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At least 1,603 records · Page 89Linked to original sources
PubMed1997

[Optimization of dose distribution of radiation in cancers of the cavum: association of an expert-system and a mathematical algorithm].

Optimization of radiation therapy in nasopharyngeal carcinoma is particularly complex due to both the proximity of at risk organs and the high dose that has to be delivered. To obtain an optimal dose distribution, a knowledge-based optimization technique has been designed that associates an expert-system, named CAVCAV, with numeric optimization (gradient projection method). Based on clinical and physical criteria, CAVCAV determines the geometric characteristics of the radiation fields (beam direction, location and shape of the shielding blocks) for the three stages of radiation therapy of nasopharyngeal carcinomas. Stage 2-treatment fields proposed by CAVCAV, though not perfectly adapted to the patient, are mathematically (beam weights, beam directions, isocenter position) and geometrically (adaptation of fields and shape of blocks by virtual simulation) optimized.

Algorithms↗
PubMed1997

Liquid ventilation: a mathematical model of gas diffusion in the premature lung.

The liquid ventilation (LV) technique was previously demonstrated to be a valuable alternative to ordinary gas ventilation, particularly for newborn patients with severely distressed lungs. This work describes a mathematical model of gas transfer phenomena occurring within the lungs of a preterm newborn baby ventilated with liquid perfluorocarbon (PFC) RM-101. The model was conceived in order to perform computer simulations of LV treatments. Its input parameters are tidal volume, respiratory frequency, oxygen and carbon dioxide tension in inlet PFC; its output data are the partial pressures of respiratory gases in the alveolar environment. Such values may be evaluated at any instant from the beginning of the treatment, in order to judge whether the therapy is able to meet the necessary conditions to arterialize properly the patient's venous blood. The model also enables optimisation procedures to be defined and performed. Quantitative results and graphs are supplied, with reference to the simulation of LV applied to a preterm newborn of 28 gestational weeks. The main results point out that a relatively short duration of initial transients is attainable (200 to 240 s) and that blood arterialization is possible even with low oxygen tension in inlet PFC (29.7 kPa (223 mmHg)).

Biomedical Engineering↗
PubMed1998

Codman's paradox of the arm rotations is not a paradox: mathematical validation.

Movement of a straight arm centred at the shoulder joint in three successive 90 degrees rotations, each around the respective orthogonal coordinate axis, leads to an apparently unrelated 90 degrees rotation around the longitudinal arm axis. This empirical fact is known as Codman's paradox, after a Bostonian surgeon who first reported it in 1934. However, by means of homogeneous coordinates, it is herein demonstrated that the phenomenon is just a mechanical property mathematically described by the equivalence between the matricial product of three orthogonal rotation matrices applied to a position vector and the matricial product of a single rotation matrix applied to the same vector. The latter rotation matrix corresponds to the middle one in the former group of three. When polar coordinates are used, the demonstration is even simpler, for the total shift vector clearly shows a single net effect on the longitudinal axis rotation. Thus, Codman's paradox is not a paradox. This property improves the muscle dynamics arm knowledge and might find applications in robotics.

Arm↗
PubMed1997

Mathematical formulation for computing the performance of self expanding helical stents.

Stents are cylindrical devices implanted inside pathologic tubular passages within the body. The stents, which are made of metal or plastic, keep the passage open for flow (of blood, urine, air etc.) by applying radial pressure on the passage walls. In most cases the stents are selected empirically for each application. We introduce here a mathematical formula for computing the radial pressure induced by self expanding helical stents. The formula was verified experimentally for an urological stent using a special device. The results correlate well with the theoretical predictions (R = 0.997; y = 1.017 x -0.06 kg; SEE = 0.034, for forces and R = 0.9988; y = 1.04 x +8.7 mmHg; SEE = 25.3 for pressures). This formula can potentially serve as an analytical tool for selecting the most suitable stent for a given application.

Angioplasty, Balloon, Coronary↗
PubMed2000

Estimating the extent of degradation of ruminant feeds from a description of their gas production profiles observed in vitro: derivation of models and other mathematical considerations.

Equations to describe gas production profiles, obtained using manual or automated systems for in vitro fermentation of ruminant feeds, were derived from first principles by considering a simple three-pool scheme. The pools represented were the potentially degradable and undegradable feed fractions, and accumulated gases. The equations derived and investigated mathematically were the generalized Mitscherlich, generalized Michaelis-Menten, Gompertz, and logistic. They were obtained by allowing the fractional rate of degradation to vary with time. The equations permit the extent of ruminal degradation (hence the supply of microbial protein to the duodenum) to be evaluated, thus linking the gas production technique to animal production.

Animal Feed↗
PubMed1995

Mathematical analysis of the relationship between blood flow and uptake of nutrients in the mammary glands of a lactating cow.

A dynamic mathematical model of blood flow regulation in the mammary glands of a lactating cow was constructed from a principle of local vasodilator release in response to changes in intracellular adenylate charge. An equation was derived to predict uptake of the milk precursors acetate, glucose, amino acids and fatty acids, as affected by mammary blood flow rate. Metabolism of the precursors to milk components and CO2 was simulated with a set of empirically derived equations. Relative rates of ATP production and utilization regulated both the number of perfused capillaries and the conductance of arteriolar segments in the mammary glands. The model simulated local control phenomena of functional and reactive hyperaemia, and simulation of autoregulation under changing arterial pressure suggested a predominance of precapillary sphincter regulation. It was predicted that an increase in blood flow without the mammary capacity to utilize blood metabolites efficiently would be detrimental to milk synthesis. Conversely, increased blood flow through changes in mammary activity resulted in predictions of higher milk production. It was proposed that the equation for uptake, [equation: see text] be used in analysis of mammary arteriovenous differences.

Acetates↗
PubMed1987

A mathematical model of the population biology of Ostertagia ostertagi in calves and yearlings.

A mathematical model of the population biology of Ostertagia ostertagi is described. The model assumes that the natural control and regulation of parasite numbers is mediated by four processes: the effect of climate on the development and survival of the free-living stages; changes in the rate of establishment of the infective larvae, and density-dependent variations in parasite survival and fecundity. The model is used to compare the course of the infection in two groups of calves. One group is assumed to have been reared under conditions typical of S.E. England and the other under conditions typical of Louisiana, USA. The more general behaviour of the model is discussed in the context of sensitivity analysis. The model is an excellent mimic of the epidemiology of bovine ostertagiasis. It can be used as a simple screening procedure to help determine which of many possible anthelmintic control strategies should be selected for more detailed examination in the field, and it provides a theoretical framework within which ideas concerning the epidemiology of parasitic gastroenteritis can be assessed and refined.

Animals↗
PubMed1986

Population dynamics in echinococcosis and cysticercosis: mathematical model of the life-cycle of Echinococcus granulosus.

A mathematical model of the life-cycle of Echinococcus granulosus in dogs and sheep in New Zealand is constructed and used to discuss previously published experimental and survey data. The model is then used to describe the dynamics of transmission of the parasite, and the means by which it may be destabilized. It is found that under the conditions that prevailed in New Zealand during the late 1950s, at the time of surveys of this parasite, the dog-sheep life-cycle was not regulated by any effective density-dependent constraint. In contrast there was evidence for an effective acquisition of immunity to reinfection by cattle. The long time to maturity of the cyst in sheep, together with the practice of feeding aged sheep to dogs, provides a time delay in the intermediate host. By comparison, the time to maturity of the adult stage in dogs is short, but it is of sufficient magnitude to be a key factor in the destabilization of the system by a regular dog-dosing programme. The model used to describe the life-cycle is a linear integrodifferential equation of the Volterra type. Such equations are intrinsically unstable in that a small perturbation in parameters can drive a previous equilibrium solution to zero. At the time of the surveys, the value of the basic reproductive rate, R0, was close to 1, and it has since been reduced below 1 by control measures.

Age Factors↗
PubMed1992

Mathematical modelling and theory for estimating the basic reproduction number of canine leishmaniasis.

The paper describes a mathematical model for canine leishmaniasis and presents formulae which can be used to estimate the basic reproduction number, R0. The primary concern has been to devise methods of estimation which make best use of those data most easily obtained by fieldwork, e.g. surveys of prevalence in dog (by age) and sandfly populations. A range of formulae are offered which are more or less demanding of data, and which consequently give more or less precise estimates of R0. They include methods for assessing the influence on R0 of heterogeneous biting rates of sandflies on dogs, in which the essence of heterogeneous transmission can be captured merely by measuring relative rather than absolute contact rates.

Animals↗
PubMedDate not supplied

Mathematical modeling of the production of cyclosporin A by Tolypocladium inflatum: effect of L-valine.

A mathematical model was developed to describe the kinetics of submerged fungal growth, consumption of nutrients, and production of the immunosuppressant drug, cyclosporin A (CyA). Special emphasis was placed on the experimentally observed stimulatory effect of L-valine on CyA production. The proposed model was based on kinetic information and emerging mechanistic data on CyA biosynthesis. It was assumed that L-valine acts as both precursor and inducer of the CyA-synthesizing multienzyme (CyA synthetase), and an unmethylated intermediate of CyA was postulated in the biosynthetic process. The model consisted of two parts: one describing cell growth and substrate consumption and the other addressing the kinetics of internal properties such as endogenous valine, biosynthetic enzyme, CyA intermediate, and CyA. The success of this extensive model was confirmed by its ability to simulate adequately the kinetic profiles of both external and internal variables. For instance, the model correctly predicted the time course of intracellular L-valine accumulation. In addition, both the optimal level and timing of exogenous L-valine addition could be predicted for maximum drug production. This study suggests rational new ways of improving the fungal production process of this important immunosuppressant.

Cell Division↗
PubMedDate not supplied

A mathematical model to predict the partitioning of peptides and peptide-modified proteins in aqueous two-phase systems.

A mathematical procedure was developed to predict the partition coefficients of the peptides AIIP, AWWP, AIIPAIIP and AWWPAWWP in poly(ethylene glycol) (PEG)/phosphate aqueous two-phase systems from amino acid hydrophobicities. In general, peptides containing tryptophan partition more into the PEG-enriched upper phase than analogous peptides containing isoleucine. Specifically, as the PEG concentration difference between the phases increased in a PEG/potassium phosphate aqueous two-phase system, the peptide AIIP was observed to have a partition coefficient ranging from 1.2 to 1.6, AIIPAIIP from 2.4 to 5.7, AWWP from 13.5 to 32.2, and AWWPAWWP from 43 to 170. The model was extended to predict the partitioning of a staphylococcal protein A derivative (ZZ) modified with these four peptides. As predicted, the protein modified with isoleucine-containing peptides had lower partition coefficients than the protein modified with tryptophan-containing peptides. The partition coefficient of the ZZ protein ranged from 0.35 to 0.20, that of ZZAIIPAIIP from 0.58 to 0.48, and that of ZZAWWPAWWP from 3.5 to 5.3 in these systems. The results show that short peptide handles can significantly enhance the partitioning of proteins in aqueous two-phase systems. The relationship between the model and the surface exposure of peptide handles and the utility of the model to aid in the design of such handles to enhance purifications are also discussed.

Amino Acid Sequence↗
PubMedDate not supplied

Mathematical model for analysis of mass transfer for immobilized cells in lactic acid fermentation.

A new mathematical model is proposed to analyze the mass transfer behavior in lactic acid fermentation using immobilized cells entrapped in calcium alginate. The model is comprised of material balance equations for glucose, free lactic acid, and several ions. The dissociation rate of lactic acid (rdiss) is involved in the proposed equations. To solve the equations numerically, a modified calculating method is proposed. Through model analysis, the possible mass transfer behavior in the gel bead was discussed. The model is validated by comparisons with the experimental results obtained from batch and continuous fermentation. The simulations using the model were made to investigate the mass transfer limitation in the gel beads. The results showed that the cell density gradient was formed in the gel beads and it was caused by the accumulation of the inhibitory product (free lactic acid), not by substrate starvation. Moreover, unusual mass transfer behavior of lactate ion in the immobilization support was pointed out.

Biotechnology↗
PubMedDate not supplied

Mathematical model of the lac operon: inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose.

A mathematical model of the lactose (lac) operon was developed to study diauxic growth on glucose and lactose. The model includes catabolite repression, inducer exclusion, lactose hydrolysis to glucose and galactose, and synthesis and degradation of allolactose. Two models for catabolite repression were tested: (i) cyclic AMP (cAMP) synthesis inversely correlated with the external glucose concentration and (ii) synthesis inversely correlated with the glucose transport rate. No significant differences in the two models were observed. In addition to synthesis, degradation and secretion of cAMP were also included in the model. Two models for the phosphorylation of the glucose produced from lactose hydrolysis were also tested: (i) phosphorylation by intracellular hexokinase and (ii) secretion of glucose and subsequent phosphorylation upon transport back into the cell. The latter model resulted in weak catabolite repression when the glucose produced from lactose was transported out of the cell, whereas the former model showed no catabolite repression during growth on lactose. Parameter sensitivity analysis indicates the importance of key parameters to lac operon expression and cell growth: the lactose and allolactose transformation rates by beta-galactosidase and the glucose concentrations that affect catabolite repression and inducer exclusion. Large values of the allolactose hydrolysis rate resulted in low concentrations of allolactose, low-level expression of the lac operon, and slow growth due to limited import and metabolism of lactose; small values resulted in a high concentration of allolactose, high-level expression of the lac operon, and slow growth due to a limiting concentration of glucose 6-phosphate formed from allolactose. Changes in the rates of all beta-galactosidase-catalyzed reactions showed similar behavior, but had more drastic effects on the growth rate. Changes in the glucose concentration that inhibited lactose transport could extend or contract the diauxic growth period during growth in the presence of glucose and lactose. Moreover, changes in the glucose concentration that affected catabolite repression affected the cAMP levels and lac operon expression, but had a lesser effect on the growth rate.

Biological Transport↗
PubMed2002

Mathematical method for the prediction of retention times of fatty acid methyl esters in temperature-programmed capillary gas chromatography.

An accurate method for identification of fatty acids in complex mixtures analyzed by temperature-programmed capillary gas chromatography is described. The method is based on a mathematical approach using regression curves obtained by plotting the relative retention times of fatty acid methyl esters (FAMEs) analyzed in isothermal and gradient temperature conditions. The method was applied to a complex biological sample (human milk), and it was possible to identify 64 fatty acids, including branched-chain and other fatty acids for which reference standards were not readily available. The identities of the majority of the peaks were confirmed by mass spectrometry. The relative residuals and the relative differences between estimated and measured relative retention times of individual FAMEs varied from 0.03 to 3.15% and from 0.0 to 2.9%, respectively. The method is useful for identification of fatty acids in routine analysis.

Chromatography, Gas↗
PubMed2006

Application of a mathematical topological pattern of antihistaminic activity for the selection of new drug candidates and pharmacology assays.

Molecular topology was used to achieve a mathematical model capable of classifying compounds according to their antihistaminic activity and low sedative effects. By application of this model of activity to databases containing chemical reagents and drugs exhibiting other pharmacological activity, we selected 30 compounds with possible antihistaminic activity. After those with possible sedative effects were discarded, activity tests were performed with five chemical reagents and three drugs searching for in vivo antihistaminic activity. The obtained results indicate that compounds such as 4-[(E)-2-(1,3-benzothiazol-2-yl)vinyl]-N,N-dimethylaniline (AH2), 2-ethyl-9,10-dimethoxyanthracene (AH4), and 2,4-bis(alpha,alpha-dimethylbenzyl)phenol (AH5) showed antihistaminic activity above terfenadine, the reference drug, whereas others, for instance, pergolide, miconazole, trihexyphenidyl, 2-(dibenzylamino-3-phenyl-1-propanol (AH1), and N-benzylquininium chloride (AH3), were less active than terfenadine.

Aniline Compounds↗
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↗
PubMed1999

Mathematical modeling of circadian cortisol concentrations using indirect response models: comparison of several methods.

Six mathematical functions to describe the chronobiology of cortisol concentrations were assessed. Mean data from a dose-proportionality study of inhaled fluticasone propionate were fitted with an indirect response model using various biorhythmic functions (single cosine, dual ramps, dual zero-order, dual cosines, and Fourier series with 2 and n-harmonics) for production rate. Data with known parameters and random variation were also generated and fitted using the ADAPT II program. Fitted parameters, model estimation criteria, and runs tests were compared. Models with preassigned functions: the dual ramps, the dual zero-order and the dual cosines provide maximum and minimum times for cortisol release rate, were suitable for describing asymmetric circadian patterns and yielding IC50 values. Fourier analysis differs from the other methods in that it uses the placebo data to recover equations for cortisol secretion rate rather than by postulation. Nonlinear regression for Fourier analysis, instead of the L2-norm method, was useful to characterize the baseline cortisol data but was restricted to a maximum of two harmonics. Apart from the single cosine function, which predicts symmetrical cortisol concentrations, all methods were satisfactory in describing the baseline and suppressed cortisol concentrations. On the other hand, Fourier series with L2-norm produced the best unbiased estimate for baseline patterns. The Fourier method is flexible, accurate, and can be extended to other drug-induced changes in normal periodic rhythms.

Androstadienes↗
PubMed1999

Relation of mathematical ability to psychosis in Iceland.

A study of mathematically gifted Icelanders demonstrates an increased risk of mental illness in their ranks. Psychotic disorders are also frequent among their relatives. Linkage of academic records with previously published data on the family distribution of psychosis reveals a pattern compatible with the hypothesis that high arousal plays a role in reasoning ability.

Achievement↗