Biomedical Engineering Reference
In-Depth Information
This problem was addressed for the first time in the study of the dynamics
of human vocal folds, and it was Ingo Titze who, in that framework, proposed
one of the most satisfactory models for the establishment of membrane os-
cillations in an airflow. According to this model, the membranes are able to
sustain lateral oscillation modes as well as flapping modes. This means that,
although the movement of the labia can be very complex as the airflow passes
between them, it is possible to decompose this movement into two simpler
ones. The first movement consists of the two masses of tissue approaching
(or moving away from) each other. In the second movement, the upper edges
of the labia move away from (or approach) each other, while the lower edges
approach (or move away from, respectively) each other. This second move-
ment can be seen as an upward propagating wave in the mucosa. In Fig. 4.4,
we show these basic motions, while Fig. 4.5 displays a series of snapshots
corresponding to successive times in the case where both movements are su-
perposed. These motions can be described as follows. Let us call a 1 half the
separation between the lower edges of the labia, and a 2 half the separation
between the upper edges. If the two modes described above are active, then
a 1 = a 10 + x + τy,
(4.10)
a 2 = a 20 + x
τy,
(4.11)
where τ is the time it takes for the propagating mucosal wave to travel a
distance of half the vertical size of the labia.
(a)
(b)
Fig. 4.4. In the flapping model, the labia move according to the coordinated dy-
namics of two global modes. The first mode is a lateral displacement ( a ), while the
second mode is an upward-propagating wave ( b ). If the labia are displaced away
from each other and have a convergent profile, or are displaced towards each other
and have a divergent profile, the labia gain energy from the airflow in each cycle.
The reason is that when they have a convergent profile, the average pressure be-
tween the labia is closer to the bronchial pressure, whereas the interlabial pressure
is closer to atmospheric pressure for a divergent profile. This results in a force in
the same direction as the velocity of displacement of the labia, which can overcome
dissipation
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