Dimensionless solutions and general characteristics of bioheat transfer during thermal therapy

The derivation and application of the general characteristics of bioheat transfer for medical applications are shown in this paper. Two general bioheat transfer characteristics are derived from solutions of one-dimensional Pennes’ bioheat transfer equation: steady-state thermal penetration depth, which is the deepest depth where the heat effect reaches; and time to reach steady-state, which represents the amount of time necessary for temperature distribution to converge to a steady-state. All results are described by dimensionless form; therefore, these results provide information on temperature distribution in biological tissue for various thermal therapies by transforming to dimension form.     

Transient bioheat simulation of the laser-tissue interaction in human skin using hybrid finite element formulation

This paper presents a hybrid finite element model for describing quantitatively the thermal responses of skin tissue under laser irradiation. The model is based on the boundary integral-based finite element method and the Pennes bioheat transfer equation. In this study, temporal discretization of the bioheat system is first performed and leads to the well-known modified Helmholtz equation. A radial basis function approach and the boundary integral based finite element method are employed to obtain particular and homogeneous solutions of the laser-tissue interaction problem. In the boundary integral based finite element formulation, two independent fields are assumed: intra-element field and frame field. The intra-element field is approximated through a linear combination of fundamental solutions at a number of source points outside the element domain. The frame temperature field is expressed in terms of nodal temperature and the corresponding shape function. Numerical examples are considered to verify and assess the proposed numerical model. Sensitivity analysis is performed to explore the thermal effects of various control parameters on tissue temperature and to identify the degree of burn injury due to laser heating.     

Application of Different Variants of the BEM in Numerical Modeling of Bioheat Transfer Problems

Heat transfer processes proceeding in the living organisms are described by the different mathematical models. In particular, the typical continuous model of bioheat transfer bases on the most popular Pennes equation, but the Cattaneo-Vernotte equation and the dual phase lag equation are also used. It should be pointed out that in parallel are also examined the vascular models, and then for the large blood vessels and tissue domain the energy equations are formulated separately. In the paper the different variants of the boundary element method as a tool of numerical solution of bioheat transfer problems are discussed. For the steady state problems and the vascular models the classical BEM algorithm and also the multiple reciprocity BEM are presented. For the transient problems connected with the heating of tissue, the various tissue models are considered for which the 1st scheme of the BEM, the BEM using discretization in time and the general BEM are applied. Examples of computations illustrate the possibilities of practical applications of boundary element method in the scope of bioheat transfer problems.     

Studies on the three-dimensional temperature transients in the canine prostate during transurethral microwave thermal therapy

Thermal therapy of benign prostatic hyperplasia requires accurate prediction of the temperature distribution induced by the heating within the prostatic tissue. In this study, the Pennes bioheat transfer equation was used to model the transient heat transfer inside the canine prostate during transurethral microwave thermal therapy. Incorporating the specific absorption rate of microwave energy in tissue, a closed-form analytical solution was obtained. Good agreement was found between the theoretical predictions and in-vivo experimental results. Effects of blood perfusion and the cooling at the urethral wall on the temperature rise were investigated within the prostate during heating. The peak intraprostatic temperatures attained by application of 5, 10, or 15 W microwave power were predicted to be 38 degrees C, 41 degrees C, and 44 degrees C. Results from this study will help optimize the thermal dose that can be applied to target tissue during the therapy.     

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy.     

Theoretical analysis of thermal damage in biological tissues caused by laser irradiation

A bioheat transfer approach is proposed to study thermal damage in biological tissues caused by laser radiation. The laser light propagation in the tissue is first solved by using a robust seven-flux model in cylindrical coordinate system. The resulting spatial distribution of the absorbed laser energy is incorporated into the bioheat transfer equation for solving temperature response. Thermal damage to the tissue is assessed by the extent of denatured protein using a rate process equation. It is found that for the tissue studied, a significant protein denaturation process would take place when temperature exceeds about 53 degrees C. The effects of laser power, exposure time and beam size as well as the tissue absorption and scattering coefficients on the thermal damage process are examined and discussed. The laser conditions that cause irreversible damage to the tissue are also identified.     

A parametric study of thermal therapy of skin tissue

A thermal therapy for cancer in skin tissue is numerically investigated using three bioheat conduction models, namely Pennes, thermal wave and dual-phase lag models. A laser is applied at the surface of the skin for cancer ablation, and the temperature and thermal damage distributions are predicted using the three bioheat models and two different modeling approaches of the laser effect. The first one is a prescribed surface heat flux, in which the tissue is assumed to be highly absorbent, while the second approach is a volumetric heat source, which is reasonable if the scattering and absorption skin effects are of similar magnitude. The finite volume method is applied to solve the governing bioheat equation. A parametric study is carried out to ascertain the effects of the thermophysical properties of the cancer on the thermal damage. The temperature distributions predicted by the three models exhibit significant differences, even though the temperature distributions are similar when the laser is turned off. The type of bioheat model has more influence on the predicted thermal damage than the type of modeling approach used for the laser. The phase lags of heat flux and temperature gradient have an important influence on the results, as well as the thermal conductivity of the cancer. In contrast, the uncertainty in the specific heat and blood perfusion rate has a minor influence on the thermal damage.     

A theoretical model for peripheral tissue heat transfer using the bioheat equation of Weinbaum and Jiji

In this paper the new bioheat equation derived in Weinbaum and Jiji is applied to the three layer conceptual model of microvascular surface tissue organization proposed in. A simplified one-dimensional quantitative model of peripheral tissue energy exchange is then developed for application in limb and whole body heat transfer studies. A representative vasculature is constructed for each layer and the enhancement in the local tensor conductivity of the tissue as a function of vascular geometry and blood flow is examined. Numerical solutions for the boundary value problem coupling the three layers are presented and these results used to study the thermal behavior of peripheral tissue for a wide variety of physiological conditions from supine resting state to maximum exercise.     

Transport lattice models of heat transport in skin with spatially heterogeneous,temperature-dependent perfusion

Background  

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach.     

Conventional and newly developed bioheat transport models in vascularized tissues: A review

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.     

Experimental validation of an inverse heat transfer algorithm for optimizing hyperthermia treatments

Hyperthermia is a cancer treatment modality in which body tissue is exposed to elevated temperatures to destroy cancerous cells. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol with the goal of isolating thermal damage to predetermined treatment areas. This paper presents an algorithm to optimize a hyperthermia treatment protocol using the conjugate gradient method with the adjoint problem. The output of the minimization algorithm is a heating protocol that will cause a desired amount of thermal damage. The transient temperature distribution in a cylindrical region is simulated using the bioheat transfer equation. Temperature and time are integrated to calculate the extent of thermal damage in the region via a first-order rate process based on the Arrhenius equation. Several validation experiments are carried out by applying the results of the minimization algorithm to an albumen tissue phantom. Comparisons of metrics describing the damage region (the height and radius of the volume of thermally ablated phantom) show good agreement between the desired extent of damage and the measured extent of damage. The sensitivity of the bioheat transfer model and the Arrhenius damage model to their constituent parameters is calculated to create a tolerable range of error between the desired and measured extent of damage. The measured height and radius of the ablated region fit well within the tolerable range of error found in the sensitivity analysis.     

Computerized planning for multiprobe cryosurgery using a force-field analogy

Cryosurgery is the destruction of undesired biological tissues by freezing. For internal organs, multiple cryoprobes are inserted into the tissue with the goal of maximizing cryoinjury within a predefined target region, while minimizing cryoinjury to the surrounding tissues. The objective of this study is to develop a computerized planning tool to determine the best locations to insert the cryoprobes, based on bioheat transfer simulations. This tool is general and suitable for all available cooling techniques and hardware. The planning procedure employs a novel iterative optimization technique based on a force-field analogy. In each iteration, a single transient bioheat transfer simulation of the cryoprocedure is computed. At the end of the simulation, regions of tissue that would have undesired temperatures apply "forces" to the cryoprobes directly moving them to better locations. This method is more efficient than traditional numerical optimization techniques, because it requires significantly fewer bioheat transfer simulations for each iteration of planning. For demonstration purposes, 2D examples on cross sections typical of prostate cryosurgery are given.     

Uncertainty analysis for temperature prediction of biological bodies subject to randomly spatial heating

An analytical solution to the Pennes bioheat transfer equation in three-dimensional geometry with practical hyperthermia boundary conditions and random heating was obtained in this paper. Uncertainties for the predicted temperatures of tissues due to approximate parameters were studied based on analyzing one-dimensional heat transfer in the biological bodies subject to a spatially decay heating. Contributions from each of the thermal parameters such as heat conductivity, blood perfusion rate, and metabolic rate of the tissues, the scattering coefficient and the surface power flux of the heating apparatus were compared and the uncertainty limit for temperature distribution in this case was estimated. The results are useful in a variety of clinical hyperthermia and biological thermal parameter measurement.     

Laser-induced hyperthermia of nanoshell mediated vascularized tissue – A numerical study

Laser-induced hyperthermia treatment of tumor in a 2-D axisymmetric tissue embedded with moderate size (100–150 µm) blood vessels is studied. Laser absorption is enhanced by embedding gold–silica nanoshells in the tumor. Heat transfer in the tissue is modeled using Weinbaum–Jiji bioheat transfer equation. With laser irradiation, the volumetric radiation is accounted in the governing bioheat equation. Radiative information needed in the bioheat equation is calculated using the discrete ordinate method, and the coupled bioheat-radiation equation is solved using the finite volume method. Effects of power density, laser exposure time, beam radius, diameter of blood vessel and volume fractions of nanoshells on temperature spread in the tissue are analyzed.     

基于动态光热作用模型的激光诱导肿瘤间质热疗中的参数选择

建立了描述温控加热方式下激光诱导肿瘤间质热疗过程中动态光热作用的二维圆柱坐标下的数学模型,采用基于网格的蒙特卡罗方法数值模拟热疗过程中激光能量在非均质生物组织内的传输过程,基于Pennes生物传热方程和Arrhen ius方程数值求解组织内的温度场和热损伤体积的变化。通过数值模拟的方法分析了激光波长、激光功率、温控范围等因素对激光诱导肿瘤间质热疗中热损伤体积的影响。数值模拟的结果表明,通过选择合适的治疗参数,可以得到各种不同大小的热疗区域。本文的结果和结论对于临床治疗方案的制定具有一定的理论指导意义。     

Estimation of surface heat flux and temperature distributions in a multilayer tissue based on the hyperbolic model of heat conduction

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent surface heat flux in a skin tissue, which is stratified into epidermis, dermis, and subcutaneous layers, from the temperature measurements taken within the medium. Subsequently, the temperature distributions in the tissue can be calculated as well. The concept of finite heat propagation velocity is applied to the modeling of the bioheat transfer problem. The inverse solutions will be justified based on the numerical experiments in which two different heat flux distributions are to be determined. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors on the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent surface heat flux can be obtained for the test cases considered in this study.     

Theoretical temperature distributions produced by an annular phased array-type system in CT-based patient models

Theoretical calculations for the specific absorption rate (SAR) and the resulting temperature distributions produced by an annular phased array (APA)-type system are made. The finite element numerical method is used in the formulation of both the electromagnetic (EM) and thermal boundary value problems. A number of detailed two-dimensional patient models based on CT-scan data from the pelvic, visceral, and thoracic regions are generated to simulate a variety of tumor locations and surrounding normal tissues. The SAR values from the EM solution are put into the bioheat transfer equation, and steady-state temperature distributions are calculated for a wide range of blood flow rates. Based on our theoretical modeling, the APA shows no preferential heating of superficial over deep-seated tumors. However, in most cases for all three regions of the human trunk only fair thermal profiles (therapeutic area near 60%) are obtained in tumors with little or no blood flow and poor temperature patterns (therapeutic area less than 50%) are found in tumors with moderate to high perfusion rates. These theoretical calculations should aid the clinician in the evaluation of the effectiveness of APA-type devices in heating tumors located in the trunk region.     

Perfused phantom models of microwave irradiated tissue

The theoretical basis, practical design considerations, and prototype testing of a perfused model suitable for simulation studies of microwave heated tissue are presented. A parallel tube heat exchanger configuration is used to simulate the internal convection effects of blood flow. The global thermal response of the phantom, on a scale of several tube spacings, is shown theoretically to be nearly identical to that predicted by Pennes' bioheat equation, which is known to give a reasonable representation of tissue under many conditions. A parametric study is provided for the relationships between the tube size, spacing and material properties and the simulated perfusion rate. A prototype with a physiologically reasonable perfusion rate was tested using a typical hyperthermia applicator. The measured thermal response of the phantom compares favorably with the numerical solution of the bioheat equation under the same irradiation conditions. This similarity sheds light on the unexpected success of the bioheat equation for modeling the thermal response of real tissue.     

A new simplified bioheat equation for the effect of blood flow on local average tissue temperature

A new simplified three-dimensional bioheat equation is derived to describe the effect of blood flow on blood-tissue heat transfer. In two recent theoretical and experimental studies [1, 2] the authors have demonstrated that the so-called isotropic blood perfusion term in the existing bioheat equation is negligible because of the microvascular organization, and that the primary mechanism for blood-tissue energy exchange is incomplete countercurrent exchange in the thermally significant microvessels. The new theory to describe this basic mechanism shows that the vascularization of tissue causes it to behave as an anisotropic heat transfer medium. A remarkably simple expression is derived for the tensor conductivity of the tissue as a function of the local vascular geometry and flow velocity in the thermally significant countercurrent vessels. It is also shown that directed as opposed to isotropic blood perfusion between the countercurrent vessels can have a significant influence on heat transfer in regions where the countercurrent vessels are under 70-micron diameter. The new bioheat equation also describes this mechanism.