Heating and cooling stages using a doubly conjugate thermal and electric asymptotic analysis between a gel and the stratum corneum

Abstract

We study by using perturbation techniques, a conjugate formulation for the heating and cooling stages related with the skin electroporation phenomenon. The fundamental idea is very simple: to analyze simultaneously the thermal and electric effects in a thin layer of gel in contact with the stratum corneum, a situation that results of the application of a uniform electric pulse in the external surface of the gel with very short duration to avoid a temperature rise induced by the Joule heating effect, which can cause irreversible tissue damage. After the application of this short time, needed to characterize the first heating stage, enters in operation a second stage where both layers are cooled because the external electric field is interrupted and the external convective ambient is sufficient to cause it.We have used perturbation techniques to solve the governing equations, identifying a dimensionless parameter denoted by γ that measures the ratio of the electrical conductivities of the two media affected by the pulse. This parameter has a direct influence on the process. Due to that the electrical conductivity of the stratum corneum is very small, γ can assume finite or usually very large values compared with unity and the theoretical predictions show the relevance that this parameter has on the increment of the temperature in both media. Therefore, we consider that this parameter guides the performance of this class of medical treatments based on electric signals and can serve to delimit under transient conditions up to where the thermal effects control the skin electroporation.We demonstrate that to achieve thermodynamic equilibrium, the cooling stage must have a much longer duration than the heating stage, in such a way that it prevents the accumulation of thermal energy in the stratum corneum and thereby prevents the formation of possible damage to the skin.