Modelling the formation of necrotic regions in avascular tumours

The mechanisms underlying the formation of necrotic regions within avascular tumours are not well understood. In this paper, we examine the relative roles of nutrient deprivation and of cell death, from both the proliferating phase of the cell cycle via apoptosis and from the quiescent phase via necrosis, in changing the structure within multicellular tumour spheroids and particularly the accumulation of dead cell material in the centre. A mathematical model is presented and studied that accounts for nutrient diffusion, changes in cell cycling rates, the two different routes to cell death as well as active motion of cells and passive motion of the dead cell material. In studying the accumulation of dead cell matter we do not distinguish between the route by which each was formed. The resulting mathematical model is examined for a number of scenarios. Results show that in many cases the size of the necrotic core is closely correlated with low levels in nutrient concentration. However, in certain cases, particularly where the rate of necrosis is large, the resulting necrotic core can lead to regions of non-negligible nutrient concentration-dependent upon the mode of cell death.

Modelling the cabling of rope systems

This paper presents a theoretical model of the torsional characteristics of parallel multi-part rope systems. In such systems, the ropes may cable, or wrap around each other, depending on the combination of applied torque, rope tension, length and spacing between the rope parts. Cabling constitutes a failure that might be retrievable but as such can seriously affect the performance of the rope system. The torsional characteristics of the system are very different before and after cabling, and theoretical models are given for both situations. Laboratory tests were performed on both two and four rope systems, with measurements being made of torque at rotations from 0 to 360 deg. Tests were run with different rope spacings, tensions and lengths and the results compared with predictions from the theoretical model. The conclusion from the test results was that the theoretical model predicts both the pre- and post-cabling torsional behaviour with an acceptable level of accuracy.

Modelling the torsional interaction of wire and polyester fibre ropes used for offshore moorings

Oil rig mooring lines have traditionally consisted of chain and wire rope. As production has moved into deeper water it has proved advantageous to incorporate sections of fibre rope into the mooring lines. However, this has highlighted torsional interaction problems that can occur when ropes of different types are joined together. This paper describes a method by which the torsional properties of ropes can be modelled and can then be used to calculate the rotation and torque for two ropes connected in series. The method uses numerical representations of the torsional characteristics of both the ropes, and equates the torque generated in each rope under load to determine the rotation at the connection point. Data from rope torsional characterization tests have been analysed to derive constants used in the numerical model. Constants are presented for: a six-strand wire rope; a torque-balanced fibre rope; and a fibre rope that has been designed to be torque-matched to stranded wire rope. The calculation method has been verified by comparing predicted rotations with measured test values. Worked examples are given for a six-strand wire rope connected, firstly, to a torque-balanced fibre rope that offers little rotational restraint, and, secondly, to a fibre rope whose torsional properties are matched to that of the wire rope.

Modelling the uptake and growth kinetics of Penicillium glabrum in a tannic acid-containing solid-state fermentation for tannase production

A mathematical growth model for the batch solid-state fermentation process for fungal tannase production was developed and tested experimentally. The unstructured model describes the uptake and growth kinetics of Penicillium glabrum in an impregnated polyurethane foam substrate system. In general, good agreement between the experimental data and model simulations was obtained. Biomass, tannase and spore production are described by logistic kinetics with a time delay between biomass production and tannase and spore formation. Possible induction mechanisms for the latter are proposed. Hydrolysis of tannic acid, the main carbon source in the substrate system, is reasonably well described with Michaelis-Menten kinetics with time-varying enzyme concentration but a more complex reaction mechanism is suspected. The metabolism of gallic acid, a tannase-hydrolysis product of tannic acid, was shown to be growth limiting during the main growth phase. (c) 2004 Elsevier Ltd. All rights reserved.

Modelling the effect of fatty acids in odour development of cooked meat in vitro: part I - sensory perception

We have investigated the contribution of muscle components to the development of cooked meat odour in an aqueous model system using trained taste panels. Reaction mixtures were prepared with oleic, linoleic and linolenic acids with or without cysteine and ribose in a buffer with or without ferrous sulphate. Odour profiles were assessed and triangular tests were used to determine the ability of panellists to discriminate between mixtures. The presence of sugar and amino acid was highly detectable by panellists independently of the fatty acid considered (P < 0.001). However, the presence of C18:3 made differences. more obvious between mixtures than the presence of C18:1 or C18:2. `Meaty' notes were only associated with cysteine and ribose. `Fishy' notes were only apparent in C18:3 mixtures with or without sugar and amino acid, although the presence of cysteine and ribose decreased the perception. The addition of Fe+ +, a pro-oxidant present in the muscle, produced a reduction in the score of the attributes although the pattern was the same as when Fe was not used in the mixtures. Only `fishy' notes that were exclusively perceived in C18:3 mixtures showed a higher score in the presence of iron. Iron also produced a better discrimination in C18:3 mixtures, which were closely related to `grassy' notes in the presence of cysteine and ribose. (C) 2002 Published by Elsevier Science Ltd.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

Grey-box radial basis function modelling: the art of incorporating prior knowledge

A basic principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: the underlying data generating mechanism exhibits known symmetric property and the underlying process obeys a set of given boundary value constraints. The class of orthogonal least squares regression algorithms can readily be applied to construct parsimonious grey-box RBF models with enhanced generalisation capability.

Modelling the likely impact of healthy eating guidelines on agricultural production and land use in England and Wales

Quadratic programming techniques were applied to household food consumption data in England and Wales to estimate likely changes in diet under healthy eating guidelines, and the consequences this would have on agriculture and land use in England and Wales. The first step entailed imposing nutrient restrictions on food consumption following dietary recommendations suggested by the UK Department of Health. The resulting diet was used, in a second step as a proxy for demand in agricultural commodities, to test the impact of such a scenario on food production and land use in England and Wales and the impacts of this on agricultural landscapes. Results of the diet optimisation indicated a large drop in consumption of foods rich in saturated fats and sugar, essentially cheese and sugar-based products, along with lesser cuts of fat and meat products. Conversely, consumption of fruit and vegetables, cereals, and flour would increase to meet dietary fibre recommendations. Such a shift in demand would dramatically affect production patterns: the financial net margin of England and Wales agriculture would rise, due to increased production of high market value and high economic margin crops. Some regions would, however, be negatively affected, mostly those dependent on beef cattle and sheep production that could not benefit from an increased demand for cereals and horticultural crops. The effects of these changes would also be felt in upstream industries, such as animal feed suppliers. While arable dominated landscapes would be little affected, pastoral landscapes would suffer through loss of grazing management and, possibly, land abandonment, especially in upland areas.

Modelling the propagation of terahertz radiation through a tissue simulating phantom

Terahertz (THz) frequency radiation, 0.1 THz to 20 THz, is being investigated for biomedical imaging applications following the introduction of pulsed THz sources that produce picosecond pulses and function at room temperature. Owing to the broadband nature of the radiation, spectral and temporal information is available from radiation that has interacted with a sample; this information is exploited in the development of biomedical imaging tools and sensors. In this work, models to aid interpretation of broadband THz spectra were developed and evaluated. THz radiation lies on the boundary between regions best considered using a deterministic electromagnetic approach and those better analysed using a stochastic approach incorporating quantum mechanical effects, so two computational models to simulate the propagation of THz radiation in an absorbing medium were compared. The first was a thin film analysis and the second a stochastic Monte Carlo model. The Cole–Cole model was used to predict the variation with frequency of the physical properties of the sample and scattering was neglected. The two models were compared with measurements from a highly absorbing water-based phantom. The Monte Carlo model gave a prediction closer to experiment over 0.1 to 3 THz. Knowledge of the frequency-dependent physical properties, including the scattering characteristics, of the absorbing media is necessary. The thin film model is computationally simple to implement but is restricted by the geometry of the sample it can describe. The Monte Carlo framework, despite being initially more complex, provides greater flexibility to investigate more complicated sample geometries.

Two methods for modelling the propagation of terahertz radiation in a layered structure

Modelling the interaction of terahertz(THz) radiation with biological tissueposes many interesting problems. THzradiation is neither obviously described byan electric field distribution or anensemble of photons and biological tissueis an inhomogeneous medium with anelectronic permittivity that is bothspatially and frequency dependent making ita complex system to model.A three-layer system of parallel-sidedslabs has been used as the system throughwhich the passage of THz radiation has beensimulated. Two modelling approaches havebeen developed a thin film matrix model anda Monte Carlo model. The source data foreach of these methods, taken at the sametime as the data recorded to experimentallyverify them, was a THz spectrum that hadpassed though air only.Experimental verification of these twomodels was carried out using athree-layered in vitro phantom. Simulatedtransmission spectrum data was compared toexperimental transmission spectrum datafirst to determine and then to compare theaccuracy of the two methods. Goodagreement was found, with typical resultshaving a correlation coefficient of 0.90for the thin film matrix model and 0.78 forthe Monte Carlo model over the full THzspectrum. Further work is underway toimprove the models above 1 THz.

A three-regime model of speculative behaviour: modelling the evolution of the S&P 500 composite index

We examine whether a three-regime model that allows for dormant, explosive and collapsing speculative behaviour can explain the dynamics of the S&P 500. We extend existing models of speculative behaviour by including a third regime that allows a bubble to grow at a steady rate, and propose abnormal volume as an indicator of the probable time of bubble collapse. We also examine the financial usefulness of the three-regime model by studying a trading rule formed using inferences from it, whose use leads to higher Sharpe ratios and end of period wealth than from employing existing models or a buy-and-hold strategy.