Numerical reconstruction of brain tumours

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose a nonlinear Landweber method for the inverse problem of locating the brain tumour source (origin where the tumour formed) based on well-established models of reaction–diffusion type for brain tumour growth. The approach consists of recovering the initial density of the tumour cells starting from a later state, which can be given by a medical image, by running the model backwards. Moreover, full three-dimensional simulations are given of the tumour source localization on two types of data, the three-dimensional Shepp–Logan phantom and an MRI T1-weighted brain scan. These simulations are obtained using standard finite difference discretizations of the space and time derivatives, generating a simple approach that performs well.

Original languageEnglish
Pages (from-to)278-298
Number of pages21
JournalInverse Problems in Science and Engineering
Issue number3
Early online date29 Mar 2018
Publication statusPublished - 1 Mar 2019

Bibliographical note

© 2018 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
(, 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


  • Inverse problems
  • landweber method
  • mathematical biology
  • medical imaging
  • nonlinear parabolic equations
  • reaction–diffusion equations
  • three-dimensional simulations of brain tumour growth


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