Three-dimensional analysis of the positional relationship between the dentition and basal bone region in patients with skeletal Class I and Class II malocclusion with mandibular retrusion

Jun Wan; Xi Wen; Jing Geng; Yan Gu

doi:10.4041/kjod23.262

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Original Article

Korean J Orthod 2024; 54(3): 171-184 https://doi.org/10.4041/kjod23.262

First Published Date April 18, 2024, Publication Date May 25, 2024

Three-dimensional analysis of the positional relationship between the dentition and basal bone region in patients with skeletal Class I and Class II malocclusion with mandibular retrusion

Jun Wan , Xi Wen , Jing Geng , Yan Gu

Department of Orthodontics, Peking University School and Hospital of Stomatology, National Center of Stomatology, National Clinical Research Center for Oral Diseases, National Engineering Research Center of Oral Biomaterials and Digital Medical Devices, Beijing Key Laboratory of Digital Stomatology, NHC Key Laboratory of Digital Stomatology, NMPA Key Laboratory for Dental Materials, Beijing, PR China

Correspondence to:Yan Gu.
Professor, Department of Orthodontics, Peking University School and Hospital of Stomatology, No. 22 Zhongguancun South Avenue, Haidian District, Beijing 100081, PR China.
Tel +86-13651078552 e-mail guyan96@126.com

How to cite this article: Wan J, Wen X, Geng J, Gu Y. Three-dimensional analysis of the positional relationship between the dentition and basal bone region in patients with skeletal Class I and Class II malocclusion with mandibular retrusion. Korean J Orthod 2024;54(3):171-184. https://doi.org/10.4041/kjod23.262

Received: December 11, 2023; Revised: April 8, 2024; Accepted: April 16, 2024

Abstract

Objective: This study aimed to determine the maxillary and mandibular basal bone regions and explore the three-dimensional positional relationship between the dentition and basal bone regions in patients with skeletal Class I and Class II malocclusions with mandibular retrusion. Methods: Eighty patients (40 each with Class I and Class II malocclusion) were enrolled. Maxillary and mandibular basal bone regions were determined using cone-beam computed tomography images. To measure the relationship between the dentition and basal bone region, the root position and root inclination were calculated using the coordinates of specific fixed points by a computer program written in Python. Results: In the Class II group, the mandibular anterior teeth inclined more labially (P < 0.05), with their apices positioned closer to the external boundary. The apex of the maxillary anterior root was positioned closer to the external boundary in both groups. Considering the molar region, the maxillary first molars tended to be more lingually inclined in females (P = 0.037), whereas the mandibular first molars were significantly more labially inclined in the Class II group (P < 0.05). Conclusions: Mandibular anterior teeth in Class II malocclusion exhibit a compensatory labial inclination trend with the crown and apex relative to the basal bone region when mandibular retrusion occurs. Moreover, as the root apices of the maxillary anterior teeth are much closer to the labial side in Class I and Class II malocclusion, the range of movement at the root apex should be limited to avoid extensive labial movement.

Keywords: Cone-beam computed tomography, Class II, Tooth movement

INTRODUCTION

A harmonized relationship between the dentition and underlying basal bone is an important orthodontic treatment goal.¹^,² The stability of the boundary of the basal bone before and after orthodontic treatment is critical; thus, teeth moved outside the basal bone boundary during orthodontic treatment can cause severe periodontal and endodontic problems, such as dehiscence, fenestration,³ and severe root resorption.⁴ Therefore, investigating the relationship between the dentition and basal bone is necessary to provide guidelines for the safe movement of teeth during orthodontic treatments in clinical practice.

Although previous studies have investigated the relationship between teeth and basal bone, the definition of basal bone varies. Andrews and Andrews⁵ proposed the Will Andrews Larry Andrews (WALA) ridge as a band of soft tissue located superior to the mucogingival junction in plastic models. However, this method is not considered sufficiently accurate to reflect the boundary of the basal bone as soft tissue thickness and model accuracy may affect the spatial position.⁶ Hwang et al.⁷ investigated the basal alveolar bone by modifying the location 7 mm apical from the alveolar crest. Rees⁸ proposed the superior border of the basal bone to be vertically 8–10 mm away from the gingival margins. However, these positions more likely correspond with alveolar than basal bone, and confirming the stability of these points during orthodontic treatment is challenging.⁹

In 1925, Lundstrom¹⁰ defined the term “apical base” as the junction of the dentition and basal bones. With the advent of cone-beam computed tomography (CBCT),¹¹^,¹² researchers have sought to determine the basal bone using CBCT images. Son et al.¹ proposed a method for determining the basal bone at the root apex level. However, this method has certain limitations. It could only be employed for comparisons of the transverse width and arch form. In 2020, Crossley et al.¹³ proposed a new method to determine the actual maxillary and mandibular areas. This method not only defined a specific scope of the basal bone but also traced a clear boundary of the basal bone region for the maxilla and mandible, making it an ideal method to analyze the three-dimensional (3D) positional relationship between the dentition and basal bone.

Several studies have focused on comparing the shape and dimensions of the dental and basal arches in patients with different skeletal patterns. Braun et al.¹⁴ found the mandibular arch to be smaller in width and depth in participants with Class II than Class I malocclusions. Arriola-Guillén and Flores-Mir¹⁵ concluded that the maxillary and mandibular incisors had greater inclination values in Class II malocclusions. However, the 3D relationship between the dentition and basal bone region in patients with Class I and Class II malocclusion remains unclear.

Therefore, this study aimed to determine the maxillary and mandibular basal bone regions and explore the 3D positional relationship between the dentition and basal bone in participants with skeletal Class I and Class II malocclusions with mandibular retrusion.

MATERIALS AND METHODS

This study was approved by the Biomedical Ethics Committee of Peking University School and Hospital of Stomatology (PKUSSIRB-202166111). The CBCT records of patients who visited the Department of Orthodontics, Peking University School and Hospital of Stomatology between January 2018 and December 2022 were obtained. The requirement to obtain informed consent was waived. A priori power analysis was considered for this retrospective study. Based on the root inclination (RI), if the most negligible difference is 1°, each group should include a minimum of 17 participants for a significance level of 5% and a power of 80% using a two-sample t test. However, the calculation based on root position (RP) indicated a minimum of 20 participants for each group at an α = 0.05, power of 80%, and effect size of 0.85. Therefore, we decided to include a minimum of 20 participants per group. The sample size was calculated using G Power software (version 3.1.9.7; Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany).

The medical histories, examination records, and CBCT images of all the participants were collected. Cephalograms were generated from the CBCT images to analyze the skeletal characteristics using Dolphin 3D Imaging software (version 11.8; Dolphin Imaging and Management Solutions, Chatsworth, CA, USA). Eighty participants aged 18–35 years were recruited. The skeletal Class II group included 20 males (mean age, 22.98 ± 5.31 years) and 20 females (mean age, 22.93 ± 4.07 years). The skeletal Class I group also included 20 males (mean age, 22.37 ± 2.51 years) and 20 females (mean age, 22.69 ± 3.34 years). The inclusion criteria for the Class II group were patients with an A point-nasion-B point angle (ANB) > 4°, sella-nasion-A point angle (SNA) > 78° and < 84°, sella-nasion-B point angle (SNB) < 76°, and Class II molar and canine relationships. Those with ANB between 0 °and 4°, SNA > 78° and < 84°, and SNB > 76° and < 82°, and Class I molar and canine relationships were classified in the Class I group. All the patients had angle between the sella-nasion and mandibular plane (MP-SN) between 27° and 37°. Additional inclusion criteria for the two groups were as follows: (1) Mongolian ethnicity, (2) aged ≥ 18 years, (3) complete permanent dentition (excluding third molars), (4) minor arch length discrepancy for both arches (spacing or crowding ≤ 3 mm). The exclusion criteria were as follows: (1) dentition with prosthetic crowns, (2) severe periodontitis, (3) history of orthodontic or orthognathic treatment, (4) cleft lip or palate, and (5) temporomandibular joint disease or other systemic diseases. Demographic information is shown in Table 1.

Table 1 . Demographic data of the participants in different groups

Measurement	Male (n = 40)			Female (n = 40)
Measurement	Class I (n = 20)	Class II (n = 20)	P value	Class I (n = 20)	Class II (n = 20)	P value
Age (yr)	22.37 ± 2.51	22.98 ± 5.31	0.648	22.69 ± 3.34	22.93 ± 4.07	0.835
SNA (°)	81.60 ± 2.74	83.02 ± 2.69	0.472	82.18 ± 2.47	82.34 ± 2.61	0.893
SNB (°)	79.15 ± 2.63	75.76 ± 2.56	< 0.001^{^***}	79.56 ± 2.76	74.88 ± 2.30	< 0.001^{^***}
ANB (°)	2.58 ± 0.93	7.30 ± 1.24	< 0.001^{^***}	2.61 ± 1.18	7.49 ± 1.00	< 0.001^{^***}
MP-SN (°)	32.01 ± 2.42	33.12 ± 2.80	0.542	32.47 ± 3.55	32.42 ± 2.69	0.985
Overjet (mm)	3.59 ± 1.16	6.30 ± 1.61	< 0.001^{^***}	3.90 ± 1.05	6.25 ± 1.63	< 0.001^{^***}

Values are presented as mean ± standard deviation.

SNA, sella-nasion-A point angle; SNB, sella-nasion-B point angle; ANB, A point-nasion-B point angle; MP-SN, angle between the sella-nasion and mandibular plane.

***P < 0.001.

Cone-beam computed tomography

All CBCT data were acquired using the same device (NewTom AG, Marburg, Germany) set: field of view, 15 × 15 cm; 110 kV; 2.81 mA; 3.6 seconds; 0.3 mm of voxel size. The CBCT images were imported into the Dolphin 3D imaging software for reconstruction and measurements.

Head reorientation

For the maxillary basal bone measurements, the axial plane was defined as the plane coinciding with the palatal plane and the anterior nasal spine (ANS) point and the center of the greater palatine foramen on the right and left sides. The midsagittal plane was perpendicular to the axial plane and passed through the ANS and basion (Ba) points. The coronal plane was perpendicular to these two planes and passed through the ANS (Figure 1A). For the mandibular basal bone measurements, the axial plane was defined as the plane coinciding with the mandibular plane by the gnathion and gonion points on the right and left sides. The coronal plane was perpendicular to the axial plane and passed through the superior most point of the coronoid process. The midsagittal plane was perpendicular to these two planes (Figure 1B).

Figure 1. Head reorientation. A, Head reorientation for maxillary basal bone measurements. B, Head reorientation for mandibular basal bone measurements.

Basal bone measurements

For the maxillary basal bone region, the axial plane was moved downward to the level of the mesiobuccal root apex of the right maxillary first molar, and the posterior most aspect of the right and left maxillary tuberosities was defined as the posterior limit. For the mandibular basal bone region, the axial plane was moved to the superior border of the right mental foramen. The posterior limit was defined as the coronal plane passing through the superior most point of the proper coronoid process. To determine the threshold number of the basal bone boundary points, 20 samples were selected and the maxillary and mandibular basal bones were traced using 90 points (the maximum number that could be uniformly distributed on the boundary). The area was denoted as S90. Using the Bootstrap sampling method, we randomly selected from 89 to 30 boundary marker points, with each number being randomly selected 1,000 times. The average areas were calculated and denoted as S89, S88, S87... S30. The number of boundary markers was selected such that the area coincided with 99.9% of the S90 values. The results revealed that a threshold number of 64 and 50 for the maxillary and mandibular basal bone region, respectively (Figure 2).

Figure 2. Bootstrap sampling method for determining the number of basal bone region boundary points. A, Threshold value of the maxillary basal area is 64. B, Threshold value of the mandibular basal region is 50.

In the axial section, the “Landmark” tool was used to define the basal bone boundary points. A total of 34 and 30 external and internal points, respectively were marked on the maxillary basal bone region. For the mandibular basal bone boundary, we used 28 external and 22 internal points. The basal bone area was calculated based on the coordinates of the boundary points. The “2D Path” tool was used to measure the midline length. The midline width and depth were measured using the “2D line” tool (Figure 3).

Figure 3. Maxillary and mandibular basal bone region and root position measurements. ra’ point, the projection points of the root apex to the basal bone plane. A, Maxillary basal bone region comprises 34 external and 30 internal boundary points. B, Mandibular basal bone region comprises 28 external and 22 internal boundary points.
DE, the distance from the ra’ point to the external boundary; DI, the distance from the ra’ point to the internal boundary.

Root position measurements

The 3D coordinates of the root apex point (ra point) were recorded for all 28 teeth. For multi-root teeth, the mean coordinates of each root apex were considered the landmark points. To obtain the RP, we converted the 3D coordinates of the 28 ra points by projecting onto the basal bone plane. The 2D coordinate values were marked as ra’ points. After projection, we calculated the distance from the ra’ point to the external boundary (DE) and internal boundary (DI) of the basal bone region (Figure 3). To determine the relative position of each tooth, we calculated the Ratio of DE to DI. Owing to the asymmetric range of the Ratio values, the Ratio was logarithmically transformed to facilitate comparison (referred to as the Log Ratio).

Root inclination measurements

RI was defined as the angle between the root axis vector and basal bone plane (Figure 4). The value of the root axis vector was obtained from the ra point to the root center point (rc point). The 3D coordinates of the midpoint of the cemento-enamel junction (single-root teeth) and root furcation (multi-root teeth) were recorded as the rc point. We calculated the RI using the coordinates of the root axis vector and basal bone boundary. All definitions of the landmarks and variables are listed in Table 2.

Figure 4. Measurements of the root inclination: the angle between the root axis vector and basal bone plane. A, Measurements of the root inclination for maxillary dentitions. B, Measurements of the root inclination for mandibular dentitions. The value of the root axis vector is obtained from the ra point to the rc point.
ra point, root apex point; rc point, root center point, the cemento-enamel junction for single-root teeth or the root furcation for multi-root teeth.

Table 2 . Definitions of the landmarks and variables of root inclination and root position for the dentition relative to the basal bone region

Landmark/variable	Definition
ra point	Root apex point, the most apical point of teeth
ra’ point	The projection point of the ra point to the basal bone plane
rc point	Root center point, the cemento-enamel junction for single-root teeth or the root furcation for multi-root teeth
Root axis vector	The value of the root axis vector was obtained from ra point to rc point
Root inclination
Single-root teeth	The angle between the root axis vector and basal bone plane. The value of the root axis vector was obtained from the ra point to the cemento-enamel junction
Multi-root teeth	The angle between the root axis vector and basal bone plane. The value of the root axis vector was obtained from the average value of ra points to the root furcation
Root position
DE	Distances from ra’ point to the external boundary of basal bone region
DI	Distances from ra’ point to the internal boundary of basal bone region
Ratio	DE/DI, indicates the relative root position of each tooth
Log Ratio	The value of Ratio after logarithmically transformation. The range of Log Ratio is symmetric, and the midpoint is 0. If the value of Log Ratio was positive, the root apex was closer to the inner boundary of the basal bone. If the value of Log Ratio was negative, the root apex was closer to the external boundary of the basal bone

Statistical analysis

To evaluate intra-examiner reliability, 20 patients were randomly selected by two investigators to measure the landmarks at 1-month intervals. The intraclass correlation coefficient was acceptable (Intraclass Correlation Coefficient (ICCs) > 0.90, P < 0.05). The Kolmogorov–Smirnov test was used to examine the normality of the outcome data. The results revealed all the variables to have a normal distribution. In each group, descriptive statistics are presented as mean ± standard deviation for the basal bone measurement, RP, and RI. Equivalence tests indicated no differences in the RI, DE, DI, Ratio (DE/DI), or Log Ratio between the left and right teeth. Thus, similar to the methodology employed in a previous study,¹⁶ we combined the left and right data according to the tooth position. An independent t test was used to determine the differences between the groups. Differences were considered statistically significant at P < 0.05. Pearson’s correlation analysis was used to evaluate the possible correlations between each group’s RI and RP. All the analyses were performed using Python (version 3.9.7; Python Software Foundation, Wilmington, DE, USA).

RESULTS

Basal bone measurements

Males had a greater basal bone area, longer midline length, and deeper midline depth than females in both the Class I and II groups for both jaws, while all the mandibular basal bone measurements demonstrated significant differences (P < 0.01; Table 3). When comparing the basal bone measurements between the Class I and Class II groups, the basal bone area and midline width revealed no significant differences for either jaw type. The midline length and depth were larger in the Class II group in the maxillary basal bone; moreover, significant differences were observed in females in the Class II group (P < 0.01). Conversely, the mandibular midline length and depth in the Class II group were significantly smaller in both sexes (P < 0.01; Table 4).

Table 3 . Comparison of the basal bone measurements between sexes in the Class I and Class II groups

Position	Measurement	Class I (n = 40)			Class II (n = 40)
Position	Measurement	Male (n = 20)	Female (n = 20)	P value	Male (n = 20)	Female (n = 20)	P value
Maxilla	Basal area (mm²)	1,577.51 ± 185.79	1,461.74 ± 372.02	0.221	1,523.53 ± 158.78	1,404.43 ± 125.77	0.012^{^*}
	Midline length (mm)	109.36 ± 6.38	103.74 ± 6.13	0.007^{^**}	111.52 ± 7.27	107.89 ± 4.78	0.070
	Midline width (mm)	49.38 ± 3.11	47.90 ± 3.20	0.147	48.64 ± 2.26	48.94 ± 2.66	0.703
	Midline depth (mm)	40.43 ± 3.37	38.16 ± 2.50	0.020^{^*}	41.91 ± 3.25	40.02 ± 2.50	0.046^{^*}
Mandible	Basal area (mm²)	1,797.58 ± 220.16	1,626.14 ± 174.79	0.010^{^*}	1,689.36 ± 201.40	1,549.40 ± 157.03	0.019^{^*}
	Midline length (mm)	130.79 ± 6.53	123.58 ± 8.10	0.004^{^**}	123.94 ± 7.35	117.74 ± 7.63	0.013^{^*}
	Midline width (mm)	83.11 ± 5.30	76.94 ± 3.82	< 0.001^{^***}	79.83 ± 4.92	76.33 ± 3.75	0.016^{^*}
	Midline depth (mm)	47.39 ± 2.43	45.28 ± 3.78	0.042^{^*}	44.15 ± 3.06	41.55 ± 3.69	0.020^{^*}

Values are presented as mean ± standard deviation.

*P < 0.05, **P < 0.01, ***P < 0.001.

Table 4 . Comparison of the basal bone measurements in the Class I and Class II groups

Position	Measurement	Male			Female
Position	Measurement	Class I (n = 20)	Class II (n = 20)	P value	Class I (n = 20)	Class II (n = 20)	P value
Maxilla	Basal area (mm²)	1,577.51 ± 185.79	1,523.53 ± 158.78	0.330	1,461.74 ± 372.02	1,404.43 ± 125.77	0.518
	Midline length (mm)	109.36 ± 6.38	111.52 ± 7.27	0.325	103.74 ± 6.13	107.89 ± 4.78	0.022^{^*}
	Midline width (mm)	49.38 ± 3.11	48.64 ± 2.26	0.395	47.90 ± 3.20	48.94 ± 2.66	0.271
	Midline depth (mm)	40.43 ± 3.37	41.91 ± 3.25	0.167	38.16 ± 2.50	40.02 ± 2.50	0.024^{^*}
Mandible	Basal area (mm²)	1,797.58 ± 220.16	1,689.36 ± 201.40	0.113	1,626.14 ± 174.79	1,549.40 ± 157.03	0.152
	Midline length (mm)	130.79 ± 6.53	123.94 ± 7.35	0.004^{^**}	123.58 ± 8.10	117.74 ± 7.63	0.024^{^*}
	Midline width (mm)	83.11 ± 5.30	79.83 ± 4.92	0.050	76.94 ± 3.82	76.33 ± 3.75	0.617
	Midline depth (mm)	47.39 ± 2.43	44.15 ± 3.06	0.001^{^**}	45.28 ± 3.78	41.55 ± 3.69	0.003^{^**}

Values are presented as mean ± standard deviation.

*P < 0.05, **P < 0.01.

Root inclination measurements

Table 5 and Figure 5 show the RI comparison between the Class I and Class II groups. Larger angles indicate crown-labial inclination. In the anterior region, the maxillary RI values demonstrated no significant differences between the two groups. The angle of the mandibular anterior teeth in the Class II group was significantly larger (P < 0.05), indicating that the mandibular anterior teeth in the Class II group were inclined more labially than those in the Class I group.

Figure 5. Means and standard deviations of the root inclination between the dentition and basal bone plane in the Class I and Class II groups. A, Root inclination for maxillary dentitions. B, Root inclination for mandibular dentitions.
1, central incisor; 2, lateral incisors; 3, canine; 4, first premolar; 5, second premolars; 6, first molar; 7, second molar.
*P < 0.05, **P < 0.01, ***P < 0.001, unpaired t tests.

Table 5 . Descriptive statistics of root inclination for dentition relative to basal bone in the Class I and Class II groups along with the results of significance testing

Position	Region	Teeth No.	Male			Female
			Class I (n = 20)	Class II (n = 20)	P value	Class I (n = 20)	Class II (n = 20)	P value
			Mean ± SD	Mean ± SD	P value	Mean ± SD	Mean ± SD	P value
Maxilla	Anterior region (°)	1	115.30 ± 6.47	112.29 ± 6.09	0.137	113.14 ± 7.18	112.50 ± 7.43	0.781
		2	113.28 ± 6.78	109.67 ± 6.57	0.095	113.86 ± 7.44	111.84 ± 6.39	0.363
		3	105.48 ± 6.81	101.68 ± 4.89	0.050	104.78 ± 7.54	102.40 ± 5.45	0.260
	Premolar region (°)	4	85.92 ± 1.63	85.74 ± 2.40	0.780	85.34 ± 2.49	85.66 ± 2.25	0.670
		5	85.02 ± 3.11	85.26 ± 2.70	0.798	84.33 ± 3.44	83.59 ± 3.23	0.488
	Molar region (°)	6	83.15 ± 3.25	80.72 ± 5.46	0.096	83.35 ± 3.91	79.70 ± 6.46	0.037^{^*}
		7	84.11 ± 3.27	83.69 ± 3.41	0.699	82.49 ± 2.81	82.54 ± 4.31	0.969
Mandible	Anterior region (°)	1	97.19 ± 4.41	106.06 ± 7.68	< 0.001^{^***}	97.51 ± 5.49	108.62 ± 7.14	< 0.001^{^***}
		2	95.85 ± 3.88	102.47 ± 6.39	< 0.001^{^***}	98.85 ± 6.23	106.97 ± 8.13	0.001^{^**}
		3	94.61 ± 3.37	98.10 ± 5.25	0.017^{^*}	95.42 ± 3.03	101.25 ± 6.14	< 0.001^{^***}
	Premolar region (°)	4	86.34 ± 1.72	84.16 ± 2.88	0.006^{^**}	85.36 ± 2.68	84.92 ± 2.42	0.585
		5	83.70 ± 3.21	83.93 ± 4.18	0.849	83.25 ± 3.49	84.62 ± 3.36	0.217
	Molar region (°)	6	73.43 ± 4.56	77.02 ± 3.61	0.009^{^**}	71.69 ± 4.41	74.93 ± 4.67	0.030^{^*}
		7	67.39 ± 7.62	73.21 ± 6.22	0.012^{^*}	68.79 ± 5.54	71.33 ± 6.71	0.199

A larger angle indicates that the crowns of the teeth are more inclined toward the lingual (anterior teeth) or labial (posterior teeth) sides.

SD, standard deviation; 1, central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar; 7, second molar.

*P < 0.05, **P < 0.01, ***P < 0.001.

In the molar region, the angle of the maxillary first molars in the Class II female group was significantly smaller than that in the Class I group (P < 0.05), indicating that the maxillary first molars inclined more lingually in the female Class II group. Meanwhile, the inclination of the mandibular molars was greater than that of the Class I group, demonstrating a more labial inclination tendency. A significant difference was observed when comparing the mandibular first molars for both sexes and the mandibular second molars for males between the two groups (P < 0.05).

The x-axis represents the horizontal distribution of the dental arch and basal bone region in Figures 6 and 7, with the left dentition and basal bone region located on the positive half-axis and the right dentition and basal bone region on the negative half-axis. The y-axis represents the vertical distribution. Zero level refers to the basal bone level. The y-axis was defined as negative when the dentition was located below the basal bone plane. Otherwise, the results were considered positive. The lateral view reflects the labial-lingual inclination of the anterior teeth, whereas the frontal view reflects the buccolingual tilt of the posterior teeth. Lateral views revealed that the mandibular anterior teeth (red, orange, and yellow lines) were more labially inclined in the Class II group in both sexes. Frontal views revealed that the mandibular first (blue lines) and second (purple lines) molars were more labially inclined in the Class II group.

Figure 6. Three-dimensional positional relationship between the dentition and underlying basal bone for the Class I and Class II groups in males. The x-axis represents the horizontal distribution, and y-axis represents the vertical distribution of the dental arch and the basal bone region. Red: central incisor; orange: lateral incisor; yellow: canine; green: first premolar; cyan: second premolar; blue: first molar; purple: second molar; grey plane: basal bone plane. A, Three-dimensional positional relationship for the maxilla. B, Three-dimensional positional relationship for the mandible.

Figure 7. Three-dimensional positional relationship between the dentition and underlying basal bone in the Class I and Class II groups in females. The x-axis represents the horizontal distribution, and y-axis represents the vertical distribution of the dental arch and basal bone region. Red: central incisor; orange: lateral incisor; yellow: canine; green: first premolar; cyan: second premolar; blue: first molar; purple: second molar; grey plane: basal bone plane. A, Three-dimensional positional relationship for the maxilla. B, Three-dimensional positional relationship for the mandible.

Root position measurements

The range of the Ratio value was not symmetrically distributed; therefore, we logarithmically calculated the Ratio value (Log Ratio). The range of Log Ratios was symmetric. If the Log Ratio was positive, the root apex was closer to the inner boundary of the basal bone. If the Log Ratio was negative, the root apex was closer to the external boundary of the basal bone.

Table 6 displays the descriptive statistics of the Log Ratios for each group. The roots of the maxillary anterior and premolar teeth were closer to the external boundary, whereas the apex of the maxillary molars was positioned more centrally relative to the basal bone boundary. This trend was observed in both the Class I and II groups, and no significant differences were observed between the two groups (Table 6 and Figure 8A). The apex of the mandibular incisors in the Class II group was positioned closer to the external boundary of the basal bone region than in the Class I group. Furthermore, although the apices of the mandibular canines, premolars, and first molars were located at the center of the basal bone, the mandibular second molars were positioned closer to the inner boundary in both groups (Table 6 and Figure 8B). In Figures 6 and 7, the vertical views visually reflect the position of the apex of the teeth relative to the basal bone region. The raw DE, DI, and Ratio data are presented in Supplementary Table 1.

Figure 8. Means and standard deviations of the Log Ratio (DE/DI) in the Class I and Class II groups. A, Log Ratio for maxillary dentitions. B, Log Ratio for mandibular dentitions.
1, central incisor; 2, lateral incisors; 3, canine; 4, first premolar; 5, second premolars; 6, first molar; 7, second molar.
*P < 0.05, unpaired t test.

Table 6 . Descriptive statistics of root position represented by Log Ratio for the dentition relative to the basal bone in the Class I and Class II groups along with the results of significance testing

Position	Region	Teeth No.	Male			Female
			Class I (n = 20)	Class II (n = 20)	P value	Class I (n = 20)	Class II (n = 20)	P value
			Mean ± SD	Mean ± SD	P value	Mean ± SD	Mean ± SD	P value
Maxilla	Anterior region (°)	1	–1.70 ± 0.90	–2.07 ± 1.09	0.246	–2.08 ± 0.91	–2.08 ± 0.86	0.986
		2	–1.02 ± 0.57	–1.39 ± 0.64	0.062	–1.26 ± 0.94	–1.24 ± 0.66	0.954
		3	–1.09 ± 0.50	–1.31 ± 0.64	0.218	–1.41 ± 0.71	–1.20 ± 0.51	0.284
	Premolar region (°)	4	–1.00 ± 0.27	–1.11 ± 0.26	0.200	–1.27 ± 0.55	–1.33 ± 0.62	0.754
		5	–0.57 ± 0.40	–0.75 ± 0.28	0.118	–0.72 ± 0.27	–0.83 ± 0.40	0.320
	Molar region (°)	6	–0.34 ± 0.24	–0.35 ± 0.20	0.886	–0.23 ± 0.27	–0.35 ± 0.30	0.183
		7	0.30 ± 0.26	0.17 ± 0.36	0.198	0.32 ± 0.37	0.18 ± 0.34	0.240
Mandible	Anterior region (°)	1	0.41 ± 0.67	–0.17 ± 1.39	0.103	0.60 ± 0.88	0.00 ± 0.82	0.032^{^*}
		2	0.36 ± 0.46	–0.00 ± 1.04	0.163	0.50 ± 0.47	0.13 ± 0.67	0.052
		3	–0.17 ± 0.37	–0.34 ± 0.35	0.152	–0.10 ± 0.28	–0.17 ± 0.32	0.414
	Premolar region (°)	4	–0.31 ± 0.34	–0.50 ± 0.30	0.079	–0.30 ± 0.37	–0.38 ± 0.28	0.470
		5	–0.07 ± 0.25	–0.27 ± 0.30	0.027^{^*}	–0.09 ± 0.39	–0.12 ± 0.25	0.780
	Molar region (°)	6	0.11 ± 0.25	0.05 ± 0.30	0.549	–0.03 ± 0.40	0.03 ± 0.26	0.616
		7	0.75 ± 0.40	0.71 ± 0.48	0.771	0.78 ± 0.52	0.98 ± 0.63	0.286

If the Log Ratio value was positive, the root apex was closer to the inner boundary of the basal bone. If the Log Ratio value was negative, the root apex was closer to the external boundary of the basal bone.

SD, standard deviation; 1, central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar; 7, second molar.

*P < 0.05.

To explore the relationship between RI and RP, Pearson correlation analysis was conducted between the RI angle and Log Ratio for each tooth. A strong positive correlation was observed in the anterior maxillary region (Table 7). Thus, more lingually inclined maxillary anterior teeth exhibited roots closer to the external boundary in each group.

Table 7 . Pearson correlations analysis between the root inclination and root position (represented by Log Ratio) for each tooth in different groups

Position	Region	Teeth No.	Class I		Class II
			Male (n = 20)	Female (n = 20)	Male (n = 20)	Female (n = 20)
			r	r	r	r
Maxilla	Anterior region (°)	1	0.581^{^**}	0.338	0.245	0.254
		2	0.706^{^***}	0.310	0.628^{^**}	0.233
		3	0.807^{^***}	0.471^{^*}	0.707^{^***}	0.569^{^**}
	Premolar region (°)	4	0.329	–0.017	–0.014	–0.275
		5	0.444^{^*}	0.508	–0.199	0.116
	Molar region (°)	6	–0.045	–0.541^{^*}	–0.183	–0.013
		7	0.422	0.364	–0.242	0.371
Mandible	Anterior region (°)	1	–0.122	–0.090	–0.352	–0.070
		2	–0.337	0.218	–0.368	–0.062
		3	0.132	0.135	–0.615^{^**}	0.120
	Premolar region (°)	4	0.057	0.541^{^*}	–0.220	0.463^{^*}
		5	–0.210	–0.452^{^*}	–0.062	–0.210
	Molar region (°)	6	–0.107	–0.280	–0.073	–0.522^{^*}
		7	0.033	–0.069	–0.293	–0.436

1, central incisor; 2, lateral incisor; 3, canine; 4, first premolar; 5, second premolar; 6, first molar; 7, second molar; r, Pearson correlation coefficient.

*P < 0.05, **P < 0.01, ***P < 0.001.

DISCUSSION

Tooth position in naturally occurring occlusions could elucidate the anatomic relationships between dentition and basal bone, which is worthy of evaluation.¹⁷ When investigating the positional relationship between the dentition and basal bone, it is crucial to define the vertical height of the basal bone. In our study, the maxillary and mandibular basal bone regions were both demonstrated at the apical level of the dentition. Located at the junction between the jawbone and dentition, the apical base possesses relatively stable characteristics and is closely related to the dentition.¹⁰

In the anterior region, the apex of the mandibular anterior teeth in the Class II group was located closer to the external boundary than that in the Class I group. Additionally, the mandibular anterior teeth in the Class II group were more labially inclined than those in the Class I group, indicating the crowns being closer to the labial side. The crown and apex positions relative to the basal bone region of the mandibular anterior teeth in the Class II group had the same tendency (labial location). Based on the comparison of the mandibular basal bone, the Class II group exhibited a shorter basal bone depth than the Class I group. We speculated the mandibular anterior dentition to have a compensatory trend of labial inclination during bodily movement in cases of mandibular retrusion. This finding is consistent with that of Kim et al.¹⁸ Longitudinal cephalometric radiographs were used to investigate the sagittal growth differences between the jaws and their effects on the changes in the occlusal relationships. Moreover, they found that when the speed of mandibular growth was slower than that of the maxilla, the mesial displacement of the mandibular dentition appeared to compensate for the growth difference. The anterior occlusal difference was adjusted by the mesial displacement and labial inclination of the mandibular incisors. However, the overjet of the anterior teeth in the Class II group was significantly greater than that in the Class I group, suggesting insufficient compensation for patients with Class II mandibular retrusion (Table 1).

In each group, the root apex of the maxillary anterior teeth was located closer to the external boundary of the maxillary basal bone. These results were consistent with the findings of Gracco et al.,¹⁹ who reported a greater thickness of the lingual alveolar bone in the apical region of the maxillary incisors. The Pearson correlation analysis also demonstrated a positive correlation for the maxillary anterior teeth (Table 7). This tendency indicates that the root apex can be displaced labially, with lingual inclination of the crown, owing to developmental or environmental factors.²⁰ Tian et al.²¹ also found that the movement of root apices can result in a change in the bone thickness of the apical region. Considering the application of this finding to clinical practice, the movement of root apices should be limited when retracting maxillary anterior teeth during orthodontic extraction treatments to avoid extensive labial movement, which may increase the risk of dehiscence and fenestration.²² Moreover, the movement of root apices can also affect the stability after treatment.¹

The buccolingual inclinations of the posterior teeth are critical when considering the establishment of ideal occlusion.²³ In our study, the maxillary first molars were more palatally positioned, while the mandibular molars were more buccally inclined in the Class II group. Our findings are consistent with those of previous studies. Hwang et al. ²⁴ and de Oliveira et al.²⁵ observed compensatory inclinations of the posterior teeth in the Class II groups. Class II malocclusions generally demonstrate a transverse dental discrepancy.²⁴ The lingual inclination of the maxillary molars in patients with Class II malocclusion might be considered a compensating factor of the transverse growth to maintain occlusal contact with a relatively distal mandible position.²⁶ This compensation can, in turn, limit the sagittal development of the mandible.²⁷ Our comparison of the mandibular basal bone measurements confirmed this assumption. The midline length and depth of the mandibular basal bone were shorter in the Class II group.

Basal bone measurements were more prominent in males than in females in both the skeletal Class I and Class II groups (Table 3). This finding was consistent with that of certain previous studies.⁷^,²⁸ The level of occlusal force may affect the morphology and size of the jaws. In general, males have greater occlusal forces than females owing to differences in the muscle strength, which may have contributed to the sex differences.²⁹ Arch forms vary among different ethnic groups.³⁰ Hasegawa et al.³¹ demonstrated variations in the arch forms between Mongolian and Japanese samples. Thus, we opted for a Mongolian sample considering the ethnic diversity.

Our study had certain limitations. Owing to the nature of the cross-sectional study, our study can only provide a method for determining the basal bone region and comparing the relationship between the dentition and basal bone region in different malocclusions. Further research on the positional change in the dentition relative to the basal bone region following different orthodontic treatments is warranted to validate our findings.

CONCLUSIONS

1. Mandibular anterior teeth in the Class II group demonstrated a labial compensatory trend both with the crown and apex relative to the basal bone region when mandibular retrusion occurs.

2. The root apex of the maxillary anterior teeth was much closer to the labial side in both the Class I and Class II groups. The range of movement of the root apex should be limited to avoid extensive labial movement when retracting the maxillary anterior teeth during extraction treatment.

3. Lingually inclined maxillary first molars and labially inclined mandibular molars were observed in the Class II groups.

AUTHOR CONTRIBUTIONS

Conceptualization: JW, YG. Data curation: JW. Formal analysis: JW. Funding acquisition: YG. Investigation: JW. Methodology: JW, XW. Software: JW, JG. Supervision: YG. Validation: JG. Visualization: YG. Writing–original draft: JW. Writing–review & editing: XW, YG.

CONFLICTS OF INTEREST

No potential conflict of interest relevant to this article was reported.

FUNDING

This work was supported by the National Natural Science Foundation of China (NSF81970979). Beijing Municipal Natural Science Foundation No. 7232217.

SUPPLEMENTARY MATERIAL

Supplementary data is available at https://doi.org/10.4041/kjod23.262.

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Article

Original Article

Korean J Orthod 2024; 54(3): 171-184 https://doi.org/10.4041/kjod23.262

First Published Date April 18, 2024, Publication Date May 25, 2024

Three-dimensional analysis of the positional relationship between the dentition and basal bone region in patients with skeletal Class I and Class II malocclusion with mandibular retrusion

Jun Wan , Xi Wen , Jing Geng , Yan Gu

Received: December 11, 2023; Revised: April 8, 2024; Accepted: April 16, 2024

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.