Identifying a response parameter in a model of brain tumour evolution under therapy
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| Názov: | Identifying a response parameter in a model of brain tumour evolution under therapy |
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| Autori: | Baravdish, George, Johansson, Tomas, Svensson, Olof, Ssebunjo, W. |
| Zdroj: | IMA Journal of Applied Mathematics. 88(2):378-404 |
| Predmety: | parameter identification, inverse problem, nonlinear conjugate gradient method, reaction-diffusion models, brain tumours |
| Popis: | A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction-diffusion type corresponding to the evolution of brain tumours under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative method is outlined as well as uniqueness of a solution to the inverse problem. Moreover, the parameter identification is recasted as the minimization of a Tikhonov type functional and the existence of a minimizer to this functional is shown. Finite-difference discretization of the space and time derivatives are employed for the numerical implementation. Numerical simulations on full 3D brain data are included showing that information about a spacewise-dependent treatment parameter can be recovered in a stable way. |
| Popis súboru: | electronic |
| Prístupová URL adresa: | https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-193706 https://liu.diva-portal.org/smash/get/diva2:1756998/FULLTEXT01.pdf |
| Databáza: | SwePub |
Nájsť tento článok vo Web of Science | Abstrakt: | A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction-diffusion type corresponding to the evolution of brain tumours under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative method is outlined as well as uniqueness of a solution to the inverse problem. Moreover, the parameter identification is recasted as the minimization of a Tikhonov type functional and the existence of a minimizer to this functional is shown. Finite-difference discretization of the space and time derivatives are employed for the numerical implementation. Numerical simulations on full 3D brain data are included showing that information about a spacewise-dependent treatment parameter can be recovered in a stable way. |
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| ISSN: | 02724960 14643634 |
| DOI: | 10.1093/imamat/hxad013 |