Cervical tooth anatomy considerations for prefabricated anatomic healing abutment design: A mathematical formulation
Bibliographic record
Abstract
STATEMENT OF PROBLEM: A custom emergence profile offers the ideal horizontal dimensions for an anatomic healing abutment. However, developing such an emergence profile can be a time-consuming and complex process. PURPOSE: The purpose of this study was to develop a mathematical formula defining horizontal cervical tooth geometry to design prefabricated, tooth-specific, healing abutments. MATERIAL AND METHODS: Cone beam computed tomography (CBCT) horizontal cross sections of 989 teeth on 54 participants were measured. For anterior and premolar teeth, 2 perpendicular ellipses were fitted onto the cervical tooth cross section that was defined by 3 parameters. The lingual ellipse followed the lingual outline of the tooth, and its diameter was the largest mesiodistal diameter of the tooth (parameter "a"); its buccolingual radius became parameter "b." The buccal ellipse was perpendicular to the lingual ellipse and followed the buccal outline of the tooth. The buccolingual radius of the smaller ellipse became parameter "c." For molars, the first ellipses followed the mesial outline of the tooth, and its larger diameter (parameter "a") matched the largest buccolingual diameter of the tooth. Its smaller radius became parameter "h1." The second ellipse was parallel to the first ellipse and followed the distal outline of the tooth. Its larger diameter became parameter "b", and its mesiodistal diameter became parameter "h2". Statistical differences between parameters were evaluated by the linear mixed model (α=.05 after Bonferroni adjustment). Pairwise comparisons were made separately for each parameter of the molars and separately for each parameter for the anterior teeth plus premolars. Teeth were put into the same parameter cluster if no significant differences were found between them for a specific parameter. If neither parameter (4 for molars and 3 for the other teeth) was different for 2 teeth, they were put into the same abutment cluster. The abutment clusters determined the type of anatomic healing abutment. The areas were calculated from the developed mathematical formula by using the parameters. In addition, cervical areas of 106 randomly chosen teeth were measured directly with a photo-editing software program. A computer algorithm was used to select 5 CBCT scans from the 54 by using the simple randomization method. The agreement between the 2 methods was evaluated by Bland-Altman analysis. RESULTS: , P=.224). Significant differences were found between most parameters among the 14 tooth types (P<.001). Based on the parameters, 12 specifically distinct clusters were defined. Two tooth types were pooled into 1 abutment cluster: the maxillary first and second premolars and the mandibular first and second molars. CONCLUSIONS: The cervical tooth cross section can be accurately defined by combining 2 elliptical elements. A comprehensive array of tooth specific emergence profiles can be provided by just 12 different prefabricated abutments, designed as per the recommended parameters.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".