Biomedical Engineering Reference
In-Depth Information
Z
Z
X
Y
X
Y
0
-8
-16
-24
-32
-40
Z
Y
X
FIGURE 4.9
(
See color insert
.) Top left: Three-turn induction coil modeled as three concentric circular loops (radii 10, 8, and 6 cm) placed
3 cm above a plane-layered fat-muscle-fat phantom. Each loop is driven by a current source at 30 MHz. Top right: Vector plot of current density
J
in planes x = 0 and y = 0. Bottom: The resulting SAR distribution (in dB relative to the maximum SAR) in the x = 0 plane.
parallel to (i.e., in the x-y plane) and 3 cm above the upper sur-
face of a planar fat-muscle phantom. The frequency is 30 MHz.
Unlike the case of capacitive electrodes, the maximum SAR is
located in the muscle region rather than in the fat layer because
the induced electric field and currents are parallel to the phan-
tom surface and the interface between the fat and muscle layers.
The boundary conditions require that the E-field is continuous
across the fat/muscle interface and so the induced current is
larger in the more-conducting muscle than in the fat. However,
due to the symmetry of the coil, there is a null in the SAR distri-
bution along the central axis.
To overcome this problem, an inductively coupled tech-
nique in which current-carrying loop is rotated (into the x-z
plane) with respect to the surface of the phantom may be used.
Figure 4.10 shows a variation of this idea in which the conductor
is U-shaped. The resulting electric field and current density are
parallel to the tissue interfaces, as in the induction coil method
above, but the circular symmetry leading to the axial null in
SAR is avoided. The SAR distribution is relatively uniform and
for practical purposes is constrained within the footprint of the
device. In practice, the current-carrying conductors form part
of a resonant circuit and such devices are therefore tuned to
a narrow-frequency band. However, this type of device, often
referred to as “current sheet applicators,” can be designed for
operation at RF and microwave frequencies. Further theoreti-
cal and practical data have been discussed by Morita and Bach
Andersen (1982), Johnson et al. (1987), Gopal et al. (1992), and
Prior et al. (1995).
transfer through radiation is increased. Several types of sources
based on hollow cylindrical waveguides of various cross sections
or on microstrip have been developed. When waves propagate
between metallic walls or dielectric surfaces, the electric and
magnetic fields must be satisfy boundary conditions. In the case
of perfectly conducting metallic walls, these conditions are that
tangential components of the electric field and normal compo-
nents of the magnetic field are zero at the surface of the conduc-
tors. In the case of a hollow metallic waveguide with rectangular
cross section, solution of Maxwell's equations shows that two
types of waves can be supported: transverse electric (TE) waves
for which the component of electric field along the guide (
E
z
) is
zero, and transverse magnetic waves for which
H
z
is zero. For TE
modes, the remaining components are:
m
a
π
n
b
π
EE
=
cos
x
sin
y
(4.43a)
x
xmn
m
a
π
n
b
π
EE
=
sin
x
cos
y
(4.43b)
y
ymn
m
a
π
n
b
π
HH
=
sin
x
cos
y
(4.43c)
x
xmn
m
a
π
n
b
π
HH
=
cos
x
sin
y
.
(4.43d)
y
xmn
In the case of a perfect (lossless) dielectric within the waveguide,
the propagation constant (along the waveguide)
γ
m,n
is
4.8.2 aperture Sources
When the wavelength of the electromagnetic field is compa-
rable to the dimensions of the source, the efficiency of energy
2
2
γ=
π
m
a
+
n
b
π
−ω µ
2
ε
(4.4 4)
m
.
