Study of the Influence of the Orientation of a 50-Hz Magnetic Field on Fetal Exposure Using Polynomial Chaos Decomposition

Abstract

Human exposure modelling is a complex topic, because in a realistic exposure scenario, several parameters (e.g., the source, the orientation of incident fields, the morphology of subjects) vary and influence the dose. Deterministic dosimetry, so far used to analyze human exposure to electromagnetic fields (EMF), is highly time consuming if the previously-mentioned variations are considered. Stochastic dosimetry is an alternative method to build analytical approximations of exposure at a lower computational cost. In this study, it was used to assess the influence of magnetic flux density (B) orientation on fetal exposure at 50 Hz by polynomial chaos (PC). A PC expansion of induced electric field (E) in each fetal tissue at different gestational ages (GA) was built as a function of B orientation. Maximum E in each fetal tissue and at each GA was estimated for different exposure configurations and compared with the limits of the International Commission of Non-Ionising Radiation Protection (ICNIRP) Guidelines 2010. PC theory resulted in an efficient tool to build accurate approximations of E in each fetal tissue. B orientation strongly influenced E, with a variability across tissues from 10% to 43% with respect to the mean value. However, varying B orientation, maximum E in each fetal tissue was below the limits of ICNIRP 2010 at all GAs.

Stochastic Dosimetry for the Assessment of Children Exposure to Uniform 50 Hz Magnetic Field with Uncertain Orientation

“…Such an assessment is indeed a challenging task, due to the intrinsic variability of the parameters that influence the exposure, as the morphology, the anatomy and the posture of the exposed subject, the dielectric properties that characterized the tissues of the subject, and the reciprocal position of the field and the exposed subject [ 12 ]. Two previous studies [ 13 , 14 ] dealt with the task of providing a description of the exposure due to 50 Hz ELF-MF in realistic scenarios, specifically in fetuses. In particular, these studies assessed how the variability of both magnetic field orientation [ 13 ] and of dielectric properties assignment to the fetal tissues at different gestational ages [ 14 ] influence the estimation of the induced electric field due to ELF-MF exposure at 50 Hz in fetal tissues using stochastic dosimetry.…”

“…Two previous studies [ 13 , 14 ] dealt with the task of providing a description of the exposure due to 50 Hz ELF-MF in realistic scenarios, specifically in fetuses. In particular, these studies assessed how the variability of both magnetic field orientation [ 13 ] and of dielectric properties assignment to the fetal tissues at different gestational ages [ 14 ] influence the estimation of the induced electric field due to ELF-MF exposure at 50 Hz in fetal tissues using stochastic dosimetry. Stochastic dosimetry is a method that combines electromagnetic computational techniques and statistics to build surrogate models that can be used to obtain, parsimoniously, the distribution of the quantity of interest (the induced electric field for instance), replacing by analytical equations the heavy numerical simulations that would be needed to characterize the highly variable exposure using only classical electromagnetic computational techniques.…”

“…Stochastic dosimetry is a method that combines electromagnetic computational techniques and statistics to build surrogate models that can be used to obtain, parsimoniously, the distribution of the quantity of interest (the induced electric field for instance), replacing by analytical equations the heavy numerical simulations that would be needed to characterize the highly variable exposure using only classical electromagnetic computational techniques. Among the statistical approaches that could be used to build surrogate models in stochastic dosimetry, the polynomial chaos (PC) theory [ 15 ] resulted in being an efficient tool to assess the variability of the EMF exposure both at radio frequency [ 16 , 17 ] and at low frequency [ 13 , 14 ]. Results obtained by [ 13 , 14 ] showed that, while variations in the dielectric properties could not be established as a decisive factor for the exposure of fetuses, the variations in the orientation of the magnetic field strongly influenced the electric field induced in the fetal tissues.…”

3D space‐dependent models for stochastic dosimetry applied to exposure to low frequency magnetic fields

“…). Analogously to the approach described by Chiaramello et al [] and Liorni et al [], in order to take into account all possible differences in the amplitude of the electric fields induced in the tissues by B ‐fields of opposite directions that could arise from anatomical asymmetries, the exposure was assessed for all the possible orientations of the B ‐field in the 3‐dimensional space, included the orthogonal ones. The ranges of variation of θ [0, 180°] and φ [−180°, 180°] were set according to the convention of unique spherical coordinates, and the two input parameters were hypothesized to be independent and uniformly distributed.…”

Sensitivity Analysis of an Implanted Antenna within Surrounding Biological Environment

“…In such a situation, the introduction of stochastic tools allows researchers to deal with the variability of all the parameters describing the electromagnetic problem. Such approaches were shown to be very efficient in the framework of the determination of specific rate absorption (SAR) in biological tissues due to mobile phones at microwaves frequencies [17][18][19] and more recently to electromagnetic compatibility problems [20].…”