Mathematical Models for Analyzing Tissue Ablation Using Short Pulse Lasers

Mathematical modeling of biological tissue ablation performed using a short pulse laser and the corresponding experimental analysis is of fundamental importance to the understanding and predicting the temperature distribution and heat affected zone for advancing surgical application of lasers. The objective of this paper is to use mathematical models to predict the thermal ablated zones during irradiation of freshly excised mouse skin tissue samples by a novel approach using a focused laser beam from a short pulse laser source. Suggested mathematical model is Stefan kind free boundary problem for the heat equation in unknown region. Temperature of the skin satisfies the classical heat equation subjected to Neumann boundary condition on the known boundary, while along the time-dependent unknown boundary, which characterizes the ablation depth, two conditions are met: (1) temperature is equal to the ablation temperature and (2) classical Stefan condition is satisfied. The latter expresses the conservation of energy at the ablation moment. A method of integral equations is used to reduce the Stefan problem to a system of two Volterra kind integral equations for temperature and ablation depth. MATLAB is used subsequently for the numerical solution. Experiments are performed using two lasers—a diode laser having a wavelength of 1552 nm and pulsewidth of 1.3 ps. The surface temperature distribution is measured using an imaging camera. After irradiation, histological studies of laser irradiated tissues are performed using frozen sectioning technique to determine the extent of thermal damage caused by the laser beam. The ablation depth and width is calculated based on the interpolated polygon technique using image processing software. The surface temperature distribution and the ablation depth obtained from the mathematical models are compared with the experimental measurements and are in very good agreement. A parametric study of various laser parameters such as time-average power, pulse repetition rate, pulse energy, and irradiation time is performed to determine the necessary ablation threshold parameters.