To read this content please select one of the options below:

Determination of the space-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer

M.A. Alosaimi (Department of Mathematics and Statistics, College of Science, Taif University, Taif, Saudi Arabia)
D. Lesnic (Department of Applied Mathematics, University of Leeds, Leeds, UK)

Engineering Computations

ISSN: 0264-4401

Article publication date: 7 March 2023

Issue publication date: 19 April 2023




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.


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.


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.


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.



M.A. Alosaimi would like to thank Taif University in Saudi Arabia and the United Kingdom Saudi Arabian Cultural Bureau (UKSACB) in London for supporting his PhD studies at the University of Leeds. D. Lesnic would like to acknowledge the support of the EPSRC grant EP/W000873/1.


Alosaimi, M.A. and Lesnic, D. (2023), "Determination of the space-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer", Engineering Computations, Vol. 40 No. 2, pp. 411-433.



Emerald Publishing Limited

Copyright © 2023, Emerald Publishing Limited

Related articles