The BEEMG research project on contact currents 2001-2011 showed that, in typical belgian residential housing, the most probable cause of high ELF internal electric fields in the human body was contact currents (see also the slides of the BBEMG study day in 2009, in French or in Dutch). However, if the qualitative link between contact currents and high internal electric field is clear, it is much more complicated to relate them quantitatively. Indeed, in order to determine the electric fields inside the human body from the contact currents, one must know the electric conductivity of all the biological tissues in the human body. These tissues are highly heterogeneous and possibly anisotropic “materials” , the properties of which change rather quickly after death  so that measurements performed in vitro on excised tissues may not be representative. Due to ethical reasons, in vivo measurements have been mostly performed on animals. The age  and the physiological condition  may also significantly alter these properties. Obtaining data for characterising a foetus is even harder .
Consequently, at ELF frequencies, the values measurements are performed either by identifying an equivalent RC circuit, or by a four-point measurement. At those frequencies, electrode polarization is a major source of errors. Some tentatives have also been performed [4, 6] for numerically estimating the conductivity and permittivity by modeling tissues as porous media, with limited success. Gabriel et al [7–9] have collected most of the existing data and built a tissue database, which is currently the reference for dosimetric computations . However, the validity of this reference data is still hugely debated, as new measurements by the same authors , as well as results obtained using a variety of novel measurement techniques based on magnetic resonance (which can be applied in vivo) [12, 13], show large discrepancies: the new values of conductivities are often higher and muscle-type tissues are found to be much less anisotropic. For example, at 50 Hz, the conductivities of the white and grey matter in  and  span, respectively, within [0.0753 ; 0.5155] and [0.0533 ; 0.302] S/m, i.e., differ by more than one order of magnitude.
It is thus crucial to quantify the effect of this uncertainty on the electromagnetic fields computed in the human body. The classical approach would be to use a time-consuming Monte-Carlo (MC) simulation to statistically characterise the induced fields—which would take several weeks of computational time for our models. In this project we investigate the use of a polynomial chaos approach to study how the uncertainty on material parameters (in this case the electric conductivity of the human body) affects the relationship between the external electromagnetic sources and the induced internal electric field. In particular, we investigate the so-called non intrusive probabilistic algorithm, which assumes that the variances of conductivities are finite  and allows to completely characterise the induced field in the probabilistic dimension with a much lower computational cost (a few hours). This method will allow us to provide confidence intervals for the internal electric field on realistic finite element models of the human body, given an external source (voltage drop leading to contact current, or ambient electric or magnetic field).
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