Visualization and modeling of cancer progression

Cancer mathematical modeling constitutes an emerging area of research aiming to predict tumors spatial and temporal evolution. Several mathematical and computational models have appeared in the literature addressing the mechanisms that govern tumor progression and invasion. Modeling techniques are initialized based either on the actual tumor geometries derived from imaging modalities (such as serial MRIs), or on virtual tumor approximation. Cancer modeling is performed using various tissue modeling and evolution techniques, which are generally classified as continuum, discrete and hybrid methods. This paper aims to present a comprehensive overview of tumor modeling approaches and based on significant trends to propose a continuum mathematical model of avascular glioma spatiotemporal evolution. This model takes under consideration the oxygen concentration inside the tumor and its surroundings, which is engaged in tumor-cell survival, proliferation and invasion. The tumor area is divided into layers that form proliferating, hypoxic and necrotic regions of tumor cells. The simulation results for different evolution times demonstrate that the proposed model may provide an essential framework for a patient-specific simulation tool towards the reliable prediction of glioma spatiotemporal progression.