Electromagnetic field-induced thermal management of biological materials

The study of temperature profiles and heat transport within the human body when subjected to electromagnetic waves is crucial for development and improvement of radiofrequency cardiac ablation treatments (radio frequency ablation). The present study provides an analytical solution for computing the temperature profiles for blood and tissue for various biological media along with heat transfer behavior during various ablation processes. The local thermal nonequilibrium model is used to characterize the bioheat transport through the biological medium. The two energy equation model for tissue and blood phase is considered. To understand the effects induced by imposed electromagnetic field, the specific absorption rate of body tissues is also studied. The results obtained have been validated against the pertinent numerical results in the literature. This study provides benchmark analytical solutions for heat transport through biological media, thereby helping in understanding the thermophysiologic response of human body toward imposed electromagnetic radiation.     

Simulation of heat transfer of biological tissue during cryosurgery based on vascular trees

During the freezing process in cryosurgery, the blood flow and blood perfusion have great influence on the heat transfer of the biological tissue. The effect of blood vessels on the temperature distribution of biological tissue is studied in this paper. The blood vessels are assumed as vascular trees using fractal methods. The method is based on the calculation of the ‘fractal dimension’ of blood vessels, considering the parameters of blood vessels and blood flows. The biological tissue is assumed as porous media and a numerical model of phase change heat transfer in biological tissue is established. The temperature distribution in biological tissue considering the effect of blood flow is simulated. The effect of the geometry of the vascular tree on the phase change heat transfer in biological tissue during cryosurgery is also analyzed.     

Numerical analysis of an equivalent heat transfer coefficient in a porous model for simulating a biological tissue in a hyperthermia therapy

An equivalent heat transfer coefficient between tissue and blood in a porous model is investigated, which is applied to the thermal analysis of a biological tissue in a hyperthermia therapy. This paper applies a finite difference method to solving the tissue temperature distribution using Pennes’ bio-heat transfer equation and a two-equation porous model, respectively, and then employs a conjugate gradient method to estimate the equivalent heat transfer coefficient in the two-equation porous model with a known perfusion rate in Pennes’ bio-heat transfer equation. The results indicate that the equivalent heat transfer coefficient is not a strong function of the perfusion rate, blood velocity and heating conditions, but is inversely related to the blood vessel diameter.     

Indirect heating strategy for laser induced hyperthermia: An advanced thermal model

A novel heating strategy based on laser irradiation of surrounding tissues as an alternative to direct irradiation of superficial tumors is proposed and analyzed for the first time. The computational analysis is based on two-dimensional axisymmetric models for both radiative transfer and transient heat transfer in the human body. A diffuse component of the radiation field is calculated using P₁ approximation. Coupled transient energy equations and kinetic equations for composite human tissue take into account the metabolic heat generation and heat conduction, blood perfusion through capillaries, the volumetric heat transfer between arterial blood and tissue, the thermal conversions in blood and tumor tissue, the periodic laser heating, and also heat exchange between a human body and ambient medium. An example problem for a superficial human cancer has been solved numerically to illustrate the relative role of the problem parameters on the transient temperature field during hyperthermia treatment. In particular, the effect of embedded gold nanoshells which strongly absorb the laser radiation is analyzed. It is shown that required parameters of tumor hyperthermia can be also reached without gold nanoshells.     

Temperature Prediction for Tumor Hyperthermia with the Behavior of Thermal Wave

In magnetic nanoparticle hyperthermia for cancer treatment, controlling the heat distribution and temperature elevations is an immense challenge in clinical applications. It is expected for treatment quality to understand the heat transport occurring in biological tissue. The non-Fourier thermal behavior in biological tissue has been experimentally observed. This work uses the thermal wave model to predict the temperature excess occurring in a two-layer concentric spherical tissue with the heat source of Gaussian distribution. The solutions to the hyperbolic bio-heat equation with the space-dependent source term in the spherical coordinate system are presented. The influences of relaxation time, blood perfusion rate, and heating strength on the thermal response in tumor and normal tissue are discussed.     

Basic natural convection in a vertical porous layer differentially heated from its sidewalls subject to lack of local thermal equilibrium

A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.     

Analysis for the dual-phase-lag bio-heat transfer during magnetic hyperthermia treatment

Magnetic fluid hyperthermia is one of hyperthermia modalities for tumor treatment. The control of temperatures is necessary and important for treatment quality. Living tissue is highly non-homogenous, and the velocity of heat transfer in it should be limited. Thus, this work analyzes the temperature rise behaviors in biological tissues during hyperthermia treatment within the dual-phase-lag model, which accounts the effect of local non-equilibrium on the thermal behavior. A small tumor surrounded by the health tissue is considered as a solid sphere. The influences of lag times, metabolic heat generation rate, blood perfusion rate, and other physiological parameters on the thermal response in tissues are investigated. While the metabolic heat generation takes little percentage of heating source, its effect on the temperature rise can be ignored. The control of the blood perfusion rate is helpful to have an ideal hyperthermia treatment. The lag times, τ_q and τ_T, affect the bio-heat transfer at the early times of heating. The total effect of τ_q and τ_T on the bio-heat transfer may be different for the same τ_T/τ_q value.     

Inductive Heating of Mg Ferrite Powder in High-Water Content Phantoms Using AC Magnetic Field for Local Hyperthermia

The purpose of this study is to elevate the temperature and induce necrosis tumor cells that include ferrite powder to 50–60°C by applying an alternating magnetic field. The achieved temperature is higher when compared to the conventional hyperthermia methods. We performed an experiment in which a high-water content agar phantom that was used as a quasi-tissue had 50 nm–10 μ m magnesium ferrite (MgFe₂O₄) dispersed in it and was then heated to a level of 190–700 kHz. The results show that the temperature of the phantom is higher for higher frequencies, larger particle sizes, and higher quantities of dispersed ferrite powder. Also, taking into account heat generation due to the magnetic powder, heat generation due to tissue metabolism, and the cooling effect of the blood flow, we solved the thermal equation related to local thermal therapy. Small differences in the distribution of ferrite powder affect the temperature increase of the tissue and the area where cell necrosis is induced.     

Influence of moving heat source on skin tissue in the context of two-temperature memory-dependent heat transport law

Abstract

Modeling and understanding heat transport and temperature variations within biological tissues and body organs are key issues in medical thermal therapeutic applications, such as hyperthermia cancer treatment. In the present analysis, the bioheat equation is studied in the context of memory responses. The heat transport equation for this problem involving the memory-dependent derivative (MDD) on a slipping interval in the context of three-phase (3P) lag model under two-temperature theory is formulated and is then used to study the thermal damage within the skin tissue during the thermal therapy. Laplace transform technique is implemented to solve the governing equations. The influences of the MDD and moving heat source velocity on the temperature of skin tissues are precisely investigated. The numerical inversion of the Laplace transform is carried out using Zakian method. The numerical outcomes of temperatures are represented graphically. Excellent predictive capability is demonstrated for identification of an appropriate procedure to select different kernel functions to reach effective heating in hyperthermia treatment. Significant effect of thermal therapy is reported due to the effect of delay time and the velocity of moving heat source as well.     

Influence of pulsatile blood flow and heating scheme on the temperature distribution during hyperthermia treatment

We conducted a numerical study to determine the influence of pulsatile laminar flow and heating protocol on temperature distribution in a single blood vessel and tumor tissue receiving hyperthermia treatment. We utilized both a physiological resting waveform at time-averaged Reynolds number of 50 and 300 and a sinusoidal waveform in this investigation. The arterial wall was modeled using the volume-averaged porous media equations. Discretization of the transport equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. We validated our numerical model by comparing it with previously published results in literature. Our results indicate that the choice of waveform significantly influences the findings concerning temperature distribution and heat transfer rate during hyperthermia treatment. A comprehensive analysis of the influence of blood velocity pulsations and blood vessel size on temperature uniformity of tissues undergoing hyperthermia treatment is presented in detail. The results of the present investigation illustrate that large vessels have a profound effect on the heat transfer characteristics in tissues receiving hyperthermia treatment. The results of this work may enhance current understanding of the factors that determine the effect of hyperthermia treatment on tumor tissues.     

Thermal action of a short light pulse on biological tissues

A simple model for optical and thermal properties of two-component biological tissues is proposed as applied to studies of thermal fields under external illumination. The model comprises a small number of varying input parameters to enable one to find all the optical characteristics required to compute light fields in tissue and to state the thermal source function. Thermal parameters of tissues determining heat transfer in a two-component medium are calculated with accounting for heat exchange conditions between the components and at the interface with various external media. A set of heat conduction equations is stated for the two-component medium simulating biological tissues. Its analytical solution is derived. Spatial distributions of the fluence rate and temperature over the tissue depth are investigated at varying time moments after the irradiation by a short light pulse. Localized absorption of light by blood vessels and its effect on optical parameters of the medium, more intense heating of blood as compared with its surrounding (basic) tissue and heat exchange between the blood and tissue, as well as heat transfer at the interface with different environments are taken into account. The solutions are derived via characteristic times of thermal processes to enable one to easy and vividly evaluate the features in tissue heating as well as the effects of optical and thermal parameters on temperature distributions of the components. The calculations are illustrated by examples.     

Analysis of temperature gradient bifurcation in porous media – An exact solution

The phenomenon of temperature gradient bifurcation in a porous medium is analyzed by studying the convective heat transfer process within a channel filled with a porous medium, with internal heat generation. A local thermal non-equilibrium (LTNE) model is used to represent the energy transport within the porous medium. Exact solutions are derived for both the fluid and solid temperature distributions for two primary approaches (Models A and B) for the constant wall heat flux boundary condition. The Nusselt number for the fluid at the channel wall is also obtained. The effects of the pertinent parameters such as fluid and solid internal heat generations, Biot number and fluid to solid thermal conductivity ratio are discussed. It is shown that the internal heat generation in the solid phase is significant for the heat transfer characteristics. The validity of the one equation model is investigated by comparing the Nusselt number obtained from the LTNE model with that from the local thermal equilibrium (LTE) model. The results demonstrate the importance of utilizing the LTNE model in the present study. The phenomenon of temperature gradient bifurcation for the fluid and solid phases at the wall for Model A is established and demonstrated. In addition, the temperature distributions for Models A and B are compared. A numerical study for the constant temperature boundary condition was also carried out. It was established that the phenomenon of temperature gradient bifurcation for the fluid and solid phases for the constant temperature boundary condition can occur over a given axial region.     

Estimation of temperature distribution in biological tissue by using solutions of bioheat transfer equation

A living body has a system for maintaining its temperature. We have investigated the heat transfer characteristics common to each organ and therapy using heat transfer. The one‐dimensional bioheat transfer equation with bioheat generation was converted into a dimensionless form and solved by Laplace transformation on the assumption that biological tissue is homogeneous. A dimensionless steady‐state solution and transient solution were derived analytically. These solutions can represent the characteristics of the temperature distribution common to each organ. Comparison with numerical solutions has confirmed that these solutions can be applied to estimate the temperature distribution of inhomogeneous biological tissue. It is proved that the size of the region where temperature change occurs, the steady‐state thermal penetration depth, is decided by biological properties. Furthermore, the time needed to reach a steady state, or the time it takes for biological tissue to reach a steady state, is calculated by using these solutions. Additionally, a temperature chart was proposed for each organ or tissue. This chart can serve as a guideline for medical doctors in formulating thermal therapy. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 374– 386, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20210     

Thermal analysis of a 2-D heat recovery system using porous media including lattice Boltzmann simulation of fluid flow

The present work deals with the fluid flow simulation and thermal analysis of a two-dimensional heat recovery system using porous media. A basic high-temperature flow system is considered in which a high-temperature non-radiating gas flows through a random porous matrix. The porous medium, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. It is desirable to have large amount of radiative heat flux from the porous segment in the upstream direction (towards the thermal system). The lattice Boltzmann method (LBM) is used to simulate fluid flow in the porous medium. The gas and solid phases are considered in non-local thermal equilibrium, and separate energy equations are applied to these phases. Convection, conduction and radiation heat transfers take place simultaneously in solid phase, but in the gas flow, heat transfer occurs by conduction and convection. In order to analyze the thermal characteristics of the heat recovery system, volume-averaged velocities through the porous matrix obtained by LBM are used in the gas energy equation and then the coupled energy equations for gas and porous medium are numerically solved using finite difference method. For computing of radiative heat flux in the porous medium, discrete ordinates method is used to solve the radiative transfer equation. Finally the effect of various parameters on the performance of porous heat recovery system is studied.     

Investigation for the dual phase lag behavior of bio-heat transfer

The success of hyperthermia treatment depends on the precise prediction and control of temperature distribution in the tissue. It was absolutely a necessity for hyperthermia treatment planning to understand the heat transport occurring in biological tissue. The tissue is highly non-homogenous, and non-Fourier thermal behavior in biological tissue has been experimentally observed. The dual phase lag model of heat conduction has been used to interpret the non-Fourier thermal behavior. This work attempts to be an extension study of Antaki [12] and explore whether the DPL thermal behavior exists in tissue. The inverse non-Fourier bio-heat transfer problem in the bi-layer spherical geometry is analyzed. In order to further address whether the dual phase lag model of bio-heat transfer merits additional study, the comparisons of the history of temperature increase among the present calculated results, the calculated values from the classical bio-heat transfer equation, and the experimental data are made for various measurement locations.     

Thermomechanical response of porous biological tissue based on local thermal non-equilibrium

Abstract

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.     

Free convection of composite porous medium in a vertical channel

A fully developed free convection flow of immiscible fluids in a vertical channel filled with a porous medium is analyzed in the presence of source/sink. The flow is modeled using the Darcy–Brinkman–Forchheimer equation model. The viscous and Darcy dissipation terms are included in the energy equation. The channel walls are maintained at two different constant temperatures. The transport properties of both fluids are assumed to be constant. Continuous conditions for velocity, temperature, shear stress, and heat flux of both fluids at the interface are employed. The resulting coupled nonlinear equations are solved analytically using regular perturbation method and numerically using finite difference method. The velocity and temperature profiles are obtained in terms of porous parameter, Grashof number, viscosity ratio, width ratio, conductivity ratio, and heat generation or heat absorption coefficient. It is found that the presence of porous matrix and heat absorption reduces the flow field. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20340     

Combined Mode Conduction and Radiation Heat Transfer in a Porous Medium and Estimation of the Optical Properties of the Porous Matrix

This article deals with the analysis of combined mode conduction and radiation heat transfer in a porous medium, and simultaneous estimation of the optical properties of the porous matrix. Simultaneous solution of the gas- and solid-phase energy equations encompasses local thermal nonequilibrium, while the convective heat exchange term couples the gas- and the solid-phase energy equations. A localized uniform volumetric heat generation zone is the source of heat transfer in the porous matrix. With volumetric radiative information needed in the solid-phase energy equation computed using the discrete transfer method, the solid- and gas-phase energy equations are simultaneously solved using the finite difference method. For a given set of boundary conditions and operating parameters, the computed temperature distribution serves as the exact temperature profile necessary in the estimation of parameters. In the estimation of parameters using inverse analysis, the objective function is minimized using the genetic algorithm. Effects of measurement error, number of generations, population size, crossover probability, and mutation probability are studied in regard to the accuracy of results and the computational time required. Reasonably accurate estimations of extinction coefficient, scattering albedo, and emissivity of the porous matrix are obtained.     

Modeling of turbulent heat transfer and thermal dispersion for flows in flat plate heat exchangers

In this paper, heat transfer and dispersion for both laminar and turbulent regimes in heat exchangers and nuclear cores are considered. Such hydraulic systems might be seen as spatially periodic porous media. The existence of a turbulent flow within a porous medium structure suggests the use of a spatial average operator, combined to a statistical average operator. Previous works [M.H.J. Pedras, M.J.S. De Lemos, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer 44 (2001) 1081–1093; F. Kuwahara, A. Nakayama, H. Koyama, A numerical study of thermal dispersion in porous medium, J. Heat Transfer 118 (1996) 756–761] have applied a double average procedure to the thermal balance equation, which led to a macroscopic turbulent transport and a subsequent macro-scale equation featuring dynamic dispersion. Considering the heat flux at the solid surfaces as a boundary condition for the fluid energy balance, the model proposed in this paper allows one to take into account this dispersion as the sum of two contributions. The first one is the classical dispersion due to velocity heterogeneities [G. Taylor, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203] and the second one is due to wall heat transfer. Applying Whitaker up-scaling method [S. Whitaker, Theory and applications of transport in porous media: the method of volume averaging, Kluwer Academic Publishers, 1999], a “closure problem” is then derived for a representative elementary volume, using the so-called Boussinesq approximation to account for small scale turbulence. The model is used to compute macro-scale heat transfer properties for turbulent flows inside a flat plate heat exchanger. It is shown that, for such flows, both dispersive fluxes strongly predominate over the macroscopic turbulent heat flux.     

A general bioheat transfer model based on the theory of porous media

A volume averaging theory (VAT) established in the field of fluid-saturated porous media has been successfully exploited to derive a general set of bioheat transfer equations for blood flows and its surrounding biological tissue. A closed set of macroscopic governing equations for both velocity and temperature fields in intra- and extravascular phases has been established, for the first time, using the theory of anisotropic porous media. Firstly, two individual macroscopic energy equations are derived for the blood flow and its surrounding tissue under the thermal non-equilibrium condition. The blood perfusion term is identified and modeled in consideration of the transvascular flow in the extravascular region, while the dispersion and interfacial heat transfer terms are modeled according to conventional porous media treatments. It is shown that the resulting two-energy equation model reduces to Pennes model, Wulff model and their modifications, under appropriate conditions. Subsequently, the two-energy equation model has been extended to the three-energy equation version, in order to account for the countercurrent heat transfer between closely spaced arteries and veins in the circulatory system and its effect on the peripheral heat transfer. This general form of three-energy equation model naturally reduces to the energy equations for the tissue, proposed by Chato, Keller and Seiler. Controversial issues on blood perfusion, dispersion and interfacial heat transfer coefficient are discussed in a rigorous mathematical manner.