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At least 847 records · Page 47Linked to original sources
PubMed1984

A mathematical model of the kinetics of 5-fluorouracil and its catabolites in freshly isolated rat hepatocytes.

A mathematical model for the kinetics of 5-fluorouracil (FUra) catabolism in liver cells is proposed. It is based on published data for the metabolism of FUra by isolated rat hepatocytes. The model relies on biochemical knowledge of the catabolic pathway. The key-steps are: the cellular uptake and the conversion of the unchanged drug to dihydrofluorouracil (FUH2) and subsequently to alpha-fluoro-beta-alanine (FBAL); the cellular fluxes of the 2 catabolites, FUH2 and FBAL. Water is partitioned between the extracellular and intracellular spaces. The first step is described by Michaelis-Menten kinetics and the other processes by first-order kinetics. Satisfactory fitting of the model validates these simplifications and provides values for the parameters describing the process. The model indicates that the kinetics of FUra disappearance are non linear, the Vmax of the first step being between 3.1 and 5.0 microM/min and the Km between 12 and 37 microM; the rate limiting step is the degradation of FUH2 (the major intracellular catabolite) with a rate constant of 0.1 to 0.02 min-1; the FUH2 transmembrane exchange is active; the exchange of the final catabolite FBAL is by diffusion.

Animals↗
PubMedDate not supplied

[Mathematical model of the postradiation recovery of the hematopoietic system].

The paper describes a mathematical model of hemopoiesis that takes into consideration postradiation arrest of mitoses and the stimulatory effect of a lack of functional cells on the yield of dividing cells into the maturing pool. Computer-aided modelling shows good agreement with the experimental data.

Bone Marrow↗
PubMed1992

Mathematical modelling and theory for estimating the basic reproduction number of canine leishmaniasis.

The paper describes a mathematical model for canine leishmaniasis and presents formulae which can be used to estimate the basic reproduction number, R0. The primary concern has been to devise methods of estimation which make best use of those data most easily obtained by fieldwork, e.g. surveys of prevalence in dog (by age) and sandfly populations. A range of formulae are offered which are more or less demanding of data, and which consequently give more or less precise estimates of R0. They include methods for assessing the influence on R0 of heterogeneous biting rates of sandflies on dogs, in which the essence of heterogeneous transmission can be captured merely by measuring relative rather than absolute contact rates.

Animals↗
PubMed1989

A mathematical model of physiological processes and its application to the study of aging.

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Aging↗
PubMed2001

A mathematical model for calculation of 90Sr absorbed dose in dental tissues: elaboration and comparison to EPR measurements.

A mathematical model for calculation of the 90Sr absorbed doses in dental tissues is presented. The results of the Monte-Carlo calculations are compared to the data obtained by EPR measurements of dental tissues. Radiometric measurements of the 90Sr concentrations. TLD and EPR dosimetry investigations were performed in animal (dog) study. The importance of the irregular 90Sr distribution in the dentine for absorbed dose formation has been shown. The dominant dose formation factors (main source-tissues) were identified for the crown dentine and enamel. The model has shown agreement with experimental data which allows to determine further directions of the human tooth model development.

Animals↗
PubMed2002

Quantitative dual-probe microdialysis: mathematical model and analysis.

Steady-state microdialysis is a widely used technique to monitor the concentration changes and distributions of substances in tissues. To obtain more information about brain tissue properties from microdialysis, a dual-probe approach was applied to infuse and sample the radiotracer, [3H]mannitol, simultaneously both in agar gel and in the rat striatum. Because the molecules released by one probe and collected by the other must diffuse through the interstitial space, the concentration profile exhibits dynamic behavior that permits the assessment of the diffusion characteristics in the brain extracellular space and the clearance characteristics. In this paper a mathematical model for dual-probe microdialysis was developed to study brain interstitial diffusion and clearance processes. Theoretical expressions for the spatial distribution of the infused tracer in the brain extracellular space and the temporal concentration at the probe outlet were derived. A fitting program was developed using the simplex algorithm, which finds local minima of the standard deviations between experiments and theory by adjusting the relevant parameters. The theoretical curves accurately fitted the experimental data and generated realistic diffusion parameters, implying that the mathematical model is capable of predicting the interstitial diffusion behavior of [3H]mannitol and that it will be a valuable quantitative tool in dual-probe microdialysis.

Agar↗
PubMed1996

[Mathematical model of supersaturation of mixed venous blood by gases on decompression].

The paper deals with the negative role of a symptomless gas-formation in the blood; there deduced an equation making it possible to calculate and limit supersaturation of the mixed venous blood and there developed a mathematical model with the use of which it is possible to assess the supersaturation of human mixed venous blood during decompression. It is established that as a result of limitation of supersaturation of the mixed venous blood under decompression there appears a series of short deep-water stops which increases the mode safety. The use of this equation in an integrated mathematical model of decompression furnishes an opportunity to develop the more adequate decompression modes.

Decompression↗
PubMed2004

Mathematical model of cylindrical form tolerance.

Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y14.5.1M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of tolerance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.

Algorithms↗
PubMed1998

Estimation of nitric oxide production and reaction rates in tissue by use of a mathematical model.

Nitric oxide (NO) produced by the vascular endothelium is an important biologic messenger that regulates vessel tone and permeability and inhibits platelet adhesion and aggregation. NO exerts its control of vessel tone by interacting with guanylyl cyclase in the vascular smooth muscle to initiate a series of reactions that lead to vessel dilation. Previous efforts to investigate this interaction by mathematical modeling of NO diffusion and reaction have been hampered by the lack of information on the production and degradation rate of NO. We use a mathematical model and previously published experimental data to estimate the rate of NO production, 6.8 x 10(-14) micromol . micron-2 . s-1; the NO diffusion coefficient, 3,300 micron2 s-1; and the NO consumption rate coefficient in the vascular smooth muscle, 0.01 s-1 (1st-order rate expression) or 0.05 microM-1 . s-1 (2nd-order rate expression). The modeling approach is discussed in detail. It provides a general framework for modeling the NO produced from the endothelium and for estimating relevant physical parameters.

Endothelium, Vascular↗
PubMedDate not supplied

Empirical and mechanistic mathematical models of temporal evolution of milk production in ruminants.

In the various sectors of animal science there has been little exploration of the theoretical mathematical aspects of data analysis and modelling. The dominant statistical methods used for the analysis of experimental data are rarely valuable for developing a deeper understanding of the problem. In addition they do not take account of the evolution over time of those variables of major interest to be studied. Only recently have more sophisticated methods of mathematical modelling begun to be used. Nonetheless attention tends to be focused exclusively on empirical models. Mathematical models with greater explanatory power, in particular those which use differential equations, are as yet little used. This work develops a mathematical approach to a problem that is of great interest in animal science: the development over time of milk production in economically important ruminant species.

Animals↗
PubMed1998

Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model.

The mechanisms underlying many important properties of the human atrial action potential (AP) are poorly understood. Using specific formulations of the K+, Na+, and Ca2+ currents based on data recorded from human atrial myocytes, along with representations of pump, exchange, and background currents, we developed a mathematical model of the AP. The model AP resembles APs recorded from human atrial samples and responds to rate changes, L-type Ca2+ current blockade, Na+/Ca2+ exchanger inhibition, and variations in transient outward current amplitude in a fashion similar to experimental recordings. Rate-dependent adaptation of AP duration, an important determinant of susceptibility to atrial fibrillation, was attributable to incomplete L-type Ca2+ current recovery from inactivation and incomplete delayed rectifier current deactivation at rapid rates. Experimental observations of variable AP morphology could be accounted for by changes in transient outward current density, as suggested experimentally. We conclude that this mathematical model of the human atrial AP reproduces a variety of observed AP behaviors and provides insights into the mechanisms of clinically important AP properties.

Action Potentials↗
PubMed1989

A mathematical model of cerebral blood flow chemical regulation--Part I: Diffusion processes.

This paper proposes a mathematical model which describes the production and diffusion of vasoactive chemical factors involved in oxygen-dependent cerebral blood flow (CBF) regulation in the rat. Partial differential equations describing the relations between input and output variables have been replaced with simpler ordinary differential equations by using mathematical approximations of the hyperbolic functions in the Laplace transform domain. This model is composed of two submodels. In the first, oxygen transport from capillary blood to cerebral tissue is analyzed to link changes in mean tissue oxygen pressure with CBF and arterial oxygen concentration changes. The second submodel presents equations describing the production of vasoactive metabolites by cerebral parenchyma, due to a lack of oxygen, and their diffusion towards pial perivascular space. These equations have been used to simulate the time dynamics of mean tissue PO2, perivascular adenosine concentration, and perivascular pH to changes in CBF. The present simulation points out that the time delay introduced by diffusion processes is negligible if compared with the other time constants of the system under study. In a subsequent work the same equations will be included in a model of the cerebral vascular bed to clarify the metabolite role in CBF regulation.

Animals↗
PubMed2003

Mathematical models of fluid and solute transport in peritoneal dialysis.

Three types of mathematical models of peritoneal transport are reviewed: distributed models, membrane models, and pore models. The distributed model described the capillary bed distributed within the tissue with two sets of transport parameters for the capillary wall and for the tissue separately. The membrane and the three pore models consider blood as a compartment separated by a transport barrier from the dialysis fluid in the peritoneal cavity. The membrane model describes the barrier using "black box" transport parameters, whereas the three pore model assumes three types of pores across the barrier (large, small, and ultra small pores) and a mathematical theory of fluid and solute transport through the pore. Each model contributes its specific share to investigations of peritoneal transport. The basic features and specific areas of application of all three types of the models are discussed.

Biological Transport, Active↗
PubMed2001

A mathematical model for chemoattractant gradient sensing based on receptor-regulated membrane phospholipid signaling dynamics.

The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring the coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of directional sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. A fundamental problem of directional sensing is its exquisite sensitivity. Even in the presence of relatively shallow chemoattractant gradients, cell projections are extended precisely in the region exposed to the highest chemoattractant concentration. This reflects the existence of a mechanism for amplifying the external signal. Recent experiments have identified a potential candidate for the seat of this amplification-membrane phosphoinositides such as PI4,5P2 and PI3,4,5P3 appear to be the first components of the signal transduction pathway to be amplified. Perturbing the cell with various chemoattractant gradients reveals a rich spectrum of phosphoinositide dynamics (Parent, C. A., and P. N. Devreotes. Science 284:765, 1999). The goal of this work is to develop a mathematical model of these phosphoinositide dynamics. Specifically, we address the following questions: (a) Which signaling pathway could lead to the localized accumulation of membrane phosphoinositides? (b) Why is this accumulation independent of the slope and mean value of the chemoattractant gradient? The model is based on the phosphoinositide cycle that transfers phosphoinositides between the plasma membrane and endoplasmic reticulum. We show that a mathematical model taking due account of receptor desensitization and the reaction-diffusion processes of the phosphoinositide cycle captures many of the experimentally observed dynamics. Having shown the plausibility of the model with respect to directional sensing, we discuss its implications for lamellipod extension, the process that follows directional sensing.

Biomedical Engineering↗
PubMed1985

Cytoplasmic and nuclear uptake of aldosterone in toad bladder: a mathematical modeling approach.

The mechanism of aldosterone uptake in the epithelial cells of toad bladder was studied using mathematical modeling. Two complementary approaches were used. The first involved analysis of cytosolic aldosterone binding at steady state according to models defined by the sum of independent noninteractive binding sites. The best model describing the experimental data corresponded to two specific binding sites with mean dissociation constant values of 0.20 and 60 nM for types 1 and 2, respectively. The second approach was based on the analysis of cytoplasmic and nuclear aldosterone uptake kinetics at 25 and 0 degrees C in intact bladder. Two models (A and B) were studied. They both implied the existence of two types of aldosterone binding sites as precursors of the corresponding chromatin bound complexes. In model A, nuclear translocation of the two types of receptors was assumed to obey first-order kinetics. In model B, the translocation process for type 1 sites involved a time lag leading to delayed binding to chromatin. Both models were found to fit the experimental data satisfactorily. The fit obtained for model B appeared to be better at low aldosterone concentrations.

Aldosterone↗
PubMed1986

Evaluation of a mathematical model analysing the relation between intradental nerve impulse activity and perceived pain in man.

In this investigation the usefulness and accuracy of the parameters of a mathematical model for the analysis of the effectiveness of different pain relieving procedures on pulpal pain were studied. The investigation was carried out using a previously developed mathematical/biological model on data from original subject recordings of Intradental Nerve Impulse Activity (INA) and pain estimations. Computer simulated INA and pain estimation curves were also used to enable calculation of the mathematical and biological conditions that are essential for the actual mathematical/biological model, and to facilitate the interpretation of the parameters of the model. It was shown by means of both real and simulated data that the mathematical model is well suited for the analysis of the effectiveness of some pain relieving procedures on pulpal pain. It was also shown that, by means of three new variables, the model could be made even more accurate and useful for this application.

Computer Simulation↗
PubMed1985

Mathematical models of metabolic systems: general principles and control of glycolysis and membrane transport in erythrocytes.

General methods for the mathematical modeling of metabolic systems are discussed. Attention is paid to the simulation of steady states as well as time dependent behaviour of biochemical reaction networks. Control coefficients are used for the quantitative evaluation of the parameter dependence of model variables. The methods are applied to the mathematical analysis of the energy metabolism of erythrocytes. New results are presented concerning the interaction of glycolysis and osmotic behaviour of the red cell (metabolic-osmotic model). A general method for the calculation of control coefficients is developed which gives the basis also for the interpretation of control coefficients using chains of causal actions.

Adenine Nucleotides↗