SEARCH · PubMed Health
Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A mathematical model describing a single contraction of a cardiac muscle strip under isometric conditions is proposed. The adequacy of the model was checked in experiments on cardiac strips from patients with chronic coronary insufficiency. It was shown that the contraction-relaxation cycle is rather completely characterized by the parameters characterizing the association-dissociation kinetics of actomyosin bridges.
A mathematical model of a chloroplast was constructed, which takes into account the inhomogeneous distribution of complexes of photosystems I and II between granal and intergranal thylakoids. The structural and functional complexes of photosystems I and II, which are localized in intergranal and granal thylakoids, respectively, and the b/f complex, which is uniformly distributed in thylakoid membranes, are assumed to be immobile. The interactions between spatially distant electron transport complexes are provided by plastoquinone and plastocyanine, which diffuse in the thylakoid membrane and intrathylakoid space, respectively. The main stages of proton transport associated with the functioning of photosystem II and oxidation-reduction transformations of plastoquinone are considered. The model takes into account the interactions of protons with membrane-bound buffer groups, the lateral diffusion of hydrogen ions in the intrathylakoid space and in the lumen between adjacent granal thylakoids, and the transmembrane proton transport associated with the function of ATP synthase and passive leakage of protons from thylakoids outside. The numerical integration of two systems of differential equations describing the behavior of some variables in two different regions: granal and intergranal thylakoids was performed. The model describes adequately the kinetics of processes being studied and predicts the occurrence of inhomogeneous lateral profiles of proton potentials and redox state of electron carriers. Modeling the electron and proton transport with allowance for the topological features of chloroplasts (lateral heterogeneity of thylakoids) is important for correct interpretation of "power-flux" interactions and the experimentally measured kinetic parameters averaged over the entire spatially inhomogeneous thylakoid system.
Different mathematical models of varying complexity have been proposed in recent years to study the cardiovascular (CV) system. However, only a few of them specifically address the response to lower body negative pressure (LBNP), a stress that can be applied in weightlessness to predict changes in orthostatic tolerance. Also, the simulated results produced by these models agree only partially with experimental observations. In contrast, the model proposed by Melchior et al., and modified by Karam et al. is a simple representation of the CV system capable of accurately reproducing observed LBNP responses up to presyncopal levels. There are significant changes in LBNP response due to a loss of blood volume and other alterations that occur in weightlessness and related one-g conditions such as bedrest. A few days of bedrest can cause up to 15% blood volume loss (BVL), with consequent decreases in both stroke volume and cardiac output, and increases in heart rate, mean arterial pressure, and total peripheral resistance. These changes are more pronounced at higher levels of LBNP. This paper presents the results of a simulation study using our CV model to examine the effect of BVL on LBNP response.
A mathematical model of microvascular exchange in the rat following a burn injury was developed by extending an existing model of normal microvascular exchange to include perturbations characteristic of burn injuries without fluid resuscitation. The changes anticipated for small (10% body surface area) and large (40% body surface area) burns are incorporated systematically into the model until there is no improvement in the statistical fit of the simulation predictions with the experimental data of Lund and Reed (Circulatory Shock 20:91-104, 1986). The "best fit" perturbations for the small burn include the experimentally measured changes in mean arterial pressure and injured tissue pressure as well as changes to plasma protein and fluid transport coefficients in the injured tissue. The larger burn "best fit" simulation required changes to the plasma protein transport coefficients in the intact tissues as well as all of the changes listed above. The simulation results are compared with the available experimental information on burn injuries as well as with the specific data of Lund and Reed (Circulatory Shock 20:91-104, 1986).
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.
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.
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.
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.
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.
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.
Explore the source record for details and available documents.
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.
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.
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.
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology.
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.
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.
Explore the source record for details and available documents.