Evaluation of the cephalometric centroid point in individuals before and after the pubertal growth peak

Objective : The purpose of this study was to evaluate the behavior of the Centroid point, known as the geometric center of the face, before and after the growth peak using lateral cephalometric x-ray. Methods : Sample consisted of 40 patients before and after pubertal peak of growth selected from the archive of the São Leopoldo Mandic Institute and Research Center, Campinas, Brazil. Anatomical structures, reference points, lines and planes were traced, and posteriorly a superimposition was performed using the palatal plane and a line perpendicular to this passage through the most posterior point of the pterygomaxillary fossa as reference. Later, the distance between the two centroid points (before and after the peak of puberty) was measured using the digital caliper, both horizontally and vertically. The palatal plane (x-axis) and a line perpendicular to this passage through the most posterior point of the pterygomaxilary fossa (y-axis) were chosen because they undergo minimal changes during growth. Results : No significant difference on the location of Centroid points on both X and Y axis (p >0.05) were observed between before and after the growth peak cephalometric tracings, showing an average change in positioning of 0.36mm on the X axis and 0.37mm on the Y axis. Conclusion : For this reason, this point can be indicated to be used clinically as a stable reference to evaluate craniofacial growth while performing superimposition methods. (antes e após o pico de puberdade) por meio de paquímetro digital tanto no sentido horizontal quanto no vertical. O plano palatal (eixo x) e a linha perpendicular a esta que passe pelo ponto mais posterior da fossa pterigomaxilar (eixo y) foram escolhidos por sofrerem mínimas alterações nas suas direções durante o crescimento. Resultados : Não foi observada diferença estatisticamente significante na localização dos pontos Centróides em ambos os eixos X e Y (p>0,05) quando comparou-se os traçados antes e depois do pico de crescimento, mostrando uma alteração, em média, no posicionamento de 0,36mm no Eixo X e 0,37mm no Eixo Y. Conclusão : Assim, este ponto pode ser utilizado como referência estável para avaliação do crescimento craniofacial nas sobreposições.


INTRODUCTION
The radiographic cephalometric method represented a major technological advance in Orthodontics, not only enhancing orthodontic diagnostic but also treatment planning allowing the study of changes on facial structures due to the growth and development of the patient. Cephalometric tracings of the same patient can be superimposed on areas of the skull base that do not suffer any or has minimal change on different time points, therefore serving as a stable reference to assess and perform measurements on teeth, maxilla and mandible, and facial structures [1]. To obtain quantitative and qualitative analyzes of the results of orthodontic treatment, which was previously done only through plaster models or non-standard radiographs [2].
The emergence of cephalometric analyzes allowed clinicians to better understand the craniofacial growth, pattern, and direction of the growth, to identify the individual's facial pattern, to study growth and development of distinct bone components at the skull and face, to analyze facial bone structures, relating it to basal bone and tooth position, to assess the soft tissue profile, as well as to help clinicians to determine the possibilities and limitations of orthodontic treatment [3].
For the cephalograms to be correctly superimposed, it is necessary to choose a certain orientation method based on points or areas located in regions with no growth, many methods indicate the use of skull basal bone as a reference [4]. In addition, anatomical structures that are easily visualized and show accuracy on the x-ray should be chosen [5].
The Centroid point, known as the geometric center of the face, is found by transforming the facial structure into a geometric figure such as a triangle or polygon and has been recommended for individual assessment of the face [6], since the Centroid point tend to show minimal changes during an increase of the shape or sides of the triangle or polygon, i.e, minimal changes during facial growth of the patient [7]. Thus, this method allows cephalomorphic and cephalometric evaluation of skeletal discrepancies without susceptibility of changes in the patient's head position during radiographic taking or variation in intracranial reference points [8].
To find the Centroid point, facial bone structure needs to be redefined into a polygon shape as so the Sella-Nasion line establishes the upper limit of the face; the posterior facial height (Sella-Gonion) represents the posterior limit of the face; the mandibular plane (Gonion-Gnathion) determines the lower limit and the facial height and lastly Nasion-Gnathion line sets the anterior limit of the face, in order to form the three-dimensional polygon. The geometric center of the polygon, thus the Centroid point, is found by connecting two lines draw from the midpoints of each side of the polygon (anterior to posterior and upper to lower) and their intersection determines the point called Centroid [9].
By drawing a horizontal line from the Centroid point to Subnasal point (both center of the face, hard and soft tissue) and later, a vertical perpendicular line in front of the profile, it is possible to use this vertical line, based on Centroid point, to estimate head position similar to the natural and reproducible rest head position of the individual [9]. The natural position of the head (NHP) obtained in photographs has been advocated as a reliable extracranial reference to avoid traditional craniofacial references which can lead to misinterpretation, particularly to the maxillomandibular relationship [10]. For this reason, a standardized method to obtain a correct position of the head is essential to accurately assess and diagnose the craniofacial structures and for longitudinal comparisons [11].
Cephalometric superimposition is a technique that aims to provide information on the changes that resulted from the craniofacial growth and/or progression of orthodontic/orthopedic treatment. For a method to be reliable the use of points or regions considered stable is essential. Thus, since previous studies have recommended using the Centroid point for cephalometric analyzes [7], the purpose of this study was to evaluate the location of Centroid point, based on the method described above, by using lateral cephalograms of individuals taken before and after the pubertal peak of growth, in order to validate its use a reliable reference for superimposition method in growing patients.

Sample selection
This prospective study was conducted after the approval of the Ethical Committee Board from Sao Leopoldo Mandic Research Center and Institute (No. 1.005.929). Eighty lateral digital radiographs of 40 individuals were selected from the archive of the Orthodontic Department at the same Institute taken before and after the pubertal peak of growth. The mean age before growth peak was 10.5 years old and the mean age after growth peak, 13 years old. In addition, in the first x-ray, patients were at Stage II of cervical vertebral maturation and in the second x-ray, at Stage IV [12]. All radiographs must have had high quality and a good contrast to be included in this study. Exclusion criteria were patients undergone any orthodontic and/or orthopedic intervention that will reduce or correct sagittal problems, patients with multiple dental absences, and patients with moderate or severe asymmetries.

Elaboration of the cephalometric tracing
The following anatomical structures were drawn by the same evaluator: sphenoid bone contour, occipital bone, frontal bone, nasal bone, soft tissue profile, maxilla, most anteriorly positioned upper and lower central incisor and first molar, symphyseal bone, mandible. Lines and Plans are described on table 1. After drawing the planes and lines as described on Table 1, an irregular polygon formed by the S-N and N-Gnc lines and Gnc-Goc and S-Goc planes was obtained. This polygon represents three-dimensionally the limits of the face. Later, four midpoints of the polygon were determined, and by connecting the upper to lower and anterior to posterior midpoints, the intersection is where Centroid point was found (figure 1) [9,10,13,14].

Method for locating the centroid points
Cephalograms from the two time-points were superimposed using the palatal plane and a line perpendicular to it passing through the most posterior point of the pterygomaxillary fossa was used as a stable reference. Both palatal plane and the line perpendicular to it that passed through the most posterior point of the pterygomaxillary fossa were chosen due to their proximity to the location of the centroid points and are considered stable [15].  The distance between the two Centroid points (before and after the pubertal peak, called C1 and C2 respectively) was calculated using a digital caliper (Mitutoyo Co., Miyazaki, Japan) on both on the X and Y-axis (figure 2). The distances from point 0 to C1 and from point 0 to C2 were measured, and their difference was calculated.
Measurements were repeated four times at different intervals to evaluate method error. Statistical tests were performed using Graphpad Prism 8 software (GraphPad Software, San Diego, CA, USA). The Smirnov-Kolmogorov test was used to investigate the normal distribution. As the assumptions of normality were not violated, a paired t-test was used. The level of significance adopted for all comparisons was 5%.

RESULTS
The characteristics of the study population are provided in table 2. Sagittal skeletal and facial type were determined based on previous studies [16,17].
To assess intra-examiner reliability, the intraclass correlation coefficient was used. Values between 0.8 and 1.0 mean excellent reliability. In this study, all measurements resulted in a value >0.999, so the test indicated the accuracy of the measurements taken by the same operator ( figure 3).
The results of location of the Centroid point obtained on tracings 1 and 2 referring to the lateral x-rays before and after the pubertal peak of growth, on X and Y axis are shown in table 3 and figures 3 and 4. There was no significant difference in the location of the centroid points on both the X and Y axis (p <0.05) when comparing both traces, showing an average change in the position of 0.36mm on the X Axis and 0.37mm on the Y Axis.

DISCUSSION
Cephalometric analysis aims to evaluate facial morphology by dividing the craniofacial complex in order to study how the skeletal parts are related to each other [18]. Most cephalometric methods use intracranial references from a normal population (no skeletal discrepancy) or extracranial references based on the natural position of the head. According to Lundström et al. [19], the intracranial method based on anatomical references can often be unreliable, as RGO, Rev Gaúch Odontol. 2022;70:e20220002 some landmarks can be difficult to identify, therefore affecting directly the interpretation of craniofacial morphology and skeletal discrepancy. When properly performed, cephalometric superimposition allows clinicians to analyze changes resulted from skeletal growth and dental arch development and orthodontic treatment progress [20].
Many studies support the use of the cranium base as a registration area for superimposition. Although several authors agree that the base of the skull, during the period when most orthodontic cases are treated (9 to 14 years old), is relatively stable and considered a satisfactory reference in the superposition of serial cephalograms [1,4,5,[21][22][23][24][25][26][27], Bjork [28] considers that this structure continues to change during adolescence. In addition, Melsen [29] reported that Sella turcica undergoes remodeling during adolescence and can move back and downwards a few millimeters, but it continues to be widely accepted as a stable area for superimposition techniques. According to McWillian [30] there is relatively good accuracy when performing superimposition using the skull base as a reference in different time intervals in adults, however greater variation can be observed when using it on individuals during growth spurt, the period when bone remodeling activity has a strong influence at the base of the skull. Baumrind et al. [31] reported that the identification of relatively stable structures is not simple, since almost all bones of the craniofacial complex undergo continuous changes during craniofacial development. Even in areas where the bone shape seems to remain relatively constant over time, growth can occur not by proportional expansion in all directions, but as a result of reabsorption and apposition of bone surfaces, which may produce different results depending on the area of evaluation. Thus, it becomes interesting to analyze whether the differences may or may not lead to significantly different interpretations.
Enlow [32] explained that no stable or fixed reference point allows accurate superimposition of cephalograms during growth, as all parts of all bone structures are subjected to greater or lesser amounts of remodeling. For this reason, better references for superimposition do not include reference points, but natural registration areas. On the other hand, as mentioned by Mathews and Payne [33], in the absence of growth or observing in a short time between x-rays, conventional superimposition methods can be used. However, the authors mention that they are not reliable for use during the adolescent growth spurt. They recommended caution when using natural landmarks for superimposition during longer periods of growth.
As for the Centroid point, Johnson and Hubbold [7] emphasized its application to assess craniofacial structures, recognizing the relative stability with traditional cephalometric analysis and described morphological changes during the growth period. They concluded that the points and lines to find Centroid tend to show less variation than anatomical points and lines such as mandibular or Frankfurt plane, or lines relating maxilla to mandible. Thus, the present study aimed to evaluate the Centroid behavior by using stable and easy-to-locate structures as well as intracranial points [9], in a simpler manner for superimposition.
According to Fishman [8] conventional cephalometric analysis evaluates facial form using numerical method comparing averages derived from pre-selected samples as ¨normal¨ and mentions the fact that there is an individual unique craniofacial development pattern and this could lead to a wide skeletal, dental, and soft tissue variation. The author was able to define and identify facial morphological features using an orientation pattern for skeletal, dental, and soft-tissue based on the Centroid point. For the author, the Centroid point represents the geometrical center of mass or gravity of a two-dimensional area or a three-dimensional volume, with minimally change in position as the geometric form increases in size, and therefore being a helpful tool to assess clinically maxillomandibular discrepancies.
By using metallic implants (pins) as reference points in longitudinal cephalometric investigations, Björk et al. [28] provided basic information about the craniofacial growth pattern in humans. Unfortunately, there have been few studies on the results of orthodontic treatment that have used the proposed tantalum implant insertion, presumably because it is an invasive method to be indicated for research purposes only. Since metallic implants are not an option, even though it is considered the gold standard for superimposition, several structures suggesting stable regions have been proposed on superimposition methods for craniofacial assessment. Gu & McNamara demonstrated that the superimposition method recommended by the American Board of Orthodontics (ABO) can underestimate the vertical displacement of the maxilla by 3mm and overestimate the anterior displacement of the maxilla by 1.5 mm when compared to the metallic implant method, measured from superimposed cephalograms of individuals with the mean age of 8.9 years and 15.3 years. In the same study superimposing cephalograms of patients from 10 to 13 years, the mean variation of the maxilla on the X-axis was found between 0.5 and 0.6 mm at the region of the posterior nasal spine [3].
The relevance of this study is the fact that the Centroid point represents a simple and objective way to assess the complex craniofacial alteration during individual development before and after the growth spurt. The results of this study showed that there was no statistically significant difference in the location of the Centroid points on both X and Y-axis (p> 0.05) when comparing the tracings 1 and 2, showing a change, on average, of 0.36mm on the X-Axis and 0.37mm on the Y-Axis. Thus, Centroid points behaved moving slightly forward and downward direction during growth of these individuals. The little amount of change during the peak of growth spurt found in the present study suggests that the proposed Centroid point can be used as a stable reference for cephalometric superimposition.
In the orthodontic daily practice, the application of the Centroid point on consecutive cephalometric tracings at different moments, can help clinicians to assess the growth of the maxilla and mandible (or results of therapy) by using it as a reference landmark and by measuring the distance from the Centroid point relative to basal bone structures, such as point A and ENA (anterior nasal spine) at the maxilla or Point B and Pogonion on the mandible point. Another way of assessing the growth or outcome of the therapy would be by superimposing two cephalograms registering on the Centroid point and by measuring the distance between each landmark on both cephalograms in order to quantify the amount of change, and also by drawing lines/plans to assess the direction of growth/change of the basal bone. Further studies should be carried out to find which method would be best indicated for assessing maxilla and mandible position, using the Centroid point as a reference.

CONCLUSION
The results of the present study demonstrated that there is no significant change from the Centroid point before and after the pubertal growth peak and suggest that Centroid point can be used as a stable reference for assessing craniofacial growth for superimposition method.
Coollaborators JSA Lee, conducting the research, data collection and writing the manuscript. H Suzuki, idea and development of method. ABS Costa, sample gathering for the experiment. AS Garcez, reviewing the manuscript. SS Suzuki, advisor, application of statistical analysis and reviewing and editing the manuscript.