Geometrical Approaches for the Accurate Identification of Normal Vertical Positions of Sella and Nasion Points in Cephalograms

Objective The aim of the study is to identify the normal vertical positions of sella (S) and nasion (N) points in subjects with a normal inclination of anterior cranial bases. Materials and Methods Lateral cephalograms of 117 subjects who had a normal ∠SN-FH plane (7° ± 1°), ∠SN-palatal plane (9° ± 2°), ∠FH-palatal plane (1° ± 1°), and cranial base angles (131° ± 4°) were included in the study. Various linear and angular parameters and ratios were evaluated to determine the normal vertical positions of S and N points. An unpaired t-test was used to identify any significant differences between males and females. The P value of 0.05 was considered as the level of significance. Results Among subjects with the normal inclinations of SN, FH, and palatal planes and cranial base angle, the mean values of ∠Ar-S-Ptm, ∠S-Ptm-Ar, and ∠S-Ar-Ptm were 59.38° ± 3.52°, 59.70° ± 3.21°, and 60.84° ± 3.56°, respectively, forming an almost equilateral triangle between S, Ar, and Ptm points. The mean values of ∠Ba-S-PNS, ∠S-PNS-Ba, and ∠S-Ba-PNS were 59.56° ± 3.17°, 59.72° ± 3.47°, and 60.76° ± 3.11°, respectively, forming another approximate equilateral triangle between S, Ba, and PNS points. The mean S-FH to N-FH ratio was 0.67 ± 0.06% for the whole sample, but it was significantly greater in males (0.69 ± 0.07%) compared to females (0.65 ± 0.06%) (P=0.002). Conclusions Two approximate equilateral triangles were formed between S, Ar, and Ptm points; and S, Ba, and PNS points in subjects with normal inclinations of SN, FH, and palatal planes and cranial base angle. The S-FH to N-FH ratio was an excellent guide to locating the normal vertical position of S and N points.

It is a well-established fact that the inclination of the SN plane can signifcantly afect the severity assessment of the malocclusion [21][22][23]27]. Te inclination of the SN plane is infuenced by the changes in the vertical position of either S or N point or both. Although one study [23] attempted to identify the normal vertical positions of S and N points, it did not provide any systematic method to determine the correct vertical locations of these points. Tus, a well-defned method is needed to identify the true vertical position of S and N points accurately so that correct SNA, SNB, and ANB values can be obtained. Te present study describes various geometrical methods to identify the normal vertical positions of S and N points among subjects with normal inclinations of anterior cranial bases.

Materials and Methods
Te study was approved by the Institute Ethics Committee (IEC No. T/IM-NF/Dentistry/21/76) and was designed as per the STROBE statement guidelines. Orthodontic record fles of 537 subjects who had either completed or were undergoing comprehensive orthodontic treatment between January, 2015, and July, 2021, were reviewed. Of 537 subjects, 117 (M � 54, F � 63) fulflled the selection criteria. Te inclusion criteria included the following: (i) Good quality pretreatment lateral cephalograms with adequate hard tissue details (ii) Age between 18-30 years (iii) Normal inclination of the SN plane to the Frankfort horizontal plane, (7°± 1°) [28] (iv) Normal inclination of the SN plane to the palatal plane, (9°± 2°) [29] (v) Normal angle between the Frankfort horizontal plane and the palatal plane, (1°± 1°) [30] (vi) Normal cranial base angle (basion-sella-nasion angle, 131°± 4°) [31] Subjects with a history of trauma to the maxillofacial region, comprehensive orthodontic treatment, functional jaw orthopedics, surgery for maxilla and mandible, congenital deformities like cleft lip and palate, facial asymmetry, and any systemic disease afecting craniofacial growth were excluded.
All cephalograms were recorded with the same machine (NewTom GiANO, Italy) with similar exposure parameters (80Kvp, 10 mAs, and 1.6 seconds). All subjects were positioned with the Frankfort horizontal plane (FH plane) parallel to the foor and teeth in centric occlusion while recording the lateral cephalograms. Te heads of all the subjects were kept erect by voice commands. Nine hard tissue landmarks were identifed on each cephalogram ( Figure 1). Te FH plane was considered a reference plane. Ten linear and 12 angular parameters and one ratio were used to establish the normal vertical positions of S and N points (Figures 2 and 3).
All the lateral cephalograms were traced manually by the same evaluator. Te linear magnifcation was corrected and calibrated according to the magnifcation factor, using the radio-opaque ruler (calibration marker). A digital caliper measured the linear parameters to the nearest 0.01 mm and the angular measurements were done using a protractor to the nearest 0.5°. Te assessment of intraobserver errors and the reproducibility of landmark location and measurement errors were analyzed by retracing the 15 randomly selected cephalograms after 3 weeks. Te intraobserver reliability of the measurements was calculated by the intraclass correlation coefcient (ICC) for the measurements obtained by the evaluator at both times.

Statistical Analyses.
All the statistical analyses were performed in the SPSS software (for Windows 7, version 20, SPSS, Chicago, Ill). Descriptive statistics were used. Te Shapiro-Wilk test was used to examine the normality of the data. An unpaired t-test determined the signifcant diferences between males and females. Te P value of 0.05 was considered as the level of signifcance.

Results
Te ICC for linear and angular measurements ranged from 0.89 to 0.95 and 0.93 to 0.97, respectively, showing excellent reliability between the measurements. Te descriptive parameters are mentioned in  Table 2 depicts the values of various linear parameters of all the subjects. All the linear parameters except N-FH distance were signifcantly greater among males compared to females. S-Ar, Ar-Ptm, and S-Ptm were of almost equal lengths while S-Ba, Ba-PNS, and S-PNS distances were nearly equal to each other. Te mean S-Ar, Ar-Ptm, and S-Ptm values were 33.79 ± 3.18 mm, 33.92 ± 2.88 mm, and 34.52 ± 3.04 mm, respectively, thus forming almost an approximate equilateral triangle between the S, Ar, and Ptm points. Similarly, the mean values of S-Ba, Ba-PNS, and S-PNS were 44.10 ± 3.36 mm, 43.75 ± 5.07 mm, and 44.77 ± 3.38 mm, respectively, forming another approximate equilateral triangle between the S, Ba, and PNS points. Te mean S-FH to N-FH ratio was 0.67 ± 0.06% for the whole sample, but it was signifcantly more in males 0.69 ± 0.07%, compared to females 0.65 ± 0.06% (P = 0.002).
From the results of all linear and angular parameters, it was found that two equilateral triangles can be drawn across the normal craniofacial structure. Te frst approximate equilateral triangle was formed among the S, Ar, and Ptm points (named as the KUKU triangle) and another between the S, Ba, and PNS points (named as the PUCHU triangle). For both the triangles, the S point was the common vertex point, and we considered the "KUKU triangle" more stable and reliable compared to the "PUCHU triangle." Hence, the "KUKU triangle" and S-FH to N-FH ratio (S-FH: N-FH) could be used as a reference triangle and ratio, respectively, for the identifcation of normal vertical positions of S and N points in subjects with aberrant anterior cranial bases.

Discussion
Efective orthodontic treatment always depends on the accurate diagnosis of malocclusion. Lateral cephalograms are one of the essential aids for the diagnosis of malocclusion. Identifying hard tissue landmarks like Sella (S), Nasion (N), Point-A, and Point-B is very easy. Te anterior cranial base completes 90% of its growth in the frst 5 years of life [32] and undergoes very minimal change during the growth period [27]; thus, the Sella-Nasion plane (SN plane) is used as a standard reference plane. For this reason, SNA, SNB, and ANB angles are the most accepted and widely used cephalometric parameters for assessing sagittal maxillary and mandibular relationships [16][17][18]. However, gradual shifting of S and N points takes place throughout the development of craniofacial structures [19], and also, the migration of N point continues for several years parallel to the craniofacial development [33]. To avoid the infuence of growth on the inclination of the SN plane, we included the lateral cephalograms of subjects who had completed their craniofacial growths for the present study. We observed in the present study that when the SN plane is normally inclined to FH and palatal planes, the cranial base angle is within normal limits; two approximately equilateral triangles are formed between S, Ar, and Ptm points (KUKU triangle) and S, Ba, and PNS points (PUCHU triangle) having S point as a common vertex. An important source of infuence on the morphology of structures surrounding sella is the growth process of the posterior cranial base [34]. Te defection of the posterior cranial base (S-Ba) could result in a greater alteration in the position of the Ba point compared to the Ar point [34]. However, a compensatory mechanism exists to make up for the position of the glenoid fossa associated with cranial base fexure [34]. Te posterior leg (S-Ba) of the cranial base angle (N-S-Ba) can be tipped anteriorly or posteriorly, and according to Andria et al. [35], these are compensated by variable lengths of the posterior cranial base, such as an acute posterior leg that places the mandible forward. Tis action is negated by a long posterior leg (S-Ba) that places both the mandible (Ar) and basion (Ba) posteriorly and vice-versa. Tus, we considered the KUKU triangle more stable and reliable than the PUCHU triangle for the identifcation of the normal vertical position of sella point. We also observed that the distance from the S point to the FH plane is approximately 69% and 65% of the distance from the N point to the FH plane among male and female subjects, respectively. Similar to our observation, Camcı and Salmanpour also reported a 69.62% S-FH to N-FH ratio among subjects with normal SN-FH angles [23].
A signifcant variation in the angle between SN and FH planes can mislead orthodontists in interpreting abnormal jaw positions, even if the jaws are normally positioned. Tus, one must be cognizant of the SN-FH angulation if the SN plane is used as a reference plane for cephalometric analyses. Tere has been no study so far in the literature assessing the normal relationships between points S, Ar, Ba, Ptm, and PNS. Tis is the frst attempt at exploring these measurements of the craniofacial skeleton. Te KUKU triangle and S-FH to N-FH ratio can be used as standard reference triangle and ratio to determine the normal vertical position of Sella and Nasion points among subjects with abnormal inclinations of anterior cranial bases.

Limitations and Future Recommendations.
Although there are newer alternatives to the conventional methods of cephalometric analysis such as the use of reduced FOV CT, this study was an audit of existing records [36][37][38][39]. Hence, future studies can be planned to explore comparisons between newer methods and our proposed methods to establish reliability.   International Journal of Dentistry 5

Conclusions
Te following conclusions were drawn from the present study: (1) Te triangles formed between S, Ar, and Ptm points and S, Ba, and PNS points were almost equilateral among subjects with normal inclinations of SN, FH, and palatal planes.

Data Availability
All data related to the study can be provided on reasonable request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.