22
Electromagnetic Fields in Biological Systems
TaBlE 1.1 Propagation Characteristics of RF Plane Waves in Biological Tissues Having
Low and High Water (H 2 O) Contents as a Function of Frequency at 37°C
Frequency
Dielectric
Conductivity
Penetration Depth
Transmission
(MHz)
Constant
(S/m)
(cm)
Coefficient (T)
H 2 O
High
Low
High
Low
High
Low
High
Low
27
113
20.0
0.61
0.03
14.3
77.0
0.14
0.56
40
97
14.6
0.69
0.03
11.2
58.8
0.17
0.62
433
53
5.6
1.43
0.08
3.6
18.3
0.36
0.82
915
51
5.6
1.60
0.10
2.5
12.8
0.40
0.83
2,450
47
5.5
2.21
0.16
1.7
8.1
0.43
0.84
5,800
43
5.1
4.73
0.26
0.8
4.7
0.44
0.85
10,000
40
4.5
10.3
0.44
0.3
2.6
0.45
0.87
Clearly, the coupling of RF energy from air into planar tissue is greater for
low-water-content tissue compared to high-water-content tissue. It is greater for higher
RFs than for lower ones and ranges from about 15% to 80%. The data given in Table 1.1
show that the penetration depth for low-water-content tissues such as bone and fat is
about five times greater than that for high-water-content tissues and that it is also frequency dependent. The transmission coefficient for air–tissue interfaces nearly doubles
for low-water-content tissues compared with high-water-content tissues. Moreover, the
transmission coefficient for tissue–tissue interfaces is generally larger than that for air–
tissue interfaces, whereas the reflection coefficient shows just the opposite trend. The
reflection coefficient varies from a low of 5% for muscle–blood interfaces to a high of
about 50% for bone–muscle interfaces (Lin and Bernardi 2007).
In a layered tissue structure having different dielectric permittivities, the coupling
behavior can be very complex. Multiple reflections can occur between tissue interfaces.
The transmitted field will combine with the reflected field to form standing waves in
each tissue layer. The peaks of the standing waves can result in greater coupling of RF
energy into the tissue layer. The standing-wave phenomenon becomes especially pronounced if the thickness of each layer is greater than the penetration depth for that tissue layer and is approximately one-half wavelength or longer at RF. This dependence of
standing-wave oscillation peaks on layer thickness is a manifestation of layer resonance,
which can enhance power transmission.
1.10.2 Radiofrequency Field Coupling to Bodies with Curvature
A plane-wave RF field in the far zone can overcome exponential losses and produce
enhanced coupling at great depths in bodies with curved surfaces. Typically, if the largest
dimension of the body is comparable to the wavelength of the impinging RF field, energy
deposition and distribution will be influenced by the surface curvature of the whole body
or the body part and tissue composition. In particular, the ratio of geometric variables and
wavelength affects the characteristics of RF energy coupling. An example of this phenomenon is given in Figure 1.11, where absorbed energy distributions inside a 9-cm-radius
homogeneous spherical model of the brain are shown. Note that the distributions have
Electromagnetic Fields in Biological Systems
TaBlE 1.1 Propagation Characteristics of RF Plane Waves in Biological Tissues Having
Low and High Water (H 2 O) Contents as a Function of Frequency at 37°C
Frequency
Dielectric
Conductivity
Penetration Depth
Transmission
(MHz)
Constant
(S/m)
(cm)
Coefficient (T)
H 2 O
High
Low
High
Low
High
Low
High
Low
27
113
20.0
0.61
0.03
14.3
77.0
0.14
0.56
40
97
14.6
0.69
0.03
11.2
58.8
0.17
0.62
433
53
5.6
1.43
0.08
3.6
18.3
0.36
0.82
915
51
5.6
1.60
0.10
2.5
12.8
0.40
0.83
2,450
47
5.5
2.21
0.16
1.7
8.1
0.43
0.84
5,800
43
5.1
4.73
0.26
0.8
4.7
0.44
0.85
10,000
40
4.5
10.3
0.44
0.3
2.6
0.45
0.87
Clearly, the coupling of RF energy from air into planar tissue is greater for
low-water-content tissue compared to high-water-content tissue. It is greater for higher
RFs than for lower ones and ranges from about 15% to 80%. The data given in Table 1.1
show that the penetration depth for low-water-content tissues such as bone and fat is
about five times greater than that for high-water-content tissues and that it is also frequency dependent. The transmission coefficient for air–tissue interfaces nearly doubles
for low-water-content tissues compared with high-water-content tissues. Moreover, the
transmission coefficient for tissue–tissue interfaces is generally larger than that for air–
tissue interfaces, whereas the reflection coefficient shows just the opposite trend. The
reflection coefficient varies from a low of 5% for muscle–blood interfaces to a high of
about 50% for bone–muscle interfaces (Lin and Bernardi 2007).
In a layered tissue structure having different dielectric permittivities, the coupling
behavior can be very complex. Multiple reflections can occur between tissue interfaces.
The transmitted field will combine with the reflected field to form standing waves in
each tissue layer. The peaks of the standing waves can result in greater coupling of RF
energy into the tissue layer. The standing-wave phenomenon becomes especially pronounced if the thickness of each layer is greater than the penetration depth for that tissue layer and is approximately one-half wavelength or longer at RF. This dependence of
standing-wave oscillation peaks on layer thickness is a manifestation of layer resonance,
which can enhance power transmission.
1.10.2 Radiofrequency Field Coupling to Bodies with Curvature
A plane-wave RF field in the far zone can overcome exponential losses and produce
enhanced coupling at great depths in bodies with curved surfaces. Typically, if the largest
dimension of the body is comparable to the wavelength of the impinging RF field, energy
deposition and distribution will be influenced by the surface curvature of the whole body
or the body part and tissue composition. In particular, the ratio of geometric variables and
wavelength affects the characteristics of RF energy coupling. An example of this phenomenon is given in Figure 1.11, where absorbed energy distributions inside a 9-cm-radius
homogeneous spherical model of the brain are shown. Note that the distributions have