A new mathematical model for accurate quantification of cryogen spray cooling in cutaneous laser surgery using realistic boundary conditions

Laser dermatologic surgery is widely used for various skin diseases. Prior to the laser treatment, transient cryogen spray cooling (CSC) is employed to prevent unwanted thermal damage of skin tissue due to melanin absorption in the epidermis. Accurate quantification on the cooling effect of CSC is essential in the subsequent laser energy dosage prediction. Based on the existing experimental data, we present a new dynamic correlation in terms of non-dimensional heat convection coefficient as a function of the dimensionless time and dimensionless spatial location. The effects of transient spray cooling and the thermal properties of experimental substrate are included in the correlation. The heat transfer within the skin tissue is calculated by a heat conduction equation. Meanwhile, the dynamic correlation of heat convection coefficient is incorporated into the heat conduction equation as a convection boundary condition. Simulation results demonstrate that the correlation correctly reflects several important characteristics of CSC and the model predictions are in consistent with the experimental observations. Numerical results indicate that the CSC time duration should be short enough to maintain selective cooling in epidermis while long enough to avoid the non-uniform spatial cooling on skin surface. A shorter spray distance (for example z = 30 mm) is found to have better cooling effect than a longer spray distance (z = 60 mm). The dynamic correlation in terms of non-dimensional heat convection coefficient proposed in this study can be used in accurate quantification of the effect of CSC. Optimal cooling duration of 75–100 ms and short spray distance of 30 mm are recommended for CSC clinical application.