What is it about?

We survey well-established models of reaction-diffusion type for studying brain tumours growth by discussing biological background and mathematical properties. We also give a variational formulation that opens the possibility of alternative derivations and modifications of the models. Moreover, we perform full 3-dimensional simulations of the tumours in time on two types of set-ups, the 3d Shepp-Logan phantom and an MRI T1-weighted brain scan from the Internet Brain Segmentation Repository (IBSR), and for both low and high grade glioma.

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Why is it important?

The reaction term is such that we have logistic growth. These simulations are obtained using standard finite difference discretisation of the space and time-derivatives with novel calculations to increase speed and accuracy, generating a simplistic approach that performs well. In fact, simulations show how the tumour deforms when it reaches regions into which it cannot grow further.

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This page is a summary of: Numerical simulations in 3-dimensions of reaction–diffusion models for brain tumour growth, International Journal of Computer Mathematics, April 2019, Taylor & Francis, DOI: 10.1080/00207160.2019.1613526.
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