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 (Lead / Corresponding author)

Mathematics

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3 Citations (Scopus)

191 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 brous 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 locallyperiodic (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
Early online date	22 Nov 2016
DOIs	https://doi.org/10.1007/s10013-016-0232-9
Publication status	Published - Mar 2017

Keywords

non-periodic microstructures
plywood-like microstructures
signalling processes
domains with non-periodic perforations
locally-periodic homogenization
unfolding operator

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10.1007/s10013-016-0232-9Licence: CC BY

Final Published Version
© The Author(s) 2016. This article is published with open access at Springerlink.com
Final published version, 477 KBLicence: CC BY

Multiscale Modelling and Analysis of Mechanical Properties of Plant Cells and Tissues
Ptashnyk, M. (Investigator)
Engineering and Physical Sciences Research Council
1/01/14 → 31/12/15
Project: Research

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 brous 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 locallyperiodic (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.",

keywords = "non-periodic microstructures, plywood-like microstructures, signalling processes, domains with non-periodic perforations, locally-periodic homogenization, unfolding operator",

author = "Mariya Ptashnyk",

note = "This research was supported by EPSRC First Grant EP/K036521/1.",

year = "2017",

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doi = "10.1007/s10013-016-0232-9",

language = "English",

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AU - Ptashnyk, Mariya

N1 - This research was supported by EPSRC First Grant EP/K036521/1.

PY - 2017/3

Y1 - 2017/3

N2 - In this paper a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic brous 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 locallyperiodic (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.

AB - In this paper a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic brous 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 locallyperiodic (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 - non-periodic microstructures

KW - plywood-like microstructures

KW - signalling processes

KW - domains with non-periodic perforations

KW - locally-periodic homogenization

KW - unfolding operator

U2 - 10.1007/s10013-016-0232-9

DO - 10.1007/s10013-016-0232-9

M3 - Article

SN - 2305-221X

VL - 45

SP - 295

EP - 316

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

IS - 1

ER -

Multiscale modelling and analysis of signalling processes in tissues with non-periodic distribution of cells

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Keywords

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Multiscale Modelling and Analysis of Mechanical Properties of Plant Cells and Tissues

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