Three-dimensional relationship between the degree of bilateral impacted mandibular third molars angulation and the mandibular dental arch parameters: a cross-sectional comparative study

The purpose of this study was to three-dimensionally evaluate the relationship between the degree of bilateral impacted mandibular third molar (IM3M) angulation and the mandibular dental arch parameters in normal skeletal and dental malocclusion patients. In this retrospective cross-sectional comparative study, 120 adult subjects’ cone-beam computed tomography (CBCT) images were three-dimensionally analyzed. The sample included 120 adults aged 20–30 years, with a gender distribution of 51 male and 69 female participants. The sample was divided into 100 adults with bilateral IM3M (study group) and 20 adults with normal bilateral erupted M3M (control group). The study group was sub-divided into three groups according to the degree of IM3M buccolingual angulation (BL°): group A, < 12° on the center of the ridge (N = 30), group B, 12–24° off-center of the ridge (N = 40), group C, > 24° off-center of the ridge (N = 30). The study group was also sub-divided into two groups according to IM3M mesiodistal angulation (MD°): group 1 from 10 to 45° (N = 36), group 2 > 45° (N = 64). Comparison within and between groups was performed using one-way ANOVA followed by Tukey’s post hoc test. The correlation between IM3M, BL, and MD angulation and the mandibular arch parameter was calculated using Pearson’s correlation coefficient. Statistically significant differences (P < 0.001) were found between the IM3M BL° and anterior teeth inclination, arch length (AL), and inter-second molar width (inter 2nd MW) as well as between the IM3M MD° with anterior crowding and the arch length (P < 0.001). A significant positive correlation was found between IM3M BL° and anterior teeth inclination and between IM3M MD° and anterior teeth crowding and inter 2nd MW. A significant negative correlation was observed between IM3M BL° and inter 1st MW and 2nd MW. The degree of buccolingual and mesiodistal angulation of the impacted mandibular third molars was related with mandibular dentoalveolar changes. Increased buccolingual angulation is generally associated with increased anterior teeth inclination and decreased 1st and 2nd inter-molar width. The increase in mesiodistal angulations was generally related with increased anterior teeth crowding and 2nd inter-molar width. Assessment of the relationship between the impacted mandibular third molars and the degree of arch discrepancy, and the position of mandibular incisors in the three planes of space might help in the decision-making process for the extraction of the impacted third molars in adult patients.


Introduction
Tooth eruption is considered a complex process; hence, tooth eruption can occur early, late, or even fail most of the time when the eruption of the tooth exceeds the scheduled time [1]. The third molar is the most commonly impacted tooth. The recorded frequency of its impaction varied greatly between populations, with the highest recorded in a Singapore Chinese population at 68.6% [2]. They are more common in the mandibular than the maxillary arch, and females are more prevalent than males [3]. The correlation between mandibular incisors crowding and the third molar impaction has been a controversial issue for a long time in the published literature [4]. The most debated question is whether third molar impaction played a role in the development or recurrence of malocclusion. Despite the discussion of this topic in literature, the question of whether impacted third molar teeth contribute to anterior dental arch crowding using three-dimensional imaging modalities remains unanswered in a comprehensive manner [5].
Panoramic radiography (OPG) has been used as a diagnostic tool. However, because of this modality's twodimensional (2D) nature, overlaps of anatomical regions are important for making decisions, which increases the chance of error. Cone-beam computed tomography (CBCT) has enabled the generation of trans-sections (i.e., perpendicular to the tangent of the dental arch) and threedimensional (3D) reconstructions from digital images in the axial, coronal, and sagittal dimensions. Its ability to capture the third dimension, the depth of the image, and the lack of overlap between nearby anatomical components makes it unique [6]. CBCT enables us to determine tooth size and arch dimension as rapidly, reliably, correctly, and reproducibly as measurements obtained by the digital method on digitalized plaster models [7,8].
A number of factors contribute to late incisor crowding. The eruption of the lower third molars is regarded as the most important etiologic factor, followed by others such as tooth size, dental arch shape, retroclination of the lower incisors, skeletal and soft tissue growth changes, mesial movement of the posterior teeth, mandibular arch length and width, jaw-to-size ratio, mandibular growth pattern, gender, forces from periodontal fibers, and natural aging [9][10][11][12]. Niedzielska et al. concluded that inadequate retromolar space exacerbates malocclusion and dental crowding of lower anterior teeth, which is produced by the eruption of the third molar, indicating the possible significance of removing the third molars [13].
Lindauer et al. concluded that the mandibular molars are expected to cause dental crowding by American orthodontists and oral and maxillofacial surgeons, and they recommended their removal [14]. According to a study by Husain et al. utilizing CBCT, there was a positive link between the crowding of the mandibular incisors and third molars, indicating that third molars are one of the etiological causes for crowding, if not the sole one [15]. On the other hand, Sidlauskas and Trakiniene evaluated 91 subjects with an average age of 21 years. Their study assessed crowding by comparing the mesiodistal widths of the individuals' teeth to the length of the corresponding segment of the mandibular dental arch [16]. The authors did not report significant differences in mandibular dental arch crowding in erupted, unerupted, and agenesis of third molar groups. They concluded that third molars and late lower dental arch crowding are not related [16]. Harradine et al. reported similar results in orthodontic treatment subjects; in a randomized controlled study, they investigated the influence of third molar extraction on the development of crowding in the anterior mandibular segment. The results reveal a negligible difference between the groups (extracted versus nonextracted group). Therefore, they concluded that extracting third molars to avoid or minimize late incisor crowding was not justifiable [11].
Even though a recently published systematic review reported that only 6 studies were selected in the quantitative synthesis, none of these studies used CBCT to evaluate such 3D problem [17]. Thus, there is a great inconsistency in studies regarding the relationship betweenbilateral impacted mandibular third molars (IM3M) and other dental arch parameters like anterior dental arch crowding. Using a more reliable diagnostic tool like 3D CBCT will add a well-designed study with comprehensive three-dimensional measurements to the existing literature. Therefore, this study aimed to three-dimensionally evaluate the relationship between the degree of bilateral IM3M angulation and the mandibular dental arch parameters in normal skeletal and dental malocclusion patients.

Study design and participants
This study was designed as a retrospective cross-sectional comparative study that was carried out at the Hospital of Stomatology, Central South University, China. Patients must consent to participate in any trial and approve the use of their data according to the institution's policy, which includes a thorough description of the procedure's advantages and risks. This study was approved by the Ethical and Clinical Scientific Research Committee at the Hospital of Stomatology, Central South University, China (LYF2022130).
This study included patients undergoing cone-beam computed tomography in the Second Xiangya Hospital of Central South University from 2019 to 2021. The inclusion criteria included the following: (1) age 20-30 years old; (2) skeletal class I according to the Chinese norms; ANB = 2.7° ± 2.0° [18] and dental (canines/molars) class I relationship; (3) complete permanent dentition; (4) lower third molar with completely formed roots; (5) reported healthy periodontium based on the recorded clinical records; (6) high-quality CBCT volumetric data. While the exclusion criteria included: (1) missing or extra teeth; (2) abnormal tooth size and morphology; (3) previous orthodontic or surgical treatment; (4) incompletely formed roots, unilateral impacted or erupted M3M; (5) interproximal caries and dental restoration, crown, and bridge; (6) noticeable alveolar bone loss; (7) cleft lip and/ or palate. The control group cases were characterized by fully formed and erupted bilateral M3M in normal or near the normal eruption, buccolingual angulations less than 12°, and mesiodistal angulation less than 10°.

Study sample size
G*power 3.0.10 software was used to determine the sample size with an alpha value of 0.05 and a power of 95% based on the study conducted by Hasegawa et al. [19], who reported Little's index of irregularity of 1.66 ± 0.83 and 4.08 ± 1.61 mm in the normal and crowded subjects in their study aimed to ascertain whether the lower third molars can affect anterior crowding and/or the inclination of teeth in the lower lateral dental arch segments. Power analysis showed a minimum sample of 18 subjects is to be included. However, the sample size was increased to a minimum of 20 subjects for each study group.
One hundred twenty young adult patients with welldocumented clinical and radiographic data fulfilled the selection criteria. The participants were divided into study groups (N = 100): who have bilateral IM3M, divided into three sub-groups according to the buccolingual inclination of the IM3M; group A, < 12° on the center of the ridge (N = 30), group B, (12-24°) off-center of the ridge (N = 40), and group C, > 24° off-center of the ridge (N = 30). The angle of the IM3M was measured buccally or lingually from the line bisecting the first and second molar in axial and coronal slices. The angle was considered positive value when the crowns of IM3M were located lingual to the root and negative value when the crown was buccal to the root (Fig. 1B, C). The study group was also divided into two sub-groups according to IM3M mesiodistal angulation ( Fig. 1A): group 1 (MD° 10-45°) (N = 36); group 2 (MD° > 45°) (N = 64). The control group (N = 20) included participants with bilateral eruption (E) M3M with buccolingual inclination less than 12° and mesiodistal angulations less than 10° in normal eruption [20,21].

Three-dimensional imaging
The following parameters were used for all CBCT imaging on an i-CAT machine (Imaging Sciences International Inc., Hatfield, PA, USA): voxel size, 0.3 mm; field of view (FOV), 16.0 × 13.0 cm; voltage, 120 kVp; filament current: 18.54 mAs; and total scan time, 8.9 s. Patients were told not to swallow while being scanned, and their heads were held in a natural head position guided by the laser guide with their teeth with maximal teeth intercuspation, the horizontal plane (HP) parallel to the ground. Digital Imaging and Communications in Medicine (DICOM) files were acquired and imported into Invivo Anatomage version 6 software (Anatomage, San Diego, CA, USA) for 3D analysis.

Outcomes assessment
The coordinate system's orientation is defined based on the skeletal midline points of the nasion (N), anterior nasal spine (ANS), and sella (S) while the horizontal coordinate was based on the right orbitale (Or) point and the two porion (Pr) points. Then, the three-dimensional landmarks were digitally digitized on the 3D volume and precisely located on the 3D slice locator. The skeletal reference lines and measurements are presented in Table 1. Table 2 shows the threedimensional measurements of angulations of impacted (I) and erupted (E) mandibular third molars (M3M) and dental arch parameters. Angulations of the third molars [22] and dental arch parameters [7] and inclination of anterior teeth [23] used in this study are presented in Figs. 1 and 2. After grouping the study group into three sub-groups (GA, GB, and GC) according to the IM3M buccolingual inclination, the means of dental arch anteroposterior and transverse parameters were compared with those in the control group. All parameters were statistically analyzed to determine the relationship between buccolingual and mesiodistal angulations of impacted and erupted M3M with the anteroposterior and transverse arch parameters.

Statistical analysis
Statistical analysis was performed using SPSS 26.0 software (IBM Corp., Armonk, NY, USA). Continuous variables are expressed as a number of observations, mean, and standard deviation. Categorical and discrete variables were presented by frequency and percentage. The Shapiro-Wilk test was used to test the normal distribution. The means of anteroposterior and transfer arch parameters were compared in both buccolingual M3M and mesiodistal M3M groups using oneway analysis of variance (ANOVA) followed by Tukey's post hoc test to compare the mean values between the groups. Pearson's correlation test was used to confirm the correlation between IM3M buccolingual and mesiodistal angulations and the anteroposterior and transverse dental arch parameters. Intra-and inter-class correlations were calculated to assess the reliability and reproducibility of the parameters. The P-value was set at 0.05 for significant differences.

Results
Both intra-and inter-observer reliability were excellent; detailed data are presented in supplementary material 1. The demographic data and descriptive statistics are presented in Table 3.
Regarding the M3M buccolingual angulations and anteroposterior parameters, there was a highly significant difference between the M3M BL° angulation and anterior teeth inclination (P < 0.001), arch length (P < 0.01), and inter 2 nd MW (P < 0.001) as shown in Table 4. The Fig. 1 The three-dimensional measurement of the mandibular third molar angulation and the mandibular incisor inclination. A The mesiodistal angle of the impacted or erupted third molar (M3M) was determined by measuring the angle between the long axis of the third molar and the vertical axis passing through the erupted second molar. B The buccolingual angulation of horizontally positioned M3M was measured buccally or lingually from the axis bisecting the first and second molars in an axial CBCT slice. C The buccolingual angulation of more vertically M3M was measured with respect to the bisecting line through the second molar. D The mandibular incisor inclination was measured in relation to the mandibular plane as observed in the sagittal view inter-group comparison revealed a significant difference in anterior teeth inclination between groups A, B, C, and D. Specifically, the inclination angle increased by 7.2° in group C compared to group A (P < 0.001). Additionally, the inclination angle in group D was found to increase by 5.1° in relation to group A (P < 0.05). Similarly, group C exhibited an increase of 3.8° in anterior teeth inclination compared to group B (P < 0.05). However, no significant difference was found when groups B and C compared with group D and when group A compared with B (P > 0.05).
Regarding the arch length, statistically significant difference was found in arch length between group A and D (P < 0.01), group B and D (P < 0.01), and group C and D (P < 0.05).
For the M3M buccolingual angulation and transverse parameters, the difference in the inter 2 nd MW was statistically significant between group A and B (P < 0.01), and group A and C (P < 0.001) as shown in Table 4.
The results of the M3M mesiodistal angulation and dental arch parameters, within group comparison, have shown a statistically significant difference in anterior teeth crowding and arch length measurement. Intergroup comparison demonstrated a statistically significant difference in anterior teeth crowding between group 2 and 3, with an increase of 0.93 mm in group 2 (P < 0.001). Additionally, there were significant differences in arch length between group 1 and 3, with an increase of 1.9 mm in group 1 (P < 0.001), and between group 2 and 3, with an increase of 2.42 mm in group 2 (P < 0.001). This suggests that group 1 and 2 had greater arch length than group 3. However, there is no significant difference between M3M MD° and transverse arch parameters ( Table 5).
The correlation between IM3M BL° and dental arch parameters was calculated and presented in Table 6. Significant positive correlation was found between IM3M Mesiodistal angle MD°The sagittal CBCT slice was used to calculate the mesiodistal angle of the impacted or erupted M3M by measuring the long axis of the third molar relative to the vertical axis through the erupted second molar (Fig. 1 A) Buccolingual angulation BL°The buccolingual BL angulation was measured as previously described by [22]. Axial CBCT slices were used to measure the buccolingual angulation of third molars in a more horizontal position (− 20° to 45°, or 136° to 180°). The buccolingual angulation was measured buccally or lingually from the axis bisecting the first and second molars in an axial CBCT slice. The angulation of IM3M was considered buccally negative value ( −) when the crown located buccal to the root, and lingually when the crown located lingual to when the crown located buccal to the root and given positive value ( +) (Fig. 1B). The coronal CBCT slices were used for more vertically angulated teeth, and buccolingual angulation was measured with respect to the bisecting line through the second molar (from the fossa through the middle of the pulp chamber). The buccal angulation of IM3M was given negative value ( −), and the lingual angulation was given positive value ( +) (Fig. 1C) Anterior teeth inclination AI The measurement of the inclination of the anterior mandibular teeth was conducted in relation to the mandibular plane, and this was also observed from a sagittal plane. Subsequently, the angle between the long axis of each mandibular anterior tooth and a vertical reference line, which was perpendicular to the horizontal reference line, was determined. [21] (Fig. 1D) Tooth size MDW The mesiodistal width which resembles to the maximum distance across the anatomic contact point of mandibular teeth ( Fig. 2A) Segment 1 S1 The distance from distal surface of the right second molar to distal surface of right canine Segment 2 S2 The distance from distal surface of canine to mesial surface of right central incisor The anterior crowding was calculated as the differences between the sum of the two anterior segments (S2 + S3) and the sum of tooth size from right to left canines Posterior dental crowding PDC The posterior arch crowding was calculated as the differences between the right and left posterior segments, and the tooth size parameters Overall arch crowding OAC The overall arch crowding was measured as the sum of anterior and posterior dental crowding BL° and anterior teeth inclination (P < 0.05), which means that the increase in the degree of IMEM angulation lingually is associated with increasing of degree of anterior teeth labial inclination. However, significant negative correlation was found between inter 1 st MW and inter 2 nd MW (P < 0.05 and P < 0.01, respectively). For correlation between IM3M MD° and dental arch parameters, significant positive correlation was found between IM3M MD° and anterior teeth crowding (P < 0.01), arch length (P < 0.01), and inter 2 nd MW (P < 0.05). It means that the increase in the degree of IM3M mesiodistal angulation is associated with increasing in anterior teeth crowding, arch length, and inter 2 nd MW as shown in Table 6.

Discussion
Crowding in the lower anterior teeth is among the most common malocclusions that need orthodontic treatment since it affects an individual's esthetics and oral health. However, identifying the etiological factors that cause crowding and relapse in this area following orthodontic treatment poses a significant challenge to orthodontists [10,20,24]. It is still unclear if the lower third molars have a role in these issues. Studies examining the association between the lower third molars and the different dental arch parameters using three-dimensional analyses are still lacking. As a result, this study aims to use a three-dimensional analysis to assess Fig. 2 The dental arch measurements. A The right side represents segment (S1) from distal surface of second molar to distal surface of canine, the anterior segment (S2) from distal surface of canine to mesial surface of central incisor that were calculated bilaterally. The left side represents tooth size measurements by measuring the maxi-mum mesiodistal width of each tooth. B The distance from the midpoint of the symphysis between the mandibular central incisors to the line that connect the disto-buccal cusp tips of the right and left second molars. C The inter-canines, premolars, and molar width; the distance from buccal cusps of the teeth on right side to those on left side the relationship between the different angulations of the impacted third molars (buccal, lingual, mesial, and distal) and the anteroposterior and transverse arch parameters (crowding, arch length, arch width) in patients with skeletal and dental class I malocclusion.
Richardson et al. examined the relationship between the original crowding and the changes in crowding after 5 years in individuals with both bilaterally impacted and erupted M3M; they concluded that the individuals with bilaterally impacted M3M tend to have more crowding of early permanent dentition, both anteriorly and posteriorly [25]. On the other hand, Gökçe et al. [26] assessed the role of impacted third molar angulation on the severity of anterior crowding. At the dentoalveolar level, they concluded that there was no relationship between the third molar inclination and the occlusal plane and the level of anterior teeth crowding too.
Our study has examined the angulation of bilateral IM3M to analyze the relationship between the degree of that angulation and dental arch parameters. The present study found a statistically significant difference between IM3M MD° and anterior teeth crowding. Additionally, Pearson's correlation has supported that idea; a significant positive correlation between IM3M MD° and anterior crowding was noticed, which means that the increasing angulation of IM3M mesially increases lower anterior teeth crowding. These results confirm those reported in the previous studies [15,27] that found a significant relation between IM3M and lower anterior crowding. In a retrospective study utilizing CBCT imaging, Husain et al. [15] analyzed the correlation between mandibular third molars and mandibular incisor crowding; they confirm a significant positive correlation between both.
Similarly, Gopalasamy et al. [27] conducted a study evaluating 537 patients with lower anterior crowding and the presence of impacted third molars, with comparable results. They found a higher prevalence of lower anterior crowding among patients with impacted third molars. They concluded that third molars play a significant role in the development of crowding in the lower anterior region. However, the current study's results contradicted those of Zigante et al. [28], who investigated the relationship between the absence, presence, and dynamics of mandibular third molar development and the occurrence and amount of late mandibular incisor crowding. The authors concluded that the occurrence and amount of mandibular late incisor crowding are not significantly influenced by the presence of mandibular third molars or their development dynamics. Similarly, Sood et al. [29] reported comparable findings when they investigated the potential relationship between mandibular anterior crowding and various factors related to the third molar, such as its eruption level, angulation, and available eruption space. They also reported that there is no significant correlation between these third molar factors and mandibular anterior crowding.
The current study has observed a significant difference between IM3M buccolingual angulation and anterior teeth inclination, which means that the increase in IM3M angulation lingually increases anterior teeth labial inclination. At the same time, the angulation of IM3M lingually was significantly associated with decreasing in inter 2 nd MW. This could be interpreted as the reduction in 2 nd MW, maybe due to the reduced arch width in the examined samples; thus, the anterior teeth were proclined to compensate for the decreased arch width.
Furthermore, in the current study, a significant difference in arch length parameters between both IM3M BL° and MD° groups was found; the increasing degree of angulation mesially or lingually was associated with decreasing arch length. However, only a significant positive correlation was found between IM3M BL° and arch length. These results support the hypothesis that the impaction of M3M, consequently the crowding in anterior teeth, was related to an increase in tooth size [30,31]. This was very clear in our study, where the arch length was significantly decreased in the control (EM3M) group compared with the impacted (IM3M) groups. Finally, this study recorded a significant negative correlation between inter 1 st and 2 nd MW and IM3M ML°; this correlation was absent in the BL° groups. This supports previous studies that hypothesize that force excreted by IM3M may cause anterior crowding [15,27]. We expect that this force can also cause slight rotation of molars buccally.

Conclusion
The degree of buccolingual and mesiodistal angulation of the impacted mandibular third molars was related with mandibular dentoalveolar changes. Increased buccolingual angulation is generally associated with increased anterior teeth inclination and decreased 1 st and 2 nd inter-molar width. The increase in mesiodistal angulations was generally related with increased anterior teeth crowding and 2 nd inter-molar width.
Acknowledgements The authors would like to thank Prof. Feng Yun Zhi, Prof. Shen gao Huang, and Dr. Bushra Sufyan Almaqrami for their consultations and assistance in accomplishing this study.
Author contribution Conception and design of study: Ohood Haider, Xiao Li Wei.