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

TL;DR

This paper develops a multiscale modeling approach for signaling in cardiac tissue with non-periodic microstructure, using locally-periodic approximations and unfolding techniques to derive macroscopic equations.

Contribution

It introduces a novel multiscale analysis method for non-periodic microstructures in biological tissues, extending existing homogenization techniques.

Findings

Derived macroscopic equations for cardiac signaling processes

Extended locally-periodic unfolding methods to non-periodic microstructures

Provided a mathematical framework for multiscale analysis in complex tissues

Abstract

In this paper a microscopic model for a signalling process in the cardiac muscle tissue of the left ventricular wall, comprising non-periodic fibrous microstructure is considered. To derive the macroscopic equations we approximate the non-periodic microstructure by the corresponding locally-periodic microstructure. Then applying the methods of 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 problem for a signalling process in the heart muscle tissue.