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A periodic model for the dynamics of cell volume

Philip Korman (2016)

Annales Polonici Mathematici

We prove the existence and uniqueness of a positive periodic solution for a model describing the dynamics of cell volume flux, introduced by Julio A. Hernández [Bull. Math. Biol. 69 (2007), 1631-1648]. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P. J. Torres [Atlantis Press, 2015].

Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions

Tomáš Vejchodský (2014)

Mathematica Bohemica

Quasi-steady state assumptions are often used to simplify complex systems of ordinary differential equations in the modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi-steady state assumptions...

Atherosclerosis Initiation Modeled as an Inflammatory Process

N. El Khatib, S. Génieys, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations...

Discrete time markovian agents interacting through a potential

Amarjit Budhiraja, Pierre Del Moral, Sylvain Rubenthaler (2013)

ESAIM: Probability and Statistics

A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport...

Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling

G. A. Koch-Noble (2011)

Mathematical Modelling of Natural Phenomena

Pharmacokinetics is an excellent way to introduce biomathematical modeling at the sophomore level. Students have the opportunity to develop a mathematical model of a biological phenomenon to which they all can relate. Exploring pharmacokinetics takes students through the necessary stages of mathematical modeling: determining the goals of the model, deciphering between the biological aspects to include in the model, defining the assumptions of the model, and finally, building, analyzing, using, and...

Formalisation and methods of analysis of the fast xenobiotic mass transfer in the body

Volodymir G. Zinkovsky, Olga V. Zhuk, Michał Teodorczyk, Natalia Karpinchik (2009)

Applicationes Mathematicae

A novel discrimination and regression method for a quantitative determination of the relative efficiency of "fast" distribution processes of xenobiotics is discussed. An integral model-independent method for estimation of equilibrium tissue-to-plasma partition ratios is proposed.

Generic principles of active transport

Mauro Mobilia, Tobias Reichenbach, Hauke Hinsch, Thomas Franosch, Erwin Frey (2008)

Banach Center Publications

Nonequilibrium collective motion is ubiquitous in nature and often results in a rich collection of intriguing phenomena, such as the formation of shocks or patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase transitions. These stochastic many-body features characterize transport processes in biology, soft condensed matter and, possibly, also in nanoscience. Inspired by these applications, a wide class of lattice-gas models has recently been considered. Building on the celebrated...

Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

Nathalie Verdiere, Lilianne Denis-Vidal, Ghislaine Joly-Blanchard, Dominique Domurado (2005)

International Journal of Applied Mathematics and Computer Science

The aim of this paper is numerical estimation of pharmacokinetic parameters of the ligands of the macrophage mannose receptor, without knowing it a priori the values of these parameters. However, it first requires a model identifiability analysis, which is done by applying an algorithm implemented in a symbolic computation language. It is shown that this step can lead to a direct numerical estimation algorithm. In this way, a first estimate is computed from noisy simulated observations without it...

Improving Cancer Therapy by Doxorubicin and Granulocyte Colony-Stimulating Factor: Insights from a Computerized Model of Human Granulopoiesis

V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski, A. Rabinovich, Y. Kogan, V. Selitser, Z. Agur (2010)

Mathematical Modelling of Natural Phenomena

Neutropenia is a significant dose-limiting toxicity of cancer chemotherapy, especially in dose-intensified regimens. It is widely treated by injections of Granulocyte Colony-Stimulating Factor (G-CSF). However, optimal schedules of G-CSF administration are still not determined. In order to aid in identifying more efficacious and less neutropenic treatment protocols, we studied a detailed physiologically-based computer model of granulopoiesis, as affected by different treatment schedules of doxorubicin...

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