Abstract | | |
**Aim:** (1) To apply the quadrilateral analysis to adult male and female Chennai population with normal occlusion, (2) To compare the results to Chennai adult male and female with anterior openbite, (3) To evaluate the correlation of the quadrilateral variables and (4) To establish additional parameters to determine an openbite tendency. **Materials and Methods:** The study was carried out from the values taken from 120 pretreatment lateral cephalograms of the selected Chennai population and divided into two groups. Group A consists of 60 lateral cephalograms of 30 male and 30 female patients with balanced anteroposterior and vertical facial proportion and normal overjet and overbite relationship. Group B consists of 60 lateral cephalograms of 30 male and 30 female patients with anterior openbite and comparision done with 2 groups. Results in normal subjects the lower facial heights are equal. In anterior openbite subjects. The facial heights. The sagittal angle. The maxillary and mandibular sagittal ratios. Lower facial height and sagittal ratio is larger than normal. **Results:** statistical analysis performed with Version 23(SPSS) and Student's t test were done to describe the mean and standard deviation. To assess the relationship pearson correlation was used.The probability value of 0.05 is consdered as significant. **Conclusion:** The malformation of the craniofacial structure in anterior openbite subjects resides in the maxillomandibular complex. The overbite depth indicator, the sagittal angle, the maxillary, and mandibular sagittal ratio can be additional parameters in determining an openbite tendency.
**Keywords:** *Cephalometric radiography, Chennai population, openbite, overbite, overjet, quadrilateral analysis*
**How to cite this article:** Dilipkumar D, Raj DS, Dayalan D, Suresh P, Sugapriya R. Quadrilateral analysis applied to a city population with anterior openbite. Indian J Dent Res 2020;31:263-76 |
**How to cite this URL:** Dilipkumar D, Raj DS, Dayalan D, Suresh P, Sugapriya R. Quadrilateral analysis applied to a city population with anterior openbite. Indian J Dent Res [serial online] 2020 [cited 2023 Mar 27];31:263-76. Available from: https://www.ijdr.in/text.asp?2020/31/2/263/284588 |
Introduction | | |
Understanding the differences in craniofacial structures between normal and openbite is important for clinical management and research purposes.
Cephalometric comparisons highlight the differences in craniofacial structure. Several studies have investigated the differences in North American whites and in North American blacks, in Chinese, and in Saudis. According to their findings, there are abnormalities in the craniofacial structures of patients with anterior openbite and, according to the quadrilateral analysis, the patient with good facial pattern shows one-to-one proportionality in the lower facial part.
The quadrilateral analysis was introduced by Di Paolo^{[1]} to relate the cephalometric characteristics of maxillary and mandibular skeletal bases in the sagittal and vertical dimensions. He suggested that a one to one ratio exists between the maxillary base length, mandibular base length, average of anterior facial height, and posterior facial height in a balanced facial pattern.^{[2],[3],[4],[5]} Tseng and Kao *et al*.^{[6],[7]} also advocated that the quadrilateral analysis is a valuable cephalometric tool for diagnosis and treatment planning of orthodontic problems.
Four linear measurements form a quadrilateral. These are the maxillary base length, mandibular base length, anterior facial height, and the posterior facial height.^{[5]}
Cephalometrics play a vital role in describing the craniofacial pattern, evaluating the changes due to growth, making proper diagnosis, obtaining appropriate treatment objective, and treatment planning. It can be used to predict the expected changes during growth.^{[8],[9],[10]}
Skeletal openbite is characterized by small anterior cranial base, increased cranial base angle, steep anterior cranial base, long lower anterior facial height, large mandibular plane angle, obtuse genial angle, short posterior facial height, anterior upward tilting of maxilla, posterior downward tilting of maxilla, increased vertical growth in posterodento-alveolar structures.^{[11],[12],[13],[14],[15]} The prevalence of anterior openbite varies among ethnic groups, age, and dentition.^{[16]}
The aim of this study was to (1) apply the quadrilateral analysis to adult male and female Chennai population with normal occlusion, (2) compare the results to Chennai adult male and female with anterior openbite, and (3) to evaluate the correlation of the quadrilateral variables.
Materials and Methods | | |
The study was carried out from the values taken from 120 pretreatment lateral cephalograms of the selected Chennai population and divided into two groups. Group A consists of 60 lateral cephalograms of 30 males and 30 females patient with balanced anteroposterior and vertical facial proportion. Normal overjet and overbite relationship. Group B consists of 60 lateral cephalograms of patient with anterior openbite. A quadrilateral analysis of the craniofacial structures of Chennai population with normal overjet and overbite was compared to Chennai population with anterior openbite.
**Group A**
A total of 60 lateral cephalograms was selected from people with normal occlusion (30 male and female patients). The sample was selected from a total of 450 lateral skull radiographs of fourth year dental students and patients:
Inclusion criteria for group A:
- Age group of 15–25 years.
- Normal occlusion.
- Balanced anteroposterior and vertical facial proportion. Normal overjet and overbite.
- Normal skeletal relationship.
- Overbite depth indicator more than 68° and less than 80°.
- No history of trauma, jaw fracture, cleft, or craniofacial syndrome.
- No previous orthodontic treatment.
**Group B**
A total of 60 lateral cephalograms was selected from patients with anterior openbite 30 male and female patients. The sample was selected from a total of 310 lateral skull radiographs of fourth year dental students and patients.
**Inclusion criteria**
- Age group of 15–20 years.
- 1 mm or more of anterior openbite measured as a perpendicular vertical distance from the tip of the mandibular incisal edge to the horizontal line passing through the tip of the upper incisal edge.
- Less than 68° of overbite depth indicator (ODI).
- For the final selection of the openbite group, each patient must be 20 years and above, upper and lower first molars should be present with the posterior teeth in occlusion
- No history of orthodontic treatment or craniofacial trauma.
**Cephalometric parameters**
The cephalometric tracings were done manually by three operators and landmarks and values were cross checked. The following landmarks were identified on the tracing for the quadrilateral analysis and to measure the overbite depth indicator: (1) nasion, (2) sella turcica, (3) orbitale, (4) porion, (5) anterior nasal spine, (6) posteriornasal spine, (7) gonion, (8) menton, (9) gnathion, (10) point A, (11) point B, (12) point A', (13) point B', (14) point C', (15) point D', and (16) point J. If the landmarks were bilateral and did not coincide with each other on the tracing, the midpoint was chosen. The landmarks used in this study follow those used by DiPaolo [Figure 1].
From the above landmarks, the following cephalometric variables were measured:
- MaxL. The maxillary base length measured in millimeters as the horizontal distance between two points (point A' and point C') projected onto the palatal plane. Point A' is a perpendicular from point A upward to the palatal plane. Point C' is a perpendicular from the most inferior portion of the pterygomaxillary fissure downward to the palatal plane [Figure 2].
- ManL. The mandibular base length measured in millimeters between two points (point B' and point D') projected onto the mandibular plane. Point B' is a perpendicular from point B, whereas point D' is a perpendicular from point J downward to the mandibular plane. Point J is located at the deepest point of the junction of anterior portion of the ramus and the base of the mandible [Figure 3].
- ALFH. The anterior lower facial height measured in millimeters from point A' to point B' [Figure 4].
- PLFH. The posterior lower facial height measured in millimeters from point C' to point D' [Figure 4]. These four measures (maxillary base length, mandibular base length, anterior lower facial height, and the posterior lower facial height) form the basis of the quadrilateral analysis [Figure 5].
- SagAng. The sagittal angle is the angle formed by the intersection of the posterior extension of the maxillary base and mandibular base.
- ALFH/PLFH. The ratio of anterior lower facial height to the posterior lower facial height.
- AUFH/TAFH. The ratio of anterior upper facial height to the total anterior facial height.
- LFHaverage. The average of the lower anterior facial height and the lower posterior facial height.
- UFAng. The upper facial angle. The angle between the line of the maxillary base length and the N-point A' line. It assesses the position of the maxilla.
- FConvAng. The angle of facial convexity formed by the line N-A' and the line A'-B' measured at point A'. It relates the quadrilateral to the upper face and gives assessment of the skeletal profile.
- AUFH. The anterior upper facial height measured in millimeters from point A' to point nasion.
- (MaxL + MaxE)/MaxE. The maxillary sagittal ratio, the sagittal ratio is a mathematical expression to assess the relative anteroposterior positioning of the maxillary and mandibular bases [Figure 5]. The ratio of A to B is called the maxillary sagittal ratio.
- (ManL + ManE)/ManE. The mandibular sagittal ratio, the ratio of C to D is called the mandibular sagittal ratio [Figure 5]. Any forward or retroposition of the base will cause unequal lengths of the posterior legs (lines A and C).
- MaxE. The maxillary extension. Posterior extension of maxillary base length.
- ManE The mandibular extension, posterior extension of mandibular base length. The maxillary and mandibular posterior extensions of base lengths determine if there is any sagittal malrelation of the mandibular base to the maxillary base.
- TPFH/TAFH. The ratio of total posterior facial height to total anterior facial height.
- ALFH/TAFH. The ratio of anterior lower facial height to the total anterior facial height.
- MaxL/ManL. The ratio of maxillary base length to mandibular base length.
- MaxL/LFHaverage. The ratio of maxillary base length to the average of lower anterior and posterior facial heights.
- MaxE/ManE. The ratio of maxillary posterior extension to the mandibular posterior extension.
- TAFH. Total anterior facial height measured in millimeters as a combination of the lower anterior facial height and the upper anterior facial height.
- TPFH. The total posterior facial height measured in millimeters from point gonion to sella turcica.
- ODI. The ODI is a combination of the angle between the AB plane to mandibular plane and the angle between the Frankfort plane to palatal plane.
| Figure 2: Construction of point A' and c' and determination of maxillary base length
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| Figure 3: Construction of point B' and D' and determination of mandibular base length
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| Figure 4: Construction of quadrilateral from point A', point B', point C' and point D' and determination of anterior lower facial height and posterior lower facial height
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| Figure 5: Construction of sagittal maxillary ratio, mandibular ratio, and sagittal angle of the quadrilateral analysis
**Click here to view** |
**Statistical analysis**
The collected data were analyzed with IBM.SPSS statistic software 23.0 version. To describe statistics mean and standard deviation were used. To find the significant difference between the bivariate samples in independent groups the unpaired sample *t* test was used. To assess relationship Pearson's correlation was used. In all the above statistical tools, the probability value. 05 is considered as significant level.
Results | | |
The results of the study showed statistical significance difference between the normal occlusion and anterior openbite group [Table 1]. | Table 1: Quadrilateral analysis of Chennai population with anterior openbite
**Click here to view** |
Discussion | | |
The study applied the quadrilateral analysis to Chennai adult patients presenting with a normal occlusion and anterior openbite.
The main finding in the Chennai adults with normal occlusion and balanced facial proportion was that the length of the maxillary base equals to the length of mandibular base and equals to average lower anterior and posterior facial heights. This finding agrees with DiPaolo^{[1],[2],[3],[4],[5]} and supports the hypothesis of equality put forward by the quadrilateral analysis.
Comparing the quadrilateral analysis of the normal occlusion group to the subjects with anterior openbite showed that the length of maxillary base and mandibular base was smaller in the openbite group [Table 2]. This was in agreement with DiPaolo *et al*.,^{[1],[2]} Chinappi *et al*.,^{[3]} DiPaolo *et al*.,^{[4],[5]} and Kao *et al*.^{[17]} who found that length of the maxillary and mandibular bases was smaller in the openbite subjects. The lower anterior facial height was significantly larger in openbite patients compared to normal patients, whereas the lower posterior facial heights were similar in the openbite and normal patients.^{[18],[19],[20],[21]} This was in agreement with several investigators^{[22],[23],[24],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34],[35],[36],[37],[38],[39],[40],[41],[42],[43],[44],[45]} who showed that the anterior openbite patients have excessively increased lower facial height. The increase in the lower anterior facial height resulted in an increase in the ratio of the lower anterior to posterior facial heights and increase in the ratio of the lower anterior facial height to the upper anterior facial height. The sagittal angle was large in the anterior openbite subjects. This was in agreement with DiPaolo *et al*.,^{[2]} Chinappi *et al*.,^{[3]} DiPaolo *et al*., and Kao *et al*.^{[17]} However, Kao *et al*.^{[17]} suggested that the sagittal angle can be used, in addition to the overbite depth indicator of Kim,^{[46]} as criteria to identify an openbite tendency. | Table 2: Results of quadrilateral analysis between Chennai adults with anterior openbite and normal occlusion
**Click here to view** |
The sagittal angle is formed by the intersection of the extensions of the maxilla and lower legs of the quadrilateral. The side legs of the quadrilateral are the anterior and posterior facial heights. An excessive increase in the lower facial heights will result in an increase in the sagittal angle. This is true if the posterior lower facial height was reduced or within normal range.^{[47],[48]} But, if the lower facial height in openbite subjects increased to a similar amount or exceeded the amount of increase in the anterior facial height then the sagittal angle will not be a good indicator for an openbite. The upper facial angle, that is, the angle formed by the palatal line and the line from point A' to point *N* measured at point A', was large in the anterior openbite group compared to normal. It was suggested that this angle will estimate the position of the maxillae.^{[5]} However, a large upper facial angle indicates a retruded maxilla or anterior upward tilting of maxilla and or posterior downward tilting of maxilla. This was in agreement with several investigators.^{[17],[25],[26],[27],[28],[29],[30],[31],[32],[33],[34],[35]} However, the small size maxilla in the openbite sample might affect the anteroposterior position of the maxilla. There was no change in convexity angle between openbite group and control group.
Correlation analysis of the measured variables ranged from 0.00 to 0.97. Wardlaw^{[49]} showed that the ODI is the most valuable parameter in diagnosing anterior openbite tendency [Table 3]. The smaller the ODI the higher the tendency for openbite. There were high correlations with significant differences at *P* < 0.01 between the ODI and the maxillary base length, anterior lower facial height, sagittal angle, facial angle, and total facial height. The correlation analysis showed a positive correlation between ODI and maxillary base length. The more openbite tendency the smaller the ODI and the smaller the maxillary base length. However, the correlation analysis shows a negative correlation between ODI and anterior lower facial height, sagittal angle, facial convexity angle, and total facial height. The more openbite tendency the smaller the ODI and the larger the anterior lower facial height, the sagittal angle, the facial convexity angle, and the total facial height. Several investigators^{[27],[28],[29],[30],[31],[32],[33],[34],[35],[36]} found that craniofacial pattern in the openbite patients was characterized by a small ODI value, increased lower and total facial heights. The finding of this study agrees with the suggestion of adding the sagittal angle as an additional indicator of an anterior openbite tendency.^{[17]}
The maxillary base length correlation analysis showed that in patients with an openbite tendency, the smaller the maxillary base length, the smaller the mandibular base length, the smaller the upper facial angle, the smaller the maxillary posterior extension, and the smaller mandibular posterior extension.^{[50]} However, a significant negative correlation indicated that the smaller the maxillary base length the larger the sagittal angle. This is in agreement with Kao *et al*.
The anterior lower facial height correlation analysis showed a positive significant correlation with the posterior lower facial height, sagittal angle, upper facial angle, and total anterior facial height. The strongest correlation was between the anterior lower facial height and the total anterior facial height. This is in agreement with Kao *et al*.^{[17]} The greater the increase in anterior facial height, the more the increase in total facial height and the sagittal angle. However, the anterior lower facial height negatively correlates with maxillary posterior extension, mandibular posterior extension and the ODI. On the contrary, the posterior lower facial height correlates positively with the anterior lower facial height, maxillary posterior extension, mandibular posterior extension, and the total posterior facial height. The posterior lower facial height negatively correlates with the sagittal angle. The smaller the posterior lower facial height the larger the sagittal angle. The total anterior facial height correlation analysis showed positive significant correlation with anterior lower facial height, sagittal angle, upper facial angle, facial convexity angle, and upper anterior facial height. However, the total anterior facial height negatively correlates with the maxillary posterior extension, mandibular posterior extension, and the ODI. The total posterior facial height correlation analysis showed positive significant correlation with posterior lower facial height, facial convexity angle, maxillary posterior extension, and mandibular posterior extension. However, the total posterior facial height correlates negatively with the sagittal angle. These findings were in agreement with Kao *et al*.^{[17]}
The sagittal angle correlation analysis showed a positive significant correlation between the sagittal angle and anterior lower facial height, the upper facial angle, and the total facial height. In the openbite tendency, the larger the sagittal angle the larger the anterior lower facial height, the upper facial angle, and the total facial height. This was in agreement with DiPaolo *et al*.,^{[2]} Chinappi *et al*.,^{[3]} DiPaolo *et al*.,^{[4],[5]} and Kao *et al*.^{[17]} However, the sagittal angle negatively correlates with maxillary base length, facial convexity angle, maxillary posterior extension, mandibular posterior extension, the total posterior facial height, and the ODI. In the anterior openbite patients, the larger the sagittal angle the smaller the maxillary base length, the facial convexity angle, the maxillary posterior extension, the mandibular posterior extension, the total posterior facial height, and the ODI. This agreed with Kao *et al*.^{[51]} The upper facial angle correlation analysis showed positive significant correlation with the maxillary base length, anterior lower facial height, sagittal angle, facial convexity angle, and total anterior facial height. The positive significant correlation of the upper facial angle indicated that in openbite patients, the greater the upper facial angle the greater the maxillary base length, the anterior lower facial height, the sagittal angle, the facial convexity angle, and the total anterior facial height. The facial convexity angle correlation analysis showed a positive significant correlation with posterior lower facial height, upper facial angle, maxillary posterior extension, mandibular posterior extension, and total anterior facial height. However, the facial convexity angle correlated negatively with the ODI. In the openbite patients, the larger the sagittal angle the smaller the maxillary base length, the facial convexity angle, the maxillary posterior extension, the mandibular posterior extension, the total posterior facial height, and the ODI. This was in agreement with DiPaolo *et al*.,^{[2]} Chinappi *et al*.,^{[3]} DiPaolo *et al*.,^{[4],[5]} and Kao *et al*.^{[21]} The maxillary and mandibular posterior extensions have positive significant correlation with the maxillary base length, posterior lower facial height, facial convexity angle, and total anterior facial height. However, the correlation analysis showed a negative significant correlation with the sagittal angle and the total anterior facial height.
The correlation analysis of the openbite patients indicated that when the ODI is small, the sagittal angle is large, the posterior extension planes of the maxilla and mandible are small, and the maxillary and mandibular sagittal ratios are large. All these measurements correlate significantly with the ODI and can therefore be used as references in diagnosing openbite tendency. These finding agreed with Kao *et al*.^{[21]}
Conclusion | | |
A quadrilateral analysis of the craniofacial structures of Chennai population with normal overjet and overbite were compared to Chennai population with anterior openbite. The results show the following.
- In normal subjects the lower facial heights are equal.
- In anterior openbite subjects compared to normal:
- The facial heights are larger.
- The sagittal angle is larger.
- The maxillary and mandibular sagittal ratios are larger.
- The average lower facial height is larger.
- Sagittal ratio is larger than normal.
**Financial support and sponsorship**
Nil.
**Conflicts of interest**
There are no conflicts of interest.
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**
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**Correspondence Address**: Dr. Dhivya Dilipkumar Department of Orthodontics and Dentofacial Orthopedics, SRM Kattankulathur Dental College and Hospital, SRM Nagar, Potheri, Chennai, Tamil Nadu - 603 203 India
**Source of Support:** None, **Conflict of Interest:** None
| **Check** |
**DOI:** 10.4103/ijdr.IJDR_867_18
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1], [Table 2], [Table 3] |