1 Introduction

Differences in tooth widths within the same jaw or between the upper and lower jaws can impact occlusion during orthodontic treatment [1]. However, this issue typically becomes apparent only in the final stages of treatment [2]. Tooth widths, especially in the anterior region, are considered crucial variables and have been identified as the seventh key to occlusion [3]. Multiple approaches have been suggested to evaluate disparities in tooth widths, although their utilization remains limited [4]. Studies conducted in the United States indicate that orthodontists frequently employ the Bolton ratio during the initial diagnosis of orthodontic cases [4]. This ratio plays a crucial role before orthodontic treatment, serving as a direct and significant indicator for assessing dental harmony and detecting irregularities in the upper or lower jaw, as well as the anterior or posterior regions [5].

The Bolton ratio directly affects overjet, overbite, crowding, and spacing [5]. Traditionally, this ratio has been manually calculated based on tooth widths (anterior/posterior width) using plaster models [6]. However, researchers are increasingly exploring modern digital alternatives and conducting tests and comparisons to determine their accuracy [7]. Digital methods are also favored for their ease, speed, and efficient image and data storage capabilities [7].

In orthodontic diagnosis, high-quality 3D digital models allow for the measurement of tooth widths and subsequent calculation of the Bolton ratio [8]. Several published studies have analyzed tooth widths using cone-beam computed tomography (CBCT), with plaster models (by alginate impressions) [9] or 2D/3D images serving as the gold standard for comparison [10], applied to either patients [10] or skulls [11]. The standardized orientation method, which involves measuring all teeth in the occlusal plane of the entire jaw, has been adopted [12]. However, the custom orientation method, based on the sagittal axis of each tooth individually, has not been used to accurately determine the anterior/posterior width.

The intraoral scanner (IOS) represents the latest innovation in dentistry for generating assessable 3D images [13]. Numerous tests have been conducted to determine the accuracy and reliability of this scanner in measuring tooth widths and the Bolton ratio, using plaster models [14] or 2D images as the gold standard [15]. However, no study has compared the accuracy and reliability of measuring tooth width and the Bolton ratio using CBCT and IOS images, with plaster models by C-silicone impressions (the gold standard) for comparison.

This study aims to be the first in the medical literature to conduct a three-way comparison of these methods.

2 Materials and methods

The study was conducted at the Department of Preventive, Orthodontic & Pedodontics, College of Dentistry, University of Duhok, from November 2021 to December 2022. It was a comparative study with three groups: the plaster model group [G(PM)], CBCT group [G(CBCT)], and the IOS group [G(IOS)]. Local Research Ethics Committee Approval was obtained from the Directorate of Health in Duhok governorate, Ministry of Health, Kurdistan Region (ID = 21082023-7-9), and the study was registered on the clinical trials database (www.clinicaltrials.gov) (ID = NCT05711160).

2.1 Sample size calculation

The sample size was determined using G*power 3.1.9.4 software (Universität Düsseldorf, Düsseldorf, Germany) with a power of 80%, and an effect size of 0.38 (based on a previous study [16]). The statistical analysis included a Repeated Measures ANOVA followed by a Bonferroni post hoc test to compare the different measurement methods. Therefore, a sample size of 72 patients was required, and informed consent was obtained from each participant.

2.2 Participants

A total of 200 patients at the Department of Preventive, Orthodontic & Pedodontics in the College of Dentistry, University of Duhok underwent examination. Out of these patients, 90 individuals who met the inclusion criteria received a detailed explanation of the study project. Information sheets were then distributed, and those patients who expressed their willingness to participate were asked to sign consent forms. Eventually, a total of 80 patients agreed to take part in the study.

Using a random selection process based on the predetermined sample size, the study selected a total of 72 patients. Each group consisted of 72 plaster models, 72 CBCT images, and 72 IOS images (Fig. 1). CBCT and IOS images, acquired from orthodontic patients at the Department of Preventive, Orthodontic & Pedodontics, College of Dentistry, University of Duhok, serve as diagnostic records for treatment initiation, extending beyond their research applications.

Fig. 1
figure 1

Diagram of the study groups

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The inclusion criteria for participants included being between the ages of 19 and 36, having a complete set of permanent teeth, and not currently undergoing orthodontic treatment. On the other hand, exclusion criteria encompassed tooth agenesis or extractions, large restorations, anomalous tooth shapes, severe carious lesions or enamel defects, and severe crowding in the dentition (> 6 mm).

2.3 Participant’s preparation

All patients underwent scaling and polishing to ensure records of clean teeth, and all diagnostic records were taken by the same trained co-authors (M.A.M).

For plaster models, impressions of the upper and lower arches were recorded using C-silicone impression material (Zetaplus, Zhermack, Italy), and Orthodontic stone class III (Orthokal, Kalabhi®, Gujarat, India) was used to create the plaster models. CBCT scans of both jaws were taken using the Smart 3D apparatus (LARGEV, China) to obtain 3D images with the following parameters: voxel size of 100 μm, tube voltage of 100 kV, tube current 3 mA, and an exposure time of 13 s. Intraoral scans of the patient’s dentition were performed using the Intraoral scanner (Trios®, 3Shape dental systems, Copenhagen, Denmark) according to the manufacturers’ instruction.

2.4 Measurement of teeth widths and Bolton’s ratios

All maximum mesiodistal width measurements were taken from the left first molar to the right first molar for both the upper and lower jaw by the trained first author (S.K).

Tooth widths were measured using a digital electronic caliper for plaster models (Fisher Scientific International Inc., Hampton, NH, USA) [17] (Fig. 2).

Fig. 2
figure 2

Taking measurements of the tooth width on the plaster model

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CBCT images were examined using smartV2-CD® software (LARGEV™, China). Images were carefully oriented for accuracy [18]. Each tooth was individually oriented, and sections were adjusted to ensure perpendicularity with the tooth’s longitudinal axis (Fig. 3). This orientation method allowed precise measurement of tooth width regardless of its position in the dental arch.

Fig. 3
figure 3

Right lower first molar (46) orientation and width measurement. a Sagittal view, b Cross-section view. IOS images were measured using ortho analyzer software (Trios®, 3Shape dental systems, Copenhagen, Denmark) [19] (Fig. 4)

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Fig. 4
figure 4

Measuring the tooth width on the digital model obtained from the IOS. a lower jaw, b upper jaw

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Bolton’s ratios were calculated for each patient using Bolton’s formula to assess the anterior and overall ratios [20].

The minimum measurable value on a digital electronic caliper is 0.01 mm, for CBCT images it is 0.1 mm, and for intraoral scanner (IOS) images, it ranges from 0.1 to 0.2 mm.

2.5 Intra-observer reliability of measurements

To determine intra-observer reliability, all measurements were repeated after one month by the same examiner (S.K).

2.6 Blinding

In this trial, the concept of participant blindness did not apply. Consequently, the only instance where blindness was implemented was during the data analysis stage, specifically by one of the co-authors (M.R.S). To maintain the assessor’s blindness, the patients’ CBCTs, IOS, and plaster models were assigned unique serial numbers, and the allocation of data was kept concealed from the investigator throughout the statistical analysis phase.

2.7 Statistical analysis

Statistical analysis was performed using 2011 IBM SPSS Statistics software (IBM©, Version 20.0, Armonk, USA). Measurement reliability (intra-observer) was assessed using the intercorrelation coefficient (ICC). Kolmogorov–Smirnov Normality tests showed normal distributions of the collected data. Repeated Measures ANOVA was used to compare the three groups, followed by post hoc tests with Bonferroni correction. The Intraclass Correlation Coefficient type2 was employed to assess the agreement among measurements across groups.

3 Results

A total of 72 participants (29 females and 43 males) with an age range of 19–36 years (mean age 26.49 ± 1.16 years) were included in the study. All patients completed the study, and data analysis was performed for all participants. Table 1 presents the basic characteristics of the patients.

Table 1 Sample basic characteristics
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Tooth width measurements were taken from the left first molar to the right first molar in the upper and lower jaws. A total of 5184 tooth width measurements (1728 per group) were recorded for all participants.

3.1 Intra-observer reliability of measurements

Regarding the intra-observer reliability of measurements, strong associations were found between the initial measurements and those taken after one month for tooth width and Bolton’s ratios in each of the three study groups (Table 2).

Table 2 Intraclass Correlation Coefficient between two-time intervals for reliability analysis
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3.2 Assessing tooth width differences among three groups

A Repeated Measures ANOVA test was conducted to evaluate the differences in mean values for teeth widths among the three groups: G(PM), G(CBCT), and G(IOS). The comparison showed no statistically significant differences in tooth widths among the groups (Tables 3 and 4).

Table 3 Comparison of accuracy and reliability of tooth widths: ANOVA and ICC Analysis among three groups (maxillary)
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Table 4 Comparison of accuracy and reliability of tooth widths: ANOVA and ICC analysis among three groups (mandibular)
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Further analysis revealed no significant differences in mean tooth widths between the G(PM) and G(CBCT) groups or between the G(PM) and G(IOS). Similarly, no significant differences were found between the G(CBCT) and G(IOS) (Table 5).

Table 5 Comparison between the three groups in the tooth widths (G(PM) + G(CBCT)), (G(PM) + G(IOS)), (G(CBCT) + G(IOS))
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Evaluation of agreement among the plaster models, CBCT, and IOS images using ICC is presented in Tables 3 and 4

3.3 Assessing Bolton ratio differences among three groups

Assessing the Bolton ratios, the G(CBCT) had slightly lower mean values compared to the plaster models group, but the differences were not statistically significant. The G(IOS) showed slightly higher mean values for the Bolton ratios, but again, no significant differences were observed (Table 6). Additional analysis indicated that there were no statistically significant differences in the mean Bolton ratios when comparing the G(PM) with the G(CBCT) or the G(PM) with the G(IOS). Likewise, there were no significant differences between the G(CBCT) and the G(IOS) (Table 7). Evaluation of agreement among the plaster models, CBCT, and IOS images using ICC is presented in Table 6.

Table 6 Accuracy and reliability comparison of Bolton ratios (AB + OB): ANOVA and ICC analysis among three groups
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Table 7 Comparison between the three groups in the measured Bolton ratios (AB + OB)
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4 Discussion

In the modern era, orthodontics plays a significant role in enhancing oral health and overall appearance [4]. One of the important advancements in orthodontic treatment is the utilization of CBCT and IOS technologies [8]. CBCT provides 3D imaging of the jaws and teeth, allowing for precise assessment and treatment planning [12]. IOS, on the other hand, utilizes digital scanning to capture accurate intraoral images without the need for traditional impressions [13]. Both CBCT and IOS offer numerous advantages in terms of diagnostic accuracy, treatment efficiency, patient comfort, and improved outcomes [8]. These advanced technologies have revolutionized the field of orthodontics by providing orthodontists with valuable tools for precise diagnosis, treatment planning, and monitoring progress [7].

The current study investigated the accuracy and reliability of using CBCT and IOS in measuring tooth widths and Bolton ratios, which are essential diagnostic elements in orthodontics. A comparison was made between the results obtained from these two techniques and the gold standard, which is plaster models by C-silicone. Plaster models, created from impressions using elastomeric materials, have been widely used as a benchmark in orthodontics due to their ability to accurately reproduce dental anatomy. These models offer a tangible and reproducible representation of the dentition, allowing for precise measurements of tooth dimensions and ratios. Over the years, they have been accepted as a reliable method for assessing tooth widths and Bolton’s ratio in orthodontic studies.

The utilization of plaster models as a gold standard in this comparative study ensures a robust foundation for evaluating the accuracy and reliability of modern imaging techniques, namely CBCT and IOS. Plaster models serve as a reference point against which the measurements obtained from CBCT and IOS images can be evaluated. This approach allows for a comprehensive assessment of the diagnostic potential and clinical applicability of these contemporary imaging methods.

The results of the present study showed that there were no statistically significant differences among the average tooth widths of the three study groups G(PM), G(CBCT), and G(IOS). When comparing G(PM) with G(CBCT), the largest difference between the mean widths was 0.03 mm, when comparing G(PM)with G(IOS), the maximum disparity between the mean widths was 0.02 mm. Additionally, when comparing G(CBCT) with G(IOS) the largest difference between the mean widths was 0.06 mm.

When comparing CBCT images with plaster models, slightly smaller mean tooth widths were observed in the CBCT images, which can be attributed to CBCT’s direct recording method without intraoral factors affecting the measurements. On the other hand, IOS images showed slightly larger mean tooth widths, possibly due to the effect of intraoral factors on scanning. However, these differences were not statistically or clinically significant. The ICC analysis of tooth widths’ results indicates a strong level of agreement among the plaster models, CBCT, and IOS images.

The results of this study suggest that the mean values of Anterior Bolton ratio did not exhibit any statistically significant differences among the three groups. A comparison of G(PM) and G(CBCT) yielded a mean difference of − 0.07%, whereas G(PM) and G(IOS) had a mean difference of − 0.01%. On the other hand, when comparing G(CBCT) and G(IOS), the mean difference was 0.05%. The results showed that there were no significant differences between the mean values of the Overall Bolton ratio among the three study groups. When comparing G(PM) with G(CBCT), the mean difference was − 0.07%. In the comparison between G(PM) and G(IOS), the mean difference was 0.001%. Lastly, when comparing G(CBCT) with G(IOS), the mean difference was 0.07%. The ICC analysis of the Bolton ratio results reveals a robust level of concordance among the plaster models, CBCT, and IOS images.

Previous studies in the medical literature compared diagnostic data extracted from CBCT or IOS images to a gold standard. No study conducted a three-way comparison of diagnostic data (tooth widths and Bolton ratios) among CBCT, IOS, and a gold standard (plaster models by C-silicon).

4.1 Comparison with CBCT studies

Regarding tooth widths, the present study agreed with the research conducted by Celikoglu et al.[21] and Kumar et al.[22], which compared CBCT with plaster models. Both studies concluded that CBCT can provide accurate tooth width values for all the groups studied. This is attributed to CBCT’s ability to directly capture data from the patient’s mouth, eliminating the influence of intraoral factors and impression materials that may impact data transfer from the patient to the diagnostician.

The present study differed from Hernandez et al.[23] and José et al. [24], which compared CBCT with 2D scanned plaster models, Furthermore, our results deviated from Kim et al.’s study [25], which compared CBCT with 3D scanned plaster models and plaster models. Although statistically significant differences were observed among the study groups, these differences were not clinically significant. The discrepancies can be attributed to the lack of clarification on their inclusion criteria in their studies. Additionally, they used a different measurement method on CBCT images compared to the present study, and Hernandez and José did not specify the Impression material used for obtaining the 2D scanned plaster models. Furthermore, Kim’s 3D models were derived from alginate impressions.

Regarding Bolton ratios, the present study aligned with Tarazona et al.’s [10] and Celikoglu et al.’s [21] studies, which compared CBCT with plaster models, as well as with Kumar et al.’s [22] and Kim et al.’s [26] studies, which compared CBCT with 3D scanned plaster models and plaster models. Both studies demonstrated that CBCT can accurately determine the anterior and overall Bolton ratios in all the groups studied. This alignment can be attributed to the use of plaster models as a gold standard for comparison with CBCT images.

4.2 Comparison with IOS studies

Regarding tooth widths, the results of the current study were consistent with the findings of Naidu et al. [19], Wiranto et al. [16], and Zhang et al. [27] who compared IOS with plaster models. They also agreed with Grünheid et al. [28] who compared IOS with 3D scanned plaster models and plaster models, and with Anne’s et al. [14] who compared IOS with stereolithographic models. These studies found no statistically significant difference in tooth width measurements between IOS and the other study groups. The agreement was attributed to the direct transfer of data from the patient’s mouth to the diagnosing doctor, as well as the confocal microscopy technology of the IOS.

Flügge et al. [29] and Camardella et al. [30] reported that IOS provides less accurate tooth width values compared to scanned plaster models and plaster models. They attributed this difference to factors related to the oral cavity, such as saliva, soft tissues, and the small size of the oral cavity. On the other hand, Tomita et al. [15] suggested that IOS is more accurate than plaster models in terms of tooth width measurements, but they used plaster models by alginate as a means of comparison.

Regarding the anterior and overall Bolton ratios, the results of the current study were in agreement with the studies by Naidu et al. [19] and Wiranto et al. [16]. These studies also found no statistically significant difference in Bolton ratio measurements between IOS and plaster models. This concurrence can be attributed to the use of the same gold standard in the current study, which is the plaster models.

In elucidating the equivalence in accuracy and reliability of dental measurements and Bolton’s ratio among traditional plaster models, CBCT images, and IOS images, we underscore the credibility of modern diagnostic methodologies. While plaster models offer limited orthodontic diagnostic insights, they impose substantial time constraints and storage demands. Additionally, transferring data between practitioners is cumbersome. In the context of IOS images, although they share a diagnostic role akin to plaster models, they present a significant advantage in terms of time efficiency and storage optimization.

CBCT images, on the other hand, assume a pivotal diagnostic role. They facilitate panoramic and cross-sectional imagery, cephalometric analyses, and diagnosis of impacted teeth. CBCT images afford meticulous precision, reliability, swift diagnosis, streamlined storage, and seamless data transfer, thereby encapsulating comprehensive orthodontic diagnostic information within a single acquisition.

Concerning the cost disparities across these diagnostic approaches, a dedicated study evaluating various devices and brands is requisite. This evaluation would provide a nuanced perspective on the financial considerations associated with each methodology, further enhancing our understanding of their practical implications.

In summation, the confluence of CBCT’s extensive diagnostic capacity, coupled with its precision, reliability, efficient time utilization, and data management, underscores its prominence. While acknowledging the diagnostic potential of IOS and the essential role of traditional plaster models, CBCT emerges as a singularly comprehensive tool for orthodontic diagnosis. Future endeavors, aimed at dissecting cost differentials among diagnostic modalities, necessitate meticulous examination across multiple devices and brands to yield an accurate assessment.

5 Limitations of the study

The study excluded teeth with composite or metal restorations, as well as prosthetic crowns or bridges. The width, depth, and length of the dental arch or the amount of overjet and overbite were not investigated. Blinding of the patients was not possible in this trial. However, this limitation is not expected to introduce bias since no patient-centered self-assessed outcomes were evaluated. The inter-examiner reliability was not assessed, and the evaluation of the impact of various CBCT imaging types or IOS devices on the extracted data quality was not undertaken.

6 Conclusions

The study demonstrates the comparable accuracy and reliability of tooth width measurements and Bolton ratios between plaster models (PM), cone beam computed tomography (CBCT), and intraoral scanner (IOS) methods. No significant differences were found among the three methods for both tooth widths and Bolton ratios. These results validate the diagnostic potential of CBCT and IOS as effective alternatives to traditional plaster models in orthodontic practice, providing clinicians with advanced tools for precise measurements. The findings encourage the integration of CBCT and IOS technologies into orthodontic diagnostics and treatment planning. Further research could focus on cost-effectiveness and device-specific considerations to enhance their practical implementation.