Mathematical Modeling of the Cancer Invasion Induced by Hypoxia

The need to understand tumor complexity has given rise to mathematical models aimed at describing the interaction between the tumor and its microenvironment. This thesis investigates the conditions governing the transition from stable to invasive growth in solid tumors, focusing on the biochemical cascade linking hypoxia to cellular motility. The mathematical model consists of a coupled system of five Partial Differential Equations (PDEs), then implemented numerically using COMSOL Multiphysics, that includes the interaction between oxygen, the transcription factor HIF, and the enzyme LOX. Initial simulations demonstrated that the LOX gradient generated by hypoxia created a strong potential for destabilization, yet was insufficient alone to break the tumor's radial symmetry. The core contribution was achieved by introducing a structural modification to the motility coefficient, making it spatially discontinuous at the tumor boundary. The result is the generation of clear dendritic and spiculated projections, known as the fingering phenomenon.