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.     

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.     

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.     

Thermal parameters for assessing thermal properties of clothing

1. The thermal parameters for describing clothing were summarized first (i.e., clo and tog unit, permeability index, evaporative transmissibility, permeation efficiency factor, index of water permeability). Their applications were then outlined for the calculation of heat exchange between human body and its environment, and for the prediction of the physiological variables under heat stress conditions.2. Nevertheless, the human body is not frequently exposed under steady-state condition, instead it is subjected to changes in environmental variables, clothing and activity. The transient thermal response of the human-clothing system plays a major role during transients. The heat exchange between the body and the environment may be affected significantly by the dynamic response of the clothing. The thermal comfort property of a clothing system during dynamic conditions should be assessed based on moisture vapor pressure alteration within the clothing, surface temperature of the clothing and heat loss from the body.3. There is a trend to develop overall thermal parameter to describe the transient thermal and moisture transfer properties of clothing system.     

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.     

Review on modeling heat transfer and thermoregulatory responses in human body

Several mathematical models of human thermoregulation have been developed, contributing to a deep understanding of thermal responses in different thermal conditions and applications. In these models, the human body is represented by two interacting systems of thermoregulation: the controlling active system and the controlled passive system. This paper reviews the recent research of human thermoregulation models. The accuracy and scope of the thermal models are improved, for the consideration of individual differences, integration to clothing models, exposure to cold and hot conditions, and the changes of physiological responses for the elders. The experimental validated methods for human subjects and manikin are compared. The coupled method is provided for the manikin, controlled by the thermal model as an active system. Computational Fluid Dynamics (CFD) is also used along with the manikin or/and the thermal model, to evaluate the thermal responses of human body in various applications, such as evaluation of thermal comfort to increase the energy efficiency, prediction of tolerance limits and thermal acceptability exposed to hostile environments, indoor air quality assessment in the car and aerospace industry, and design protective equipment to improve function of the human activities.     

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.     

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.     

Regression models in physiological research

Regression models play a significant role for appropriate interpretations of complex phenomena of biomedical sciences. In the present paper an attempt has been made to critically review the applications of regression models in physiological research pertaining to the solutions of various defence oriented problems of indirect estimation of human endurances, fitness, physical work capacity, energy expenditure at different work rates, body density and lean body mass from body measurements at high altitude, ventilatory 'norms' for wider age groups from physical characteristics, heat output and index finger temperature from ambient temperature, leg muscle volume and fat free mass from X-ray radiographs and stature, total body volume from anthropometric measurements, thermoregulatory efficiency at different environmental situations etc. These regression models are of practical significance for screening personnel in defence services, mines, industrial work, sports and the like.     

A self-heated thermistor technique to measure effective thermal properties from the tissue surface

A microcomputer based instrument to measure effective thermal conductivity and diffusivity at the surface of a tissue has been developed. Self-heated spherical thermistors, partially embedded in an insulator, are used to simultaneously heat tissue and measure the resulting temperature rise. The temperature increase of the thermistor for a given applied power is a function of the combined thermal properties of the insulator, the thermistor, and the tissue. Once the probe is calibrated, the instrument accurately measures the thermal properties of tissue. Conductivity measurements are accurate to 2 percent and diffusivity measurements are accurate to 4 percent. A simplified bioheat equation is used which assumes the effective tissue thermal conductivity is a linear function of perfusion. Since tissue blood flow strongly affects heat transfer, the surface thermistor probe is quite sensitive to perfusion.     

The physiological equivalent temperature – a universal index for the biometeorological assessment of the thermal environment

With considerably increased coverage of weather information in the news media in recent years in many countries, there is also more demand for data that are applicable and useful for everyday life. Both the perception of the thermal component of weather as well as the appropriate clothing for thermal comfort result from the integral effects of all meteorological parameters relevant for heat exchange between the body and its environment. Regulatory physiological processes can affect the relative importance of meteorological parameters, e.g. wind velocity becomes more important when the body is sweating. In order to take into account all these factors, it is necessary to use a heat-balance model of the human body. The physiological equivalent temperature (PET) is based on the Munich Energy-balance Model for Individuals (MEMI), which models the thermal conditions of the human body in a physiologically relevant way. PET is defined as the air temperature at which, in a typical indoor setting (without wind and solar radiation), the heat budget of the human body is balanced with the same core and skin temperature as under the complex outdoor conditions to be assessed. This way PET enables a layperson to compare the integral effects of complex thermal conditions outside with his or her own experience indoors. On hot summer days, for example, with direct solar irradiation the PET value may be more than 20 K higher than the air temperature, on a windy day in winter up to 15 K lower. Received: 14 December 1998 / Accepted: 26 May 1999     

Theory on thermal probe arrays for the distinction between the convective and the perfusive modalities of heat transfer in living tissues

Recent suggestions for an improved model of heat transfer in living tissues emphasize the existence of a convective mode due to flowing blood in addition to, or even instead of, the perfusive mode, as proposed in Pennes' "classic" bioheat equation. In view of these suggestions, it might be beneficial to develop a technique that will enable one to distinguish between these two modes of bioheat transfer. To this end, a concept that utilizes a multiprobe array of thermistors in conjunction with a revised bioheat transfer equation has been derived to distinguish between, and to quantify the perfusive and convective contribution of blood to heat transfer in living tissues. The array consists of two or more temperature sensors one of which also serves to locally insert a short pulse of heat into the tissue prior to the temperature measurements. A theoretical analysis shows that such a concept is feasible. The construction of the system involves the selection of several important design parameters, i.e., the distance between the probes, the heating power, and the pulse duration. The choice of these parameters is based on computer simulations of the actual experiment.     

哺乳动物毛被传热性能及其影响因素

毛被能够加强或减弱动物向周围环境的热量散失,毛被的形态结构和颜色是传热性能的决定因素,其传热过程往往是传导、对流和辐射3个过程的耦合。以往研究发现环境因子中,风可增加机体向环境中的散热速率,且散失量与风速正相关,且动物通过调节在风场中的姿态来适应不同风向。动物体与环境间的温差是影响散热速率的另一因素,不同环境中的动物通过改变毛被结构来适应温差变化。毛被含水率上升会引起导热和蒸发冷却作用加强,动物通过行为或毛被结构变化来调节毛被含水率。毛色决定毛被吸收和反射热辐射的能力。毛被传热性能直接把动物的生理特点与环境因子关联起来,这对揭示动物的适应、进化都具有重要意义。同时提出,毛被结构和传热性能的研究还有助于仿生学意义的挖掘。因此,今后应重点在毛被结构和物理性能、研究技术与方法以及毛被生物学和仿生学意义等方面开展研究。     

Heat transfer analysis of skin during thermal therapy using thermal wave equation

Specifying exact geometry of vessel network and its effect on temperature distribution in living tissues is one of the most complicated problems of the bioheat field. In this paper, the effects of blood vessels on temperature distribution in a skin tissue subjected to various thermal therapy conditions are investigated. Present model consists of counter-current multilevel vessel network embedded in a three-dimensional triple-layered skin structure. Branching angles of vessels are calculated using the physiological principle of minimum work. Length and diameter ratios are specified using length doubling rule and Cube law, respectively. By solving continuity, momentum and energy equations for blood flow and Pennes and modified Pennes bioheat equations for the tissue, temperature distributions in the tissue are measured. Effects of considering modified Pennes bioheat equation are investigated, comprehensively. It is also observed that blood has an impressive role in temperature distribution of the tissue, especially at high temperatures. The effects of different parameters such as boundary conditions, relaxation time, thermal properties of skin, metabolism and pulse heat flux on temperature distribution are investigated. Tremendous effect of boundary condition type at the lower boundary is noted. It seems that neither insulation nor constant temperature at this boundary can completely describe the real physical phenomena. It is expected that real temperature at the lower levels is somewhat between two predicted values. The effect of temperature on the thermal properties of skin tissue is considered. It is shown that considering temperature dependent values for thermal conductivity is important in the temperature distribution estimation of skin tissue; however, the effect of temperature dependent values for specific heat capacity is negligible. It is seen that considering modified Pennes equation in processes with high heat flux during low times is significant.     

Heat transport mechanisms in vascular tissues: a model comparison

We have conducted a parametric comparison of three different vascular models for describing heat transport in tissue. Analytical and numerical methods were used to predict the gross temperature distribution throughout the tissue and the small-scale temperature gradients associated with thermally significant blood vessels. The models are: an array of unidirectional vessels, an array of countercurrent vessels, and a set of large vessels feeding small vessels which then drain into large vessels. We show that three continuum formulations of bioheat transfer (directed perfusion, effective conductivity, and a temperature-dependent heat sink) are limiting cases of the vascular models with respect to the thermal equilibration length of the vessels. When this length is comparable to the width of the heated region of tissue, the local temperature changes near the vessels can be comparable to the gross temperature elevation. These results are important to the use of thermal techniques used to measure the blood perfusion rate and in the treatment of cancer with local hyperthermia.     

Cadmium-containing quantum dots: properties,applications, and toxicity

The marriage of biology with nanomaterials has significantly accelerated advancement of biological techniques, profoundly facilitating practical applications in biomedical fields. With unique optical properties (e.g., tunable broad excitation, narrow emission spectra, robust photostability, and high quantum yield), fluorescent quantum dots (QDs) have been reasonably functionalized with controllable interfaces and extensively used as a new class of optical probe in biological researches. In this review, we summarize the recent progress in synthesis and properties of QDs. Moreover, we provide an overview of the outstanding potential of QDs for biomedical research and innovative methods of drug delivery. Specifically, the applications of QDs as novel fluorescent nanomaterials for biomedical sensing and imaging have been detailedly highlighted and discussed. In addition, recent concerns on potential toxicity of QDs are also introduced, ranging from cell researches to animal models.

     

Human males and females body thermoregulation: Perfusion effect analysis

Skin temperature is a common physiological parameter that reflects thermal responses. Blood perfusion is an important part of the physiological processes that the human body undergoes in order to maintain homeostasis. This study focuses on the effect of perfusion on the temperature distribution in human males and females body in different thermal environment. The study has been carried out for one dimensional steady cases using finite element method. The input parameter of the model is the blood perfusion or volumetric flow rate within the tissue. The appropriate physical and physiological parameters together with suitable boundary conditions that affect the heat regulations have been incorporated in the model. The study is to have a better understanding that how does thermoregulation change in human males and females skin layered due to perfusion.     

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.