Heat Transfer In Biological Tissues Research Articles

Mathematical modeling of heat transfer in tissues with skin tumor during thermotherapy.

The study of thermal therapy to tumors and the response of living cells to this therapy used to treat tumor is very important due to the complexity of heat transfer in biological tissues. In the past few years, there has been a growing interest among clinicians, mathematicians, and engineers regarding the use of computational and mathematical methods to simulate biological systems. Numerous medical proceedings also employ mathematical modeling and engineering techniques as a means to guarantee their safety and evaluate the associated risks effectively. This manuscript provides an analytical solution used for the first time to study the mechanism of biological thermal response during heat therapy on spheroidal skin tumor. The proposed method used a generalized thermoelasticity model with one relaxation time. The influence of relaxation times on the responses of diseased and healthy tissues is studied and interpreted graphically. Also, the impact of different laser irradiance on the thermal profile of the malignant tumor cells over a period of 2 minutes is interpreted graphically. To investigate the transfer of heat within biological tissues during the thermal therapy, the Laplace transform and inverse Laplace transform methods were applied. A comparison of the present generalized thermoelasticity model and different models based on Pennes bioheat transfer PBT shows that our proposed model yields more realistic and accurate predictions. The current model can be used to explain various therapeutic methods.

Effect of inclined magnetic field and chemical reaction on Casson fluid flow over a stretching surface with Cattaneo–Christov double diffusion

This investigation discusses the significance of studying the behavior of non-Newtonian fluids, specifically the Casson fluid, subjected to an electrically conducting and stretching sheet. The study also explores the effects of an aligned magnetic field, Cattaneo–Christov double diffusion, viscous dissipation and chemical reactions on heat and mass transfer, respectively. The partial differential equations governing the flow problem are transformed into ordinary differential equations through the utilization of similarity transformations. Furthermore, the shooting technique is implemented in MATLAB to solve the ODEs. The influence of physical parameters, such as the magnetic field parameter, Eckert number, Prandtl number and chemical reaction parameter, on the velocity profile, temperature distribution, concentration profile, skin friction coefficient, Nusselt number and Sherwood number is studied and presented in graphical and tabular forms. It is found that increasing the Prandtl number causes a drop in the temperature profile. Moreover, the presence of thermal radiation and the Eckert number significantly amplifies the temperature distribution. When the magnetic number undergoes a substantial increase, there is a notable decrease in the velocity profile, and simultaneously, the temperature profile experiences a noticeable rise. Additionally, increase in the chemical reaction parameters leads to a decrease in the concentration profile. The skin friction coefficient, local Nusselt number and Sherwood number exhibit significant reductions as the Casson parameter increases. Additionally, a MATLAB built-in function named bvp4c is incorporated to verify the computed results. The practical implications of the Cattaneo–Christov heat flux model include microelectronics, microfluidic devices, processes involving rapid heating or cooling, such as laser welding or pulsed laser ablation and heat transfer in biological tissues.

Non-destructive estimation of temperature field during laser-induced tumor hyperthermia based on Kalman filtering

Laser-induced thermal therapy (LITT) is an emerging minimally invasive treatment technique for tumors. Non-destructive acquisition of the transient temperature field in the target tissue is a key in studying and developing LITT technology. In this paper, a non-destructive temperature field estimation scheme based on Kalman filtering theory is proposed to address the challenge of temperature field monitoring during the LITT process. This scheme establishes a state space model that corresponds to the fundamental equations of heat transfer in biological tissues. Subsequently, the real-time estimation of the transient temperature field within the target tissue is conducted by integrating the temperature observations on the surface of the tissue with the state space model of heat transfer in biological tissues and the Kalman filtering theory. Numerical experiments are conducted in this study to estimate the transient temperature field inside the target tissue during the therapy of LITT. The effect of the number of temperature observation points on the surface of the target tissue, laser irradiation conditions, and measurement noise on the estimation results of the transient temperature field within the target tissue is also discussed.

Bioheat Transfer with Thermal Memory and Moving Thermal Shocks

This article investigates the effects of thermal memory and the moving line thermal shock on heat transfer in biological tissues by employing a generalized form of the Pennes equation. The mathematical model is built upon a novel time-fractional generalized Fourier’s law, wherein the thermal flux is influenced not only by the temperature gradient but also by its historical behavior. Fractionalization of the heat flow via a fractional integral operator leads to modeling of the finite speed of the heat wave. Moreover, the thermal source generates a linear thermal shock at every instant in a specified position of the tissue. The analytical solution in the Laplace domain for the temperature of the generalized model, respectively the analytical solution in the real domain for the ordinary model, are determined using the Laplace transform. The influence of the thermal memory parameter on the heat transfer is analyzed through numerical simulations and graphic representations.

Methods of Finite Differences in the Domain of Time Applied to the Equation of Heat Biotransfer in Ocular Tissues

This article presents a methodology for two-dimensional modeling of the human eye to analyze the heat transfer in biological tissues, in this case, ocular tissues. The technique used was the finite differences method in the time domain. With a proposal for a numerical simulation of the problem, see that this type of work aims to promote the development of tools that help detect errors in biomedical engineering. Several medical procedures, including surgical ones that use laser, whose main limiting factor is the increase in temperature in living tissue, a fact that can cause irreversible damage, even evaporating. For example, refractive eye surgery using a laser. The simulation is intended to calculate the temperature gradient to guide the physician more precisely before an intervention. An example of this is certain types of inoperable tumors that can be irradiated with laser sources. Their function is to cause a rise in local temperature to destroy cancer cells without thermal damage to the healthy region.

Thermal Simulations of Cancerous Breast Tumors and Cysts on a Realistic Female Torso.

Medical thermography has been around for several decades however due to its low specificity it has not become a popular medical diagnostic technique. The development of computational models of heat transfer in biological tissue can provide a deeper knowledge of healthy and nonhealthy thermal patterns which could increase the specificity of this technique increasing its usefulness in clinical diagnosis. In this work, the thermal pattern of cancerous tumors and cysts are calculated through finite element computer simulations using a real human female torso. The simulation results show a thermal pattern that agrees with infrared thermal images taken from female subjects, the simulated thermal patterns show real thermal features that do not appear in simulations performed using other approximate geometries of the breast. Results show that the temperature on the region of the skin closest to the tumor decreases for cysts while it increases for malignant tumors. The temperature patterns show a 20% deviation from thermal simulations using a hemispherical model of the breast, these results reinforce the notion that the geometry used for thermal simulation plays an important role in the accuracy of the simulations. These results are a first step in understanding benign and malignant thermal processes of the breast which might help increase the usefulness of infrared imaging in breast clinical diagnosis.

Numerical Analysis of Breast Cancer Cell with Gold Nanoparticles Necrosis by Laser Hyperthermia

Laser hyperthermia treatment of cancer tissue is widely used in cancer treatment to destroy cancer cells. This study focus on the mechanisms of heat transfer in biological tissues to minimize damage to the tissues resulting from extra heat applied. The important feature of this method is heating of specific region to raise its temperature to a threshold temperature and destroying cancer cells without to destroy surrounding tissue. In this study, we have used the combinations of laser light and gold nanoparticles to investigate the influence of nanoparticles on the spatial distribution of temperature in the tumor and healthy tissues. Accurate simulations and solving Penne’s bio-heat transfer equation were used to solve and model the thermal tumor breast cancer in the presence of gold. Nanoparticles of some particular sizes and concentrations were selected. We would like here to stress that our attempt was a theoretical and computer model with some real and hypothesized parameters and homogeneous target. The results of this study help the doctors in the study for results of hyperthermia treatment before using it on the vivo by known the properties of the laser used and the properties of the breast tumor trying to reduce the damage of the treatment.

Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data.

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.

An analytical solution of the bioheat model in a spherical tissue due to laser irradiation

This article studies an analytical approach associated with Laplace transform, experimental temperature data and a sequential concept over time to obtain the thermal damage and the temperature in living tissue due to laser irradiation. The effects of blood perfusion and the thermal relaxation time on the temperature of skin tissues and the resulting of thermal damage are investigated. The resulting of thermal damage to the tissue is assessed by the denatured protein range using the formulation of Arrhenius. The outcomes show that the hyperbolic bioheat model is reduced to the parabolic bioheat model when the relaxation time is close to zero. The numerical outcomes of thermal injuries and temperatures are graphically introduced. In conclusion, the comparison between the numerical computations and the existing experimental study displays that a current mathematical model is an effective tool for evaluating the biological heat transfer in biological tissues.

A thermometry software tool for monitoring laser-induced interstitial thermotherapy.

The purpose of this study was to develop a thermometry software tool for temperature monitoring during laser-induced interstitial thermotherapy (LITT). C++ programming language and several libraries including DICOM Toolkit, Grassroots DICOM library, Insight Segmentation and Registration Toolkit, Visualization Toolkit and Quasar Toolkit were used. The software's graphical user interface creates windows displaying the temperature map and the coagulation extent in the tissue, determined by the magnetic resonance imaging (MRI) thermometry with the echo planar imaging sequence and a numerical simulation based on the radiation and heat transfer in biological tissues, respectively. The software was evaluated applying the MRI-guided LITT to ex vivo pig liver and simultaneously measuring the temperature through a fiber-optic thermometer as reference. Using the software, the temperature distribution determined by the MRI method was compared with the coagulation extent simulation. An agreement was shown between the MRI temperature map and the simulated coagulation extent. Furthermore, the MRI-based and simulated temperatures agreed with the measured one - a correlation coefficient of 0.9993 and 0.9996 was obtained, respectively. The precision of the MRI temperature amounted to 2.4°C. In conclusion, the software tool developed in the present study can be applied for monitoring and controlling the LITT procedure in ex vivo tissues.

Determination of an additive time- and space-dependent coefficient in the heat equation

PurposeThe purpose of this study is to provide an insight and to solve numerically the identification of an unknown coefficient of radiation/absorption/perfusion appearing in the heat equation from additional temperature measurements.Design/methodology/approachFirst, the uniqueness of solution of the inverse coefficient problem is briefly discussed in a particular case. However, the problem is still ill-posed as small errors in the input data cause large errors in the output solution. For numerical discretization, the finite difference method combined with a regularized nonlinear minimization is performed using the MATLAB toolbox routine lsqnonlin.FindingsNumerical results presented for three examples show the efficiency of the computational method and the accuracy and stability of the numerical solution even in the presence of noise in the input data.Research limitations/implicationsThe mathematical formulation is restricted to identify coefficients which separate additively in unknown components dependent individually on time and space, and this may be considered as a research limitation. However, there is no research implication to overcome this, as the known input data are also limited to single measurements of temperature at a particular time and space location.Practical implicationsAs noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Social implicationsThe identification of the additive time- and space-dependent perfusion coefficient will be of great interest to the bio-heat transfer community and applications.Originality/valueThe current investigation advances previous studies which assumed that the coefficient multiplying the lower-order temperature term depends on time or space separately. The knowledge of this physical property coefficient is very important in biomedical engineering for understanding the heat transfer in biological tissues. The originality lies in the insight gained by performing for the first time numerical simulations of inversion to find the coefficient additively dependent on time and space in the heat equation from noisy measurements.

Design, confection and calibration of a flow phantom with ultrasound applications

Ultrasound phantoms are standardized biological tissue models with well-defined acoustic properties, dimensions, and internal characteristics. Despite blood flow is a relevant factor in heat transfer in biological tissues, flow phantoms applied to therapeutic ultrasound are scarce in the literature. Therefore, this work aims to develop an ultrasound flow phantom capable of generating continuous flow with values similar to brachial artery. The phantom was made of agar based material with a tube of 4.6 mm of inner diameter inserted within, including a region of interest. The flow was produced with a linear flow propulsion system, generated by a peristaltic pump and an equalizing pressure system of milimetric graduated columns.The phantom was capable of generating adjustable and continuous flows rate. The flow rate generated by flow phantom propulsion system range between 20.85 ± 0.95 m3.s−1 and 118.36 ± 1.18 m3.s−1. Those values are similar to flow rate values in the brachial artery. We expect to apply the ultrasonic flow phantom to therapeutic ultrasound safety evaluation in testing houses.

Flow and heat transfer in biological tissue due to electromagnetic near-field exposure effects

Electromagnetic fields (EMF) have been a vital part of our daily life over the past decade. Therefore, people are continuously exposed to electromagnetic (EM) sources in their vicinity generated by electronic devices such as those emitted by Wi-Fi, mobile phones, portable wireless router and other wireless services. This study aims to investigate the SAR, fluid flow and heat transfer in biological tissue due to EM near-field exposure. In a tissue model, the effects of distance to an EMF source and tissue permeability on natural convection in the biological tissue are systematically investigated. The specific absorption rate (SAR), fluid flow and the temperature distributions in the tissue during exposure to EM fields are obtained by numerical simulation of EM wave propagation and heat transfer equations. The EM wave propagation is expressed mathematically by Maxwell’s equations. The heat transfer model used in this study is developed based on bioheat model and porous media model. By using the porous media model, the distribution patterns of temperature are quite different from the bioheat model by the strong blood dissipation effect of the porous media model. The exposure distance significantly influences the SAR, velocity field and temperature distribution. Moreover, the tissue permeability also affects the temperature distribution patterns within the tissue. The obtained results may be of assistance in determining exposure limits for the power output of the wireless transmitter, and its distance from the human body. The results can also be used as a guideline to clinical practitioners in EM relates the interaction of the radiated waves with the human body.

基于有限元分析的组织光热耦合相互作用模型

本文基于有限元分析方法，使用COMSOL Multiphysics 4.4软件，将生物组织光传输的物理场与热传输的物理场相耦合，运用间接耦合求解法和全耦合求解法分别模拟了静态光热参数和动态光热参数下生物组织的光分布和温度分布随时间的变化特征；并将静态光热参数和动态光热参数的情况相比较。结果表明：通过分析不同温度的静态光热参数下的光分布和温度分布能定性说明组织光分布和温度分布的变化趋势；使用动态光热参数进行模拟时，随着加热时间的增加，光分布范围和温度分布范围在逐渐变大，入射点的光通量密度和温度在增大，而温度随加热时间的增长变化的越来越慢。同时还表明COMSOL Multiphysics软件能够方便的求出任意时刻的温度分布及此时所对应的光分布。 This paper is based on the finite element analysis method and it couples the physical field of optical transmission with the physical field of heat transfer in biological tissue by using COMSOL Multiphysics 4.4 software. The temporal distributions of light and temperature in biological tissue were studied in the case of statically photothermal parameters and dynamically photothermal parameters by using indirectly coupled solution method and fully coupled solution method, respectively. In addition, the case of statically photothermal parameters was compared with the case of dynamically photothermal parameters. The results present that the change of light distribution and change rate of temperature in tissue can be described qualitatively by analyzing the distribution of light and temperature in the case of statically photothermal parameters of different temperature; the range of light distribution and temperature distribution are increased in the course of heating when the dynamically photothermal parameters were employed. At the same time, the light flux density and temperature of the incident point will be increased, but the change rate of temperature will be decreased when the heating time goes by. It also shows that the temperature profile at any time and the corresponding light distribution can be easily obtained by using COMSOL Multiphysics software.

The electromagnetic-thermal dosimetry for the homogeneous human brain model

The electromagnetic-thermal dosimetry model of the human brain exposed to electromagnetic (EM) radiation is developed. The EM model based on the surface integral equation (SIE) formulation is derived using the equivalence theorem for the case of a lossy homogeneous dielectric body. The thermal dosimetry model of the brain is based on the form of Pennes׳ equation for heat transfer in biological tissue. The numerical solution of the EM model is carried out using the Method of Moments (MoM) while the bioheat equation is solved using the finite element method (FEM). Developed EM-thermal model has been applied for the internal dosimetry of the human brain to assess the absorbed EM energy and the consequent temperature rise due to the exposure of 900MHz plane wave. Due to the variability of various parameters, the sensitivity of the maximum, minimum and the average steady-state temperature, on the various thermal parameters have been examined, as well as the influence of the parameters variation on the temperature distribution in case of EM exposure. The proposed model may be found useful in the rapid assessment of the temperature distribution in the human brain, prior to having to deal with a tedious development of a more complex models.

Electromagnetic-thermal dosimetry comparison of the homogeneous adult and child brain models based on the SIE approach

The results of the absorbed electromagnetic (EM) energy in brain models of adults and children due to incident plane wave of 900 MHz and 1800 MHz are presented in this paper. The specific absorption rate (SAR) in the human brain is determined using the EM model based on the surface integral equation formulation. The thermal dosimetry model is based on the form of Pennes’ equation of heat transfer in biological tissue featuring the homogeneous Neumann boundary conditions. The thermal model is handled via the finite elements method. The models of a 10-year and a 5-year-old child brain, respectively, are obtained by linearly reducing the adult one. Although the anatomical accuracy of these models is low compared to MRI-based child models, they may be found useful for rapid dosimetric assessment. The models take into account age-dependent parameters of the brain tissue via total body water concept. The numerical results of the surface electric field obtained by the three brain models are compared, as well as the calculated results of the peak and average SAR and the related temperature increase.

Bioheat transfer analysis of biological tissues induced by laser irradiation

This paper develops an analytical solution for a generalized dual phase lag (DPL) model based on the nonequilibrium heat transfer in biological tissues during laser irradiation achieved by performing volume average to the local instantaneous energy equation for blood and tissue. The obtained energy equation is solved by employing the separation of variables and Duhamel's integral method for both absorbing and scattering tissues. The generalized DPL model anticipates different results than that of the predicted by the classical DPL and Pennes bioheat transfer (parabolic) models. It is found that the generalized DPL model calculates lower temperature than that of obtained by the classical DPL model due to considering heat convection between blood vessels and tissue. The obtained analytical results are also compared with existing numerical and experimental data to verify the accuracy of the analytical solution. The results indicate that the generalized DPL model reduces to Pennes bioheat transfer model when both thermal lag times are zero. It is shown that effects of blood perfusion rate, coupling factor and the lag time τT on the temperature response of tissue are similar. Furthermore, the comparison between the analytical results and existed experimental data shows that the present mathematical model is an efficient tool for evaluation of bioheat transfer in biological tissues.

Numerical Study on non-Fourier Bio heat Transfer During Thermal Ablation

In this paper, a mathematical model describing the process of non-Fourier heat transfer in biological tissues for generalized coordinate system during thermal ablation by electromagnetic radiation with Gaussian external heat source is studied. The boundary value problem governing this process has been solved using hybrid numerical method taking Legendre wavelet basis function. The result obtained from finite element Legendre wavelet Galerkin method (FELWGM) is compared with exact analytical solution and shows a good agreement. The effect of variability of time, generalized coordinate system, location of tumor or cancer, relaxation time and external heat source coefficient on temperature distribution is discussed in detail. It has been observed that treatment of tumor or cancerous cell is independent of the generalized coordinate system at the thermal ablation position.

Simulation and Study of Temperature Distribution in Living Biological Tissues under Laser Irradiation.

With the rapid increase in use of lasers in medical treatments, it is important to understand the mechanisms of heat transfer in biological tissues in order to minimize damage to the tissues resulting from extra heat applied. The aim of this study is to investigate the temperature distribution in living biological tissues when laser irradiation is used in a treatment. In this work a model was suggested to study the impact of several parameters such as (laser power, exposure time, laser spot size) on the temperature distribution within skin tissues when subjected to a laser source. A three-dimensional finite element thermal model of biological tissues was developed using bio-heat equation to describe heat transfer in living tissues. Temperature distribution within skin tissues subjected to laser heating is calculated in details using the Finite element method and a suggested model; the results are presented in figures and tables showing the effects of Laser spot size, power and exposure time on temperature distribution within treated tissue. the results presented in this work are expected to be useful in optimizing Laser spot size, power and exposure time for a variety of laser applications medicine and surgery.

Non-Fourier bio heat transfer modelling of thermal damage during retinal laser irradiation

Study of non-Fourier energy transport is important in various biomedical applications, in the understanding of heat transfer in biological tissues. One such biomedical application that involves non-Fourier heat conduction is laser irradiation of the retina, where a high heat flux is typically applied for a short period of time. In the present study, retinal laser irradiation is analysed using the dual phase lag model for heat conduction. A simplified one-dimensional model of the human eye with seven layers is used in the simulation. The laser heating is modelled as a volumetric heat source and the respective magnitudes are calculated based on the absorptivities of the various layers. Apart from the temperature distribution, the damage distribution is also computed using the Arrhenius damage integral approach. The effect of the two phase lags τq and τT on the temperature and damage distributions are analysed. Small τT/τq ratios (⩽0.01) indicate a thermal wave like behaviour, which diminishes as the ratio increases (i.e. for τT/τq⩾0.1). The results are also compared with corresponding results from the Fourier model. Choroidal blood perfusion rate is found to have no significant effect on the unsteady temperature and damage distributions.