Treatment-induced shrinking of tumour aggregates: A nonlinear volume-filling chemotactic approach

TL;DR

This paper presents a nonlinear chemotactic model to study how chemotherapy affects tumour aggregate size by altering cell mechanics and proliferation, supported by stability analysis and numerical simulations.

Contribution

It introduces a novel volume-filling chemotactic PDE model incorporating cell elasticity and treatment effects, analyzing aggregate shrinking under therapy.

Findings

Chemotherapy induces mechanical changes leading to aggregate shrinking.

The model predicts pattern formation and stability under different treatment scenarios.

Numerical simulations confirm the reduction of tumour aggregates with treatment.

Abstract

Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we develop a mathematical model where tumour aggregate formation is obtained as the result of nutrient-limited cell proliferation coupled with chemotaxis-based cell movement. The introduction of a chemotherapeutic treatment induces mechanical changes at the cell level, with cells undergoing a transition from rigid bodies to semi-elastic entities. We analyse the influence of these individual mechanical changes on the properties of the aggregates obtained at the population level by introducing a nonlinear volume-filling chemotactic system of partial differential equations. The elastic properties of the cells are taken into account through the so-called squeezing probability, which allows us to change the packing capacity of the aggregates, depending on the concentration of the treatment in the extracellular microenvironment. We explore two scenarios for the effect of the treatment: firstly, the treatment acts only on the mechanical properties of the cells and, secondly, we assume it also prevents cell proliferation. A linear stability analysis enables us to study the ability of the system to create patterns. We provide numerical simulations in 1D and 2D that illustrate the shrinking of the aggregates due to the presence of the treatment.