Coupling Characteristic of Adult and Children with Non-uniform Magnetic Field
Kei Maruyama1,3, Yukihisa Suzuki2, Masao Taki2, Kanako Wake3, Soichi Watanabe3, Osamu Hashimoto1
1
Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan, Email: maru@nict.go.jp
2
Tokyo Metropolitan University, 1-1 Minamiosawa, Hachioji, Tokyo 192-0397, Japan
3
National Institute of Information and Communications Technology, 4-2-1
Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan
Abstract
In this paper, we investigated normalized induction factor for adult and child exposed to non-uniform
magnetic fields. Two anatomical human models (adult and 3-year-old child) were used to calculate induced current
densities. The normalized induction factors were computed for head and torso separately and were plotted in relation to
the distance between the magnetic dipole and the human body. The dependence of the normalized induction factors on a
distance is different between head and torso in the adult case. On the other hand, the normalized induction factors for
the head of the child are always larger than that of the torso of the child.
1. Introduction
Electronic article surveillance (EAS) systems are widely used in the world to prevent unjustified making off the
product in the store. There are several types of systems in EAS; magnetic systems, acousto-magnetic systems, radiofrequency systems, microwave systems. The magnetic systems which have advantage in cost are more popular among
them. The magnetic systems are based on time-varying magnetic field at the frequency range from low frequency to
intermediate frequency. On the other hand, induction heating (IH) hobs which also use time-varying magnetic field for
heating process has became popular as cooking device. These devices are used in the proximity of human bodies. There
are growing concerns of general public about possible health effects of time-varying magnetic field of these devices.
There are several guidelines to limit electromagnetic fields. The guidelines established by ICNIRP [1] and by
IEEE [2, 3] are well known. In these guidelines, the limitation of the magnetic field at the frequency used by these
devices mentioned above is induced current density (in ICNIRP) or electric field (in IEEE). Since it is difficult to
measure the induced current densities or electric fields within human body, the reference levels are also provided as
incident magnetic or electric fields.
The reference levels in the guidelines are assumed that the exposed magnetic field is uniform. However actual
magnetic fields from various electrical equipments are not uniform. Therefore it is not easy to compare the magnetic
field generated by the devices with the reference level. One of simple assessment is to compare the maximum magnetic
flux density with the reference level. However this way overestimates the level of magnetic field from the devices. In
order to assess the compliance with the reference level, we have to convert the non-uniform magnetic field into
equivalent uniform magnetic field. From these backgrounds, the normalized induction factor has been proposed to
convert the non-uniform magnetic field into the uniform magnetic field in terms of induced current densities [4].
Additionally, in the IEC documents, the coupling factor with the same function is described [5].
2. Normalized Induction Factor
The normalized induction factor is the fraction of the maximum current densities induced by non-uniform
magnetic field and that induced by uniform magnetic field [4]. Thus the factor K J can describe as
KJ =
J max −nonuniform
J max −uniform
,
(1)
where J max −nonuniform is the maximum induced current density obtained from the exposure to the non-uniform magnetic
field;
J max −uniform is the maximum induced current density obtained from exposure to the uniform magnetic field. The
amplitude of the uniform magnetic field is adjusted to the maximum value of non-uniform magnetic field within the
human body.
Equation (1) means that, if the exposed magnetic field is close to uniform, the denominator becomes equal to the
numerator; K J ≅ 1 .
3. Models and Method
Anatomical human models were used in the calculation to evaluate induced current density inside human bodies.
We used adult male model and 3-year-old child model. The adult model is based on MRI images of Japanese adult male
with average height and weight. The 3-year-old child model is developed by transforming adult male model [8, 9]. Both
models have over 50 tissues and organs with 2 mm cubic voxels. The height and weight of adult male are 172.8 cm and
65.0 kg, respectively; those of the child model are 88.2 cm and 13.4 kg, respectively.
Figure 1 shows the location of the magnetic dipole and the human model. The magnetic dipole is located at 800
mm height from the ground in front of the models. The frequency of the magnetic field is set at 20 kHz. The distance
between the magnetic dipole and the human models are changed form 10 mm to 30 m.
Induced current densities within the human models were calculated by the impedance method [6]. In this method,
the biological tissues or organs are represented by cubic cells, and each edge of the cells is attempted impedance. The
electrical properties of individual tissues and organs are obtained from parametric model developed by Gabriel [7].
Since the frequency of magnetic fields we investigate is 20 kHz, the imaginary part of impedance (ωε) is negligible
compared with the conductivity (σ). Therefore we took into account only real part of the impedance in the calculation.
According to the ICNIRP guidelines, current densities should be averaged over a cross-section of 1cm2
perpendicular to the current direction. The specific procedure for computing the 1 cm2 averaged value is not mentioned
in the guidelines. In this work, we obtained the averaged value of 1 cm2 by following steps. First, each component of
current density vector were averaged over 5×5 cells (the area equals to 1cm2) as shown in Fig. 2. Then, the magnitude
is obtained by root-sum-square of three components calculated with procedure mentioned above.
4. Results
The dependences of peak current densities on the distance are shown in Fig. 3. Figure 3 (a) is the adult case and
(b) is 3-year-old child case respectively. Dashed lines indicate peak current densities in the head, and solid lines are
peak in the torso. Since the magnetic field decays as increase of the distance, the magnitudes of current densities
decrease in both cases. Both of the peak current densities induced in the head and torso in child case is larger than those
of the adult case. In the child case, the magnetic dipole is located closer to the head (refer to Fig. 1). Head contains
cerebral spinal fluid (CSF), which has very high conductivity (2.0 S/m at 20 kHz); thus the peak current density more
likely to be observed in head. For the adult, in contrast, the magnetic dipole is located close to torso. Thus the high
conductivity tissue in the region near the magnetic dipole is muscle. The conductivity of muscle (0.34 S/m at 20 kHz) is
lower than the value of CSF.
Figure 4 shows normalized induction factors of adult and 3-year-old child. Dashed lines are normalized
induction factors obtained from peak current densities in the head, and solid lines are obtained from the values of the
torso. On the calculation of normalized induction factors, the uniform magnetic field incident from the top to bottom
(TOP) is assumed.
In the adult case, the normalized induction factors for body of adult are larger than that for torso at the
approximately of the magnetic dipole (region (Ι)). At the distances between 1 and 10 m (region (ΙΙ)), the normalized
induction factors for the head are larger. This can be described that the direction of the dominant component of the
magnetic field vector in the head varies, if the distance between the magnetic dipole and the human body changes. At
the distance under 1 m and over 10m (region (Ι) and (ΙΙΙ)), the direction of dominant component in head is parallel to
the TOP. On the other hand, at the distances in the region (ΙΙ), the dominant components in head are TOP and the
direction from front to back. The component of the uniform magnetic field is only TOP direction; hence the induction
factors are become larger.
The normalized induction factors for child of the head are always larger than those of torso at any distance. In
the child case, the magnetic dipole is located closer to the head than the body. Additionally, the head has higher
conductivity tissue (CSF) than the torso. Therefore the peak current densities are found in the head.
6. Summary
This paper presents the characteristics of the induced current density in adult and child exposed to non-uniform
magnetic field. The peak current densities are observed in different region of the body in adult case depending on the
distance from the source. In the child case, the peaks in 3-year-old child are observed in head at any distance. These
differences are caused by the position of the magnetic dipole. From the results, it is found that the coupling
characteristics for adult and child are different by the distance from the magnetic dipole.
7. References
1. International Commission on Non-Ionizing Radiation Protection, “Guidelines for Limiting Exposure to Time-varying
Electric, Magnetic, and Electromagnetic Fields (up to 300 GHz)”, Health Phys., 74, pp.494-522, 1998.
2. IEEE, “IEEE Standard for Safety Levels with Respect to Human Exposure to Electromagnetic Fields, 0–3 kHz”,
IEEE Std. C95.6, 2002.
3. IEEE, “IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic
Fields, 3 kHz to 300 GHz”, IEEE Std. C95.1, 2005.
4. T. Dan Bracken and Trevor Dawson, “Evaluation of Nonuniform 60-Hertz Magnetic-Field Exposures for
Compliance with Guidelines”, Journal of occupational and environmental Hygiene, Vol.1, pp.629-638, 2004.
5. IEC, “Exposure to electric or magnetic fields in the low and intermediate frequency range – Methods for calculating
the current density and internal electric field induced it the human body, Part2-1:”, IEC 62226-2-1, 2004.
6. N. Orcutt and O. P. Gandhi, “A 3-D impedance Method to Calculate power Deposition in Biological Bodies
Subjected to Time Varying magnetic Field”, IEEE Trans. Biomed. Eng., Vol.35, pp.577-583, 1988.
7. S. Gabriely, R. W. Lau and C. Gabriel, “The dielectric properties of biological tissues: III. Parametric models for the
dielectric spectrum of tissues”, Physics in Medicine and Biology, Vol.41, pp.2271–2293, 1996.
8. T. Nagaoka, S. Watanabe et al., “Development of realistic high-resolution whole-body voxel models of Japanese
adult males and females of average height and weight, and application of models to radio-frequency electromagneticfield dosimetry”, Physics in Medicine and Biology, Vol.49, pp.1-15, 2004.
9. Tomoaki Nagaoka, Etsuo Kunieda, Jianquing Wang, Osamu Fujiwara, and Soichi Watanabe, “Development of
Whole-body Child Models Based on Japanese Body Dimensions Data”, Bioelectromagnetics Proceedings, abstract
#230, 2006.
Fig. 1 Location of the magnetic dipole and the human model
Fig. 2 Region averaged over the area of the 1 cm2. This is a
case of averaging area for z-axis direction.
(a) Adult
(b) 3-year-old child
Fig. 3 Peak current density in head and torso for adult and 3-year-old child
(a) Adult
(b) 3-year-old child
Fig. 4 Normalized induction factor for maximum current density in head and torso