Biomedical Engineering Reference
In-Depth Information
0
-8
-16
-24
-32
-40
Z
Y
X
0
-0.6
-1.2
-1.8
-2.4
-3
FIGURE 4.10
Current sheet device. Top left: The U-shaped conductor is placed 3 cm above a plane-layered fat-muscle-fat model and driven by
a 30 MHz current source. Top right: The resulting SAR distribution (in dB relative to the maximum SAR) in the
y
= 0 plane. Bottom: SAR in the
uppermost plane of the muscle-like medium (in dB relative to the maximum in that plane) showing a relatively uniform SAR distribution that is
essentially constrained within the footprint of the conductor parallel to the upper surface of the phantom.
where
m
and
n
are integers and describe different modes of
propagation. If
in designing aperture sources is to achieve a large effective field
size. Parameters that may be considered include extending the
end of the waveguide into a horn structure, dielectric loading
of the waveguide, and the use of waveguides of differing cross
sections.
An example of a superficial hyperthermia applicator that
produces a larger EFS than a simple waveguide applicator is
the lucite cone applicator (LCA), a water-filled rectangular
waveguide terminated by a modified horn antenna (van Rhoon
et al. 1998; Samaras et al. 2000). The waveguide operates in
the TE
10
mode at 433 MHz, and the metallic walls of the horn
section that are parallel to the E-field are replaced by poly-
methyl methacrylate walls. A polyvinyl chloride cone located
centrally in the aperture is also inserted into the applicator as
shown in Figure 4.12. In use, a water bolus is placed between
the aperture and the tissue to be heated. Laboratory testing
shows that the nonmetallic walls and an appropriate choice
(
)
+
()
2
2
2
π
π
then
γ
m,n
is real and there is
no significant propagation since the fields for these evanescent
modes decay rapidly along the guide. If
m
a
n
b
>ωµ
ε
(
)
+
()
2
2
π
π
,
then
γ
m
,
n
is imaginary and the fields propagate along the wave-
guide. The transition occurs when
m
a
n
b
2
<ωµ
ε
(
)
+
()
2
2
π
π
. he
frequency
f
c
m
,
that satisfies this condition is known as the cut-
off frequency and is given by
m
a
n
b
2
=ωµ
ε
2
2
1
m
a
π
+
n
b
π
f
=
πµ
.
(4.45)
c
m
,
2
ε
The mode with the lowest cut-off frequency is known as the
dominant mode, and the dimensions of the waveguide are often
chosen so that only this mode can propagate. For a waveguide
of rectangular cross section, the TE
10
mode is the dominant
one and Figure 4.11 shows the dependence of
E
y
as a func-
tion of distance across the wide dimension of the rectangular
cross-section waveguide for this mode. A parameter that has
been proved useful in assessing the effectiveness of hyperther-
mia devices is the effective field size (EFS), defined as the area
that is enclosed within the contour at 50% maximum SAR at
a depth of 1 cm in a flat homogeneous phantom (Hand et al.
1989). If an aperture source supporting a TE
10
mode is placed
directly onto a lossy medium, since
E
y
b
y
sin
()
, the SAR distribu-
tion immediately beneath the aperture will be nonuniform vary-
ing approximately as
sin
2
0
x
a
0
a
x
()
and consequently the EFS is small
compared to the footprint of the aperture. One of the challenges
x
FIGURE 4.11
Electric field
E
y
(
x
) for TE
10
mode in rectangular wave-
guide of cross-sectional dimensions
a
×
b
.
