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At least 253 records · Page 14Linked to original sources
PubMedDate not supplied

[Mathematical models in hemostasis physiology].

A mathematical model of spatial propagation of blood coagulation is proposed. The control mechanism of advancement of the activation zone is established. The intrinsic and extrinsic pathways of blood coagulation are considered. Blood flow transfer of the activated factors is shown to play a significant role in stopping advancement of the activation zone. This effect is amplified by the coagulation cascade. Propagation of the concentration wave is related to the model indices.

Animals↗
PubMedDate not supplied

[Mathematical model of histamine bronchospasm].

A mathematical model of changes in histamine concentration in the wall of human bronchiole was constructed. The parameters of the model adequately characterize the state of patients with bronchial asthma.

Asthma↗
PubMed2001

Delayed fluorescence induction transients: mathematical modelling based on the chosen kinetic models.

The paper deals with mathematical modelling of the transients obtained by fitting of delayed fluorescence (DF) induction trace. The transients are in certain, doubtless connection with electrochemical gradient (ECG) formed across thylakoid membranes upon illumination. The fitting of the C and D transients by using consecutive model for first-order reactions (A --> B --> C) showed that they might play a role of the intermediate (B), according to scheme down bellow: ("A1 state")ECG (k1(C transient))--> C transient (k2(C transient))--> products, ("A2 state")ECG (k1(D transient))--> D transient (k2(D transient))--> products. The two ECG controlled "states" (A1 & A2) are not the same, which does not exclude some sort of proportionality. On the other hand, the E band, contributing mainly to the stationary level of DF induction trace, may be fitted by parallel model of at least two first-order reactions.

Electrochemistry↗
PubMedDate not supplied

[Mathematical model of children mortality].

A mathematical model of infantile mortality is proposed. The model is based on the probability principle of organism-environment interactions assuming that the organism is able to remember the diseases encountered previously and resist them. The adequacy of the model was assessed using the demographic database for two countries. The dynamics of the model parameters during the last century is presented.

Algorithms↗
PubMed1976

Computer simulation of local anesthetic effects using a mathematical model of myelinated nerve.

A mathematical model of myelinated axon was programmed for digital computer solution of the consequences of the conduction characteristics when the model membrane was affected by local anesthetics simulated by alteration of the ionic conductance parameter. The effects of tetrodotoxin on impulse conduction were studied in detail by means of a systematic reduction in sodium conductance in 1 to 10 nodes of Ranvier. Rhis technique simulates the method used experimentally and clinically to achieve a conduction block with the circumscribed application of local anesthetics to segments of nerve axons or nerve trunks. The analysis of the tetrodotoxin "dose-response" relationships revealed the fact that the model myelinated axon could support three types of conduction when depressed by this drug. One type of conduction of a subnormal impulse at the nodes of Ranvier; a second is characterized by a form of decremental conduction in which the rate of decrement of the nodal impulse is linear with distance. The third type is a second form of decremental conduction which is exponential in configuration and is seen when the g(Na) at the nodes of Ranvier is reduced to less than 27% of normal. Parallel experiments were performed to simulate the effects of lidocaine and some significant differences were observed. Analysis of the action potentials within the internodel region suggests that, although immune to drug action in the model, the internodal segment affects the generation of action potentials at the nodes. A commentary is presented on the limitations of the model as it reflects known pharmacologic relationships in real myelinated axons.

Anesthetics, Local↗
PubMed1998

Kinetics of T cell proliferation: a mathematical model and data analysis.

A mathematical model of in vitro T cell proliferation controlled by IL-2 internalization is presented. The model describes the T cell transition from G1 to S+G2+M stages of the cell cycle and introduces "molecular" equations for the G1-S phase control. These equations consider current knowledge of the biochemical mechanisms of receptor synthesis, ligand-receptor binding, and internalization of ligand-receptor complexes. The model describes the kinetic data for in vitro T cell proliferation at various IL-2 concentrations (50-500 pM) for various exposure time (6-26 h). The kinetic parameters were calculated based on the model. The results obtained suggest that increase in the IL-2 concentration and exposures decrease the critical ligand-receptor concentration in the cells which control proliferation. The time tau, which characterizes the delay in the G1-S transition, was constant at various IL-2 concentrations.

Animals↗
PubMed2004

A theory of drug tolerance and dependence II: the mathematical model.

The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

Adaptation, Physiological↗
PubMed1991

Mathematical modelling in nuclear medicine.

Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms.

Computer Simulation↗
PubMedDate not supplied

[A mathematical model of the biomechanics of respiration during artificial ventilation of the lungs].

The authors review a mathematic model of the respiratory biomechanics during artificial lung ventilation, presenting a subsystem of the mathematic model of respiration designed at the All-Union Research Surgery Center of the USSR AMS and used in the medical information diagnostic system elaborated for the Department of Resuscitation and Intensive Care, provide differential equations of the mathematic model, the results of the numerical solution of the model and an example of using the model for solving a private problem of selecting an adequate mode of artificial lung ventilation.

Biomechanical Phenomena↗
PubMed1988

Mathematical models of cumulative effect and optimization of fractionation regimes.

Different (most known) mathematical models are shortly described and basic assumptions the individual models are based on are discussed and critically examined. Advantages and shortages of individual models are mentioned. A semiphenomenological model is then used to demonstrate some possibilities how to make use of the mathematical models in attempts of optimizing the fractionation approaches in individual cases.

Dose-Response Relationship, Radiation↗
PubMed1991

On the use of mathematical models of malaria transmission.

The key conclusions of several mathematical models of malaria are reviewed with emphasis on their relevance for control. The Ross-Macdonald model of malaria transmission has had major influence on malaria control. One of its main conclusions is that endemicity of malaria is most sensitive to changes in mosquito imago survival rate. Thus malaria can be controlled more efficiently with imagicides than with larvicides. An extension of this model shows that the amount of variability in transmission parameters strongly affects the outcome of control measures and that predictions of the outcome can be misleading. Models that describe the immune response and simulate vaccination programs suggest that one of the most important determinants of the outcome of a vaccine campaign is the duration of vaccine efficacy. Apparently malaria can be controlled only if the duration of efficacy is in the order of a human life-span. The models further predict that asexual stage vaccines are more efficient than transmission-blocking vaccines. Directions for further applications of mathematical models are discussed.

Animals↗
PubMed1989

[A mathematical model for predicting the efficacy of glucocorticoid therapy of glomerulonephritis].

A mathematical model is proposed for prediction of the efficacy of glucocorticoid therapy developed on the basis of the Bayes theorem and successive Wald's analysis. The model uses the retrospective values of the results of radioligand determination of the number of glucocorticoid receptor of lymphocytes and static renal scintigraphy. By means of the blind method the informative value of the mathematical model to predict the inefficacy of glucocorticoid therapy in nephrotic glomerulonephritis was 96%. A nomogram was developed.

Algorithms↗
PubMedDate not supplied

[Mathematical modeling of the interaction of local anesthetics with the surface of nerve fiber biomembranes].

Theoretical analysis and mathematical modelling of conductor anesthesia has been performed. It has been established that mathematical models explicity taking into account the form and the size of molecules (through molar volumes) and the energy of intermolecular interaction with biomembrane surface of a nerve fiber (through normal boiling temperatures) are the most close to electrophysiology data obtained by measuring of minimal blocking concentrations of anesthetics in inter- or intracell solutions, causing complete isolation of a pain spike in the fiber. Computation based on an improved additive systematics produced physical-chemical descriptors for construction of mathematical models. The determined parameters conform to experimental data in crucial features molar volumes and normal boiling temperatures for analyzed compounds. Predictions possibilities and restrictions of suggested approach for search for new effective anesthetics and structures with higher indices of biological activity has been analyzed.

Anesthetics, Local↗
PubMed1975

Quantitative evaluation of hemodialysis therapy using a simple mathematical model and a programmable pocket calculator.

1. A single pool mathematical model has been clinically tested and found to give values similar to those previously reported for volumes of distribution of creatinine and urea. 2. Calculated generation rates for creatinine and urea approximated values obtained by independent measurement of removal rate. 3. Preliminary observations suggest that the model may be empirically useful in predicting interdialytic serum creatinine urea concentrations. 4. The potential clinical usefulness of the mathematical model has been enhanced by development of a solution suitable for a programmable pocket calculator.

Adult↗
PubMed2004

Concerted regulation of all hyphal tips generates fungal fruit body structures: experiments with computer visualizations produced by a new mathematical model of hyphal growth.

Filamentous hyphal growth is inherently suited to kinetic analysis, and in many respects the fungal mycelium can be viewed as a very mechanical biological system, which lends itself to mathematical modelling. The mathematics of hyphal tip extension growth are well-established. However, even though a hyphal growth equation can be written with confidence, and we have a good understanding of the effects of tropisms on growth, it is not easy to form a mental picture of the behaviour of large populations of hyphal tips. What is required, and what we believe we have produced, is a mathematical model that is sufficiently sophisticated to produce a realistic visualization of fungal hyphal growth. This provides us with a cyberfungus that can be used for experimentation on the theoretical rules that might govern hyphal patterning, hyphal interactions, and tissue formation and organ development by actually visualizing the virtual hyphal growth patterns that result from different regulatory scenarios. From a series of model experiments the most significant observation is that complex fungal fruit body shapes can be simulated by applying the same regulatory functions to all of the growth points active in a structure at any specific time. No global control of fruit body geometry is necessary. No localized regulation is necessary. The shape of the fruit body emerges from the concerted response of the entire population of hyphal tips, in the same way, to the same signals.

Computer Graphics↗
PubMed1980

A mathematical model representing the extraneuronal O-methylating system of the perfused rat heart.

1. A mathematical model was developed to mimic the function of the extraneuronal O-methylating system of the rat heart. Its essential features are: a saturable uptake process (uptake 2), a saturable, intracompartmental enzyme (COMT), the ability of the catecholamine to penetrate the membrane of the model compartment by a diffusional flux obeying first-order kinetics, and the ability of the metabolite to leave the compartment by an efflux obeying first-order kinetics. 2. Of the six kinetic constants of the model compartment five are known from experiments with hearts perfused with 3H-isoprenaline (Kmuptake, Vmaxuptake, Vmaxenzyme, k for amine, k for metabolite); only one constant is unknown (Kmenzyme) for the intact heart cells. 3. Results calculated with the help of the mathematical model were compared with results obtained from rat hearts perfused with 3H-isoprenaline. Although full congruency of results cannot be expected, there was satisfactory agreement between the two sets of results. Apparently, the mathematical model is able to simulate the function of the O-methylating system of the rat heart. 4. Comparison of the two sets of results leads to a definition of the function of the O-methylating system of the perfused rat heart. if all cells of the rat heart participate in the O-methylating system, the Km of the COMT of intact heart cells must be very low (i.e., somewhere between 2 and 5 microM isoprenaline). However, if the O-methylating system comprises only a small fraction of all cells, the COMT of the intact heart cells may well have a correspondingly higher Km.

Animals↗
PubMed2006

Mathematical modelling of the composting process: a review.

In this paper mathematical models of the composting process are examined and their performance evaluated. Mathematical models of the composting process have been derived from both energy and mass balance considerations, with solutions typically derived in time, and in some cases, spatially. Both lumped and distributed parameter models have been reported, with lumped parameter models presently predominating in the literature. Biological energy production functions within the models included first-order, Monod-type or empirical expressions, and these have predicted volatile solids degradation, oxygen consumption or carbon dioxide production, with heat generation derived using heat quotient factors. Rate coefficient correction functions for temperature, moisture, oxygen and/or free air space have been incorporated in a number of the first-order and Monod-type expressions. The most successful models in predicting temperature profiles were those which incorporated either empirical kinetic expressions for volatile solids degradation or CO2 production, or which utilised a first-order model for volatile solids degradation, with empirical corrections for temperature and moisture variations. Models incorporating Monod-type kinetic expressions were less successful. No models were able to predict maximum, average and peak temperatures to within criteria of 5, 2 and 2 degrees C, respectively, or to predict the times to reach peak temperatures to within 8 h. Limitations included the modelling of forced aeration systems only and the generation of temperature validation data for relatively short time periods in relation to those used in full-scale composting practice. Moisture and solids profiles were well predicted by two models, but oxygen and carbon dioxide profiles were generally poorly modelled. Further research to obtain more extensive substrate degradation data, develop improved first-order biological heat production models, investigate mechanistically-based moisture correction factors, explore the role of moisture tension, investigate model performance over thermophilic composting time periods, provide more information on model sensitivity and incorporate natural ventilation aeration expressions into composting process models, is suggested.

Biodegradation, Environmental↗
PubMed1986

Mathematical modelling of lipid production by oleaginous yeasts in continuous cultures.

A mathematical model was constructed to describe the influence of the carbon to nitrogen ratio (C/N-ratio) of the growth medium on lipid production by oleaginous yeasts. To test this model and to determine some relevant model parameters, the oleaginous yeast Apiotrichum curvatum ATCC 20509 was grown in continuous cultures at various C/N-ratios and dilution rates. It appeared that when nitrogen is limiting for the formation of biomass, the remaining glucose can be converted to storage carbohydrate and storage lipid. No clear dependence of carbohydrate yield on the C/N-ratio could be demonstrated, but lipid yield increased gradually with increasing C/N-ratios. The maximal dilution rate for lipid producing yeast cells appeared to be optimal at relatively low C/N-ratios. It can be concluded that the experimental results fitted well with the mathematical model. By using this model, lipid yield and lipid production rate can be calculated at any C/N-ratio of the growth medium and optimum operation conditions can be predicted for the production of microbial lipids.

Candida↗