The impact of spatial resolution and respiratory motion on MR imaging of atherosclerotic plaque.

PURPOSE: To examine the impact of spatial resolution and respiratory motion on the ability to accurately measure atherosclerotic plaque burden and to visually identify atherosclerotic plaque composition. MATERIALS AND METHODS: Numerical simulations of the Bloch equations and vessel wall phantom studies were performed for different spatial resolutions by incrementally increasing the field of view. In addition, respiratory motion was simulated based on a measured physiologic breathing pattern. RESULTS: While a spatial resolution of > or = 6 pixels across the wall does not result in significant errors, a resolution of < or = 4 pixels across the wall leads to an overestimation of > 20%. Using a double-inversion T2-weighted turbo spin echo sequence, a resolution of 1 pixel across equally thick tissue layers (fibrous cap, lipid, smooth muscle) and a respiratory motion correction precision (gating window) of three times the thickness of the tissue layer allow for characterization of the different coronary wall components. CONCLUSIONS: We found that measurements in low-resolution black blood images tend to overestimate vessel wall area and underestimate lumen area.

Multi-slice three-dimensional myocardial strain tensor quantification using zHARP.

In this article we propose a novel method for calculating cardiac 3-D strain. The method requires the acquisition of myocardial short-axis (SA) slices only and produces the 3-D strain tensor at every point within every pair of slices. Three-dimensional displacement is calculated from SA slices using zHARP which is then used for calculating the local displacement gradient and thus the local strain tensor. There are three main advantages of this method. First, the 3-D strain tensor is calculated for every pixel without interpolation; this is unprecedented in cardiac MR imaging. Second, this method is fast, in part because there is no need to acquire long-axis (LA) slices. Third, the method is accurate because the 3-D displacement components are acquired simultaneously and therefore reduces motion artifacts without the need for registration. This article presents the theory of computing 3-D strain from two slices using zHARP, the imaging protocol, and both phantom and in-vivo validation.

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge.

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l2, l1TV norm of the prior knowledge of the edges of the object, one over-determined multiple orientation method (COSMOS) and anewly proposed modulated closed-form solution (MCF). The performance of these methods was compared using a numerical phantom and in-vivo high resolution (0.65mm isotropic) brain data acquired at 7T using a new coil combination method. For all QSM methods, the relevant regularization and prior-knowledge parameters were systematically changed in order to evaluate the optimal reconstruction in the presence and absence of a ground truth. Additionally, the QSM contrast was compared to conventional gradient recalled echo (GRE) magnitude and R2* maps obtained from the same dataset. The QSM reconstruction results of the single orientation methods show comparable performance. The MCF method has the highest correlation (corrMCF=0.95, r(2)MCF =0.97) with the state of the art method (COSMOS) with additional advantage of extreme fast computation time. The l-curve method gave the visually most satisfactory balance between reduction of streaking artifacts and over-regularization with the latter being overemphasized when the using the COSMOS susceptibility maps as ground-truth. R2* and susceptibility maps, when calculated from the same datasets, although based on distinct features of the data, have a comparable ability to distinguish deep gray matter structures.

Fourth order pseudo maximum likelihood methods

We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux et al. (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods [Authors]

Imputation in data fusion of heterogeneous data sets a model-based numerical experiment

Given the very large amount of data obtained everyday through population surveys, much of the new research again could use this information instead of collecting new samples. Unfortunately, relevant data are often disseminated into different files obtained through different sampling designs. Data fusion is a set of methods used to combine information from different sources into a single dataset. In this article, we are interested in a specific problem: the fusion of two data files, one of which being quite small. We propose a model-based procedure combining a logistic regression with an Expectation-Maximization algorithm. Results show that despite the lack of data, this procedure can perform better than standard matching procedures.

Segmentation and grid generation for numerical simulations of vad connections with patient-specific data

Objectives: We are interested in the numerical simulation of the anastomotic region comprised between outflow canula of LVAD and the aorta. Segmenta¬tion, geometry reconstruction and grid generation from patient-specific data remain an issue because of the variable quality of DICOM images, in particular CT-scan (e.g. metallic noise of the device, non-aortic contrast phase). We pro¬pose a general framework to overcome this problem and create suitable grids for numerical simulations.Methods: Preliminary treatment of images is performed by reducing the level window and enhancing the contrast of the greyscale image using contrast-limited adaptive histogram equalization. A gradient anisotropic diffusion filter is applied to reduce the noise. Then, watershed segmentation algorithms and mathematical morphology filters allow reconstructing the patient geometry. This is done using the InsightToolKit library (www.itk.org). Finally the Vascular Model¬ing ToolKit (www.vmtk.org) and gmsh (www.geuz.org/gmsh) are used to create the meshes for the fluid (blood) and structure (arterial wall, outflow canula) and to a priori identify the boundary layers. The method is tested on five different patients with left ventricular assistance and who underwent a CT-scan exam.Results: This method produced good results in four patients. The anastomosis area is recovered and the generated grids are suitable for numerical simulations. In one patient the method failed to produce a good segmentation because of the small dimension of the aortic arch with respect to the image resolution.Conclusions: The described framework allows the use of data that could not be otherwise segmented by standard automatic segmentation tools. In particular the computational grids that have been generated are suitable for simulations that take into account fluid-structure interactions. Finally the presented method features a good reproducibility and fast application.

Orthotropic active strain models for the numerical simulation of cardiac biomechanics

An active strain formulation for orthotropic constitutive laws arising in cardiac mechanics modeling is introduced and studied. The passive mechanical properties of the tissue are described by the Holzapfel-Ogden relation. In the active strain formulation, the Euler-Lagrange equations for minimizing the total energy are written in terms of active and passive deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiac cells. The well-posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed and different mechanical activation functions are considered. In addition, the active strain formulation is compared with the classical active stress formulation from both numerical and modeling perspectives. Taylor-Hood and MINI finite elements are employed to discretize the mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main key features of the phenomenon, while allowing savings in computational costs.

Total knee arthroplasty - a clinical and numerical study of the micromovements of the tibial implant

Introduction The importance of the micromovements in the mechanism of aseptic loosening is clinically difficult to evaluate. To complete the analysis of a series of total knee arthroplasties (TKA), we used a tridimensional numerical model to study the micromovements of the tibial implant.Material and Methods Fifty one patients (with 57 cemented Porous Coated Anatomic TKAs) were reviewed (mean follow-up 4.5 year). Radiolucency at the tibial bone-cement interface was sought on the AP radiographs and divided in 7 areas. The distribution of the radiolucency was then correlated with the axis of the lower limb as measured on the orthoradiograms.The tridimensional numerical model is based on the finite element method. It allowed the measurement of the cemented prosthetic tibial implant's displacements and the microvements generated at bone-ciment interface. A total load (2000 Newton) was applied at first vertically and asymetrically on the tibial plateau, thereby simulating an axial deviation of the lower limbs. The vector's posterior inclination then permitted the addition of a tangential component to the axial load. This type of effort is generated by complex biomechanical phenomena such as knee flexion.Results 81 per cent of the 57 knees had a radiolucent line of at least 1 mm, at one or more of the tibial cement-epiphysis jonctional areas. The distribution of these lucent lines showed that they came out more frequently at the periphery of the implant. The lucent lines appeared most often under the unloaded margin of the tibial plateau, when axial deviation of lower limbs was present.Numerical simulations showed that asymetrical loading on the tibial plateau induced a subsidence of the loaded margin (0-100 microns) and lifting off at the opposite border (0-70 microns). The postero-anterior tangential component induced an anterior displacement of the tibial implant (160-220 microns), and horizontal micromovements with non homogenous distribution at the bone-ciment interface (28-54 microns).Discussion Comparison of clinical and numerical results showed a relation between the development of radiolucent lines and the unloading of the tibial implant's margin. The deleterious effect of lower limbs' axial deviation is thereby proven. The irregular distribution of lucent lines under the tibial plateau was similar of the micromovements' repartition at the bone-cement interface when tangential forces were present. A causative relation between the two phenomenaes could not however be established.Numerical simulation is a truly useful method of study; it permits to calculate micromovements which are relative, non homogenous and of very low amplitude. However, comparative clinical studies remain as essential to ensure the credibility of results.

Selection methods regulate evolution of cooperation in digital evolution.

A key, yet often neglected, component of digital evolution and evolutionary models is the 'selection method' which assigns fitness (number of offspring) to individuals based on their performance scores (efficiency in performing tasks). Here, we study with formal analysis and numerical experiments the evolution of cooperation under the five most common selection methods (proportionate, rank, truncation-proportionate, truncation-uniform and tournament). We consider related individuals engaging in a Prisoner's Dilemma game where individuals can either cooperate or defect. A cooperator pays a cost, whereas its partner receives a benefit, which affect their performance scores. These performance scores are translated into fitness by one of the five selection methods. We show that cooperation is positively associated with the relatedness between individuals under all selection methods. By contrast, the change in the performance benefit of cooperation affects the populations' average level of cooperation only under the proportionate methods. We also demonstrate that the truncation and tournament methods may introduce negative frequency-dependence and lead to the evolution of polymorphic populations. Using the example of the evolution of cooperation, we show that the choice of selection method, though it is often marginalized, can considerably affect the evolutionary dynamics.

Prothèses totales de genoux. Analyse clinique et numérique des micromouvements de l'implant tibial [Total knee prosthesis. Clinical and numerical study of micromovements of the tibial implant].

INTRODUCTION: The importance of the micromovements in the mechanism of aseptic loosening is clinically difficult to evaluate. To complete the analysis of a series of total knee arthroplasties (TKA), we used a tridimensional numerical model to study the micromovements of the tibial implant. MATERIAL AND METHODS: Fifty one patients (with 57 cemented Porous Coated Anatomic TKAs) were reviewed (mean follow-up 4.5 year). Radiolucency at the tibial bone-cement interface was sought on the AP radiographs and divided in 7 areas. The distribution of the radiolucency was then correlated with the axis of the lower limb as measured on the orthoradiograms. The tridimensional numerical model is based on the finite element method. It allowed the measurement of the cemented prosthetic tibial implant's displacements and the micromovements generated at bone-ciment interface. A total load (2000 Newton) was applied at first vertically and asymetrically on the tibial plateau, thereby simulating an axial deviation of the lower limbs. The vector's posterior inclination then permitted the addition of a tangential component to the axial load. This type of effort is generated by complex biomechanical phenomena such as knee flexion. RESULTS: 81 per cent of the 57 knees had a radiolucent line of at least 1 mm, at one or more of the tibial cement-epiphysis jonctional areas. The distribution of these lucent lines showed that they came out more frequently at the periphery of the implant. The lucent lines appeared most often under the unloaded margin of the tibial plateau, when axial deviation of lower limbs was present. Numerical simulations showed that asymetrical loading on the tibial plateau induced a subsidence of the loaded margin (0-100 microns) and lifting off at the opposite border (0-70 microns). The postero-anterior tangential component induced an anterior displacement of the tibial implant (160-220 microns), and horizontal micromovements with non homogenous distribution at the bone-ciment interface (28-54 microns). DISCUSSION: Comparison of clinical and numerical results showed a relation between the development of radiolucent lines and the unloading of the tibial implant's margin. The deleterious effect of lower limbs' axial deviation is thereby proven. The irregular distribution of lucent lines under the tibial plateau was similar of the micromovements' repartition at the bone-cement interface when tangential forces were present. A causative relation between the two phenomenaes could not however be established. Numerical simulation is a truly useful method of study; it permits to calculate micromovements which are relative, non homogenous and of very low amplitude. However, comparative clinical studies remain as essential to ensure the credibility of results.

Integrated application of geochemical and geophysical methods for hydrogeological impact assessment for tunneling in fractured rock

The interaction of tunneling with groundwater is a problem both from an environmental and an engineering point of view. In fact, tunnel drilling may cause a drawdown of piezometric levels and water inflows into tunnels that may cause problems during excavation of the tunnel. While the influence of tunneling on the regional groundwater systems may be adequately predicted in porous media using analytical solutions, such an approach is difficult to apply in fractured rocks. Numerical solutions are preferable and various conceptual approaches have been proposed to describe and model groundwater flow through fractured rock masses, ranging from equivalent continuum models to discrete fracture network simulation models. However, their application needs many preliminary investigations on the behavior of the groundwater system based on hydrochemical and structural data. To study large scale flow systems in fractured rocks of mountainous terrains, a comprehensive study was conducted in southern Switzerland, using as case studies two infrastructures actually under construction: (i) the Monte Ceneri base railway tunnel (Ticino), and the (ii) San Fedele highway tunnel (Roveredo, Graubiinden). The chosen approach in this study combines the temporal and spatial variation of geochemical and geophysical measurements. About 60 localities from both surface and underlying tunnels were temporarily and spatially monitored during more than one year. At first, the project was focused on the collection of hydrochemical and structural data. A number of springs, selected in the area surrounding the infrastructures, were monitored for discharge, electric conductivity, pH, and temperature. Water samples (springs, tunnel inflows and rains) were taken for isotopic analysis; in particular the stable isotope composition (δ2Η, δ180 values) can reflect the origin of the water, because of spatial (recharge altitude, topography, etc.) and temporal (seasonal) effects on precipitation which in turn strongly influence the isotopic composition of groundwater. Tunnel inflows in the accessible parts of the tunnels were also sampled and, if possible, monitored with time. Noble-gas concentrations and their isotope ratios were used in selected locations to better understand the origin and the circulation of the groundwater. In addition, electrical resistivity and VLF-type electromagnetic surveys were performed to identify water bearing fractures and/or weathered areas that could be intersected at depth during tunnel construction. The main goal of this work was to demonstrate that these hydrogeological data and geophysical methods, combined with structural and hydrogeological information, can be successfully used in order to develop hydrogeological conceptual models of the groundwater flow in regions to be exploited for tunnels. The main results of the project are: (i) to have successfully tested the application of electrical resistivity and VLF-electromagnetic surveys to asses water-bearing zones during tunnel drilling; (ii) to have verified the usefulness of noble gas, major ion and stable isotope compositions as proxies for the detection of faults and to understand the origin of the groundwater and its flow regimes (direct rain water infiltration or groundwater of long residence time); and (iii) to have convincingly tested the combined application of a geochemical and geophysical approach to assess and predict the vulnerability of springs to tunnel drilling. - L'interférence entre eaux souterraines et des tunnels pose des problèmes environnementaux et de génie civile. En fait, la construction d'un tunnel peut faire abaisser le niveau des nappes piézométriques et faire infiltrer de l'eau dans le tunnel et ainsi créer des problème pendant l'excavation. Alors que l'influence de la construction d'un tunnel sur la circulation régionale de l'eau souterraine dans des milieux poreux peut être prédite relativement facilement par des solution analytiques de modèles, ceci devient difficile dans des milieux fissurés. Dans ce cas-là, des solutions numériques sont préférables et plusieurs approches conceptuelles ont été proposées pour décrire et modéliser la circulation d'eau souterraine à travers les roches fissurées, en allant de modèles d'équivalence continue à des modèles de simulation de réseaux de fissures discrètes. Par contre, leur application demande des investigations importantes concernant le comportement du système d'eau souterraine basées sur des données hydrochimiques et structurales. Dans le but d'étudier des grands systèmes de circulation d'eau souterraine dans une région de montagnes, une étude complète a été fait en Suisse italienne, basée sur deux grandes infrastructures actuellement en construction: (i) Le tunnel ferroviaire de base du Monte Ceneri (Tessin) et (ii) le tunnel routière de San Fedele (Roveredo, Grisons). L'approche choisie dans cette étude est la combinaison de variations temporelles et spatiales des mesures géochimiques et géophysiques. Environs 60 localités situées à la surface ainsi que dans les tunnels soujacents ont été suiviès du point de vue temporel et spatial pendant plus de un an. Dans un premier temps le projet se focalisait sur la collecte de données hydrochimiques et structurales. Un certain nombre de sources, sélectionnées dans les environs des infrastructures étudiées ont été suivies pour le débit, la conductivité électrique, le pH et la température. De l'eau (sources, infiltration d'eau de tunnel et pluie) a été échantillonnés pour des analyses isotopiques; ce sont surtout les isotopes stables (δ2Η, δ180) qui peuvent indiquer l'origine d'une eaux, à cause de la dépendance d'effets spatiaux (altitude de recharge, topographie etc.) ainsi que temporels (saisonaux) sur les précipitations météoriques , qui de suite influencent ainsi la composition isotopique de l'eau souterraine. Les infiltrations d'eau dans les tunnels dans les parties accessibles ont également été échantillonnées et si possible suivies au cours du temps. La concentration de gaz nobles et leurs rapports isotopiques ont également été utilisées pour quelques localités pour mieux comprendre l'origine et la circulation de l'eau souterraine. En plus, des campagnes de mesures de la résistivité électrique et électromagnétique de type VLF ont été menées afin d'identifier des zone de fractures ou d'altération qui pourraient interférer avec les tunnels en profondeur pendant la construction. Le but principal de cette étude était de démontrer que ces données hydrogéologiques et géophysiques peuvent être utilisées avec succès pour développer des modèles hydrogéologiques conceptionels de tunnels. Les résultats principaux de ce travail sont : i) d'avoir testé avec succès l'application de méthodes de la tomographie électrique et des campagnes de mesures électromagnétiques de type VLF afin de trouver des zones riches en eau pendant l'excavation d'un tunnel ; ii) d'avoir prouvé l'utilité des gaz nobles, des analyses ioniques et d'isotopes stables pour déterminer l'origine de l'eau infiltrée (de la pluie par le haut ou ascendant de l'eau remontant des profondeurs) et leur flux et pour déterminer la position de failles ; et iii) d'avoir testé d'une manière convainquant l'application combinée de méthodes géochimiques et géophysiques pour juger et prédire la vulnérabilité de sources lors de la construction de tunnels. - L'interazione dei tunnel con il circuito idrico sotterraneo costituisce un problema sia dal punto di vista ambientale che ingegneristico. Lo scavo di un tunnel puô infatti causare abbassamenti dei livelli piezometrici, inoltre le venute d'acqua in galleria sono un notevole problema sia in fase costruttiva che di esercizio. Nel caso di acquiferi in materiale sciolto, l'influenza dello scavo di un tunnel sul circuito idrico sotterraneo, in genere, puô essere adeguatamente predetta attraverso l'applicazione di soluzioni analitiche; al contrario un approccio di questo tipo appare inadeguato nel caso di scavo in roccia. Per gli ammassi rocciosi fratturati sono piuttosto preferibili soluzioni numeriche e, a tal proposito, sono stati proposti diversi approcci concettuali; nella fattispecie l'ammasso roccioso puô essere modellato come un mezzo discreto ο continuo équivalente. Tuttavia, una corretta applicazione di qualsiasi modello numerico richiede necessariamente indagini preliminari sul comportamento del sistema idrico sotterraneo basate su dati idrogeochimici e geologico strutturali. Per approfondire il tema dell'idrogeologia in ammassi rocciosi fratturati tipici di ambienti montani, è stato condotto uno studio multidisciplinare nel sud della Svizzera sfruttando come casi studio due infrastrutture attualmente in costruzione: (i) il tunnel di base del Monte Ceneri (canton Ticino) e (ii) il tunnel autostradale di San Fedele (Roveredo, canton Grigioni). L'approccio di studio scelto ha cercato di integrare misure idrogeochimiche sulla qualité e quantité delle acque e indagini geofisiche. Nella fattispecie sono state campionate le acque in circa 60 punti spazialmente distribuiti sia in superficie che in sotterraneo; laddove possibile il monitoraggio si è temporalmente prolungato per più di un anno. In una prima fase, il progetto di ricerca si è concentrato sull'acquisizione dati. Diverse sorgenti, selezionate nelle aree di possibile influenza attorno allé infrastrutture esaminate, sono state monitorate per quel che concerne i parametri fisico-chimici: portata, conduttività elettrica, pH e temperatura. Campioni d'acqua sono stati prelevati mensilmente su sorgenti, venute d'acqua e precipitazioni, per analisi isotopiche; nella fattispecie, la composizione in isotopi stabili (δ2Η, δ180) tende a riflettere l'origine delle acque, in quanto, variazioni sia spaziali (altitudine di ricarica, topografia, etc.) che temporali (variazioni stagionali) della composizione isotopica delle precipitazioni influenzano anche le acque sotterranee. Laddove possibile, sono state campionate le venute d'acqua in galleria sia puntualmente che al variare del tempo. Le concentrazioni dei gas nobili disciolti nell'acqua e i loro rapporti isotopici sono stati altresi utilizzati in alcuni casi specifici per meglio spiegare l'origine delle acque e le tipologie di circuiti idrici sotterranei. Inoltre, diverse indagini geofisiche di resistività elettrica ed elettromagnetiche a bassissima frequenza (VLF) sono state condotte al fine di individuare le acque sotterranee circolanti attraverso fratture dell'ammasso roccioso. Principale obiettivo di questo lavoro è stato dimostrare come misure idrogeochimiche ed indagini geofisiche possano essere integrate alio scopo di sviluppare opportuni modelli idrogeologici concettuali utili per lo scavo di opere sotterranee. I principali risultati ottenuti al termine di questa ricerca sono stati: (i) aver testato con successo indagini geofisiche (ERT e VLF-EM) per l'individuazione di acque sotterranee circolanti attraverso fratture dell'ammasso roccioso e che possano essere causa di venute d'acqua in galleria durante lo scavo di tunnel; (ii) aver provato l'utilità di analisi su gas nobili, ioni maggiori e isotopi stabili per l'individuazione di faglie e per comprendere l'origine delle acque sotterranee (acque di recente infiltrazione ο provenienti da circolazioni profonde); (iii) aver testato in maniera convincente l'integrazione delle indagini geofisiche e di misure geochimiche per la valutazione della vulnérabilité delle sorgenti durante lo scavo di nuovi tunnel. - "La NLFA (Nouvelle Ligne Ferroviaire à travers les Alpes) axe du Saint-Gothard est le plus important projet de construction de Suisse. En bâtissant la nouvelle ligne du Saint-Gothard, la Suisse réalise un des plus grands projets de protection de l'environnement d'Europe". Cette phrase, qu'on lit comme présentation du projet Alptransit est particulièrement éloquente pour expliquer l'utilité des nouvelles lignes ferroviaires transeuropéens pour le développement durable. Toutefois, comme toutes grandes infrastructures, la construction de nouveaux tunnels ont des impacts inévitables sur l'environnement. En particulier, le possible drainage des eaux souterraines réalisées par le tunnel peut provoquer un abaissement du niveau des nappes piézométriques. De plus, l'écoulement de l'eau à l'intérieur du tunnel, conduit souvent à des problèmes d'ingénierie. Par exemple, d'importantes infiltrations d'eau dans le tunnel peuvent compliquer les phases d'excavation, provoquant un retard dans l'avancement et dans le pire des cas, peuvent mettre en danger la sécurité des travailleurs. Enfin, l'infiltration d'eau peut être un gros problème pendant le fonctionnement du tunnel. Du point de vue de la science, avoir accès à des infrastructures souterraines représente une occasion unique d'obtenir des informations géologiques en profondeur et pour échantillonner des eaux autrement inaccessibles. Dans ce travail, nous avons utilisé une approche pluridisciplinaire qui intègre des mesures d'étude hydrogéochimiques effectués sur les eaux de surface et des investigations géophysiques indirects, tels que la tomographic de résistivité électrique (TRE) et les mesures électromagnétiques de type VLF. L'étude complète a été fait en Suisse italienne, basée sur deux grandes infrastructures actuellement en construction, qui sont le tunnel ferroviaire de base du Monte Ceneri, une partie du susmentionné projet Alptransit, situé entièrement dans le canton Tessin, et le tunnel routière de San Fedele, situé a Roveredo dans le canton des Grisons. Le principal objectif était de montrer comment il était possible d'intégrer les deux approches, géophysiques et géochimiques, afin de répondre à la question de ce que pourraient être les effets possibles dû au drainage causés par les travaux souterrains. L'accès aux galeries ci-dessus a permis une validation adéquate des enquêtes menées confirmant, dans chaque cas, les hypothèses proposées. A cette fin, nous avons fait environ 50 profils géophysiques (28 imageries électrique bidimensionnels et 23 électromagnétiques) dans les zones de possible influence par le tunnel, dans le but d'identifier les fractures et les discontinuités dans lesquelles l'eau souterraine peut circuler. De plus, des eaux ont été échantillonnés dans 60 localités situées la surface ainsi que dans les tunnels subjacents, le suivi mensuelle a duré plus d'un an. Nous avons mesurés tous les principaux paramètres physiques et chimiques: débit, conductivité électrique, pH et température. De plus, des échantillons d'eaux ont été prélevés pour l'analyse mensuelle des isotopes stables de l'hydrogène et de l'oxygène (δ2Η, δ180). Avec ces analyses, ainsi que par la mesure des concentrations des gaz rares dissous dans les eaux et de leurs rapports isotopiques que nous avons effectués dans certains cas spécifiques, il était possible d'expliquer l'origine des différents eaux souterraines, les divers modes de recharge des nappes souterraines, la présence de possible phénomènes de mélange et, en général, de mieux expliquer les circulations d'eaux dans le sous-sol. Le travail, même en constituant qu'une réponse partielle à une question très complexe, a permis d'atteindre certains importants objectifs. D'abord, nous avons testé avec succès l'applicabilité des méthodes géophysiques indirectes (TRE et électromagnétiques de type VLF) pour prédire la présence d'eaux souterraines dans le sous-sol des massifs rocheux. De plus, nous avons démontré l'utilité de l'analyse des gaz rares, des isotopes stables et de l'analyses des ions majeurs pour la détection de failles et pour comprendre l'origine des eaux souterraines (eau de pluie par le haut ou eau remontant des profondeurs). En conclusion, avec cette recherche, on a montré que l'intégration des ces informations (géophysiques et géochimiques) permet le développement de modèles conceptuels appropriés, qui permettant d'expliquer comment l'eau souterraine circule. Ces modèles permettent de prévoir les infiltrations d'eau dans les tunnels et de prédire la vulnérabilité de sources et des autres ressources en eau lors de construction de tunnels.

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier-Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.