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Displacement and stress distribution of mandibular incisors after orthodontic treatment in the presence of alveolar bone loss under occlusal loads: A finite element analysis

Displacement and stress distribution of mandibular incisors after orthodontic treatment in the presence of alveolar bone loss under occlusal loads: A finite element analysis



American Journal of Orthodontics and Dentofacial Orthopedics, 2022-05-01, Volume 161, Issue 5, Pages e456-e465, Copyright © 2022 American Association of Orthodontists


Introduction

This study evaluated the initial stress produced in the periodontal ligament (PDL) and the displacements of mandibular incisors under masticatory force in patients with alveolar bone loss (ABL) after orthodontic treatment.

Methods

Four horizontal absorption models (zero, one third, one half, and two thirds of root length) and 2 labiolingual absorption models (labial two thirds, lingual one third of root length, and vice versa) of the mandibular anterior segment were constructed. A total force of 285.3 N was applied vertically to the edges of incisors. The tooth displacement and principal stresses in the PDL were evaluated in a finite element analysis.

Results

In all models, the labial movements of the central incisors ascended more significantly, whereas there was obvious compressive stress and tensile stress concentrated in the labial and lingual cervical margins of the PDL, respectively. For the lateral incisors, augmentation of the distal motions was more evident. Compressive stress was apparent in the labial-distal margin, and tensile stress was concentrated in the lingual-mesial cervical margin. With the same proportion of ABL, more significant displacement and stress concentration in the PDL occurred in the central incisors. In labiolingual absorption models, labial ABL caused greater incisors displacement and periodontal stress concentration. When horizontal ABL extended from one half to two thirds of the root length, mobility of the central incisors and stresses in the PDL increased significantly.

Conclusions

Mandibular incisors follow the different movement and stress distribution patterns under occlusal loads. Special consideration should be given to the retention of mandibular incisors when horizontal ABL exceeds half of the root length.

Highlights

  • Four horizontal and 2 labiolingual absorption models of the mandibular anterior segment were constructed.

  • Whether in horizontal or labiolingual alveolar bone absorption, the mandibular central and lateral incisors follow the different movement and stress distribution patterns under masticatory force.

  • Special consideration should be given to the retention of the mandibular incisors with alveolar bone horizontal absorption exceeding half of the root length.

Periodontitis is an inflammatory disease characterized by tissue destruction and subsequent attachment loss. When the balance among the factors that maintain physiological tooth position is disturbed by diminished supportive tissue, tooth displacement occurs, defined as pathologic tooth migration, usually manifested as proclination, diastema, rotation, extrusion, and drifting. Periodontal therapy alone can control inflammation. Nevertheless, it cannot release the occlusal trauma and esthetic problems caused by tooth displacement, whereas the strength of orthodontic treatment is in relieving crowding, closing gaps, improving occlusal relations, and eliminating occlusal trauma. Therefore, combined periodontal and orthodontic treatment (CPOT) is vital to prevent further periodontal tissue damage and achieve long-term stability for periodontitis. Studies have shown that combination therapy has good clinical efficacy, reducing the inflammatory levels in serum and gingival crevicular fluid and improving the morphology of bone defects. , With the improvements in living standards and esthetic requirements, an increasing number of patients with periodontitis have sought orthodontic treatment in recent years.

Expanding the range of tooth movement based on controlled inflammation is an area worth exploring and has aroused the interest of many researchers. Orthodontic treatment plans, biomechanics, and appliance systems should be modified to address teeth surrounded by reduced periodontal support. , Nowadays, with adequate plaque control and appropriate orthodontic treatment implementation, severe periodontitis is no longer a contraindication for orthodontic therapy.

In orthodontic patients with good periodontal health, tooth movement is limited by strict physiological and anatomic boundaries, which, if infringed, can result in reduced periodontal and alveolar bone support. Furthermore, adult patients are more prone to periodontal complications because these boundaries cannot be pushed as far as adolescents. Patients with CPOT often suffer from periodontal bone defects, usually horizontally, and are characterized by an even reduction in the bone height around 1 or more tooth. Although orthodontic treatment-related alveolar bone loss (ABL) usually occurs at the labial or lingual sides of the incisors as a result of proclination or retroclination of the incisors, both of these situations can lead to reduced alveolar bone support of incisors after orthodontic treatment.

The necessity of wearing a retainer after comprehensive orthodontic treatment is indisputable. However, few studies on retention of orthodontic patients with reduced alveolar bone height. Although some biomedical agents and low-level laser therapy show great potential for orthodontic retention experimentally, conventional approaches such as fixed lingual retainers, removable thermoplastic retainers, and acrylic retainers remain the most commonly used retainers in the clinic. There is no consensus on the ideal mode of retention after orthodontic treatment, which remains one of the greatest challenges of orthodontic treatment.

Alveolar bone resorption of patients may not be repaired after orthodontic treatment. Their tooth mobility is usually more apparent than orthodontic patients without ABL because of decreased supportive periodontal tissues. Thus, fixed retainers are typically recommended for these orthodontic patients with reluctant alveolar bone conditions. Nevertheless, the wide variation in the severity of bone resorption may impede establishing a “one size fits all” approach to retention for those patients. However, there are no available data about the extent of tooth displacement and the stress distribution exerted on periodontal tissues in patients with reduced alveolar bone height, which are vital for doctors to determine a retention regime.

Finite element analysis (FEA) is a mathematical approximation method for solving the mechanical problems of constitutive models that allow stresses and displacement to be identified. With the advantages of being noninvasive, accurate, and providing quantitative data on possible reactions occurring in internal structures that can hardly be measured in vivo, it has been widely used in the study of tooth movement biomechanics, orthodontic treatment planning, and properties of orthodontic materials. ,

Attachment loss more often presents in the lower anterior region. Mandibular incisor crowding and irregularity are risk factors in periodontal disease progression. Therefore, after active orthodontic treatment, orthodontists should pay special attention to the retention of patients whose mandibular incisors with reduced alveolar bone height to prevent relapse. This study intended to evaluate the initial stress produced in the periodontal ligament (PDL) and the displacement of mandibular incisors in patients without or with varying types of ABL in the mandibular anterior area after orthodontic treatment under occlusal loads by means of FEA to provide a reference for the consideration of retention schemes for orthodontic patients with reduced alveolar bone height.

Material and methods

An adult patient with a 90° angle between the mandibular central incisors and the mandibular plane, who had just removed the bracket and had no ABL, was selected. A cone-beam computed tomography (CBCT) scan was conducted by a 3-dimensional (3D) examination device (Kavo Dental GmbH, Biberach, Germany) using the default technical parameters (120 kV; 37.07 mA; 26.9 seconds; field of view, 13 × 16 cm; and voxel size of 0.25 mm). All CBCT data were exported to digital imaging and communications in medicine format, then imported to Mimics Software (version 17.0; Materialise, Leuven, Belgium) for reconstruction. The anterior segment of the mandible was isolated, and a 3D model of the cortical bone, trabecular bone, tooth, and PDL was extracted. Anterior teeth were segmented by automatic thresholding (1458-3307), and artifactual connections between opposing or adjacent tooth crowns were manually removed. To reconstruct the PDL, the roots of mandibular anterior teeth were isolated by manual segmentation 1.0-1.5 mm below the enamel cementum junction. Considering the widening of the PDL after orthodontic treatment, the PDL was obtained by expanding the roots outwardly by 0.5 mm. Then, the cortical bone was isolated by gray value thresholding (231-1998), and the Boolean operation subtracted the tooth and PDL. The cancellous bone was created by filling the inner space of the cortical bone. Using 3-Matic software (version 10.0; Materialise, Leuven, Belgium), 3D datasets of the cortical bone, cancellous bone, tooth, and PDL were converted into ∗.x_t files. These files were then imported into the HyperMesh program (version 2019; Altair Company, Troy, Mich) to trim obvious defects and spikes, fill gaps between each part, then build and generate grids for 6 distinct models.

Model 1 simulated mandibular anterior teeth with no ABL. In addition, 2 types of alveolar bone resorption models were established. In the first type, models 2-4 characterized alveolar bones of mandibular anterior teeth absorbing one third, one half, two thirds of root length, which replicated horizontal alveolar bone absorption deriving from periodontitis. In addition, models 5 and 6 depicted orthodontic treatment-related labiolingual alveolar bone resorption, with the alveolar bone absorbing one third of root length on the labial side and two thirds on the lingual side in model 5 and the opposite in model 6 ( Fig 1 ). Models 2-6 were established by the removal of alveolar bone from the crest in the buccolingual and mesiodistal directions according to the corresponding proportions established in model 1. Tetrahedral elements were used to form the mesh and to ensure the accuracy and efficiency of the calculation. The size near the PDL was approximately 0.3 mm, whereas the size far from the PDL was approximately 1 mm. The average total number of elements and nodes of the 6 models was 759,272 and 179,407, respectively. The convergence of the mesh was successfully tested for all finite element models.

Finite element models of mandibular anterior segment. Model 5 is the lingual view, whereas the other models are the labial view.
Fig 1
Finite element models of mandibular anterior segment. Model 5 is the lingual view, whereas the other models are the labial view.

The next phase was to transfer the models to Abaqus software (version 2019; Dassault Systèmes, Johnston, RI) for calculation. The local coordinate system of each model was established. The x-axis represented the direction of the coronal plane with the origin at the mesial incisal points of the central incisors, the y-axis represented the sagittal plane with the positive direction toward the lingual surface of the tooth, and the z-axis represented the vertical plane with the positive direction toward the incisor edge.

The tooth, cortical bone, and cancellous bone were considered elastic, homogeneous, and isotropic linear materials. Young’s modulus and Poisson's ratio were taken from the literature ( Table I ). , The PDL was assumed to be hyperelastic according to the V-W hyperelastic model reported by Huang et al , and implemented in Abaqus software through a user-defined material subroutine. The relevant parameters are listed in Table II . For the boundary condition, all nodes at the base and distal extremes of the model were fixed in all directions to constrain free-body motion. The tie constraint was used for the tooth-PDL, PDL-cortical bone, and cortical-cancellous bone interfaces in all models. A total force of 285.3 N (as a maximum occlusal force usually exerted on the mandibular incisors) was applied vertically to the edges of the 4 mandibular incisors on average ( Fig 2 ). The nodal displacement of the labial midpoint of the edge of 4 incisors, the principal stress distribution of the PDL, the maximum value of the first principal stress (S1, maximum tensile stress), and the minimum value of the third principal stress (S3, maximum compressive stress) of the PDL nodes were recorded for each model.

Table I
Material properties used in this study
Material Young’s modulus (MPa) Poisson’s ratio
Tooth 20,000 0.3
Cortical bone 13,700 0.31
Cancellous bone 1370 0.31

Table II
Material parameters for V-W model
C1(MPa) C2 C3(MPa)
6.21197 1.19493 −0.808983

Boundary conditions and force system applied to teeth. Red, force; orange , boundary conditions were applied to the models.
Fig 2
Boundary conditions and force system applied to teeth. Red, force; orange , boundary conditions were applied to the models.

Informed consent for research participation was acquired, and the use of the CBCT data was approved by the Ethics Committee. All experiments were approved and performed according to relevant guidelines and regulations.

Results

For a better comparison, the average displacement of the bilateral mandibular central and lateral incisors is displayed in Table III and Figure 3 .

Table III
The incisal displacement of mandibular incisors in various models (in mm)
Tooth Direction Model 1 Model 2 Model 3 Model 4 Model 5 Model 6
Central Distal 0.017 0.077 0.172 0.780 0.053 0.110
Labial 0.115 0.394 0.686 2.388 0.398 0.531
Inferior 0.045 0.115 0.193 0.818 0.122 0.193
Total 0.124 0.418 0.733 2.642 0.420 0.576
Lateral Distal 0.047 0.153 0.315 0.754 0.164 0.224
Labial 0.059 0.121 0.247 0.551 0.157 0.180
Inferior 0.030 0.061 0.115 0.271 0.074 0.101
Total 0.081 0.204 0.416 0.973 0.239 0.304

Total displacement and displacement in coordinator directions of the mandibular incisors in ( A ) horizontal absorption models and ( B ) labiolingual absorption models. The solid line represents the displacement of the mandibular central incisors, whereas the dotted line signifies the displacement of the mandibular lateral incisors.
Fig 3
Total displacement and displacement in coordinator directions of the mandibular incisors in ( A ) horizontal absorption models and ( B ) labiolingual absorption models. The solid line represents the displacement of the mandibular central incisors, whereas the dotted line signifies the displacement of the mandibular lateral incisors.

In model 1, with no alveolar resorption, the average displacement of the central incisors was 0.124 mm, and that of the lateral incisors was 0.081 mm. In horizontal absorption models, with the increase of the ABL, the mobility of central and lateral incisors increased gradually. In horizontal absorption models, represented by models 2 to 4, the mobility of the central incisors increased by 3.4, 5.9, and 21.3 times, respectively. In addition, the mobility of the lateral incisors increased by 2.5, 5.1, and 12.0 times, compared with model 1. In labiolingual absorption models, labial alveolar bone resorption in the lower anterior area (model 6) exerted a greater impact on the tooth mobility under the maximum bite force. Compared with model 1, the mobility of mandibular central incisors and lateral incisors increased by 3.4 and 2.9 times in model 5 and 4.6 and 3.7 times in model 6, respectively.

In periodontally healthy subjects, the total displacement of the mandibular central incisors was greater than that of the lateral incisors; the labial movements of the central incisors were dominant, whereas those of the lateral incisors were only slightly larger than the distal direction. With the aggravation of ABL, regardless of the resorption type, the labial movements of central incisors increased more significantly than in other directions, the augmentation of distal motions of lateral incisors was more evident than labial displacement. However, regardless of the presence or absence of alveolar resorption, central and lateral incisors shifted very little in the vertical direction except in model 4.

The numeric findings of principal stresses in the PDL are presented in Tables IV and V and Figures 4-6 .

Table IV
The maximum value of the first principle force (MPa) in the PDL of mandibular incisors
Site Model Right lateral incisor Right central incisor Left central incisor Left lateral incisor
Cervical margin Model 1 0.328 0.537 0.370 1.172
Model 2 1.650 2.889 4.773 4.378
Model 3 5.672 6.176 6.245 5.833
Model 4 15.752 36.750 /150.208 ∗∗ 29.536 /169.822 ∗∗ 15.478
Model 5 1.958 1.840 1.632 1.214
Model 6 16.349 31.392 28.820 10.967
Apical one third Model 1 −2.212 −1.001 −1.109 −1.875
Model 2 1.298 4.952 12.064 0.684
Model 3 6.604 27.305 9.912 6.503
Model 4 20.152 184.299 83.287 11.327
Model 5 2.319 12.514 5.688 2.065
Model 6 3.396 6.923 5.338 2.556

Lingual cervical margin.

∗∗ Labial cervical margin.

Table V
The minimum value of the third principle force (MPa) in the PDL of mandibular incisors
Site Model Right lateral incisor Right central incisor Left central incisor Left lateral incisor
Cervical margin Model 1 −10.249 −8.010 −8.012 −7.554
Model 2 −11.469 −18.019 −26.749 −10.612
Model 3 −21.921 −75.053 −111.601 −17.845
Model 4 −48.484 −371.272 −344.549 −56.181
Model 5 −14.697 −18.247 −18.802 −11.869
Model 6 −16.709 −19.798 −15.285 −12.007
Apical one third Model 1 −5.708 −6.486 −5.795 −5.524
Model 2 −9.502 −20.065 −16.071 −9.021
Model 3 −14.985 −30.281 −20.442 −11.526
Model 4 −69.665 −218.639 −57.290 −20.980
Model 5 −8.967 −15.081 −14.323 −10.050
Model 6 −15.053 −30.225 −17.761 −12.266

The first principal stress distribution in the PDL of all finite element models (MPa). Note that legends differ from model to model.
Fig 4
The first principal stress distribution in the PDL of all finite element models (MPa). Note that legends differ from model to model.

The third principal stress distribution in the PDL of all finite element models (MPa). Note that legends differ from model to model.
Fig 5
The third principal stress distribution in the PDL of all finite element models (MPa). Note that legends differ from model to model.

The maximum principal stress (abs) (ie, the principal stress with the maximum absolute value) distribution in the PDL of all finite element models (MPa). Note that legends differ from model to model.
Fig 6
The maximum principal stress (abs) (ie, the principal stress with the maximum absolute value) distribution in the PDL of all finite element models (MPa). Note that legends differ from model to model.

In all models, the stress magnitudes in the PDL of the right incisors were not identical to their left counterparts. However, the distribution of compressive stress and tensile stress had good symmetry. Stress concentration was more likely to occur in the cervical margin and apical one third of the PDL of incisors, especially in the central incisors. The distribution of stress in the cervical margin of the PDL was consistent with the tooth displacement. The PDLs of lingual cervical margins were subjected to apparent tensile stress for central incisors, whereas the labial cervical margins were subjected to tremendous compression stress. For lateral incisors, considerable compressive stress was observed in the labial-distal cervical margins of the PDL, and pronounced tensile stress was observed in the lingual-mesial cervical margins.

In horizontal absorption models, with the aggravation of the ABL, the compressive and tensile stresses in the PDL were raised. It should also be noted that there were prominent stress concentration areas in the labial cervical margin of the PDL of central incisors in model 4, with the maximum tensile stresses of 150.208 MPa and 169.822 MPa and the maximum compressive stresses of −371.272 MPa and −344.549 MPa, respectively. Compared with the absolute value, the compressive stress was still dominant at this site.

In labiolingual absorption models, an increase of tensile and compressive stress was also observed compared with the nonalveolar bone absorption model. Model 6 exhibited a greater stress concentration than model 5 at the cervical margin and the apical one third of the PDL. In addition, the apparent concentration of tensile stress at the cervical margin of model 6 was significant. The tensile stress of central incisors at the cervical margin in model 6 was 17.4 times that of model 5 and 8.7 times greater in the lateral incisors.

With variations in the amount and type of alveolar bone absorption, a change in stress patterns was also observed. The labial apical one third of the PDL of incisors was subjected to compressive stress in model 1 and model 6 but tensile stress in model 2 to model 5.

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