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Couple stresses and discrete potentials in the vertex model of cellular monolayers
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers....
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10511640/ https://www.ncbi.nlm.nih.gov/pubmed/36201070 http://dx.doi.org/10.1007/s10237-022-01620-2 |
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author | Jensen, Oliver E. Revell, Christopher K. |
author_facet | Jensen, Oliver E. Revell, Christopher K. |
author_sort | Jensen, Oliver E. |
collection | PubMed |
description | The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers. Here, we consider the stress attributed to the neighbourhood of each tricellular junction, evaluating in particular its leading-order antisymmetric component and the associated couple stresses, which characterise the degree to which individual cells experience (and resist) in-plane bending deformations. We develop discrete potential theory for localised monolayers having disordered internal structure and use this to derive the analogues of Airy and Mindlin stress functions. These scalar potentials typically have broad-banded spectra, highlighting the contributions of small-scale defects and boundary layers to global stress patterns. An affine approximation attributes couple stresses to pressure differences between cells sharing a trijunction, but simulations indicate an additional role for non-affine deformations. |
format | Online Article Text |
id | pubmed-10511640 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-105116402023-09-22 Couple stresses and discrete potentials in the vertex model of cellular monolayers Jensen, Oliver E. Revell, Christopher K. Biomech Model Mechanobiol Original Paper The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers. Here, we consider the stress attributed to the neighbourhood of each tricellular junction, evaluating in particular its leading-order antisymmetric component and the associated couple stresses, which characterise the degree to which individual cells experience (and resist) in-plane bending deformations. We develop discrete potential theory for localised monolayers having disordered internal structure and use this to derive the analogues of Airy and Mindlin stress functions. These scalar potentials typically have broad-banded spectra, highlighting the contributions of small-scale defects and boundary layers to global stress patterns. An affine approximation attributes couple stresses to pressure differences between cells sharing a trijunction, but simulations indicate an additional role for non-affine deformations. Springer Berlin Heidelberg 2022-10-06 2023 /pmc/articles/PMC10511640/ /pubmed/36201070 http://dx.doi.org/10.1007/s10237-022-01620-2 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Original Paper Jensen, Oliver E. Revell, Christopher K. Couple stresses and discrete potentials in the vertex model of cellular monolayers |
title | Couple stresses and discrete potentials in the vertex model of cellular monolayers |
title_full | Couple stresses and discrete potentials in the vertex model of cellular monolayers |
title_fullStr | Couple stresses and discrete potentials in the vertex model of cellular monolayers |
title_full_unstemmed | Couple stresses and discrete potentials in the vertex model of cellular monolayers |
title_short | Couple stresses and discrete potentials in the vertex model of cellular monolayers |
title_sort | couple stresses and discrete potentials in the vertex model of cellular monolayers |
topic | Original Paper |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10511640/ https://www.ncbi.nlm.nih.gov/pubmed/36201070 http://dx.doi.org/10.1007/s10237-022-01620-2 |
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