Biomedical Engineering Reference
In-Depth Information
therapy applications tissues are closer to the source (certainly
less than a wavelength away), or even in contact with it. Under
these conditions, a parameter often referred to as the effective
penetration depth,
d
ef
, is used, which is not only less than
d
but
is also dependent upon the distance from the device. Figure 4.6
shows the dependence of
d
ef
upon frequency and the size of
source, assuming that the source has a square aperture and irra-
diates muscle-like tissue. For relatively large sources (
a
~ 20 cm),
d
ef
is dependent upon frequency and approaches the plane wave
penetration
d
. However,
d
ef
generally decreases as the size of
the aperture decreases. For relatively small apertures (a ~ 4 cm),
there is little dependence of
d
ef
on frequenc y.
The human body is comprised of many tissue types, each
with differing dielectric properties (see Tables 4.1 and 4.2).
Electromagnetic fields must satisfy Maxwell's equations in each
tissue type and at boundaries between tissues. The boundary
conditions that must be met at an interface between two tissues,
tissue A and tissue B, are:
Muscle
Fat
11
10
9
8
7
6
5
4
3
2
1
0
5
6
7
8
Log
10
(Frequency(Hz))
Muscle
Fat
0.4
0.36
0.32
0.28
0.24
0.2
0.16
0.12
0.08
0.04
0
(
)
×=0
EE n
AB
−
(4.40a)
(
)
×=
ε
E
−
ε
E
n
ρ
(4.40b)
AA
BB
(
)
×=
HH nJ
A
−
(4.40c)
B
8
9
10
(
)
Log
10
(Frequency(Hz))
− ×=
(4.40d)
µ
HH n
0
0
A
B
FIGURE 4.5
Frequency dependence of plane wave penetration depth
in muscle and fat tissues. Upper: 100 kHz to 100 MHz. Lower: 100 MHz
to 10 GHz.
where
n
is a unit vector normal to the interface. In Equation
4.40d it is assumed that the permeability of each tissue is equal
to that of free space μ
0
. When there are no surface charges or
currents, ρ and
J
are zero, and it follows from Equations 4.40a
to 4.40d that the components of
E
and
H
parallel to the interface
are continuous:
where
M
is the total mass of the body. The local SAR at a given
location is
2
EE
A
B
and
HH
A
B
(4 .41)
SAR
σ
E
0
=
.
(4.38)
local
2
ρ
while the components perpendicular to the interface satisfy
If the penetration depth
d
is taken to be the distance into a
medium over which the electric field is reduced by a factor
e
, the
corresponding reduction in the SAR is by a factor
e
2
(i.e., by a
factor of 7.39 or to approximately 13.5%). In the clinically related
literature, a measure of penetration that is of more practical use
in thermal therapy is
d
½
, the distance over which SAR is reduced
by a factor of 2. The determination of penetration in practice
requires further comment, since in most cases tissues are located
in the near field of the electromagnetic source. For example, if
SAR is measured at two depths,
z
1
and
z
2,
beneath a source, then
ε
E
=
ε
E
and
HH
A
=
B
.
(4.42)
AA
⊥
BB
⊥
⊥
⊥
4.6 principles of Electromagnetic
Heating techniques
A general term for the production of heat in body tissues is dia-
thermy. In the literature medical diathermy refers to the moder-
ate heating of tissues used to treat sports injuries and in other
forms of rehabilitation where the induced temperature rise
remains below the patient's pain threshold. Surgical diathermy
refers to more extreme heating such as that used to cut tissue or
to produce coagulation. More specific thermal therapies include
hyperthermia and thermal ablation. Heating techniques employ
frequencies from those in the RF range through to microwaves.
Sources may use predominantly electric or magnetic fields and
may be located externally to the body or can be implanted within
the tissues to be heated.
(
)
(
)
SARat
z
/
AR at
z
=
exp
2
zzd
.
−
/
(4.39)
2
1
2
1
If
z
1
and
z
2
are approximately equal to or greater than the
wavelength in tissue, then for a constant (
z
1
−
z
2
), this ratio is
independent of the actual depth. Under these conditions, the
determination of
d
is clearly defined. However, in most thermal
