Good manners in good modeling: mathematical models and computer simulations of physiological systems.
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Computers↗
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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↗
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↗
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↗
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↗
[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↗
Carbon monoxide exchanges between the human fetus and mother: a mathematical model.
A mathematical model was developed to calculate maternal and fetal carboxyhemoglobin concentrations, [HbCO], as functions of time during and after exposure of the mother to various inspired CO concentrations. Effects of variation in alveolar ventilation rates, pulmonary and placental fiffusing capacities, cardiac output, endogenous carbon monoxide production and other factors were studied. Following a change in the inspired CO concentration, fetal HbCO lags behind maternal HbCO by several hours. During CO uptake, fetal HbCO eventually overtakes maternal, and approaches an equilibrium value as much as 10% higher than the mother's. During CO washout the fetal levels again lag behind the mothers. Results indicate that treatment of pregnant women who have elevated HbCO levels with 100% oxygen reduces the time necessary to reduce the maternal HbCO level as expected, but that the rate of fetal CO elimination is not increased as much as that of the mother. Changes in maternal and fetal HbCO were also calculated for a representative exposure to changing inspired CO levels produced by fluctuating levels of air pollution. Finally, the effects of carboxyhemoglobin on fetal oxygenation were studied, including the effects of high altitude and exercise.
Carbon Monoxide↗
[Nerve impulse conduction along myelinated fibers while internodal vary (mathematical model)].
The mathematical model of a myelinated fibre (Hille, 1971) was used to study the dependence of the velocity of nerve impulse propagation (theta) and of some parameters of the action potential on the properties of internodes. Calculations have shown that with increasing of the length (L) of internodes over the range of 0.75-3 mm, theta rises and then declines; in the fibre with the external diameter, D = 14 mu the maximum of theta falls on L = 1.5 mm. With decreasing of d/D (d = internal diameter of the fibre) at expense of D (simulation of the myelin sheath thickening) theta grows up monotonically, while the safety factor N (defined as the ratio of the potential (V) in the 6th node to V in the 8th node at a moment when V in the 8th node reaches its maximum) rises steeply only up to d/D approximately 0.75; with further increasing of D, N increases insignificantly. The raising of the longitudinal resistance (ri + r0) leads to the gradual decrease of theta; at ri + r0 = 70 mohm/cm the nerve impulse propagation ceased. The estimation of the longitudinal resistance of the intercellular clefts suggests that in the nerve trunks with a compact packing of nerve fibres the flow of the local currents through the axoplasm of the neighbouring fibres is a prerequisite for impulse conduction. The possibility of electrical (electronical) interaction between the membranes of nodes and internodes has been studied. Calculations have shown that if the generation of a membrane potential in the internode were absent, the resting potential of the node would by 10 mv lower than the potential created by the nodal "generator".
Action Potentials↗
Mathematical modelling and field trials of an inexpensive endoskeletal above-knee prosthesis.
The swing-phase motion of the shank of an above-knee prosthesis has been modelled mathematically. An inexpensive endoskeletal prosthesis was designed using the Jaipur foot and conduit pipes with a hinge joint for the knee. Results of field trials and the modelling indicate that a very simple above-knee prosthesis can give near normal gait at "normal" walking speeds on flat surfaces. The swing of the shank is most sensitive to the timing of toe-off.
Acceleration↗
[Effect of NAD recirculation on the mechanism of ATP stabilization in cytoplasm. Mathematical models].
A mathematical model of the glycolytic system with the cytoplasmic coenzymes NAD+ and NADH as essential variables is proposed. It has been shown that any increase in the steady-state concentration of NADH will reduce the range of activity of the "generalized" ATPase, wherein the level of ATP is stabilized. Such a reduction in the range of ATP stabilization may be caused by an increasing rate of the pyruvate loss into non-glycolytic pathways, in particular, into mitochondria. This effect may be compensated by increasing oxidation of NADH by the dehydrogenases of H+-transferring cytosol-mitochondrial shuttles (malate-aspartate or alpha-glycerophosphate). The properties of the complete model were compared with those of its simplified version, which takes account only of the phosphotransferase reactions of glycolysis. The effects of various factors, which do not alter the level of NADH in the system, may be studied within the scope of the simplified model.
Adenosine Triphosphatases↗
[Kinetic study of a heterogeneous tumor cell population using a mathematical model].
A mathematical model of a heterogenous tumor as a system of interrelating cell populations is described, including a pool of quiescent cells, cell-to-cell variability in maturation rates, and cell migration from growth area to necrotic one. Computer simulation results are given, model labeled mitoses and labeled index curves for the Lewis carcinoma are compared with experimental data.
Animals↗
Drug elimination interactions: analysis using a mathematical model.
A mathematical model was developed to analyze the elimination kinetics of drug interactions in the rat. The model is based on physiological blood flow rates and organ weights and includes Michaelis-Menten equations for enzymatic processes which are involved in the elimination of the drug; competitive inhibition interactions are computed for shared pathways. Using data from the single drugs, the model can simulate the results of experiments of the acute warfarin-BSP interactions in rats.
Animals↗
Measurement, analysis, and modelling of the caloric response. 1. A descriptive mathematical model of the caloric response over time.
A mathematical model for describing the caloric response over time offers many important advantages over the commercially-available qualitatively-fitted curves that are now used by the clinician for evaluating caloric results. In this report advances in the development of a nonlinear least-squares mathematical model are discussed and the roles and derivations of fitting parameters and curve-derived indices are outlined. This model provides a rigorous and objective description of the caloric response in its entirety with four continuous parameters. These fitting parameters make it possible to 1) describe individual caloric responses precisely and uniquely, 2) compare pairs of individual caloric responses or groups of caloric responses statistically, 3) extract information not previously available, 4) quantify variability within the caloric response, and 5) model physical properties of the caloric stimulus and physiological variables affecting the caloric response. Results from this model are compared with the results from our earlier models and with traditional multiparameter caloric results.
Caloric Tests↗
[Mathematical model of autoimmunity].
A mathematical model of autoimmunity is developed. This model is a system of two nonlinear differential equations, which describe the concentration dynamics of tissue cells and agressive lymphocytes. An analysis of the solutions shows that this model reproduces general behaviour of autoimmune diseases.
Autoimmune Diseases↗