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Mathematical modeling of morphogenesis in living materials. (English) Zbl 1353.92017
Preziosi, Luigi (ed.) et al., Mathematical models and methods for living systems, Levico Terme, Italy 2014. Based on lectures given at the C.I.M.E.-C.I.R.M. summer school. Cham: Springer; Florence: Fondazione CIME (ISBN 978-3-319-42678-5/pbk; 978-3-319-42679-2/ebook). Lecture Notes in Mathematics 2167. CIME Foundation Subseries, 211-274 (2016).
Summary: From a mathematical viewpoint, the study of morphogenesis focuses on the description of all geometric and structural changes which locally orchestrate the underlying biological processes directing the formation of a macroscopic shape in living matter. In this chapter, we introduce a continuous chemo-mechanical approach of morphogenesis, deriving the balance principles and evolution laws for both volumetric and interfacial processes. The proposed theory is applied to the study of pattern formation for either a fluid-like or a solid-like biological system model, using both theoretical methods and simulation tools.
For the entire collection see [Zbl 1358.92011].
MSC:
92C15 Developmental biology, pattern formation
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