Numerical simulations in 3-dimensions of reaction–diffusion models for brain tumour growth

Rym Jaroudi*, Freddie Åström, B. Tomas Johansson, George Baravdish

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1151-1169
Number of pages19
JournalInternational Journal of Computer Mathematics
Issue number6
Early online date9 May 2019
Publication statusPublished - 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://, 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


Dive into the research topics of 'Numerical simulations in 3-dimensions of reaction–diffusion models for brain tumour growth'. Together they form a unique fingerprint.

Cite this