Heat transfer in tissue

The exact description of convective heat transfer in tissues is mathematically intractable. In most cases, therefore, a simplified scalar term is used to describe the heat dissipation by blood. 

In the first approach, the convection term is replaced by a diffusion type" of term, and the heat transfer in tissues is described in terms of an... 

While the bio-heat transfer equation, as it stands, appears to give adequate results in several applications, a precise description of heat transfer in tissues remains a tedious but challenging problem. 

Huang, H.W., Z.P. Chen, and R.B. Roemer, A counter current vascular network model of heat transfer in tissues. /. Biomech. Eng., 1996,118 120-129. 

In the fifth part of this article (Section VI), heat transfer in tumors is discussed with application in thermography and hyperthermia. Similar to mass transfer, two theoretical approaches—lumped and distributed parameter—to describing heat transfer in normal and neoplastic tissues are described and used to predict temperature distributions during normo-and hyperthermia. Various techniques to induce localized and whole-body hyperthermia are also summarized. 

Currently, there are six major methods available for cancer treatment surgery, radiotherapy, chemotherapy, immunotherapy, hyperthermia, and photodynamic therapy. The first three are the most widely used, and the last three are under development. Surgery, radiotherapy, hyperthermia, and photodynamic therapy are primarily local, while chemotherapy and immunotherapy are primarily systemic methods. In most cases a combination of methods is used for cancer treatment. Except for surgery, the application of the remaining five methods can be improved considerably by developing quantitative understanding of mass and/or heat transfer in tumors and normal tissues. In what follows, we will discuss the problems and promises of each of these five techniques from the point of view of mass and heat transfer, and mention anti-angiogenic approaches. 

There are four major problems in analyzing heat transfer in normal and neoplastic tissues during hyperthermia ... 

It is assumed that there is perfect heat transfer between tissue and blood in the capillaries and the temperature of blood leaving the capillaries is equal to the local tissue temperature. This is not strictly correct, but it seems to be a reasonable approximation. Recently Keller (30) has pointed out that blood flowing through small vessels may serve as an effective heat transfer medium which, in effect, increases the apparent thermal conductivity of tissue. 

Thermal interaction between blood and tissue can be studied either experimentally or theoretically. However, for the following reasons it is difficult to evaluate heat transfer in a biological system ... 

The complexity of the vasculature. It is not practical to develt a comprehensive model that includes the effect of all thermally significant vessels in a tissue. Therefore, the most unusual and difficult basic problem of estimating heat transfer in living biologic systems is modeling the effect of blood circulation. 

The effects of blood flow on heat transfer in living tissue have been examined for more than a century, dating back to the experimental studies of Bernard in 1876. Since then, mathematical modeling of the complex thermal interaction between the vasculature and tissue has been a topic of interest for numerous physiologists, physicians, and engineers. A major problem for theoretical prediction of temperature distribution in tissue is the assessment of the effect of blood circulation, which is the dominant mode of heat removal and an important cause of tissue temperature inhomogeneity. 

Weinbaum-Jiji Bioheat Equation. Since 1980, researchers (Chen and Holmes, 1980 Chato, 1980 Weinbaum et al., 1984) have begun to question the validity of the Pennes bioheat equation. Later, Weinbaum and Jiji (1985) developed a new equation for microvascular blood tissue heat transfer, based on the anatomic analysis (Weinbaum et 1984), that illustrated that the predominant mode of heat transfer in the tissue was the countercurrent heat exchange between a thermally significant artery and vein pair. The near-perfect countercurrent heat exchange mechanism implies that most of the heat leaving the artery is transferred to its countercurrent vein rather than released to the sur-... 

The main limitations of the Weinbaum-Jiji equation are associated with the importance of the countercurrent heat exchange. It was derived to describe heat transfer in peripheral tissue only, where its fundamental assumptions are most applicable. In tissue area containing a big blood vessel (>200 /rm in diameter), the assumption that most of the heat leaving the artery is recaptured by its countercurrent vein could be violated, thus, it is not an accurate model to predict the temperature field. In addition, this theory was primarily developed for closely paired microvessels in muscle tissue, which may not always be the main vascular structure in other tissues, such as the renal cortex. Furthermore, unlike the Pennes equation, which requires only the value of blood perfusion, the estimation of the enhancement in thermal conductivity requires that detailed anatomical studies be performed to estimate the vessel number density, size, and artery-vein spacing for each vessel generation, as well as the blood perfusion rate (Zhu et al., 1995). These anatomic data are normally not available for most blood vessels in the thermally significant range. 

Baish, J. W., 1994, Formulation of a Statistical Model of Heat Transfer in Perfused Tissue, ASME Journal of Biomechanical Engineering, 116 521-527. 

Arkin, M., L.X. Xu, and K.R. Holmes, Recent developments in modeling heat transfer in blood perfused tissues. IEEE Trans. Biomed. Eng., 1994,41 97 107. 

Baish, J.W., Formulation of a statistical model of heat transfer in perfused tissue. J. Biomech. Eng., 1994,116 521-527. 

Assuming that skin tissue above an isothermal core is maintained at a constant body temperature, Pennes [54] proposed one of the first bioheat models to deseribe heat transfer in... 

Khaled, A.-R.A. and K. Vafai, The role of porous media in modeling flow and heat transfer in biological tissues. International Journal of Heat and Mass Transfer, 2003. 46 4989-5003. 

Van Leeuwen, G.M.J. et al.. Accuracy of geometrical modelling of heat transfer from tissue to blood vessels. Physics in Medicine and Biology, 1997. 42 1451-1460. 

Liquid metal bums are known as projections from blast furnace tap or the situation of loading with delivery of bulk into liquid metal. Metal is normally of low viscosity like water and spreads on skin and eye. Thus projections of liquid metal do not behave like viscous materials but like water and spread their enormous heat onto wide areas. When eventually cooling down, liquid metal is trapped in the conjunctival sac. When this happens, there is a maximum heat transfer with high thermoconductivity from metallic surfaces to the conjunctiva with immediate water evaporation and consecutive heat transfer from the metal to the eye up to carbonization of the tissues [16,17],... 

One of the most important factors to consider in designing a fermenter is the provision for adequate mixing of its contents. The main objectives of mixing in fermentation are to disperse the air bubbles, to suspend the microorganisms (or animal and plant tissues), and to enhance heat and mass transfer in the medium. 

PCBs are industrial compounds which were widely used as organic diluents, plasticizers, pesticide extenders, adhesives, dust-reducing agents, cutting oils, flame retardants, heat transfer fluids, dielectric fluids for transformers and capacitors, hydraulic lubricants, sealants and in carbonless copy paper. PCBs have entered the environment via multiple pathways and residues of these compounds have been identified in air, water, wildlife and human adipose tissue, serum and milk.89-91 Like many other aromatic hydrocarbons, PCBs are highly lipophilic and chemically stable and this has contributed to their environmental persistence and bioconcentration in the food chain. PCBs were originally... 

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