Microvascular Heat Transfer

Continuum models of microvascular heat transfer are intended to average over the effects of many vessels so that the blood velocity field need not be modeled in detail. Such models are usually in the form of a modified heat diffusion equation in which the effects of blood perfusion are accounted for by one or more additional terms. These equations then can be solved to yield a local average temperature that does not include the details of the temperature field around every individual vessel, but provides information on... 

Baish, J.W. (2000). Microvascular heat transfer. In The Biomedical Engineering Handbook, Bronzino, J.D. 

The value of the continuum models is that they do not require a separate solution for the blood subvolume. In each continuum formulation, the behavior of the blood vessels is modeled by introducing assumptions that allow solution of only a single differential equation. But by solving only one equation, all detailed information on the temperature of the blood in individual blood vessels is lost. Several investigators have introduced multiequation models that typically model the tissue, arteries, and veins as three separate, but interacting, subvolumes [13,17,38-40]. As with the other non-Pennes formulations, these methods are difficult to apply to particular clinical applications, but provide theoretical insights into microvascular heat transfer. 

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