Bridging the gap between individual-based and continuum models of growing cell populations
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Publication:2297289
DOI10.1007/s00285-019-01391-yzbMath1432.92007arXiv1812.05872OpenAlexW3100217212WikidataQ92648031 ScholiaQ92648031MaRDI QIDQ2297289
Fiona R. Macfarlane, Tommaso Lorenzi, Mark A. J. Chaplain
Publication date: 18 February 2020
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.05872
continuum modelsindividual-based modelsgrowing cell populationspressure-driven cell movementpressure-limited growth
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Developmental biology, pattern formation (92C15) Cell movement (chemotaxis, etc.) (92C17) Traveling wave solutions (35C07)
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Cites Work
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- A history of the study of solid tumour growth: the contribution of mathematical modelling
- Free boundary problems for tumor growth: a viscosity solutions approach
- On the mechanics of a growing tumor
- On interfaces between cell populations with different mobilities
- Models of dispersal in biological systems
- Large systems of interacting particles and the porous medium equation
- A user's guide to PDE models for chemotaxis
- On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
- Derivation of a porous medium equation from many Markovian particles and the propagation of chaos
- A two-phase model of solid tumour growth
- A new mathematical model for avascular tumour growth
- The influence of growth-induced stress from the surrounding medium on the development of multicell spheroids
- Exclusion processes on a growing domain
- From short-range repulsion to Hele-Shaw problem in a model of tumor growth
- A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis
- Growth of necrotic tumors in the presence and absence of inhibitors
- Growth of nonnecrotic tumors in the presence and absence of inhibitors
- Modelling the movement of interacting cell populations
- Derivation of a Hele-Shaw type system from a cell model with active motion
- Individual-based and continuum models of growing cell populations: a comparison
- A Hele-Shaw problem for tumor growth
- The Hele-Shaw asymptotics for mechanical models of tumor growth
- Invasion and adaptive evolution for individual-based spatially structured populations
- The Diffusion Limit of Transport Equations II: Chemotaxis Equations
- Computational Modeling of Solid Tumor Growth: The Avascular Stage
- Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development
- Mathematical Models of Avascular Tumor Growth
- Spatial segregation limit of a competition–diffusion system
- Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
- Free boundary value problems associated with the growth and development of multicellular spheroids
- The Derivation of Chemotaxis Equations as Limit Dynamics of Moderately Interacting Stochastic Many-Particle Systems
- The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes
- Finite Volume Methods for Hyperbolic Problems
- Porous medium equation to Hele-Shaw flow with general initial density
- ON THE CLOSURE OF MASS BALANCE MODELS FOR TUMOR GROWTH
- Cancer Modelling and Simulation
- Modelling solid tumour growth using the theory of mixtures
- Composite Waves for a Cell Population System Modeling Tumor Growth and Invasion
- COARSE GRAINING IN SIMULATED CELL POPULATIONS
- Nonlinear modelling of cancer: bridging the gap between cells and tumours
