60
Electromagnetic Fields in Biological Systems
ε′′
ε′
ε′, ε′′
0
1 2
2
1
3
3
5
10
15
20
25
20
40
60
80
Frequency (GHz)
FigurE 1.34 Measured skin permittivity (solid lines 2) for ε′ and ε″ of human (forearm) skin:
Shown in the figure for comparison are dotted (1) and dashed (3) lines representing predicted frequency dependence of skin permittivity calculated by Gandhi and Riazi (1986) and Gabriel, Lau,
and Gabriel (1996), respectively. (From Alekseev, S. I., and M. C. Ziskin. 2007. Human skin permittivity determined by millimeter wave reflection measurements. Bioelectromagnetics 28:331–9.
With permission.)
It should be noted that skin tissue is not homogeneous but consists of a multilayer of
stratum corneum (SC), epidermis, and dermis. Moreover, it is differentiated according
to body location; for example, forearm and palm skins have thin and thick SC, respectively. Similar to Equation 1.53, it has been shown that the mmW permittivity of different skin layers may be described by the Debye equation with a single relaxation time
such that (Alekseev, Gordiienko, and Ziskin 2008):
ε ι * (ω) = ε hi + (ε li − ε hi )/(1 + jωτ) + σ i /jωε 0
(1.69)
The values of τ, ε hi = ε ∞ , Δε ι = ε li − ε hi , and σ i for each of the skin layers in the models
are given in Table 1.8.
Some measured power reflection coefficients (R 2 ) for human forearm and palm skins
are given in Figure 1.35. The fraction of transmitted power (T 2 ) is found from T 2 = 1 −
R 2 (see Equations 1.44 and 1.45). It can be seen that reflections from the palm are lower
than those from the forearm (Alekseev and Ziskin 2007). The disjuncture for the two
sets of data obtained in the two frequency ranges of 37−53 and 54−74 GHz is the result
of measuring the magnitude of reflection with two waveguides of different sizes and different cutoff wavelengths. Given the trend toward lower values for higher frequencies,
perhaps the gap may be bridged by extrapolating between the two segments; in each
case, there would be a reasonable continuum of reflection as a function of frequency.
Thus, the reflection coefficients for frequencies from 37 to 74 GHz decreased from 60%
to 45% and from 40% to 20% for skin on the forearm and the palm, respectively.
Calculations of mmW power transmission coefficients for skin on the forearm
showed an increase from 55% to 65% between 30 and 90 GHz (Alexseev et al. 2008).
A thick SC in the palm causes an increase in transmission as a result of layer matching phenomenon at higher mmW frequencies. The transmitted power density profile,
Electromagnetic Fields in Biological Systems
ε′′
ε′
ε′, ε′′
0
1 2
2
1
3
3
5
10
15
20
25
20
40
60
80
Frequency (GHz)
FigurE 1.34 Measured skin permittivity (solid lines 2) for ε′ and ε″ of human (forearm) skin:
Shown in the figure for comparison are dotted (1) and dashed (3) lines representing predicted frequency dependence of skin permittivity calculated by Gandhi and Riazi (1986) and Gabriel, Lau,
and Gabriel (1996), respectively. (From Alekseev, S. I., and M. C. Ziskin. 2007. Human skin permittivity determined by millimeter wave reflection measurements. Bioelectromagnetics 28:331–9.
With permission.)
It should be noted that skin tissue is not homogeneous but consists of a multilayer of
stratum corneum (SC), epidermis, and dermis. Moreover, it is differentiated according
to body location; for example, forearm and palm skins have thin and thick SC, respectively. Similar to Equation 1.53, it has been shown that the mmW permittivity of different skin layers may be described by the Debye equation with a single relaxation time
such that (Alekseev, Gordiienko, and Ziskin 2008):
ε ι * (ω) = ε hi + (ε li − ε hi )/(1 + jωτ) + σ i /jωε 0
(1.69)
The values of τ, ε hi = ε ∞ , Δε ι = ε li − ε hi , and σ i for each of the skin layers in the models
are given in Table 1.8.
Some measured power reflection coefficients (R 2 ) for human forearm and palm skins
are given in Figure 1.35. The fraction of transmitted power (T 2 ) is found from T 2 = 1 −
R 2 (see Equations 1.44 and 1.45). It can be seen that reflections from the palm are lower
than those from the forearm (Alekseev and Ziskin 2007). The disjuncture for the two
sets of data obtained in the two frequency ranges of 37−53 and 54−74 GHz is the result
of measuring the magnitude of reflection with two waveguides of different sizes and different cutoff wavelengths. Given the trend toward lower values for higher frequencies,
perhaps the gap may be bridged by extrapolating between the two segments; in each
case, there would be a reasonable continuum of reflection as a function of frequency.
Thus, the reflection coefficients for frequencies from 37 to 74 GHz decreased from 60%
to 45% and from 40% to 20% for skin on the forearm and the palm, respectively.
Calculations of mmW power transmission coefficients for skin on the forearm
showed an increase from 55% to 65% between 30 and 90 GHz (Alexseev et al. 2008).
A thick SC in the palm causes an increase in transmission as a result of layer matching phenomenon at higher mmW frequencies. The transmitted power density profile,