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At least 541 records · Page 30Linked to original sources
PubMed1993

Mathematical modelling and quantification of the autoinhibitory feedback control of noradrenaline release in brain slices.

Concentration-response curves, reflecting alpha 2-autoreceptor-mediated inhibition of [3H]-noradrenaline release by exogenous noradrenaline in rat cerebral cortex and rabbit hippocampus slices, were analysed in order to test the usefulness of a mathematical model describing the relation between the independent variable, exogenous noradrenaline, and the dependent variable, inhibition of release. This model was based on the assumption of direct proportionality between receptor occupation and response, implying that there is correspondence between the shape of a concentration-binding curve and a concentration-response curve. The experimental concentration-response curves were obtained by different approaches: noradrenaline release from brain slices prelabelled with [3H]-noradrenaline was elicited electrically either by pseudo-one-pulse (POP) stimulation or by stimulation with 36 pulses applied with a frequency of 3 Hz. POP stimulation avoids autoinhibition by released noradrenaline and, therefore, was a suitable touchstone for the applied mathematical model which evaluates by nonlinear regression analysis two primary parameters: the dissociation constant between noradrenaline and the alpha 2-adrenoceptor and the biophase concentration of noradrenaline which reflects the extent of autoinhibition and should be zero under POP conditions. In rat cerebral cortex tissue, the corresponding biophase concentration of endogenous noradrenaline was indeed estimated to be zero and the dissociation constant was Kd = 10(-7.62 +/- 0.14) mol/l. With 3 Hz stimulation, the biophase concentration was 10(-7.80 +/- 0.05) mol/l, which has to be interpreted with respect to a simultaneously estimated Kd of 10(-7.63 +/- 0.12) mol/l.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1995

A mathematical analysis of a model for tumour angiogenesis.

In order to accomplish the transition from avascular to vascular growth, solid tumours secrete a diffusible substance known as tumour angiogenesis factor (TAF) into the surrounding tissue. Neighbouring endothelial cells respond to this chemotactic stimulus in a well-ordered sequence of events comprising, at minimum, of a degradation of their basement membrane, migration and proliferation. A mathematical model is presented which takes into account two of the most important events associated with the endothelial cells as they form capillary sprouts and make their way towards the tumour i.e. cell migration and proliferation. The numerical simulations of the model compare very well with the actual experimental observations. We subsequently investigate the model analytically by making some relevant biological simplifications. The mathematical analysis helps to clarify the particular contributions to the model of the two independent processes of endothelial cell migration and proliferation.

Angiogenesis Inducing Agents↗
PubMed1978

Systems-matching by degeneration. II. Interpretation of the generation and degeneration of retinal ganglion cells in the chicken by a mathematical model.

Quantitative data on generation and degeneration of retinal ganglion cells during development (Rager and Rager, 1978) are interpreted in terms of a mathematical model which consists of a system of differential equations. By these equations we attempt to describe the formation of retinal ganglion cells and their termination domains in the tectum. Since ganglion cells seem not to degenerate before their axons have arrived at their termination site and start branching, from the arrival time on they may become competent either to continue to mature or to die. Therefore, to find the actual number of competent cells the extension of the fiber pathway between the retina and the optic tectum had also to be measured and computed. The differential equations are united by the principle that at any given time cells in excess of the number of termination domains have to die. By this model the mathematical function was determined. Several parameter values of this function were optimized with the Gauss-Newton method by which the curve was fitted to the measured values. The high correlation obtained by this method allows to conclude that, to a first approximation, the model may be satisfactory. The evidence of competition for termination sites and of systems-matching by cell death is discussed.

Age Factors↗
PubMed1989

On a mathematical model for body tissue inflammation.

In the present paper I will try to prove the mathematical validity of a model on the localized bacterial infection for tissue inflammation. This model was proposed by Lauffenburger and Kennedy, and it describes the inflammatory response to bacterial invasion of body tissue. I prove the mathematical validity of the model by means of a positivity theorem, an existence theorem and a uniqueness theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension.

Humans↗
PubMed1989

On the solution of mathematical models of herd immunity in human helminth infections.

The general solution of the mathematical model of herd immunity to human helminth infections recently proposed by Anderson and May is obtained. The numerical solution of a more accurate biological model is indistinguishable from the corresponding exact solution of a more tractable mathematical model. Computer simulations of some particular cases of this model support the notion that both ecological and immunological factors determine the observed convex patterns of age-prevalence and age-intensity curves of human helminth infections.

Animals↗
PubMed1978

A mathematical model of air and water caloric nystagmus.

A mathematical model is proposed to explain the induction of nystagmic eye movements in response to thermal stimulation of the ear by air and water. Laplace-transformed equations are set up to describe heat flow in the meatus lumen to the ear-drum and heat transmission into meatus wall. Heat transport to the lateral semicircular canal, resulting in convective endolymph flow, and the induction of reflectory eye movements are included in the mathematical description. Input of the model is the time-course of temperature at the irrigating tip, output is the time-course of eye position (in correspondence to experimental nystagmogramms). The predicted nystagmus is in good agreement with experimental results, thus supporting our assumptions on the thermal effects of air and water irrigations.

Air↗
PubMed1986

Mathematical modelling of lipid production by oleaginous yeasts in continuous cultures.

A mathematical model was constructed to describe the influence of the carbon to nitrogen ratio (C/N-ratio) of the growth medium on lipid production by oleaginous yeasts. To test this model and to determine some relevant model parameters, the oleaginous yeast Apiotrichum curvatum ATCC 20509 was grown in continuous cultures at various C/N-ratios and dilution rates. It appeared that when nitrogen is limiting for the formation of biomass, the remaining glucose can be converted to storage carbohydrate and storage lipid. No clear dependence of carbohydrate yield on the C/N-ratio could be demonstrated, but lipid yield increased gradually with increasing C/N-ratios. The maximal dilution rate for lipid producing yeast cells appeared to be optimal at relatively low C/N-ratios. It can be concluded that the experimental results fitted well with the mathematical model. By using this model, lipid yield and lipid production rate can be calculated at any C/N-ratio of the growth medium and optimum operation conditions can be predicted for the production of microbial lipids.

Candida↗
PubMed1993

Mathematical models for multidrug resistance and its reversal.

Mathematical models describing drug resistance are briefly reviewed. One model which describes the molecular function of the P-glycoprotein pump in multidrug resistant (MDR) cell lines has been developed and is presented in detail. The pump is modeled as an energy dependent facilitated diffusion process. A partial differential equation linked to a pair of ordinary differential equations forms the core of the model. To describe MDR reversal, the model is extended to add an inhibitor. Equations for competitive, one-site noncompetitive, and two-site noncompetitive inhibition are derived. Numerical simulations have been run to describe P-glycoprotein dynamics both in the presence and absence of these kinds of inhibition. These results are briefly reviewed. The character of the pump and its response to inhibition are discussed within the context of the models. All discussions, descriptions, and conclusions are presented in nonmathematical terms. The paper is aimed at a scientifically sophisticated but mathematically innocent audience.

ATP Binding Cassette Transporter, Subfamily B, Mem↗
PubMed1988

Antigenic relationships between avian paramyxoviruses. III. A mathematical model of antigenic drift and a computer-assisted approach for construction of a phylogenetic tree.

The suggested model of antigenic kinship between related paramyxoviruses is based on another concept of antigenic determinant, as compared to the previously suggested combinatorial mathematical model by the authors. According to it, antigenic changes of any determinant do not proceed by "leaps" but can be changed gradually. Such changed determinant can induce a correspondingly changed type of antibodies which still preserve a certain kinship to the original type of the determinant (before its changing) revealed by cross reaction serological tests. Accordingly, there can be "families" of the determinants differing by degree of relatedness to (or, reversely, by antigenic distance from) the "original" ("ancestor") determinant. In addition to another interpretation of the antigenic kinship, the new mathematical model was used as an approach for revealing phylogenetic relationships between antigenically related viruses.

Antigens, Viral↗
PubMed1979

Evolutionary potential: a mathematical hypothesis of mouse hemoglobin beta chain evolution.

This paper examines the possibility that the linkage arrangements and regulatory properties of genes may be influenced by selection. A mathematical hypothesis is developed in order to show how selective properties of hemoglobin beta chains could have influenced the linkage and regulation of their structural genes. The hypothesis is applied to the case of mouse hemoglobin beta chains. In most mice, closely-linked pairs of loci (doublets) code for two structurally divergent beta chains in unequal amounts. Some mouse strains have singlet alleles, however, coding for another beta chain variant. With the mathematical hypothesis, one can show that selectively determined "evolutionary potentials" may have favored changes in proportions of major and minor chains produced by a doublet allele. In the extreme case, zero production of the minor chain may give a selective advantage, leading to a singlet; conversely, selection may favor linking another gene to the singlet locus to give a doublet. A specific prediction of the model is the stable maintenance under certain conditions of multiple alleles at regulatory loci. The concept of evolutionary potential thus suggests that selection could have influenced the evolution of genotypic fitnesses, in addition to causing changes in gene frequencies as in standard population genetics models

Animals↗
PubMedDate not supplied

Analytical approach to mathematical modelling of the isometric contraction of the hypertrophied myocardium.

It is attempted on the basis of the Hill two-element model to simulate mathematically the rising phase of the isometric mechanogram in the pressure-hypertrophied rat myocardium (Goldblatt II). The evaluation is based on the experimentally determined force-velocity relation as well as on the characteristic of the series-elastic stiffness. The changes in the isometric mechanogram of the hypertrophied heart muscle observed in the experiment can be mathematically predicted solely by means of the alterations in the force-velocity relationships induced by the hypertrophy, whereby the characteristic of the series-elastic stiffness is considered to be unchanged.

Cardiomegaly↗
PubMed1990

Mathematical model of chest wall mechanics: a phenomenological approach.

A mathematical model of chest wall mechanics, based on a phenomenological approach to force balances, provides a quantitative framework for analyzing many types of chest wall movements by using orthogonal displacement coordinates. The moveable components of the ventilatory system include the rib cage, diaphragm, and abdomen. A distinction is made between the lung-apposed and diaphragm-apposed actions on the rib cage. The model equations are derived from "pressure" balances and geometrical relations of the compartments; the stress-displacement relations are hyperbolic. With this model we simulated stiff and flaccid chest wall behavior under normal and constrained conditions associated with abdominal compression, a Mueller maneuver, and a diaphragmatic isometric inspiration. We also examined situations that produce paradoxical as well as orthodox inspiratory movements. The results of these simulations were quantitatively consistent with available data from the literature. A phenomenon predicted by the stiff-wall model during quasi-static inspiration is that the rib cage displacement is negligible near residual volume, but then increases dramatically with lung volume. Since this mathematical model has a sound physical basis and is more comprehensive than previous models, it can be used to predict and analyze the behavior of the chest wall under a wide variety of circumstances.

Abdominal Muscles↗
PubMed1994

Analysis of mathematical model for osseous factors in difficult intubation.

A two-dimensional model of the factors relevant to difficult laryngoscopy was analysed mathematically to determine clinical implications and limitations. The model describes the space into which the "inevitable residual volume" of the tongue (that part remaining anterior to the blade at laryngoscopy) can be displaced to permit a view of the larynx. Four points are used: the tip of the upper incisors; a point on the anterior airway just above the larynx; the mid-point between the mandibular condyles and the internal mid-point of the symphysis. The number, F, was defined by a formula developed from their spacial relationships. Decreasing F values imply an increasing likelihood of difficult laryngoscopy. The analysis investigated the effects of: translation of individual points; plotting individual point positions for specified F-values; translating adjacent pairs of points; treating any three points as a triangle which rotates about each of its apices; and lastly, translating three points independently. During manipulations the model behaved well mathematically. Single point analysis implied that jaw recession and a non-protruding mandible were comparable in effect. Closing the mouth around the laryngoscope blade maximised F-values. Prominence of the maxilla required greater forward displacement than backward movement of the symphysis for equivalent F-value change. One particular triangular rotation suggested an entirely novel mechanism for difficulty (the "hi-slung mandible") where the condyles are positioned more rostral than normal. An otherwise normal jaw with this configuration recedes markedly on opening. Further studies are required to validate the model. Accurate quantification of individual factors in difficult laryngoscopy may then be feasible.

Adult↗
PubMed1999

Evaluation of a mathematical model to predict intrapulmonary shunt non-invasively.

PURPOSE: We have previously published a mathematical model of oxygen transport. Using several physiological assumptions, the model provides a non-invasive estimate of intrapulmonary shunt. During a larger study of lung injury in a pig model, we had the opportunity to check the validity of our assumptions and the accuracy of the model's predictions. METHODS: We used six female pigs, average weight 12.8 kg. Following general anesthesia, tracheostomy and insertion of pulmonary venous and arterial lines, lung injury was induced by repeated saline lung lavage. Using hemodynamic measurements made at different levels of inspired oxygen, intrapulmonary shunt was calculated both by the traditional shunt equation and also by our mathematical model based on non-invasive measurements of FIO2 and SaO2. RESULTS: There was good agreement between the two methods of shunt calculation. Using linear regression the correlation coefficient was 0.95. Bland and Altman analysis showed a bias of -0.8 and precision of 12%. CONCLUSION: In a controlled setting, intrapulmonary shunt can be estimated from non-invasive measurements to a reasonable degree of accuracy. However, the calculation requires too many assumptions to be of general clinical value. The equations used provide a validated physiological model that acts as a useful tool for teaching cardiorespiratory physiology.

Animals↗
PubMed1991

Mathematical model for in vivo pharmacodynamics integrating fluctuation of the response: application to the prolactin suppressant effect of the dopaminomimetic drug DCN 203-922.

We propose a general pharmacokinetic-pharmacodynamic model that integrates the rhythmic fluctuation of hormone secretion for the description of the hormone-lowering effect of a drug. The mathematical model takes into account the variation in response observed after administration of a placebo and the drug. It is assumed that the change with time in the physiological response during the placebo period results from fluctuations in the concentration of hypothetical endogenous molecules. The mathematical formulation for predicting the response after drug intake is derived assuming competitive interaction of these "molecules" with the active species for binding to receptors. The suggested "fluctuation model" was implemented in order to describe the time course of the prolactin (PRL) plasma level after administration of two oral doses (2.5 and 5.0 mg) of the dopaminomimetic compound DCN 203-922 (DCN) to 9 healthy male subjects. Its performance was compared with that of conventional modeling approaches, in which the circadian changes after placebo are neglected and the hormone baseline is assumed to be constant. The new model provided a better description of the time course of PRL in most subjects. It was used for prediction of the amplitude and duration of the PRL suppressant effect after single and chronic administration of DCN at various dosage regimens as well as after changes in drug absorption.

Adult↗
PubMed2004

[Interaction between mathematics and melancholy].

The copperplate Melencolia I engraved by Dürer in 1514 illustrates various interdependencies between mathematics and melancholy. Dürer's engraving is one of the best known works of art in our western history. Up to our own times it has been interpreted repeatedly. The significance of Dürer's Melencolia I for our cultural history is subject of this essay. On the one hand the various changes of the conception of melancholy from antiquity up to Dürer' s times will be called in mind. In addition to it some examples will assert that during the last five centuries the correlation between mathematics and melancholy has been contemplated and shaped as well.

Depressive Disorder↗
PubMed2005

Group size determined by fusion and fission. A mathematical modelling with inclusive fitness.

We consider a mathematical model for the group size determination by the intra-reactions, self-growth, ostracism and fission within a group, and by the inter-reactions, immigration and fusion between two groups. In some group reactions, a conflict between two groups occurs about the reaction to change the group size. We construct a mathematical model to consider such conflict, taking into account the inclusive fitness of members in each group. In the conflict about the fusion between two groups, our analysis shows that the smaller group wants to fuse, while the larger does not. Also the criterion to resolve the conflict is discussed, and some numerical examples are given, too. It is concluded that, depending on the deviation in the total cost paid for the conflict by counterparts, the group reactions could result in a terminal group size different from that reached only by a sequence of outsider's immigrations into a group.

Animals↗
PubMed1996

A mathematical model of activity-dependent, anatomical segregation induced by competition for neurotrophic support.

Mathematical or computational models of activity-dependent neural competition typically impose competition in anatomically fixed networks by the use of synaptic normalisation, for which there is very little experimental support. Recent experimental evidence, however, strongly implicates neurotrophic factors in neural plasticity and competition, in addition to their well-known potent effects on neurite outgrowth and synaptogenesis. We therefore present a simple, mathematical model of anatomical segregation induces by activity-dependent competition for a limited supply of a neurotrophic factor provided by target cells to afferents. We extract the behaviour of the model in various regimes, in which the neurotrophic factor is either in critical supply or in abundant supply, by a combination of analytical and numerical methods, and study the effects of correlations in afferent inputs on competition. We apply the model to three different systems: ocular dominance column formation; elimination of polyneuronal innervation at the vertebrate neuromuscular junction; trigeminal brain stem whisker-related structure formation. Several classes of related predictions emerge, including the prediction that kittens reared with strabismus should require a higher concentration of neurotrophic factor infusion into their primary visual cortex than normally reared cats in order to induce the anatomical desegregation of ocular dominance columns. We also speculate on the mechanisms of support of inhibitory rather than excitatory neurons, and suggest the existence of a separate, (Cl-)-mediated activity-dependent pathway for their neurotrophic support.

Animals↗