liquide nonaqueuse et les résultats obtenus montrent que le modèle d'erreur permet une forte réduction du temps de calcul tout en estimant correctement l'incertitude. De plus, pour chaque réponse approximée, une prédiction de la réponse complexe est fournie par le modèle d'erreur. Le concept de modèle d'erreur fonctionnel est donc pertinent pour la propagation de l'incertitude, mais aussi pour les problèmes d'inférence bayésienne. Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont les algorithmes les plus communément utilisés afin de générer des réalisations géostatistiques en accord avec les observations. Cependant, ces méthodes souffrent d'un taux d'acceptation très bas pour les problèmes de grande dimensionnalité, résultant en un grand nombre de simulations d'écoulement gaspillées. Une approche en deux temps, le "MCMC en deux étapes", a été introduite afin d'éviter les simulations du modèle complexe inutiles par une évaluation préliminaire de la réalisation. Dans la troisième partie de la thèse, le modèle d'écoulement approximé couplé à un modèle d'erreur sert d'évaluation préliminaire pour le "MCMC en deux étapes". Nous démontrons une augmentation du taux d'acceptation par un facteur de 1.5 à 3 en comparaison avec une implémentation classique de MCMC. Une question reste sans réponse : comment choisir la taille de l'ensemble d'entrainement et comment identifier les réalisations permettant d'optimiser la construction du modèle d'erreur. Cela requiert une stratégie itérative afin que, à chaque nouvelle simulation d'écoulement, le modèle d'erreur soit amélioré en incorporant les nouvelles informations. Ceci est développé dans la quatrième partie de la thèse, oú cette méthodologie est appliquée à un problème d'intrusion saline dans un aquifère côtier. -- Our consumption of groundwater, in particular as drinking water and for irrigation, has considerably increased over the years and groundwater is becoming an increasingly scarce and endangered resource. Nofadays, we are facing many problems ranging from water prospection to sustainable management and remediation of polluted aquifers. Independently of the hydrogeological problem, the main challenge remains dealing with the incomplete knofledge of the underground properties. Stochastic approaches have been developed to represent this uncertainty by considering multiple geological scenarios and generating a large number of realizations. The main limitation of this approach is the computational cost associated with performing complex of simulations in each realization. In the first part of the thesis, we explore this issue in the context of uncertainty propagation, where an ensemble of geostatistical realizations is identified as representative of the subsurface uncertainty. To propagate this lack of knofledge to the quantity of interest (e.g., the concentration of pollutant in extracted water), it is necessary to evaluate the of response of each realization. Due to computational constraints, state-of-the-art methods make use of approximate of simulation, to identify a subset of realizations that represents the variability of the ensemble. The complex and computationally heavy of model is then run for this subset based on which inference is made. Our objective is to increase the performance of this approach by using all of the available information and not solely the subset of exact responses. Two error models are proposed to correct the approximate responses follofing a machine learning approach. For the subset identified by a classical approach (here the distance kernel method) both the approximate and the exact responses are knofn. This information is used to construct an error model and correct the ensemble of approximate responses to predict the "expected" responses of the exact model. The proposed methodology makes use of all the available information without perceptible additional computational costs and leads to an increase in accuracy and robustness of the uncertainty propagation. The strategy explored in the first chapter consists in learning from a subset of realizations the relationship between proxy and exact curves. In the second part of this thesis, the strategy is formalized in a rigorous mathematical framework by defining a regression model between functions. As this problem is ill-posed, it is necessary to reduce its dimensionality. The novelty of the work comes from the use of functional principal component analysis (FPCA), which not only performs the dimensionality reduction while maximizing the retained information, but also allofs a diagnostic of the quality of the error model in the functional space. The proposed methodology is applied to a pollution problem by a non-aqueous phase-liquid. The error model allofs a strong reduction of the computational cost while providing a good estimate of the uncertainty. The individual correction of the proxy response by the error model leads to an excellent prediction of the exact response, opening the door to many applications. The concept of functional error model is useful not only in the context of uncertainty propagation, but also, and maybe even more so, to perform Bayesian inference. Monte Carlo Markov Chain (MCMC) algorithms are the most common choice to ensure that the generated realizations are sampled in accordance with the observations. Hofever, this approach suffers from lof acceptance rate in high dimensional problems, resulting in a large number of wasted of simulations. This led to the introduction of two-stage MCMC, where the computational cost is decreased by avoiding unnecessary simulation of the exact of thanks to a preliminary evaluation of the proposal. In the third part of the thesis, a proxy is coupled to an error model to provide an approximate response for the two-stage MCMC set-up. We demonstrate an increase in acceptance rate by a factor three with respect to one-stage MCMC results. An open question remains: hof do we choose the size of the learning set and identify the realizations to optimize the construction of the error model. This requires devising an iterative strategy to construct the error model, such that, as new of simulations are performed, the error model is iteratively improved by incorporating the new information. This is discussed in the fourth part of the thesis, in which we apply this methodology to a problem of saline intrusion in a coastal aquifer.

Percutaneous drainage versus emergency cholecystectomy for the treatment of acute cholecystitis in critically ill patients : does it matter ?

RESUME DE THESEContexte de l'étudeLe but de cette étude est de comparer le drainage percutané (DP) et la chirurgie d'urgence (CU) de la vésicule biliaire (VB) pour le traitement de la cholécystite aiguë lithiasique/alithiasique dans un groupe homogène de patients gravement malades et hospitalisés aux soins intensifs (SI).Patients et méthodeEntre les années 2001 et 2007, tous les patients successivement traités par DP ou CU pour cholécystite aiguë aux SI ont été rétrospectivement analysés. Les cas ont été collectés à partir d'une base de données prospective. Le DP était effectué par voie trans-hépatique et la chirurgie par voie ouverte ou laparoscopique. L'état général des patients et la dysfonction des organes étaient évalués par deux scores validés (SAPS Π et SOFA, respectivement). L'analyse des données s'est portée sur les complications à court terme (morbidité, mortalité hospitalière) et à long terme (récurrence des symptômes) après drainage ou chirurgie en urgence.RésultatsQuarante-deux patients (âge médian 65 ans, 32-94 ans) ont été inclus dans l'étude ; 45% ont eu une CU (10 laparoscopics, 9 voies ouvertes) et 55% un DP (n=23) de la vésicule biliaire. Le DP et la CU ont eu des taux de succès respectifs de 91 et 100% pour la résolution du sepsis lié à la cholécystite aigiie. Après drainage et chirurgie de la VB, la dysfonction des organes secondaire au sepsis s'est résolue dans les 3 jours. Malgré le drainage, deux patients ont nécessité une cholécystectomie en urgence pour cholécystite gangréneuse. Le taux de conversion de la laparoscopic à la voie ouverte était de 20%. La morbidité majeure était de 0% après drainage et 21% après chirurgie en urgence (p=0.034). Finalement, la mortalité hospitalière était similaire (13% après DP vs. 16% après CU, p=1.0) et uniquement liée aux co-morbidités des patients. La récurrence des symptômes liés à la VB n'est apparue que chez des patients initialement drainés pour cholécystite lithiasique.ConclusionsChez les patients gravement malades des soins intensifs, le drainage percutané et la chirurgie en urgence de la VB sont tous deux efficaces pour la résolution d'un sepsis lié à une cholécystite aigiie. Cependant, la chirurgie d'urgence est associée à une morbidité majeure accrue et l'approche par laparoscopic n'est pas toujours réalisable. Le drainage percutané de la VB est donc une modalité de traitement valable, mais nécessite à distance de l'épisode aigu une cholécystectomie par laparoscopic, surtout après une cholécystite lithiasique.

Accuracy of a new transmittance-reflectance pulse oximetry sensor in critically ill neonates.

OBJECTIVE: To test the accuracy of a new pulse oximeter sensor based on transmittance and reflectance. This sensor makes transillumination of tissue unnecessary and allows measurements on the hand, forearm, foot, and lower limb. DESIGN: Prospective, open, nonrandomized criterion standard study. SETTING: Neonatal intensive care unit, tertiary care center. PATIENTS: Sequential sample of 54 critically ill neonates (gestational age 27 to 42 wks; postnatal age 1 to 28 days) with arterial catheters in place. MEASUREMENTS AND MAIN RESULTS: A total of 99 comparisons between pulse oximetry and arterial saturation were obtained. Comparison of femoral or umbilical arterial blood with transcutaneous measurements on the lower limb (n = 66) demonstrated an excellent correlation (r2 = .96). The mean difference was +1.44% +/- 3.51 (SD) % (range -11% to +8%). Comparison of the transcutaneous values with the radial artery saturation from the corresponding upper limb (n = 33) revealed a correlation coefficient of 0.94 with a mean error of +0.66% +/- 3.34% (range -6% to +7%). The mean difference between noninvasive and invasive measurements was least with the test sensor on the hand, intermediate on the calf and arm, and greatest on the foot. The mean error and its standard deviation were slightly larger for arterial saturation values < 90% than for values > or = 90%. CONCLUSION: Accurate pulse oximetry saturation can be acquired from the hand, forearm, foot, and calf of critically ill newborns using this new sensor.

Fractional hepatic de novo lipogenesis in healthy subjects during near-continuous oral nutrition and bed rest: a comparison with published data in artificially fed, critically ill patients.

BACKGROUND AND AIMS: In critically ill patients, fractional hepatic de novo lipogenesis increases in proportion to carbohydrate administration during isoenergetic nutrition. In this study, we sought to determine whether this increase may be the consequence of continuous enteral nutrition and bed rest. We, therefore, measured fractional hepatic de novo lipogenesis in a group of 12 healthy subjects during near-continuous oral feeding (hourly isoenergetic meals with a liquid formula containing 55% carbohydrate). In eight subjects, near-continuous enteral nutrition and bed rest were applied over a 10 h period. In the other four subjects, it was extended to 34 h. Fractional hepatic de novo lipogenesis was measured by infusing(13) C-labeled acetate and monitoring VLDL-(13)C palmitate enrichment with mass isotopomer distribution analysis. Fractional hepatic de novo lipogenesis was 3.2% (range 1.5-7.5%) in the eight subjects after 10 h of near continuous nutrition and 1.6% (range 1.3-2.0%) in the four subjects after 34 h of near-continuous nutrition and bed rest. This indicates that continuous nutrition and physical inactivity do not increase hepatic de novo lipogenesis. Fractional hepatic de novo lipogenesis previously reported in critically ill patients under similar nutritional conditions (9.3%) (range 5.3-15.8%) was markedly higher than in healthy subjects (P&lt;0.001). These data from healthy subjects indicate that fractional hepatic de novo lipogenesis is increased in critically ill patients.

Diagnostic accuracy of G-CSF, IL-8, and IL-1ra in critically ill children with suspected infection.

OBJECTIVE: To elucidate the diagnostic accuracy of granulocyte colony-stimulating factor (G-CSF), interleukin-8 (IL-8), and interleukin-1 receptor antagonist (IL-1ra) in identifying patients with sepsis among critically ill pediatric patients with suspected infection. DESIGN AND SETTING: Nested case-control study in a multidisciplinary neonatal and pediatric intensive care unit (PICU) PATIENTS: PICU patients during a 12-month period with suspected infection, and plasma available from the time of clinical suspicion (254 episodes, 190 patients). MEASUREMENTS AND RESULTS: Plasma levels of G-CSF, IL-8, and IL-1ra. Episodes classified on the basis of clinical and bacteriological findings into: culture-confirmed sepsis, probable sepsis, localized infection, viral infection, and no infection. Plasma levels were significantly higher in episodes of culture-confirmed sepsis than in episodes with ruled-out infection. The area under the receiver operating characteristic curve was higher for IL-8 and G-CSF than for IL-1ra. Combining IL-8 and G-CSF improved the diagnostic performance, particularly as to the detection of Gram-negative sepsis. Sensitivity was low (<50%) in detecting Staphylococcus epidermidis bacteremia or localized infections. CONCLUSIONS: In this heterogeneous population of critically ill children with suspected infection, a model combining plasma levels of IL-8 and G-CSF identified patients with sepsis. Negative results do not rule out S. epidermidis bacteremia or locally confined infectious processes. The model requires validation in an independent data-set.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Quantifying uncertainty: physicians' estimates of infection in critically ill neonates and children.

To determine the diagnostic accuracy of physicians' prior probability estimates of serious infection in critically ill neonates and children, we conducted a prospective cohort study in 2 intensive care units. Using available clinical, laboratory, and radiographic information, 27 physicians provided 2567 probability estimates for 347 patients (follow-up rate, 92%). The median probability estimate of infection increased from 0% (i.e., no antibiotic treatment or diagnostic work-up for sepsis), to 2% on the day preceding initiation of antibiotic therapy, to 20% at initiation of antibiotic treatment (P&lt;.001). At initiation of treatment, predictions discriminated well between episodes subsequently classified as proven infection and episodes ultimately judged unlikely to be infection (area under the curve, 0.88). Physicians also showed a good ability to predict blood culture-positive sepsis (area under the curve, 0.77). Treatment and testing thresholds were derived from the provided predictions and treatment rates. Physicians' prognoses regarding the presence of serious infection were remarkably precise. Studies investigating the value of new tests for diagnosis of sepsis should establish that they add incremental value to physicians' judgment.

Enteral nutrition in critically ill patients with severe hemodynamic failure after cardiopulmonary bypass.

BACKGROUND & AIMS: The study was designed to investigate and quantify nutritional support, and particularly enteral nutrition (EN), in critically ill patients with severe hemodynamic failure. METHODS: Prospective, descriptive study in a surgical intensive care unit (ICU) in a university teaching hospital: patients aged 67+/-13 yrs (mean+/-SD) admitted after cardiac surgery with extracorporeal circulation, staying 5 days in the ICU with acute cardiovascular failure. Severity of disease was assessed with SAPS II, and SOFA scores. Variables were energy delivery and balance, nutrition route, vasopressor doses, and infectious complications. Artificial feeding delivered according to ICU protocol. EN was considered from day 2-3. Energy target was set 25 kcal/kg/day to be reached stepwise over 5 days. RESULTS: Seventy out of 1114 consecutive patients were studied, aged 67+/-17 years, and staying 10+/-7 days in the ICU. Median SAPS II was 43. Nine patients died (13%). All patients had circulatory failure: 18 patients required intra-aortic balloon-pump support (IABP). Norepinephrine was required in 58 patients (83%). Forty patients required artificial nutrition. Energy delivery was very variable. There was no abdominal complication related to EN. As a mean, 1360+/-620 kcal/kg/day could be delivered enterally during the first 2 weeks, corresponding to 70+/-35% of energy target. Enteral nutrient delivery was negatively influenced by increasing dopamine and norepinephrine doses, but not by the use of IABP. CONCLUSION: EN is possible in the majority of patients with severe hemodynamic failure, but usually results in hypocaloric feeding. EN should be considered in patients with careful abdominal and energy monitoring.

Copper, selenium, zinc, and thiamine balances during continuous venovenous hemodiafiltration in critically ill patients.

BACKGROUND: Acute renal failure is a serious complication in critically ill patients and frequently requires renal replacement therapy, which alters trace element and vitamin metabolism. OBJECTIVE: The objective was to study trace element balances during continuous renal replacement therapy (CRRT) in intensive care patients. DESIGN: In a prospective randomized crossover trial, patients with acute renal failure received CRRT with either sodium bicarbonate (Bic) or sodium lactate (Lac) as a buffering agent over 2 consecutive 24-h periods. Copper, selenium, zinc, and thiamine were measured with highly sensitive analytic methods in plasma, replacement solutions, and effluent during 8-h periods. Balances were calculated as the difference between fluids administered and effluent losses and were compared with the recommended intakes (RI) from parenteral nutrition. RESULTS: Nineteen sessions were conducted in 11 patients aged 65 +/- 10 y. Baseline plasma concentrations of copper were normal, whereas those of selenium and zinc were below reference ranges; glutathione peroxidase was in the lower range of normal. The replacement solutions contained no detectable copper, 0.01 micromol Se/L (Bic and Lac), and 1.42 (Bic) and 0.85 (Lac) micromol Zn/L. Micronutrients were detectable in all effluents, and losses were stable in each patient; no significant differences were found between the Bic and Lac groups. The 24-h balances were negative for selenium (-0.97 micromol, or 2 times the daily RI), copper (-6.54 micromol, or 0.3 times the daily RI), and thiamine (-4.12 mg, or 1.5 times the RI) and modestly positive for zinc (20.7 micromol, or 0.2 times the RI). CONCLUSIONS: CRRT results in significant losses and negative balances of selenium, copper, and thiamine, which contribute to low plasma concentrations. Prolonged CRRT is likely to result in selenium and thiamine depletion despite supplementation at recommended amounts.

Metabolic effects of parenteral nutrition enriched with n-3 polyunsaturated fatty acids in critically ill patients

BACKGROUND & AIMS: n-3 fatty acids are expected to downregulate the inflammatory responses, and hence may decrease insulin resistance. On the other hand, n-3 fatty acid supplementation has been reported to increase glycemia in type 2 diabetes. We therefore assessed the effect of n-3 fatty acids delivered with parenteral nutrition on glucose metabolism in surgical intensive care patients. METHODS: Twenty-four surgical intensive care patients were randomized to receive parenteral nutrition providing 1.25 times their fasting energy expenditure, with 0.25 g of either an n-3 fatty acid enriched-or a soy bean-lipid emulsion. Energy metabolism, glucose production, gluconeogenesis and hepatic de novo lipogenesis were evaluated after 4 days. RESULTS: Total energy expenditure was significantly lower in patients receiving n-3 fatty acids (0.015+/-0.001 vs. 0.019+/-0.001 kcal/kg/min with soy bean lipids (P<0.05)). Glucose oxidation, lipid oxidation, glucose production, gluconeogenesis, hepatic de novo lipogenesis, plasma glucose, insulin and glucagon concentrations did not differ (all P>0.05) in the 2 groups. CONCLUSIONS: n-3 fatty acids were well tolerated in this group of severely ill patients. They decreased total energy expenditure without adverse metabolic effects.