Biomedical Engineering Reference
In-Depth Information
END OF CHAPTER SUMMARY
9.1
The respiratory system provide the means for gas exchange between the atmospheric air and
the cardiovascular system. It is divided into a conducting pathway (composed of the nasal
cavity, the pharynx, the larynx, the trachea, and the bronchi) and a branching pathway,
which eventually diverges into the alveolar sacs. The alveoli are the locations for gas
exchange and provide approximately 70 square meters of area for exchange. The respiratory
boundary is composed of the alveoli epithelial cell, the capillary endothelial cell, and the
fused laminae between these cells. Each lung is surrounded by a pleural membrane that
facilitates the changes in lung volume to account for the movement of gases into and out of
the lungs. This is based on Boyle's Law, which for a constant temperature system is repre-
sented as
P
1
V
1
5
P
2
V
2
9.2
The lungs go through an approximate 20% change in volume, which significantly affects the
blood vessel area within the lungs. Due to these large stresses, the Kirchhoff stress and the
Green's strain are most applicable to relate the forces to the deformation. This is experimen-
tally found to be represented as
S
xx
5
a
1
E
xx
1
0
:
6429E
yy
S
yy
5
a
2
E
yy
1
0
:
6429E
xx
The separation distance for the respiratory boundary is also affected by the pressure of
the respiratory and vascular system. This distance can be modeled as
<
Δ
P
,2
:
0
0
7 mmHg
0
:
5
μ
m
0
:
5
μ
m
1
7 mmHg
Δ
P
2
0
:
7 mmHg
, Δ
P
,
0 mmHg
0
:
h
ðΔ
P
Þ 5
m
75 mmHg
Δ
P
2
μ
:
0
:
5
μ
m
1
0 mmHg
, Δ
P
,
30 mmHg
1
:
3
μ
m
Δ
P
.
30 mmHg
9.3
The pressure and the volume of the lungs are altered based on the movement of the ribs and
the diaphragm. As the diaphragm moves downward and the ribs move outward the lungs
expand and experience a temporal reduction in pressure. The reverse movements of the dia-
phragm and lungs cause the lungs to shrink and experience an increase in pressure. Under
normal conditions, the tidal volume is approximately 500 mL (of which 350 mL is used for
gas exchange), and there are approximately 12 to 15 breaths per minute. In extreme condi-
tions, the lungs can move approximately 4800 mL of air per breath, which is using all of the
inspiratory reserve and the expiratory reserve. There is 1200 mL of residual volume which
maintains the alveolar space open.
9.4
Oxygen and carbon dioxide diffusion is based on the solubility of the gas within blood.
Henry's Law formulates this as
Gas Concentration
Solubility Coefficient
P
5
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