On the mechanical theory for biological pattern formation

DOI10.1016/0167-2789(93)90153-RzbMath0778.92006OpenAlexW2052871172MaRDI QIDQ1803798

James D. Murray, Daniel E. Bentil

Publication date: 29 June 1993

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(93)90153-r

zbMATH Keywords

pattern formationsimulationswound healingexamplesstanding wavesconservation equationsspatio-temporal oscillationsembryologycell density equationscell-matrix equationdermatoglyphic patternsfingerprint patternslong-range traction forcesOster-Murray modelspurely local cell-matrix interactionsstationary stable patternstissue extracellular matrix

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Developmental biology, pattern formation (92C15) Applications to the sciences (65Z05)

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Fingerprint formation

Cites Work

• Spatial and spatio-temporal patterns in a cell-haptotaxis model
• A mechanical model for mesenchymal morphogenesis
• Cell traction models for generating pattern and form in morphogenesis
• Pattern selection in biological pattern formation mechanisms
• Nonlinear pattern selection in a mechanical model for morphogenesis
• A generalized diffusion model for growth and dispersal in a population
• Mathematical analysis of a basic model for epidermal wound healing
• Analysis of a Model for Complex Skin Patterns
• A Nonlinear Analysis of a Mechanical Model for Biological Pattern Formation
• The chemical basis of morphogenesis
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