Biomedical Engineering Reference
In-Depth Information
The physical interpretation of counterion polarization is rather simple [10].
The motion of an ion in the bulk electrolyte near the particle depends greatly
on whether its sign is the same or opposite than of the ions in the counterion
layer. Ions of the same sign can enter the counterion layer and their charge is
quickly conducted to the opposite side of the particle: The particle acts as a
good conductor. Those of opposite sign are excluded from the layer and must
travel around the particle in the bulk electrolyte surrounding the particle: The
particle acts as an insulator. As a result, charges accumulate in the electrolyte
near the particle, giving rise to an induced dipole moment of the system and
hence a large permittivity of the suspension.
2.2.3
Dielectric Dispersion in Tissues
The Kramer and Kronig equations [Eqn. (1.12)] relate the real (imaginary)
part of the permittivity to the imaginary (real) part of the permittivity through
an integral over the whole frequency range. One may also say that they relate
the conductivity of materials, including biological tissues, to their permittivity.
It has been observed in Section 1.3.1 that for the imaginary part to exist, the
permittivity has to vary as a function of frequency. When a material has param-
eters such as permittivity, conductivity, and/or permeability varying as a func-
tion of frequency, it is said to be
dispersive
; this property is called
dispersion
.
Evaluating dielectric dispersion consists in considering the variation of the
properties as a function of frequency. On the other hand, when a material
has a nonzero imaginary part of the permittivity (or of the permeability), it
exhibits losses and is said to be
dissipative
(or
lossy
); this property is called
dissipation
. It can easily be proven that dissipation induces dispersion and
reciprocally, but in a universe satisfying causality [18].
In Section 1.3.1, Eqns. (1.15) and (1.16) formulated the correspondence
between the conductivity
s
and the imaginary part of permittivity
e≤
of a mate-
rial; in particular,
[
(
)
]
ss e
sswe
=¢+ ¢
S m
Eq. 1.15
-
1
eff
¢¢ =
+ ¢¢
F m
[
Eq. 1.16
(
)
]
-
1
eff
and for most
practical purposes only their conductivity must be taken into account. This is
not true at higher frequencies, as will be shown below. Equations (1.15) and
(1.16) show that an increase of conductivity with frequency is associated with
a decrease of permittivity.
It has already been said that water is the major constituent in most tissues.
The water contained in tissues is sometimes called
biological water
. It is obvi-
ously difficult to evaluate the differences between bulk tissue water and bulk
water. Dielectric relaxation, conductivity, and diffusion have however been
investigated for the sake of comparison. For instance, Cole-Cole representa-
tions show a relaxation time of the water in muscle tissue 1.5 times longer than
This shows that in tissues at low frequencies one has
e
eff
>> e¢,
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