Biomedical Engineering Reference
In-Depth Information
Use a more general form of Boyle's Law to determine the tidal volume needed at body tem-
perature/pressure:
P
B
V
B
T
B
5
P
M
V
M
T
M
T
B
P
M
V
M
P
B
T
M
5
310 K
ð
480 mmHg
Þð
750 mL
Þ
V
B
5
5
520 mL
760 mmHg
ð
283 K
Þ
Twenty-one percent of this volume is oxygen and of that, your body can only use 35%:
520 mL
0
:
21
0
:
35
5
38
:
22 mL
T
T
Thus, the body takes in 38.22 mL O
2
/breath under normal conditions.
The number of breaths needed on the mountain top would be
270 mL O
2
=
min
breath
5
7 breaths
=
min
38
:
22 mL O
2
=
To model the diffusion of oxygen into blood or that of carbon dioxide out of blood, let
us consider the respiratory boundary as a semipermeable membrane (
Figure 9.6
). Blood
flows along one side of the membrane and gas flows along the other side. For simplicity,
let us assume that the membrane is only permeable to one respiratory gas (O
2
for this
example). The net movement of oxygen across this channel will be from the gas side to the
blood side. If we take the mass balance of the gas within each chamber across this semi-
permeable membrane, assuming that
the concentration of oxygen is constant
(i.e.,
1
C
O
2
2
blood
5
C
O
2
2
gas
constant), we get
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
ð
9
:
7
Þ
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
ð
9
:
8
Þ
where J is the flux of oxygen across the membrane defined by
D
h
ð
C
O
2
2
gas
2
C
O
2
2
blood
Þ
J
5
ð
9
:
9
Þ
where h is the thickness of the respiratory boundary. If
Δ
x approaches zero,
Equations 9.7
and 9.8
become
dC
O
2
2
gas
dx
52
D
Ru
G
h
ð
C
O
2
2
gas
2
C
O
2
2
blood
Þ
ð
:
Þ
9
10
FIGURE 9.6
Respiratory boundary modeled
as a semipermeable membrane. Using this type
of model, the diffusion of respiratory gases
across the respiratory boundary can be calcu-
lated if we assume that the total concentration
of the gas remains constant along the channel.
Gas velocity, u
G
C
O
2
−
gas
(
X
)
R
O
2
R
C
O
2
−
blood
(
X
)
Blood velocity, u
B
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