RF/Microwave Interaction Mechanisms in Biological Materials - RF/Microwave Interaction with Biological Tissues - page 65

system and the investigated dielectric effect. Nonlinearity thresholds have
been evaluated elsewhere [12].
Dipolar Orientation Dipolar orientation has been described in Sections 1.6
and 1.7. The basic theory is macroscopic and does not strictly apply to molec-
ular systems. It applies poorly to liquids, especially to water. In tissues, several
dipolar effects may be anticipated. Globular proteins typically exhibit total
dielectric increments of the order of 1-10 per gram of protein per 100 g of solu-
tion, with relaxation frequencies in the range 1-10 MHz. Polar side chains on
protein relax at some higher frequencies. However, these are likely to be rel-
atively small effects in tissues at RFs and below for which charging phenom-
ena or counterion effects dominate the dielectric properties.
Water is the major constituent in most tissues, and in several respects the
dielectric properties of tissues reflect those of water. At RFs, the conductivity
of tissue is essentially that of its intracellular and extracellular fluids. At
microwave frequencies the dielectric dispersion arises from the dipolar relax-
ation of the bulk tissue water. Dipolar relaxation of water is a dominant effect
in tissues at microwave frequencies. Pure water undergoes nearly single time
constant relaxation centered at 20 GHz at room temperature and 25 GHz at
37°C. Water associated with protein surfaces has a lower relaxation frequency
than that of the bulk liquid, and this water fraction contributes noticeably to
the dielectric dispersion at frequencies near 1 GHz.
Interfacial Relaxation If a material is electrically heterogeneous, charges do
appear at the interfaces within the material because of boundary conditions
at the interfaces. Interfacial effects typically dominate the dielectric proper-
ties of colloids and emulsions. Evaluating the effect of interfaces within a mate-
rial is a classical EM problem, in particular for evaluating the transmission and
reflection of EM waves, solved in a number of textbooks [e.g., 13-15]. Simple
models can easily be analyzed.
Cartesian configurations are most easy to evaluate, for instance two semi-
infinite media in contact with each other, one slab of a given thickness inserted
into an infinite medium separated in two parts by the slab, two slabs in contact
with each other, and so on. The bulk permittivity and conductivity of the com-
posite material can easily be calculated. When the bulk material properties of
the constituent phases vary with frequency, the frequency dependence of the
heterogeneous material can no longer be characterized by a single relaxation
time.
The conductivity of a dilute suspension of spherical particles has been cal-
culated by Maxwell as a function of the volume fraction of the suspended
particles. His analysis has been extended by Wagner to the case of alternating
currents, which led to a set of dispersion equation in the form of Eqn. (1.9).
These results clearly show that the presence of heterogeneity introduces dis-
persion in the material. This is often termed the Maxwell-Wagner theory.
Fricke extended it to the case of prolate or oblate spheroids for which a