Multi-scale modeling of tissue freezing during cryogen spray cooling with R134a, R407c and R404a
In laser dermatologic surgery, cryogen spray cooling (CSC) has been proved to be an efficient cooling technique to avoid thermal damage from skin burning due to the light energy absorption by melanin in epidermis. R134a is now the only cooling agent in commercial laser and has been proved to be effective for light pigmented skin. R407c and R404a could provide better cooling effect for darkly pigmented skin than R134a because both of them have much lower boiling point. In order to investigate the potential cold injury mechanism prior to the further clinic use, this paper presents a multi-scale model to simulate the cooling process of the skin and estimate the potential cold injury. In the model, the skin tissue is treated as multi-layered geometry and the heat transfer within this multi-layer skin is described by a macro-scale bio-heat transfer model. A general dynamic relation is introduced on the surface of skin to quantify the convective cooling of CSC with various cooling agents. Meanwhile, the micro-scale mass transfer and the ice formation in cell during the cooling are evaluated in a Krogh unit. The cold injury is recognized once the cell is dehydrated or the ice formed intracellularly. The results show that the surface cooling effect of spray cooling is well related with the boiling point of cryogen. Much lower surface and inner skin temperature will be achieved by using cryogens with lower boiling poring, e.g. R404a and R407c, which is benefit to thermal damage protection for darkly pigmented skin. Recognized as cell dehydration, the spray durations to cause cold injury are 3.3 s, 2.2 s and 1.9s for R134a, R407c and R404a, which proved that three cooling agents are all safe for epidermis protection in CSC with spurt duration of tens of milliseconds in clinic. (C) 2014 Elsevier Ltd. All rights reserved.