Lesnic, D. orcid.org/0000-0003-3025-2770 and Alosaimi, M. (2024) Retrieving the time-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer. Engineering Computations, 41 (7). pp. 1824-1838. ISSN 0264-4401
Abstract
Purpose
In order to include the non-negligible lag relaxation time feature that is characteristic of heat transfer in biological bodies, the classical Fourier's law of heat conduction has to be generalized as the Maxwell–Cattaneo law resulting in the thermal-wave model of bio-heat transfer. The purpose of the paper is to retrieve the unknown time-dependent blood perfusion coefficient in such a thermal-wave model of bio-heat transfer from (non-intrusive) measurements of the temperature on an accessible sub-portion of the boundary that may be taken with an infrared scanner.
Design/methodology/approach
The nonlinear and ill-posed problem is reformulated as a nonlinear 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. Numerical results for a benchmark test example are presented and thoroughly discussed, shedding light on the performance and effectiveness of the proposed methodology.
Findings
The inverse problem of obtaining the time-dependent blood perfusion coefficient and the temperature in the thermal-wave model of bio-heat transfer from extra boundary temperature measurement has been solved. In particular, the uniqueness of the solution to this inverse problem has been established. Furthermore, our proposed computational method demonstrated successful attainment of the perfusion coefficient and temperature, even when dealing with noisy data.
Originality/value
The originalities of the present paper are to account for such a more representative thermal-wave model of heat transfer in biological bodies and to investigate the possibility of determining its time-dependent blood perfusion coefficient from non-intrusive boundary temperature measurements.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2024, Emerald Publishing Limited. This author accepted manuscript is provided for your own personal use only. It may not be used for resale, reprinting, systematic distribution, emailing, or for any other commercial purpose without the permission of the publisher. |
Keywords: | Inverse problem, Bio-heat transfer, Blood perfusion coefficient, Tikhonov regularization, Thermal-wave model |
Dates: |
|
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: | 22 Jul 2024 10:54 |
Last Modified: | 24 Sep 2024 04:26 |
Published Version: | https://www.emerald.com/insight/content/doi/10.110... |
Status: | Published |
Publisher: | Emerald |
Identification Number: | 10.1108/EC-01-2024-0013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:214959 |