Biomedical Engineering Reference
In-Depth Information
SAR
¼
1
2
r
q
j
2
ð
7
:
1
Þ
where E is the root mean square (RMS) electric field strength, q is the mass density
(in kg/m
3
), and r is the conductivity of the tissue. The electric field and the
magnetic field in the frequency domain can be described by Maxwell's curl
equations in the frequency domain as below:
r
E
ðÞ¼
jxlH
ðÞ
ð
7
:
2
Þ
r
H
ðÞ¼
jxe
0
e
r
ðÞ
E
ðÞ
ð
7
:
3
Þ
where j
¼
p
is the imaginary unit, x is the angular frequency, E
ðÞ
and H
ðÞ
are time-harmonic electric and magnetic fields, l is the permeability, e
0
is the free
space permittivity and e
r
ðÞ
is the frequency dependent complex relative per-
mittivity. Because of the dependency of the electric field one
r
ðÞ
;
the SAR var-
iation inherently depends on the relative permittivity of the material, which itself
depends on the incident frequency of the electromagnetic signal. The behavior of
the complex relative permittivity for different tissue types differs from each other,
especially at higher frequency ranges such as UWB. Hence, it is not advised to use
straightforward homogeneous body models to simulate the electromagnetic effects
at higher frequencies. The simulations presented in this chapter use the CST Studio
voxel human model, which is a human body model consisting of a mixture of
tissue materials such as brain, bone, intestinal tissue, colon tissue, fat and skin. It
also considers blood flow for thermal calculations.
The
1
frequency
dependent
dielectric
permittivity
of
human
tissue
can
be
expressed as [
33
]:
r
e
0
x
¼
e
0
1
xs
e
r
ðÞ¼
e
0
je
00
¼
e
0
j
1
j
ð
7
:
4
Þ
where e
0
is the relative permittivity of the tissue material, e
00
is the out of phase loss
factor, which can be expressed as e
0
¼
r
e
0
x
and s
¼
e
0
e
0
r
is the relaxation time
constant. In the expression for e
00
, r represents the total conductivity of the
material, which might be partially attributed by frequency dependent ionic con-
ductivity r
i
, e
0
= 8.85 9 10
-12
F/m is the permittivity of the free space and x is
the angular frequency. Based on this equation, Gabriel et al. have proposed a
method of evaluating the frequency dependent relative permittivity of a material
by so-called 4-Cole Cole model approximation given in the equation below [
30
]:
ðÞ¼
e
1
þ
X
4
1
þð
jxs
n
Þ
1
a
n
þ
r
i
De
n
e
r
ð
7
:
5
Þ
jxe
0
n
¼
1
