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PubMedDate not supplied

[Mathematical model of Thiobacillus ferrooxidans growth on a medium with ferrous iron].

A mathematical model is proposed for the growth of Thiobacillus ferrooxidans in the process of Fe2+ oxidation depending on the active acidity and temperature of the medium. The model was used to establish the correlation between the action of temperature and pH of the medium on the bacterial growth and oxidation of Fe2+. The range of pH values which had no effect on the bacterium is broader at 28 degrees C (from 2.5 to 2.8) than at 12 degrees C (from 2.3 to 2.4). Apparently, the growth of the bacterium and the enzymatic processes of Fe2+ oxidation are more susceptible to changes in the pH than in temperature, at least when it is lowered to 12 degrees C.

Culture Media↗
PubMed1991

A mathematical model for the rate of oxygenation of blood in pulmonary capillaries using nth-order one-step kinetics of oxygen uptake by haemoglobin.

A mathematical model is described for the process of gas exchange in pulmonary capillaries by taking into account the transport mechanisms of molecular diffusion, convection, and the facilitated diffusion due to haemoglobin. The nth-order one-step kinetics of oxygen uptake by haemoglobin has been incorporated. The rate k at which blood becomes oxygenated is determined by setting up an appropriate eigenvalue problem. This method eventually leads to a transcendental equation in k. A multiprecision technique due to Verma and Sharan (1980) is employed to obtain a physically acceptable solution. It is shown that, at equilibrium, the saturation of haemoglobin with oxygen computed from the analysis is fairly close to the data of Severinghaus (1966). It was found that 97.15% of the total haemoglobin combined with oxygen. The blood is oxygenated well before it leaves the pulmonary capillary. The dissolved oxygen takes longer to achieve equilibration whereas the carbon dioxide traverses a comparatively smaller distance in the capillary.

Biological Transport↗
PubMed1994

A mathematical model for the prediction of the impact of HIV infection on tuberculosis.

A mathematical model is introduced to study the accelerating impact of HIV infection on the incidence rates of tuberculosis (TB) disease. A sexually active population (15-49 years) is followed cross-sectionally over a period of time. Beginning with the year in which HIV infection was probably first present in the population, the model calculates the growing yearly incidence rates of new TB disease in HIV-positive and in HIV-negative individuals. Model equations, derived by an actuarial method, are developed recursively. Input information required for the calculations includes the age distribution of the study population, pre-HIV annual TB infection rates, annual HIV infection and mortality rates, and estimates of annual TB disease breakdown rates in the absence and in the presence of HIV infection. With correct input data, the model provides a useful blueprint for health agencies in designing effective programmes for curbing the future course of these dual epidemics in the population.

AIDS-Related Opportunistic Infections↗
PubMed1999

A mathematical model on germinal center kinetics and termination.

We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics are extended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes, and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we study the role of GC T cells in GC kinetics, GC termination, and B cell selection. We find that GC T cells play a major role in GC formation, but that the maintenance of established GC reactions requires very few T cells only. The results therefore suggest that the termination of a GC reaction is largely caused by lack of Ag on the follicular dendritic cells and is hardly influenced by Th cells. Ag consumption by centrocytes is the major factor determining the decay rate of the antigenic stimulus during a GC reaction. Investigating the effect of the Ag dose on GC kinetics, we find that both the total size of the GC and its duration are hardly influenced by the initial amount of Ag. In the model this is due to a buffering effect by competition for limited T cell help and/or competition between proliferating centroblasts.

Antigen-Antibody Complex↗
PubMed1991

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.

Animals↗
PubMed2001

Mathematical models as tools for evaluating the effectiveness of interventions: a comment on Levin.

Possible interventions to minimize resistance rates are numerous and can involve reduction and/or change in antimicrobial use, infection control, and vaccinations. As mathematical models are becoming more realistic they can be useful to quantitatively evaluate the relative contribution of individual risk factors and for the planning of future intervention strategies. The fitness cost associated with resistance is an important parameter and small differences can have a profound effect on the results. The mathematical models presented for communities predicted that even with cessation of antibiotic use, the decline in resistance frequency would be slow. This contrasts with successful interventions in Finland and Iceland. Future models have to include important variables such as herd immunity and take into account the heterogeneity of open communities. Provision of susceptible strains from areas with low resistance rates to areas with high resistance rates can have a profound effect on the success of interventions to minimize resistance.

Anti-Bacterial Agents↗
PubMed2005

A mathematical model of aircraft for evaluating the effects of shielding structure on aircrew exposure.

To investigate the influence of the aircraft structures and contents on the exposure of aircrew to the galactic component of cosmic rays, a mathematical model of an aeroplane has been developed. The irradiation of the mathematical model in the cosmic ray environment has been simulated using the Monte Carlo transport code FLUKA. Effective dose andambient dose-equivalent rates have been determined inside the aircraft at several locations along the fuselage at a typicaI civil aviation altitude. A significant effect of the shielding of aircraft structures has been observed on the ambient dose-equivalent rates, while the impact on the effective dose rates seems to be minor. Care should be taken in positioning the detectors onboard when the measurements are aimed at validating the codes.

Aerospace Medicine↗
PubMed1980

Cross-sectional echocardiography. II. Analysis of mathematic models for quantifying volume of the formalin-fixed left ventricle.

Cross-sectional echocardiography was used to quantify volume in 21 canine left ventricles that were fixed in formalin and immersed in mineral oil. Area, length and diameter measurements were obtained from short- and long-axis cross-sectional images of the left ventricle and volume was calculated by seven mathematic models. Calculated volume was then compared, by linear regression and percent error analyses, with fluid volume of the left ventricle, obtained by filling the chamber with a known amount of fluid. Volumes ranged from 13-146 ml. Mathematic models using short-axis area and long-axis length gave higher correlation coefficients (r = 0.982 and r = 0.969) and lower mean errors (10-20%) than standard formulas previously used for M-mode echo and angiography. Thus, short-axis area analysis with cross-sectional echocardiography is well-suited for quantifying left ventricular volumes in dogs.

Animals↗
PubMed2000

Improvement of internal dose calculations using mathematical models of different adult heights.

In internal dosimetry for both nuclear medicine and radiation protection, the adult morphology is represented by a limited number of anthropomorphic models that may not be suitable for all patients. To develop more patient-specific dosimetry, we derived six mathematical models for adults of different height. Three male models (160 cm, 170 cm and 180 cm) and three female models (150 cm, 160 cm and 170 cm), based on the MIRD model design, were developed from the statistical analysis of anthropometric data gathered from autopsies. Monte Carlo calculations were used to provide an example of estimations of S value for these new models for iodine 131 uniformly distributed successively in the stomach or in the urinary bladder. On average, for both male and female models, an increase in the model height of 10 cm leads to a mean reduction in the S value for iodine-131 by 20% and 29% when the stomach and the urinary bladder respectively are selected as source regions. Similarly, when the model height increases by 20 cm, the S values decrease on average by 35% and 48%. This study presents the use of anthropometric data to develop new mathematical models for adults of different height, and shows the significant influence of the morphology on dosimetric parameters.

Adult↗
PubMed2002

A mathematical model for the role of cell signal transduction in the initiation and inhibition of angiogenesis.

Neovascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In two previous papers, [Levine, H.A. and Sleeman, B.D. (1997) "A system of reaction diffusion equations arising in the theory of reinforced random walks" SIAM J. AppL Math. 683-730; Levine, H.A., Sleeman, B.D. and Nilsen-Hamilton, M. (2001b) "Mathematical modelling of the onset of capillary formation initiating angiogenesis." J. Math. Biol. 195-238] the authors introduced a new approach to angiogenesis, based on the theory o f reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial vascular endothelial cell growth factor (VEGF) receptors as the catalyst for transforming into a proteolytic enzyme in order to model the first stage. It is the purpose of this paper to present a more descriptive yet not overly complicated mathematical model of the biochemical events that are initiated when VEGF interacts with endothelial cells and which result in the cell synthesis of proteolytic enzyme. We also delineate via chemical kinetics, three mechanisms by which one may inhibit angiogenesis (inhibition of growth factor, growth factor receptor and protease function).

Animals↗
PubMed2000

A method for quantification of absolute amounts of nucleic acids by (RT)-PCR and a new mathematical model for data analysis.

Accurate quantification of nucleic acids by competitive (RT)-PCR requires a valid internal standard, a reference for data normalization and an adequate mathematical model for data analysis. We report here an effective procedure for the generation of homologous RNA internal standards and a strategy for synthesizing and using a reference target RNA in quantification of absolute amounts of nucleic acids. Further, a new mathematical model describing the general kinetic features of competitive PCR was developed. The model extends the validity of quantitative competitive (RT)-PCR beyond the exponential phase. The new method eliminates the errors arising from different amplification efficiencies of the co-amplified sequences and from heteroduplex formation in the system. The high accuracy (relative error <2%) is comparable to the recently developed real time detection 5'-nuclease PCR. Also, corresponding computer software has been devised for practical data analysis.

Cell Line↗
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↗
PubMed2003

[Dosage regimen optimization in cancer chemotherapy using a 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 could minimize the tumor burden while limiting toxicity on the white blood cells. Simulation suggests that the optimal drug administration is an initial high dose chemotherapy up to saturation of constraints associated with normal cell toxicity followed by a maintenance continuous infusion at a moderate rate. Data related to etoposide investigations were next used in a feasibility study. Simulations made with the usual clinical protocols and optimized protocols revealed that model-based optimal drug doses lead to greater cytoreduction. Also, examples showed how to use this new approach for the dose ranging problem and they evaluated the sensitivity of the optimized protocols with respect to the clinical constraints.

Antineoplastic Agents↗
PubMed2003

Mathematical models for the evaluation of antibiotic resistance in hospitals: a systematic review.

As the appearance and spread of antibiotic resistance is becoming an increasingly serious public health problem, there is a definite need for further studies by simulation, experiment and observation. Mathematical models may provide very useful tools to develop a rationale to extend the effective life of existing and newly introduced antimicrobial agents. In this work we systematically reviewed a number of mathematical models recently presented in the literature, in order to provide a brief and informative tool for public health policy makers, regarding the spread of antibiotic resistance, worldwide.

Bacteria↗
PubMed1983

[Mathematical model of baroreflex regulation of hemodynamics in the dog].

A non-linear mathematical model of dog hemodynamics regulation was developed including descriptions of the cardiovascular system, the arterial baroreflex and the Beinbridge reflex. Model calculated arterial and venous pressure, blood flow, and heart rate are in good agreement with experimental data.

Animals↗
PubMed1993

[A mathematical model for the dynamics of primitive biological macromolecules and its evolutionary implications].

A mathematical model, adopted from the logistic equations for population growth and interspecific competition in ecology, was proposed for the dynamics of primitive biological macromolecules: [formula: see text] where Nm is the copy number of a kind of biological macromolecule in primitive environment at time t. rm is the intrinsic replicating capacity (rate) of the macromolecule. Km is the carrying capacity (resource limit) of the primitive environment. dNm/dt is the instantaneous rate of increase of copy number of the primitive biological macromolecule beta 12 and beta 21 are competition coefficients concerning the inhibition of macromolecule 2 on macromolecule 1 (beta 12), and macromolecule 1 on macromolecule 2 (beta 21) other lower indexes in the equations refer to macromolecule 1 or 2. By analysing the possible competition outcomes deduced from the model, a conclusion with evolutionary implications could be drawn that the biological diversity would be very low shortly after the origin of life in the primitive biosphere. In other words, the abundant biological macromolecules capable of replicating in the primitive biosphere would be quite unique in kinds, and this uniqueness would therefore be the initial basis of biological evolution which would then go from low biological diversity to high biological diversity. The model is also helpful for the understanding of the origin of repeated sequences which are widely present in the genomes of modern organisms.

Animals↗
PubMedDate not supplied

A new implemented version of program MIR (MIR II): analysis and identification of mathematical models in enzyme and transport kinetic studies.

The computer program MIR previously described (R. Bianchi, G.M. Hanozet and M. Pilone Simonetta, Comput. Prog. Biomed. 16 (1983) 189) that fits trial rate laws to enzyme and transport steady-state kinetic data by the least-squares method has been enhanced. The new version MIR II is an interactive program and it consists of five major routines and a larger number of smaller program elements to perform the linear (three different functional forms) and non-linear (eleven mathematical models) regression analysis of kinetic data from enzyme and transmembrane transport experiments, also in the presence of inhibitors. Other features of the new program include a set of statistics and tests useful for the model building process, for the development of the mathematical model and for its validation and maintenance. An algorithm for fitting a straight line taking into account errors in both x and y is also provided.

Algorithms↗