Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Quantitative integration of geophysical and hydraulic data : from the local towards the regional scale range

Des progrès significatifs ont été réalisés dans le domaine de l'intégration quantitative des données géophysique et hydrologique l'échelle locale. Cependant, l'extension à de plus grandes échelles des approches correspondantes constitue encore un défi majeur. Il est néanmoins extrêmement important de relever ce défi pour développer des modèles fiables de flux des eaux souterraines et de transport de contaminant. Pour résoudre ce problème, j'ai développé une technique d'intégration des données hydrogéophysiques basée sur une procédure bayésienne de simulation séquentielle en deux étapes. Cette procédure vise des problèmes à plus grande échelle. L'objectif est de simuler la distribution d'un paramètre hydraulique cible à partir, d'une part, de mesures d'un paramètre géophysique pertinent qui couvrent l'espace de manière exhaustive, mais avec une faible résolution (spatiale) et, d'autre part, de mesures locales de très haute résolution des mêmes paramètres géophysique et hydraulique. Pour cela, mon algorithme lie dans un premier temps les données géophysiques de faible et de haute résolution à travers une procédure de réduction déchelle. Les données géophysiques régionales réduites sont ensuite reliées au champ du paramètre hydraulique à haute résolution. J'illustre d'abord l'application de cette nouvelle approche dintégration des données à une base de données synthétiques réaliste. Celle-ci est constituée de mesures de conductivité hydraulique et électrique de haute résolution réalisées dans les mêmes forages ainsi que destimations des conductivités électriques obtenues à partir de mesures de tomographic de résistivité électrique (ERT) sur l'ensemble de l'espace. Ces dernières mesures ont une faible résolution spatiale. La viabilité globale de cette méthode est testée en effectuant les simulations de flux et de transport au travers du modèle original du champ de conductivité hydraulique ainsi que du modèle simulé. Les simulations sont alors comparées. Les résultats obtenus indiquent que la procédure dintégration des données proposée permet d'obtenir des estimations de la conductivité en adéquation avec la structure à grande échelle ainsi que des predictions fiables des caractéristiques de transports sur des distances de moyenne à grande échelle. Les résultats correspondant au scénario de terrain indiquent que l'approche d'intégration des données nouvellement mise au point est capable d'appréhender correctement les hétérogénéitées à petite échelle aussi bien que les tendances à gande échelle du champ hydraulique prévalent. Les résultats montrent également une flexibilté remarquable et une robustesse de cette nouvelle approche dintégration des données. De ce fait, elle est susceptible d'être appliquée à un large éventail de données géophysiques et hydrologiques, à toutes les gammes déchelles. Dans la deuxième partie de ma thèse, j'évalue en détail la viabilité du réechantillonnage geostatique séquentiel comme mécanisme de proposition pour les méthodes Markov Chain Monte Carlo (MCMC) appliquées à des probmes inverses géophysiques et hydrologiques de grande dimension . L'objectif est de permettre une quantification plus précise et plus réaliste des incertitudes associées aux modèles obtenus. En considérant une série dexemples de tomographic radar puits à puits, j'étudie deux classes de stratégies de rééchantillonnage spatial en considérant leur habilité à générer efficacement et précisément des réalisations de la distribution postérieure bayésienne. Les résultats obtenus montrent que, malgré sa popularité, le réechantillonnage séquentiel est plutôt inefficace à générer des échantillons postérieurs indépendants pour des études de cas synthétiques réalistes, notamment pour le cas assez communs et importants où il existe de fortes corrélations spatiales entre le modèle et les paramètres. Pour résoudre ce problème, j'ai développé un nouvelle approche de perturbation basée sur une déformation progressive. Cette approche est flexible en ce qui concerne le nombre de paramètres du modèle et lintensité de la perturbation. Par rapport au rééchantillonage séquentiel, cette nouvelle approche s'avère être très efficace pour diminuer le nombre requis d'itérations pour générer des échantillons indépendants à partir de la distribution postérieure bayésienne. - Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending corresponding approaches beyond the local scale still represents a major challenge, yet is critically important for the development of reliable groundwater flow and contaminant transport models. To address this issue, I have developed a hydrogeophysical data integration technique based on a two-step Bayesian sequential simulation procedure that is specifically targeted towards larger-scale problems. The objective is to simulate the distribution of a target hydraulic parameter based on spatially exhaustive, but poorly resolved, measurements of a pertinent geophysical parameter and locally highly resolved, but spatially sparse, measurements of the considered geophysical and hydraulic parameters. To this end, my algorithm links the low- and high-resolution geophysical data via a downscaling procedure before relating the downscaled regional-scale geophysical data to the high-resolution hydraulic parameter field. I first illustrate the application of this novel data integration approach to a realistic synthetic database consisting of collocated high-resolution borehole measurements of the hydraulic and electrical conductivities and spatially exhaustive, low-resolution electrical conductivity estimates obtained from electrical resistivity tomography (ERT). The overall viability of this method is tested and verified by performing and comparing flow and transport simulations through the original and simulated hydraulic conductivity fields. The corresponding results indicate that the proposed data integration procedure does indeed allow for obtaining faithful estimates of the larger-scale hydraulic conductivity structure and reliable predictions of the transport characteristics over medium- to regional-scale distances. The approach is then applied to a corresponding field scenario consisting of collocated high- resolution measurements of the electrical conductivity, as measured using a cone penetrometer testing (CPT) system, and the hydraulic conductivity, as estimated from electromagnetic flowmeter and slug test measurements, in combination with spatially exhaustive low-resolution electrical conductivity estimates obtained from surface-based electrical resistivity tomography (ERT). The corresponding results indicate that the newly developed data integration approach is indeed capable of adequately capturing both the small-scale heterogeneity as well as the larger-scale trend of the prevailing hydraulic conductivity field. The results also indicate that this novel data integration approach is remarkably flexible and robust and hence can be expected to be applicable to a wide range of geophysical and hydrological data at all scale ranges. In the second part of my thesis, I evaluate in detail the viability of sequential geostatistical resampling as a proposal mechanism for Markov Chain Monte Carlo (MCMC) methods applied to high-dimensional geophysical and hydrological inverse problems in order to allow for a more accurate and realistic quantification of the uncertainty associated with the thus inferred models. Focusing on a series of pertinent crosshole georadar tomographic examples, I investigated two classes of geostatistical resampling strategies with regard to their ability to efficiently and accurately generate independent realizations from the Bayesian posterior distribution. The corresponding results indicate that, despite its popularity, sequential resampling is rather inefficient at drawing independent posterior samples for realistic synthetic case studies, notably for the practically common and important scenario of pronounced spatial correlation between model parameters. To address this issue, I have developed a new gradual-deformation-based perturbation approach, which is flexible with regard to the number of model parameters as well as the perturbation strength. Compared to sequential resampling, this newly proposed approach was proven to be highly effective in decreasing the number of iterations required for drawing independent samples from the Bayesian posterior distribution.

A gamma camera count rate saturation correction method for whole-body planar imaging.

Whole-body (WB) planar imaging has long been one of the staple methods of dosimetry, and its quantification has been formalized by the MIRD Committee in pamphlet no 16. One of the issues not specifically addressed in the formalism occurs when the count rates reaching the detector are sufficiently high to result in camera count saturation. Camera dead-time effects have been extensively studied, but all of the developed correction methods assume static acquisitions. However, during WB planar (sweep) imaging, a variable amount of imaged activity exists in the detector's field of view as a function of time and therefore the camera saturation is time dependent. A new time-dependent algorithm was developed to correct for dead-time effects during WB planar acquisitions that accounts for relative motion between detector heads and imaged object. Static camera dead-time parameters were acquired by imaging decaying activity in a phantom and obtaining a saturation curve. Using these parameters, an iterative algorithm akin to Newton's method was developed, which takes into account the variable count rate seen by the detector as a function of time. The algorithm was tested on simulated data as well as on a whole-body scan of high activity Samarium-153 in an ellipsoid phantom. A complete set of parameters from unsaturated phantom data necessary for count rate to activity conversion was also obtained, including build-up and attenuation coefficients, in order to convert corrected count rate values to activity. The algorithm proved successful in accounting for motion- and time-dependent saturation effects in both the simulated and measured data and converged to any desired degree of precision. The clearance half-life calculated from the ellipsoid phantom data was calculated to be 45.1 h after dead-time correction and 51.4 h with no correction; the physical decay half-life of Samarium-153 is 46.3 h. Accurate WB planar dosimetry of high activities relies on successfully compensating for camera saturation which takes into account the variable activity in the field of view, i.e. time-dependent dead-time effects. The algorithm presented here accomplishes this task.

Error estimate and control in the MSFV method for multiphase flow in porous media

n this paper the iterative MSFV method is extended to include the sequential implicit simulation of time dependent problems involving the solution of a system of pressure-saturation equations. To control numerical errors in simulation results, an error estimate, based on the residual of the MSFV approximate pressure field, is introduced. In the initial time steps in simulation iterations are employed until a specified accuracy in pressure is achieved. This initial solution is then used to improve the localization assumption at later time steps. Additional iterations in pressure solution are employed only when the pressure residual becomes larger than a specified threshold value. Efficiency of the strategy and the error control criteria are numerically investigated. This paper also shows that it is possible to derive an a-priori estimate and control based on the allowed pressure-equation residual to guarantee the desired accuracy in saturation calculation.

A study of the cambial zone and conductive phloem of common beech (Fagus sylvatica L.) using an image analysis method. I. Influence of tree age on the structure

Quantification is a major problem when using histology to study the influence of ecological factors on tree structure. This paper presents a method to prepare and to analyse transverse sections of cambial zone and of conductive phloem in bark samples. The following paper (II) presents the automated measurement procedure. Part I here describes and discusses the preparation method, and the influence of tree age on the observed structure. Highly contrasted images of samples extracted at breast height during dormancy were analysed with an automatic image analyser. Between three young (38 years) and three old (147 years) trees, age-related differences were identified by size and shape parameters, at both cell and tissue levels. In the cambial zone, older trees had larger and more rectangular fusiform initials. In the phloem, sieve tubes were also larger, but their shape did not change and the area for sap conduction was similar in both categories. Nevertheless, alterations were limited, and demanded statistical analysis to be identified and ascertained. The physiological implications of the structural changes are discussed.

Trabecular Bone Score: A Noninvasive Analytical Method Based Upon the DXA Image.

The trabecular bone score (TBS) is a gray-level textural metric that can be extracted from the two-dimensional lumbar spine dual-energy X-ray absorptiometry (DXA) image. TBS is related to bone microarchitecture and provides skeletal information that is not captured from the standard bone mineral density (BMD) measurement. Based on experimental variograms of the projected DXA image, TBS has the potential to discern differences between DXA scans that show similar BMD measurements. An elevated TBS value correlates with better skeletal microstructure; a low TBS value correlates with weaker skeletal microstructure. Lumbar spine TBS has been evaluated in cross-sectional and longitudinal studies. The following conclusions are based upon publications reviewed in this article: 1) TBS gives lower values in postmenopausal women and in men with previous fragility fractures than their nonfractured counterparts; 2) TBS is complementary to data available by lumbar spine DXA measurements; 3) TBS results are lower in women who have sustained a fragility fracture but in whom DXA does not indicate osteoporosis or even osteopenia; 4) TBS predicts fracture risk as well as lumbar spine BMD measurements in postmenopausal women; 5) efficacious therapies for osteoporosis differ in the extent to which they influence the TBS; 6) TBS is associated with fracture risk in individuals with conditions related to reduced bone mass or bone quality. Based on these data, lumbar spine TBS holds promise as an emerging technology that could well become a valuable clinical tool in the diagnosis of osteoporosis and in fracture risk assessment. © 2014 American Society for Bone and Mineral Research.

Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method.

We present a method for segmenting white matter tracts from high angular resolution diffusion MR. images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.

Standardisation of 18F by a coincidence method using full solid angle detectors.

A solution of (18)F was standardised with a 4pibeta-4pigamma coincidence counting system in which the beta detector is a one-inch diameter cylindrical UPS89 plastic scintillator, positioned at the bottom of a well-type 5''x5'' NaI(Tl) gamma-ray detector. Almost full detection efficiency-which was varied downwards electronically-was achieved in the beta-channel. Aliquots of this (18)F solution were also measured using 4pigamma NaI(Tl) integral counting and Monte Carlo calculated efficiencies as well as the CIEMAT-NIST method. Secondary measurements of the same solution were also performed with an IG11 ionisation chamber whose equivalent activity is traceable to the Système International de Référence through the contribution IRA-METAS made to it in 2001; IRA's degree of equivalence was found to be close to the key comparison reference value (KCRV). The (18)F activity predicted by this coincidence system agrees closely with the ionisation chamber measurement and is compatible within one standard deviation of the other primary measurements. This work demonstrates that our new coincidence system can standardise short-lived radionuclides used in nuclear medicine.

F+0 renography in neonates and infants younger than 6 months: an accurate method to diagnose severe obstructive uropathy.

We studied the response to F+0 renography and the relative and absolute individual kidney function in neonates and < 6-mo-old infants before and after surgery for unilateral ureteropelvic junction obstruction (UJO). METHODS: The results obtained at diagnosis and after pyeloplasty for 9 children (8 boys, 1 girl; age range, 0.8-5.9 mo; mean age +/- SD, 2.4 +/- 1.5 mo) with proven unilateral UJO (i.e., affected kidney [AK]) and an unremarkable contralateral kidney (i.e., normal kidney [NK]) were evaluated and compared with a control group of 10 children (6 boys, 4 girls; age range, 0.8-2.8 mo; mean age, 1.5 +/- 0.7 mo) selected because of symmetric renal function, absence of vesicoureteral reflux or infection, and an initially dilated but not obstructed renal pelvis as proven by follow-up. Renography was performed for 20 min after injection of (123)I-hippuran (OIH) (0.5-1.0 MBq/kg) immediately followed by furosemide (1 mg/kg). The relative and absolute renal functions and the response to furosemide were measured on background-subtracted and depth-corrected renograms. The response to furosemide was quantified by an elimination index (EI), defined as the ratio of the 3- to 20-min activities: An EI > or = 3 was considered definitively normal and an EI < or = 1 definitively abnormal. If EI was equivocal (1 < EI < 3), the response to gravity-assisted drainage was used to differentiate AKs from NKs. Absolute separate renal function was measured by an accumulation index (AI), defined as the percentage of (123)I-OIH (%ID) extracted by the kidney 30-90 s after maximal cardiac activity. RESULTS: All AKs had definitively abnormal EIs at diagnosis (mean, 0.56 +/- 0.12) and were significantly lower than the EIs of the NKs (mean, 3.24 +/- 1.88) and of the 20 control kidneys (mean, 3.81 +/- 1.97; P < 0.001). The EIs of the AKs significantly improved (mean, 2.81 +/- 0.64; P < 0.05) after pyeloplasty. At diagnosis, the AIs of the AKs were significantly lower (mean, 6.31 +/- 2.33 %ID) than the AIs of the NKs (mean, 9.43 +/- 1.12 %ID) and of the control kidneys (mean, 9.05 +/- 1.17 %ID; P < 0.05). The AIs of the AKs increased at follow-up (mean, 7.81 +/- 2.23 %ID) but remained lower than those of the NKs (mean, 10.75 +/- 1.35 %ID; P < 0.05). CONCLUSION: In neonates and infants younger than 6 mo, (123)I-OIH renography with early furosemide injection (F+0) allowed us to reliably diagnose AKs and to determine if parenchymal function was normal or impaired and if it improved after surgery.

Accuracy profile validation of a new method for carbon monoxide measurement in the human blood using headspace-gas chromatography-mass spectrometry (HS-GC-MS).

The aim of our study was to provide an innovative headspace-gas chromatography-mass spectrometry (HS-GC-MS) method applicable for the routine determination of blood CO concentration in forensic toxicology laboratories. The main drawback of the GC/MS methods discussed in literature for CO measurement is the absence of a specific CO internal standard necessary for performing quantification. Even if stable isotope of CO is commercially available in the gaseous state, it is essential to develop a safer method to limit the manipulation of gaseous CO and to precisely control the injected amount of CO for spiking and calibration. To avoid the manipulation of a stable isotope-labeled gas, we have chosen to generate in a vial in situ, an internal labeled standard gas ((13)CO) formed by the reaction of labeled formic acid formic acid (H(13)COOH) with sulfuric acid. As sulfuric acid can also be employed to liberate the CO reagent from whole blood, the procedure allows for the liberation of CO simultaneously with the generation of (13)CO. This method allows for precise measurement of blood CO concentrations from a small amount of blood (10 μL). Finally, this method was applied to measure the CO concentration of intoxicated human blood samples from autopsies.

A New Method for ECG Tracking of Persistent Atrial Fibrillation Termination during Stepwise Ablation

Stepwise radiofrequency catheter ablation (step-CA) has become the treatment of choice for the restoration of sinus rhythm (SR) in patients with long-standing persistent atrial fibrillation (pers-AF). Its success rate appears limited as the amount of ablation to achieve long term SR is unknown. Multiple organization indexes (OIs) have been previously developed to track the organization of AF during step-CA, however, with limited success. We report an adaptive method for tracking AF termination (AF-term) based on OIs characterizing the relationship between harmonic components of atrial activity from the surface ECG of AF activity. By computing their relative evolution during the last two steps preceding AF-term, we found that the performance of our OIs was superior to classical indices to track the efficiency of step-CA "en route" to AF-term. Our preliminary results suggest that the gradual synchronization between the fundamental and its first harmonic of AF activity appears as a promising parameter for predicting AF-term during step-CA.