Analysis of non-Fourier Heat Transfer Behavior of Cylindrical Shaped Living Tissue During Laser Based Photo Thermal Therapy

Abstract

The application of lasers in the medical field has increased drastically in recent decades. One such field is laser-based photothermal therapy for cancer treatment. The study of laser-tissue interaction is essential to reduce the thermal damage of nearby healthy tissue and enhance the efficacy of photothermal therapy. The present work is mainly concerned with the thermal response of cylindrical-shaped laser-irradiated living tissue embedded with optical inhomogeneity. The phenomena of light propagation through the cylindrical-shaped living tissue have been mathematically modeled using the transient radiative transfer equation. This equation has been solved using the modified discrete ordinate method to obtain the intensity field in the living tissue irradiated by a short-pulsed laser. The laser energy absorbed by the living tissue behaves like a source term in the bio-heat transfer equation. Researchers have experimentally found that the Fourier heat conduction model predicts inaccurate results in the case of biological tissue. So, they modified the Fouier heat conduction model by considering the relaxation time associated with heat flux and temperature gradient, known as the non-Fourier heat conduction model. In the present study, the non-Fourier modelbased bio-heat transfer equation has been numerically solved using the finite volume method to determine the temperature distribution inside the living tissue irradiated by a short-pulsed laser. The two different types of optical inhomogeneity, such as absorption inhomogeneity (mimics malignant cells) and scattering inhomogeneity (mimics benign cells), are considered in the current study. The inhomogeneity's optical and thermophysical properties may be the same/different from the homogeneous living tissue, making the problem a conjugate heat transfer problem. This conjugate heat transfer problem is solved using the harmonic mean technique. The present results have been verified with the results from the literature, and good agreement was found between them. Then, the independent study is performed to select the optimum grid size, control angle size, and time step. A comparative analysis of results (temperature distribution) between the traditional Fourier and non-Fourier (dual phase lag, hyperbolic) models has been performed. The effect of different parameters like relaxation times corresponding to the temperature gradient and heat flux, metabolic heat generation, and blood perfusion on the resultant temperature distribution inside the axisymmetric living tissue exposed to short-pulsed laser has been discussed. Subsequently, the effect of inhomogeneity's optical properties on the temperature distribution is investigated. A comparative study is performed between the same and different thermophysical properties of inhomogeneity from the living tissue. Although the non-Fourier heat conduction model-based bio-heat transfer equation has been widely utilized to determine the temperature distribution, it is essential to carry out the second law analysis to investigate any unphysical behavior. In this context, the equilibrium entropy production rates have been calculated based on the hypothesis of classical irreversible thermodynamics, which may have negative values and violate the second law of thermodynamics. So, the entropy production rate based on classical irreversible thermodynamics is modified using the extended irreversible thermodynamics hypothesis in the present study, and its solution gives the nonequilibrium entropy production rate. A comparative analysis of the entropy production rate corresponding to the Fourier and non-Fourier models was performed. The values of equilibrium and nonequilibrium entropy production rate for the Fourier model are found to be positive. In contrast, the equilibrium entropy production rate is negative for non-Fourier heat conduction and does not satisfy the second law of thermodynamics. On the other hand, the nonequilibrium entropy production rate is always a positive value for Fourier and non-Fourier models and satisfies thermodynamics second law. It has been investigated how thermal relaxation times affect the temperature field and entropy production rates in tissue subjected to laser light. The thermal relaxation parameters associated with the non-Fourier heat conduction model significantly affect the heat transfer process in the laser-irradiated living tissue. Hence, a part of the present work also comprises the numerical solution of the inverse heat transfer problem to estimate the thermal relaxation parameters corresponding to the non- Fourier model-based heat transfer in laser-irradiated living tissue. The inverse heat transfer problem solution has been obtained using the Levenberg–Marquardt algorithm. The direct problem is the non-Fourier heat conduction model-based bio-heat transfer equation in combination with the transient radiative transfer equation. The analytical solution of the non-Fourier heat conduction model-based bio-heat transfer equation is obtained using the finite integral transform technique. The computer code developed for estimating unknown thermal relaxation parameters using the Levenberg–Marquardt algorithm has been tested using data from the literature. The influence of sensor position on the sensitivity of the inverse heat transfer problem solution has been discussed. The impact of the total transient readings and the measurement error on estimating the unknown parameters have been investigated. The present study's findings can significantly contribute to various parameter estimation problems where the conventional methods for direct parameter measurements are impossible or very difficult. The work reported in the present thesis holds its importance in understanding the non-Fourier heat transfer behavior of living tissue during laser-based photo-thermal therapy, which may help to improve its efficacy.