The brain cancer is a very serious disease and difficult to treat. There are over 120
different types of brain tumors, which is making treatment complicated. Therefore, numerical
approaches based on mathematical models of the drug penetration into the brain
tumor can give results much faster than real experiments, which is very important if a
tumor is progressive.
In our work, the governing system of equations consists of the mass conservation equation,
the momentum equation and an equation of the drug concentration into the brain tumor.
This system describes the penetration of drugs into the brain tumor (there is a cavity
after surgical removal of a cancer tumor), which fill up the cavity after a surgery. The
mathematical model of drug delivery to brain tumors is not new, there are various configurations
of different complexity, but we consider full mass conservation and momentum
equations which are coupled with the concentration equation depending on the velocity.
We use techniques of computational fluid dynamics (CFD) to get a solution of the derived
partial differential equations (Navier-Stokes equation with the added equations and
terms). We obtain a saddle point problem after discretization of the governing system
of equations with finite elements and use modern CFD tools like FEATFLOW to get
numerical solutions of this problem