We first used a two-layer fininte element model (FEM-2, Fig. 2), which was also used in a human study,11 to represent the skin of the rat’s paw. However, the simulation results were not satisfactory (see Sec. 3). Instead, we used a three-layer model (FEM-3, Fig. 2), which contains stratum corneum. The thickness of stratum corneum was 40 μm, and the remaining epidermis was 50 μm.20 The dermis was 800 μm thick.19 The thermal conductivity of stratum corneum and the viable epidermis was 0.1 (Refs. 24 and 25) ( is the absolute temperature). The other parameters were set according to Frahm et al.11 The temperature distribution was based on Pennes’s bioheat equation [Eq. (1)].26 The heat source (, ) was assumed as exclusively contributed by the laser, which is described by Eq. (2). The equation was solved by FEM in MatLab (pdetool, MathWorks, Natick, MA). We chose 3313 triangular elements to solve the equation. The lowest boundary of dermis was assumed as a constant temperature (Dirichlet condition, ). The other boundary conditions were assumed to be thermal-isolated (Neumann condition, heat ). The heat-transfer coefficient () of every boundary was .27Display Formula
(2)where is tissue density, is specific heat of tissue, is tissue temperature, is time, is thermal conductivity, is laser power (), is the absorption coefficient of tissue assumed to contain 35% or 40% water (30,000 or 35,000 ), is the depth from skin surface, is the standard deviation of Gaussian fit of the laser profile (0.875 mm), and is the distance from the axis of the laser beam.