Modeling of One-Dimensional Thermoelastic Dual-Phase-Lag Skin Tissue Subjected to Different Types of Thermal Loading

The heat transfer in skin tissues under the general two-temperature three-phase-lag model of heat conduction with a comparative study

In this paper, a new and more general model of heat conduction that depends on the drift velocity due to thermomass motion assumption will be established and will be applied to the skin tissue. Four different heat conduction models will be incorporated into a unified equation of heat conduction: the Pennes, Vernotte-Cattaneo, dual-phase-lag of Tzou, and the general two-temperature three-phase-lag of Youssef. The governing partial differential equations of the general two-temperature three-phase-lag model of bioheat conduction will be implemented and solved directly in the domain of the Laplace transformation. The numerical solutions of the Laplace transform will be calculated by executing the Tzou iteration formula. The ramp-type heat on the surface of the skin tissue will be considered as thermal loading. The conductive and dynamic temperature increment reactions have been studied and discussed with different values of ramp-time heat, characteristic length, and drift velocity parameters. The novelty of this work is to introduce some comparisons of the four under-studied bioheat conduction models and show the differences between them in the figures. The numerical results show that the ramp-time heat, drift velocity, and characteristic length parameters have major impacts on the increment of both dynamical and conductive temperature distributions.

Influence of thermal relaxation time on thermomechanical interactions in biological tissue during hyperthermia treatment

This study presents an analytical analysis of thermo-mechanical interactions within living tissues using a generalized biothermoelastic model with one thermal relaxation time. Utilizing Laplace transforms and associated techniques, we investigate the response of living tissue to a pulse boundary heat flux that decays exponentially on a traction-free surface. Through detailed graphical illustrations, we elucidate the influence of key parameters such as thermal relaxation time, blood perfusion rate, and the characteristic time of the pulsing heat flux on temperature distribution, displacement, and thermal strain. Our results are presented through comprehensive graphical representations. Furthermore, a parametric analysis is conducted to guide the selection of optimal design factors, enhancing the accuracy of hyperthermia treatments.

Investigation of memory influences on bio-heat responses of skin tissue due to various thermal conditions

Advancement of new technologies such as laser, focused ultrasound, microwave and radio frequency for thermal therapy of skin tissue has increased numerous challenging situations in medical treatment. In this article, a new meticulous bio-heat transfer model based on memory-dependent derivative with dual-phase-lag has been developed under different thermal conditions such as thermal shock and harmonic-type heating. Laplace transform method is acquired to perceive the analytical consequences. Quantitative results are evaluated for displacement, strain and temperature along with stress distributions in time domain by adopting the technique of inverse Laplace transform. Impacts of the constituents of memory-dependent derivatives-kernel functions along with time-delay parameter are analysed on the studied fields (temperature, displacement, strain and stress) for both thermal conditions separately using computational results. It has been found that the insertion of the memory effect proves itself a unified model, and therefore, this model can better predict temperature field data for thermal treatment processes.

Mathematical Modelling with the Exact Solution of Three Different Bioheat Conduction Models of a Skin Tissue Shocked by Thermoelectrical Effect

This research deals with the temperature increment and responsiveness of skin tissue to a continuous flow of surface heat induced by a constant-voltage electrical current. The exact analytical solution for the dual-phase-lag (DPL) of bioheat transfer has been obtained. It is used to confine the variables to a limited domain to solve the governing equations. The transition temperature reactions have been measured and investigated. The figures provide a comparison of the Pennes, Tzou models, and Vernotte-Cattaneo models. The numerical results demonstrate the values of the voltage, resistance, electric shock time, and dual-phase-lag time parameters which have significant influences on the distributions of the dynamic and conductive temperature rise through the skin tissue.

Refined Dual-Phase-Lag Theory for the 1D Behavior of Skin Tissue under Ramp-Type Heating

In this article, a mathematical analysis of thermoelastic skin tissue is presented based on a refined dual-phase-lag (DPL) thermal conduction theory that considers accounting for the effect of multiple time derivatives. The thin skin tissue is regarded as having mechanically clamped surfaces that are one-dimensional. Additionally, the skin tissue undergoes ramp-type heating on its outer surface, whereas its inner surface keeps the assessed temperature from vanishing. Some of the previous generalized thermoelasticity theories were obtained from the proposed model. The distributions of temperature, displacement, dilatation, and stress are attained by applying the Laplace transform and its numerical reversal approaches. The outcomes are explicitly illustrated to examine the significant influences on the distributions of the field variables. The refined DPL bioheat conduction model in this study predicts temperature, and the findings revealed that the model is located among the existing generalized thermoelastic theories. These findings offer a more thorough understanding of how skin tissue behaves when exposed to a particular boundary condition temperature distribution.

Analytical and numerical analysis of the dual-pulse lag heat transfer in a three-dimensional tissue subjected to a moving multi-point laser beam

An extensive algorithm based on both analytical and numerical solution methodologies is proposed to obtain transient temperature distributions in a three-dimensional living tissue subjected to a moving single-point and multi-point laser beam by considering metabolic heat generation and blood perfusion rate. Here, the dual-phase lag/Pennes equation is analytically solved by using the method of Fourier series and the Laplace transform. The ability to model single-point or multi-point laser beams as an arbitrary function of place and time is a significant advantage of the proposed analytical approach, which can be used to solve similar heat transfer problems in other living tissues. Besides, the related heat conduction problem is numerically solved based on the finite element method. The effects of laser beam transitional speed, laser power, and the number of laser points on the temperature distribution within the skin tissue are investigated. Moreover, the temperature distribution predicted by the dual-phase lag model is compared with that of the Pennes model under different working conditions. For the studied cases, it is observed that the maximum tissue temperature decreased about 63% by an increase of 6mm/s in the speed of the laser beam. An increase in the laser power from 0.8W/cm³ to 1.2W/cm³ results in a 28 °C increase in the maximum temperature of the skin tissue. It is observed that the maximum temperature predicted by the dual-phase lag model is always lower than that of the Pennes model and the temperature variations over time are sharper, while their results are entirely consistent over the simulation time. The obtained numerical results indicated that the dual-phase lag model is preferred in heating processes occurring at short intervals. Among the investigated parameters, the laser beam speed has the most considerable effect on the difference between the results of the Pennes and the dual-phase lag models.

Thermo-vibrational analyses of skin tissue subjected to laser heating source in thermal therapy

Laser-induced thermal therapy, due to its applications in various clinical treatments, has become an efficient alternative, especially for skin ablation. In this work, the two-dimensional thermomechanical response of skin tissue subjected to different types of thermal loading is investigated. Considering the thermoelastic coupling term, the two-dimensional differential equation of heat conduction in the skin tissue based on the Cattaneo–Vernotte heat conduction law is presented. The two-dimensional differential equation of the tissue displacement coupled with the two-dimensional hyperbolic heat conduction equation in the tissue is solved simultaneously to analyze the thermal and mechanical response of the skin tissue. The existence of mixed complicated boundary conditions makes the problem so complex and intricate. The Galerkin-based reduced-order model has been utilized to solve the two-sided coupled differential equations of vibration and heat transfer in the tissue with accompanying complicated boundary conditions. The effect of various types of heating sources such as thermal shock, single and repetitive pulses, repeating sequence stairs, ramp-type, and harmonic-type heating, on the thermomechanical response of the tissue is investigated. The temperature distribution in the tissue along depth and radial direction is also presented. The transient temperature and displacement response of tissue considering different relaxation times are studied, and the results are discussed in detail.