ANALYSIS OF COUGHING MECHANISM
M3
Bindu George
Jocelyn Poruthur
Chunpang Shen
Jeffrey Wu
ABSTRACT
The coughing mechanism of collapsible and non-collapsible trachea models, with varying
diameter sizes, was observed. The mechanism was studied using a pressurized tank, solenoid
valve, and trachea setup. Nitrogen gas ranging from 1 to 8 psi was expelled through the trachea
models. Water, 30%, 60%, and 90% glycerol-water solutions were used to simulate bronchial
mucus. The percentage efficiency of mucus removal from the large collapsible trachea model
was found to be 4.8% to 10% higher than the rigid trachea. No significant difference in
percentage efficiency was found between the small collapsible and non-collapsible tracheas.
During the coughs, the percentage expansions of the large and small collapsible tracheas were
found to be ranging from –6.25% to –17.01% and –0.015% to 2.95%, respectively. The collapse
observed in the large collapsible trachea led to higher velocity of the escaping nitrogen gas and
higher percentage efficiency.
BACKGROUND
Coughing is a normal reflex that helps clear the respiratory tract of secretions and foreign
material. It can be caused by an irritation of the airway or from stimulation of receptors in the
lung, diaphragm, ear (tympanic membrane), and stomach. The bronchi and trachea are
extremely sensitive to even the smallest amounts of foreign matter. The following picture
illustrates the structure of the trachea and bronchi.
Figure 1 Trachea
The point where the trachea divides into the bronchi, the larynx and carina, are the most
sensitive locations. When this region is irritated, vagus nerves in the respiratory passages
transmit impulses and trigger the neuronal circuits of the medulla. This results in the following
chain of events. First, about 2.5 liters of air are rapidly inspired. Then the epiglottis closes and
the vocal cords shut causing entrapment of air in the lungs. The abdominal muscles then
contract, pushing the diaphragm. As a result, lung pressure rises to 100mm Hg. The vocal cords
and epiglottis suddenly open allowing the release of the built up pressure in the lungs at velocity
of about 75-100 miles per hour. The compressive force induced by the lungs causes the bronchi
and trachea to collapse by causing the noncartilaginous parts to fold inward. The air coming out
carries the foreign object in the bronchi and trachea out.
In this experiment, the rates of collapse of the noncartilaginous parts were determined
using video taping technology. Also the efficiency of cough was studied using non-collapsible
and collapsible tubing of varying diameters. The cough wase simulated by using a pressurized
tank as lungs and diaphragm, a solenoid valve as glottis, tubing as trachea, and a small amount of
viscous fluid as mucus.
METHODS AND MATERIALS








Nitrogen Gas
Clamps, Ring Stands
Glycerol-Water Solutions: 30% and 60%
Scale
Camera, VCR
Tygon Tubing, Penrose Tubing
12 cm Syringes
300 cc Graduated Cylinder
Experimental Setup
Figure 2 Large collapsible trachea model
Figure 2 (a) Top: Small, collapsible trachea (b) Bottom: Ruler setup with large collapsible trachea
Four different models of trachea were used. Two types of trachea models were madeone that is half-collapsible and half-rigid and the second being completely rigid. For the two
models of the collapsible-rigid tracheas, the collapsible part of the trachea was made from
Penrose tubes with diameters of 0.5” and 1”. A half-cylindrical syringe modeled the rigid
portion. The Penrose tubes were cut into 12 cm length pieces. Syringes of 50 cc and 25 cc were
sawed into half along their lengths. Using a rat-tail, the sawed surfaces were polished for safety.
The inside surfaces of the tubes were also etched using the rat-tail to aid in adhesion of the
cylinder to the Penrose tubing. For the smaller syringe, the two halves were joined together at
the ends with epoxy glue. The half cylindrical syringes were then sawed to a length of 12 cm
with the non-cylindrical parts removed. Afterwards, the Penrose tubing was glued onto the rigid
half-cylindrical syringe with contact cement. For the totally rigid trachea, only the noncylindrical parts of the syringe were removed. The cylindrical syringes were sawed to length of
12 cm.
The tank, solenoid valve, and Tygon tubing configuration of the project was modeled
after the setup in Experiment 1. The trachea was clamped to the end of the Tygon tubing. The
double Y fittings were used to simulate airflow from the two main stem bronchi into the trachea.
A 300 cc graduated cylinder with a parafilm top was used as the collection apparatus.
Finally, a camera was set up to record the collapse of the half rigid, half collapsible
tracheas. The camera was positioned at the same level as the trachea models and was secured
onto a ring stand. The camera was focused on the trachea to capture the side view of the collapse.
The camera was connected to a VCR to enable recording of the experiment. The motion of the
Penrose tubing in the collapsible models was determined by noting the displacement of the
tubing during each cough as captured by the camera. The displacement was determined by
noting the position of the tubing relative to a fixed ruler that was placed behind the trachea
models during the cough. (Figures 2a and 2b) Note that the large collapsible model was inverted
to prevent the solution from exiting prematurely.
A source gas tank was connected to a steel tank and two pressure gauges (one electronic,
one non-electronic), which were attached to determine the pressure inside the tank. The steel
tank was connected to a solenoid valve, which can be opened and closed electrically. The
trachea models were attached next in series after the valve.
The LabView program “cough2001.vi” read changes in the pressure transducer. The
voltage readings from the pressure transducer were calibrated with the pressure gauge by
creating a 0 pressure and a 10 psig environment with the gas tank. LabView also controlled the
duration at which the solenoid valve was opened (the length of the cough).
Nitrogen gas was used for all trials since it is the major component of expired air (~74%).
Four series of cough solutions were used: 0% glycerol (water), 30% glycerol, 60% glycerol and
90% glycerol. Air in the lungs is expelled at high pressures of approximately 100 mmHg for a
cough. The cough pressures at which the experiments were conducted were determined by
finding the maximum pressure that would allow for the determination of the rate of collapse
while insuring that the trachea would not collapse completely. The maximum pressures at which
the large and small tracheas could be tested were 8 psi and 2 psi, respectively. The large tracheas
were tested at 4, 6 and 8 psi while the small tracheas were tested at 1 and 2 psi.
A cough was simulated by opening the solenoid valve for 0.15 seconds while having 15
cc of cough solution in the tubing for the large tracheas and 5 cc for the small tracheas. First, the
tubing was filled with 0% glycerol solution. The pressure in the steel tank was raised to 8 psig of
nitrogen. A cough was simulated and the solution forced out of the large collapsible trachea was
collected and weighed in a 300 cc graduated cylinder to determine the amount of solution
emitted. Three trials were conducted under this condition. The procedure was repeated using
30% glycerol, 60% glycerol, and 90% glycerol for two collapsible trachea designs and two non-
collapsible tracheas. Then, one trial of a long cough in which the tank pressurized at the
maximum pressure for the respective trachea size was emptied until the pressure in the tank was
0 gage.
RESULTS
The percentage of liquid coughed out of the trachea was calculated using the following
relationship:
% Efficiency 
Mass f , bucket  Massi, bucket
 Liquid  V0, Liquid
x100%
The percentage efficiency is the quotient of the mass of the coughed out liquid and the mass of
the original liquid slug. The efficiency was calculated for all completed trials.
The dimensionless parameter employed for this project is defined by the following equation:
where  is the gas density, U is the mean gas velocity,  is the flow pulse duration (cough
Dimensionl ess Parameter 
  U 2 

duration equal to 0.15 sec), and  is the liquid viscosity. The dimensionless parameter consists of
properties of both the gas and the liquid. The value of U2 term was found using the following
Bernoulli’s relationship:
P( 0)Tank  Patm 
1
 gasU gas 2
2
 gasU gas 2  2 P( 0)Tank
The above relationship is derived with the assumptions of gage pressure, negligible velocity of
the escaping gas with in the tank, and no elevation changes.
With the appropriate unit conversions, all the units of the dimensionless parameter cancelled out.
The unit conversions are summarized in Figure 4.
5
2
2
 1P  0.02089lbf  s  2.089 x10 lb f  s
 [ ] 1cP 


 100cP  10 P  ft 2 
ft 2
 [] s
1lb f  12in  2 144lb f
  U [ ] 2 
 
in  ft 
ft 2
2
Figure 4 Unit Conversion
The plots of the percentage efficacy versus the dimensionless parameter were constructed. The
plots below are for the large and small tracheas. The results for both collapsible and rigid
tracheas could be found in the following figures as well.
Large Trachea: % Efficiency v. Dimensionless Parameter
90
y = 11.465Ln(x) - 115.28
80
2
R = 0.7327
70
%
Eff 60
ici 50
en 40
cy
30
y = 13.197Ln(x) - 147.09
2
R = 0.9251
20
10
0
0.E+00
2.E+06
4.E+06
6.E+06
8.E+06
1.E+07
1.E+07
1.E+07
2.E+07
Dim Param
Collapsible
Non-collapsible
Figure 5 Large Collapsible and Non-collapsible: Percent Efficiency v. Dimensionless Parameter
Small Trachea: % Efficiency v. Dimensionless Parameter
100
90
80
y = 9.4004Ln(x) - 53.488
2
R = 0.7851
% Efficiency
70
60
50
y = 11Ln(x) - 76.357
2
R = 0.8642
40
30
20
10
0
0.E+00
5.E+05
1.E+06
2.E+06
2.E+06
3.E+06
3.E+06
4.E+06
4.E+06
Dim Par
Non-collapsible
Collapsible
Figure 6 Small Collapsible and Non-collapsible: Percent Efficiency v. Dimensionless Parameter
The motion of the collapsible trachea model was studied by converting the video of the cough
into a digital format. The height of the tubing at each frame of the video was measured. The
percent expansion of the tube was calculated and graphed as a function of time. Figure 7
displays the percent expansion of the large collapsible model when under two different pressures
(8 psig and 4 psig) for 2 seconds with no fluid inside.
10
5
% Expansion
0
-5
-10
-15
-20
-25
-30
-35
-40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Time (sec)
8 psig
4 psig
Figure 7 Percent Expansion of Large Collapsible Model at 8 and 4 psig without Fluid
Figure 7 shows the percent expansion of the large collapsible model under the cough condition
(pressure applied at 0.15 seconds) with no fluid inside.
15
% Expansion
10
5
0
-5
-10
-15
-20
-25
-30
-35
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (sec)
8 psig
4 psig
Figure 8 Percent Expansion in Large Collapsible Model at 8 and 4 psig without Fluid
0.35
The collapses for all trials performed were examined in the same fashion. Graphs for all trials
are displayed in the Appendix for reference. Figure 8 is representative graphs of the cough
through the large collapsible model with various test fluids under 4 psig.
4 psig
5
% Expansion
0
-5
-10
-15
-20
-25
-30
0
0.04
0.08
0.12
0.16
0.2
0.24
Time (sec)
Water
30% glycerol
60% glycerol
Figure 9 Percent Expansion in Small Collapsible Model at 4 psig
Figure 9 is representative graphs of the cough through the small collapsible model with various
test fluids under 2 psig.
2 psig
% Expansion
10
5
0
-5
-10
-15
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
Water
30% glycerol
60% glycerol
Figure 10 Percent Expansion in Small Collapsible Model at 2 psig
The percent expansions of the large and small collapsible trachea models under the various
testing conditions are summarized by the average percent expansion throughout the duration of
the cough. These values are displayed in Tables 1 and 2.
8 psig
6 psig
4 psig
Large Collapsible
Water
30% glycerol
-11.07
-17.01
-7.65
-7.66
-7.17
-6.45
60% glycerol
-7.89
-7.26
-6.25
Table 1 Average Percent Expansion in Large Collapsible Model
Small Collapsible
Water
30% glycerol 60% glycerol
2 psig
0.30
1.06
2.95
1 psig
0.62
2.17
-0.15
Table 2 Average Percent Expansion in Small Collapsible Model
ANALYSIS
The effect of the tracheas’ collapsibility on the amount of liquid coughed out was
observed. It was found that the large collapsible trachea possessed vertical oscillating motion
during a cough. Furthermore, the oscillations decreased the cross sectional area of the trachea
while increasing the velocity of the gas. The increased velocity in the large collapsible trachea
led to higher percentage efficiency. The large collapsible trachea had a 4.8% to 10% higher
efficiency compared to the large non-collapsible trachea (Figure 5). A comparison between the
small collapsible and non-collapsible tracheas, however, yielded no significant difference in
percentage efficiency between the two tracheas (Figure 6). Furthermore, it was found that the
small collapsible trachea did not collapse as much as the large collapsible trachea. The above
observation suggested that there was not a significant increase in gas velocity in the small
trachea.
Figure 7 shows that as air flow through the large collapsible trachea model, the Penrose
tubing oscillates up and down. Figure 8 shows a similar motion for a cough simulation without
test fluids. On average, the model remained at a negative percent expansion (i.e., cross sectional
area decreased), but there was initial expansion.
This motion intuitively makes sense. Two forces are of concern when analyzing the
motion of the collapsible tubing. The first is the difference in pressure inside the tubing and
outside the tubing. Based on the conservation of energy through the tubing, the velocity of air
inside the tubing is greater than the outside. When applying Bernoulli’s principle across the
tubing, pressure inside is less than the pressure outside. Thus, there is a force causing the tubing
to collapse. On the other hand, the pressure applied by the gas tank creates a net force on the
tubing, thus causing the tube to expand. This second force dominates during the initial onset of
the cough because the velocity inside the tube has not had a chance to increase (i.e., no Bernoulli
effect yet). As the cough progresses, the force from the Bernoulli effect competes with the force
of the applied pressure. The velocity of the inside air increases because of the pressure, thus
causing the tube to collapse. However, when the tube is collapsed, there is an increase in surface
area normal to the pressure force, thus pushing the tubing walls outward (expansion). When the
tubing is not collapsed, the pressure force normal to the surface area is reduced, allowing the
Bernoulli pressure gradient to collapse the tubing again. This competition of the two forces is
the likely cause of the oscillation of the collapsible tubing.
From Figures 7 and 8, it appears that the frequency of oscillation decreases as the applied
pressure increases. This assertion is a tentative one, however. The frame rate of the digital video
format is thirty frames per second. With this small frame rate, much of the motion has not been
captured. If the actually frequency of oscillation was in fact greater than 30 Hz, then the data
collected cannot be used to make an assertion about the frequencies.
Figures 9 and 10 as well as the figure shown in the Appendix are graphs of the motion of
the collapsible tubing during each trial. When examining each graph, one can find no concrete
trend in the effects of fluid viscosity on the percent expansion of the tubing. Also, the motion of
the tubing cannot be predicted. However, one major trend that can be stated is that on average,
the large collapsible model remains at a collapsed state during a cough. The small collapsible
model remains at an expanded state during a cough, although it does collapse at the end of the
cough.
Table 1 illustrates that on average throughout the cough, the large collapsible tubing
remains at a negative percent expansion (collapsed state). This explains the greater efficiency of
the collapsible model over the non-collapsible model shown in Figure 5. On average, the cross
sectional area is smaller during a cough, thereby increasing the average velocity of the flow. The
increased velocity helps to remove more of the fluid.
Table 2 shows that on average throughout the cough, the small collapsible tubing remains
at a positive percent expansion. However, these expansions are all less than 3%. The average
cross-sectional areas for the collapsible and non-collapsible models are not significantly
different. Thus, there is no advantage in using the small collapsible model, as shown in Figure 6.
Referring back to Figure 5, the dimensionless parameter for the large collapsible model
was calculated assuming that the velocity of air through the tube was identical to the velocity of
air through the non-collapsible model. However, on average during a cough, the large
collapsible model had a cross-sectional area less than that of the non-collapsible model. The
dimensionless parameter used for the large collapsible model is incorrect because the velocity of
the airflow is greater. Using the data from Table 1, the dimensionless parameter could be
recalculated. The corrected graph of efficiency verses dimensionless parameter for the large
collapsible model should match that for the large non-collapsible model.
The only term that needs to be corrected in the dimensionless parameter is the velocity
value U. Using conservation of mass (continuity), we have:
A1U 1  A2U 2
2
r 
AU
  r12
U2  1 1 
 U 1   1   U 1
2
A2
  r2
 r2 
If U1 and r1 are the velocity and radius of the non-collapsible tubing respectively, then U2 and r2
are the average velocity and radius of the collapsible tubing. Making a rough assumption that
the shape of the collapsed tubing remains circular (the exact shape of the cross section cannot be
uniformly determined), the two radii can be equated based on the collapse data:
r2 
100  percent expansion
100
 r1
Substituting into the continuity equation, we have:
2


2


 r1 
r1
100

  U  
U 2     U 1 
1
 100  percent expansion
 100  percent expansion

 r2 

 r1 

100


2

 U1


The dimensionless parameter is dependent of U2. Therefore, the dimensionless parameter can be
corrected by the following manner:
Parametercorrected

100
 
 100  percent expansion
4

  Parameteroriginal


Figure 11 is the resultant graph when making this modification.
Large Trachea: % Efficiency v. Dimensionless Parameter
90
80
% Efficiency
70
60
50
40
30
20
10
0
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
2.5E+07
Dim Param
Collapsible
Non-collapsible
Corrected Collapsible
Figure 11 Revised Version of Figure 5
The logarithmic trendline for the non-collapsible curve closely matches that of the corrected
collapsible curve.
IMPROVEMENTS

Devise a method to collect all solution coughed out

Obtain a frame grabber with a higher rate of frames/second

Construct a dip within the trachea model so that the loaded solution would stay in the
tube as opposed to dripping out
Several actions can be taken by experimenters to reduce uncertainty in results and obtain
more conclusive data. First, a more efficient method of collecting solution after coughing
should be devised. The method utilized in this project did not allow for collection all of the
expelled solution. As a result, the calculated percent efficiency was lower than the actual
percent. Second, a dip within the trachea model needs to be constructed so that the loaded
solution will stay in the tube as opposed to dripping out. Heat treatment of the syringe could
be performed prior to completing the model, so that there would be an indentation for the
water to collect. Otherwise Tygon tubing, that is more flexible, could be used to model the
non-collapsible side. Third, video equipment that can capture at a higher rate
(frames/second) needs to be obtained. In this experiment, a frame grabber was used to
capture stills at 3 frames/second. If a higher capturing rate was available, more data points
could be collected and analyzed for the determination of the collapse rate or pattern.
CONCLUSION
The large collapsible trachea model showed a higher efficiency (4.8-10% greater)
compared to its respective non-collapsible model. This was due to the higher velocity obtained
when the cross sectional area decreased during oscillation. However, the small collapsible
trachea model did not show an advantage in terms of efficiency over its respective noncollapsible model. Theses results correspond to the degree in which the Penrose tubing
collapsed during the cough. The Penrose tubing oscillates up and down during a cough. The
large collapsible model expands on average by -6.25% to -17.01% during the cough trials. The
small collapsible model collapses on average by -0.15% to 2.95%.
APPENDIX
Percent Expansion versus Time for Large Collapsible Model During Cough
Trials
% Expansion
4 psig
5
0
-5
-10
-15
-20
-25
-30
0
0.04
0.08
0.12
0.16
0.2
0.24
Time (sec)
Water
30% glycerol
60% glycerol
% Expansion
6 psig
0
-5
-10
-15
-20
-25
-30
-35
0
0.04
0.08
0.12
0.16
0.2
0.24
Time (sec)
Water
30% glycerol
60% glycerol
8 psig
% Expansion
10
0
-10
-20
-30
-40
0
0.04
0.08
0.12
0.16
0.2
Time (sec)
Water
30% glycerol
60% glycerol
0.24
Percent Expansion versus Time for Small Collapsible Model During Cough
Trials
1 psig
% Expansion
6
4
2
0
-2
-4
0
0.05
0.1
0.15
0.2
0.25
Time (sec)
Water
30% glycerol
60% glycerol
2 psig
% Expansion
10
5
0
-5
-10
-15
0
0.05
0.1
0.15
0.2
Tim e (sec)
Water
30% glycerol
60% glycerol
0.25