Ultrafast laser radiation and conduction heat transfer in biological tissues

Ultrafast laser radiation heat transfer in biological tissues is governed by time-dependent equation of radiative transfer and modeled using the transient discrete ordinates method. The divergence of radiative heat flux is then obtained and used for predicting the local temperature response due to radiation energy absorption within the ultrashort time period. To this end, the lumped method is employed and heat diffusion is negligible. Both single pulse and pulse train irradiations are considered. For the single pulse irradiation, the transient radiation field is obtained and the local temperature keeps rising until a time of about 20 times of the short pulse width; and then a stable local temperature profile is reached and maintained until the start of heat conduction. For the pulse train case (10⁴ ultrashort pulses until 1 ms), the local temperature response is an accumulation of continuous single pulses because the thermal relaxation time of biological tissues was reported in the range of 1-100 sec and is much longer than the pulse train duration (1 ms). After a stable local temperature field is achieved, the hyperbolic heat conduction model is adopted to describe the heat conduction. MacCormark's scheme is utilized for solving the thermal wave equations. Thermal wave behavior is observed during the heat transfer process. It is found that the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. After several thermal relaxation times the thermal wave behavior is substantially weakened and the predictions between the hyperbolic and diffusion models match.