Inclination of Mandibular Molars and Alveolar Bone in Untreated Adults and Its Relationship with Facial Type

Abstract

To date, there is no solid agreement on the relationship between mandibular molars, mandibular alveolar bone, and vertical facial types. Therefore, we aim to assess the buccolingual inclination of mandibular first molars and respective alveolar bones and their relationship with different vertical skeletal patterns. The CBCT data from fifty-four untreated Caucasian adult patients (12 males and 42 females, 18–65 years old) were obtained from a private orthodontic practice. We measured the inclination of the tooth and alveolar bone of the right and left mandibular first molars using CBCT. From the two-dimensional lateral cephalometric radiographic images extracted from CBCT, we assessed FMA, SN-GoGn, and PFH:AFH. All subjects showed lingual inclinations of the mandibular molars and alveolar bones which were significantly correlated with each other. However, there was no significant correlation between the inclination of alveolar bone and vertical facial types. Our study supports the conclusion that a proper curve of Wilson is physiological and should be maintained during orthodontic treatment.

1. Introduction

George H. Wilson first described a curve that contacts the buccal and lingual cusps of the left and right molars viewed from the coronal section (curve of Wilson) [1]. Such curvature exists due to the lingual inclination of mandibular molars. Dempster conducted a study that further supported the lingual inclination of mandibular molars by inserting wires into the root canals of the posterior teeth of skulls [2]. More recently, Alkhatib and Chung studied cone-beam computed tomography (CBCT) images of untreated adults and reported the tendency of buccal inclination of maxillary first molars and lingual inclination in mandibular molars [3]. Yang and Chung studied CBCT images of untreated children and adults and compared their buccolingual inclinations of maxillary and mandibular first molars [4]. They found that both children and adults had lingually inclined mandibular molars and buccally inclined maxillary first molars. However, the adults showed a lesser degree of inclinations, and concluded that first molars, both maxillary and mandibular, become more upright with growth.

Several studies assessed the association between the molar inclination and vertical facial types. However, these studies were inconclusive. For example, Tsunori et al. measured the buccolingual inclinations of mandibular molars on dry skulls in different facial types and concluded that mandibular molars were significantly lingually inclined in the hypodivergent group [5]. Masumoto et al. reported no difference in the mandibular first molar inclinations and facial type [6]. Eraydin et al. used CBCT images in their study and found that the inclinations of mandibular molars in different facial types were similar [7].

Other studies investigated the relationship between mandibular alveolar bone inclination and facial types. Tsunori et al. concluded that the mandibular alveolar bone was significantly more lingually inclined in the hypodivergent group [5]. Wagner and Chung studied longitudinal transverse growth of the maxilla and mandible in girls aged 6 to 18 with different vertical facial types [8]. They found that the low mandibular plane angle in hypodivergent children had a wider skeletal maxillary and mandibular transverse dimension at age 6 and the trend continues until age 18. This difference in transverse growth pattern may have an effect on the final mandibular alveolar bone and tooth inclinations. Hwang et al. and Forster et al. found that the hyperdivergent group was associated with narrow mandibular arches [9,10]. By using CBCT scans, Ahn et al. evaluated the relationship between mandibular shape and the three-dimensional (3D) skeleton [11]. They found no significant effect of the vertical component of the skull on mandibular morphology.

To date, there are conflicting results in the literature on the relationship of the inclination of mandibular molars and mandibular alveolar bone, and different vertical facial types. The existing literature only compared either the inclination of mandibular molars or alveolar bone to the vertical skeletal pattern. In addition, some studies used dry skulls to investigate the relationship. In our study, we examined the buccolingual inclination of mandibular first molars and alveolar bones and compared their association with different vertical skeletal patterns. The null hypothesis is that the buccolingual inclination of mandibular first molars and alveolar bones is not related to vertical skeletal patterns.

2. Materials and Methods

Institutional review board approval (#829885) from the University of Pennsylvania was approved prior to collecting any CBCT information. CBCT scans of 54 untreated Caucasian adult patients (12 males and 42 females) between the ages of 18 and 65 were obtained from a private orthodontic practice with an I-CAT machine (Imaging Sciences International, Hatfield, PA, USA) in 0.3 mm voxel size. The inclusion criteria were: (1) no prior orthodontic treatment; (2) minimal dental wear; (3) no missing teeth other than third molars; and (4) less than 5 mm crowding per arch. The exclusion criteria were: (1) presences of remaining primary dentition; (2) posterior crossbite; (3) crowns or significant restorations on any first molars; (4) extensive dental restorations and wear; and (5) craniofacial deformities. The sample size was pre-determined based on the previous studies [3,4]. In addition, the sample size was calculated based on an alpha significance level of 0.05 and 80% power to detect an effect size (ρ) of 0.36 between measurements. The power analysis showed that at least 46 patients were needed.

Using Dolphin Imaging 3D software (version 10.5, Dolphin Imaging and Management Solutions, Chatsworth, CA, USA), each image was oriented so that the occlusal plane was parallel to the floor. To extract a two-dimensional (2D) lateral cephalogram, each scan was compressed from the right outermost portion of the patient’s head to the center of the left central incisor, as described by Habeeb et al. [12]. This 2D extracted lateral cephalogram was used to make vertical cephalometric measurements. The following measurements were taken and evaluated for each patient’s lateral cephalograms: FMA (FH to mandibular plane, in degrees), SN-GoGn (SN to GoGn, in degrees), and PFH:AFH (poster facial height to anterior facial height ratio):

• Porion (Po): the most superior point of the external auditory meatus.
• Orbitale (Or): the most inferior point of the orbital rim.
• Sella (S): the geometric center of the pituitary fossa located by visual inspection.
• Nasion (N): the most anterior point of the frontonasal suture.
• Gonion (Go): the mid-point between the best fit lines tangent to the posterior and inferior border of the mandible.
• Gnathion (Gn): the midpoint between the most anterior and inferior points of the symphysis.
• Menton (Me): the most inferior point on the mandibular symphysis.
• Frankfort horizontal (FH) plane: the line connecting the porion and orbitale.
• Mandibular plane: the line tangent to the lower border of mandible.
• SN: the line connecting the sella and nasion.
• GoGn: the line connecting the gonion and gnathion.
• Poster facial height to (PFH): S to Go* mm (*constructed Gonion).
• Anterior facial height (AFH): N to Me**mm (**Menton).
• Frankfort-mandibular plane angle (FMA): the angle formed by the intersection of the FH plane and the mandibular plane.
• SN-GoGn: the angle between a line through sella to nasion and a line through gonion and gnathion.

The axial section at the mandibular first molar was taken at the furcation. In this view, the anteroposterior and mesiolateral midpoints were determined. The sagittal section at the mandibular first molar was confirmed at the line through the midpoint of mesiodistal crown width and midpoint between mesial and distal roots at 1/3 the distance from apex. The coronal section obtained at 0.5 mm slice was to measure tooth and bone inclination. Separate left and right coronal sections were taken for higher accuracy. Tooth inclination was obtained by measuring the angle between the vertical line and a line made by connecting the midpoint of the buccal and lingual cusp tips and the midpoint of the buccolingual width at the level of the cementoenamel junction, as described by Alkhatib and Chung (Figure 1a,b) [3]. Alveolar bone inclination was also measured in the same 0.5 mm coronal section obtained to measure first molar inclinations. The angle was defined by the angle between the vertical line and a line connecting the midpoint of the alveolar crest and the midpoint of the buccolingual width at 1/3 of the distance from the inferior border of the mandible (Figure 2a,b). As with first molar inclination, left and right alveolar bone inclinations were measured in separate coronal sections for greater accuracy.

Fifteen subjects were randomly selected and all measurements were retaken following a 3-week interval by the same examiner (Y.L.). A paired t-test was used to determine the intra-examiner reproducibility. Correlation analysis was performed to determine the presence of significant differences between the original and repeated measurements. The mean, standard deviation, and range were obtained for each measurement. In addition, correlation and regression analyses were performed. The significance was determined at p < 0.05.

3. Results

The buccolingual inclinations of mandibular first molars and their alveolar bones are shown in

Table 1. The measurements of inclinations of lower first molars and their alveolar bones, and vertical cephalometric measurements.

	LR6	LL6	LR Bone	LL Bone	FMA	SN-GoGn	PFH:AFH
N	54	54	54	54	54	54	54
Mean	−14.0	−14.9	−14.9	−13.3	22.6	30.7	65.0
SD a	6.5	6.0	6.1	7.2	7.4	8.5	7.01
Min	−30.1	−29.5	−32.7	−33.4	1.8	6.9	52.8
Max	−2.3	−2.6	−0.6	−1.9	37.2	44.4	85

^a SD indicates standard deviation.

. No statistically significant differences were found between the measurements of male and female groups (p > 0.05). All of the subjects had lingual inclinations of the molars and alveolar bones.

The correlation tests between lower first molars, alveolar bone, and vertical cephalometric measurements were carried out (

Table 2. Correlation coefficient (r) among mandibular first molars, alveolar bones, and vertical cephalometric measurements.

	LR6	LL6	LR Bone	LL Bone	FMA	SN-GoGn	PFH:AFH
LR6	1
LL6	0.34 *	1
LR Bone	0.34 *	0.16	1
LL Bone	0.13	0.33 *	0.76 *	1
FMA	−0.16	−0.27 *	0.16	0.10	1
SN-GoGn	−0.12	−0.29 *	0.22	0.15	0.93 *	1
PFH:AFH	0.18	0.36 *	−0.15	−0.12	−0.91 *	−0.98 *	1

* represents statistically significant (p < 0.05).

). The inclinations of mandibular first molars and alveolar bones, and of molars and bones between left and right are closely correlated (p < 0.05). The lower right first molar and lower right bone inclinations were significantly related (p < 0.05), as with the lower left first molar and lower left bone inclinations (p < 0.05). The lower left first molar and FMA, SN-GoGn, and PFH:AFH were also significantly related (p < 0.05), but other cephalometric measurements showed no significant relations with the first molar and bone inclinations. Mandibular bone inclinations and vertical cephalometric measurements did not show significant relationships (p > 0.05).

The intra-examiner reliability test revealed no statistical difference between the original and repeated measurements. The correlation value was 0.92–0.99, suggesting a very strong correlation between the measurements at two different time points.

4. Discussion

With the use of 3D CBCT imaging, we can easily obtain a cross-section image of the teeth and alveolar bone. This advancement bypasses the need of dental casts or dry skulls and is clinically useful. As shown in our results, all subjects showed a lingual inclination of mandibular first molars, 14.0° and 14.9°, for right and left molars, respectively. This result agrees with Alkhatib and Chung [3], who found that mandibular first molars had an average of 12.60° of lingual inclination. It also agrees with Yang and Chung [4], who reported a mean of 13° lingual inclinations of each mandibular first molar in adults.

Dawson [13] opined on the anatomical and functional significance of the lingual inclination of mandibular molars. He observed that the buccal inclination of maxillary molars and lingual inclination of mandibular molars mimicked the inclination of the internal pterygoid muscles. As a result, he suggested that teeth could better resist the loading placed during mastication. In addition, the lingual inclination of mandibular molars enables the tongue to direct food to the occlusal surface without the interference of the lingual cusps. As described, the curve of Wilson is essential for anatomical stability as well as masticatory function.

There have been several studies on the relationship between vertical facial pattern and occlusal function. For example, Proctor et al. examined the relationship of the masseter muscle position relative to dentofacial form [14]. In hyperdivergent groups, the masseter muscle was attached more horizontally relative to the SN, FH plane and the palatal plane, implying that the vertical component of the masseter muscle was greater in the hypodivergent group, hence presenting a higher masticatory bite force in the low angle group. Ingervall et al. experimented on the effects of the facial growth by training masticatory muscles of long-faced children [15]. One year of masticatory training resulted in an increased bite force and higher masticatory muscle activity. The training also produced forward mandibular rotation, which resulted in decreased mandibular plane angle and increased posterior to anterior facial height. Braun et al. assessed the association between bite force and various cephalometric measurements [16]. They concluded that subjects with higher bite force had lower mandibular plane angles, higher posterior to anterior facial height ratios, and higher mandibular dentoalveolar heights.

In our study, we found a significant correlation between mandibular left first molar and facial type (p < 0.05). As the correlation coefficient was quite low, it may not be clinically significant. We also found there was no significant correlation between mandibular right first molar and facial type (p > 0.05). Our findings agree with Janson et al. [17], Ross et al. [18], Masumoto et al. [6], and Eraydin et al. [7], who supported no significant correlation between the buccolingual inclination of mandibular molars and vertical facial types. Our results do not support Tsunori et al. [5], who found the significantly lingually inclined mandibular molars in the hypodivergent group.

We found no significant correlation between the inclination of mandibular alveolar bone and vertical facial type (p > 0.05). Our findings agree with Ahn et al. [11], who reported that there was no significant correlation between mandibular bone morphology and facial types. Our findings disagree with Tsunori et al. [5] and Kohakura et al. [19], which examined dry skulls of male Asiatic Indians. Tsunori et al. [5] found more lingually inclined bone in the hypodivergent group and Kohakura et al. [19] reported increased buccal cortical bone thickness in the hypodivergent group.

In our study, no statistically significant differences were found between the male and female groups on all the measurements. Thus, we combined the male and female data with a total number of 54 subjects.

In the current literature, there are different philosophies regarding the curve of Wilson. Andrews [20] suggests that the goal of molar inclination is to have an optimally inclined occlusal surface that allows for proper occlusal function with the opposing teeth. Some straight-wire appliances have built-in torque that aims to upright the molars and level the curve of Wilson. In our study, we found a statistically significant correlation between lower molar inclination and alveolar bone inclination (p < 0.05). This finding further supports the claim by Dawson [13] that it is clinically important to maintain this natural tooth inclination in orthodontic treatment, as proper buccolingual inclination is physiological and relates to proper function.

5. Conclusions

The following conclusions can be made for this study:

• Mandibular first molars presented lingual inclination, with an average angle of 14.5°.
• Mandibular alveolar bone on first molar presented lingual inclination, with an average angle of 14.1°.
• Mandibular molar inclinations were significantly correlated to mandibular alveolar bone inclinations.
• There was no significant correlation between the inclination of alveolar bone and vertical facial type.
• The proper curve of Wilson is physiological and should be maintained during orthodontic treatment.