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 made- one 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 non-cylindrical 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:

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

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:


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.

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.


Figure 5Large Collapsible and Non-collapsible: Percent Efficiency v. Dimensionless Parameter


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.

Figure 7Percent 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.

Figure 8 Percent Expansion in Large Collapsible Model at 8 and 4 psig without Fluid

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.

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.

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.

Table 1 Average Percent Expansion in Large Collapsible Model

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:

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:

Substituting into the continuity equation, we have: