Pennes bioheat equation

Pennes Bioheat Transfer Model. It is known that one of the primary functions of blood flow in a biological system is its ability to heat or cool the tissue, depending on the relative local tissue temperature. The existence of a temperature difference between the blood and tissue is taken as evidence of its function to remove or release heat. On the basis of this speculation, Pennes [Pennes, 1948] proposed his famous bioheat transfer model, which is called Pennes bioheat equation. Pennes suggested that the effect of blood flow in the tissue be modeled as as heat source or sink term added to the traditional heat conduction equation. The Pennes bioheat equation is given by... 

Despite the limitations of the Pennes bioheat equation, reasonable agreement between theory and experiment has been obtained for the measured temperature profiles in perfused tissue subject to various heating protocols. This equation is relatively easy to use, and it allows the manipulation of two blood-related parameters, the volumetric perfusion rate and the local arterial temperature, to modify the results. Pennes performed a series of experimental studies to validate his model. Over the years, the validity of the Pennes bioheat equation has been largely based on macroscopic thermal clearance measurements in which the adjustable free parameter in the theory, the blood perfusion rate [Xu and Anderson, 1999] was chosen to provide reasonable agreement with experiments for the temperature decay in the vicinity of the thermistor bead probe. Indeed, if the limitation of Pennes bioheat equation is an inaccurate estimation of the strength of the perfusion source term, an adjustable blood perfusion rate will overcome its limitations and provide reasonable agreement between experiment and theory. 

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-... 

FIGURE 6.2 One-dimensional steady-state solution of Pennes bioheat equation for constant parameter values. 

The transient solution of Pennes bioheat equation with constant perfusion rate for an initial uniform... 

In 1948, physiologist Harry Pennes modeled the temperature profile in the human forearm by introducing the assumptions that the primary site of equilibration was the capillary bed and that each volume of tissue has a supply of arterial blood that is at the core temperature of the body. The Pennes bioheat equation has the form [25]... 

Typically, the Pennes bioheat transfer equation is used to predict the temperature transient. It is assumed fiiat the thermistor bead is small enough to be considered a point source inserted into the center of an infinitively large medium. The governing equation and initial condition for this thermal process are described as... 

Temperature Pulse Decay Technique. As described in Sec. 2.4 under Temperature Pulse Decay (TPD) Technique, local blood perfusion rate can be derived from the comparison between the dieoretically predicted and experimentally measured temperature decay of a thermistor bead probe. The details of the measurement mechanism have been described in that section. The temperature pulse decay technique has been used to measure the in vivo blood perfusion rates of different physical or physiological conditions in varimis tissues (Xu et al., 1991 1998). The advantages of this technique are that it is fast and induces little trauma. Using the Pennes bioheat transfer equation, the intrinsic thermal conductivity and blood perfusion rate can be simultaneously measured. In some of the applications, a two-parameter least-square residual fit was first performed to obtain the intrinsic therm conductivity of the tissue. This calculated value of thermal conductivity was then used to perform a one-parameter curve fit for the TPD measurements to obtain the local blood perfusion... 

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