Computational fluid dynamic analysis of the nasal respiratory function before and after postero-superior repositioning of the maxilla.

Morphological changes in the upper airway and the resulting alteration in the nasal respiratory function after jawbone repositioning during orthognathic surgery have garnered attention recently. In particular, nasopharyngeal stenosis, because of the complex influence of both jaws, the effects of which have not yet been clarified owing to postero-superior repositioning of the maxilla, may significantly impact sleep and respiratory function, necessitating further functional evaluation. This study aimed to perform a functional evaluation of the effects of surgery involving maxillary repositioning, which may result in a larger airway resistance if the stenosis worsens the respiratory function, using CFD for treatment planning. A model was developed from CT images obtained preoperatively (PRE) and postoperatively (POST) in females (n = 3) who underwent maxillary postero-superior repositioning using Mimics and ICEM CFD. Simultaneously, a model of stenosis (STENOSIS) was developed by adjusting the severity of stenosis around the PNS to simulate greater repositioning than that in the POST. Inhalation at rest and atmospheric pressure were simulated in each model using Fluent, whereas pressure drop (ΔP) was evaluated using CFD Post. In this study, ΔP was proportional to airway resistance because the flow rate was constant. Therefore, the magnitude of ΔP was evaluated as the level of airway resistance. The ΔP in the airway was lower in the POST compared to the PRE, indicating that the analysis of the effects of repositioning on nasal ventilation showed that current surgery is appropriate with respect to functionality, as it does not compromise respiratory function. The rate of change in the cross-sectional area of the mass extending pharynx (α) was calculated as the ratio of each neighboring section. The closer the α-value is to 1, the smaller the ΔP, so ideally the airway should be constant. This study identified airway shapes that are favorable from the perspective of fluid dynamics.

Introduction

The goal of orthognathic surgery involving the resection of the jawbone is to improve masticatory function and achieve stable occlusion when orthodontic treatment alone cannot correct discrepancies related to the dentition, jawbone, or face. This surgery entails repositioning of the jawbone, which is a hard tissue, along with changes in the soft tissues and airway. Postoperative airway stenosis may have a significant impact on sleep and respiratory function [1, 2]. Therefore, the morphological changes in the airway and the resulting alteration in nasal respiratory function have recently attracted the attention of researchers [3, 4].

Morphological evaluation of nasal respiratory function has been performed using nasal tests [5-7] (e.g., rhinomanometry and acoustic rhinometry), roentgenographic cephalometric analysis [1, 8, 9], and computed tomography (CT) [3, 10, 11]. However, functional or morphological evaluation of a specific site of the airway cannot be generalized to that of the ventilation of the entire airway, owing to its morphological characteristics (i.e., long, narrow, and complicated tubular structure). Moreover, the optimal evaluation method remains elusive because airway obstruction due to airway stenosis can occur at any site, including the nasal cavity, nasopharynx, oropharynx, and hypopharynx. The jawbone and the soft tissues and airway that are moved during orthognathic surgery can be associated with all of these source sites because of their location. Mouth breathing during sleep in the presence of nasal respiratory problems reduces the activity of the airway dilator muscles and the diameter of the airway lumen, increasing the risk of obstructive sleep apnea (OSA) [12].

OSA has also been associated with maxillofacial morphology [9, 13, 14]. A high incidence of mandibular skeletal prognathism (Class III) has been reported in Japan; it is treated using posterior repositioning of the mandible (single-jaw mandibular setback osteotomy). When upper and lower jaw osteotomy (two-jaw surgery) is applied because of a severe discrepancy of the jaws, the maxilla is moved upward and/or backward and the mandible is moved backward. Although there is a lack of clear evidence that corrective jaw surgery causes OSA, it is clear that posterior surgical repositioning of the mandible leads to postoperative narrowing of the upper airway. Therefore, except nasopharynx, several studies have reported the relationship between stenosis of the nasal cavity, oropharynx, or hypopharynx and OSA [3, 8, 15, 16]. On the other hand, in the case of maxillary skeletal prognathism (Class II), the maxilla is moved upward and/or backward or the mandible is moved forward in single-jaw surgery. If two-jaw surgery is required, the maxilla is moved upward and/or backward and the mandible is moved forward. One study reported that patients with Class II have smaller pharyngeal airway volume due to the maxillofacial morphology, which is more likely to lead to OSA compared to the Class I and III skeletal relationships [17]. However, the effect of surgical repositioning of the jaw on OSA has not been elucidated. Despite maxillary impaction, anterior repositioning of the mandible in patients with a Class II skeletal relationship may improve the respiratory status during sleep by expanding the volume of the pharynx. On the other hand, in Class II, posterior and/or superior repositioning of the maxilla may lead to narrowing of the nasal cavity and nasopharynx as was observed in Class III with a reduction in the volume of the airway in the nasal cavity and the most posterior point on the posterior nasal spine (PNS) [4]. Nasal airflow and the cross-sectional area of the nasal cavity decrease when the degree of maxillary impaction exceeds a certain limit [2]. Thus, repositioning of the maxilla may reduce the volume of the entire upper airway changes with the degree of maxillary impaction and mandibular position. The nasopharynx is thought to be susceptible to the movement of both jaws due to its location. Therefore, preventing the reduction in overall ventilation of the upper airway necessitates the evaluation of the nasopharynx, on which the effects of stenosis have not yet been clarified.

Therefore, this study focused on corrective jaw surgery involving the postero-superior repositioning of the maxilla, which is accompanied by a high risk of morphological changes in the nasopharyngeal airway. Maxillary prognathism and vertical maxillary excess (VME) without significant mandibular anomalies is an indication for corrective jaw surgery with postero-superior repositioning with maxillary osteotomy alone, without osteotomy of the mandibular ramus. Operative stress arising from osteotomy of the mandibular ramus and repositioning of the distal fragments of the mandible (e.g., the body of the mandible) may lead to postoperative development or exacerbation of progressive condylar resorption in patients with maxillary prognathism, VME, and significant deformation of the condyle [18-20]. Therefore, maxillary osteotomy alone (without mandibular osteotomy) is recommended to prevent relapse of the mandible [21, 22]. The maxilla is repositioned posteriorly with impaction to improve the facial appearance and occlusion, whereas the mandible undergoes reactionary counter-clockwise rotation during postero-superior repositioning, to achieve occlusion with the maxilla (Fig 1). The improvements in the safety of surgical methods owing recent advancements and development of the ultrasonic osteotomy device have facilitated an increase in the degree of postero-superior repositioning of the maxilla [23-25] (as shown in Fig 1, pink area), leading to higher deformation and narrowing of the nasopharyngeal airway and a higher risk of nasopharyngeal stenosis. However, it is difficult to predict the morphological changes in the airway before surgery. Therefore, the aim of this study was to perform a functional evaluation of the effects of corrective jaw surgery involving postero-superior repositioning of the maxilla on nasal respiratory function using computational fluid dynamics for the purpose of treatment planning. The new insights acquired in this study may improve understanding of the pathogenesis of OSA and the effect of orthognathic surgery.

Fig 1

Postero-superior repositioning of the maxilla and mandibular autorotation.

Surgical impaction of the maxilla and the reaction of the mandible and the associated changes in the airway are illustrated schematically. Notes: black line, pre-surgery (before mandibular autorotation); red line, post-surgery; blue circle, center of mandibular autorotation; blue arrow, direction of autorotation; green line, after mandibular autorotation; gray line; post-surgery in the figure of airway changes; pink area, preoperative nasal cavity; pink hatched area, postoperative nasal cavit; pink arrow, direction of nasal cavity change; purple area, preoperative nasopharyngeal airway; purple hatched area, postoperative nasopharyngeal airway; purple arrow, direction of pharyngeal change.

Materials and methods

Participants

This study was conducted under approval of the Ethics Committee of Tokyo Medical and Dental University (TMDU) (approval number: D2018-003) and the Institutional Ethical Review Board of the School of Medicine, Yokohama City University (approval number: B110512003). All patients provided written informed consent prior to participation.

This study enrolled three patients, all female, diagnosed with maxillary skeletal prognathism, who underwent Le Fort I osteotomy including postero-superior repositioning of the maxilla [the amount of repositioning was measured with the maxillary central incisor (U1) and first maxillary molar (U6) as reference], and complete postoperative orthognathic surgery (age at surgery, 21 to 36 years and body mass index (BMI) 17.8 to 19.4 kg/m2) at the Yokohama City University Medical Center between 2012 and 2015.

The exclusion criteria were as follows: patients who underwent repositioning of the mandible; patients with a history of facial fractures, tumors, cystic lesions, etc.; patients with congenital anomalies or endocrine disease; patients with significant deviation of the jawbone; and patients with significant nasal deviation.

Three-dimensional models

This study utilized CT images acquired immediately before and 1 year after surgery using the Aquilion 16 scanner (Toshiba Medical Systems, Tokyo, Japan). The slice thickness was set at 1.0 mm, and the slice width and height were 512 × 512 pixels. The pixel size was 4.68 × 10−4 m. Imaging was performed while the patient was awake. The head was positioned with the Frankfort horizontal (FH) plane horizontal to the floor. Imaging was performed with the teeth in occlusion, while the breath held and the mouth closed as much as possible. The CT imaging data were saved in the Digital Imaging and Communications in Medicine (DICOM) format.

Segmentation of the upper airways was performed on the basis of the Hounsfield unit, a measure of the electron density of the tissue, assigned to each pixel of the saved DICOM images imported into Mimics (Materialise, Leuven, Belgium) to generate a three-dimensional (3D) model. The threshold was adjusted to obtain a clear image of the airway after eliminating the imaging artifacts. The 3D model was generated in the area between the nasal aperture and subglottis, except for the paranasal sinus, and a “driver” was added to reduce the effect of the inlet and outlet boundary conditions (Fig 2).

Fig 2

Development of the driver.

Three-dimensional model of the nasal airway with the tubes projecting from the nostrils and subglottis indicating the “driver” region (encompassed by orange circles). The area surrounded by the pink oval is the nose area. The area surrounded by the purple oval is the pharynx area.

The generated 3D model data were imported into 3-matic (Materialise, Leuven, Belgium), followed by smoothing to generate a surface mesh. Subsequently, the mesh was imported into the ICEM CFD software (Ansys Inc, Canonsburg, PA, USA). The volume mesh of the airway had around　7 400 000 elements. The unstructured tetrahedral/prism hybrid mesh of the airway model was generated. Three layers of the prism mesh was placed near the wall so that even the area near the wall possessed sufficient resolution (Fig 3). The cell size of the prism region was adjusted to attain a dimensionless wall distance (y+) value less than 1.

Fig 3

Three-dimensional mesh cross-section of the nasal cavity.

The front section of the nasal cavity with a focus on the wall. The unstructured tetrahedral/prism hybrid mesh of the airway model was generated. Three layers of the prism mesh were placed near the wall.

Airflow simulation

The above-mentioned analytical model was used to simulate function during inhalation. The conditions for analysis in this study were as follows: inhalation at rest at 20°C and atmospheric pressure (1.013×105 Pa). The following physical properties were set in the model: steady flow of an incompressible Newtonian fluid with a density of 1.205 kg/m3 and viscosity of 1.822 × 10−5 Pa·s based on a previous study [26]. Lee et al. [26] explained that significant change was not observed in flow pattern distribution between steady and unsteady calculation at the inhalation phase.

The governing equations for the velocity and pressure of the flow field were solved using Fluent (version 14.0, ANSYS Inc., Canonsburg, PA, USA). The governing equations consist of the continuity Eq (1) and Navier-Stokes Eq (2) as follows.

Continuity equation:

Navier-Stokes equation: Here, U is the velocity vector, i, j = 1, 2, 3, Ui = ith component of the velocity vector, P = static pressure of the flow field, and S = ith component of the source.

The finite volume method was used for the discretization of the governing equations. A semi-implicit method was used for time integration. The velocity and pressure fields were calculated using the SIMPLE algorithm (Semi-Implicit Pressure Linked Equation). The Launder-Sharma low Reynolds number k-ε model [27] was used as the turbulent flow model given by the following equations.

Turbulent kinetic energy equation (k): Turbulence dissipation rate model (ε): where Cε1, Cε2, Cμ, σk and σε are model constants. The damping functions fμ, f1, and f2 and the extra source terms D and E are only active close to the solid walls, which makes it possible to solve k and ε down to the viscous sublayer. fμ = exp-3.4/(1+Ret/50)2, f1 = 1, f2 = 1–0.3exp-Ret2, Ret≡k2/vε, εwall = 0, D = 2v(∂k1/2/∂y)2, E = 2vvt(∂2u/∂y2)2. The constants appearing in (3), (4), (5), and (6) are Cμ = 0.09, σk = 1.0, σε = 1.30, Cε1 = 1.44, and Cε2 = 1.92, respectively.

The inlet boundary conditions were set at a flow rate of 2.000 × 10−4 m3/s based on previous studies on the peak respiratory flow at rest [28] and simulation of upper airway flow [29-31]. The inflow velocity was calculated using the flow rate and area of the inlet. The free outflow boundary condition was used as the outlet boundary condition. However, a pressure of P = 0 was used in the high-stenosis model with an inverse pressure gradient near the outlet. Because back flow occurred at the outflow boundary, the pressure boundary condition (P = 0) was adapted in the high-stenosis model based on reality. The wall was defined as non-slip.

Areas and methods of evaluation

A simulation was performed using the model of the preoperative airway shape (PRE), which was developed using the preoperative CT data, and the model of the postoperative airway shape (POST), which was developed using CT data obtained 1 year after surgery. The effect of airway stenosis of the nasopharynx was examined using the 3D stenosis model (STENOSIS) with different amounts of trimming around the area extending from the POST to the PNS (Fig 4). In each model, the nasopharynx was trimmed as much as possible until it was divided into the nasal and laryngeal parts. As shown in Fig 4, the nasopharynx of the STENOSIS model (indicated by the rectangle in the inset) was trimmed mainly around the PNS by the amount indicated by the red asterisks (where each asterisk equals the amount of trimming for each model, e.g., in the STENOSIS -1 mm model, the asterisk means narrowing the thickness by 1 mm).

Fig 4

STENOSIS model.

With a focus on the nasopharynx region of the STENOSIS model, the area (surrounded by the orange dotted circle) was trimmed by the length of the asterisk around the posterior nasal spine (PNS) in the sagittal plane. The red asterisk indicates the amount of trimming for the nasopharynx of the STENOSIS model.

Imaging simulation was performed using post-processing software (CFD-Post 14.0, ANSYS, Canonsburg, PA, USA). The generated morphologies and boundaries of the airway and sites of evaluation are shown in Fig 5. The inlet was perpendicular to the driver wall. The outlet was perpendicular to the subglottis wall. The nasal cavity was defined as the area extending from the nostril (Nos) to the posterior nasal aperture (PNA). The entity NP represents the cross-section of the flow crossing the PNS. PAt denotes the cross-section horizontal to the FH plane traversing the lower edge of the posterior nasal cavity. PAmin denotes the narrowest part of the pharynx. PAt’ is the cross-sectional area horizontal to the FH plane that divides the region extending from the PAt to PAmin into two halves. PAb was defined as the horizontal plane crossing the tip of the epiglottis. The area extending from the PNA to the PAt’ (mainly around the PNS) was trimmed in the STENOSIS model (Fig 4). The definitions of landmarks and measurement variables are listed in Tables 1 and 2.

Fig 5

Cross-section of the upper airway and nasopharynx.

Lateral view of the upper airway, nasopharynx and cross-section of the reference planes.

Table 1

Definitions of landmarks.

Symbol	Definition
PNS	The cutting edge of the posterior nasal spine
U1	The most anterior point on the incisal edge of the maxillary central incisor
U6	The center of the occlusal surface of the maxillary first molar
FH	Frankfort horizontal plane
NOS	The nostrils
NV	The nasal valve
PNA	The posterior nasal aperture
CSA	The cross-sectional area of the upper airway on each CT sagittal plane
ΔP	The pressure drop
α	The rates of change in cross-sectional area

Table 2

Definitions of measurements variables.

Symbol	Definition
PRE	three-dimensional pre-surgery model
POST	three-dimensional post-surgery model
STENOSIS	three-dimensional stenosis model
NP	cross-section of the flow crossing the PNS
PAt	cross-section horizontal to the FH plane crossing the lower edge of the posterior nasal cavity
PAmin	the most constricted region of the pharyngeal airway
PAt’	cross-section horizontal to the FH plane that divides the area extending from the PAt to PAmin into two halves
PAb	horizontal plane crossing the tip of the epiglottis
CSA-x	cross-sectional area of each region of airway
ΔPAll	pressure drop in the whole upper airway
ΔPNose	pressure drop in the nasal cavity
ΔPPharynx	pressure drop in the nasopharynx
ΔP1	pressure drop from the PNA to the NP
ΔP2	pressure drop from the NP to the PAt’
ΔP3	pressure drop from the PAt’ to the PAmin
ΔP4	pressure drop from the PAmin to the PAb
α1	calculated as CSA-NP /CSA-PNA
α2	calculated as CSA-PAt’/CSA-NP
α3	calculated as CSA-PAt’/CSA-PAmin
α4	calculated as CSA-PAmin/CSA-PAb

Airway resistance was evaluated by measuring the pressure drop (ΔP), which was calculated by multiplying the airway resistance by the volumetric flow rate. A stable flow rate of 2.000 × 10−4 m3/s was maintained constant in this study. Therefore, airway resistance was proportional to the ΔP. ΔP was calculated as the difference in the mean pressure between two cross-sections obtained from the airway. Pressure drops in the nasal cavity and nasopharynx were defined as ΔPNose (i.e., pressure drop from the NOS to the PNA) and ΔPPharynx (i.e., pressure drop from the PNA to the PAb), respectively. ΔPAll (i.e., pressure drop from the NOS to the PAb) was calculated as the sum of ΔPNose and ΔPPharynx. The cross-sectional area (CSA) of the NOS, nasal valve (NV), PNA, NP, PAt’, PAmin, and PAb (as shown in Fig 5) was CSA-NOS, CSA-NV, CSA-PNA, CSA-NP, CSA-PAt’, CSA-PAmin, and CSA-PAb, respectively. As shown in Fig 6, ΔPPharynx was divided into the following four segments:ΔP1 (pressure drop from the PNA to the NP), ΔP2 (pressure drop from the NP to the PAt’), ΔP3 (pressure drop from the PAt’ to the PAmin), and ΔP4 (pressure drop from the PAmin to the PAb). The rates of change in the CSA of the mass extending from the nasopharynx to oropharynx (α) were calculated as follows: α1, CSA-NP /CSA-PNA; α2, CSA-PAt’/CSA-NP; α3, CSA-PAt’/CSA-PAmin; and α4, CSA-PAmin/CSA-PAb.

Fig 6

Segments in which the pressure drop was evaluated.

Lateral view of the nasopharynx and oropharynx. Pressure drop was defined by the pressure at any two cross-sectional areas.

Results

Pressure effort

In the narrowest stenosis model (patients 1 and 2 in the STENOSIS model), ΔPAll was higher in POST than that in PRE (Table 3 and Fig 7). The ratio of ΔPNose to ΔPAll (ΔPNose/ΔPAll) was higher than that of ΔPPharynx to ΔPNose in all cases, except for patient 2 in the STENOSIS -10 mm model and patient 3 in the PRE model (Table 3 and Fig 7).

Table 3

Pressure drop (ΔP).

			U1	U6	ΔPAll
			posterior/vertical impaction (mm)			ΔPNose (Pa)	ΔPPharynx (Pa)	ΔPNose/ ΔPAll	ΔP1+ΔP2 (Pa)			ΔP3+ΔP4 (Pa)
										ΔP1 (Pa)	ΔP2 (Pa)		ΔP3 (Pa)	ΔP4 (Pa)
Patient No.	Model
1	PRE	BMI:17.8			11.318	9.009	2.309	0.80	0.485	0.033	0.452	1.823	2.800	-0.977
	POST		2.5 / 4.0	3.0 / 5.5	9.179	8.953	0.226	0.98	0.023	0.068	-0.045	0.203	0.550	-0.347
	STENOSIS	-1 mm			9.148	8.917	0.231	0.97	0.047	0.081	-0.034	0.183	0.554	-0.371
		-2 mm			9.197	8.922	0.275	0.97	0.139	0.137	0.002	0.136	0.478	-0.342
		-3 mm			9.265	8.952	0.313	0.97	0.156	0.187	-0.031	0.157	0.497	-0.340
		-10 mm			10.901	9.445	1.456	0.87	1.772	1.780	-0.008	-0.317	1.018	-1.335
		-15 mm			21.751	11.842	9.908	0.54	10.315	10.238	0.077	-0.406	1.487	-1.893
2	PRE	BMI:19.4			12.254	9.869	2.385	0.81	0.479	0.116	0.363	1.905	4.973	-3.068
	POST		4.0 / 0	2.5 / 0	8.368	7.557	0.811	0.90	0.851	-4.467	5.318	-0.039	0.614	-0.653
	STENOSIS	-1 mm			8.509	7.594	0.915	0.89	0.866	-3.716	4.582	0.049	0.640	-0.591
		-2 mm			8.299	7.520	0.779	0.91	0.842	-3.852	4.694	-0.063	0.641	-0.704
		-3 mm			8.417	7.600	0.817	0.90	1.055	-4.259	5.314	-0.238	0.567	-0.805
		-5 mm			9.546	7.434	2.112	0.78	1.974	-4.956	6.930	-0.505	0.137	-0.642
		-10 mm			28.291	8.004	20.287	0.28	20.486	-6.523	27.009	-0.517	-0.199	-0.318
3	PRE	BMI:18.3			31.591	15.387	16.204	0.49	-0.036	-0.178	0.142	16.241	9.624	6.617
	POST		7.5/2.2	8.0/2.5	28.729	22.728	6.001	0.79	0.034	-0.163	0.197	5.968	5.315	0.653
	STENOSIS	-1 mm			28.759	22.685	6.074	0.79	0.019	-0.174	0.193	6.055	5.396	0.659
		-2 mm			28.647	22.695	5.952	0.79	0.020	-0.084	0.104	5.933	5.296	0.637
		-3 mm			28.542	22.557	5.985	0.79	0.118	-0.182	0.300	5.867	5.254	0.613
		-5 mm			28.289	22.864	5.425	0.81	0.142	-0.200	0.342	5.984	5.282	0.702
		-10 mm			30.595	22.829	7.766	0.75	4.037	0.277	3.760	4.706	3.725	0.981

Fig 7

Pressure drop in the nasal cavity and nasopharynx.

The line chart shows the CSA-NP. Abbreviations: -1 mm, STENOSIS -1 mm; -2 mm, STENOSIS -2 mm; -5 mm, STENOSIS -5 mm; -10 mm, STENOSIS -10 mm; -15 mm, STENOSIS -15 mm. Notes: pink bar, ΔPNose; purple bar, ΔPPharynx; gray line, CSA-NP.

Cross-sectional area

The comparison between PRE and POST showed that the CSA-NOS and CSA-Val were lower and CSA-PAmin and CSA-PAb were higher in POST than those in PRE in all cases (Table 3). CSA PNA’ and CSA-NP increased and decreased at different time points and under different conditions (Table 4). The results of the analyses of the shapes are depicted in Fig 8.

Table 4

Cross-sectional area and ratio of the cross-sectional area.

			CSA-NOS (cm2)	CSA-NV (cm2)	CSA-PNA′ (cm2)	CSA-NP (cm2)	CSA-PAt’ (cm2)	CSA-PAmin (cm2)	CSA-PAb (cm2)	α1	α2	α3	α4
Patient No.	Model
1	PRE	36 years 4 months	1.323	2.016	3.388	3.592	2.125	0.963	2.038	1.06	0.59	0.45	2.12
	POST		1.177	1.861	2.946	2.972	2.915	1.831	3.665	1.01	0.98	0.63	2.00
	STENOSIS	-1 mm	1.177	1.861	2.906	2.846	2.912	1.831	3.665	0.96	1.02	0.63	2.00
		-2 mm	1.177	1.861	2.946	2.630	2.891	1.831	3.665	0.89	1.10	0.63	2.00
		-3 mm	1.177	1.861	2.960	2.427	2.911	1.831	3.665	0.82	1.20	0.63	2.00
		-10 mm	1.177	1.861	2.812	1.431	2.812	1.831	3.665	0.49	1.96	0.65	2.00
		-15 mm	1.177	1.861	2.812	0.668	2.812	1.831	3.665	0.23	4.21	0.65	2.12
2	PRE	21 years 1 month	1.069	1.936	2.985	2.201	2.222	0.674	2.047	0.74	1.01	0.30	0.92
	POST		1.021	1.930	3.655	2.441	1.424	1.116	2.435	0.67	0.58	0.78	2.18
	STENOSIS	-1 mm	1.021	1.930	3.651	2.308	1.424	1.116	2.435	0.63	0.62	0.78	2.18
		-2 mm	1.021	1.930	3.655	2.174	1.424	1.116	2.435	0.60	0.66	0.78	2.18
		-3 mm	1.021	1.930	3.655	1.896	1.425	1.116	2.434	0.52	0.75	0.78	2.18
		-5 mm	1.021	1.930	3.655	1.800	1.424	1.116	2.435	0.49	0.79	0.78	2.18
		-10 mm	1.021	1.930	3.655	0.516	1.425	1.116	2.434	0.14	2.76	0.78	2.18
3	PRE	21 years	1.238	1.901	4.001	3.964	3.768	0.584	1.328	0.99	0.95	0.16	2.27
	POST		1.233	1.673	3.777	4.055	2.058	0.736	1.024	1.07	0.51	0.36	1.39
	STENOSIS	-1 mm	1.233	1.673	3.761	3.890	2.057	0.735	1.024	1.03	0.53	0.36	1.39
		-2 mm	1.232	1.673	3.672	3.747	2.020	0.736	1.025	1.02	0.54	0.36	1.39
		-3 mm	1.230	1.671	3.669	3.556	1.909	0.736	1.023	0.97	0.54	0.39	1.39
		-5 mm	1.233	1.673	3.376	3.017	2.019	0.736	1.024	0.89	0.67	0.36	1.39
		-10 mm	1.233	1.673	3.666	1.535	2.022	0.736	1.024	0.42	1.32	0.36	1.39

Fig 8

Cross-sectional shape of the upper airway.

Cross-sectional shape of the upper airway in patients 1, 2 and patient 3.

The rates of change in cross-sectional area (α) were calculated as follows: α1, CSA-NP/CSA-PNA; α2, CSA-PAt’/CSA-NP; α3, CSA-PAt’/CSA-PAmin; and α4, CSA-PAmin/CSA-PAb. The relationship between ΔP (ΔP1+ΔP2 and ΔP3+ΔP4) and α for the four intervals of the nasopharynx in all models are shown in Fig 9 and the schematic is presented in Fig 10. The closer the α-value is to 1, the smaller the pressure drop irrespective of the area (Fig 9).

Fig 9

Pressure drop and the rate of changes in the cross-sectional area (α).

Correlation between pressure drop and α. The horizontal axis indicates α and the vertical axis represents the pressure drop. Notes: blue, α1; orange, α2; grey, α3; green, α4.

Fig 10

Schematic illustration of the pharynx.

The arrow points toward the direction of airflow.

Flow field

The flow field of the sagittal section of the nasopharynx for each model is shown in Fig 11. In the severe STENOSIS model, a jet was observed through the aperture stenosis, whereas vortices were observed downstream. In the STENOSIS -15mm model of patient 1 and the STENOSIS -10mm model of patient 2 in Fig 11, the Reynolds numbers of the nasopharynx region were about 11 200 and 6800, respectively.

Fig 11

Flow fields of the sagittal section of the nasopharynx for each model.

The direction of flow is from the lower right (nasal cavity side) to the left (oropharyngeal side).

Discussion

A comparison of the PRE and POST models in this study revealed a lower ΔPAll in the POST model than in the PRE model (Fig 7 and Table 3). The airway resistance was proportional to ΔP because the flow rate was constant in this study. Therefore, the magnitude of ΔP was evaluated as the level of airway resistance, so the pre- and postoperative comparisons in this study revealed a postoperative improvement in the ventilation of the entire upper airway (Fig 7). In patient 3, ΔPNose was increased, but ΔPAll, which represents the ΔP in the entire upper airway, was lower in the POST model than that in the PRE model. Our previous study [29] found that the nasal cavity has a greater influence on the ΔP compared to the pharynx after surgery for mandibular prognathism (i.e., Class III skeletal relationship of the jaws). These findings are consistent with those of the present study, in which the ratio of ΔPNose to ΔPAll was higher (Table 3) than that of ΔPPharynx to ΔPAll in maxillary prognathism (i.e., Class II skeletal relationship of the jaws).

The results of our study suggest that changes in the nasopharynx do not have a substantial impact on the ΔPAll pressure drop, except in the extremely high STENOSIS model. The nasopharynx and oropharynx can be considered as a cylinder (Fig 8); thus, airway resistance is inversely proportional to the fourth power of the airway radius based on the Hagen–Poiseuille law (7) given by where Q is the flow rate (m3/s), ΔP is the pressure difference between the ends of the cylinder (Pa), r is the internal radius of the cylinder (m), μ is the viscosity of the fluid (Pa s), and L is the length of the cylinder (m). As the CSA of a cylinder is calculated by A = πr2, ΔP is inversely proportional to the square of the CSA (i.e., ΔP = 8πμQL/A2).

The CSA of the nasopharynx (PNA, NP) is larger than that of the nasal cavity (NOS, NV) and the cross-sectional morphology of the nasopharynx closely resembles a cylindrical tube, while the nasal cavity is a narrow and complex structure. Thus, the nasopharynx has a lower impact on ΔP in case of equivalent amount of jaw repositioning (Fig 8). Hence, it can be inferred that the effect of the nasopharynx on postero-superior repositioning of the maxilla is smaller than that of the nasal cavity. In the extremely high STENOSIS model, e.g., the STENOSIS -15 mm model of patient 1, when A in Eq (7) is less than one-fourth of that in POST, the calculated value of ΔP is larger than the square of 4. However, stenosis of such extreme severity does not occur clinically, owing to the presence of the descending palatine artery and pterygoid process, which regulate the postero-superior repositioning of the maxilla in Le Fort I osteotomy.

Note that in this study, we have assumed a rigid wall and steady state. The mechanical properties of the pharynx wall are difficult to determine, because it is regulated by a complex interplay between whether enclosed in a bony structure, wall thickness, airspace cross-sectional areas, and tissue pressure [32, 33]. Therefore, the compliance effects have not been considered and have been simplified. This behavior is an important aspect that should be taken in consideration in future studies. According to Hahn et al. [34], the upper airway wall can be assumed to be a rigid body for the purpose of simplification, ignoring the effects of the vibrissae, humidity, etc. Therefore, the ΔP, which mainly occurs in the upper airway, comprises a ΔP due to viscosity and ΔP due to turbulent flow. Air flow in the airway during breathing creates a resisting force due to the airflow viscosity in the upper airway. The presence of stenosis in the upper airway may lead to flow separation, which may lead to the formation of flow-separation zones as in the throat airflow structures [35, 36]. As shown in Fig 12, the flow velocity in the A-B interval is low due to a ΔP, whereas the flow velocity in the B-C interval is high due to an increase in the ΔP (albeit without flow-separation zones). This separation leads to a significantly higher amount of energy loss, in addition to airway resistance, depending on the size of the cross-section due to vortices created downstream of the separation point by reflux. According to the results of this study, separation and vena contracta in the narrower area (equivalent to the A-B interval in Fig 12) and separation and turbulent flow in a wider area (equivalent to the B-C interval in Fig 12) resulted in a ΔP due to turbulent flow in ΔPPharynx, as seen in the STENOSIS -15 mm model of patient 1 and STENOSIS -10 mm model of patient 2 in Fig 11. On the other hand, the changes in ΔP were insignificant due to a significant ΔP caused by viscosity due to the tapering of the pharyngeal airway toward the narrowest part of the pharynx in the POST/STENOSIS models of patients 2 and 3. Previous studies [30, 37] examined the CSA of stenosis of the upper airway, but failed to evaluate the changes in the pre- and postoperative diameters of the upper airway. Yajima et al. [30] found that the ΔP increased substantially when the stenotic region in the oropharynx (CSA-PAmin) was less than 1 cm2. Conversely, for the nasopharynx (CSA-NP), ΔP increased below 1 cm2 (Table 4 and Fig 7). The rate of changes in the CSA (α) was calculated to facilitate objective comparisons between the pre- and postoperative states using ΔP (Figs 9 and 10). The greater the proximity of the value of α to 1, the smaller the changes in airway diameter and ΔP. On the other hand, the further the value of α from 1, the greater the changes in airway diameter and pressure drop. Consider the α2 of the STENOSIS model of patient 1: -1 mm and -2 mm are both close to 1, α2 is > 1, and the pressure drop is also higher in the -10-mm and -15-mm models. These results suggest that the closer the morphology of the airway is to a straight tube, the lower the risk of reduction of airway ventilation. Therefore, ideally the airway diameter should be constant. In this study, the α-value and CSAs were sufficient, so that all values of ΔPAll in the POST model were smaller than their PRE counterparts and there was no reduction in nasal respiratory function.

Fig 12

Stenosis image.

The arrow points toward the direction of airflow. Notes: A, inlet; B, stenosis; C, outlet.

The prediction of the changes in airway morphology due to the repositioning of bone fragments may be necessary, to apply the present findings of the airway morphology to surgical practice in the future. It is thought that the direction of repositioning of the maxilla during corrective jaw surgery affects the nasopharyngeal airway [38], whereas repositioning of the mandible affects the lower part of the pharyngeal airway [39]. However, the sample size of this study was small because the indications for maxillary osteotomy alone are few, so larger sample sizes and further analyses are needed to accurately predict changes in the airway morphology, which varies according to the maxillofacial morphology and amount of surgical repositioning. We will endeavor to investigate this aspect in a future study. If it becomes clear that there are no functional problems with surgical methods that involve the large posterior and/or superior movement of the jawbone, which is expected to have an adverse effect on the upper airway, it will be possible to improve surgical planning and develop new treatments. This would lead to the enhancement of patients’ quality of life and the further development of orthognathic surgery. Individual differences exist in the morphological changes in the airway even after equivalent amount of repositioning. Furthermore, a reduction in the airway CSA may lead to stenosis, while flattening of the airway may reduce the anteroposterior diameter, also leading to stenosis. However, the patterns of airway changes have not been elucidated. Therefore, in the present study, we added fluid considerations from a case study with a small sample size by mimicking the airway constriction caused by jaw movement and changing it numerically. What we learned from that consideration is highly versatile as it can be applied to other patients if the relationship holds. Elucidation of the airway morphology and prediction of the changes in respiratory function using preoperative CT in future studies, along with the findings of the present study, may aid surgical planning, with considerations for occlusion, maxillofacial morphology, and respiratory function. Not only can we develop surgical methods to prevent the onset of OSA, but we can develop clinical research that incorporates model simulations of soft tissue changes including the upper airway associated with general orthognathic surgery.

The current study of the effect of postero-superior repositioning of the maxilla on nasal ventilation using computational fluid dynamics showed that current surgical methods are appropriate with respect to functionality and do not reduce nasal respiratory function, irrespective of the nature of the surgery. The greater the proximity of the value of α to 1, the smaller the changes in airway diameter and ΔP, so ideally the airway diameter should be constant without stenosis. This study identified airway shapes that are preferable from the perspectives of flow dynamics. We found that our results may be applicable to other patients.

12 Jan 2022

Submitted filename: review.docx

Click here for additional data file.

25 Feb 2022

Here is a point-by-point response to the journal requirements and the reviewers’ comments.

Journal Requirements

1. When submitting your revision, we need you to address these additional requirements.Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

Reply:

We have ensured that our manuscript meets PLOS ONE's style requirements, including those for file naming.

2. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Reply:

We have ensured that our reference list is complete and correct. Additional references have been noted in specific replies and as follows:

1. Tselnik M, Pogrel MA. Assessment of the pharyngeal airway space after mandibular setback surgery. J Oral Maxillofac Surg. 2000;58: 282–5 discussion 285. doi: 10.1016/s0278-2391(00)90053-3 (line 42).

2. Mirmohamadsadeghi H, Zanganeh R, Barati B, Tabrizi R. Does maxillary superior repositioning affect nasal airway function? Br J Oral Maxillofac Surg. 2020;58: 807-811 doi: 10.1016/j.bjoms.2020.04.020 (line 42).

3. Engboonmeskul T, Leepong N, Chalidapongse P. Effect of surgical mandibular setback on the occurrence of obstructive sleep apnea. J Oral Biol Craniofac Res. 2020;10: 597-602 doi: 10.1016/j.jobcr.2020.08.008. (line 43).

4. Hsieh YJ, Chen YC, Chen YA, Liao YF, Chen YR. Effect of bimaxillary rotational setback surgery on upper airway structure in skeletal class III deformities. Plast Reconstr Surg. 2015;135: 361e-369e doi: 10.1097/PRS.0000000000000913 (line 43).

32. White DP, MK Younes. Obstructive sleep apnea. Compr Physiol. 2012;2: 2541–2594 doi: 10.1002/cphy.c110064 (line 309).

33. Woodson BT. A method to describe the pharyngeal airway. Laryngoscope 2015;125: 1233–1238 doi: 10.1002/lary.24972. (line 309).

35. Kleinstreuer C, Zhang Z. Airflow and particle transport in the human respiratory system. Annu Rev Fluid Mech. 2010; 42: 301–334 doi: 10.1146/annurev-fluid-121108-145453 (line 316).

36. Cui XG, Gutheil E. Large eddy simulation of the unsteady flow-field in an idealized human mouth-throat configuration. J Biomech. 2011; 44: 2768–2774 doi: 10.1016/j.jbiomech.2011.08.019 (line 316).

3. We note that you have indicated that data from this study are available upon request. PLOS only allows data to be available upon request if there are legal or ethical restrictions on sharing data publicly. For more information on unacceptable data access restrictions, please see

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In your revised cover letter, please address the following prompts:

a) If there are ethical or legal restrictions on sharing a de-identified data set, please explain them in detail (e.g., data contain potentially sensitive information, data are owned by a third-party organization, etc.) and who has imposed them (e.g., an ethics committee). Please also provide contact information for a data access committee, ethics committee, or other institutional body to which data requests may be sent.

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We will update your Data Availability statement on your behalf to reflect the information you provide.

Reply:

a) There is an ethical restriction. Upon reasonable request, the data that support the findings of this study are available from the ethics committee as follows:

Dental Research Ethics Committee of Tokyo Medical and Dental University

E-mail: d-hyoka.adm@tmd.ac.jp

Url: https://tmdu-berc.jp

Comments from Reviewer #1

We wish to express our appreciation to the reviewer for your insightful comments, which have helped us significantly improve the paper.

1. The significance of the study is not clear, and it should be explained better in the Abstract, Objectives, as well as the Discussion/Conclusion.

Reply:

In accordance with the reviewer's comment, we have added the explanation in the manuscript as follows:

“In particular, nasopharyngeal stenosis, because of the complex influence of both jaws, the effects of which have not yet been clarified owing to postero-superior repositioning of the maxilla may significantly impact sleep and respiratory function, necessitating further functional evaluation.” (in the Abstract, lines 18-21)

“The jawbone and the soft tissues and airway that are moved during orthognathic surgery can be associated with all of these source sites because of their location.” (in the Introduction, lines 50-51)

“Therefore, in the present study, we added fluid considerations from a case study with a small sample size by mimicking the airway constriction caused by jaw movement and changing it numerically. What we learned from that consideration is highly versatile as it can be applied to other patients if the relationship holds.” (in the Discussion, lines 356-358)

“We found that our results may be applicable to other patients.” (in the Discussion section, conclusion, line 369)

2. The authors explain that the sample size for the study has been small and they tend to study a larger sample size in future. Adding more explanations on how the results of this study or the knowledge obtained in this research can facilitate future research or bring insights into an efficient future work can be helpful.

Reply:

In accordance with the reviewer's comment, we have added the explanation in the manuscript as follows:

“The new insights acquired in this study improves understanding of the pathogenesis of OSA and the effect of orthognathic surgery.” (in the Introduction, lines 94-95)

“If it becomes clear that there are no functional problems with surgical methods that involve the large posterior and/or superior movement of the jawbone, which is expected to have an adverse effect on the upper airway, it will be possible to improve surgical planning and develop new treatments. This would lead to the enhancement of the patients’ quality of life and the further development of orthognathic surgery.” (in the Discussion, lines 349-352)

“Therefore, in the present study, we added fluid considerations from a case study with a small sample size by mimicking the airway constriction caused by jaw movement and changing it numerically. What we learned from that consideration is highly versatile as it can be applied to other patients if the relationship holds.” (in the Discussion, lines 356-358)

“Not only can we develop surgical methods to prevent the onset of OSA, but we can develop clinical research that incorporates model simulations of soft tissue changes including the upper airway associated with general orthognathic surgery.” (in the Discussion, lines 361-363)

3. In the abstract, the observation of “ΔP in the upper airway was lower in the POST model compared to the PRE model” can be more elaborated before concluding that the current surgical methods “do not compromise nasal respiratory function”. For instance, why the change in pressure drop cannot make any change on respiratory function? Could it not affect the air flow rate? Or, what changes were they expecting that were not observed?

Reply:

As reported by Mirmohamadsadeghi H et al. [2] and Hsieh YJ et al. [4], nasal airflow, cross-sectional area, and volume are decreased by maxillary movement. Therefore, in the present study, it was feared that postoperative orthognathic surgery with postero-superior repositioning of the maxilla would result in a larger ΔPAll due to these decreases, which would worsen the respiratory function. However, according to the results, ΔPAll in the upper airway was lower in the POST model than in the PRE model. As shown in Fig. 8, this can be explained by focusing on the change in airway cross-section.

We have therefore changed and added the following text:

From

“This study aimed to perform a functional evaluation of the effects of corrective jaw surgery involving postero-superior repositioning of the maxilla on nasal respiratory function using computational fluid dynamics for treatment planning.”

to

“This study aimed to perform a functional evaluation of the effects of surgery involving maxillary repositioning, which may result in a larger airway resistance due to the stenosis would worsen the respiratory function, using CFD for treatment planning.” (in abstract, lines 21-23)

“A comparison of the PRE and POST models in this study revealed a lower ΔPAll in the POST model than in the PRE model (Fig. 7, Table 3).” (in discussion, lines 280-281)

4. In the Abstract and Discussion, it is mentioned that “this study identified airway shapes that are preferable from the perspectives of flow dynamics”. However, the text does not provide explanations about this identification and it is not mentioned in the text what criteria are considered for evaluating an airway shape as favourable from fluid dynamics perspective. It will be good if authors provide more explanations on that.

Reply:

In accordance with the reviewer's comment, we have added the explanation in the Abstract as follows:

“The closer the α-value is to 1, the smaller the ΔP, so ideally the airway should be constant.” (line 34)

Also, we have added the explanation in the Discussion as follows:

“The greater the proximity of the value of α to 1, the smaller the changes in airway diameter and ΔP, so ideally the airway diameter should be constant without stenosis.” (in discussion, lines 366-368)

5. The first paragraph of the introduction requires references (lines 43-45).

Reply:

We have added references [1,2] (line 42) and [3,4] (line 43) in the paragraph.

The introduction section of the manuscript now contains the following references:

1. Tselnik M, Pogrel MA. Assessment of the pharyngeal airway space after mandibular setback surgery. J Oral Maxillofac Surg. 2000;58: 282–5

2. Mirmohamadsadeghi H, Zanganeh R, Barati B, Tabrizi R. Does maxillary superior repositioning affect nasal airway function? Br J Oral Maxillofac Surg. 2020;58: 807-811.

3. Engboonmeskul T, Leepong N, Chalidapongse P. Effect of surgical mandibular setback on the occurrence of obstructive sleep apnea. J Oral Biol Craniofac Res. 2020;10: 597-602.

4. Hsieh YJ, Chen YC, Chen YA, Liao YF, Chen YR. Effect of bimaxillary rotational setback surgery on upper airway structure in skeletal class III deformities. Plast Reconstr Surg. 2015;135: 361e-369e.

6. The purpose of the lines 68-69 is not clear and the grammatical structure requires amendment.

Reply:

We are sorry that this part was not clear in the original manuscript. We have revised the contents of this part from:

“Prevention the reduction in overall ventilation of the upper airway necessitates the evaluation of the nasopharynx, the site of the original stenosis.”

to

“Therefore, preventing the reduction in overall ventilation of the upper airway necessitates the evaluation of the nasopharynx, on which the effects of stenosis have not yet been clarified." (lines 74-76)

7. Authors may clarify figure 1 by improving the image quality and showing the rotations with arrows and probably the position of the nasal cavity and nasopharyngeal airway.

Reply:

We have improved the image quality and added new explanations to Figure 1 (line 97-103).

Changes:

Added rotations with blue arrows and the position of the nasal cavity (pink area) and nasopharyngeal airway (purple area).

8. In line 134, the atmospheric pressure mentioned is inaccurate.

Reply:

In accordance with the reviewer's comment, we have corrected from " 1.013×10-5 Pa" to "1.01325×10-5 Pa ". (in Airflow simulation section, line 152)

9. All the terms such as Pamin, Pabp, Paup, and CSA-PNA are recommended to be denoted in a more clear and readable way.

Reply:

We have changed the terms throughout the manuscript including figures as follows:

Symbol (change from) Symbol (change to)

Nos NOS

Nval NV

PNA・PNS NP

Paup PAt

Pamin PAmin

Paup’ PAt’

Pabp PAb

ΔP nose ΔPNose

ΔP pharynx ΔPPharynx

ΔP all ΔPAll

10. All figure captions should be re-written in the form of complete sentence(s) and not phrases, where possible. Also, figure captions are better to be written as one single paragraph and not multiple paragraphs.

Reply:

In accordance with the reviewer's comment, all figure captions have been rewritten in the form of complete sentences and/or a single paragraph. We have summarized correction of the caption in the file labeled “figure captions.docx”.

11. All parameters studied in the model can be presented in a nomenclature in the beginning or a table in the text to avoid repeating the definitions in every figure caption and at the end of each Table. For instance, alpha is defined in both lines 261 and 270 repeatedly.

Reply:

We have added new Tables (Tables 1 and 2, please see pages 14-16), which outline definitions of landmarks and measurements variables, and removed the definitions.

12. In Table 1, units should be mentioned in front of each parameter rather than in separate cells.

Reply:

As requested, we have removed units in separate cells and placed it in front of each parameter in Table 1 (changed to Table 3), and in Table 2 (changed to Table 4), too (Please see pages 19-20 and 22-23).

13. The quality of all figures should be improved.

Reply:

We have corrected the quality issues pointed out in the figures.

14. Table 1 should be cross-referenced in line 243, where the data is reported.

Reply:

We have cross-referenced Table 1 (change to Table 3) in line 251.

15. In figure 8, appropriate labels should be added to both X and Y axes instead of explaining in the figure caption.

Reply:

We have added a label for “α”on the x-axis and “Pressure drop” on the y-axis in Figure 9 (changed from Figure 8).

16. The statement in lines 264-265 needs to be edited. Also, Figure 9 should be cross-referenced as the data is reported in lines 264-265.

Reply:

We have revised the contents of this part to clarify and cross-referenced.

"The closer the α-value is to 1, the smaller the pressure drop irrespective of the area (Fig. 9). " (line 262).

17. The two statements in lines 301 to 304 give the same message and hence, can be merged into one sentence.

Reply:

In accordance with the reviewer's comment, we have merged the sentences into one sentence as follows:

“Therefore, the magnitude of ΔP was evaluated as the level of airway resistance, so the pre- and postoperative comparisons in this study revealed a postoperative improvement in the ventilation of the entire upper airway (Fig. 7).” (lines 282-284)

18. The statement in lines 299-300 seems to disagree with the statement in lines 310-312. Please clarify.

Reply:

The airway resistance was proportional to ΔP because the flow rate was constant in this study, so we could compare the PRE and POST models. The airway resistance is inversely proportional to the airway radius based on the H–P law. The CSA of the nasopharynx (PNA, NP) is larger than that of the nasal cavity (NOS, NV). Thus, the nasopharynx has a lower impact on ΔPAll. If the stenosis is not large, the pressure drop will also be low when a is close to 1, as shown in Fig. 9 (changed from Fig. 8).

19. The statements in lines 329-331 need references.

Reply:

We have added references [35,36] in the paragraph (line 316).

The discussion section of the manuscript now contains the following references:

35. Kleinstreuer C, Zhang Z. Airflow and particle transport in the human respiratory system. Annu Rev Fluid Mech. 2010; 42: 301–334.

36. Cui XG, Gutheil E. Large eddy simulation of the unsteady flow-field in an idealized human mouth-throat configuration. J Biomech. 2011; 44: 2768–2774.

20. In line 337, please specify how it was found that the flow was turbulent. Please report the Re number if that is used.

Reply:

In accordance with the reviewer's comment, we have added the explanation in the Result as follows:

“In the STENOSIS -15mm model of patient 1 and the STENOSIS -10mm model of patient 2 in Fig. 11, the Reynolds numbers of the nasopharynx region were about 11200 and 6800, respectively.” (in Results, Flow field, lines 273-274)

We appreciate all of your insightful comments. We worked hard to be responsive to them. Thank you for taking the time and energy to help us improve the paper.

Comments from Reviewer #2

The manuscript offers good insights into the effect of changes in airway morphology due to the repositioning of bone fragments which is beneficial in predicting the effect of such operation on patients ventilation, but the number of cases used in the study is quite small which makes it quite hard to get more generalized conclusions. However, the study approach is quite promising for the future of corrective surgeries.

Reply:

Thank you very much for your invaluable comments. We found them quite useful as we approached our revision.

1- In the abstract, page (2) line (32-33),” the rate of change in the cross-sectional area of the mass extending from the nasopharynx to oropharynx approximated 1”. It is not clear how the rate of change in the cross-sectional area was calculated?

Reply:

We have rewritten an explanation of α in the abstract (lines 33-34).

2- In the second paragraph in the introduction, page (4) line (55-69), this paragraph is a bit confusing to the reader, as it is not clear what the authors are trying to address in this paragraph and how it is related to the current work.

Reply:

As pointed out by the reviewer, we have rewritten the whole paragraph to clarify its meaning. The changes are as underlined as follows:

“A high incidence of mandibular skeletal prognathism (Class III) has been reported in Japan: it is treated using posterior repositioning of the mandible (single-jaw mandibular setback osteotomy). When upper and lower jaw osteotomy (two-jaw surgery) is applied because of a severe discrepancy of the jaws, the maxilla is moved upward and/or backward and the mandible is moved backward. Although there is a lack of clear evidence that corrective jaw surgery causes OSA, it is clear that posterior surgical repositioning of the mandible leads to postoperative narrowing of the upper airway. Therefore, except nasopharynx, several studies have reported the relationship between stenosis of the nasal cavity, oropharynx, or hypopharynx and OSA [3,8,15,16]. On the other hand, in the case of maxillary skeletal prognathism (Class II), the maxilla is moved upward and/or backward or the mandible is moved forward in single-jaw surgery. If two-jaw surgery is required, the maxilla is moved upward and/or backward and the mandible is moved forward. One study reported that patients with Class II have smaller pharyngeal airway volume due to the maxillofacial morphology, which is more likely to lead to OSA compared to the Class I and III skeletal relationships [17]. However, the effect of surgical repositioning of the jaw on OSA has not been elucidated. Despite maxillary impaction, anterior repositioning of the mandible in patients with a Class II skeletal relationship may improve the respiratory status during sleep by expanding the volume of the pharynx. On the other hand, in Class II, posterior and/or superior repositioning of the maxilla may lead to narrowing of the nasal cavity and nasopharynx as was observed in Class III with a reduction in the volume of the airway in the nasal cavity and the most posterior point on the posterior nasal spine (PNS) [4]. Nasal airflow and the cross-sectional area of the nasal cavity decrease when the degree of maxillary impaction exceeds a certain limit [2]. Thus, repositioning of the maxilla may reduce the volume of the entire upper airway changes with the degree of maxillary impaction and mandibular position. The nasopharynx is thought to be susceptible to the movement of both jaws due to its location. Therefore, preventing the reduction in overall ventilation of the upper airway necessitates the evaluation of the nasopharynx, which the effects of stenosis have not yet been clarified.” (in introduction, lines 54-76)

3- Figure (1) need to be more intuitive by adding a color legend to address reactionary counter-clockwise rotation during postero-superior repositioning.

Reply:

In accordance with the Reviewer’s comment, Fig. 1 has been revised to show the movement more clearly and the associated changes in the airway. We have also added the following notes (lines 99-103):

black line, pre-surgery (before mandibular autorotation); red line, post-surgery; blue circle, center of mandibular autorotation; blue arrow, direction of autorotation; green line, after mandibular autorotation; gray line; post-surgery in the figure of airway changes ; pink area, preoperative nasal cavity; pink hatched area, postoperative nasal cavity； pink arrow, direction of nasal cavity change; purple area, preoperative nasopharyngeal airway; purple hatched area, postoperative nasopharyngeal airway; purple arrow, direction of pharyngeal change

4- typo error line (90) page (6),” Surgical impaction of the maxilla and the reaction of the mandible ae illustrated schematically”.

Reply:

This error has been corrected in accordance with the reviewer's comment from "ae" to "are." (in introduction, line 98)

5- It has to be mentioned clearly that the study was performed on females only because the authors mentioned that the study was performed on 3 females.( page 7, line 100).

Reply:

Accordingly, we have added “females” to abstract section (line 24). As well, we have specified “three patients, all female” in the participants section (line 112).

6- Figure illustrating the mesh is needed to provide information regarding this information “Three layers of the tetrahedral/hybrid tetrahedral-prism”, mentioned in line 129, page(8).

Reply:

In accordance with the reviewer's comment, we have included a new Figure 3 to illustrate the mesh (lines 146-148 and Figure 3).

7- Information about the element size and mesh independence study need to be added.

Reply:

We have changed the following text to the Three-dimensional models section (lines 141-144) from:

“Three layers of the tetrahedral/hybrid tetrahedral-prism meshes were generated so that even the area near the wall possessed sufficient resolution.”

to

“The volume mesh of the airway had around 7400000 elements. The unstructured tetrahedral/prism hybrid mesh of the airway model was generated. Three layers of the prism mesh was placed near the wall so that even the area near the wall possessed sufficient resolution (Fig. 3). The cell size of the prism region was adjusted to attain a dimensionless wall distance (y+) value less than 1.”

8- Reason for choosing these assumptions is steady and need to be clarified in the text. Line (135), page (9).

Reply:

Lee et al explained that significant change was not observed in flow pattern distribution between steady and unsteady calculation at inhalation phase. Therefore, we have chosen steady flow to simplify calculations. We have also added the following underlined text and reference (lines 152-156):

“The following physical properties were set in the model: steady flow of an incompressible Newtonian fluid with a density of 1.205 kg/m3 and viscosity of 1.822 × 10-5 Pa·s based on a previous study [26]. Lee et al. [26] explained that significant change was not observed in flow pattern distribution between steady and unsteady calculation at the inhalation phase.”

26. Lee JH, Na Y, Kim SK, Chung SK. Unsteady flow characteristic through a human nasal cavity. Respiratory Physiology & Neurobiology. 2010;172: 136-146.

9- In page (10) line (162-163), the Outlet boundary condition is used a free outlet and p=0 in one of the cases, can you clarify the reason behind using different outlet boundary conditions.

Reply:

Thank you for this comment. We have also added the following underlined text and reference (lines 184-185):

“Because back flow occurred at the outflow boundary, the pressure boundary condition (P=0) was adapted in the high-stenosis model based on reality.”

10- Figure (6), a y-axis label need to be added and the x-axis.

Reply:

We have added a label for “Model”on the x-axis. Also, “Pressure drop” and “CSA” have been added on the y-axis in Figure 7 (changed from Figure 6).

11- Can you indicate how the STENOSIS -1mm, -3mm is measured in the figure (3), it seems to be a distance, so can you clarify how this is measured

Reply:

We have added the following text to clarify how to create the STENOSIS models:

“As shown in Fig.4, the nasopharynx of the STENOSIS model (indicated by the rectangle in the inset) was trimmed mainly around the PNS by the amount indicated by the red asterisks (where each asterisk equals to the amount of trimming for each model, e.g., in STENOSIS -1 mm model, the asterisk means narrowing the thickness by 1 mm).” (lines 193-196)

“With a focus on the nasopharynx region of the STENOSIS model, the area (surrounded by the orange dotted circle) was trimmed by the length of the asterisk around the posterior nasal spine (PNS) in the sagittal plane. The red asterisk indicates the amount of trimming for the nasopharynx of the STENOSIS model.” (lines 198-200)

12- In page (25), line (327), the assumption of rigid upper airways is quite obsolete; as some studies have investigated the effect of upper airways tissue motion (The effects of upper airway tissue motion on airflow dynamics). Also, most of the experimental studies use flexible materials for manufacturing upper airway replicas’.

Reply:

The use of a rigid model may be a limitation of the present study. The influence of model conditions will be a consideration for our future study. We have therefore added the following text and references (in discussion, lines 307-311):

“Note that in this study, we have assumed a rigid wall and steady state. The mechanical properties of the pharynx wall are difficult to determinate, because it is regulated by a complex interplay between whether enclosed in a bony structure, wall thickness, airspace cross-sectional areas, and tissue pressure [32,33]. Therefore, the compliance effects have not been considered and have been simplified. This behavior is an important aspect that should be taken in consideration in future studies.”

32. White DP, MK Younes. Obstructive sleep apnea. Compr Physiol. 2012;2: 2541–2594.

33. Woodson BT. A method to describe the pharyngeal airway. Laryngoscope 2015;125: 1233–1238.

13- Body mass index (BMI) for the cases tested in this study needs to be mentioned.

Reply:

We have supplemented the Materials and Methods section (line 115) and Table 3 with data of BMI.

Thank you once again for your valuable comments and suggestions.

Submitted filename: Response to Reviewers.doc

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8 Apr 2022

11 Apr 2022

Thank you for giving me the opportunity to submit a revised draft of my manuscript titled “Computational fluid dynamic analysis of the nasal respiratory function before and after postero-superior repositioning of the maxilla” to PLOS ONE.

We appreciate the time and effort that you and the reviewers have dedicated to providing your valuable feedback on our manuscript. We have revised the manuscript according to the comments from editors and reviewers.

We have highlighted the changes within the manuscript.

Here is a point-by-point response to the journal requirements and the reviewers’ comments.

Journal Requirements

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Reply:

We have ensured that our reference list is complete and correct. Additional reference lists have noted as follows:

20. Hoppenreijs TJ, Stoelinga PJ, Grace KL, Robben CM. Long-term evaluation of patients with progressive condylar resorption following orthognathic surgery. Int J Oral Maxillofac Surg. 1999;28: 411-418. doi: 10.1034/j.1399-0020.1999.280602.x.

Comments from Reviewer #1

The manuscript is significantly improved.

However, the atmospheric pressure mentioned in page 10 line 152 is still inaccurate and should be changed to 1.013 x 10^+5 Pa.

Reply:

Thank you very much for your kind suggestion.

In accordance with the reviewer's comment, we have corrected from " 1.013×10-5 Pa" to "1.013×105 Pa ". (in Airflow simulation section, page 10 line 152)

Comments from Reviewer #2

(No Response)

Reply:

Thank you very much for reviewing our manuscript.

We look forward to hearing from you in due time regarding our submission and to respond to any further questions and comments you may have.

Sincerely,

Marie Oshima

Submitted filename: Response to Reviewers.doc

Click here for additional data file.

13 Apr 2022

Computational fluid dynamic analysis of the nasal respiratory function before and after postero-superior repositioning of the maxilla

PONE-D-21-36984R2

Dear Dr. Oshima,

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Academic Editor

PLOS ONE

18 Apr 2022

PONE-D-21-36984R2

Computational fluid dynamic analysis of the nasal respiratory function before and after postero-superior repositioning of the maxilla

Dear Dr. Oshima:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

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