This study was conducted because it was based on the general objective of comparing the results of the diagnosis of dentocraniofacial symmetry of patients in two-dimensional and three-dimensional methods. While in specific, the purpose of this study is to compare the results of the diagnosis of symmetry of the anterior nasal spine, upper first incisor, lower first incsior, pterygomaxillary fissure, orbita, menton, porion, upper first molar, condyle, lower first molar, coronoid process, gonion, zygoma, latero nasale, jugulare in two-dimensional and three-dimensional methods.

The diagnosis of dentocraniofacial asymmetry is crucial in orthodontic treatment planning. Previous literature has extensively explored the comparative analysis of two-dimensional and three-dimensional techniques in assessing dentocraniofacial asymmetry. These studies have contributed to the understanding of the diagnostic accuracy of different methods in evaluating dentocraniofacial asymmetry. The field of dentocraniofacial asymmetry diagnosis is largely focused on comparing two-dimensional and three-dimensional methods, but there is a lack of comprehensive research comparing the specific dentocraniofacial parameters using these methods. Existing studies have not provided a detailed comparison of the diagnosis of symmetry in parameters such as the anterior nasal spine, upper and lower first incisors, pterygomaxillary fissure, orbita, menton, porion, upper and lower first molars, condyle, coronoid process, gonion, zygoma, latero nasale, and jugulare. This research aims to fill this gap by conducting a comprehensive assessment of these specific parameters, leading to a more thorough understanding of dentocraniofacial asymmetry diagnosis.

This study was an analytic observational study with a cross-sectional approach. The clinical examination of the research subjects was carried out at the Dental Hospital of the Faculty of Dentistry, University of Indonesia in March - April 2023. The population of this study were patients with dentocraniofacial asymmetry before orthodontic treatment at the RSKGM FKG UI Orthodontic Specialist Clinic in 2023. The participants in the study were within the age range of 15 to 25 years. This age range was chosen considering the growth and development of the dentocraniofacial structures during adolescence and early adulthood, which can significantly impact the measurements and diagnosis of dentocraniofacial asymmetry. Researchers used 15 people to be sampled based on the Dahlan formula (2010). The study was approved by the Dental Research Ethics Committee, Faculty of Dentistry, Universitas Indonesia with (Protocol no: 050180223) has approved the study on February 12th, 2023. A written informed consent was obtained from all the participants. The clinical examinations were conducted meticulously, following standardized procedures to ensure accuracy and reliability of the data collected. Each participant underwent a thorough assessment of their dentocraniofacial features, allowing the researchers to gather valuable insights into the nature of the asymmetry present in the study population.

In processing the data (Siswoyo, 2023), the researcher conducted a categorical comparative analytic hypothesis test to compare the proportion between the dependent variables, namely with Fisher's Exact Test to determine the difference in the results of the diagnosis of dentocraniofacial symmetry between the two-dimensional technique and the three-dimensional method with the calculation of the Katsumata asymmetry index. Kappa Cohen analysis was performed to see the strength of agreement between the diagnosis of dentocraniofacial symmetry of the two-dimensional and three-dimensional methods on each parameter 11.

The hypothesis for this study is that there is no significant difference in the diagnosis of dentocraniofacial symmetry between two-dimensional and three-dimensional methods when assessing the specific dentocraniofacial parameters including the anterior nasal spine, upper and lower first incisors, pterygomaxillary fissure, orbita, menton, porion, upper and lower first molars, condyle, coronoid process, gonion, zygoma, latero nasale, and jugulare. The 2D dimensions were obtained through traditional orthodontic cephalometric radiographs, which provide a two-dimensional representation of the patient's dental and skeletal structures. On the other hand, the 3D dimensions were obtained through cone-beam computed tomography (CBCT) scans, which provide a three-dimensional visualization of the patient's dental and skeletal anatomy, allowing for a more comprehensive assessment of dentocraniofacial asymmetry. Furthermore, the measurements were specifically conducted on bone-based dimensions to ensure clarity and precision in the diagnosis of dentocraniofacial symmetry. By focusing on bone-based dimensions, the study aimed to provide valuable insights for general practitioners and specialists in accurately identifying and addressing asymmetry within the craniofacial complex.

Fifteen samples that have been obtained in the form of DICOM CBCT are processed using Carestream 3D Imaging v3.87 software ( https://www.carestream.com/en/us/medical/software/imageview-software?gclid=CjwKCAiA3JCvBhA8EiwA4kujZoh1Jaj95uopjgV3gCOLnHA5FjN9FsDVOCl9sfi7hVGM2KIjMtR_qxoCMpkQAvD_BwE) to produce a reconstructed posteroanterior cephalogram image on a 168.3 mm image slice.

A categorical comparative test was performed with Fisher's Exact Test to see if there was a difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the fifteen parameters studied. The results of the analysis of each parameter will be presented in each table.

Fisher's exact test results of two-dimensional and three-dimensional methods on ANS parameters conducted on fifteen samples showed a p value> 0.05. This indicates that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on ANS parameters ( Table 1).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on the parameters of the upper first incisor in fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the upper first incisor parameter ( Table 2).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on the parameters of the lower first incisor conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the lower first incisor parameter ( Table 3).

Fisher's exact test results of two-dimensional and three-dimensional methods on pterygoid fissure parameters conducted on fifteen samples showed p> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the pterygoid fissure parameter ( Table 4).

Fisher's exact test results of two-dimensional and three-dimensional methods on orbita parameters conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the orbita parameters ( Table 5).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on the menton parameter conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the menton parameter ( Table 6).

Fisher's exact test results of two-dimensional and three-dimensional methods on porion parameters conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the porion parameter ( Table 7).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on the parameters of the upper first molar conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the parameters of the upper first molar ( Table 8).

Fisher's exact test results of two-dimensional and three-dimensional methods on condyle parameters conducted on fifteen samples showed p> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the condyle parameter ( Table 9).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on the parameters of the lower first molar conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the parameters of the lower first molar ( Table 10).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on coronoid parameters conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the coronoid parameter ( Table 11).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on gonion parameters conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the gonion parameter ( Table 12).

The results of Fisher's exact test of two-dimensional and three-dimensional methods on zygoma parameters conducted on fifteen samples showed a p value> 0.05. This shows that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the zygoma parameter ( Table 13).

Fisher's exact test results of two-dimensional and three-dimensional methods on lateronasale parameters conducted on fifteen samples showed a p value> 0.05. This indicates that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods in the lateronasale parameter ( Table 14).

Fisher's exact test results of two-dimensional and three-dimensional methods on the jugulare parameter conducted on fifteen samples showed a p value> 0.05. This indicates that there is no difference in the diagnosis of dentocraniofacial symmetry in the two- and three-dimensional methods on the jugulare parameter ( Table 15).

The study results revealed significant differences between Grummon standard and Katsumata index readings for the measured dentocraniofacial features. This finding suggests that there are notable distinctions in the diagnosis of dentocraniofacial symmetry when using the two-dimensional and three-dimensional methods for assessing these features.

In general, the test results obtained are p>0.05 in all parameters measured, so it can be concluded that there is no significant difference in the diagnosis of dentocraniofacial symmetry between the two- and three-dimensional methods on all fifteen dentocraniofacial parameters measured.

This is in line with research conducted by Kumar (2007); Katsumata et al. (2005) and Robben et al (2017) which states that the reconstruction of two-dimensional cephalogram images from CBCT imaging results is able to provide an image similar to conventional cephalogram results with linear and angular size accuracy and the same precision. ¹ The results of this posteroanterior cephalogram reconstructed image will be analyzed for dentocraniofacial symmetry using the software. Research by Meldenik et al (2011) stated that the use of carestream 3D imaging is able to provide good contrast and resolution as well as good accuracy during the analysis process which can affect visualization in determining craniometric points. ^{2 , 3 , 9} The analysis procedure was carried out using the Grummon technique on all fifteen parameters by measuring the linear discrepancy of each side against the midsagittal reference line. At a single parameter point, only the distance from the parameter point to the midsagittal reference line was measured. If the linear discrepancy value obtained was more than two millimeters, a diagnosis of asymmetry was made. ^{1 , 2}

Three-dimensional analysis was carried out by processing the fifteen samples of CBCT results into multiplanar reconstruction and volumetric rendering. This is supported by the research of Barreto et al (2020) which states that cephalometric measurements in multiplanar reconstruction have good accuracy in linear and angular measurements. 81 The analysis process is carried out by measuring the fifteen parameters against a three-dimensional reference plane whose values will be calculated into an asymmetry index as described by Katsumata. The asymmetry index obtained will be compared with the Katsumata index table to assess whether it is categorized as asymmetry or not for each parameter. ³

The results of the Fisher's exact test on fifteen parameters showed a p value> 0.05, meaning that there was no significant difference between the diagnosis of dentocraniofacial symmetry of the two-dimensional method and the three-dimensional method of calculating the asymmetry index. Kappa Cohen analysis was performed to see the agreement of dentocraniofacial symmetry diagnosis of two-dimensional and three-dimensional methods. The highest agreement value was seen in the parameters of jugular, lateronasale, zygoma, lower first incisor. The next category in near perfect agreement is the lower first molar parameter. Menton, porion, upper first molar, orbita, and anterior nasal spine are included in the substantial agreement category. Upper first incisor, condyle, and gonion are included in moderate agreement. Lastly, the pterygoid fissure and coronoid are in fair agreement.

The anterior nasal spine parameters in the fifteen samples analyzed, fourteen samples were diagnosed with symmetry and one sample was diagnosed with asymmetry in both methods. One sample was diagnosed with asymmetry in the three-dimensional method but symmetry in the two-dimensional method. This may be due to the difference in the standard deviation range of the Katsumata asymmetry index value and the Grummon standard. The discrepancy of 1.8 mm in ANS is still categorized as symmetry in the two-dimensional method because it is still below 2 mm but the value is above the standard Katsumata asymmetry index in the ANS category. In the parameters of upper first incisor, lower first incisor, pterygoid fissure, orbita, menton, porion, upper first molar, condyle, lower first molar, coronoid, and gonion, the same thing was found in the form of a difference in diagnosis between the two-dimensional and three-dimensional methods of calculating the Katsumata asymmetry index. This difference can occur due to several things, including the placement of the craniometric points of the measured parameters due to differences in the definition of each parameter and differences in procedures and standard values for diagnosis in the two- and three-dimensional methods. ⁵

Cephalometric analysis errors can be systematic errors and random errors. Systematic errors are measurement errors that occur consistently throughout the study. In this study, only one exposure to the patient was used, namely by using a CBCT machine so that the radiographic image can minimize the occurrence of magnification and distortion. Two-dimensional image reconstruction was performed using the same CBCT results and the same software, namely carestream 3D imaging v 3.87 at a slicing split view of 168.3 mm to minimize systematic errors. The study measurements were performed by one researcher (SS) with clear operational definitions so that according to Lisboa et al (2014), systematic errors in craniometric point identification do not affect the results of the study if supported by a good intrarater reliability assessment.

The second error is random error. This error is a difference in the measurement data due to inaccuracy and/or difficulty in measurement. Random errors can always occur in a measurement. In cephalometric analysis, random errors can occur due to imprecise craniometric point placement. The imprecision of craniometric point placement can be influenced by several things such as the brightness and contrast level settings of the posteroanterior reconstructed cephalogram image and CBCT results and operator fatigue factors. To anticipate this, researchers ensure that sufficient brightness and contrast levels are used during the analysis process and give a minimum distance of 1 day between each pointing to avoid fatigue.

There are some craniometric points that are difficult to identify in both two and three dimensions and researchers' opinions on the accurate positioning of craniometric points may vary. Although the operational definition of parameter points has been determined, points with the definition of “most anterior/posterior/inferior” on curved planes such as the orbita or gonion have high subjectivity (Chien et al, 2009). This is in line with the research of Oliveira et al (2009) who said that the orbital point is located on a curved surface so that the three-dimensional identification process can provide accurate placement. In addition to the orbital point, the condyle point also often has difficulty in point placement. This is due to the lack of detailed definition of the parameter point due to its curved anatomical area. ⁶ Vlijmen et al (2010) also added that differences in diagnosis results between two- and three-dimensional methods can occur due to the addition of second and third-dimensional assessments that can affect the diagnosis. In three-dimensional analysis, anatomical structures can be observed as they actually are in all three viewpoints rather than two-dimensional imaging. ^{7 , 8} The addition of the third dimension requires additional precision for the researcher in determining points according to the three-dimensional definition, especially points located on curved planes. ^{3 , 4 , 6}

This identification difficulty in craniometric points also affects the taking of the reference sagittal plane in the two-dimensional and three-dimensional methods. In the two-dimensional method, the center reference line is determined using the midsagittal reference (MSR) formed from the point on the crest gallii. In the three-dimensional method, the center plane is determined using the sella and nasion reference points. Identification of the sella point on a two-dimensional posteroanterior cephalogram image is not possible due to the superimposition of anatomical structures from the frontal direction. This difference allows for different transverse size values in the two-dimensional and three-dimensional methods. The sella point is located at the base of the cranii which undergoes very minimal expansion during growth after the age of five and only undergoes growth in the inferior anterior direction. The nasion point is also a relatively stable point and only undergoes growth in the vertical and sagittal directions but not in the transverse. The anterior region of the base of the cranii from the sella turcica to the frontal bone is quite stable and does not undergo much change after the age of seven years, so using this point as a reference plane is considered good. ¹⁰

This identification difficulty in craniometric points also affects the taking of the reference sagittal plane in the two-dimensional and three-dimensional methods. In the two-dimensional method, the center reference line is determined using the midsagittal reference (MSR) formed from the point on the crest gallii. In the three-dimensional method, the center plane is determined using the sella and nasion reference points. Identification of the sella point on a two-dimensional posteroanterior cephalogram image is not possible due to the superimposition of anatomical structures from the frontal direction. This difference allows for different transverse size values in the two-dimensional and three-dimensional methods. The sella point is located at the base of the cranii which undergoes very minimal expansion during growth after the age of five and only undergoes growth in the inferior anterior direction. The nasion point is also a relatively stable point and only undergoes growth in the vertical and sagittal directions but not in the transverse. The anterior region of the base of the cranii from the sella turcica to the frontal bone is quite stable and does not undergo much change after the age of seven years.

The results of this study showed no difference in the diagnosis of dentocraniofacial symmetry in two-dimensional and three-dimensional methods with the calculation of the Katsumata asymmetry index. The level of agreement of the diagnosis results of the two- and three-dimensional methods varied in all fifteen parameters. Orthodontists are expected to utilize three-dimensional dentocraniofacial symmetry diagnosis for patients who are indicated using cone beam computed tomography for examination and preparation of surgical and non-surgical combined orthodontic treatment plans. Orthodontists are also expected to analyze the symmetry of the dentocraniofacial structure in depth in three dimensions to determine the shape of the dentocraniofacial asymmetry whether it is purely translational or there is a combination of rolling, yawing, and pitching that can affect the treatment plan. This is in accordance with Ko's research (2022) which states that to obtain optimal treatment results in asymmetry patients, a comprehensive dentocraniofacial evaluation is needed including from the outer to the inner dentoskeletal components which can be done on a three-dimensional cone beam computed tomography examination.

The study was focused on comparing the Grummon standard for the analysis of two-dimensional (2D) measurements and the Katsumata index for three-dimensional (3D) measurements. These standards were utilized as references to determine whether the measurements exhibited symmetry or asymmetry. In the case of the Grummon standard, it is a well-established method used to assess dentocraniofacial asymmetry in 2D measurements. Meanwhile, the Katsumata index is specifically designed for 3D measurements and has been widely recognized in the field of orthodontics. The Grummon standard assesses the symmetry or asymmetry of specific dentocraniofacial parameters in 2D measurements, including the anterior nasal spine, upper first incisor, lower first incisor, pterygomaxillary fissure, orbita, menton, porion, upper first molar, condyle, lower first molar, coronoid process, gonion, zygoma, latero nasale, and jugulare. Symmetry or asymmetry is determined based on the measurements in relation to established norms. On the other hand, the Katsumata index is used to evaluate the symmetry or asymmetry of dentocraniofacial parameters in 3D measurements. This index considers the spatial relationships and dimensions of various craniofacial structures. Using this index, researchers were able to assess the symmetry or asymmetry of the same set of parameters in their three-dimensional form. By employing these standardized methods, the study aimed to provide a comprehensive comparison of the diagnosis of dentocraniofacial asymmetry in both 2D and 3D methods, thus contributing to the advancement of orthodontic diagnostic techniques. Diagnosis showed no statistically significant difference in the two-dimensional method with the Grummon comparison technique and the three-dimensional method with the calculation of the Katsumata asymmetry index.

The clinical examination of the research subjects was carried out at the Dental Hospital of the Faculty of Dentistry, University of Indonesia in March - April 2023.

The study was approved by the Dental Research Ethics Committee, Faculty of Dentistry, Universitas Indonesia with (Protocol no: 050180223) has approved the study on February 12th, 2023. A written informed consent was obtained from all the participants.

Figshare:STROBE Checklist for Comparison of two-dimensional Grummons’ analysis and three-dimensional asymmetry index measurement in diagnosis of dentocraniofacial asymmetry, https://doi.org/10.6084/m9.figshare.24331090.v2. ¹¹