Three-dimensional position changes of unopposed molars before implant rehabilitation: a short-term retrospective cohort analysis

Subjects

The study is a retrospective cohort study. Subjects were selected from 321 patients with one or more missing molars seeking replacement and rehabilitation by implant restoration; these patients visited the Department of Periodontology, Peking University School and Hospital of Stomatology from January 2013 to December 2020. Molars opposing the missing molars were selected as target teeth. The inclusion criteria were as follows: (a) ≥ 25 years old; (b) patients with at least one molar missing, with records showing the time of extraction clearly, as well as evidence of the existing antagonist teeth; (c) the unopposed teeth had no contact with any opposite teeth according to the plaster models and clinical occlusal photographs; (d) there were CBCT radiographs including the target teeth within three months before extraction of the antagonist (baseline) and after extraction. The patients were excluded if they (a) wore an occlusal guard; (b) had a history of orthodontic treatment prior to the tooth extraction; (c) had history of drug therapy or radiation therapy that severely affects bone metabolism; (d) had uncontrolled systemic diseases. All the patients in the study had periodontitis. 69.5% of the patients were diagnosed as stage 3, grade C according to new classification [23]. Initially, 146 patients were not included due to lacking records showing the time of extraction. Then, 6 patients were excluded because of orthodontic history, or the tooth extracted without any antagonist teeth. The screening for CBCT radiographs meeting the requirements further reduced the sample size by 67 patients. Then, plaster models and clinical occlusal photographs were used to identify whether the unopposed teeth had no contact with any opposite teeth; 43 patients were excluded at this step. Finally, a total of 59 patients with 68 target teeth were included in this study. Written informed consent about the application of medical information for research was obtained from all participants. The study was conducted in full accordance with the ethical principles established in the World Medical Association Declaration of Helsinki of 1975 as revised in 2000 and approved by the Institutional Review Boards of the (Approval Number: 201949134).

3D reconstruction of CBCT and coordinates establishment for measurements

All participants received a pre-operative CBCT examination using a New Tom 9000 CBCT (Aperio Services, Italy) within 3 months before extracting the antagonist of the target tooth to confirm the indication for extraction or the possibilities of socket preservation. All scans were taken at 110 kV, 12–17 mA, with 0.1–0.3 mm slice thickness and pixel size of 0.125 mm, and this pre-operative data was recorded as To. The postoperative CBCT was performed before the definitive restoration of the edentulous space using the same CBCT machine and protocol; this time was documented as Tn. The Digital Imaging and Communications in Medicine (DICOM) file from the CBCT examination was imported and merged in a volumetric imaging software (Mimics 20.0, Materialise, Belgium), in which 3D images of models were constructed. Thresholding was used to obtain the 3D models under the applicable thresholds of crown, alveolar bone, and root. The mask in each threshold was named as "Crown", "Root", and "Alveolar bone", respectively (Fig. 1a–c). The unit in Boolean operations was used to unite the masks, and a window around the apical region of target tooth was made to expose the root in the model (Fig. 1d). The final 3D models were generated into the Standard Tessellation Language (STL) files. Postoperative images (Tn) were superimposed with pre‐operative (To) CBCT images using automated surface best fit aligning with the iterative closest point algorithm in the treatment evaluation mode of a reverse engineering software (Geomagic Control 2015, 3D Systems, Inc., USA) (Fig. 1e). All crowns of the dentition, except the target teeth and the stable alveolar bone area not containing the crest of the alveolar ridge and the open window area, were selected as the align area.

Fig. 1figure 1

Processing in extracting CBCT 3D model information. a Crown: extracting 3D model under the experience threshold of crown; b Root: extracting 3D model under experience threshold of root with removing part of cusps; c Alveolar bone: extracting 3D model under the experience threshold of alveolar bone with removing the crown part; d Model for measurement after uniting; e The alignment of preoperative and postoperative CBCT images

According to the method established by Chen et al. [24], the 3D coordinates of target teeth were established by confirming three mutually perpendicular reference planes on the baseline model (To): Occlusal Plane, Mesio-Distal Plane, and Bucco-Lingual Plane (Fig. 2). Occlusal Plane was calculated by matching all the cusp tips of the posterior teeth in the quadrant of target tooth. A line perpendicular to the Occlusal Plane and across the midpoint of the line connecting the midpoint of the mesial and distal marginal crests was defined as the z-axis. The original point was the meeting point of the z-axis and Occlusal Plane. The original point was assigned as 0. The Mesio-Distal Plane was a plane passing through the z-axis and the midpoint of the distal marginal crest. The Bucco-Lingual Plane was a plane passing through the original point and was perpendicular to the two aforementioned planes. The positive direction of x-axis, y-axis, and z-axis was set in mesial, lingual, and occlusal direction, respectively.

Fig. 2figure 2

Determination of three reference planes and establishment of 3D coordinate system of the target tooth. 0, original point; Mm, midpoint of mesial marginal crest; Md, midpoint of distal marginal crest

Determination of the reference points and parameters

Points of reference were determined on each 3D model (Fig. 3a). Cusp tips were used as reference points, and the average coordinate values of all the cusp tips were taken to obtain the centroid of cusp tips (CC). The average coordinate values of the root apex were taken to obtain the centroid of apex (CA). The midpoints of the mesial and distal marginal crest were assigned as Mm and Md, respectively. The vector from CA to CC was defined as the tooth axis (Fig. 3b). The parameters related to spatial changes such as overeruption and tipping were shown from Fig. 3c to f. The values of the parameters were derived from coordinate calculations. The detailed definition of each parameter is as follows:

Fig. 3figure 3

Determination of reference points and parameters. a LC1, LC2, BC1, and BC2 were cusp tips, in which LC and BC means lingual cusp and buccal cusp; Mm and Md were midpoints of the mesial and distal marginal crests, respectively. b CC: centroid of cusp tips; CA: centroid of root apexes; Tooth axis, line from CA to CC. c OEmean, mean overeruption of cusps d OEmax, maximum overeruption of cusps. e BLT, Bucco-Lingual tipping angle. f MDT, Mesio-Distal tipping angle

As the vector CC1 to CC2 reflects the displacement of the centroid of cusp tips (Fig. 3c), its value in the occlusal direction can be used to describe the overeruption. Mean overeruption of cusps (OEmean): the occlusal movements of the centroid of cusp tips in the z-axis direction between Tn and To (Fig. 3c). Maximum overeruption of cusps (OEmax): the maximum displacements among cusp tips in the z-axis direction (Fig. 3d). Bucco-Lingual tipping angle (BLT) represents the angle between the tooth axis and Mesio-Distal Plane (Fig. 3e). Mesio-Distal tipping angle (MDT) represents the angle between the tooth axis and Bucco-Lingual Plane (Fig. 3f). The difference between the angle of tipping at Tn and To is the outcome index, named as Bucco-Lingual tipping change (cBLT) or Mesio-Distal tipping change (cMDT).

Statistical analysis

Statistical evaluation was undertaken with the Statistical Package for Social Sciences, version 22.0 (SPSS Inc., Chicago, Illinois, USA). Statistical analyses were performed at tooth level. Data obtained from coordinate values were expressed in terms of means and ranges. Frequency (percentages) were computed for categorical variables. A one-sample t-test was performed, and the zero value was used as a reference to compare with the averages of the evaluated parameters. As the normal distribution of the parameters was observed using the graphical method, one-way analysis of variance (ANOVA) was used to compare the degree of overeruption and tipping of different molar types based on a significant level at α = 0.05. The specific data distribution was displayed by bar chart, box chart, and line chart.

Error of method

All assessments were repeated on 10 randomly selected subjects after 2 weeks. The consistency between the two measurements was assessed using intra-class correlation efficient (ICC), and a two-way mixed model was chosen. A high consistency of OEmean and OEmax obtained from the two measurements (ICC = 0.965 and 0.973, respectively) was found. The size of the combined method error in locating the landmarks and the measuring procedure was evaluated using Dahlberg’s (1940) formula and the results were as follows: the OEmean was 0.074 mm, and the OEmax was 0.092 mm, respectively. There was compliance with the STROBE checklist.

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