Airway turbulence and changes in upper airway hydraulic diameter can be estimated from the intensity of high frequency inspiratory sounds in sleeping adults

Abstract

Obstructive sleep disordered breathing can cause death and significant morbidity in adults and children. We previously found that children with smaller upper airways (measured by magnetic resonance imaging while awake) generated loud high frequency inspiratory sounds (HFIS, defined as inspiratory sounds > 2 kHz) while they slept. The purpose of this study was (1) to determine what characteristics of airflow predicted HFIS intensity, and (b) to determine if we could calculate changes in hydraulic diameter (D) in both an in vitro model and in the upper airways of sleeping humans. In an in vitro model, high frequency sound intensity was an estimate of airflow turbulence as reflected by the Reynold's number (Re). D of the in vitro model was calculated using Re, the pressure gradient, Swamee–Jain formula and Darcy formula. D was proportional to but smaller than the actual diameters (r² = 0.94). In humans, we measured HFIS intensity and the pressure gradient across the upper airway (estimated with oesophageal pressure, P_es) during polysomnography in four adult volunteers and applied the same formulae to calculate D. At apnoea termination when the airway opens, we observed (1) an increase in HFIS intensity suggesting an increase in turbulence (higher Re), and (2) a larger calculated D. This method allows dynamic estimation of changes in relative upper airway hydraulic diameter (D) in sleeping humans with narrowed upper airways.

Key points

• Adults and children with obstructive sleep disordered breathing make loud high frequency inspiratory sounds (HFIS, defined as inspiratory sounds >2 kHz) while sleeping.

• In an in vitro model, the intensity of high frequency sounds was found to be an estimate of airflow turbulence as reflected by the Reynold's number (Re).

• Hydraulic diameter (D) of the in vitro model could be calculated using Re determined by sound intensity, the pressure gradient, the Swamee–Jain formula and the Darcy formula.

• In four adult humans, D was calculated from measured HFIS intensity and the pressure gradient across the upper airway (estimated with oesophageal pressure, P_es).

• At apnoea termination when the airway opens, we observed (1) an increase in HFIS intensity suggesting an increase in turbulence (higher Re), and (2) a larger calculated D.

• This method allows dynamic estimation of changes in relative upper airway D in sleeping humans with narrowed upper airways.

Introduction

We previously observed that children suspected of having obstructive sleep disordered breathing (OSDB) made loud high-pitched inspiratory sounds (HFIS) during sleep (Rembold & Suratt, 2004). We defined HFIS as a sound during an inspiration that has discrete harmonics at frequencies >2 kHz. Parents of these children described these sounds as snoring. These children also had narrow upper airways as measured by magnetic resonance imaging (MRI) when the children were awake (Rembold & Suratt, 2005). The frequency peaks of the HFIS predicted a resonant chamber that had a length similar to the length of the children's upper airways (Rembold & Suratt, 2005). Louder HFIS were found in the children who had smaller upper airways measured by MRI while awake (Rembold & Suratt, 2005). The children who made many HFIS had more episodes of airway closures and narrowing (obstructive apnoeas + hypopneas per hour of sleep) than those who did not.

In this study, we first evaluated which characteristic(s) of moving air predicted the intensity of HFIS. In a previous study, we postulated that HFIS intensity was an index of inspiratory effort in people with a narrowed but not entirely collapsed upper airways (Rembold & Suratt, 2005). In the current study, we found that the pressure gradient across the upper airways (estimated by oesophageal pressure, P_es) was not the primary predictor of HFIS intensity. We found that HFIS intensity primarily reflected the degree of turbulence as estimated by the Reynolds number (Re).

Our second objective was to determine whether we could calculate hydraulic diameter (D) in an in vitro model and in the upper airways of sleeping humans with narrowed but not occluded upper airways. D is a theoretical physics/engineering conception that describes a minimum circular region that has the same airflow characteristics as an obstruction, which is not an ideal circle. In the in vitro model, calculated D was proportional to measured diameters. In humans, we found that we could calculate dynamic changes in relative airway hydraulic D from the degree of turbulence (Re as estimated by HFIS intensity) and the inspiratory effort as estimated by oesophageal pressure (P_es). D was larger at and following apnoea termination than before apnoea termination, i.e. during the apnoea.

Methods

In vitro model

We created a simple model of inspiratory airflow obstruction by sucking air at a constant rate through various small internal diameter (i.d.) tubes that were placed in a resonating chamber (mimicking the upper airways). We measured sound outside the resonating chamber, flow through the system and pressure on the vacuum side of the small tubes compared to ambient pressure. The model, shown in Fig. 1, had the following linear setup: hospital suction, an Ohio vacuum regulator, 7 m of 7.9 mm i.d. plastic tubing (the long length suppressed some of the noise from the vacuum regulator and vacuum source), an electronic flow meter (Timeter Series RT200, setting 32, St. Louis, MO, USA), 1 m of 7.9 mm i.d. plastic tubing, a 7.9 mm i.d. T junction with the side arm of the T junction attached to the low pressure port of a Timeter model T300 electronic pressure meter (Allied, St. Louis, MO, USA), followed by one of several 2 cm long cylindrical tubes each with a different i.d. (2.4, 3.2, 4.0, 4.8 and 7.9 mm) to generate obstructions. These 2 cm long tubes were placed in one end of a 12 cm long, 25.4 mm i.d. plastic PVC resonating pipe. A recording microphone was placed 0.3 m from the other end of the resonating pipe. The recording system had the same settings employed as in the previously described human studies. For each small i.d. tube, the vacuum regulator was adjusted to generate ∼5, ∼10, ∼15, ∼20, ∼25 and ∼30 l min⁻¹ flow while we simultaneously measured flow, pressure at the T-junction and high frequency sound (HFS) intensity. With a larger obstructive i.d., these flow rates did not generate as low a pressure as that seen with a smaller obstructive i.d.

Figure 1.

Schematic diagram of the in vitro model

Human study

Subjects

The study was approved by the University of Virginia Human Institutional Review Board and were performed in accordance with the Declaration of Helsinki. Four subjects with the highest number of apnoeas hourly were chosen from a larger trial of 21 subjects. These four subjects had 63% of the apnoeas detected in the 21 subjects. All were adults who signed informed consent.

Polysomnography and sound recording

The four subjects had overnight polysomnography using conventional techniques, including electroencephalograms, electro-occulograms, submental electromyograms, nasal airflow measured with a nasal cannula attached to a pressure transducer, oral airflow measured with a thermister, pulse oximetry and chest/abdominal movement detected by respiratory inductance plethysmography as previously described (Suratt et al. 2006). We measured oesophageal pressure (P_es) to approximate the driving pressure across the upper airways. P_es was measured with a water-filled oesophageal catheter that was placed through the nose into the oesophagus as previously described (Kushida et al. 2002). The catheter was a soft 2 mm paediatric feeding tube (PEDI-TUBE, Kendall; Tyco Healthcare Group, Mansfield, MA, USA) whose end was placed approximately 40 cm from the nares. Appropriate placement was confirmed by appropriate changes in pressure during breathing (Kushida et al. 2002). The oesophageal catheter was calibrated with a water manometer at −50, 0 and +50 cmH₂O. Apnoeas and hypopneas were detected using the criteria of the American Academy of Sleep Medicine Manual for the Scoring of Sleep and Associated Events (Iber et al. 2007). The definition of apnoea and hypopnoea is complicated: in general terms, an apnoea is defined as a total or near total cessation of airflow for ≥10 s and hypopnoea is a decrease in airflow for ≥10 s followed by either a fall in oxyhaemoglobin saturation or an arousal. To simplify the text, the term ‘apnoea’ includes obstructive apnoeas, mixed apnoeas and hypopnoeas.

During polysomnography, sounds were recorded from a microphone suspended 1.2 m above the bed as described (Rembold & Suratt, 2004). Sounds were sampled and digitally stored at 44 kHz for 8 h. We analysed 6 h of the recordings (the first hour included P_es calibration and the eighth hour typically included awakening of the subject, so they were not included in analysis). P_es, nasal flow, chest motion and abdominal motion signals were stored at 1 kHz in the same files.

Data analysis

Sounds were later analysed in Matlab (Mathworks, Inc., Natick, MA, USA) with fast Fourier transforms at 0.1 s intervals for frequencies between 0 and 10 kHz at 0.1 kHz intervals. The mean intensity of sounds both <2 kHz (low frequency sounds) and >2 kHz (HFS) was then averaged for each 0.1 interval. HFS intensity was normalized by subtracting background HFS intensity that was determined for each subject. Background HFS intensity was determined by visually inspected each subject's recording to find periods when ventilation was stable and HFS intensity did not vary with ventilation. The mean HFS intensity was calculated for these periods for each subject and this value was subtracted from all HFS intensity measurements for each subject. Therefore, the background sound intensity for each subject was 0 and HFIS intensities are positive numbers. In this study, HFIS were defined as HFSs that occurred during inspiration (the presence of harmonics was not required).

Scored sleep stage, apnoeas and arousal data from Sandman software was imported into the sound data files. Inspirations were identified by negative deflections in the P_es signal (an algorithm written in Matlab). For purposes of this study, we defined an inspiration as a negative deflection in P_es regardless of whether there was visible nasal airflow. Thus, a negative deflection in P_es during an apnoea when there was no visible nasal airflow was called an inspiration. We excluded inspirations that occurred when subjects were awake as defined by polysomnography. For the entire 6 h of recording, we compared the lowest P_es for each breath during sleep to the HFIS intensity and calculated hydraulic diameter (D, see below for definition) that occurred at the same time during that breath. We calculated HFIS at the lowest P_es, as the force collapsing the airway would be maximal at that point so that measurements would reflect minimal D.

Unless otherwise noted, all values are reported as means ± 1 s.e.m. Statistical significance testing was performed by t test if there were two groups or ANOVA if more (calculated in Sigmastat). P < 0.05 was the criterion for significance.

Results

Prediction of high frequency inspiratory sounds intensity using an in vitro model

To determine which characteristics of sound generated by moving air through an in vitro obstruction were responsible for increases in HFS intensity, we considered the following: (1) airflow rate across the obstruction; (2) pressure gradient across the obstruction; and (3) turbulence within the obstruction. To test this, we created a simple in vitro model of inspiratory airflow obstruction by sucking air at a constant rate through various i.d. obstructive tubes that were placed in a resonating chamber while flow and pressure were continuously measured (setup described in Methods and Fig. 1).

Flow

As more suction was applied across the small tubes in the resonating chamber, both flow and HFS intensity increased (Fig. 2A). HFS intensity was highly dependent on the i.d. of the obstruction; at any given flow rate, a smaller i.d. produced a higher HFS intensity. These data suggest that HFS intensity was not a simple function of airflow.

Figure 2. Prediction of HFS intensity from flow (A), pressure (B) and estimated Reynolds numbers (C) at various internal diameters (see inset legend) in the in vitro model.

Overall, HFS intensity was best predicted by Reynolds numbers, suggesting HFS intensity is an estimate of the amount of turbulence. HFS, high frequency sound.

Pressure

The dependence of HFIS intensity on i.d. and pressure was complicated (Fig. 2B). Specifically we found:

1. With the smallest orifice i.d. (2.4 mm), higher HFS intensity was observed with increasing pressure gradient, i.e. with more negative pressures (Fig. 2B, filled squares).

2. With a larger orifice i.d., the pressure gradients that could be generated at the tested flow rates were smaller than those generated by the smaller orifices. In general, larger orifice i.d. had lower peak HFIS intensities than that observed with smaller orifice i.d.

3. At equivalent pressures, larger orifice i.d. had higher HFS intensities than with smaller orifice i.d. This reflects the higher flow rates at equivalent pressure with higher orifice i.d. This was clearly shown in Fig. 2B at −3 cmH₂O where HFS intensity was higher with the 4.8 mm i.d. orifice (open circle) than with the 2.4 mm i.d. orifice (filled square).

4. With the largest orifice i.d., pressure could not be lowered below −1 cmH₂O because our suction source could not generate sufficient flow. Nevertheless, at the equivalent pressure of 0.7 cmH₂O pressure, the largest i.d. orifice (8.0 mm, Fig. 2B, open diamonds) produced a higher HFS intensity than that produced by smaller i.d.

These data suggest that HFS intensity was not a simple function of pressure within the physiological pressure range as HFS intensity was also influenced by orifice diameter.

Reynold's number

Finally, we calculated the Reynold's number (Re) for each combination of flow, pressure and i.d. Re is a dimensionless number that reflects whether flow is laminar or turbulent. Re <2000 occur with laminar flow while Re >4000 occur with turbulent flow; values in between reflect transitional flows. Re can be calculated as:

(1)

where i.d. is internal diameter of the obstruction, kinematic viscosity of air at 37°C is 1.57 × 10⁻⁵ m² s⁻¹, and area is the cross-sectional area of the obstruction. There was a linear relation between HFS intensity and Re with HFS intensity increasing with Re >2000 (Fig. 2C, r² = 0.88). When Re was <2000, HFS intensity was low or not detected indicating there was no measured sound generation when flow was laminar. As Re values between 2000 and 4000 predict the onset of turbulent flow and as turbulent flow would be expected to induce oscillations in air pressure that are detected as sound, these data suggest that HFS intensity is probably a manifestation of turbulent flow as measured by Re. The relationship between Re and HFS intensity in Fig. 2C is described by the following regression equation, which predicted Re from HFS intensity with r² = 0.88 (note that this relation is only valid for turbulent flow, i.e. when Re >2000):

(2)

Calculation of hydraulic diameter

We tested whether we could calculate obstruction hydraulic diameter in our in vitro model. The hydraulic diameter (D) is a theoretical physics/engineering conception that describes a minimum circular region that has the same airflow characteristics as an obstruction, which is not an ideal circle. D can be calculated from the empirically derived Darcy formula as detailed in Moody's classic paper (Moody, 1944):

(3)

Rearranging we get:

(4)

Where P is the pressure drop (as an absolute value in kg m⁻²), l is obstruction length (assumed to be 2 cm), g is the gravitational constant, f is friction factor described below in eqn (5) and Re is derived from HFS intensity using eqn (2). f can be calculated from the empirically derived Swamee–Jain formula:

(5)

For these studies, we made the assumption that the airway was not rough, i.e. e = 0 (so the term e/3.7 × D in eqn (5) becomes zero). With this assumption, calculated D in the in vitro model were smaller but proportional to actual obstruction i.d. with a regression showing D = 0.28 × i.d. + 0.0006, (r² = 0.94). The difference in calculated D and actual i.d. probably results from our assumptions, particularly that roughness (e) = 0. Importantly, these data show that HFS intensity can proportionally predict calculated D in vitro. Note that calculated D from eqn (4) is a hydraulic diameter and does not imply that the obstruction has a circular cross-section.

Equations (3)–(5) were derived empirically – these equations are quite complicated and non-intuitive. By assuming f is a constant and combining the other constants, calculated D from eqns (4) and (5) can be approximated with a simplified equation that is easier to understand (using calculated Re from HFS intensity in eqn (2):

(6)

The variance in hydraulic diameter of eqn (6) from eqns (4) and (5) when calculated using the data in Fig. 2 had a standard deviation of 0.066. This more intuitive function reveals that increases in Re will have a larger effect to increase D than will decreases in P to decrease D. This occurs because Re is raised to the 2/3 power whereas the absolute value of P is raised to the negative 1/3 power. Note that the effect of P on D is confusing because P values are negative given the vacuum source and the absolute value of P is raised to the negative 1/3 power.

Equation (6) shows the complicated dependence of D on both HFIS intensity (through Re) and P:

1. At any given pressure, low D values predict low Re values and hence by eqn (2), low HFS intensities. Larger D at any given pressure is associated with louder HFS because the larger D allows greater flow generating more turbulence (higher Re) and hence more sound.

2. As D gets very large flow becomes laminar with higher flow and less negative pressure. With the onset of laminar flow, HFIS intensity decreases (note that eqns (3)–(6) are only valid when flow is turbulent, so are not valid when D is very large and flow is laminar). This seems counterintuitive but it is well known that the elimination of turbulence increases flow at any given pressure.

3. The highest HFS intensities are associated with intermediately size Ds. Low HFS intensity are associated with either (1) low D (flow is limited), or (2) with high D (flow is high and laminar). This is what is generally thought to occur in sleeping humans with obstructive sleep apnoea. Loud inspiratory noises during sleep are only heard when the airway is narrowed but not occluded. When the airway is not narrowed during sleep, loud breathing noses are not heard.

4. At any given HFIS intensity, low D is associated with more negative P (higher |P|, so lower |P|^−1/3). Higher D is associated with less negative P (lower |P|, so higher |P|^−1/3). As D gets very large, flow becomes laminar and P gets closer to zero, flow becomes laminar and eqns (3)–(6) are no longer valid.

Human studies and calculation of hydraulic diameter from high frequency inspiratory sound intensity and pressure

Testing the hypothesis that HFIS intensity predicts turbulence (Re) in sleeping humans was difficult. In humans, we measure HFIS rather than HFS. Driving pressure, the gradient across the upper airways, can be approximated by comparing ambient pressure to intrathoracic pressure measured with an oesophageal catheter (P_es, note that during inspiration P_es is a negative number so that larger P gradients are seen with lower P_es). Airflow measurement during sleep is difficult to measure without interfering with breathing sounds. It is most accurately measured by placing a tightly fitting mask over the nose and mouth and attaching this to a flow meter. This interferes with measurement of sound. Relative airway hydraulic diameter (D) was calculated by: (1) measuring HFIS intensity to estimate Re; (2) measuring intrathoracic pressure with an oesophageal catheter (P_es) to approximate the driving pressure drop (P) across the upper airways; and (3) eqns (2), (4) and (5) at 0.1 s intervals during inspiration in four sleeping subjects. D cannot be calculated when HFIS intensities were low because low HFIS values are associated with either (1) low Re numbers suggesting laminar flow, i.e. no turbulence, Re <2000, i.e. high D, or (2) very low or no flow, i.e. very low D. Therefore, calculated D values only occur with intermediate D values when there is turbulent flow. D was not calculated during expiration as our interest was in airway collapse during inspiration.

We analysed the time course of HFIS intensity, P_es, and calculated hydraulic diameter (D) in each of the four subjects for three breaths before (termed breath −3, −2 and −1), the breath at apnoea termination (termed breath 0) and the three breaths after apnoea termination (termed breath +1, +2 and +3, Fig. 3). For this analysis, obstructive hypopnoeas, obstructive apnoeas and mixed apnoeas were scored in a blinded manner without knowledge of HFIS intensity and subsequently analysed for HFIS intensity, P_es and calculated D for 6 h of each of the four subjects. The end of the apnoea was defined as the return of airflow during inspiration without reference to HFIS intensity or P_es. HFIS intensity, P_es and D are presented as the value when the P_es value was minimal for each breath (see Methods). Figure 3 shows data from each of the four subjects with the vertical line denoting the scored apnoea termination. In all four subjects, mean HFIS intensity peaked at apnoea termination (* indicates significant difference vs. apnoea termination). Minimal P_es occurred either one breath before (subjects 8 and 12) or at apnoea termination or one breath after (subjects 4 and 5).

Figure 3. Mean time course of HFIS amplitude (A), minimal P_es (B) and D calculated hydraulic diameter (C) for the three breaths before, breath at and three breaths after apnoea termination in the four subjects.

The subject number and number of apnoeas are shown at the top. The vertical lines represent the breath at apnoea termination. Data are presented as means ± 1 s.e.m. Significance: *above error bars indicates significance by t testing versus the data at apnoea termination and *below error bars indicate significant in paired D measurements. Mean HFIS intensity and P_es data for all data are plotted as filled circles in (A) and (B). D could only be calculated when HFIS intensity was high enough to predict turbulence; therefore, mean D (C) was calculated in two ways. (1) The open circles reflect mean D for all measurements when D could be calculated; therefore, n for D was lower than for HFIS intensity and P_es (for subject 8, n = 67, 89, 148, 276, 249, 174 and 178; for subject 12, n = 32, 36, 37, 110, 87, 60 and 35; for subject 4, n = 42, 46, 65, 96, 40, 32 and 28; and for subject 5, n = 33, 40, 46, 59, 60, 38 and 45 for breaths −3, −2, −1, 0, 1, 2 and 3, respectively. (2) The filled circles reflect paired D values in which only D values were included when data are present before and at apnoea termination (see text). HFIS, high frequency inspiratory sounds.

The open symbols in Fig. 3C show the mean of calculated D at each breath and demonstrate that mean D significantly increased at apnoea termination in each subject. Equations (2)–(5) require that HFIS intensity must be high enough to predict a Re >2000 to calculate D. Many breaths did not have D calculated because the apnoea was complete and there was no airflow to generate sound. In these four subjects, only 15–53% of apnoeas had calculated D values (the highest was 53% of breaths with calculated D values at apnoea termination and the lowest was 15% of breaths with calculated D values three breaths before apnoea termination).

As averaging data with missing values can produce misleading results, we also compiled paired D values when there were data both before apnoea termination (mean of D for breaths −2 and −3) and at apnoea termination (mean of D for breaths 0 and +1). The implication of calculated D before apnoea termination is that the ‘apnoea’ did not totally block airflow as some airflow was required to increase HFIS intensity for calculation of D. The filled symbols in Fig. 3C show the mean of calculated D for paired data demonstrate that D significantly increased at apnoea termination in each of the four subjects (n = 90, 36, 51 and 44 paired breaths before and at apnoea termination with P = 4 × 10⁻¹⁶, 4 × 10⁻⁷, 8 × 10⁻⁶ and 0.003 for the change before and at apnoea termination, respectively). This result suggests that average data with missing values was not the cause of the increased D at apnoea termination.

The human data in Fig. 3 show that before apnoea termination, D was small so a higher driving pressure (lower P_es) was required to produce a small airflow, which only caused a relatively low HFIS intensity (as airflow was low, little sound was generated in the upper airway). At apnoea termination, D increased allowing increased airflow at similar or less effort (less negative P_es), which allowed more sound generation (higher HFIS intensity). The breath after apnoea termination did not require as much driving pressure (P_es nearer to 0) but had louder sound generation (higher HFIS intensity) given the increased airflow. These findings agree with both our in vitro model and with the known physiology of airways obstruction in OSDB, specifically than the airways are small during apnoeas/hypopneas and increase in size with the termination of apnoeas/hypopnoeas.

As the data in Fig. 3 involved comparison of two variables (P_es and HFIS intensity) that both changed, we reanalysed data at similar P_es values one breath before and one breath after the end of the apnoea (breath −1 and +1 in Fig. 3, which was an excellent idea suggested by one of the referees). The first two subjects (08 and 12) had enough data for this type of analysis. At a ‘constant’ P_es, both HFIS intensity and calculated D increased from breath −1 to breath +1 (Table 1).

Table 1.

HFIS and calculated hydraulic D at matched P_es

	Pes (cmH2O)		HFIS intensity		Hydraulic D (mm)
Subjects	Breath −1	Breath +1	Breath −1	Breath +1	Breath −1	Breath +1
08	−32.52 ± 0.65	−32.50 ± 0.75	3.41 ± 3.56	6.92 ± 1.14	2.10	2.49
	P = 0.73		P = 0.0006*
12	−45.68 ± 1.57	−45.70 ± 2.53	0.97 ± 1.84	3.72 ± 1.68	1.60	1.91
	P = 0.92		P = 0.0002*

Data are shown as mean ± 1 s.d., n = 21, P values per paired t test. Abbreviation: HFIS, high frequency inspiratory sounds. *Statistically significant. For patients 08 and 12 shown in Fig. 3, there were enough data points to match different breaths HFIS at nearly equivalent P_es values. We chose to match P_es values to near the mean value of all P_es at the −1 breath for each subject. The data were then sorted by P_es for breath −1 and breath +1 so that 21 breaths with P_es values nearest to the goal P_es would be analysed. Then mean HFIS intensity was calculated for these breaths and hydraulic D was calculated from the mean P_es and mean HFIS intensity.

Discussion

We previously found that children with OSDB made louder HFIS intensity during sleep than children without OSDB (Rembold & Suratt, 2004). According to classic acoustic theory (Rossing et al. 2002), sound is created when a high-velocity turbulent jet of air, such as that generated by a narrowed upper airway with a high driving pressure, is injected into a resonating chamber. The resonant chamber creates a set of sounds (harmonics) with resonant frequencies dependent on the length of the resonating chamber. As the velocity of the jet of air increases, the amplitude (loudness) of the sound increases at all of the resonant frequencies, but the frequencies themselves do not change. The amplitude of generated sound is generally louder with a higher airflow velocity, a higher airflow volume and/or a better resonant chamber. A previous study in children showed that the predominant harmonic pattern of HFIS predicted resonant chamber lengths that were the distance from the larynx to the lips in about half of the subjects and length the distance from the soft palate to the lips in the remainder (Rembold & Suratt, 2005). This indicated that the pharynx of these children was acting as a resonating chamber. Therefore, in the upper airway, narrowing and/or increasing the driving pressure should increase the velocity of the jet of air resulting in louder resonant sounds.

In this study, we investigated which characteristic(s) of moving air predicted the intensity of HFIS. We found that HFIS intensity is an estimate of airflow turbulence (Fig. 2C). HFIS intensity did not predict the effort of breathing (P_es). This is not surprising, as some apnoeas will have no airflow, so no sound is generated despite a low P_es. Other apnoeas/hypopneas will have some airflow, so sound will be generated. We also found in sleeping humans that the hydraulic diameter (D) was larger at apnoea termination compared to during apnoea, as would be expected from the accepted physiology of OSDB. D is a theoretical physics/engineering conception based on the physics of airflow; it describes an ideal circular region that has the same airflow characteristics (pressure gradient, P_es, and degree of turbulence, Re) as the non-circular obstruction in the airways. Calculation of D has some intrinsic advantages over imaging because the physics of airflow automatically finds the characteristics of the obstruction regardless of its location. This is not true with imaging, which (1) assumes the obstruction is in a two-dimensional plane (it could be saddle shaped), and (2) imaging requires a lot of manipulation to get an image perpendicular to the region with the minimal area. However, D could only be calculated when HFIS were present. HFIS occur only when there is some airflow and a moderate to high inspiratory effort. HFIS will not occur when the airways are completely occluded. HFIS are also unlikely to occur when the airways are of normal calibre as flow is generally laminar. Only when inspiratory effort becomes higher than normal would air move fast enough to create turbulent flow and generate sound. These data suggest that HFIS intensity is an index of upper airway turbulence and that relative changes in upper airway hydraulic diameter can be qualitatively estimated from HFIS intensity and P_es.

There are several assumptions that affect our calculations of D and may account for our underestimation of D in our in vitro model. First, we assumed no roughness in vitro or in vivo (i.e. e = 0 in eqn (5)). This is a better assumption in sleeping humans, who have wetted upper airways, than in our in vitro model. If we are correct that roughness was lower in sleeping humans, then calculated D should be proportionally larger than our estimate based on our in vitro model. Second, we assumed that P_es equals driving pressure where in fact it equals driving pressure plus the pressure to move the lung. As driving pressure will be less than P_es, D will be larger than what we calculated. Third, HFIS intensity depends on the resonating chamber, which will vary in different people; therefore, calculation of relative changes in D for a single person would be more accurate than comparisons among people. Therefore, we suggest that D values calculated from HFIS intensity and P_es should be considered qualitative, not quantitative measures. Fourth, this study is also limited based on the sample size of four subjects.

We have not measured actual minimum airways size. Therefore, we cannot claim our estimates of D reflect minimal airways size. Measuring dynamic changes in airways size during sleep is extremely difficult and beyond the scope of this study. CT scanning would be a radiation hazard. At present, MRI imaging is the most promising technique, but has multiple challenges: (1) the upper airways are dynamic and the region with the smallest diameter will probably be in different parts of the upper airways and be present in different imaging planes in different subjects; (2) the changes in upper airways size can be very rapid (given the large region that needs to be scanned, speeding up time resolution will reduce spatial resolution); (3) MRI scanners generate a loud banging sound during active scanning that both interferes with sleep and makes detection of HFIS difficult; and (4) documenting sleep in the scanner is difficult because the MRI scanner induces noise in electroencephalographic signals that confirm sleep. Despite these issues, dynamic MRI of the upper airways is actively being researched. At present, the most promising study involved dynamic three-dimensional MRI imaging of the upper airways of awake subjects who had external airways occlusion induced by a mask (Kim et al. 2014). They found a decrease in pharyngeal volume with external airways occlusion. They also showed some cross-sectional images that partly collapsed during external airways occlusion. Importantly, these studies were not done during obstructive apnoea or when the subject was asleep. In addition, they did not calculate the minimum diameter (which can be in different locations during a breath). Another promising development is that of a microphone that is MR compatible and a computer algorithm that eliminates MR sounds in the speech range by correlation subtraction (Inouye et al. 2014). In the future, both of these methods could probably be modified to measure minimal airway size and detect HFIS during sleep in subjects with OSDB. We suggest that HFIS intensity is a qualitative measure of the degree of airway turbulence. It is a non-invasive measure as no instruments touch the patient. When combined with a measure of ventilatory effort (P_es), it allows qualitative estimation of changes in airway hydraulic diameter (D).

Additional information

Competing interests

None

Author contributions

Both authors read, wrote and approved the final submitted manuscript and were involved in the conception of the manuscript. C.M.R. did the maths and performed the data analysis and P.M.S. the patient recruitment and sleep studies. All authors approved the final version of the manuscript.

Funding

This work was supported by the University of Virginia General Clinical Research Center M01 RR00847.