Reliability of a Centroid method to estimate head position in cephalometric diagnosis

Objective: The objective of this study was to 1) evaluate the reproducibility of natural head position (NHP) in different professional groups; 2) compare three cephalometric methods of estimating head position to the established natural head position and 3) investigate the applicability of a new method to estimated head position using a Centroid method. Methods: The sample consisted of 105 individual cephalometric tracings and photographs. For the first evaluation, copies of the lateral photographs were reproduced for each patient and 3 professionals with different expertise (experienced orthodontists, orthodontic students and orthognatic surgeon) were instructed to position the photographs in NHP. Later, 3 different methods to obtain NHP were assessed: 1) the Frankfort Horizontal Plane (FRANK), 2) Sella-Nasion 7o Line (SN7) and 3) proposed Horizontal Reference Line based on Centroid. Angles formed by the evaluated planes/lines and True Vertical Line obtained were measured. Gender and skeletal discrepancy were considered. Results: The results showed a significant difference between NHP obtained from orthodontists and surgeons compared to students (p<0.0001). Also results showed no effect of skeletal classification and gender did on measurement (p>0.05). Both SN minus 7o and FRANK methods showed a high variability (p < 0,01) compared to Centroid method. Conclusion: NHP may be affected by the professional experience. The proposed horizontal line based on Centroid is a valid method for estimating head position, thus, may be indicated to use as a diagnostic tool in Orthodontics and Orthognatic Surgery. Indexing terms: Orthodontics. Diagnosis. Orthognatic surgery.


INTRODUCTION
Cephalometric analyses have become indispensable in clinical Orthodontics and orthognatic surgery in order to obtain a proper diagnosis, treatment planning, therapy monitoring and evaluation of treatment results, as well as, craniofacial growth follow-up [1].
In order to determine skeletal maxillomandibular relationship by cephalometric analysis, two methods are most commonly used to guide head position, either using intracranial or extracranial references [2,3]. Intracranial reference, such as the Sella-Nasion line [1] and Frankfort horizontal [4] are widely used. However, landmarks used to determine these intracranial references may not be stable and may change continuously during growth, leading to greater variability among individuals. Therefore, these lines/planes are inherently unreliable and likely to mislead orthodontic diagnosis and treatment planning [3]. A recent study has shown that skeletal cephalometrics may lead to a different diagnosis of patient's facial characteristics [5].
Natural head position (NHP) is considered the most appropriate reference for skeletal discrepancies diagnosis and treatment planning and is the method of choice by many clinicians since is relatively easy to obtain [2,3,5,6]. NHP is a standardized and reproducible position, with patient in an upright head posture and eyes focused on a point at some distance and at eye level, in a horizontal vision axis [5,6]. A number of studies evaluating NHP registered in photographs and lateral radiographs recommend it as a reasonably stable position that could be used as a reference [7][8][9]. NHP obtained during x-ray acquisition seems more difficult that taken by photograph, probably due to the ear rods and the nasal support from the cephalostat which might disturb the natural position of the head [9]. In a recent review, Cassi et al. cited that assessment of craniofacial morphology is influenced by the experience and perceptions of the examiner, so the standard positioning of the patient is crucial for objective assessment, especially with use of Cone Beam Computed Tomography (CBCT) and 3D photographs [10].
Variability of less than 5° may be considered acceptable and a variation between 2° and 3° can be found in most studies [6,7,11,12]. Madsen et al. [13] found that approximately 68% of individuals will reproduce NHP within a variation of ±3° and 95% of individuals within ±6° of difference from zero which means that for 2/3 of the subjects. Thus, NHP reproducibility ranged within ±3°, but 1/3 ranged within ±6º which is clinically meaningful and could alter diagnosis and treatment plan 11 . In order to have more understanding of this issue, in figure 1A, we can observe a lateral facial photograph that has been modified in clockwise and counter-clockwise rotation every 1º from the original head position to illustrate the clinical significance of this variability during NHP acquisition. In Figure B and C, it is possible to better visualize how much a ±3° and ±6° variation in NHP can be misinterpreted in daily clinical practice.
Centroid is a mathematical point that describes the geometric center of a polygon or also described in physics as the center of gravity of an object's shape. It has been introduced fifty years ago and its use in cephalometric research has been reported by a few investigators [14][15][16][17][18]. The explanation of why use Centroid in cephalometric research lies in that, Centroid represents the least variable, therefore, the most stable point of any area or volume, and it is not affected by increasing in size and/or changing in shape [17].
The purpose of this study was: 1) to evaluate the reproducibility of natural head position between three RGO, Rev Gaúch Odontol. 2020;68:e20200045 groups of clinicians with different professional experience; 2) to assess two methods of estimating head position using intracranial references and comparing them to the established natural head position and 3) to investigate the reliability and applicability of an estimated head position using a Centroid reference method.

Sample
This prospective study was conducted after the approval of the St. Leopoldo Mandic Dental Research Center Ethical Committee of Human Studies # 07/115.
The sample consisted of lateral photographs and cephalometric radiographs of 212 subjects, age varying from 12 to 48 years old divided in 4 groups: Group 1 consisted in 60 skeletal Class I patients (mean age 22.3 years old), Group 2 in 79 skeletal Class II and III patients (mean age 22.1 years old) and Group 3 in 73 patients presenting vertical discrepancies (mean age 18.5 years old). Inclusion criteria included: no orthodontic/orthopedic treatment, complete permanent dentition, no congenitally missing, extracted teeth or extensive restorations or prosthesis and no physically handicapped or visually impaired individuals. Study 1 -For the lateral photograph, each patient was instructed to keep teeth gently in occlusion and to look at a mirror at eye level located at a 2m distance. Patient was instructed to remain in a natural and relaxed body position. In the photograph, soft tissue of the patient facial profile was fully observed.
In order to evaluate and establish the correct natural head position obtained in the photographs, from the overall sample, 100 patients were selected and seven copies of the photograhs, seven copies of the photograph were reproduced for each patient, resulting in a total of 700 photographs that were cropped in a round shape, in order to avoid the effect of the paper margins during head positioning. After sample preparation, each set of 100 photographs were submitted for evaluation by: Group A) three orthodontists with more than 15 year of clinical experience; Group B) three students enrolled in the orthodontic program for 2 years and Group C) one experienced orthognatic surgeon.
All professionals were instructed to place the photographs in natural head position based on his/her own criteria and fixed it. After proper attachment of the photographs, Ricketts' E-line (a line drawn from nose tip to chin) was traced on the photograph and the angle between the E-line and a vertical line (VL) parallel to the paper margin was measured (figure 2A). Study 2 -Lateral radiographs were taken, and tracings were performed including soft and hard tissue drawings. Lines and planes used in this study included: Sella-Nasion line (SN); Sella-Constructed Gonion line (S-Goc); Nasion-Constructed Gnation Line (N-Gnc), mandibular plane (MP), Frankfort horizontal, and horizontal line (HL), perpendicular to the vertical line.
For the Centroid method, a polygon geometric figure was traced using: anterior cranial base SN line representing the ceiling of the face, S-Goc representing the posterior limit of the face, N-Gnc representing the anterior limit of the face and MP as the floor (lower bound) of the face. In order to obtain a regular geometric form, middle points of each line were found and by tracing the transversal and vertical lines that connects the middle points, the Centroid point was found. A line was then constructed passing through the Centroid point and the Subnasal and extending it until it reached the VL, this line was called Centroid Reference Line (CRL) (figure 2F). Additionally, two conventional methods, traditionally used, based on intracranial references were traced: SN7º and Frankfort horizontal.
All three methods were evaluated considering NHP as the gold standard method. Mean values of the angles obtained from NHP achieved by the four experienced professionals (orthodontists and the surgeon) in the first study of this study were used as reference to transfer the VL obtained in the photograph to the cephalometric tracing by using E-line as the common line to both photograph and tracing (figure 2B-C).
After transferring the VL to the tracing, a HL was drawn perpendicular to VL, passing through the Sella, Porion and Centroid points in order to measure the angles for SN7º, Frankfort horizontal and CRL, respectively ( Figure  2D-F). When the HL was above CRL, FRANK or SN7º, values were considered negative and positive when HL was underneath them. Also individuals were divided in 2 groups categorized by the measured angle: individuals presenting angles higher than +4º and lower than -4º (x-≤-4º or x-≥+4º) were considered non-acceptable and angles varying between -4º and +4º (-4º < x <+4º) were considered acceptable.

Statistical Analysis
Normality of the data distribution was assessed with the Shapiro-Wilk test. Kruskal-Wallis and Dunn Multiple Comparison nonparametric tests were used to compare NHP determined by the three professionals. Same non-paremetric test was used to compare the three skeletal groups for each method. Mann-Whitney was used for gender comparison. Friedman test to compare three compare the 3 methods to estimate head position with no

Error of method
To test the method error, 43 cephalometric tracings, representing 20% of the overall sample, were randomly selected and re-traced, as well as all the landmarks and measures. The Wilcoxon Matched Pairs test were applied and did not show a p value< 0.05 for all the three methods (SN7º, p=0.72; Frankfort horizontal, p=0.085; Centroid method, p=0.32).

RESULTS
The results showed that there was a significant difference between NHP experienced orthodontists x orthodontic students (p=0.0058) and surgeon x orthodontic students groups (p=0.0073). No difference was found between experienced orthodontist and orthognatic surgeon (p>0.9999) and the difference between values found were less than 1º (figure 3).  Table 1 shows median, minimum and maximum values for all the three methods, distributed by skeletal classification groups and genders. There were no   statistically differences related to skeletal classification and gender (p>0.05). Table 2 shows the results general results, including all skeletal discrepancies and gender. Both tables show that the three methods differ from each other (p<0.01) and that the median for the Centroid method is close to zero, which means that it is extremely compatible with the true horizontal line. SN7º and Frankfort horizontal showed a higher variability for median and standard deviation.
Since HL obtained from NHP found by experienced professionals was used as reference, angles found larger or lower than 4º were considered non-acceptable (high variability). A higher number and percentage of individuals  When the methods were compared separately in pairs, SN7º and Frankfort horizontal were found not statistically different (p=0.3203), but both methods were significantly different from the Centroid method (p<0.001) (table 3).
The Centroid method can be applied as the method of choice in cases when the clinician does not have the profile photograph of the patient or may be insecure on using the NHP taken by a non-experienced professional. A clinical example is shown in figures 4 and 5, of facial and dental records of a 14 year-old patient. Study model shows a Class III Angle malocclusion with proclined upper incisors and lingual inclination of lower incisors, confirmed by the lateral xray. Such characteristics are usually found as dentoalveolar compensation on Class III skeletal patients. On the contrary, facial images, especially the profile picture allegedly taken in natural head position shows a convex profile with retrognatic mandible, which is contradictory with the clinical and xray findings (figure 4). When Wits measurement was performed based on NHP obtained on the photograph, a positive 4o was found, indicating a Class I maxillomandibular relationship ( Figure 5). After tracing the cephalogram, head position was estimated using the Centroid method, by correcting the Centroid Reference Line (Centroid point to Subnasal), Wits was once again measured, but this time, the obtained value was -3o, thus expressing a skeletal Class III relationship which seems to corroborate with clinical findings.

DISCUSSION
Cephalometrics aims to evaluate facial morphology by segmenting the craniofacial complex in order to study how skeletal compartments relate to each other [19,20]. Most common cephalometrics use intracranial landmarks relating to normal population (with no skeletal disorders) or extracranial references based on the natural head position. According to Lundström et al. [3], the intracranial method based on anatomical landmarks can often be unreliable since some landmarks can be hard to distinguish, thus, having a direct effect on the interpretation of the craniofacial morphology and skeletal discrepancy.
Our results showed that comparing Centroid method and Frankfort, there was a significant difference and the same result was found when comparing the Centroid method to SN7º. No difference was found when comparing Frankfort horizontal to SN7º. Since median value of the measured angle obtained from Centroid method was equal 0, this indicate that the proposed method to estimate head position has a close relation to the NHP established by the experienced professionals. Frankfort and SN7º presented greater variability. Probably due to a difficulty in locating precisely Porion point in the petrous portion of temporal bone [6] or a high variation to demarcate orbit point [21] in Frankfort horizontal. As to SN, Moorrees [4] considered it as highly variable and mentioned that when the SN line is markedly inclined downward or upward, SNA (Sella-Nasion-Apoint) and SNPg (Sella-Nasion-Pogonion) angles may vary greatly. Another downside of using SN line is that nasion point is a established in a suture that changes during active growth in children, thus it may move forward and upward, or even downward during growth [22]. It might explain the high variation for SN7º and Frankfort horizontal references found in our study.
Studies have shown that extracranial reference using NHP minimizes intracranial variations, leading to a more accurate assessment of growth and dentocraniofacial anomalies and considered NHP method more reliable and highly reproducible [1,2,4,6,8,11,23]. Negreiros & Smith [24] and Özbek & Köklü [25] reported that angular and linear measurements show significant changes when NHP changed more than 5º. It is known that the change in head position equal or more than 5º may conduct to an error in linear measurement as large as 10cm [26], and thus incorrectly establishing facial morphology and as consequence, an incorrect diagnosis and treatment plan. Based on this, the present study used 4º as a reference to consider variation of head position as acceptable (-4º < x <+4º) or non-acceptable (x≤-4º ou x≥+4º). It was observed in our study that for all three groups, the number of individuals with acceptable values was greater than the non-acceptable values. Centroid method showed the highest number of individuals presenting angles varying between -4º and 4º (88.2%) compared to the other methods. Frankfort method [27] showed 38.7% of indivuduals categorized as non-acceptables, thus greater variability of head position.
In addition, the minimum and maximum values related to the Centroid method were lower than SN minus 7 and Frankfort horizontal, +13º to -5º and -11º to 9º respectively ( Table 2). Confirming this data, Torres et al. [28] found minimum and maximum values of the angle formed by the Frankfurt Horizontal to vary between -11.5º and +8º in all 60 cases studied. The Centroid method showed the lowest variation of minimum and maximum values compared to other methods (-6º to 4º ). Therefore, the use of Centroid Reference Line showed less variation between the minimum and maximum values, and seems to be the most reliable method to estimate head position.
If the clinician does not have patient's lateral photograph or may be insecure on using the NHP taken by a non-experienced professional, Centroid method can be applied. A number of factors affects head posture, including craniofacial morphology [29], respiratory resistance, rapid maxillary expansion [30]. As explained previously at the results section, if photograph is not taken in a correct natural head position which at the majority of times, head needs to be adjusted by the clinician, it may mislead to interpretation of patient's facial profile, therefore the diagnosis of the skeletal problems. The method using the E-line angle to transfer head position from cephalogram to photograph and from photograph to cephalogram has been recommended by Park et al suggested the use of E-line angle found in profile photograph to be transfer to CBCT 3D image aiming to adjust head position and therefore, more accurately access anteroposterior skeletal relationships [31].
The relevance of this study lies on the fact that Centroid method represents a simple and objective approach for clinicians to evaluate the craniofacial complex. More research on the proposed method based on Cone Beam computed tomography should be encouraged to estimate head position on 3D model, increasing its applicability to benefit a more proper diagnosis of sagittal and vertical skeletal discrepancies and more accurate treatment plan.

CONCLUSION
-NHP seems to be dependent on professional experience. -Reorientation of cephalometric tracings using the Centroid method is a reliable, simple and objective method to estimate head position. -The Centroid method had the least variation compared to Frankfort horizontal and SN7º methods, thus it may assist clinicians to obtain a proper diagnosis and treatment plan.
Collaborators H SUZUKI, idea and development of method, reviewing the manuscript; SS SUZUKI, application of statistical analysis, writing the manuscript; AS GARCEZ, development and design of the methodology,reviewing the manuscript; JM CARVALHAES, conducting the research and data collection; DN FUJII, sample gathering for the experiment; YBL ARSATI, advisor and reviewing and editing the manuscript.