Romain Guibert

Cerebral blood flow modeling in primate cortex

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.

Computational Permeability Determination from Pore-Scale Imaging: Sample Size, Mesh and Method Sensitivities

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.

An open-source toolbox for multiphase flow in porous media

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.

A Comparison of Various Methods for the Numerical Evaluation of Porous Media Permeability Tensors from Pore-Scale Geometry

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 obtained with the various methods is thoroughly discussed.

Blood Flow Simulations for the Design of Stented Valve Reducer in Enlarged Ventricular Outflow Tracts

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.

On the normalization of cerebral blood flow.

Cerebral blood flow (CBF) is the most common parameter for the quantification of brains 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.

Analysis of vascular homogeneity and anisotropy on high-resolution primate brain imaging

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.

Efficiency of a two-step upscaling method for permeability evaluation at Darcy and pore scales

This work presents a new subdivision method to upscale absolute permeability fields. This process, called two-step method, consists in (i) solving micro-scale equations on subdomains obtained from the full domain regular decomposition and (ii) solve a second upscaling with Darcy’s law on the permeability fields obtained in the first step. The micro-scale equations used depend on the case studied. The two-step upscaling process is validated on randomly generated Darcy-scale permeability fields by measuring the numerical error induced by upscaling. The method is then applied to real domains obtained from sandstone micro-tomographic images. The method specificities due to pore-space structure are discussed. The main advantage of the two-step upscaling method resides in the drastic reduction of computational costs (CPU time and memory usage) while maintaining a numerical error similar to that of other upscaling procedures. This new upscaling method may improve permeability predictions by the use of finer meshes or larger sample volumes.

Steady streaming confined between three-dimensional wavy surfaces

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 σ h 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.