Biomedical Engineering Reference
In-Depth Information
d
s
1
e
1
(I)
E
1
SG
E
2
d
s
2
e
2
(II)
FIGURE 4.6
Modeling for analysis with two-layer medium.
dielectric heating are generated, based both on an ionic current and the dielec-
tric constant.
Using the analytical model of a two-layer medium shown in Figure 4.6,
heating is described as follows. (A more detailed investigation will be given in
Section 4.2.6). The complex dielectric constant of this two-layer medium, to
compare with a single-layer medium, is shown by the equation
k
s
we
wet
wt
k
Ê
Ë
ˆ
¯
-
Ê
Ë
ˆ
¯
˙
ee ee
e
=- =
¢
j
≤
1
+
+
j
+
(4.4)
S
S
S
e
1
wt
22
1
+
22
0
where
e
0
is the permittivity in free space, e
e
=
e
1
e
2
/(e
1
+ e
2
), t =
(e
1
+ e
2
)e
0
/(s
1
+
(e
1
s
2
+ e
2
s
1
)
2
/[e
1
e
2
(s
1
+ s
2
)
2
], s = s
1
s
2
/(s
1
+ s
2
).
Therefore, the electric power loss per unit volume is obtained as follows by
substituting the imaginary part of the complex dielectric constant of Eqn. (4.4)
in Eqn. (4.3):
s
2
), and
k
=
s
we
wet
wt
k
weet
wt
k
Ê
Ë
ˆ
¯
Ê
Ë
ˆ
¯
e
0
e
W
=
we
+
E
2
=+
+
s
E
2
(4.5)
0
0
1
+
1
22
22
0
Under the ideal material condition, when there is no energy absorption and
exothermic reaction accompanying the chemical or physical change in the
dielectric, heat is generated according to the above expressions. The first term
in Eqn. (4.5) shows Joule's heat, while the second is loss caused by the RF. As
suggested by this simple model, for a medium in which the dielectric constant,
permittivity, and conductivity heterogeneously intermingle, Joule's heat
contributes to heat generation when the RF electric field is applied to the
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