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PubMedDate not supplied

[Mathematical model of radiation inactivation of cells].

The analysis was made of the compatibility of several mathematical models for radiation inactivation of mammalian cells with a large number of experimental data and some statistical correlations were revealed between the model survival curve and the approximated experimental dependence. It was shown that the statistical agreement between some model and some set of the experimental data was not a sufficient condition for the theoretical significance of the model. For the most plausible model to be reliably defined by the statistical criteria experimental data should be obtained on many millions of similar biological objects. So one of the theoretical models for radiation inactivation of cells was chosen to give the best description of the known variety of data on mammalian cell inactivation by different types of radiation.

Animals↗
PubMed1990

Thermodynamics and mathematical modeling of the partitioning of chlorpromazine between n-octanol and aqueous buffer.

The distribution of chlorpromazine (CPZ) between aqueous buffer solutions and 1-octanol was studied over a wide range of pH, buffer concentration, and temperature. A mathematical model was developed to simulate the distribution profiles. It is assumed that only monomers of CPZ exist in the organic phase, whereas in the aqueous phase, association equilibria were assumed to occur. The model predicted the formation of dimers and no higher aggregates over most of the concentration range covered in this study. Thermodynamic parameters for the partition equilibria were evaluated from the equilibrium partition coefficients measured as a function of temperature. Positive values of delta H and delta S were obtained for the transfer of CPZ from the aqueous to the organic phase. The process is entropy controlled indicative of a hydrophobic interaction between CPZ and the aqueous solvent.

1-Octanol↗
PubMed2003

Towards a mathematical model of the aortic reservoir.

It is well known from experiments that the circulation is going on under physiological parameters, only if the rigidity of the aortic wall is sufficiently small. We show that the result can be confirmed by the one-dimensional mathematical model describing the dynamics of the aortic reservoir (AR) by means of a hyperbolic system of PDE.

Aorta↗
PubMed1981

[Mathematical model on the development of progesterone in the cow: application and proof of differences between breeds].

Peripheral plasma progesterone levels were compared in "Normandy" (6), "Charolais" (6) and French Friesian (6) heifers. The progesterone curves were fitted to mathematical models for the luteal phase (a logistic function) and for the luteolytic phase (an exponential model). 1. Discriminating and multivariate analyses showed a breed difference in luteal phase duration (17.8 +/- 1.1, 16.8 +/- 2.3, 16.1 +/- 1.06 days, respectively, for Normandy, Charolais and French Friesian heifers) and in the rate of progesterone level increase (1.1 +/- 0.4, 1.09 +/- 0.3, 1.3 +/- 0.3 ng/ml/day, respectively) (chi 2 = 22.5; P less than 0.02). 2. Progressive multiple regression showed the duration of the luteal phase was highly correlated to oestrous cycle duration (20.8 +/- 1.7, 20.5 +/- 2.8, 19.2 +/- 1.5 days, respectively) (r = 0.89). It appears that breed differences in bovine oestrous cycle duration are due to differences in luteal phase duration. 3. The rate of progesterone level increase reached a maximum at 7.2 +/- 0.8, 6.9 +/- 1.1 and 6.4 +/- 0.6 days, respectively, concomitant with maximal corpus luteum secretion. 4. The reproducibility of these parameters, summarizing the progesterone pattern during two consecutive oestrous cycles, showed that each animal had an individual secretion pattern.

Animals↗
PubMed1992

Mechanical work rate minimization and freely chosen stride frequency of human walking: a mathematical model.

The interplay between the work done to move the body centre of mass with respect to the environment (external work) and the work done to move the limbs with respect to the body (internal work) has been shown experimentally partially to determine the freely chosen stride frequency during walking. A mathematical model that estimates the two components of the mechanical work is proposed. The model, according to the criterion of work rate minimization (both positive and positive plus negative), is able to predict the natural stride frequency as a function of the average progression speed. The adequacy of the model and the validity of the assumptions have been checked against measurements of natural stride frequency in 11 subjects walking on a treadmill at several speeds (range 1-3 m s-1). Comparison with theoretical predictions shows good agreement with the minimization of positive work rate at low speeds, while at high speeds the stride frequency is better explained by the model for minimum positive plus negative work rate.

Biomechanical Phenomena↗
PubMedDate not supplied

[Mathematical model of fluid transport in the convoluted portion of the proximal kidney tubules and surrounding capillaries].

Simulating transport of fluid and ions among proximal tubule, interstice and capillaries the mechanism of fluid transport in the kidney was studied. A mathematical model as a system of differential equations was processed with a numerical method by a digital computer. The results showed that 96% of fluid from the proximal convolution into interstice were reabsorbed because of the difference of osmotic pressures caused by HCO3-, ions and 4% -- at the expense of oncotic pressure gradient. Fluid transport from interstice into capillaries is realized by the higher oncotic pressure caused by proteins as a result of previous plasma filtration in the nephron glomerulus.

Biological Transport↗
PubMed1991

A mathematical model of interference for use in constructing linkage maps from tetrad data.

In determining genetic map distances it is necessary to infer crossover frequencies from the ratios of recombinant and parental progeny. To do this accurately, in intervals where multiple crossovers may occur, a mathematical model of chiasma interference must be assumed when mapping in organisms displaying such interference. In Saccharomyces cerevisiae the model most frequently used is that of R.W. Barratt. An alternative to this model is presented. This new model is implemented using a microcomputer and standard numerical methods. It is demonstrated to fit ranked tetrad data from Saccharomyces more closely than the Barratt model and thus generates more accurate estimates of map distances when used with two-point data. A computer program implementing the model has been developed for use in calculating map distances from tetrad data in Saccharomyces.

Chromosome Mapping↗
PubMed1991

Kinetic investigation and mathematical modeling of methanogenesis of glucose.

The kinetic regularities of anaerobic conversion of glucose, and intermediates of its decomposition (ethanol, butyrate, and acetate) by a microbial methanogenic association from anaerobic digester were investigated. Kinetic scheme for conversion of glucose is suggested, and the mathematical model based on the scheme is evolved. The model includes growth and metabolism of three kinds of microorganisms--acid producents, and acetate- and hydrogen-utilizing methane producents; of cell lysis with consequent fermentation of "died biomass" to acetate, hydrogen, and carbon dioxide; of induction and repression of the enzyme responsible for decomposition of butyrate, and for a number of regulations depending on the concentrations of intermediates in glucose metabolism. The values of parameters of the model have been calculated, sufficiently describing the experimental regularities. The numerical experiments have enabled us to reveal and describe the principal regulating factors of glucose methanogenesis.

Anaerobiosis↗
PubMed2005

Clinical implications of a mathematical model of benign paroxysmal positional vertigo.

Benign paroxysmal positional vertigo (BPPV) is the most commonly diagnosed vertigo syndrome. It is caused by movement of detached otoconia within the inner ear (canalithiasis) or otoconia adherent to the cupula (cupulolithiasis). A mathematical model incorporating fluid dynamics of BPPV, which results in the following insights, has been developed recently: (1) The characteristic latency of BPPV is explained by movement of detached otoconia through the ampulla, as pressure caused by moving otoconia is negligible until otoconia enter the narrow duct of the semicircular canal. Typical otoconia move at a rate of 0.2 mm/s, or about 1% of the circumference of the canal each second. (2) Particle-wall interactions can account for the considerable variability in duration and latency of BPPV. (3) Dispersion of a clump of otoconia creates more rather than less nystagmus. Thus, dispersion is not a viable explanation of fatigability. (4) Cupulolithiasis is predicted to cause a far weaker nystagmus than canalithiasis. (5) Inertial effects of treatment maneuvers cause negligible movement of otoconia.

Ear, Inner↗
PubMed2005

Changes in hematocrit based on incremental blood sampling: mathematical models perform poorly.

PURPOSE: Excessive blood sampling, with its inherent risks, is of growing concern among clinicians. We performed this study to measure the changes in hematocrit (Hct) during a laboratory investigation where multiple blood samples are collected. The performance of a simple mathematical model, used in clinical practice to predict Hct changes, is evaluated. METHODS: Eight healthy male volunteers participated in this study. The equation Hct(f) = Hct(i)*(EBV-BL)/EBV is used to predict changes in Hct. Where Hct(f) and Hct(i) are, respectively, the final and initial Hct, EBV is the estimated blood volume and BL is the blood loss. RESULTS: Thirty-five pharmacokinetic samples per subject were collected totalling 314 mL of BL. The Hct decreased from 44.2% +/- 2.2% to 39.9% +/- 2.5% (P = 0.001). On average, model predictions tended to have a discrete tendency to underestimate the Hct changes (-0.5% points of bias). While the predictions of the Hct were very accurate in 50% of the subjects, the discrepancy of the Hct predictions was clinically significant in the other 50% of the subjects. CONCLUSION: Consistent with the model prediction, this study demonstrated a significant reduction in the Hct values in healthy subjects undergoing incremental phlebotomy. On average, the model successfully predicted the decrease in Hct. However, the inter- and intra-individual variabilities in the Hct changes are clinically significant. In clinical settings, which are not well controlled environments, the variability is likely to be greater and the clinical use of the model cannot replace the need to monitor the Hct.

Adult↗
PubMed1982

[Mathematical model of a learning process by biofeedback].

The aim of Biofeedback is to teach a subject to control some of his biological functions. This experimental method was numerous therapeutic applications. General laws of these particular learning processes have not yet been well understood. Mathematical models can be used in order to make evident these laws can lead to an optimization of the learning processes. The stochastic model presented here underlines the shortcomings of certain experimental procedures. Although it has been performed from one of our particular experiments, it can be applied to analogous experiments.

Biofeedback, Psychology↗
PubMed1989

Mathematical modelling of trabecular bone structure: the evaluation of analytical and quantified surface to volume relationships in the femoral head and iliac crest.

The three-dimensional architecture of trabecular bone has structural trends related to physical function as described by Wolff's law. Mathematical modelling provides a means of analysing these structures through the use of simplified representations. A single measure of mineralized bone volume per unit volume of structure (Vv) and the surface area of mineralized bone per unit volume of structure (Sv) does not identify a particular architecture in any detail; the way in which Sv changes in relation to Vv does provide this information as the structure remodels. A series of structures using the elements of plates and rods were created. The rates of change of Sv with respect to Vv for trabecular structures give insight into differences in such models. Structures in the femoral head and iliac crest were analysed by power curve regression. In the principal compressive region, just above the medial cortex, advanced osteoarthritis was associated with a preferential loss of rods from the normal trabecular structure, resulting in a more plate-like architecture. The iliac crest remodelling that takes place in the osteoporotic appears to be the result of a generalised bone loss with some of the thinner elements of the structure being removed completely, resulting in an increase in unit cell dimension. The consequence of changing unit cell size has a major impact on surface availability for osteoblastic and osteoclastic activity. The simple plate model as a basis for the stereological analysis of trabecular structures is therefore limited because of the mixed plate and rod nature of trabecular architecture.

Anthropometry↗
PubMed1977

[A mathematical model of the pyruvate oxidation in liver mitochondria. 1. Regulation of the Krebs cycle by adenine and pyridine nucleotides].

A mathematical model is proposed to describe the behavior of the pyruvate metabolic reactions, Krebs cycle and oxidative phosphorylation over a wide range of changes in the pyruvate influx rate and the activities of ATPase and NADH-reoxidating dehydrogenase. The role of adenine and pyridine nucleotides in various allosteric regulations of the Krebs cycle enzymes is discussed. The accumulation of ATP and NADH has been shown to proceed in definite succession, which makes the allosteric regulation of the Krebs cycle enzymes successive too. First "works" the inhibition by ATP, then by NADH. It has been shown that the properties of the model are in qualitative agreement with the experimental data (Garber A., Hanson R. [1]) on pyruvate oxidation by mitochondria from guinea pig liver, when allosteric regulation of isocitrate dehydrogenase by adenine nucleotides is taken into account.

Adenine Nucleotides↗
PubMed1989

Mathematical model of CD4+ lymphocyte depletion in HIV infection.

The CD4+ lymphocyte depletion in human immunodeficiency virus (HIV)-infected persons seems to be affected by HIV products. As the dynamics of the concentration of HIV products is reciprocal to that of non-replicating antigen used for induction of tolerance, the mathematical model of immunological tolerance can be used to describe the dynamics of CD4+ lymphocyte depletion. To stimulate the clinically observed dynamics, it is necessary to include the limitation of HIV growth by the corresponding cytotoxic T cells and their dependence on the helper effect of CD4+ lymphocytes. Simulation analysis suggests that qualitatively similar results are obtained if immature, mature, or both categories of CD4+ lymphocytes considered in the model are depleted by the HIV products.

Acquired Immunodeficiency Syndrome↗
PubMed1977

[Formulation and evalution of a mathematical model to predict losses of nutrients during the thermal processing of canned food].

The purpose of this paper was the development of a mathematical model to predict losses of nutrients with first orden degradation kinetics during the thermal processing of conduction-heated foods. The model do not require experimental heat penetration data and operate for any possible case. It was evaluated experimentally for different thermal processes, being all the results within the 90% confidence interval on the mean experimental values. These results were obtained with a Fortran IV computer program elaborated for this purpose. The duration of this program was two minutes and tem seconds in a PDP 11/45 computer and was more efficient than others presented in the literature.

Evaluation Studies as Topic↗
PubMed1993

Mathematical modelling of the human cardiovascular system in the presence of stenosis.

This paper reports a theoretical study on the distribution of blood flow in the human cardiovascular system when one or more blood vessels are affected by stenosis. The analysis employs a mathematical model of the entire system based on the finite element method. The arterial-venous network is represented by a large number of interconnected segments in the model. Values for the model parameters are based upon the published data on the physiological and rheological properties of blood. Computational results show how blood flow through various parts of the cardiovascular system is affected by stenosis in different blood vessels. No significant changes in the flow parameters of the cardiovascular system were found to occur when the reduction in the lumen diameter of the stenosed vessels was less than 65%.

Blood Circulation↗
PubMed1993

A mathematical model for the elimination of carbon monoxide in humans.

Carboxyhaemoglobin (COHb) build-up in the blood as a result of exposures to carbon monoxide (CO) affects human beings. It is important to eliminate CO from the blood for treatment and health safety. A mathematical model is proposed to compute COHb level in the blood as a function of post-exposure time as CO is eliminated. The model takes into account molecular diffusion, facilitated diffusion, convection, non-equilibrium kinetics of CO with haemoglobin and the important physiological parameters, such as ventilation rate, blood flow rate and the total volume of blood in the body. Endogenous production of CO in the body is included in the formulation. The resulting coupled system of non-linear partial differential equations with physiologically relevant initial, entrance and boundary conditions is solved numerically. The COHb levels computed from our model agree with those measured experimentally (Pace et al., 1950; Peterson & Stewart, 1970). The half-life of COHb, i.e. the time required for the blood COHb to decrease from the initial level to its half-value is computed. The half-life values of COHb computed from our model are in good agreement with those based on experimental data collected under different physiological conditions (Pace et al., 1950). Also, the results predicted from our model give better approximation to the experimental values than the CFK equation (Coburn et al., 1965). It is found that the rate of elimination of CO increases with the increase of inspired PO2 and ventilation rate.

Carbon Monoxide↗