ArticleJournal of mathematical biology2020
Bridging the gap between individual-based and continuum models of growing cell populations.
Article in Journal of mathematical biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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13 citing papers in PubMed.
- The Role of Viral Dynamics and Infectivity in Models of Oncolytic Virotherapy for Tumours with Different Motility.Bulletin of mathematical biology · 2026Article
- Advances in surrogate modeling for biological agent-based simulations: trends, challenges, and future prospects.Journal of mathematical biology · 2025Review
- Equations describing semi-confluent cell growth (II) colony formation on a flat surface.European biophysics journal : EBJ · 2025Article
- Spatial Segregation Across Travelling Fronts in Individual-Based and Continuum Models for the Growth of Heterogeneous Cell Populations.Bulletin of mathematical biology · 2025Article
- Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.Journal of mathematical biology · 2025Review
- Agent-Based and Continuum Models for Spatial Dynamics of Infection by Oncolytic Viruses.Bulletin of mathematical biology · 2023Article
- A global method for fast simulations of molecular dynamics in multiscale agent-based models of biological tissues.iScience · 2022Article
- Derivation of continuum models from discrete models of mechanical forces in cell populations.Journal of mathematical biology · 2021Article
- Learning differential equation models from stochastic agent-based model simulations.Journal of the Royal Society, Interface · 2021Article
- Comparative analysis of continuum angiogenesis models.Journal of mathematical biology · 2021Article
- Population dynamics with spatial structure and an Allee effect.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Predicting population extinction in lattice-based birth-death-movement models.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- From a discrete model of chemotaxis with volume-filling to a generalized Patlak-Keller-Segel model.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
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3 authors.
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Abstract
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population growth. Little prior work has explored the relation between such continuum models and related single-cell-based models. We present here a simple stochastic individual-based model for the spatial dynamics of multicellular systems whereby cells undergo pressure-driven movement and pressure-dependent proliferation. We show that nonlinear partial differential equations commonly used to model the spatial dynamics of growing cell populations can be formally derived from the branching random walk that underlies our discrete model. Moreover, we carry out a systematic comparison between the individual-based model and its continuum counterparts, both in the case of one single cell population and in the case of multiple cell populations with different biophysical properties. The outcomes of our comparative study demonstrate that the results of computational simulations of the individual-based model faithfully mirror the qualitative and quantitative properties of the solutions to the corresponding nonlinear partial differential equations. Ultimately, these results illustrate how the simple rules governing the dynamics of single cells in our individual-based model can lead to the emergence of complex spatial patterns of population growth observed in continuum models.
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