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[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↗

Determinants of distortions in CO2 catheter sampling systems: a mathematical model.

A mathematical model was developed to predict the distortions in the measured expiratory CO2 concentration time profile caused by catheter sampling systems. Parameters considered included the expiratory flow and concentration profiles, the sample flow rate, the sample tube dimensions and the sample cell volume. Unless care is taken in choosing the parameters of a catheter sampling system, particularly in the presence of low expiratory flow rates and short expiratory times, the CO2 concentration profile may be severely distorted. In worst case situations end tidal CO2 plateaux may not be recognized or alternately artifactual plateaux may be produced. Sample flow rate and sample cell volume are the most important parameters while distortion within the sample tube itself is relatively less important.

Carbon Dioxide↗

[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↗

Enhancement of neutrophil-mediated phagocytosis by human granulocyte-macrophage colony-stimulating factor demonstrated using a novel mathematical model.

A mathematical model is presented which may be applied to describe and analyse data from microscopic phagocytosis assays. The method has been used to investigate the phagocytosis of opsonized yeast by peripheral blood neutrophils treated with purified recombinant human granulocyte-macrophage colony-stimulating factor (rH GM-CSF) in vitro. Under limiting conditions of serum opsonization, rH GM-CSF decreased the proportion of non-phagocytic cells and increased the mean number of ingested yeast per cell. Stimulation of phagocytosis was dose-dependent and occurred with concentrations of rH GM-CSF in the range 10-320 units/ml. The effect was dependent on a heat-labile component in serum and was not attributable to endotoxin contamination of the preparation.

Colony-Stimulating Factors↗

Asbestos body concentrations in human lung: predictions from asbestos body counts in tissue sections with a mathematical model.

A mathematical model for predicting the concentration (Nv) of asbestos bodies (AB) in human tissue from the count (No) of these bodies in planar tissue sections is presented. The result is the equation Nv = No/[0.54 X A X (La + t)], giving the concentration of AB in numbers per gram of wet lung tissue. La, the average length (in microns) of the AB, is specific for each case; A is the area (square millimeters) of the tissue counted, and t is the thickness of the section (in microns). This equation fits experimental digestion results to a multiplicative error factor of less than 3. When an estimate of La, such as 51.6 microns, is used, the equation is less accurate but probably sufficiently accurate for the screening of lung specimens.

Asbestos↗

[The key role of fructose-2,6-bis-phosphate in the temporal organization of carbohydrate metabolism. An auto-oscillating mathematical model].

A mathematical model describing the periodical temporal organization of the open futile cycle fructose-6-phosphate in equilibrium fructose-1,6-bisphosphate (F6P in equilibrium F1,6P2) is investigated. The oscillations in this cycle are caused by the regulatory cycle F6P in equilibrium fructise-2,6-bisphosphate (F2,6P2), catalyzed by phosphofructokinase-2 (PFK-2) with a cascade of covalent chemical modification. The apparent product activation of PFK-2 by F2,6P2 together with the F2,6P2 outflux from the regulatory cycle create square-shaped oscillations in the concentration of F2,6P2, a powerful reciprocal regulator of the enzymes of the futile cycle F6P in equilibrium F1,6P2. Compared to the mechanisms of the autonomous regulation of the F6P in equilibrium F1,6P2 cycle suggested previously, the new one provides an excellent temporal separation of the glycolytic and gluconeogenic pathways and possesses a considerably larger region of existence of the self-oscillatory behaviour.

Carbohydrate Metabolism↗

[Ratio between carbohydrate and lipid metabolism in muscle cell energy metabolism during ATPase loading. Mathematical model].

A mathematical model is proposed to describe the interaction between glycolysis, the Krebs cycle and 3-oxidation (beta OX). The model incorporates the activations of phosphofructokinase by AMP and of isocitrate dehydrogenase by ADP as well as the inhibitions of citrate synthase by citrate, of acyl CoA synthase by excess CoAsAcyl, of pyruvate dehydrogenase (PDH) and the beta OX helix by the products CoAsAc and NADH. These regulations have been shown to provide consecutive triggering of the fatty acid and glucose oxidation systems with an increase in the ATPase load, the beta OX of fatty acids being a major source of energy at small loads. The steady state rates of glycolysis and PDH-reaction begin to increase at larger loads when the rate of beta OX is close to its maximum value. At maximum ATPase loads, the glucose oxidation accounts for more than 80% of the total energy production. Under limited fatty acid supply, the transfer to glucose oxidation gives rise to a region of the ATPase loads, where in the steady state levels of NADH and CoAsAc increase with load.

Adenosine Triphosphatases↗

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↗

[Mechanisms of the regulation of muscle energy metabolism on oxidation of glucose and fatty acids. A mathematical model].

A mathematical model was used to study the role of various allosteric regulatory mechanisms in the oxidation of glucose and fatty acids by muscle energy metabolism. A large number of such mechanisms were shown to be involved in simultaneous oxidation of both substrates: glycolysis is regulated by the ATP/ADP ratio at the phosphofructokinase (PFK) step; the control over pyruvate dehydrogenase is exercised by the NADHm/NADm+ and CoAsAc/CoAsH ratios as well as by the level of pyruvate; the Krebs cycle is regulated by oxaloacetate and citrate concentrations in the citrate synthase reaction and by the ATP/ADP and NADHm/NADm+ ratios in the isocitrate dehydrogenase reaction. The inhibition of PFK and pyruvate dehydrogenase by excess of CoAsAcyl as well as the inhibition of PFK by citrate are additional equivalent regulatory mechanisms. When glucose alone is oxidized, the levels of citrate, CoAsAcyl, NADHm and CoAsAc decrease drastically within the whole range of physiological ATPase loads; the only regulating factors that remain efficient are the ATP/ADP ratio in glycolysis, the level of pyruvate at the pyruvate dehydrogenase step, the ATP/ADP ratio and the levels of CoAsAc, oxaloacetate and isocitrate in the Krebs cycle.

Adenosine Diphosphate↗

[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↗

Quantitative analysis of interleukin-2-induced proliferation in the presence of inhibitors using a mathematical model.

The proliferative response of CTLL-2 cells to human recombinant interleukin-2 (IL-2) can be modeled mathematically using enzyme kinetic equations. This approach has been used to analyze dose-response curves (IL-2 concentration vs. level of proliferation) measured by MTT and [3H]TdR assays. The values of functional dissociation constants, equivalent to IL-2 concentrations giving 50% of the maximal response, depended on the cell concentration and increased from 4 to 60 pM for the [3H]TdR assay and from 40 to 140 pM for the MTT assay when the cell concentration was increased from 2 x 10(3) to 4 x 10(4) cells/well. The types of inhibition and dissociation constants for various inhibitors of IL-2-dependent proliferation such as mAbs against IL-2 receptor (7D4 and AMT13) and normal mouse serum (NMS) were also analyzed. Both mAbs exhibited competitive mechanisms of inhibition whereas NMS inhibited IL-2-driven proliferation in a mixed manner. Two gel-filtration fractions of NMS with inhibitory activity manifested different types of inhibition: purely competitive type of inhibition in the case of a 10-15 kDa fraction and a mixed type of inhibition for a 100-150 kDa fraction. The proposed model can also be used for quantitative analysis of the influence of various factors (pH, temperature, cultivation condition) on the level of proliferation.

Animals↗

Mathematical model of corneal surface smoothing after laser refractive surgery.

PURPOSE: To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction. DESIGN: Experimental study, interventional case series, and meta-analysis of literature. METHODS: A theory of epithelial smoothing in response to corneal contour change is derived from differential equations that describe epithelial migration, growth, and loss. Computer simulations calculate the effects on postoperative epithelial thickness, topography, refraction, and spherical aberration. Model parameter is matched with laser in situ keratomileusis (LASIK) outcome in literature and in a retrospective study of primary spherical myopic (77 eyes) and hyperopic (19 eyes) corrections. Surgically induced refractive change was the main outcome measure. RESULTS: Simulated epithelial remodeling after myopic ablation produces central epithelial thickening, reduction in achieved correction, and induction of oblate spherical aberration. Simulation of hyperopic ablation shows peripheral epithelial thickening, a larger reduction in correction, and induction of prolate spherical aberration. Simulation using a minus cylinder laser ablation pattern shows decreased astigmatism correction and increased hyperopic shift. In the LASIK series, linear regression of achieved correction vs ablation setting in hyperopic and minus cylinder corrections shows slopes of 0.97, 0.71, and 0.74, respectively. These clinical results match model predictions when the smoothing constant is set at 0.32, 0.63, and 0.55 mm, respectively. CONCLUSIONS: Epithelial thickness modulations after ablation can be modeled mathematically to explain clinically observed regression and induction of aberration. The cornea appears to smooth over ablated features smaller than approximately 0.5 mm. The model provides an approach for designing ablation patterns that precompensate for the smoothing to improve final outcome.

Astigmatism↗

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↗

Endometrial thermal balloon ablation using a high temperature, pulsed system: a mathematical model.

A new endometrial thermal balloon ablation treatment for menorrhagia is modeled mathematically to predict its efficacy and safety. A device preheats a fluid to 173 degrees C within a reservoir external to the uterus, and then pulses this fluid without further heating between the reservoir and the balloon for 2.1 min of treatment time. The model predicted this treatment to result in consistent immediate tissue death (coagulation) depths of 3.4 +/- 0.1 mm for uterine cavities of 7 to 26 mL, and that eventual necrosis (tissue death that would occur 1-5 days post burn) may occur to depths of 6.5 +/- 0.2 mm. Whereas, burn depths varied with uterine cavity volume when a low temperature treatment (constant 75 degrees C for 15 min) was modeled (2.3-2.9 mm and 6.8-8.2 mm, for immediate tissue death and eventual necrosis respectively). Similarly, the high temperature, pulsed treatment was less sensitive to blood perfusion rate than the low temperature treatment. Predicted eventual necrosis depth was 1.5 mm less for the high temperature, pulsed treatment than that predicted for a low temperature treatment (constant 87 degrees C for 7 min) for the same immediate tissue death depth (3.5 mm), indicating that the new high temperature treatment may result in less damage to non targeted tissues.

Body Temperature Regulation↗

[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↗