Cervical tooth anatomy considerations for prefabricated anatomic healing abutment design: A mathematical formulation

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.

The purpose of this study was to develop a mathematical formula defining horizontal cervical tooth geometry to design prefabricated, tooth-specific, healing abutments.

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.

The lower and upper limits of agreement between the 2 methods were -8.57 and 7.36 mm², respectively, with no bias (-0.61 mm², 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.

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.