This section first presents the flow rate, then the direction of breathing jet, and finally the area of nose/mouth opening for normal breathing. The normal breathing flow rate can be best represented by a sine wave for all the subjects, and for all the breathings shown in Table 1, although the time of inhalation was shorter than that of exhalation. Figure 1 shows the typical flow rate variation over time.
The functional form of the flow rate during breathing can be expressed as:
The MV and RF can vary with the subject, organ of breathing or human posture, and so will ‘a’ and ‘β’. We conducted statistical tests to investigate the influence of organ of breathing and human posture on MV and RF. The RF and thus MV can change with the organ of breathing due to the differences in the routes of respiration (Douglas et al., 1983), but the hypothesis testing through the paired t-tests indicated no significant differences in the current data. Human posture affects the activity of the abdominal muscle and thus may influence the breathing (Kera and Maruyama, 2005). The paired t-test indicated no significant differences in the MV and RF due to the change in the posture. This is in agreement with studies by Kera and Maruyama, 2005. Therefore, further analysis was performed on the nose breathing in sitting posture.
Our study indicated that the MV increases with the BSA, which is in agreement with the literature (Baldwin et al., 1948; Goldman and Becklake, 1959; and Robinson, 1938). The BSA can be obtained from the height and weight of a person (Gehan and George, 1970). Figure 2a, b show the variation of MV with the BSA of the male and female subjects, respectively. All the values lie between the confidence intervals from several previous studies. One of the main reasons for the wide spread could be the wide variation in ethnicity of the subjects in the current study. It was found that the MV for the female subjects was lower than that for the male subjects.
Figure 2. Variation of minute volume with the body surface area of (a) the male subjects and (b) the female subjects
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The earlier investigation by Baldwin et al. (1948) and Robinson (1938) suggested a linear relationship between the MV and the BSA. Thus, a linear regression analysis was performed to obtain the relationship between the MV and the BSA. The correlation coefficient for both groups of the subjects was found to be more than 0.4 for a p less than 0.05. The relationship for the male and female subjects can be described by Equations 5 and 6 respectively.
The confidence interval for the slope for the male and female subjects was from 4.838 to 5.868 l/m2 and 4.421 to 5.16 liter/m2, respectively.
Figure 3a, b show the variation in respiratory frequency for the male and female subjects, respectively. The exhalation time was longer than the inhalation for both of the genders. The multiple regression analysis showed that the respiratory frequency was mainly dependent on the height. With an increased height that may be associated with an increased lung capacity, the frequency would be decreased for the same MV. For the male subjects, a slight dependency on weight was also found. An increase in weight increased the frequency and, hence, reduced the time period of each breath. Therefore, a heavier person typically has a shorter breath. Equations 7–10 give the relationship between the RF and the physiological parameters for the male and female subjects.
where RF is respiration frequency, H body height, and W body weight.
Thus, with physiological parameters of a person, the MV and respiratory frequencies can be obtained using Equations 5–10. The amplitude and frequency of the breathing sine wave can then be calculated from the MV, RFin, and RFout through Equations 2–4. Finally, the flow rate over time can be obtained with the a and β-values via Equation 1.
The nose breathing direction was investigated by visualizing the jets from the front and side views. The jets can be better defined with two angles from each view. Figure 4 shows these views and the angles for one of the jets. The θm and φm are the mean side and front angle, while the θs and φs are the front and side spreading angle, respectively.
The mean side and front angles did not vary much among the subjects as shown in Figure 5. Hence, an average angle calculated from these mean angles could be used for the nose breathing direction. Equations 11 and 12 give a 95% confidence bound for the side and front mean angles.
Similar variation was observed for the spreading angle though there was variation among the subjects as shown in Figure 5. Thus, averaged mean and spreading angles with 95% confidence bounds are proposed and are given by Equations 13 and 14 respectively.
Figure 6 shows a mouth breathing jet. The mouth breathing jet was discharged approximately in the horizontal direction with a spreading angle of 300. Table 2 shows variations of the mouth breathing angles among the subjects.
Table 2. Variation in jet angle from mouth breathing among different subjects
|Subjects||θ1||θ2||Spreading angle θs (=θ1 + θ2)|
The mouth breathing jet was observed to have a negligible spread from the front and, hence, the side-angle is deemed sufficient to define the direction of the jet. The side spread can be described by a single value:
This investigation found that the nose opening area did not change during normal breathing for a subject but variation existed among some of the subjects as shown in Figure 7. The mean nose opening area for the female subjects was smaller than that of the male subjects. Equations 16 and 17 give the mean nose opening area with 95% confidence bounds for the male and female subjects respectively.
The mouth opening was measured over time during normal mouth breathing and did not change with during the process, thus can be modeled as a constant. Figure 8 shows the results obtained in correlation with the BSAs for all the subjects. The results do not show a correlation. Thus, an average value is proposed for modeling the mouth breathing. Equations 18 and 19 shows the average value of the mouth opening area with 95% confidence bound for the male and the female subjects respectively.
This section first discusses the flow rate, jet direction and mouth opening area measured or observed during talking. As mentioned in the research design, the talking study consisted of three parts: counting from 1 to 10, pronouncing six letters, and reading a passage.
Figure 9 shows the flow rate over time for all the three exercises. It was observed that the time required for enunciating an alphabet or a number was around 1 s while the total time required for reading the passage was around 2 min. The peak flow rates of counting three times consecutively numbers two, three, eight, and ten were higher than others. The same was observed for alphabets F, S, and T than the other alphabets. The flow rate over time for the passage was found to be irregular. The positive flow rates indicate the exhalation while the negative flow rates indicate inhalation. The exhaled and inhaled volume is thus calculated by integrating the positive and negative flow rates over the exhalation and inhalation time respectively. Table 3 shows the volume of exhalation and inhalation from the nose and mouth of a subject. It is evident from Table 3 that most of the outflow (i.e. exhalation) took place from the mouth, while inhalation through the nose. The air volume imbalance was probably due to the leakages from the mask used to collect the flow. The peak flow rates during talking (Figure 9c, d) are higher than the peak flow rate during normal breathing (Figure 1). But the total volume exhaled/inhaled during talking (∼27 l in 2 min) is comparable to breathing (∼12 l in 1 min, it is the MV for the subject). As it would be difficult to accurately describe the irregular flow, a time averaged flow rate was obtained from this study by dividing the exhaled air volume with the total time of the event (exhalation and inhalation). As most of the exhalation took place through mouth, this average flow rate can be used as boundary conditions for the mouth for modeling the exhalation of talking. Similarly, as most of the inhalation took place from the nose, the average flow rate can be used as a boundary condition at the nose for modeling inhalation of talking.
Figure 9. Flow rate measured for a subject: (a) from the mouth by counting the numbers three times consecutively, (b) from the mouth by pronouncing the alphabets three times consecutively, (c) from the mouth for reading the passage, and (d) from the nose for reading the passage
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Table 3. Air volume inhaled and exhaled from the nose and mouth of a subject during the passage reading
|Volume inhaled (l)||4.02||23.92||27.94|
|Volume exhaled (l)||21.96||3.89||25.85|
Figure 10a, b show the measured airflow rate for pronouncing the alphabets (Aavg), counting the numbers (Navg) and reading the passage (Pavg) for the male and female subjects respectively. It was found that the Aavg, Navg and Pavg for both genders increase with the BSA. The average flow rate for talking, i.e. the average amount of air exhaled/inhaled over a time period is in a way similar to breathing MV, i.e. the volume exhaled/inhaled in a minute. The breathing MV is linearly related to the BSA (body surface area) (Baldwin et al., 1948 and Robinson, 1938). Thus, a linear regression analysis was performed on the talking flow rate data to obtain a relationship similar to breathing (Equation 5 or 6). Equation 20 shows the relationship for various talking flow rates. Table 4 shows the value of the slope (m) for various exercises for the male and female populations.
Figure 10. Measured airflow rate for counting the numbers (Navg), pronouncing the alphabets (Aavg) and reading the passage (Pavg) vs. body surface area (BSA) for (a) the male subjects and (b) the female subjects
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Table 4. Value of slope (m) as defined in Equation 20 obtained from the regression analysis
|Male||(3.8 ± 0.9) × 10−1||(4.31 ± 1.2) × 10−1||(9.7 ± 0.7) × 10−2|
|Female||(3.0 ± 0.8) × 10−1||(2.6 ± 0.6) × 10−1||(8.9 ± 1) × 10−2|
The talking process was visualized to determine jet directions. As no single event can define a talking process, its direction should be determined by Equation 15 for mouth breathing jet. The mouth opening during talking is the area between the lips when certain words/letters are said. As the lip movement is continuous during talking, the mouth opening varies over time. Figure 11 shows the change in the mouth opening area over time for a subject when he/she counted numbers from one to ten. Initially, the mouth opening area increased and then stayed almost unchanged and finally reduced to zero. The variation in the mouth opening area while reading the rainbow passage would be the sequence of the variations in mouth opening areas when the words in the passage are said. Thus, the average of these mouth opening areas can be used to model the talking process. The variation in the mouth opening area when numbers from 1 to 10 are said could be a representative of mouth opening area for various words in the rainbow passage. Hence, this study recommends using a time averaged area, averaged over all the numbers for modeling the talking process with passage flow rates.
Figure 12 shows the variation in this average area of mouth opening with the height for all the subjects. No clear trend with height or any other physiological parameter was observed. Thus, an average area of mouth opening is proposed for both of the genders and is given by Equation 21.