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In some cases of proclined maxillary incisors, the proclination can be corrected by a fixed prosthesis. The aim of this study was to investigate the magnitude and distribution of (i) principal stresses in the adjacent alveolar bone and (ii) direct and shear stresses that are normal and parallel, respectively, to the bone-tooth interface of a normal angulated maxillary incisor, a proclined one, and a proclined one corrected with an angled prosthetic crown. 2D finite-element models were constructed, and a static load of 200 N on the palatal surface of the maxillary incisor at different load angles was applied. Load angles (complementary angle to interincisal angle) ranging from 20° to 90° were applied. The results indicate that the load angle could have a more significant impact on the overall stress distributions in the surrounding alveolar bone and along the bone-tooth interface than the proclination of the maxillary incisor. Provided that the resulting interincisal angle is 150° or smaller, the stresses in the surrounding bone and at the bone-tooth interface are similar between a proclined maxillary incisor and the one with prosthodontic correction. Hence, such a correction, when deemed appropriate clinically, can be undertaken with confidence that there is little risk of incurring additional stresses over that already in existence, in the supporting bone and at the tooth-bone interface.

Facial appearance, function, and competence of the lips are greatly influenced by the alignment (or malalignment) of the maxillary incisor, and its protrusion, especially, has a negative impact on appearance and psychosocial wellbeing. In addition, excess overjet and overbite due to protrusion may also increase the vulnerability of the front teeth to injury and periodontal damage. Thus, the index of orthodontic treatment need (IOTN), which defines the severity of malocclusion and priority for treatment, considers excess overjet the second worst type of malocclusion [

The aim of this study is therefore to perform finite-element (FE) analysis to compare the stress distributions in the supporting tissues, especially those at the bone-tooth interface, between a normal angulated maxillary incisor, a proclined one, and a proclined one with an angle-corrected prosthetic crown. The results will help determine whether such prosthodontic correction is a viable treatment option for proclined maxillary incisors.

The finite-element method is a numerical tool ideal for analyzing the mechanical behavior of manmade and biological structures, including their combinations. It can help us better understand the potential risks or benefits of a dental treatment such as the aforementioned angle correction of a protruded maxillary incisor using a prosthetic crown.

In this study, linear-elastic static analyses were performed to calculate the stress distributions in the surrounding bone and at the bone-tooth interface for a maxillary incisor during occlusion, with or without malalignment, and in the former, with or without angle correction.

2D rather than 3D finite-element models will be used in this study as it has been found previously that the numerical differences observed between 2D and 3D analyses of dental restorations in a single tooth unit are small [

Two-dimensional finite-element models of a human maxillary central incisor and the surrounding PDL and bone were constructed by using the software SolidWorks (version 2016; Dassault Systèmes SOLIDWORKS Corp, Waltham, MA, USA) based on data in the literature [

Models for (a) normal tooth (Case 1), (b) proclined tooth (Case 2), and (c) corrected tooth (Case 3).

The mechanical properties of the materials were considered to be linearly elastic, isotropic, and homogeneous. The material properties of each part are shown in Table

Material properties used in the FE models.

Young’s modulus (MPa) | Poisson’s ratio | Ref. | |
---|---|---|---|

Enamel | 84100 | 0.3 | [ |

Dentin | 18600 | 0.33 | [ |

Cortical bone | 13700 | 0.33 | [ |

Cancellous bone | 1370 | 0.33 | [ |

Periodontal ligament | 6.89 | 0.45 | [ |

Pulp | 2.07 | 0.45 | [ |

In the present study, the direction of the load was assumed to follow the long axis of the lower incisor with the load angle being the complementary angle to the interincisal angle (Figure ^{9}. Class II division 1 cases of incisor relationships usually have a smaller than average interincisal angle, whereas Class II division 2 cases usually have a larger than average interincisal angle. In order to simulate a range of interincisal angles, load angles ranging from 20° to 90° were considered.

Cephalometric diagram illustrating the interincisal angle and load angle (modified from Figure

A concentrated load of 200 N was applied to simulate the occlusal force. The position of the load for Case 1 was 3 mm above the incisal edge, corresponding to an overjet of 2 mm. An overjet of 4.75 mm was assumed for Case 2, which corresponded to a moderate need for orthodontic treatment (3.5–6.0 mm) [

Positions of the load in Cases 2 and 3. Point 1: load position in corrected tooth. Point 2: load position in proclined tooth. Angle 3: angle subtended by the load vector with respect to the long axis of the tooth.

Principal stresses within the cortical and the cancellous bone and the normal and shear stresses at the bone-tooth interface were assessed.

For ease of comparison between the three cases, the interfacial stresses were averaged over all the nodes along the interface. For the interfacial normal stresses, the tensile and compressive values were considered separately and in combination (by averaging the absolute values). For the interfacial shear stresses, only the absolute values were considered as the sign or direction of a shear stress was not important as far as the biomechanical response was concerned.

The alveolar bone is subjected to both axial compression and a counterclockwise bending moment. The larger the load angle, the larger the bending moment and the smaller the axial compression (Figure

Maximum principal stress distributions in the alveolar bone under 20°, 30°, 50°, and 90° load angles for Cases 1, 2, and 3.

Minimum principal stress distributions in the alveolar bone under 20°, 30°, 50°, and 90° load angles for Cases 1, 2, and 3.

The magnitudes of the stresses along the tooth-bone interface are much lower than those in the bone (Figures

Distributions of stress normal to the bone-tooth interface for Cases 1, 2, and 3 at 20° (a), 30° (b), 50° (c), and 90° (d) load angles.

Average (a) and maximum (b) of the normal stresses (tensile and compressive) along the bone-tooth interface at different load angles.

Distributions of shear stress at the bone-tooth interface for Cases 1, 2, and 3 at 20° (a), 30° (b), 50° (c), and 90° (d) load angles.

Average (a) and maximum (b) of the shear stresses along the bone-tooth interface at different load angles.

Figure

The direct stress normal to the bone-tooth interface on the labial tooth socket is mostly compressive but becomes tensile towards the apex where there is stress concentration. It then changes sharply to being compressive on the palatal side of the apex before reversing back to being tensile towards the alveolar crest. The stresses on the palatal side are generally higher than those on the labial side in Case 1 (normal tooth), but the opposite is true for Cases 2 and 3 (proclined tooth and corrected tooth). The distribution and magnitude of the normal stress in Cases 2 and 3 are similar to increasing load angle, except at the apical area under the smaller load angles of 20° and 30° where the stresses in Case 3 are higher than those in Case 2. The magnitude of the interfacial normal stress at both the labial and palatal sides of the apex increases with increasing load angle for all three cases, with the increase on the palatal side of the apex for Case 3 being the least pronounced.

The average tensile and compressive interfacial stresses increase with the load angle, with the average tensile stress increasing faster than the average compressive stress (Figure

Table

Average of the absolute values of stresses (MPa) normal to the bone-tooth interface at different load angles.

20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° | Avg. | |
---|---|---|---|---|---|---|---|---|---|

Normal tooth | 1.1700 | 1.4616 | 1.7678 | 2.0634 | 2.3207 | 2.5200 | 2.6808 | 2.7289 | 2.0891 |

Proclined tooth | 1.3394 | 1.5739 | 1.8151 | 2.0283 | 2.1913 | 2.2934 | 2.3497 | 2.3322 | 1.9904 |

Corrected tooth | 1.5664 | 1.7347 | 1.9526 | 2.1453 | 2.3194 | 2.4115 | 2.4479 | 2.4163 | 2.1243 |

The shear stress at the bone-tooth interface is minimal at the apical area and is mainly present on the labial and palatal sides of the tooth socket (Figure

The average of the absolute values of the shear stress over all the nodes along the bone-tooth interface (Figure

Average of the absolute values of shear stresses (MPa) along the bone-tooth interface at different load angles.

20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° | Avg. | |
---|---|---|---|---|---|---|---|---|---|

Normal tooth | 0.4052 | 0.6167 | 0.8152 | 0.9863 | 1.1268 | 1.2316 | 1.2598 | 1.2849 | 0.9658 |

Proclined tooth | 0.6233 | 0.8168 | 0.9836 | 1.1187 | 1.2179 | 1.2790 | 1.2757 | 1.2479 | 1.0704 |

Corrected tooth | 0.7904 | 0.9176 | 1.0627 | 1.1841 | 1.2492 | 1.3034 | 1.3043 | 1.2903 | 1.1378 |

This study evaluated the effect of prosthodontic correction on the stresses of the bone surrounding a proclined maxillary incisor using the FE method. Some previous FE analysis investigating the effect of maxillary incisor proclination suggested that the bigger the proclination of the incisor, the higher the stress at the root apex. External root resorption has been shown to occur when stresses induced by intrusion at the apex exceed the resistance and reparative ability of periapical tissues [

The results of this study indicate that, during chewing, the load angle, and hence the interincisal angle, could have a more significant impact on the overall stress distributions in the surrounding bone and along the bone-tooth interface than the proclination angle. Considering the Class I interincisal edge relationship and the position of loading according to the average overjet distance [

The present study shows that the stresses in the surrounding tissues of the proclined incisors, with and without prosthodontic correction, are similar except at the apical area for the smaller load angles of 20° and 30° (Figures

The normal and shear stresses along the tooth-bone interface were analyzed separately as they may be responsible for different modes of biomechanical responses. Furthermore, the tensile and compressive normal stresses were considered separately. This is because the strength of the bone depends on the mode of loading [

During biting or chewing, the lower incisor moves along the occlusal surface of the upper one, changing both the direction and position of contact. If a bolus of food is considered, the tooth-loading process would be more complicated. These are things that have not been considered in this study. In addition, the current model did not take into consideration endodontically treated dentine and the usage of a post, as the scope of this study was to study the distribution of stresses in the supporting tissues. Indeed, clinically, failure can occur in the restoration used to correct the proclination. Effects on the patient’s mastication of the prosthodontic correction will also need to be assessed. Further studies will need to be conducted on the impact of the above scenario on the stress distributions of the supporting tissues, the endodontically treated tooth, and the prosthodontic crown used to correct the angle.

Provided that the resulting interincisal angle is 150° or smaller, the stresses in the surrounding bone and at the bone-tooth interface are similar between a proclined maxillary incisor and the one with prosthodontic correction. Hence, such a correction, when deemed appropriate clinically, can be undertaken with confidence that there is little risk of incurring additional stresses over that already in existence, in the supporting bone and at the tooth-bone interface.

The finite-element model data used to support the findings of this study are available from the corresponding author upon request.

The authors do not have any conflicts of interest in the content and results of this paper.

The authors would like to acknowledge 3M gives in the provision of financial support to Yiting He with the Key Opinion Leaders Scholarship. This work was also supported by the National Natural Science Foundation of China (Grant No. 81571015), Science and Technology Innovation Committee of Guangzhou (Grant No. 2017010011), and Science and Technology Plan Funds of Guangdong (2016A050502012).