  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.
