Biomedical Engineering Reference
In-Depth Information
where e
?
is the permittivity when x ? ? (permittivity in Terahertz frequencies
in practical scenarios), De
n
is the change in the permittivity in a specified fre-
quency range during nth iteration, s
n
is the relaxation time during the nth iteration,
a
n
is the nth iteration of the distribution parameter which is a measure of the
broadening of dispersion and r
i
is the static ionic conductivity. Due to the high
computational complexity involved when calculating the SAR in the time domain,
for example when using the FDTD method, most of the literature available for
SAR variation in body tissues used an approximation method such as the Debye
approximation [
9
] or the so called 4 9 L Cole Cole approximation [
22
] instead of
the more accurate 4-Cole Cole model of tissue properties. This is mainly due to the
fact that obtaining a time domain expression for e
r
ðÞ
for 0 \ a
n
\ 1 is compu-
tationally intensive. The approach followed in this chapter has been to compute the
SAR in the frequency domain, which enables to use the more accurate 4-Cole Cole
approximation in the obtained calculations.
Apart from the frequency dependent dispersive nature of the tissue materials,
the human age affects the electromagnetic behavior of body tissues. This is mainly
due to the change in the water content of tissue with age [
34
,
35
]. Methods
presented in [
36
] follow the Lichtenecker's exponential law for the complex
permittivity based on the water content of the human tissue materials [
37
].
According to the information given in [
37
], the relative permittivity of any tissue
material (i.e. real part of the complex relative permittivity (e
0
in (
7.4
)) can be
calculated as:
e
0
¼
e
w
e
1
b
ð
7
:
6
Þ
t
where e
W
is the permittivity of water, e
t
is the age independent relative permittivity
of the tissue organic material and b is the hydrate rate for the tissue material. b can
h
i
2
5
ðÞ
6
:
9589
AGE
ln
be expressed as b
¼
q
TBW , where TBW
¼
784
241
e
is the
total body water index (''AGE'' is the age of the tissues sample in years) [
36
,
38
].
After some primary operations, the frequency dependent complex permittivity for
body tissues can be expressed as follows [
36
]:
b
b
A
1
b
A
w
1
b
1
b
A
A
1
xs
e
r
ðÞ¼
e
e
1
j
ð
7
:
7
Þ
where e
A
is the age dependent relative permittivity of a reference adult tissue
material which can be expressed as e
A
¼
e
b
w
e
1
b
t
by replacing e
0
¼
e
A
in (
7.6
) (for
present simulations, the tissue parameters of a 55 year old adult are used as ref-
erence) and b
A
is the hydrate rate for adult tissues (all other parameters are
described in (
7.4
) and (
7.6
)). By using the 4-Cole Cole approximation in combi-
nation with the age related tissue parameter approximations it is possible to
characterize the human tissue properties with sufficient precision. This approach
has been utilized in the present study. This study also considers the relative
