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At least 73 records · Page 4Linked to original sources
PubMed1987

Prediction of the range of hand positions available to a patient with movement restrictions at the joints of the upper limb--a mathematical model.

A mathematical model has been constructed to predict the workspaces available to patients with reduced ranges of motion at the joints of the upper limb. The model uses the inverse kinematic method of Benati et al. (1982) together with simplified anatomical data. Comparisons with experimental data (Dempster, 1955) show significant discrepancies which are believe to be due to differences in scapular constraint and to simplified anatomical modelling. It is intended to improve the anatomical model by the use of the published data of Eyclesheimer and Shoemaker (1911). Despite the discrepancies, the model already detects significant differences between normal workspaces and those of patients with restriction at the joints of the upper limb. It is believed that this model could, when incorporated with empirical data, form the basis of an "expert" system to assist the therapist and clinician in the planning of rehabilitation of the upper limb.

Activities of Daily Living↗
PubMedDate not supplied

[Formation of gas bubbles in biological tissues in decompression (a mathematical model)].

A mathematical model simulating transport of gases between a bubble resulted from decompression and tissue around is presented. With the help of the model the influence of gas mixture and density of the bubble forming centres upon the growth rate was studied. An important part of CO2 in the bubble forming was found out. The bubbles with He have been shown to grow faster than those with N2. At a 5-10-fold decrease of the outer pressure during 1-2 seconds the bubbles can reach sizes which violate hemodynamics in the system of microcirculation.

Animals↗
PubMed1983

[Kinetic study of prostaglandin biosynthesis. A mathematical model].

A mathematical model has been suggested to describe the kinetics of the prostanoid biosynthesis in the Plexaura homomalla coral. It allows to predict the changes in prostaglandin A2 concentration at various pH and concentration of sodium ions citrate when the latter is not too high. The degradation of prostaglandin biosynthesis intermediates is shown to proceed as two consecutive first-order reactions. For the second step the reaction rate grows into the raise of prostaglandin A2 concentration, apparently due to autocatalytic character of the process.

Animals↗
PubMedDate not supplied

[Checking of some hypotheses of the pathogenesis of diabetes mellitus by mathematical modeling].

A mathematical model of normal regulation of carbohydrate metabolism by the pancreas endocrine apparatus is presented. In a numerical experiment the model imitated changed levels of sucrose, insulin glucagon and gastrointestinal hormones in the blood in response to the ingested 50 g of glucose. The model of normal regulation was damaged in the way which theoretically should result in diabetes development. Then an estimation was made to what extent the disturbances of carbohydrate metabolism characteristic of diabetes were reproduced by the changed model. It has been shown that disturbances specific for diabetes appear when the sensitivity of beta-cells to glucose stimulus or hyperproduction of glucagon decreased. No changes in the behaviour of blood glucose typical of diabetes were obtained in the model when a decrease of the sensitivity of insulin receptors due to hyperinsulinemia in insulin-dependent tissues was imitated, as well as an increased activity of liver insulinase or hyposecretion of gastrointestinal hormones. These results point to the necessity of further development of these hypotheses.

Blood Glucose↗
PubMed1995

[Hematopoietic dynamics in mammals under combined radiation exposures (mathematical modelling)].

The mathematical models describing the dynamics of hemopoiesis in the mammals exposed to a combination of chronic irradiation are devised and studied. The models reproduce the increased radiosensitivity of the systems of thrombocytopoiesis, erythropoiesis and lymphopoiesis in the animals resulting from prolonged radiation exposure. Succeeding acute radiation exposure causes a more severe damage of the above-mentioned systems than it occurs for the species not being previously exposed to radiation. The model of granulocytopoiesis simulates both the decrease and the increase in radiosensitivity of this system due to the effect of chronic exposure using low and somewhat higher radiation doses, respectively. The postchronic acute radiation exposure has respectively the decreased or increased damaging effect. Within the limits of the models an interpretation of these effects is suggested. The results of modelling have an important theoretical significance in studies of the mechanisms of an effect of small doses of radiation on the mammalian organism as well as point to the perspectives of simulation experiments when evaluating the real radiation risks during long-term space missions.

Acute Disease↗
PubMedDate not supplied

[Analysis of geometric parameters and mechanical properties of erythrocytes by filtration through nuclear membrane filters. I. A mathematical model].

A mathematical model is constructed, which quantitatively describes the rate of erythrocyte passage through pores of nuclear membrane filters during filtration of a diluted erythrocyte suspension upon action of a constant hydrostatic pressure. The following main factors have been taken into account: geometrical constraints linking the surface area of the erythrocyte membrane, the erythrocyte volume and the geometrical parameters of the filter pores; mechanical characteristics of the erythrocyte membrane; viscosity of the intracellular content. Analysis of the model allows us to conclude that it is possible to extract information about all above erythrocyte characteristics from the experimental curves describing, dependency of the filtration rate of the erythrocyte suspension from the osmoticity of the outer medium.

Erythrocytes↗
PubMed1997

Mathematical modeling of pharmacy systems.

Mathematical modeling and its potential applications in pharmacy are discussed. A model is a simplified representation of the real world. As an experimental approach, modeling minimizes expense, risk, and disruption, but its validity can be hard to ascertain. Mathematical models describe numerically the relationships among elements of a system and are a powerful tool in making decisions affecting that system. There are two types of mathematical models: analytical models, which directly describe the relationships between system inputs and outputs using mathematical equations (such as pharmacokinetic models), and simulation models, which involve the replication, usually with a computer, of events as they occur in the real world. Analytical models are easier to develop but are not appropriate for describing highly complex systems. In continuous-time simulation, the system is represented as an uninterrupted flow of material; in discrete-event simulation, it is assumed that events occur only at distinct times. Various simulation programs are commercially available. The stages of a mathematical modeling study are (1) formulate the problem, (2) determine the model's structure, (3) collect and analyze initial data, (4) develop the model further, (5) validate the model, (6) experiment using the model, and (7) use the results. There have been many applications of modeling in health care, but relatively few have involved the study of pharmacy systems. Mathematical modeling offers pharmacists a low-risk, low-cost tool for aiding decisions about pharmacy systems by predicting alternative futures.

Models, Organizational↗
PubMed1990

[Possibilities of mathematical models of pharmacokinetics].

Mathematical modelling is currently the most rapidly developing branch of pharmacokinetics. Along with such traditional pharmacokinetic aspects as drug absorption, distribution, metabolism, and elimination, the pharmacodynamic area is also becoming actively involved in mathematical modelling. Complex pharmacokinetic-dynamic models are becoming a tool that finds wider application in drug therapy optimization. Current approaches to the pharmacokinetic modeling are discussed and classification of various model types presented, each type being briefly specified and compared to the others. Mention is made of the major problems that are encountered in pharmacokinetics and that require modelling to find a proper solution. Future tasks calling for the use of modelling are also considered.

Models, Biological↗
PubMed1994

Prediction of the comparative intensity of pneumoconiotic changes caused by chronic inhalation exposure to dusts of different cytotoxicity by means of a mathematical model.

A multicompartmental mathematical model has been used to simulate variations in the cytotoxicity of dusts in the kinetics of the retention, in the pulmonary region and tracheobronchial lymph nodes, of practically insoluble quartzite and titanium dioxide dust particles deposited on the free surfaces of the acini from alveolar air. Experiments with these dusts were conducted on rats exposed to virtually the same dust concentrations in the air for an experimental period of 20 weeks and a period of 10 weeks after exposure. Satisfactory approximation to the experimental data on the retention of these dusts is obtained by using the model parameters that depend either on damage to lung macrophages by phagocytosed particles or on the response of the host organism to this damage by enhanced recruitment of neutrophilic leucocytes; all the other variables of the model being unchanged. The values of the "action integral" computed from this model and multiplied by the index of comparative cytotoxicity of particles in vitro satisfactorily approximate to quantitative differences in the intensity of pneumoconioses caused by the dusts under study by the end of the experimental period. On the whole, the results of the mathematical model agree with the hypothesis that the cytotoxicity of particles plays a key part in both the process of retention of dust in the lung parenchyma and lung associated lymph nodes, and the pathological process caused by the retained dust. Thus given the factors and conditions on which the deposition of practically insoluble dusts in the pulmonary region depends, it is necessary to take into account the multiplicative nature of these two effects of cytotoxicity when predicting the comparative risk of pneumoconiosis.

Animals↗
PubMed1980

Corneal curvature changes associated with penetrating keratoplasty: a mathematical model.

A mathematical derivation of the effect of penetrating keratoplasty on corneal curvature was used to examine many variables in corneal surgery. The amount of wound disparity taken up by the recipient cornea was found to be the major factor in determining the amount of astigmatism induced by host wound/donor tissue size disparities. The amount of disparity showed as essentially linear relationship with the amount of astigmatism, approximately 0.4 diopters for each 0.1 mm of wound disparity for each 10% of the amount of the distortion taken up by the cornea (7.5 mm trephine). The smaller the trephine, the more distortion could be expected for each increment of wound disparity. Variations in the corneal curvature of the donor cornea had a minimal effect on the amount of keratoplasty-induced astigmatism.

Astigmatism↗
PubMed1980

[Mathematical models in epizootiology].

Mathematical modelling in epizootology makes it possible to forecast the occurrence and spreading of infection, to learn the main factors of the origin and spread of infection, or to test hypotheses on these factors. Therefore epizootological models must be correct from the biological and mathematical view-point. They should not contradict to experimental facts, must be sufficiently sensitive to important factors, and must be able to approximate real epizootological phenomena and processes. Examples of the construction of simple deterministic and stochastic models of exogenous infections whose etiological agents meet the conditions of Henle-Koch's postulates are used for demonstrating the basic approaches to the use of mathematical models for the evaluation of epizootological analyses and programmes of infection control.

Animals↗
PubMed1986

Models of spinal cord injury: Part 2. A mathematical model.

A mathematical model was constructed to predict motor performance in rats for 8 weeks after spinal cord injury. The model is based on experimental data generated from an investigation of the static-load technique of inducing cord injury and was derived using multiple linear regression. The regression coefficients for weight of the injury-producing load were statistically significant (P less than 0.001), and it was found that the weight of the load contributes over 95% of the posttrauma motor deficit, whereas the time duration of the load resting on the cord contributes less than 5% to the deficit. Sex, pretrauma motor performance, and pretrauma body weight are insignificant covariates. The model may be used to establish expected motor deficits and to derive dose-response curves.

Animals↗
PubMed1995

Photosynthetic oscillations and the interdependence of photophosphorylation and electron transport as studied by a mathematical model.

A simple mathematical model of photosynthetic carbon metabolism as driven by ATP and NADPH has been formulated to analyse photosynthetic oscillations. Two essential assumptions of this model are: (i) reduction of 3-phosphoglycerate to triosephosphate in the Clavin cycle is limited by ATP, not by NADPH, and (ii) photophosphorylation is affected by the availability of both ADP and NADP, while electron transport is limited by NADP only. The model produces oscillations of observed damping and period in ATP and NADP concentrations which are about 180 degrees out of phase, while three alternative proposals regarding coupling of electron transport and photophosphorylation do not produce oscillatory model solutions. The phases of ATP and NADPH are in reasonable agreement with the available experimental data. The model (which assumes that redox control of photophosphorylation is part of the oscillatory mechanism) is compared with an alternative proposal (that oscillations are due to interdependence of turnover of adenylates and Calvin cycle intermediates). From the similarity of the mathematical structures of both models it is inviting to speculate that both models are partial aspects of 'the oscillatory mechanism'.

Adenosine Triphosphate↗
PubMed1985

[Description of Na, K-ATPase activation by monovalent cations using a simplified mathematical model].

A simple mathematic model describing the activation Na,K-ATPase system by univalent cations is proposed. The constants for the enzyme activation values by each of the ions in the presence of a fixed concentration of the other ion have been calculated. The substitution of these values into the common equation describing the behaviour of the whole system according to the given model gives the curve of Na,K-ATPase activity change in dependence of Na/K ration at the same total concentration 150 mM. The experimental points correspond to the curve.

Cations, Monovalent↗
PubMed1988

Continuous arteriovenous hemofiltration: an in vitro simulation and mathematical model.

In vitro and mathematical models of continuous arteriovenous hemofiltration (CAVH) have been developed. Human erythrocytes resuspended in normal saline containing 5% bovine albumin were used to perfuse the circuit from a gravity driven pressure source. Membrane hydraulic permeability was observed to decline from 31.2 x 10(-5) +/- 11.9 x 10(-5) cm/(min.mm Hg) before use to 12.3 x 10(-5) +/- 3.3 x 10(-5) (mean +/- SD) after use. This fall occurred during the first one to two hours whether perfused with blood or 5% albumin alone. Pressure-flow relationships of each circuit component, measured with 40% sucrose as a calibration medium, conformed to Poiseuille's equation. Use of high resistance blood access on the venous end of the circuit resulted in a low blood flow rate and high filtration fraction. The same access, when placed on the arterial end, produced both low blood flow rate and low filtration fraction. These results were a consequence of pressure distribution within the circuit as demonstrated by measurements of perfusion, prefilter, and postfilter pressures. The importance of negative pressure applied to the filter chamber in order to maintain favorable Starling forces, when the system was operated with a small bore arterial access, was demonstrated by similar methods. Enhancement of urea clearance by predilution was verified. Model simulations suggest that predilution will be of less benefit or even detrimental for other solutes which fail to distribute across the erythrocyte membrane. Comparison of results with predictions of a mathematical model demonstrated good agreement, but with some tendency to overestimate filtrate production. The latter was attributed to neglect of concentration polarization of plasma proteins in model development.

Hemofiltration↗