Analytical characterization of heat transport through biological media incorporating hyperthermia treatment

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. The biological media can be treated as a blood saturated tissue represented by a porous matrix. A comprehensive analytical investigation of bioheat transport through the tissue/organ is carried out including thermal conduction in tissue and vascular system, blood–tissue convective heat exchange, metabolic heat generation and imposed heat flux. Utilizing local thermal non-equilibrium model in porous media theory, exact solutions for blood and tissue phase temperature profiles as well as overall heat exchange correlations are established for the first time, for two primary tissue/organ models representing isolated and uniform temperature conditions, while incorporating the pertinent effective parameters, such as volume fraction of the vascular space, ratio of the blood and the tissue matrix thermal conductivities, interfacial blood–tissue heat exchange, tissue/organ depth, arterial flow rate and temperature, body core temperature, imposed hyperthermia heat flux, metabolic heat generation, and blood physical properties. A simplified solution based on the local thermal equilibrium between the tissue and the blood is also presented.     

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.     

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 thermal analysis of skin tissue using parabolic and hyperbolic approaches

The understanding of heat transfer in skin tissue is of utmost significance in various areas. Especially in medicine is required a precise determination of the temperature distribution for not thermally damaging healthy tissue when any region of the body is subjected to a heat treatment. The accuracy in predicting temperatures is linked to the use of adequate thermal and numerical methods. In this way, this study presents the results of a two-dimensional model to calculate transient temperature and burn injury distributions in skin tissue. Heat transfer was modeled using the Pennes' thermal model, and the mechanism of heat conduction assessed through two different approaches, classical Fourier law and non-Fourier law, characterized mathematically as parabolic and hyperbolic, respectively. The numerical solutions of the two approaches were compared to analytical solutions reported in the literature, as well as are shown various numerical results under various conditions to evaluate the differences between the two approaches to predict the temperature distribution and thermal damage.     

Transient heat transfer in a U-tube borehole heat exchanger

A transient heat transfer model has been development for a thermal response test (TRT) on a vertical borehole with a U-tube. Vertical borehole heat exchangers are frequently coupled to ground source heat pumps, which heat and cool buildings. The model provides an analytical solution for the vertical temperature profiles of the circulating fluid through the U-tube, and the temperature distribution in the ground. The model is verified with data sets from a laboratory sandbox and field TRTs, as well as a previously reported numerical solution. Unlike previous analytical models, the vertical profiles for the circulating fluid are generated by the model without any assumption of their functional form.     

Analytical solution of forced convective heat transfer in tubes partially filled with metallic foam using the two-equation model

In this study, an analytical solution for fully developed forced convection in a tube partially filled with open-celled metallic foams is presented. In the foam region, the Brinkman flow model is used to describe the fluid transport, and the local thermal non-equilibrium model is adopted to represent the fluid–solid energy exchange. At the foam–fluid interface, interfacial coupling conditions for temperature are proposed and used to derive the analytical solution. Velocity and temperature profiles are derived from this solution, and explicit expressions for the friction factor and the Nusselt number are obtained. A parametric study is conducted to study the influences of various factors on flow resistance and heat transfer performance. The present analytical solution establishes a benchmark for similar work hereafter.     

NUMERICAL STUDY ON 3-D LIGHT AND HEAT TRANSPORT IN BIOLOGICAL TISSUES EMBEDDED WITH LARGE BLOOD VESSELS DURING LASER-INDUCED THERMOTHERAPY

Tissue vasculature plays an important role in the temperature responses of biological bodies subject to laser heating. For example, interfaces between blood vessel and its surrounding tissues may lead to reflection or absorption of the coming laser light. However, most of the previous efforts just treat this by considering a collective model. To date, little attention has been paid to the effect of a single blood vessel on tissue temperature prediction during laser-induced thermotherapy. To resolve this important issue in clinics, we propose to simultaneously solve the three-dimensional (3-D) light and heat transport in several typical tissue domains with either one single blood vessel or two countercurrent blood vessels running through. Both surface and intervenient laser irradiations are considered in these studies. The 3-D heat transfer and blood flow models are established to characterize the temperature transients over the whole area. Coupled equations for heat and blood flow in multiple regions are solved using the blocking-off method. In particular, the Monte Carlo method is introduced to calculate the light transport inside the tissues as well as the blood vessel. Theoretical algorithms to deal with the complex interfaces between the tissues and vessels, and the tissue–air interface, are given. The heat generation pattern due to absorption of laser light is thus obtained by Monte Carlo simulation and then adopted into the heat and flow transport equations to predict the 3-D temperature transients over the whole domain. It is demonstrated that without considering large-size blood vessels inside the tissues, a very different temperature response is induced when subject to the same laser heating. Detailed temperature developments for the aforementioned vessel configurations are comprehensively analyzed. Implementation of the laser irradiation pattern to the clinical practices is discussed. We also test the effects of the buoyancy-driven blood flow due to laser heating on the tissue temperature response. This study may raise new issues to evaluate the contribution of a single blood vessel in modeling laser–tissue interaction. Such information is expected to be critical for accurate treatment planning in clinics.     

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.     

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.     

Analytical study of the combustion waves propagation under filtration of methane–air mixture in a packed bed

The study of combustion waves during the filtration of lean methane–air mixtures in inert porous media is carried out using the one-temperature approximation in a semi-infinite canal. The analytical solution is built in three different regions, the pre-heating region, the reaction region and the region occupied by the combustion products. By means of the solution, the temperature and mass fraction profiles of the methane are built for three regions, as well as the longitudinal extension of the reaction region, the ignition temperature of the mixture and the combustion wave propagation velocity in the system. The results obtained are validated by means of comparisons with the known numerical and analytical solutions and experimental results found in literature. Finally, an analysis of the built analytical solution in terms of five dimensionless parameters is made, which define heat and mass transport in mathematical model.     

A general bioheat model at macroscale

We develop a general bioheat transport model at macroscale for biological tissues with the required closure provided. The model shows that both blood and tissue macroscale temperatures satisfy the dual-phase-lagging (DPL) energy equations. Due to the coupled conduction between the blood and the tissue, thermal waves and possibly resonance may appear in bioheat transport. The blood–tissue interaction yields a very rich effect of the interfacial convective heat transfer, the blood velocity, the perfusion and the metabolic reaction on blood and tissue macroscale temperature fields. Examples include: (i) the spreading of tissue metabolic effect into the blood DPL bioheat equation, (ii) the appearance of the convection term in the tissue DPL bioheat equation due to the blood velocity, and (iii) the appearance of sophisticated heat source terms in energy equations for blood and tissue temperatures.     

An analytical solution for thermally fully developed combined pressure – electroosmotically driven flow in microchannels

An analytical solution is presented to study the heat transfer characteristics of the combined pressure – electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier–Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt number is obtained for a constant wall heat flux boundary condition. The fully-developed temperature profile and the Nusselt number depend on velocity field, channel height, solid/liquid interface properties and the imposed wall heat flux. A parametric study is presented to evaluate the significance of various parameters and in each case, the maximum heat transfer rate is obtained.     

Study on the Heat and Fluid Transport inside the Biological Tissues Subject to Boiling Saline-Based Tumor Hyperthermic Injection

Percutaneous hot saline injection therapy (PSIT) is becoming a very effective way of killing the target tumor in deep human body through direct heat deposition. Although the old-style injector may scald the healthy tissues along the insertion path of the needle during the operation, the newly proposed concentric tube structure of syringe by incorporating a cooling film will make the PSIT a practical method. However, as a relatively young clinical strategy for tumor treatment, the operational features of the PSIT received little attention up to now. In particular, little is known about its heating performances, and no mathematical model was ever established to characterize this behavior. To better understand the temperature responses of the living tissues subject to PSIT, this paper presents research on the modeling of heat and fluid transport inside the biological tissues when injected with hot water. Following the operational features of the new-style syringe, a one-dimensional mathematical model in spherical coordinate was proposed. Preliminary experiments through a single or multiple injections on pork tissues were performed to validate the theoretical predictions. The obtained results indicate that this model can predict well the heat and fluid transport process in the tissues heated by the injected flowing hot water and thus provide very useful information for the clinical practices. Further, parametric studies were performed to test the effects of a series of either physiological or heating parameters, such as tissue porosity, tissue and blood absorption coefficient, blood perfusion rate, injector diameter, injection velocity of hot water, or tissue position. Their implementations in PSIT are discussed, and some useful instructions for operating the PSIT are suggested. The results also indicate that the influence of blood perfusion rate may be negligible if a high degree of accuracy is not especially required. This study may find significant applications in the treatment planning of a PSIT on destroying a certain specific target tumor.     

Horizontal recirculation in water bodies due to thermal discharge

An analytical study of the steady horizontal recirculation generated due to heat rejection to a shallow water body, through a heated discharge, is carried out. The effect on the cold water intake temperature and the dependence of the flow on various governing parameters are studied. The horizontal spread of the flow is determined for various configurations and flow rates. The resulting recirculation is obtained in terms of streamlines and isotherms. The study also considers a simpler one-dimensional model. The relevance of the results obtained to practical heat rejection systems is also discussed.     

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.     

Approximate analytical solution for one-dimensional tissue freezing around cylindrical cryoprobes

An approximate analytical solution for the temperature distribution and interface motion is determined for the freezing of blood-perfused tissue around a cylindrical cryoprobe. The solution is based on an improved quasi-steady model in which assumed temperature profiles in the frozen and unfrozen tissue are used to determine the interface motion. The approximate solution satisfies all temperature boundary conditions as well as the transient heat equations at the interface. Due to blood perfusion in the unfrozen tissue, a steady state is reached where the interface becomes stationary. The solution converges to the exact steady state interface location. Improvement over the quasi-steady solution and the accuracy of the present theory are verified by comparison with numerical solutions for the limiting case of zero blood perfusion and metabolic heat production. Results show that a typical quasi-steady error of 73% is reduced to 8% using the present theory. Parametric charts are presented to evaluate the effect of the governing parameters on interface location.     

Numerical and linear regression analysis on MHD two-phase flow in an asymmetric nonuniform channel

The flow through asymmetric nonuniform (convergent) channels with the effect of the magnetic field have a pronounced impact in engineering and biological fields such as chemical and food industries, blood flow through capillaries, and arteries, and so forth. With this motivation, the present study focuses on convective hydromagnetic particulate suspension flow in an asymmetric convergent channel under the heat generation effect. The numerical method is applied to solve the nondimensionalized equations governing the transport process of fluid and particle flow and its heat. To check the convergence of the computational results, a grid independence test has been performed. A comparison test has been made to validate the results and an admirable agreement is noticed with published results. Computation results are reported for the influence of emerging parameters on the fluid as well as particle velocity and temperature profiles through graphs and tables. A method of slope linear regression through data points is presented to study the impact of various parameters on skin friction and Nusselt number. The study pioneers the investigation on the significance of the combined influence of cross-flow Reynolds number and magnetic field on fluid and particle in the convergent channel and also reports its importance on drag coefficient and rate of heat transfer at the walls. It is perceived that a reduction in fluid velocity takes place with an increment in Magnetic parameter, Grashof number, and Reynolds number. An augmentation in fluid temperature is noted with an increment in Prandtl number and heat source parameter.     

Effect of the body position on natural convection within the anterior chamber of the human eye during exposure to electromagnetic fields

ABSTRACT

Heating is the main biological effect of the electromagnetic (EM) fields to human eye. This study intends to focus attention on the differences in the heat transfer characteristics of the human eye induced by EM fields in different body positions. The effect of three different body positions – sitting, supine, and prone – on natural convection of aqueous humor (AH) in the anterior chamber of the eye is systematically investigated. The specific absorption rate (SAR) value, fluid flow, and the temperature distribution in the eye during exposure to EM fields are obtained by numerical simulation of EM wave propagation. In this study, the frequencies of 900 and 1,800 MHz are chosen for the investigations. The heat transfer model used in this study is developed based on natural convection and porous media theories. The results show that the AH temperature inside the anterior chamber is the highest in the supine position at both frequencies. It is found that during exposure to EM fields, body position plays an important role on AH natural convection and the heat transfer process within the anterior chamber and its periphery in the front part of the eye. However, the body position has no significant effect on temperature distribution for the middle part of the eye. The obtained results provide information on the body position and thermal effects from EM fields exposure.     

Fully developed electro-osmotic heat transfer in microchannels

Thermally fully developed, electro-osmotically generated convective transport has been analyzed for a parallel plate microchannel and circular microtube under imposed constant wall heat flux and constant wall temperature boundary conditions. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The result is a combination of unique electro-osmotic velocity profiles and volumetric heating in the fluid due to the imposed voltage gradient. The exact solution for the fully developed, dimensionless temperature profile and corresponding Nusselt number have been determined analytically for both geometries and both thermal boundary conditions. The fully developed temperature profiles and Nusselt number are found to depend on the relative duct radius (ratio of the Debye length to duct radius or plate gap half-width) and the magnitude of the dimensionless volumetric source.     

An experimental and theoretical study of the nonlinear heat conduction in dry porous media

Heat transfer in porous media is important in various engineering fields, including contaminated soil incineration. Most heat transfer models are theoretical in nature. Consequently, this study was undertaken to perform both theoretical and experimental studies of heat transfer in two different sand matrices. A mathematical model based on Fourier's law of heat conduction for a one‐dimensional system with the variable thermal conductivity was developed. The experimental part included heating sand samples placed in a small reactor within an infrared furnace. The transient temperature profiles of the sand layers were monitored by thermocouples. The bulk thermal conductivity was estimated to be linearly proportional to the temperature. The temperature profiles predicted by the model of heat conduction with a variable bulk thermal conductivity was compared by the observed temperatures in Quartz and Sea sands matrices up to 1300 K. Copyright © 1999 John Wiley & Sons, Ltd.