Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Close packed transitions in slit-shaped pores: Density functional theory study of methane adsorption capacity in carbon

An important feature of improving lattice gas models and classical isotherms is the incorporation of a pore size dependent capacity, which has hitherto been overlooked. In this paper, we develop a model for predicting the temperature dependent variation in capacity with pore size. The model is based on the analysis of a lattice gas model using a density functional theory approach at the close packed limit. Fluid-fluid and solid-fluid interactions are modeled by the Lennard-Jones 12-6 potential and Steele's 10-4-3, potential respectively. The capacity of methane in a slit-shaped carbon pore is calculated from the characteristic parameters of the unit cell, which are extracted by minimizing the grand potential of the unit cell. The capacities predicted by the proposed model are in good agreement with those obtained from grand canonical Monte Carlo simulation, for pores that can accommodate up to three adsorbed layers. Single particle and pair distributions exhibit characteristic features that correspond to the sequence of buckling and rhombic transitions that occur as the slit pore width is increased. The model provides a useful tool to model continuous variation in the microstructure of an adsorbed phase, namely buckling and rhombic transitions, with increasing pore width. (C) 2002 American Institute of Physics.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

Development of a generic crop model template in the cropping system model APSIM

The Agricultural Production Systems slMulator, APSIM, is a cropping system modelling environment that simulates the dynamics of soil-plant-management interactions within a single crop or a cropping system. Adaptation of previously developed crop models has resulted in multiple crop modules in APSIM, which have low scientific transparency and code efficiency. A generic crop model template (GCROP) has been developed to capture unifying physiological principles across crops (plant types) and to provide modular and efficient code for crop modelling. It comprises a standard crop interface to the APSIM engine, a generic crop model structure, a crop process library, and well-structured crop parameter files. The process library contains the major science underpinning the crop models and incorporates generic routines based on physiological principles for growth and development processes that are common across crops. It allows APSIM to simulate different crops using the same set of computer code. The generic model structure and parameter files provide an easy way to test, modify, exchange and compare modelling approaches at process level without necessitating changes in the code. The standard interface generalises the model inputs and outputs, and utilises a standard protocol to communicate with other APSIM modules through the APSIM engine. The crop template serves as a convenient means to test new insights and compare approaches to component modelling, while maintaining a focus on predictive capability. This paper describes and discusses the scientific basis, the design, implementation and future development of the crop template in APSIM. On this basis, we argue that the combination of good software engineering with sound crop science can enhance the rate of advance in crop modelling. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Polyethylene flow prediction with a differential multi-mode Pom-Pom model

We report the first steps of a collaborative project between the University of Queensland, Polyflow, Michelin, SK Chemicals, and RMIT University; on simulation, validation and application of a recently introduced constitutive model designed to describe branched polymers. Whereas much progress has been made on predicting the complex flow behaviour of many - in particular linear - polymers, it sometimes appears difficult to predict simultaneously shear thinning and extensional strain hardening behaviour using traditional constitutive models. Recently a new viscoelastic model based on molecular topology, was proposed by McLeish and Larson (1998). We explore the predictive power of a differential multi-mode version of the pom-pom model for the flow behaviour of two commercial polymer melts: a (long-chain branched) low-density polyethylene (LDPE) and a (linear) high-density polyethylene (HDPE). The model responses are compared to elongational recovery experiments published by Langouche and Debbaut (1999), and start-up of simple shear flow, stress relaxation after simple and reverse step strain experiments carried out in our laboratory.

Application of the Williams-Landel-Ferry model to the viscosity-temperature relationship of Australian honeys

The rheological behaviour of nine unprocessed Australian honeys was investigated for the applicability of the Williams-Landel-Ferry (WLF) model. The viscosity of the honeys was obtained over a range of shear rates (0.01-40 s(-1)) from 2degrees to 40 degreesC, and all the honeys exhibited Newtonian behaviour with viscosity reducing as the temperature was increased. The honeys with high moisture were of lower viscosity, The glass transition temperatures of the honeys, as measured with a differential scanning calorimeter (DSC), ranged from -40degrees to -46 degreesC, and four models (WLF. Arrhenius, Vogel-Tammann-Fulcher (VTF), and power-law) were investigated to describe the temperature dependence of the viscosity. The WLF was the most suitable and the correlation coefficient averaged 0.999 +/- 0.0013 as against 0.996 +/- 0.0042 for the Arrhenius model while the mean relative deviation modulus was 0-12% for the WLF model and 10-40% for the Arrhenius one. With the universal values for the WLF constants, the temperature dependence of the viscosity was badly predicted. From non-linear regression analysis, the constants of the WLF models for the honeys were obtained (C-1 = 13.7-21.1: C-2 = 55.9-118.7) and are different from the universal values. These WLF constants will be valuable for adequate modeling of the rheology of the honeys, and they can be used to assess the temperature sensitivity of the honeys. (C) 2002 Elsevier Science Ltd. All rights reserved.

MR image-based measurement of rates of change in volumes of brain structures. Part 1: Method and validation

A detailed analysis procedure is described for evaluating rates of volumetric change in brain structures based on structural magnetic resonance (MR) images. In this procedure, a series of image processing tools have been employed to address the problems encountered in measuring rates of change based on structural MR images. These tools include an algorithm for intensity non-uniforniity correction, a robust algorithm for three-dimensional image registration with sub-voxel precision and an algorithm for brain tissue segmentation. However, a unique feature in the procedure is the use of a fractional volume model that has been developed to provide a quantitative measure for the partial volume effect. With this model, the fractional constituent tissue volumes are evaluated for voxels at the tissue boundary that manifest partial volume effect, thus allowing tissue boundaries be defined at a sub-voxel level and in an automated fashion. Validation studies are presented on key algorithms including segmentation and registration. An overall assessment of the method is provided through the evaluation of the rates of brain atrophy in a group of normal elderly subjects for which the rate of brain atrophy due to normal aging is predictably small. An application of the method is given in Part 11 where the rates of brain atrophy in various brain regions are studied in relation to normal aging and Alzheimer's disease. (C) 2002 Elsevier Science Inc. All rights reserved.

Mixed gas equilibrium adsorption on zeolites and energetic heterogeneity of adsorption volume

A model for binary mixture adsorption accounting for energetic heterogeneity and intermolecular interactions is proposed in this paper. The model is based on statistical thermodynamics, and it is able to describe molecular rearrangement of a mixture in a nonuniform adsorption field inside a cavity. The Helmholtz free energy obtained in the framework of this approach has upper and lower limits, which define a permissible range in which all possible solutions will be found. One limit corresponds to a completely chaotic distribution of molecules within a cavity, while the other corresponds to a maximum ordered molecular structure. Comparison of the nearly ideal O-2-N-2-zeolite NaX system at ambient temperature with the system Of O-2-N-2-zeolite CaX at 144 K has shown that a decrease of temperature leads to a molecular rearrangement in the cavity volume, which results from the difference in the fluid-solid interactions. The model is able to describe this behavior and therefore allows predicting mixture adsorption more accurately compared to those assuming energetic uniformity of the adsorption volume. Another feature of the model is its ability to correctly describe the negative deviations from Raoult's law exhibited by the O-2-N-2-CaX system at 144 K. Analysis of the highly nonideal CO2-C2H6-zeolite NaX system has shown that the spatial molecular rearrangement in separate cavities is induced by not only the ion-quadrupole interaction of the CO2 molecule but also the significant difference in molecular size and the difference between the intermolecular interactions of molecules of the same species and those of molecules of different species. This leads to the highly ordered structure of this system.

Distribution kinetics of solutes in the isolated in-situ perfused rat head using the multiple indicator dilution technique and a physiological two-barrier model

The purpose of this study was to determine the pharmacokinetics of [C-14]diclofenac, [C-14]salicylate and [H-3]clonidine using a single pass rat head perfusion preparation. The head was perfused with 3-[N-morpholino] propane-sulfonic acid-buffered Ringer's solution. Tc-99m-red blood cells and a drug were injected in a bolus into the internal carotid artery and collected from the posterior facial vein over 28 min. A two-barrier stochastic organ model was used to estimate the statistical moments of the solutes. Plasma, interstitial and cellular distribution volumes for the solutes ranged from 1.0 mL (diclofenac) to 1.6 mL (salicylate), 2.0 mL (diclofenac) to 4.2 mL (water) and 3.9 mL (salicylate) to 20.9 mL (diclofenac), respectively. A comparison of these volumes to water indicated some exclusion of the drugs from the interstitial space and salicylate from the cellular space. Permeability-surface area (PS) products calculated from plasma to interstitial fluid permeation clearances (CLPI) (range 0.02-0.40 mL s(-1)) and fractions of solute unbound in the perfusate were in the order: diclofenac>salicylate >clonidine>sucrose (from 41.8 to 0.10 mL s(-1)). The slow efflux of diclofenac, compared with clonidine and salicylate, may be related to its low average unbound fraction in the cells. This work accounts for the tail of disposition curves in describing pharmacokinetics in the head.

Cyclosporin A pretreatment in a rat model of warm ischaemia/reperfusion injury

Background/Aims: These studies investigated the role of apoptosis following ischaemia/reperfusion (I/R) injury to the liver and the effect of pretreatment with Cyclosporin A. Methods: Male Sprague-Dawley rats received 30 min of warm ischaemia followed by a period of reperfusion of 6 h. Rats were given olive oil or Cyclosporin A (30 mg/kg p.o.) the day before surgery. Neutrophil numbers were assessed in haematoxylin-eosin-stained sections of liver. In situ staining of sections using TdT-mediated dUTP-fluoreseein nick-end labelling was carried out to determine the extent of apoptosis, followed by electron microscopy. Semi-quantitative polymerase chain reaction (PCR) analysis of the transcript for Fas antigen was performed. Results and Conclusions: High levels of apoptosis were observed in I/R injury, which were greatly ameliorated in Cyclosporin A-pretreated groups. PCR analysis indicated a reduction in the level of expression of Fas transcript in Cyclosporin A-treated rats. Histological analysis showed a significant increase in the number of neutrophils infiltrating I/R-injured tissue (62 +/- 10.69, it = 16), which was markedly reduced by Cyclosporin A pretreatment (16 +/- 7, n = 6, P < 0.05). These results indicate a role of parenchymal apoptosis in the pathogenesis of I/R injury, which occurs in association with neutrophil infiltration, both of which can be significantly reduced by Cyclosporin A pretreatment. (C) 2002 European Association for the Study of the Liver. Published by Elsevier Science B.V. All rights reserved.

The E(NK) model: extending the NK model to incorporate gene-by-environment interactions and epistasis for diploid genomes

The haploid NK model developed by Kauffman can be extended to diploid genomes and to incorporate gene-by-environment interaction effects in combination with epistasis. To provide the flexibility to include a wide range of forms of gene-by-environment interactions, a target population of environment types (TPE) is defined. The TPE consists of a set of E different environment types, each with their own frequency of occurrence. Each environment type conditions a different NK gene network structure or series of gene effects for a given network structure, providing the framework for defining gene-by-environment interactions. Thus, different NK models can be partially or completely nested within the E environment types of a TPE, giving rise to the E(NK) model for a biological system. With this model it is possible to examine how populations of genotypes evolve in context with properties of the environment that influence the contributions of genes to the fitness values of genotypes. We are using the E(NK) model to investigate how both epistasis and gene-by-environment interactions influence the genetic improvement of quantitative traits by plant breeding strategies applied to agricultural systems. © 2002 Wiley Periodicals, Inc.

Simulation of the load-unload response ratio and critical sensitivity in the lattice solid model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.