Abstract:

One of the subjects taught in many engineering degrees is the subject called Modelling, in which students learn how to model a problem mathematically and how to solve it using mathematical software. Some problems are modelled using Partial Differential Equations (PDEs), which is a relation that involves an unknown function of several independent variables and its partial derivatives with respect to those variables. Problems such as the heat transfer or the vibrating string are two typical problems modelled in engineering courses using PDEs. Different problems may have similar mathematical formulations. In this work we will see how the diffusion-reaction model can be used not only to calculate the temperature distribution in materials but also to simulate the glioma expansion. Gliomas are tumours that constitute more than 50% of all brain cancers. According to the latest advances, the diffusion-reaction equation can be used to simulate their expansion.

Keywords:

Reaction-diffusion equation, modelling gliomas, partial differential equations.