A novel technique to parametrize shell-like deformations inside biological membranes

Biological structures like organs or embryos usually have irregular forms. The analytical description of their geometry constitutes then a major issue when numerical modeling is used to simulate their behavior. The novel technique presented here allows to parametrize many three-dimensional objects w...

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Bibliographic Details
Published in:Computational mechanics Vol. 47; no. 4; pp. 409 - 423
Main Authors: Allena, R., Aubry, D.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2011
Springer
Springer Nature B.V
Springer Verlag
Subjects:
Biological
Biomechanics
Classical and Continuum Physics
Computational Science and Engineering
Computer simulation
Deformation
Domains
Electric potential
Electricity
Embryos
Engineering
Engineering Sciences
Fruit flies
Geometry
Kinematics
Mathematical analysis
Mathematical models
Mechanics
Mechanics of materials
Organs
Original Paper
Physics
Shells
Theoretical and Applied Mechanics
Morphogenesis
Electric potential
Biological shells
Simply and multiply connected domains
ISSN:0178-7675, 1432-0924
Online Access:Get full text
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Summary:Biological structures like organs or embryos usually have irregular forms. The analytical description of their geometry constitutes then a major issue when numerical modeling is used to simulate their behavior. The novel technique presented here allows to parametrize many three-dimensional objects whose shape can be approximated by the one of a general shell. The main idea of the present work lies on the coupling between electricity, geometry and mechanics because the electric potential inside an object has properties inherited from the geometrical representation. Based on this fundamental property, we are able to describe both simply and multiply connected domains. Two forms of the theoretical formulation are proposed. First, we present a partial version for which the electric potential is employed to compute only one of the principal variables, which compose the general curvilinear system. Second, we introduce an extended version for which the complete covariant and contravariant bases are obtained and the conventional kinematics and mechanics for a thick general shell are redefined. Finally, for illustrative purpose, we propose a biomechanical application on a rather complex structure such as Drosophila embryo. In particular, we show how the new technique fits well when a parametrical description of the system geometry is required to simulate the morphogenetic movements.
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ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-010-0551-8