Discrete mechanical growth model for plant tissue.

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass poin...

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Main Authors: Louis D Weise, Kirsten H W J Ten Tusscher
Format: Article
Language:English
Published: Public Library of Science (PLoS) 2019-01-01
Series:PLoS ONE
Online Access:https://doi.org/10.1371/journal.pone.0221059
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spelling doaj-279d552cfe8f422f89428a11030edb932021-03-03T19:51:35ZengPublic Library of Science (PLoS)PLoS ONE1932-62032019-01-01148e022105910.1371/journal.pone.0221059Discrete mechanical growth model for plant tissue.Louis D WeiseKirsten H W J Ten TusscherWe present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke's law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.https://doi.org/10.1371/journal.pone.0221059
collection DOAJ
language English
format Article
sources DOAJ
author Louis D Weise
Kirsten H W J Ten Tusscher
spellingShingle Louis D Weise
Kirsten H W J Ten Tusscher
Discrete mechanical growth model for plant tissue.
PLoS ONE
author_facet Louis D Weise
Kirsten H W J Ten Tusscher
author_sort Louis D Weise
title Discrete mechanical growth model for plant tissue.
title_short Discrete mechanical growth model for plant tissue.
title_full Discrete mechanical growth model for plant tissue.
title_fullStr Discrete mechanical growth model for plant tissue.
title_full_unstemmed Discrete mechanical growth model for plant tissue.
title_sort discrete mechanical growth model for plant tissue.
publisher Public Library of Science (PLoS)
series PLoS ONE
issn 1932-6203
publishDate 2019-01-01
description We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke's law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.
url https://doi.org/10.1371/journal.pone.0221059
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AT kirstenhwjtentusscher discretemechanicalgrowthmodelforplanttissue
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