Biomedical Engineering Reference
In-Depth Information
length
l
is obtained by multiplying the expression in (4.54) by
l
:
(
)
¢(
) +
(
)
¢(
)
gr
p
aAl
H
2
ber
g
r
ber
g
a
bei
g
a
bei
g
a
2
0
0
0
0
0
P
=
2
(4.55)
a
(
) +
(
)
16
g
a
ber
g
a
bei
g
a
2
2
2
0
0
0
where
A
= p
a
2
. This expression is then transformed by defining
(
)
¢(
) +
(
)
¢(
)
2
ber
g
a
ber
g
a
bei
g
a
bei
g
a
(
) =
0
0
0
0
Qa
g
g
=
8
pms
2
f
0
(
) +
(
)
0
g
a
ber
2
g
a
bei
2
g
a
0
0
0
Finally, we obtain
1
(
)
Pf HQa
=
m
g
l
(4.56)
2
a
0
2
Now, using the relation on the skin depth of current, the definition of
Q
(g
0
a
)
can be transformed into
a
p
Ê
Ë
ˆ
¯
(
) =
QaQ
g
0
2
a
p
a
p
a
p
a
p
Ê
Ë
ˆ
¯
¢
Ê
Ë
ˆ
¯
+
Ê
Ë
ˆ
¯
¢
Ê
Ë
ˆ
¯
ber
2
ber
2
bei
2
bei
2
p
a
=
2
(4.57)
a
p
a
p
Ê
Ë
ˆ
¯
+
Ê
Ë
ˆ
¯
ber
2
bei
2
2
2
where the skin depth of current is
p
=
2
g
. Expression (4.56) can then be
0
transformed into the simple form
a
p
Ê
Ë
ˆ
¯
1
Pf HQ
=
m
2
2
Al
(4.58)
a
2
In all these expressions, cgs units such as
f
(Hz),
A
(cm
2
), and
H
a
(Oe) have been
used because of the small size of the conducting cylinder. Therefore, the
present power loss is expressed in units of (ergs per second).
Accordingly, when watts are used, the power loss in (4.56) is finally given
by the expression
Pf HQ
a
p
Ê
Ë
ˆ
¯
1
=
m
2
2
Al
¥
10
-
7
W
(4.59)
a
2
This is the expression (4.11) obtained in the previous section.
4.3
HYPERTHERMIA
The first paper on hyperthermia was published by W. Bush in 1886 [33].
According to Bush, the sarcoma that occurred on the face of a 43-year-old lady
was cured when fever was caused by erysipelas. F. Westermark in Sweden tried
to circulate high-temperature water for the treatment of an inoperable cancer
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