A mathematical modeling of tumor progression based on the availability of oxygen, glucose, VEGF and other conditions

Abstract

Tumors are one of the most active areas of research in the world, and that is why a lot of research is focusing on mathematical modeling in this area, to help with production, treatment, and finding solutions to help manage tumors, whether malignant or benign. The importance of our model is that it helps to study tumor growth on the basis of several nutritional factors, namely oxygen, glucose, and VEGF. It also uses a generic equation that we have modified to fit our model, the generic equation that deals with tumor growth, the source of which is already cited in the article. So our model was applied to simulate the growth of the tumor, and we found that the size of the tumor increases with time under the triggering of VEGF, the increase in oxygen, its reaction with glucose and then finally by calculating it with the capillary network CN and the flow Q(t).