Biomedical Engineering Reference
In-Depth Information
The diameter of the trachea is 20 mm, which makes its cross sectional area 314 mm
2
and
the air flow velocity 2.38 m/s for the same breathing rate. In this case the Reynolds number
will be
ρv
d
R
e
=
η
10
−
3
1
.
2
×
2
.
38
×
20
×
=
10
−
5
.
×
1
78
=
3208
This is larger than 2300; therefore, the flow through the trachea will be turbulent.
9.3.4 Inertia
When the respiratory muscles contract, they must produce sufficient force to accelerate
the lung-chest cage system and move the air in the airway from a standstill to some final
velocity. The opposing force of inertia is related to the mass of the object and its rate
of acceleration,
Q
(L/min
2
)
. While the lung and chest cage both have considerable mass,
their acceleration is small during normal breathing. In contrast, air can be accelerated to a
high velocity, but its mass is very small. The effects of inertia are therefore small for both
the lung-chest cage structures and air moving through the air passages—typically about
5% of the total forces that oppose respiratory muscle contraction.
9.4
ENERGY REQUIRED FOR BREATHING
Breathing requires that physical work be performed by the respiratory muscles. While
the opposing forces of elastance (compliance), frictional resistance, and inertia have been
discussed, the amount of work the respiratory muscles must perform to overcome each
of these three opposing forces as a portion of the total work performed needs to be
considered. As summarized in the Table 9-1, about 60 to 66% of the total work performed
by the respiratory muscles is used to overcome the elastic or compliance characteristics
of the lung-chest cage, 30 to 35% is used to overcome frictional resistance, and only 2
to 5% of the work is used for inertia. However, this partitioning of the opposing forces is
altered by changes in tidal volume or breathing frequency.
TABLE 9-1
Summary of the Contributions to the Work Done in Breathing
Type of Work
Contributing Components
% of Total
Surface tension 50 to 80%
Tissue 20 to 50%
Lung 50%
Elastic (compliance)
60 to 66%
Chest cage 50%
Viscous 20%
Airways 80%
30 to 35%
Frictional
Lung
2 to 5%
Inertia
Chest cage
Air
