Autowaves in the model of avascular tumour growth

TL;DR

This paper presents a mathematical model of avascular tumor growth incorporating cell dynamics and nutrient effects, demonstrating autowave solutions that explain tumor invasion patterns and align with experimental data.

Contribution

It introduces a novel model capturing nutrient-dependent tumor growth and analyzes autowave solutions, extending understanding of tumor invasion mechanisms.

Findings

Existence of automodel solutions in tumor growth model

Nutrient distribution influences autowave speed and relaxation

Model aligns with experimental tumor growth data

Abstract

A mathematical model of infiltrative tumour growth taking into account cell proliferation, death and motility is considered. The model is formulated in terms of local cell density and nutrient (oxygen) concentration. In the model the rate of cell death depends on the local nutrient level. Thus heterogeneous nutrient distribution in tissue affects tumour structure and development. The existence of automodel solutions is demonstrated and their properties are investigated. The results are compared to the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. Influence of the nutrient distribution on the autowave speed selection as well as on the relaxation to automodel solution is demonstrated. The model adequately describes the data, observed in experiments.