On impact of oxygen distribution on tumor necrotic region: A Multiphase Model

Background and Objective: In an in-vivo situation, the tissue near the blood vessels is rich in oxygen supply compared to the one far from blood vessels. Hence, non-uniform oxygen distribution is observed in biological tissues. Our objective is to explore the influence of non-uniform oxygen supply in the development of necrotic core and, also to examine the effects of necrotic core on tumor growth. Methods: The research is processed through a mathematical approach based on the multiphase mathematical model. To simulate the model, a finite difference numerical method based on the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is adopted. Results: The necrotic core starts to form at the boundary of the tumor with lower oxygen concentration from the initial time. Investigations reveal that the position of the necrotic core varies depending on the oxygen supply through the tumor boundary. The results predict asymmetrical tumor growth under unequal oxygen supply at tumor boundaries. Also, it is hinted that a tumor with a larger size of necrotic core grows slowly as compared to a tumor containing a smaller size of necrotic core. Conclusions: The formulated model has the potential to cast the situation of the tumor growth in an in-vivo and in-vitro situations. This study provides an idea about the location and shape of the necrotic core and the impact of the necrotic core on tumor growth. This information will be beneficial to the clinicians and medical practitioners in predicting the stage of the disease.