A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments

Thermal wave and Pennes' models of bioheat transfer in human skin: A transient comparative analysis

The primary focus of this study is to analyze comparative heat transfer in a two-dimensional (2D) multilayered human skin using thermal waves and Pennes' bioheat transfer models. The model comprises the epidermis, dermis, hypodermis tissue, and inner cells, and aims to understand their response to microwave (MW) power and electromagnetic (EM) frequency. The system of equations involves EM wave frequency and bioheat equations and uses the finite element method (FEM) for solving. It encompasses a range of microwave power levels (4-16 W), frequencies (0.9-4 GHz), and exposure durations (0-180 s). It examines how MW power and frequency affect temperature predictions due to different relaxation times. The results are visually represented, illustrating microwave power dissipation, isothermal profiles within the skin tissue, temperature trends at several locations, relaxation times, specific absorption rate (SAR), and the mean surface temperature of the multilayered dermal cell. Thermal analysis shows that Pennes' equation predicts higher temperatures than the thermal wave model of bioheat transfer (TWMBT). A notable disparity in temperature evolution is observed between the two models, especially in high-frequency transient heating scenarios. The TWMBT forecasts a delay in heat transfer, offering valuable insights into the more realistic short-term thermal behavior that the classical Pennes' model fails to capture. This comparative study underscores the significance of selecting an appropriate bioheat transfer model for precise thermal analysis in biomedical applications, such as hyperthermia treatment and thermal diagnostics. The findings emphasize the potential of the TWMBT to enhance the accuracy of thermal treatments in clinical settings.

An improved analytical model for heat flow in cancerous tumours to avoid thermal injuries during hyperthermia

The present study highlights an analytical hybrid scheme consisted of a shift of variables and finite integral transform for analysing a local thermal non-equilibrium (LTNE) bioheat model. This model can have utilised to be a betterment of prediction of the temperature field in the localised hyperthermia therapy (LHT) for the treatment of cancer patients. As the hyperthermia treatment is only the application in living tissues, an appropriate initial condition for the therapeutic thermal response is proposed instead of a constant temperature taken in the previous studies based on the 1-D heat flow. The present analysis suggests the therapeutic exposure time of 7776.8s (2.16 h) with constant heat flux and the exposure time of 10969.9s (3.06 h) with a sinusoidal heat flux within the usual temperature range of the hyperthermia (in a combination of thermal ablation and medium temperature hyperthermia) to be more effective in the treatment protocol. The presented results show that fatal injuries (tissue trauma, thermal burn, etc.) of internal organs might be possible to avoid by the current therapeutic condition. Therefore, this study may nullify the adverse effect of the existing model with the constant heating and consequently, the repercussion of the several therapeutic variables is to estimate with the development of a thermal profile for the suitability of a therapeutic condition. On the other hand, the present study well matches with the published analysis in case of both the theoretical and experimental (live tissues of the pig due to unavailability of real-time data on the human body) studies and it found the maximum deviation of the thermal response as 2.26% and 2.66%, respectively.

Two-dimensional closed-form model for temperature in living tissues for hyperthermia treatments

This research article determines an exact analytical expression for 2-D thermal field in single layer living tissues under a therapeutic condition by means of Fourier and non-Fourier heat transfer approaches. An actual spatially dependent initial condition has been adopted to analyze the heat propagation in tissues. The exact analytical determination for this actual initial condition for temperature may be difficult. However, in this study, an approximate analytical method has newly been established for an appropriate initial condition. With this initial expression, an exact temperature distribution for 2-D heat conduction in plane co-ordinates has been investigated for the predefined therapeutic boundary condition to have knowledge for practical aspects of the thermal therapy. Laplace Transform Method (LTM) in conjunction with the Inversion Theorem is used for the analytical solution treatment. We have utilized both Pennes' bioheat equation (PBHE) and thermal wave model of bioheat equation (TWMBHE) for the analysis. The influence of thermo-biological behavior on 2-D heat conduction in tissues has been studied with the variation of several dependable parameters in relation to the Hyperthermia treatment protocol in a moderate temperature range (42-45°C). The result in the present study has been evidenced for the biological heat transfer for the enforcement of different circumstances and also has been validated with the published value where the maximum temperature deviation of 2.6% has been recorded. We conclude that the temperature curve for TWMBHE model shows a higher waveform nature for low thermal relaxation time and this wavy nature gradually diminishes with an increase in relaxation time. The maximum peak temperature attains 46.3°C for the relaxation time = 2s and with the increase in the relaxation time the peak temperature gradually falls. The impact of blood perfusion rate on the relaxation time has also been established in this paper.