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Updated: Mar 17, 2026
07:08
Modeling and Imaging 3-Dimensional Collective Cell Invasion
Published on: December 7, 2011
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Modelling collective invasion with reaction-diffusion equations: When does domain curvature matter?
J J Pollacco1,2, R E Baker2, P K Maini2
1Department of Biochemistry, University of Oxford, Oxford, OX1 3QU, United Kingdom.
Applied Mathematics Letters
|March 16, 2026
Summary
Neglecting curved geometry in reaction-diffusion models can lead to inaccuracies. This study quantifies when it
Area of Science:
- Mathematical Biology
- Computational Science
- Physics
Background:
- Cellular invasion often occurs in curved environments.
- Simplifying models by ignoring curvature can introduce prediction errors.
Purpose of the Study:
- To determine criteria for validly neglecting curved geometry in reaction-diffusion models.
- To analyze the impact of curvature on invasion dynamics.
Main Methods:
- Analytical exploration of reaction-diffusion equations (RDEs) on an annular geometry.
- Asymptotic expansion to derive conditions for ignoring curvature.
- Numerical simulations of the Fisher-KPP model on annular and rectangular domains.
Main Results:
- Derived conditions for when domain curvature can be ignored in RDEs.
- Quantified deviations in invasion dynamics between curved and flat geometries.
- Showcased how deviations vary across annulus width and with geometric parameters (r0, δ).
Conclusions:
- Provides crucial insights into the validity of simplifying assumptions in reaction-diffusion modeling.
- Offers guidance on when to account for curved geometries in studying traveling wave phenomena.
- Highlights the importance of geometric considerations in biological invasion models.
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