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Unsaturated water flows at watershed scale or Darcy-scale are generally described by the Richardson-Richards equation. This equation is highly non-linear and simulation domains are limited by computational costs. The porousMultiphaseFoam toolbox, is a Finite Volume tool capable of modeling multi-phase flows in porous media, including the solving of the Richardson-Richards equation combined with the transport equation. As it has been developed using the OpenFOAM environment, the software is natively fully parallelized and can be used on super computers. Despite all its perks, the toolbox still suffer from expensive computational cost in 3D, highlighted by a calibration method developed last year to validate the 3D model against the historic 2D and 1D+2D models. In an attempt to reduce those, Adaptive Mesh Refinement (AMR) method has been included into the toolbox. The main issue faced by the method is the highly anisotropic mesh, with cells having horizontal characteristic lengths up to 100 times bigger than the vertical one. We present here the results obtained using the AMR, and tools to evaluate its efficiency on anisotropic meshes. Particularly, we take interest in the total CPU time, the mesh size and the number of linear iteration required to solve the problem. We show results using both 3D hydrological and transport solvers.

The objective of this work is to develop and apply a numerical workflow for the simultaneous determinations of the effective porosity and the dispersion coefficient from core flood taking chemical reactions into account. This approach consists of modeling the species transport at the core scale coupled with the chemical reactions, as involved in alkali flooding core experiments. Then, the one-dimensional model is compared with experimental breakthrough curves of tracer and pH, and the optimization process based on a genetic algorithm permits to identify the optimal parameter combination of effective porosity and dispersion coefficient. This approach is validated for an artificial case, then investigated on two distinct experimental configurations of core flooding. The proposed workflow, which involves an additional experimental measurement for pH, provides both an estimate of the kinetic porosity that is lower than the measured porosity, as well as an estimate of the dispersion coefficient that is significantly different from the usual single signal approach. The tests performed in this work do not take the interactions of the fluid with the rock into account.

Unsaturated water flows at watershed scale or Darcy-scale are generally described by the Richardson-Richards equation. This equation is highly non-linear and simulation domains are limited by computational costs. The porousMultiphaseFoam toolbox is a Finite Volume tool capable of modeling multiphase flows in porous media, including the solving of the Richardson-Richards equation. As it has been developed using the OpenFOAM environment, the software is natively fully parallelized and can be used on super computers. By using experimental data from real site with geographical informations and piezometrics values, an iterative algorithm is set up to solve an inverse problem in order to evaluate an adequate permeability field. This procedure is initially implemented using simplified aquifer model with a 2D saturated modeling approach. A similar procedure using a full 3D model of the actual site is performed (handling both saturated and unsaturated area). The results are compared between the two approaches (2D and 3D) for steady simulations and new post-processing tools are also introduced to spatialize the error between the two models and define the areas for which the behaviour of the models is different. In a second part, an optimization of the Van Genuchten parameters is performed to reproduce transient experimental data. The 3D numerical results at the watershed scale are also compared to the reference simulations using a 1D unsaturated + 2D satured modeling approach.

International audience; An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat’s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image–based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.

Background The clustering of data produced by liquid chromatography coupled to mass spectrometry analyses (LC-MS data) has recently gained interest to extract meaningful chemical or biological patterns. However, recent instrumental pipelines deliver data which size, dimensionality and expected number of clusters are too large to be processed by classical machine learning algorithms, so that most of the state-of-the-art relies on single pass linkage-based algorithms. Results We propose a clustering algorithm that solves the powerful but computationally demanding kernel k-means objective function in a scalable way. As a result, it can process LC-MS data in an acceptable time on a multicore machine. To do so, we combine three essential features: a compressive data representation, Nyström approximation and a hierarchical strategy. In addition, we propose new kernels based on optimal transport, which interprets as intuitive similarity measures between chromatographic elution profiles. Conclusions Our method, referred to as CHICKN, is evaluated on proteomics data produced in our lab, as well as on benchmark data coming from the literature. From a computational viewpoint, it is particularly efficient on raw LC-MS data. From a data analysis viewpoint, it provides clusters which differ from those resulting from state-of-the-art methods, while achieving similar performances. This highlights the complementarity of differently principle algorithms to extract the best from complex LC-MS data.

Using a systematic investigation of brain blood volume, in high-resolution synchrotron 3D images of microvascular structures within cortical regions of a primate brain, we challenge several basic questions regarding possible vascular bias in high-resolution functional neuroimaging. We present a bilateral comparison of cortical regions, where we analyze relative vascular volume in voxels from 150 to 1000 lm side lengths in the white and grey matter. We show that, if voxel size reaches a scale smaller than 300 mm, the vascular volume can no longer be considered homogeneous, either within one hemisphere or in bilateral comparison between samples. We demonstrate that voxel size influences the comparison between vessel-relative volume distributions depending on the scale considered (i.e., hemisphere, lobe, or sample). Furthermore, we also investigate how voxel anisotropy and orientation can affect the apparent vascular volume, in accordance with actual fMRI voxel sizes. These findings are discussed from the various perspectives of high-resolution brain functional imaging

International audience; The term "spectral clustering" is sometimes used to refer to the clustering of mass spectrometry data. However, it also classically refers to a family of popular clustering algorithms. To avoid confusion, a more specific term could advantageously be coined.

The IMplicit Pressure Explicit Saturation (IMPES) method is a prevalent way to simulate multiphase flows in porous media. The numerical stability of this sequential method implies limitations on the time step, which may depend on the flow regime studied. In this note, three stability criteria related to the IMPES method, that differ in their construction on the observed variables, are compared on homogeneous and heterogeneous configurations for different two-phase flow regimes (viscous/capillary/gravitational). This highlights that there is no single optimal criterion always ensuring stability and efficiency. For capillary dominated flows, the Todd's condition is the most efficient one, while the standard Coat condition should be preferred for viscous flows. When gravity effects are present, Coat's condition must be restricted, but remains more efficient than the Todd's condition.

International audience; Multiphase flow in porous media provides a wide range of applications: from the environmental understanding (aquifer, site-pollution) to industrial process improvements (oil production, waste management). Modeling of such flows involve specific volume-averaged equations and therefore specific computational fluid dynamics (CFD) tools. In this work, we develop a toolbox for modeling multiphase flow in porous media with OpenFOAM®, an open-source platform for CFD. The underlying idea of this approach is to provide an easily adaptable tool that can be used in further studies to test new mathematical models or numerical methods. The package provides the most common effective properties models of the literature (relative permeability, capillary pressure) and specific boundary conditions related to porous media flows. To validate this package, a solvers based on the IMplicit Pressure Explicit Saturation (IMPES) methodare developed in the toolbox. The numerical validation is performed by comparison with analytical solutions on academic cases. Then, a satisfactory parallel efficiency of the solver is shown on a more complex configuration.

Using a systematic investigation of brain blood volume, in high‐resolution synchrotron 3D images of microvascular structures within cortical regions of a primate brain, we challenge several basic questions regarding possible vascular bias in high‐resolution functional neuroimaging. We present a bilateral comparison of cortical regions, where we analyze relative vascular volume in voxels from 150 to 1000 μm side lengths in the white and grey matter. We show that, if voxel size reaches a scale smaller than 300 µm, the vascular volume can no longer be considered homogeneous, either within one hemisphere or in bilateral comparison between samples. We demonstrate that voxel size influences the comparison between vessel‐relative volume distributions depending on the scale considered (i.e., hemisphere, lobe, or sample). Furthermore, we also investigate how voxel anisotropy and orientation can affect the apparent vascular volume, in accordance with actual fMRI voxel sizes. These findings are discussed from the various perspectives of high‐resolution brain functional imaging. Hum Brain Mapp 38:5756–5777, 2017. © 2017 Wiley Periodicals, Inc.

In this study, a two-step upscaling method, already validated for absolute permeability determination, is extended to non-Darcy flows. Inertial regime is generally observed near wellbores. The upscaling process consists in evaluating the Forchheimer factor and induces several simulations in each spatial directions. The method is applied on two different porous media (sphere packing and rock sample). These configurations are used to quantify the accuracy and demonstrate the convergence of the method.

In this work, several boundary value problems used to numerically evaluate the absolute permeability tensors of porous media using core-scale images are compared and discussed. The various configurations differ by the type of boundary conditions used to compute the flow at the micro-scale. The issue is the ability of the method to capture anisotropy correctly and to avoid possible percolation artifacts. This study is carried on two-dimensional synthetic, isotropic or anisotropic, porous media, that are chosen to illustrate the various difficulties mentioned above. A new method is proposed which consists in embedding the porous medium in question in a homogenized one. Using an iterative optimization procedure on the surrounding permeability, the method determines the absolute permeability tensor of the original medium. The equivalent permeability tensor that minimizes the effect on the surrounding porous medium is, unlike that of classical methods, de facto symmetrical due to the use of periodic boundary conditions and exhibits significantly lower permeabilities. The way in which non-diagonal terms of the permeability tensor are obtainedwith the various methods are thoroughly discussed.

The aim of this work is the evaluation of numerical methods to estimate longitudinal effective dispersion coefficients on pore-space images using a Lagrangian Particle Tracking method. The pore-space imaging is done using a X-ray Microscope Computed Tomograph. Equations are then directly solved in the mesh respecting the binary image using the open-source platform OpenFOAM. After a short reminder of the LPT method and a description of the samples used, the LPT algorithm is validated in idealized media. The use of simple 2D and 3D geometries allow the comparison to theoretical laws. But in order to ensure the validity of our method, we also cross compare our results with the Volume Averaging Method. The impact of the mesh quality on statistical moments will be also presented showing some effects on the first moment. The main part of the presented study focus on the comparison of three different estimators of dispersion coefficients which treat boundary conditions differently. This allows to determine dispersivity in non periodic samples.

A computational approach is proposed for efficient design study of a reducer stent to be percutaneously implanted in enlarged right ventricular outflow tracts (RVOT). The need for such a device is driven by the absence of bovine or artificial valves which could be implanted in these RVOT to replace the absent or incompetent native valve, as is often the case over time after Tetralogy of Fallot repair. Hemodynamics are simulated in the stented RVOT via a reduce order model based on proper orthogonal decomposition (POD), while the artificial valve is modeled as a thin resistive surface. The reduced order model is obtained from the numerical solution on a reference device configuration, then varying the geometrical parameters (diameter) for design purposes. To validate the approach, forces exerted on the valve and on the reducer are monitored, varying with geometrical parameters, and compared with the results of full CFD simulations. Such an approach could also be useful for uncertainty quantification. Device design, percutaneous pulmonary valve replacement, proper orthogonal decomposition (POD), finite element method, blood flow CFD, repaired Tetralogy of Fallot.

International audience; Tetralogy of Fallot is a congenital heart disease characterized over time, after the initial repair, by the absence of a functioning pulmonary valve, which causes regurgitation, and by progressive enlargement of the right ventricle outflow tract (RVOT). Due to this pathological anatomy, available transcatheter valves are usually too small to be deployed there. To avoid surgical valve replacement, an alternative consists in implanting a reducer prior to or in combination with the valve. It has been shown in animal experiments to be promising, but with some limitations. The effect of a percutaneous pulmonary valve reducer on hemodynamics in enlarged RVOT is thus studied by computational modeling. To this aim, blood flow in the RVOT is modeled with CFD coupled to a simplified valve model and 0D downstream models. Simulations are performed in an image-based geometry and boundary conditions tuned to reproduce the pathological flow without the device. Different device designs are built and compared with the initial device-free state, or with the reducer alone. Results suggest that pressure loss is higher for the reducer alone than for the full device, and that the latter successfully restores hemodynamics to a healthy state and induces a more symmetric flow in the pulmonary arteries. Moreover, pressure forces on the reducer and on the valve have the same magnitudes. Migration would occur towards the right ventricle rather than the pulmonary arteries. Results support the thesis that the reducer does not introduce clinically significant pressure gradients, as was found in animal experiments. Such study could help transfer to patients.

We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude σh where σ ~ O(1), but long-wavelength variations λ, with h/λ ≪ 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel's wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.

The modeling of blood flows confined in micro-channels or micro-capillary beds depends on the interactions between the cell-phase, plasma and the complex geometry of the network. In the case of capillaries or channels having a high aspect ratio (their longitudinal size is much larger than their transverse one), this modeling is much simplified from the use of a continuous description of fluid viscosity as previously proposed in the literature. Phase separation or plasma skimming effect is a supplementary mechanism responsible for the relative distribution of the red blood cell’s volume density in each branch of a given bifurcation. Different models have already been proposed to connect this effect to the various hydrodynamics and geometrical parameters at each bifurcation. We discuss the advantages and drawbacks of these models and compare them to an alternative approach for modeling phase distribution in complex channels networks. The main novelty of this new formulation is to show that albeit all the previous approaches seek for a local origin of the phase segregation phenomenon, it can arise from a global non-local and nonlinear structuration of the flow inside the network. This new approach describes how elementary conservation laws are sufficient principles (rather than the complex parametric models previously proposed) to provide non local phase separation. Spatial variations of the hematocrit field thus result from the topological complexity of the network as well as nonlinearities arising from solving a new free boundary problem associated with the flux and mass conservation. This network model approach could apply to model blood flow distribution either on artificial micro-models, micro-fluidic networks, or realistic reconstruction of biological micro-vascular networks.

International audience; In this work, a complete work flow from pore-scale imaging to absolute permeability determination is described and discussed. Two specific points are tackled, concerning (1) the mesh refinement for a fixed image resolution and (2) the impact of the determination method used. A key point for this kind of approach is to work on enough large samples to check the representativity of the obtained evaluations, which requires efficient parallel capabilities. Image acquisition and processing are realized using a commercial micro-tomograph. The pore-scale flows are then evaluated using the finite volume method implemented in the open-source platform OpenFOAM®. For this numerical method, the influence of the different aspects mentioned above are studied. Moreover, the parallel efficiency is also tested and discussed. We observe that the level of mesh refinement has a non-negligible impact on permeability tensor. Moreover, increasing the refinement level tends to reduce the gap between the methods of computational measurements. The increase in computation time with the mesh is balanced with the good parallel efficiency of the platform.

International audience; 3D computational fluid dynamics (CFD) in patient-specific geometries provides complementary insights to clinical imaging, to better understand how heart disease, and the side effects of treating heart disease, affect and are affected by hemodynamics. This information can be useful in treatment planning for designing artificial devices that are subject to stress and pressure from blood flow. Yet, these simulations remain relatively costly within a clinical context. The aim of this work is to reduce the complexity of patient-specific simulations by combining image analysis, computational fluid dynamics and model order reduction techniques. The proposed method makes use of a reference geometry estimated as an average of the population, within an efficient statistical framework based on the currents representation of shapes. Snapshots of blood flow simulations performed in the reference geometry are used to build a POD (Proper Orthogonal Decomposition) basis, which can then be mapped on new patients to perform reduced order blood flow simulations with patient specific boundary conditions. This approach is applied to a data-set of 17 tetralogy of Fallot patients to simulate blood flow through the pulmonary artery under normal (healthy or synthetic valves with almost no backflow) and pathological (leaky or absent valve with backflow) conditions to better understand the impact of regurgitated blood on pressure and velocity at the outflow tracts. The model reduction approach is further tested by performing patient simulations under exercise and varying degrees of pathophysiological conditions based on reduction of reference solutions (rest and medium backflow conditions respectively).

International audience; Cerebral blood flow (CBF) is the most common parameter for the quantification of brain's function. Literature data indicate a widespread dispersion of values that might be related to some differences in the measurement conditions that are not properly taken into account in CBF evaluation. Using recent high-resolution imaging of the complete cortical microvasculature of primate brain, we perform extensive numerical evaluation of the cerebral perfusion. We show that blood perfusion associated with intravascular tracers should be normalized by the surface of the voxel rather than by its volume and we consistently test this result on the available literature data.

International audience; Vascular domains have been described as being coupled to neuronal functional units enabling dynamic blood supply to the cerebral cyto-architecture. Recent experiments have shown that penetrating arterioles of the grey matter are the building blocks for such units. Nevertheless, vascular territories are still poorly known, as the collection and analysis of large three-dimensional micro-vascular networks are difficult. By using an exhaustive reconstruction of the micro-vascular network in an 18mm(3) volume of marmoset cerebral cortex, we numerically computed the blood flow in each blood vessel. We thus defined arterial and venular territories and examined their overlap. A large part of the intracortical vascular network was found to be supplied by several arteries and drained by several venules. We quantified this multiple potential to compensate for deficiencies by introducing a new robustness parameter. Robustness proved to be positively correlated with cortical depth and a systematic investigation of coupling maps indicated local patterns of overlap between neighbouring arteries and neighbouring venules. However, arterio-venular coupling did not have a spatial pattern of overlap but showed locally preferential functional coupling, especially of one artery with two venules, supporting the notion of vascular units. We concluded that intra-cortical perfusion in the primate was characterised by both very narrow functional beds and a large capacity for compensatory redistribution, far beyond the nearest neighbour collaterals.

International audience; We report new results on blood flow modeling over large volumes of cortical gray matter of primate brain. We propose a network method for computing the blood flow, which handles realistic boundary conditions, complex vessel shapes, and complex nonlinear blood rheology. From a detailed comparison of the available models for the blood flow rheology and the phase separation effect, we are able to derive important new results on the impact of network structure on blood pressure, hematocrit, and flow distributions. Our findings show that the network geometry (vessel shapes and diameters), the boundary conditions associated with the arterial inputs and venous outputs, and the effective viscosity of the blood are essential components in the flow distribution. In contrast, we show that the phase separation effect has a minor function in the global microvascular hemodynamic behavior. The behavior of the pressure, hematocrit, and blood flow distributions within the network are described through the depth of the primate cerebral cortex and are discussed.

International audience; Cerebral micro-vascular networks control the blood pressure distribution when considering in vitro blood rheology models. Blood rheology is complex and non-linear. In small vessels, the effective viscosity variations are important due to red blood cells packing in capillaries, the so-called Fåhræus-Lindquist effect, whilst concomitantly phase segregation appears in bifurcations. Direct numerical simulations of different non-linear rheological models of the blood are performed on realistic three-dimensional micro-vascular networks. These simulations exhibit two significant results. First, various rheological models lead to very similar pressure distribution over the whole range of physiologically relevant hematocrits. Secondly, different models for phase segregation lead to very distinct hematocrit distributions in the micro-vacular network. Nevertheless, the hematocrit distribution very weakly affects the pressure distribution. Hence, our results suggest that the micro-vacular network structure mainly controls the pressure distribution in micro-circulation, whilst the effect of hematocrit distribution is weak.

1361-8415/$ see front matter 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.media.2014.01.007 DOI of original article: http://dx.doi.org/10.1016/j.media.2013.09.003 ⇑ Corresponding author. Tel.: +49 3