Reconstruction of the thermal properties in a wave-type model of bio-heat transfer

Abstract

Purpose This study aims to at numerically retrieve five constant dimensional thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements. Design/methodology/approach The thermal-wave model of bio-heat transfer is used as an appropriate model because of its realism in situations in which the heat flux is extremely high or low and imposed over a short duration of time. For the numerical discretization, an unconditionally stable finite difference scheme used as a direct solver is developed. The sensitivity coefficients of the dimensionless boundary temperature measurements with respect to five constant dimensionless parameters appearing in a non-dimensionalised version of the governing hyperbolic model are computed. The retrieval of those dimensionless parameters, from both exact and noisy measurements, is successfully achieved by using a minimization procedure based on the MATLAB optimization toolbox routine lsqnonlin. The values of the five-dimensional parameters are recovered by inverting a nonlinear system of algebraic equations connecting those parameters to the dimensionless parameters whose values have already been recovered. Findings Accurate and stable numerical solutions for the unknown thermo-physical properties of a biological tissue from dimensionless boundary temperature measurements are obtained using the proposed numerical procedure. Research limitations/implications The current investigation is limited to the retrieval of constant physical properties, but future work will investigate the reconstruction of the space-dependent blood perfusion coefficient. Practical implications As noise inherently present in practical measurements is inverted, the paper is of practical significance and models a real-world situation. Social implications The findings of the present paper are of considerable significance and interest to practitioners in the biomedical engineering and medical physics sectors. Originality/value In comparison to Alkhwaji et al. (2012), the novelty and contribution of this work are as follows: considering the more general and realistic thermal-wave model of bio-heat transfer, accounting for a relaxation time; allowing for the tissue to have a finite size; and reconstructing five thermally significant dimensional parameters.

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

“…We investigate the governing hyperbolic partial differential equation (1) subject to appropriate initial and boundary conditions when the unknown perfusion coefficient w b (x) is not constant, but it depends on the space variable. Therefore, this generality allows extending previous analyses (Alosaimi et al, 2020(Alosaimi et al, , 2021a by the authors to investigate heterogeneous tissues which are more general/realistic than the homogeneous ones. For simplicity, all the other thermal parameters are assumed to be known and constant, and we shall consider the one-dimensional time-dependent case of equation ( 1) only although a similar analysis holds also in higher dimensions.…”

Determination of the thermo-physical properties of multi-layered biological tissues

“…Baghban and Ayani [2] estimated the intensity of a laser applied to a three-layered skin tissue using the parabolic Pennes' bio-heat model and a sequential method. Very recently, the retrieval of several thermo-physical properties of a single-layer tissue entering a thermal-wave model of bioheat transfer has been investigated by Alosaimi et al [20]. These previous studies either neglected the stratified structure of the tissues investigated or did not consider the thermalwave model of bio-heat transfer.…”