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On the Dynamics of an Impulsive Model of Hematopoiesis

C. Kou, M. Adimy, A. Ducrot (2009)

Mathematical Modelling of Natural Phenomena

We propose and analyze a nonlinear mathematical model of hematopoiesis, describing the dynamics of stem cell population subject to impulsive perturbations. This is a system of two age-structured partial differential equations with impulses. By integrating these equations over the age, we obtain a system of two nonlinear impulsive differential equations with several discrete delays. This system describes the evolution of the total hematopoietic stem cell populations with impulses. We first examine...

On the global dynamics of the cancer AIDS-related mathematical model

Konstantin E. Starkov, Corina Plata-Ante (2014)

Kybernetika

In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...

On the Influence of Discrete Adhesive Patterns for Cell Shape and Motility: A Computational Approach

C. Franco, T. Tzvetkova-Chevolleau, A. Stéphanou (2010)

Mathematical Modelling of Natural Phenomena

In this paper, we propose a computational model to investigate the coupling between cell’s adhesions and actin fibres and how this coupling affects cell shape and stability. To accomplish that, we take into account the successive stages of adhesion maturation from adhesion precursors to focal complexes and ultimately to focal adhesions, as well as the actin fibres evolution from growing filaments, to bundles and finally contractile stress fibres.We use substrates with discrete patterns of adhesive...

On the Mathematical Modelling of Microbial Growth: Some Computational Aspects

Markov, Svetoslav (2011)

Serdica Journal of Computing

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...

On two methods for the parameter estimation problem with spatio-temporal FRAP data

Papáček, Štěpán, Jablonský, Jiří, Matonoha, Ctirad (2015)

Programs and Algorithms of Numerical Mathematics

FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model...

Optimal Proliferation Rate in a Cell Division Model

P. Michel (2010)

Mathematical Modelling of Natural Phenomena

We consider a size structured cell population model where a mother cell gives birth to two daughter cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a...

Oxygen exchange between multiple capillaries and living tissues: An homogenisation study

Andro Mikelić, Mario Primicerio (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.

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