Nitric oxide transmission from the maxillary sinus to the nasal cavity
Figure 2 shows the NO concentration in the nasal cavity when the breath was held for 10–60 s. The result shows that there was no airflow in the nasal cavity when the breath is held, and NO entered the nasal cavity by diffusion from the maxillary sinus. When the breath was held for 10 s, NO filled the nasal cavity. As the breath-holding time increased, NO continuously entered the nasal cavity from the maxillary sinus, and the concentration of NO in all parts of the nasal cavity increased. However, the overall distribution law was that closer the proximity to the maxillary sinus ostium, the higher was the NO concentration. NO concentration was lower in the nasal threshold and nasopharynx, which are situated far from the maxillary sinus ostium.
Airflow distribution in the nasal cavity and maxillary sinus
An expiratory flow of 10 mL/s was set for the nasopharynx, and the maxillary sinus wall was set as the NO generation source at a concentration of 10000 ppb. Figure 3 shows the airflow streamline in the maxillary sinus and nasal cavity during breathing. Owing to the difference of several orders of magnitude between the airflow velocity in the nasal meatus and in the maxillary sinus, the color scale in Fig. 3 is logarithmic. Because the maxillary sinus model has only one outlet and is a closed cavity, there was almost no convective flow observed in the maxillary sinus (Fig. 3). During breathing, the airflow velocity in the maxillary sinus was very low; it was approximately 3–4 orders of magnitude lower than that in the nasal airway. Multiple vortices were generated in the maxillary sinus, and their axes were in different directions. When the gas containing NO exited the maxillary sinus along the ostium into the middle meatus, it flowed with the airflow in the middle nasal passage, the speed increased rapidly, and finally flowed out through the nostrils or into the lower respiratory tract. Therefore, NO concentration in the nasal cavity was affected by NO concentration in the maxillary sinus as well as by the airflow rate in the nasal cavity.
Distribution of NO concentration in the nasal cavity at different NO concentrations in the maxillary sinus
The boundary condition in the nasopharynx was set at the expiratory flow rate of 10 mL/s, and the maxillary sinus wall was set to produce NO at a concentration of 1000–23000 ppb (Lundberg et al. 1994). The distribution of NO concentration in the nasal cavity under different NO concentrations in the maxillary sinus can be obtained by calculation. As shown in Fig. 4, NO concentration in the nasal cavity increased with an increase in NO concentration in the maxillary sinus, but the distribution pattern of NO in the nasal cavity did not change significantly. Because this was an expiratory process, NO was distributed only in the anterior part of the nasal cavity bounded by the maxillary sinus ostium. NO diffused from the maxillary sinus and it was transported by the expiratory airflow. It then diffused in the front half of the nasal cavity and finally flowed out through the nostrils. Figure 5 shows NO concentration of the exhaled airflow from the nostrils under different NO concentrations in the maxillary sinus; a linear relationship was observed between them.
Distribution of NO concentration in the nasal cavity under different airflow rates
NO concentration from the maxillary sinus wall was set at 10000 ppb, and the expiratory flow rate in the nasopharynx was set at 5–100 mL/s. The effects of different airflow rates on the distribution of NO concentration in the nasal cavity were investigated. The simulation results in Fig. 6 show that lower the airflow rate, higher was the NO concentration in the nasal cavity, and greater was the diffusion range in the nasal cavity. As shown in Fig. 7, NO concentration in the nostrils decreased with an increase in the airflow rate. NO concentration at the airflow rate of 5 mL/s was approximately 6.6 times that at the airflow rate of 100 mL/s. However, NO content in the exhaled airflow increased with an increase in the airflow rate. NO content at the airflow rate of 100 mL/s was approximately three times that at the airflow rate of 5 mL/s. Thus, in addition to NO concentration in the maxillary sinus, the distribution pattern of NO concentration in the nasal cavity is associated with the respiratory airflow rate. At an airflow rate of 100 mL/s, as soon as NO entered the nasal airway through the maxillary ostia, it flowed out through the nostrils with the expiratory airflow. However, when the airflow rate was 5 mL/s, it took a long time for NO to flow out of the nasal cavity; hence, it diffused in the anterior half of the nasal cavity.
Distribution of NO concentration in the nasal cavity during normal respiration
A numerical simulation was performed for the distribution of NO concentration in the nasal cavity during the entire breathing process. One breathing cycle was set for 4 s with a sinusoidal variation of the airflow rate and a tidal volume of 600 mL. Figure 8 shows the changes in the distribution of NO concentration in the nostrils and nasopharynx during the entire breathing process after two cycles of calculations. It was observed that during 0–2 s and 4–6 s of inspiration NO flows from maxillary sinus to nasopharynx, and the NO concentration in the nostril was 0. At the beginning (4 s) and end (6 s) of inspiration, NO concentration increased to approximately 432 ppb and 336 ppb, respectively, in the nasopharynx. However, in the mid-inspiratory phase (5 s), which is the time of peak inspiratory flow, NO concentration was low (approximately 300 ppb). The total amount of airflow and NO content during inspiration were calculated, and the average NO concentration was calculated as approximately 320 ppb. This amount of NO would return to the nasal cavity during expiration and would finally flow out through the nostrils. It is assumed that during exhalation, the inhaled NO was mixed sufficiently with the air in the lungs, and its content was not reduced. NO flowed into the nasal cavity with the expiratory airflow from the nasopharynx, and NO continued to enter the nasal cavity from the maxillary sinus. During the entire expiratory phase, there was a mixed constant concentration of NO in the nasopharynx. At the beginning (6 s) and end (8 s) of expiration, NO concentration increased to approximately 433 ppb and 424 ppb, respectively, in the nostrils. However, in the mid-inspiratory phase (7 s), which is the time of peak expiratory flow, NO concentration was low (approximately 393 ppb). NO concentration in the nostrils was higher than that in the nasopharynx throughout the expiratory phase. Figure 9 shows the NO concentration profile in the nasal cavity during respiration. Figure 9 (a) represents the case of lower airflow at 4.1 s; it shows that only the nasal airway in the posterior part of the maxillary sinus ostium had NO during inspiration, and the range of distribution of NO in the nasal cavity was large. Figure 9 (b) shows the distribution of NO at the peak of inspiratory airflow at 5 s, and it can be seen that the range of NO distribution was small. As the airflow rate in the nasal cavity was quite high, a large amount of NO was removed to the extent that NO content in the middle of the maxillary sinus began to decrease significantly. Figure 9 (c) shows that during exhalation, as inhaled NO was well mixed with air in the lungs, the exhaled NO was diffusely distributed throughout the nasal cavity in uniform concentrations. NO concentration was high in the maxillary sinus ostium because of NO continuing to enter the nasal cavity from the maxillary sinus ostium.
Comparison between numerical simulation results and experimental test results
Nasally exhaled NO concentrations of 50 healthy volunteers from the Dalian region were recorded, and the results are shown in Fig. 10 and Table 1. The measurements showed a general agreement between the measurements of the left and right nostrils (approximately 390 ppb). When the right nostril was the test nostril, the air entered the left nasal cavity from the left nostril, flowed through the left middle meatus, and carried NO from the left maxillary sinus into the nasopharynx. The air then entered the right nasal cavity, carried NO from the right maxillary sinus into the right nostril, and finally entered the NO analyzer. When tested for the nostril of the other side, the process of the airflow transport of NO was reversed. This means that the measured NO concentration in the experiment represents the transport rate of NO from the bilateral maxillary sinuses into the nasal cavity. Therefore, whether measured from the left or right nostril, the measurement results may differ only slightly. NO concentration in the maxillary sinus wall was adjusted to 3500 ppb, and the calculated NO concentration in the right nostril was 394 ppb, which was close to the experimental data recorded. Since the NO concentration set as 3500 ppb in the maxillary sinus was within the normal range, the reliability of the numerical simulation results could be verified to some extent.
Table 1
Statistical analysis of nitric oxide concentrations in 50 healthy adults from Dalian, China in 2021
Sides
|
N
|
Mean ± standard deviation
|
95% confidence interval
|
LnNO
|
50
|
383.32 ± 126.35
|
347.41–419.23
|
RnNO
|
50
|
395.26 ± 124.32
|
359.93–430.59
|
nNO
|
100
|
389.29 ± 124.85
|
364.52–414.06
|
(nNO, nitric oxide concentration in the nostrils; LnNO, nitric oxide concentration in the left nostril; RnNO, nitric oxide concentration in the right nostril) |
Different types of NO concentration test equipment show different sampling flow rates. At the beginning of the NO test, NO concentration was unstable; hence, it needed to be pumped for some time so that NO concentration reached a plateau, and it could then be measured. At different sampling flow rates, the time taken to reach the plateau was different. Figure 12 shows the numerical simulation of the NO test experiment and the calculated value of NO concentration output from the right nostril within 10 s for different sampling flow rates. It can be observed that as the sampling flow rate increased, the time required for NO concentration in the nostrils to reach a stable value decreased. When the sampling flow rate was 100 mL/s, it took approximately 2 s for NO concentration to reach a stable value. When the sampling flow rate was 50 mL/s, it took approximately 4–5 s for NO concentration to reach a stable value. However, when the sampling flow rate was 5 mL/s, NO concentration had not plateaued at 10 s. These computational results are in general agreement with the experimental results of Muchmore et al. (2017). Figure 13 shows the numerical results of NO concentration in the right nostril at sampling flow rates of 5–100 mL/s, corresponding to the results of the measured plateau. It can be seen from the numerical results in Fig. 13 that with an increase in the sampling flow rate, NO concentration in the right nostril decreased, and many previous studies showed this trend (Lundberg et al. 1996; Imada et al. 1996). At the sampling flow rates of 5 mL/s and 100 mL/s, the numerical results of NO concentration in the right nostril were approximately 547 ppb and 158 ppb, respectively.
It is difficult to measure NO concentration directly in the maxillary sinus using the current experimental methods. The NO analyzer can test the overall concentration of NO entering the nasal cavity from the maxillary sinus. In this study, volunteer was asked to hold his breath for a certain time, and then the trend of NO concentration in the nostrils for different breath-holding times was assessed to study the ability of the maxillary sinus to transmit NO into the nasal cavity. In the experiment, the volunteer was asked to hold his breath for 10–30 s. NO concentration was then measured in the right nostril at the sampling flow rate of 10 mL/s for 6 s. Simultaneously, a numerical simulation of this breath-holding test was performed. In the established numerical model of the nasal cavity, the flow rate in the right nostril (sampling side in the test) was first set at 0 for 10–60 s, and then the change in NO concentration in the right nostril was calculated at the sampling flow rate of 10 mL/s for 10 s. Figure 14 shows that with an increase in the breath-holding time, NO concentration in the nostrils increased continuously. Each of the trend lines showing changes in NO concentration first increased and then decreased continuously, and finally tended to reach a stable value, which was close to 400 ppb at 10 s. By dividing the total amount of exhaled NO in the first 6 s by the total exhaled air flow, the average concentration of exhaled NO in the first 6 s can be obtained. The numerical results in Fig. 15 show that NO concentration did not reach a plateau in the first 6 s and increased with an increase in the breath-holding time. The experimental results (Fig. 15) also show that when the test time lasted only 6 s, the NO concentration was affected by the breath-holding time, which increased with the breath-holding time. Comparing the experimental and numerical results shows that although there are some differences in value, the slopes are approximately the same between the two results. In other words, the rates of NO transport from the maxillary sinus to the nasal cavity were close.