Abstract

1. Introduction

Cone-beam computed tomography (CBCT) is an imaging technology that has been increasingly used in the last decade. During the procedure, the CBCT rotates around the patient’s head, using a cone-shaped beam to obtain many two-dimensional images. The scanning software reconstructs the data to produce values on a regular grid in three-dimensional space, and these values can be manipulated and visualized with specialized software [1]. Due to its high spatial resolution, isotropic voxel, adequate contrast between the soft tissue and empty space, and the relatively low radiation dose compared to conventional CT, CBCT can be used to analyze the anatomical parameters three-dimensionally [1]. CBCT is well suited for imaging the craniofacial area [1,2]. Depending on the size of the acquisition field, CBCT can show the soft and hard anatomical structures such as the maxillo-facial region, the base of the skull, the viscerocranium and the upper airway [1,2]. CBCT is consequently a tool for the diagnosis, assessment, planning, and delivery of treatment in various specialties in dentistry (e.g., endodontics, periodontology, orthodontics, oral and maxillofacial surgery and implantology, temporomandibular joint disorders) [3].

Compared with multidetector computed tomography (MDCT), CBCT is less costly, uses lower radiation doses for a higher resolution, and produces more detailed images of hard tissues, even if it provides less soft tissue contrast. Consequently, CBCT imaging could replace MDCT in otolaryngology-related applications, for instance for the evaluation of the upper airway, at standard or low-dose protocols [4,5].

The upper airway comprises the nasopharynx, the oropharynx, and the hypopharynx. Several hard and soft tissue particularities constrain the aerial flow. According to the literature, CBCT is an accurate tool for upper airway evaluation [6,7,8,9,10,11,12,13,14,15,16]. Indeed, CBCT provides insights into the anatomical anomalies found along craniofacial structures and has been used to measure soft and hard anatomical structures. It has been suggested that anatomical abnormalities of the upper airway, including upper-airway collapsibility, alterations in craniofacial structures (i.e., the anteroposterior position of the mandible), and enlargements of surrounding soft tissue structures (i.e., tongue and lateral pharyngeal walls, soft palate, and hyoid bone) play an important role in the development of Obstructive Sleep Apnea (OSA) [6,7,8,9,10,11,12,13,14,15,16]. This pathology is characterized by the temporary cessation of breathing (apnea) or shallow breathing (hypopnea) with decreased hemoglobin oxygen saturation [9,10,11,16]. Increased interest in upper airway morphology can be attributed to the appreciation that the upper airway configuration is associated with OSA as well as its general relationship to craniofacial morphology.

Although several studies using CBCT have been carried out to determine the upper-airway configuration, they used various anatomical structures without investigating the role of all these structures taken simultaneously [6,7,8,9,10,11,12,13,14,15,16]. In the literature, anatomical landmarks seem easily identifiable without superimposition or distortion on CBCT exams [17,18,19,20,21,22,23,24,25,26,27,28,29]. The upper airway volume can be obtained by the automatic segmentation method [8,9,13]. It would be interesting to analyze the different variables and see how they are linked to each other, specifically exploring the placement of variables related to the upper airway. Moreover, in recent years, the use of Machine Learning (ML) methods has made it possible to accurately estimate the observed dynamics by learning automatically from several variables. In this study, in addition to the classical statistical approach, we use a special branch of ML, namely symbolic regression (SR). SR is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits data. SR works by randomly combining mathematical building blocks to obtain models understandable from a human perspective.

The aim of this study was to assess on CBCT exams the correlation between hard and soft anatomical parameters and their impact on the characteristics of the upper airway using symbolic regression as a machine learning strategy.

2. Materials and Methods

3. Results

3.4. Bi-Variate Analysis

The correlation matrix was presented in Figure 1. The anteroposterior position of the mandible (Na–B distance) was significantly correlated with the characteristics of the upper airway (volume, CSAmin and its anteroposterior and lateral dimension), the hyoid bone position (S–H distance), the position of the tongue (BEP–A distance) and the anteroposterior position of the maxilla, with $\tau$ correlation coefficients around +0.4.

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Figure 1

The correlation matrix plot between the variables two by two using Kendall’s $\tau$ correlation coefficient. The level of significance was set at 5% (p < 0.05). The colormap indicates the values of the correlation (from strong positive correlation in deep blue to strong negative correlation in deep red). A cross means non-significance at the 5% threshold.

The height of the nasal cavity (Na-ANS distance) was slightly but significantly correlated with the characteristics of the upper airway and the localization of the soft palate (TUV–PNS) ($\tau$ around +0.2). It was moderately associated with the dimension of the tongue (BEP–A), the width of the mandible (rGo–lGo), the dimension of the cranial basis (S–Na), the position of hyoid bone (S–H, PNS–H), the dimension of vertical soft palate (PNS–VSP) and the anteroposterior position of the maxilla (Na–A), with $\tau$ values around +0.4.

The horizontal soft palate (PNS-LP) was significantly correlated with the characteristic of upper airway with $\tau$ correlation coefficients around −0.3, and it was moderately correlated with the dimension of the tongue (BEP-A) with $\tau$ values around +0.4. Furthermore, age was significantly correlated with $\tau$ values around +0.4 with the anteroposterior dimension of the CSAmin, the pharyngeal hypertrophy (Ba-Tph) and the hyoid bone position (C3–H). There was a negative correlation between these two variables ($\tau$ = −0.3, p < 0.05).

3.5. Results from the Principal Component Analysis

This analysis highlights the most important variables which are associated in each dimension to explain the variability of the sample subjects. Most of the variability was explained by the first two dimensions, with 22.6% and 15.5% of the explained variance, respectively (Figure 2). We observed that the variables which were the most correlated to the upper airway characteristics were: for soft tissues, the dimension of the tongue (BEP–A), the hyoid bone position (C3–H, S–H), pharyngeal hypertrophy (Ba–Tph), and the soft palate (PNS–LP, PNS–VSP); for hard tissues, the position of the anteroposterior mandible (Na–B), and the length of the nasal cavity (Na–ANS).

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Figure 2

Results of the principal component analysis (PCA) for the dimensions 1 and 2. Variables well represented by the PCA are located next to the periphery of the circle (and have a high value of cos2). Positively correlated variables are found closely, while negatively correlated variables are found in the opposite quadrant.

3.6. Machine Learning Analysis

Since numerous variables are highly correlated or weakly informative to explain volume or CSAmin, symbolic regression analyses were performed to determine the importance of variables to model the upper airway characteristics. Models converged quickly. Figure 3A,B presents the variables ranked by normalized fitness-weighted importance to explain the CSAmin and the volume, respectively. This metric is related to the importance of the variables, i.e., the proportion of equations in which these variables appear, weighted by their fit (the mean absolute error). All equations obtained for each experimental run were provided in Supplementary Tables S1 and S2. The distance PNS–LP mostly influenced both CSAmin and volume. Other outcomes were related to the hyoid bone (distance C3–H, angle H–Na–S), the soft palate (distance PNS–VSP), the tongue (distance BEP–A, BEP–TUV) or the mandibular or maxillary position (distance Na–B, angle S–Na–A). In order to evaluate the direction of the effect of these parameters on the volume or CSAmin, a sensitivity analysis was performed. Distances PNS–LP, BEP–TUV and angle H–Na–S had a negative mean magnitude on the CSAmin with −0.91, −0.14 and −0.07 (variables found in 10, 2 and 2 of the best models, respectively). Distance PNS–LP and angle H–Na–S had a negative mean magnitude on the airway volume with −0.97 and −0.39, respectively, meaning that an increase in the variable induces a decrease in the volume (variables found in 10/10 of the best models). Conversely, distances BEP–A, PNS–VSP and angle S–Na–A had a positive mean magnitude on the airway volume with 0.27, 0.29 and 0.37, respectively (variables found in 6 to 10 of the best models).

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Figure 3

Results for the symbolic regression analysis. (A) The variables are ranked by decreasing normalized fitness-weighted variable importance to explain the CSAmin of the upper airway. (B) The variables are ranked by decreasing normalized fitness-weighted variable importance to explain the volume (Vol) of the upper airway.

In summary, the results from symbolic regression analyses strengthen the results from the descriptive analysis. Soft tissues that are the most important to explain the upper airway are the horizontal soft palate, the tongue, and the position of the hyoid bone. The hard anatomical structure that is the most important to explain the upper airway is the anteroposterior position of the mandible and the maxilla related to the base of the skull.

4. Discussion

In this study, the aim was to assess the correlation between hard and soft anatomical parameters and their impact on the characteristics of the upper airway on CBCT scans.

The upper airway is a complex structure. The superior boundary of the upper airway is defined by a plane passing by PNS and ANS (to define the hard palate) and parallel to the FH plane [6,7,8,9,10,11,12,13,14,15,16,17,18]. In contrast, the position of the inferior boundary is not absolute. Indeed, some authors consider the BEP parallel to the FH plane [13,16,23], others consider it to be the superior part of the trachea [6,7,10,33], the anteroinferior point of C3 [34,35], the anteroinferior point of C2 [9,36,37] or the anteroinferior point of C4 [15,38]. In this study, the inferior boundary was defined as the anteroinferior point of C3 and parallel to the FH plane [34,35]. To compensate for the potential head incline during acquisition, all examinations were reoriented according to the FH and the midsagittal planes. To our knowledge, no study has performed an upper airway region analysis using validated soft and hard anatomical parameters simultaneously.

The upper airway is generally defined by its volume, its minimal section [7,8,9,15,16,32,36,37,39]. The volume of the upper airway and the CSAmin are obtained by automatic segmentation in Avizo software (Supplementary Text). In this study, the width of the nasal cavity was added as a hard-anatomical parameter even if such a parameter was not commonly reported in the literature. It made sense to add the nasopharynx, as its anatomy may participate directly or indirectly in the characteristics of the upper airway. All the other angles and distances were justified by the scientific literature [6,7,8,9,10,11,12,14,15,16,23]. The rationale for the mathematical computation of distances and angles from the spatial position of landmarks rather than measurements directly on Avizo was to improve the reproducibility of measures.

Several studies, such as that of de Oliveira et al., pointed out a more important reproducibility when using anatomical landmarks on a CBCT scan, if a protocol for operator training and calibration was followed [27,32]. Finally, the intra-observer reproducibility of this study was good to excellent with ICC values > 0.7. The possibility of both obtaining a 3D visualization from CBCT scans, and working on the three planes of space, may also have improved landmarks positioning more easily than using 2D radiography [1,17,19,20,21,22,25,40,41].

The literature reports that there are craniofacial morphological characteristics in OSA patients such as reduced upper airway space, anteroposterior position of the mandible (Na-B), abnormal long soft palate and tongue dimension, and low position of the hyoid bone [6,7,8,9,10,11,12,14,15,16,23,34,37,39,42,43,44]. Some authors have compared patients with and without OSA [7,9,10,11,16,23,32,36,37,39,43,44,45,46]. In this study, the analysis of the upper airway was carried out in a general population, irrespective of their medical pathology. However, CBCT exams were performed for medical reasons, such as sinus pathology and orthodontic disorders, and nothing excludes that the prescription of these examinations could not be directly or indirectly linked to an upper airway pathology (selection bias of the population).

The aim of the symbolic regression was to seek an optimal model between a set of different types of predefined mathematical functions and their combinations. This kind of methodology opens new perspectives in terms of flexibility and accuracy for statistical modeling [47]. Such an innovative approach has made it possible here to demonstrate the predominant importance of the horizontal soft palate to predict both the airway volume and minimal cross-section area. Our results are also in accordance with the literature. The soft tissues are predominately responsible for the reduction of the upper airway, especially the tongue, the soft palate and the hyoid bone position [8,9,16,32,44]. For the hard structures, the anteroposterior position of the mandible is also an important feature linked to the characteristics of the upper airway [8,12,34,35,37]. A significant correlation between the volume and the CSAmin, and its anteroposterior and lateral dimensions has been also reported [36].

This study shows that a few simple parameters, concerning both bone and soft tissues, can give information on the volume and restriction of the section of the airway. It is therefore important that the CBCT volume, often performed for dento-maxillary issues, be read in full with a systematic approach [48]. This implies strengthening the training of dental medical doctors to make them aware of incidental findings, and in particular of the airway and the risk of OSA. This will go together with the automation of linear or volume measurement by artificial intelligence [49,50]. Exposing the patient to the smallest possible amount of radiation is a major concern in medical imaging. If an acquisition is to be made specifically for the upper airway, CBCT low-dose protocols could be considered [51,52] as well as other types of imaging such as “Black Bone” magnetic resonance [53].

5. Conclusions

The upper airway is an important and complex anatomic structure in relationship with the development of pathogenesis such as OSA. In a general population, the soft tissues that are predominately responsible for the upper airway morphology are the soft palate and the hyoid bone position. For the hard structures, the anteroposterior of the mandible and the maxilla are also important features linked to the characteristics of the upper airway. Thus, although the volume of the airway is not accessible on all CBCT exams performed by dental practitioners, this study demonstrates that a small number of anatomical elements may be markers of the reduction of the upper airway, with potentially an increased risk of OSA. This could help the dentist refer the patient to a suitable physician.

Acknowledgments

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/jcm12010084/s1.

Funding Statement

We gratefully acknowledge the Programme d’Investissements d’Avenir and the Agence Nationale pour la Recherche for the support of the national infrastructure “ECELLFrance: Development of mesenchymal stem cell-based therapies” (PIA-ANR-11-INBS-005).

Author Contributions

Conceptualization, F.V., D.M. and P.M.; methodology, C.d.B., F.V., N.T., D.M. and P.M.; software, D.B., J.D. and P.M.; validation, F.V., N.T., S.C.-B. and D.M.; formal analysis, C.d.B. and P.M.; investigation, C.d.B. and D.M.; data curation, C.d.B., D.B., J.D. and P.M.; writing—original draft preparation, C.d.B., D.B., D.M. and P.M.; writing—review and editing, F.V., N.T. and S.C.-B.; supervision, N.T., D.M. and P.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

The study was conducted according to the guidelines of the Declaration of Helsinki. According to the French ethics and regulatory laws, studies that use routine care data do not have to be submitted to an ethics committee but must be declared or covered by the reference methodology defined by the French National Commission for Informatics and Liberties (CNIL). Toulouse University Hospital signed a commitment of compliance to the reference methodology MR-004 of the CNIL (number: 2206723 v0).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

References