ArticleProceedings. Mathematical, physical, and engineering sciences2021
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- Brillouin Microscopy of Breast tumor Spheroids On-a-Chip: Mechanical and Transcriptional Responses to Microfluidic-Induced Rapid Deformations.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Tumor Growth, Proliferation and Diffusion in Osteosarcoma.Acta biotheoretica · 2025Article
- Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist.Frontiers in cell and developmental biology · 2024Review
- Quantifying tissue growth, shape and collision via continuum models and Bayesian inference.Journal of the Royal Society, Interface · 2023Article
- A Continuum Mathematical Model of Substrate-Mediated Tissue Growth.Bulletin of mathematical biology · 2022Article
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Authors and funding
5 authors.
Funding
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Abstract
In this paper, we carry out a travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion. We consider two types of invasive fronts of tumour tissue into extracellular matrix (ECM), which represents healthy tissue. These types differ according to whether the density of ECM far ahead of the wave front is maximal or not. In the former case, we use a shooting argument to prove that there exists a unique travelling-wave solution for any positive propagation speed. In the latter case, we further develop this argument to prove that there exists a unique travelling-wave solution for any propagation speed greater than or equal to a strictly positive minimal wave speed. Using a combination of analytical and numerical results, we conjecture that the minimal wave speed depends monotonically on the degradation rate of ECM by tumour cells and the ECM density far ahead of the front.
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Registered trials
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