Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

An optimized model for rat liver perfusion studies

Conditions which influence the viability, integrity, and extraction efficiency of the isolated perfused rat liver were examined to establish optimal conditions for subsequent work in reperfusion injury studies including the choice of buffer, use of oncotic agents, hematocrit, perfusion flow rate, and pressure. Rat livers were perfused with MOPS-buffered Ringer solution with or without erythrocytes. Perfusates were collected and analyzed for blood gases, electrolytes, enzymes, radioactivity in MID studies, and lignocaine in extraction studies. Liver tissue was sampled for histological examinations, and wet:dry weight of the liver was also determined. MOPS-buffered Ringer solution was found to be superior to Krebs bicarbonate buffer, in terms of pH control and buffering capacity, especially during any prolonged period of liver perfusion. A pH of 7.2 is chosen for perfusion since this is the physiological pH of the portal blood. The presence of albumin was important as an oncotic agent, particularly when erythrocytes were used in the perfusate. Perfusion pressure, resistance, and vascular volume are how-dependent and the inclusion of erythrocytes in the perfusate substantially altered the flow characteristics for perfusion pressure and resistance but not vascular volume. Lignocaine extraction was relatively flow-independent. Perfusion injury as defined by enzyme release and tissue fine structure was closely related to the supply of O-2. The optimal conditions for liver perfusion depend upon an adequate supply of oxygen. This can be achieved by using either erythrocyte-free perfusate at a how rate greater than 6 ml/min/g liver or a 20% erythrocyte-containing perfusate at 2 ml/min/g. (C) 1996 Academic Press, Inc.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Binding and internalization of the melanocyte stimulating hormone receptor ligand [Nle(4), D-Phe(7)]alpha-MSH in B16 melanoma cells

The current study aims to ascertain the fate of the melanocyte stimulating hormone (MSH) receptor and its ligand [Nle(4), D-Phe(7)]alpha-MsH (NDP-MSH) following binding to murine B16 melanoma cells. Cells were incubated with [I-125]-NDP-MSH for up to 180 min and binding, internalization and degradation determined. Intracellular trafficking of the radiolabel was assessed !using Percoll density gradient centrifugation of homogenized cells. Receptor down-regulation and receptor mRNA levels were also measured over 96 hr after exposure to 1 mu M ligand. NDP-MSH accumulation increased with time in a temperature-dependent manner and was inhibited by excess peptide. The ligand was rapidly internalized and translocated to the lysosomal compartment where it was degraded. Internalization was accompanied by a loss or down-regulation of cell surface receptors, suggesting internalization of the NDP-MSH-receptor complex. No recycling of the receptors between the plasma membrane and intracellular compartments could be detected in this cell-hue. Approximately 15% of the surface receptors were resistant to down-regulation, possibly indicating receptor heterogeneity. Down-regulation persisted ibr up to 96 hr and was accompanied by a decrease in MSH receptor mRNA levels 48 hr after treatment. However, before this time, transcript levels were the same in treated and control cells. In contrast to what was seen with NDP-MSH, cell surface receptors removed with trypsin wc:re rapidly replaced. These results show that NDP-MSH not only induced MSH receptor :internalization but also inhibited receptor turnover, resulting in a prolonged down-regulation. It is concluded that, in B16 cells, the MSH receptor undergoes ligand-dependent internalization, resulting in a prolonged down-regulation. Copyright (C) 1996 Elsevier Science Ltd

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Modelling of cold-formed purlin-sheeting systems .1. Full model

Purlin-sheeting systems used for roofs and walls commonly take the form of cold-formed channel or zed section purlins, screw-connected to corrugated sheeting. These purlin-sheeting systems have been the subject of numerous theoretical and experimental investigations over the past three decades, but the complexity of the systems has led to great difficulty in developing a sound and general model. This paper presents a non-linear elasto-plastic finite element model, capable of predicting the behaviour of purlin-sheeting systems without the need for either experimental input or over simplifying assumptions. The model incorporates both the sheeting and the purlin, and is able to account for cross-sectional distortion of the purlin, the flexural and membrane restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The validity of the model is shown by its good correlation with experimental results. A simplified version of this model, which is more suitable for use in a design environment, is presented in a companion paper. (C) 1997 Elsevier Science Ltd.

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

Isolated limb perfusion with melphalan for human melanoma xenografts in the hindlimb of nude rats: A surviving animal model

We have established a surviving model of isolated limb perfusion using xenografts of the human melanoma cell line MM 96L injected subcutaneously into the hindlimb of a nude rat, The femoral artery and vein were cannulated via the left renal artery and vein and the hind limb was isolated using tourniquets. The limb was perfused with Krebs Heinseleit buffer at 37 degrees C containing 4.7% bovine serum albumin at a constant flow rate of 4 mi per min for 30-60 min with 100% survival of the animals, Tumour vascularization and blood flow were demonstrated using vascular casts and [Cr-51]-microspheres. Following the addition of melphalan (15 or 100 mu g/ml), drug concentrations in the perfusate, tissues and systemic circulation were determined using high pressure liquid chromatography (HPLC), Systemic leakage, assessed using [I-125]albumin and melphalan and detected by a gamma-counter and HPLC respectively, was <0.5%. The melphalan concentration and tissue flow rate in the tumour deposits were 40 and 30% respectively, when compared with the surrounding subcutaneous tissue, At a dose of 15 mu g/ml, melphalan caused a reduction in tumour growth after 60 min perfusion, and a significant reduction in tumour size was seen when the melphalan dose was 100 mu g/ml. The surviving nude rat model of isolated limb perfusion for recurrent melanoma will allow examination of optimal perfusion conditions, along with the pharmacokinetics, pharmacodynamics and efficacy of melphalan and other drugs.

A continuum model for periodic two-dimensional block structures

A continuum model for regular block structures is derived by replacing the difference quotients of the discrete equations by corresponding differential quotients. The homogenization procedure leads to an anisotropic Cosserat Continuum. For elastic block interactions the dispersion relations of the discrete and the continuous models are derived and compared. Yield criteria for block tilting and sliding are formulated. An extension of the theory for large deformation is proposed. (C) 1997 by John Wiley & Sons, Ltd.

Melphalan dosing regimens for management of recurrent melanoma by isolated limb perfusion: Application of a physiological pharmacokinetic model based on melphalan distribution in the isolated perfused rat hindlimb

The optimal dosing schedule for melphalan therapy of recurrent malignant melanoma in isolated limb perfusions has been examined using a physiological pharmacokinetic model with data from isolated rat hindlimb perfusions (IRHP), The study included a comparison of melphalan distribution in IRHP under hyperthermia and normothermia conditions. Rat hindlimbs were perfused with Krebs-Henseleit buffer containing 4.7% bovine serum albumin at 37 or 41.5 degrees C at a flow rate of 4 ml/min. Concentrations of melphalan in perfusate and tissues were determined by high performance liquid chromatography with fluorescence detection, The concentration of melphalan in perfusate and tissues was linearly related to the input concentration. The rate and amount of melphalan uptake into the different tissues was higher at 41.5 degrees C than at 37 degrees C. A physiological pharmacokinetic model was validated from the tissue and perfusate time course of melphalan after melphalan perfusion. Application of the model involved the amount of melphalan exposure in the muscle, skin and fat in a recirculation system was related to the method of melphalan administration: single bolus > divided bolus > infusion, The peak concentration of melphalan in the perfusate was also related to the method of administration in the same order, Infusing the total dose of melphalan over 20 min during a 60 min perfusion optimized the exposure of tissues to melphalan whilst minimizing the peak perfusate concentration of melphalan. It is suggested that this method of melphalan administration may be preferable to other methods in terms of optimizing the efficacy of melphalan whilst minimizing the limb toxicity associated with its use in isolated limb perfusion.

A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

Interconnected-tubes model of hepatic elimination

The distributed-tubes model of hepatic elimination is extended to include intermixing between sinusoids, resulting in the formulation of a new, interconnected-tubes model. The new model is analysed for the simple case of two interconnected tubes, where an exact solution is obtained. For the case of many strongly-interconnected tubes, it is shown that a zeroth-order approximation leads to the convection-dispersion model. As a consequence the dispersion number is expressed, for the first time, in terms of its main physiological determinants: heterogeneity of flow and density of interconnections between sinusoids. The analysis of multiple indicator dilution data from a perfused liver preparation using the simplest version of the model yields the estimate 10.3 for the average number of interconnections. The problem of boundary conditions for the dispersion model is considered from the viewpoint that the dispersion-convection equation is a zeroth-order approximation to the equations for the interconnected-tubes model. (C) 1997 Academic Press Limited.

Crystal structure at 1.1 angstrom resolution of alpha-conotoxin PnIB: Comparison with alpha-conotoxins PnIA and GI

Conotoxins are small, cysteine-rich peptides isolated from the venom of Conus spp. of predatory marine snails, which selectively target specific receptors and ion channels critical to the functioning of the neuromuscular system. alpha-Conotoxins PnIA and PnIB are both 16-residue peptides (differing in sequence at only two positions) isolated from the molluscivorous snail Conus pennaceus. In contrast to the muscle-selective alpha-conotoxin GI from Conus geographus, PnIA and PnIB block the neuronal nicotinic acetylcholine receptor (nAChR). Here, we describe the crystal structure of PnIB, solved at a resolution of 1.1 Angstrom and phased using the Shake-and-Bake direct methods program. PnIB crystals are orthorhombic and belong to the space group P2(1)2(1)2(1) with the following unit cell dimensions: a = 14.6 Angstrom, b = 26.1 Angstrom, and c = 29.2 Angstrom. The final refined structure of alpha-conotoxin PnIB includes all 16 residues plus 23 solvent molecules and has an overall R-factor of 14.7% (R-free of 15.9%). The crystal structures of the alpha-conotoxins PnIB and PnIA are solved from different crystal forms, with different solvent contents. Comparison of the structures reveals them to be very similar, showing that the unique backbone and disulfide architecture is not strongly influenced by crystal lattice constraints or solvent interactions. This finding supports the notion that this structural scaffold is a rigid support for the presentation of important functional groups. The structures of PnIB and PnIA differ in their shape and surface charge distribution from that of GI.