Tumor boundary instability induced by nutrient consumption and supply

TL;DR

This paper models tumor boundary stability considering nutrient dynamics, revealing that in vitro conditions stabilize tumor boundaries while aggressive nutrient consumption in vivo can induce instability.

Contribution

It introduces a Hele-Shaw based model to analyze tumor boundary stability under different nutrient supply regimes and consumption rates.

Findings

In vitro regime stabilizes tumor boundaries.

Aggressive nutrient consumption can cause boundary instability.

In vivo regime may induce boundary instability under certain conditions.

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.