| Mathematical models are developed to quantitatively analyze tissue and cellular responses to chronic in vivo heating in calves. Disks for heating and temperature measurements are implanted in the thoracic cavity. A constant heat flux is maintained at the disk surface for up to seven weeks. Tissue temperatures are measured by thermistors placed in needles at various distances from the disk surface. From temperature responses with the heat turned off and on for less than 1 hour, tissue perfusion is estimated by optimal fitting the output from a bio-heat equation to the experimental data. A quasi-steady thermal model is established to predict muscle tissue temperature for heating at 0.06--0.12 W/cm2 up to seven weeks. For chronic heating with initial tissue temperature less than 47°C, tissues adapt by increasing capillary density, which allows more capillary blood flow and reduce tissue temperature. After seven weeks of heating at 0.08 W/cm2, perfusions of muscle and lung tissues show a statistically significant increase of 3-fold and 2-fold, respectively. At a heat flux of 0.06 W/cm2, the changes are less apparent. At a heat flux of 0.04 W/cm2, the changes are negligible.;Immuno-histochemical data from muscle tissue provides the basis for quantitative analysis of cellular responses to chronic heating. With an input of 0.08 W/cm 2, capillary density significantly increases under chronic heating, i.e., angiogenesis. Above normal body temperature and below 43°C, cells express heat shock protein 70 (HSP70), proliferate, and secrete angiogenic factors, such as basic fibroblast growth factor and vascular endothelial growth factor. A mathematical model is developed to analyze the mechanistic process associated with chronic heating responses of endothelial cells, HSP70-expressing cells, and growth factors. With longer heating, the cell number densities and growth factor concentrations increase while their spatial distributions move closer to the heat source. Conversely, the thickness of heat-induced necrotic region next to the heating disk decreases with heating duration and become negligible after seven weeks. In conclusion, cellular responses to chronic heating allow tissue adaptation by increasing perfusion and heat loss, which lead to lower tissue temperature and elimination of necrotic regions. |
