Computer Modelling of Bioheat Transfer for the Analysis of Brightness Temperature Distributions

TL;DR

This work tackles the challenge of accurately interpreting microwave radiometry brightness temperatures by developing a coupled biothermics–electrodynamics model for multilayer biological tissues. The authors formulate a non-stationary bioheat equation alongside a frequency-domain electromagnetic description, using a four-layer axisymmetric breast geometry and a finite element–Crank-Nicolson numerical workflow to compute $T_B( u)=\int_{V_b} W(oldsymbol{r}; \nu) T(oldsymbol{r}) \, dV$, where the weight function $W$ is derived from the dissipated power density via the Helmholtz equation. Key findings show a linear sensitivity of brightness temperature to ambient conditions $T_{air}$ and convective coefficient $h$, as well as to tissue conductivity $k$, with an $8^\circ$C rise in $T_{air}$ causing roughly a $2^\circ$C change in $T_B$ and a $0.2 ext{ W/(m·°C)}$ increase in $k$ producing ~1.5°C change in $T_B$; model validation yields temperature errors $\le 0.1^\circ$C. The dedicated C++ software, validated against analytical solutions and field data, enables accurate diagnostics and sets the stage for integrating radiometry with machine learning for automated interpretation and for extending the approach to other organs and therapeutic planning.

Abstract

This paper presents a comprehensive computer simulation of thermal processes in multilayered biological tissues for the analysis of luminance temperature distributions recorded by microwave radiometry. A mathematical model combining the bioheat transfer equation with the electrodynamic description of electromagnetic field propagation in an inhomogeneous medium has been developed. The model accounts for variations in the thermophysical and dielectric properties of tissues, as well as convective heat exchange with the environment. A parametric analysis was performed to investigate the effects of ambient temperature, heat transfer coefficient, and tissue thermal conductivity on brightness temperature formation. Computational experiments revealed a clear linear dependence of the radiometric signal on both external and internal parameters. It was found that an increase in air temperature by 8 °C causes a shift in the brightness temperature by about 2 °C, which exceeds the typical error of the microwave radiometry method and emphasises the need for strict temperature control of the measurement conditions. The developed software system was validated against analytical solutions and experimental data, confirming the accuracy of the calculated temperature fields to within 0.1 °C. The obtained results lay the groundwork for refining heat transfer models in biological tissues, improving the accuracy of non-invasive thermodiagnostic methods, and integrating computer modelling with machine learning algorithms to enable the automated interpretation of radiometric data.

Figures (6)

• Figure 1: Schematic representation of a multilayered geometric model of the breast: $\Omega_1$ is the skin, $\Omega_2$ is the subcutaneous adipose tissue, $\Omega_3$ is the glandular tissue, and $\Omega_4$ is the muscle tissue (a). The scheme of radiometric examinations of the breast (b).
• Figure 2: Software class diagram for modelling the coupled problem of biothermics and electrodynamics
• Figure 3: Dependence of the maximum relative error of the numerical solution $\xi$ on the number of calculation cells $N$ (grid elements) during sequential refinement of the calculation grid
• Figure 4: Dependence of brightness temperature $T_B$ on heat transfer coefficient $h$ (a); ambient temperature $T_{air}$ (b): the red line corresponds to point "0" on the breast, the blue line corresponds to point "3", and the green line corresponds to point "7".
• Figure 5: Dependence of brightness $T_B$ and infrared $T_{IR}$ temperatures on ambient temperature $T_{air}$ in field experiments for point "0": right breast (a-b), left breast (c-d).