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At least 775 records · Page 43Linked to original sources
PubMed1990

[A mathematical model of age distribution of malignant tumours mortality].

There was a tendency that the mortality of malignant tumours increased with age. In order to explore the law of this tendency, the data of malignant tumours mortality from disease monitoring points in Shandong Province were mathematically analogized, and the mathematical model of age distribution of malignant tumours mortality was established by using the exponential curve, y = 10a + bx. The model was also tested and verified by using national data, to observe the universal significance of the model. The model gave a theoretical account of the law of age distribution of malignant tumours mortality from a population, and provided an initial method to predict malignant tumours mortality. The increment quantity of malignant tumours mortality in various age groups when age increased one year could be calculated by using the differential equation from the exponential curve equation, y = 10a + bx. Further, "an increment multiple constant" of the increment quantity of malignant tumours mortality could be calculated. The constant could be used as an Index for comparison in risk degree and age distribution law of malignant tumours mortality among various age groups and the same age group in different periods, and provided leads for further research of the causes of malignant tumours.

Age Factors↗
PubMedDate not supplied

[The use of mathematical modelling and prediction for assessing the efficacy of the treatment of periodontitis].

The statistical prediction and mathematical modelling techniques were applied to the analysis of the results of treatment of periodontitis. The afflicted focus cross-sectional area (as measured by X-ray film) was taken as a variable. A total of 40 patients were divided into 2 groups. Computer analysis allowed developing a mathematical model of the afflicted focus ossification under different therapeutical approaches.

Administration, Topical↗
PubMed1989

[Mathematical prediction of indicators of toxicity and hygienic standardization of phenylurea compounds].

The relation between physical and chemical constants and toxicometric indicators has been used as the basis of mathematical simulation both of separate indices of toxicity and preliminary safety exposure levels of the compounds of phenylurea series, thus it becomes possible to apply the derived mathematical links for rapid hygienic norm-setting of new substances of the above group. Multiple regression equations have been derived for calculating LD50, Limac, Limch and MACs of phenylurea in the work zone air. The proposed approach to MAC substantiation provides the opportunity to predict MACs for similar chemical compounds in the work zone air with sufficient accuracy.

Air Pollutants, Occupational↗
PubMed1989

[Biomathematical aspects of numerical evaluation and mathematical modelling of non-monotonous exponential measuring processes].

Measurements of endocrinological and pharmacological processes often yield courses of time series with exponentially saturated increasing first part followed by an exponentially decreasing part. Such measured courses may be mathematically modelled by the so-called BATEMAN function type, an expression consisting of 2 e-function terms. In this paper, the method of locally adjusted functional approximation for model-free quantitative evaluation of measured time series is sketched. By means of 2 real examples of measured data, it will be demonstrated how the results of the model-free evaluation may serve for internal regression to estimate starting parameter values for an iterative fitting of a BATEMAN function to measured data courses. Furthermore, it is shown that the model-free approach of data evaluation may give substantial hints for the mathematical model building process and for model verification.

Animals↗
PubMedDate not supplied

Nasal provocation test (NPT) through previously active rhinomanometry: physical and mathematical reasons.

Rhinomanometry is a technique which studies the resistance of the nasal airways. It also permits us to measure their variations during NPT. This work has analysed the different methods of rhinomanometry (previously active, previously passive and late), commenting on its advantages and disadvantages. Bearing in mind that the European Committee for the standardizing of rhinomanometry has suggested the use of AAR, we have analysed it's physical and mathematical principles, as well as the bases of NPT through AAR. On these principles we present our technique, highly standardized, showing the comparative data with other diagnostic methods, as well as it's diagnostic value and we compare it with other proposed systems. We have also considered it useful to include a mathematical development of TPN which informs us of the equations of regression for the dose and nasal responses.

Airway Resistance↗
PubMed1989

Mathematical simulation of an enzyme-based glucose sensor with pO2-basic sensor.

In the design of enzyme-based sensors, the measuring characteristics are mostly obtained by the trial-and-error method. An alternative is provided by mathematical simulation of the behaviour of the sensors. For this, a mathematical model was outlined which is described by two coubled inhomogeneous partial differential equations for each layer of the sandwich membrane structure and by a set of boundary conditions. This model was used to simulate the dependence of the measuring characteristics (calibration curves, response time) on the design parameters (geometry, transport properties of the membranes, enzyme activity) of the enzyme-based glucose sensor. The simulated and the measured calibration curves are in good correspondence. With decreasing pO2, a stoichiometric limitation appears, and the linear range of measurement is reduced. If catalase is coimmobilized with glucose oxidase, the oxygen consumption is halved and the measuring range is doubled. The influences of diffusion coefficients and of specific enzyme activities on the sensitivity and response time are simulated. The results are in good accordance with theoretical statements and experimental results. The limits of the model are determined by its convergence properties.

Biosensing Techniques↗
PubMed1989

[A complex of mathematical models in the radionuclide diagnosis of the status of the urinary system].

Various mathematical models describing the process of transport of nephrotropic radiopharmaceutic drugs in the body of patients are used at present on a wide scale in processing the results of radionuclide studies of the urinary system functional status. The authors propose to give an objective quantitative assessment on the basis of a complex consisting of 3 mathematical models.

Humans↗
PubMed1989

[A mathematical analysis of the interconnection between the titer and avidity of antibodies].

The study made by the methods of mathematical statistics (regression and dispersion analysis) and the calculation of correlative relationship have shown that the titers of antibodies and their avidity in immune rabbit sera, used as a model, are unrelated; changes in the titers and avidity of antibodies in the dynamics of immune response at different schemes of immunization have been mathematically described by means of regressive equations.

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

[Cyclicity and the prognosis of tick-borne encephalitis morbidity in the Krasnoyarsk Territory: expert and mathematical assessments].

Long-term extrapolative prognosis is presented, which is based on 30-year data on tick-borne encephalitis infection rates in the Krasnoyarsk Territory. Mathematical analysis of many-year ranges was performed later by a maximum entropy method with further frequency filtration, its results allowing to predict the infection rate. Disease rate changes for the last 4 years demonstrated that extrapolative prognosis based both on expert and mathematical assessment (by the entropy maximum method) agreed well with the real data.

Disease Outbreaks↗
PubMedDate not supplied

Mathematical modelling of stimulus-secretion coupling in the pancreatic B-cell. V. Threshold phenomenon for the response to cyclic AMP.

Recent experimental data suggest that a rise in cyclic AMP content of pancreatic islet cells may have little effect upon cytosolic Ca2+ activity. Hence, a mathematical model for stimulus-secretion coupling was designed in which cyclic AMP fails to affect Ca2+ movements in the islet cells, but augments the responsiveness to cytosolic Ca2+ of the effector system for insulin release. Provided that the latter effect of cyclic AMP becomes operative only when the nucleotide concentration exceeds a critical threshold value, the mathematical model was found suitable to predict the dynamics of both insulin release and 45Ca fluxes in islets deprived of or exposed to D-glucose, Ca2+ and a phosphodiesterase inhibitor.

Animals↗
PubMed1985

Mathematical models of metabolic systems: general principles and control of glycolysis and membrane transport in erythrocytes.

General methods for the mathematical modeling of metabolic systems are discussed. Attention is paid to the simulation of steady states as well as time dependent behaviour of biochemical reaction networks. Control coefficients are used for the quantitative evaluation of the parameter dependence of model variables. The methods are applied to the mathematical analysis of the energy metabolism of erythrocytes. New results are presented concerning the interaction of glycolysis and osmotic behaviour of the red cell (metabolic-osmotic model). A general method for the calculation of control coefficients is developed which gives the basis also for the interpretation of control coefficients using chains of causal actions.

Adenine Nucleotides↗
PubMedDate not supplied

[Changes in the levels of paramagnetic centers in the mouse liver and a mathematical model of synchronized auto-oscillations].

Investigations of circadian rhythms in paramagnetic particles (free radicals and metal complexes) (PP) concentration variations in tissues are under continuation. A mathematical model advanced considers PP biorhythms as self-induced oscillations subjected to weak synchronization by an external source, by geomagnetic field intensity daily variations for example. By computation parameters of the model were obtained giving good agreement between the theory and experimental data. Due to the mathematical model the amplitude of external synchronizer influence is ten times less than the self-amplitude of PP biorhythm. The experiment was performed on the normal mouse liver. ESR signals g = 1.94, 2.00 and 2.25 were studied.

Animals↗
PubMed1986

[Biotyping of pathogenic cocci using mathematical methods].

The differential information content of biological signs in the ecology of different staphylococcal and streptococcal species has been studied by the mathematical method. The method for the intraspecific differentiation of staphylococci, streptococci and gonococci into pathovars with the use of programs for the computerized analysis of the material has been proposed. The mathematical models of strain virulence in different coccal species are described.

Bacteriological Techniques↗
PubMed1988

[Parametric identification of mathematical models of population genetics taking into account the geographical dispersion in finite samples].

A method for parameter identification of population genetics' mathematical models, taking account of geographical disperse at limited samples of experimental data on mutant frequency values has been developed. The existence of the MLS (method of the least squares) estimations of the models' parameters studied has been proved, zero approach of the looked for estimations found and the iterative procedure of making them precise shown. A means of building up the a posteriori function of probability density of the zero and following approximations of the models' parameters is pointed out. The possibility of application of the proposed method to find estimations of mathematical models' parameters of population genetics, taking account of geographical disperse, has been shown on the particular example.

Animals↗
PubMed1987

Mathematical models from laws of growth to tools for biologic analysis: fifty years of "Growth".

Mathematical models of size and shape have played a prominent role in the first half century of Growth. In honor of the fiftieth anniversary of the journal, this paper reviews the development of these models. An historical perspective is taken with a focus on the changing context in which mathematical models have been studied. Early models were thought to represent principles or laws of growth. Today, models are viewed as tools for biologic analysis. We trace this contextual shift through specific models developed and used in Growth.

Growth↗
PubMed1988

[A mathematical model for describing radiation complications].

The paper is devoted to the development of a mathematical model for describing probabilities of occurrence of radiation complications on the skin (as well as in other normal organs and tissues) during its irradiation with homogeneous and inhomogeneous dose fields as a function of an irradiated skin area. The model naturally necessitates the isolation of an equivalent dose (an equidosimetric value) introduced by I. B. Keirim-Marcus which can be effectively used for comparison of homogeneous and inhomogeneous dose fields in normal organs and tissues. The development of mathematical models describing probabilities of occurrence of radiation complications in normal organs and tissues opens up new opportunities for improvement of methods of cancer radiotherapy design.

Humans↗
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↗