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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...
Our aim is to show a class of mathematical models in application to some problems of cell biology. Typically, our models are described via classical chemical networks. This property is visualized by a conservation law. Mathematically, this conservation law guarantees most of the mathematical properties of the models such as global existence and uniqueness of solutions as well as positivity of the solutions for positive data. These properties are consequences of the fact that the infinitesimal generators...
When invading the tissue, malignant tumour cells (i.e. cancer cells) need to detach from
neighbouring cells, degrade the basement membrane, and migrate through the extracellular
matrix. These processes require loss of cell-cell adhesion and enhancement of cell-matrix
adhesion. In this paper we present a mathematical model of an intracellular pathway for
the interactions between a cancer cell and the extracellular matrix. Cancer cells use
similar...
This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–
359/2008.We consider a nonlinear model of a continuously stirred bioreactor
and study the stability of the equilibrium points with respect to practically
important model parameters. We determine regions in the parameter
space where the steady states undergo transcritical and Hopf bifurcations.
In the latter case, the stability of the emerged limit cycles is also studied.
Numerical simulations in the computer algebra...
This paper presents a semi-global mathematical model for an analysis of a signal of amperometric biosensors. Artificial neural networks were applied to an analysis of the biosensor response to multi-component mixtures. A large amount of the learning and test data was synthesized using computer simulation of the biosensor response. The biosensor signal was analyzed with respect to the concentration of each component of the mixture. The paradigm of locally weighted linear regression was used for retraining...
Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical...
In this paper we propose a mathematical model to describe the evolution of leukemia
in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous
medium. We show the existence of two stationary solutions, one of them corresponds to the normal
case and another one to the pathological case. The leukemic state appears as a result of a bifurcation
when the normal state loses its stability. The critical conditions of leukemia development
are determined by the proliferation...
We develop and test a relatively simple enhancement of the classical model reduction method applied to a class of chemical networks with mass conservation properties. Both the methods, being (i) the standard quasi-steady-state approximation method, and (ii) the novel so-called delayed quasi-steady-state approximation method, firstly proposed by Vejchodský (2014), are extensively presented. Both theoretical and numerical issues related to the setting of delays are discussed. Namely, for one slightly...
A pharmacodynamic model introduced earlier in the literature for in silico prediction of rifampicin-induced CYP3A4 enzyme production is described and some aspects of the involved curve-fitting based parameter estimation are discussed. Validation with our own laboratory data shows that the quality of the fit is particularly sensitive with respect to an unknown parameter representing the concentration of the nuclear receptor PXR (pregnane X receptor). A detailed analysis of the influence of that parameter...
We propose a new approach to the mathematical modelling of
microbial growth. Our approach differs from familiar Monod type models by
considering two phases in the physiological states of the microorganisms and
makes use of basic relations from enzyme kinetics. Such an approach may
be useful in the modelling and control of biotechnological processes, where
microorganisms are used for various biodegradation purposes and are often
put under extreme inhibitory conditions. Some computational experiments
are...
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