A “new vista” in the assessment of anteroposterior jaw relationship

,
Abstract
Aim
The purpose of this investigation was to (1) compare the credibility of four recently introduced cephalometric measurements in assessing the anteroposterior jaw relationship; (2) To assess the correlation between various measurements used for assessment of anteroposterior discrepancy, including Yen linear, Yen angle, W angle and Pi angle.Materials and Methods
The sample size for the study consisted of 45 subjects with age group of 1519 years (mean age 17 ± 2.1) and was subdivided into Skeletal Class I, II and III groups of 15 each based upon the ANB angle derived from the pre treatment lateral cephalogram. Landmarks were located and Yen angle, Yen linear, W angle and Pi angle were assessed for each group. All the lateral cephalograms were traced by a single examiner. Intra examiner reliability was assessed by Intraclass coefficient correlation (ICC) test. Correlation coefficients were obtained for each of parameters to compare their relationship with other parameters in Class I group. Receiver operating characteristics (ROC) curves were run to examine sensitivity and specificity of all the angles.Results
The results showed that ICC for all the groups were ≥0.90 showing good repeatability of the measurements. There was statistically significant correlation between Yen angle and ANB angle, Yen linear and Yen angle for Class I group, between W angle and Yen angle for Class II group, between Yen angle, Yen linear and ANB for Class III group. ROC curves showed that Pi angle had 100% sensitivity and specificity to discriminate a Class II and a Class III group from a Class I and a Class III group from a Class II. Yen linear and W angle showed very low specificity to differentiate a Class II from a Class I group.Interpretation and Conclusion
The new parameters considered in the study were found to be equally reliable and are not affected much by local remodeling due to tooth movements or by occlusal or Frankfurt horizontal plane. These parameters measure the anteroposterior discrepancy more consistently and accurately, with Pi angle being the most accurate.Keywords
INTRODUCTION
Malocclusions are classified broadly based on dental and skeletal discrepancies. Skeletal discrepancies are further sub classified based on the plane of discrepancy present, that is, sagittal, transverse and vertical discrepancies.^{[1]} An accurate anteroposterior measurement of the jaw relationship is critically important in orthodontic diagnosis and treatment planning of these skeletal discrepancies. Since Broadbent’s introduction of the cephalostat in 1931, a number of geometrical parameters, such as ANB angle,^{[2]} WITS appraisal,^{[3]} AFBF^{[4]} linear, APDI^{[5]} angular measurement and Beta angle^{[6]} have been defined and used effectively for the evaluation of anteroposterior discrepancies affecting the apical bases of the jaws.^{[1520]} However, various studies have questioned the reliability of these parameters as none of them currently gives a definitive picture of the anteroposterior jaw relationship. ANB angle has been found to be affected by rotation of the SellaNasion (SN) plane, the relative length of the SN plane and the rotation of the jaws during growth and treatment.^{[2]} As an alternative, it was suggested that perpendiculars be drawn from points A to B on the occlusal plane (WITS appraisal), but misinterpretation of WITS value can be encountered due to variability in the occlusal plane, which is easily affected by tooth eruption and orthodontic treatment.^{[7]} Although Beta angle does not use the cranial reference planes but it uses point A, which is affected by the orthodontic tooth movement of upper incisors and also point C is difficult to be located on the lateral cephalogram.^{[8]}
Various cranial reference planes, such as FrankfortHorizontal (FH) plane and SN plane have been used in determination of anteroposterior jaw dysplasia: However, measurements related to cranium do not provide a wholly reliable estimation of the anteroposterior jaw relationship within the dentofacial complex.^{[2]} Thus, calibrations independent of cranial reference planes or dental occlusion were introduced to determine the apical base relationship, reflecting true skeletal anteroposterior relationship without being influenced by changes in other parameters. These measurements included Yen angle,^{[9]} Yen linear,^{[1]} W angle^{[10]} and Pi angle.^{[11]} They utilize skeletal landmarks G and M points, to represent the mandible and maxilla respectively, which will be discussed later in this article.
However, despite introduction of the newer angles the orthodontist is in a dilemma over choosing the right parameter for assessment of anteroposterior jaw relationship. Therefore, the aims of this study were:
To compare the credibility of four cephalometric measurements in assessing the anteroposterior jaw relationship and.
To assess the correlation between various measurements used for anteroposterior discrepancy, including Yen linear, Yen angle, W angle and Pi angle.
MATERIALS AND METHODS
The sample size for the study consisted of 45 subjects (age 1519 years) who had reported for orthodontic treatment in the Department of Orthodontics and Dentofacial Orthopedics, MS Ramaiah Dental College, Bengaluru, India. The subjects were subdivided into Skeletal Class I, II and III groups of 15 each based upon the ANB angle derived from the pretreatment cephalogram. Inclusion criteria for subjects were:
ANB angle between 1° and 4° for Class I; >4° for Class II and ≤0° for Class III.^{[11]}
Permanent dentition with no missing teeth;
Patients with age group between 15 and 19 years.
Exclusion criteria included:
No previous history of orthodontic treatment;
No cranial or facial malformation and no history of craniofacial trauma;
Poor quality of cephalograms.
The cephalostat with following specifications was used for all subjects to obtain lateral cephalograms in Natural Head PositionPlanmecca PM 2002 CC Proline Pan/ Ceph (manufactured in Helinski, Finland, with voltage of 70 kV, current 10 mA and exposure time of 1.2 s). All the radiographs were hand traced by a single investigator (D. M.). To determine Yen angle, Yen linear, W angle and Pi angle, Points G and M were located using a transparent template containing number of circles whose inner diameter increased in 1 mm increments.^{[11]} These landmarks were utilized to represent the maxilla and mandible respectively. Each center was identified by a pinhole in the template.
Point M was determined by the center of the largest bestfit circle tangent to anterior, superior, and palatal surface of premaxilla in each radiograph.
Point G was determined by the center of the largest best fit circle tangent to the internal, anterior, inferior, and posterior surfaces of mandibular symphysis.^{[12,13]}
The Yen angle, Yen linear, W angle and Pi angle were calculated for all the subjects in all the groups [Figures 1 and 2]. All the tracings and measurements were repeated after 3 weeks to evaluate the intraexaminer reliability and the mean values were tabulated in Microsoft Excel sheet (Microsoft, Redmond, Washington, USA).
Statistical analysis
All statistical analysis was performed using SPSS Statistics Version 10.0.5 (SPSS Inc., Chicago, IL). Intra examiner reliability was assessed by intraclass coefficient correlation test. Descriptive data that included arithmetic means and standard deviations of all the four angles were calculated. Receiver operating characteristics curves were run to examine sensitivity and specificity of all the angles. Correlation coefficients were obtained for each of parameters to compare their relationship with other parameters in Class I group. The level of statistical significance was established at P < 0.05.
RESULTS
The mean values for all the angles in the three skeletal groups are listed in the Table 1. Oneway ANOVA showed statistically significant differences between mean values of all the angles among the three skeletal groups. Mean values of Yen angle were 126.36 ± 3.02, 117.57 ± 2.44, 137.79 ± 4.93, For Yen linear, −1.93 ± 1.68, 1.07 ± 1.97, −11.71 ± 4.48, For Pi angle, 2.71 ± 1.43, 8.36 ± 1.69, −9.79 ± 4.11 and For W angle, 55.5 ± 1.95, 52.14 ± 1.91, 67.29 ± 3.14 respectively for Class I, II and III groups. There was statistically significant correlation between Yen angle and ANB angle, Yen linear and Yen angle for Class I, between W angle and Yen angle for Class II, between Yen angle, Yen linear and ANB for Class III [Table 2]. Table 3 gives the cutoff values for all the 4 angles to determine Class I, Class II and Class III skeletal groups. The results show that Pi angle has 100% sensitivity and specificity to discriminate a Class II and a Class III case from a Class I to a Class III case from a Class II. Yen linear and W angle showed very low specificity to differentiate a Class II from a Class I.
Group  n  Mean ± SD 

ANB  
Class I  15  1.321±1.0116 
Class II  15  5.857±1.7913 
Class III  15  −7.071±3.4522 
Yen angle  
Class I  15  126.36±3.028 
Class II  15  117.57±2.441 
Class III  15  137.79±4.933 
Yen linear  
Class I  15  −1.93±1.685 
Class II  15  1.07±1.979 
Class III  15  −11.71±4.48 
Pi angle  
Class I  15  2.71±1.437 
Class II  15  8.36±1.692 
Class III  15  −9.79±4.117 
W angle  
Class I  15  55.5±1.951 
Class II  15  52.14±1.916 
Class III  15  67.29±3.148 
SD – Standard deviation
Group  Yen angle  Yen linear  Pi angle  W angle 

Class I  
ANB  
Correlation  −0.643  0.459  −0.170  −0.633 
P  0.013  0.099  0.561  0.015 
Yen angle  
Correlation  −0.759  −0.311  0.631  
P  0.002  0.280  0.015  
Yen linear  
Correlation  0.263  −0.526  
P  0.363  0.053  
Pi angle  
Correlation  −0.219  
P  0.451  
Class II  
ANB  
Correlation  −0.191  0.198  0.018  −0.330 
P  0.513  0.497  0.951  0.249 
Yen angle  
Correlation  −0.152  0.021  0.722  
P  0.603  0.942  0.004  
Yen linear  
Correlation  −0.330  −0.226  
P  0.250  0.437  
Pi angle  
Correlation  0.197  
P  0.500  
Class III  
ANB  
Correlation  −0.706  0.777  0.412  −0.529 
P  0.005  0.001  0.143  0.052 
Yen angle  
Correlation  −0.759  −0.403  0.589  
P  0.002  0.153  0.027  
Yen linear  
Correlation  0.205  −0.830  
P  0.482  <0.001  
Pi angle  
Correlation  −0.248  
P  0.392 
Cut off  Class II from Class I  Class III from Class I  Class III from Class II  

Sensitivity (%)  Sensitivity (%)  Sensitivity (%)  Sensitivity (%)  Sensitivity (%)  Sensitivity (%)  
ANB  >3  100  100  100  100  100  100 
Yen angle  <120  92.9  100  92.9  92.9  100  100 
Yen linear  >2  92.9  71.4  100  100  100  100 
Pi angle  >5  100  100  100  100  100  100 
W angle  <54  92.9  64.3  100  100  100  100 
DISCUSSION
In orthodontic diagnosis and treatment planning, the evaluation of the anteroposterior jaw relationship is an indispensable step and this relationship is generally determined by using lateral cephalograms, which have been used for many decades now for this purpose. Various angular and linear measurements have been incorporated into the various cephalometric analyses for diagnosing these anteroposterior discrepancies. However, these can be erroneous as angular measurements are affected by changes in facial height, jaw inclination, and total jaw prognathism, whereas linear variables can be affected by the inclination of the reference line.^{[8]} ANB is still widely used but it has its own demerits as already discussed. To overcome some of the deficits of previous parameters, measurements such as W angle, Pi angle, Yen linear and Yen angle were introduced. These do not utilize A and B points as skeletal landmarks, which are affected by local remodeling due to orthodontic treatment. Instead they utilize points M and G which are not affected by local remodeling and they approximate to being centroid points similar to sella. Concept of centroid was given by Johnson. It’s the center of an area of an image representing the mean point within the shape, about which it varies and is subject to least variation relative to nonmean anatomic points and therefore provides more stable reference points.^{[14]}
In the current study, we traced the lateral cephalograms of 45 patients who fulfilled the inclusion and exclusion criteria, after which a transparent template was used to determine points M and G, centroid points of anterior maxilla and mandible respectively, which are not subjected to local remodeling due to tooth movements, unlike point A and B. Once these reference points were marked, all four measurements  Yen angle, Yen linear, W angle and Pi angle were made for the three skeletal groups, along with ANB angle which was the control.
All the parameters were found to be equally significant in assessing the anteroposterior discrepancy, however localization of the skeletal defect was ineffective. Pi angle is helpful in this regard as it utilizes true horizontal and nasion and thus gives a more accurate picture of which jaw is at fault. The results in the present study revealed that all the 4 parameters considered in the study are accurate in determining the anteroposterior jaw discrepancy with Pi angle being 100% sensitive and specific for discriminating a Class I from Class II, Class III malocclusion and also Class II from Class III malocclusion. In a similar study the overall accuracy for discriminating skeletal Class II from skeletal Class I was found to be 85% and for discriminating skeletal Class III from skeletal Class I, was found to be 90%.^{[10]} Thus, a cutoff point between Class I and II groups was considered a Pi angle of approximately 5° and between Class I and III approximately 1.3°.^{[11]}
The second objective of this study was to assess the correlation between various parameters used to measure the anteroposterior discrepancyincluding ANB angle, W angle, Yen angle, Yen linear and Pi angle. For this purpose, multiple correlation analysis was performed between the various parameters used in this study. There was statistically significant correlation between Yen angle and ANB angle, Yen linear and Yen angle for Class I, between W angle and Yen angle for Class II, between Yen angle, Yen linear and ANB for Class III. The correlation of Pi angle with other angles was weak for all the skeletal groups. In a similar study Horowitz and Hixon stated that a correlation coefficient better than 0.8 can be used in clinical predictions, on this basis the Pi angle may be considered highly interchangeable in the assessment of anteroposterior jaw relationship.^{[11]}
Although this study proves that all the parameters were efficient in determining anteroposterior skeletal discrepancy, Pi angle being the most credible angle, the study has some limitations. The fact that this study was performed on a smaller sample size was probably a reason why most of the parameters assessed were effective in determining the skeletal discrepancy with a uniform outcome. Further investigation with the larger sample size might provide a better overview of determining the preferred parameter among others to evaluate the skeletal discrepancy
CONCLUSION
Previously established parameters for assessing the anteroposterior jaw discrepancy have inaccuracies associated with them. The new parameters considered in the study were found to be equally reliable and are not affected much by local remodeling due to tooth movements or by occlusal or FH plane. These measure the anteroposterior discrepancy more consistently and accurately, with Pi angle being the most accurate. However, there is large variability among human populations and a single cephalometric analysis cannot assess the true skeletal relationship consistently in all situations.
Financial support and sponsorship
Nil.Conflicts of interest
There are no conflicts of interest.References
 J World Fed Orthod. 2013;2:5760YENLinear: A sagittal cephalometric parameter.
 [Google Scholar]
 Angle Orthod. 1998;68:50311Determining cephalometric norms for caucasians and African Americans in Birmingham.
 [Google Scholar]
 Eur J Orthod. 2002;24:47783Properties of the ANB angle and the Wits appraisal in the skeletal estimation of angle’s class III patients.
 [Google Scholar]
 Am J Orthod Dentofacial Orthop. 1987;92:11722Assessment of anteroposterior jaw relationship.
 [Google Scholar]
 Am J Orthod. 1978;73:61933Anteroposterior dysplasia indicator: An adjunct to cephalometric differential diagnosis.
 [Google Scholar]
 Am J Orthod Dentofacial Orthop. 2004;126:1005A new approach of assessing sagittal discrepancies: The Beta angle.
 [Google Scholar]
 Pak J Orthod. 2012;4:1723Correlation of overjet, ANB and Wits appraisal for assessment of sagittal skeletal relationship.
 [Google Scholar]
 Am J Orthod Dentofacial Orthop. 2003;124:4709The “Wits” appraisal of jaw disharmony 1975.
 [Google Scholar]
 World J Orthod. 2009;10:14751A new sagittal dysplasia indicator: The YEN angle.
 [Google Scholar]
 Eur J Orthod. 2013;35:6670A new approach of assessing sagittal dysplasia: The W angle.
 [Google Scholar]
 J Orthod. 2012;39:2629An evaluation of the Pi analysis in the assessment of anteroposterior jaw relationship.
 [Google Scholar]
 Angle Orthod. 2004;74:32831The Gaxis: A growth vector for the mandible.
 [Google Scholar]
 Am J Orthod Dentofacial Orthop. 1994;105:32844Cephalometric assessment of sagittal relationship between maxilla and mandible.
 [Google Scholar]
 Angle Orthod. 1989;59:28390The stability of anatomical and centroid reference points in cephalometric analysis.
 [Google Scholar]
 People’s J Sci Res. 2012;5:18Predictability of Yen Angle and Appraisal of Various Cephalometric Parameters.
 [Google Scholar]
 Indian J Dent Sci 4Comparison of Different Angular Measurements to Assess Sagittal Skeletal Discrepancy  A Cephalometric Study.
 [Google Scholar]
 Am J Orthod. 1984;85:41123Analysis of factors affecting angle ANB.
 [Google Scholar]
 Am J Orthod Dentofacial Orthop. 2006;129:6418Influence of occlusal plane inclination on ANB and Wits assessments of Antero posteriour jaw relationships.
 [Google Scholar]
 Am J Orthod Dentofacial Orthop. 1988;93:21323A summary five factor cephalometric analysis based on natural head posture and the true horizontal.
 [Google Scholar]
 Angle Orthod. 1981;51:16171Adjusting ANB angle to reflect the effect of maxillary position.
 [Google Scholar]