Thomas Radulesco
email: thomas.radulesco@ap-hm.fr

Lionel Meister

Gilles Bouchet

Arthur Varoquaux

Jérome Giordano

Julien Mancini

Patrick Dessi

Pierre Perrier

Justin Michel

| Gilles Bouchet

| Arthur Varoquaux

Jérôme Giordano

Correlations between computational fluid dynamics and clinical evaluation of nasal airway obstruction due to septal deviation: An observational study

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

| INTRODUC TI ON

Nasal airway obstruction (NAO) is a common symptom leading many patients to seek a medical consultation and occasionally undergo surgical procedures. [START_REF] Villwock | Diagnostic algorithm for evaluating nasal airway obstruction[END_REF] Septal deviation (SD) is one of the main causes of NAO. [START_REF] Teixeira | Nasal septal deviations: a systematic review of classification systems[END_REF] Clinical evaluation of NAO is usually carried out by patient interview, self-questionnaires and various physical tests designed to quantify NAO. [START_REF] Rhee | A systematic review of patient-reported nasal obstruction scores: defining normative and symptomatic ranges in surgical patients[END_REF] Anterior active rhinomanometry is a physical test performed in many centres to calculate resistance to the airflow in the nasal cavity. [START_REF] Vogt | Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements[END_REF] Computational fluid dynamics (CFD) is a recent tool for modelling the nasal cavity as well as for analysing air conditioning and airflow. [START_REF] Kim | Patient specific CFD models of nasal airflow: overview of methods and challenges[END_REF] Over the past 10 years, more and more authors have assessed the nasal airway using CFD. [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF] New measurements, such as heat flux (HF) and wall shear stress (WSS), are computable by CFD in addition to usual data such as nasal resistances. [START_REF] Leong | A review of the implications of computational fluid dynamic studies on nasal airflow and physiology[END_REF] However, only a few publications have attempted to correlate CFD with clinical evaluation of NAO and these studies were usually based on a limited number of cases or on healthy subjects. [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF][START_REF] Lu | Accuracy evaluation of a numerical simulation model of nasal airflow[END_REF] In our view, the correlation between CFD and clinical evaluation of NAO (patient perception and rhinomanometry) would permit validation and improved interpretation. Regarding NAO, patients often complain of unilateral impairment. This is convenient for correlating CFD data as they can be easily calculated on each side: the more obstructed side (MOS) and the less obstructed side (LOS). However, the most frequently used self-questionnaires are quality-of-life evaluation tools, which is why they do not investigate lateralisation of the functional impairment, thus making it difficult to correlate them with CFD-calculated data. [START_REF] Rhee | A systematic review of patient-reported nasal obstruction scores: defining normative and symptomatic ranges in surgical patients[END_REF] The primary objective of this study was to determine how CFD could be correlated to clinical evaluation of NAO in a population of patients with symptomatic SD. To do so, we researched the correlations between CFD and patient perception on one hand, and CFD and rhinomanometric data on the other for each of the nasal cavities.

The secondary objective of the study was to determine whether CFD could define which side was the MOS and the LOS.

| ME THODS

| Ethical standards

All patients gave written consent before participating in the study, which was conducted according to the Declaration of Helsinki.

Authorisation to conduct this study was obtained from the Ethical Committee of our institution (Assistance Publique des Hôpitaux de Marseille, N°2017-14-12-005).

| Patient selection

All patients were referred for septal surgery at our centre between January 2017 and September 2018. Age range was 19-58 years (mean 37 years). Preoperative CT scans were obtained using a low dose protocol on a multi-detector CT scanner (Aquilion Prime, Canon Medical Systems) using a cranio-caudal helical acquisition. Fixed parameters were used in accordance with the industrial engineer: 80 × 0.5 mm detectors, FOV: extra-small 180 mm, 40 mm collimation, 0.5 seconds revolution time, pitch of 0.625 mm/rotation, 100 kV tube voltage, DPL target of 50 mGy cm, scout view auto-exposure of mAs intensity, FC30 bone filter, Adaptive Iterative Dose Reduction-3D standard reconstruction. Voxel dimensions were 0.35 × 0.35 × 0.5 mm (0.61 mm 3 ).

| Exclusions

All patients with non-structural causes of NAO such as rhinitis, sinusitis or tumoral/autoimmune processes (ie, not due to anatomic obstruction) were excluded. We excluded patients presenting symptoms alternating from one side to the other as this can create bias, especially regarding CFD-NR [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF] We also excluded patients with the same perception score on both sides, in order to clinically determine a MOS and a LOS for each patient. correlated to patient perception in cases of SD. It also helps to distinguish the more obstructed side from the less obstructed side and could contribute to further CFD studies.

Keypoints

• Septal deviation is one of the main causes of nasal airway obstruction.

• Computational fluid dynamics is a recent tool for modelling the nasal cavity as well as for analysing air conditioning and airflow. Thanks to developments and technical progress in recent years, it is now possible to perform computational fluid dynamics on the nasal airway.

• The correlation between computational fluid dynamics and clinical evaluation of nasal airway obstruction would permit validation and improved interpretation.

• This study aims to enhance our ability to interpret CFDcalculated data in the nasal airway. It highlights and confirms that heat flux measures are very closely correlated to patient perception in cases of SD.

• We found that CFD-computed nasal resistances were strongly correlated with patient perception. However, CFD-calculated nasal resistances had low correlations with rhinomanometry in our series.

| Clinical evaluation of NAO

| Patient perception scores

In all patients, subjective perception of nasal airflow was quantified separately on each nasal cavity: 0 = "no obstruction," 1 = "slight obstruction," 2 = "moderate obstruction," 3 = "severe obstruction" and 4 = "total obstruction." The more obstructed side was abbreviated to MOS. The less obstructed side was abbreviated to LOS. The definition of the LOS and MOS was based on the subjective scores. Clinical evaluation was performed 1 month before surgery, in the absence of any intercurrent infectious episode.

| Rhinomanometry

Anterior active rhinomanometry (without vasoconstriction) was performed before surgery. No procedures (eg, Cottle or Bachman tests) were performed in order to avoid deforming the nasal anatomy. The same rhinomanometer was used for all patients (Otopront ® Rhinon-sys © Happersberger Otopront GmbH 2008). Right and left nasal resistances were calculated. Nasal resistances obtained using rhinomanometry were measured at a pressure drop of 150 Pa and are abbreviated to RMM-NR

| Creation of 3-dimensional models

3D reconstructions were obtained using itk-snap (3.6.0). The procedure was as follows: (a) importation of CT scan images (DICOM formats), (b) segmentation process using the half-maximum height protocol (imagej software version 1.44o) to determine the boundaries of anatomical structures and (c) nasal surface extraction. No smoothing algorithm was applied. The half-maximum height protocol offers an objective process to delimit a reproducible interface between two tissues. [START_REF] Spoor | Linear measurements of cortical bone and dental enamel by computed tomography: applications and problems[END_REF] This method included pixels from -1024 to -400 Hounsfield Units. Paranasal sinuses were removed manually during the segmentation process.

| CFD protocol

CFD was performed using star-ccm+ ® software (CD-ADAPCO-www. cd-adpaco.com). The computational domain was the Boolean union of extracted surface and a 3 cm-diameter sphere centred on the tip of the nose. The aim of this sphere was to impose a pressure boundary condition far from the nostrils, thus allowing a non-imposed airflow close to the nasal entrance. Volume mesh was performed using a polyhedral mesher with parameters defined after a convergence mesh study: the prism layer (total thickness = 0.16 mm) included 10 prismatic cells with 1.1 prism layer stretching ratio.

We defined the following computational hypothesis: airflow to standard conditions for temperature (19°C) and atmospheric pressure (101 325 Pa). Air was considered to be an incompressible Newtonian fluid with density ρ = 1.225 kg/m 3 and viscosity μ = 1.8 × -5 Pa seconds.

We considered the flow to be laminar. Steady computation was used, with a segregated solver and second-order accuracy in space.

Sinonasal surface was a non-slip wall. Wall temperature was 34°C. [START_REF] Lindemann | Impact of menthol inhalation on nasal mucosal temperature and nasal patency[END_REF] An imposed atmospheric pressure value) defined on the sphere surface (101 325 Pa). We analysed total pressure (TP)

where TP = static pressure + dynamic pressure. Nasopharynx was a pressure outlet with an imposed pressure. In case of re-entry, the temperature of air in the nasopharynx was 37°C. The differential pressure imposed in the nasopharynx was -150 Pa. CFD-calculated nasal resistances were called CFD-NR CFD-NR were calculated for the right and left side. Nasal resistances were expressed as R = ΔP/V, where ΔP is the pressure differential between the nostril and the rhinopharynx and V is the airflow rate, expressed in Pa s/mL. The pressure drop used to compute nasal resistance was total pressure differential.

A total of 30 CFD variables were collected for each patient, 15 on each side (Figure 1 Average HF measures were mean HF values calculated for both sides.

WSS was measured 0.1 cm before the junction between upper lateral and lower lateral cartilages (nasal valve area; WSS1) and at the maximum SD, depending on patient's deviation (WSS2).

Maximum velocity was assessed for each nasal fossa (Vmax).

Temperatures were recorded in ambient air (T1), in the middle meatus (after the SD for MOS, symmetrically for LOS; T2) and at the choana (T3).

| Statistical analyses

Results were analysed using Microsoft Office Excel. Statistical calculations were performed using past software (Oyvind Hammer, University of Oslo, Norway). To compare CFD-NR and RMM-NR, statistical differences were assessed using a paired t test. Comparisons between NAO and CFD variables were made using the Spearman correlation test (r s ). The correlation was considered perfect if

|r s | = 1,

| RE SULTS

| Population

We selected 22 patients complaining of NAO with SD. Most of them had an anterior SD. We were thus able to perform 44 analyses comparing each side with its CFD data. Regarding patient perception scores, we found for MOS a severe obstruction score (mean score ± standard deviation = 3.18 ± 0.80); For LOS, we found a low obstruction score (mean score ± standard deviation = 0.95 ± 0.79).

The difference between MOS and LOS was statistically significant (P < 0.001).

| Correlation of CFD with subjective perception of nasal airflow

| Pressures, heat flux, temperatures, velocities, wall shear stress

Regarding correlations with patient perception, we found a very strong correlation for heat flux values after SD (HF3; Figures S2 andS3;

Table 1). We also found a strong correlation with all other HF values, T2 and WSS2. Moderate correlations were found for P2, P3, P4, T3 and Vmax. Correlations were low or non-significant for P5, WSS1 and Vmax.

After Bonferroni correction, only P2 became non-significant (P > 0.004).

| RMM-NR and CFD-NR

Both RMM-NR and CFD-NR had strong correlations with subjective scores (r s = 0.75, P < 0.001 and r s = 0.6, P < 0.001, respectively).

F I G U R E 2 Lateral views of MOS (Right side) and LOS (Left side) according to (A) total pressure (Pa), (B) heat flux (W/m2), (C) wall shear stress (Pa) and (D) streamlines. Streamlines are coloured according to total pressure. The patient complained of right side "Total Obstruction" (4/4). On the left side, he reported "No obstruction" (0/4). On the MOS, we observed a strong Pressure drop and decreased Heat Flux. WSS1 and 2 were null and lower, respectively, on the MOS

| Comparison between MOS and LOS

| Pressures, heat fluxes, temperatures, velocities, wall shear stress

Regarding total pressure, we found a big pressure drop after SD (P3) in MOS (Figures 2,3, and 4A; Table 23.1; Video S1). The difference was statistically significant comparing MOS and LOS for P3 (P < 0.001). However, we found no statistically significant differences for P2, P4 and P5. There was a strong modification of HF, moving closer to 0 2 , after SD on MOS (HF3, Figure 4B).

The difference was statistically significant comparing MOS and LOS for HF1, HF2, HF3 and HF4 (P < 0.001). Average heat flux measures in LOS were higher than MOS thus allowing us to identify LOS and MOS in 100% of patients. At T2 (Figure 4C), mean temperatures were 28.5 ± 3.6°C and 23.3 ± 2.8°C, respectively, for MOS and LOS. At T3, mean temperatures were 30.9 ± 1.9°C and 29 ± 2.3°C, respectively, for MOS and LOS.

Differences were statistically significant at T2 between MOS and LOS (P < 0.001). We also found a strong correlation between HF and temperatures (r s = 0.56, P < 0.001). Maximum velocities were higher on MOS. The difference between MOS and LOS was not statistically significant (P = 0.039). Comparing WSS, they were statistically higher on MOS in WSS2 values but not in WSS1 (P = 0.065; Figure 4D).

| RMM-NR and CFD-NR

RMM-NR were mean 1.8 ± 2.2 Pa s/mL for MOS. RMM-NR were mean 0.6 ± 0.37 Pa s/mL for LOS (P = 0.01). CFD-NR were mean ± 1.17 Pa s/mL for MOS. CFD-NR were mean 0.23 ± 0.1 Pa s/mL for LOS (P = 0.03).

We found a statistically significant difference between RMM-NR and CFD-NR (P = 0.003, Figure S1). The Pearson correlation coefficient was r = 0.145 (P = 0.3) between RMM-NR and CFD-NR RMM-NR in LOS were lower than MOS in 91% of analyses. CFD-NR in LOS were lower than MOS in 82% of analyses. CFD-calculated flow rates in LOS were higher than MOS in 82% of analyses.

| D ISCUSS I ON

| Synopsis of new findings

The ability to analyse airflow and air conditioning within the nasal cavities offers new perspectives in rhinology. Over the past 10 years, many CFD studies have investigated the nose, first in healthy or cadaveric subjects, and then in patients. [START_REF] Li | Investigation of the abnormal nasal aerodynamics and trigeminal functions among empty nose syndrome patients[END_REF][START_REF] Liu | Effects of septal deviation on the airflow characteristics: using computational fluid dynamics models[END_REF][START_REF] Shadfar | Characterization of postoperative changes in nasal airflow using a cadaveric computational fluid dynamics model: supporting the internal nasal valve[END_REF] The analysis and interpretation of CFD-calculated data must be correlated with the patient's clinical experience. [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF] To that end, CFD must be compared with already existing tests or examinations, especially relative to new data such as HF or WSS.

| Clinical applicability of the study

Clinical evaluation of NAO remains difficult. Many tools have been developed in recent years, and patient reported outcome has become more and more important in functional procedures. Evaluation can be performed subjectively, often by self-questionnaires. The NOSE, SNOT-22 and ENS6Q self-questionnaires are the most used in the literature. [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF][START_REF] Shadfar | Characterization of postoperative changes in nasal airflow using a cadaveric computational fluid dynamics model: supporting the internal nasal valve[END_REF][START_REF] Li | Computational fluid dynamics and trigeminal sensory examinations of empty nose syndrome patients[END_REF] Despite being widely validated in the literature, these questionnaires do not lateralise MOS and LOS although, in most cases, patients with NAO complain more about one side than about the other. Furthermore, CFD analysis is predominantly performed unilaterally. [START_REF] Kimbell | Computed nasal resistance compared with patient-reported symptoms in surgically treated nasal airway passages: a preliminary report[END_REF] It is not logical, therefore, to compare a F I G U R E 3 A, Temperatures (°C) and (B) velocities (m/s). in axial view for the same patient (Right-side obstruction). Temperatures were lower in the LOS. However, velocities were higher on the LOS when NAO was total unilateral CFD analysis with a global clinical feeling. For this reason, we found it useful to make separate clinical evaluations of MOS and LOS so as to compare with their CFD data. Establishing the correlation between CFD data and patients' clinical perceptions appears fundamental in order to better interpret CFD. Our study used a convenience sample of patients presenting a septal deviation, without any other cause of nasal involvement. This must be kept in mind when interpreting our results.

| Comparison with other studies

Kimbell et al [START_REF] Kimbell | Computed nasal resistance compared with patient-reported symptoms in surgically treated nasal airway passages: a preliminary report[END_REF][START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF] and Kim et al 18 also found big changes in airflow characteristics on MOS after SD (Video S1). Similarly for HF, which decreased after SD and was closely correlated with patient perception (Figures 2 and4). The decrease of HF after SD can be explained by reduced airflow in this area responsible for less heat exchange between cool air (19°C) and mucosa (34°C).

Although there are different ways of measuring HF (Total HF, Peak HF, SAHF50), many authors have found a strong correspondence between HF and patient perception, [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF][START_REF] Sullivan | Perception of better nasal patency correlates with increased mucosal cooling after surgery for nasal obstruction[END_REF][START_REF] Zhao | Regional peak mucosal cooling predicts the perception of nasal patency[END_REF] whatever the method adopted. We also noted this strong correlation. This finding reinforces the idea that the mucosal cooling effect plays a large part in NAO perception, and that the latter is probably multifactorial and not dependent exclusively on nasal resistances as suggested for many years. [START_REF] Lindemann | Impact of menthol inhalation on nasal mucosal temperature and nasal patency[END_REF] In our study, average heat flux measures were always higher in LOS, thus suggesting that heat flux measures can distinguish MOS from LOS. Since HF is dependent on air and wall temperatures, it is scientifically logical to find a strong correlation between HF and temperatures (r s = 0.56). It is also logical that temperature differences between MOS and LOS are lower at T3 than at T2 as air temperature has nearly achieved the wall temperature in both sides by the time inspired air reaches the choana.

Regarding WSS, there was a good correlation with subjective scores for the WSS2 measured on the maximum SD but not in the

F I G U R E 4
Mean values in the cohort of 22 patients: total pressure, heat flux, temperatures and wall shear stress are compared using boxplots according to MOS and LOS. A huge total pressure and heat flux drop (P3, HF3) were found after the septal deviation in MOS nasal valve area (WSS1). Kimbell et al [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF] reported a correlation with patient perception measuring WSS on the entire MOS.

Regarding velocities, discordant results were found in our series which sometimes displayed higher velocities in LOS. [START_REF] Liu | Effects of septal deviation on the airflow characteristics: using computational fluid dynamics models[END_REF] Moreover, Vmax was poorly correlated with patient perception. Velocity and WSS are very dependent on anatomic variations. These discrepancies for WSS1 and Vmax can be explained by an "ON-OFF" effect in the event of total NAO. Logically, the greater the deviation, the higher the WSS1 and Vmax. However, in the event of absence of airflow due to totally obstructive septal deviation, WSS1 and Vmax are necessarily null and therefore lower in MOS than in LOS (Figure 3).

Nasal resistance is one of the most used data for assessing NAO perception prior to surgery (septoplasty, inferior turbinate hypertrophy or functional rhinoplasty). However, few studies have sought to compare RMM-NR and CFD-NR. Those studies that have been performed analyse only small cohorts or healthy subjects. [START_REF] Lu | Accuracy evaluation of a numerical simulation model of nasal airflow[END_REF][START_REF] Zhao | In response: regional peak mucosal cooling predicts the perception of nasal patency: Mucosal Cooling and Nasal Patency[END_REF][START_REF] Zachow | Visual exploration of nasal airflow[END_REF] This is the first study to compare CFD-NR and RMM-NR in a large cohort of patients with NAO. While establishing a good correlation between patient perception and both RMM-NR and CFD-NR, the correlation between CFD-NR and RMM-NR was poor (r = 0.14) in our series and lower than in Zhao's studies (r = 0.41 and r = 0.53). [START_REF] Zhao | Regional peak mucosal cooling predicts the perception of nasal patency[END_REF][START_REF] Zhao | In response: regional peak mucosal cooling predicts the perception of nasal patency: Mucosal Cooling and Nasal Patency[END_REF] However, Zhao analysed only healthy volunteers. In our study, we used total pressure differential to compute nasal resistance. This can explain in part why CFD-NR was statistically different from RMM-NR More studies need to be performed on this topic, on larger series, including NAO causes such as inferior turbinate hypertrophies or nasal valve collapses.

Indeed, using a small convenient sample clearly limits the statistical power of our study. Great care is needed when calculating CFD-NR: using a steady flow and a non-deformable model may have an impact on CFD-NR Moreover, the presence of a strong nasal cycle could bias CFD-NR analysis. Although the inferior turbinates can be reduced by applying vasoconstrictors, this procedure distorts reality. To overcome this problem, Gaberino et al 9 proposed virtual modelling to correct the nasal cycle: the correlation between CFD-NR and patient perception was greatly increased.

| Limits

To date, CFD can only analyse static disorders related to nasal ventilation. However, it is well known that ventilatory disorders can be dynamic, especially regarding the nasal valve. [START_REF] Maalouf | A functional tool to differentiate nasal valve collapse from other causes of nasal obstruction: the FRIED test[END_REF] These disorders appear only above an airflow threshold involving dynamic nasal valve collapse. To date, CFD in the nasal airway does not assume deformable walls.

We used a steady flow simulating continuous inspiration. This model is quite different from clinical reality. [START_REF] Vogt | Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements[END_REF] CFD can calculate these inspiration/expiration cycles, even if the computing times are much longer. Importantly, we analysed inspiratory and not expiratory resistance. This choice was made because, in most cases, patients complain only of impairment due to inspiration. We acknowledge using a small series (in terms of statistical power) and a non-validated perception score. Moreover, patients and assessors were not blinded to the findings. We used a convenience sample subject to selection bias, which is not representative of the global population.

| CON CLUS ION

This study aimed to enhance our ability to interpret CFD-calculated data in the nasal airway. Despite the small number of patients, this study highlights and confirms that heat flux measures are closely correlated to patient perception in cases of SD. It also helps to distinguish the more obstructed side from the less obstructed side. This should encourage further CFD studies, on larger series, including other NAO causes such as inferior turbinate hypertrophies or nasal valve collapses.

ACK N OWLED G EM ENTS

To Amidex and Mr Morgan for linguistic assistance.

CO N FLI C T O F I NTE R E S T

None to declare.

O RCI D

Thomas Radulesco https://orcid.org/0000-0002-5939-5372

R E FE R E N C E S

F I G U R E 1

 1 Example of CT scan in axial and coronal view showing where CFD data were calculated on the more obstructed side. P1 = 0 Pa and T1 = 19°C for every patient. HF, Heat Flux; T, Temperature; TP, Total Pressure; WSS, Wall Shear Stress TA B L E 1 Correlations of CFD data with patient perception

  ):All measurements in axial view were performed 1.5 cm from the nasal floor on the septal wall. Total pressure, heat flux and WSS were measurement averages within a circular wall region of 1 cm 2 . P1, P2, P3, P4 and P5 were the pressure differentials with respect to atmospheric pressure. Pressures were measured in the ambient air (atmospheric pressure = 101 325 Pa, P1 = 0 Pa), 0.1 cm before the junction between upper lateral and lower lateral cartilages (nasal valve area; P2), 1 cm after maximum SD on MOS (or symmetrically for LOS; P3), 2 cm before the choana (the posterior third of the nasal septum; P4) and at the choana (P5). Heat flux (ie, the rate of heat transfer across a surface per unit of time and area) was measured at the entrance to the nose (1 cm before the junction between upper lateral and lower lateral cartilages, on the nostril side; HF1), 0.1 cm before the junction between upper lateral and lower lateral cartilages (nasal valve area; HF2), 1 cm after maximum SD on MOS (or symmetrically for LOS; HF3) and 2 cm before the choana (posterior third of the nasal septum; HF4).

  very strong if |r s | > 0.8, strong if 0.5 > |r s | > 0.8, moderate if 0.2 > |r s | > 0.5, low if |r s | < 0.2 and null if r s = 0. The 95% confidence intervals of Spearman's rank correlation coefficients were computed by bootstrapping using the RVAideMemoire package for

r3.5 (R Foundation for Statistical Computing). Comparisons between nasal cavity MOS and LOS were made using paired Wilcoxon test. P values < 0.004 were considered to be statistically significant after Bonferroni correction. Pearson correlation coefficient was used to compare RMM-NR and CFD-NR

  TA B L E 2 Comparisons between mean CFD values for more obstructed side and less obstructed side Note: P2, P4 and P5 and WSS1 showed no statistical difference between MOS and LOS. Abbreviations: LOS, Less Obstructed Side; MOS, More Obstructed Side.

		MOS	LOS	P
	Subjective scores
		3.18 ± 0.80	0.95 ± 0.79	<0.001*
	Total pressure (Pa)
	P2	-34.6 ± 40.0	-42.9 ± 31.8	0.52
	P3	-128.5 ± 47.6	-75.4 ± 42.0	0.003*
	P4	-114.9 ± 33.7	-99.3 ± 38.5	0.11
	P5	-123.6 ± 24.9	-123.8 ± 24.6	0.775
	Heat flux (W/m 2 )
	HF1	1069 ± 872	2192 ± 867	<0.001*
	HF2	731 ± 941	1952 ± 864	0.001*
	HF3	153 ± 212	1290 ± 947	<0.001*
	HF4	276 ± 308	944 ± 709	<0.001*
	Temperature (°C)
	T2	28.5 ± 3.6	23.3 ± 2.8	<0.001*
	T3	30.9 ± 1.9	29.0 ± 2.3	0.007
	Velocity (m/s)
	Vmax	13.0 ± 4.0	10.2 ± 4.0	0.039
	Wall shear stress (Pa)
	WSS1	5.68 ± 6.15	2.54 ± 1.99	0.065
	WSS2	7.21 ± 4.78	2.89 ± 2.23	0.002*

*Significant results (P < 0.004 after Bonferroni correction).

S U PP O RTI N G I N FO R M ATI O N

Additional supporting information may be found online in the Supporting Information section at the end of the article.


Thomas Radulesco
email: thomas.radulesco@ap-hm.fr

Lionel Meister

Gilles Bouchet

Jérome Giordano

Patrick Dessi

Pierre Perrier

Justin Michel

| Gilles Bouchet

Jérôme Giordano

Functional relevance of computational fluid dynamics in the field of nasal obstruction: A literature review

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

| INTRODUC TI ON

Nasal airway obstruction is a common symptom affecting patient quality of life. [START_REF] Rhee | Quality of life assessment in nasal airway obstruction[END_REF] It may involve different aetiologies including septal deviations, nasal valve collapse or inferior turbinal hypertrophy. [START_REF] Do | Predicting postsurgery nasal physiology with computational modeling: current challenges and limitations[END_REF] To date, the evaluation of nasal obstruction has been subjective, through self-questionnaires (NOSE, SNOT 22) and/or the visual analog scale (VAS), or has been performed using various physical tests such as rhinomanometry and peak nasal inspiratory flow (PNIF). [START_REF] Rhee | A systematic review of patient-reported nasal obstruction scores: defining normative and symptomatic ranges in surgical patients[END_REF][START_REF] Vogt | Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements[END_REF][START_REF] Pendolino | Comparison between unilateral PNIF and rhinomanometry in the evaluation of nasal cycle[END_REF] The use of fluid dynamics to simulate airflow in the nasal cavity was widely adopted during the 2000s. Computational fluid dynamics (CFD) consists in analysing fluid flows, or their effect, by numerical solution of equations governing fluids. Applied to nasal cavities, CFD is designed to produce accurate models of airflow and air-conditioning. The CFD process includes the importation of DICOM data (most often from CT scans), three-dimensional modelisation and definition of boundary conditions. Boundary conditions define the inputs of the simulation model (ie pressure, air and wall temperature), thus allowing nasal breathing to be simulated. In this way, CFD offers practitioners a new tool for nasal ventilation analysis.

Over the past 10 years, many studies have been published focusing on CFD in the nasal airway. [START_REF] Chen | Numerical simulation of the effects of inferior turbinate surgery on nasal airway heating capacity[END_REF][START_REF] Dayal | Impact of middle versus inferior total turbinectomy on nasal aerodynamics[END_REF] Computational fluid dynamics has enabled a better understanding of nasal physiology, computing wellknown variables such as nasal airflow and nasal resistances, as well as new variables, for example, heat flux, which represents heat transfers between air and nasal mucosa, or wall shear stress (WSS), which measures friction between the fluid and the wall. These variables are not currently in use in the medical field or in clinical routine. [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF][START_REF] Rhee | Role of virtual surgery in preoperative planning: assessing the individual components of functional nasal airway surgery[END_REF] As a new tool, CFD is confronted by existing gold standards in the field of nasal obstruction assessment. However, to date, it remains unclear how CFD variables can be correlated with patient perception or with physical measurements carried out in clinical routine. [START_REF] Otto | Computational fluid dynamics evaluation of posterior septectomy as a viable treatment option for large septal perforations[END_REF] The correlation between clinical evaluation of nasal breathing and CFD is a key to improving interpretation of the latter. In the published literature, there is a dearth of comparative studies analysing correlations between patient nasal breathing perception and CFD, as reported by Leite et al in their recent literature review. [START_REF] Leite | The clinical implications of computerised fluid dynamic modelling in rhinology[END_REF][START_REF] Shadfar | Characterization of postoperative changes in nasal airflow using a cadaveric computational fluid dynamics model: supporting the internal nasal valve[END_REF] We conducted a literature review of CFD studies regarding the nasal airway, focusing on articles comparing clinical data with CFD. The goal was to define correlations between CFD variable and patient nasal obstruction perception or physical measurements. We also aimed to identify the most reliable CFD variable (heat flux, WSS, total pressure, temperature…) characterising nasal obstruction.

| ME THODS

| Selection of studies

The literature review was performed according to PRISMA guidelines. [START_REF] Moher | Preferred reporting items for systematic review and meta-analysis protocols (PRISMA-P) 2015 statement[END_REF] The selected studies were obtained from the US National Library of Medicine (PubMed) online database, MEDLINE (Ovid), Google Scholar and Cochrane Library using a combination of MeSH terms (nose, paranasal sinus, fluid dynamics, rhinology) and non-MeSH terms (CFD, nasal airway, nasal airflow, numerical, nasal symptoms). Studies that did not incorporate more than 5 subjects and objective or subjective clinical assessment were excluded. 1). The present review summarised the correlation between clinical assessment of nasal obstruction and CFD results. No time filter was used on included studies.

Ranges of

| RE SULTS

| Article selection

| Nasal airway obstruction: clinical assessment

Clinical assessment of nasal obstruction can be performed using many tools. For subjective assessment, most authors used the NOSE (Nasal Obstruction Symptom Evaluation) questionnaire and/or the VAS scale. [START_REF] Floyd | Systematic review and meta-analysis of studies evaluating functional rhinoplasty outcomes with the NOSE Score[END_REF][START_REF] Hsu | Evaluation of nasal patency by visual analogue scale/nasal obstruction symptom evaluation questionnaires and anterior active rhinomanometry after septoplasty: a retrospective one-year follow-up cohort study[END_REF] The NOSE questionnaire is a disease-specific quality-of-life instrument for nasal obstruction that has been validated in the literature. [START_REF] Stewart | Development and validation of the nasal obstruction symptom evaluation (NOSE) scale[END_REF][START_REF] Lipan | Development of a severity classification system for subjective nasal obstruction[END_REF] Other authors used the SNOT-22 questionnaire or • The correlation between clinical evaluation of nasal breathing and CFD is a key to improving the interpretation of the latter. In the published literature, there is a lack of comparative studies analysing correlations between patient nasal breathing perception and CFD.

• Heat flux appears to be the best CFD variable correlated with patient perception. Total pressure, wall shear stress and velocities are also useful and show good correlations.

• CFD-calculated nasal resistances are heterogeneously correlated with patient impairment.

• CFD must integrate new types of variable such as hygrometry, which measures the humidity in the atmosphere, or take into account variations of nasal mucosal temperature according to inspiration or expiration. more specific surveys such as the ENS6Q questionnaire for empty nose syndrome (ENS) patients. [START_REF] Erskine | SNOT-22 in a control population[END_REF][START_REF] Velasquez | The Empty Nose Syndrome 6-Item Questionnaire (ENS6Q): a validated 6-item questionnaire as a diagnostic aid for empty nose syndrome patients[END_REF] Among the physical tests, the most frequently used tool remains rhinomanometry, which measures pressure and flow through the nose during normal inspiration and expiration. [START_REF] Vogt | Four-phase rhinomanometry: a multicentric retrospective analysis of 36,563 clinical measurements[END_REF] Acoustic rhinometry measures the cross-sectional area and length of the nose and the nasal cavity by means of acoustic reflections. It can be correlated with minimal cross-sectional area (MCAs) and is also used for functional assessment, although it is in fact a morphological examination. [START_REF] Geißler | Rhinomanometry and acoustic rhinometry[END_REF] We found no study related to PNIF.

F I G U R E 1 PRISMA flow diagram

| CFD calculations

The main data measured using CFD were as follows:

• Airflow (uni-or bilateral, in mL/s), and airflow partitioning (%) corresponding to the balance between obstructed and non-obstructed nasal fossae.

• Nasal resistance (CFD-NR) to uni-or bilateral inspiration and expiration, (sPa/mL): Nasal resistances were expressed as R = ΔP V , where ΔP is the pressure differential between the nostril and the rhinopharynx and V is the airflow rate.

• Heat transfer (measure of the heat loss from the nasal mucosa to the inspired air) can be studied by: o Total heat flux (W/m 2 ), calculated as the rate of heat loss from the nasal mucosa to inspired air between entry of the nostrils and the choana, divided by the corresponding surface area. o SAHF50, that is, the surface area where heat flux >50 W/m 2 .

o Peak heat flux defined as the value above which only 1 cm 2 of mucosa is exposed.

• Total pressure (Pa), that is, the measure of total energy of the airstream, is equal to static pressure plus velocity pressure.

• Wall shear stress (WSS) (Pa), that is, a friction force generated when moving air enters into contact with the nasal walls.

• Air velocity (m/s) and maximal velocity (Vmax), that is, the distance travelled per unit of time.

Streamlines corresponding to intranasal airflow distribution and allowing airflow visualisation (Video S1).

| Correlation between CFD and clinical assessment

| Airflow

Casey et al [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF] found strong correlations between unilateral nasal airflow and NOSE (r = -0.55, P = 0.0016) and moderate correlations between unilateral nasal airflow and VAS (r = -0.49, P = 0.0056).

For Gaberino et al, [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF] correlations with NOSE and VAS were strong after virtual correction of the nasal cycle (r = -0.61, P = 0.002 and r = 0.56, P = 0.04, respectively). Before virtual correction, airflow was moderately correlated with NOSE (r = -0.41, P = 0.048) but not significantly correlated with VAS. Kimbell reported a strong correlation between NOSE and airflow (r = -0.70). [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF] In patients improved after surgery for nasal obstruction, several studies found improved airflow on the narrow side and deteriorated airflow on the non-narrow side after surgery. [START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF][START_REF] Chen | Assessments of nasal bone fracture effects on nasal airflow: A computational fluid dynamics study[END_REF][START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF]

| CFD-calculated nasal resistances

Nasal resistances are among the most analysed data in the literature concerning nasal obstruction. [START_REF] Keeler | Measuring nasal obstruction[END_REF] Authors found heterogeneous results for correlations between CFD-calculated nasal resistances (CFD-NR) and nasal airflow sensation. Casey et al found statistically significant higher CFD-NR in patients complaining of nasal obstruction compared to patients without nasal obstruction (P = 0.0006). [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF] However, in their study on 30 individuals (15 patients with nasal obstruction and 15 without), no correlation was found between CFD-NR and NOSE or VAS. Before virtual correction of the nasal cycle, Gaberino et al found no correlation between CFD-NR and NOSE or VAS. However, after virtual correction of the nasal cycle, CFD-NR was strongly correlated with NOSE and VAS (r = 0.55, P = 0.005 and r = -0.58, P = 0.003, respectively). [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF] Kimbell et al 8 found a moderate correlation between CFD-NR and both NOSE and VAS (r = 0.48 and r = -0.42, respectively).

Regarding comparison between rhinomanometry and CFD-NR,

Zhao et al [START_REF] Zhao | Regional peak mucosal cooling predicts the perception of nasal patency[END_REF] found a moderate correlation (r = 0.41, P < 0.05). Lu et al [START_REF] Lu | Accuracy evaluation of a numerical simulation model of nasal airflow[END_REF] found no significant differences between rhinomanometry and CFD-NR, but correlations were not evaluated (P > 0.05).

| Heat transfer: total heat flux, SAHF50, peak heat flux

Heat flux analysis now occupies a major place in CFD applied to nasal obstruction. Different methods are available to calculate heat transfer, and results seem to correlate well with patient perception, whatever the method used. In Casey's study, NOSE and VAS were moderately correlated with total unilateral heat flux (r = -0.48, P = 0.0075 and r = 0.43, P = 0.0166, respectively) and strongly with SAHF50 (r = -0.55, P = 0.0016 and r = -0.51, P = 0.0038, respectively). [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF] Sullivan et al reported that, among all heat flux measures, SAHF50 had the best correlation with NOSE (r = -0.76, P < 0.0001) and VAS (r = 0.63, P = 0.002). [START_REF] Lu | Accuracy evaluation of a numerical simulation model of nasal airflow[END_REF] Gaberino et al found a statistically significant difference between pre-and postoperative analyses for heat flux (P = 0.027). In their study, after correction of the nasal cycle, heat flux was strongly correlated with NOSE and VAS (r = -0.51 and r = 0.51, respectively, P = 0.011) but SAHF50 was only moderately correlated with NOSE (r = -0.43, P = 0.34). [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF] For Zhao et al, [START_REF] Zhao | Regional peak mucosal cooling predicts the perception of nasal patency[END_REF] only peak nasal mucosal heat loss posterior to the nasal valve was moderately correlated with VAS score (r = -0.46, P < 0.01).

| Pressure

Kim et al [START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF] compared three symptomatic patients with three asymptomatic patients. They also found a greater pressure drop in patients with nasal obstruction (P < 0.05). The pressure distribution led this author to conclude that the nasal valve is a key zone for nasal obstruction, as shown elsewhere. [START_REF] Naughton | Effect of nasal valve shape on downstream volume, airflow, and pressure drop: importance of the nasal valve revisited[END_REF]

| Maximum velocity

For Kim et al, [START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF] Maximum velocity (Vmax) was higher in patients with septal deviation (P = 0.05). Vmax was also correlated with anatomical findings: when the septal deviation was caudal, Vmax and symptoms were higher than in posterior septal deviation. [START_REF] Liu | Effects of septal deviation on the airflow characteristics: using computational fluid dynamics models[END_REF]

TA B L E 2 The table reports all CFD-calculated values

Authors

| Intranasal airflow distribution

Regarding the nasal airway, in patients with nasal obstruction, middle pathway airflow was lower than in individuals without nasal obstruction (31 ± 18 mL/s vs 68 ± 10 mL/s, P < 0.001); middle pathway airflow was strongly correlated with NOSE (r = -0.76, P < 0.001) and VAS scores (r = 0.64, P < 0.0001). [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF] In a more specific population of ENS patients, Li et al [START_REF] Li | Investigation of the abnormal nasal aerodynamics and trigeminal functions among empty nose syndrome patients[END_REF] found an unexpected change in airflow when the inferior turbinate was missing: they observed a strong diminution of airflow in the inferior region and an augmentation of airflow in the middle region (P < 0.05).

| D ISCUSS I ON

| Synopsis of new findings

One of the difficulties regarding outcomes of aesthetic and/or functional surgery is the objectivity of the evaluations carried out and their correlation with patient perception. [START_REF] Barone | A systematic review of patient-reported outcome measures after rhinoplasty[END_REF] While self-evaluation using quality-of-life questionnaires remains the gold standard, results of objective measurements such as rhinomanometry remain controversial. [START_REF] Pawar | Objective measures in aesthetic and functional nasal surgery: perspectives on nasal form and function[END_REF] CFD offers a new method for evaluating nasal airflow that shows an interesting correlation with current patient-reported outcomes. The advantage of CFD lies not only in the airflow analysis it provides but also in airflow conditioning. [START_REF] Zhao | Perceiving nasal patency through mucosal cooling rather than air temperature or nasal resistance[END_REF] This innovative approach is very useful since data such as heat flux are not measurable by conventional investigations.

| Summary of main results

Recent studies evidenced the great interest showsn in heat flux in rhinology. [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF][START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF][START_REF] Li | Computational fluid dynamics and trigeminal sensory examinations of empty nose syndrome patients[END_REF][START_REF] Li | Investigation of the abnormal nasal aerodynamics and trigeminal functions among empty nose syndrome patients[END_REF][START_REF] Inthavong | Geometry and airflow dynamics analysis in the nasal cavity during inhalation[END_REF][START_REF] Lindemann | Impact of menthol inhalation on nasal mucosal temperature and nasal patency[END_REF] Heat flux could be likened to the feeling of cold felt by the patient during inspiration. In the studies reviewed, all data allocated a major role to heat flux in the genesis of nasal obstruction perception (Table 2). Different versions of heat flux can be used (total heat flux, SAHF50, peak heat flux), each of which has shown a statistically significant correlation with patient perception. [START_REF] Sullivan | Perception of better nasal patency correlates with increased mucosal cooling after surgery for nasal obstruction[END_REF] This suggests that nasal obstruction is related to a lack of cooling effect rather than to high nasal resistance. Perhaps, after all, the truth lies in a combination of both. [START_REF] Zhao | Perceiving nasal patency through mucosal cooling rather than air temperature or nasal resistance[END_REF] Regarding comparisons between patient perception and nasal resistances, several authors concorded that unilateral evaluation All results are presented for the most obstructed side.

Authors

Bold and * indicates a statistically significant correlation or difference (P < 0.05).

NS = non-significant test. If empty, not analysed. Abbreviations: NVC, nasal valve collapse; ITH, inferior turbinate hypertrophy; SD, septal deviation.

TA B L E 2 (Continued) | 7 RADULESCO Et AL.
is more reliable than bilateral evaluation. [START_REF] Roithmann | Acoustic rhinometry, rhinomanometry, and the sensation of nasal patency: a correlative study[END_REF] Consequently, it is necessary to focus on narrow side and non-narrow side rather than on total airflow or total nasal resistance. [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF] The main criticism that can be directed at questionnaires (except the VAS scale) is that they do not lateralise the more obstructed side, whereas CFD data focus most often on unilateral exploration. We therefore compare overall perception with unilateral analyses. In most studies, there was a significant improvement after surgery on the narrow side although contralateral deterioration was often found (due to medialisation of the nasal septum), while patients did not report nasal impairment. Therefore, it appears important to take into account the balance of airflow partitioning. Analysis of correlations between CFD-NR and patient perception reveals heterogeneous results. Many reasons can account for these discrepancies. Firstly, the sensation of nasal obstruction is not only due to an increase in nasal resistances. This is why clinical measurements such as rhinomanometry are discussed. [START_REF] Naito | The effect of Lmenthol stimulation of the major palatine nerve on subjective and objective nasal patency[END_REF][START_REF] Chandra | Diagnosis of nasal airway obstruction[END_REF] Secondly, it is necessary to pay close attention to the nasal cycle in CFD studies as this can constitute a confounding factor. [START_REF] Gaberino | Estimates of nasal airflow at the nasal cycle mid-point improve the correlation between objective and subjective measures of nasal patency[END_REF][START_REF] Kahana-Zweig | Measuring and characterizing the human nasal cycle[END_REF][START_REF] Patel | Simulating the nasal cycle with computational fluid dynamics[END_REF] Thirdly, tissue compliance is currently not considered in CFD studies, which assumes only rigid walls. It is acknowledged that nasal obstruction problems due to the nasal valve may be either static or dynamic. [START_REF] Bloching | Disorders of the nasal valve area[END_REF][START_REF] Aksoy | Role of nasal muscles in nasal valve collapse[END_REF] If static (architectural), problems can be efficiently explored using CFD; simulation of a nasal valve collapse appearing during breathing would entail modelling deformable walls according to the airflow.

The nasal valve area is key in the perception of nasal obstruction, in which pressure and velocity analyses are linked to nasal obstruction perception. [START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF][START_REF] Liu | Effects of septal deviation on the airflow characteristics: using computational fluid dynamics models[END_REF][START_REF] Bloching | Disorders of the nasal valve area[END_REF][START_REF] Nyte | Hyaluronic acid spreader-graft injection for internal nasal valve collapse[END_REF][START_REF] Xavier | Spreader grafts: functional or just aesthetical?[END_REF] Measuring pressures and velocities is not difficult and should be systematically undertaken when performing

CFD.

Wall shear stress increases in cases of septal deviation or nasal valve collapse and diminishes to minimum value in the absence of obstruction. [START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF][START_REF] Li | Investigation of the abnormal nasal aerodynamics and trigeminal functions among empty nose syndrome patients[END_REF][START_REF] Balakin | Aerodynamic evaluation of the empty nose syndrome by means of computational fluid dynamics[END_REF] However, while the above-mentioned results seem interesting, WSS suffers from a major limitation in as far as it is invalid in the presence of total nasal obstruction. Indeed, when there is septal deformation, findings are generally increased, whereas, in the absence of airflow, WSS is null and therefore difficult to correlate with clinical discomfort.

Concerning intranasal airflow distribution, several authors reported a strong correlation between the patient's obstruction and the path taken by the air inside the nasal cavity: patients with a decreased flow at the middle meatus appeared more uncomfortable. [START_REF] Casey | Correlation between subjective nasal patency and intranasal airflow distribution[END_REF] Conversely, in ENS patients, the flow in the middle meatus increases. [START_REF] Li | Investigation of the abnormal nasal aerodynamics and trigeminal functions among empty nose syndrome patients[END_REF][START_REF] Nyte | Hyaluronic acid spreader-graft injection for internal nasal valve collapse[END_REF] Thus, modifying the passage of air through the nasal cavity, even without deterioration of nasal resistance, changes patient perception and can trigger nasal obstruction perception.

We found no major difference between NOSE and VAS in their correlation with CFD, their degree of correlation varying according to the different studies. We recommend using both, as well as more targeted questionnaires such as the ENS6Q for ENS.

| Limitations

Comparing clinical data with CFD remains a difficult exercise. To do so, however, authors have several options: they can either compare healthy and pathological subjects or compare the same patient before and after surgery. Alternatively, they can compare clinical tests with CFD. There are many reasons why such studies are still difficult to perform on large populations of subjects. Firstly, postoperative CT scans are not always justified since CT scans expose patients to additional radiation. Moreover, calculation and implementation times are still long and often require the presence of an IT specialist as the currently available software is not user-friendly for surgeons.

Recent software appears to be easier to use, including automatic generation of the nasal geometry and computational mesh in the nasal cavity. [START_REF] Xavier | Spreader grafts: functional or just aesthetical?[END_REF] The software can perform CFD in the nasal cavity (solving the Navier-Strokes equation) using different boundary conditions, types of airflows (laminar or turbulent) and breathing phases (inspiration or expiration).

| Potential biases in the review

Of the studies reviewed, one did not include a validated assessment of nasal obstruction but simply reported a difference in clinical impairment between the compared groups. [START_REF] Kim | Correlation between nasal airflow characteristics and clinical relevance of nasal septal deviation to nasal airway obstruction[END_REF] However, given the number of studies, we incorporated all those that report patient perception. In some cases, correlations occasionally appear to be present although their significance remains unconfirmed by a satisfactory statistical test due to the small number of patients included.

It is essential therefore to conduct further studies on larger populations of patients.

| Implication for research

In future, we must be able to perform more frequent inspiratory and expiratory simulations based on normal breathing (and not on a constant incoming airflow). This is essential to allow deformation of nasal walls, which play a major role in nasal valve collapse, and in order to integrate new types of data such as hygrometry to measure the humidity in the atmosphere and to vary the temperature of the nasal mucosa according to inspiration or expiration. This will help generate more reliable extrapolation of CFD results. Application of CFD protocols to clinical cases of nasal obstruction will help define the best treatment of the disease (surgery, non-invasive or minimally invasive therapy).

| CON CLUS ION

The growing number of CFD studies involving the nose is helping to improve our understanding of nasal obstruction. The clinical interpretation of previously unknown data, such as WSS and heat flux, is opening up new horizons in our knowledge regarding this symptom.

Heat fluxes are among the most accurate CFD values correlated with patient perception. Further studies on larger cohorts of patients are needed.

CO N FLI C T O F I NTE R E S T S

None to declare.

O RCI D

Thomas Radulesco https://orcid.org/0000-0002-5939-5372

R E FE R E N C E S

Keypoints•

  Computational fluid dynamics (CFD) consists in studying fluid flows, or their effect, by numerical solution of equations governing fluids. It can be used to study nasal ventilation modalities.

3 . 4 . 6 |

 346 Wall shear stressKimbell et al[START_REF] Kimbell | Changes in nasal airflow and heat transfer correlate with symptom improvement after surgery for nasal obstruction[END_REF] found that wall shear stress (WSS) calculated on the obstructed side was strongly correlated with NOSE (r = -0.51) and moderately with VAS (r = 0.32). Kim et al 24 reported higher shear stress values in symptomatic patients than in asymptomatic patients (0.564-0.943 Pa vs 0.368-0.461 Pa, P = 0.050). In patients with nasal airway obstruction due to ENS, WSS was lower in the inferior region, due to absence of inferior turbinates.[START_REF] Li | Computational fluid dynamics and trigeminal sensory examinations of empty nose syndrome patients[END_REF][START_REF] Li | Investigation of the abnormal nasal aerodynamics and trigeminal functions among empty nose syndrome patients[END_REF]

  Comparison between CFD and: -NOSE and VAS scores; -symptomatic and non-symptomatic patients; -pre-vs postoperative situations.

Table 1

 1 lists all selected studies and their assessment method for clinical evaluation of nasal obstruction. Of the 258 articles selected, 47 dealt with CFD and nasal airway. Ten out of 47 included CFD and subjective or objective nasal obstruction clinical measurements data (Figure

  TA B L E 1 Clinical assessment of NAO in the 10 published studies included in this review

		Number of		Clinical evaluation of NAO
	Article	patients	Type of patient	Subjective	Objective
	Casey et al 21	30	Anatomic nasal obstruction (deviated septum, turbi-	NOSE/ VAS	/
			nate hypertrophy or nasal valve dysfunction) versus
			healthy subjects
	Gaberino et al 22	12	Anatomic nasal obstruction (deviated septum, turbi-	NOSE/ VAS	/
			nate hypertrophy) with significant nasal cycle
	Kim et al 24	6	Patients with nasal obstruction versus healthy subject Clinical data	/
	Kimbell et al 8	10	Anatomic nasal obstruction (deviated septum ± turbi-	NOSE/ VAS	/
			nate hypertrophy)
	Li, Farag, Leach et al 30 28	Empty nose syndrome versus healthy subject	NOSE/ SNOT-22/ ENS6Q Rhinomanometry/
					Acoustic rhinometry
	Li, Farag, Maza et al 31	69	Empty nose syndrome versus healthy subject	NOSE/ SNOT-22/ ENS6Q /
	Liu et al 29	19	Anatomic nasal obstruction (deviated septum) versus	VAS	/
			healthy subject
	Lu et al 27	10	Healthy subjects	/	Rhinomanometry/
					Acoustic rhinometry

Sullivan et al 37 10 Anatomic nasal obstruction (deviated septum, turbinate hypertrophy or nasal valve dysfunction) NOSE/ VAS / Zhao et al 26 22 Healthy subject VAS Rhinomanometry

S U PP O RTI N G I N FO R M ATI O N

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