In this study, a nasal airway of a 3-year-old patient who was diagnosed with adenoid hypertrophy (AH) was reconstructed from 269 CT images (DICOM format) with a resolution of 512 × 512 pixels and 0.5 mm intervals. The set of clinical images were taken at the end of inhalation processes and the patient was required to hold breath during scanning, which provides a clear vision of original nasal airway. The imaging data was collected by project members in Xi'an Jiaotong University, which was conducted with written informed consent from the parents and was approved by the Human Research Ethics Committee at the Second Affiliated Hospital of Xi'an Jiaotong University.To facilitate the computational simulation application, the set of medical imaging data was imported into 3D-slicer version 5.0.3 [open-source platform (available http://www.slicer.org)] for nasal geometry segmentation and registration purpose. Detailed reconstruction process has been reported in our previous work (32).

To better restore the flow patterns and particle transport behaviors which were jointly influenced by the external nares and surrounding environment, the realistic facial features around nares that enclosed by a spherical breathing zone has been attached to the nasal passage (33). The larynx region was preserved to obtain the fully developed outstream and better numerical convergence.

To facility visualized the influence of adenoidectomy on nasal flow patterns and aerosols transport, a virtual surgery was conducted on the adenoid region and removed the enlarged adenoid tissue artificially as shown in Figure 1. Except for the artificially restored adenoid region, the post-operative geometry keeps consistence with the pre-operative geometry.

Figure 2 is a configuration preview of mesh details with two typical slices respectively located at nostrils and middle of the passage to highlight the internal mesh refinement. In each model, ANSYS Fluent Meshing (ANSYS, INC., CANONSBURG, Pennsylvania) was used for mesh generation, where polyhedral elements were employed to solve the flow fields. Compared with unstructured tetrahedral element, polyhedron scheme performs several advantages including less sensitive to stretching, better numerical convergence and more effective computational time. Meanwhile, 5 prism layers were attached to nasal walls and the face to provide an accurate prediction of particle behaviour in the near wall region. Subsequently, a mesh independence test was conducted by solving the average velocity at vestibule region under the inhalation flow rate of 9.5 LPM, where a stable solution was achieved when the global elements in main nasal cavity sized between 0.2 mm to 0.3 mm. Finally, 0.96 million and 1.19 million elements were used respectively for pre- and post-operative model, which achieved a balance between computational efficiency and accuracy. Overall, both pre- and post-operative model employed a hybrid prism-polyhedral mesh scheme to accomplish numerical accuracy while minimize computation cost.

Figure 3 illustrated the details of boundary conditions in this case. The attached breathing zone in front of the cavity was set as zero-gauge pressure inlet to imitate the ambient environment. The outlet of the airway was set as velocity outlet by dividing the physiological volumetric flow rate with the area of the outlet. International Commission on Radiological Protection (ICRP) publication 66 suggests a tidal volume of 0.244 L with a frequency of 39 per minute for children subjects under light exercise condition. Therefore, the equivalent volumetric flow rate of 9.5 litre per minute (LPM) was employed for light exercise condition. Respiratory conditions are determined by human exercise and physical activity. To consider different physiological conditions, numerical simulations under three levels of inhalation flow rates, representing, respectively, resting (3.1 LPM), light exercise (9.5 LPM), heavy exercise (18.9 LPM) circumstances were performed in this study. For the nasal surface as well as surrounding face, it was assumed to be no-slip, stationary and perfect absorbed when predict particle transport.

In this study, the fluid flow was simulated by ANSYS-FLUENT 2020 R2 (ANSYS, INC., CANONSBURG, Pennsylvania). During quiet and moderate breathing, airflow is primarily laminar in nasal passages. However, the airflow may exhibit higher level of disturbances at locations with drastic changes in cross-sectional areas (such as the nasal valve or nasopharynx sections). Therefore, to capture all flow patterns in nasal airways including the laminar-turbulence transition, Shear-Stress Transport (SST) k-ω model was employed in present study (34, 35). Due to the presence of swirls and eddies, stronger mixing effect are expected in turbulent flow, which causes higher flow resistance. In addition, flow fluctuations also cause particles to undergo changes in both magnitude and direction of their trajectories and to eventually deposit on airway walls. To account for the role of turbulence in deposition, the Discrete Random Walk (DRW) model can be added when conducting air-particle simulations using Discrete Phase Model (DPM). According to our predictions of the total particle deposition efficiencies for 1 μm, 5 μm and 10 μm particles with and without the DRW model, the largest value disparity is 0.32% for 1 μm particles. Therefore, the effect of turbulent mixing on deposition is considered as insignificant and negligible.

For the assuming steady incompressible fluid, continuity and momentum equations were solved to govern the fluid motion and shown as below:(1)∂∂xi(ρui)=0(2)ρuj∂ui∂xj=−∂p∂xi+∂∂xj[μ∂ui∂xj]

Where ρ represents density, u represents velocity and p represents pressure of the air.

Previous studies have revealed that there is an increasing trend in adopting medical nebulizer and Metered-Dose Inhaler (MDI) approaches in adenoid hypotrophy therapy, and the resultant drug aerosol size distribution is generally below 20 µm (36–40). Therefore, micrometer particles ranged between 1 and 20 μm were employed to evaluate the aerosols transport and deposition performance. Micron-particle sized 1, 2, 3, 4, 5, 6, 7, 8, 10, 15, 20 µm were tracked. For each particle size, 50,000 were passively released based on a series of particle number independence tests with a variation less than 0.1% for predicted of deposition efficiency. Particles were uniformly released from a spherical surface with a radius of 30 mm centered at the nose tip, which fully overlay the nostril and its surrounding area. The particles were released with a zero initial velocity and inhaled along the inhalation streamlines. Primary mechanisms of aerosol deposition in respiratory airways include inertial impaction, gravitational sedimentation, Brownian diffusion, and to a lesser extent, by turbulence, electrostatic precipitation, and interception (41). The relative contribution of these mechanisms is a function of the physical characteristics of the particles, the airway anatomy, and the physiological airflow patterns. Inertial impaction mainly occurs in the upper respiratory tract when there is a sudden change in the airflow direction, which causes large micron particles to deviate from the air streamlines as the inertia of the particles keeps them on their initial trajectories. For gravitational sedimentation, it results from the settling of the particles under that action of gravity. This mechanism is most efficient in the small airways and alveoli where the residence time is high and the travel distance of particles is small. The third main mechanism of deposition is Brownian diffusion, it results from the random motions of the particles caused by their collisions with gas molecules. Unlike impaction and sedimentation, deposition by Brownian diffusion increases with decreasing particle size and becomes the dominant mechanism for particles smaller than 0.5 µm. For aerosol particles (micron-particle in a range between 1 and 20 µm) considered in this study, inertial impaction is the dominant mechanism of deposition, as previous studies have demonstrated that the very short residence time in the nasal passage (smaller than 0.1 s) do not permit micron-particles to deposit by sedimentation (42).

In this case, one-way coupled Lagrangian discrete phase model (DPM) was used to predict the individual particle trajectories which occupies a low volume fraction, equating the particle inertia with drag force, gravity force and Brownian force:(3)duiPdt=FD+FG+FBwhere uiP represents the particles velocity, FD is the drag force per unit particle mass described as:(4)FD=18μ(uig−uip)Ccdp2ρphere u is the airflow velocity, μ is the air viscosity, dP is the particle diameter, ρP is the particle density and Cc is the Cunningham correction factor given by:(5)Cc=1+2λdP(1.257+0.4e(−1.1dp2λ))here λ is the air molecular mean free path defined as 67 mm in this case.

FB is Brownian force defined as ξi√((πSo)/Δt), where Δt is the particle integration time-step and ξi is a zero-mean, unit-variance-independent Gaussian random numbers. So is a spectral intensity function explained as:(6)So=216vkBTπ2ρdp5(ρPρ)2Cc

Here v is the kinematic viscosity, kB is the Boltzmann constant, T is the Kelvin temperature of inhaled air set as 293 K in this case and Cc is the Cunnigham correction factor.

Particles that absorbed by trap nasal surface were statistically process as particle deposition efficiency (particle number trapped by regional nasal wall divided by total number inhaled into nasal chamber).

To verify the reliability of the computational model, an in-vivo rhinomanometry measurement was conducted on the patient by project members in Xi'an Jiaotong University and the detailed measurement theory has been explained in our previous work (43). Figure 4 shows the measurement and numerical simulation results of the pressure drop-flow curves with comparison data from previous literature. Both of the prediction and measurement trans-nasal pressure drop trends to increase with the increasing inhalation flow rate. For a fixed flow rate, the numerical pressure-drop shows minimize tolerance with measurement results especially when flow rate is less than 10LPM while the difference slightly increases when inhalation at a higher rate. Overall, the numerical prediction curve shows great consistence with measurement curves both in magnitude and trend, which indicates convincing reliability of numerical model.

There are several clinical methods of adenotonsillar hypertrophy (AH) assessment to describe the degree of nasal airway obstruction. In this study, the lateral neck x-ray (LNX) was used for defining the degree, which is the most accepted method for assessing AH (44). Moideen, Mytheenkunju (45) reported that LNX assessment method has significant correlation with patient's symptoms and key landmarks of assessment according to the reference have been highlighted in the Figure 5A. Line B-B is the line drawn along straight part of anterior margin of basi-occiput, on which following measurement bases. Moideen defines the adenoid thickness (line L_A) starts from line BB and then perpendicularly reaches most conves part of adenoid tissue. Nasopharynx depth (line L_N) was measured from line BB to the spheno-occipital synchondrosis. Following Moideen's method, adenoid-to-nasopharyngeal ratio was then calculated as L_A divided by L_N. In this study, 75% adenoid-to-nasopharyngeal ratio was measured, which belongs to Grade IV that enlargement tissue practically obstructs the airway.

Using original diseased model as reference location, shape deviation was investigated as Figure 5B, where red part indicates that adenoid tissue is reduced away from the airway after virtual surgery. The operation only performed virtual reduction of the enlarged tissue, and the blocked nasopharyngeal channel gradually widened that larger deformation was observed at the center of the adenoid pad. Relatively mild change about 1–2 mm was measured at the edge of the tissue, and the peak change near the center reached about 6 mm.

Figure 6 shows cross-sectional area vs. normalized arc-length away from nostril measured pre- and post-virtual surgery. Since virtual operation only conducted at the enlarged adenoid region, the cross-sectional area of the anterior nasal passage (normalized length before 0.7) was remained in same condition. Key anatomical region has been marked with the rectangle wireframe, which covers the whole adenoid area. Within the marked region, the size of the nasopharyngeal channel performs sharp narrow after a moderate increase. The cross-sectional area of the airway after surgery is significantly larger than that of pre surgery, and the difference become greater as the direction away from the nostrils. At normalized distance 0.75, the regional cross-section area reached peak value, 2.2 cm² pre-operation and 2.5 cm² post-operation. After dramatically constriction, the narrowest airway pathway was observed around distance 0.9, which increased from 0.21 cm² to 0.85 cm² after the virtual operation. More than 4-times airway widening brings a non-negligible improvement in nasal airway patency.

Figure 7 compares velocity streamlines under three inhalation conditions, including 3.1 LPM, 9.5 LPM and 18.9 LPM, which represent different activity levels (resting, light exercise, heavy exercise) before and after virtual surgery. Airflow streamlines analysis provides surgeons with more accurate understanding of the improvement of the nasal airflow after surgery and helps to standard objective judgement of the surgery.

Overall, the flow stream mainly allocated into the middle passage for all inhalation conditions while relatively moderate flow entered the inferior passage. Rare flow reached and formed recirculation stream around the upper anterior site, limited by the vestibule notches and the narrow slit-like anatomical features. As shown in Figure 7, airflow suddenly accelerated at the nasopharyngeal region in the diseased model due to the severely compressed passage. In contrast, the dramatical acceleration situation was significantly alleviated by virtually removing the enlarged tissue, thus more breathing effort is anticipated in diseased nasal cavity to combat the flow resistance while satisfying the respiratory needs. For resting condition (3.1 LPM), local peak velocity of diseased model was measured as 5.1 m/s and it reduced to 1.2 m/s after surgery, which provides the patient with the most noticeable respiratory improvement (more than 4 times) among all activity conditions. Under light exercise condition (9.5 LPM), local peak velocity at nasopharynx region reached 7.8 m/s and the virtual surgery helps to reduce to a half (3.9 m/s). It indicates the operation could achieve considerably satisfying performance in the most common respiratory activity. For heavy exercise condition (18.9 LPM), the extremely high local flow stream was released from 13.1 m/s to 9.3 m/s after virtual surgery. In addition, the distribution of inhaled flow throughout the nasal cavity is more spread out after removing the abnormal tissue since more airflow distributed into olfactory region and superior meatus, which is of great advantage of the nasal ventilation and maintaining stable nasal function.

To further quantify the anatomical effect of the narrowed nasopharynx airway, detailed comparison of pressure drop between original (pre-operative) and virtually restored (post-operative) nasal airways under various inhalation status was performed. As listed in Table 1, the local pressure drop across the nasopharynx region shows obvious variability between pre- and post-operative models. Under all breathing conditions investigated, high pressure drop values were dramatically reduced in the post-operative model, which indicates breathing efforts were reduced and healthier respiratory resistance was restored (46). Among all conditions, the most significant improvement was found under heavy exercise (18.9 LPM), where local pressure drop decreased from 208.66 Pa to 35.52 Pa with an 83% resistance reduction increment.

The nasal epithelium is constantly subjected to wall shear stress (WSS) induced by respiratory airflows, and WSS has an important role in the mechanical regulation of the nasal epithelium function. For example, one major source of the mucus secretion is the nasal epithelial goblet cells, which rapidly discharge mucus in response to various biological stimuli. In-vitro cell based assays conducted by Even-Tzur, Kloog (47). has revealed that mucus secretion levels were directly related to the WSS magnitudes and exposure time duration. Abnormal shear stress patterns and prolonged inhalation exposure may lead to permanent cell damage and impaired nasal physiology and defence functions. In this study, WSS at the air-wall interface of the nasal airways were numerically compared between the pre- and post-operation nose subjects (Figure 8). Overall, increased stress occurred at the posterior vestibule region and nasopharynx region due to the 90° turn and constriction of the airway. By the contrary, extremely low magnitude of WSS was observed at the olfactory region and inferior meatus. Specially, it is noticeable that the abnormal enlargement of adenoid tissue caused obviously varying stress pattern that has been marked by red rectangle in Figure 8. For resting breathing condition (3.1 LPM), shear stress at nasopharynx region exhibits slight increase with peak value of 0.5 Pa while 0.07 Pa was measured after virtual surgery which only accounts 14% of the original case. For light exercise condition (9.5 LPM), abnormally high WSS was observed for diseased model with local peak magnitude of 2.1 Pa, and the value reduce to a quarter after virtual surgery. Extremely high WSS was prevalent in marked region in diseased model under active inhalation situation with local peak of 6.7 Pa and it reduced to 22% of diseased case. Obvious relief of WSS variation support patient maintain more stable nasal function under active situation as less stimulation is imposed. In addition, relatively increased stress exhibits in the middle passage since rapid near-wall velocity variation owing to fast flow stream passing through.

In order to accurately analyze the improvement of airflow distribution by the virtual surgery, a cross-sectional slice was taken in the middle passage, where the middle and inferior meatus were divided and statistical volume flow for pre- and post- surgery is shown in Table 2 [Improvements in airflow distribution are measured using increments: (post-surgery—pre-surgery)/pre-surgery × 100]. It can be observed that the increment of the inferior meatus post-surgery is much larger than that of the middle meatus. From the perspective of data analysis, the virtual surgery has a stronger effect on the improvement of the airflow into the inferior meatus, which is due to the smaller value of the measured volume flow. For heavy exercise (18.9 LPM), the passing flow increases most, reaching 28.7%. However, in various breathing states, the amount of airflow entering the middle meatus is significantly more than that of the inferior meatus, showing a law that increases with the higher inhalation rate. When the child was breathing vigorously, the most abundant flow through middle meatus increased from 11.15 m³/s to 12.11 m³/s, with an increment of 8.61%. The improvement in virtual surgery is most pronounced in the light exercise condition (9.5 LPM), because 11.05% more flow was apportioned into the middle meatus.

Nasal airflow that effectively transports ambient odours to the olfactory receptors is important for human olfaction. On the other hand, the olfactory region itself is a portal for intranasal drug aerosol delivery that targets the Central Nervous System (CNS). To evaluate the anatomical changes (i.e., normal and obstructed nasopharynx region due to the presence of adenoid hypertrophy) on airflow that enters the olfactory slits, the ventilation status of pre- and post-operation nose subjects were numerically compared (Figure 9). Overall, weak flow enters olfactory region and the situation shows limited improvement with more active respiratory conditions. Under 3.1 LPM breathing condition, rarely gentle flow entered olfactory region in original model with a local velocity of 0.19 m/s and it is improved 160% after virtual operation. For general breathing condition (9.5 LPM), relatively limited enters olfactory slit before operation with the local peak velocity of 0.71 m/s while inter-chamber difference is slightly eliminated with local velocity increasing by 136% after surgery. Compared with gentle and general condition, relatively effective flux flows into that region with measured local velocity of 1.32 m/s which rises to 1.53 m/s after operation. The weak improvement exhibited under active respiratory condition was owing to the anatomical limitation effect.

Figure 10 describes micro-particle (with diameter of 5, 10, 15 μm) deposition patterns under the light exercise inhalation condition (9.5 LPM), from which noticeable variation of the spatial deposition performance is observed between pre- and post-surgery models. Overall, higher nasal deposition intensity appeared for larger particle size because of the inertia-dominated deposition mechanism. Surface deposition for 5 μm exhibited a relatively dispersed pattern while that for other two particle sizes were more concentrated at the middle passage since the large inertia particles were more likely to transport along the inhaled flow and hit nasal surface. Similarly, the larger the particle inertia, the higher deposition distribution at anterior passage. There was rare deposition spot being observed in the inferior and upper passage since limited flow distribution here. However, 10 μm showed the most concentrated pattern in the olfactory region compared to the 5 μm and 15 μm.

It is observed that 5 μm is preferred to deposit in the vestibule region while 10 μm and 15 μm were more likely to escape from the filtration of this region and direct into main passage. The localized deposition behaviour could be characterized by Stokes number which is considered as a significant non-dimensional parameter for describing particle motion (48). It suggests that particles become increasingly sensitive to the flow with smaller Stokes numbers. Particles of 5 μm has smallest Stokes number that is proportional to the square of the particle diameter, resulting in the highest fidelity of flow tracer behaviour. Figure 11 describes the secondary flow motion on a cross-sectional plane in vestibule region, from where discernible vortices is observed at the top of plane due to the local airway changes. Consequently, particles of 5 μm are most likely to comply the local flow changes and hit onto the wall, forming the most concentrated deposition at the roof top of vestibule region. This unique finding may distinguish from other literature that reported higher deposition efficiency for larger micron-particles in vestibule region by the different definition of vestibule region and inter-subject anatomical feature of nasal vestibule (19, 49). It was more commonly that defining the entrance and nasal valve as vestibule, which provides the deposition results that measured within a quite larger area than this study. Furthermore, the cylindrical shape of children nasal vestibule and the nearly parallel cross-sections of nostrils and nasal valves facilitate extensive contact between inhaled flow and vestibule surface, enhancing the possibility of airflow responding to local airway changes. This encourages that there is still valuable research potential in the morphological features of children nasal cavity and its associated flow and aerosol dynamics.

For all particle sizes, pre-surgery nasal geometry shows higher possibility of capturing micron-particles compared with post-surgery. In addition, deposition patterns for pre-surgery model spread further into the posterior passage compared to post-surgery model, which may owe to a relatively plain flow jet path from nostril to pharynx that formed by severely blocked nasopharynx. Besides, more particles tended to deposit into olfactory region pre-surgery, which was particularly obvious for 10 μm particles. This funding may provide more evidence to help the nasal-brain related drug delivery research.

Furthermore, it needs to be noted that the deposition pattern and regional disparities were discussed based on the assumption of constant flow rate under 9.5 LPM, which neglects the instantaneous deposition of microparticles because of unsteady accelerating and decelerating flow. For instance, overprediction of deposition in anterior nasal passage was reported under steady condition when particle size is between 1 and 20 μm (50). A higher deposition with particle sized between 1 and 10 μm for steady condition was found by Häußermann, Bailey (51). However, our previous study also demonstrated that the quansi-steady airflow assumption in the nasal cavity was reasonable when the instantaneous Strouhal number was smaller than 0.2 (52). Therefore, in present study, the instantaneous deposition features were not considered, and future studies should consider addressing this research limitation.

Figure 12 measured total nasal deposition efficiency (DE) and clearly present the contrast between pre- and post- virtual surgery vs. impact factor. For the overall trend, the number of particles captured by the nasal surface wall was significantly positively correlated with the impact factor, and DE increased at a greater rate when the particle diameter exceeded about 4 μm. Before the virtual operation, DE gradually approaches 99.9% from lower levels (10.2%) with increasing particle diameter up to 10 μm. Comparing the results before and after surgery, total nasal deposition of each particle diameter is reduced to varying degrees. The higher velocity streamlines resulting from the narrow airway before surgery makes inertial-dominated transport of micro-sized particles more easily captured by the complex nasal structure. The deposition curves exhibit greater difference (approximately 3.2 times difference) when inhaled particle size larger than 5 μm and the curve approaches peak until 15 μm.

Although adenoidectomy is the most common treatment for severe cases, a few studies indicated that using nasal steroids including budesonide, mometasone furoate is also considered as an effective therapeutic method for adenoid hypertrophy treatment specially for decreasing diseased tissue before surgery or preventing regrowth after surgery (27, 40, 53). Several possibilities have been raised about its mechanism, including a lympholytic action on adenoids, anti-inflammatory effect, or reduction the risk of the adenoids for infection. Since intranasal steroids is considered as a therapeutic treatment or adjunctive treatment after surgery, the adenoid region that lesion occurs should be paid attention to as the destination for drug delivery. Figure 13 is comparison of regional DE in adenoid tissue area for pre- and post- virtual surgery vs. impact factor (for convenience of observation, the value range of the ordinate becomes 0 to 3). Overall, similar lower deposition results occurs when particle diameter smaller than 5 μm or larger than 15 μm while peak-shaped deposition curves appear in the middle of this range (reaches peak at 10 μm). It is worth noting that DE measured after virtual adenectomy is higher than that before virtual surgery, especially when particle diameter is 10 μm. The enlarged adenoids tissue forms a locally high-speed airflow and jet to the back of the pharynx, so that a more linear streamline transports the particles through the target area.