Biomedical Engineering Reference
In-Depth Information
TABLE 3.1
Specific Heat Capacity and Density
Specific Heat Capacity
Density
(J kg
-1
°C
-1
)
(kg m
-3
)
Tissue
Skeletal muscle
3470
70
Fat
2260
940
Bone, cortical
1260
1790
Bone, spongy
2970
1250
Blood
3890
1060
Source:
From [1].
have to be made. As an example, when investigating the effect of microwaves
on the spinal cord, because of the narrowness of the medium and imperfect
knowledge of the power deposition in the nearby tissues of the spinal cord
(bone, skin, and muscle), only the longitudinal two-dimensional section of the
spinal cord has been considered, assuming a homogeneous medium [8]. With
this approximation, the bioheat equation can be written as
(
)
∂
Txyt
t
,,
[
]
r
xycxy
(
,
) (
,
)
=
k xy
(
,
)
—
Txyt
(
,
,
)
+
v xy T
(
,
)
-
Txyt
(
,
,
)
2
t
s
a
∂
(
) +
(
)
(3.7)
+
Qxy Qxyt
,
,
,
m
where
T
is the temperature inside the medium at the considered point (°C),
r(
x
,
y
) the volume mass of the tissues (1020 kg m
-3
),
c
(
x
,
y
) the specific heat of
the tissues (3500 J kg
-1
°C
-1
),
k
t
the thermal conductivity of the tissues (0.6 W
m
-1
°C
-1
),
v
s
the blood heat exchange coefficient (= 14560 W m
-3
°C
-1
),
T
a
the
arterial temperature (37°C),
Q
m
the heat generated by the metabolic activity
(W m
-3
),
Q
the heat generated by the absorption of the electromagnetic energy
(W m
-3
),
t
the time (
s
), and
2
1
Qxyt
(
,,
)
=
s
(
xyE xy gt
,
)
(
,
)
( )
(3.8)
2
where
g
(
t
) = 1 during the microwave exposure and
g
(
t
) = 0 otherwise. In the
absence of adequate information about the thermal constants of the spinal
cord, the thermal constants of white matter have been used. The terms
c
,
v
s
,
k
t
, and
Q
m
depend on the type of tissues. They were assumed to be independ-
ent of temperature. The usual practice of assuming that
Q
m
may be neglected
when compared to
Q
has been followed. Finally, it has been assumed that the
spinal cord is evenly perfused. As can be seen, solving the bioheat equation
even in a simplified case requires skill.
Possible
nonthermal effects
are under question. This is not a new question
[9, 10]. It will be examined in more detail in Section 3.8. In fact, some of the
so-termed nonthermal effects might actually be microthermal effects [11].
Also, one needs to be very careful about the conditions of an experimental
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