ArticleProceedings. Mathematical, physical, and engineering sciences2019
A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Mechanical Cell Interactions on Curved Interfaces.Bulletin of mathematical biology · 2025Article
- Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation.Journal of mathematical biology · 2024Article
- Multiscale Asymptotic Analysis Reveals How Cell Growth and Subcellular Compartments Affect Tissue-Scale Hormone Transport.Bulletin of mathematical biology · 2023Article
- Derivation of continuum models from discrete models of mechanical forces in cell populations.Journal of mathematical biology · 2021Article
- Mechanical Pressure Driving Proteoglycan Expression in Mammographic Density: a Self-perpetuating Cycle?Journal of mammary gland biology and neoplasia · 2021Review
- A free boundary mechanobiological model of epithelial tissues.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Identifying density-dependent interactions in collective cell behaviour.Journal of the Royal Society, Interface · 2020Article
- Reversible signal transmission in an active mechanical metamaterial.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
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Authors and funding
4 authors.
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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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