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Results for “Mathematical Model”

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At least 1,099 records · Page 61Linked to original sources
PubMed1998

Role of the net architecture in piriform cortex activity: analysis by a mathematical model.

We present a mathematical analysis of the piriform cortex activity in rats. Experimental data were obtained by means of optical recording of fluorescent signals driven by neuronal activity. From these data, we determined the numerical value of the relaxation time for the pyramidal cell activity in layers II and III and the time latency map for bulb activation. Our model for the piriform cortex is based on pairs of excitatory and inhibitory neurons which correspond to pyramidal cells of layers II and III and to their inhibitory associated interneurons respectively; pyramidal cells are also interconnected through short and long range association fiber systems. Under such conditions, the model outputs resemble closely the experimental observations: (1) a double-bumped response to a strong and short stimulation; (2) oscillatory behavior under weak sustained stimulation conditions; (3) propagation of traveling activity waves; and (4) pacemaker activity when clusters of neurons are preferentially coupled.

Animals↗
PubMedDate not supplied

[Design of a mathematical model of the formation of erythrocyte shape as an autowave process].

The phenomenological model of T. Teorell's "biomembrane generator" underlies the mathematical model of erythrocyte forms as an autowave process. For a distributed system the model is formulated as a differential equation of the second order in partial derivatives with a small parameter. It is stated that a substantial thing in the model is the presence of mass-transfer through a pore membrane determined by its electrostatic and hydrostatic permeabilities, as well as the fact that mass-transfer through the membrane results in a non-uniform distribution of the liquid current through it. It is suggested that as a consequence of this process there appears mechanical instability of the spherical membrane, which is the cause of the autowave process. Due to the membrane elasticity this process can be compared with the movement of "tank caterpillar".

Erythrocyte Membrane↗
PubMed1988

[Bayesian estimates of unknown parameters of mathematical models of the dynamics of the mutation process and changes in the ratio of cells having passed different numbers of divisions in a culture].

With the help of Bayesian methods, the conditions of solving experimental data samples and their divisions were established, equivalence of estimations of unknown linear dynamic models parameters proved, the estimations having been worked out by both accounting calculation errors and using their compensations with additional noise in the original model's discrete analog. The results are used in mathematical modeling of changing intensity of the process of hereditary pathology frequencies, and the process of changing the ratio of cells having passed different numbers of divisions in the culture.

Bayes Theorem↗
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↗
PubMed2002

[Mathematical modeling -- an objective assessment of new medicines and treatment technologies].

An objective method of studying effectiveness of new medicines and methods of treatment is mathematical modeling. On the basis of mathematical processing of the pooled data obtained in the control group of patients an individual prognostic formula can be made which predicts the only outcome for each patient. When studying a new medicine or method of treatment in each patient under test his prognostic outcome is compared to the real one. An improvement of the real outcome as compared to the prognostic one points to the effectiveness of the new medicine used. An objective and individual approach to the assessment of the result after the end of each case of treatment allows the further perspectiveness of the work done and the number of necessary tests to be efficiently estimated.

Drug Therapy↗
PubMed2007

A mathematical model for predicting controlled release of bioactive agents from composite fiber structures.

A mathematical model for predicting bioactive agent release profiles from core/shell fiber structures was developed and studied. These new composite fibers, which combine good mechanical properties with desired protein release profiles, are designed for use in tissue regeneration and other biomedical applications. These fibers are composed of an inner dense polymeric core surrounded by a porous bioresorbable shell, which encapsulates the bioactive agent molecules. The model is based on Fick's second law of diffusion, and on two major assumptions: (a) first-order degradation kinetics of the porous shell, and (b) a nonconstant diffusion coefficient for the bioactive agent, which increases with time because of degradation of the host polymer. Three factors are evaluated and included in this model: a porosity factor, a tortuosity factor, and a polymer concentration factor. Our study indicates that the model correlates well with in vitro release results, exhibiting a mean error of less than 2.2% for most studied cases. In this study, the model was used for predicting protein release profiles from fibers with shells of various initial molecular weights and for predicting the release of proteins with various molecular weights. This new model exhibits a potential for simulating fibrous systems for a wide variety of biomedical applications.

Biocompatible Materials↗
PubMedDate not supplied

Mathematical modelling of changes in circulating insulin and C-peptide concentrations.

A simple mathematical model is proposed to assess the validity of methods currently used in clinical investigation to detect short-term or long-term alterations in insulin and/or C-peptide clearance. This model draws attention to unwarranted conclusions which resulted from the analysis of insulin and C-peptide plasma concentrations.

C-Peptide↗
PubMed2000

A mathematical model of the stress induced during avascular tumour growth.

In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stress to the strain directly). By studying three model problems which differ in detail, certain characteristic features are identified. First, cells near the tumour boundary, where nutrient levels and cell proliferation rates are high, are under compression. By contrast, cells towards the centre of the tumour, where nutrient levels are low and cell death dominant, are under tension. The implications of these results and possible model developments are also discussed.

Humans↗
PubMed2004

A mathematical model for the growth of the abdominal aortic aneurysm.

We present the first mathematical model to account for the evolution of the abdominal aortic aneurysm. The artery is modelled as a two-layered, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model. It is subject to a constant systolic pressure and a physiological axial prestretch. The development of the aneurysm is assumed to be a consequence of the remodelling of its material constituents. Microstructural 'recruitment' and fibre density variables for the collagen are introduced into the strain energy density functions. This enables the remodelling of collagen to be addressed as the aneurysm enlarges. An axisymmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodelling of the fibre variables, is simulated numerically. Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm are consistent with those observed in vivo. An asymmetric aneurysm with spinal contact is also modelled, and the stress distributions are consistent with previous studies.

Aortic Aneurysm, Abdominal↗
PubMed1984

A mathematical model for lambda dv plasmid replication: analysis of wild-type plasmid.

A mathematical model for lambda dv plasmid replication in a growing single cell of Escherichia coli has been formulated and solved numerically. Quantitative description of the molecular control mechanism for initiation of lambda dv replication presumes regulatory functions of repressor and initiator proteins and transcriptional activation of the origin region. Random selection of a single plasmid for activation and replication is assumed, as is regular plasmid segregation to daughter cells. The model is capable of simulating the periodic changes in each regulatory element and the plasmid copy number during the cell cycle. The calculated average copy number, repressor concentration, and timing of plasmid replication agree well with experimental data. The simulated lambda dv plasmid replication rate is controlled primarily by transcription frequency. Initiation of plasmid replication is not related to variations in the levels of repressor or initiator proteins during the cell cycle. Simulation studies of perturbations in plasmid and repressor segregation indicate that replication regulation of the lambda dv plasmid compensates to readjust copy number to normal values in a few generations. Implications of these studies relative to the molecular mechanisms of replication control are discussed.

DNA Replication↗
PubMed1977

A mathematical model of periodic processes in membranes (with application to cell cycle regulation).

A mathematical model of the regulation of the cell cycle by the plasma membrane is suggested. The model is based on the hypothesis that structural transitions of the cell membrane play an important role in the regulation of cell division. Conditions of transition from the proliferating state to the resting state and back are investigated. Possible qualitative differences between models of the cell cycle of a normal and a tumour cell are pointed out.

Cell Cycle↗
PubMed2005

A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin's lymphoma: investigation of the current protocol through theoretical modelling results.

Doxorubicin treatment outcomes for non-Hodgkin's lymphomas (NHL) are mathematically modelled and computationally analyzed. The NHL model includes a tumor structure incorporating mature and immature vessels, vascular structural adaptation and NHL cell-cycle kinetics in addition to Doxorubicin pharmacokinetics (PK) and pharmacodynamics (PD). Simulations provide qualitative estimations of the effect of Doxorubicin on high-grade (HG), intermediate-grade (IG) and low-grade (LG) NHL. Simulation results imply that if the interval between successive drug applications is prolonged beyond a certain point, treatment will be inefficient due to effects caused by heterogeneous blood flow in the system.

Cell Cycle↗
PubMed1987

Mathematical modeling of electrical activity of the heart.

This paper reviews the literature on mathematical models of cardiac activation and evaluates these approaches against an analytical approach that includes both structure and membrane properties. The advantages and disadvantages of each methodology are described and directions for future research suggested.

Animals↗
PubMed1999

Mathematical modelling of drug permeation through a swollen membrane.

This work proposes two different mathematical models (linear and numerical) able to simulate the drug permeation through a swollen membrane sandwiched by two external layers (trilaminate system). Moreover, a solid drug dissolution phenomenon in the donor compartment may be accounted for. Indeed, this is a situation that may often occur in permeation experiments. An insufficient stirring of the donor and of the receiver volume may give rise to two sandwiching layers and the target of a constant drug concentration in the donor compartment may be accomplished by putting a solid drug amount in the saturated donor solution. The linear model shows the advantage of having an analytical expression which extremely simplifies the calculation of the drug diffusion coefficient D inside the membrane. Its main drawback lies in the fact that it works only for thin trilaminate systems. The numerical model is more general than the linear one, as it works for all kind of trilaminate thickness and it may account for a solid powder dissolution in the donor compartment. Of course, it does not have an analytical solution and, thus, the D determination is less easy to perform as the numerical model is more time consuming than the linear one. These two models are then compared with the classical approach developed by Flynn and Barrie in order to better define its validity limits.

Diffusion↗
PubMed1986

On the choice of mathematical models for the estimation of lethal gene equivalents in man.

A range of mathematical models and error distributions was used to examine the validity of linear regression methods for the calculation of lethal gene equivalents. Because of the restricted span of inbreeding coefficient F values available in human studies and the limited number of data points, equivalent results were obtained with all combinations tested. It was concluded that linear regressions should be employed only for the detection of significant inbreeding effects in man and that their application to the estimation of lethal gene equivalents was not warranted.

Female↗
PubMed1996

What does mathematical modeling tell us about harm reduction?

This paper argues, primarily by example, that mathematical modeling can contribute to harm reduction-orientated drug policy making in three ways: by contributing to quantitative evaluations of effectiveness, by improving data and understanding of the underlying drug-related phenomena, and by encouraging precise thinking about the goals and objectives of harm reduction.

Journal Article↗
PubMed2005

Mathematical models of cancer dormancy.

The objective of this paper is to present preliminary mathematical models of the interaction between tumor and antibody for the murine BCL1 lymphoma and illustrate how this interaction leads to dormancy of the tumor. We explicitly model the induction by the immune response of cell cycle arrest and apoptosis of the tumor cells. In the absence of large amounts of quantitative data and because the models are preliminary, they are deliberately simple. We neglect, for example, spatial effects on this lymphoid tumor and the synergistic effect of antigen-specific T cells. A comparison of alternative models shows that, although vaccination is necessary to stimulate a sufficient immune response to control tumor growth, boosting of the antibody response by the tumor itself is vital to the mechanisms that maintain dormancy. We determine parameters that control the size of the dormant tumors, and the fraction of proliferating cells. Finally, we discuss the implications for tumor immunotherapy.

Animals↗
PubMed1997

A mathematical model that predicts skeletal muscle force.

This study demonstrates the validity of a mathematical model that predicts the force generated by rat skeletal muscles during brief subtetanic and tetanic isometric contractions. The model consists of three coupled differential equations (ODE's). The first two equations represent the calcium dynamics and the third equation represents force dynamics. The model parameters were identified from brief trains of regularly spaces pulses [constant-frequency trains (CFT's)] that produce subtetanic muscle responses. Using these parameters, the model was able to predict isometric forces from other stimulation patterns. For the gastrocnemius muscles predictions were made for responses to CFT's with interpulse intervals (IPI's) ranging from 10 to 50 ms and variable-frequency trains (VFT's), where the initial IPI = 10 ms and the remaining IPI's were identical to those used for the CFT's. For the soleus muscles predictions were made for 10-100-ms CFT's. The shape of the predicted responses closely match the experimental data. Comparisons between experimental and modeled force-time integrals, peak forces, and time-to-peak also suggest excellent agreement between the model and the experiment data. Many physiological parameters predicted by the model agree with values obtained independently by others. In conclusion, the model accurately predicts isometric forces generated by rat gastrocnemius and soleus muscles produced by brief stimulation trains.

Actins↗