Predicting the growth of glioblastoma multiforme spheroids using a multiphase porous media model

Tumor spheroids constitute an effective in vitro tool to investigate the avascular stage of tumor growth. These three-dimensional cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. In the last years, new experimental techniques have been developed to determine the effect of mechanical stress on the growth of tumor spheroids. These studies report a reduction in cell proliferation as a function of increasingly applied stress on the surface of the spheroids. This work presents a specialization for tumor spheroid growth of a previous more general multiphase model. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the stress are formulated on the basis of experimental observations. A set of experiments is performed, investigating the growth of U-87MG spheroids both freely growing in the culture medium and subjected to an external mechanical pressure induced by a Dextran solution. The growth curves of the model are compared to the experimental data, with good agreement for both the experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is presented at the end of the paper. This new law is validated against experimental data and provides better results compared to other expressions in the literature.     

Towards optimum permeability reduction in porous media using biofilm growth simulations

While biological clogging of porous systems can be problematic in numerous processes (e.g., microbial enhanced oil recovery—MEOR), it is targeted during bio‐barrier formation to control sub‐surface pollution plumes in ground water. In this simulation study, constant pressure drop (CPD) and constant volumetric flow rate (CVF) operational modes for nutrient provision for biofilm growth in a porous system are considered with respect to optimum (minimum energy requirement for nutrient provision) permeability reduction for bio‐barrier applications. Biofilm growth is simulated using a Lattice‐Boltzmann (LB) simulation platform complemented with an individual‐based biofilm model (IbM). A biomass detachment technique has been included using a fast marching level set (FMLS) method that models the propagation of the biofilm–liquid interface with a speed proportional to the adjacent velocity shear field. The porous medium permeability reduction is simulated for both operational modes using a range of biofilm strengths. For stronger biofilms, less biomass deposition and energy input are required to reduce the system permeability during CPD operation, whereas CVF is more efficient at reducing the permeability of systems containing weaker biofilms. Biotechnol. Bioeng. 2009;103: 767–779. © 2009 Wiley Periodicals, Inc.     

Kinetic investigation of microbial souring in porous media using microbial consortia from oil reservoirs

Microbial souring (H2S production) in porous media was investigated in an anaerobic upflow porous media reactor at 60 degrees C using microbial consortia obtained from oil reservoirs. Multiple carbon sources (formate, acetate, propionate, iso- and n-butyrates) found in reservoir waters as well as sulfate as the electron acceptor was used. Kinetics and rates of souring in the reactor system were analyzed. Higher volumetric substrate consumption rates (organic acids and sulfate) and a higher volumetric H(2)S production rate were found at the from part of the reactor column after H(2)S production had stabilized. Concentration gradients for the substrates (organic acids and sulfate) and H(2)S were generated along the column. Biomass accumulation throughout the entire column was observed. The average specific sulfate reduction rate (H(2)S production rate) in the present reactor after H(2)S production had stabilized was calculated to be 11062 +/-2.22 mg sulfate-S/day g biomass. (c) 1994 John Wiley & Sons, Inc.     

Insulin adsorption into porous charged membranes: Effect of the electrostatic interaction

Insulin adsorption into a series of porous charged membranes was investigated by batch adsorption experiments, and the experimental results were analyzed by the homogeneous diffusion model. The membranes used in this study were prepared by pore‐surface modification of porous poly(acrylonitrile) (PAN) membranes by grafting with weak acidic and basic functional groups. The amount of insulin adsorbed into the membrane was determined from the material balance of insulin. The insulin partition coefficient K between the membrane and solution was estimated from the equilibrium adsorption amount, and the effective diffusion coefficient D was estimated by matching the model with the experimental data as a fitting parameter. The dependence of K and D on the charge properties of the insulin and membrane is observed and discussed. The partition coefficient K increased when the insulin and the membrane carried opposite charges, on the other hand, the effective diffusion coefficient D was reduced. These results indicate that the electrostatic interaction between the insulin and the membranes played an important role in the insulin adsorption. © 2009 American Institute of Chemical Engineers Biotechnol. Prog. 2009     

Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory

This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue (phase), together with the physical stresses in each component. The theory requires constitutive relations to specify the material properties of each phase, and also requires relations to specify the stresses developed due to mechanical interactions, both within each phase and between different phases. An application of the theory is given to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. Stability analysis techniques show that the interplay of the forces between the tissue constituents results in two different regimes: either the cells form aggregates or disperse through the scaffold.     

A method for obtaining equilibrium tautomeric mixtures of reducing sugars via glycosylamines using nonaqueous media

Equilibrium tautomeric mixtures of several mono- and disaccharides are obtained in anhydrous form, without the use of water, by reacting the commercially available reducing sugars with ammonia gas in dry methanol, followed by the concentration of the resultant solution to dryness. Mutarotation and hydrolysis of the initially formed glycosylamine in the resultant medium account for the transformation. Equilibrium anomeric mixtures enriched in the beta-form of commercially available sugars such as alpha-D-glucose and alpha-lactose have not only vastly increased solubility, but are also synthetically valuable as these can be readily converted to the methyl/benzyl/trimethylsilyl ether and other derivatives for further transformations.     

Chemotactic migration of bacteria in porous media

Chemotactic migration of bacteria—their ability to direct multicellular motion along chemical gradients—is central to processes in agriculture, the environment, and medicine. However, current understanding of migration is based on studies performed in bulk liquid, despite the fact that many bacteria inhabit tight porous media such as soils, sediments, and biological gels. Here, we directly visualize the chemotactic migration of Escherichia coli populations in well-defined 3D porous media in the absence of any other imposed external forcing (e.g., flow). We find that pore-scale confinement is a strong regulator of migration. Strikingly, cells use a different primary mechanism to direct their motion in confinement than in bulk liquid. Furthermore, confinement markedly alters the dynamics and morphology of the migrating population—features that can be described by a continuum model, but only when standard motility parameters are substantially altered from their bulk liquid values to reflect the influence of pore-scale confinement. Our work thus provides a framework to predict and control the migration of bacteria, and active matter in general, in complex environments.     

Markedly improving Novozym 435-mediated regioselective acylation of 1-beta-D-arabinofuranosylcytosine by using co-solvent mixtures as the reaction media

A comparative study was made of Novozym 435-catalyzed regioselective acylation of 1-beta-D-arabinofuranosylcytosine with vinyl propionate for the preparation of the 5'-O-monoester in eleven co-solvent mixtures and three pure polar solvents. Novozym 435 displayed low or no acylation activity toward 1-beta-D-arabinofuranosylcytosine in pure polar solvents, although those solvents can dissolve the nucleosides well. When a hexane-pyridine co-solvent system was adopted, both the initial rate and the substrate conversion were enhanced markedly. The polarity of co-solvent mixtures had significant effect on the reaction. Among the solvent mixtures investigated, the higher the polarity of the solvent mixture, the lower the initial reaction rate and the substrate conversion. It was also found that the acylation was dependent on the hydrophobic solvent content, the water activity and the reaction temperature. The most suitable co-solvent, initial water activity, and reaction temperature were hexane-pyridine (28:72, v/v), 0.07, and 50 degrees C, respectively. Under these conditions, the initial rate, the substrate conversion and the regioselectivity were as high as 91.1 mM h(-1), >97% and >98%, respectively, after a reaction time of 6 h. Among the reaction mediums examined, the lowest apparent activation energy was achieved with hexane-pyridine (28:72, v/v), in which Novozym 435 also exhibited good thermal stability.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

Non-destructive analysis of root growth in porous media

A technique is described for non-destructive observations and analysis of root growth in granular media, using time-lapse video in conjunction with a pressure cell. The pressure cell consists of one half of a traditional triaxial cell with a flat clear perspex front allowing growth of the root to be monitored using a video camera. The cell is connected to an external pressure supply, which is used to regulate precisely the confining pressure, and hence, the physical impedance to root growth. Preliminary results of the growth of root axes and the emergence of laterals of peas over a range of physical impedances are presented to illustrate the potential of this technique in studying root growth.     

Effect of temperature on adsorption of mixtures in porous materials

The effect of temperature on the adsorption of a simple mixture (Ar/Kr) in disordered porous materials is investigated by means of molecular simulation. In the larger mesopores of porous silica glasses, capillary condensation occurs upon decreasing the temperature. At temperatures above the capillary condensation temperature, Kr is preferentially adsorbed at the pore surface and Ar adsorption occurs in regions of low Kr density. For temperatures below the capillary condensation temperature, Ar density surprisingly increases as temperature increases, the behaviour that is consistent with an over-solubility effect. In contrast, in the disordered sub-nanoporous carbon, filling of the pores occurs in a reversible and continuous way upon decreasing the temperature, owing to the small size and amorphous shape of the pores. These results show that the crossover between capillary condensation and continuous reversible filling observed for pure fluids in pores also exists for mixtures. We also show that the Kr selectivity exhibits a minimum in the disordered porous silica that is located at the capillary condensation temperature. In contrast, in the disordered porous carbon where no capillary condensation occurs, the selectivity decreases monotonically with increasing the temperature. These results shed light on low-temperature adsorption of mixtures confined in porous materials and provide a guide to design efficient phase separation processes.     

DC-ELF characterization of random mixtures of piecewise nonlinear media

Biological tissues are ensembles of linear and nonlinear, symmetric and asymmetric constituents. As far as their electromagnetic characterization is concerned, they can be modeled as microscopic mixtures of the corresponding material media. Any medium volume can be properly discretized in a finite number of cells which can be modeled as an equivalent three dimensional network of lumped components, in order to characterize its electromagnetic behavior at wavelengths much longer than the relevant average linear size of the constitutive cells. Therefore, any mixture and the corresponding tissue can be characterized in terms of its effective conductance at extremely low frequency, with respect to a reference set of electrodes (ports of the equivalent network). When the above procedure is implemented for evaluating any of the aforesaid conductances, a resulting nonlinear characteristic should be expected. In reality, it may happen that the effect of the constitutive nonlinearities and the related asymmetries are smeared out by the randomness of the interconnections of the lumped components, leading at a macroscopic level to an isotropic constant equivalent conductance, i.e., to an isotropic constant equivalent conductivity of the mixture. The closed form analysis of a random network of nonlinear (piecewise linear) resistors offers a simple but clear cut example of such a property. This result, if extrapolated to biological media, suggests a new hint for explaining why there is no inconsistency between the typical electric characterization of biological tissues as almost linear macroscopic media, by means of their effective conductivity and permittivity, and the nonlinearities of the biochemical processes occurring in the tissue cells. In fact, the nonlinearities may not be observable by means of macroscopic electrical measurements because of the randomized spatial orientation and location of the processes.     

Conductance of porous media depends on external electric fields

In obstacle-filled media, such as extracellular or intracellular lumen of brain tissue, effective ion-diffusion permeability is a key determinant of electrogenic reactions. Although this diffusion permeability is thought to depend entirely on structural features of the medium, such as porosity and tortuosity, brain tissue shows prominent nonohmic properties, the origins of which remain poorly understood. Here, we explore Monte Carlo simulations of ion diffusion in a space filled with overlapping spheres to predict that diffusion permeability of such media decreases with stronger external electric fields. This dependence increases with lower medium porosity while decreasing with radial (two-dimensional or three-dimensional) compared with homogenous (one-dimensional) fields. We test our predictions empirically in an electrolyte chamber filled with microscopic glass spheres and find good correspondence with our predictions. A theoretical insight relates this phenomenon to a disproportionately increased dwell time of diffusing ions at potential barriers (or traps) representing geometric obstacles when the field strength increases. The dependence of medium ion-diffusion permeability on electric field could be important for understanding conductivity properties of porous materials, in particular for the accurate interpretation of electric activity recordings in brain tissue.     

Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric—a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.     

多孔介质中的微生物迁移行为与影响因素研究进展

微生物在地下水和土壤环境中的迁移与地下水资源保护、地下水污染修复及土壤污染防治等息息相关。自然界中多孔介质具有结构复杂性和空间异质性。这导致微生物在其中的迁移易受多重环境因素的影响。本文总结了几种典型多孔介质中微生物迁移模型、理论与研究方法,并对多孔介质中影响微生物迁移行为的3种因素——物理、化学和生物因素进行了梳理。其中物理因素的影响主要包括多孔介质的粒径、表面粗糙度、饱和度、环境温度、水体流速等相关;化学因素主要包含流体pH、离子种类与强度、可溶性有机物含量、多孔介质自身化学性质等;生物因素不但涉及微生物种类、细胞大小和细胞表面特性,还与胞外聚合物的分泌、鞭毛运动及趋化性等相关。本综述旨在总结近年来有关微生物在多孔介质中迁移的相关研究,深入理解微生物在多孔介质中的迁移行为,为其在地下水和土壤污染修复中的实际应用提供理论依据。     

Numerical study of hemodynamics in brain aneurysms treated with flow diverter stents using porous medium theory

Conventional approaches of implementing computational fluid dynamics to study aneurysmal hemodynamics after treatment with a flow diverter stent are computationally expensive. Cumbersome meshing and lengthy simulation runtimes are common. To address these issues, we present a novel volume penalization method that considers flow diverters as heterogeneous porous media. The proposed model requires a considerably smaller number of mesh elements, leading to faster simulation runtimes. Three patient-specific aneurysms were virtually treated with flow diverters and aneurysmal hemodynamics were simulated. The results of the virtual deployments including aneurysmal hemodynamics were compared to corresponding results from conventional approaches. The comparisons showed that the proposed approach led to 9.12 times increase in the speed of simulations on average. Further, aneurysmal kinetic energy and inflow rate metrics for the proposed approach were consistent with those from conventional approaches, differing on average by 3.52% and 3.78%, respectively.     

Estimating the species accumulation curve using mixtures

As a significant tool in ecological studies, the species accumulation curve or the collector's curve is the graph of the expected number of detected species as a function of sampling effort. The problem of estimating the species accumulation curve based on an empirical data set arising from quadrat sampling is studied in a nonparametric binomial mixture model. It will be shown that estimating the species accumulation curve not only is independent of the unknown number of species but also includes estimating the number of species as a limiting case. For the purpose of interpolation, moment-based estimators, associated with asymptotic confidence intervals, are developed from several points of view. A likelihood-based procedure is developed for the purpose of extrapolation, associated with bootstrap confidence intervals. The proposed methods are illustrated by ecological data sets.