Tumor boundary instability induced by nutrient consumption and supply

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.

arXiv comment33 pages, 10 figures

References in corpus (7)

• The Hele-Shaw asymptotics for mechanical models of tumor growth
• Incompressible limit of mechanical model of tumor growth with viscosity
• An accurate front capturing scheme for tumor growth models with a free boundary limit
• A Hele-Shaw limit without monotonicity
• Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis
• Complex Far-Field Geometries Determine the Stability of Solid Tumor Growth with Chemotaxis
• Nonlinear simulation of an elastic tumor-host interface