Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion
| Autor: | Chloé Colson, Faustino Sánchez-Garduño, Helen M. Byrne, Philip K. Maini, Tommaso Lorenzi |
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| Rok vydání: | 2021 |
| Předmět: |
Quantitative Biology::Tissues and Organs
General Mathematics 35Q92 35K57 35C07 Physics::Medical Physics travelling-wave solutions General Engineering General Physics and Astronomy degenerate and cross-dependent diffusion tumour invasion Quantitative Biology::Cell Behavior Mathematics - Analysis of PDEs FOS: Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 477 |
| ISSN: | 1471-2946 1364-5021 |
| DOI: | 10.1098/rspa.2021.0593 |
| Popis: | 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. 41 pages (21 for the main paper, 17 for the supplementary material and 3 for the bibliography) with 6 figures (4 in the main paper and 2 in the supplementary material) |
| Databáze: | OpenAIRE |
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