Biomedical Engineering Reference
In-Depth Information
trachea
m 2
labium
m 1
bronchus
Fig. 6.4. The two-mass model of the labia. The hypothesis in the simple model
described in Chap. 4 is that only two modes of oscillations are needed to account for
the dynamics of the labia. A more subtle model would require us to allow different
parts of the labia to display their dynamics without being constrained to generate
an upward wave. The solutions of the models described so far can be generated by
this new model of labial oscillation, but now, new and richer solutions can also be
found
6.3.2 The Two-Mass Model
The set of hypotheses for the values of the interlabial pressure in this new
model is compatible with the set corresponding to the flapping model. In the
two-mass model, it is assumed that, if the labia form a convergent profile
(the lower parts of the opposing labia are more separated than the upper
parts), the pressure between the upper parts of the opposing labia is basi-
cally the vocal-tract pressure. On the other hand, the pressure between the
lower parts of the opposing labia is a fraction of the bronchial pressure. This
occurs because in this situation, the airflow is almost laminar (by laminar,
we mean that the air particles travel in an orderly fashion, following smooth
trajectories over the entire space available). In this regime, the pressure of
the air decreases as the fluid velocity increases. Moreover, the air will travel
faster as it moves from the bronchi to the interlabial space, since the passage
is narrower between the labia. If there is no accumulation of air, this should
further increase the air velocity. This is why the pressure between the lower
parts of the labia will be a fraction of the bronchial pressure.
Let us now pay attention to the hypothesis for the case in which the labia
form a divergent profile (i.e., the labia are “opened” to the trachea). It is
considered that the air acquires a velocity in its passage through the space
between the lower parts of the labia such that a laminar regime cannot be
established in the region between the upper parts. On the contrary, a jet is
established, so that the actual value of the distance between the upper parts
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