Bioheat transfer in a spherical biological tissue: a comparison among various models

Abstract

The investigation of bioheat transfer is a difficult issue because it entails a mixture of many mechanisms to take into account, such as thermal conduction in tissues, convection and blood perfusion, metabolic heat generation, vascular structure, changing of tissue properties depending on physiological condition and so on. This topic has a key role to predict accurately the temperature distribution in tissues, especially during biomedical applications. In this paper, different bioheat transfer models are resumed and compared. The biological tissue is modelled as a porous sphere and liver tissue properties are used. Governing equations are averaged over a Representative Elementary Volume (REV) of the living tissue. Transient bioheat equations based on models like, for example, Pennes model, Local Thermal Non-Equilibrium equations (LTNE model), are employed. In the employed equations, radiative heat transfer is also considered. Governing equations with the appropriate boundary conditions are solved with the finite-element code COMSOL Multiphysics®. The effects of hyperthermia on the living tissue are included with a source term in the tissue energy equation. Results are presented in terms of temperature profiles in the biological tissue; the aim is to appreciate differences due to the various bioheat models.

Pennes’ bioheat equation vs. porous media approach in computer modeling of radiofrequency tumor ablation

“…The results of the LTE and LTNE models at the same porosity value were almost identical. As all the cases referred to a tissue with infiltrating terminal arteries, as described in Section "Modified LTNE model", the values of blood vessel diameter and blood velocity in the LTNE model were small enough to validate the local thermal equilibrium assumption, in agreement with the results reported in 7,21,22 , which all confirmed that the LTE temperature distributions agree with those of LTNE only when small blood vessels are considered (up to 3.00 × 10 -5 m) and blood velocity is less than 4.00 × 10 -3 m s -1 , showing that blood does not act as a heat sink in these cases. Note that the LTNE and LTE equations are not limited to modeling vessels smaller than 1 mm, but can also model larger vessels, which were not taken into account in this work.…”

“…(8) and (9) were combined the perfusion term disappeared. Note that in this case local thermal equilibrium should be a good approximation for temperature distributions because of the small size of the vessels considered (as described in 2,7,22 ), while this assumption would not be valid in the presence of larger vessels. Even if the two phases are at the same temperature, they have different water contents, as in the LTNE model, so that vaporization was included as in Eqs.…”

Fractal Pennes and Cattaneo–Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

“…We expect that the fractal solutions will give rise to some new insights in tumour growth dynamics. In general, one can neglect the metabolic heat generation in the tissue since it is expected to be much slighter than the power density released during hyperthermia treatment [110][111][112]. But this will not affect the solution of the fractal Pennes bioheat transfer equation.…”

Numerical Investigation of a Thermal Ablation Porous Media-Based Model for Tumoral Tissue with Variable Porosity

“…Thus, different models applied to thermal therapies have been developed trying to overcome these limitations, and they have been resumed in various review studies [7][8][9][10]. Furthermore, other thermodynamic approaches to cancer cell behaviors have been developed, such as the application of the constructal law [11,12].…”