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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.

Free boundary problems arising in tumor models

Avner Friedman (2004)

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

We consider several simple models of tumor growth, described by systems of PDEs, and describe results on existence of solutions and on their asymptotic behavior. The boundary of the tumor region is a free boundary. In §1 the model assumes three types of cells, proliferating, quiescent and necrotic, and the corresponding PDE system consists of elliptic, parabolic and hyperbolic equations. The model in §2 assumes that the tumor has only proliferating cells. Finally in §3 we consider a model for treatment...

Free Boundary Problems Associated with Multiscale Tumor Models

A. Friedman (2009)

Mathematical Modelling of Natural Phenomena

The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary...

From Quasispecies Theory to Viral Quasispecies: How Complexity has Permeated Virology

E. Domingo, C. Perales (2012)

Mathematical Modelling of Natural Phenomena

RNA viruses replicate as complex and dynamic mutant distributions. They are termed viral quasispecies, in recognition of the fundamental contribution of quasispecies theory in our understanding of error-prone replicative entities. Viral quasispecies have launched a fertile field of transdiciplinary research, both experimental and theoretical. Here we review the origin and some implications of the quasispecies concept, with emphasis on internal interactions...

Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation

Weihua Geng, Shan Zhao (2013)

Molecular Based Mathematical Biology

The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and stably solve the nonlinear PB equation in a pseudo-transient continuation approach. The operator splitting...

Fusion based analysis of ophthalmologic image data

Jiří Jan, Radim Kolář, Libor Kubečka, Jan Odstrčilík, Jiří Gazárek (2011)

Kybernetika

The paper presents an overview of image analysis activities of the Brno DAR group in the medical application area of retinal imaging. Particularly, illumination correction and SNR enhancement by registered averaging as preprocessing steps are briefly described; further mono- and multimodal registration methods developed for specific types of ophthalmological images, and methods for segmentation of optical disc, retinal vessel tree and autofluorescence areas are presented. Finally, the designed methods...

Generalised filtering.

Friston, Karl, Stephan, Klaas, Li, Baojuan, Daunizeau, Jean (2010)

Mathematical Problems in Engineering

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...

Genetic and Tabu search algorithms for peptide assembly problem

Jacek Błażewicz, Marcin Borowski, Piotr Formanowicz, Tomasz Głowacki (2010)

RAIRO - Operations Research

Determining amino acid sequences of protein molecules is one of the most important issues in molecular biology. These sequences determine protein structure and functionality. Unfortunately, direct biochemical methods for reading amino acid sequences can be used for reading short sequences only. This is the reason, which makes peptide assembly algorithms an important complement of these methods. In this paper, a genetic algorithm solving the problem of short amino acid sequence assembly is presented....

Global classical solutions in a self-consistent chemotaxis(-Navier)-Stokes system

Yanjiang Li, Zhongqing Yu, Yumei Huang (2024)

Czechoslovak Mathematical Journal

The self-consistent chemotaxis-fluid system n t + u · n = Δ n - · ( n c ) + · ( n φ ) , x Ω , t > 0 , c t + u · c = Δ c - n c , x Ω , t > 0 , u t + κ ( u · ) u + P = Δ u - n φ + n c , x Ω , t > 0 , · u = 0 , x Ω , t > 0 , is considered under no-flux boundary conditions for n , c and the Dirichlet boundary condition for u on a bounded smooth domain Ω N ( N = 2 , 3 ...

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