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At least 865 records · Page 48Linked to original sources
PubMed2006

A mathematical model for the evaluation of amplitude of hemoglobin fluctuations in elderly anemic patients affected by myelodysplastic syndromes: correlation with quality of life and fatigue.

Therapy with RBC transfusions and rHuEPO for management of anemia in patients with myelodysplastic syndromes causes recurrent fluctuations in hemoglobin levels. The purpose of this study was to elaborate a mathematical model for the interpretation of hemoglobin fluctuations and to correlate the resulting numerical parameter (Variaglobin Index) with quality of life and fatigue. In 32 myelodysplastic patients, lower amplitude of the Variaglobin Index was found significantly correlated with a better quality of life and less fatigue. The mathematical model proposed here makes it easy to monitor anemia in myelodysplastic patients and to adjust therapy accordingly.

Aged↗
PubMed1993

Mathematical model for comparison of time-killing curves.

The relevance of mathematical modeling to investigations of the bactericidal effects of antimicrobial agents has been emphasized in many studies of killing kinetics. We propose here a descriptive model of general use, with four parameters which account for the lag phase, the initial number of bacteria, and the limit of effectiveness and bactericidal rate of antimicrobial agents. The model has been applied to several kinetic datum sets with amoxicillin, cephalothin, nalidixic acid, pefloxacin, and ofloxacin against two Escherichia coli strains. It is a useful tool to compare killing curves by taking into account model parameter confidence limits. This can be illustrated by studying drug effects, strain effects, and concentration effects. For the antibiotics used here, concentration effects had an influence mainly on the length of the lag phase and the minimum number of living cells observed. It is therefore clear that differences in the killing curves with changes in one or more parameters could occur.

Amoxicillin↗
PubMed1999

Independent prediction of naphthalene transport and biodegradation in soil with a mathematical model.

Experiments were performed to test the ability of a mathematical model to predict naphthalene transport and biodegradation. Pseudomonas putida G7, a model bacterial strain capable of degrading naphthalene, was added to a column packed with the soil that had been pre-equilibrated with naphthalene. Model prediction for transport and degradation were based on predetermined parameters that described naphthalene desorption kinetics and the utilization of naphthalene by the test bacterium. However, initial prediction for naphthalene biodegradation was high, and the formation of cell aggregates is advanced as a plausible explanation. Access of substrate to cells in the interior of an aggregate would be restricted. When the numerical simulation was conducted with a factor to account for cell aggregation, it successfully described the experimental data. Thus, with a single adjustable parameter (an average effectiveness factor), the model predicted macroscopic responses of naphthalene in soil-columns where naphthalene was subject to transport and biodegradation.

Adsorption↗
PubMed1976

A mathematical model for microbial growth under limitation by conservative substrates.

A mathematical model is suggested for growth of microorganisms under limitation by "conservative" substrates such as inorganic ions or vitamins that are not broken down after uptake into the cells, but that wholely or partly remain available for production of biomass. The specific growth rate is expressed here as a function of the intracellular "concentration" of the limiting substrate, defined as the amount of substrate within the cells per unit of cell dry weight. In the model, the intracellular substrate is divided into two parts. One part is a "structural" substrate not available for further growth. The other part is an "excess" or "functional" substrate that is used for biomass production and is assumed to be converted into structural substrate proportionally to growth. The rate of growth is believed to be controlled by the intracellular concentration of excess substrate.

Bacteria↗
PubMed2001

A mathematical model of auxin-mediated radial growth in trees.

A mathematical model is presented to describe the coupling between the concentration of indole-3-acetic acid (IAA) in the cambial region of a tree branch and the radial expansion of the branch during active growth. The main features of the model are (1) the branch cambium is treated as an approximately cylindrical surface of negligible thickness, (2) the rate of radial growth is proportional to the mass of IAA per unit area on the cambial surface, and (3) IAA is transported basipetally through the cambium at a constant speed. We neglect the role of elastic strains in the determination of branch shape, and the effects of IAA synthesis and metabolization in the cambium, so the model is not quantitatively accurate. However, the model does reproduce several important qualitative features of tree growth including the approximate area-preserving property of tree branch junctions and the ability of a branch to maintain its shape despite perturbations due to injury.

Indoleacetic Acids↗
PubMed1980

Limited usefulness of mathematical models for assessing the carcinogenic risk of minute doses.

No mathematical model for carcinogenesis can cover all the exigencies of life. The usefulness of any model is consequently limited. A model may provide a basis for graduating data, though it need not be altogether valid to give reasonable graduations in the observable range and competing models could do as well. Or for providing useful insights into situations, a model need not be completely valid. But for the problematic issue of extrapolating to minute doses, the question of validity is crucial. A variety of related issues and approaches are discussed, beginning with a kinetic model proposed by Cornfield. Other discussions relate to the empirical relationship described by Druckrey, the linear model approach espoused by Crump and Guess and their associates, the safe dose estimation procedure of Hartley and Sielken and the relation of these approaches to the Mantel-Bryan approach. Issues like between-species extrapolation, limiting concern to near lifetime risks, occupational exposures vs. general population exposures are also considered.

Carcinogens↗
PubMed1979

Mathematical modeling -- guide to high-dose methotrexate infusion therapy.

A mathematical model that describes methotrexate pharmacokinetics has been refined for use as a guide to dose escalation during high-dose methotrexate infusion therapy. Parameters for the model are adjusted for a patients by the SAAM computer program of Berman and Weiss, on the basis of plasma concentrations obtained during the initial course of therapy. Various dose escalations can be simulated by the computer and a print-out of predicted plasma concentrations obtains. The model has been used successfully to predict plasma concentrations after high-dose infusions in patients, including those with abnormal creatinine clearances. The program is designed to allow comparisons among infusions of any duration. This can be helpful when a change from a 24-hour infusion to a 6-hour infusion is contemplated for a patient. Deviations of observed values from those predicted are used to warn of the possibility of delayed toxicity secondary to methotrexate and alert the physician that increased amounts of rescue agent may be required.

Carcinoma, Squamous Cell↗
PubMed1986

Mathematical model for the control of ColE1 type plasmid replication.

A mathematical model for the molecular events controlling replication of ColE1 type plasmids is described. All the model parameters can be evaluated independently. The model simulates plasmid replication and accurately predicts the copy-number of ColE1 plasmids carrying a variety of regulatory mutations. The model is used to test the plausibility of hypotheses concerning the interactions of regulatory elements involved in the replication apparatus. The model favorably supports the mechanism proposed by Tomizawa and co-workers concerning the nature of RNA-RNA interactions and that the Rom protein increases the binding between the two RNA species. The hypothesis that the interactions of RNA I-II increases the susceptibility of RNA II to the action of endonucleases is not a plausible mechanism.

DNA Replication↗
PubMed1994

Mathematical modelling of the enteric nervous network. 1: Cholinergic neuron.

A mathematical model is proposed to describe the coupled electrochemical mechanisms of nerve-pulse transmission via cholinergic synapse. Based on pharmacological and morphophysiological data, the model describes the dynamics of the propagation of the electric signal along the unmyelinated geometrically non-uniform axon of the neuron and the chemical mechanisms of the transformation of the electrical signal in the synaptic zone into the postsynaptic output. The combined nonlinear system of partial and ordinary differential equations has been obtained and solved numerically. The results of numerical simulation of the function of the cholinergic neuron quantitatively and qualitatively describe the dynamics of Ca2+ ions influx into the terminal, acetylcholine release from the vesicles, accumulation of its free fraction, diffusion into the synaptic cleft, and binding with the receptors on the postsynaptic structures with the generation of the fast excitatory postsynaptic potential. They are in good agreement with the observed experimental findings.

Acetylcholine↗
PubMed2004

Optimum force magnitude for orthodontic tooth movement: a mathematic model.

The aim of this study was to develop a mathematic model to describe the relationship between magnitude of applied force and rate of orthodontic tooth movement. Initially, data were extracted from experimental studies in dogs (beagles), in which controlled, standardized forces were used to move mandibular second premolars distally. Curve-fitting by nonlinear regression analysis provided an equation describing the relationship between force magnitude and rate of tooth movement in beagles. A similar equation was subsequently used to analyze the limited available data from the literature on human canine retraction. The maximum rates of tooth movement in humans and dogs are very similar. A threshold for force magnitude that would switch on tooth movement could not be defined. The model showed that a wide range of forces can be identified, all of which lead to a maximum rate of tooth movement.

Animals↗
PubMed2000

Mathematical modeling of citric acid production by repeated batch culture.

A mathematical model has been created for the process of citric acid biosynthesis by yeast (mutant strain Yarrowia lipolytica) cultivated by the repeated batch (RB) method on ethanol under conditions of nitrogen limitation. The model accounts for cell growth as a function of nitrogen concentration in the culture liquid; nitrogen uptake by growing cells; citric acid production; pH control in the fermentor by means of NaOH addition; and changes in system volume. The model represents a system of five nonlinear differential equations. Experimental measurements of cell concentration, citric acid concentration, and cultivation broth volume were used with the least squares method to determine the values of eight model parameters. The parameter values obtained were consistent with literature data and general concepts of cell growth and citric acid biosynthesis. The model has been used to predict optimum RB culture conditions.

Journal Article↗
PubMed1999

Planning chemotherapy based schistosomiasis control: validation of a mathematical model using data on Schistosoma haematobium from Pemba, Tanzania.

A mathematical model, based on a deterministic differential equation framework, has been developed to predict the impact of community chemotherapy programmes for human schistosomiasis. Here, this model is validated using data collected from a long-term control programme for urinary schistosomiasis on the island of Pemba, Zanzibar, United Republic of Tanzania, initiated in 1986 and still ongoing, in which schoolchildren were offered praziquantel chemotherapy every 6 months. Prevalence of infection and blood in urine were monitored in all the schools (total 26000 children from 60 schools) and more detailed data were collected in selected evaluation schools. Model predictions were run by using the initial prevalence as input. The predictions were very close to the observed decreases in prevalence and in prevalence of blood in urine. The correspondence improved further when the data were combined, going from single school level to district, and when the entire data set was combined. The accuracy of the predictions suggests that this model could be used as a tool to predict the consequences of chemotherapy control programmes. It is currently in press as a Windows software package under the name of 'EpiSchisto'.

Adolescent↗
PubMedDate not supplied

A simple structured mathematical model for biopolymer (PHB) production.

Economic production technology for a biodegradable polymer (poly-beta-hydroxybutyrate, PHB) is urgently required to replace conventional polymers, which have an inherent disadvantage of staying in the environment forever. Various approaches have been applied for improving the productivity and reducing the production cost, which are considered to be the two major problems associated with industrial production of PHB. One of the engineering approaches to improve PHB productivity could be to design and implement model-based fed-batch cultivations to provide desirable nutrient availability. In the present study, growth and intracellular biopolymer storage kinetics of Ralstonia eutropha was studied in a batch cultivation process. It featured 19.7 g/L biomass and 10.89 g/L PHB with a productivity of 0.18 g/L.h. The effect of carbon, nitrogen, and phosphate limitations and inhibitions on growth was studied in detail. A structured model featuring typical growth limitations and/or possible inhibitions was then proposed. The value of the model parameters was found by minimizing the difference between experimental value and model simulation at all data points and for all process variables. The optimal batch model parameter values obtained above were used to solve the differential equations numerically. The simulated data obtained in this way was then compared with the experimental data to establish the validity of the batch model. The proposed model was then compared with literature reported mathematical models to reconfirm its accuracy. Statistical validity of the developed model and historical models to describe the observed experimental kinetics was then investigated to reinforce the accuracy of the developed simple model.

Bioreactors↗
PubMed2002

Mathematical model for meso- and thermophilic anaerobic sewage sludge digestion.

A mathematical model is developed to describe the dynamic behavior of mesophilic (35 +/- 5 degrees C) and thermophilic digestion (55 +/- 5 degrees C). Special emphasis is given to acetotrophic methanogenesis and propionate degradation, as the steps that determine the stability of anaerobic digestion, as well as to hydrolysis rate, which determines the degradation efficiency of particulate degradable organic carbon. Within the range of 6-20 (mesophilic) and 2-8 d (thermophilic) hydraulic retention time (HRT), the observed maximum growth rates for acetotrophic methanogens are 0.33 and 1.3 d(-1), respectively, with a 15% decay rate. Temperature and pH dependence as well as ammonia inhibition of acetate and propionate conversion are determined and included in the model, which allows us to simulate the effect of protein- and nitrogen-rich waste addition and the consequences of temporarily increased free ammonia at high pH. No inhibition of hydrogen conversion was observed in the same free ammonia range. The pH optimum is between 6.6 and 7.3. Acetotrophic methanogenesis is strongly inhibited below pH 6.2, whereas above pH 7.4 it can be inhibited by free ammonia. For digesters fed with ordinary municipal sewage sludge, free ammonia inhibition of acetate conversion leads to an increase in acetate at about 35 and 140 mg of N/L for mesophilic (HRT = 20 d) and thermophilic (HRT = 6 d) conditions, respectively. The hydrolysis rate constant is 0.25 and 0.4 d(-1) respectively for these two conditions. The model is validated with load variation experiments in laboratory and full-scale digesters for step and shock loads.

Bacteria, Anaerobic↗
PubMed1977

Mathematical models for the evolution of multigene families by unequal crossing over.

Mathematical models of homologous but unequal crossing over between sister chromatids are presented. For mispairing by one repeat, the evolution of a multigene family by unequal crossing over can be represented by a linear birth-death process. The fixation rate of one repeat in a multigene family is estimated. For mispairing by more than one repeat, some approximate results are obtained.

Alleles↗
PubMed1997

A nonlinear mathematical model of electrically stimulated skeletal muscle.

A new biophysically based mathematical model for a human musculotendon system is presented. This model is developed specifically for skeletal muscle activated by functional electrical stimulation (FES). The reverse-order recruitment dynamics of FES activated systems are modeled, as are the underlying processes of force generation in mammalian muscle. The resulting system model is both nonlinear and highly coupled, reflecting the fundamental structure and behavior of skeletal muscle. A new heterogeneous model structure for a contractile element is also presented that overcomes many of the problems which arise when attempting to describe all possible contraction modes. It is found that the new model is robust, numerically stable, and easily implemented. Simulation results are presented that demonstrate the model's ability to capture a variety of nonlinear behaviors observed in skeletal muscle activated by FES. Significant insight into the internal dynamics of force development in FES muscle may also be gained from the model. This model is intended as a possible alternative to those currently available in the literature. It may be of use to those conducting research into the modeling, control and optimization of FES generated motion, and neural feedback systems.

Electric Stimulation↗
PubMed1999

Computer-controlled heart rate increase by isoproterenol infusion: mathematical modeling of the system.

The purpose of this study was mathematical modeling of the heart rate (HR) response to isoproterenol (Iso) infusion. We developed a computerized system for the controlled increase of HR by Iso, based on a modified proportional-integral controller. HR was measured in conscious, freely moving rats. We found that the steady-state HR can be described as a hyperbolic power function of the steady-state Iso flow rate. This dependence was coupled with a first-order difference equation to form a pharmacodynamic model that reliably describes the relationship between HR and Iso flow for any arbitrary form of Iso flow function. In simulation studies, we showed that the model continued to follow the HR curve from real-time experiments far beyond the initial "learning interval" from which its parameters were calculated. Our results suggest that the predictive ability and the simplicity of calculating the parameters render this pharmacodynamic model appropriate for use within future advanced, model-based, adaptive control systems and as a part of larger cardiovascular models.

Animals↗
PubMed1980

Mathematical model of the fetal cardiovascular system: the uncontrolled case.

A mathematical model was developed to study and to interpret the results of different experiments undertaken in the field of fetal cardiovascular physiology. This model consists of a total of six peripheral blood compartments and a detailed description of the heart. The unique characteristics of the fetal circulation, particularly the ductus arteriosus, the foramen ovale, and the placenta are incorporated into this model. No control mechanisms are incorporated. The model was validated by simulating several previously described experiments. First, the performance of the individual ventricles was measured. The results indicate that, in the normal physiological situation, the right ventricle is working near the upper limits of its function while the left ventricle works below its limits. Second, the circulatory system was stressed by increasing the blood volume and the results show a shift from right to left in the relative contributions of each ventricle to the total cardiac output. Finally, effects of clamping the several blood vessels of the umbilical cord were studied.

Animals↗