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Investigation of the Spinal Cord as a Natural Receptor
Antenna for Incident Electromagnetic Waves and
Possible Impact on the Central Nervous System
Sevaiyan Balaguru, Rajan Uppal, Ravinder Pal Vaid &
Balasubramaniam Preetham Kumar
Department of Electrical and Electronic Engineering, California State University,
Sacramento, California, USA
The effects of electromagnetic field (EMF) exposure on biological systems have been studied
for many years, both as a source of medical therapy and also for potential health risks.
In particular, the mechanisms of EMF absorption in the human or animal body is of
medical/engineering interest, and modern modelling techniques, such as the Finite Difference
Time Domain (FDTD), can be utilized to simulate the voltages and currents induced in different
parts of the body. The simulation of one particular component, the spinal cord, is the focus
of this article, and this study is motivated by the fact that the spinal cord can be modelled
as a linear conducting structure, capable of generating a significant amount of voltage from
incident EMF.
In this article, we show, through a FDTD simulation analysis of an incoming electromagnetic
field (EMF), that the spinal cord acts as a natural antenna, with frequency dependent induced
electric voltage and current distribution. The multi-frequency (100 –2400 MHz) simulation
results show that peak voltage and current response is observed in the FM radio range around
100 MHz, with significant strength to potentially cause changes in the CNS. This work can
contribute to the understanding of the mechanism behind EMF energy leakage into the CNS,
and the possible contribution of the latter energy leakage towards the weakening of the blood
brain barrier (BBB), whose degradation is associated with the progress of many diseases,
including Acquired Immuno-Deficiency Syndrome (AIDS).
INTRODUCTION
The effects of electromagnetic field (EMF) radiation on biological systems have
been studied for decades, both for therapeutic applications such microwave
hyperthermia treatment of cancer (National Cancer Institute, 2011), and also health
risks associated with prolonged exposure (SCENIHR, 2007). Very recently, the World
Health Organization (WHO) listed mobile phone use in the same “carcinogenic
hazard” category as lead, engine exhaust, and chloroform.
In the U.S., the Federal Communications Commission (FCC) regulates EMF
exposure according to table (Table 1) below (FCC, 1997), which sets limits on
electric/magnetic field strengths and power density in the vicinity of human and
animal population.
Address correspondence to B. P. Kumar, Department of Electrical and Electronic Engineering,
California State University, 6000 J Street, Sacramento, CA-95819-6019; E-mail: kumarp@ecs.csus.edu
Electromagnetic Biology and Medicine, Early Online: 1–11, 2012
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ISSN: 1536-8378 print / 1536-8386 online
DOI: 10.3109/15368378.2011.624653
1
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However, to obtain accurate estimates of voltages and currents induced in
biological systems, and also EMF absorption (measured by the Specific Absorption
Rate or SAR), specific simulation studies have to be performed and the results
analyzed to conclude if the above FCC regulations are maintained.
Effects of Electromagnetic Fields on CNS Pathologies
Exposure to electromagnetic fields has been associated with health risks (Johansen,
2000; Nikitina, 2000), which include neurological diseases such as amyotrophic lateral
sclerosis, senile dementia, Parkinson’s disease, and Alzheimer’s disease (Johansen,
2000). In a Russian study (Nikitina, 2000), for example, the aim was to examine
the health of workers exposed to HF and microwave range (3 and 10 cm wavelength)
EMF. The results of the Johansen study are summarized in Table 2 below.
Such studies show that EMF exposure affects the CNS to a major extent, thereby
increasing the importance of focusing on this part of the human or animal system.
The mechanisms of EMF entry and absorption in the body are not very clearly
understood, and require study of key elements of the CNS system such as the Blood
Brain Barrier (BBB), brain system, and the spinal cord. The aim of this article is to
examine if the antenna-like properties of the spinal cord enhances the EMF
absorption of the CNS, as compared to other systemes in the human or animal system.
Direct Effects of EMF Exposure and Absorption
Experimental studies on animals have clearly shown that electromagnetic fields have
the capacity to alter, and weaken, the structure of the Blood Brain Barrier (BBB)
TABLE 1 FCC Guidelines for EMF exposure (FCC, 1997).
FCC Limits for Maximum Permissible Exposure (MPE)
Frequency
Range (MHz)
Electric Field
Strength (E) (V/m)
Magnetic Field
Strength (H) (A/m)
Power Density (S)
(mW/cm
2
)
Averaging
Time jEj
2
,jHj
2
or S (minutes)
(A) Limits for Occupational/Controlled Exposure
0.3–3.0 614 1.63 (100)*6
3.0–30 1842/f 4.89/f (900/f
2
)*6
30–300 61.4 0.163 1.0 6
300–1500 – – f/300 6
1500–100,000 – – 5 6
(B) Limits for General Population/Uncontrolled Exposure
0.3–1.34 614 1.63 (100)*30
1.34–30 824/f 2.19/f (180/f
2
)*30
30–300 27.5 0.073 0.2 30
300–1500 – – f/1500 30
1500–100,000 – – 1.0 30
NOTE 1: See Section 1 for discussion of exposure categories. f¼frequency in MHz. *Plane-wave
equivalent power density.
TABLE 2 Pathological changes pattern and rate in workers exposed to 3–30 MHz EMF and control
groups (%) (Johansen, 2000).
Pathological changes Basic groups n¼72 Control groups n¼45 P
Central nervous system disturbances 50.0 13.3 ,0.01
Cardiovascular system diseases 34.7 6.7 ,0.01
Gastrointestinal tract diseases (gastritis,
cholecystitis)
19.4 11.1 ,0.1
Peripheral nervous system diseases 9.7 6.7 NS
Respiratory organs diseases 12.5 4.4 NS
2 S. Balaguru et al.
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(Baureus Koch et al., 2003; NIH, 1995; Deeken and Lo
¨scher, 2007). The blood-brain
barrier (BBB) is an intricate cellular system composed of vascular endothelial cells
and perivascular astrocytes that restrict the passage of molecules between the blood
stream and the brain parenchyma. Specifically, as reported in Deeken and Lo
¨scher
(2007), 344 rats were exposed in a transverse electromagnetic transmission line
chamber to microwaves of 915 MHz as continuous wave (CW) and pulse-modulated
with repetition rates of 8, 16, 50, and 200 Hz. The specific energy absorption rate
(SAR) varied between 0.016 and 5 W/kg. The results showed albumin leakage in 5 of
62 of the controls and in 56 of 184 of the animals exposed to 915 MHz microwaves.
A continuous wave resulted in 14 positive findings of 35, which differ significantly
from the controls. Hence, it has been shown experimentally that even small values of
SAR can potentially damage or alter the BBB properties.
Other investigations have detected abnormalities in the human BBB permeability
in association with HIV infection, which suggest that abnormal permeability of the
BBB is associated with HIV infection. However, the exact role the perturbation of the
BBB plays in HIV neuropathogenesis and in disease progression is unclear. For
example, one would like to know whether the perturbation of the BBB precedes or
succeeds the entry of HIV into the parenchyma (Deeken and Lo
¨scher, 1993). Hence,
the study of any process that weakens the BBB in humans or animals is of vital
importance in the understanding of the mechanisms behind the evolution of AIDS,
in addition to other neurological disorders in the human or animal system.
Proposed Theory and Modeling of Increased EMF Absorption in the CNS
This article is motivated to provide understanding of the mechanism of EMF
induction in the human body, specifically focusing on the modelling of the human
spinal cord structure as a natural antenna receptor for incident EMF, by taking into
account its wire-like and conductive properties. Accurate models of the spinal cord
structure have been developed in the past (Salford et al., 1994; Wesselink et al., 1998;
Struijk et al., 1993a,b), especially for its stimulation in clinical neurological
applications; however, in this article, a concentric cylindrical layer model for the
spinal cord structure is employed, and FDTD analysis carried out for an incident
plane wave. This study will help in understanding significant effects of EMF on
nervous system components such as the Blood-Brain Barrier (BBB), which serves as
a vital block between the human physiological and neurological systems.
FDTD MODELLING OF PLANE WAVE INCIDENCE ON SPINAL CORD
Brief Background on the FDTD Method
The finite-difference time-domain (FDTD) formulation of EMF problems is a
convenient tool for solving scattering problems. The FDTD method, first introduced
by Yee (1996), is a direct solution of Maxwell’s time-dependent curl equation.
Yee’s Finite Difference Algorithm
In an isotropic medium, Maxwell’s equation can be written as:
7£E¼2
m
›
H
›
tð1aÞ
7£H¼
s
Eþ1
›
E
›
tð1bÞ
Using Yee’s notation, we define a grid point in the solution region as:
ði;j;kÞ¼ðiDx;jDy;kDzÞð2Þ
Investigation of the Spinal Cord 3
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We determine the scattered fields as follows. At t ,0, the program is started by
setting all the field components at the grid points equal to zero:
E0
xði;j;kÞ¼E0
yði;j;kÞ¼E0
zði;j;kÞ¼0ð3aÞ
H0
xði;j;kÞ¼H0
yði;j;kÞ¼H0
zði;j;kÞ¼0ð3bÞ
If we know
Hn21
xði;j;kÞ;Hn21
yði;j;kÞ;Hn21
zði;j;kÞ;En21
xði;j;kÞ;En21
yði;j;kÞand En21
zði;j;kÞ
for all grid points in the solution region, then we can determine new Hn
xði;j;k) and
En
xði;j;k) everywhere from the Eqs. (4a) –(4f) below:
Hn
xði;j;kÞ¼Hn21
xði;j;kÞþEn21
yði;j;kþ1Þ2En21
yði;j;kÞ2En21
xði;jþ1;kÞ
þEn21
xði;j;kÞð4aÞ
Hn
yði;j;kÞ¼Hn21
yði;j;kÞþEn21
xðiþ1;j;kÞ2En21
xði;j;kÞ2En21
xði;j;kþ1Þ
2En21
xði;j;kÞð4bÞ
Hn
xði;j;kÞ¼Hn21
xði;j;kÞþ
,
En21
xði;jþ1;kÞ2
,
En21
xði;j;kÞ2En21
yðiþ1;j;kÞ
þEn21
yði;j;kÞð4cÞ
En
xði;j;kÞ¼CaðmÞEn21
xði;j;kÞþCbðmÞ½Hn21
xði;j;kÞ2Hn21
xði;j21;kÞ
2Hn21
yði;j;kÞþHn21
yði;j;k21Þ ð4dÞ
En
yði;j;kÞ¼CaðmÞEn21
yði;j;kÞþCbðmÞ½Hn21
xði;j;kÞ2Hn21
xði;j;k21Þ
2Hn21
xði;j;kÞþHn21
xði21;j;kÞ ð4eÞ
En
xði;j;kÞ¼CaðmÞEn21
xði;j;kÞþCbðmÞ½Hn21
yði;j;kÞ2Hn21
yði21;j;kÞ
2Hn21
xði;j;kÞþHn21
xði;j21;kÞ ð4fÞ
where, following Taflove et al. (1995), we define the following constants:
R¼
m
0=210ð5aÞ
Ra¼c
d
t=
d
2ð5bÞ
Rb¼
d
t=
m
o
d
ð5cÞ
Cb¼Rb=1ði;j;kÞþ
fR
s
ði;j;kÞgð5dÞ
where
m
0
denotes the permeability of free space, 1,
s
, respectively, the permittivity
and conductivity. The spatial increment is
d
¼Dx¼Dy¼Dz, and time increment
d
t
¼nDt.
4 S. Balaguru et al.
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The initial field components are obtained by simulating a single-frequency, z
polarized plane wave, traveling along the positive x-direction. A desirable plane
wave condition takes into account the scattered fields at the source plane. For a
three-dimensional case, a typical wave source condition at the plane
j¼js;ðnear y ¼0Þis
En
zði;j;kÞˆsin ð2
p
fn
d
tÞð6Þ
where fis the irradiation frequency, Equation (2.9) is a modification of the algorithm
for all the points on the plane j¼j
s
. Thus, at t¼0, the plane wave source frequency,
fis assumed to be turned on (Taflove et al., 1995). Time stepping simulates the
propagation of waves from this source, which is repeatedly implementing Yee’s finite
difference algorithm on lattice points. The incident wave is then tracked as it first
propagates to the scatterer and then interacts with it via surface current excitation,
diffusion, penetration, and diffraction. Time stepping is continued until the
sinusoidal steady state is achieved at each point.
Modelling of the Spinal Cord
The modelling and study of electromagnetic field (EMF) interaction with the human
spinal cord is motivated by the fact that the spinal cord structure possesses the
following important antenna like properties:
.The spinal cord has an almost linear structure with cylindrical cross-section.
.The innermost region of the spinal cord, such as the cerebro-spinal fluid (CSF), is
conductive, and hence the current can be induced by incident electromagnetic
radiation.
Given the above properties, the two important applications, which would require
an accurate and fast modelling of the EMF interaction with the spinal cord, are
neural therapeutic systems, and EMF hazard study application.
The spinal cord is modelled as a concentric multi-layer cylinder, based on the
cross-section of the spinal cord illustrated in Fig. 1 (Thuery, 1992). The cross-section
is comprised of different biological media, starting with the outer skin layer, and
Gray matter
Ventral End of Spinal Column
Dorsal End of Spinal Column
White matter
Cerebro-spinal fluid (CSF)
Epidural fat
Vertebral bone
Skin
5 mm
FIGURE 1 Transverse section of midcervical spinal cord model (National Cancer Institute, 2011).
Investigation of the Spinal Cord 5
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converging to the innermost central canal of the spinal cord. The detailed electrical
and magnetic properties of the spinal cord model layers are given in Table 3. The
reference medium air is given as the first item in the latter table, and the innermost
central canal of the spinal cord is the last item.
The conduction current density induced in the spinal cord is given by:
J¼
s
Eð7Þ
where Jis the electric current density vector (A/m
2
), E(x,y,z) is the electric field
vector, and
s
is the electricity conductivity distribution, Siemens/m. The voltage
induced in the length of the spinal cord is given by:
V¼2ð
L
0
E†dl ð8Þ
where the integration is carried out over the length of the spinal cord.
In addition to the induced voltage and current in the spinal cord, the specific
absorption rate or SAR was also calculated in this study. The SAR is a measure of the
energy absorption and is given by:
SAR ðWatts=kgÞ¼
s
jEj2
2
r
ð9Þ
where the density
r
is usually taken to be approximately equal to that of water
(
r
¼10
3
kg/m
3
).
SIMULATION RESULTS
The FD-TD simulation grid is divided into 30 £30 £30 cells along the x-y-zaxis,
with the cell size Dx¼Dy¼Dz¼D¼6.7 mm, and time step Dt¼1.9 picoseconds.
The simulation time step Dtwas selected based upon the FD-TD method (Taflove,
1995) where:
umax Dt
D#ffiffiffi
1
n
rð10Þ
where n¼3 is the maximum number of space dimensions, u
max
is the maximum
velocity of the electromagnetic plane wave in the biological medium, and DT
and Dare the space step and the time step respectively. The simulation was
performed in MATLABQfor an average spinal cord length of 45 cm (Balaguru
et al., 2001).
TABLE 3 Material properties and dimensions of spinal model.
No. Medium
Thickness
(mm)
Dielectric
constant (1
r
)
Permeability
(
m
H/m)
Conductivity
s
S/m
1 Air – 1 4
p
£10
27
0.0
2 Skin 5/3 44.5 4
p
£10
27
0.01
3 Bone 15 6.4 4
p
£10
27
0.02
4 Epidural Fat 8/3 6.4 4
p
£10
27
0.04
5 Cerebro-spinal Fluid (CSF) 4 60 4
p
£10
27
1.7
6 White Matter (WM) 2 15 4
p
£10
27
0.6
7 Grey Matter (GM) 2 10 4
p
£10
27
0.23
Layer Number 8: Central Canal of the Spinal Column
6 S. Balaguru et al.
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Voltage and Current Density Distribution
Fig. 2 shows the current density magnitude jJj¼jJ
z
jdistribution induced in
the spinal cord model corresponding to an z-polarized incident plane wave of
magnitude 1 V/m, and frequency 400 MHz. Fig. 2a shows the 3-dimensional current
density distribution, whereas Fig. 2b depicts the cross-sectional top view in the x-y
plane. Similarly, Fig. 3 illustrates the current density distribution (3-dimensional
and top view) at incident plane wave frequency of 1800 MHz. The peak current
density and induced voltage are listed in Table 4 in a frequency range of
100–2400 MHz, and it is observed that the peak current density decreases from
30.9 mA/m
2
at 100 MHz to 3.9 mA/m
2
at 2400 MHz. The increasing attenuation of
the electric field with frequency, as demonstrated by the decrease in induced
current and voltage with frequency, is consistent with current knowledge of
electromagnetic fields, and their dependence of penetration depth in media with
frequency (Salford et al., 1994).
Specific Absorption Rate (SAR) distribution
The SAR distribution was simulated at two frequencies of 400 MHz and 1800 MHz,
and the results are graphically illustrated in Figs 4 and 5, respectively. The SAR
0.2
0.2
0.15
0.1
0.05
0
–0.05
–0.1
–0.15
–0.2
–0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2
0.1
0
–0.1
–0.2
0.2
z, meter
y, meter
y, meter
x, meter
x, meter
(a) 3-dimensional view
Top view (b)
Ventral end Dorsal end
Ventral end Dorsal end
Current density
(mA/m2)
0.00–1.90
1.90–3.80
3.80–5.70
5.70–7.60
7.60–9.50
0.1 0–0.1 –0.2 –0.2 –0.1 00.1 0.2
FIGURE 2 Current distribution in the spinal cord for plane wave incidence: Frequency ¼400 MHz,
Electric field amplitude ¼1 V/m.
Investigation of the Spinal Cord 7
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decreases from a peak value of 0.085 W/kg at 400 MHz to a peak value of 0.035W/kg
at 1800 MHz.
CONCLUSIONS
This article describes the FDTD simulation of plane wave interaction with the
stratified model of the human spinal column and the resultant induced current
TABLE 4 Peak current density, induced voltage, and SAR in spinal column.
Frequency (MHz) Peak Current Density (mA/m
2
) Induced Voltage (millivolts)
100 30.9 8.2
400 9.5 2.5
700 4.9 1.3
1000 4.3 1.1
1800 3.7 0.97
2400 3.4 0.9
0.2
0.2
0.15
0.1
0.05
0
–0.05
–0.1
–0.15
–0.2
–0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2
0.1
0
–0.1
–0.2
0.2
z, meter
y, meter
y, meter
x, meter
x, meter
Ventral end Dorsal end
Ventral end Dorsal end
Current density
(mA/m2)
0.00–0.74
0.74–1.48
1.48–2.22
2.22–2.96
2.96–3.70
0.1 0–0.1 –0.2 –0.2 –0.1 00.1 0.2
FIGURE 3 Current distribution in the spinal cord for plane wave incidence: Frequency ¼1800 MHz,
Electric field amplitude ¼1 V/m.
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and voltage at various frequencies. Preliminary results show that incident EMF
frequencies in the FM band of ,100 MHz show increased response on the spinal
cord structure generating significant voltage of ,8 mV, which could have potential
impact on the CNS processes, including the Blood Brain Barrier.
It cannot be definitely surmised if the purported BBB leakage could occur in the
spinal cord itself or in the main brain region. However, since the voltage generated
by the integrative effect of the cord would be maximum at the upper end of the cord,
it would support the theory that the BBB weakening could potentially occur at the
junction of the brain and spinal cord. Future work will focus on the effects of the
induced voltage and current on the central nervous system, and if it does have
significant impact on the Blood-Brain-Barrier (BBB), which is an area of great
interest in the study of immunological diseases.
Declaration of interest
The authors report no conflicts of interest. The authors alone are responsible for the
content and writing of the paper.
0.2
0.2
0.15
0.1
0.05
0
–0.05
–0.1
–0.15
–0.2
–0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2
0.1
0
–0.1
–0.2
0.2
z, meter
y, meter
y, meter
x, meter
x, meter
Top view
3-dimensional view (a)
(b)
Ventral end Dorsal end
Ventral end Dorsal end
SAR values (W/kg)
0.000–0.017
0.017–0.034
0.034–0.051
0.051–0.068
7.068–0.085
0.1 0–0.1 –0.2 –0.2 –0.1 00.1 0.2
FIGURE 4 Specific Absorption Rate (SAR) distribution in spinal cord for plane wave incidence at
400 MHz.
Investigation of the Spinal Cord 9
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0.2
0.2
0.15
0.1
0.05
0
–0.05
–0.1
–0.15
–0.2
–0.2 –0.15 –0.1 –0.05 0 0.05 0.1 0.15 0.2
0.1
0
–0.1
–0.2
0.2
z, meter
y, meter
y, meter
x, meter
x, meter
3-dimensional view (a)
(b) Top view
Ventral end Dorsal end
Ventral end Dorsal end
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0.014–0.021
0.021–0.028
0.028–0.035
0.1 0–0.1 –0.2 –0.2 –0.1 00.1 0.2
FIGURE 5 Specific Absorption Rate (SAR) distribution in spinal cord for plane wave incidence at
1800 MHz.
10 S. Balaguru et al.
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