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 starti...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2019
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| In: |
Inverse problems in science and engineering
Year: 2018, Volume: 27, Issue: 3, Pages: 278-298 |
| ISSN: | 1741-5985 |
| DOI: | 10.1080/17415977.2018.1456537 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1080/17415977.2018.1456537 Verlag, Volltext: https://doi.org/10.1080/17415977.2018.1456537 
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| Author Notes: | Rym Jaroudi, George Baravdish, B. Tomas Johansson & Freddie Åström |
| Summary: | 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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| Item Description: | Published online: 29 Mar 2018 Gesehen am 14.02.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1741-5985 |
| DOI: | 10.1080/17415977.2018.1456537 |