In this paper we studied the effects of external fields' polarization on the coupling of pure magnetic fields into human body. Finite Difference Time Domain (FDTD) method is used to calculate the current densities induced in a 1 cm resolution anatomically based model with proper tissue conductivities. Twenty different tissues have been considered in this investigation and scaled FDTD technique is used to convert the results of computer code run in 15 MHz to low frequencies which are encountered in the vicinity of industrial induction heating and melting devices. It has been found that external magnetic field's orientation due to human body has a pronounced impact on the level of induced currents in different body tissues. This may potentially help developing protecting strategies to mitigate the situations in which workers are exposed to high levels of external magnetic radiation

A Taflove

Behzad Elahi

CM Furse

DA Savitz

F Gustrau

Jalil Rashed-Mohassel

JC Weaver

JD Sahl

JP Berenger

KA DeBruin

Laleh Golestani-Rad

OP Gandhi

TW Dawson

English

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BioMed Central
BioMagnetic Research and 
Technology
ssOpen AcceResearch
Investigating the effects of external fields polarization on the 
coupling of pure magnetic waves in the human body in very low 
frequencies
Laleh Golestani-Rad*1, Behzad Elahi2 and Jalil Rashed-Mohassel3
Address: 1Laboratory of Electromagnetics and Acoustics (LEMA), Ecole Polytechnique Fédérate de Lausanne (EPFL), Switzerland, 2School of 
Medicine, Tehran University of Medical Sciences, Tehran, Iran and 3Center of Excellence on Applied Electromagnetic Systems, Department of 
Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Iran
Email: Laleh Golestani-Rad* - laleh.golestanirad@epfl.ch; Behzad Elahi - elahi.behzad@gmail.com; Jalil Rashed-Mohassel - jrashed@ut.ac.ir
* Corresponding author    
Abstract
In this paper we studied the effects of external fields' polarization on the coupling of pure magnetic
fields into human body. Finite Difference Time Domain (FDTD) method is used to calculate the
current densities induced in a 1 cm resolution anatomically based model with proper tissue
conductivities. Twenty different tissues have been considered in this investigation and scaled FDTD
technique is used to convert the results of computer code run in 15 MHz to low frequencies which
are encountered in the vicinity of industrial induction heating and melting devices. It has been found
that external magnetic field's orientation due to human body has a pronounced impact on the level
of induced currents in different body tissues. This may potentially help developing protecting
strategies to mitigate the situations in which workers are exposed to high levels of external
magnetic radiation.
Background
Coupling of external electromagnetic fields into the
human body has been subject of many investigations in
recent years especially with several epidemiological stud-
ies linking higher rates of incidence of certain cancers with
electromagnetic radiation [1,2]. Many investigations have
been made to evaluate EM waves coupling into different
organs of body and many international guidelines and
standards have been set up for exposure limits in order to
protect workers against nonionizing radiation in their
workplaces.
Regarding the fact that many cancer associations have
referred to magnetic radiation and considering the fact
that magnetic fields are not shielded by conventional
shielding structures, has led to a dominant interest in
exploring potential hazards of magnetic induction.
There are many studies in recent years evaluating levels of
current densities induced in different body tissues when
exposed to low frequency EM waves. The well known
scaled FDTD technique has been used widely since pro-
posed by Gandhi [3-5] to convert the results of a simula-
tion performed in a higher frequency (in the range of
mega hertz) to the results of very low frequency coupling
caused by power line radiation in 50 and 60 Hz. Other
studies considering the effects of uniform and nonuni-
form magnetic fields with various polarizations are also
performed at 60 Hz using quasi-static impedance method
[6].
Published: 15 May 2007
BioMagnetic Research and Technology 2007, 5:3 doi:10.1186/1477-044X-5-3
Received: 25 January 2007
Accepted: 15 May 2007
This article is available from: http://www.biomagres.com/content/5/1/3
© 2007 Golestani-Rad et al; licensee BioMed Central Ltd. 
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), 
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Page 1 of 5
(page number not for citation purposes)
BioMagnetic Research and Technology 2007, 5:3 http://www.biomagres.com/content/5/1/3Different combinations of incident waves, including pure
magnetic fields with different polarizations and both elec-
tric and magnetic fields in the form of a uniform plane
wave have been studied in Gandhi's works at power line
frequencies. Other studies have explored effects of very
low frequency pure electric fields using high resolution
models (with cubic voxels of 3.6 mm edges) [6]. Indus-
trial frequencies in the range of kilo hertz have been also
studied due to potential risks imposed on workers near
induction heating and melting devices and it has also
been shown that for low frequency dosimetric applica-
tions, using 1 cm resolution model with realistic shape
but relatively lower resolution in discrimination of inter-
nal tissues may give good results with acceptable accuracy
[7].
In this paper a 1 cm resolution anatomically based model
with 20 different organs/tissues has been used to evaluate
current densities induced in different parts of body when
exposed to pure magnetic fields in frequency of 1 KHz.
This particular frequency is of interest for two major rea-
sons: first, this is the frequency mostly radiated by indus-
trial heating and melting devices in work places for which
many basic restrictions indicating the maximum permissi-
ble values of electric and magnetic field inside the human
body have already been established. The second, this is
the frequency proven to have a remarkable impact on the
phenomenon of cell electroporation [8,9]. In this phe-
nomenon, tiny pores will be formed on the membrane of
cells exposed to electric fields with a particular frequency
and magnitude. These pores are formed in several micro-
seconds and may last up to some seconds and the process
is irreversible if the voltage induced on the cell membrane
exceeds a critical value and cell death will occur. There-
fore, studying the magnitude of induced electric fields in
different body tissues may potentially help obtaining a
better control and insight into potential occurrence of
electroporation phenomenon.
The model is manually prepared by converting MRI
images of a 46-year old man with the height of 178 cm
into suitable matrixes of electrical properties of computa-
tional space to be used in FDTD algorithm. MRI images
were T1-weighted and obtained with a 1.5T unit and the
following parameters: TR = 300–450 ms, TE = 12–15 ms,
matrix size = 256 × 256.
20 different tissues and related organs have been identi-
fied by an expert physician and a consulting radiologist
and have been discriminated due to variations in their
conductivities. Pure magnetic radiation is simulated using
two plane waves traveling in opposite directions with elec-
tric components canceling each other.
It is shown that the orientation of magnetic vector in
respect with the body may have a considerable impact on
the coupling of external fields into different organs. This
may be useful to be considered when seeking for appro-
priate protective strategies against unwanted effects of
external radiation.
FDTD algorithm and human body modeling
The anatomic based human body model used in our work
has been prepared manually using data from MRI images
of a 46-year old man with the height of 178 cm. These
images have been then converted to thee dimensional
matrixes introducing electrical properties of human body
to the computational environment in FDTD algorithm.
Fig. 1 shows some sensitive organs included in the model.
Related conductivities for different parts of body are
obtained from [10] for the frequency of 1 KHz.
The whole FDTD computational space has been divided
into 80 × 80 × 200 = 1280000 cubic cells with the cell size
of 1 cm. The human body is suspended in the air and the
computational space is terminated to a 10-layer PML (Per-
fectly Matched Layer) with a grading profile and the opti-
mum conductivity as described in [11].
To simulate the interaction of low frequency incident
waves with human body, scaled FDTD method is used as
described in [4]. According to Gandhi, in this case the
electric fields outside the body depend not on the internal
tissue properties, but only on the shape of the body as
long as the quasi-static approximation is valid, i.e., the
size of the body is a factor of 10 or more smaller the wave-
length, and |σ + jωε| >> ωε0 where σ and ε are the conduc-
tivity and permittivity of the tissues, respectively. Under
these conditions electric fields in air are normal to the
body surface and the internal electric fields are given from
the boundary conditions in terms of the fields outside:
A higher quasi-static frequency of f' maybe therefore used
for irradiation of the model and the induced electric fields
E' thus calculated may be scaled back to the frequency of
interest f.
From the equation (1) we can write:
Assuming that σ + jωε ≅ σ at both f and f'
In many cases if σ' and σ are close enough we can simplify
the equation (2) to
j n E j n Eair tissueωε σ ωε0
 G  G
. ( ) .= + (1)
G G G
E f
j
j
E f
f
f
ETissue Tissue Tiss( )
( )
( )
( )=
′
′ + ′
+
′ ′ ≅
′
′
′ω
ω
σ ωε
σ ωε
σ
σ ue
f( )′
(2)Page 2 of 5
(page number not for citation purposes)
BioMagnetic Research and Technology 2007, 5:3 http://www.biomagres.com/content/5/1/3In our program the actual FDTD program is performed at
a frequency of f' = 15 MHz and afterwards the induced
electric field E' in the frequency of f' is scaled to the fre-
quency of interest f using equation (3). As it is obvious
from (2) the permittivity of tissues doesn't affect the
results significantly, therefore the value of εr = 1 has been
set for the whole environment to hasten the speed of wave
propagation.
In order to generate a homogeneous magnetic field the
model is exited simultaneously by two plane waves
traveling in opposite directions. With the appropriate ori-
entation of plane waves electric field components cancel
out and the magnetic components superpose construc-
tively. Two different orientations for magnetic field vector
are studied: front to back and foot to head and the magni-
tude of electric field of each plane wave is 100 V/m.
The total average electric current for different layers of
body height is obtained from the equation (4). When
FDTD runs, the magnitude of electric fields inside the
body reaches an overshoot during the beginning time
steps and then follows a sinusoidal pattern with lower
amplitude. This overshoot has not been considered when
calculating the temporal maximum of currents. To calcu-
late the average of total electric current for each layer we
have simply added elemental currents of each cell in the
layer and divided the result by the number of contributing
cells.
Numerical results
Fig. 2 shows the layer-averaged induced currents com-
puted for two different polarizations of magnetic field. It
is obvious that orientation of the body with respect to
E r
f
f
E r( ) ( )=
′
′ (3)
J Etotal k i j k
i j
m
i j k
m x y z
=
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥∑ ∑=
σ , ,
,
, ,
, ,
2
1
2 (4)
Views of anatomic model of human body used in the simulationF gure 1
Views of anatomic model of human body used in the simulation.Page 3 of 5
(page number not for citation purposes)
BioMagnetic Research and Technology 2007, 5:3 http://www.biomagres.com/content/5/1/3external fields has a pronounced impact on the coupling
of fields into body.
For different organs, the organ-averaged electric current
has been also calculated for two magnetic field's polariza-
tions. Fig. 3 shows the results of this calculation. It is
observed that for most of organs the front to back mag-
netic vector orientation has more powerful coupling
effects than side to side magnetic vector, though this trend
is reversed for some specific parts of body. In [4] also, dif-
ferent orientations of fields due to human body are stud-
ied for 60 Hz pure magnetic fields, but the results do not
show such pronounced differences between curves of
layer averaged electric currents. This may be because of the
fact that in [4] a more homogeneous human model is
used and less discrete tissue/organs are considered.
The differences are more pronounced for some specific
organs like thymus and thyroid glands. If it is clinically
proven that electric currents may some how affect the
function of these organs, then the results obtained from
this study may help suggesting some mitigating tech-
niques to reduce the potential hazardous effects of
unwanted external radiation, i.e. by setting some restric-
tions on workers orientations due to industrial devices.
To verify the model, the results are compared with the
results presented in [7]. In this work, a pure magnetic field
with the vector oriented from front to back of the body is
Table 1: Electrical properties of different body organs/tissues in
Organ/Tissue Conductivity in 1000 Hz
Aorta 0.26
Lung 0.15
Bone 0.05
Kidney 0.11
Liver 0.04
Heart 0.11
Atrium 0.11
Artery 1.5
Skin 0.02
Bladder 0.2
Brain 0.075
Trachea 0.3
Tongue 0.27
Thyroid 0.52
Spleen 0.1
Gi 0.52
Vein 1
Pancreas 0.52
Muscle 0.32
Eye orbit 0.5
Layer-averaged electric current for two different polariza-tions of magnetic fieldFigure 2
Layer-averaged electric current for two different polariza-
tions of magnetic field.
Organ-averaged electric current for different parts of bodyFigure 3
Organ-averaged electric current for different parts of body.
Maximum of total electric current for different parts of bodyFigure 4
Maximum of total electric current for different parts of body.Page 4 of 5
(page number not for citation purposes)
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simulated to produce B = 30.7 μT. The electric field of each
of the two plane waves must therefore be 0.92 V/m. Fig. 4
shows the maximum of electric current induced in differ-
ent body parts. If we scale the results presented in Fig. 4 by
dividing them to the scale factor 1087, they will show a
good agreement with results presented in [7]. Slight differ-
ences between results may be due to differences in weight
and height of actual models.
Conclusion
In this work the effects of external magnetic fields' orien-
tation on the coupling of fields into human body in very
low frequencies have been studied using an inhomogene-
ous anatomic human model. It has been shown that the
coupling of external fields into different organs and tis-
sues may be affected considerably by changing the orien-
tation of external filed vectors. This effect is more
pronounced for some specific organs like thyroid and thy-
mus gland and calls for further studies on potential effects
of electric currents on function of these organs.
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Investigating the effects of external fields polarization on the coupling of pure magnetic waves in the human body in very low frequencies

Crossref

A perfectly matched layer for the absorption of electromagnetic waves.

Chizmadzhev YA: Theory of electroperation: A review. Bioelectrochemistry and Bioenergetics

Cohort and nested case-control studies of hematopoietic cancers and brain cancer among electric utility workers. Epidemiology

Currents Inducedin Anatomic Models of the Human for Uniformand Nonuniform Power Frequency Magnetic Fields. Bioelectromagnetics

DP: Magnetic field exposure in relation to leukemia and brain cancer mortality among electric utility workers.

Hagness SC: Computational Electrodynamics: The Finite-difference Time-domain Method Artech

JY: Numerical dosimetry at power-line frequencies using anatomically based models.

Krassowska W: Modeling Electroporation in a Single Cell. I. Effects of Field Strength and Rest Potential. Biophysical Journal

OP: Calculation of electric fields and currents induced in a millimeter-resolution human model at 60 Hz using the FDTD method.

Simulation of induced current densities in the human body at industrial induction heating frequencies.

Stuchly MA: High-resolution organ dosimetry for human exposure to low-frequencymagnetic fields.

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Investigating the effects of external fields polarization on the coupling of pure magnetic waves in the human body in very low frequencies

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