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.     

Numerical modeling of non-Fourier heat transfer and fluid flow during plasma arc welding of AISI 304 stainless steel

ABSTRACT

This paper is an attempt to study the evolution of temperature profiles and weld pool geometry during plasma arc welding (PAW) by solving the transient Navier–Stokes and Energy equations. The analysis for an AISI 304 stainless steel rectangular plate was carried out using a flexible written program in Fortran. Due to the low accuracy of the Fourier heat transfer equation for short times and large dimensions, a non-Fourier form of heat transfer equation was used. Gaussian heat source is considered as the heat source model. The fluid flow in the molten pool is of interest because it can change the temperature distribution in and around the molten zone. The governing equations for fluid flow were solved by the finite-volume method in which the SIMPLE method was utilized for pressure–velocity coupling. The effects of heat conduction, fluid flow, and force actions at the weld pool were considered. Thermo-physical properties such as thermal conductivity, specific heat, and dynamic viscosity vary as a function of temperature. There are two mechanisms involved which actively cause heat transfer to the surroundings: radiation and convection heat transfer. The numerical results are compared to the experimental data. The results corroborate that the weld pool thickness in the cross section of PAW and the time taken by molten metal to reach the end of thick metal are in good agreement with the experimental measurements. Finally, the results obtained from the assumed Fourier heat transfer are compared for the same study.     

Bio-heat transfer analysis during short pulse laser irradiation of tissues

The objective of this paper is to analyze the temperature distributions and heat affected zone in skin tissue medium when irradiated with either a collimated or a focused laser beam from a short pulse laser source. Experiments are performed on multi-layer tissue phantoms simulating skin tissue with embedded inhomogeneities simulating subsurface tumors and as well as on freshly excised mouse skin tissue samples. Two types of lasers have been used in this study – namely a Q-switched pulsed 1064 nm Nd:YAG short pulse laser having a pulse width of 200 ns and a 1552 nm diode short pulsed laser having a pulse width of 1.3 ps. Experimental measurements of axial and radial temperature distribution in the tissue medium are compared with the numerical modeling results. For numerical modeling, the transient radiative transport equation is first solved using a discrete ordinates method for obtaining the intensity distribution and radiative heat flux inside the tissue medium. Then the temperature distribution is obtained by coupling the bio-heat transfer equation with either hyperbolic non-Fourier or parabolic Fourier heat conduction model. The hyperbolic heat conduction equation is solved using MacCormack’s scheme with error terms correction. It is observed that experimentally measured temperature distribution is in good agreement with that predicted by hyperbolic heat conduction model. The experimental measurements demonstrate that converging laser beam focused directly at the subsurface location can produce desired high temperature at that location compared to that produced by collimated laser beam for the same laser parameters. Finally the ablated tissue removal is characterized using histological studies as a function of laser parameters.     

A Reduced Numerical Model for the Thermit Rail Welding Process

In this article, a reduced numerical model for the heat transfer in a commonly used Thermit rail welding procedure is presented. A geometrically reduced calculation domain was deduced from the welding system consisting of rails, weld material and mold. The geometrical domain is restricted to heat transfer in the rail web. Unsteady heat conduction in base rail and weld regions undergoing melting and solidification are modeled using the finite difference method. Therefor the consecutive periods of the process are described by specified initial and boundary conditions: preheating, tapping time, pouring and the final cooling. The solid-liquid phase change occurring during pouring and cooling is described using the enthalpy method. Thermal radiation between rail and mold surfaces is considered. Validation is carried out against results of models using computational fluid dynamics and solidus temperature isothermal positions in micrographs of longitudinal weld cuts from experiments. A sensitivity analysis was performed for the reduced model. The temperature of the liquid steel melt and the specific heat of the rail steel have the largest impact on the fusion zone width whereas mold material properties show negligible influences. The calculated width of the final fusion zone agrees within a deviation of 16% to experimental results.     

Transient simulations of heat transfer in human eye undergoing laser surgery

A validated two-dimensional computational model of the human eye solving the discretized form of the bio-heat transfer equation using finite volume formulation has been developed. Using the model, the transient temperature evolution and associated thermal effects in various regions of the human eye subjected to laser radiation during retinopathy are investigated. It is shown that the transient evolution of the retinal temperature during laser heating could reach values higher than that required for irreversible cell damage. This is because the time scale for spatial diffusion of heat towards the choroid, containing blood vessels for cooling, is much larger than that of the actual laser surgical process (100 ms). This excess temperature could cause cell damage to the adjoining retinal region due to heat diffusion. Based on the simulation results, a method is proposed to maintain the retinal pigmented epithelium (RPE) temperature close to the required 60 °C by pulsating the laser source between suitable maximum and minimum heat flux values.     

各向异性散射介质的辐射传热分析

利用Ｍｏｎｔｅ－ＣａｒｌｏＺｏｎｅ相结合的数值计算方法（简称ＭＣＺ方法）分析各向同性和各向异性散射介质的辐射换热。为了便于对照,本文选取了一维平板系统,利用编程序对各向同性散射吸收介质和线性相函数各向异性纯散射介质的半球透射率和半球反射率以及线性相函数各向异性散射吸收介质的平板中辐射传热分别进行了计算,获得了较好的结论。     

生物组织热边界条件反演研究

对肿瘤热疗过程中生物组织表面热流及内部温度协同反演进行了研究。首先介绍了激光辐照下生物组织内部光热传输模型，并采用有限体积法和离散坐标法相结合求解生物组织内光热传输问题。然后介绍了模糊推理方法基本原理，并采用改进分散模糊推理方法同时反演了激光诱导肿瘤热疗过程中生物组织表面入射热流及内部温度场。最后分析了热流形式和测量误差对反演结果的影响。结果表明，改进分散模糊推理方法可以准确地同时反演组织表面热流及内部温度分布，并具有较强稳定性和抗误差干扰能力。     

An investigation of heat transfer and fluid flow on laser micro-welding upon the thin stainless steel sheet (SUS304) using computational fluid dynamics (CFD)

A transient three-dimensional model is numerically developed using the method of computational fluid dynamics (CFD) to characterize some thermal phenomena and characterization of heat transfer and fluid flow in laser micro-welding by considering the heat source and the material interaction leads to rapid heating, melting and thermal cycles in the heating zone. The application of developed thermal models has demonstrated that the laser parameters, such as laser power, scanning velocity and spot diameter, have considerable effects on the peak temperature and resulted weld pool. The heat source model is consisted of surface heat source and adaptive volumetric heat source that could be well represented the real laser welding as the heat penetrates into the material. In the computation of melt dynamics, mass conservation, momentum and energy equations have been considered to compute the effects of melt flow and the thermo-fluid energy heat transfer. The simulation results have been compared with two sets of experimental research to predict the weld bead geometry and solidification pattern, which laser welds are made on thin stainless steel sheet (SUS304). The shape comparison describes those parameters relevant to any changes in the temperatures and melt dynamics are of great importance on the heat distribution and formation of weld pool during laser micro-welding process. The fair agreement between simulated and experimental results, demonstrates the reliability of the computed model.     

Lattice Boltzmann simulations of a radiatively participating fluid in Rayleigh–Benard convection

Thermal radiation is an integral part of the heat transfer process but it is often neglected due to the complexity involved in the analysis of radiative transfer. We use the lattice Boltzmann method as a common computational tool to solve all three modes of heat transfer: conduction, convection, and radiation. This tool is then used to analyze the effect of radiatively participating medium on Rayleigh–Benard convection. We find that increasing the effects of radiation (i) increases the critical Rayleigh number required for the onset of Rayleigh–Benard convection and (ii) affects the temperature and flow patterns of convection rolls significantly changing the net heat transfer between the hot and cold plates. Both these effects are due to the presence of radiation available as an additional mode of heat transfer. Thus, we establish that the unified lattice Boltzmann framework is an effective computational tool for heat transfer and propose to use this method for a large range of problems in science and engineering involving radiative heat transfer.     

RADIATION MODELING OF STATIONARY FUSED SILICA RODS AND FIBERS HEATED BY CO2 LASER IRRADIATION

This study presents a heat transfer model for a stationary fused silica rod heated by a CO₂ laser. During laser heating, the effect of fused silica being modeled to be opaque or semitransparent to laser irradiation is studied. The radiative heat transfer caused by the emission of fused silica is modeled using the zonal method, and compared to the Rosseland diffusion approximation. The spectral dependence of the fused silica absorption coefficient in semitransparent wavelengths is approximated by a two-band model. The weighted-sum-of-gray-gas (WSGG) method is used to calculate the radiative source term. The governing equation with conduction and radiation heat transfer is solved by the finite-volume method. The importance of modeling the effects of laser energy penetration below the fused silica surface during heating, especially for small diameter fibers, is discussed. The importance of radiative heat transfer in fused silica is also discussed. Around 25 K in temperature difference is observed when the diffusion approximation is used in place of the zonal method to model the radiative transfer in fused silica.     

RADIATION ELEMENT METHOD FOR TRANSIENT HYPERBOLIC RADIATIVE TRANSFER IN PLANE-PARALLEL INHOMOGENEOUS MEDIA

In this study the radiation element method is formulated to solve transient radiative transfer with light radiation propagation effect in scattering, absorbing, and emitting media with inhomogeneous property. The accuracy of the method is verified by good agreement between the present calculations and Monte Carlo simulations. The sensitivity of the method against element size, ray emission number, and time increment size is examined. The transient effect of radiation propagation is essential in short-pulse laser radiation transport when the input pulse width is not considerably larger than the system radiation propagation time. The transient characteristics of radiative transfer are investigated in the media subject to collimated laser irradiation and/or diffuse irradiation withtemporal Gaussian and/or square profiles. The inhomogeneous profile of extinction coefficient of the medium affects strongly the transient radiative flux divergence inside the medium.     

Multiscale Investigation of Femtosecond Laser Pulses Processing Aluminum in Burst Mode

Megahertz is the highest femtosecond laser repetition rate that the state-of-the art technology can achieve. In this article, a single femtosecond laser pulse is burst into multiple femtosecond laser pulses to process aluminum. The temporal gap between two consecutive burst pulses is 2 picoseconds, which is much shorter than the temporal gap between two consecutive pulses at the repetition rate of megahertz. By taking the thermophysical scenarios of femtosecond laser induced of electron thermalization, electron heat conduction, electron–phonon-coupled heat transfer and atomic motion into account, a multiscale framework integrating ab initio quantum mechanical calculation, molecular dynamics and two-temperature model are constructed. The effect of femtosecond laser pulse number on the incubation phenomenon is studied. Comparing with the single pulse-processing aluminum film, the femtosecond laser in burst mode leads to smaller thermal stress, which is favorable to reduce the thermal mechanical damage of the material beneath the laser-irradiated surface. Appreciable differences among the simulation results by using electron thermophysical parameters from ab initio quantum mechanical calculation and those from experimental measurement, empirical estimation and calculation are found, indicating the essentials to precisely model the electron thermal response subject to femtosecond laser excitation.     

辐射离散传播法在三维圆柱腔体辐射传热计算中的应用

运用空间解析几何理论与数值计算相结合的方法,实现了辐射离散传播法（OTM）在三维圆柱腔体内辐射传热计算的应用。采用坐标转换建立了辐射射线方程,通过直接求解所有发射点上各立体角内的辐射射线与各辐射单元体的交点,确定射线经过的路径及各交点与发射点的距离,然后按距离远近对交点进行排序,得到适合DTM法求解辐射能量传递方程的交点顺序。运用该方法对圆柱腔体内辐射换热进行三维计算,得到与精确解基本相符的结果;将DTM法运用于煤粉燃烧火焰辐射换热的计算,得到的温度场与实验结果基本一致,表面辐射热流密度分布合理,由此表明本文设计的方法是可行的。     

Successive laser-induced breakdowns in atmospheric pressure air and premixed ethane–air mixtures

Two successive focused laser pulses are employed to experimentally simulate laser-induced breakdown plasmas at high repetition rates. We find that energy absorption of the second laser pulse by the plasma produced by the first laser pulse is enhanced slightly when the time interval between the pulses is shorter than several tens of nanoseconds but falls to almost zero when the time interval is between a few hundreds of nanoseconds and several tens of microseconds. This behavior is attributed to gas heating by the first breakdown event. In premixed ethane–air mixtures, we identify another strong reduction in the second laser pulse absorption when this pulse coincides with the heat released by combustion, typically milliseconds after the first laser pulse. The fuel–air equivalence ratio (?) and base flow speed are also varied in this study. The results show that the window of reduced absorption coinciding with heat release due to combustion is narrowed when the base flow speed is increased, and also under fuel lean and fuel rich conditions. These results suggest that the use of pulsed high frequency laser breakdowns for premixed combustion stabilization is optimized when laser pulse repetition rates below a certain frequency (e.g., 500 Hz at the conditions that ? is 1 and the base flow speed is 4.9 m/s) to maximize laser energy coupling and for improved anchoring of the flame base.     

Radiative heat transfer in preforms for microstructured optical fibres

Air inclusions in any preform for microstructured optical fibres can greatly reduce conductive heat transfer. Modelling the heat transfer therefore requires that radiation be properly included. In this paper we use the Rosseland approximation to consider radiative heat transfer within the matrix material and present a method of including radiative heat transfer across the air inclusions for the first time. We apply the thermal model to the transient heating process of a silica preform with a hole structure that restricts conduction. The resultant heat transfer model yields realistic heating times.     

DSG太阳能槽式集热器动态特性

采用数值模拟方法,分析了以水,水蒸气为工质的DSG槽式集热器的动态流动与传热特性.首先建立了管内流体的一维多相流动与传热模型,并利用差分法对该模型进行求解,计算结果与现有文献数据吻合较好.分析了稳态条件下,集热器出口流体工质参数受太阳辐射强度、流体质量流量、人口温度和入口压力的影响规律.在动态分析中,研究了辐射强度变化所导致的出口参数变化特性.从阶跃响应和脉冲响应的分析中得出,虽然热惯性存在,但短期的辐射强度波动对出口温度仍有较大影响,但对出口压力的影响较小.辐射波动将对一次直通DSG系统出口温度产生很大波动.     

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.     

LASER SHORT-PULSE HEATING: INFLUENCE OF LASER POWER INTENSITY ON TEMPERATURE FIELDS

High-power-intensity and short-pulse laser heating of metallic surfaces results in thermal separation of electron and lattice subsystems. In this case, energy transport between the subsystems is governed mainly by the collisional process. Moreover, electron and lattice subsystems respond differently for different pulse intensities, despite the fact that the laser pulses have the same energy content. Consequently, in the present study, laser step-input pulse heating of gold substrate is considered and the thermal response of electron and lattice subsystems to four different intensity pulses with the same energy content is examined. The electron kinetic theory approach is introduced to model the nonequilibrium energy transport in the substrate material. It is found that electron temperature rises rapidly in the heating cycle while lattice temperature rise is gradual, which is more pronounced for laser short pulse lengths. In the cooling cycle (time after the laser pulse diminishes), electron temperature decay rate differs from the rate of lattice site temperature rise due to the specific heat ratios of electron and lattice sites.     

The influences of thermophysical properties of porous media on superadiabatic combustion with reciprocating flow

The influences of thermophysical properties of porous media on superadiabatic combustion with reciprocating flow is numerically studied in order to improve the understanding of the complex heat transfer and optimum design of the combustor. The heat transfer performance of a porous media combustor strongly depends on the thermophysical properties of the porous material. In order to explore how the material properties influence reciprocating superadiabatic combustion of premixed gases in porous media (short for RSCP), a two‐dimensional mathematical model of a simplified RSCP combustor is developed based on the hypothesis of local thermal non‐equilibrium between the solid and the gas phases by solving separate energy equations for these two phases. The porous media is assumed to emit, absorb, and isotropically scatter radiation. The finite‐volume method is used for computing radiation heat transfer processes. The flow and temperature fields are calculated by solving the mass, moment, gas and solid energy, and species conservation equations with a finite difference/control volume approach. Since the mass fraction conservation equations are stiff, an operator splitting method is used to solve them. The results show that the volumetric convective heat transfer coefficient and extinction coefficient of the porous media obviously affect the temperature distributions of the combustion chamber and burning speed of the gases, but thermal conductivity does not have an obvious effect. It indicates that convective heat transfer and heat radiation are the dominating ways of heat transfer, while heat conduction is a little less important. The specific heat of the porous media also has a remarkable impact on temperature distribution of gases and heat release rate. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 336–350, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20120     

An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

Vessel–vessel and vessel–tissue heat transfer rates are defined and explicitly quantified, for the first time, for a uniformly heated, finite, circular tissue region with two arbitrarily imbedded circular vessels and general Dirichlet boundary conditions. These heat transfer rates are obtained using an exact analytical solution for the tissue temperature field that is derived herein. Based on these heat transfer rates two different types of Poisson conduction shape factors (PCSFs) are defined. One is related to the vessel–vessel heat transfer rate (VVPCSF) and the other is related to the vessel–tissue heat transfer rates (VTPCSF). Two, conventional, alternative formulations for the VTPCSFs are studied; one is based on the difference between the average vessel wall and tissue boundary temperatures, and the other on the difference between the average vessel wall and the average tissue matrix temperatures. The effects of the angularly varying, non-uniform boundary conditions, the source term and the diameters and locations of the two vessels on these heat transfer rates and PCSFs are studied for the typical case of vessels cooling a tissue; i.e., when the average vessel wall boundary temperatures are lower than the average tissue boundary temperature. Results show that first, the effects of vessel wall temperature fluctuations on both the vessel–vessel and the vessel–tissue heat transfer rates are significant. Second, unlike the vessel wall temperature fluctuations, fluctuations at the outer tissue boundary affect only the vessel–tissue heat transfer rates. They do not affect the vessel–vessel heat transfer rates. Third, when strong fluctuations are present on the vessel walls and outer tissue boundary the shape factors are dependent on the shape of the fluctuations, and are thus very problem specific. Further, the analytical solution procedure used to derive the solution for the temperature field and the methodology developed to quantify the heat transfer rates are general and can be extended for the case of ‘N’ arbitrarily located vessels.