Biomedical Engineering Reference
In-Depth Information
close to and parallel to the line of the fundamental frequency in Fig. 6.1b.
The interesting thing about this complex model, involving so many masses
and springs to emulate the labial motion, is that it gives us room to study
what happens when we change somewhat the symmetry of the problem. Now
we can afford to play with the possibility that the right and left labia might
not be exactly equal. This allows us a greater degree of realism, since the
bipartite nature of the syrinx does not allow, for each half, the same degree
of symmetry between labia as what is present in the case of human vocal folds.
Steinecke et al. [Steinecke and Herzel 1995] studied what kinds of oscillations
exist for different values of the pressure and for various degrees of asymmetry
in this model.
There are wide ranges of pressure for which (despite the asymmetries) the
solutions are regular, but for sublabial pressures larger than a certain value -
which depends on the degree of asymmetry of the problem - the solutions
become very complex. In Fig. 6.6, we compare the syringeal flows that are
predicted by the model for two different values of the pressure (and a fixed
degree of asymmetry). In the case illustrated, the values of the masses and
the coupling constant between them on the left side are 52% of the values for
the right side. As can be seen in the figure, for the first pressure condition, the
airflow is regular, with a certain period. For the second condition, the airflow
does not repeat itself until a time lapse three times larger than in the previous
case, despite the fact that the change in sublabial pressure was very slight.
The computed spectra denote the additional complexity of the airflow. The
origin of this complexity is in the dynamics of the masses, which can in fact
become completely aperiodic for appropriate values of the sublabial pressure
(a)
1.0
2
F
T
1.5
1
0.5
0
0.0
0
25
50
0.0
frequency (Hz)
500
time (ms)
(b)
1.0
2
T' ~ 3T
F' ~ F/3
1.5
1
0.5
0.0
0
0.0
frequency (Hz)
500
0
25
50
time (ms)
Fig. 6.6.
Assymetric two-mass model showing dramatic changes in flow periodicity
as the pressure parameter is changed slightly. The masses and coupling constants
for the left side are 52% those for the right-side. (
a
) “Normal” oscillation with
frequency
F
.(
b
) When the pressure is raised 10% above the value in (
a
), the
frequency of the oscillation suddenly changes to
F/
3
