A nonlinear electrical-thermal model of the skin

Abstract
This work presents a model for the skin which accounts for both the nonlinearities and the asymmetries in its voltage-current characteristic. This model consists of an electrical submodel and a heat transfer submodel. The electrical submodel uses nonlinear devices in which some parameters depend on skin temperature. The heat transfer submodel models the heat exchange between the skin, the surrounding tissues, and the ambient medium and calculates the temperature of the skin to update the necessary parameters of the electrical submodel. The model is based on experiments designed to determine: 1) the dry skin voltage-current characteristic; 2) the changes in the skin breakdown voltage with location; 3) the moist skin voltage-current characteristic; 4) the changes in the voltage-current characteristic of the skin with duration after the onset of stimulation; and 5) the effect of skin temperature on its voltage-current characteristic. During these experiments we used 84-mm2 square Ag-AgCl electrodes to apply sinusoidal voltage of 0.2 and 20 Hz. The simulations were performed using the Advanced Continuous Simulation Language (ACSL), capable of solving differential and integral equations with variable coefficients. The model predicted the skin behavior satisfactorily for a large range of amplitudes and frequencies. We found that the breakdown occurred when the energy delivered to the skin exceeded a threshold. Above this threshold the voltage-current characteristic of the skin became nonlinear and asymmetric and, in a real situation, the subject would experience an uncomfortable sensation which could rapidly develop into pain.