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At least 991 records · Page 55Linked to original sources
PubMed2003

Dynamic mathematical model of high rate algal ponds (HRAP).

This article presents a mathematical model to describe High-Rate Algal Ponds (HRAPs). The hydrodynamic behavior of the reactor is described as completely mixed tanks in series with recirculation. The hydrodynamic pattern is combined with a subset of River Water Quality Model 1 (RWQM1), including the main processes in liquid phase. Our aim is to develop models for WSPs and aerated lagoons, too, but we focused on HRAPs first for several reasons: Sediments are usually less abundant in HRAP and can be neglected, Stratification is not observed and state variables are constant in a reactor cross section, Due to the system's geometry, the reactor is quite similar to a plugflow type reactor with recirculation, with a simple advection term. The model is based on mass balances and includes the following processes: *Phytoplankton growth with NO3-, NO2- and death, *Aerobic growth of heterotrophs with NO3-, NH4+ and respiration, *Anoxic growth of heterotrophs with NO3-, NO2- and anoxic respiration, *Growth of nitrifiers (two stages) and respiration. The differences with regard to RWQM1 are that we included a limiting term associated with inorganic carbon on the growth rate of algae and nitrifiers, gas transfers are taken into account by the familiar Adeney equation, and a subroutine calculates light intensity at the water surface. This article presents our first simulations.

Bioreactors↗
PubMedDate not supplied

[Mathematical modelling of apoptosis and necrosis processes in in vitro cell culture].

Mathematical models of apoptosis and necrosis in in vitro cultured cells for different ways of indication of phenotypical manifestations of these processes are proposed. The models make it possible to calculate the probability of apoptosis and necrosis programming of cells, to appraise and compare intensities of these processes using experimental data.

Apoptosis↗
PubMedDate not supplied

[Reproducibility of a mathematical model for calculating survival in multiple myeloma].

The reliability of the mathematical model for calculating survival proposed by Merlini, Waldenstrom e Jayakar (1980) was tested in a group of 80 patients with multiple myeloma. The observed and calculated survivals were compared using univariate regression analysis. The results show that a significant (p less than 0.001) relationship between observed and calculated survival exists in the study patient group. These observations confirm that this useful and reliable clinical staging system can be a basis for individualization of a new treatment approach for each stage in order to reach an optimal treatment for multiple myeloma patients.

Adult↗
PubMed1984

Determining hepatic transport kinetics by mathematical modeling.

Three approaches to the measurement of hepatic transport kinetics by mathematical modeling are briefly reviewed. The so-called lumped, two-compartment model and the single-pass multiple-indicator dilution method enjoy a long history of wide application, but each is subject to important errors inherent in their underlying assumptions. An understanding of the reasons for these errors, as revealed by simulation analysis, suggests a third approach that can substantially improve the previous difficulties.

Animals↗
PubMedDate not supplied

[A mathematical model of the seasonal morbidity of shigellosis].

A new epidemiologically significant mathematical model for the prognosis of seasonal morbidity in dysentery caused by S. flexneri and S. sonnei has been developed. This model may be used for solving problems on the epidemiology of Shigella infections. In this model quantitative ratios are determined by means of the system of nonlinear integral-differential equations in partial derivatives of the first order with edge conditions of the integral type. This model makes it possible to make multiple calculations with a view to obtaining the most probable picture of the development of the epidemic process at individual territories, to ascertain and make prognosis the terms and peaks of morbidity rises year after year in succession. The model permits the evaluation of specific features of the course of dysentery in patients of different ages in different groups of the population, affected by various nosological forms of shigellae. The relationships indicated by the model have been realized in the form of the computer program "SHIGELLA C" permitting multiple calculations of dysentery morbidity by means of an IBM PC/AT.

Dysentery, Bacillary↗
PubMed1997

A mathematical model of T lymphocyte proliferation controlled by interleukin-2 internalization.

A mathematical model of the first in vitro IL-2-controlled division cycle of T lymphocytes is presented. The model describes the population dynamics of T cells at different stages of the cell cycle and introduces "molecular" equations for the G1-S phase control. These equations are based on the current knowledge of the biochemical mechanisms of ligand-receptor binding, ligand and receptor synthesis, and internalization of the ligand-receptor complexes. The temporal order in the biosynthesis of IL-2 and IL-2R during the G1a and G1b phases is investigated. We show numerically that the maximum number of cells in the S-phase depends on the reversibility of the G1a-G1b transitions, on the rates of ligand-receptor binding, ligand and receptor synthesis, and internalization of the ligand-receptor complexes. The phase portraits for different hypotheses on the temporal order of the IL-2 and high affinity receptor synthesis at the G1 phase of the cell cycle are qualitatively different. On this basis, simple kinetic experiments to distinguish between these alternatives are proposed.

Animals↗
PubMed1997

[Current issues of mathematical modeling and advancement in radiology].

An analysis of certain issues in mathematical support and optimization of radiological procedures has pointed to many criteria involved in designing effective schedules of radiotherapy of neoplasms. TDF, CRE and ETD may be used for relevant evaluations. The greatest promise is held by such criteria as tumor tissue ablation (TTA) and radiation injury complications (RIC) in normal organs and tissue. This calls for development of suitable methods. Considering the high complexity of the body. It should be expected that body responses to radiation are determined by irradiation parameters and condition of target tissues. The report deals with a procedure for adapting mathematical models to on-line requirements. Newly-developed programming complexes are designed to help the medical radiologist integrate available data with his or her clinical findings.

Models, Theoretical↗
PubMed1999

The value of oxygen-carrying solutions in the operative setting, as determined by mathematical modeling.

BACKGROUND: The use of oxygen carriers (red cell [RBC] substitutes) in acute trauma and in surgery, with or without the use of acute normovolemic hemodilution (ANH), is being investigated. Mathematical modeling was used to assess the impact of RBC substitutes, with or without ANH, in the elective surgical setting. STUDY DESIGN AND METHODS: Mathematical equations and computer models were developed on the basis of previously described mathematical principles, for better understanding of the potential efficacy of RBC substitutes for blood needs with or without ANH. Savings were calculated for a patient with a blood volume of 5000 mL and an initial hematocrit (Hct) of 45 or 30 percent. RESULTS: Substantial increases in the tolerable blood losses (or reduced allogeneic RBC needs) were most evident when the use of an RBC substitute to achieve severe ANH to a Hct that the patient might not otherwise have been able to tolerate was combined with the use of RBC substitutes as replacement for the surgical blood subsequently lost. However, the benefit was greatly dependent on the patient's initial Hct. For example, for a patient with a blood volume of 5000 mL and an initial Hct of 45 percent, a blood loss of approximately 2500 mL resulted in a final Hct of 28 percent without the use of an RBC substitute or ANH. In contrast, with the combined use of staged ANH with an RBC substitute and the RBC substitute for lost surgical blood, a blood loss of up to 14.5 L could be tolerated. However, in an anemic patient (blood volume 5000 mL, initial Hct 30%), a Hct of 28 percent cannot be sustained without the use of allogeneic RBCs for any of the described strategies, even when blood losses were as low as 1 L. CONCLUSION: The use of RBC substitutes has the potential to result in a substantial reduction in allogeneic RBC exposure. This benefit is essentially limited to the nonanemic patient when the use of an RBC substitute is combined with severe ANH and there is concomitant large perioperative blood loss. Anemic patients can be expected to have only limited benefit, because of an inability to sequester an adequate volume of autologous RBCs via ANH.

Blood Substitutes↗
PubMed2003

New mathematical model for the correct prediction of the exchangeable blood volume during acute normovolemic hemodilution.

BACKGROUND: The blood volume that has to be exchanged for crystalloids and/or colloids during acute normovolemic hemodilution (ANH) in order to reach a preset target hemoglobin concentration (hb) is usually predicted by the Bourke and Smith formula developed in 1974. This formula systematically overestimates the 'true' exchangeable blood volume (EBV), a fact that may potentially endanger patients because the target hb will be missed and the normovolemic anemia might turn out to be more severe than a priori intended. Our objective was to develop a more accurate mathematical model of hemodilution kinetics and to validate this new model in animals and in patients undergoing ANH. METHODS: Twenty-two anesthetized beagle dogs and 18 patients under balanced anesthesia underwent isovolemic hemodilution with hydroxyethyl starch (HAES 6%, 200 000) to a target hb of 7 g dl-1 or 9 g dl-1, respectively. Exchangeable blood volume predicted by use of the different mathematical models was compared with the blood volume actually exchanged to meet the preset target hb. RESULTS: Calculation of EBV by the Bourke and Smith formula (EBVB + S) systematically overestimated the volume actually exchanged (overestimation: dogs 15%, patients 20%), whereas our new iterative model predicted EBV (EBViterative) more reliably (overestimation: dogs 1%, patients 8%). In both cases EBVB + S differed significantly from the EBViterative. CONCLUSION: Exchangeable blood volume is predicted more accurately by the new iterative model than by the Bourke and Smith formula. The iterative model leads to an improvement in patient safety and provides a physiologically adequate basis for future studies investigating the efficacy of ANH in reducing allogenic blood transfusions.

Algorithms↗
PubMed1994

DNA damage and the proliferation and aging of cells in culture: a mathematical model with time lag.

This paper is an extension of an earlier one by the same author in which a mathematical model was presented to describe the proliferation and aging of cells in culture. The model consists of a group of ordinary differential equations with a time lag. In the previous paper, the time lag was omitted for simplicity and the resulting differential equations were resolved analytically. It was shown that the model explains the behavior of a cell culture reasonably well. In this paper, the analytical solution of the original differential equations is presented without omitting the time lag. An analytical description of the variations in doubling capability between sister cells that was only simulated numerically in the earlier paper is given.

Animals↗
PubMed2002

Mathematical modelling of antifungal action.

In this paper a simplified modelling approach indicated that yeast growth was inhibited by an antifungal drug according to an exponential function. In addition, the corresponding inhibition rate followed a hyperbolic function the parameters of which permit us to determine the percentage of maximum inhibition and the minimum inhibitory concentration for 80%. From the equation of a hyperbola it was also possible to calculate an affinity constant Kaff corresponding to the inverse of the concentration of antifungal drugs giving half the maximal inhibition. The affinity constant was demonstrated to be characteristic of the yeast strain and of the antifungal drug employed. Simulation of the mathematical modelling enabled determination of a theoretical inhibition level corresponding to strong concentrations of antifungal drugs which cannot be carried out for technical reasons (precipitates, opacity etc.). The interest of this mathematical modelling of growth and inhibition to predict the doses of antifungals which can act synergistically is discussed.

Amphotericin B↗
PubMed1998

Parameterization of inoculum effect via mathematical modeling: aminoglycosides against Staphylococcus aureus and Escherichia coli.

Inoculum effect describes the inoculum size dependent changes in minimum inhibitory concentrations (MIC) exhibited by antibiotic-bacterium combinations demonstrating such effect. Traditionally, inoculum effect has been loosely defined based on the extent of increase in the MIC with respect to the increase in inoculum size. In most studies, assessment of MIC data has relied on the arbitrary selection of a point of reference for both baseline MIC and inoculum size. More importantly, this conventional method of assessment does not permit information conveyed in a complete MIC versus inoculum size profile to be fully explored. To undertake these issues, a mathematical model was developed for the description of the entire inoculum effect profile. With the employment of three key parameter estimates, i.e., the baseline MIC, the threshold inoculum size at which the increase in MIC commences, and the rate of increase in MIC with respect to inoculum size, both the shape and location of the profile could be adequately defined. To verify the application of this model, a series of four aminoglycosides were tested against standard strains of E. coli and S. aureus. Results showed a good degree of organism specificity and antibiotic-class dependency of the inoculum effect profiles. Analysis of the parameter estimates obtained provided further support for these observations. In conclusion, the mathematical model developed in the present study adequately described the inoculum effect exhibited by the various aminoglycoside-bacterium combinations tested. The parameter estimates generated by the modeling approach allowed comparison and quantitative analysis of the inoculum effect profiles with minimal difficulties.

Amikacin↗
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↗
PubMed1999

A mathematical model predicting the frequency of aberrant rearrangements in the T-cell receptor gene.

The T-cell receptor (TCR) genetic loci undergo an orderly process of recombination in ontogeny in order to generate a diverse array of antigen receptors. Normally occurring, out-of-frame and incomplete rearrangements produce non-productive TCR transcripts. Abnormalities in the rearrangement process occur at very low frequencies but may predominate in inborn errors of recombination. Detecting these abnormalities in surviving pools of lymphocytes is difficult and typically focuses on identification of abnormally rearranged alleles or on detecting abnormalities in recombinase proteins. Thus, there currently exists no rapid screening method to identify aberrant V(D)J recombination. To address this issue, a mathematical model was developed to predict the error rate from the measured proportions of different non-productive TCR alleles. Since the proportions of different non-productive rearrangements vary in a characteristic fashion in response to abnormalities in the recombination process, the mathematical model presented here provides a tool to indirectly assess the error rate of TCR recombination. The model was applied to a group of patients with Omenn's syndrome, most of whom had an unknown primary defect. The results indicate that these patients had a > 90% rate of aberrant TCR recombination.

Alleles↗
PubMed2005

A mathematical model of the euglycemic hyperinsulinemic clamp.

BACKGROUND: The Euglycemic Hyperinsulinemic Clamp (EHC) is the most widely used experimental procedure for the determination of insulin sensitivity, and in its usual form the patient is followed under insulinization for two hours. In the present study, sixteen subjects with BMI between 18.5 and 63.6 kg/m(2) were studied by long-duration (five hours) EHC. RESULTS: From the results of this series and from similar reports in the literature it is clear that, in obese subjects, glucose uptake rates continue to increase if the clamp procedure is prolonged beyond the customary 2 hours. A mathematical model of the EHC, incorporating delays, was fitted to the recorded data, and the insulin resistance behaviour of obese subjects was assessed analytically. Obese subjects had significantly less effective suppression of hepatic glucose output and higher pancreatic insulin secretion than lean subjects. Tissue insulin resistance appeared to be higher in the obese group, but this difference did not reach statistical significance. CONCLUSION: The use of a mathematical model allows a greater amount of information to be recovered from clamp data, making it easier to understand the components of insulin resistance in obese vs. normal subjects.

Blood Glucose↗
PubMedDate not supplied

[Mathematical model of electrogenic transport through biomembranes via oligomeric channels capable of conformational transitions].

A mathematical model of electrogenic ion transport across biomembranes by oligomeric channels liable to conformational transformations has been derived. The model describes changes with time of the membrane potential and near--membrane ion concentrations. Different types of the channel conductance regulation such as activation or inhibition by the permeating ions and membrane potential have been considered. It appears that in the presence of such regulations 1) the channel voltage-current curves have negative resistance regions; 2) the dependence of the quasisteady state (or resting) potential on the ion concentrations in the solution is of hysteresis nature; 3) the model may have multiple steady-state and oscillating solutions.

Cell Membrane Permeability↗
PubMed2003

[High resolution fluorescence microscopy in combination with mathematical modelling. First evidence of sub-cellular anesthetic effects on Ca2+ sparks in situ].

Volatile anesthetics used in daily clinical routine, are associated with a rare but life-threatening disease, malignant hyperthermia. To date it is well known that, with the exception of xenon and nitrous oxide, all volatile anesthetics have the potential to trigger calcium (Ca(2+)) release from the sarcoplasmic reticulum, thereby influencing the Ca(2+) homeostasis in muscle fibers. The effects of volatile anesthetics have been previously studied by recording Ca(2+)-activated force transients in muscle fibers and by quantifying the effects on isolated intracellular Ca(2+)-release channels (ryanodin receptors). The use of high resolution fluorescence microscopy methods in combination with spatio-temporal mathematical models allows the effects of volatile anesthetics on functional clusters of ryanodin receptors in mammalian skeletal muscle fibers to be studied in situ for the first time.Thus, the analysis of cellular Ca(2+)-activated force production and single channel properties in conjunction with mathematical models allows the quantification of the effects of volatile anesthetics on Ca(2+)-release in the natural physiological environment on the basis of the underlying molecular architecture. In addition to the basic understanding of alterations in the Ca(2+) homeostasis induced by volatile anesthetics in muscle and nerve cells, the results are also of direct clinical importance for the understanding of the pathogenesis of malignant hyperthermia,where ryanodin receptor mutations are currently thought to result in an increased Ca(2+) release under the influence of volatile anesthetics.

Anesthetics, Inhalation↗