Biomedical Engineering Reference
In-Depth Information
The solubility coefficients for oxygen and carbon dioxide in blood are 0.024 and 0.57, respec-
tively. Gas diffusion can also be modeled as the movement of gases across a semi-permeable
boundary. In general, we would write the mass balance equations (for oxygen) as
Ru
G
ð
C
O
2
2
gas
ð
x
1Δ
x
Þ 2
C
O
2
2
gas
ð
x
ÞÞ 1
J
Δ
x
5
0
and:
Ru
B
ð
C
O
2
2
blood
ð
x
1Δ
x
Þ 2
C
O
2
2
blood
ð
x
ÞÞ 2
J
Δ
x
5
0
assuming that the concentration of the gas remains constant within the channel.
9.5
Oxygen has a very low solubility in blood and therefore another mechanism for oxygen
transport is needed. As we know, oxygen diffuses into the red blood cell and becomes asso-
ciated with the heme groups of hemoglobin. Carbon dioxide has a much more complicated
transport mechanism. Approximately 70% of the carbon dioxide enters the red blood cells
and interacts with carbonic anhydrase to form hydrogen and bicarbonate ions; 25% of carbon
dioxide associates with free amino groups on the hemoglobin protein. The remaining carbon
dioxide is transported directly in the blood.
9.6
Gases are fairly compressible, and it is important to develop the relationships for compress-
ible fluid flow. For a steady isentropic flow, the governing equations are
ρ
1
v
1
A
1
5
ρ
2
v
2
A
2
5
m
R
x
1
p
1
A
1
2
p
2
A
2
5
mv
2
2
mv
1
v
1
2
5
h
2
1
v
2
2
5
h
0
s
1
5
s
2
5
s
h
1
1
For an ideal gas, we can make use of the following relationships
p
5
ρ
RT
h
2
2
h
1
5
c
p
ð
T
2
2
T
1
Þ
p
ρ
k
5
constant
If there is friction without heat transfer, we need to consider
R
x
1
F
x
1
p
1
A
1
2
p
2
A
2
5
mv
2
2
mv
1
and:
2
Rln
T
2
T
1
p
2
p
1
s
2
2
s
1
5
c
p
ln
If there is heat transfer without friction, then we need to consider
v
2
2
2
h
1
2
v
1
2
Q
5
_
mh
2
1
9.7
Emphysema and tuberculosis are two common diseases that affect the respiratory system.
Emphysema is characterized as a destruction of the respiratory boundary, and therefore,
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