RF/Microwave Interaction Mechanisms in Biological Materials - RF/Microwave Interaction with Biological Tissues - page 69

Permittivity The relative permittivity of tissues at frequencies as low as 50-
60 Hz is extraordinary large, being of the order of 10 5 -10 7 , typically 10 6 . Figure
1.9 illustrates the variation of tissue permittivity as a function of frequency.
There are three major dispersion regions where the value of permittivity is
varying strongly with frequency, called alpha, beta, and gamma, at relaxation
frequencies in the ranges of kilohertz, hundreds of kilohertz, and gigahertz,
respectively. The permittivity undergoes an almost monotonous decrease over
the entire frequency range.
The astonishingly high value of the permittivity at very low frequency
(ELF), due to alpha dispersion, can be largely ascribed to counterion diffu-
sion effects. Indeed, theory predicts a dielectric increment of the order of 10 6
[16, 17]. The alpha dispersion also results from other contributions: active
membrane conductance phenomena, charging of intracellular membrane-
bound organelles that connect with the outer cell membrane, and perhaps fre-
quency dependence in the membrane impedance itself [19]. Although alpha
dispersion is very striking in the permittivity, it does not appear in the con-
ductivity. Assuming a dielectric increment of 10 6 and a relaxation frequency
of 100 Hz, the Kramer and Kronig relations yield a total increase in conduc-
tivity associated with alpha dispersion of about 0.005 S m -1 while the ionic
conductivity is about 200 times larger. Thus, at low frequencies, tissues are
essentially resistive despite their tremendous permittivity values.
Beta dispersion occurs at RFs. It arises principally from the capacitive
charging of cellular membranes in tissues. A small contribution might also
come from dipolar orientation of tissue proteins at high RFs. As an example,
blood exhibits a total dielectric increment of 2000 and a beta relaxation fre-
quency of 3 MHz [12]. The associated increase in ion conductivity is about
0.4 S m -1 . For tissues, the static permittivity and relaxation times of this dis-
persion are typically larger than in blood.
Gamma dispersion occurs with a center frequency near 25 GHz at body
temperature. It is due to the dipolar relaxation of the water, which accounts
for 80% of the volume of most soft tissues, yielding a total dielectric incre-
ment of 50. These values of dielectric increment and relaxation frequency yield
a total increase in conductivity of about 70 S m -1 [12].
Some authors have called delta dispersion a small dispersion occurring in
tissues and other biological materials between 0.1 and 3 GHz. The lack of a
single dominant mechanism makes the interpretation of this dispersion region
difficult.

2.2.4 Measurements

Tissues A good knowledge of the complex permittivity of biological media is
necessary for adequately determining the action of EM fields, in biological
effects as well as in medical applications. Hyperthermia is only one example.
Dielectric properties of a variety of selected tissues can be found in three main