This is a retrospective cohort study. All methods were carried out in accordance with the declaration of research involving human subjects and the regional ethical and scientific guidelines in vestland region, Norway. Data for all patients who had undergone RME were retrospectively collected at the Department of Orthodontics (Stomatological hospital, Dalian, China) between January 2013 and December 2016. The inclusion criteria were patients younger than 15 years old who had both pre- and post- CBCT scans due to orthodontic indication. The pre-RME CBCTs were taken within seven days prior to fixing the expander (T0) and the post-RME CBCTs at the removal of expanders (T1). The exclusion criteria were severe abnormalities of maxillofacial tissue, previous surgery on skeletal and soft tissue related to respiration, and previous orthodontic or orthopaedic treatment. Eventually, 17 patients (mean age 12 years, 11 male/6 female) were eligible for inclusion in the study. An experienced radiologist viewed all CBCT scans and ensured that the images were qualified to construct 3D models of the upper airway.
RME
A fixed Hyrax expander was used for RME, banded to the maxillary first premolars and first molars. The patient, or their guardian, rotated the expansion screw twice a day at home and a clinical check-up was performed by orthodontists once a week. After achieving the desired expansion, the expander remained in place for at least three months to stabilise the expansion.
CFD simulation
Figure 1 demonstrates the stepwise procedure of the CFD modelling and simulation, including 3D segmentation, mesh generation, and aerodynamic results.
CBCT imaging
The examination protocol of CBCT scans was as follows: field of view (FOV) 16x13 cm; tube potential 120 kVp and tube current 5 mA; scanning time 14.7 seconds (3D eXam; KaVo, Biberach an der Riss, Germany). The voxel size was set at 0.2 mm, and the contrast resolution had a 14-bit depth. All CBCT examinations were performed according to the standardised clinical routine, i.e. with the Frankfort horizontal plane parallel to the floor, teeth in maximum intercuspation, and peaceful nasal breathing without swallowing. We divided the patients into two groups according to the AN ratio at baseline (T0): group 1 was comprised of individuals with an AN ratio < 0.6 and group 2 encompassing those with an AN ratio ≥ 0.6. The CBCT images were imported to MIMICS software (MIMICS, Materialise, Belgium) in the digital imaging and communications in medicine (DICOM) format for later analysis. To segment the 3D UA, one author (XF) orientated the CBCT image. An appropriate threshold was set from -1024 to -500 to involve the UA without defection, which was called a “mask”. The superior boundary was defined on the mask as perpendicular to the horizontal plane through the most posterior point of middle turbinate in the sagittal view; the inferior boundary was parallel the horizontal plane through the most anterior-inferior point of cervical vertebra 4. The 3D UA was then calculated from the defined mask. The superior and inferior boundaries were extended by 20mm to avoid flow reversing [23]. The extended 3D model was used to create a surface model for further mesh generation.
Mesh generation
Mesh generation is the practice of creating a mesh by computer algorithms. The continuous geometric UA space may be subdivided into discrete geometric cells. Mesh cell is the fundamental element of the reconstructed space that contains a local approximation of aerodynamic characteristics, which will be used for a later calculation. We chose tetrahedral and prismatic cells to construct the main body and boundary layer of the UA (ANSYS, Inc., Canonsburg, Pennsylvania). Each UA mesh had five boundary layers and an average of 2 million elements. The inlet and outlet of UA were defined at the extended superior and inferior boundary, as earlier described.
Aerodynamic analysis
ANSYS Fluent (ANSYS, Inc.) was applied to simulate the airflow of UA, and the SST κ-ω model was used to calculate the aerodynamic characteristics of UA. The wall of UA was defined as no-slip, stationary, and rigid, and the temperature and density of air were set as fixed [24]. In the inspiratory phase, the inlet was set with pressure 0 Pa and the outlet a flow rate of - 200 mL/s [21]. The corresponding values were - 200 mL/s and 0 Pa at inlet and outlet for the expiratory phase. Over 2000 iterations were performed to ensure the resulting residuals were less than 10-6. A radiologist (XF) performed all the simulations under the technical supervision of an engineer (YCC).
Data Analyses
We calculated the aerodynamic characteristics at inspiratory and expiratory phases, including mean pressure at the four planes defined on UA (Fig. 2). The parameters included are the pressure drop from plane 1 to plane 4, the maximum velocity of the midsagittal slice, and maximum wall shear stress at T0 and T1. Data were processed using the Statistical Package for the Social Sciences (SPSS Statistics, version 25.0, IBM, New York, NY, USA). Significance was set at p less than 0.05. Independent samples t-test was used to compare the differences of the aerodynamic characteristics between the two groups at T0 and T1.