This study investigates the transient temperature response in biological tissue with sinusoidal temperature oscillation on the skin surface. Based on the Laplace transform, an exact solution of the Pennes bioheat transfer equation has been derived which includes the whole time domain from the initial transient oscillation to the final steady periodic oscillation. Furthermore, the exact solutions of special cases under no perfusion rate, constant temperature, and the combination of those two assumptions are demonstrated in this study. The primary application for this type of analysis is to assess the blood perfusion rate in the skin by imposing a periodic temperature load onto the skin surface. Through the noninvasive measurement of the maximum heat flux or minimum heat flux on the skin, equation (15) can be utilized to estimate the blood perfusion rate in living tissues. The results show that both the larger perfusion rate and greater tissue depth decrease the amplitude of the sinusoidal temperature response. A larger perfusion rate can also reduce the unstable duration for the estimation of the blood perfusion rate. Meanwhile, the shift of phase angle related to the sinusoidal temperature variation increases with tissue that is deeper and has lower perfusion rate.

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