A Comparative Study on the Induced Current Density in Humans Exposed to ELF Electric Fields

JOURNAL OF COMMUNICATIONS SOFTWARE AND SYSTEMS, VOL. 3, NO. 1, MARCH 2007 17 A Comparative Study on the Induced Current Density in Humans Exposed to ELF Electric Fields Vitantonio Amoruso, Giovanna Calò, Francesco Lattarulo, Dragan Poljak, Andres Peratta, Cristina Gonzalez Abstract: A comparison between two theoretical methods, recently adopted for evaluating induced currents in a human body, is here presented. In both cases, a vertical ELF electric field is assumed for the coupling to a standard human subject. Specifically, the diakoptic method (DM), applied to a homogeneous multi-sphere model of man with low partitioning degree, and the Boundary Element Method (BEM), applied to a non-homogeneous model with high partitioning degree, have been selected. The analytical and numerical formulations, respectively distinctive of the above methods, are carefully described and a number of data are reported and commented upon. Index terms: Boundary Element Method, diakoptic method, ELF human exposure, induced currents I. INTRODUCTION The electromagnetic fields produced at extremely low frequency (ELF) by power installations, at radiofrequency for radio and television broadcasting and at microwaves by GSM mobile phones are of primary interest regarding environmental problems involving human beings. Assessing the radiation hazard is still an open problem at ELFs since the currently claimed correlation between exposure and serious pathologies, such as neoplastic disease [1]-[4], is still subject to debate. The above harmful correlation essentially derives from some epidemiological studies on involved population groups. On the other hand, a large amount of laboratory research on ELF-field carcinogenesis has so far produced controversial results. A human body exposed to electric fields,is subject to an induced current. In the high frequency range, specific absorption rate (SAR) and temperature increase in the tissue due to electromagnetic effects are good indicators of exposure intensity. However, in the quasistatic case, the resultant internal electric fields and current densities, mutually correlated by means of the tissue conductivity, are often considered as exposure indicators, this is due to the negligible thermal effects at low frequency and field intensities. The current distribution on the exposed surface of the Manuscript received September 16, 2006 and revised November 20, 2006. V. Amoruso, G. Calò and F. Lattarulo are with Politecnico di Bari, Dipartimento di Elettrotecnica ed Elettronica, Bari, Italy (e-mail: ). D. Poljak is with the University of Split, Department of Electronics, Split, Croatia (e-mail: ). A.Peratta and C. Gonzalez are both with the Wessex Institute of Technology, UK (e-mail: ). human body is essentially non-uniform and strongly dependent on the actual exposure conditions, namely on the field orientation and magnitude and the human body’s size, posture, connection to ground and relative position with respect to influencing nearby conductors. In the following, reference will only be made to the canonical case study of a grounded man either isolated from or above a conducting plane (no presence of nearby conductors appart from the plane will be taken into account). At ELFs, the human body behaves essentiatlly as a perfect conductor from a point of view external to it, and as a pure resistance from an internal point of view. Moreover, provided that inner conductance inhomogeneities can be disregarded (see, later, Sect V), the internal current density only results dependent on the body configuration. This implies that the prerequisite for a good reproduction of a human exposure to a quasistatic electric field reduces to assigning an optimum sophistication degree to a perfectly conducting model of man. Either analytical [1]-[2], [5-6], or numerical techniques [710] have previously been developed for evaluating, with different degree of accuracy, the current density induced by ELF exposures. To this end, oversimplified [6, 10] and, on the other hand, computationally expensive solvers, the latter often based on the Finite Element Method (FEM) [8] and Finite Difference Time Domain (FDTD) method [7], [9], have been adopted. This paper aims to compare the features of a pair of so far overlooked, even though efficient, methods. One of them applies the Diakoptic method (DM) [10]-[11] to the human dosimetry after having adopted a low partitioning degree to a human model externally behaving as a perfect conductor. The assumed homogeneity of the internal conductivity also contributes to make the computational effort required quite modest. Such a performance especially promotes investigations on the dynamic dosimetry, namely the theoretical monitoring of the induced current distribution when the human posture progressively changes. The Boundary Element Method (BEM) [14], has also been applied with success to the problem of human exposure to ELF fields [13],[15]. BEM results more involved than a computationally equivalent FDTD but less expensive than FEM at equal sophistication degree assumed for the object representation. Another attractive feature of BEM is that it avoids a volume mesh discretisation. The formulation is based on the quasi-static approximation of the electric field and the related equation of continuity. The general continuity equation is simplified to the Laplace equation form for the 1845-6421/07/6146 © 2007 CCIS 18 JOURNAL OF COMMUNICATIONS SOFTWARE AND SYSTEMS, VOL. 3, NO. 1, MARCH 2007 electric scalar potential, which is numerically handled via BEM with the domain decomposition concept [14]. BEM will accommodate inner conducting inhomogeneities, a supplementary general feature which will be discussed with specific application to ELF studies. The model requires to be imaged owing to the presence of the conducting plane. Each sphere is dimensioned according to anthropometric criteria applied to a 1.75-m tall subject. The connection between nearby spheres are ensured by unperturbing wires, see Fig. 1 a). II. ANALYTICAL AND NUMERICAL MODELS OF THE HUMAN BODY By virtue of the diakoptic theory, the originally assembled structure, represented by eleven spheres, is subdivided into as many elements by cutting the wiring terminals. A. Diakoptic Theory The DM applied to the analysis of composite electrode structures offers an efficient and effective solution to electrostatic or quasi-static problems, regardless of the complexity of the system under examination and the low degree of partialisation a priori adopted. According to the original Greek word διαχòπτω (to cut), the diakoptic method is based on initially tearing a connected structure into large dimensioned elemental blocks. In other words, the exposed human body is assimilated to a multi-element receiving antenna whose elemental blocks are electrically small although comparable with the main anatomic parts. The current contribution of each single element, represented by an equivalent c (...truncated)