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A study on thermomechanical interactions in two-dimensional tissues without energy dissipation
... The influence of fractional calculus on thermal therapy modeling was addressed by Alsisi et al. [49], who applied a fractional-order approach to simulate thermomechanical effects in two-dimensional biological tissues during hyperthermia treatment. Expanding on this, Almuneef et al. [50] analyzed thermomechanical behavior in biological tissues under non-dissipative conditions, contributing to the understanding of energy-efficient thermal processes in biomedical applications. Collectively, these studies underscore the growing importance of incorporating fractional derivatives, graded material properties, and laser-induced effects in analyzing wave propagation and thermal response across diverse engineering and biomedical domains. ...
... (ii) In hydro-photo-thermoelastic theory, the motion equation accounts for combined thermal, mechanical, hydraulic, and photoinduced effects resulting from heat generated by laser excitation [49,50]: ...
... (iv) In porous semiconductors, water excess pore pressure is described by an equation that models fluid movement driven by temperature gradients [50]: where m = n 0 ρ w C w + (1 − n o )ρ s C s , e = ∂u ∂x + ∂w ∂z and b = gρ w k d . The constitutive relation captures the coupling between thermal, mechanical, and fluid effects, where charge carrier motion affects the material's mechanical response, and mechanical changes influence carrier dynamics in the semiconductor [51]: ...
The laser irradiation of living tissues poses a risk of thermal damage, making it a critical factor in medical procedures such as laser surgery and thermal therapies. Effectively predicting and managing this damage, particularly in hyperthermia therapy, is essential for maximizing treatment efficacy while protecting surrounding healthy tissues. In this context, theoretical and computational models of biological heat transfer, especially the enhanced Pennes bioheat transport equation, have attracted significant research interest. This study contributes to the field by providing a novel analytical solution to the refined Pennes bioheat model, incorporating the three-phase lag (TPL) concept. The research examines heat transfer in a one-dimensional region, where the outer surface is exposed to laser heating while the inner surface remains thermally insulated. It explores the mechanical effects of thermal shock induced by laser treatment, focusing on heat generation patterns across different laser intensities in diseased human skin tissues. To validate the model, numerical inverse and Laplace transform techniques were applied, producing results consistent with existing literature. The findings not only advance the theoretical understanding of bioheat transfer but also enhance the safety and effectiveness of laser-based medical therapies.
The use of thermal conduction models, particularly the double-phase lag thermal wave model, is vital for improving thermal therapies in biological tissues. However, existing models have limitations that hinder their practical application. This paper introduces a modified Pennes fractional thermal equation for biological heat transfer that integrates the double-phase lag concept and the fractional Atangana-Baleanu operator with a non-singular kernel. The model’s predictions were validated against measured temperature responses of laser-irradiated skin tissue and compared to established models. A one-dimensional layer of human skin tissue was analyzed using the Laplace transform method, with graphical results for each scenario. The comparative analysis showed that the AB fractional model outperforms other fractional models in capturing memory effects related to temperature variations and accurately models thermal interactions in living tissues while considering time delays. These findings highlight the model’s potential to improve the design and optimization of thermal therapies in clinical practice.
In order to address various clinical applications within living tissue, the aim of this work is to analytically study the thermomechanical interaction for a living tissue which is subjected to variable thermal loadings. Human tissues undergoing regional hyperthermia treatment for cancer therapy is based on graded changes of the cells, and as a consequences, the constitutive equations have been formulated using the nonlocal elasticity theory. The heat transport equation for the present problem is formulated in the context of Moore‐Gibson‐Thompson theory of generalized thermoelasticity assimilating the memory‐dependent derivative within a slipping interval. Both the boundaries of the tissue is maintaining the condition of zero traction. The lower boundary of the tissue is subjected to prescribed thermal loading while, the upper boundary is kept at zero temperature. Utilizing the Laplace transform mechanism, the governing equations have been solved and the general solutions have been obtained in the transformed domain. In order to arrive at the solutions in the real space‐time domain, suitable inversion of the Laplace transform has been carried out numerically using the method of Zakian. Numerical findings suggest that thermomechanical waves propagate through skin tissue over finite distances, which helps mitigate the unrealistic predictions made by the Pennes' model. Significant effect due to different effective parameter such as nonlocal parameter and the time‐delay parameter is reported. Also, how a nonlinear kernel function can be more effective in bio‐heat transfer, is outlined in the study also.
Understanding the biothermal response of skin tissue exposed to electromagnetic (EM) radiation and variable thermal fields is crucial for mitigating risks associated with such exposures. This knowledge can empower the development of safe and efficacious evidence‐based treatments for various skin conditions within the medical field. This study employs the fourth‐order Moore–Gibson–Thomson (MGT) concept to establish a theoretical framework for biothermal analysis. This investigation aims to elucidate the biothermal response of skin tissues to EM radiation. The developed model facilitates the prediction of thermal reactions within human skin and the subsequent evaluation of bioheat transfer efficiency in biological tissues. The proposed model is implemented on a one‐dimensional representation of a skin layer and incorporates the effects of an induced electric field and a time‐harmonic heat source. Additionally, a linear dependence of metabolic heat generation on tissue temperature is considered. By employing Laplace transforms, the analytical solutions for tissue temperature are presented. The derived analytical solutions are compared with established theories to assess the accuracy of the proposed model. The results reveal that the modified MGT bioheat transfer model predicts lower temperatures compared to the conventional Pennes model, attributable to the incorporation of the thermal relaxation time constant.
This investigation aims to employ a modified fractional two-phase thermal conductivity (DPL) model to elucidate the influence of temperature variations on the thermophysical properties of human skin tissue. The model incorporates the fractional Atangana–Baleanu (AB) derivative operator, characterized by its non-local and non-singular kernel. This specific choice enables the model to capture non-local effects and memory phenomena within the context of skin tissue thermal conductivity. A segment of human skin tissue is subjected to a ramp-type thermal load for analysis using the modified fractional two-phase DPL model. The investigation focuses on the exterior surface, with the opposing surface assumed to be thermally insulated and free of external mechanical interactions. The governing equations are employed within the Laplace transform domain to describe and solve for the thermophysical response of the skin tissue. Subsequently, a parametric study is conducted to elucidate the influence of phase delays, fractional order, and the ramp heating profile on the behavior of the tissue under various scenarios.
This study provides analytical solutions for the non-Fourier theory, which accounts for bioheat transfer in biological tissue when exposed to laser irradiation. To perform thermal treatment procedures effectively, a thorough comprehension of both the heat transmission mechanism and the subsequent thermal and mechanical interaction within the patient's human tissue is essential. The assessment of thermal injuries to the tissue involves determining the extent of denatured proteins using the Arrhenius formulation. The bio-thermoelastic model presented employs Laplace transforms and analytical techniques to establish governing formulations. Subsequently, an eigenvalues scheme is utilized to derive solutions to these equations. Graphical representations of the results for temperature, displacements, and stress are provided. The analytical solution's accuracy is verified through a comparison with numerical and experimental data. Results indicate that, when both have zero thermal lag times, the generalized non-Fourier model aligns with the Pennes bioheat transfer model. Furthermore, the effectiveness of the mathematical model in evaluating bioheat transfer in biological tissues is validated by comparing it with established experimental data.
Medical scientists frequently employ the Pennes bioheat equation as a computational tool to comprehend the intricate dynamics of thermal energy dispersion within living tissues. This equation, endowed with pronounced utility, finds paramount significance in the realm of therapeutic interventions, notably hyperthermia, wherein regulated elevation of tissue temperatures is administered for multifarious medical objectives. The utilization of this technology significantly enhances the optimization of treatment protocols and the preservation of temperature levels within crucial anatomical regions of the human body. To ensure the effectiveness of therapies and to uphold the utmost welfare of patients, meticulous monitoring of the thermal response of tissues subjected to thermal stimuli becomes imperative. This study introduces a mathematical formulation of the Pennes equation, specifically tailored for capturing the biothermal conduction phenomena transpiring in the intricate structure of skin tissue by employing the Moore–Gibson–Thompson (MGT) equation. This model enables accurate predictions of the thermal response of human skin to temperature variations. The key differentiating factor of this model is the incorporation of the concept of time delay. This inclusion serves the purpose of minimizing the rapid propagation of thermal energy within biological tissues, ultimately restricting its diffusion at limited rates. The proposed model is employed to characterize the intricacies of heat transfer in a slender, constrained stratum of skin tissue that is subject to a harmonic thermal stimulus. The computational outcomes are presented with the aid of illustrative figures, effectively highlighting the impact of model parameters on the temperature and deformation distributions within the material.
Simple Summary
Heat transport in biological tissue is mediated through a variety of phenomenological processes, involving tissue heat exchange, blood-tissue convection, blood perfusion or advection and diffusion across microvascular beds, and metabolic heat production. In recent years, many physicians and engineers have taken an interest in applying computational and mathematical techniques to model biological systems. The objective of the current paper is to provide an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time. The suggested model is used to examine heat transport in biological tissues as an infinite concentric spherical region during magnetic fluid hyperthermia. This method is used to investigate the influence of heat generation through heat treatment on a skin tumor a spherical layered structure. The present model can explain the effect of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences including transfer, metabolism support, blood perfusion, and other similar treatments.
Abstract
Hyperthermia therapy is now being used to treat cancer. However, understanding the pattern of temperature increase in biological tissues during hyperthermia treatment is essential. In recent years, many physicians and engineers have studied the use of computational and mathematical models of heat transfer in biological systems. The rapid progress in computing technology has intrigued many researchers. Many medical procedures also use engineering techniques and mathematical modeling to ensure their safety and assess the risks involved. One such model is the modified Pennes bioheat conduction equation. This paper provides an analytical solution to the modified Pennes bioheat conduction equation with a single relaxation time by incorporating in it the (MGT) equation. The suggested model examines heat transport in biological tissues as forming an infinite concentric spherical region during magnetic fluid hyperthermia. To investigate thermal reactions caused by temperature shock, specifically the influence of heat generation through heat treatment on a skin tumor [AEGP9], the Laplace transformation, and numerical inverse transformation methods are used. This model was able to explain the effects of different therapeutic approaches such as cryotherapy sessions, laser therapy, and physical occurrences, transfer, metabolism support, and blood perfusion. Comparison of the numerical results of the suggested model with those in the literature confirmed the validity of the model’s numerical results.
In this work, numerical estimations of a nonlinear hyperbolic bioheat equation under various boundary conditions for medicinal treatments of tumor cells are constructed. The heating source components in a nonlinear hyperbolic bioheat transfer model, such as the rate of blood perfusions and the metabolic heating generations, are considered experimentally temperature-dependent functions. Due to the nonlinearity of the governing relations, the finite element method is adopted to solve such a problem. The results for temperature are presented graphically. Parametric analysis is then performed to identify an appropriate procedure to select significant design variables in order to yield further accuracy to achieve efficient thermal power in hyperthermia treatments.
This investigation is focused on the effects of nonlocality due to 2-D deformations arising in a nonlocal homogeneous isotropic thermoelastic solid which is subjected to a ramp type heat source with two temperature. There has been the use of Laplace and Fourier transforms for solving the equations. The expressions for displacement components, stress components and conductive temperature have been computed in the transformed domain. The numerical inversion technique has been used for obtaining the results in the physical domain. The effect of nonlocal parameter on the displacement components, conductive temperature and stress components have been represented graphically.
The present paper aims to study the influence of the magnetic field and initial stress on the 2-D problem of generalized thermo-viscoelastic material with voids subject to thermal loading by a laser pulse in the context of the Lord-Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord-Shulman and the coupled theories in the presence and absence of the initial stress and the magnetic field.
The present study utilizes the generalized thermoelasticity theory, with one thermal relaxation time (TR), to examine the thermoelastic problem of a functionally graded thin slim strip (TSS). The authors heated the plane surface bounding using a non-Gaussian laser beam with a pulse length of 2 ps. The material characteristics varied continually based on exponential functions. Moreover, the equations governing the generalized thermoelasticity for a functionally graded material (FGM) are recognized. The problem’s ideal solution was primarily obtained in the Laplace transform (LT) space. The LTs were converted numerically because of the considerable importance of the response in the transient state. For a hypothetical substance, the numerical procedures calculating the displacement, stress, temperature and strain were given. The analogous problem solution to an isotropic homogeneous material was provided by defining the parameter of non-homogeneity adequately. The obtained results were displayed using graphs to illustrate the extent to which non-homogeneity affected displacement, stress, temperature and strain. A comparison was been made between the present study and those previously obtained by others, when the new parameters vanish to show the impact of the non-homogeneity, TSS and laser parameters on the phenomenon. The results obtained indicate a significant strong impact of FGM, TSS and laser parameters.
This work is devoted to the investigation of a two-dimensional porous material under weak, strong and normal conductivity, using the eigenvalues method. By using Laplace–Fourier transformations with the eigenvalues technique, the variables are analytically obtained. The derived technique is assessed with numerical results that are obtained from the porous mediums using simplified symmetric geometry. The results, including the displacements, temperature, stresses and the change in the volume fraction field, are offered graphically. Comparisons are made among the outcomes obtained under weak, normal and strong conductivity.
INTRODUCTION: Thermal processes are the essence of living organisms and are necessary for understanding life. The study of Transfer of heat in tissues is known as Bioheat transfer. Many techniques are developed for the thermal treatment of skin and other disease such as skin cancer, skin burns and injured skin tissue with laser. The tissue is inhomogeneous and at times anisotropic with complex thermal properties. Moreover, there may be skin tissue damage when irradiated with a laser beam.OBJECTIVES: In this research a novel one-dimensional (1-D) bioheat model has been used with memory-dependent derivative (MDD) in Pennes’ bioheat transfer equation due to laser radiation and the thermal damage in tissue caused due to laser heating has been examined.METHODS: Bioheat transfer model has been used with memory-dependent derivative (MDD) in Pennes’ bioheat transfer equation. The problem is solved using Laplace transform technique.RESULTS: The temperature and thermal damage in the skin exposed to heating with laser radiation is calculated and obtained in physical form. The thermal reaction of skin tissues during laser radiation is studied under memory-dependent derivative (MDD) in Pennes’ bioheat transfer equation.CONCLUSION: Analyzed a novel bioheat mathematical model on the basis of MDD involving time-delay parameter 𝜒𝜒 for the Pennes’ bioheat transfer equation and applied to examine the thermal properties of the skin tissue for burns caused due to laser radiations. The thermal damages can be measured in a better way with the MDD model. The blood perfusion prevent the tissue damage by developing the cooling function. Effect of memory dependent derivatives and time delay parameter are represented graphically and analysed.
Understanding of heat transfer and related thermomechanical interaction in biological tissue is very important to clinical applications. It is quite natural to treat the living tissue as a porous medium, such as the living tissue in the presence of blood. Based on a non-equilibrium heat transfer model, the thermomechanical response of porous biological tissue exposed to an instantaneous thermal shock is investigated in this work. The governing equations are established based on local thermal non-equilibrium model in the context of the generalized thermoelastic theory and solved by time-domain finite-element method. The effect of porosity coefficient on the thermal-mechanical response of the porous tissue is studied and illustrated graphically. Comparisons are made between the proposed results and those from the local thermal equilibrium models to reveal the difference of these two models in terms of thermoelastic response.
The model of coupled plasma and thermo-elastic wave were used to investigate the wave propagation in a two-dimensional semiconducting half space by using eigenvalues approach. By using Fourier and Laplace transformations with the eigenvalues techniques methodology, the exact solution of all physical quantities is obtained. The boundary edge of the plane is due to a heat flux with a pulse that decays exponentially and is taken as free of tractions. A semiconductor media such as silicon has been studied. The outcomes have been verified numerically and are represented graphically. Keywords: Photo-thermal waves, Laplace-fourier transforms, Eigenvalues approach
A mathematical model is proposed to study the influence of elasticity on the peristaltic flow of a generalized Newtonian fluid in a tube. A power-law model is considered in the present study to understand the effect of elasticity on the peristaltic flow of blood through arteries. Application of blood flow through arteries is studied by expressing a relationship between pressure gradient and volume flow rate in an elastic tube. The results show the significant effect of elasticity on flow quantities. It is observed that the flux increases as the fluid behaviour index increases and that the flux is more for a Newtonian fluid when compared to non-Newtonian cases. The trapping phenomenon is presented graphically for various physical parameters. The results obtained in the present study are compared with an earlier investigation of Vajravelu et al. (Peristaltic transport of a Herschel–Bulkley fluid in an elastic tube. Heat Transf-Asian Res. 2014;44:585–598).
This paper deals with a mathematical model describing the inward solidification of a melt of phase change material within a container of different geometrical configuration like slab, circular cylinder or sphere under the most generalized boundary conditions. The thermal and physical properties of melt and solid are assumed to be identical. To solve this mathematical model, the finite difference scheme is used to convert the problem into an initial value problem of vector matrix form and further, solving it using the Legendre wavelet Galerlcin-method. The results thus obtained are analyzed by considering particular cases when one might impose either a constant/time varying temperature or a constant/time varying heat flux or a constant heat transfer coefficient on the surface. The whole analysis is presented in dimensionless form. The effect of variability of shape factor, condition posed at the boundary, Stefan number, Predvoditelev number, Kirpichev number, and Biot number on dimensionless temperature and solid-layer thickness are shown graphically. Furthermore, a comparative study of time for complete solidification is presented.
The problem of two-temperature generalized thermoelastic thin slim strip is investigated in the context of Green and Lindsay theory. As an application of the problem, a particular type of moving heat source is considered and the problem is solved analytically by using the eigenvalue approach in the Laplace transforms domain. The displacement, conductive temperature, thermodynamic temperature, and stress are obtained. The resulting quantities are depicted graphically.
This article aims to employ an analytical approach to analyze the thermal and mechanical responses of biological tissues due to instant heating, considering the dual phase-lag (DPL) model. To effectively carry out thermal treatment procedures, it is imperative to have a deep understanding of both the mechanism of heat transmission and the resulting thermomechanical interactions within the patient’s human tissues. The governing formulations of this extended bio-thermoelastic model are established using analytical methods and Laplace transforms. The eigenvalue approach is then employed to obtain solutions to these formulations. The results for temperature, displacement and stresses are presented graphically. A comparative analysis has been conducted between two bioheat transfer models: the DPL and the Pennes bioheat (Pennes) models.
This paper is related to the study of two temperature parameter effect for the axisymmetric deformation in a two-dimensional nonlocal homogeneous isotropic thick circular plate without energy dissipation. The plate is subjected to a cubical thermal source with a unit magnitude normal force. Laplace and Hankel transforms have been used to find the analytical solutions to the problem. The expressions for physical quantities such as displacement components, stress components and conductive temperature have been obtained in the transformed domain. The resulting quantities in the physical domain have been obtained with the use of inversion technique. The numerical simulated results have been depicted graphically for studying the effect of nonlocal parameter along with two temperature on the components of displacements, stresses and conductive temperature. The results obtained in this paper can be very useful for the researchers working in the field of nonlocal theory of thermoelasticity, in the fields of geophysics and various other scientific fields.
In our present study, we approach a linear theory for the thermoelasticity of type III for Cosserat media. At the beginning we introduce the equations and conditions, specific for a mixed problem in this context, namely the motion and energy equations, the initial condition and boundary relations. After that, we establish two results regarding the solution unique to the problem and two results on the continuous dependence of solutions, for the same mixed problem. Both problems that we address in our paper (uniqueness and continuous dependence) are not based on the material symmetries of the medium. Moreover, our results concern the theory of type III thermoelasticity for Cosserat media in their most general form, namely anisotropic.
The paper is devoted to the study of the axisymmetric deformations in a two-dimensional nonlocal homogeneous isotropic thermoelastic solid without energy dissipation. The effect of two temperature has been added with normal force over the circular region, concentrated normal force, thermal source over the circular region and concentrated thermal point source as an application. Analytical solutions to the field equations have been obtained using Laplace and Hankel transforms. The expressions for physical fields such as conductive temperature distribution, stress components and displacement components and have been obtained in the transformed domain. Numerical inversion technique has been used to obtain the resulting quantities in the physical domain. In this paper the numerical simulated results have been depicted graphically to show the effect of nonlocal parameter on various components along with the discussion of some particular cases. A great difference in the deformation of nonlocal isotropic thermoelastic body has been found while considering the effect of presence and absence of nonlocal parameter. The variation of r causes various components to follow an oscillatory pattern.
Here, in this research we have studied a two dimensional problem in a homogeneous orthotropic magnetothermoelastic medium with higher order dual-phase-lag heat transfer with combined effects of rotation and hall current in generalized thermoelasticity due to time harmonic sources. As an application the bounding surface is subjected to uniformly distributed and concentrated loads (mechanical and thermal source). Fourier transform technique is used to solve the problem.
The expressions for displacement components, stress components and temperature change are derived in frequency domain. Numerical inversion technique has been used to obtain the results in physical domain. The effect of frequency has been depicted with the help of graphs.
Although there have been numerous reports in several articles about the viscoelastic properties of biological tissues, no effort has been made to investigate the combined thermal and mechanical behavior of the viscoelastic tissue. At present, the model of thermo-viscoelasticity theory with variable thermal conductivity and rheological properties of the volume is considered to investigate bio-thermo-mechanics behavior in living tissue within the context of the Lord-Shulman theory. The model is applied to a limited thickness, cancerous layer problem. The problem was solved analytically in the transformed domain using Laplace transform as a tool. The exact solution is obtained in the context of transformation Laplace. Numerical results are given and illustrated graphically for the distributions of temperature, displacement, and stress. Some correlations are produced with the results obtained for the absence of the thermal relaxation parameter. The effects of variable thermal and volume materials properties, blood perfusion rate on the behavior of various fields are examined.
This paper presents an analytical approach associated with Laplace transformation, experimental temperature data, and a sequential concept over time to obtain the thermal damage and the temperature in a living tissue due to laser irradiation. The analytical solutions in the Laplace domain are appreciably obtainable. The thermal damage to the tissue is completely assessed by the denatured protein range using the formulation of Arrhenius. Numerical outcomes for temperatures and the thermal damages are graphically introduced. Besides, the comparison between the numerical computations and the existing experimental study shows that a current mathematical model is an effective tool for evaluating the biological heat transfer in biological tissues.
Advancements in the use of laser technology in the medical field have motivated the widespread use of thermal energy to treat a wide variety of diseases and injuries. During laser-induced thermotherapy, the tissue gains heat from laser irradiation and its shape is deformed due to non-uniform temperature distribution. To describe the phenomenon adequately, the mathematical model that considers both heat transfer and mechanical deformation is needed. In this study, the formulation of mathematical model describing coupled heat transfer and mechanical deformation of tissue subjected to laser-induced thermotherapy is numerically implemented. The effects of laser irradiation time, wavelength, laser intensity, laser beam radius and blood perfusion rate on temperature distribution, Von Mises stress distribution, and displacement of the layered skin during laser irradiation are systematically investigated. The values obtained provide an indication of limitations that must be considered in administering laser-induced thermotherapy.
Biothermomechanics involves bioheat transfer, biomechanics, burn damage and physiology. Comprehension of biothermomechanics in living tissue is very important to clinical applications. In present work, the generalized thermoelastic theory without energy dissipation is used to investigate bioheat transfer and heat-induced mechanical response in bi-layered human skin with variable thermal material properties. The governing equations of skin tissue with temperature-dependent material properties are solved by Kirchhoff and Laplace transformation.The transient thermoelastic responses and thermal damage of the skin tissue are obtained and illustrated graphically. The influences of interface and variable thermal material parameters on the responses are also discussed.
Electromagnetic heating is widely used in medical treatments, such as microwave, radiofrequency, laser, etc. Recent advances in these technologies resulted in remarkable developments of thermal treatments for a multitude of diseases and injuries involving skin tissue. The comprehension of heat transfer and related thermomechanics in skin tissue during these treatments is thus of great importance, and can contribute to the further developments of these medical applications. Biothermomechanics of skin is highly interdisciplinary, involving bioheat transfer, burn damage, biomechanics and physiology. The aim of this study is to develop a computational approach to examine the heat transfer process, heat-induced mechanical response as well as the associated pain level, so that the differences among the clinically applied heating modalities can be quantified. In this paper, numerical simulations with the finite difference method (FDM) was used to analyze the temperature, burn damage and thermal stress distributions in the skin tissue subjected to various thermal treatments. The results showed that the thermo-mechanical behavior of skin tissue is very complex: blood perfusion has little effect on thermal damage but large influence on skin temperature distribution, which, in turn, influences significantly the resulting thermal stress field; for laser heating, the peak temperature is higher for laser with shorter wavelength, but the peak is closer to the skin surface; the thermal stress due to laser and microwave heating is mainly limited to the top epidermis layer due to the exponential decrease of heat generation along skin depth; the thin (and commonly overlooked) stratum corneum layer dominates the thermomechanical response of skin tissue.
A three-dimensional model of the generalized thermoelasticity without energy dissipation under temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of the reference temperature. The resulting formulation in the context of Green and Naghdi model II is applied to a half-space subjected to a time-dependent heat source and traction free surface. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled equations. Numerical results for the field quantities are given in the physical domain and illustrated graphically. The results are also compared to results obtained in the case of temperature-independent modulus of elasticity.
For a free vibration problem of a thermoelastic hollow sphere into the context of the generalized thermoelasticity theory with one relaxation time, exact analytic solutions are obtained with the use of eigenvalue approach. Both the inner and outer curved surfaces of the sphere are considered stress-free and isothermal surfaces. The dispersion relations for the existence of various types of possible modes of vibrations in the considered hollow sphere are derived. The numerical results have been presented graphically in respect of natural frequencies, thermoelastic damping, and frequency shift.
Non-linear Pennes’ bioheat equation including the thermal wave model of bioheat transfer as well as the dual-phase-lag model has been discretized using a mesh-free Smoothed-Particle Hydrodynamics (SPH) procedure. The time evolution of the temperature distribution within a living tissue and effect of non-linearity in the PDEs on the solution have been investigated. The thermal conductivities for Fourier and non-Fourier based bioheat models are varied. The results obtained using the SPH method were compared with the previously published data for benchmark problems. It is shown that these SPH results show an excellent agreement in comparison with the previous results obtained using other numerical methods which proves suitability of SPH scheme towards simulations for bioheat equation.
In this work, we study the effect of the magnetic field, rotation, thermal field, and the initial stress and also voids on the reflection of P-wave with one relaxation time. The formulation is applied to generalization, the Lord–Shulman theory with one relaxation time.
The electromagneto-thermoelastic interactions in perfectly conducting plane is subjected to a uniform axial magnetic field with voids and rotation. It is shown that there exist four plane waves; P
1-, P
2-, P
3- and P
4-.
In addition, the reflection coefficients from insulated stress-free surface for the incident P-wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of magnetic field, initial stress, rotation,
thermal relaxation time and voids parameters and displayed graphically. In the case of neglecting the effect of the magnetic field, and made clear the impact of other variables on the reflection coefficients, which is considered a special case of this study and displayed graphically.
The fundamental equations of the problems of generalized thermoelasticity with one relaxation time parameter including heat sources have been written in the form of a vector-matrix differential equation in the (i) Laplace transform domain for a one dimensional problem, and in the (ii) Laplace-Fourier transform domain for a two dimensional problem and they re solved by the eigenvalue approach. The results are compared with the existing literature.
During laser-assisted photo-thermal therapy, the temperature of the heated tissue region must rise to the therapeutic value (e.g., 43°C) for complete ablation of the target cells. Large blood vessels (larger than 500 micron in diameter) at or near the irradiated tissues have a considerable impact on the transient temperature distribution in the tissue. In this study, the cooling effects of large blood vessels on temperature distribution in tissues during laser irradiation are predicted using finite element based simulation. A uniform flow is assumed at the entrance and three-dimensional conjugate heat transfer equations in the tissue region and the blood region are simultaneously solved for different vascular models. A volumetric heat source term based on Beer-Lambert law is introduced into the energy equation to account for laser heating. The heating pattern is taken to depend on the absorption and scattering coefficients of the tissue medium. Experiments are also conducted on tissue mimics in the presence and absence of simulated blood vessels to validate the numerical model. The coupled heat transfer between thermally significant blood vessels and their surrounding tissue for three different tissue-vascular networks are analyzed keeping the laser irradiation constant. A surface temperature map is obtained for different vascular models and for the bare tissue (without blood vessels). The transient temperature distribution is seen to differ according to the nature of the vascular network, blood vessel size, flow rate, laser spot size, laser power and tissue blood perfusion rate. The simulations suggest that the blood flow through large blood vessels in the vicinity of the photothermally heated tissue can lead to inefficient heating of the target.
In this work, we have constructed the equations for generalized thermoelasticity of an unbounded fiber-reinforced anisotropic medium with a circular hole. The formulation is applied in the context of Green and Naghdi (GN) theory. The thermoelastic interactions are caused by (I) a uniform step in stress applied to the boundary of the hole with zero temperature change and (II) a uniform step in temperature applied to the boundary of the hole which is stress-free. The solutions for displacement, temperature and stresses are obtained with the help of the finite element procedure. The effects of the reinforcement on temperature, stress and displacement are studied. Results obtained in this work can be used for designing various fiber-reinforced anisotropic elements under mechanical or thermal load to meet special engineering requirements.
Heat transfer in a biological system is a complex process and its analysis is difficult. Heterogeneous vascular architecture, blood flow in the complex network of arteries and veins, varying metabolic heat generation rates and dependence of tissue properties on its physiological condition contribute to this complexity. The understanding of heat transfer in human body is important for better insight of thermoregulatory mechanism and physiological conditions. Its understanding is also important for accurate prediction of thermal transport and temperature distribution during biomedical applications. During the last three decades, many attempts have been made by researchers to model the complex thermal behavior of the human body. These models, viz., blood perfusion, countercurrent, thermal phase-lag, porous-media, perturbation, radiation, etc. have their corresponding strengths and limitations. Along with their biomedical applications, this article reviews various contextual issues associated with these models. After brief discussion of early bioheat models, the newly developed bioheat models are discussed in detail. Dependence of these models on biological properties, viz., thermophysical and optical properties are also discussed.
This paper presents the capacitive hyperthermia from physical perspective focusing on the geometric dimensions as parameters. For this purpose six parameters having three levels each, including two tunable parameters i.e. applied voltage, frequency together with four geometric parameters i.e. size of the tumor, location of the tumor, electrode size and relative position of the electrodes w.r.t tumor were considered for analysis. Taguchi based design of experiments approach was used for the aforementioned six parameters. Using Taguchi's standard L27 orthogonal array, the required results could be obtained employing least number of experiments. For this study temperature was taken as the quality characteristic to be optimized. Furthermore, analysis of variance (ANOVA) was performed to quantify the effect of each parameter on the response variable and results were presented. To deal with the extent of thermal damage to the healthy tissue and tumor, the fraction of tissue experiencing thermal damage was calculated. For this purpose two indices namely treatment index and damage index were formulated. Finally it was concluded that maximum achieved temperature alone does not depict the effectiveness of the treatment. Rather, the combination of the maximum achieved temperature and accompanied thermal damage to the surrounding healthy tissue which should be considered.
In this article, a mathematical model describing the process of heat transfer in biological tissues with blood perfusion having different values under different temperature range for various coordinate system and different boundary conditions during thermal therapy by electromagnetic radiation is studied. Using the method of finite differences, the boundary value problem governing this process has been converted to an initial value problem of ordinary differential equations, which is solved by the Adomian decomposition method. The effects of blood perfusion rate intended for a different temperature range of temperature at target point during thermal therapy for different boundary conditions are discussed in detail. And we have also checked our results with the result of exact solutions for one case and it shows a good agreement.