Theoretical analysis of coupled thermal and denaturation processes in living tissues subject to a uniform surface heating condition

Abstract

In this work, we develop a theoretical study of the thermal and denaturation processes in a biological tissue subject to a surface heating, when coupled effects of dynamic changes of blood perfusion and temperature-dependent physical properties are taken into account. To analyze this phenomenon, the governing equations were appropriately nondimensionalized, where a suitable Damköhler number appears, which measures the competition between the denaturation time and the characteristic thermal diffusive time of tissue. In order to determine the denaturation front, situation that occurs when tissue has been completely denatured, we show the existence of a critical value of this dimensionless number for each time, which represents an eigenvalue in the mathematical model. Important results of the proposed model indicate that the denatured region, and the time required for carrying out this thermal process are substantially modified in comparison with the case of constant physical properties. In addition, the magnitude of the applied thermal energy source, the biological resistance of tissue to thermal attack and the blood perfusion are very important aspects that must be considered in those medical treatments that make use of rehabilitation therapies by thermal processes.