Temperature response in biological tissue by alternating heating and cooling modalities with sinusoidal temperature oscillation on the skin

This study investigates the transient temperature response in biological tissue immersed in warm and cold water alternately with a sinusoidal temperature oscillation on the skin surface to simulate the contrast therapy which uses alternatively heat and cold modalities in subacute and chronic conditions. In addition, this type of analysis is also applied to assessing the blood perfusion rate in the skin through noninvasive technology by imposing a periodic temperature load onto the skin surface and then measuring the phase shift of the resulting surface heat flux. Based on the Pennes bio-heat transfer equation, the Laplace transform is used to derive an exact solution to the temperature variation in the tissue from the initial oscillation to the final steady periodic oscillation. Furthermore, the solutions to special cases under no perfusion rate, constant temperature, and the combination of these two assumptions are demonstrated in this study. The results show that both a larger perfusion rate and a greater tissue depth decrease the amplitude of the sinusoidal temperature response. Meanwhile, a larger perfusion rate can reduce the phase angle related to the sinusoidal surface temperature oscillation and surface heat flux.