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

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.

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.

中文翻译：

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预制解剖愈合基台设计的颈牙解剖考虑：数学公式

问题陈述

定制的出现轮廓为解剖愈合基台提供了理想的水平尺寸。然而，开发这样的出现概况可能是一个耗时且复杂的过程。

目的

本研究的目的是开发一个定义水平颈牙几何形状的数学公式，以设计预制的、牙齿特定的愈合基台。

材料与方法

测量了 54 名参与者的 989 颗牙齿的锥形束计算机断层扫描 (CBCT) 水平横截面。对于前磨牙和前磨牙，将 2 个垂直椭圆拟合到由 3 个参数定义的颈牙横截面上。舌椭圆沿着牙齿的舌侧轮廓，其直径为牙齿的最大近远中直径（参数“a”）；它的颊舌半径变成了参数“b”。颊侧椭圆垂直于舌侧椭圆并遵循牙齿的颊侧轮廓。较小椭圆的颊舌半径成为参数“c”。对于臼齿，第一个椭圆遵循牙齿的近中轮廓，其较大的直径（参数“a”）与牙齿的最大颊舌直径相匹配。它的较小半径成为参数“h1。” 第二个椭圆平行于第一个椭圆，并遵循牙齿的远端轮廓。其较大的直径成为参数“b”，其近中直径成为参数“h2”。通过线性混合模型评估参数之间的统计差异（Bonferroni 调整后α=.05）。分别对磨牙的每个参数和前牙加前磨牙的每个参数进行成对比较。如果在特定参数上没有发现牙齿之间的显着差异，则将牙齿放入相同的参数组中。如果两颗牙齿的两个参数（臼齿为 4，其他牙齿为 3）都不同，则将它们放入同一个基台群中。基台簇决定了解剖愈合基台的类型。通过使用参数从开发的数学公式计算面积。此外，使用照片编辑软件程序直接测量了 106 颗随机选择的牙齿的颈部区域。使用计算机算法通过简单随机化方法从 54 个 CBCT 扫描中选择 5 个。通过 Bland-Altman 分析评估 2 种方法之间的一致性。

结果

两种方法之间的一致下限和上限分别为 -8.57 和 7.36 mm ²，没有偏差（-0.61 mm ²，P =.224）。在 14 种牙齿类型中，大多数参数之间存在显着差异（P <.001）。根据这些参数，定义了 12 个特别不同的集群。两种牙齿类型汇集到一个基台群中：上颌第一和第二前磨牙以及下颌第一和第二磨牙。

结论

可以通过组合 2 个椭圆元素来准确定义颈牙横截面。仅 12 种不同的预制基台就可以提供全面的牙齿特定出现轮廓，根据推荐的参数进行设计。