Extending a Gray Lattice Boltzmann Model for Simulating Fluid Flow in Multi-Scale Porous Media

Abstract A gray lattice Boltzmann model has previously been developed by the authors of this article to simulate fluid flow in porous media that contain both resolved pores and grains as well as aggregates of unresolved smaller pores and grains. In this model, a single parameter is introduced to prescribe the amount of fluid to be bounced back at each aggregate cell. This model has been shown to recover Darcy-Brinkman flow but with effective viscosity and permeability correlated through the model parameter. In this paper, we prove that the model parameter relates to the fraction of the solid phase of a sub-pore system for a specific set of bounce-back conditions. We introduce an additional parameter to the model, and this enables flow simulation in which cases with variable effective viscosity and permeability can be specified by selecting the two parameters independently. We verify and validate the model for layered channel cases and mathematically analyze fluid momentum and energy losses for the single- and two-parameter models to explain the roles of the parameters in their conservation. We introduce a strategy to upgrade our model to an isotropic version. We discuss the fundamental differences between our model and the Brinkman body-force LBM scheme

An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media

A lattice Boltzmann (LB) model is proposed for simulating fluid flow in porous media by allowing the aggregates of finer-scale pores and solids to be treated as ‘equivalent media’. This model employs a partially bouncing-back scheme to mimic the resistance of each aggregate, represented as a gray node in the model, to the fluid flow. Like several other lattice Boltzmann models that take the same approach, which are collectively referred to as gray lattice Boltzmann (GLB) models in this paper, it introduces an extra model parameter, ns, which represents a volume fraction of fluid particles to be bounced back by the solid phase rather than the volume fraction of the solid phase at each gray node. The proposed model is shown to conserve the mass even for heterogeneous media, while this model and that model of Walsh et al. (2009) [1], referred to the WBS model thereafter, are shown analytically to recover Darcy–Brinkman’s equations for homogenous and isotropic porous media where the effective viscosity and the permeability are related to ns and the relaxation parameter of LB model. The key differences between these two models along with others are analyzed while their implications are highlighted. An attempt is made to rectify the misconception about the model parameter ns being the volume fraction of the solid phase. Both models are then numerically verified against the analytical solutions for a set of homogenous porous models and compared each other for another two sets of heterogeneous porous models of practical importance. It is shown that the proposed model allows true no-slip boundary conditions to be incorporated with a significant effect on reducing errors that would otherwise heavily skew flow fields near solid walls. The proposed model is shown to be numerically more stable than the WBS model at solid walls and interfaces between two porous media. The causes to the instability in the latter case are examined. The link between these two GLB models and a generalized Navier–Stokes model [2] for heterogeneous but isotropic porous media are explored qualitatively. A procedure for estimating model parameter ns is proposed

Role of up-regulation of IK1 in action potential shortening associated with atrial fibrillation in humans

Objectives: Although previous studies in dogs have indicated a minimal role for changes in IK1 in the shortening of action potential duration (APD) associated with atrial fibrillation (AF), in humans, there is evidence for significant AF-induced up-regulation of this current. In this computer model study, we investigated the relative contributions of the remodeling of IK1, L-type calcium current, and other remodeled ionic channel currents to AF-induced APD reduction in human atrium. \ud \ud Methods: Two computer models of electrical activity of human atrial cell were modified by incorporating experimental data of AF-induced changes in human atrial ionic channel conductance and kinetics reported by Bosch et al. (ICaL, Ito, IK1, and INa) (AF-1) and Workman et al. (ICaL, Ito, and IK1) (AF-2). The roles and relative importance of individually remodeled ion channels in the APD reduction in human atrium were evaluated by the removal and exclusive methods, in which remodeling of specific currents was omitted, or considered in isolation, in the two models. \ud \ud Results: When tested together, previously reported AF-induced changes in sarcolemmal ion currents result in marked shortening of atrial APD90. With the AF-1 remodeled parameters, there is a 62% reduction in APD90 for the Nygren et al. model, and a 68% reduction for the Courtemanche et al. model, which are comparable to experimental results of 60% reduction seen in humans. When tested individually, AF-1-induced changes in ICaL, IK1, or Ito alone result in APD90 reduction of 20%, 64%, and –10%, respectively, for the Nygren et al. model, and 27%, 40%, and 11.6%, respectively, for the Courtemanche et al. model. With the AF-2 remodeled parameters, there is a 47% reduction in APD90 for the Nygren et al. model and a 49% reduction for the Courtemanche et al. model, which are also comparable to experimental results of 45% reduction. When tested individually, AF-2-induced changes in ICaL or IK1 alone result in APD90 reduction of 20% and 40%, respectively, for the Nygren et al. model, and 14% and 21%, respectively, for the Courtemanche et al. model. \ud \ud Conclusion: Previously reported changes in L-type Ca2+ current are insufficient to account for the observed reduction in atrial APD associated with persistent AF. Up-regulation of IK1 has a greater influence on atrial APD in the human model

The Potent Antioxidant MitoQ Protects Against Preeclampsia During Late Gestation but Increases the Risk of Preeclampsia When Administered in Early Pregnancy.

AIMS:Although preeclampsia (PE) has been attributed to excessive oxidative stress (OS) in the placenta, mild antioxidants failed to prevent PE in clinical trials. As mitochondria are a major source of OS, this study assessed the potential of a potent mitochondria-targeting antioxidant MitoQ in the prevention of PE. RESULTS:Placentas from women with PE and from reduced uterine perfusion pressure (RUPP) mice demonstrated significantly higher OS, along with increased mitochondrial damage and compromised glutathione peroxidase (GPx) activities. MitoQ administration during late gestation alleviated RUPP-induced PE, while early-pregnancy MitoQ treatment not only exacerbated BP, fetal growth restriction and proteinuria, but also reduced the labyrinth/spongiotrophoblast ratio and blood sinuses in the labyrinth. Invasion (Matrigel transwell) and migration (wound healing assay) of trophoblasts were greatly improved by 1 µM H2O2, but this improvement was abolished by MitoQ or MitoTempo. Mild OS enhanced the expression of miR-29b-3p, which regulates 5 genes involved in viability and mobility, in HTR8-S/Vneo cells. Innovation and Conclusions: Although the potent mitochondrial-targeting antioxidant MitoQ protects against hypertension and kidney damage induced by RUPP in mice when administered in late gestation, it exacerbates the PE-like phenotype when given in early gestation by interfering with placenta formation because mild OS is required to stimulate trophoblast proliferation, invasion and migration. Eliminating trophoblastic OS during early pregnancy may lead to compromised placentation and a risk of diseases of placental origin. Therefore, antioxidant therapy for pregnant women should be considered carefully