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PubMed2002

A mathematical model of human atrioventricular nodal function incorporating concealed conduction.

This work develops a mathematical model for the atrioventricular (AV) node in the human heart, based on recordings of electrical activity in the atria (the upper chambers of the heart) and the ventricles (the lower chambers of the heart). Intracardiac recordings of the atrial and ventricular activities were recorded from one patient with atrial flutter and one with atrial fibrillation. During these arrhythmias, not all beats in the atria are conducted to the ventricles. Some are blocked (concealed). However, the blocked beats can affect the properties of the AV node. The activation times of the atrial events were regarded as inputs to a mathematical model of conduction in the AV node, including a representation of AV nodal concealment. The model output was compared to the recorded ventricular response to search for and identify the best possible parameter combinations of the model. Good agreement between the distribution of interbeat intervals in the model and data for durations of 5 min was achieved. A model of AV nodal behavior during atrial flutter and atrial fibrillation could potentially help to understand the relative roles of atrial input activity and intrinsic AV nodal properties in determining the ventricular response.

Atrial Fibrillation↗
PubMed2000

Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model.

In cancer chemotherapy, it is important to design treatment strategies that ensure a desired rate of tumor cell kill without unacceptable toxicity. To optimize treatment, we used a mathematical model describing the pharmacokinetics of anticancer drugs, antitumor efficacy, and drug toxicity. This model was associated with constraints on the allowed plasma concentrations, drug exposure, and leukopenia. Given a schedule of drug administrations, the mathematical model optimized the drug doses that can minimize the tumor burden while limiting toxicity at the level of the white blood cells. The main result is that the optimal drug administration is an initial high-dose chemotherapy up to saturation of constraints associated with normal cell toxicity and a maintenance continuous infusion at a moderate rate. Data related to etoposide investigations were used in a feasibility study. Simulations with the optimized protocol showed better performances than usual clinical protocols. Model-based optimal drug doses provide for greater cytoreduction, while limiting the risk of unacceptable toxicity.

Antineoplastic Agents↗
PubMed1996

Self-Efficacy Beliefs and Mathematical Problem-Solving of Gifted Students

Path analysis was used to test the predictive and mediational role that self-efficacy beliefs play in the mathematical problem-solving of middle school gifted students (n = 66) mainstreamed with regular education students (n = 232) in algebra classes. Self-efficacy of gifted students made an independent contribution to the prediction of problem-solving in a model that controlled for the effects of math anxiety, cognitive ability, mathematics GPA, self-efficacy for self-regulated learning, and sex. Gifted girls surpassed gifted boys in performance but did not differ in self-efficacy. Gifted students reported higher math self-efficacy and self-efficacy for self-regulated learning as well as lower math anxiety than did regular education students. Although most students were overconfident about their capabilities, gifted students had more accurate self-perceptions and gifted girls were biased toward underconfidence. Results support the hypothesized role of self-efficacy in A. Bandura's (1986) social cognitive theory.

Journal Article↗
PubMed2001

Preservice Teachers' Self-Esteem and Mathematics Achievement.

The purpose of this article is to examine the relationship between preservice teachers' general self-esteem and mathematics achievement through the inclusion of variables that are supported by recent research in psychology and social cognitive theory. A structural equation model is used to examine the paths from mathematics achievement to general self-esteem and vice versa. To this end, the concepts of self-esteem and the relationships between self-esteem and academic achievement are first explained, followed by a description of the baseline model that was used for the analysis of the data. The methodology of the study, with emphasis on the description of the intervening variables, is then summarized. Last, the results of the study are discussed and conclusions are drawn from the main findings. Copyright 2001 Academic Press.

Journal Article↗
PubMedDate not supplied

Mechanistic and mathematical inactivation studies of food spoilage fungi.

Fungal spoilage forms an increasing economic problem in the food industry. Chemical antifungals are becoming less attractive as food preservatives and hygiene agents due to the development of resistance and due to stricter legal regulations concerning the permitted concentrations. Finally, consumers tend to demand more "naturally preserved" or preservative-free products. Here we review our understanding of the mechanisms of action and resistance to classical antifungals. Next, we evaluate the scientific basis underlying the application of novel, natural antifungals. Finally, we discuss the mathematical modelling of fungal growth and the development of preliminary predictive lag-time models. The eventual aim of the reviewed work is to generate mathematical lag-time models in real foods that predict the microbiological stability of the food and are based on a mechanistic understanding of the chain of events that leads to cell death, or an extension of lag-time of the initiation of outgrowth.

Antifungal Agents↗
PubMed2000

Mathematical Modeling of Drug Release from Microemulsions: Theory in Comparison with Experiments.

The topic of this paper is the study of the drug release from a drug-loaded microemulsion by reverting to a new mathematical model overcoming some drawbacks of previously proposed models. In particular, attention is focused on the mathematical expression of the drug fluxes existing between the oil and water phases during drug release. Indeed, not only the drug release kinetics, but also the drug oil-water partition coefficient strongly depend on these fluxes. Two microemulsion are considered: the first is composed by water, Tween80 as surfactant, and Triacetin as oil phase, while the second is composed by water, Tween80 as surfactant, and a Triacetin-benzylic alcohol mixture (1 : 1) as oil phase. Both of them are loaded by Nimesulide, an oil-soluble drug of considerable industrial relevance. The drug release is performed by resorting to a permeation experiment (Franz cells apparatus) as it demonstrated to be the most reliable methodology. The good agreement between the experimental permeation data and the model best-fitting ensures that the most important phenomena ruling this kind of drug release were properly accounted for by the new proposed model. Copyright 2000 Academic Press.

Journal Article↗
PubMed1998

Comparative kinetic analysis of FLP and cre recombinases: mathematical models for DNA binding and recombination.

The integrase class site specific recombinases FLP from Saccharomyces cerevisiae, and Cre from bacteriophage P1, have been extensively used to direct DNA rearrangements in heterologous organisms. Although their reaction mechanisms have been relatively well characterised, little comparative analysis of the two enzymes has been published. We present a comparative kinetic analysis of FLP and Cre, which identifies important differences. Gel mobility shift assays show that Cre has a higher affinity for its target, loxP (7. 4x10(10) M-1), than FLP for its target, FRT (8.92x10(8) M-1). We show that both recombinases bind the two halves of their target sites cooperatively, and that Cre shows approximately threefold higher cooperativity than FLP. Using a mathematical model describing the sequential binding of recombinase monomers to DNA, we have determined values for the association and dissociation rate constants for FLP and Cre.FLP and Cre also showed different characteristics in in vitro recombination assays. In particular, approximately tenfold more active FLP was required than Cre to optimally recombine a given quantity of excision substrate. FLP was able to reach maximum excision levels approaching 100%, whilst Cre-mediated excision did not exceed 75%. To investigate possible reasons for these differences a mathematical model describing the excision recombination reaction was established. Using measured DNA binding parameters for FLP and Cre in the model, and comparing simulated and experimental recombination data, the values of the remaining unknown parameters were determined. This analysis indicates that the synaptic complex is more stable for Cre than for FLP.

Allosteric Regulation↗
PubMed1997

Stress Caused by Waiting: A Theoretical Evaluation of a Mathematical Model

According to cognitive stress theories, stress caused by waiting is influenced by two components, the (psychological) cost of waiting, that is, a function C of time, and a probability distribution over waiting times. Osuna (1985a) suggested a model by which stress as a function of time could be calculated from these constituents. The aim of this paper is (1) to generalize the model, (2) to investigate its mathematical properties, (3) to derive predictions for experimental tests of the model, and (4) to give a precise meaning to the variability and duration hypothesis discussed in the experimental literature. In particular, several theorems are derived which specify situations in which the model enables the user to compare conditions for their stress inducing potential. Such conditions are the duration of the waiting time and the predictability of the length of a waiting period. The core of the mathematical derivations is an identity for expected stress which simplifies the calculations of the Osuna model considerably. Copyright 1997 Academic Press

Journal Article↗
PubMed1996

Mathematical modeling of helper T lymphocyte/antigen-presenting cell interactions: analysis of methods for modifying antigen processing and presentation.

Helper T lymphocytes (Th cells) are activated by contact with antigen-presenting cells (APCs) that have processed and presented the appropriate MHC-peptide complexes. Two experimental methods for modifying antigen processing and presentation include altering the properties of the antigen and altering the method of antigen uptake. Mathematical modeling was used to investigate the effects of these two methods on the Th cell response. Two mathematical models were used, one for relating the external antigen concentration to the number of MHC-peptide complexes to the number of bound T cell receptors (TCRs) on the Th cell. Large values of MHC/peptide affinity were predicted to compensate for small values of TCR/MHC-peptide affinity in particular parameter ranges. Similarly, large values of antigen receptor number were predicted to compensate for small values of antigen receptor affinity in particular parameter ranges. Results were shown to agree with a variety of experimental data. In addition, model predictions suggest that knowledge of MHC/peptide, TCR/MHC-peptide, and receptor/antigen affinities is not sufficient to accurately describe an experimental system; the kinetic rate constants can dramatically affect antigen processing and presentation, the Th-APC interaction, and the Th cell response. This theoretical approach is useful not only for interpreting experimental data but also for guiding future experiments aimed at manipulating the Th cell response.

Antigen Presentation↗
PubMed1997

A mathematical model to determine the optimal number of fragments for comparison of bacterial chromosomic macrorestriction patterns.

To our knowledge, although comparison of chromosomic macrorestriction patterns has become one of the most feasible molecular tools of the current microbial taxonomy, a mathematical approach to optimize the choice of a restriction enzyme among the endonucleases tested for such comparison has not been previously described. The coincidence of restriction patterns for two tested bacterial strains with this chosen endonuclease will ensure a high genetic relatedness between them. We report a mathematical model to determine the probability of hazardously obtaining a particular chromosomic macrorestriction pattern by PFGE and to calculate the optimal number of fragments for its comparison. The model presented allows us to determine the optimal number of fragments in order to compare chromosomic restriction patterns. The model calculates this values as a function of the chromosome size and the restriction site length. The model is not useful for choosing a restriction enzyme previous to experimental steps, but as a tool for the choice of the restriction enzyme that yields the lowest probability of hazardously obtaining coincidences of chromosomic patterns. The applicability of this model has been exemplified by determining the optimal number of fragments for some well-characterized bacteria and by comparing these values with those that have been experimentally used.

Bacteria↗
PubMed1998

Mathematical modelling of 3-(3',4'-dichlorophenyl)-1,1-dimenthylurea action in plant leaves

A mathematical model of the action of a photosystem II herbicide 3-(3',4'-dichlorophenyl)-1, 1-dimenthylurea, DCMU, in plant leaves upon an external application is presented. The diffusion of DCMU in a plant tissue is described with the help of Fick's laws and the following reaction of the herbicide with the QB-binding site of photosystem II by the mass action theory. The model is used for a description of the effect of the herbicide on chlorophyll fluorescence induction (the O-J-I-P curve) measured with spring barley primary leaves submerged in the herbicide solution. The increase of the J step during the herbicide action is ascribed to an increase of the number of photosystem II centres with bound herbicide molecules and malfunctioning in the electron transport to the plastoquinone pool. The experimental data were fitted with the help of the mathematical model. Values of the diffusion coefficient and the second order rate constant of the reaction of the herbicide with photosystem II, obtained by the fitting procedure, are discussed.Copyright 1998 Academic Press Limited

Journal Article↗
PubMed1998

A mathematical model for Neanderthal extinction.

A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed; nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solutions (fronts) confirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).

Animals↗
PubMed1998

The humoral immune response to Haemophilus influenzae type b: a mathematical model based on T-zone and germinal center B-cell dynamics.

Through careful mapping of the physiology of the T-zone and GC B-blast dynamics to a mathematical representation of the cell processes including proliferation, migration, differentiation, and cell death, a mathematical model is constructed to capture the dominant nominal primary, late follicular, and secondary humoral response to Haemophilus influenzae Type b. This model explicitly incorporates the dynamics of memory B-cells, T-zone and GC B-dynamics, IgM and IgG antibodies, avidity maturation, and IC presentation by FDCs into a coherent framework. This paper describes the relevant immunology, the pertinent physiological assumptions, the developed model, and the parameter identification procedure. The model parameters were found using a parameter identification procedure that capitalizes on the timing and interactions of certain dominant physiological attributes. Simulation results and validation tests indicate that the model reflects not only a nominal primary and secondary humoral immune response but also the tertiary and T-independent responses. The model shows robustness to variations in infection dosage, bacterial growth rate (virulence of the strain), and onset-timing of the secondary response. The utility of this model in studying the humoral immune response is demonstrated through suggested physiological assumptions, mechanisms, and rates to be eventually clinically evaluated as well as insights into vaccination design. The model and parameter identification techniques are easily adapted to other diseases which primarily evoke a humoral immune response.

Antibodies, Bacterial↗
PubMed2000

Mathematical modeling the kinetics of cell distribution in the process of ligand-receptor binding.

A statistical approach is presented to model the kinetics of cell distribution in the process of ligand-receptor binding on cell surfaces. The approach takes into account the variation of the amount of receptors on cells assuming the homogeneity of monovalent binding sites and ligand molecules. The analytical expressions for the kinetics of cell distribution have been derived in the reaction-limited approximation. In order to demonstrate the applicability of the mathematical model, the kinetics of binding the rabbit, anti-mouse IgG with Ig-receptors of the murine hybridoma cells has been measured. Anti-mouse IgG was labeled with fluorescein isothiocyanate (FITC). The kinetics of cell distribution on ligand-receptor complexes was observed during the reaction process by real-time measuring of the fluorescence and light-scattering traces of individual cells with the scanning flow cytometer. The experimental data were fitted by the mathematical model in order to obtain the binding rate constant and the initial cell distribution on the amount of receptors.

Animals↗
PubMed2000

A mathematical expectation model for bird navigation based on the clock-and-compass strategy.

We present here a mathematical formula for the directional distribution of migratory birds if they use a vector navigation/clock-and-compass strategy to find their winter quarters. It is based on mathematical expectation theory and shows that a simple parabola can describe the expected geographical spread of clock-and-compass birds as a function of migratory distance. Predictions based on this model are then tested against all same autumn ringing recoveries of first-season Pied Flycatchers, Ficedula hypoleuca, ringed in Scandinavia and European Robins, Erithacus rubecula, ringed in Sweden and Finland and recovered north of the Sahara Desert. We find that the predictions of our analytical model fit the ringing recovery distribution of freely migrating conspecifics extremely well.

Animals↗
PubMed2001

A mathematical framework to study the effects of growth factor influences on fracture healing.

During fracture healing, multipotential stem cells differentiate into specialized cells responsible for producing the different tissues involved in the bone regeneration process. This cell differentiation has been shown to be regulated by locally expressed growth factors. The details of their regulatory mechanisms need to be understood. In this work, we present a two-dimensional mathematical model of the bone healing process for moderate fracture gap sizes and fracture stability. The inflammatory and tissue regeneration stages of healing are simulated by modeling mesenchymal cell migration; mesenchymal cell, chondrocyte and osteoblast proliferation and differentiation, and extracellular matrix synthesis and degradation over time. The effects of two generic growth factors on cell differentiation are based on the experimentally studied chondrogenic and osteogenic effects of bone morphogenetic proteins-2 and 4 and transforming growth factor-beta-1, respectively. The model successfully simulates the progression of healing and predicts that the rate of osteogenic growth factor production by osteoblasts and the duration of the initial release of growth factors upon injury are particularly important parameters for complete ossification and successful healing. This temporo-spatial model of fracture healing is the first model to consider the effects of growth factors. It will help us understand the regulatory mechanisms involved in bone regeneration and provides a mathematical framework with which to design experiments and understand pathological conditions.

Bone Morphogenetic Protein 2↗
PubMed2002

A mathematical model of chemoreception for odours and taste.

We propose a mathematical model based on the occupation theory and on the hypothesis that, for a given stimulus, there exist two kinds of receptors. The receptors of the first kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active depolarizing form (this scheme was already used by Del Castillo & Katz, 1957). In the same way, the receptors of the second kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active hyperpolarizing form. The response is assumed to be proportional to the difference between the fraction of the active depolarizing compound and that of the active hyperpolarizing compound. The present paper deals only with the time course of the intensity of the response: in the first part, when a continuous flow of stimulus is applied and in the second part, when this continuous flow is removed. It does not deal with the quality and the discrimination of odours. The proposed mathematical model accounts for the depolarizing responses (which are the most frequent ones), the hyperpolarizing responses, the mixed responses reported by Patte et al. (1989), the off-responses reported by Takagi & Shibuya (1959) and for their variability, and the latent period in the olfactory response (Ottoson, 1974).

Chemoreceptor Cells↗
PubMed2002

A mathematical model of pattern formation in the vascular cambium of trees.

The beautiful patterns apparent in wood grain have their origin in the alignment of fusiform initial cells in the vascular cambium of trees. We develop a mathematical model to describe the orientation of fusiform initial cells, and their interaction with the plant hormone indole-3-acetic acid (auxin). The model incorporates the following four assumptions: (1) auxin is actively transported parallel to the long axis of the initials, (2) auxin diffuses perpendicular to the long axis of the initials, (3) the initials tend to orient parallel to the flux of auxin through the cambium, and (4) adjacent initials tend to orient parallel to one another. Each assumption is justified on the basis of available evidence and cast in mathematical form. Our main result is a pair of nonlinear differential equations that describe the coupling between the distribution of auxin in the cambium and the orientation of fusiform initials. Numerical solutions to the equations show qualitative resemblance to the wood grain patterns observed at branch junctions, wounds and knots, and topological defects.

Diffusion↗