Good manners in good modeling: mathematical models and computer simulations of physiological systems.
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Computers↗
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Results for “Mathematical Model”
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[The hematopoietic system during chronic irradiation with high dose rates (mathematical modeling)].
Mathematical models have been developed to describe dynamics of some haemopoietic compartments in mammals subjected to long-term irradiation. Within the framework of the models developed an equation has been obtained for a critical dose-rate (Ncr) of chronic irradiation, leading to complete depletion of certain haemopoietic compartments, that helps to prognose the dangerous Ncr values without preliminary experiments.
Animals↗
[A study of the effect of radiation on megakaryocytopoiesis using a mathematical model].
Mathematical modelling used in analysing the postirradiation changes in megakaryocytopoiesis permitted to determine the level of radiation-induced injury in each experiment conducted and to show that megakaryocytopoiesis regulation followed the same mechanism after irradiation as it does normally and after the effect of hydroxyurea and anti-thrombocyte serum. The analysis has demonstrated that after the stem cell death induced by ionizing radiation, the regeneration can be provided by the committed cells, and the level of regeneration is determined by the maturity of precursors.
Animals↗
[Study of the combined action of an antibiotic and an immunostimulator using mathematical modeling].
A mathematical model of antibiotic and immunostimulator (IMS) combined effect on various elements of the immune system and general state of patients with infectious diseases is described. The model was constructed as a system including 6 usual differential equations of the 1st order. With the use of this model and a computer many diverse variants of infection development under conditions of treatment with IMS at the background of antibiotic therapy were modeled. Ii was shown that IMS-antibiotic complexes markedly improved the indices of antibiotic therapy as compared to the use of the antibiotics alone. In combined use of IMS and antibiotics it was possible to lower the antibiotic doses without lowering the antimicrobial effect. The use of IMS at the optimal period led to balanced activation of the host specific and nonspecific resistance factors at the background of antibacterial therapy. The results of the mathematical modeling corresponded to the data on protective effect of salmozan (IMS) and doxycycline (antibiotic) combination in animals (albino mice). It was concluded that the described mathematical model was adequate for validation and optimization of schemes for combined use of IMS and antibacterial agents.
Adjuvants, Immunologic↗
Physical properties of resistance vessel wall in peripheral blood flow regulation--I. Mathematical model.
A mathematical model is introduced to investigate the influence of the physical properties of the resistance vessel wall on the metabolic and myogenic mechanisms. The resistance vessel wall is assumed to have an elastic property and the elastic modulus to be a function of pressure (myogenic) and flow (metabolic). Blood is Poiseuille's flow. The resulting mathematical equations for pressure-flow, pressure-diameter, pressure-wall tension and pressure-wall elastic modulus relationships introduced obey Laplace's law. Poiseuille's law and Hooke's law. In comparison with the experimental data (pressure diameter), the mathematical model is confirmed to explain well the dynamic behavior of the resistance vessel wall in vivo.
Elasticity↗
Epidermal cell proliferation. II. A comprehensive mathematical model of cell proliferation and migration in the basal layer predicts some unusual properties of epidermal stem cells.
The clustering of 3HTdR labelled cells in the epidermal basal layer and their changes with time have been modelled mathematically and cannot be adequately fitted by an earlier model of the cell kinetic organisation of the skin. A more refined model analysis was performed based on Monte Carlo computer simulations of cell layers which take cell division, cell aging and lateral as well as vertical cell migration into account. A large variety of hypothetical scenarios was tested to see if each could provide a fit to the clustering data. The analysis provides further support for the concept of a cell kinetic heterogeneity with a stem-transit-postmitotic differentiation scheme. In the best overall model scheme three transit divisions are predicted but unlike in the earlier model it is now postulated that postmitotic cells can be produced at all stages in the lineage rather than only at the end of the amplification scheme. Most important, the model predicts that stem cells and most of the transit cells differ in the way they process 3HTdR label. Grain dilution is an important mechanism to explain the fate of some labelled cells in the tissue, but on its own it can only consistently explain the data if the stem cells have a very low labelling index (LI less than or equal to 1%) which implies a very short biologically unreasonable S-phase. If a higher LI (longer S-phase) is assumed for the stem-cells other mechanisms must be predicted to explain the lack of large clusters and the increase in time of the singles. The selective segregation of chromosomes at mitosis is one such mechanism. However, on its own a large number of cells would have to behave in this way (i.e. both stem and T1 cells). If combined with other assumptions such as some grain dilution this selective segregation may be restricted only to stem cells. In addition the model allows cell production and migration rates to be estimated and the analysis can be related to the EPU-concept. Indeed the model itself would tend to automatically generate an EPU like structure. The model quantitatively reproduces LI, PLM, CL and clustering data.
Autoradiography↗
Mathematical modelling of the elastic properties of retina: a determination of Young's modulus.
The retina can be regarded as an elastic membrane or sheet which stretches and deforms when a force is applied to it. Isolated bovine retina was taken and a graded traction force applied to determine retinal profile as a function of force. The resulting profile can be modelled mathematically and the model then used to determine a value for the elastic constant. The value of the elastic constant obtained by this method is approximately 2 N/m. This value of the elastic constant, combined with the observed retinal thickness, yields a value of Young's modulus for retina of approximately 2 x 10(4) Pa, which is about 2 orders of magnitude weaker than typical rubber. This value can then be used in modelling retinal behaviour in vivo when forces are applied to detached retina.
Animals↗
Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells.
A mathematical model of glycolysis in human erythrocytes is proposed to study the influence of a pyruvate kinase deficiency on the energy metabolism. The model takes into account the main regulatory properties of the non-equilibrium enzymes and the magnesium-complex formation by the adenine nucleotides and by 2,3-bisphosphoglycerate. In the normal case (no enzyme defect) the calculated flux rates and metabolite concentrations are in a good agreement with experimental data. It is shown that a severe pyruvate kinase deficiency manifested in a tenfold diminished activity of that enzyme leads to a remarkable decrease of the glycolytic flux and the ATP concentration of about 50% of the normal values. On the other hand a lowering of the pyruvate kinase activity to half of the normal value, characteristic for the heterozygotes, gives no significant alterations of the metabolite concentrations and the flux rates compared with the normal case which is in accordance with the lack of clinical symptoms for a metabolic disease of these probands. For three patients with known alterations of their pyruvate kinase mutants the calculated metabolite concentrations and the control characteristics permit estimation of the degree of disorder of the glycolytic pathway. The resulting classification corresponds well to other independent experimental and clinical findings. In particular, the calculation demonstrates that there is no simple correlation between the lowered enzyme activity and the reduced flux rate through the affected pathway.
Adenosine Triphosphate↗
Flow characteristics of red cell containing fluids through pores. The effect of filter plugging, a mathematical model.
A mathematical model was developed that describes the effects of filter plugging on flow through 3 micron pore polycarbonate filters as a function of time, pressure, and cell concentration, both under stirring and nonstirring conditions. The mathematical constants for the model were derived from experimental data generated with a filtration apparatus, and were tested by using various concentrations of cells that are able to plug filter pores. A computer simulation program was written to test the model over a wide range of nonfilterable cell concentrations.
Blood Flow Velocity↗
Determination of the mechanism of retrotransfer by mechanistic mathematical modeling.
Two mathematical models to elucidate the mechanism of retromobilization (or retrotransfer), that is, the ability of conjugative plasmids to mobilize genes into the cell containing the conjugative plasmid, were developed. This study deals with retromobilization of nonconjugative plasmids (Tra-Mob+). Plasmid transfer was modeled by two mass action models. The first is based on the hypothesis that retromobilization of the Tra-Mob+ vector occurs in one step, by means of the pilus formed by the Tra+ plasmid in the original host. In the second model, retromobilization is considered to be a two-step process involving two transfer events. The first step involves the transfer of the Tra+ plasmid from the recipient cell to the donor of the nonconjugative vector, and during the second encounter the nonconjugative vector is mobilized toward the recipient. Since the relationships between the number of transconjugants and the number of recipients for the two models are different, filter matings were performed for short time periods with different initial densities of the recipient population. Comparison of the numbers of transconjugants with the results of the mathematical equations confirmed the hypothesis that retromobilization is a one-step conjugation process.
Conjugation, Genetic↗
[Oscillations and trigger phenomena in fructose-2,6-bis-phosphate metabolism. A mathematical model].
A mathematical model describing metabolism of fructose-2,6-bisphosphate (F2, 6P2), which is a powerful mediator in glycolysis, is investigated. The model takes into account inhibitory effect of F2, 6P2 and fructose-6-phosphate (F6P) on protein kinase, which phosphorylates the bifunctional enzyme fructose-6-phosphate-2-kinase/fructose-2,6-bisphosphatase. Such a mechanism of enzyme chemical modification in the presence of F2, 6P outflow from the F6P in equilibrium with F2, 6P2 cycle, caused by nonspecific phosphatases, can display trigger phenomena and sustained oscillations in F2, 6P2 metabolism and in the whole glycolytic system. The results obtained suggest that earlier models of the generation of glycolytic oscillations should be revised.
Fructosediphosphates↗
Development of phage populations in a bacterial culture: a mathematical model.
A mathematical model for the interaction kinetic in phage-bacterium culture is proposed. An appropriate analytical relationship between phage and bacterial concentrations has been derived. Characteristic kinetic constants have been obtained by comparing the experimental growth curves with computer-simulation analysis. The model allows also to evaluate the phage-yield as a function of the initial concentrations.
Bacterial Physiological Phenomena↗
[Double-frequency oscillation in the glycolytic system. Mathematical model].
A mathematical model describing the generation mechanism of double-frequency oscillations in the glycolytic system is proposed. Interaction of two connected glycolytic oscillation generators are put in the basis of this mechanism. It is assumed in the model that the first oscillation generator is formed due to product activation of phosphofructokinase (PFK) with adenosine diphosphate (ADP), while the second one is based on substrate inhibition of glyceraldehydephosphatededhydrogenase (GAPDH) with glyceraldehydephosphate (GAP).
Adenosine Diphosphate↗
[An analysis of the intracellular distribution of glucocorticoid hormones by using a mathematical model].
A mathematic model depicting the interaction of glucocorticoids with the target cell is proposed. Specific features of cortisol and dexamethasone distributions in thymocytes in a wide range of hormonal concentrations have been analyzed. It has been established that specific action of glucocorticoids is dependent on the binding affinity and the number of the binding sites of hormones in the topographically different cell receptor systems (intracellular and membrane glucocorticoid receptors).
Animals↗
[Dynamics of O2 and CO2 tensions in the brain (mathematical modeling)].
The mathematical model for description of the circulation and gas exchange dynamics in the brain is suggested. The model is based on a cell of two compact parallel capillary network with a brain tissue within. The equation system describing the model was calculated on a computer. The simulation showed that steady state pO2 in the cell during blood flow changes from 0.5 mm/sec to 0.25 or 1 mm/sec is reached within 2--5 sec. The dynamics of pCO2 is more inert. It was shown that the main factor in the dynamics of pO2 in the brain is the velocity of blood flow in capillaries. The dynamic pattern of pCO2 depends on haemodynamical condition, the structure of capillary network and physical properties of CO2.
Brain↗
[Compensatory reactions of the oxygen-transport systems of the body with hemic hypoxia (studies on a mathematical model].
The mathematical model suggested by the authors and results of experiments have been used to study the significance of basic oxygen-transport systems in regulation of oxygen conditions of the organism with acute and chronic hemic hypoxia of different seriousness, to determine a relative contribution of each of them to compensation of this hypoxic state, to estimate specific weight of proper "hypoxic" (induced by the effect on oxygen-transport blood function) and "toxic" (caused by the total toxic effect) action of sodium nitrite in the development of hemic hypoxia.
Animals↗
[Assessment of the regulatory resources of the pial and intracerebral arteries by using mathematical modeling].
A mathematical model for estimation of regulatory abilities of pial and intracerebral arteries was used for studying the pressure - radius relationships for arteries of various calibres in passive and active states. In passive state the arteries were found to be characterized by high elasticity and low tensile force. The radius of the artery depends mainly on the smooth muscle contractile force. The data obtained suggest that the wall structure of small pial and intracerebral arteries well correspond to their function: the control of the adequate and rapid cerebral blood flow.
Biophysical Phenomena↗
[Substrate inhibition as a cause of oscillations in an open irreversible enzymic reaction S1 + S2 in the presence of E(R,T) leads to S1' + S2'. A mathematical model].
A mathematical model of an open irreversible reaction S1 + S2 (formula: see text) catalysed by an olygomeric enzyme E(R, T) has been analysed. It is assumed that the enzyme undergoes the concerted conformational transitions R in equilibrium T in conformity with the theory of Monod, Wyman and Changeux, and one of the substrates (S2) produces inhibition of the enzyme, thus shifting the equilibrium between the two enzyme forms in the direction of T formation. A simple graphical explanation is given to the hysteresis of the input characteristic approximately v ([S1]) (approximately v is the reaction rate at d[S2]/dt=O) which gives rise to self--oscillations. The hysteresis occurs both in the case of allosteric and isosteric substrate inhibition.
Allosteric Regulation↗