Bio-heat transfer equations

The most common representation of the spatial and temporal distribution of temperature in living systems is the so-called bio-heat transfer equation (BHTE). It was first suggested by Pennes (1948) in the following form ... 

The bio-heat transfer equation with both of these assumptions has been solved for various tissue geometries and initial and boundary conditions (Shitzer and Eberhart, 1985). Because of scalar treatment of the convective heat transport by blood, the use of the bio-heat transfer equation has been questioned repeatedly (Charny, 1992). Considering tissue as porous media, Wulff (1974, 1980) introduced the blood velocity vector ub, in the bio-heat transfer equation. Unfortunately, the complex nature of the system defies any attempt to specify the circulation vector at the microscopic level. As non-invasive technologies (e.g., MRI) provide improved spatial resolution, it may be possible to incorporate such data numerically (Dutton et al., 1992). 

A second criticism of the bio-heat transfer equation originates from the fact that it does not account for the countercurrent heat exchange in the capillary bed. Assuming that the velocity vector is one-dimensional, Mitchell and Myers (1968), and later, Keller and Seiler (1971), analyzed... 

While these various improvements in the bio-heat transfer equation provide new insight into the heat transfer process in the microvascular bed, mathematical complexity in describing the microcirculation and vascular topology makes their application to normal and neoplastic tissues... 

Once all the model parameter values are specified, the geometry of the model system must be defined. Depending upon the information desired, either a particular organ (or tissue region) or the whole mammalian body may be considered as the region in which the bio-heat transfer equation must be solved. Both of these approaches have been discussed in depth elsewhere (Shitzer and Eberhart, 1985) for application in the normal tissues therefore, we will focus our attention on tumors. 

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. 

In Chitrphiromsri and Kuznetsov s model [47] heat and moisture transport in fire fighters protective clothing dining a flash fire exposure are investigated. The garment consists of three fabric layers (outer shell, moisture barrier and thermal barrier). The skin also has three layers epidermis, dermis and subcutaneous. The bio-heat transfer equation for the skin, based on the Pennes model [54], is written as ... 

Heat efficacy is defined as the difference between the amount of heat produced and the amount of heat lost. Therefore, effective ablation can be achieved by optimizing heat production and minimizing heat loss within the area to be ablated. The relationship between these factors has been characterized as the bio-heat equation. The bio-heat equation governing RF-induced heat transfer through tissue has been previously described by Pennes (1948), with this equation simplified to a first approximation by Goldberg et al. (2000b) as follows ... 

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