FI shows the greatest occurrence rate on mandibular first molars, and its main clinical manifestations include the formation of periodontal pocket, loss of connective tissue attachment and intra-radicular bone [22]. Previous studies demonstrated that the complexity of furcation anatomy is an important contributory factor in the progress of furcation lesions [3, 7].

In this study, we found that the separating angle between the DB and DL roots of 3RM1s (in the distal view) is the greatest, and the mean value (~ 60°) is approximately two-folds larger than that between mesial and distal/DB roots in the buccal view. According to an in vivo CBCT study on a Hong Kong population, Ho et al. [23] found the vertical separation angle between DB and DL roots was 62.8° ± 11.4°, which is very close our data. Another CBCT investigation on Chinese children indicated that the DL root could also occur in deciduous mandibular second molars, and the distal furcation angle was 67.4° ± 14.4°, significantly greater than that of the permanent 3RM1s [24]. The great separating angle between DB and DL roots indicates that the orientation of the endodontic instrument may significantly deviate from the axis of the tooth as it is inserted into the DB/DL canal, and overzealous drilling or instrumentation may easily lead to perforation at the pulp floor or root furcation area. Additionally, care should be taken to preserve pericervical dentin during coronal preflaring or post space preparation, as a wider root separation increases the vulnerability to root fractures. Table 1 shows that the angle between the mesial and DL roots is the smallest, and is even significantly less than the angle between mesial and DB roots. This finding also suggests that the DL root is generally located at the mesial side of the DB root in the mesio-distal direction. A deep understanding of the location and morphology of DL roots can be useful for clinicians to carry out furcation probing or periodontal treatment on 3RM1s with FI. In the buccal view, although only one fifth of the DL root was completely overlapped by the DB root, it is still prone to missed diagnosis or misdiagnosis on conventional radiographs due to superimposition of adjacent alveolar bone, and the use of multiple angled radiographs or CBCT [1, 23] allows for more reliable detection of this root trait. Wang et al. [25] carried out an ex vivo experiment to evaluate the X-ray projection angulation for successful detection of the extra DL root in 3RM1s (n = 25). On the orthoradial radiographs, correct assessment could only be found in 7 teeth (28%), and in the other 18 specimens, the DL roots were moderately (n = 8) or severely (n = 10) overlapped by the DB roots; while an additional 25° mesial horizontal angulation radiograph, but not the 25° distal angulation radiograph, yielded a 100% correct assessment rate [25]. Recently, convolutional neural network based deep learning system was applied for the detection of 3RM1s on panoramic radiographs, significantly improving diagnostic accuracy compared to that of clinicians [26]. The presence of the DL root could affect the efficiency of the periodontal instrumentation and plaque control, and a small separation angle was unfavorable to gaining access for debridement in the furcation area [23, 27].

To examine the furcation ridges, Everett et al. [27] divided 328 extracted mandibular molars into three groups, and by grinding off the mesial/distal half of the tooth, or amputating the tooth roots, the root furcations were observed under the microscope in three different views. For the first time they reported the presence of a distinct “intermediated bifurcational ridge”, as well as the “buccal and lingual bifurcation ridges”. Our current study was non-invasive, and by modifying the transparency of the tooth model into semi-transparent, the anatomic features of the furcation roof could be displayed vividly (Fig. 2). In the proximal (distal) view, the type V furcation accounted for nearly half of the total teeth, and a pronounced intermediate ridge could be detected; while in the study of Everett et al. [28], intermediated bifurcational ridge was found to be pronounced in 44%, noticeable in 29%, and absent in 27%, and primarily consisted of cement. In regard to Type W furcation, which only accounted for one fifth of our sample teeth, the buccal and lingual ridges were located near the buccal and lingual entrance of the furcation, respectively, which were mainly formed by dentine and covered with a thin layer of cement [28]. In regard to type U furcation (approximately accounting for one fourth of total teeth), the buccal and lingual ridges were not apparent, and neither protrusion nor furcation concave was formed. Everett et al. [28] reported that in 37% of cases, there was no noticeable differences between the buccal and lingual ridges or these ridges were not apparent. The concave at the center of inter-radicular area may act as an ecological niche for biofilm, and would pose challenge for proper debridement [28, 29]. In the current study, neither gender nor age was found to significantly influence the proportion of furcation types (Tables S1 and S2), although both factors may affect cement deposition and furcation configurations. Further studies with larger sample sizes and a more diverse age range are warranted. The anatomical complexity of furcation ridges presents significant challenges in diagnosing periodontal involvement. Clinicians must consider these structures carefully when assessing FI using clinical and radiographic methods. Precise identification of the furcation type is crucial for effective treatment planning, which may include procedures such as scaling and root planing, furcation debridement, or surgical interventions.

In terms of root trunk length, earlier studies reported that molars with short root trunks were susceptible to FI due to the increased likelihood of plaque retention, and conversely, a longer root trunk meant that the furcation area was located deeper within the bone, which may offer some protection against early FI in periodontal disease [9, 10]. In restorative dentistry, root trunk length can influence the design and success of restorations. Particular attention is required when restoring teeth with shorter root trunks to avoid exacerbating periodontal issues. However, FI detected in molars with long root trunks means an advanced stage of periodontitis, difficulties in diagnosis and treatment, and a poor prognosis [7]. The current study found that the mean distal trunk length is 0.7 mm longer than that of the buccal/lingual root trunk (3.0 mm). Our data is lower than those (distal trunk: 5.2 mm; buccal/lingual trunk: 4.0 mm) reported by Ho et al. [23], and the discrepancy can be due to the differences in the research method and geological reagion of populations. A short root trunk is mandatory when the clinician considers root resection or tunneling procedures as treatment options for molars with FI, while molars with long root trunks are unsuitable for such procedures [30]. Hou et al. [10] proposed a classification of molar FI based on root trunk and horizontal and vertical attachment loss, and the root trunks were classified into three types according to the ratio of vertical length of root trunk to root length (types A, B and C indicate root trunk involving the cervical third, the cervical half, and the cervical two thirds of roots, respectively), which were associated with guidelines in diagnosis and treatment of FI. When performing periodontal surgery, such as flap surgery or regenerative procedures, the length of the root trunk must be considered. Shorter root trunks may require more precise surgical techniques to effectively manage FI and to ensure adequate healing and bone regeneration.

Root concavities are clinically significant because they increase the root’s surface area, thereby aiding in the tooth’s stability within the alveolar bone. However, previous scholars have also demonstrated that root concavities may serve as an ecological niche for bacterial plaque and contribute to the formation of deeper periodontal pockets [30]. After surgical periodontal treatment, plaque, calculus and contaminated cementum should be removed adequately by periodontal instruments, and a smooth root surface that is more biologically acceptable to soft tissue should be created, which can ensure long-term fate of the involved teeth [27]. The presence of the root concavity may compromise the treatment outcome due to its inaccessibility to cleaning. Additionally, deep root concavities may predispose the tooth to fractures, particularly if significant bone loss occurs around the tooth. This is especially relevant in molars subjected to high occlusal forces. Root concavities often cannot be detected in the conventional buccolingual radiographs [31, 32], while in vivo CBCT examination [33] or ex vivo micro-CT imaging can three-dimensionally visualize its detailed configuration. To assess the depth of root concaves, many previous studies, based on tooth sections or micro-CT/CBCT scans, frequently took measurements in several or a series of horizontal (axial) root slices [16, 33, 34], and therefore, the measurement data were discrete along the root. In the current study, in buccal view of the mesial root, the continuous distribution of the distal concavity depth, as well as the corresponding canal wall thickness in the mesio-distal direction, could be displayed along the root length in one screenshot (Fig. 3). We found there was no difference between the three- and two-rooted tooth groups; averagely, the maximum depth was located at 2.8 mm below furcation or the coronal third level of the whole root length. While several other scholars arbitrarily defined that in the mesial roots of mandibular molars, the distal furcal root dentine 2 mm below furcation was the danger zone [35, 36]. Based on CBCT images, Bolbolian et al. [37] measured the dentin thickness and depth of distal concavity of the mesial roots from the furcation to 5 mm below. The area with the greatest depth of concavity was used to calculate the minimum dentin thickness and regarded as the danger zone. They demonstrated that danger zone was in the range of 0 to 3 mm below furcation with a probability of 93.4% [37]. However, the current data indicate that the maximum depth of the distal concavity does not always correspond to the minimum canal wall thickness along the root (Fig. 3B). In determining the site of danger zone, the canal curvature, dentine wall thickness, and distal root concavity should all be considered, and this issue deserves further investigations.

Ectopic enamel can be detected on the root either as cervical enamel projection, or by enamel pearl, which can induce accumulation of plaque, and are associated with rapid progression of pocket formation, periodontal attachment loss and occurrence of FI [38]. The prevalence of enamel projections can be influenced by ethnicity; it ranges from 8.6 to 85% worldwide [39], and Asian subjects have a higher prevalence rate as compared with other races [30]. Hou et al. [40] reported that the mandibular first molar exhibited the highest occurrence rate among different molars, while Grewe et al. [41] reported the most common site was the buccal side of mandibular second molars. Similar to coronal enamel, the fibers of the periodontal ligament are unable to attach to enamel projections [42]. When guided tissue regeneration is performed on molars with FI, the enamel projections should be removed via enameloplasty for a better outcome [11]. Masters and Hoskinsdean [43] classified the severity of these projections into three grades: Grade 1, short but distinct change in contour of CEJ toward furcation; Grade 2, the enamel projection approaches furcation, but no actually making contact with it; Grade 3, the enamel projection extends into the furcation; while the current study allows for accurate quantitative assessment of the 3D length of enamel projections. Table 5 shows that the mean length of the buccal enamel projections is significantly longer than that of the lingual ones, suggesting that our concerns should be put on the buccal side. Its length varies over a wide range from 0.65 to 6.47 mm, which indicates that the dentist should evaluate the status of cervical enamel projections (CEPs) for each patient carefully, and individualized clinical management of this dental anomaly should be considered regarding the eminent individual difference in severity of CEPs. The treatment decisions also depend the specific situation of the subject [17]. Figure 6 shows more than half of the buccal enamel projects are longer than 3 mm; considering the mean buccal/lingual root trunk length is also 3 mm, we estimate that Masters and Hoskinsdean’s Grade 3 may account for the largest proportion. These data can be useful for clinicians in management of CEPs during periodontal treatment, especially for treatments of Chinese patients. It is difficult to accurately determine the severity of enamel projections clinically, especially for those periodontally-healthy molars. Theoretically, CBCT imaging can best display the extent of enamel projections in the furcation, though CBCT is not routinely performed to assess furcation due to the extra radiation dose exposed and its use should apply with the principle of ALARA (as low as reasonably achievable).

Previous studies have demonstrated that both gender and age can influence the root morphology. However, concerning the prevalence of 3RM1s, gender differences have generally not been observed [44], a finding corroborated by our recent in vivo study based on CBCT examinations [24]. As shown in Tables S1 and S2, neither gender nor age significantly impact the incidence of furcation types, which may be attributed to the small sample size. Age, along with various pathological factors, may impact the deposition of cementum in the furcation area, thereby altering furcation morphology (e.g., the thickness of furcation ridges and the depth of root concaves). In this study, the mean age of subjects was 48 years, with a significant proportion of the sample teeth collected from elderly patients. Thus, our results are particularly relevant for guiding dental treatments in elderly patients.

This study has several limitations. First, all the sample teeth were collected from a Chinese population. Since ethnicity is an important influencing factor, further studies on teeth from other ethnic populations are essential to validate our conclusions. Second, the DL roots are often curved and tiny, and prone to fracture during tooth extraction, which may result in small sample size and introduce bias into the conclusions. In the future, in vivo CBCT studies with larger sample sizes may mitigate this limitation, and the impacts of the age or pathological factors can also be analyzed. Third, although all odontometric analyses were performed on 3D tooth models reconstructed from high-resolution micro-CT scans, to simplify the measurement process, the furcation angle, canal curvature, and furcation type were evaluated in the buccal-lingual view and/or proximal view, which does not constitute a true “3D” measurement. Finally, micro-CT images are unable to clearly distinguish between cementum and dentine in the furcation areas, while pathological factors and the aging processes may affect the deposition or absorption of the cement, thereby altering root furcation morphology. Clinicians should be aware of these limitations when comparing our findings with other studies or applying them to clinical practice.