We work with a well-known model of reaction–diffusion type for brain tumour growth and accomplish full 3-dimensional (3d) simulations of the tumour in time on two types of imaging data, the 3d Shepp–Logan head phantom image and an MRI T1-weighted brain scan from the Internet Brain Segmentation Repository. The source term is such that we have logistic growth. These simulations are obtained using standard finite difference approximations with novel calculations to increase speed and accuracy. Moreover, biological background to the model, its well-posedness together with a variational formulation are given. The variational formulation enable the feasibility of different derivations and modifications of the model.
|Number of pages||19|
|Journal||International Journal of Computer Mathematics|
|Early online date||9 May 2019|
|Publication status||Published - 2 Jun 2020|
Bibliographical note© 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://
creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the
original work is properly cited, and is not altered, transformed, or built upon in any way
Funding: The first author is grateful for support by the EU funding under the program ALYSSA (ERASMUS MUNDUS Action
2, Lot 6).
- 3-dimensional simulations of brain tumour growth
- mathematical biology
- medical imaging
- Nonlinear parabolic equations
- reaction–diffusion equations