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

Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we propose a novel mechano-transduction mechanism where the introduction of a chemotherapeutic treatment induces mechanical changes at the cell level. We analyse the influence of these individual mechanical changes on the properties of the aggregates obtained at the population level. We employ a nonlinear volume-filling chemotactic system of partial differential equations, where the elastic properties of the cells are taken into account through the so-called squeezing probability, which depends on the concentration of the treatment in the extracellular microenvironment. We explore two scenarios for the effect of the treatment: first, we suppose that the treatment acts only on the mechanical properties of the cells and, in the second one, we assume it also prevents cell proliferation. We perform a linear stability analysis which enables us to identify the ability of the system to create patterns and fully characterize their size. Moreover, we provide numerical simulations in 1D and 2D that illustrate the shrinking of the aggregates due to the presence of the treatment.