Deterministic-Stochastic Boundary Element Modeling of the Brain and Eye Exposed to High-Frequency Radiation

Abstract

The paper reviews the influence of the variability in the morphology and the tissue properties of the human brain and eye, respectively, exposed to high-frequency (HF) radiation. Deterministic-stochastic modeling enables one to estimate the effects of the parameter uncertainties on the maximum induced electric field and Specific Absorption Rate (SAR). Surface Integral Equation (SIE) scheme applied to the brain exposed to HF radiation and hybrid boundary element method (BEM)/finite element method (FEM) scheme used to handle the eye exposure to HF radiation are discussed.Furthermore, a simple stochastic collocation (SC), through which the relevant parameter uncertainties are taken into account, is presented. The SC approach also provides the assessment of corresponding confidence intervals in the set of obtained numerical results. The expansion of statistical output in terms of the mean and variance over a polynomial basis (via SC approach) is shown to be robust and efficient method providing a satisfactory convergence rate. Some illustrative numerical results for the maximum induced field and SAR in the brain and eye, respectively, are given in the paper, as well.Keywords: boundary integral equations, deterministic modeling, human exposure to electromagnetic fields, stochastic modeling. INTRODUCTIONHuman exposure to artificial electromagnetic fields has raised many questions regarding potential adverse effects [1], particularly for the brain and eye exposure to high-frequency (HF) radiation. The assessment of HF exposure is based on the evaluation of specific absorption rate (SAR) distribution and related temperature rise in a tissue. As a measurement of fields induced in the body is not possible, human exposure assessment is carried out via sophisticated computational models [2][3][4][5]. Contrary to the simple canonical models used in the 60s and 70s (plane slab, cylinders, homogeneous and layered spheres and prolate spheroids [6]) modern realistic, anatomically based computational models comprising cubical cells are mostly related to the use of the Finite Difference Time Domain (FDTD) methods [7]. The Finite Element Method (FEM) and Boundary Element Method (BEM) are generally used to a somewhat lesser extent [3,8].One of the significant difficulties arising in the area of computational bioelectromagnetics is the appreciable variation of the input parameter set, i.e. possible differences in individual size and age (morphology), or the general variability of permittivity and conductivity, due to difference in age or sex. The uncertainty of the input parameters set eventually leads to the