Quantitative Mathematical Model Research Articles

A Risk Assessment Model for Importation of United States Milling Wheat Containing Tilletia contraversa.

Dwarf bunt of wheat, caused by the fungus Tilletia contraversa, is a pathogen historically limited in distribution by its very specific climatic requirements for establishment. In an effort to both address the need for adequate protection and eliminate unwarranted trade barriers, a number of countries have examined restrictions on importing milling wheat containing teliospores of T. contraversa. Pest risk analysis (PRA), under the guidelines of the World Trade Organization and Food and Agriculture Organization, has become an internationally accepted process for evaluating such issues. As a component of a dwarf bunt PRA, our objective was to develop a quantitative mathematical model to evaluate and communicate the potential risk of dwarf bunt establishment from the importation of U.S. milling wheat containing teliospores of T. contraversa. A T. contraversa–risk model (TCK-risk model) was developed using new data, historic literature, and industry statistics to estimate teliospore diversion from transport and milling processes, spore contamination levels, grain handling, and end-product usage. A climatic model was developed to identify potential regions where the environment was favorable for disease development. The likelihood of disease establishment and wheat yield loss was determined using the model to conduct Monte Carlo simulations of 100,000 wheat shipping-years. The model is dynamic in that individual components can be easily updated or modified in order to determine the effect of numerous scenarios (e.g., climate changes, shipping tonnage, contamination levels, mitigation strategies) on the probability of dwarf bunt establishment. TCK-risk model evaluation scenarios previously conducted for the People's Republic of China, Brazil, Mexico, and Peru are presented as examples.

Cellular signaling is potentially regulated by cell density in receptor trafficking networks

Previous work has shown that receptor trafficking is a potential site for the control of signaling pathways. In most biological experiments, the ligand concentration and cell density vary within a wide range among different systems. However, there is less attention to systematically analyze how much cellular signal response is affected by cell densities. Here, we use a quantitative mathematical model to investigate signal responses in different receptor trafficking networks by simultaneous variations of ligand concentration and cell density. Computational analysis of the model revealed that receptor trafficking networks have potential sigmoid responses to ratio between ligand and surface receptor number per cell, which is a key factor to control the signaling responses in receptor trafficking networks. Furthermore, cell density also affects the robustness of dose–response curve upon the variation of binding affinity.

Design of an integrated supplier selection and multi-echelon distribution inventory model in a built-to-order supply chain environment

The paper deals with the development of an integrated supplier selection and multi-echelon distribution inventory model (MEDIM) for the original equipment manufacturing company in a built-to-order supply chain environment using fuzzy analytical hierarchy process (FAHP) and a genetic algorithm. The main objective is to design the integrated qualitative decision-making of the supplier selection model using FAHP with that of the quantitative mathematical model for the distribution inventory supply chain using a genetic algorithm to the built-to-order environment. The proposed model is validated by considering the case study in a tyre industry in Southern India. The software used for programming is C++ language.

Scale and scalability

Scale and scalability

Investigation on silicon–glass electrostatic bonding time

To simulate the process of anodic bonding and lay foundation for the computer aided design (CAD) of anodic bonding, this paper presents an approach to study anodic bonding time. In order to describe the relationship of bonding time, bonding voltage, and temperature on the basis of experiments, the concept of critical bonding time is introduced, and the measuring method of critical time is given. Based on anodic bonding mechanism and the bonding experiments, the formula of the critical time is deduced. Experimental results show that the mean-root-square error from the formula is less than 5%. The formula concretely explains the relationship of bonding time, bonding voltage, and bonding temperature. Accordingly a quantitative mathematical model for the simulation of anodic bonding technology is proposed.

Quantitative model for anisotropy and reorientation thickness of the magnetic moment in thin epitaxially strained metal films

A quantitative mathematical model for the critical thickness of strained epitaxial metal films is presented, at which the magnetic moment experiences a reorientation from in-plane to perpendicular magnetic anisotropy. The model is based on the minimum of the magnetic anisotropy energy with respect to the orientation of the magnetic moment of the film. Magnetic anisotropy energies are taken as the sum of shape anisotropy, magnetocrystalline anisotropy and magnetoelastic anisotropy, the two latter ones being present as constant surface and variable volume contributions. Other than anisotropy materials constants, readily available from literature, only information about the strain in the films for the determination of the magnetoelastic anisotropy energy is required. Application of the epitaxial Bain path allows to express the strain in the film in terms of substrate lattice constant and film lattice parameter, and thus to obtain an approximate closed expression for the reorientation thickness in terms of lattice mismatch. The model can predict the critical spin reorientation transition thickness with surprising accuracy.

Model simulation of the patient flow through a screening centre for diabetic retinopathy

To construct a quantitative, flexible and simplified mathematical model of the patient flow through the Eye Clinic at the Steno Diabetes Centre (SDC) in order to enable rational dimensioning and assess the effects of modifications. Patient data were drawn from the Eye Care database at the SDC. A simple patient flow model was constructed, allowing simultaneous adjustments of all variables, and the model was tested. Two scenarios were simulated: (1) adjusting the algorithm that assigns the follow-up intervals, and (2) increasing the population size to include all patients with diabetes in Copenhagen County. The model can describe the patient flow under steady state conditions, but is less precise in predicting transient changes with the present set-up. Accordingly all simulations were run for a substantial number of iterations. The two scenarios illustrate the usefulness of the model by calculating the required photographic examination capacity for the specific population, thereby allowing better estimations of future dimensioning of the organization. The study presents a patient flow model that can be used to illustrate the effects of proposed changes prior to their implementation, specifically with respect to the capacity of the system.

Mathematical Frameworks for Modeling Listeria Cross‐contamination in Food‐

ABSTRACT: The possibility of modeling the cross‐contamination of Listeria species, total Listeria monocytogenes, or specific L. monocytogenes strains using a quantitative mathematical model using Monte Carlo simulation techniques is proposed. This article illustrates this approach using 2 different models: one that tracks L. monocytogenes number and prevalence for 4 different strains (Model I) and one that tracks only prevalence for a single strain (Model II). These models have been developed to provide a starting framework for predictive modelers and scientists studying L. monocytogenes to begin research together with the ultimate goal of understanding and controlling L. monocytogenes in food‐processing plants.

Kinetics of Factor X activation by the membrane-bound complex of Factor IXa and Factor VIIIa.

Intrinsic tenase consists of activated Factors IX (IXa) and VIII (VIIIa) assembled on a negatively charged phospholipid surface. In vivo, this surface is mainly provided by activated platelets. In vitro, phosphatidylcholine/phosphatidylserine vesicles are often used to mimic natural pro-coagulant membranes. In the present study, we developed a quantitative mathematical model of Factor X activation by intrinsic tenase. We considered two situations, when complex assembly occurs on either the membrane of phospholipid vesicles or the surface of activated platelets. On the basis of existing experimental evidence, the following mechanism for the complex assembly on activated platelets was suggested: (i) Factors IXa, VIIIa and X bind to their specific platelet receptors; (ii) bound factors form complexes on the membrane: platelet-bound Factor VIIIa provides a high-affinity site for Factor X and platelet-bound Factor IXa provides a high-affinity site for Factor VIIIa; (iii) the enzyme-cofactor-substrate complex is assembled. This mechanism allowed the explanation of co-operative effects in the binding of Factors IXa, VIIIa and X to platelets. The model was reduced to obtain a single equation for the Factor X activation rate as a function of concentrations of Factors IXa, VIIIa, X and phospholipids (or platelets). The equation had a Michaelis-Menten form, where apparent V(max) and K(m) were functions of the factors' concentrations and the internal kinetic constants of the system. The equation obtained can be used in both experimental studies of intrinsic tenase and mathematical modelling of the coagulation cascade. The approach of the present study can be applied to research of other membrane-dependent enzymic reactions.

Quantitative analyses of bifunctional molecules.

Small molecules can be discovered or engineered to bind tightly to biologically relevant proteins, and these molecules have proven to be powerful tools for both basic research and therapeutic applications. In many cases, detailed biophysical analyses of the intermolecular binding events are essential for improving the activity of the small molecules. These interactions can often be characterized as straightforward bimolecular binding events, and a variety of experimental and analytical techniques have been developed and refined to facilitate these analyses. Several investigators have recently synthesized heterodimeric molecules that are designed to bind simultaneously with two different proteins to form ternary complexes. These heterodimeric molecules often display compelling biological activity; however, they are difficult to characterize. The bimolecular interaction between one protein and the heterodimeric ligand (primary dissociation constant) can be determined by a number of methods. However, the interaction between that protein-ligand complex and the second protein (secondary dissociation constant) is more difficult to measure due to the noncovalent nature of the original protein-ligand complex. Consequently, these heterodimeric compounds are often characterized in terms of their activity, which is an experimentally dependent metric. We have developed a general quantitative mathematical model that can be used to measure both the primary (protein + ligand) and secondary (protein-ligand + protein) dissociation constants for heterodimeric small molecules. These values are largely independent of the experimental technique used and furthermore provide a direct measure of the thermodynamic stability of the ternary complexes that are formed. Fluorescence polarization and this model were used to characterize the heterodimeric molecule, SLFpYEEI, which binds to both FKBP12 and the Fyn SH2 domain, demonstrating that the model is useful for both predictive as well as ex post facto analytical applications.

Microdialysis of dopamine interpreted with quantitative model incorporating probe implantation trauma.

Although microdialysis is widely used to sample endogenous and exogenous substances in vivo, interpretation of the results obtained by this technique remains controversial. The goal of the present study was to examine recent criticism of microdialysis in the specific case of dopamine (DA) measurements in the brain extracellular microenvironment. The apparent steady-state basal extracellular concentration and extraction fraction of DA were determined in anesthetized rat striatum by the concentration difference (no-net-flux) microdialysis technique. A rate constant for extracellular clearance of DA calculated from the extraction fraction was smaller than the previously determined estimate by fast-scan cyclic voltammetry for cellular uptake of DA. Because the relatively small size of the voltammetric microsensor produces little tissue damage, the discrepancy between the uptake rate constants may be a consequence of trauma from microdialysis probe implantation. The trauma layer has previously been identified by histology and proposed to distort measurements of extracellular DA levels by the no-net-flux method. To address this issue, an existing quantitative mathematical model for microdialysis was modified to incorporate a traumatized tissue layer interposed between the probe and surrounding normal tissue. The tissue layers are hypothesized to differ in their rates of neurotransmitter release and uptake. A post-implantation traumatized layer with reduced uptake and no release can reconcile the discrepancy between DA uptake measured by microdialysis and voltammetry. The model predicts that this trauma layer would cause the DA extraction fraction obtained from microdialysis in vivo calibration techniques, such as no-net-flux, to differ from the DA relative recovery and lead to an underestimation of the DA extracellular concentration in the surrounding normal tissue.

Haemostasis with haemodilution -- a quantitative mathematical model of thrombocytes and fibrinogen in haemodilution

Haemostasis with haemodilution -- a quantitative mathematical model of thrombocytes and fibrinogen in haemodilution

Health service capacity modelling

This paper aims to describe a modelling tool that gives a framework for the estimation of future bed demand for hospital services. It also outlines some issues regarding the application of the model. A quantitative mathematical model was constructed that was based on two years of seasonally adjusted inpatient data. To calculate the number of beds required five years into the future, ten factors were applied to the number of bed-days used for each service. In the example given (Figure 1), 7,924 bed-days used in 1998-99 translated into a requirement for twenty-six beds in 2004. The value of this approach lies in the ability to describe and delineate each of the varying factors, and thus allowing clinicians, healthcare managers, the purchasers of health services and other stakeholders to be involved in a clear and explicit decision-making process.

AN INTERNAL DOSE MODEL FOR INTERSPECIES EXTRAPOLATION OF IMMEDIATE INCAPACITATION RISK FROM INHALATION OF FIRE GASES

A quantitative mathematical model assesses incapacitation risk in humans from toxic gas inhalation. A body-mass-normalized internal dose for each gas is calculated from an inhalation equation in which ventilation is a function of species, activity, and the gases inhaled. Uptake in the dead space considers U.S. Environmental Protection Agency (EPA) gas categories. The probability of incapacitation is a function of normalized internal dose and follows a cumulative distribution curve whose parameters are found from small-animal incapacitation data. No internal interaction of gases is modeled, and probabilities are combined independently. The model compares favorably with combined gas and large-animal incapacitation data.

Redox equilibrium between guanyl radicals and thiocyanate influences base damage yields in gamma irradiated plasmid DNA. Estimation of the reduction potential of guanyl radicals in plasmid DNA in aqueous solution at physiological ionic strength

Purpose : Gamma irradiation of an aqueous solution containing thiocyanate ions produces the strongly oxidizing intermediate (SCN) 2 £ -. Reaction of this species with plasmid DNA produces damage that is revealed as strand breaks after incubation with the Escherichia coli base excision repair endonuclease formamidopyrimidine-DNA N -glycosylase (FPG). It has been previously reported that the yield of damage is highly sensitive to the experimental conditions, leading to the suspicion that electron transfer between DNA and (SCN) 2 £ - is reversible. In principle this makes it possible to determine the oxidation potential for plasmid DNA (more formally the reduction potential of oneelectron oxidized plasmid DNA), a fundamental parameter describing the reactivity of DNA towards electron transfer reactions. Materials and methods : Aqueous solutions of plasmid DNA and thiocyanate ions were subjected to 137 Cs n -irradiation. After irradiation, the plasmid was incubated with the E. coli base excision repair endonuclease formamidopyrimidine-DNA N -glycosylase (FPG). The yield of this damage was quantified by using agarose gel electrophoresis to identify the fraction of the plasmid population that contains strand breaks. Results : The yield of FPG-sensitive sites decreases with increasing thiocyanate concentration, decreasing DNA concentration, and increasing dose rate. By making some simple assumptions about the chemical reactions that produce DNA damage, it is possible to derive a quantitative mathematical model for the yield of FPG-sensitive sites. A good agreement was found between this model and the experimental observations over a wide range of conditions (thiocyanate concentrations, DNA concentrations, and dose rates that vary by 20-, 40-, and 150-fold respectively). Conclusions : It was possible to assign a value to the equilibrium constant for the one electron transfer reaction between the two radical species (SCN) 2 £ - and DNA-G £ +. This leads to an estimate of the reduction potential at pH 7 for the couple DNA G £ + /DNA of E 7 = +1.39 - 0.01V.

A model for energy flow in the inner ear of the bullfrog (Rana catesbeiana).

We present a quantitative mathematical model that represents the main features of the bullfrog inner ear. Calculated responses based on this model predict the observed frequency separation between the amphibian papilla and basilar papilla responses. The origin of this separation can be traced to the effect of the contact membranes on the impedance of the respective paths. Additionally, we calculated the input impedance of the periotic canal and showed that at low frequencies it acts as a bypass for most of the energy entering the ear, shunting it away from the amphibian-basilar papilla complex. As this shunting decreases with increasing frequency, we propose that the periotic canal functions as a protection mechanism to prevent overload of the amphibian papilla and basilar papilla during ventilation and for quasi-static pressure equalization. Our model explains the main features of the empirical data obtained from direct measurement of the amphibian papilla and basilar papilla contact membranes reported in an accompanying paper (this issue).

A Fuzzy FDI Decision Making System for the Support of the Human Operator

The goal of Fault Detection and Isolation (FDI) is to decide whether and where a fault in the system under consideration has occurred avoiding wrong decisions that cause false alarms. To achieve a fault detection scheme which is robust in the sense of false alarms a combined quantitative/qualitative supervision system will be used to detect and isolate faults. The quantitative part will be used to generate fault symptoms (residuals) using a quantitative (mathematical) model of the process. These residuals contain the information whether a fault has occured or not. The next step in the FDI process is the residual evaluation . There exists a number of different residual evaluation techniques, for example simple threshold logic tests, statistical decision making, pattern recognition, decision making based on fuzzy logic or neural networks. The fundamental difficulty with residual evaluation is that residuals are normally uncertain, corrupted by noise, disturbances and, if the residuals are generated by model-based techniques, by modelling uncertainties. In order to select from the given residual data the important fault information a human support tool for the generation of a knowledge base for fault diagnosis will be presented in this paper.

Spontaneous electrical and calcium oscillations in unstimulated pituitary gonadotrophs

Single pituitary cells often fire spontaneous action potentials (APs), which are believed to underlie spiking fluctuations in cytosolic calcium concentration ([Ca2+]i). To address how these basal [Ca2+]i fluctuations depend on changes in plasma membrane voltage (V), simultaneous measurements of V and [Ca2+]i were performed in rat pituitary gonadotrophs. The data show that each [Ca2+]i spike is produced by the Ca2+ entry during a single AP. Using these and previously obtained patch-clamp data, we develop a quantitative mathematical model of this plasma membrane oscillator and the accompanying spatiotemporal [Ca2+]i oscillations. The model demonstrates that AP-induced [Ca2+]i spiking is prominent only in a thin shell layer neighboring the cell surface. This localized [Ca2+]i spike transiently activates the Ca2(+)- dependent K+ current resulting in a sharp afterhyperpolarization following each voltage spike. In accord with experimental observations, the model shows that the frequency and amplitude of the voltage spikes are highly sensitive to current injection and to the blocking of the Ca(2+)-sensitive current. Computations also predict that leaving the membrane channels intact, the firing rate can be modified by changing the Ca2+ handling parameters: the Ca2+ diffusion rate, the Ca2+ buffering capacity, and the plasma membrane Ca2+ pump rate. Finally, the model suggests reasons that spontaneous APs were seen in some gonadotrophs but not in others. This model provides a basis for further exploring how plasma membrane electrical activity is involved in the control of cytosolic calcium level in unstimulated as well as agonist-stimulated gonadotrophs.

The analysis of relaxed criteria for erosion-control filters

To optimize the design of erosion-control filters a transport model is presented for moving base material in horizontally loaded filters that are not geometrically stable. Supporting experimental work is used to obtain the parameters in a descriptive quantitative mathematical model. A set of three fixed parameters describes most experiments. Exceptions are where the filter to base grain-size ratio is so small that geometrical obstruction takes place and where this ratio is so large that the turbulences in the flow cause the sand surface under the filter to ripple. The latter case is described with a slightly amended parameter to allow for the amount of fluctuation in the problem. Key words : filtration, transport, experiments, theory, granular material, barriers.

Modelling of near-field subsurface displacements for generalized faults and fault arrays

A quantitative mathematical model using elastic dislocation theory has been developed to model the near-field subsurface displacement field associated with faults and fault arrays within an elastic layer above an elastic half-space. The three components of displacement in the spatial domain are expressed as a sum of Fourier-Bessel integrals in the wave number domain. A numerical technique using matrix decomposition has been used to obtain near-field stable solutions. Fault displacements may be dip-slip, strike-slip and oblique-slip. The model has been used to determine the three-dimensional surface and subsurface displacement fields for a rectangular fault with constant slip, and for an elliptical fault on which the slip varies from the point of maximum displacement at the centre to zero displacement at an elliptical tip-line. The three-dimensional displacement field may be determined for individual slip events on a fault, or for cumulative fault displacements. The model has also been applied to multiple fault arrays.