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

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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 languageEnglish
Pages (from-to)295-316
Number of pages22
JournalVietnam Journal of Mathematics
Volume45
Issue number1-2
Early online date22 Nov 2016
DOIs
Publication statusPublished - 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

  • Mathematics(all)

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