

RESEARCH ARTICLE 

Year : 2015  Volume
: 6
 Issue : 1  Page : 125130 


Reliability of Beta angle in assessing true anteroposterior apical base discrepancy in different growth patterns
Shobha Sundareswaran, Vinay Kumar
Department of Orthodontics, Government Dental College, Calicut, Kerala, India
Date of Web Publication  14Jan2015 
Correspondence Address: Dr. Shobha Sundareswaran Department of Orthodontics, Government Dental College, Calicut  673 008, Kerala India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09769668.149109
Abstract   
Introduction: Beta angle as a skeletal anteroposterior dysplasia indicator is known to be useful in evaluating normodivergent growth patterns. Hence, we compared and verified the accuracy of Beta angle in predicting sagittal jaw discrepancy among subjects with hyperdivergent, hypodivergent and normodivergent growth patterns. Materials and Methods: Lateral cephalometric radiographs of 179 patients belonging to skeletal Classes I, II, and III were further divided into normodivergent, hyperdivergent, and hypodivergent groups based on their vertical growth patterns. Sagittal dysplasia indicators  angle ANB, Wits appraisal, and Beta angle values were measured and tabulated. The perpendicular point of intersection on line CB (CondylionPoint B) in Beta angle was designated as 'X' and linear dimension XB was evaluated. Results: Statistically significant increase was observed in the mean values of Beta angle and XB distance in the vertical growth pattern groups of both skeletal Class I and Class II patients thus pushing them toward Class III and Class I, respectively. Conclusions: Beta angle is a reliable indicator of sagittal dysplasia in normal and horizontal patterns of growth. However, vertical growth patterns significantly increased Beta angle values, thus affecting their reliability as a sagittal discrepancy assessment tool. Hence, Beta angle may not be a valid tool for assessment of sagittal jaw discrepancy in patients exhibiting vertical growth patterns with skeletal Class I and Class II malocclusions. Nevertheless, Class III malocclusions having the highest Beta angle values were unaffected. Keywords: Beta angle, sagittal dysplasia, vertical growers
How to cite this article: Sundareswaran S, Kumar V. Reliability of Beta angle in assessing true anteroposterior apical base discrepancy in different growth patterns. J Nat Sc Biol Med 2015;6:12530 
How to cite this URL: Sundareswaran S, Kumar V. Reliability of Beta angle in assessing true anteroposterior apical base discrepancy in different growth patterns. J Nat Sc Biol Med [serial online] 2015 [cited 2020 Jun 5];6:12530. Available from: http://www.jnsbm.org/text.asp?2015/6/1/125/149109 
Introduction   
Assessment of jaw relationship in all three planes (anteroposterior, transverse, and vertical) is an integral part of orthodontic treatment planning. Of the several analyses attempted to assess the anteroposterior discrepancy with numerous angular and linear measurements, ^{[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]} the ANB angle, ^{[3],[13]} Wits appraisal ^{[4]} and Beta angle ^{[10]} are commonly used. However, the validity of ANB angle and Wits appraisal is questionable due to a number of distorting factors such as rotation of jaws, ^{[4]} variation in the position of nasion, ^{[14],[15],[16],[17],[18]} length of cranial base ^{[15]} and vertical distance of points A and B from the cranial base. ^{[15]} Although the Wits appraisal, overcomes some of these limitations, ^{[4]} it is affected by tooth eruption, ^{[19],[20]} Curve of Spee, open bite and is not easily identifiable or reproducible. ^{[21]}
Beta angle is yet another method for determining true sagittal apical base relationships independent of cranial reference planes or functional occlusal plane. It uses three skeletal landmarkspoint A, point B and apparent axis of the condylepoint C. Angle formed between AB line and point A perpendicular to CB line (CondylionB point) is the Beta angle. ^{[10]} The sample used for development of this new parameter comprised of cases with normal vertical components, based on mandibular occipital (MOCC) angle and hypothesize that the Beta angle would remain relatively stable even when the jaws are rotated downward and backward. ^{[10]} When point B is rotated backwards, the CB line is also rotated in the same direction carrying the perpendicular from point A with it. The Beta angle is presumed to remain relatively stable because the AB line is also rotating in the same direction. Hence, it is believed that Beta angle would accurately assess the sagittal relationship in skeletal patterns even if clockwise or counterclockwise rotation of the jaws tended to camouflage it. This would be geometrically true if the mandible were to rotate like a steering wheel with every point on it being displaced to the same extent and same direction. However, internal rotation of the mandible is different and has two components i.e., (a) matrix rotation centered around the condyle, (b) intramatrix rotation centered within the body of the mandible. ^{[22]} Hence, it is essential to understand and investigate the degree to which vertical dysplasia can affect the Beta angle. Moreover, projection of perpendicular from point A to CB line (named Point X) results in the formation of a right angle triangle, AXB. Angle XAB forms the Beta angle under consideration. Since in any right angled triangle, each side is proportional to the angle diametrically opposite to it, we also decided to evaluate the linear dimension of mandible pertaining to line XB to assess its effect on Beta angle.
Materials and Methods   
This crosssectional study was based on departmental pretreatment records containing high definition lateral cephalometric radiographs of only those patients who had no previous history of trauma, orthodontic treatment or orthognathic surgery and no missing teeth, functional mandibular shifts or congenital defects.
Sample size was determined using a power calculation based on mean Beta angle value of Class I occlusion (31.1° ± 2°). ^{[10]} To detect a change of 2° from this mean value with 95% confidence and 80% power, we required a sample size of 16 in each group.
Cephalometric landmarks used in this study included Sella(S), Nasion(N), Point A(A), Point B(B), Gnathion(Gn), Menton(Me), Gonion(Go), Articulare(Ar), and projection of perpendicular from point A to CB line (X).
Linear and angular measurements used
 Wits appraisal
 Angle ANB
 XB distance  the linear distance between point X and B point
 Beta angle  the angle between the perpendicular from point A to CB line and the AB line
 Angle GoGn (GonionGnathion) to SN plane.
All radiographs were traced by a single investigator and Sagittal dysplasia indicators  angle ANB, Wits appraisal, and Beta angle values were measured and tabulated. Vertical growth pattern was assessed using angles GoGn to SN plane ^{[23]} and MOCC as used by Margolis. ^{[24]} The point of intersection obtained by the perpendicular drawn from point A to the CB line (condylion to point B) was designated as 'X' and linear distance XB measured and recorded [Figure 1].  Figure 1: Cephalometric parameters analyzed in study  Beta angle (XAB) and XB distance
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Angular and linear measurements were obtained nearest to 0.01 mm and 0.5° using digital Vernier caliper (Hangzhou United Bridge Tools Co., Ltd.) and semicircular protractor respectively. From a total of 264 patients initially selected, 179 radiographs were included in the study based on specific inclusion criteria. Age range was between 15 and 25 years.
Criteria for a patient to be included in Class I skeletal pattern:
 Angle ANB of 13°, ^{[10]}
 Wits appraisal of 0 to −3 mm, ^{[10]}
 Angle's Class I molar relationship,
 Orthognathic, Class I profile.
Criteria for Class II group:
 Angle ANB was above 4°, ^{[10]}
 Wits appraisal greater than 0 mm, ^{[10]}
 Molar relationship was Angle's Class II and
 Retrognathic, Class II profile.
Criteria for Class III group:
 Angle ANB was lesser than 1°, ^{[10]}
 Wits reading equal to or lesser than −4 mm, ^{[10]}
 Molar relationship Angle's Class III and
 Prognathic, Class III profile.
Based on vertical growth pattern as evidenced by MOCC angle ^{[24]} and angle GoGn to SN, ^{[23]} each skeletal class was further divided into three groups.
 Normodivergent/normal growth pattern  MOCC between −4 and +4°; GoGn2836°
 Hyperdivergent/vertical growth pattern  MOCC >4°; GoGn >36°
 Hypodivergent/horizontal growth pattern  MOCC <4°; GoGn <28°
The final sample distribution is shown in [Table 1].  Table 1: Distribution of the sample based on growth pattern and skeletal classification
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After an interval of 2 weeks, 20 randomly selected radiographs were retraced by the same investigator and repeatability of Beta angle and XB distance was measured by intraclass correlation coefficient (ICC) as shown in [Table 2], indicating a good agreement between two different time interval observations.
Statistical analysis
The measured values of Beta angle and XB distance in each group were evaluated for statistical significance using Statistical Package for Social Sciences (SPSS version 16, IBM). Data are represented as means ± standard deviations (SD). Oneway analysis of variance was used to identify overall differences in mean values of Beta angle and XB distance in each group. The level of significance was set at P < 0.05. When differences between groups were found to be significant, the Bonferroni test for multiple comparisons was applied. Receiver operating characteristics (ROC) curves were run to examine the sensitivity and specificity of XB linear distance as a test to discriminate between the three different skeletal pattern groups. Kappa statistics were used to measure the agreement between skeletal classes and Beta angle category in different growth patterns, and ICC was used to measure repeatability of quantitative variables (Beta angle and XB distance) to examine intraexaminer bias.
Results   
Mean (±SD) values for Beta angle and XB distance for Class I and Class II but not Class III with normal, horizontal, and vertical growth patterns were significantly different (P < 0.05) [Table 3].  Table 3: Descriptive statistics for mean value of Beta angle and XB distance in all skeletal class groups
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Significant (P < 0.05) increase in Beta angle values in vertical growth patterns of both Class I and II cases [Table 4] was observed. The XB distance also showed significant differences among the various groups for both Class I and Class II cases. Skeletal Class III cases however showed no statistical difference among the three growth patterns.  Table 4: Bonferroni test for multiple comparisons among three different growth patterns
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Horizontal growth pattern showed maximum agreement for Beta angle with 100% reliability in Class III, 83.3% in Class I and 73.7% in Class II (K = 0.778, P < 0.001) [Table 5] and [Table 6]. Normal growth patterns were also found to be 100% reliable in Class III and 80% in Class I but only 69.2% in Class II (K = 0.747, P < 0.001). Vertical growth patterns on the other hand showed only 47.4% reliability of Beta angle as a sagittal parameter in Class II cases and 47% in Class I cases (K = 0.474, P < 0.001). However, Class III showed 100% reliability [Table 5] and [Table 6].  Table 5: Agreement between skeletal class and Beta angle category in different growth patterns
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 Table 6: Kappa statistics to measure the agreement of Beta angle in different growth patterns with the original study
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Average XB value in skeletal Class II was 17.4 mm (±4.5). It increases to 21.9 mm (±3.1) in Class I and further to 29.2 mm (±6.4) in Class III [Table 7].  Table 7: Descriptive statistics of XB distance (mm) for different skeletal groups
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ROC curve analysis for XB distance to identify the cutoff to differentiate Class II from the other classes is represented in [Figure 2]. Similarly, ROC curve for XB distance to discriminate skeletal Class III from the other groups is presented in [Figure 3]. The optimum cutoff with corresponding sensitivity and specificity are presented in [Table 8]. A cutoff of 20.75 will delineate Class II from Class I and Class III together. Similarly, a cutoff of 22.25 will delineate Class III from Class I and Class II together.  Figure 2: Receiver operating characteristics curve for XB distance to discriminate skeletal Class II group from other groups
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 Figure 3: Receiver operating characteristic curve for XB distance to discriminate skeletal Class III from other groups
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 Table 8: Validity and optimum cutoff value for XB distance by ROC curve
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Discussion   
Accurate anteroposterior analysis of jaw relationships is critically important in planning orthodontic treatment. Many linear and angular measurements are proposed in cephalometrics for this purpose. It is important that vertical growth patterns do not affect such parameters as it could mislead the clinician and make interpretation very complex. The Beta angle purports to be unaffected by vertical growth patterns. Verification of the accuracy of this parameter in different growth patterns, is therefore necessary.
Subjects with horizontal and normal growth patterns showed good adherence to Beta angle values. However, individuals with vertical growth patterns and skeletal Class I relationship exhibited only 47% reliability with respect to Beta angle values. A similar lack of reliability was observed in skeletal Class II vertical growth patterns (47.4%) as well. Hence, use of Beta angle as a true indicator of sagittal dysplasia is reliable only in individuals with horizontal to normal growth patterns. Only 47% of vertical growers in both Class I and Class II exhibited true sagittal discrepancy, which may be because steep mandibular planes had a strong tendency to increase the Beta angle values. This finding is however not in agreement with a previous report ^{[10]} in patients with normal growth patterns (evidenced by Margolis MOCC angle) ^{[24]} and had a cutoff point between Class I and Class II of 27.5° and between Class I and Class III of 35.5° with 95% sensitivity.
Our findings also do not support the theory that Beta angle would remain stable even when jaws are rotated. Clockwise growth rotation significantly increased Beta angle values, thus pushing Class I and Class II subjects toward Class III and Class I, respectively. However, skeletal Class III obviously remained unaffected because the already high Beta angle values were unaffected by vertical growth patterns making it a reliable parameter for such cases.
The linear dimension XB is another variable that showed a statistically significant increase from skeletal Class II (17.4 ± 4.5 mm) through Class I (21.9 ± 3.1 mm) to Class III (29.2 ± 6.4 mm). In Class I and Class II, XB distance was significantly higher in the vertical growers as compared to normal and horizontal groups. No such difference was seen for the three growth patterns in Class III [Table 3].
When a perpendicular is dropped from point A to CB line intersecting it at 'X', AXB forms a right angled triangle. In a vertical grower, mandibular plane is steep with short ramus height leading to a steep CB line. Keeping point A constant, to maintain angle AXB at 90°, the point of intersection, X has to move distally to X'. This leads to an increase in the linear dimension X'B and decrease in dimension AX'. In a right angled triangle, each angle is always proportional to the length of the opposite side. Hence, irrespective of the skeletal class, Beta angle values showed an increase in values whenever the XB linear dimension was increased. This is in contrast to previous findings, which state that when mandible rotates, the perpendicular rotates with it leading to stable Beta angle values in the face of clockwise or counter clockwise growth rotations. Hence, Beta angle value is apparently dependent on linear dimension XB. For the same mandibular length, a person with vertical growth pattern and clockwise rotation of the mandible, Beta angle values may become higher because XB distance increases. This might place an individual with Class I anteroposterior discrepancy in skeletal Class III and a Class II discrepancy may be pushed to Class I. This effect will be negated only if point A also moves downwards and forwards to the same extent.
Limitations
The present study was done assuming point A to be constant. When point A varies, Beta angle values are liable to change. This has not been included in this study.
Scope for future studies
Further studies are needed to assess the vertical change in the position of point A and its effect on Beta angle. This can be done by using the simplistic equation of trigonometry as follows:
Angle AXB in [Figure 4] is a right angled triangle, and angle XAB represents Beta angle under consideration. Angle XAB or Beta angle can be calculated by the following equation:
tan θ = Perpendicular/base = XB/AX
Beta angle which is a function of both AX and XB can easily be calculated and the effect of the ratio of XB:AX can be seen in Beta angle value.
Conclusions   
Clockwise rotation of the mandible affected the reliability of Beta angle as a sagittal discrepancy assessment tool. Hence, Beta angle may not be a reliable tool for assessment of sagittal jaw discrepancy in patients exhibiting vertical growth patterns with skeletal Class I and Class II malocclusions. However, Beta angle is a reliable indicator of sagittal dysplasia in normal and horizontal patterns of growth. Interestingly, skeletal Class III malocclusions showed 100% adherence to Beta angle values irrespective of the growth pattern.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8]
