On the mechanical theory for biological pattern formation
type: Item
instance of: scholarly article
title: On the mechanical theory for biological pattern formation
zbMATH Open document ID: 0778.92006
DOI: 10.1016/0167-2789(93)90153-R
published in: Physica D
publication date: 1993-06-29T00:00:00Z
review text: The pattern formation potential of the purely mechanical Oster-Murray models [see \textit{J. D. Murray} and \textit{G. F. Oster}, IMA J. Math. Appl. Med. Biol. 1, 51-75 (1984; Zbl 0611.92003)] in embryology is investigated. These consist of 3 nonlinear PDE's: conservation equations for cells and extracellular matrix, respectively, and a cell-matrix equation. Numerical solutions yield standing waves for the case of purely local cell-matrix interactions, whereas stationary stable patterns (in one and two dimensions) are achieved when biologically realistic long-range traction forces are included. Biological examples are discussed, among which are wound healing and formation of fingerprint patterns.
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 65Z05
zbMATH DE Number: 221907
zbMATH Keywords: tissue extracellular matrix
zbMATH Keywords: cell density equations
zbMATH Keywords: spatio-temporal oscillations
zbMATH Keywords: dermatoglyphic patterns
zbMATH Keywords: simulations
zbMATH Keywords: pattern formation
zbMATH Keywords: Oster-Murray models
zbMATH Keywords: embryology
zbMATH Keywords: conservation equations
zbMATH Keywords: cell-matrix equation
zbMATH Keywords: standing waves
zbMATH Keywords: purely local cell-matrix interactions
zbMATH Keywords: stationary stable patterns
zbMATH Keywords: long-range traction forces
zbMATH Keywords: examples
zbMATH Keywords: wound healing
zbMATH Keywords: fingerprint patterns
author: Daniel E. Bentil
author: J. D. Murray
reviewed by: Michael Baake
MaRDI profile type: Publication
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full work available at URL: 0167-2789(93)90153-r
OpenAlex ID: W2052871172
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description: scientific article; zbMATH DE number 221907