Analysis of 'Investigating an extended multiphase flow model that includes specific interfacial area', Computer Methods in Applied Mechanics and Engineering, 418:116594, 2024

Comments are provided on the recent paper by Ebadi et al. [3], which demonstrates that the formulated model that was solved contains misconceptions or errors that render the work unsuitable for describing the evolution of interfacial areas in two-fluid porous medium systems. The need for kinematic equations is described and components of a theoretically consistent approach are summarized.

A continuum mechanical framework for modeling tumor growth and treatment in two- and three-phase systems

The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions

The thermodynamically constrained averaging theory (TCAT) is a comprehensive theory used to formulate hierarchies of multiphase, multiscale models that are closed based upon the second law of thermodynamics. The rate of entropy production is posed in terms of the product of fluxes and forces of dissipative processes. The attractive features of TCAT include consistency across disparate length scales; thermodynamic consistency across scales; the inclusion of interfaces and common curves as well as phases; the development of kinematic equations to provide closure relations for geometric extent measures; and a structured approach to model building. The elements of the TCAT approach are shown; the ways in which each of these attractive features emerge from the TCAT approach are illustrated; and a review of the hierarchies of models that have been formulated is provided. Because the TCAT approach is mathematically involved, we illustrate how this approach can be applied by leveraging existing components of the theory that can be applied to a wide range of applications. This can result in a substantial reduction in formulation effort compared to a complete derivation while yielding identical results. Lastly, we note the previous neglect of the deviation kinetic energy, which is not important in slow porous media flows, formulate the required equations to extend the theory, and comment on applications for which the new components would be especially useful. This work should serve to make TCAT more accessible for applications, thereby enabling higher fidelity models for applications such as turbulent multiphase flows.

Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems

Multiphase flows in porous medium systems are typically modeled at the macroscale by applying the principles of continuum mechanics to develop models that describe the behavior of averaged quantities, such as fluid pressure and saturation. These models require closure relations to produce solvable forms. One of these required closure relations is an expression relating the capillary pressure to fluid saturation and, in some cases, other topological invariants such as interfacial area and the Euler characteristic (or average Gaussian curvature). The forms that are used in traditional models, which typically consider only the relationship between capillary pressure and saturation, are hysteretic. An unresolved question is whether the inclusion of additional morphological and topological measures can lead to a nonhysteretic closure relation. Relying on the lattice Boltzmann (LB) method, we develop an approach to investigate equilibrium states for a two-fluid-phase porous medium system, which includes disconnected nonwetting phase features. A set of simulations are performed within a random close pack of 1964 spheres to produce a total of 42 908 distinct equilibrium configurations. This information is evaluated using generalized additive models to quantitatively assess the degree to which functional relationships can explain the behavior of the equilibrium data. The variance of various model estimates is computed, and we conclude that, except for the limiting behavior close to a single fluid regime, capillary pressure can be expressed as a deterministic and nonhysteretic function of fluid saturation, interfacial area between the fluid phases, and the Euler characteristic. To our knowledge, this work is unique in the methods employed, the size of the data set, the resolution in space and time, the true equilibrium nature of the data, the parametrizations investigated, and the broad set of functions examined. The conclusion of essentially nonhysteretic behavior provides support for an evolving class of two-fluid-phase flow in porous medium systems models.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot.

Averaging Theory for Description of Environmental Problems: What Have We Learned?

Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

Averaging Theory for Description of Environmental Problems: What Have We Learned?

Advances in Water Resources has been a prime archival source for implementation of averaging theories in changing the scale at which processes of importance in environmental modeling are described. Thus in celebration of the 35th year of this journal, it seems appropriate to assess what has been learned about these theories and about their utility in describing systems of interest. We review advances in understanding and use of averaging theories to describe porous medium flow and transport at the macroscale, an averaged scale that models spatial variability, and at the megascale, an integral scale that only considers time variation of system properties. We detail physical insights gained from the development and application of averaging theory for flow through porous medium systems and for the behavior of solids at the macroscale. We show the relationship between standard models that are typically applied and more rigorous models that are derived using modern averaging theory. We discuss how the results derived from averaging theory that are available can be built upon and applied broadly within the community. We highlight opportunities and needs that exist for collaborations among theorists, numerical analysts, and experimentalists to advance the new classes of models that have been derived. Lastly, we comment on averaging developments for rivers, estuaries, and watersheds.

A multiphase model for three-dimensional tumor growth

Several mathematical formulations have analyzed the time-dependent behaviour of a tumor mass. However, most of these propose simplifications that compromise the physical soundness of the model. Here, multiphase porous media mechanics is extended to model tumor evolution, using governing equations obtained via the Thermodynamically Constrained Averaging Theory (TCAT). A tumor mass is treated as a multiphase medium composed of an extracellular matrix (ECM); tumor cells (TC), which may become necrotic depending on the nutrient concentration and tumor phase pressure; healthy cells (HC); and an interstitial fluid (IF) for the transport of nutrients. The equations are solved by a Finite Element method to predict the growth rate of the tumor mass as a function of the initial tumor-to-healthy cell density ratio, nutrient concentration, mechanical strain, cell adhesion and geometry. Results are shown for three cases of practical biological interest such as multicellular tumor spheroids (MTS) and tumor cords. First, the model is validated by experimental data for time-dependent growth of an MTS in a culture medium. The tumor growth pattern follows a biphasic behaviour: initially, the rapidly growing tumor cells tend to saturate the volume available without any significant increase in overall tumor size; then, a classical Gompertzian pattern is observed for the MTS radius variation with time. A core with necrotic cells appears for tumor sizes larger than 150 μm, surrounded by a shell of viable tumor cells whose thickness stays almost constant with time. A formula to estimate the size of the necrotic core is proposed. In the second case, the MTS is confined within a healthy tissue. The growth rate is reduced, as compared to the first case - mostly due to the relative adhesion of the tumor and healthy cells to the ECM, and the less favourable transport of nutrients. In particular, for tumor cells adhering less avidly to the ECM, the healthy tissue is progressively displaced as the malignant mass grows, whereas tumor cell infiltration is predicted for the opposite condition. Interestingly, the infiltration potential of the tumor mass is mostly driven by the relative cell adhesion to the ECM. In the third case, a tumor cord model is analyzed where the malignant cells grow around microvessels in a 3D geometry. It is shown that tumor cells tend to migrate among adjacent vessels seeking new oxygen and nutrient. This model can predict and optimize the efficacy of anticancer therapeutic strategies. It can be further developed to answer questions on tumor biophysics, related to the effects of ECM stiffness and cell adhesion on tumor cell proliferation.

Tumor growth modeling from the perspective of multiphase porous media mechanics

Multiphase porous media mechanics is used for modeling tumor growth, using governing equations obtained via the thermodynamically constrained averaging theory (TCAT). This approach incorporates the interaction of more phases than legacy tumor growth models. The tumor is treated as a multiphase system composed of an extracellular matrix, tumor cells which may become necrotic depending on nutrient level and pressure, healthy cells and an interstitial fluid which transports nutrients. The governing equations are numerically solved within a Finite Element framework for predicting the growth rate of the tumor mass, and of its individual components, as a function of the initial tumor-to-healthy cell ratio, nutrient concentration, and mechanical strain. Preliminary results are shown.

TCAT Analysis of Capillary Pressure in Non-equilibrium, Two-fluid-phase, Porous Medium Systems

Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 8. Interface and Common Curve Dynamics

This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 8. Interface and Common Curve Dynamics

This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 7. Single-Phase Megascale Flow Models

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 4. Species Transport Fundamentals

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 4. Species Transport Fundamentals

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 4. Species Transport Fundamentals

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.

Dental caries trends in primary teeth among third-grade children in Harris County, Texas

PURPOSE

The purpose of this study was to assess trends in dental caries in the primary dentition of third-grade children in suburban Harris County, Texas.

METHODS

The study populations for the 2 cross-sectional surveys consisted of 1,584 third-grade children in 1991 and 1,039 in 1998. Trained dentists collected data on decayed and filled tooth surfaces (dfs). Chi-square tests analyzed the differences in proportions of children with and without dental caries experience in 1991 and 1998 by demographic subgroups: (1) gender; (2) ethnicity; and (3) socioeconomic status (SES). Student's t test investigated the differences in mean dfs scores in subgroups.

RESULTS

The prevalence of caries decreased significantly from 59% to 54% between 1991 and 1998 (P = .01). The caries prevalence was lower in 1998 than 1991 in certain subgroups: 1) females; 2) Caucasians; and 3) low SES. The mean dfs score decreased significantly from 4.81 to 3.16, and lower dfs scores were seen in certain demographic subgroups between the 2 studies (P < .05). Children from a low SES had high levels of untreated caries in both studies.

CONCLUSIONS

Despite a decline in primary teeth caries of study participants, intergroup disparities exist, emphasizing the need for preventive strategies, especially for the low SES children.

Examination of Darcys law for flow in porous media with variable porosity

Henry Darcy's experimental studies in 1856 of saturated water flowthrough a homogeneous porous medium contained in a vertical column have provided the basis for the quantitative description of fluid flow in a wide variety of both natural and engineered porous medium environmental systems. Extrapolation of Darcy's original observations and conclusions has led to several commonly applied equations used to model flow in porous media. This work examines this original experimental study, summarizes the appropriate mathematical expressions that ensue directly from the data, and indicates expressions in common use that are suggested, but not actually supported, by the data. The paradoxes that exist in the common approaches for the case of a porous medium with a spatiallyvariable porosity are illustrated. A modified form of Darcy's law, and also of the Hubbert potential, is derived based upon fundamental notions of averaging. The modified form of Darcy's law derived here reduces to the conventional form for a homogeneous porous medium.

Stability of a fluid–fluid interface in a biconical pore segment

Pore networks that include biconical pore segments are frequently used to model two-phase flow. In this work, we describe in detail the displacement of a fluid-fluid interface in such a pore segment. We assume sharp edges in the throat, inlet, and outlet of the pore segment to be the limiting cases of round edges, the radii of which vanish. We account for interfacial and lineal tensions that cause nonconstant contact angles. For zero lineal tension, we provide analytical solutions for flow induced by changing infinitesimally slowly either capillary pressure or the volume of one fluid. In diverging and converging cones, the common line among the two fluids and the solid phase slides while it is pinned in the throat, inlet, and outlet. We observe hysteresis within the pore segment, and drainage entry pressures deviate from prior work.

Thermodynamic fundamental equation of contact lines: selection of independent variables

In this work we review the development of the generalized theory of capillarity. When considering the theory of contact lines, we find that the theory developed by Boruvka and Neumann (BN) requires significant modifications. Their choice of parameters (independent variables) for a line is insufficient for formulating the fundamental equation. Furthermore, there are differential geometric constraints on these geometric parameters but not included in their analysis. As a result, their independent variables are in fact dependent. To describe the geometry of contact lines properly, we present a new set of parameters from the differential geometry viewpoint and subsequently give the fundamental equation for the thermodynamic system of contact lines.

Hydrogeological research: just getting started

This paper comments on the current state of knowledge in the field of hydrogeology and claims that fundamental understandings must be developed if creative research is to have maximum impact. Problems of great importance to society include water development and quality, waste disposal, and global cycling of resources. These problems cannot be addressed effectively unless significant advances are made in understanding of a range of challenging scientific issues including fundamental physics, the importance of scale, modeling, and chemical and biological processes. Meaningful advances in hydrogeologic research will require an increased emphasis on fundamental understanding, interdisciplinary approaches, educational reforms, and the attraction of excellent researchers to the field.

Bisphenol a binds to the low-affinity estrogen binding site

Environmental estrogens are suspected of being involved in the current increase in the incidence of human reproductive malfunctions, such as a decrease in male reproductive capacity and an increased incidence of breast cancer in women. The influences of these compounds have been proposed to be mediated through binding to macromolecules, such as estrogen receptor alpha or beta. In this study we examined whether the low-affinity Type II estrogen binding site (Type II EBS), originally identified in the rat uterus, is a possible mediator of environmental estrogens such as bisphenol A (BPA). Analysis of BPA's binding to an enriched fraction of Type II EBS, using a competition assay, indicated that BPA was able to compete with estradiol in binding to this site. At a concentration of 10-15 microM (comparable to that required to induce uterine proliferation), BPA inhibited the binding of estradiol to Type II EBS by greater than 50%. The binding affinity of BPA for the Type II EBS was only 8-10-fold lower than that of the synthetic estrogen diethylstilbestrol. The binding of BPA to Type II EBS appeared specific to BPA, in that endosulfan, another environmental estrogen, failed to displace estradiol from the site. A comparison of the relative binding affinities of BPA for rat uterine estrogen receptor alpha to that of the Type II EBS implies that BPA preferentially binds to the Type II EBS.

Comment on "Dynamics of wetting fronts in porous media"

A new method to model unsaturated flow in porous media was presented in Phys. Rev. E 58, R5245 (1998). We analyze the proposed approach and illustrate some significant shortcomings.

Estrogen receptor alpha requires no accessory factors for high-affinity binding to a consensus response element

Estrogen receptor (ER) alpha is commonly thought to bind to a consensus estrogen response element (ERE) as a homodimer, but previous experiments have not ruled out the presence of other proteins in the ERalpha/ERE complex. To characterize this interaction in more detail, we overexpressed mouse (m) ERalpha in a baculovirus system, using the selective advantage of the apoptosis inhibitor p35. Recombinant mERalpha possesses the predicted molecular weight and binds 17beta-estradiol and an oligonucleotide containing a consensus vitellogenin ERE with high affinity. Over a wide concentration range of mERalpha protein (0.1-50 nM), only one complex was detected between mERalpha and vitellogenin ERE in gel shift assays. The ratio of E2:vitellogenin ERE bound by mERalpha was close to 2:1, and each complex contained only one ERE. The molecular weight of the complex was determined to be 160 000, very close to that predicted for two mERalpha proteins and one ERE oligonucleotide, therefore providing strong evidence that no other proteins were present. Recombinant mERalpha was purified such that it was the only protein observable by silver stain. Purified mERalpha and mERalpha in a nuclear extract behaved identically in Ferguson analysis, providing more evidence that only mERalpha was binding to the ERE. Purified mERalpha bound vitellogenin ERE with high affinity (Kd = 0. 92 +/- 0.20 nM), indicating that no other proteins are necessary for high-affinity mERalpha interaction with a consensus ERE. To determine whether ERalpha in an estrogen-responsive mammalian tissue behaves the same as the overexpressed mERalpha, we tested rat uterine cytosol by Ferguson analysis. ERalpha in rat uterine cytosol behaved identically to overexpressed mERalpha, suggesting that ERalpha in the uterine extract also binds to DNA predominantly as a homodimer with no additional proteins.

Phytoestrogens act as estrogen agonists in an estrogen-responsive pituitary cell line

There is renewed interest in the medicinal value of natural plant products. One group of plant compounds, the phytoestrogens (PE), has been given considerable attention due to their ability to decrease the incidence of certain estrogen-dependent cancers. In this study, we evaluate the effects of PE on estrogen-dependent pituitary tumor cells by using the immortalized pituitary cell line PR1. Several PE were found to be active in PR1 cells, in that they bound to the estrogen receptor (ER), stimulated growth of PR1 cells, and induced an estrogenic response, prolactin secretion. The PE genistein, coumestrol, and zearalenone bound to the ER present in PR1 cells with an affinity 100-times lower than that of estradiol. However, resveratrol, a plant antitumor agent found in grapes, showed no significant binding to the ER. Zearalenone, coumestrol, and genistein were found to induce prolactin secretion and to stimulate growth, whereas resveratrol showed prolactin secretion but no growth stimulation. The estrogenic effects of PE in PR1 cells were ER dependent, in that addition of the antiestrogen ICI-182,780 inhibited prolactin response. Although resveratrol did not bind to the ER or stimulate growth, it induced prolactin secretion in both a dose- and time-dependent manner. The data presented here demonstrate that PE are active in lactotroph cells of the pituitary.

Identification and characterization of an estrogen-responsive element binding protein repressed by estradiol

Cytosolic proteins from uteri of 19-day-old rats were analyzed by an electrophoresis mobility shift assay (EMSA) using a 31 base pair DNA probe containing an estrogen-responsive element (ERE) from the vitellogenin A2 gene. EMSA identified three distinct cytosolic protein-DNA complexes that are separable by Q-Sepharose anion exchange chromatography into an estrogen receptor (ER)-containing fraction (150 mM NaCl eluate) and a non-ER-containing fraction (250 mM NaCl eluate). We thus refer to the non-ER fraction as the ERE binding protein (ERE-BP). The ERE-BP-containing fraction was repressed to 40-50% of its normal levels following a single injection of estradiol. In addition, ERE-BP levels were repressed to the same extent (greater than 50%) by day 20 of the rat's gestational period. Examination of the expression pattern of ERE-BP shows that this activity is differentially expressed in both estrogen-responsive and nonresponsive tissues, with the highest levels of expression occurring in the pituitary. We next examined the specificity of ERE-BP binding by competition analysis using DNA sequences corresponding to binding sites of several known transcription factors. ERE-BP was found to be specific for both the ER binding site (ERE) and TATA binding protein binding sites. Furthermore, saturation analysis demonstrated that ERE-BP binds to the ERE and TATA binding protein sequences with an apparent Kd of 1.2 and 0.12 nM, respectively. Partial purification of ERE-BP using three chromatography steps (Q-Sepharose, hydroxyapatite, and Sephacryl S300) followed by sodium dodecyl sulfate analysis indicated the presence of three major protein bands (p102, p81, and p48) as judged by Coomassie staining. UV cross-linking of the ERE-BP/DNA complex followed by sodium dodecyl sulfate analysis-polyacrylamide gel electrophoresis analysis indicates that the 48 kDa band seen in the final, partially purified fraction correlates with the ERE-BP activity. Thus, this study has identified a unique uterine cytosolic protein that binds to the ER binding site and may influence ER binding.

A low-affinity estrogen-binding site in pregnant rat uteri: analysis and partial purification

We have identified a low-affinity (type II) estrogen-binding site (EBS) that is expressed at high levels during pregnancy in rat uteri. Although this activity was detectable in nonpregnant rat uteri, it was present in amounts (0.094 pmol/g of uteri) that were severalfold lower than the high-affinity type I estrogen receptor (0.57 pmol/g of uteri). During pregnancy, at 19-20 days of gestation, the low-affinity type II EBS became the major (> or = 88%) estrogen-binding site in rat uteri. The increase in the level of low-affinity EBS (7.9 pmol/g) in uteri was approximately 85-fold with an approximately 20-fold increase in the specific activity (0.39 pmol/mg) of this form, whereas the high-affinity form remained relatively unchanged. We report here a method of purification of type II EBS from pregnant rat uteri and present an analysis of its DNA and steroid-binding properties. Estradiol-binding studies and Scatchard analysis showed that the type II EBS had an apparent estradiol-binding affinity of > or = 24 nM. Gel filtration and SDS/PAGE analysis indicated that the type II EBS was a monomeric 73-kDa protein. The estradiol binding remained apparently uninhibited in the presence of a large excess of tamoxifen, nafoxidine, or dihydrotestosterone. Estradiol, diethylstilbestrol, and quercitin (a type II EBS-specific inhibitor) competed efficiently. The purified low-affinity EBS did not have sequence-specific DNA-binding activity with the estrogen-responsive element, which indicated that it differs in function from the type I estrogen receptor.

A Numerical Model Study of Ground-Water Contamination from Price's Landfill, New Jersey - II. Sensitivity Analysis and Contaminant Plume Simulation

A numerical model of flow and transport in the vicinity of Price's Landfill and the Atlantic City public water-supply wells is used to estimate the extent of the existing contamination problem. Model parameters such as boundary conditions, pumping rates, permeability, and dispersivity are varied to demonstrate the sensitivity of the model to these quantities. A historical simulation of the past ten years of contamination is obtained and two schemes for remediation of the contamination problem are compared. In the light of this work, additional data requirements are revealed.

A Numerical Model Study of Ground-Water Contamination from Price's Landfill, New Jersey- I. Data Base and Flow Simulation

Toxic waste contamination is currently threatening the Atlantic City, New Jersey public water-supply wells. The geohydrologic data for this region are presented and organized into a format suitable for a numerical model study of the contamination problem. Presentation of the data in light of numerical work reveals the importance of good estimates of boundary conditions, historical pumping records, reliable water-quality data, accurate well logs, and reasonable parameter estimates. One set of measured head data is simulated.