Modeling invasion patterns in the glioblastoma battlefield

Glioblastoma is the most aggressive tumor of the central nervous system, due to its great infiltration capacity. Understanding the mechanisms that regulate the Glioblastoma invasion front is a major challenge with preeminent potential clinical relevances. In the infiltration front, the key features of tumor dynamics relate to biochemical and biomechanical aspects, which result in the extension of cellular protrusions known as tumor microtubes. The coordination of metalloproteases expression, extracellular matrix degradation, and integrin activity emerges as a leading mechanism that facilitates Glioblastoma expansion and infiltration in uncontaminated brain regions. We propose a novel multidisciplinary approach, based on in vivo experiments in Drosophila and mathematical models, that describes the dynamics of active and inactive integrins in relation to matrix metalloprotease concentration and tumor density at the Glioblastoma invasion front. The mathematical model is based on a non-linear system of evolution equations in which the mechanisms leading chemotaxis, haptotaxis, and front dynamics compete with the movement induced by the saturated flux in porous media. This approach is able to capture the relative influences of the involved agents and reproduce the formation of patterns, which drive tumor front evolution. These patterns have the value of providing biomarker information that is related to the direction of the dynamical evolution of the front and based on static measures of proteins in several tumor samples. Furthermore, we consider in our model biomechanical elements, like the tissue porosity, as indicators of the healthy tissue resistance to tumor progression.