Numerical reconstruction of brain tumours

Rym Jaroudi; George Baravdish; B. Tomas Johansson; Freddie Åström

doi:10.1080/17415977.2018.1456537

Numerical reconstruction of brain tumours

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	278-298
Number of pages	21
Journal	Inverse Problems in Science and Engineering
Volume	27
Issue number	3
Early online date	29 Mar 2018
DOIs	https://doi.org/10.1080/17415977.2018.1456537
Publication status	Published - 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
(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

Keywords

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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10.1080/17415977.2018.1456537Licence: CC BY-NC-ND 3.0

Numerical reconstruction of brain tumours
© 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 (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
Final published version, 3.91 MBLicence: CC BY-NC-ND 3.0

Cite this

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title = "Numerical reconstruction of brain tumours",

abstract = "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.",

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AU - Åström, Freddie

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AB - 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.

KW - Inverse problems

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KW - medical imaging

KW - nonlinear parabolic equations

KW - reaction–diffusion equations

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Numerical reconstruction of brain tumours

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