Biomedical Engineering Reference
In-Depth Information
bronchi. If this is not the case, the portion of the bronchus between the
trachea and the valve will be seen by the valve as a pipe. Fletcher and
Tarnopolsky computed the bronchial resonance associated with this anatomy
[Fletcher and Tarnopolsky 1999]. These formants have been identified by
Suthers [Suthers 1994] in a study of the oilbird (
Steatornis caripensis
). He
identified frequencies which could be associated with the bronchial segments,
and showed that they were behaving as quarter-wave pipe resonators.
6.3 Labia with Structure
6.3.1 The Role of the Dynamics
There are other mechanisms that allow us to account for the spectral com-
plexity described above. But we shall have to enrich our model of the labial
oscillations in order to address them. In our discussion in Chap. 4, the up-
per part of a labium moves in a way that is perfectly correlated with the
lower part. This is due to our description of the labial movement in terms
of a superposition of two simple modes. The first mode consisted of a global
displacement, and the second one of an upward wave, together making up
a kind of flapping motion. In this situation, the upper and lower parts of a
labium move a little out of phase, the upper part always following the lower
part.
A model that allows for richer behavior can be built if the upper and lower
parts of each labium are thought of as two masses attached to each other by
means of a spring. In such a model, the labia can show more complex behavior,
beyond the behavior described above [Herzel et al. 1995, Herzel et al. 1996].
This was the strategy followed by Fee et al. [Fee et al. 1998] to explain the
existence of subharmonics in the song of zebra finches (
Taeniopygia guttata
).
The interesting aspect of this observation is that the acoustic properties of the
song are not uniquely controlled by the nervous system of the bird. The me-
chanical properties of the vocal organ can contribute to generating new prop-
erties of the sound when a small change in the control parameters is made.
In fact, the work by Fee et al. was performed on a syrinx in vitro. There-
fore, the appearance of subharmonics for certain values of the pressure does
not require delicate muscular control. The model used by Fee and coworkers,
known as the “two-mass model” (first proposed in [Ishizaka et al. 1972]) and
illustrated in Fig. 6.4, is capable of generating fluctuations in the airflow of
a higher complexity than those generated by the simple model (4.5). The
reason is that the motion of the upper part of the labium, represented by
the mass
m
2
in the figure, is affected (due to elastic coupling) to the lower
part. This allows solutions different from the ones analyzed so far, in which a
small distance between the upper parts of the opposed labia implied a large
separation between the lower parts.
