The problem of heat transfer in a single blood vessel is well understood because of its similarity to the case of duct flow. But the collective effects of the entire vasculature are not easily modeled. The primary difficulties arise from the large number of vessels, their wide range of sizes, their complicated, tree-like geometry and the time dependence of the blood flow due to thermoregulation. Most existing models are based on some sort of volume average of the energy equation that yields an effective medium theory. Typically, the blood is assumed to act as a distributed heat sink or an enhancement to the thermal conductivity of the tissue. But there has been considerable debate over the proper form of such models with the earlier work of the author suggesting that no single model is valid under all circumstances. In fact, effective medium theories may need to be discarded entirely in some cases. The aim of this research is to explore new ways of modeling heat transfer in tissue. As one approach to this problem, concepts from fractal geometry will be used to represent various vascular architectures. Another approach will be based on a recent proof of the author that blood vessels often act like conductive fibers. A new concept of bioheat transfer results: the tissue and vasculature may be viewed as a composite of conductive materials. The implications of this model have yet to be fully explored. Finally, a control systems approach will be used to investigate the role of thermoregulation on tissue-level heat transfer. This will extend existing studies of thermoregulation that emphasize the whole body or regional response. An experimental program is also planned to supplement the analytical and numerical studies. The outcome of this research will be immediately valuable to the designers of clinical equipment. A reliable underlying theory is essential to the intelligent design of heating applicators and thermal sensors. New technologies that improve safety and comfort in thermally stressful environments may also result.
