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

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.