The prognosis of a DBD of the M2M after M3M coronectomy has not been studied systematically and accurately previously. Only the effect of root migration and short-term complications of DBD variations have been analyzed with overlapped 2D radiography . The influences of rotation, eruption status, and re-contact with adjacent teeth of the M3M root complex have been ignored, which are important and common coronectomy-related cofactors . In addition, Vignudelli observed 4 ± 4 mm of bone regeneration 9 months after coronectomy, and claimed it was comparable with guided tissue regeneration after M3M extraction. They used a value of 3.59 ± 1.14 mm reported by Hassan  as a comparison. A new study with three-dimensional (3D) measurements should be applied to validate these results.
We combined digital technology and CBCT (which overcame the limitation of periodontal probing and 2D radiography) to measure bone-level changes in three dimensions accurately. Our main finding was that periodontal healing of the M2M after M3M coronectomy would not be disturbed by the remaining root complex. The volume of bone regenerated in the distal 2 mm of the M2M was an effective indicator in three dimensions.
After registration of CBCT at baseline and Po.6 m, digital technology showed a significantly lower deviation (0.01 ± 0.25 mm) than that using 2D radiography (± 0.5 mm) . Eliminating overlap in 2D radiography, all distal sites (DL, DM, DB) of the M2M were assessed and a significant difference in the PD and DBD depth was found (P ≤ 0.001) (Table 1). Po.6 m was chosen because the major part of periodontal healing occurs within 3 months after surgery . The mean reduction in the DBD depth was 1.28 ± 1.24 mm, which is slightly higher than that documented in other studies (0.62–1.25 mm) [4, 6, 13]. Hence, the root complex did not disturb periodontal healing of the M2M. The change in the DBD depth (r ≥ 0.54) and PD (r ≥ 0.38) in all sites was corelated significantly with the mean value (Fig. 2). It was acceptable to use the mean value in subsequent statistical analyses.
The factors influencing periodontal healing of the M2M reported previously were analyzed in the present study. No significant difference was found between the DBD depth in patients younger than 25 years (4.08 ± 1.77 mm) and those older than 25 years (4.45 ± 1.56 mm) (P = 0.105). However, 6 months later, patients younger than 25 years (1.55 ± 1.35 mm) obtained a greater reduction in the DBD than their older counterparts (1.07 ± 1.10 mm) (P = 0.045). Correlation and regression analyses also showed a negative relationship between age and DBD reduction, and these observations were consistent with data from various studies [7, 29]. The original DBD depth has been reported to be a risk factor for periodontal healing of the M2M . In the present study, a close correlation was shown between baseline and Po.6 m (r = 0.67, P ≤ 0.001) for DBD depth. Besides, the higher DBD in our study (5.43 ± 2.29 mm at baseline, 72.8–45.1%) explains why the decrease in the number of DB sites of DBD depth ≥ 4 mm was less than that reported in the study by Faria (4.54 ± 1.87 mm at baseline, 76.9–15.3%) . However, the DBD depth at baseline showed a positive correlation with DBD reduction, with the highest correlation coefficients being reported among all the factors evaluated in our study (r = 0.59, P ≤ 0.001). These data suggested that compensatory bone formation would occur in patients with a large DBD depth at baseline, but their prognosis would not be better than that of patients with small DBD depth at baseline. These cases of coronectomy are important because the deeper the impaction of M3Ms preoperatively, the larger was the DBD depth at baseline. Similarly, deep impaction and large angulation of the M3M could contribute to a large DBD depth at baseline, as shown previously [3, 10, 30], and are related positively with DBD reduction (r ≥ 0.20, P ≤ 0.003).
Some factors related to coronectomy and periodontal healing have not been studied before. The RMS reflects whether the width for M3M eruption is sufficient . The RMS was corelated negatively with the depth of M3M impaction (r = − 0.28, P ≤ 0.001). Significant correlation was observed between the RMS and reduction in DBD depth (r = − 0.36, P ≤ 0.001). Thus, it is reasonable to assume that, after coronectomy of the M3M, patients with a small RMS could obtain a narrow and deep pocket distal to the M2M.  Sculean reported that that a narrow and deep pocket would gain more bone than a wide and shallow defect. Hence, a patient with a small RMS could gain more bone than a patient with a large RMS. Rotation of the root complex can be observed in 65% of patients after coronectomy . The positive relationship between root rotation and reduction in DBD depth has been considered to be orthodontic traction . A bony impacted root complex regenerated more bone distal to the M2M than that observed for soft tissue-impacted roots (r = 0.27, P ≤ 0.001), data that are in accordance with results from a study by Yeung . A correlation was not found between reduction in DBD depth and root migration, as reported previously [14, 31]. Analyses of the coronectomy-related factors mentioned above suggested that the remaining root complex did not disturb periodontal healing of the M2M. Re-contact of the root complex and distal surface of the M2M was a potential risk factor for the periodontal condition of the M2M; it caused two in five patients to undergo secondary surgery after coronectomy in a study by Monaco . Meanwhile, a M3M with a complete root apex can erupt upon application of mechanical force to a M2M  and increase the risk of external root resorption . Surgeons should note that the remaining enamel increased the risk of re-contact by 5.9-fold (OR = 6.93, P = 0.037) and, for each 1-mm decrease in the RMS, the risk of re-contact increased by 33% (0.67, 0.035).
Healing processes among DB, DM and DL sites might have been different because of three different causes of bony defect. First, the periodontal condition at the DL site was much better than that at DM and DB sites. Periodontal healing at the DL site showed much less relevance than that at DM and DB sites (Fig. 2). DBD depth at the DL site (1.91 ± 1.19 mm at Po.6 m) was in accordance with the periodontal-healing standard that alveolar-bone height must be restored to within 2 mm of the CEJ . Periodontal healing here could be characterized as normal healing of alveolar sockets. Second, defects at DM and DB sites were much deeper than those at the DL site (Table 1), and might have been caused by M3M growth. Chen studied 421 CBCT images of M3Ms and found that 96.2% of M3Ms were at median or buccal sides distal to M2Ms . Conversely, we found that PD reduction could be due more to soft-tissue variation than hard-tissue variation (Table 4). Most participants in the present study were asymptomatic, and a thickness of soft tissue > 5 mm at DM and DB sites (difference in reduction of DBD depth and PD reduction is shown in Table 1) would be considered to be the long junctional epithelium . Also, the lack of keratinized gingival coverage might account for the vulnerability of the M3M region to periodontal diseases . It would be better to prevent reduced growth of the epithelium and improve periodontal healing of the M2M with guided tissue regeneration . Third, a defect at the DB site is also created (at least in part) by iatrogenic removal of buccal bone during M3M surgery . A significant correlation between reduction in DBD depth and PD reduction was found between DM and DB sites (Fig. 2). However, the percentage of severe bone loss (DBD depth ≥ 4 mm) was greater at the DB site (72.8% at baseline, 45.1% at Po.6 m) than that at the DM site (63.4% at baseline, 27.7% at Po.6 m) (Table 1).
Healing of a periodontal defect is based on recovery of surrounding alveolar bone . Previous periodontal probing and 2D radiographs are not sufficient to evaluate morphology of bone pockets, which is critical for prediction of periodontal healing . Furthermore, bone height does not to indicate the stability of periodontal healing. A more accurate and predictable index in three dimensions is necessary.
We proposed, for the first time, the volume of bone regenerated in the distal 2 mm of the M2M to be such an index. This parameter reflects the minimum thickness of bone required to prevent resorption of surrounding bone, and denotes the stability of bone distal to the M2M. Our postulation is based on two main observations. First, Porto reported, in an anatomic study, that the minimum thickness of stable alveolar bone in posterior teeth is 1.98 ± 1.33 mm . Second, it is widely accepted that 2 mm of alveolar width around the implant is the minimum volume to prevent further bone resorption . When using digital software to measure bone volume, the error between the measured value and real value is relatively small. According to Liu’s study , the deviation was < 7%. Therefore, the accuracy of our new 3D index (the volume of bone regenerated in the distal 2 mm of the M2M) was sufficient for clinical application. The morphology of bone pockets is presented in Fig. 1G. A significantly high correlation was found between the volume of bone regenerated in the distal 2 mm and reduction in the DBD depth (r = 0.74, P༜0.001). In addition, all statistical analyses involving these two factors revealed similar results, which provides further evidence of the effectiveness of this new index. Conversely, the volume of bone regenerated in the distal 2 mm showed a weak correlation with the total volume of bone regenerated in the alveolar socket (r = 0.20, P = 0.004) whereas reduction in DBD depth did not (r = − 0.01, P = 0.871). Our new index might bridge the healing of the alveolar socket of the M3M and repair of distal periodontal tissue of the M2M.
Our study had two main limitations. First, a control group (total extraction of the M3M) was not included. The reason was because coronectomy is widely accepted as an effective alternative to prevent IAN injury . Also, our ethics committee suggested that random grouping might not suitable in our study. Second, age is a critical factor for DBD healing , but the patients recruited for our study were relatively young.