Modeling the pharyngeal pressure during adult nasal high flow therapy

Accepted Manuscript Title: Modeling of pharyngeal pressure during adult nasal high flow therapy Author: Haribalan Kumar Callum J.T. Spence Merryn H. Tawhai PII: DOI: Reference:

S1569-9048(15)30012-4 http://dx.doi.org/doi:10.1016/j.resp.2015.06.011 RESPNB 2518

To appear in:

Respiratory Physiology & Neurobiology

Received date: Revised date: Accepted date:

9-2-2015 22-6-2015 22-6-2015

Please cite this article as: Kumar, Haribalan, Spence, Callum J.T., Tawhai, Merryn H., Modeling of pharyngeal pressure during adult nasal high flow therapy.Respiratory Physiology and Neurobiology http://dx.doi.org/10.1016/j.resp.2015.06.011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Modeling of pharyngeal pressure during adult nasal high flow therapy Haribalan Kumar1, Callum J.T. Spence2, Merryn H. Tawhai1 1

Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand 2

Fisher and Paykel Healthcare Limited, Auckland, New Zealand

Address: Auckland Bioengineering Institute The University of Auckland Private Bag 92019 Auckland 1142 New Zealand

Highlights

• • • •

We model pharyngeal pressure during nasal high flow therapy in adult nasal airway We simulate flow in realistic and simplified nasal airway geometry Pressure is strongly dependent on NHF rate Pressure is also dependent on nasal valve cross-section

Introduction Nasal High Flow (NHF) is a non-invasive ventilation therapy that provides respiratory support through the delivery of medical gas via wide bore nasal cannula. The therapy is postulated to provide benefit by promoting slow deep breathing or by flushing of CO2 from the nasal cavity dead space (Dysart et al., 2009). The NHF offering from Fisher & Paykel Healthcare Ltd. (Auckland, New Zealand), OptiflowTM provides flows of heated and humidified gas at rates

upto to 60 L/min, and delivers a low-level flow-dependent positive airway pressure (Dysart et al., 2009; Moller et al., 2015; Mundel et al., 2013). While NHF systems such as OptiflowTM – which delivers heated and humidified gas - are clinically attractive due to improved patient comfort and compliance (Maggiore et al., 2014; Roca et al., 2010), the lack of control of the delivered airway pressure has been noted as a clinical concern. Previous studies have measured airway pressure and velocity at the oropharynx, nasopharynx, and via tracheostomy during NHF in patients and healthy volunteers (Dysart et al., 2009; Franke et al., 2014; Gerald et al., 2013; Groves and Tobin, 2007; Parke et al., 2009; Parke and McGuinness, 2013; Spence et al., 2012; Spence et al., 2011). There is considerable variation in measured airway pressure in these studies, for example mean expiratory pressure of 2.7 ± 1.0 cmH2O in post-cardiac surgery patients for NHF at 35 L/min (Parke et al., 2009), and mean of 7.4 cmH2O (range 5.5 - 8.8 cmH2O) for NHF at 60 L/min in healthy volunteers (Groves and Tobin, 2007). The NHF system OptiFlowTM is typically used with cannula flow rates between 20-60 L/min in the adult population. In a clinical setting, if a patient is not responding satisfactorily to NHF, the clinician may choose to increase NHF rate, resulting in an increase of positive end-expiratory pressure (PEEP). Informing the process of titrating an efficacious delivered pressure with NHF is clinically very significant in terms of effect on both cardiovascular and lung function. The geometry of the nasal airways in the adult population varies widely, although with some consistent trends (Liu et al., 2009; Taylor et al., 2010). For example, the nasal valve – is a constriction located posterior to the nasal vestibule and generally represents the minimum crosssectional area of the nasal airway. The nasal valve may generally vary in range of 40 to 120 mm2 (Liu et al., 2009; Taylor et al., 2010) and the nostril area between 80 to 150 mm2. Groves and

Tobin (Groves and Tobin, 2007) observed a linear increase in expiratory pressure with flow, and they postulated that the facial features, particularly the smaller nares of females, could explain the higher pressure observed in some groups (Parke and McGuinness, 2013). Hence it is plausible that a relationship between airway pressure, nasal airway geometry, and cannula flow can be quantified. Computational fluid dynamics (CFD) uses numerical methods and algorithms to run computer simulations of fluid flows and is now frequently used to simulate airflow in nasal or bronchial airways (Bates et al., 2015; Doorly et al., 2008a; Doorly et al., 2008b; Elad et al., 2008; Quadrio et al., 2014; Schroeter et al., 2014; Subramaniam et al., 1998; Tawhai and Lin, 2010; Taylor et al., 2010). In the current study we have used CFD to elucidate the producing mechanism and maximum expected magnitudes of nasopharyngeal pressures during supply of NHF. Maximum steady-state inspiratory and expiratory nasopharyngeal pressures during supply of NHF are estimated during mouth closed breathing. Although in clinical practice a patient receiving NHF may breathe with their mouth open, highest airway pressures are generated with the mouth closed (Parke et al., 2011). Flow trajectories and static pressure in an anatomically structured 3D model of a single nasal airway are considered in detail. The construction of anatomically-structured geometry to simulate pharyngeal pressures across patient populations is challenging due to limited access to imaging (when imaging is available) and the time involved in image processing, 3D model construction, and CFD simulation. To address this issue, a ‘minimal’ airway is presented that captures the important geometric properties of the anatomical airway. Previous studies have adopted a similar approach to estimate nasal resistance (Javaheri et al., 2013; Schreck et al., 1993). The minimal airway geometry is derived by simplifying the cross-sectional shapes of the detailed anatomical airway. The geometry is then manipulated to

investigate the effect of subject variability in nasal valve area and external nostril area on static pressure drop along the airway. Investigating variability has potential clinical relevance for efficacy across the differing patient demographic.

Methods Anatomical model geometry Volumetric computed tomography (CT) imaging was used to obtain a three-dimensional (3D) geometry of a human nasal airway. The reconstructed 3D geometry is shown in Figure 1. The cross-sectional area along the model centerline is plotted in Figure 1(b) and cross-sectional shapes along the nasal passage are shown in Figure 1(c). The airway has nostril areas of 119 and 133 mm2 for left and right nostril, respectively, and nasal valve areas of 94 (left) and 96 (right) mm2. Since closed-mouth breathing was assumed in this study the oral cavity was not included. With closed mouth breathing the highest pressure scenario is therefore simulated. The nasal air was assumed to have the same density and dynamic viscosity as the 37oC 100% relative humidity air delivered by the cannula’s nasal prongs into each nostril. The cannula geometry was based on Fisher & Paykel Healthcare’s medium sized adult OptiflowTM cannula (OPT844) that has an elliptical prong cross-section (major axis 5.5 mm and minor axis 3.4 mm). The presence of the nasal cannula prong reduced the nostril space to 104 mm2 (left) and 118 mm2 (right), respectively.

Figure 1. Reconstructed 3D geometry of an adult nasal airway. (a) Lateral view. (b) Crosssectional area along downstream locations. (c) Cross-sectional shapes within the nasal passage. ‘V’ is nasal valve. ‘O’ is nostril. ‘N’ is nasopharynx Minimal model geometry A 3D minimal airway model was developed for one half of the nasal airway, using the cross-sectional area at 11 locations along the anatomical nasal passage. At these locations, the complex nasal airway cross-sectional shape was replaced with simple shapes as shown in Figure 2, while maintaining the cross-sectional area at these relative locations. The nasal airway geometry was created in SolidWorksTM using interpolation and B-spline surface extrusion. To study the impact of geometry differences, nasal valve areas of 98, 70 and 50 mm2, and nostril areas of 120, 90 and 72 mm2 were selected while cross-sectional areas in other locations were not changed. The centerline cross-sectional areas for different combinations are given in Figure 2(b). Each combination was assigned a geometry number: 11, 12, 13, 22, 23 and 32. For example, geometry 11 has nostril area of 120 mm2 and valve size of 98 mm2 and so on. Details of these geometries are given in Table 2.

2

Figure 2. (a) Geometry of simplified nasal airway. (b) Centerline cross-sectional area (in mm ) of

various nasal airway geometry used in this study.

Numerical methods Steady-state inspiratory and expiratory flows were simulated using ANSYS CFX 14.0 (ANSYS, Inc.), a fluid-dynamics solution package. The tracheal flow rate and NHF (or cannula flow) rate are inputs to the simulation. NHF has been reported to reduce respiratory rate (Rittayamai et al., 2014; Roca et al., 2010; Sztrymf et al., 2011), increase tidal volume (Corley et al., 2011; Mundel et al., 2013) and reduce minute ventilation (Braunlich et al., 2013). In practice, meeting or exceeding peak inspiratory volumes ensures accuracy of delivered oxygen concentrations when there is no requirement to entrain air to meet demand (Ritchie et al., 2011). Steady flowrates representing peak inspiration and peak expiration of 36 L/min and 20 L/min, respectively, were assumed (Spence, 2011). Neglecting flow bias these flows corresponded to 18 L/min and 10 L/min through each nostril, respectively. The flow rates do not correspond to a particular minute volume, as only steady-state flows were considered and not the time period over which the flow would occur. Nevertheless, the flowrates of Spence et al were taken on a healthy 23-year old male (height 184cm, weight 85kg) with a resting minute volume of

7.0L/min. Three NHF rates (QC = 20, 40 and 60L/min) were considered in our study. A NHFReynolds number equal to

may be defined at the prong where

of air, D is the equivalent diameter (=

is the kinematic viscosity

) of cannula prong, and AC is the prong cross-

sectional area. For NHF rates of QC = 20, 40 and 60 L/min, the NHF-Reynolds numbers are 6069, 12139 and 18208, respectively. NHF QC=60 L/min implies 30 L/min through each cannula. Flow is assumed turbulent at these Reynolds numbers. In practice this turbulence is thought to contribute to the CO2 washout effect seen with this therapy. Turbulence prediction was performed using a Shear Stress Transport (SST) model with automatic wall treatment. 5% turbulence intensity was specified at all inlet and outlet boundaries. The mesh for the 3D model from the human subject used in this study was predominantly tetrahedral with 3.1 million nodes and 16.8 million elements. The mesh in near wall region included 12 prismatic inflation layers. The simplified nasal airway used in this study had ~3 million nodes and ~9 million elements, and included 10 prismatic inflation layers. For all cases, the first mesh point was at distance of ~0.02 mm from the wall boundary. The following boundary conditions were applied. A zero-gauge pressure opening-type boundary condition was prescribed on the curved mask-like surface. A steady incoming cannula flow rate was specified at the prong. At the other end of the model, the tracheal velocity profile was specified. For nasal high flow, the cannula jet velocity vector is taken as pointing to the center of the nasal valve region. A steady state solution was sought. Although input boundary values of cannula and lung flow did not vary with time, in some simulations a steady-state solution was not obtainable. In such cases, a suitable initial condition was first obtained before an unsteady solution was carried out. In all these cases, the solution reached a periodic quasisteady state. Pressure at different locations in the airway was monitored. The solution was

assumed to have converged when a periodicity was reached in pressure. The variation in observed pressure differed within 20 Pa. The final reported solution is the time-average of the unsteady solution. For purpose of clinical relevance, pressure drop has been reported in both Pascal and cmH2O where applicable.

Results and Discussion: NHF is an open-system wherein a leakage or buffer region exists in the nose around the cannula. Depending on the magnitude of lung and cannula flow rates, breathing may be active or passive. Figure 3 is a schematic of the possible airflow directions. Consider a peak inspiratory flow rate of 36 L/min. With NHF rate of 20 L/min, the patient’s inspiratory drive spontaneously inhales at 16 L/min (see Figure 3a). At NHF rate of 40 L/min, an excess of 4 L/min is flushed out through the nasal leakage region (Figure 3b). Hence during inspiration, the region in the nasal vestibule around the prong acts as a buffer. During expiration, the subject exhales against a steady incoming cannula flow. For a NHF rate of 40 L/min, a lung flow rate of 20L/min would result in 60L/min exhaled out through the leakage region in both nostrils (see Figure 3c).

Figure 3. Interaction of cannula flow and tracheal flow (a) and (b) Inspiration at 36 L/min. (c) Expiration at 20 L/min. Arrow with solid circle at its head is the leakage flow.

NHF differs from other ventilation strategies mainly in providing a facility to breathe in or out through a leakage region formed around the cannula. For a medium 16mm2 cannula, the leakage of air out of the nose is typically present at higher NHF rates during both inspiration and expiration. Although the mechanism and characteristics of airflow during inspiration and expiration are different, the presence of leakage region highlights a similarity.

Airflow inside the nasal passage Compared to unassisted natural breathing, the characteristics of airflow are altered in the presence of NHF, and the air flow streamlines are also different between inspiration and expiration. Figure 4 shows the flow streamlines at inspiration and expiration at NHF of 60 L/min. In Figure 4(a), the red streamlines are the cannula flow and the white lines are tracheal flow. In Figure 4(b), the red lines and white lines represent airflow in left and right nasal passages, respectively. The results agree with previous observations using PIV (Spence et al., 2011). For the expiratory flow, jet from the cannula (red line in Figure 4) flows deeper into the left nasal passage than the right. There are two recirculating vortices, a smaller one formed above the cannula jet and a larger one below. Flow in the posterior regions of the nasal airway near the nasopharynx is not affected by the cannula flow. At NHF of 60 L/min, the streamlines during inspiration also have two recirculating vortices, a larger one above the jet and a smaller one below. The size of the recirculation depends on the cannula jet direction. An important consequence of NHF is to ‘washout’ the anterior nasal cavity during both inspiration and expiration. Dead space washout has been postulated as one beneficial mechanism of nasal high flow therapy (Dysart et al., 2009), however modeling the magnitude of the washout and its impact on arterial blood gases is beyond the scope of this work. What has been reported in many

NHF clinical studies is an improved PaO2 to FiO2 ratio and a reduced PaCO2 (Corley et al., 2011; Maggiore et al., 2014; Sztrymf et al., 2011)

Figure 4: (a) Streamlines at exhalation for NHF = 60 L/min. Red lines is the cannula flow. White lines are the tracheal flow (b) Streamlines at inhalation for NHF = 60 L/min. Red and white lines represent flow in left and right nasal airway, respectively. Black arrows indicate approximate flow direction.

Figure 5. NHF=60 L/min. (a) Pressure at various streamwise sections during inspiration and (b) during expiration. (c) Velocity magnitude on a mid-sagittal section during inspiration and expiration.

Nasopharyngeal pressure At tracheal flow rate of 36 L/min, pressure drop during natural inspiration (absence of cannula flow) in the model is 30.9 Pa (0.31 cmH2O) below atmospheric. Taylor et al (Taylor et al., 2010) simulated airflow in a unilateral nasal airway with nostril area of 150 mm2 and nasal valve area of 95.6 mm2 and observed 1.7 Pa pressure drop at 6L/min lung flow rate. Our mask boundary condition is similar to their ‘face’ boundary condition. In a separate simulation (results not shown here) steady inspiratory flow at a lung flow rate of 12 L/min (equivalent to 6L/min through each nasal airway) was computed and a pressure drop of 4.2 Pa was observed. Pressure drop observed through the left side airway was about 6% higher than the right. Many flow

features such as a high local velocity near the nasal valve region agreed well with Taylor et al., although differences associated with anatomy are to be expected. Inspiratory Pharyngeal Pressures (IPP) and Expiratory Pharyngeal Pressures (EPP) are reported in Table 1. Here IPP and EPP are the average pressure measured at the nasopharynx on plane (‘N’) shown in Figures 1 and 2. At NHF of 20 L/min, IPP was negative with respect to ambient. At NHF rate of 40 L/min or above, IPP was positive and hence the lungs would experience a positive airway pressure. IPP was 160.5 Pa (1.64 cmH2O) at NHF of 60L/min. During expiration, pharyngeal pressure was always positive with either unassisted or NHF breathing. EPP increased by 124 Pa (1.26 cmH2O) from NHF 20 to 40 L/min and by 206 Pa (2.1 cmH2O) from NHF 40 to 60 L/min. Hence the increase of EPP with NHF rate is not linear. Pressure and velocity at different cross-sections is shown in Figure 5 for NHF=60 L/min. The high flow jet from the cannula creates localised regions of negative pressure during inspiration. This adverse pressure gradient points to reversal in flow direction and recirculation. Negative pressures were observed near the base of the nasal valve region. Its location on the septal wall will be specific to the geometry used here. Flow in the meatus and beyond did not show significant changes in pressure although differences between left and right sides are present, due to shape and difference in patency of the airway at these locations. For example, in Figure 5(b), pressure at sections 2 and 3 vary between 350 Pa and 380 Pa. This observation motivated simplifying the complex anatomically structured nasal airway geometry to a more simple geometry that permitted further analysis of geometric influences on the nasal flow. Figure 5(c) shows the high speed jet from cannula for NHF 60L/min. Velocity at cannula prong outlet was 39m/s. During expiration, high flow velocity in buffer region was observed. The nasal

septum was curved around the nasal valve region and hence mid-sagittal section does not show the complete jet. Significant flushing of the anterior nasal cavity can be noted.

Figure 6. Streamlines for simplified airway geometry 11 during (a) inspiration and (b) expiration. NHF=60 L/min.

Airflow simulations were performed for simplified airway geometries given in Table 2. Pharyngeal pressures during inhalation and exhalation for different combinations of nostril area and valve area are reported. Nostril area was normalised by nasal prong area as the nasal prong effectively occludes part of the outer nose, e.g. for A*=8, the nostril is 14% occluded by the cannula. The results of airflow simulations are qualitatively similar to the more complex geometry, and streamlines in Figure 6 compare well with those in Figure 4 supporting the use of the simplified model to understand the basic pressure-flow relationship in the cannulated nasal airway. From simulations in the simplified model, the following observations can be made about IPP: i.

NHF rate of 20 L/min is insufficient for delivering a positive IPP. This was true for all configurations chosen in this study. This observation is partially in agreement with

Groves and Tobin (Groves and Tobin, 2007), who measured mean -0.2 cmH2O at 20L/min. ii.

At NHF 60 L/min, airway-32 generates the highest IPP of ~274.6 Pa (2.8 cmH2O). This result is consistent with Groves and Tobin who measured mean IPP of 2.9 cmH2O in female subjects (i.e. assumed to have smaller airway dimensions) and 1.5 cmH2O in male subjects. While our model was consistent with the mean value for females, the chosen combinations of airways could not generate high IPP as observed in Groves and Tobin (for example, 5.3 cmH2O in one subject).

iii.

IPP increases with cannula flow rate. The rate of increase of IPP with increase in NHF is a function of the nasal valve area: the smaller the nasal valve area, the greater the increase.

iv.

IPP increases nonlinearly with cannula flow rate, i.e. the proportional increase in IPP due to increase in NHF from 40 to 60 L/min is higher than the increase in NHF from 20 to 40 L/min.

v.

IPP showed a weak correlation with nostril area (the nostril area (A*) is normalised with prong area (AC) in Table 2). For example, with nasal valve area of 70 mm2, a reduction in nostril area (i.e. a more occluded nostril) by 25% increased IPP by only 4%. The increase in IPP may become more pronounced with further decrease in nostril area, however only nostril-valve area combinations that were in the physiological range and gave acceptable airway geometries were chosen for analysis here.

From Table 2, the following observations were made about EPP: i.

EPP is positive and increases with NHF rate.

ii.

For case 11, as NHF increases from 20 to 40 L/min, EPP increases by 79.6 Pa (0.81 cmH2O). For an additional 20 L/min step increase in NHF (from 40 to 60 L/min), a further 123.7 Pa (1.26 cmH2O) EPP is generated.

iii.

Similar to trends in IPP, EPP increases significantly with NHF rate. The rate of increase is a function of the nasal valve size: smaller the nasal valve area, larger the percentage increase.

iv.

The effect following change in nostril area is different from the effect of valve area. The EPP increases with reduction in nostril area. Compared to the effect of reducing nasal valve area, only a weak correlation exists between A* and pressure. In the theoretical limit of a fully occluded nostril, the pressure will be infinitely large.

v.

Groves and Tobin (Groves and Tobin, 2007) observed a linear increase in EPP with flow rate. They also surmised that the facial features - particularly the smaller nares of females - could explain the higher pressure observed. Our results are in good agreement with these observations for changes in nostril size. Some of the measurements by Groves and Tobin in female volunteers resulted in EPP upto 9 cmH2O at NHF rate of 60L/min. Our simplified nasal airway geometry is not able to predict such high pressure although the anatomy of the subjects measured in their study was not known.

Although the mean EPP across subjects from Groves and Tobin increased with NHF rate, the standard deviation also increased, indicating that subject response differs markedly at higher NHF rates. Our results are in agreement: EPP varied between 240-600 Pa at NHF 60L/min and between 40-80 Pa at NHF 20L/min.

Correlation for pressure using multiple linear regression Results from Table 2 were used to obtain simple and predictive relations for pressure. Multiple regression was performed to obtain correlation for nasopharyngeal pressure as a

function of chosen nasal anatomical dimensions. The simulation data points from Table 2 were utilized for regression. Due to inverse correlation of pressure with area, (m,n)>0 is enforced during regression.

IPP or EPP(model) =

(a + bQ ) A (A − 1) 2 C

m V

*

n

=

(a + bQ ) 2 C

AVm AC−n ( AN − AC )

n

Here QC is in L/min, AV in mm2 and A* is non-dimensional. a, b, m, and n are coefficients fitted to the model. Regression was carried out using MATLAB®. For inspiration, the coefficient vector (a,b,m,n) = (-40.598, 0.0818,1.0835,0.204) with RMS = 0.29. It may be noticed that IPP is near zero at NHF 20L/min, hence coefficient ‘a’ will be nearly equal to 400b. This dependency created instability in the regression. Hence a = b a* was imposed during optimization where a* was an intermediate variable. For expiration, the coefficient vector (a,b,m,n) = (3.9688,0.1332,1.0574,0.1762) with RMS = 0.46.

Study Limitations The simplified nasal airway model used in this study is a substitute for reconstructing an anatomically realistic geometry from imaging data across a population of subjects who have variation in nostril and/or nasal valve size. It is hypothesized that this modelling approach based only on cross-sectional areas (and not subject specific shape details of nasal anatomy) is sufficient for understanding how the nasopharyngeal pressure relates to the NHF rate and the combination of cross-sectional areas. In its current context this approach is useful for estimating the maximum PEEP that would be established by NHF. In the current study, only the effect of nostril area and nasal valve area were studied. Although results of fluid flow simulations in the anatomical nasal airway indicated that nostril area and valve area may have the most effect, other

geometrical parameters might contribute to variability in peak pressure. These include (i) nostril and vestibule shape (ii) nasal valve orientation with respect to the nostril plane, (iii) meatus region shape and size and (iv) differences between left and right nasal airway. Alternatively, standardized geometry (Liu et al., 2009) of the human nasal cavity may also be used in future studies. The exact location of the prong in the nasal vestibule and direction of jet into the nose is not known and could affect the peak pressure. The tracheal flow rate fluctuates during the breathing cycle and has not been taken into account in this study. Nevertheless, this study highlights the effect of anatomical features on the peak pharyngeal pressure during high flow therapy. We reiterate that our model observations are based on the assumption of closed-mouth breathing. In the clinical setting the patient is likely to open their mouth, at least intermittently. The maximum pressures induced by NHF will occur when the mouth is closed, therefore this is the appropriate situation to consider in the current study.

Conclusions Constant positive airway pressure (CPAP) or PEEP are controlled at clinicallydetermined levels during conventional invasive or non-invasive ventilation. In conventional therapies the measurement of pressure is trivial; however for NHF the pressure imposed by the therapy requires invasive instrumentation. The analysis here suggests that pressures larger than 6 cmH2O are not typical, even for the highest level of NHF (60 L/min). On this basis NHF is unlikely to provide pressure at concerningly high levels. Our study provides a predictive equation for the relationship between key geometric parameters of the nasal airway, NHF rate, and IPP or EPP. This relationship has potential application in designing individualised NHF

ventilation protocols for patient groups in whom a relatively low level of additional pressure is beneficial.

Acknowledgements The authors wish to thank Jane O'Donnell from Fisher & Paykel Healthcare Ltd. for valuable clinical advice and suggestions. Authors also thank Karthik Subramanian from the Auckland Bioengineering Institute for help with regression and Alexandra Rommerskirchen for assistance with 3D modeling. This project was funded by a Ministry of Business, Innovation and Employment grant number ROP-20959-NMTS-UOA.

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List of Figures:

Figure 1. Reconstructed 3D geometry of an adult nasal airway. (a) Lateral view. (b) Cross-sectional area along downstream locations. (c) Cross-sectional shapes within the nasal passage. ‘V’ is nasal valve. ‘O’ is nostril. ‘N’ is nasopharynx.

Figure 2: (a) Geometry of simplified nasal airway. (b) Centerline cross-sectional area (in mm2) of various nasal airway geometry used in this study. Figure 3. Interaction of cannula flow and tracheal flow (a) and (b) Peak inspiration at 36 L/min. (c) Peak expiration at 20 L/min. Arrow with solid circle at its head is the leakage flow. Figure 4: (a) Streamlines at peak exhalation for NHF = 60 L/min. Red lines are for the cannula flow. White lines originate from the tracheal flow. (b) Streamlines at peak inhalation. NHF = 60 L/min. Red and white lines represent flow in left and right nasal airway, respectively. Black arrows indicate approximate flow direction. Figure 5. NHF=60 L/min. (a) Pressure at various streamwise sections during inspiration and (b) during expiration. (c) Velocity magnitude on a sagittal section during inspiration and expiration. Figure 6. Streamlines for simplified airway geometry 11 during (a) inspiration and (b) expiration. NHF=60 L/min. List of Tables:

Table 1: Nasopharyngeal pressure (Pascals, value in cmH2O is given in parenthesis) in an adult human airway model. Table 2. Nasopharyngeal pressure (Pascals, value in cmH2O is given in parenthesis) in reduced nasal models. A* is the nostril area normalised by prong area. AV is the nasal valve area.

Cannula flow rate

Inspiratory Expiratory pharyngeal pharyngeal pressure (IPP) pressure (EPP) (L/min) Pa (cmH2O) Pa (cmH2O) 0 -30.9 (-0.31) 7.1 (0.07) 20 -13.0 (-0.13) 60.3 (0.61) 40 38.3 (0.39) 184.4 (1.88) 60 160.5 (1.64) 390.5 (3.98) Table 1: Measurements of static nasopharyngeal pressure (Pascals, values in cmH2O is given in parenthesis) in an adult human airway model.