Biomedical Engineering Reference
In-Depth Information
Physical work,
W
(J), can be computed by multiplying the force by the distance an
object is moved or by multiplying the change in pressure by the change in volume. In
general terms this can be written in terms of an integral
V
2
=
P
(
V
)
dV
W
(9.6)
V
1
where
P
(Pa) is the pressure, and
V
1
and
V
2
are the start and end volumes (m
3
)
, respectively.
In the compliance curve for the lung-chest cage system, the change in total volume is
plotted as a function of the intrapleural pressure. From the compliance curve, it is possible
to estimate the amount of elastic work performed by the respiratory muscles.
For the inspiration of an average tidal volume of 500 ml, the elastic work,
W
el
(J), would
be proportional to the triangular area a-b-c-a in Figure 9-14. By making some assumptions,
the same plot can be used to estimate the frictional work for this tidal volume. During
inspiration the intrapleural pressure would initially fall below atmospheric pressure and
then gradually return to atmospheric pressure as the lung fills with air at end inspiration.
Thus, the friction work,
W
insp
(J), is proportional to the curved segment a-i-b-a labeled
resistive work during inspiration.
In the example shown, the total elastic work performed by the muscles is equal to the
area of the triangle a-b-c-a
W
el
=
P
×
V
2
=
500
×
500
×
10
−
6
/
2
=
0
.
125 J
From the relaxation curve, it is apparent that most of the work during inspiration is elastic
work, with a smaller amount of frictional work. During inspiration, the lung is stretched
and sufficient (potential) energy is stored to do the work needed to overcome the frictional
resistance encountered during expiration. The elastic work performed during inspiration
is recovered and is normally sufficient to overcome the frictional resistance work,
W
exp
(J),
associated with expiration, shown as the curved segment a-b-e-a labeled resistive work
during expiration. The negative work,
W
neg
(J) (done on the inspiratory muscles during
expiratory air flow), is proportional to the area a-e-b-c-a.
FIGURE 9-14
Work done to
overcome elastic
and frictional
components during
normal breathing.
[Adapted from (Fenn
and Rahn 1965).]
