Russian Journal of Numerical Analysis and Mathematical Modelling

Published by De Gruyter

Volume 29 Issue 5

Issue of Russian Journal of Numerical Analysis and Mathematical Modelling

Contents
Journal Overview

Publicly Available October 11, 2014

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Page range: i-iv

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October 11, 2014

The Method for Identification of Hierarchical Organization of Protein Sequences

Anastasia A. Anashkina, Alexei N. Nekrasov

Page range: 265-273

Abstract

The paper describes a newmethod of Information Structure Analysis (ISAN) for protein sequences. The method uses a new approximation for description of protein sequences, which allows us to detect hierarchically organized elements (Information Structure Elements (ISEL)) in them. It is shown that elements of the higher hierarchy level of information structure correspond to stable elements in the spatial structure of globular proteins. Based on the ISAN method, we propose an approach to design of the new sequences of recombinant proteins. The proposed approach was confirmed experimentally in the case of obtaining functionally active recombinant proteins.

October 11, 2014

Electro-Mechanical Coupling in a One-Dimensional Model of Heart Muscle fiber

Leonid B. Katsnelson, Natalia A. Vikulova, Alexander G. Kursanov, Olga E. Solovyova, Vladimir S. Markhasin

Page range: 275-284

Abstract

We developed a mathematical model that describes heart muscle fiber as a one-dimensional continuous medium of electrically and mechanically coupled cardiomyocytes through which electrical excitation propagates and initiates muscle contraction. The generic model simulates bilateral relations between the electrical and the mechanical activity of cardiomyocytes in the tissue and accounts for both intracellular and intercellular electro-mechanical couplings and mechano-electric feedback mechanisms.

October 11, 2014

Analysis of a Stochastic Model for the Spread of Tuberculosis with Regard to Reproduction and Seasonal Immigration of Individuals

Nikolay V. Pertsev, Vasiliy N. Leonenko

Page range: 285-295

Abstract

A stochastic model for the spread of tuberculosis is proposed taking into account the reproduction and seasonal immigration of individuals. The system of difference equations majorating the system of equations for mathematical expectations of sizes of considered cohorts of individuals is studied. Conditions for the parameters of the model are obtained so that under those conditions the sizes of cohorts of afflicted individuals do not exceed the given mean level. The results of numerical experiments are presented for the study of dynamics of mean sizes of cohorts of individuals subject to parameters of immigration inflow.

October 11, 2014

The Use of Evolution Optimality Principles in Simulation of Structured Biosystems

Valery N. Razzhevaikin

Page range: 297-305

Abstract

Approaches to use the theory of evolutionary optimality in the study of structured models of biological communities are proposed. Relations of this theory to the stability of equilibrium states are indicated and the formulation of its main result for the case of a quasilinear dynamical systems in normed spaces is presented. For models of communities with age, spatial, and age-spatial structure, functionals optimized over parameters of evolutionary selection are constructed. The functionals are calculated on the basis of the available information concerning steady stationary distributions. The sets of parameters obtained as the result of this optimization can serve for identification of models.

October 11, 2014

Nonstationary Hemodynamics Modelling in a Cerebral Aneurysm of a Blood Vessel

Arseny A. Yanchenko, Alexander A. Cherevko, Alexander P. Chupakhin, Alexey L. Krivoshapkin, Kirill Yu. Orlov

Page range: 307-317

Abstract

Computer simulation is carried out for unsteady hemodynamics in a cerebral aneurysm of a blood vessel. Using the data of a real patient obtained in medical examination and during surgery, we reconstruct the 3D geometry of the anomaly, calculate hydrodynamic parameters of blood flow (flow velocity, streamline distribution, pressure, shear stress on walls, energy flux) and the deformation and stresses of the vessel walls. The calculations were performed for the following three cases: in the presence of an aneurysm, immediately after stent deployment changing the geometry of the vessel, and one year after the surgery. It is shown what changes of hydrodynamic and mechanical quantities characterize a successful surgery.

October 11, 2014

Hybrid Cellular Automaton Method for Homogeneous Tumour Growth Modelling

Kirill M. Zapolski, Yury B. Admiralskiy, Alexander S. Bratus

Page range: 319-329

Abstract

In this paper a discrete planar model of the tumour growth is presented. The model is based on hybrid cellular automaton and describes the tumour in a homogeneous tissue. The tissue consists of healthy cells and can have irregular vasculature. The model simulates proliferation processes and necrotic cells appearance which depends on the oxygen supply. There exists a stable solution, which may be used as an approximation of the tissue. Described HCA model can be extended with angiogenesis, nutrients and factors fields.

About this journal

Objective
The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest.

Topics

numerical analysis
numerical linear algebra
finite element methods for PDEs
iterative methods
Monte-Carlo methods
mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences

Article formats
Research articles

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