Timing selection for loosened tooth fixation based on degree of alveolar bone resorption: a finite element analysis

The experimental volunteer was selected from the 2nd generation of Chinese virtual person (living digital-human) "No.23" volunteer, with complete dentition.

CT image data of mandible of the volunteer was imported into the medical three-dimensional image reconstruction software Materialise Mimics 10.0 (Materialise Company, Belgium) in DICOM format to generate the bone tissue surface profile. The gap between the tooth root and mandible was filled with a 0.2 mm periodontal membrane structure, and in combination with various software tools and clinical anatomical features, the profile curve of each structure was manually plotted. The three-dimensional digital anatomy model of mandible was reconstructed (including the separation of cortical bone and cancellous bone, enamel, dentin-cementum complex, periodontal membrane, dental pulp, temporomandibular joint condyle and other structures), then imported into reverse engineering software Geomagic Studio12.0 (Geomagic Company, USA) in STL format, using polygon editing tools to optimize the mesh of each independent anatomical structure. Alveolar bone resorption in chronic periodontitis is generally described by the ratio of resorption area to the length of tooth root, and usually divided into three degrees. In order to unify bone resorption of each tooth position in the sample models, the critical value of bone resorption in varying degrees of periodontitis was used as the standard for division. The model was trimmed, and the total length of the measured tooth root was subtracted from the distance of enamel-cementum boundary and alveolar ridge to calculate the root length of the inner alveolar bone of each tooth. The height of alveolar bone was reduced to 0, 1/3, 1/2 and 2/3 of the inner length of the root bone. The edge was trimmed to make it smooth and continuous. Four models were established to simulate (a) non-periodontitis (b) mild periodontitis (c) moderate periodontitis and (d) severe periodontitis of the mandible models, and to simulate the stable state of bone resorption after periodontal treatment. The model was imported into the finite element pre-processing software HyperMesh 11.0 (Altair Company, USA) for materialization. After the Boolean operation, finite element models of a mandible with varying degrees of alveolar bone resorption were constructed (Fig. 1).

Take the non-periodontitis model vertical loading as an example. The initial mesh size of teeth and surrounding tissues adopted 0.5 mm, and the maximum stress error percentage between 0.5 mm and 0.25 mm was 1.4% (Table 1). Given the calculation efficiency, the four modles (Fig. 2) were established using 0.5 mm mesh size. There were 283,886 tetrahedrons and 53,718 nodes in the non-periodontitis model, 274,913 tetrahedrons and 52,382 nodes in the mild periodontitis model, 273,965 tetrahedrons and 52,719 nodes in the moderate periodontitis model, and 261,095 tetrahedrons and 50,911 nodes in the severe periodontitis model.

All materials were considered linear-elastic, isotropic and homogeneous [10‐16]. The applied material properties (elastic modulus and Poisson's ratio) were obtained from the literature (Table 2).

Different teeth play diverse roles in chewing function, same loading was applied to the teeth of same region. Therefore, the loading of 100 N, 50 N and 25 N were loaded on the occlusal surfaces of molars, premolars, and anterior teeth, respectively [10]. In this study, a certain distributed point on the occlusal surface of each tooth was selected for concentrate loading [17], and the chewing cycle was simplified to vertical loading and oblique loading. Under loading conditions, the edge of the mandible was fixed to prevent the jaw from displacement in the X, Y and Z directions [13, 15] (Fig. 3).

During vertical loading, the von Mises stress distribution on the root surface was concentrated on the root labial side of the lower anterior teeth. The maximum Von Mises stress (MVMS) of mandibular dentition was concentrated on the incisor. The MVMS of the root interface of normal mandible was 13.43 MPa; the MVMS of the root interface of mild periodontitis was 15.60 MPa; the MVMS of the root interface of moderate periodontitis was 21.79 MPa; the MVMS of the root interface of severe periodontitis was 29.97 MPa (Fig. 4, Table 3). During 45° oblique loading, the stress was concentrated on the root surface of mesiolingual posterior teeth, and the MVMS was concentrated on the root surface of the mandibular first molar. The stress was 2–3 times than when vertical loading (Fig. 5, Table 4). In addition, during both vertical and oblique loading, the MVMS was increased with aggravation of periodontitis, and stress was increased more significantly with moderate to severe periodontitis.

During vertical loading, the von Mises stress distribution of the periodontal membrane was concentrated at the corresponding position of periodontal membrane on the labial side of the lower anterior tooth root close to the neck. The MVMS was concentrated in the incisor. The MVMS of the periodontal membrane of a normal mandibular was 1.35 MPa; the MVMS of the periodontal membrane with mild periodontitis was 1.65 MPa; the MVMS of the periodontal membrane with moderate periodontitis was 2.33 MPa; the MVMS of the periodontal membrane with severe periodontitis was 3.15 MPa (Fig. 6, Table 5). During 45° oblique loading, stress was concentrated at the corresponding position of the periodontal membrane on the lingual side of the lower anterior tooth root close to the neck. The MVMS was concentrated on the mandibular first molar, and the stress was 2–4 times than during vertical loading (Fig. 7, Table 6). It was found that during vertical and oblique loading, the MVMS increased with the aggravation of periodontitis, and stress of the periodontal membrane was increased more significantly in moderate to severe periodontitis.

During vertical loading, occlusal force was transmitted to the mandible via the periodontal membrane of the tooth. When the cortical bone of the mandible was stressed, the maximum Von Mises stress was located in the corresponding cortical bone area of the labial neck of the incisor root; the minimum stress was located in the corresponding cortical bone area of the neck of the canine root (Fig. 8, Table 7). With 45° oblique loading, stress was concentrated in the corresponding cortical bone area of the mesiolingual neck of the posterior tooth (Fig. 9, Table 8). It was found that during vertical and oblique loading, the MVMS was increased with aggravation of periodontitis. In mild to moderate periodontitis, stress was increased slowly; in severe periodontitis, cortical bone stress was increased more significantly.

When the cancellous bone of the mandible was stressed, the stress was mainly distributed in the corresponding cancellous area of the root apex. During vertical and oblique loading, the MVMS was increased with aggravation of periodontitis. The maximum Von Mises stress was located in the apical area of the second molar. In mild to moderate periodontitis, stress increased slowly. In severe periodontitis, stress of cancellous bone increased more significantly (Figs. 10, 11, Tables 9, 10).