Numerical reconstruction of brain tumours


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.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > School of Informatics and Digital Engineering > Mathematics
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: © 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
Uncontrolled Keywords: Inverse problems,landweber method,mathematical biology,medical imaging,nonlinear parabolic equations,reaction–diffusion equations,three-dimensional simulations of brain tumour growth,Engineering(all),Computer Science Applications,Applied Mathematics
Publication ISSN: 1741-5985
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://www.tan ... 77.2018.1456537 (Publisher URL)
PURE Output Type: Article
Published Date: 2019-03-01
Published Online Date: 2018-03-29
Accepted Date: 2018-03-13
Authors: Jaroudi, Rym
Baravdish, George
Johansson, B. Tomas (ORCID Profile 0000-0001-9066-7922)
Åström, Freddie

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