Agreement between rhinomanometry and computed tomography-based computational fluid dynamics

Active anterior rhinomanometry (AAR) is an international standardized method for the evaluation of nasal obstruction [1, 2]. AAR measures nasal pressure and airflow during inspiration and expiration. Specifically, it measures pressure differences between the nasal entrance (ambient pressure) and the nasopharynx. AAR can be influenced by alternating congestion and decongestion of the nasal mucosa, a physiologic process that is termed “nasal cycle” [3, 4]. The nasal cycle results into different mucosal congestion status between the left and right nasal side [5]. Another important tool for evaluation of nasal obstruction is computed tomography (CT).

Recently, the importance of computational fluid dynamics (CFD) in rhinology has been highlighted [6]. CFD uses numerical methods to analyze and solve problems that involve fluid flows, e.g., aerodynamics. In their recent review, Leite and coauthors concluded that CFD may become a viable diagnostic tool in the future for studying nasal physiology [7]. Recently, Radulesco and coauthors searched for data to compare nasal obstruction with CFD variables. Among CFD-calculated resistances, airflow, heat flux, wall shear stress, total pressure, velocities and streamlines, the authors reported the heat flux as the most correlated CFD variable with subjective nasal obstruction. Total pressure and velocities were also useful [8].

In an attempt to investigate the correlation between AAR and CT-based CFD, Kaneda and coauthors compared the nasal patency computed by solving the Navier–Stokes equations with the AAR-measured nasal patency [9]. Despite the unsatisfactory correlation, the authors reported similar qualitative tendencies between both methods. Cherobin and coauthors investigated the correlation and agreement between the resistances derived from AAR and CFD [10]. The authors reported a weak correlation between the values of nasal resistance derived from AAR and CFD (r = 0.41, p = 0.003).

In our study, we investigated the correlations and agreements between the results from AAR and an in-house developed CT-based CFD approach for multiple subjects. Our CFD simulations of nasal airflow were previously validated with laser Doppler anemometry (LDA) [11]. LDA is a fluid flow measurement technique that captures the velocity of particles in the flow field. LDA is noninvasive and does not influence the flow field. Since fluid flow phenomena are difficult to simulate accurately (turbulence, separation), LDA was used to determine the accuracy of the simulated nasal airflow. LDA requires optical accessibility to the flow field. Therefore, in vivo measurements were not possible. A simplified 3D printed model (Dremel 3D20, Dremel, Racine, USA), based on a CT dataset of a septal deviation CT dataset, was investigated with LDA. Optical accessibility was guaranteed by acrylic glass elements. The measurement results were then compared to those of the LB simulations. On a line introduced near the nasal valve for evaluation, the maximum velocity difference between LDA and the LB simulation was below 15%, which was considered acceptable.

In this Pilot study, we investigated whether the clinically performed AAR could correlate with a simulated AAR generated from CT-based CFD. For this purpose, we compared the pressure values derived from clinical AAR and simulated AAR. Our results revealed an excellent correlation between pressures derived from both methods (r = 0.93; p < 0.001), after removing the variations due to subjects, nasal sides and respiration phases. However, this was a trivial, even misleading finding, as the flow rate necessarily increases when the pressure drop increases. In addition, the high number of observations increased the observed correlation. To cope with this issue, we compared the more commonly clinically used resistance by 150 Pa pressure drop during inspiration, derived from clinical and simulated AAR. Our results revealed a moderate correlation between resistances derived from both methods (r = 0.65, p = 0.041; Fig. 5).

Since correlation does not necessarily indicate agreement, we further investigated this issue by the Bland–Altman method in line with similar studies [10]. This statistical method is used to assess agreement between two methods of measurements with repeated data. To precisely describe how smaller or greater pressure and resistance values of AAR were in comparison with pressure and resistance values of the simulation, we logarithmically transformed the pressure and resistance values. The Y-Axis of the Bland–Altman plot was the difference between two methods of measurements. The difference of logarithmic RhinoPress and logarithmic SimPress is equal to the proportional deviation of logarithmic RhinoPress and logarithmic SimPress. This led to easy calculation of the proportional deviation of RhinoPress and SimPress. Similarly, the same approach was followed for the RhinoRes150 and SimRes150.

The proportional deviation of pressure values was computed separately for each nasal side and respiration phase. A low value for the logarithm of the proportional deviation would indicate a high degree of agreement. Our results revealed a logarithm of the proportional deviation of 1–29% (Table 1). This implied that the RhinoPress was 1–2 times greater than SimPress (Table 1). This variation was more crucial for higher \({\Delta }p\). This suggested an inverse proportionality (“the lower the \({\Delta }p\), the higher the agreement”). Similarly, the documented value for the logarithm of the proportional deviation of RhinoRes150 from SimRes150 was 3%, which implied that the RhinoRes150 was similar to the SimRes150.

Substantial side predominance was noted. On the left side, RhinoPress was similar to SimPress. On the right side, RhinoPress was two times greater than SimPress. Septal deviation to the right was present in 4/5 subjects. These results could indicate a better agreement on the less obstructed and a worse agreement on the more obstructed nasal side. Indeed, the agreement between RhinoPress and SimPress for subject 5 (left septal deviation) was slightly better on the right side (5.0%) than in the left side (5.3%; data not shown).

The first problem we encountered was the mucosal status. We were obliged to choose either the congested or decongested AAR as clinical AAR. We based this decision on the agreement between either the congested or the decongested AAR and the simulated AAR. This agreement depended on the nasal mucosa status. The simulated AAR was generated from a CT scan. At the time of the CT, the nasal mucosa was in either a congested or a noncongested state. This depended on the nasal cycle, resulting in one congested and one noncongested state of the nose. Therefore, we noted a high agreement between the simulated AAR and either the congested or the decongested AAR, but not both. Indeed, visual inspection of the congested, decongested and simulated AARs (Fig. 2) supported this observation.

In all subjects, AAR was performed according to international standards [1], and the same imaging protocol (DVT) was chosen. DVT provided approximately 400 DICOM files in total for the axial, coronal and sagittal planes, substantially useful for application in CFD. With the lattice Boltzmann package Sailfish CFD, the segmented 3D data structure in DICOM file format can be used for simulations without any preprocessing. Sailfish CFD is numerically stable with the complex shapes of the nasal airway passage in the airflow range of AAR.

The digitization of the AAR pdf data resulted in pixel-based pictures with a pixel density of 200 dots per inch (dpi). For printing, 300 dpi is standard; 150 dpi is considered acceptable to separate raw AAR data curves [19]. For data extraction, RGB color thresholds with ± 10 range were chosen. The color was specified by visual selection with the graphical user interface pipette. The colors of the AAR curves were unique in the original pdf file; a larger threshold range provided no additional benefits. The extracted AAR analysis depended on the discretization window applied to the original pdf file; a discretization window of 5 × 5 pixels resulted in an extracted AAR resolution of more than 1500 x–y points. For this, the computational time was less than a second. A larger discretization window with less computational time—but also with lower AAR resolution—was not considered. Since the extracted AAR resolution was considered acceptable, a smaller discretization window with an even higher extracted AAR resolution was not needed.

The nasal air space extraction was programmed in Python and performed based on thresholding at -460 HU [13]. The simple thresholding segmentation led to occasional artificial connections between the three nasal meatus, artificial septal perforations or bad connectivity to paranasal sinuses in anatomical sites with very thin tissues. Here, a slight effect at the results cannot be ruled out. This might explain the worse agreement between AAR and CT-based CFD on the more obstructed nasal side, in which the borders between structures are not as easily outlined as on the less obstructed nasal side. The simulation of the airflow at the nasal tip was critical [20]. For this reason, a sphere was positioned at the nasal tip. The sphere extended the simulation area without ‘hurting’ the anatomical integrity of the anterior nose, which is crucial for the airflow. Therefore, the airflow at the nasal tip reflected real-life conditions. We set the sphere diameter to 70 mm [21]; a larger diameter would merely increase the computational time without any additional advantages, and a smaller diameter might influence the integrity of the anterior nasal structures. The cuboid at the outlet was considered the appropriate geometrical element to define flow rate \(\dot{V}\) by a “Dirichlet” velocity boundary condition (constant velocity at the outlet boundary condition). The Python script allowed automatic segmentation without user interaction for all CT datasets. One single manual correction was performed in order to reflect AAR conditions. Specifically, one nostril was locked manually during simulation.

The accuracy of the LB fluid flow simulations depends on the fluid properties and the resolution of the spatial discretization. Air was simulated with a constant temperature of 20 °C, which was specified by a constant density and viscosity. During inspiration, the air temperature increases, which results in an increase in viscosity and a reduction in density. This change is not reflected within the LB simulation [22]. The resolution of the spatial discretization was considered sufficient and mesh independent [11]. However, the resolution was not sufficient to resolve sub-millimetric turbulent flow phenomena, especially when the air-space cross section was smaller than 3–5 cells (0.702–1.17 mm). In our study, we focused on nasal airflow in general. We did not perform a turbulent spectrum analysis. We performed LDA measurements to determine the accuracy of the velocity vector field and a mesh convergence study to guarantee that the pressure between sphere and oropharynx was independent of the grid size. Within the simulations, pressure extraction was performed in the sphere and the cuboid in the oropharynx (Fig. 1b). Significant pressure changes were not observed in either the sphere or the cuboid. This reassures the accuracy of the pressure extraction. Moreover, the computational time of the simulation using Sailfish CFD on a NVIDIA GTX 980 Ti was less than six minutes. Furthermore, the pressure drop is an extremely robust parameter, tolerant at coarse meshes. Despite the nose complex geometry, the nasal airflow is a simple fluid dynamical problem.

In contrast to Cherobin and coauthors [10], we examined the pressure scalar field. The investigation was performed with the LB code. Here, the air segmented CT datasets are used without any further meshing process, which simplifies the workflow [14]. The LB code is simple and fast when run on a GPU [14]. The LES Smagorinsky subgrid model used is more accurate than k-omega [23]. The disadvantages of LB include greater memory usage and numerical stability only in a defined velocity range [14]. Furthermore, Cherobin and coauthors compared 50 left and right resistance measurements and 50 left and right conductance measurements of 25 patients, derived from CFD and AAR, also by the Bland–Altman method of agreement. The authors reported a weak to moderate correlation between CFD and AAR. The comparison was performed only at \({\Delta }p\) = 75 Pa [10]. In our study, we compared the complete clinical AAR curve with the complete simulated AAR curve. Here, we analyzed grouped pairs of flow and pressure measurements that covered the complete spectrum of flow (− 625 to 625 ml/s) and pressure (Fig. 2; supplementary material 1 in raw form), thus presenting a more representative comparison of both methods. Obviously, \({\Delta }p\) = 150 Pa or near it remains the most useful clinical measurements [24]. Therefore, we also examined the resistance by \({\Delta }p\) = 150 Pa during inspiration. Here, we noted a moderate correlation between CFD and AAR. Resistance values did not differ significantly between both methods. However, this might be related to the small sample size, since we noted a tendency for lower resistance values in CFD than in AAR.

Limitations of our pilot study included the small sample size and the effect of the nasal cycle. Initially, we intended to investigate the correlation and agreement of CT-CFD and AAR by a new approach. Most steps of the processing pipeline were automated and did not require much computational power. Usually, pilot studies investigate small samples for feasibility. The first results were the graphical presentation of simulation data and AAR data (similar to Fig. 2) that indicated a promising visual agreement. For statistical investigation, AAR data were digitized, aggregated, redistributed and analyzed. This was an elaborate process, since we compared paired values of flow and pressure of the complete flow/pressure spectrum and not only around \({\Delta }p\) = 150 Pa. Furthermore, the limited funding for this preliminary investigation did not allow increasing the study sample size.

In conclusion, despite the advantages of the LB simulation, our results were close to the results described by other studies. The pressure and resistance values derived from CT-based CFD and AAR were similar, yet not same. The presence of a sphere at the tip of the nose ensured the anatomical integrity of the anterior nose. The LB simulation was applicable for the complicated geometry of the nose and required low computational time. Most importantly, the LB simulation was validated with LDA to assure the validity of the simulation approach. Improvements may include a larger sample size and the decongestion of the nasal mucosa.