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A simple mathematical model of the human liver

Lenka Čelechovská (2004)

Applications of Mathematics

The parameter estimation problem for a continuous dynamical system is a difficult one. In this paper we study a simple mathematical model of the liver. For the parameter identification we use the observed clinical data obtained by the BSP test. Bellman’s quasilinearization method and its modifications are applied.

A simultaneous localization and tracking method for a worm tracking system

Mateusz Kowalski, Piotr Kaczmarek, Rafał Kabaciński, Mieszko Matuszczak, Kamil Tranbowicz, Robert Sobkowiak (2014)

International Journal of Applied Mathematics and Computer Science

The idea of worm tracking refers to the path analysis of Caenorhabditis elegans nematodes and is an important tool in neurobiology which helps to describe their behavior. Knowledge about nematode behavior can be applied as a model to study the physiological addiction process or other nervous system processes in animals and humans. Tracking is performed by using a special manipulator positioning a microscope with a camera over a dish with an observed individual. In the paper, the accuracy of a nematode's...

A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes

J. Dyson, R. Villella-Bressan, G. Webb (2010)

Mathematical Modelling of Natural Phenomena

A model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of...

A stochastic extension of R. Thomas regulatory network modelling

Bartek Wilczyński (2008)

Banach Center Publications

In this paper we present the extension of the kinetic logic proposed by René Thomas for analysis of genetic regulatory gene networks. We consider the case with a Gaussian noise added to the regulation function and propose a method of analyzing the resulting model with a discrete time Markov model.

A theoretical comparison of disco and CADIAG-II-like systems for medical diagnoses

Tatiana Kiseliova (2006)

Kybernetika

In this paper a fuzzy relation-based framework is shown to be suitable to describe not only knowledge-based medical systems, explicitly using fuzzy approaches, but other ways of knowledge representation and processing. A particular example, the practically tested medical expert system Disco, is investigated from this point of view. The system is described in the fuzzy relation-based framework and compared with CADIAG-II-like systems that are a “pattern” for computer-assisted diagnosis systems based...

A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates

Christian Bourdarias, Stéphane Gerbi, Jacques Ohayon (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...

A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates

Christian Bourdarias, Stéphane Gerbi, Jacques Ohayon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...

A time-dependent best choice problem with costs and random lifetime in organ transplants

Anna Krasnosielska (2010)

Applicationes Mathematicae

This paper develops and analyzes a time-dependent optimal stopping problem and its application to the decision making process concerning organ transplants. Offers (organs for transplant) appear at jump times of a Poisson process. The values of the offers are i.i.d. random variables with a known distribution function. These values express the degree of histocompatibility between the donor and the recipient. The sequence of offers is independent of the jump times of the Poisson process. The decision...

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