Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Mariya Ptashnyk

doi:10.1007/s10013-016-0232-9

Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Mariya Ptashnyk^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

36 Downloads (Pure)

Abstract

In this paper, a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic fibrous microstructure, is considered. To derive the macroscopic equations, the non-periodic microstructure is approximated by the corresponding locally periodic microstructure. Then, applying the methods of locally periodic homogenization (the locally periodic (l-p) unfolding operator, locally periodic two-scale (l-t-s) convergence on oscillating surfaces and l-p boundary unfolding operator), we obtain the macroscopic model for a signalling process in the heart tissue.

Original language	English
Pages (from-to)	295-316
Number of pages	22
Journal	Vietnam Journal of Mathematics
Volume	45
Issue number	1-2
Early online date	22 Nov 2016
DOIs	https://doi.org/10.1007/s10013-016-0232-9
Publication status	Published - Mar 2017

Keywords

Domains with non-periodic perforations
Locally periodic homogenization
Non-periodic microstructures
Plywood-like microstructures
Signalling processes
Unfolding operator

ASJC Scopus subject areas

General Mathematics

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Cite this

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title = "Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells",

abstract = "In this paper, a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic fibrous microstructure, is considered. To derive the macroscopic equations, the non-periodic microstructure is approximated by the corresponding locally periodic microstructure. Then, applying the methods of locally periodic homogenization (the locally periodic (l-p) unfolding operator, locally periodic two-scale (l-t-s) convergence on oscillating surfaces and l-p boundary unfolding operator), we obtain the macroscopic model for a signalling process in the heart tissue.",

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AB - In this paper, a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic fibrous microstructure, is considered. To derive the macroscopic equations, the non-periodic microstructure is approximated by the corresponding locally periodic microstructure. Then, applying the methods of locally periodic homogenization (the locally periodic (l-p) unfolding operator, locally periodic two-scale (l-t-s) convergence on oscillating surfaces and l-p boundary unfolding operator), we obtain the macroscopic model for a signalling process in the heart tissue.

KW - Domains with non-periodic perforations

KW - Locally periodic homogenization

KW - Non-periodic microstructures

KW - Plywood-like microstructures

KW - Signalling processes

KW - Unfolding operator

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EP - 316

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 1-2

ER -

Multiscale Modelling and Analysis of Signalling Processes in Tissues with Non-Periodic Distribution of Cells

Abstract

Keywords

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