446 Chapter 25
1980 ; Stuchly and Stuchly 1980 ; Schwan
1981 ; Foster and Schwan 1986 ; Pethig and
Kell 1987 ; Duck 1990 ; Foster and Schwan
1996 ; Gabriel 1996, 2006 ; Gabriel and
Gabriel 1996 ; Gabriel et al. 1996a, b, c ).
The γ - dispersion, also called orientation
polarization, is located at the GHz region,
and it is due to the polarization dipoles,
fundamentally free water molecules. The
β - dispersion or interfacial polarization is
mainly due to the Maxwell - Wagner effect.
This effect is produced due to interfacial phe-
nomena on heterogeneous materials (Feldman
et al. 2003 ). Other dispersions can be pro-
duced by proteins or other macromolecules
at frequencies between the β and γ diper-
sions, depending on the size and charge of
the molecules (Gabriel 2006 ). Another addi-
tional relaxation ( δ ) is located between the β
and γ dispersions. This relaxation is caused
by the rotation of amino acids, the rotation of
charged side groups of proteins, and the
relaxation of protein - bound water (Schwan
1981 ). The α - dispersion dominates between
millihertz and a few kilohertz, and is not yet
completely understood. Some hypotheses
remark the counter - ion effects near the mem-
The conductivity of most tissues rises
from a low value at low frequencies that
depend strongly on the volume fraction of
extracellular fl uid up to a plateau in the 10 –
100MHz frequency range, which mainly
corresponds to the conductivity of intra -
and extracellular ions. Conductivity then
rises dramatically, due to the dielectric relax-
ation of water (Rigaud et al. 1996 ) (Fig.
25.4 ).
This increase in conductivity is associated
with a decrease in permittivity, from very
high values at low frequencies in different
steps called dispersions. It is important to
highlight that these dispersions are not pro-
duced instantaneously and are characterized
by the correspondent relaxation phenomena
(Schwan 1988 ). In biological systems, there
are four main relaxation regions: α , β , δ and
γ (Fig. 25.3 ). Each of these steps character-
izes a type of relaxation that occurs in a spe-
cifi c frequency range and which allows the
identifi cation of different phenomena. The
dispersions of biological systems have been
widely studied by many authors (Grant et al.
1978 ; Schanne and P - Ceretti 1978 ; Pethig
1979 ; Stuchly 1979 ; Schwan and Foster
1,00E+08
e¢
s (S/m)
¶ (Hz)
1,00E+07
1,00E+06
1,00E+05
1,00E+04
1,00E+03
1,00E+02
1,00E+01
1,00E+00
1,00E–01
1,00E–02
1,00E
–01
1,00E
+01
1,00E
+03
3,00E
+05
1,00E
+07
1,00E
+09
1,00E
+11
1,00E
+13
Figure 25.4. Ideal representation of electric conductivity and dielectric constant spectra.