The mechanical properties of a cell-based numerical model of epithelium.

In this work we use a computational cell-based model to study the influence of the mechanical properties of cells on the mechanics of epithelial tissues. We analyze the effect of the model parameters on the elasticity and the mechanical response of tissues subjected to stress loading application. We compare our numerical results with experimental measurements of epithelial cell monolayer mechanics. Unlike previous studies, we have been able to estimate in physical units the parameter values that match the experimental results. A key observation is that the model parameters must vary with the tissue strain. In particular, it was found that, while the perimeter contractility and the area elasticity of cells remain constant at lower strains (<20%), they must increase to respond to larger strains (>20%). However, above a threshold of 50% extension, the cells stop counteracting the tissue strain and reduce both their perimeter contractility and area elasticity.

Noise source identification with the lattice Boltzmann method.

In this paper the sound source identification problem is addressed with the use of the lattice Boltzmann method. To this aim, a time-reversed problem coupled to a complex differentiation method is used. In order to circumvent the inherent instability of the time-reversed lattice Boltzmann scheme, a method based on a split of the lattice Boltzmann equation into a mean and a perturbation component is used. Lattice Boltzmann method formulation around an arbitrary base flow is recalled and specific applications to acoustics are presented. The implementation of the noise source detection method for two-dimensional weakly compressible (low Mach number) flows is discussed, and the applicability of the method is demonstrated.

Towards a physical interpretation of the entropic lattice Boltzmann method.

The entropic lattice Boltzmann method (ELBM) is one among several different versions of the lattice Boltzmann method for the simulation of hydrodynamics. The collision term of the ELBM is characterized by a nonincreasing H function, guaranteed by a variable relaxation time. We propose here an analysis of the ELBM using the Chapman-Enskog expansion. We show that it can be interpreted as some kind of subgrid model, where viscosity correction scales like the strain rate tensor. We confirm our analytical results by the numerical computations of the relaxation time modifications on the two-dimensional dipole-wall interaction benchmark.

Straight velocity boundaries in the lattice Boltzmann method.

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocity Dirichlet boundary conditions, and to straight on-lattice boundaries which are aligned with the horizontal and vertical lattice directions. The boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes. This procedure makes it possible to compare boundary conditions on an equal footing, although they were originally derived from very different principles. It is concluded that all five boundary conditions exhibit second-order accuracy, consistent with the accuracy of the lattice Boltzmann method. The five methods are then compared numerically for accuracy and stability through benchmarks of two-dimensional and three-dimensional flows. None of the methods is found to be throughout superior to the others. Instead, the choice of a best boundary condition depends on the flow geometry, and on the desired trade-off between accuracy and stability. From the findings of the benchmarks, the boundary conditions can be classified into two major groups. The first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations. Boundary conditions in this group are found to be exceptionally accurate at low Reynolds number. Boundary conditions of the second group replace all variables on boundary nodes by new values. They exhibit generally much better numerical stability and are therefore dedicated for use in high Reynolds number flows.

Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media.

This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

Determination of a shear rate threshold for thrombus formation in intracranial aneurysms.

BACKGROUND: Particular intra-aneurysmal blood flow conditions, created naturally by the growth of an aneurysm or induced artificially by implantation of a flow diverter stent (FDS), can potentiate intra-aneurysmal thrombosis. The aim of this study was to identify hemodynamic indicators, relevant to this process, which could be used as a prediction of the success of a preventive endovascular treatment. METHOD: A cross sectional study on 21 patients was carried out to investigate the possible association between intra-aneurysmal spontaneous thrombus volume and the dome to neck aspect ratio (AR) of the aneurysm. The mechanistic link between these two parameters was further investigated through a Fourier analysis of the intra-aneurysmal shear rate (SR) obtained by computational fluid dynamics (CFD). This analysis was first applied to 10 additional patients (4 with and 6 without spontaneous thrombosis) and later to 3 patients whose intracranial aneurysms only thrombosed after FDS implantation. RESULTS: The cross sectional study revealed an association between intra-aneurysmal spontaneous thrombus volume and the AR of the aneurysm (R(2)=0.67, p<0.001). Fourier analysis revealed that in cases where thrombosis occurred, the SR harmonics 0, 1, and 2 were always less than 25/s, 10/s, and 5/s, respectively, and always greater than these values where spontaneous thrombosis was not observed. CONCLUSIONS: Our study suggests the existence of an SR threshold below which thrombosis will occur. Therefore, by analyzing the SR on patient specific data with CFD techniques, it may be potentially possible to predict whether or the intra-aneurysmal flow conditions, after FDS implantation, will become prothrombotic.

Estimating allele age and selection coefficient from time-serial data.

Recent advances in sequencing technologies have made available an ever-increasing amount of ancient genomic data. In particular, it is now possible to target specific single nucleotide polymorphisms in several samples at different time points. Such time-series data are also available in the context of experimental or viral evolution. Time-series data should allow for a more precise inference of population genetic parameters and to test hypotheses about the recent action of natural selection. In this manuscript, we develop a likelihood method to jointly estimate the selection coefficient and the age of an allele from time-serial data. Our method can be used for allele frequencies sampled from a single diallelic locus. The transition probabilities are calculated by approximating the standard diffusion equation of the Wright-Fisher model with a one-step process. We show that our method produces unbiased estimates. The accuracy of the method is tested via simulations. Finally, the utility of the method is illustrated with an application to several loci encoding coat color in horses, a pattern that has previously been linked with domestication. Importantly, given our ability to estimate the age of the allele, it is possible to gain traction on the important problem of distinguishing selection on new mutations from selection on standing variation. In this coat color example for instance, we estimate the age of this allele, which is found to predate domestication.