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Numerical simulations in 3-dimensions of reaction-diffusion models for brain tumour growth
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering. Univ Tunis El Manar, Tunisia.
Heidelberg Univ, Germany.
Linköping University, Department of Science and Technology, Physics, Electronics and Mathematics. Linköping University, Faculty of Science & Engineering. Aston Univ, England.
Linköping University, Department of Science and Technology, Physics, Electronics and Mathematics. Linköping University, Faculty of Science & Engineering.
2019 (English)In: International Journal of Computer Mathematics, ISSN 0020-7160, E-ISSN 1029-0265Article in journal (Refereed) Epub ahead of print
Abstract [en]

We work with a well-known model of reaction-diffusion type for brain tumour growth and accomplish full 3-dimensional (3d) simulations of the tumour in time on two types of imaging data, the 3d Shepp-Logan head phantom image and an MRI T1-weighted brain scan from the Internet Brain Segmentation Repository. The source term is such that we have logistic growth. These simulations are obtained using standard finite difference approximations with novel calculations to increase speed and accuracy. Moreover, biological background to the model, its well-posedness together with a variational formulation are given. The variational formulation enable the feasibility of different derivations and modifications of the model.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD , 2019.
Keywords [en]
Nonlinear parabolic equations; reaction-diffusion equations; 3-dimensional simulations of brain tumour growth; mathematical biology; medical imaging
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-158572DOI: 10.1080/00207160.2019.1613526ISI: 000470588800001OAI: oai:DiVA.org:liu-158572DiVA, id: diva2:1334800
Note

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

Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-11-06

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