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 ).
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 .
| 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 |
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