Lesnic, D orcid.org/0000-0003-3025-2770 and Alosaimi, M (2023) Determination of the space-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer. Engineering Computations, 40 (2). pp. 411-433. ISSN 0264-4401
Abstract
Purpose When modeling heat propagation in biological bodies, a non-negligible relaxation time (typically between 15-30 s) is required for the thermal waves to accumulate and transfer, i.e. thermal waves propagate at a finite velocity. To accommodate for this feature that is characteristic to heat transfer in biological bodies, the classical Fourier's law has to be modified resulting in the thermal-wave model of bio-heat transfer. The purpose of the paper is to retrieve the space-dependent blood perfusion coefficient in such a thermal-wave model of bio-heat transfer from final time temperature measurements.
Design/methodology/approach The non-linear and ill-posed blood perfusion coefficient identification problem is reformulated as a non-linear minimization problem of a Tikhonov regularization functional subject to lower and upper simple bounds on the unknown coefficient. For the numerical discretization, an unconditionally stable direct solver based on the Crank–Nicolson finite difference scheme is developed. The Tikhonov regularization functional is minimized iteratively by the built-in routine lsqnonlin from the MATLAB optimization toolbox. Both exact and numerically simulated noisy input data are inverted.
Findings The reconstruction of the unknown blood perfusion coefficient for three benchmark numerical examples is illustrated and discussed to verify the proposed numerical procedure. Moreover, the proposed algorithm is tested on a physical example which consists of identifying the blood perfusion rate of a biological tissue subjected to an external source of laser irradiation. The numerical results demonstrate that accurate and stable solutions are obtained.
Originality/value Although previous studies estimated the important thermo-physical blood perfusion coefficient, they neglected the wave-like nature of heat conduction present in biological tissues that are captured by the more accurate thermal-wave model of bio-heat transfer. The originalities of the present paper are to account for such a more accurate thermal-wave bio-heat model and to investigate the possibility of determining its space-dependent blood perfusion coefficient from temperature measurements at the final time.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023, Emerald Publishing Limited. This is an author produced version of a paper published in Engineering Computations. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Inverse problem, bioheat transfer, blood perfusion coefficient, Tikhonov regularization, thermal-wave model. |
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) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/W000873/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Jan 2023 07:45 |
Last Modified: | 04 Aug 2023 14:54 |
Status: | Published |
Publisher: | Emerald |
Identification Number: | 10.1108/EC-07-2022-0467 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:194796 |