Investigation of Mathematical Modeling for the general treatment of Glioblastoma

The purpose of this research is to validate various forms of mathematical modeling
of glioblastoma multiforme (GBM) expressed as differential equations, numerically.
The first work was involved in the numerical solution of the reaction-convection
model, efficacy of which is expressed in terms of survival time. It was calculated using
simple numerical scheme for the standard-of-care treatment in clinics which includes
surgery followed by the radiation and chemotherapy. Survival time using all treatment
options increased significantly to 57 weeks compared to that of surgery close
to 14 weeks. It was also observed that survival time increased significantly to 90
weeks if tumor is totally resected. In reaction-diffusion model using simple numerical
scheme, tumor cell density patterns due to variation in patient specific tumor
parameters such as net proliferation rate and diffusion coefficient were computed.
Significant differences were observed in the patterns while using dominant diffusion
and proliferation rate separately. Numerical solution of the tumor growth model
under the anti-angiogenic therapy revealed some impacts in optimum tumor growth
control however it was not significant.