Cao, K and Lesnic, D (2018) Reconstruction of the space-dependent perfusion coefficient from final time or time-average temperature measurements. Journal of Computational and Applied Mathematics, 337. pp. 150-165. ISSN 0377-0427
Abstract
Knowledge of the blood perfusion in biomedicine is of crucial importance in applications related to hypothermia. In this paper, we consider the inverse bio-heat transfer nonlinear problem to determine the space-dependent perfusion coefficient from final time or time-average temperature measurements, which are themselves space-dependent quantities. In other applications this coefficient multiplying the temperature function represents a reaction rate. Uniqueness of solution holds but continuous dependence on the input data is violated. The problem is reformulated as a least-squares minimization whose gradient is obtained by solving the sensitivity and adjoint problems. The newly obtained gradient formula is used in the conjugate gradient method (CGM). This is the first time that the CGM is applied to solve the inverse problems under investigation. For exact data, we investigate the convergence of the iterative CGM. We also test that the iterative algorithm is semi-convergent under noisy data by stopping the iteration using the discrepancy principle criterion to produce a stable solution. Furthermore, because the search step size is computed using an optimization scheme at each iteration the CGM is very efficient. Three examples are investigated to verify the accuracy and stability of the numerical method.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier B.V. This is an author produced version of a paper published in Journal of Computational and Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problem; Heat transfer; Conjugate gradient method; Perfusion coefficient |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 12 Jan 2018 11:07 |
Last Modified: | 31 Jan 2019 01:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.cam.2018.01.010 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:126162 |