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Numerical reconstruction of brain tumours
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Tunis El Manar Univ, Tunisia.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Aston Univ, England.
Heidelberg Univ, Germany.
2019 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 27, no 3, p. 278-298Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD , 2019. Vol. 27, no 3, p. 278-298
Keywords [en]
Inverse problems; landweber method; nonlinear parabolic equations; reaction-diffusion equations; mathematical biology; medical imaging; three-dimensional simulations of brain tumour growth
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-153952DOI: 10.1080/17415977.2018.1456537ISI: 000454930700001OAI: oai:DiVA.org:liu-153952DiVA, id: diva2:1281582
Note

Funding Agencies|EU under the program ALYSSA (ERASMUS MUNDUS Action 2, Lot 6)

Available from: 2019-01-22 Created: 2019-01-22 Last updated: 2019-01-22

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