Biomedical Engineering Reference
In-Depth Information
the impedance of the membranes is so small that cells are essen-
tially short-circuited, and ε′ and σ are then determined by the
water, salt, and protein content of the tissue. As the frequency
increases further to around 1 GHz there is a small decrease in
ε′ due to the interaction of the field with large polar molecules.
The rapid increase in σ above about 1 GHz and decrease in ε′
above 3 GHz are due to the polar properties of water within the
tissue. Values of ε′ and σ for several tissue types at 0.1, 1, 127, 100,
433, 915, and 2450 MHz are listed in Tables 4.1 and 4.2. These
are based on measurements and theoretical models described by
Gabriel (1996) and Gabriel et al. (1996a,b,c) and were computed
online from http://niremf.ifac.cnr.it/tissprop/.
The question of uncertainty regarding values of ε′ and σ has
been addressed by Gabriel and Peyman (2006). They suggested
that random variations from repeat measurements were the
major contribution to uncertainty in the case of biological tis-
sues and reported total uncertainties ranging from 0.8% to 7.1%
for ε and 1.3% to 10.6% for σ regarding measurements made
on porcine gray and white matter, cornea, long bone, cartilage,
liver, and fat over the frequency range 50 MHz to 20 GHz. Many
dielectric data are based on
ex vivo
measurements of animal
tissues. Stuchly et al
.
(1982) compa red
in vivo
measurements over
the range 100 MHz to 10 GHz made on several tissues in cats
and rats and found relatively small differences between species.
However, O'Rourke et al
.
(2007) measured dielectric proper-
ties of
in vivo
and
ex vivo
human liver tissues between 500 MHz
and 20 GHz. Measurements indicated that properties of nor-
mal liver tissue
in vivo
were
16% and 43% higher than those
ex
vivo
at 0.915 and 2.45 GHz. Lazebnik et al
.
(2007) carried out a
large-scale multi-institutional study in which the dielectric prop-
erties of normal breast tissue samples obtained from reduction
surgeries were measured over the frequency range 500 MHz to
20 GHz. Results showed that the dielectric properties of breast
tissue are primarily determined by the adipose content of each
tissue sample and that the dielectric properties of some types of
normal breast tissues are much higher than previously reported.
They also found no statistically significant difference between the
within-patient and between-patient variability in ε′ and σ.
Muscle
Fat
10,000
9,000
8,000
7,000
6,000
5,000
100
90
80
70
60
50
40
4,000
3,000
2,000
1,000
0
30
20
10
0
5
6
7
8
9
10
Log
10
(Frequency (Hz))
FIGURE 4.2
Frequency dependence of relative permittivity of typical
high- and low-water-content tissues (muscle and fat, respectively).
Both ε′ and σ are dependent upon the frequency of the field
and electrolyte content of the tissue as shown in Figures 4.2 and
4.3, respectively. At low frequencies (lower than approximately
100 MHz) the cell membranes present a high impedance and
essentially restrict the flow of current to extracellular regions
within the tissue. In this case the capacitance and permittivity
of the tissue are relatively high since the cell membranes can be
charged and discharged during each cycle of the applied field.
Most tissues can be classed as either being of low or high water
content. Fat and bone lie in the first group, while muscle and
brain are typical of the second group. Large variations in ε′
and σ of tissues of low water can be caused by relatively small
variations in free water and bound water close to biological
macromolecules.
In all types of tissue, the impedance of the membranes
decreases as the frequency of the field increases, giving rise to
an increase in the conductivity. There is also insufficient time
to charge and discharge the cell membranes as the frequency
increases, and this leads to the decrease in ε′ observed. In the
case of fields of frequency greater than approximately 100 MHz,
4.5 propagation of Electromagnetic
Fields in tissues
Muscle
Fat
11
1.1
10
9
8
7
6
5
4
3
2
1
0
5
1
0.9
To describe fields within lossy dielectric media such as tissues,
the permittivity ε in Equations 4.15a to 4.15d is replaced by the
complex permittivity ε*. The plane travelling wave solution anal-
ogous to Equation 4.19 becomes
0.8
0.7
0.6
0.5
0.4
0.3
or
(4.27)
−γ
.
r
−γ
.
r
E
()
rEe
=
B
()
rBe
=
0.2
0
0
0.1
with a complex propagation constant γ (m
−1
) given by
10
0
6
7
8
9
Log
10
(Frequency (Hz))
.
ε−
σ
ωε
γ= ωµ ε
j
j
(4.28)
FIGURE 4.3
Frequency dependence of conductivity of typical high-
and low-water-content tissues (muscle and fat, respectively).
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