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At least 325 records · Page 18Linked to original sources
PubMed1980

Mathematical model of synaptic plasticity: II. Habituation.

A mathematical model of the phenomenon of habituation as a homosynaptic depression of the amount of transmitter release is proposed. The model is based on the physiological studies of habituation in invertebrates and in the spinal cord of vertebrates, where a single synapse has been isolated and some of the physiological mechanisms of this process have been elucidated. The model simulates the following properties of habituation: (1) reduced amount of transmitter release attributed to a repetitive stimulus through changes in the membrane permeability to Ca2+ ions; (2) spontaneous recovery by rest; (3) the amplitude and frequency dependence of habituation; (4) modulation of habituation: sensitization, through an increase in membrane Ca2+ permeability, and presynaptic inhibition, through a reduced depolarization of the physiological stimulus; (5) long-term habituation attributed to repetitive trials of habituation and spontaneous recovery.

Animals↗
PubMedDate not supplied

[Mathematical modelling of perorally induced immunological tolerance].

A mathematical model of the mechanism of development of orally induced immunologic tolerance has been suggested. The model presents a system of differential non-linear equations, and it is realized as a program in FORTRAN. The model describes primary and secondary immune responses, reflects the main features of the immune system response to antigen intake with food. The immune system model response to varying doses and frequency of the antigen intake with food has been studied. It has been established that repeated administration of small doses of the food antigen leads to a deeper tolerance due to lower stimulation of the immune system. The existence of optimal tolerogenic doses of the food antigen has been proved. Qualitative changes in the immune system response to the food antigen have been recorded in case of increased permeability of the intestinal wall.

Administration, Oral↗
PubMed1984

Inhibition of calcium by magnesium in the contraction of rat aortic smooth muscle. I. Mathematical model of calcium and magnesium binding.

A mathematical model of the effect of calcium and magnesium binding on muscle tension was developed. The model was tested on aortic smooth muscle tissue obtained from rats fed magnesium-sufficient (Mg: 650 ppm) and magnesium-deficient (Mg: 4.5 ppm) diets. Ca2+ binding constants of 2.51 X 10(3) and 2.3 X 10(3) M-1 were obtained for aortae from magnesium-sufficient and magnesium-deficient rats, respectively. The corresponding Mg2+ binding constants were 0.6 X 10(3) and 0.4 X 10(3) M-1. The data indicate that Mg2+ is a competitive inhibitor of Ca2+ in tension development in rat aortic smooth muscle tissue.

Animals↗
PubMed1994

A nonlinear mathematical model for the development and rupture of intracranial saccular aneurysms.

Mathematical models of aneurysms are typically based on Laplace's law which defines a linear relation between the circumferential tension and the radius. However, since the aneurysm wall is viscoelastic, a nonlinear model was developed to characterize the development and rupture of intracranial spherical aneurysms within an arterial bifurcation and describes the aneurysm in terms of biophysical and geometric variables at static equilibrium. A comparison is made between mathematical models of a spherical aneurysm based on linear and nonlinear forms of Laplace's law. The first form is the standard Laplace's law which states that a linear relation exists between the circumferential tension, T, and the radius, R, of the aneurysm given by T = PR/2t where P is the systolic pressure. The second is a 'modified' Laplace's law which describes a nonlinear power relation between the tension and the radius defined by T = ARP/2At where A is the elastic modulus for collagen and t is the wall thickness. Differential expressions of these two relations were used to describe the critical radius or the radius prior to aneurysm rupture. Using the standard Laplace's law, the critical radius was derived to be Rc = 2Et/P where E is the elastic modulus of the aneurysm. The critical radius from the modified Laplace's law was R = [2Et/P]2At/P. Substituting typical values of E = 1.0 MPa, t = 40 microns, P = 150 mmHg, and A = 2.8 MPa, the critical radius is 4.0 mm using the standard Laplace's law and 4.8 mm for the modified Laplace's law.(ABSTRACT TRUNCATED AT 250 WORDS)

Aneurysm, Ruptured↗
PubMed1989

[A complex of mathematical models in the radionuclide diagnosis of the status of the urinary system].

Various mathematical models describing the process of transport of nephrotropic radiopharmaceutic drugs in the body of patients are used at present on a wide scale in processing the results of radionuclide studies of the urinary system functional status. The authors propose to give an objective quantitative assessment on the basis of a complex consisting of 3 mathematical models.

Humans↗
PubMed2002

Mathematical modelling for the new millenium: medicine by numbers.

Physicists, engineers and mathematicians are accustomed to the combination of elegance, rigour and utility that characterise mathematical models. They are familiar with the need to dip into their mathematical toolbox to select the technique of choice. However, medicine and biology have not been characterised, in general, by a mathematical formalism. The relative paucity of mathematical models in biology and medicine reflects in part the difficulty in making accurate and appropriate experimental measurements in the field. Signal noise, the lack of appropriate sensors, and uncertainty as to what constitutes the significant measurements are largely to blame for this. The purpose of this paper is to characterise a 'good' model, encourage the development and application of such models to new areas, and outline future developments in the field. It is proposed that a good model will be accurate, predictive, economical, unique and elegant. These principles will be illustrated with reference to four models: radiosensitisation of tumours, modelling solute clearance in haemodialysis, the myogenic response in reactive hyperaemia and cardiac electrical activity. It is suggested that, in the immediate future, the mathematical model will become a useful adjunct to laboratory experiment (and possibly clinical trial), and the provision of 'in silico' models will become routine.

Arrhythmias, Cardiac↗
PubMed1990

Solute transport in continuous arteriovenous hemodiafiltration: a new mathematical model applied to clinical data.

A mathematical model of continuous arteriovenous hemodiafiltration is presented, by which the diffusive mass transfer coefficient (Kd) for a solute may be calculated from blood, filtrate and dialysate flow rates and solute concentrations. The model was applied to clinical data obtained with 0.6-m2 AN69 capillary dialyzers that had been used for up to 5 days. The diffusive mass transfer coefficient proved to depend on dialysate flow rate. Furthermore, it was related to the membrane index of ultrafiltration, as measured in the clinic, and to the filter resistance to blood flow. Measurement of these filter characteristics allowed a reasonable prediction of solute clearance.

Data Interpretation, Statistical↗
PubMed2006

A mathematical model for simulating the bone remodeling process under mechanical stimulus.

OBJECTIVES: Among the current mathematical models for bone remodeling, few can consider bone resorption due to overload. The objective of this paper is to develop a new bone remodeling model which can simulate both underload and overload resorptions that often occur in dental implant treatments. METHODS: Based on the traditional model, a new mathematical equation relating the density change rate with mechanical stimulus has been developed. The new equation contains an additional quadratic term which can produce reduction in bone density at high load levels. In addition, to fully exploit the characteristics of this model, a range of different bone remodeling behaviors were studied under the load cases with both constant and varying stress magnitudes. Finally, the model was applied in conjunction with the finite element method to a practical case of dental implant treatment. RESULTS: The FE analysis results showed that bone resorption at the neck of the implant occurred due to occlusal overload but then resorption stopped after some time before reaching the coarse threads. Meanwhile, the density of the bone deeper into the mandible increased slightly due to the additional mechanical stimulus provided by the occlusal load. This phenomenon is observable in some clinical situations. SIGNIFICANCE: The new model can describe the bone overload resorption, a feature which is absent in most of the current models. And by simulating the dental implant treatment using FE method, the ability of the new mathematical model to simulate overload bone resorption has been clearly demonstrated.

Biomechanical Phenomena↗
PubMed1994

Tumor growth in vivo and as multicellular spheroids compared by mathematical models.

In vivo volume growth of two murine tumor cell lines was compared by mathematical modeling to their volume growth as multicellular spheroids. Fourteen deterministic mathematical models were studied. For one cell line, spheroid growth could be described by a model simpler than needed for description of growth in vivo. A model that explicitly included the stimulatory role for cell-cell interactions in regulation of growth was always superior to a model that did not include such a role. The von Bertalanffy model and the logistic model could not fit the data; this result contradicted some previous literature and was found to depend on the applied least squares fitting method. By the use of a particularly designed mathematical method, qualitative differences were discriminated from quantitative differences in growth dynamics of the same cells cultivated in two different three-dimensional systems.

Animals↗
PubMedDate not supplied

[Mathematical model of adaptation of the energy metabolism of a cell. Calculation of the influence of ATP on the activity and concentration of the initiator stage enzyme].

A simple kinetic model was constructed to study the adaptation of cell energy metabolism to a varying loading. In this model the initiatory step of energy metabolism, in which the initial substrate S is activated at the expense of ATP molecule energy, is catalyzed by an oligomeric enzyme E dissociable at high ATP concentration to monomers E1. It is assumed that the steady state level of monomers E1 in the cell is maintained by constitutive synthesis of E1 molecules, which balances their continuous hydrolysis by proteases. The properties of the kinetic model were studied using a mathematical model which is a system of nonlinear differential equations describing the change with time of the total enzyme E concentration and the concentration of ATP. The main isoclines of this system can intersect in one, two or three points. The mathematical analysis shows that the kinetic model considered exhibits adaptive properties. A sharp increase of the ATPase activity in the model initiates a transient process which leads to a rise in the total enzyme E concentration and in the efficiency of energy metabolism. As a result, the concentration of ATP drops only slightly. The establishment of a new level of the enzyme E concentration may proceed in the oscillatory fashion.

Adaptation, Physiological↗
PubMedDate not supplied

Mathematical modelling of angiogenesis.

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network. Subsequent cell proliferation near the sprout-tips permits further extension of the capillaries and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this article we first of all present a review of a variety of mathematical models which have been used to describe the formation of capillary networks and then focus on a specific recent model which uses novel mathematical modelling techniques to generate both two- and three-dimensional vascular structures. The modelling focusses on key events of angiogenesis such as the migratory response of endothelial cells to exogenous cytokines (tumour angiogenic factors, TAF) secreted by a solid tumour; endothelial cell proliferation; endothelial cell interactions with extracellular matrix macromolecules such as fibronectin; capillary sprout branching and anastomosis. Numerical simulations of the model, using parameter values based on experimental data, are presented and the theoretical structures generated by the model are compared with the morphology of actual capillary networks observed in in vivo experiments. A final conclusions section discusses the use of the mathematical model as a possible angiogenesis assay.

Animals↗
PubMed2002

A mathematical model of chemoreception for odours and taste.

We propose a mathematical model based on the occupation theory and on the hypothesis that, for a given stimulus, there exist two kinds of receptors. The receptors of the first kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active depolarizing form (this scheme was already used by Del Castillo & Katz, 1957). In the same way, the receptors of the second kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active hyperpolarizing form. The response is assumed to be proportional to the difference between the fraction of the active depolarizing compound and that of the active hyperpolarizing compound. The present paper deals only with the time course of the intensity of the response: in the first part, when a continuous flow of stimulus is applied and in the second part, when this continuous flow is removed. It does not deal with the quality and the discrimination of odours. The proposed mathematical model accounts for the depolarizing responses (which are the most frequent ones), the hyperpolarizing responses, the mixed responses reported by Patte et al. (1989), the off-responses reported by Takagi & Shibuya (1959) and for their variability, and the latent period in the olfactory response (Ottoson, 1974).

Chemoreceptor Cells↗
PubMed2001

Mathematical model of a hybrid dispersed network-membrane-based controlled release system.

A mathematical model with an exact solution is presented for the controlled release of a drug from a hybrid dispersed network-membrane based system. Both hollow fiber and flat membrane device geometries are considered. The reservoir is loaded with a drug dispersed in a liquid phase. This reservoir is bounded by a microporous membrane, the pores of which are filled with liquid immiscible with the reservoir phase liquid. The drug dissolves from the solid network into the reservoir liquid and migrates through the reservoir toward the microporous membrane. At the interface between the reservoir and the pore, the solute partitions between the reservoir and the pore liquid phases, before diffusing outward through the membrane pore. Experimental results are in close agreement with the release profiles predicted by the mathematical model. Parametric studies reveal the interaction between system parameters and the controlled release behavior. The presence of a dispersed drug phase in the reservoir results in the release of drug for an extended time. The release rate of the drug may be controlled by its rate of diffusion through the membrane pores or by its rate of dissolution into the reservoir liquid.

Chemistry, Pharmaceutical↗
PubMed2004

Mathematical modelling of tumour-induced angiogenesis: network growth and structure.

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organise themselves into a branched, connected network. Subsequent cell proliferation near the sprout-tips permits further extension of the capillaries and ultimately completes the process. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this chapter we first of all present a review of a variety of mathematical models which have been used to describe the formation of capillary networks and then focus on a specific recent model which uses novel mathematical modelling techniques to generate both 2 and 3 dimensional vascular structures. The modelling focusses on key events of angiogenesis such as the migratory response of endothelial cells to exogenous cytokines (tumour angiogenic factors, TAF) secreted by a solid tumour; endothelial cell proliferation; endothelial cell interactions with extracellular matrix macromolecules such as fibronectin; matrix degradation; capillary sprout branching and anastomosis. Numerical simulations of the model, using parameter values based on experimental data, are presented and the theoretical structures generated by the model are compared with the morphology of actual capillary networks observed in in vivo experiments. A final section discusses the use of the mathematical model as a possible angiogenesis assay and implications for chemotherapy regimes.

Animals↗
PubMed1988

[A mathematical model for describing radiation complications].

The paper is devoted to the development of a mathematical model for describing probabilities of occurrence of radiation complications on the skin (as well as in other normal organs and tissues) during its irradiation with homogeneous and inhomogeneous dose fields as a function of an irradiated skin area. The model naturally necessitates the isolation of an equivalent dose (an equidosimetric value) introduced by I. B. Keirim-Marcus which can be effectively used for comparison of homogeneous and inhomogeneous dose fields in normal organs and tissues. The development of mathematical models describing probabilities of occurrence of radiation complications in normal organs and tissues opens up new opportunities for improvement of methods of cancer radiotherapy design.

Humans↗
PubMed2001

Mathematical modeling for functional divergence after gene duplication.

In this paper, I present a statistical framework for modeling the functional divergence after gene duplication. A rate-component model to describe the rate covariation among homologous genes of a gene family is implemented when a phylogenetic tree is known. The Markov chain model is rigorous but may require a huge amount of computational time when the number of sequences is large. On the other hand, the Poisson-based model is mathematically analytical so that computation is very fast even for a large dataset. Moreover, under the posterior framework, we have developed a site-specific profile for predicting important amino acid residues responsible for these functional differences between member genes of a gene family. Our study may have great potential for functional genomics because it is cost-effective, and these predictions can be further tested by biological experimentation.

Biological Evolution↗
PubMed2006

Mathematical modeling and simulation of drug release from microspheres: Implications to drug delivery systems.

This article aims to provide a comprehensive review of existing mathematical models and simulations of drug release from polymeric microspheres and of drug transport in adjacent tissues. In drug delivery systems, mathematical modeling plays an important role in elucidating the important drug release mechanisms, thus facilitating the development of new pharmaceutical products by a systematic, rather than trial-and-error, approach. The mathematical models correspond to the known release mechanisms, which are classified as diffusion-, swelling-, and erosion-controlled systems. Various practical applications of these models which explain experimental data are illustrated. The effect of gamma-irradiation sterilization on drug release mechanism from erosion-controlled systems will be discussed. The application of existing models to nanoscale drug delivery systems specifically for hydrophobic and hydrophilic molecules is evaluated. The current development of drug transport modeling in tissues utilizing computational fluid dynamics (CFD) will also be described.

Bone and Bones↗