An integrated mathematical model to evaluate nutrient partition in dairy cattle between the animal and its environment

In the past decade, a number of mechanistic, dynamic simulation models of several components of the dairy production system have become available. However their use has been limited due to the detailed technical knowledge and special software required to run them, and the lack of compatibility between models in predicting various metabolic processes in the animal. The first objective of the current study was to integrate the dynamic models of [Brit. J. Nutr. 72 (1994) 679] on rumen function, [J. Anim. Sci. 79 (2001) 1584] on methane production, [J. Anim. Sci. 80 (2002) 2481 on N partition, and a new model of P partition. The second objective was to construct a decision support system to analyse nutrient partition between animal and environment. The integrated model combines key environmental pollutants such as N, P and methane within a nutrient-based feed evaluation system. The model was run under different scenarios and the sensitivity of various parameters analysed. A comparison of predictions from the integrated model with the original simulation models showed an improvement in N excretion since the integrated model uses the dynamic model of [Brit. J. Nutr. 72 (1994) 6791 to predict microbial N, which was not represented in detail in the original model. The integrated model can be used to investigate the degree to which production and environmental objectives are antagonistic, and it may help to explain and understand the complex mechanisms involved at the ruminal and metabolic levels. A part of the integrated model outputs were the forms of N and P in excreta and methane, which can be used as indices of environmental pollution. (C) 2004 Elsevier B.V All rights reserved.

Revised QUICKI provides a strong surrogate estimate of insulin sensitivity when compared with the minimal model

OBJECTIVE: To compare insulin sensitivity (Si) from a frequently sampled intravenous glucose tolerance test (FSIGT) and subsequent minimal model analyses with surrogate measures of insulin sensitivity and resistance and to compare features of the metabolic syndrome between Caucasians and Indian Asians living in the UK. SUBJECTS: In all, 27 healthy male volunteers (14 UK Caucasians and 13 UK Indian Asians), with a mean age of 51.2 +/- 1.5 y, BMI of 25.8 +/- 0.6 kg/m(2) and Si of 2.85 +/- 0.37. MEASUREMENTS: Si was determined from an FSIGT with subsequent minimal model analysis. The concentrations of insulin, glucose and nonesterified fatty acids (NEFA) were analysed in fasting plasma and used to calculate surrogate measure of insulin sensitivity (quantitative insulin sensitivity check index (QUICKI), revised QUICKI) and resistance (homeostasis for insulin resistance (HOMA IR), fasting insulin resistance index (FIRI), Bennetts index, fasting insulin, insulin-to-glucose ratio). Plasma concentrations of triacylglycerol (TAG), total cholesterol, high density cholesterol, (HDL-C) and low density cholesterol, (LDL-C) were also measured in the fasted state. Anthropometric measurements were conducted to determine body-fat distribution. RESULTS: Correlation analysis identified the strongest relationship between Si and the revised QUICKI (r = 0.67; P = 0.000). Significant associations were also observed between Si and QUICKI (r = 0.51; P = 0.007), HOMA IR (r = -0.50; P = 0.009), FIRI and fasting insulin. The Indian Asian group had lower HDL-C (P = 0.001), a higher waist-hip ratio (P = 0.01) and were significantly less insulin sensitive (Si) than the Caucasian group (P = 0.02). CONCLUSION: The revised QUICKI demonstrated a statistically strong relationship with the minimal model. However, it was unable to differentiate between insulin-sensitive and -resistant groups in this study. Future larger studies in population groups with varying degrees of insulin sensitivity are recommended to investigate the general applicability of the revised QUICKI surrogate technique.

A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Multi‐method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi-method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL-2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model.

Mathematical model for NF-kappaB-driven proliferation of adult neural stem cells

Neural stem cells (NSCs) are early precursors of neuronal and glial cells. NSCs are capable of generating identical progeny through virtually unlimited numbers of cell divisions (cell proliferation), producing daughter cells committed to differentiation. Nuclear factor kappa B (NF-kappaB) is an inducible, ubiquitous transcription factor also expressed in neurones, glia and neural stem cells. Recently, several pieces of evidence have been provided for a central role of NF-kappaB in NSC proliferation control. Here, we propose a novel mathematical model for NF-kappaB-driven proliferation of NSCs. We have been able to reconstruct the molecular pathway of activation and inactivation of NF-kappaB and its influence on cell proliferation by a system of nonlinear ordinary differential equations. Then we use a combination of analytical and numerical techniques to study the model dynamics. The results obtained are illustrated by computer simulations and are, in general, in accordance with biological findings reported by several independent laboratories. The model is able to both explain and predict experimental data. Understanding of proliferation mechanisms in NSCs may provide a novel outlook in both potential use in therapeutic approaches, and basic research as well.

Multi-method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes

When studying hydrological processes with a numerical model, global sensitivity analysis (GSA) is essential if one is to understand the impact of model parameters and model formulation on results. However, different definitions of sensitivity can lead to a difference in the ranking of importance of the different model factors. Here we combine a fuzzy performance function with different methods of calculating global sensitivity to perform a multi-method global sensitivity analysis (MMGSA). We use an application of a finite element subsurface flow model (ESTEL-2D) on a flood inundation event on a floodplain of the River Severn to illustrate this new methodology. We demonstrate the utility of the method for model understanding and show how the prediction of state variables, such as Darcian velocity vectors, can be affected by such a MMGSA. This paper is a first attempt to use GSA with a numerically intensive hydrological model

Improvement and sensitivity analysis of thermal thin-ice thickness retrievals

Considering the sea ice decline in the Arctic during the last decades, polynyas are of high research interest since these features are core areas of new ice formation. The determination of ice formation requires accurate retrieval of polynya area and thin-ice thickness (TIT) distribution within the polynya.We use an established energy balance model to derive TITs with MODIS ice surface temperatures (Ts) and NCEP/DOE Reanalysis II in the Laptev Sea for two winter seasons. Improvements of the algorithm mainly concern the implementation of an iterative approach to calculate the atmospheric flux components taking the atmospheric stratification into account. Furthermore, a sensitivity study is performed to analyze the errors of the ice thickness. The results are the following: 1) 2-m air temperatures (Ta) and Ts have the highest impact on the retrieved ice thickness; 2) an overestimation of Ta yields smaller ice thickness errors as an underestimation of Ta; 3) NCEP Ta shows often a warm bias; and 4) the mean absolute error for ice thicknesses up to 20 cm is ±4.7 cm. Based on these results, we conclude that, despite the shortcomings of the NCEP data (coarse spatial resolution and no polynyas), this data set is appropriate in combination with MODIS Ts for the retrieval of TITs up to 20 cm in the Laptev Sea region. The TIT algorithm can be applied to other polynya regions and to past and future time periods. Our TIT product is a valuable data set for verification of other model and remote sensing ice thickness data.

A mathematical model of the in vitro keratinocyte response to chromium and nickel exposure

A mathematical model describing the main mechanistic processes involved in keratinocyte response to chromium and nickel has been developed and compared to experimental in vitro data. Accounting for the interactions between the metal ions and the keratinocytes, the law of mass action was used to generate ordinary differential equations which predict the time evolution and ion concentration dependency of keratinocyte viability, the amount of metal associated with the keratinocytes and the release of cytokines by the keratinocytes. Good agreement between model predictions and existing experimental data of these endpoints was observed, supporting the use of this model to explore physiochemical parameters that influence the toxicological response of keratinocytes to these two metals.

Understanding post-operative temperature drop in cardiac surgery: a mathematical model

A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central core containing the majority of organs, the rectal region containing the intestines and the outer peripheral region of skin and muscle. In particular, we focus on the issue of afterdrop: a drop in core temperature following patient re-warming, which can lead to serious post-operative complications. Model results for a typical cooling and re-warming procedure during surgery are in qualitative agreement with experimental data in producing the afterdrop effect and the observed dynamical variation in temperature between the core, rectal and peripheral regions. The influence of heat transfer processes and the volume of each compartmental region on the afterdrop effect is discussed. We find that excess fat on the peripheral and rectal regions leads to an increase in the afterdrop effect. Our model predicts that, by allowing constant re-warming after the core temperature has been raised, the afterdrop effect will be reduced.

Combined affinity labelling and mass spectrometry analysis of differential cell surface protein expression in normal and prostate cancer cells

Differences in the expression of cell surface proteins between a normal prostate epithelial (1542-NP2TX) and a prostate cancer cell line (1542-CP3TX) derived from the same patient were investigated. A combination of affinity chromatographic purification of biotin-tagged surface proteins with mass spectrometry analysis identified 26 integral membrane proteins and 14 peripheral surface proteins. The findings confirm earlier reports of altered expression in prostate cancer for several cell surface proteins, including ALCAM/CD166, the Ephrin type A receptor, EGFR and the prostaglandin F2 receptor regulatory protein. In addition, several novel findings of differential expression were made, including the voltage-dependent anion selective channel proteins Porin 1 and 2, ecto-5'-nucleotidase (CD73) and Scavenger receptor B1. Cell surface protein expression changed both qualitatively and quantitatively when the cells were grown in the presence of either or both interferon INFalpha and INFgamma. Costimulation with type I and II interferons had additive or synergistic effects on the membrane density of several, mainly peripherally attached surface proteins. Concerted upregulation of surface exposed antigens may be of benefit in immuno-adjuvant-based treatment of interferon-responsive prostate cancer. In conclusion, this study demonstrates that differences in the expression of membrane proteins between normal and prostate cancer cells are reproducibly detectable following vectorial labelling with biotin, and that detailed analysis of extracellular-induced surface changes can be achieved by combining surface-specific labelling with high-resolution two-dimensional gel electrophoresis and mass spectrometry.

Combined affinity labelling and mass spectrometry analysis of differential cell surface protein expression in normal and prostate cancer cells

Differences in the expression of cell surface proteins between a normal prostate epithelial (1542-NP2TX) and a prostate cancer cell line (1542-CP3TX) derived from the same patient were investigated. A combination of affinity chromatographic purification of biotin-tagged surface proteins with mass spectrometry analysis identified 26 integral membrane proteins and 14 peripheral surface proteins. The findings confirm earlier reports of altered expression in prostate cancer for several cell surface proteins, including ALCAM/CD166, the Ephrin type A receptor, EGFR and the prostaglandin F2 receptor regulatory protein. In addition, several novel findings of differential expression were made, including the voltage-dependent anion selective channel proteins Porin 1 and 2, ecto-5'-nucleotidase (CD73) and Scavenger receptor B1. Cell surface protein expression changed both qualitatively and quantitatively when the cells were grown in the presence of either or both interferon INF alpha and INF gamma. Costimulation with type I and II interferons had additive or synergistic effects on the membrane density of several, mainly peripherally attached surface proteins. Concerted upregulation of surface exposed antigens may be of benefit in immuno-adjuvant-based treatment of interferon-responsive prostate cancer. In conclusion, this study demonstrates that differences in the expression of membrane proteins between normal and prostate cancer cells are reproducibly detectable following vectorial labelling with biotin, and that detailed analysis of extracellular-induced surface changes can be achieved by combining surface-specific labelling with high-resolution two-dimensional gel electrophoresis and mass spectrometry.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Exchange rate pass-through to prices in macrodata: a comparative sensitivity analysis

This paper compares exchange rate pass-through to aggregate prices in the US, Germany and Japan across a number of dimensions. Building on the empirical approaches in the recent literature, our contribution is to perform a thorough sensitivity analysis of pass-through estimates. We find that the econometric method, data frequency and variable proxy employed matter for the precision of details, yet they often agree on some general trends. Thus, pass-through to import prices has declined in the 1990s relative to the 1980s, pass-through to export prices remains country-specific and pass-through to consumer prices is nowadays negligible in all three economies we considered.