An inverse problem in estimating the laser irradiance and thermal damage in laser-irradiated biological tissue with a dual-phase-lag model

The aim of this study is to solve an inverse heat conduction problem to estimate the unknown time-dependent laser irradiance and thermal damage in laser-irradiated biological tissue from the temperature measurements taken within the tissue. The dual-phase-lag model is considered in the formulation of heat conduction equation. The inverse algorithm used in the study is based on the conjugate gradient method and the discrepancy principle. The effect of measurement errors and measurement locations on the estimation accuracy is also investigated. Two different examples of laser irradiance are discussed. Results show that the unknown laser irradiance and thermal damage can be predicted precisely by using the present approach 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.     

Long-term estimation of soil heat flux by single layer soil temperature

Soil heat flux is one of the important components of surface energy balance. In this study, long-term estimation of soil heat flux from single layer soil temperature was carried out by the traditional sinusoidal analytical method and the half-order time derivative method of Wang and Bras [Wang and Bras (1999) J Hydrol 216:214–226]. In order to understand the characteristics of soil heat flux and to examine the performances of the two methods, a field experiment was conducted at a temperate and humid grassland in Cork, Ireland. Our results show that the soil heat flux had the same magnitude as the sensible heat flux at this grassland site. It was also demonstrated that the analytical method did not predict the soil heat flux well because the sinusoidal assumption for the temporal variation in soil heat flux was invalid. In contrast, good agreement was found between the soil heat flux measurements and predictions made by the half-order time derivative method. This success suggests that this method could be used to estimate soil heat flux from long-term remotely sensed surface temperature.     

季节性干旱对中亚热带人工林显热和潜热通量日变化的影响

植被与大气间的显热和潜热通量的日变化是大气过程和植被生理过程的显著标志。本研究利用ChinaFLUX千烟洲站典型的夏季雨热不同季的季节性干旱的试验条件,探讨了2003年季节性干旱对该生态系统显热和潜热通量日变化变异幅度和峰值时间的影响。研究表明：显热通量的日变化变异幅度年平均值为176 W/m2。潜热通量的日变化变异幅度年平均值为171 W/m2。显热通量到达日变化峰值的时间平均为11:57。全年潜热通量的日变化都在午后达到峰值,平均值为12:33。季节性干旱造成显热通量的日变异幅度明显增大,从144W m-2增加到321 W m-2。而潜热通量的日变异幅度明显降低,从324 W/m2减小到198 W/m2。,显热和潜热通量日变异幅度的相对变化明显增大,从-165 W/m2增加到76 W/m2,气温和饱和水汽压差是影响显热和显热日变异幅度及其相对变化的主要控制因素。干旱胁迫期,深层水对显热通量日变化变异幅度及其与潜热通量日变化变异幅度的相对变化的作用更显著,而潜热通量日变化变异幅度与气象要素关系不显著。季节性干旱造成显热通量日变化的峰值时间和显热和潜热通量日变化峰值时间的相对变化明显向下午偏移,显热通量日变化的峰值从上午11:31到中午12:17,相对变化从1小时到1小时20分钟。季节性干旱对潜热通量日变化峰值时间没有显著的影响。非干旱胁迫期,显热通量日变化峰值时间和显热及潜热通量日变化峰值时间的相对变化均与气温负相关,而干旱胁迫期,则与气温正相关。潜热通量日变化峰值时间与气象要素关系均不显著。该生态系统显热和潜热通量日变化峰值的相对变化主要受降水量的季节分配控制,在干旱胁迫期降水的作用更加明显。潜热和显热通量日变化峰值时间的相对变化总体上都受植被与大气间的耦合程度控制。     

Evaluation of photobioreactor heat balance for predicting changes in culture medium temperature due to light irradiation

Microalgal photosynthesis requires appropriate culture medium temperatures to achieve high photosynthetic performance and to maintain production of a high-quality biomass product. Enclosed systems, such as our conical, helical tubular photobioreactor (HTP), can accomplish high photosynthetic efficiency and the small amount of culture medium used by these systems means that the culture medium temperature may be effectively controlled. On the other hand, because a high ratio of surface area to culture medium volume leads to rapid heating under the illumination condition and substantial heat loss at night, maintaining a suitable culture medium temperature is necessary to achieve efficient, commercially practical biomass production. In order to predict changes in the culture medium temperature caused by changes in solar irradiance and ambient temperature, it is necessary to understand the heat balance within the photobioreactor. We therefore investigated the heat balance in three major parts (photostage, degasser, and helical heat exchanger) of our conical HTP, analyzed the time-dependent changes in medium temperature at various room temperatures and radiant energy inputs, and predicted changes in the culture medium temperature based on the characteristics of heat transfer among the three parts. Using this model, the predicted changes in culture medium temperature were very similar to the changes observed experimentally in the laboratory and under field conditions. This means that by calculating the time-dependent changes in the culture medium temperature, based on measurements of solar energy input and ambient temperature, we should be able to estimate the energy required to maintain the culture medium temperature within a range where photosynthetic performance of microalgae is high.     

城市公园绿地水、热与CO2通量观测与分析

水、热和CO2通量是评价城市绿地生态效益的重要指标。在北京海淀公园中部和边缘架设涡度相关系统,连续观测和定量研究城市公园绿地影响下的通量变化特征。结果表明,公园绿地所获得的净辐射在植被生长季节大部分用于植被的蒸散作用,潜热大于显热;而在植被非生长季节大部分用于显热,潜热数值非常小。晴天显热与潜热的比值在春季随着植被枝叶的生长逐渐减少,到夏季达到最小值约1/3,在秋季随着植被叶片枯黄逐渐变大,冬季达到数倍。公园绿地能量平衡率在52%～83%,普遍存在能量不平衡。公园中部的潜热观测值大于公园边缘,而显热小于公园边缘;公园中部CO2通量日均值为负,公园绿地是CO2汇。公园绿地在植被生长季节具有明显的降温增湿、吸收CO2等生态效应。     

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.     

New mathematical model to estimate tissue blood perfusion, thermal contact resistance and core temperature

Analytical solutions were developed based on the Green's function method to describe heat transfer in tissue including the effects of blood perfusion. These one-dimensional transient solutions were used with a simple parameter estimation technique and experimental measurements of temperature and heat flux at the surface of simulated tissue. It was demonstrated how such surface measurements can be used during step changes in the surface thermal conditions to estimate the value of three important parameters: blood perfusion (w(b)), thermal contact resistance (R"), and core temperature of the tissue (T(core)). The new models were tested against finite-difference solutions of thermal events on the surface to show the validity of the analytical solution. Simulated data was used to demonstrate the response of the model in predicting optimal parameters from noisy temperature and heat flux measurements. Finally, the analytical model and simple parameter estimation routine were used with actual experimental data from perfusion in phantom tissue. The model was shown to provide a very good match with the data curves. This demonstrated the first time that all three of these important parameters (w(b), R", and T(core)) have simultaneously been estimated from a single set of thermal measurements at the surface of tissue.     

Cutaneous heat flux models do not reliably predict metabolic rates of marine mammals

Heat flux models have been used to predict metabolic rates of marine mammals, generally by estimating conductive heat transfer through their blubber layer. Recently, Kvadsheim et al. (1997) found that such models tend to overestimate metabolic rates, and that such errors probably result from the asymmetrical distribution of blubber. This problem may be avoided if reliable estimates of heat flux through the skin of the animals are obtained by using models that combine calculations of conductive heat flux through the skin and fur, and convective heat flux from the surface of the animal to the environment. We evaluated this approach based on simultaneous measurements of metabolic rates and of input parameters necessary for heat flux calculations, as obtained from four harp seals (Phoca groenlandica) resting in cold water. Heat flux estimates were made using two free convection models (double-flat-plate and cylindrical geometry) and one forced convection model (single-flat-plate geometry). We found that heat flux estimates generally underestimated metabolic rates, on average by 26-58%, and that small variations in input parameters caused large variations in these estimates. We conclude that cutaneous heat flux models are too inaccurate and sensitive to small errors in input parameters to provide reliable estimates of metabolic rates of marine mammals.     

下挖式日光温室土墙温度和热流的变化规律

2011年12月-2012年3月,在山东寿光对下挖式日光温室土质后墙不同厚度层的温度、热流进行连续测试,分析了下挖式日光温室土墙温度和热流的变化规律,确定了土墙的合理厚度.结果表明: 冬季,研究区温室墙体内侧表面、外侧覆盖层表面温度、热流的变化幅度较大,且与室内外气温的变化趋势相同.墙体温度总体上由内侧表面到外侧表面呈不断降低的趋势,墙体内侧温度、热流变化幅度较大的层次多于外侧.墙体温度、热流的变化幅度从浅层到深层依次减小.连阴天条件下,墙体内侧各层温度都有不同程度的下降,向室内放热的层次不断加深,而外侧各层次以向室外放热为主.根据墙体温度和热流的变化规律,在墙体外侧有覆盖层的情况下,把墙体从内到外划分为蓄热层、过渡层和御冷层,其厚度分别为0.8～1.0 m、2.2～2.6 m和0.4～0.6 m.在不考虑过渡层的条件下,寿光日光温室土墙厚度以1.4～1.6 m为宜.     

Parametric studies on the three-layer microcirculatory model for surface tissue energy exchange

The new three-layer microvascular mathematical model for surface tissue heat transfer developed in, which is based on detailed vascular casts and tissue temperature measurements in the rabbit thigh, is used to investigate the thermal characteristics of surface tissue under a wide variety of physiological conditions. Studies are carried out to examine the effects of vascular configuration, arterial blood supply rate, distribution of capillary perfusion, cutaneous blood circulation and metabolic heat production on the average tissue temperature profile, the local arterial-venous blood temperature difference in the thermally significant countercurrent vessels, and surface heat flux.     

Addressing the influence of instrument surface heat exchange on the measurements of CO2 flux from open-path gas analyzers

There is a growing concern in the flux community that using the eddy covariance method with open‐path CO₂ analyzers often leads to measurements of an apparent ecosystem CO₂ uptake during off‐season periods, especially in cold climates. Such uptake has not been observed when measurements were made with closed‐path analyzers, chambers, or profile methods, suggesting it is an artifact due in some way to the use of open‐path analyzers. In this study, a series of laboratory tests and field experiments were conducted to determine the magnitude of the instrument surface heat exchange in the open path and its relationship with the measured CO₂ flux. Results showed that (1) the surface of an open‐path instrument became substantially warmer than ambient due to electronics and radiation load during daytime, while at night, radiative cooling moderated temperature increases in the path; (2) high‐frequency temperature measurements inside the path were correlated with vertical wind speed producing sensible heat flux inside the instrument path exceeding the ambient heat flux by up to 14%; (3) enclosing the open‐path instrument eliminated the sensible heat flux in the path, and caused measured CO₂ flux to match a closed‐path reference; (4) using sensible heat flux measured directly inside the open path in the WPL term instead of the ambient sensible heat flux also led to a match in CO₂ flux between open‐path instrument and closed‐path reference; and (5) correcting previously collected open‐path CO₂ flux data was possible by estimating the instrument heating effect with a semi‐empirical model using standard weather variables. Results showed that all proposed techniques led to a significant reduction in apparent CO₂ uptake during off‐season periods and to a reduction of the underestimation of CO₂ release in other periods. Close agreement between the open‐path measurements and closed‐path references was achieved in all cases.     

Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet

This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.     

Coupled field analysis of heat flow in the near field of a microwave applicator for tumor ablation

Microwave tumor ablation (MTA) offers a new approach for the treatment of hepatic neoplastic disease. Reliable and accurate information regarding the heat distribution inside biological tissue subjected to microwave thermal ablation is important for the efficient design of microwave applicators and for optimizing experiments, which aim to assess the effects of therapeutic treatments. Currently there are a variety of computational methods based on different vascular structures in tissue, which aim to model heat distribution during ablation. This paper presents results obtained from two such computational models for temperature distributions produced by a clinical 2.45 GHz MTA applicator immersed in unperfused ex vivo bovine liver, and compares them with measured results from a corresponding ex vivo experiment. The computational methods used to model the temperature distribution in tissue caused by the insertion of a 5.6 mm diameter "wandlike" microwave applicator are the Green's function method and the finite element method (FEM), both of which provide solutions of the heat diffusion partial differential equation. The results obtained from the coupled field simulations are shown to be in good agreement with a simplified analysis based on the bio-heat equation and with ex vivo measurements of the heat distribution produced by the clinical MTA applicator.     

Computational hip joint simulator for wear and heat generation

This paper presents a computational simulator for the hip to compute the wear and heat generation on artificial joints. The friction produced on artificial hip joints originates wear rates that can lead to failure of the implant. Furthermore, the frictional heating can increase the wear. The developed computational model calculates the wear in the joint and the temperature in the surrounding zone, allowing the use of different combinations of joint materials, daily activities and different individuals. The pressure distribution on the joint bearing surfaces is obtained with the solution of a contact model. The heat generation by friction and the volumetric wear is computed from the pressure distribution and the sliding distance. The temperature is obtained from the solution of a transient heat conduction problem that includes the time-dependent heat generated by friction. The contact and heat conduction problems are solved numerically with the Finite Element Method. The developed computational model performs a full simulation of the acetabular bearing surface behaviour, which is useful for acetabular cup design and material selection. The results obtained by the present model agree with experimental and clinical data, as well as other numerical studies.     

A combined heat clearance method for tissue blood flow measurement.

Tissue Blood Flow is measured by applying a combined procedure of two independent approaches based on heat clearance: the Pulse Decay Method and the Continuous Method. The Pulse Method allows absolute assessment of tissue BF with no need for calibration, and can be applied only if the tissue BF is steady during the period of measurement. On the other hand, the Continuous Method enables the observation of rapid changes in tissue BF, and can be applied under non steady-state conditions. Using the combined method, a continuous quantitative measurement of transient changes in tissue BF can be obtained. For this purpose, we have developed two experimental systems consisting of independent electronic units: a Pulse Unit and a Continuous Unit. A micro-computer with dedicated software controls the operation of the electronic units and calculates tissue BF on-line. In vitro measurements are performed and demonstrate the reliability of the methods. In vivo measurements in rat brain tissue are also performed and include physiological and pharmacological changes of local tissue BF. The results of the two heat clearance methods correlate well with tissue BF values measured by a third independent method, the Hydrogen Clearance Method.     

土壤-植物-大气连续体水热、CO2通量估算模型研究进展

土壤-植物-大气连续体(SPAC)水热、CO2通量的准确估算对理解陆地和大气的物质和能量交换过程有着重要意义.重点阐述了基于过程的土壤-植物-大气连续体水热、CO2通量模型,综述了统计模型、综合模型及基于遥感的模型的发展过程.其中水热通量统计模型包括基于温度和湿度以及基于温度和辐射的方法;CO2通量统计模型包括基于气候因子或蒸散因子以及基于光能利用率的方法.水热通量过程模型包括大叶、双源、多源和多层的水热传输物理模型;CO2通量过程模型包括叶片尺度及由大叶、双叶和多层方法扩展到冠层尺度的生理生态模型以及光合-蒸腾耦合模型.综合模型包括生物物理模型、生物化学模型和生物地理模型.统计模型形式简单,资料易得,对大范围的水热通量模拟具有指导意义;过程模型准确的揭示了水热和CO2通量传输的物理和生理过程,是大尺度综合模型的基础.未来生态系统水热、CO2通量估算模型将集成各种技术手段进行多尺度网络观测和大尺度机理模拟.     

The heat transfer analysis of nanoparticle heat source in alanine tissue by molecular dynamics

The purpose of this study is to simulate the heat transfer problem when the 3-D Alanine tissue is heated by the gold nanoparticle in the field of molecular dynamics. In this paper, the Alanine molecule is adopted and its parameters are available in the GROMACS protein data bank. A computing algorithm is developed to evaluate the heat transfer phenomena in the nano-scale biological system based on the molecular dynamics and the protein data bank. The value of the thermal conductivity of Alanine is calculated from the autocorrelation function of the Green-Kubo formalism and this result has a roughly approximation with the bulk thermal conductivity reported by experimental data . Two kinds of problems are investigated in the paper. One is the Alanine tissue heated by the constant heat source and the other is by the time-varying heat source. The numerical results show that a temperature jump exists around the source and the temperature profiles drop to the environmental temperature within a very short distance. It concludes that only a small region around the nano-scale heat source is affected by the heated process. Therefore, the results of the nanoparticle-heated method could be applied to the clinical therapy of tumor, and the normal cells are destroyed only within a smaller region than those of chemotherapy or surgery.     

Eddy-correlation system for long-term monitoring of fluxes of heat, water vapour and CO2

An eddy-correlation system is presented that was designed with special focus on long-term measurements of turbulent fluxes in the atmospheric boundary layer. It consists of a SOLENT sonic anemometer, a fast temperature sensor, and a LI-COR LI 6262 closed-path infrared gas analyser. The use of a fast temperature sensor turned out to be necessary because of errors in the sound virtual temperature measured by the sonic anemometer at high wind speeds. The components are combined with special attention paid to protection against lightning and other environmental stresses. The data acquisition program SOLCOM runs on standalone systems or in a network environment and performs ‘quasi on-line’ data processing, on-line graphical display of single data and fluxes, and on-line correction of the raw data. Raw data can be stored continuously on DAT tapes. All data handling can be done by remote access, thus only a minimum amount of m situ maintenance is required. Power spectra of vertical and longitudinal wind speed, air temperature, air humidity and carbon dioxide concentration showed to follow the -2/3 law quite well. There was some noise in the high frequency range of the carbon dioxide spectrum. However, the corresponding cross spectra with the vertical wind component showed less deviation from a straight line in the high frequency range. The sum of convective heat fluxes and soil heat flux showed good agreement with the measured net radiation for several months and it was concluded that the system described here constitute a good platform for long-term flux measurements over forest.     

Temperature heterogeneity over leaf surfaces: the contribution of the lamina microtopography

Temperature is spatially heterogeneous over leaf surfaces, yet the underlying mechanisms are not fully resolved. We hypothesized that the 3D leaf microtopography determines locally the amount of incoming irradiation flux at leaf surface, thereby driving the temperature gradient over the leaf surface. This hypothesis was tested by developing a model of leaf temperature heterogeneity that includes the development of the leaf boundary layer, the microtopography of the leaf surface and the physiological response of the leaf. Temperature distributions under various irradiation loads (1) over apple leaves based on their 3D microtopography, (2) over simulated flat (2D) apple leaves and (3) over 3D leaves with a transpiration rate distributed as in 2D leaves were simulated. Accuracy of the predictions was quantified by comparing model outputs and thermographic measurements of leaf surface temperature under controlled conditions. Only the model with 3D leaves predicted accurately the spatial heterogeneity of surface temperature over single leaves, whereas the mean temperature was well predicted by both 2D and 3D leaves. We suggest that in these conditions, the 3D leaf microtopography is the primary driver of leaf surface heterogeneity in temperature when the leaf is exposed to a light/heat source.