Identifying a response parameter in a model of brain tumour evolution under therapy

Abstract 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 a...

Full description

Saved in:

Bibliographic Details
Published in:	IMA journal of applied mathematics Vol. 88; no. 2; pp. 378 - 404
Main Authors:	Baravdish, G, Johansson, B T, Svensson, O, Ssebunjo, W
Format:	Journal Article
Language:	English
Published:	Oxford University Press 01-06-2023
Subjects:	inverse problem nonlinear conjugate gradient method parameter identification reaction-diffusion models brain tumours
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	Abstract 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.
ISSN:	0272-4960 1464-3634 1464-3634
DOI:	10.1093/imamat/hxad013