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Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that enc...

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Autores principales: Mathias, Sonja, Coulier, Adrien, Bouchnita, Anass, Hellander, Andreas
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7538447/
https://www.ncbi.nlm.nih.gov/pubmed/33025278
http://dx.doi.org/10.1007/s11538-020-00810-2
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author Mathias, Sonja
Coulier, Adrien
Bouchnita, Anass
Hellander, Andreas
author_facet Mathias, Sonja
Coulier, Adrien
Bouchnita, Anass
Hellander, Andreas
author_sort Mathias, Sonja
collection PubMed
description Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.
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spelling pubmed-75384472020-10-19 Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models Mathias, Sonja Coulier, Adrien Bouchnita, Anass Hellander, Andreas Bull Math Biol Original Article Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level. Springer US 2020-10-06 2020 /pmc/articles/PMC7538447/ /pubmed/33025278 http://dx.doi.org/10.1007/s11538-020-00810-2 Text en © The Author(s) 2020 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/.
spellingShingle Original Article
Mathias, Sonja
Coulier, Adrien
Bouchnita, Anass
Hellander, Andreas
Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
title Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
title_full Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
title_fullStr Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
title_full_unstemmed Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
title_short Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models
title_sort impact of force function formulations on the numerical simulation of centre-based models
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7538447/
https://www.ncbi.nlm.nih.gov/pubmed/33025278
http://dx.doi.org/10.1007/s11538-020-00810-2
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