Stochastic analysis of epithelial/absorbed power density in multilayered planar skin model with uncertain tissue electric properties

Abstract

Stochastic analysis of the absorbed power density (APD) on skin surface exposed to radiation of halfwave dipole at 10, 30 and 90 GHz and for different antenna-body distances is presented. Skin tissue is modeled as a half-space consisting of one layer (skin) or three layers (skin, fat and muscle) whose permittivities and conductivities are uncertain. Deterministic part is based on numerical solution of Pocklington equation via Galerkin Bubnov Indirect Boundary Element method (GB-IBEM) and numerical integration of the corresponding field integrals. Uncertainty from tissue electric parameters is propagated to APD via nonintrusive Stochastic Collocation method (SCM) in order to compute stochastic moments of APD. For 1-layered model APD stochastic moments are computed with 3 deterministic simulations. On the other hand APD mean and variance for 3 layered model are successfully computed with 13 deterministic simulations while skewness and kurtosis require 85 deterministic simulations. The ratio of APD standard deviation and mean decreases with frequency thus indicating that the uncertainty in the tissue electric properties has smaller effect on APD uncertainty at higher frequencies. Finally, sensitivity analysis carried out for both 1-layered and 3-layered models indicates the same conclusions. At 10 GHz skin permittivity and conductivity are the two most important parameters. However, as frequency increases the impact of skin conductivity prevails. This indicates that in frequency range 10-90 GHz the APD uncertainty quantification and sensitivity analysis can be carried out by using only 2-dimensional stochastic model.