All procedures in this study were conducted in accordance with the Universiti Malaysia Perlis Research Ethics Committee, Perlis, Malaysia-UniMAP/PTNC(P&I)/JKETIKA (10/11/2021) approved protocols. Written informed consents were received from all the patients, and the study was conducted according to the tenets of the Declaration of Helsinki for research involving human subjects. The upper airway geometry is extracted from CT scan images of 24-year-old female nonsmoking OSA patient volunteers. The BMI of the patient is 70.3 kg/m², and the AHI is 99.5. The summarized characteristics of the OSA subject that were selected for the conduction of the upper airway CT scan. According to previous works, the focus of the subject of interest was decided to be from the nostril until the pharyngeal [13]. A total of 431 frames with 0.3 mm of slice thickness covering the upper airway CT scan of the subject were performed using an i-CAT Cone Beam 3D Dental Imaging System (version 3.1.62 supplied by Imaging Science International, Hatfield, USA), as shown in Fig. 2.

The airway boundary is identified from the CT scan images via a threshold based on the intensity of the grey image. The thresholding method divides images into sub-images and then determines the threshold value for each portion in order to find different threshold values for various parts of the images. The results of the thresholding are then combined for each component of the image. This technique splits an image into vertical and horizontal parts containing a section of the object’s background. Finally, interpolation is required to achieve the desired outcomes [21]. The images were captured while the patient was awake and lying down with their face upward, as explained in the works of Chan et al. [22]. Each CT scan has 534 pixels × 534 pixels, and the pixel spacing is 0.3 mm × 0.3 mm. A series of CT scan images were stored in a Digital Imaging and Communications in Medicine (DICOM) format. Then, the DICOM images were imported into a three-dimensional (3D) medical image processing MIMICS software (version 15.0; Materialise, Leuven, Belgium). The image segmentation of the upper airway was carried out to identify the 3D airway region based on the pixel value (Hounsfield unit) from the DICOM image series. The airway surface model was generated using segment airway in pulmonary function test, as shown in Fig. 2. Then, the 3D volume of the pharyngeal airway was created and exported for the 3D model mesh generation.

The model generated by the MIMICS software was transferred to 3-Matic (version 15.0; Leuven, Belgium) to create the volume mesh. The preprocessor, ICEM (ANSYS, USA), generated unstructured tetrahedral meshes for airway volume. The mesh quality was controlled to ensure the highest level of result accuracy. The surfaces of the pharyngeal airway have meshed with 2.0 mm of Maximum face size. The maximum and minimum size of the mesh is 2 mm and 0.002 mm, respectively. An inflation of the pharyngeal airway mesh was considered around the wall boundary to increase the accuracy of the simulation. This consideration also ensures an excellent fine mesh is created next to the wall, thus providing an adequately small mesh close to the size of the wall mesh. The y+ (dimensionless distance) approach was used to accurately estimate the initial boundary layer thickness [12] that corresponds to the near-wall cell size (0.272). The quality of the meshed airway model was examined in ANSYS, where the quality of the mesh is measured by the average skewness value and standard deviation. The skewness value is 0.2142, which indicates an excellent cell quality (0–0.25), as recommended by ANSYS. Then, the mesh sensitivity grid study was performed on the 3D airway model with different grid scales. The 5-grid size was performed to establish acceptable accuracy, as shown by the previous research approach.

Inhalation and exhalation breathing involve the airflow passing through the pharyngeal airway. The airflow characteristics may vary due to the uniqueness of the pharyngeal airway. Thus, in the simulation analysis, the flow field in the pharyngeal airway for OSA patients is computed by using a steady-state Reynolds-averaged Navier-Stokes (RANS) formulation, with the k–ω shear stress transport (SST) turbulence model with low Reynolds number correction [23]. The popular k–ω SST turbulence model was considered in this work instead of the k–ϵ model due to the greater accuracy of the former in viscous near-wall region treatment while considering the effects of adverse pressure gradient [24]. The solver used in the simulation had been validated in our previous studies [1]. The comparison of the simulation and previous experimental results showed a good agreement on the wall static pressure induced by the airflow 1.

The minimum area is crucial for patients with sleep apnea. Contraction of the cross-sectional area influences the smoothness of the airflow when passing through the upper airway. This situation is also defined as the obstruction of airflow during inhalation. The narrow airway area in a patient with OSA might have been caused by the collapse or laxity of airway tissue. Most researchers, such as Lantz et al. [28], Chouly et al. [29], and Djukic et al. [30], have discussed and employed the flow values (i.e., velocity, pressure, and wall shear stress) to describe the characteristics of the upper airway. In this work, the additional flow parameter, TKE, is considered to describe the characteristics of the upper airway. Other flow parameters were also considered to visualize the phenomena and flow patterns in the upper airway.

Fig. 4a depicts the axial velocity contour (m/s) and streamlines along the upper airway's midsagittal plane in the nasopharynx, oropharynx, and hypopharynx. The results show that the highest velocity began after the airflow at the oropharynx. As the airflow approached the minimum cross-sectional area of the airway (retropalatal pharynx), the velocity increased, and the airflow seemed to have developed a turbulent flow pattern that also generated the flow recirculation regions (negative axial velocity), as shown in Fig. 4b. The dilation of the cross-sectional area after the narrow area had affected the airflow in the OSA patient's airway. Thus, the flow recirculation is concentrated around this region, typically formed downstream with obstructions (narrow area). The existence of negative axial velocity may lead to the vibration of airway tissue due to continuous breathing. Hence, it is highly likely that this region will generate vibration, causing the snoring. Snoring is known to reduce the strength of the tissue in patients with sleep apnea [31].

Fig. 4b exhibits the recirculation region phenomenon caused by a narrow breathing area. Narrowed breathing area gives the exact definition of hypopnea in calculating the degree of blockage of breathing airway during sleep. By understanding the recirculation region, a new tool may be introduced in calculating the degree of blockage from the simulation of the upper airway without requiring the patient to sleep all night. Fig. 5 shows the maximum velocity and area distribution around the upper airway’s maximum narrowing. The maximum velocity in maximum narrowing is also known as “pharyngeal jet”, whereby it creates a compact region and induces recirculation flow. The average velocity also indicates the maximum velocity around the narrow region. In this situation, the high-velocity airflow had induced a high fluctuation that contributes to the vortices in a turbulent flow. Thus, the TKE, as explained in Eq. (4), is used to describe the mean kinetic energy per unit mass of vortices after the maximum narrowing in the upper airway is reached.

The correlation between velocity and the area of the upper airway was investigated in this study. The region of interest (ROI) was focused on positions ranging from 0.01 to 0.028 m and 0.03 to 0.04 m. The airflow velocity passing from 0.01 to 0.028 experienced the convergence of the cross-sectional area of the upper airway. In contrast, after position 0.028 m, the cross-sectional area of the upper airway is increased; this can be observed in Fig. 5. Fig. 6 shows the correlation between airflow velocity and area. The simulation results revealed that the airflow velocity decreased with the increasing area under the fitting of the power function at positions from 0.01 to 0.028 m. The coefficient of determination (R²) is 0.9981 and indicates the excellent data fit in the regression model. However, the correlation between velocity and area is in the polynomial behavior after the airflow passes through the narrow area. The R² is 0.9854, demonstrating the excellent data fitting of the polynomial function to describe the relationship between velocity and area (positions 0.03 to 0.04 m). The change in the correlation between velocity and airflow was attributed to the airflow characteristic after passing through the narrow area, as aforementioned in Figs. 4 and 5.

The airway wall or tissue experiences the variation of pressure when airflow passes through the airway. Pressure variation may lead to the vibration of airway tissue. Figs. 7a and 7b illustrate the pressure on the airway wall (unit: Pa) during the inspiration and expiration breathing phase, respectively. It is observed that the inhale and exhale breathing have the low-pressure region around the narrow area. This observation corresponded to the large velocity around the narrow area. Higher velocity gives the higher pressure drop.

The TKE value will be high if the velocity fluctuation is in a randomized direction, with high magnitude impacting the blockage in the breathing area, as visualized in Fig. 4; there is low pressure at the narrow cross-sectional breathing area the exhale. The high wall shear stress is mainly observed in the obstructed regions, contributing to high turbulent energy near the wall [24]. In a recent study, Gupta et al. [32] found that shear stress generates fluctuating velocity and produces TKE in this region. The fluctuating velocity and turbulent flow near the wall will induce vibration and simultaneously generate snoring. As such, the severity of snoring directly corresponds to the TKE. The occurrence of snoring in the long term would cause reduced tissue strength for the pharyngeal, which will lead to the laxity or collapse of tissue due to gravitational effects when the patient sleeps in a lying down position. Consequently, this makes it a contributing factor to sleep apnea. Besides, the velocity gradient affects the wall shear stress. The changes in velocity around the obstructed regions indicated the higher wall shear stress in those regions. The upper airway walls’ exposure to high wall shear stress may play a significant role in the respiratory disease's inflammatory process [33,34].

The turbulent Reynolds number and Reynolds number were considered in this work to describe the airflow characteristics of the airway of an OSA patient. The severe vibration of airway tissue leads to snoring, where long-term snoring weakens the airway tissue, thus leading to the blockage of airflow (i.e., sleep hypopnea and apnea). Previous researchers often employ the Reynolds number to express the flow condition in the study of the airway. The subject mainly breathed in a turbulent region expressed in the Reynolds number shown in Fig. 8. The flow develops a turbulent region at 0.014 m from the inlet with the Reynolds number 4096. The flow reaches a peak at 0.04 m from the inlet with the value of the Reynolds Number 7534, but for the healthy person in normal breathing, the Reynolds number is estimated around 2084. High turbulent Reynolds number was identified around a region after the narrow area. Both Reynolds (Re) and turbulent Reynolds (Re_y) were concentrated in a similar region. The results indicate that Re corresponded to the Re_y. This situation can be observed at the first peak of the plot (at the position ~0.04 m) for Re and Re_y in Fig. 8, respectively. The Re_y is helpful for the identification of the turbulence level of airflow in an airway.

Turbulent Reynolds number was considered to explain the intensity of turbulence or energy of the Reynolds number, as expressed in Eq. (6). The turbulent Reynolds number reflects the level of turbulence in each area (cross-sectional area of the airway). The high-velocity intensity in the upper airway indicates high turbulence generated from friction work, as expressed in Eq. (6). High-velocity intensity is generated from the critical cross-sectional area, while the recirculation region (Fig. 4) is attributable to the mechanism of hypopnea in clinical areas. High turbulent Reynold number contour is observed around inhale and exhale breathing outlets after the narrow-area (Fig. 9). The high turbulent Reynolds number is higher during exhale breathing (Fig. 9) than inhale breathing around that narrow area. This situation may lead to the high tendency of sound-producing in exhaling breathing. The explanation of the turbulent Reynolds number will provide a new tool in establishing the severity of the OSA through the consideration of AHI as the evaluation method.

The turbulent kinetic energy is associated with the kinetic energy of vortices (velocity fluctuation) generated in the turbulent flow, which quantifies the turbulence level in the airway. In the clinical study, the index to measure the severity of OSA is the apnea-hypopnea index called AHI, a diagnosis of the periodic breathing of a patient during sleep. Hypopnea is when the patient undergoes shallow breathing due to a constricted airway. The constricted airway will induce the intensity of the flow, causing high turbulent flow that creates velocity fluctuation, as shown in Fig. 10. The fluctuation of velocity (Eq. (3)) and TKE (Eq. (4)) are related to hypopnea, which causes shallow breathing during sleep in measure of the AHI and TKE in CFD simulation.

The CFD analysis computes TKE, and turbulent Reynolds number Re_y. Figs. 8 and 10 show the distribution of TKE obtained from the velocity fluctuation, as shown in Eq. (4); whereas the turbulent Reynolds number was computed from Eq. (6), following the works by Calmet et al. [7]. The airflow motion in the airway is predominantly by the energy in turbulent flow; therefore, the application of TKE is deemed suitable to describe the vortex and quantify the turbulence level. The results show high turbulent kinetic energy concentrated after the narrow region. In addition, the formation of a jet stream was observed in the pharynx of the airway. The jet stream formed had hit the wall in the inhalation area, which may have caused velocity remodeling near the airway wall. Fig. 10 portrays the occurrence of TKE at high-velocity fluctuation induced by the recirculation phenomenon. TKE value helps provide new information on airflow characteristics. TKE can be used as a new parameter to characterize, as well as in the detection of the patient with OSA. Turbulent flow is generated when the airflow passes through the critical sectional area (Fig. 3) in the patient's upper airway. The severity of the turbulence can be explained more impressively and accurately by visualizing the TKE parameter (maximum TKE 77.19, in Fig. 10), which is similar to the clinical parameter, AHI of the patient (99.5). The TKE and AHI parameters are related to the OSA phenomenon, which will be helpful in the measurement of the severity of OSA.

The advent of high-resolution three-dimensional TKE able to be constructed from a synthesis of standard two-dimensional cross-sectional images, and of “Volume Render Mode,” a technique to analyze information inside a three-dimensional volume by digitally enhancing individual flow, promises to revolutionize the diagnosis of obstructive sleep apnea in patients, and the level severity of AHI. Using the different post-processing display parameters, the volume-rendered image provides better visualization performance when there are no significant differences in the signal levels of the conventional approach, as shown in Fig. 11. In Fig. 11, the TKE occurs after the critical area for both breathing conditions, either inspiration or expiration.

The biomechanical aspect during the inhale and exhale breathing is focused on the body forces exerted on the upper airway. During breathing, the deterioration of the airflow pattern creates pressure variation, velocity, and TKE in the upper airway. as shown in Figs. 4, 7, 9, and 11. The pressure variation leads to the variation of body forces acting on the upper airway. The forces acting on the upper airways during inhale and exhale breathing are depicted in Fig. 12. The simulation results (Fig. 12) demonstrated that the forces exerted on the upper airway during inhaling are greater than exhaling. The forces are concentrated on the upper airway after the narrow region. This phenomenon also corresponded to the high turbulent kinetic energy (TKE) found in Fig. 10 (in Section 3.5), indicating that the high TKE could increase body forces. The pressure variation, velocity, and TKE corresponded with the biomechanical aspect of the upper airway. The phenomenon is synchronous with the findings in the previous work [35]. The width of the pharyngeal airway [35] crucially influenced the vortex formation, aerodynamic pressure, and pharyngeal wall force.