  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.
