Deformations of acid-mediated invasive tumors in a model with Allee effect

TL;DR

This paper models invasive tumor deformations considering an Allee effect, analyzing the stability of tumor fronts and revealing how acellular gaps can cause complex interface dynamics like finger-like protrusions.

Contribution

It extends existing tumor invasion models by analyzing the stability of planar fronts with acellular gaps, providing new criteria for transverse instability and complex interface behaviors.

Findings

Acellular gaps often lead to transverse instability of tumor fronts.

Stability criteria for tumor interface perturbations are derived.

Complex invasion patterns such as finger-like protrusions can develop.

Abstract

We consider a Gatenby--Gawlinski-type model of invasive tumors in the presence of an Allee effect. We describe the construction of bistable one-dimensional traveling fronts using singular perturbation techniques in different parameter regimes corresponding to tumor interfaces with, or without, acellular gap. By extending the front as a planar interface, we perform a stability analysis to long wavelength perturbations transverse to the direction of front propagation and derive a simple stability criterion for the front in two spatial dimensions. In particular we find that in general the presence of the acellular gap indicates transversal instability of the associated planar front, which can lead to complex interfacial dynamics such as the development of finger-like protrusions and/or different invasion speeds.