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A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation

R. J. Murphy, P. R. Buenzli, R. E. Baker, M. J. Simpson
doi: https://doi.org/10.1101/485276
R. J. Murphy
1Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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P. R. Buenzli
1Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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R. E. Baker
2Mathematical Institute, University of Oxford, Oxford, UK
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M. J. Simpson
1Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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  • For correspondence: matthew.simpson@qut.edu.au
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Abstract

Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

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  • https://github.com/ryanmurphy42/Murphy2019

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Posted June 11, 2019.
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A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation
R. J. Murphy, P. R. Buenzli, R. E. Baker, M. J. Simpson
bioRxiv 485276; doi: https://doi.org/10.1101/485276
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A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation
R. J. Murphy, P. R. Buenzli, R. E. Baker, M. J. Simpson
bioRxiv 485276; doi: https://doi.org/10.1101/485276

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