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Mathematics > Analysis of PDEs

arXiv:2210.01359 (math)
[Submitted on 4 Oct 2022]

Title:Tumor boundary instability induced by nutrient consumption and supply

Authors:Yu Feng, Min Tang, Xiaoqian Xu, Zhennan Zhou
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Abstract:We investigate the tumor boundary instability induced by nutrient consumption and supply based on a Hele-Shaw model derived from taking the incompressible limit of a cell density model. We analyze the boundary stability/instability in two scenarios: 1) the front of the traveling wave; 2) the radially symmetric boundary. In each scenario, we investigate the boundary behaviors under two different nutrient supply regimes, in vitro, and in vivo. Our main conclusion is that for either scenario, the in vitro regime always stabilizes the tumor's boundary regardless of the nutrient consumption rate. However, boundary instability may occur when the tumor cells aggressively consume nutrients, and the nutrient supply is governed by the in vivo regime.
Comments: 33 pages, 10 figures
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:2210.01359 [math.AP]
  (or arXiv:2210.01359v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2210.01359
Related DOI: https://doi.org/10.1007/s00033-023-02001-0

Submission history

From: Yu Feng [view email]
[v1] Tue, 4 Oct 2022 03:57:45 UTC (481 KB)
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