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[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↗
PubMed2000

Mathematical modelling of metabolism.

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.

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↗
PubMed1992

Measurement, analysis, and modelling of the caloric response. 1. A descriptive mathematical model of the caloric response over time.

A mathematical model for describing the caloric response over time offers many important advantages over the commercially-available qualitatively-fitted curves that are now used by the clinician for evaluating caloric results. In this report advances in the development of a nonlinear least-squares mathematical model are discussed and the roles and derivations of fitting parameters and curve-derived indices are outlined. This model provides a rigorous and objective description of the caloric response in its entirety with four continuous parameters. These fitting parameters make it possible to 1) describe individual caloric responses precisely and uniquely, 2) compare pairs of individual caloric responses or groups of caloric responses statistically, 3) extract information not previously available, 4) quantify variability within the caloric response, and 5) model physical properties of the caloric stimulus and physiological variables affecting the caloric response. Results from this model are compared with the results from our earlier models and with traditional multiparameter caloric results.

Caloric Tests↗
PubMed1985

The coordination of arm movements: an experimentally confirmed mathematical model.

This paper presents studies of the coordination of voluntary human arm movements. A mathematical model is formulated which is shown to predict both the qualitative features and the quantitative details observed experimentally in planar, multijoint arm movements. Coordination is modeled mathematically by defining an objective function, a measure of performance for any possible movement. The unique trajectory which yields the best performance is determined using dynamic optimization theory. In the work presented here, the objective function is the square of the magnitude of jerk (rate of change of acceleration) of the hand integrated over the entire movement. This is equivalent to assuming that a major goal of motor coordination is the production of the smoothest possible movement of the hand. Experimental observations of human subjects performing voluntary unconstrained movements in a horizontal plane are presented. They confirm the following predictions of the mathematical model: unconstrained point-to-point motions are approximately straight with bell-shaped tangential velocity profiles; curved motions (through an intermediate point or around an obstacle) have portions of low curvature joined by portions of high curvature; at points of high curvature, the tangential velocity is reduced; the durations of the low-curvature portions are approximately equal. The theoretical analysis is based solely on the kinematics of movement independent of the dynamics of the musculoskeletal system and is successful only when formulated in terms of the motion of the hand in extracorporal space. The implications with respect to movement organization are discussed.

Arm↗
PubMed1990

The true canalicular angle: a mathematical model.

A mathematical formula that allows for the computation of the true angle between the upper and lower canaliculi using dacryocystograms is described. It was used to determine the true canalicular angle in 33 patients. The mean calculated angle at the 1.0 mm distance was 57.2 degrees +/- 13.0 degrees, and at the 0.5 mm distance was 65.2 degrees +/- 16.2 degrees. The true calculated angle was highly correlated with the angle measured in the Waters view. There was no statistically significant correlation between the right and left sides in the same patient. There was no statistically significant difference between the canalicular angle in males and females, and there was no correlation between canalicular angle and patient's age. A clinical application of this model is discussed.

Adult↗
PubMed1988

Autoimmunity and its therapy: mathematical modelling.

A mathematical description of autotolerance and autoimmunity based on the previous model of immune response for normal antigen stimulation is given. In particular, the clonal deletion theory and non-specific stimulation of T-helper cells are included. Thus, an idea about the origin of autoimmune disease and the qualitative description of its course is presented. Possible therapies, such as immunosuppression and extracorporeal removal of autoantibodies, are also discussed.

Antigens↗