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Research Article
Erratum Notice
Important: There has been an erratum issued for this article. View Erratum Notice
Retraction Notice
The article Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size (LEfSe) in Microbiome Data (10.3791/61715) has been retracted by the journal upon the authors' request due to a conflict regarding the data and methodology. View Retraction Notice
This study investigates a modified digital technique for the individualized zirconia crown restoration of posterior teeth.
This study employed a modified digital technique to evaluate parameters of molar preparations for monolithic zirconia crown restoration, investigating whether clinical preparations with different tooth positions influence restorative outcomes. A total of 238 prepared posterior abutments were analyzed using an intraoral scanner, with parameters including total occlusal convergence (TOC) angle, margin perimeter, and mean abutment height assessed for statistical analysis. The results revealed that the average TOC angle of each posterior tooth exceeded 6°, with the maximum average observed in the mandibular left second molar (35.96 ± 20.21°) and the minimum in the maxillary right first premolar (10.97 ± 6.84°). Statistically significant differences were found in the TOC angle of homonymous second premolars (p < 0.05), where the mandibular left second molar was significantly larger than the other homonymous teeth. Additionally, significant differences existed between teeth in the same quadrant with different positions (p < 0.05), showing a linear increase in TOC angle as the tooth position moved backward. A positive correlation was observed between TOC angle and margin perimeter, while a negative correlation existed between TOC angle and mean abutment height. The findings indicate that clinical zirconia crown preparations often deviate from theoretical TOC recommendations, particularly requiring tailored criteria for mandibular teeth. The developed software integrates digital acquisition with clinical analysis, demonstrating its relevance in prosthodontic practice and education.
High-quality zirconia-crown preparation is crucial for the long-term success of dental restoration1,2,3. It has been observed that the total occlusal convergence (TOC) angle, diameter, and abutment height are correlated1,4,5. Several in vitro studies have indicated that these factors substantially influence the fit, retention, resistance, and longevity of restoration5,6,7. The TOC angle in crown preparation is defined as the angle formed by the convergence of two opposing axial walls in the same plane. Inadequate tooth preparation may result in both mechanical and biological complications. Mechanical failures can manifest as restoration loosening, debonding, or fracture, as well as tooth structure fracture. Biological complications may include periodontal inflammation and mucosal soft tissue infections8. The TOC angle is often influenced by manual operation, unlike abutment height and diameter, which are determined by anatomical variables9. Due to its variations, the TOC angle is essential for determining the retention and resistance quality of the preparation. During tooth preparation, the angulation and taper of the bur determine the tooth preparation angle at each location on the tooth10.
Pioneers like Ward were the first to support the TOC angle measurement for preparations, proposing a convergence angle between 3° and 12°11. Subsequent in vitro studies by Jorgensen12 and Kaufman13 revealed that retention force decreases with increased convergence angle, indicating a higher TOC beyond 5°. Furthermore, Ohm and Silness preliminarily measured the TOC angle on clinically prepared teeth and revealed significantly larger values than the recommended range14. A systematic review (1978-2013) showed that the ideal TOC angle of 2°-5° was practically unachievable and suggested that a realistic TOC angle of 10-22°15. Moreover, it has been suggested that qualified dentists typically achieve a TOC angle between 15° and 25°16,17,18,19,20,21,22,23. Shillingburg HT proposed specific convergence angles for different tooth positions, ranging from 10 to 24°24. Nordlander et al. examined data from 10 dentists comprising 208 cases and proposed a minimum angle of 17.3° in the anterior region and a maximum of 27.3° in the posterior region25. The literature also suggests that preparation's axial surfaces should be parallel to each other, or with a convergence angle of <6° 26. However, teeth are complex and unique, and those with different positions should be treated with a clinically recommended value tailored to their individual needs. The statistical analysis by Janine Tiu on >100 stone dies prepared for glass-ceramic crown restorations showed that the greatest mean TOC angle for the maxillary left second molar was 74.49° (n = 4)27. However, the low strength of glass-ceramic crown materials limited their application in the molar region28. Therefore, it is crucial to comprehensively analyze statistics on the posterior restoration based on zirconia crowns.
Recent advancements in ceramic materials and digital dentistry have made monolithic zirconia ceramic crowns a favored option for posterior fixed restorations using intraoral optical scanning (IOS) systems for tooth defect restoration, particularly because of their high strength, biocompatibility, and aesthetic qualities29. Conventional digital techniques capture only limited geometric parameters and, when combined with traditional 3D scanning methods that are unable to directly assess internal preparation features, demonstrate significant limitations30. This study introduces an individualized modified digital technique to evaluate zirconia crown restorations for posterior teeth, offering a clinically applicable method to optimize fit and longevity. The proposed technique can be specifically employed for customized crown adaptation, such as for teeth with reduced abutment height, uneven marginal configurations, or non-ideal taper. This method systematically analyzes TOC angle variations across different posterior tooth positions, helping clinicians achieve optimal preparation guidelines and reducing the risk of mechanical failure or cementation issues. Furthermore, comparing TOC angles with recommended values offers practical insight for dental practitioners during tooth preparation, ensuring better clinical outcomes. Moreover, the correlation analysis between TOC angle, margin line length, and average abutment height provides valuable insights for restorative planning. Clinicians can use these findings to adjust preparation techniques or select alternative restorative solutions in cases of short clinical crowns or excessive taper. This technique's digital workflow enhances accuracy and reduces chairside time. This approach supports more predictable and durable zirconia crown restorations in posterior dentition by bridging the gap between digital design and real-world restorative challenges.
All experiments were conducted in accordance with a protocol approved by the Institutional Review Board (IRB) of Beijing Shijitan Hospital, Capital Medical University. The ethical approval reference number was IIT2023-021-001.
1. Experiment preparation
2. Data acquisition
3. Data preprocessing
4. Measurement procedure
5. Quality control
6. Statistical analysis
General characteristics
The number of maxillary specimens (n = 132) was greater than that of mandibular specimens (n = 106), with the maxillary right first molar being the most frequently prepared tooth (n = 24). The angles exhibiting a negative value were deemed invalid and omitted from statistical analysis. Table 2 delineates the quantity and classification of invalid TOC angle specimens. Table 3 presents the mean TOC angle for each posterior tooth. Furthermore, clinical TOC angles are compared with recommended values (Figure 3), which revealed that the average TOC angle of each posterior tooth exceeded the recommended value of 6°, consistent with the literature26. Most TOC angles were close to those recommended by Shillingburg et al.24, although the mandibular left second molar showed significantly higher values.
This study observed that the maximum value of the average TOC angle was the mandibular left second molar (tooth 37, TOC-BL = 35.96 ± 20.21°, TOC-MD = 35.12 ± 14.67°, n = 14), with similar mean values in both BL and MD perspectives. Whereas the minimum TOC angle value was found in the maxillary right first premolar (tooth 14, TOC-BL = 10.97 ± 6.84°, n = 14), the maxillary left second premolar (tooth 25, TOC-MD = 14.96 ± 7.34°, n = 14), and the mandibular right second premolar (tooth 45, TOC-MD = 14.96 ± 8.99°, n = 10).
The margin perimeter for each posterior tooth is presented in Table 3. The maxillary left second molar had the longest margin perimeter (tooth 27, 34.73 ± 3.4 mm, n = 17), while the mandibular left second premolar had the shortest (tooth 35, 21.42 ± 2.03 mm, n = 13).
Table 3 displays the average abutment height for each posterior tooth. The mandibular left first premolar demonstrated the greatest height (tooth 34, 3.53 ± 0.94 mm, n = 8), while the mandibular left second molar displayed the least height (tooth 37, 2.34 ± 0.83 mm, n = 14).
Comparison of TOC-BL and TOC-MD in a single tooth position
The analysis of variance between TOC-BL and TOC-MD at a single tooth position (Figure 3) indicated that TOC-MD exceeded TOC-BL primarily in teeth 14 and 46, with a statistically significant difference (p < 0.05), and no significant difference was observed between TOC-BL and TOC-MD in other dental positions (p > 0.05).
Comparison of TOC angle in the same quadrant
The linear trend analysis of TOC angles for teeth in the same quadrant but different positions (Table 4 and Figure 4) indicated a linear increase in TOC-BL in the maxillary right (Figure 4A) and mandibular left (Figure 4C) quadrants as the tooth position moves backward. Furthermore, TOC-MD exhibited a linear rise according to tooth position in the posterior direction in the maxillary right (Figure 4A), maxillary left (Figure 4B), mandibular left (Figure 4C), and mandibular right (Figure 4D) quadrants.
Comparison of the TOC angle in homonymous tooth positions
Statistically significant differences were observed among homonymous tooth positions between 17, 27, 37, and 47 for TOC-BL (p = 0.002) and TOC-MD (p = 0.013) (Table 5 and Figure 5). Moreover, post-hoc pairwise comparisons showed significant differences (p < 0.05) in TOC-BL between maxillary right second molar (tooth 17) and mandibular left second molar (tooth 37), between maxillary left second molar (tooth 27) and mandibular left second molar (tooth 37), as well as mandibular left second molar (tooth 37) and mandibular right second molar (tooth 47). The TOC-BL of the mandibular left second molar (tooth 37) was significantly greater than that of other corresponding teeth. Moreover, significant differences (p < 0.05) in TOC-MD were identified between maxillary right second molar (tooth 17) and mandibular left second molar (tooth 37), as well as between maxillary left second molar (tooth 27) and mandibular left second molar (tooth 37). The TOC-MD of mandibular left second molar (tooth 37) was larger than that of maxillary right second molar (tooth 17) and maxillary left second molar (tooth 27). No statistical differences were found between the mandibular left second molar (tooth 37) and the mandibular right second molar (tooth 47) in TOC-MD.
Correlation analysis
Pearson correlation analysis revealed a positive association between TOC-BL and TOC-MD, as well as between TOC-BL and margin perimeter, whereas a negative relationship was observed between TOC-BL and mean abutment height. TOC-MD exhibited a positive correlation with margin perimeter and a negative correlation with mean abutment height. The margin perimeter exhibited an inverse association with the mean abutment height (Figure 6).

Figure 1: Clinical case presentation of tooth preparation and monolithic zirconia crown restoration. (A-F) Monolithic zirconia crown restoration of the maxillary left first molar. (G-L) Monolithic zirconia crown restoration of the maxillary right second premolar. Please click here to view a larger version of this figure.

Figure 2: Flow chart of digital evaluation. Please click here to view a larger version of this figure.

Figure 3: Total occlusal convergence (TOC) angles with 95% confidence intervals, categorized by tooth type and compared to recommended values. Significant differences were observed in tooth 14 (TOC-MD = 15.21 ± 4.6°, TOC-BL = 10.97 ± 6.84°) and tooth 46 (TOC-MD = 27.77 ± 13.41°, TOC-BL = 17.72 ± 6.10°), *p < 0.05. Please click here to view a larger version of this figure.

Figure 4: Comparison of TOC angle within the same quadrant. (A) Maxillary right quadrant: TOC-BL differed in tooth 14 (10.97 ± 6.84°) vs. 16 (20.80 ± 9.59°), and 14 (10.97 ± 6.84°) vs. 17 (21.23 ± 8.17°), *p < 0.05. (B) Maxillary left quadrant. (C) Mandibular left quadrant: TOC-BL differed in tooth 34 (16.03 ± 7.59°) vs. 37 (35.96 ± 20.21°), 35 (15.94 ± 9.65°) vs. 37 (35.96 ± 20.21°), and 36 (25.57 ± 11.6°) vs. 37 (35.96 ± 20.21°), *p < 0.05. TOC-MD differed in tooth 34 (18.08 ± 6.88°) vs. 37 (35.12 ± 14.67°), 35 (16.22 ± 10.64°) vs. 37 (35.12 ± 14.67°), and 36 (24.09 ± 10.97°) vs. 37 (35.12 ± 14.67°), *p < 0.05. (D) Mandibular right quadrant: TOC-BL differed in tooth 45 (14.98 ± 5.48°) vs. 47 (22.99 ± 8.95°), and 46 (17.72 ± 6.10°) vs. 47 (22.99 ± 8.95°), *p < 0.05. TOC-MD differed in tooth 45 (14.96 ± 8.99°) vs. 46 (27.77 ± 13.41°), and 45 (14.96 ± 8.99°) vs. 47 (28.34 ± 12.32°), *p < 0.05. Please click here to view a larger version of this figure.

Figure 5: Comparison of TOC angle in homonymous tooth positions. (A) First premolars. (B) Second premolars. (C) First molars. (D) Second molars: TOC-BL differed in tooth 17 (21.23 ± 8.17°) vs. 37 (35.96 ± 20.21°), 27 (19.37 ± 9.83°) vs. 37 (35.96 ± 20.21°), and 37 (35.96 ± 20.21°) vs. 47 (22.99 ± 8.95°), *p < 0.05. TOC-MD differed in tooth 27 (23.17 ± 9.95°) vs. 37 (35.12 ± 14.67°), and 17 (22.16 ± 9.48°) vs. 37 (35.12 ± 14.67°), *p < 0.05. Please click here to view a larger version of this figure.

Figure 6: Pearson correlation analysis for TOC angle, margin perimeter, and mean abutment height. Correlations were examined between TOC-BL and TOC-MD, TOC-BL and margin perimeter, TOC-BL and mean abutment height, TOC-MD and margin perimeter, and TOC-MD and mean abutment height. *p < 0.05. Please click here to view a larger version of this figure.
Table 1: Reproducibility testing. Please click here to download this Table.
Table 2: Number of valid and invalid measurements of TOC angle, margin perimeter, and mean abutment height. Please click here to download this Table.
Table 3: TOC angle for each posterior tooth. Please click here to download this Table.
Table 4: Linear trend analysis of the TOC angle within the same quadrant. Please click here to download this Table.
Table 5: Differences in TOC angle among homonymous teeth. a: p < 0.05 between tooth 37 and 17; b: p < 0.05 between tooth 37 and 27; c: p < 0.05 between tooth 47 and 37. Please click here to download this Table.
Supplementary Figure 1: Scanner calibration. Please click here to download this File.
Supplementary Figure 2: Visual illustration of preprocessing outcomes. Please click here to download this File.
This study aimed to evaluate the total occlusal convergence (TOC) angle of monolithic zirconia crowns using digital technology and analyze its relationship with tooth position, an area still lacking in research. Additionally, the application of digital techniques in the preparation and assessment of these crowns remains underexplored. Clinical samples were collected based on tooth location, and for each posterior tooth, the TOC angle, margin perimeter, and mean abutment height were measured. The findings revealed that monolithic zirconia crown preparations often fall short of optimal standards, even when performed by experienced dentists, as clinically achieved TOC angles frequently deviate from theoretical recommendations. These results highlight the need for improved preparation techniques in routine prosthetic practice. Furthermore, digital technology demonstrates potential for refining crown design, suggesting that future studies should investigate tooth-specific parameters to enhance clinical outcomes.
The IOS has become increasingly popular in clinical dentistry and has replaced traditional impression-taking methods. In the past decades, digital technologies, including IOS, have transformed the clinical practices in medicine and dentistry30,34. Monolithic zirconia crowns do not require veneering ceramics for posterior tooth repair and necessitate minimal tooth preparation35. This is facilitated by Computer-Aided Design (CAD) and Computer-Aided Manufacturing (CAM) technologies, which can manufacture anatomically tailored crowns from zirconia ceramic blocks with enhanced mechanical qualities, thus eliminating the requirement for veneering ceramic, and therefore avoiding veneer-chipping problems36. Currently, the most common restorations of defective teeth in clinical practice involve using intraoral optical scans for tooth preparation and CAD/CAM technology to fabricate monolithic zirconia ceramic crowns35. This progress in materials has resulted in reduced dental preparation and enhanced preservation of tooth tissue; however, meticulous tooth preparation remains essential37.
In the past, most research investigated the TOC angle rather than any other parameter, highlighting its importance for clinical success. In contrast to limited samples in previous studies27, the presented study analyzed 238 posterior teeth, including premolars and molars, for parameter analysis. Furthermore, the included data were harvested from IOS rather than from gypsum casts for more precise measurement. The accuracy and reproducibility of the measurements were ensured through critical protocol steps, comprising standardized IOS, meticulous software calibration, and 15 repeated measurements/tooth with established standard deviation thresholds by experienced prosthodontists. Moreover, the TOC angle values significantly differed from the recommended textbook values (0-6°)26. Most mean TOC angle values for posterior teeth were consistent with Shillingburg et al.'s recommendations24. This suggests that the standard TOC angle setting associated with the tooth position was closer to the clinical operation.
This study showed that the maxillary right first premolar (10.97 ± 6.84°) had the minimum TOC angle, whereas the larger TOC angles were observed in maxillary molars (23.17 ± 9.95°) and mandibular molars (35.96 ± 20.21°), consistent with previous studies (27.03 ± 15.00°38, 30.44 ± 10.61°39, 37.20 ± 13.50°40). Furthermore, the TOC angles of mandibular molars were greater than those of maxillary teeth, in line with reports from Al-Omari and Al-Wahadni40, Janine Tiu27, Conrad Winkelmeyer32, and Leempoel et al.17. These findings suggest that tooth position and anatomic shape substantially affect the accuracy of tooth preparation, which warrants comprehensive research.
It was also observed that the TOC angles of the second molars of homonymous teeth had statistically significant differences (TOC-BL: p = 0.002 and TOC-MD: p = 0.013). Significant TOC angles were found in the mandibular left second molar following post hoc pairwise comparisons (p < 0.05). Furthermore, the different axes of the TOC angles surface were as follows: The mandibular left second molar had significantly larger TOC angles in the BL direction than other homonymous teeth. The tissues of the floor of the mouth, the masticatory and buccinator muscles, constituted a complex environment during tooth production in the mandibular molar region. Moreover, a dental mirror is essential to prevent tongue injury during tooth preparation, which frequently limits dentists' visibility. Moreover, no significant difference was observed between the mandibular left and right second molars. Al-Omari and Al-Wahadni proposed that prepared mandibular molars incline mesially and lingually, thus resulting in higher mean TOC values36. Pathologically, proximal surface erosion frequently results in mesial inclination of the mandibular molars41,42. Moreover, the resin restoration of the distal cavity in second molars also promotes a mesially inclined plane. Furthermore, the retromolar pad and its adjacent tissues anatomically influence the procedure at the mandibular second molar locations. The resulting TOC angles were mostly linked to the operator's posture, tooth accessibility, direct or indirect visibility, and the type and size of the burs employed43. However, long-term stable crown restoration is also influenced by other geometrical shapes.
Here, the Pearson correlation analysis revealed a negative correlation between TOC angle and mean abutment height, consistent with Sato et al.19 and Al-Omari40. In the 1980s, Parker et al. developed a "limiting taper" concept, a mathematical model primarily based on the height-to-base ratio of the preparation10. According to this concept, when the acquired TOC angle exceeds the "limiting taper," retention resistance is lost. To ensure retention resistance, an expanded cervical region of the abutment, increased height, and reduced TOC are essential. This study demonstrated a positive link between TOC angles and margin perimeter, while a negative correlation was observed between margin perimeter and mean abutment height. However, due to daily abrasion, molars often exhibit a decreased height, and their anatomical morphology results in a relatively large margin perimeter. The limited abutment height (<3 mm) fails to provide adequate bur stabilization during preparation, leading to increased bur deflection. This technical challenge frequently forces physicians to utilize adjacent teeth as fulcrums, accidentally producing a lever effect that intensifies bur tilt and ultimately leads to progressive inclination with increased TOC angles44. To compensate for the resultant loss of retention, practitioners frequently resort to pulp-chamber retention aids or employ specialized zirconia cements when restoring these molar prostheses45.
Furthermore, suitable measuring equipment is essential for data collection, parameter analysis, and evaluation46,47,48. The clinical application of IOS received extensive acknowledgment among dentists as a benchmark for fixed prosthodontics. These sophisticated technologies emphasize scanning precision, with their measurement algorithms precisely optimized for essential preparation parameters, including occlusal clearance35. Furthermore, the educational IOS software is widely employed in tooth preparation on the Dental Simulation Manikin for educational guidance30. Researchers are trying to develop software that is not only appropriate for healthcare data collection but also proficient in assessing diverse IOS impressions. This study modified a measurement system, which could input data from any IOS equipment and assess standard preparation characteristics, including TOC angles, margin perimeter, abutment height, volume reduction, depth of undercut, area of undercut, path of insertion, and degrees of smoothness. This modified software ensures exceptionally accurate assessment of these clinically significant parameters, which are fundamental to successful prosthetic outcomes. Moreover, this modified software system demonstrates multifaceted practical value in clinical applications. The incorporation of digital workflow in prosthodontic optimization offers real-time feedback on preparation quality (like taper angles and margin adaptation, etc.), providing prompt changes before final impression taking and significantly decreasing remake rates. Its multi-scanner compatibility feature enables it to function as a universal quality control instrument for clinics employing various scanning systems. Future integration of machine learning algorithms could further enable intelligent preparation recommendations based on accumulated clinical data. In educational applications, this modified software system provides transformative tools for dental training. For preclinical skill assessment, an objective grading system can be implemented in dental simulation labs to automatically evaluate student-prepared tooth characteristics (e.g., TOC angle, margin sharpness), replacing traditional subjective faculty evaluations. Furthermore, it compares student preparations against ideal parameters and generates personalized learning reports pinpointing specific areas requiring improvement, thus significantly improving teaching effectiveness.
This study has certain limitations. The clinical adoption of digital measurements may face practical barriers such as cost and training requirements, though these could be addressed through phased training programs and cost-sharing models. As a single-center study with standardized operators, the findings may have limited generalizability. Additionally, the long-term clinical impact of TOC variations on restoration longevity requires further validation. Future research should incorporate mechanical testing (e.g., finite element analysis) to assess TOC-related stress distribution, as well as multicenter studies to evaluate preparation variability across different clinical settings.
In conclusion, this study highlighted significant clinical challenges in monolithic zirconia crown preparations, indicating that even experienced dentists frequently fail to achieve theoretically recommended TOC angles in routine prosthetic work. Therefore, there is an urgent need for tooth-specific preparation criteria based on anatomical features, particularly for mandibular molars, which necessitate special attention. This study developed a software system that effectively connected digital data acquisition with clinically relevant analysis, displaying diverse applications in prosthodontic practice, education, and research. Future advancements should integrate AI, cloud-based cooperation, and automation enhancement to fully harness its disruptive potential in modern digital dentistry.
The authors declare that they have no competing interests.
The authors were financially supported by the Beijing Municipal Administration of Hospitals Incubating Program (PX2024028), Capital Medical University (grant number 2023JYY349), the National Natural Science Foundation of China (Grant No.81901001), and the National Natural Science Foundation of China (Grant No.62002033).
| DentalEngineerV1.0 | SuZhou, China | Dental measurement software | |
| 3Shape TRIOS3 | 3Shape, Danmark | Intraoral scanner | |
| Geomagic Studio12.0 | 3D Systems, USA | Intraoral scanning data processing |