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Computational fluid dynamics study of the pharyngeal airway space before and after mandibular setback surgery in patients with mandibular prognathism

Computational fluid dynamics study of the pharyngeal airway space before and after mandibular setback surgery in patients with mandibular prognathism



International Journal of Oral & Maxillofacial Surgery, 2017-07-01, Volume 46, Issue 7, Pages 839-844, Copyright © 2017 International Association of Oral and Maxillofacial Surgeons


Abstract

The purpose of this study was to investigate the relationship between the pressure drop in the pharyngeal airway space ( ΔP PAS ) and the minimum cross-sectional area (minCSA) of the pharyngeal airway before and after mandibular setback surgery using computational fluid dynamics, in order to prevent iatrogenic obstructive sleep apnoea. Eleven patients with mandibular prognathism underwent bilateral sagittal split osteotomy for mandibular setback. Three-dimensional models of the upper airway were reconstructed from preoperative and postoperative computed tomography images, and simulations were performed using computational fluid dynamics. ΔP PAS and the minCSA of the pharyngeal airway were calculated, and the relationship between them was evaluated by non-linear regression analysis. In all cases, the minCSA was found at the level of the velopharynx. After surgery, ΔP PAS increased significantly and the minCSA decreased significantly. The non-linear regression equation expressing the relationship between these variables was ΔP PAS = 3.73 × minCSA −2.06 . When the minCSA was <1 cm 2 , ΔP PAS increased greatly. The results of this study suggest that surgeons should consider bimaxillary orthognathic surgery rather than mandibular setback surgery to prevent the development of iatrogenic obstructive sleep apnoea when correcting a skeletal class III malocclusion.

In orthognathic surgery, the bilateral sagittal split osteotomy (BSSO) is commonly performed for mandibular setback or advancement. Such surgery can improve occlusion, masticatory function, and aesthetics by changing the mandibular position . Because patients with obstructive sleep apnoea (OSA) have a narrower pharynx compared with healthy subjects, and mandibular setback surgery for mandibular prognathism reduces the pharyngeal airway space (PAS) , mandibular setback may induce sleep-disordered breathing, typified by obstructive sleep apnoea syndrome (OSAS), in some patients . OSA is characterized by repetitive collapse of the upper airway, which decreases its intraluminal diameter and increases airway resistance in accordance with the Hagen–Poiseuille law . This increased airway resistance causes hypopnoea or apnoea, and OSA is associated with metabolic disturbances and sleep fragmentation . Additionally, OSA is related to excessive daytime sleepiness, fatigue, and cardiovascular and cerebrovascular disease. In patients who have a large mandibular setback, obesity, short neck, large tongue, and/or excessive daytime sleepiness and snoring, surgeons should consider the possibility of OSA when planning orthognathic surgery .

Narrowing of the PAS after orthognathic surgery has the potential to lead to the development of OSA , and has thus received increasing attention in recent years. Many studies have assessed changes in the PAS after orthognathic surgery; however most have investigated the PAS only morphologically, using lateral cephalograms and/or computed tomography (CT) scans , and morphological analyses cannot show the airflow condition or airway pressure. Narrowing of the PAS leads to increased airflow velocity and subsequently to a further reduction in intraluminal pressure and further pharyngeal narrowing .

Airflow simulations using computational fluid dynamics (CFD) have recently been applied to patients with OSA who have received treatment with mandibular advancement devices or who have undergone adenotonsillectomy, maxillomandibular advancement, or genioglossal advancement . The information provided by CFD can help clarify the pathogenesis of OSAS , and CFD analysis has been combined with the pharyngeal airway geometries obtained before and after treatment to calculate the pressure drop or flow resistance .

Few studies to date have used CFD to assess the possibility of OSA caused by mandibular setback surgery. The purpose of this study was to investigate the relationship between the pressure drop in the pharyngeal airway space ( ΔP PAS ) and the minimum cross-sectional area (minCSA) of the pharyngeal airway before and after mandibular setback surgery using CFD, in order to help prevent iatrogenic OSA.

Materials and methods

This study was approved by the Institutional Review Board of Yokohama City University. The participants were 11 Japanese patients with mandibular prognathism who underwent BSSO for mandibular setback. Three of these patients were male and eight were female, and they ranged in age from 17 to 42 years (mean age 23.8 years). All operations were performed by one surgeon, and semi-rigid fixation during BSSO was achieved with titanium miniplates and screws. The mean mandibular setback was 6.5 mm (range 3.5–9.0 mm). Patient selection criteria were skeletal class III malocclusion and symmetry. Patients with a history of facial fracture, syndrome, obesity, OSAS, or complete airway obstruction identified on CT imaging were excluded.

A CT scan was performed with a 16-slice CT scanner (Aquilion 16; Toshiba Medical Systems, Tokyo, Japan) a few weeks before and 1 year after mandibular setback surgery. The slice thickness was set to 1.0 mm, and the slice width and height were 512 × 512 pixels; the pixel size was 4.68 × 10 −4 m. CT scanning was performed while patients were awake in the supine position and with the Frankfort horizontal plane perpendicular to the floor. Patients were asked to hold their breath at the end of inspiration. CT data were stored in DICOM format (Digital Imaging and Communications in Medicine). The DICOM images were then entered into Mimics software (version 15.0; Materialise, Leuven, Belgium). Image segmentation of the upper airway was performed based on the Hounsfield units assigned to each pixel in the DICOM image series. Threshold values were adjusted to eliminate imaging artefacts and to refine the selected airway region. The three-dimensional airway model was created for the region between the nostrils and the infraglottic cavity without the paranasal sinuses and was converted to a smooth model without losing the patient-specific characteristic of the upper airway shape. Each inlet plane was vertical to the nasal cavity wall at the left or right nostril, and the outlet plane was vertical to the infraglottic cavity wall. The surface mesh was created from the three-dimensional airway model using Mimics software. The surface mesh was imported into a fluid analysis pre-processor (ICEM-CFD; Ansys Inc., Canonsburg, PA, USA) to create a volume mesh. An unstructured tetrahedral/prism hybrid mesh of the airway model was generated, and a three-layer prism mesh was placed on the wall. The volume mesh of the airway had around 1 800 000 elements.

Ansys Fluent commercial CFD software (Ansys Inc.) was used to solve the governing equations of the flow and to calculate the distributions of the flow variables, such as velocity and pressure, in each airway model generated. The governing equations consisted of the continuity and Navier–Stokes equations of incompressible flow, and they were discretized on the computational domain using second-order finite-volume schemes. For the time integration, a second-order implicit scheme was used. The coupling between the velocity and pressure fields was realized using the semi-implicit method for pressure-linked equations (SIMPLE) algorithm on a collocated grid. A low Reynolds number k-ε model was used as the turbulence model.

Simulations were performed using the post-processor software CFD-Post (Ansys Inc.) on a PC running the Microsoft Windows 7 Professional operating system. The CPU was a quad-core Intel Xeon E5-1620 (clock frequency 3.60 GHz) with 64 GB of RAM per core. The simulation was designed for human inspiration at rest and at atmospheric pressure (1.013 × 10 5 Pa) and atmospheric temperature (20 °C). The coefficients of viscosity (1.822 × 10 −5 Pa·s) and density (1.205 kg/m 3 ) were provided as fluid data. The inflow condition was prescribed as the velocity perpendicular to the surface. The inlet velocity magnitude was calculated from the flow rate (2.000 × 10 −4 m 3 /s) and the area of two nasal inlets. The outlet condition was prescribed as the free outflow boundary condition. The non-slip boundary condition was imposed at the wall, which was assumed to be a rigid body. The PAS was defined as extending from the nasopharynx to the tip of the epiglottis, with the upper plane located between the nasal cavity and the nasopharynx. The bottom plane was perpendicular to the streamline through the tip of the epiglottis ( Fig. 1 ).

Pharyngeal and nasal airway space.
Fig. 1
Pharyngeal and nasal airway space.

The magnitude of the pressure gradient in the PAS was regarded as the pressure drop ( ΔP ) . Airway resistance was evaluated by ΔP , which was defined as the product of the airway resistance and the volume flow rate. In this study, the volume flow rate was fixed (2.000 × 10 −4 m 3 /s); therefore, ΔP was proportional to airway resistance. ΔP was obtained by calculating the difference between the average pressures on the designated two planes. Pressure drop in the PAS was defined as ΔP PAS . The minCSA was defined as the narrowest cross-sectional area perpendicular to the streamline of the airflow in the pharyngeal airway and providing the maximum airflow velocity, because narrowing of the PAS leads to increased airflow velocity and a further reduction in intraluminal pressure. ΔP PAS and the minCSA were calculated and the relationship between them was evaluated by non-linear regression analysis.

The statistical analysis was performed with the Wilcoxon signed rank test using IBM SPSS Statistics 21 for Windows (IBM Japan Ltd, Tokyo, Japan). Differences were considered significant at P < 0.05.

Results

Each simulation took approximately 18 h to complete. The results are summarized in Table 1 . In all cases, the minCSA was found at the level of the soft palate (velopharynx). After mandibular setback surgery, ΔP PAS increased significantly ( P = 0.003), whereas the minCSA decreased significantly ( P = 0.003). The non-linear regression equation describing the relationship between ΔP PAS and the minCSA was ΔP PAS = 3.73 × minCSA −2.06 . This relationship is shown by the fitted curve of the preoperative and postoperative data in Fig. 2 . The coefficient of determination ( R 2 ) between ΔP PAS and minCSA was 0.959. ΔP PAS increased greatly when the minCSA was <1 cm 2 .

Table 1
Minimum cross-sectional area (minCSA) and pressure drop in the pharyngeal airway space ( ΔP PAS ) before and after mandibular setback surgery.
Case Setback (mm) Phase MinCSA (cm 2 ) ΔP PAS (Pa)
1 8.0 Preoperative 2.03 0.64
Postoperative 0.62 9.32
2 5.0 Preoperative 2.45 0.40
Postoperative 1.03 2.72
3 9.0 Preoperative 2.21 0.54
Postoperative 1.31 2.35
4 6.5 Preoperative 2.37 0.67
Postoperative 1.42 2.15
5 4.5 Preoperative 2.55 0.71
Postoperative 1.68 1.81
6 5.5 Preoperative 1.02 3.00
Postoperative 0.48 16.26
7 3.5 Preoperative 1.64 2.48
Postoperative 1.33 3.00
8 7.5 Preoperative 2.81 0.34
Postoperative 1.61 1.31
9 6.0 Preoperative 4.76 0.12
Postoperative 3.68 0.23
10 8.5 Preoperative 1.88 1.40
Postoperative 1.14 3.60
11 8.0 Preoperative 0.65 7.54
Postoperative 0.45 16.10

Correlation between pressure drop ( ΔP ) and minimum cross-sectional area (minCSA) of the pharyngeal airway space.
Fig. 2
Correlation between pressure drop ( ΔP ) and minimum cross-sectional area (minCSA) of the pharyngeal airway space.

Discussion

Changes in the PAS after orthognathic surgery have attracted much attention because both airflow resistance and the risk of snoring and OSA increase if the airway is narrowed when the skeletal and soft tissues are altered by the surgery . Many studies on mandibular setback or advancement surgery have analyzed these PAS changes using lateral cephalograms and/or CT . Two-dimensional cephalometric analyses by Hochban et al. revealed that the correlation between mandibular setback and soft tissue pharyngeal changes was not as strong as expected. In their study, none of the patients was obese and mean mandibular setback was 7.5 mm, with a range of 3–12 mm. They suggested that sleep-related breathing disorders after mandibular setback surgery may be rare despite a decrease in the PAS . In contrast, several other studies have demonstrated the possibility of the iatrogenic development of OSAS . Tselnik and Pogrel showed a strong correlation between the amount of mandibular setback and the decrease in the PAS; in that study, the mean mandibular setback was 9.7 mm. Kawamata et al. reported that the size of the pharyngeal airway after surgery might be predictable at the time of treatment planning, because a significant correlation was found between the amount of mandibular setback and the reduction in the lateral pharyngeal width. Chen et al. proposed an equation for predicting the change in the PAS after mandibular setback surgery that was based on changes in the A-point–nasion–B-point (ANB) angle, mandibular length (gonion–gnathion (Go–Gn)), and mandibular plane (sella–nasion to Go–Gn (SN–GoGn)) derived from preoperative and postoperative cephalograms. However, prediction of the PAS size after mandibular setback surgery using two-dimensional anatomical measurements does not necessarily predict the development of OSA.

CT allows not only linear measurements, but also planar measurements such as the CSA of the airway in three planes of space, or volumetric measurements. Degerliyurt et al. reported that anteroposterior and CSA dimensions of the PAS at the level of the soft palate and tongue base were significantly decreased on CT images after mandibular setback surgery. Similarly, the minCSA was significantly decreased after mandibular setback surgery in this study. Volumetric analysis with CT showed that the dimension of the oropharynx decreased after mandibular setback surgery . According to a meta-analysis by Mattos et al. , moderate evidence was found to support a significant reduction in the oropharyngeal airway after mandibular setback surgery. Although narrowing of the PAS is caused by inferior or posterior repositioning of the hyoid bone and a posterior shift of the tongue and soft palate after mandibular setback surgery , most two- and three-dimensional studies of the PAS have not been physiological or functional evaluations but merely morphological evaluations, such as linear, planar, or volumetric measurements . Polysomnography (PSG) has also been used to measure several physiological characteristics after mandibular setback surgery , but it is difficult to predict the development of OSAS preoperatively.

Riley et al. described setback of 7 mm and 10 mm in two patients who developed OSAS after mandibular setback surgery. According to Demetriades et al. , postoperative PSG showed that patients who underwent mandibular setback of ≥5 mm had a higher incidence of mild to moderate OSAS than those who underwent maxillary advancement and mandibular setback surgery. A strategy to prevent OSA after mandibular setback surgery is therefore needed, because patients who are obese, have potential sleep-disordered breathing, and have a large mandibular setback may be prone to developing OSA in the future . Uesugi et al. reported that patients who are obese, have a large mandibular setback, and/or are of relatively advanced age may be more likely to develop sleep-disordered breathing after mandibular setback surgery. A two-jaw surgery, which decreases the amount of PAS reduction, should therefore be considered in patients with a skeletal class III malocclusion who have these risk factors. Demetriades et al. also suggested that when preoperative planning indicates a mandibular setback of ≥5 mm, mandibular setback surgery combined with maxillary advancement should be performed to decrease the possibility of the iatrogenic development of OSAS.

In subjects with and without OSA, the velopharynx—the portion of the nasopharynx bounded ventrally by the soft palate—is the most constricted part of the PAS . The present study also showed that the CSA in the PAS was lowest at the velopharynx in all patients without OSA. Previous imaging studies have shown a relationship between the severity of OSA and morphological features of the airway, such as velopharyngeal size . However, it remains difficult to distinguish patients with OSA from healthy individuals using only geometric features of the airway .

Airflow simulations using CFD were recently applied to patients with OSA who had undergone treatment with mandibular advancement devices or sleep surgery, including orthognathic surgery . The information provided by CFD can help clarify the pathogenesis of OSAS , and CFD analysis has been combined with the pharyngeal airway geometries obtained before and after treatment to determine the effects on parameters such as pressure drop and flow resistance . Several CFD studies have shown that the correlation between the pressure drop and the apnoea–hypopnoea index (AHI) is consistent with models of the pharyngeal airway with mandibular advancement devices for OSAS patients . The pressure drop may be a useful index for internal airway loading due to anatomical narrowing, and may be better correlated with the AHI than direct anatomical measurements of the airway . CFD simulations may therefore reveal flow features that allow subjects with OSA to be differentiated from healthy subjects .

The human upper airway can be considered a cylinder ( Fig. 3 ), and thus resistance to airflow is inversely proportional to the fourth power of the airway radius and directly proportional to the airway length based on the Hagen–Poiseuille law (equation 2 in Table 2 ) . Because the CSA of a cylinder is described by equation 3 in Table 2 , ΔP (the pressure drop) is inversely proportional to the square of the CSA (equation 4 in Table 2 ). However, the theoretical relationships described by these equations cannot be simply applied to the human upper airway, which has a complicated geometry and weak turbulence. Nevertheless, ΔP PAS was found to correlate closely with minCSA in the present study and could be estimated from the measurement of the minCSA according to the fitted curve equation ΔP PAS = 3.73 × minCSA −2.06 . Moreover, because the present study suggests a high correlation between the pressure drop and the minCSA of the PAS, and several studies have shown a correlation between the pressure drop and the AHI, there may be a correlation between the minCSA of the PAS and the AHI.

Laminar flow through a cylinder. The relationship between the pressure drop and cross-sectional area is shown in Table 2 .
Fig. 3
Laminar flow through a cylinder. The relationship between the pressure drop and cross-sectional area is shown in Table 2 .

Table 2
Equations for laminar flow through a cylinder.
Equations Variables
(1) ΔP = Q × Rs ΔP = pressure drop across resistance
Q = flow rate (volume of air moved per unit time)
Rs = resistance
(2) Rs = 8 μL / πr 4 μ = viscosity
L = length of cylinder
r = radius of cylinder
(3) A = πr 2 A = cross-sectional area (CSA) of cylinder
(4) ΔP = 8 πμQL / A 2

Butterfield et al. investigated the minCSA and the AHI before and after maxillomandibular advancement surgery for patients with OSA using cone beam CT. The mean minCSA increased from 0.79 cm 2 to 2.47 cm 2 , and the mean AHI score improved from 45.5 to 7.7. In previous studies, the mean minCSA of patients with OSA (0.39 cm 2 to 0.79 cm 2 ) was found to be narrower than that of patients without OSA (1.08 cm 2 to 2.47 cm 2 ) . In the present CFD study, the pressure drop increased greatly when minCSA was <1 cm 2 . Taken together, these findings suggest that CFD simulations may allow the discrimination of subjects with and without OSA.

The minCSA of the PAS is essential to simulate airflow and evaluate respiratory function . Many prior CT- and CFD-based studies have calculated the minCSA using axial planes or the CSA of some undefined portion of the PAS, which does not provide the true minimum area . Accurate determination of the minCSA requires measurement of the CSA perpendicular to the pharyngeal airway centreline. However, this is challenging because the pharyngeal airway is not a warped cylindrical shape. The minCSA of the PAS was therefore measured perpendicular to the streamline of airflow in the pharyngeal airway and it was possible to show a high correlation between this and the pressure drop.

A large mandibular setback could inhibit biological adaptation and cause sleep-disordered breathing . The proposed treatment plan should be modified according to the risk of airway compromise. Surgeons should consider bimaxillary orthognathic surgery rather than mandibular setback surgery to prevent the development of iatrogenic OSA when treating skeletal class III patients with a large anteroposterior discrepancy and/or hypoplasia, because bimaxillary orthognathic surgery has a smaller effect on the reduction of the pharyngeal airway than mandibular setback surgery alone.

In conclusion, this study used CFD to investigate the influence of mandibular setback surgery on the PAS and showed a high correlation between the minCSA and pressure drop in the PAS. When the minCSA was <1 cm 2 , the pressure drop increased greatly; such a drop may result in iatrogenic OSA. Although further studies involving a large number of subjects are still required to predict the possibility of OSA from the minCSA in the PAS on CT imaging before mandibular setback surgery, the present study offers a new perspective for treatment based on changes in the minCSA of the PAS.

Funding

This study was supported by a Grant-in-Aid for Scientific Research (C) from the Ministry of Education, Culture, Sports and Technology of Japan (No. 23592933 ).

Competing interests

None declared.

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