Fluid and Thermal Dynamics of Cryogen Sprays Impinging on a Human Tissue Phantom

Cryogen spray cooling (CSC) protects the epidermis from unintended heating during cutaneous laser surgery. The present work investigated the time-dependent flow characteristics of cryogen sprays and correspondent thermal dynamics at the surface of a human tissue phantom. First, a numerical analysis was carried out to evaluate an epoxy block substrate as a human tissue phantom. Next, the velocity and diameter of cryogen droplets were measured simultaneously and correlated with surface temperature of the human tissue phantom during CSC. Finally, velocity and diameter measurements were used to compute the spray number, mass, and kinetic energy fluxes, and temperature measurements were used to compute the surface heat flux. Numerical modeling showed that the thermal response of our phantom was qualitatively similar to that of human stratum corneum and epidermis; quantitatively, thermal responses differed. A simple transformation to map the temperature response of the phantom to that of tissue was derived. Despite the relatively short spurt durations (⁠$10ms$⁠, $30ms$⁠, and $50ms$⁠), cryogen delivery is mostly a steady state process with initial and final fluid transients mainly due to the valve dynamics. Thermal transients $(16ms)$ are longer than fluid transients $(4ms)$ due to the low thermal diffusivity of human tissues; steady states are comparable in duration (⁠$≈10ms$⁠, $30ms$⁠, and $50ms$⁠) although there is an inherent thermal delay $(≈12ms)$⁠. Steady state temperatures are the lowest surface temperatures experienced by the substrate, independent of spurt duration; hence, longer spurt durations result in larger exposures of the tissue surface to the same lower, steady state temperature as in shorter spurts. Temperatures in human tissue during CSC for the spray system and parameters used herein are estimated to be $≈−19°C$ at the stratum corneum surface and $>0°C$ across the epidermis.