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.     

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.     

Numerical investigation of thermal response of laser-irradiated biological tissue phantoms embedded with gold nanoshells

The work presented in this paper focuses on numerically investigating the thermal response of gold nanoshells-embedded biological tissue phantoms with potential applications into photo-thermal therapy wherein the interest is in destroying the cancerous cells with minimum damage to the surrounding healthy cells. The tissue phantom has been irradiated with a pico-second laser. Radiative transfer equation (RTE) has been employed to model the light-tissue interaction using discrete ordinate method (DOM). For determining the temperature distribution inside the tissue phantom, the RTE has been solved in combination with a generalized non-Fourier heat conduction model namely the dual phase lag bio-heat transfer model. The numerical code comprising the coupled RTE-bio-heat transfer equation, developed as a part of the current work, has been benchmarked against the experimental as well as the numerical results available in the literature. It has been demonstrated that the temperature of the optical inhomogeneity inside the biological tissue phantom embedded with gold nanoshells is relatively higher than that of the baseline case (no nanoshells) for the same laser power and operation time. The study clearly underlines the impact of nanoshell concentration and its size on the thermal response of the biological tissue sample. The comparative study concerned with the size and concentration of nanoshells showed that 60 nm nanoshells with concentration of 5×10¹⁵ mm⁻³ result into the temperature levels that are optimum for the irreversible destruction of cancer infected cells in the context of photo-thermal therapy. To the best of the knowledge of the authors, the present study is one of the first attempts to quantify the influence of gold nanoshells on the temperature distributions inside the biological tissue phantoms upon laser irradiation using the dual phase lag heat conduction model.     

计算强激光作用下生物组织中烧蚀深度的新公式

本文采用强激光对生物组织热作用的一维Stefan数学模型和反问题辨识方法,并充分考虑实际多维问题的复杂性,提出了确定强激光作用下烧蚀深度的计算关系式。由该公式得出的理论计算结果与实验数据符合得较好。     

Dual phase lag bio-heat transfer during cryosurgery of lung cancer: Comparison of three heat transfer models

The Pennes bio-heat model is based on Fourier's law of heat conduction, which assumed that a thermal signal propagate with infinite speed. This gives contradiction in physical situation. Also, the hyperbolic bio-heat model considers the micro scale response in time, but it does not explain the micro scale response in space. Therefore, to consider the thermal behaviour which is not captured by the Fourier's law and to take into account the microstructural effect in space, a dual phase lag (DPL) bio-heat conduction model would be advantageous. In this paper, a two dimensional DPL model is proposed to study the phase change heat transfer process during cryosurgery of lung cancer. The governing equations are solved numerically by enthalpy based finite difference method. The non-ideal behaviour of tissue and heat source terms, metabolism and blood perfusion are also considered. This study is made to examine the effects of phase lags in heat flux and temperature gradient on interface positions and temperature distribution during freezing process. A comparative study of DPL, parabolic and hyperbolic conduction models is thoroughly investigated. It is found that the phase lags of temperature gradient and heat flux have significant effect on interface positions and temperature distribution.     

Fast inverse prediction of the freezing front in cryosurgery

Cryosurgery has become a well-established technique for the ablation of undesirable tissues such as tumors and cancers. The motivation for this study is to improve the efficacy and safety of this technique. This study presents an inverse heat transfer method for monitoring the motion of the freezing front from a cryoprobe. With the help of a thermocouple inserted into the layer of diseased tissue, the inverse heat transfer method estimates simultaneously the blood perfusion rate and the thermal conductivities of both frozen and unfrozen tissues. This information is then fed to the Pennes bioheat equation that: (1) calculates the time-varying temperature distribution inside the layer of tissue and (2) predicts the motion of the freezing front. The effect of the most influential parameters on the inverse predictions is investigated. These parameters are (1) the initial guesses for the unknown Levenberg-Marquardt polynomial parameters of the thermo-physical properties; (2) the temperature of the cryoprobe; (3) the heat transfer coefficient of the impinging jet of liquid nitrogen; and (4) the noise on the temperature data recorded by the thermocouple probe. Results show that the proposed inverse method is a promising alternative to ultrasound and Magnetic Resonance Imaging (MRI) for monitoring the motion of the freezing front during cryosurgery. For all the cryogenic scenarios simulated, the predictions of the inverse model remain accurate and stable.     

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.     

激光照射猪肝组织的温度场研究

研究了激光照射下猪肝组织传热过程温度场空间分布的动态规律。采用有限元分析法,利用激光分布公式获得猪肝组织的温度场空间分布,并采用K型热电偶和热电偶放大器来测量猪肝组织表面和内部温度,实验测量结果和模拟结果基本吻合,同时得出血液灌注率和猪肝组织温度的关系。研究结果对于激光临床应用中激光参数的合理选择有一定的指导意义。     

Chorioretinal thermal behavior

Chorioretinal thermal response to intense light exposure is calculated for light sources with a wide variety of spatial and temporal characteristics. Transient temperature distributions are computed by means of an alternating directions implicit method for solving cylindrically symmetric heat conduction problems in biological media. Chorioretinal thermal distributions are discussed in terms of a maximum temperature damage criterion for ocular tissue.     

Laser-induced heating of dextran-coated mesocapsules containing indocyanine green

Indocyanine green (ICG) is a photosensitive reagent with clinically relevant diagnostic and therapeutic applications. Recently, ICG has been investigated for its utility as an exogenous chromophore during laser-induced heating. However, ICG's effectiveness remains hindered by its molecular instability, rapid circulation kinetics, and nonspecific systemic distribution. To overcome these limitations, we have encapsulated ICG within dextran-coated mesocapsules (MCs). Our objective in this study was to explore the ability of MCs to induce thermal damage in response to laser irradiation. To simulate tumorous tissue targeted with MCs, cylindrical phantoms were prepared consisting of gelatin, intralipid emulsion, and various concentrations of MCs. The phantoms were embedded within fresh chicken breast tissue representing surrounding normal tissue. The tissue models were irradiated at lambda = 808 nm for 10 min at constant power (P = 4.2 W). Five hypodermic thermocouples were used to record the temperature at various depths below the tissue surface and transverse distances from the laser beam central axis during irradiation. Temperature profiles were processed to remove the baseline temperature and influence of light absorption by the thermocouple and subsequently used to calculate a damage index based on the Arrhenius damage integral. Tissue models containing MCs experienced a maximum temperature change of 18.5 degrees C. Damage index calculations showed that the heat generation from MCs at these parameters is sufficient to induce thermal damage, while no damage was predicted in the absence of MCs. ICG maintains its heat-generating capabilities in response to NIR laser irradiation when encapsulated within MCs. Such encapsulation provides a potentially useful methodology for laser-induced therapeutic strategies.     

Numerical study on the thawing process of biological tissue induced by laser irradiation

Most of the laser applications in medicine and biology involve thermal effects. The laser-tissue thermal interaction has therefore received more and more attentions in recent years. However, previous works were mainly focused on the case of laser heating on normal tissues (37 degrees C or above). To date, little is known on the mechanisms of laser heating on the frozen biological tissues. Several latest experimental investigations have demonstrated that lasers have great potentials in tissue cryopreservation. But the lack of theoretical interpretation limits its further application in this area. The present paper proposes a numerical model for the thawing of biological tissues caused by laser irradiation. The Monte Carlo approach and the effective heat capacity method are, respectively, employed to simulate the light propagation and solid-liquid phase change heat transfer. The proposed model has four important features: (1) the tissue is considered as a nonideal material, in which phase transition occurs over a wide temperature range; (2) the solid phase, transition phase, and the liquid phase have different thermophysical properties; (3) the variations in optical properties due to phase-change are also taken into consideration; and (4) the light distribution is changing continually with the advancement of the thawing fronts. To this end, 15 thawing-front geometric configurations are presented for the Monte Carlo simulation. The least-squares parabola fitting technique is applied to approximate the shape of the thawing front. And then, a detailed algorithm of calculating the photon reflection/refraction behaviors at the thawing front is described. Finally, we develop a coupled light/heat transport solution procedure for the laser-induced thawing of frozen tissues. The proposed model is compared with three test problems and good agreement is obtained. The calculated results show that the light reflectance/transmittance at the tissue surface are continually changing with the progression of the thawing fronts and that lasers provide a new heating method superior to conventional heating through surface conduction because it can achieve a uniform volumetric heating. Parametric studies are performed to test the influences of the optical properties of tissue on the thawing process. The proposed model is rather general in nature and therefore can be applied to other nonbiological problems as long as the materials are absorbing and scattering media.     

Critical evaluation of indications for the holmium:YAG laser and the neodymium:YAG laser in orthopedic surgery based on an in vitro study]

This is an in vitro study of the biophysical effects of holmium:YAG and neodymium-YAG lasers that was prompted by the poor clinical results obtained with lumbar percutaneous laser discus decompression (PLDD). In the absence of adequate cooling, ablation of tissue with the holmium:YAG laser causes thermal damage to the surrounding tissues. Utilizing the immediate colour-independent laser coupling effect, the holmium:YAG laser removes soft and hard tissue immediately. The low tissue penetrating power (max. 0.32 mm), together with the use of irrigation, avoids thermal problems, and this laser type with its high pulse energy and frequency is to be recommended for arthroscopic surgery. In contrast, the effects of the neodymium:YAG laser are highly dependent on tissue colour. Using this laser on light-coloured tissue only diffuse warming but no ablation of soft tissue was often seen. The depth of tissue penetration seen in our study was 0.58 mm, but is greatly dependent on the duration of application, and is much larger with long application times. In conclusion, we believe that the neodymium:YAG laser is more suitable for percutaneous intradiscal procedures than the holmium:YAG laser. For arthroscopic surgery, the holmium:YAG laser will be the better choice. The effect of each type of laser depends not only on its physical properties, but also on tissue properties (light or dark-coloured, thermal conductivity) and duration of application.     

Equations of heat distribution within the body

A vector integral equation describing heat distribution within the body has been derived. The factors considered are heat conduction, forced convection via the circulatory system, environmental exchange, metabolic heat production, and change in heat content. The vector partial differential equation and alternative forms incorporating boundary conditions were also developed. A difference equation based on a first-order approximation to the fundamental equations was derived to form the basis of a model for heat distribution within the body. It has been shown that factors involving conduction and convection must be considered independently unless the temperature of the blood flowing from a region of the body is equal to the average temperature of the tissue in that region. If this relation between tissue and blood temperature does exist, only a single temperature from each eleeent is needed to describe the heat distribution. In this latter case, models which ascribe all heat transfer to “equivalent” conduction or to convection can give valid predictions.     

Simulation and investigation of quantum dot effects as internal heat-generator source in breast tumor site

The Pennes bio-heat transfer equation, which introduces the exchange magnitude of heat transfer between tissue and blood, is often used to solve the temperature distribution for thermal imaging and sensing. Near-infrared light has the ability to be used as a non-invasive means of diagnostic imaging within the woman's breast. Due to the diffusive nature of light in different tissue, computational model-based methods are required for functional imaging within the breast. In this article, the time-dependent bio-heat transfer is solved by a numerical method. In our model, the heat generation source (intrinsic and extrinsic) involves laser, metabolism, and quantum dot that the metabolism and heat generated by QDs are considered as intrinsic. We supposed the injected quantum dots would target the tumor site by a passive targeting process and then by interaction of laser radiation and quantum dot, the photoluminescence of quantum dot is converted to heat in the tumor site. The extra generated heat can impact on the extracted heat profile. One of the important applications of this research has led to a sensitivity improvement of the imaging system, which is potentially useful in the diagnosis and detection of breast cancer.     

Heat transfer simulation using energy conservative dissipative particle dynamics

Dissipative particle dynamics with energy conservation (eDPD) was used to investigate conduction heat transfer in two dimensions under steady-state condition. Various types of boundary condition were implemented to the conduction domain. Besides, 2D conduction with internal heat generation was studied and the heat generation term was used to measure the thermal conductivity and diffusivity of the eDPD system. The boundary conditions used include both the Neumann and Dirichlet boundary conditions. The Neumann boundary condition was applied via adiabatic surfaces and surfaces exposed to convection heat transfer. The DPD simulations were compared to analytical solutions and finite-difference techniques. It was found that DPD appropriately predicts the temperature distribution in the conduction regime. Details of boundary condition implementation and thermal diffusivity measurement are also described in this paper.     

A transient heating technique for the measurement of thermal properties of perfused biological tissue

Knowledge of tissue thermal transport properties is imperative for any therapeutic medical tool which employs the localized application of heat to perfused biological tissue. In this study, several techniques are proposed to measure local tissue thermal diffusion by heating with a focused ultrasound field. Transient as well as near steady-state heat inputs are discussed and examined for their suitability as a measurement technique for either tissue thermal diffusivity or perfusion rate. It is shown that steady-state methods are better suited for the measurement of perfusion; however the uncertainty in the perfusion measurement is directly related to knowledge of the tissue's intrinsic thermal diffusivity. Results are presented for a transient thermal pulse technique for the measurement of the thermal diffusivity of perfused and nonperfused tissues, in vitro and in vivo. Measurements conducted in plexiglas, animal muscle, kidney and brain concur with tabulated values and show a scatter from 5-15 percent from the mean; measurements made in perfused muscle and brain compare well with the nonperfused values. An estimate of the error introduced by the effect of perfusion shows that except for highly perfused kidney tissue the effect of perfusion is less than the experimental scatter. This validation of the tissue heat transfer model will allow its eventual extension to the simultaneous measurement of local tissue thermal diffusivity and perfusion.     

射频消融中温度场建立的探讨

提出了建立在射频电流组织加热和热传导基础上的射频消融中温度场建立的理论模型,初步分析了血流对温度分布提影响,得出稳定后的温度场在径向的分布基本上与ｒ及血流速度成反比;近场的温度场的建立过程的时间常数与血流速度成反比。     

The response of living tissue to pulses of a surgical CO2 laser

The response of living tissue to surgical lasers was studied numerically. An algorithm computed the crater boundaries formed by a single laser pulse and the thermochemical damage around this crater. Heat conduction and beam attenuation by tissue vapors were found to be the major factor in the reduction of cutting efficiency.     

Characterization of Thermal Transport in One-dimensional Solid Materials

The TET (transient electro-thermal) technique is an effective approach developed to measure the thermal diffusivity of solid materials, including conductive, semi-conductive or nonconductive one-dimensional structures. This technique broadens the measurement scope of materials (conductive and nonconductive) and improves the accuracy and stability. If the sample (especially biomaterials, such as human head hair, spider silk, and silkworm silk) is not conductive, it will be coated with a gold layer to make it electronically conductive. The effect of parasitic conduction and radiative losses on the thermal diffusivity can be subtracted during data processing. Then the real thermal conductivity can be calculated with the given value of volume-based specific heat (ρc_p), which can be obtained from calibration, noncontact photo-thermal technique or measuring the density and specific heat separately. In this work, human head hair samples are used to show how to set up the experiment, process the experimental data, and subtract the effect of parasitic conduction and radiative losses.