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At least 613 records · Page 34Linked to original sources
PubMed2000

On mathematical models of microdialysis: geometry, steady-state models, recovery and probe radius.

Commonly used methods for microdialysis recovery measurement are reviewed and the zero flow and no net flux methods are suggested as the most robust in practice. Six different mathematical models of microdialysis assumptions are investigated and compared for varying dialysis probe radius. One transmitter (dopamine), three metabolites (DOPAC, HVA and 5HIAA) and two drugs (caffeine and theophylline) were studied. Histology and functional response to a drug were measured. Deficiencies were demonstrated for several of the models, the one best explaining experimental data includes both passive diffusion and active tissue regulation in a cylindrical symmetric geometry. The recovery decreased with decreasing probe radius but smaller probes caused less tissue injury. It is concluded that a mathematical model of microdialysis must include diffusional and physiological processes in order to accurately account for experimentally observed phenomena. The experiments also demonstrated that, for small brain nuclei, the size of the nucleus may influence the recovery.

Animals↗
PubMed1987

Development of mathematical models for an in vitro-phagocytosis test system.

Phagocytosis tests have been carried out by many authors using different methods under different conditions. The results have been interpreted in different ways, as well sometimes with conflicting notations. In order to get to a more systematic data analysis and to separate intrinsic from methodic influences, the possibility to apply mathematical models to a phagocytosis test has been studied. In agreement with previous experiences that phagocytosis can well be represented by a mathematical treatment as Michaelis-Menten-type enzyme kinetics concerning its initial rate and by an exponential function under in vivo conditions, in vitro-phagocytosis was phenomenologically described as an analogon of an irreversible bimolecular chemical reaction. In this way, rate and capacity of phagocytosis may be quantified separately. On the basis of systematic deviations of the data from this model, modifications have been developed which could be connected with pertinent observations. The design of further experiments from preliminary results on the basis of our models is discussed.

Granulocytes↗
PubMedDate not supplied

[The efficacy of universal vaccination against the hepatitis B virus. Simulation with a mathematical model].

We present a mathematical model of the hepatitis B virus (HBV) infection in a community. The main object is to analyze the effects of two different strategies of mass vaccination: newborns or adolescents. It appears that adolescents mass vaccination produces in the short-term a bigger effect than in the newborns. Mathematically, the model is a system of non linear first order differential equations, in which each function is a related class of individuals (susceptible, infectious, carrier, immune and death by HBV) in the evolution of the HBV. The solution of system is obtained in a numerical way. It should be pointed out that the model explains neatly the herd immunity effect of the vaccine and can be used in the simulation of possible changes in the HBV infection such that generalized use of discarded needles by the drug addicted population, changes in the sexual habits, etc.

Adolescent↗
PubMed1998

Soft mathematics and information dynamics.

We present a brief overview of a new framework for interdisciplinary collaboration toward understanding the fundamentals of information dynamics in social systems. The need for a new mathematics is noted, and a promising component, soft mathematics, is described.

Information Science↗
PubMed1999

TWODEE: the Health and Safety Laboratory's shallow layer model for heavy gas dispersion. Part 1. Mathematical basis and physical assumptions.

The Major Hazard Assessment Unit of the Health and Safety Executive (HSE) provides advice to local planning authorities on land use planning in the vicinity of major hazard sites. For sites with the potential for large scale releases of toxic heavy gases such as chlorine this advice is based on risk levels and is informed by use of the computerised risk assessment tool RISKAT [C. Nussey, M. Pantony, R. Smallwood, HSE's risk assessment tool RISKAT, Major Hazards: Onshore and Offshore, October, 1992]. At present RISKAT uses consequence models for heavy gas dispersion that assume flat terrain. This paper is the first part of a three part paper. Part 1 describes the mathematical basis of TWODEE, the Health and Safety Laboratory's shallow layer model for heavy gas dispersion. The shallow layer approach used by TWODEE is a compromise between the complexity of CFD models and the simpler integral models. Motivated by the low aspect ratio of typical heavy gas clouds, shallow layer models use depth-averaged variables to describe the flow behaviour. This approach is particularly well suited to assess the effect of complex terrain because the downslope buoyancy force is easily included. Entrainment may be incorporated into a shallow layer model by the use of empirical formulae. Part 2 of this paper presents the numerical scheme used to solve the TWODEE mathematical model, and validated against theoretical results. Part 3 compares the results of the TWODEE model with the experimental results taken at Thorney Island [J. McQuaid, B. Roebuck, The dispersion of heavier-than-air gas from a fenced enclosure. Final report to the US Coast Guard on contract with the Health and Safety Executive, Technical Report RPG 1185, Safety Engineering Laboratory, Research and Laboratory Services Division, Broad Lane, Sheffield S3 7HQ, UK, 1985].

Diffusion↗
PubMed1999

[Short-term dynamics of intertidal microphytobenthos biomass. Mathematical model].

We formulate a deterministic mathematical model to describe the dynamics of the microphytobenthos of intertidal mudflats. It is 'minimal' because it only takes into account the essential processes governing the functioning of the system: the autotrophic production, the active upward and downward migrations of epipelic microalgae, the saturation of the mud surface by a biofilm of diatoms and the global net loss rates of biomass. According to the photic environment of the benthic diatoms inhabiting intertidal mudflats, and to their migration rhythm, the model is composed of two sub-systems of ordinary differential equations; they describe the simultaneous evolution of the biomass 'S' concentrated in the mud surface biofilm--the photic layer--and of the biomass 'F' diluted in the topmost centimetre of the mud--the aphotic layer. Qualitatively, the model solutions agree fairly well with the in situ observed dynamics of the S + F biomass. The study of the mathematical properties of the model, under some simplifying assumptions, shows the convergence of solutions to a stable cyclic equilibrium, whatever the frequencies of the physical synchronizers of the production. The sensitivity analysis reveals the necessity of a better knowledge of the processes of biomass losses, which so far are uncertain, and may further vary in space and time.

Biomass↗
PubMed1998

Feto-maternal circulation: mathematical model and comparison with Doppler measurements.

OBJECTIVES: Clinicians are more and more frequently studying fetal blood flow velocity curves recorded by Doppler ultrasound in vital organs such as the placenta and fetal brain to evaluate fetal well-being. We have therefore developed a mathematical model of the utero-placental and fetal circulations which could be used for teaching and for a better understanding of regulatory mechanisms. METHODS: The model is based on two basic elements-an arterial segment and a bifurcation-and we have reproduced the major arteries of the feto-maternal circulation combining these basic elements. The mathematical model of the system is based on the Navier-Stokes equations. The peripheral areas such as the brain, kidneys and placenta are modeled by a simple Windkessel model and the model computes instantaneous flow and pressure at any point in the fetal arterial tree and the uterine arteries. RESULTS: We have compared the computed instantaneous flow curves and pressure with in vivo data and our results agree with the findings in physiological situations and in gravidic hypertension. CONCLUSIONS: Our model provides new interesting insights into fetal hemodynamics such as a better understanding of the mismatch impedance phenomena and is a promising model for the study of blood redistribution mechanisms in hypoxic situations.

Blood Vessels↗
PubMed1996

A mathematical model for analysis of pharmacologically induced changes in the kinetics of cardiac muscle.

A mathematical model of the isometric contraction of cardiac muscle is developed and utilized to characterize the inotropic and lusitropic effects of cardioactive compounds in isolated guinea pig left atria. In contrast to metrics that are based on minima and maxima of an isometric twitch and its derivative function, the entire time course of the twitch is used to quantify the kinetics of the contraction-relaxation cycle. The model relates observed tension to a time-dependent activation function that describes generation of internal force and a coupling function that determines mechanical response to the activation function. The model is structured so that it is suitable for nonlinear curve fitting to observed data. Results obtained using the model for fitting experimental data from tissues treated with different classes of cardioactive compounds agree with more qualitative results presented by other authors. Experiments using the model to fit data over an extended (90 min) time course revealed differences in the kinetic profiles of milrinone and forskolin. Computer simulations that demonstrate the effect of each model parameter on twitch kinetics are presented, and the relationships between the model and other theoretical and empirical models of cardiac muscle are discussed. The mathematical model is useful to enable a more quantitative understanding of the kinetics of cardiac muscle contraction and relaxation and identify compounds that may be selective for inotropic or lusitropic effects.

Animals↗
PubMed2002

Contribution of a mathematical modelling approach to the understanding of the ovarian function.

The biological meaning of folliculogenesis is to free fertilisable oocytes at the time of ovulation. We approached the study of the control of follicular development at the level of follicular granulosa cells, on the experimental as well as mathematical modelling grounds. We built a mathematical model allowing for the processes of proliferation, differentiation and apoptosis. State variables correspond to the numbers of cells undergoing these different processes, while control variables correspond to the cellular transition rates. The model results raised the notion of proliferative resources, which leads to consider the optimal management of these resources and has motivated the settling of an experiment investigating the changes in the growth fraction within the granulosa throughout terminal development. We are now investigating the way gonadotrophins, and especially FSH, operate on granulosa cells, in order to account for the hormonal control of the divergent commitment of granulosa cells towards either proliferation, differentiation or apoptosis. We are thus focusing on the dynamics of cAMP production, which appears to be a keypoint in FSH signal transduction.

Animals↗
PubMed1990

Qualitative and quantitative aspects on mathematics achievement in MZ and DZ twins.

Mathematics achievement test results have been collected for 22 MZ and 24 DZ same-sex twin pairs in the Swedish compulsory school. The twins were approximately 11-13 years of age and attended grades 4, 5, or 6. The twin pairs were part of a larger collaborative study between Israel and Sweden (the KAM-project). Teachers were asked how they planned and evaluated their work in the subjects Swedish and Mathematics. In addition to this, results for the twins on Maths tests given by the teachers in their regular work were collected. These tests were thus used by the teachers as an instrument to evaluate the educational process. Intrapair similarity for MZ and DZ twins has been compared for qualitative and quantitative aspects of the Maths tests. Different tests were used by the teachers but the same criteria have been used in the comparison. MZ twins are somewhat more similar than DZ twins for both the qualitative and quantitative aspects. Only one quantitative aspects, however, percentage of correct answers, shows a significant difference between the twin categories. A comparison was also made of intrapair similarity in classes, where the teachers differed according to planning and evaluation of their education. Irrespective of that, the MZ twins seemed to be more similar than the DZ twins in number of correct answers on the Maths tests. Educational implications are discussed.

Adolescent↗
PubMed1997

The kinetics of immunological responses to microfilariae in a murine host: experimental and mathematical studies.

We present a mathematical model which is used to interpret the dynamics of the immunological response of a mouse host to infection with the filarial worm Onchocerca lienalis. The model mimics changes in worm burden over time post-infection and after reinfection and its behaviour provides a good description of experimental results. Measured production of T-cells and eosinophils is also compared with the predictions of the model. Our results show that the immune response mechanism proposed on the basis of experimental results, involving CD4+ T-cells and eosinophil destruction of the parasite, is supported by the insights gained from the mathematical model. Also, using the parameters estimated to describe the primary infection dynamics, the degree of acquired immunity to secondary infection is also well described by the model. Our analysis highlights the importance of obtaining quantitative measures of the many rate parameters involved in even the simplest interpretations of immunological responses to parasitic infection.

Animals↗
PubMedDate not supplied

Mathematical model for the effects of epidermal growth factor receptor trafficking dynamics on fibroblast proliferation responses.

We apply a mathematical model for receptor-mediated cell uptake and processing of epidermal growth factor (EGF) to analyze and predict proliferation responses to fibroblastic cells transfected with various forms of the EGF receptor (EGFR) to EGF. The underlying conceptual hypothesis is that the mitogenic signal generated by EGF/EGFR binding on the cell surface, via stimulation of receptor tyrosine kinase activity, is attenuated when the receptors are downregulated and growth factor is depleted by endocytic internalization and subsequent intracellular degradation. Hence, the cell proliferation rate ought to depend on receptor/ligand binding and trafficking parameters as well as on intrinsic receptor signal transduction properties. The goal of our modeling efforts is to formulate this hypothesis in quantitative terms. The mathematical model consists of kinetic equations for binding, internalization, degradation, and recycling of EGF and EGFR, along with an expression relating DNA synthesis rate to EGF/EGFR complex levels. Parameter values have been previously determined from independent binding and trafficking kinetic experiments on B82 fibroblasts transfected with wild-type and mutant EGFR. We show that this model can successfully interpret literature data for EGF-dependent growth of NR6 fibroblasts transfected with wild-type EGFR. Moreover, it successfully predicts the literature observation that NR6 cells transfected with a delta 973 truncation mutant EGFR, which is kinase-active but internalization-deficient, require an order of magnitude lower EGF concentration than cells with wild-type EGFR for half-maximal proliferation rate. This result demonstrates that it may be feasible to genetically engineer mammalian cell lines with reduced growth factor requirements by a rational, nonempirical approach. We explore by further model computations the possibility of exploiting other varieties of EGFR mutants to alter growth properties of fibroblastic cells, based on relationships between changes in the primary structure of the EGF receptor and the rates of specific receptor/ligand binding and trafficking processes. Our studies show that the ability to predict cell proliferation as a function of serum growth factors such as EGF could lead to the designed development of cells with optimized growth responses. This approach may also aid in elucidation of mechanisms underlying loss of normal cell proliferation control in malignant transformation, by demonstrating that receptor trafficking dynamics may in some cases play as important a role as intrinsic signal transduction in determining the overall resulting mitogenic response.

Cell Division↗
PubMedDate not supplied

Mathematics as a basis for chemistry.

Mathematicians are increasingly publishing papers in which mathematics is applied to chemical problems. Examination of some of these papers reveals that while they contain genuine contributions to chemistry they tend to avoid the more interesting and difficult problems. The "forward" problem of estimation of physical properties from a compound's structure, for example, has seen many publications, a proportion of which have been successful. The "reverse" problem, prediction of the structures which possess given properties, is only rarely examined and never by mathematicians. This is unfortunate because these problems are mathematically complex and mathematicians could make significant contributions by bringing their skills to bear on such questions.

Algorithms↗
PubMed2002

Sequencing surgery, radiotherapy and chemotherapy: insights from a mathematical analysis.

We present results from a mathematical analysis that is aimed at finding the best way to sequence the three traditional cancer treatments: surgery (S), chemotherapy (C), and radiotherapy (R). The mathematical model tracks the temporal evolution of the primary tumor and its associated metastases, and incorporates the primary tumor's effect on the dormancy and growth of the metastases. We show that the SCR schedule (i.e., surgery followed by chemotherapy followed by radiotherapy) achieves a higher cure probability than SRC if the primary tumor is sufficiently large or if the metastatic population is sufficiently large relative to the primary tumor. We also show that a novel schedule, SRCR, which splits the radiotherapy regimen into two disjoint portions, is optimal among all schedules, provided that the patient's dormant metastatic tumors do not become vascularized within about 40 days after surgery.

Breast Neoplasms↗
PubMed1997

New mathematical implementation of generalized pharmacodynamic models: method and clinical evaluation.

A new method and experimental design are presented to unambiguously estimate the transduction function (phi) and the conduction function (psi) of the generalized pharmacodynamic model: E = phi (psi * r), when measured pharmacokinetic response r is (i) drug plasma concentration and (ii) drug input rate into the systemic circulation. phi relates the observed pharmacologic effect E to the concentration at the effect site: ce = (psi * r), psi defines transfer of drug from plasma site to effect site or from input site to effect site, and * represents the convolution integral. The model functions psi and phi were expressed as cubic splines giving a very flexible description of those processes which is not biased by the structured assumptions of more conventional models, e.g., effect compartment models. The experimental design proposed addresses the problem of ambiguous identification of the model functions typical of these models; that is, there is more than one pair of very different functions describing the effect data collected after a single drug administration. We tested the hypothesis that the simultaneous fitting of at least two administrations allows the unambiguous identification of the model functions without the need for unlikely or cumbersome constraints. The performance of the mathematical implementation and the robustness of the methods with respect to measurement noise and possible failure of some assumptions, such as intraindividual variability, were tested by computer simulations. The method was then applied to the results of a clinical study of verapamil pharmacodynamics in 6 healthy subjects. Results of these studies demonstrated that the mathematical implementation does not introduce bias or artifact into the estimated functions and that the models and the proposed methods are suitable for application to clinical research. Two drug administrations were sufficient to unambiguously describe verapamil pharmacodynamics in the 6 human subjects studied.

Adult↗
PubMed1998

Sample timing and mathematical considerations for modeling breath elimination of volatile organic compounds.

Real-world exposure measurements are a necessary ingredient for subsequent detailed study of the risks from an environmental pollutant. For volatile organic compounds, researchers are applying exhaled breath analysis and the time dependence of concentrations as a noninvasive indicator of exposure, dose, and blood levels. To optimize the acquisition of such data, samples must be collected in a time frame suited to the needs of the mathematical model, within physical limitations of the equipment and subjects, and within logistical constraints. Additionally, one must consider the impact of measurement error on the eventual extraction of biologically and physiologically relevant parameters. Given a particular mathematical model for the elimination kinetics (in this case a very simple pharmacokinetic model based upon a multiterm exponential decay function that has been shown to fit real-world data extremely well), we investigated the effects on synthetic data caused by sample timing, random measurement error, and number of terms included in the model. This information generated a series of conditions for collecting samples and performing analyses dependent upon the eventual informational needs, and it provided an estimate of error associated with various choices and compromises. Though the work was geared specifically toward breath sampling, it is equally applicable to direct blood measurements in optimizing sampling strategy and improving the exposure assessment process.

Air Pollutants↗
PubMed1991

Mathematical problem solving by analogy.

We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.

Adult↗
PubMed1990

Assessing spurious "moderator effects": Illustrated substantively with the hypothesized ("synergistic") relation between spatial and mathematical ability.

The traditional methodology for assessing moderator variables (hierarchical multiple regression analysis) is examined. Possible drawbacks of this technique for corroborating psychological theories (cf. Busemeyer & Jones, 1983), are illustrated empirically on the basis of an analysis of 400,000 subjects. This article tested a well-known (and currently popular) substantive hypothesis: A synergistic relation exists between mathematical ability and spatial visualization in the prediction and development of sophisticated levels of advanced mathematics. Using the traditional methodology, this hypothesis was confirmed; however, on further analysis, using a more systematic approach, it was demonstrated that this finding was spurious. Suggestions are offered for modifying the traditional methodology used for assessing moderator effects (for both applied and theoretical purposes). These amount to ways for minimizing Type I and Type II errors.

Adolescent↗