Investigation of effective intrusion and extrusion force for maxillary canine using finite element analysis

Trabecular Bone Component Assessment under Orthodontic Loads and Movements during Periodontal Breakdown-A Finite Elements Analysis

This numerical analysis, by employing Tresca and Von Mises failure criteria, assessed the biomechanical behavior of a trabecular bone component subjected to 0.6, 1.2, and 2.4 N orthodontic forces under five movements (intrusion, extrusion, tipping, rotation, and translation) and during a gradual horizontal periodontal breakdown (0-8 mm). Additionally, they assessed the changes produced by bone loss, and the ischemic and resorptive risks. The analysis employed eighty-one models of nine patients in 405 simulations. Both failure criteria showed similar qualitative results, with Tresca being quantitatively higher by 1.09-1.21. No qualitative differences were seen between the three orthodontic loads. Quantitatively, a doubling (1.2 N) and quadrupling (2.4 N) were visible when compared to 0.6 N. Rotation and translation followed by tipping are the most stressful, especially for a reduced periodontium, prone to higher ischemic and resorptive risks. In an intact periodontium, 1.2 N can be safely applied but only in a reduced periodontium for extrusion and intrusion. More than 0.6 N is prone to increasing ischemic and resorptive risks for the other three movements. In an intact periodontium, stress spreads in the entire trabecular structure. In a reduced periodontium, stress concentrates (after a 4 mm loss-marker for the stress change distribution) and increases around the cervical third of the remaining alveolar socket.

Three-dimensional finite element analysis of retracting pathological migration of the right upper central incisor with a clear aligner

We aimed to explore the best orthodontic step distance of the right upper central incisor with mild, moderate, and severe pathological displacement achieved via a clear aligner. Three-dimensional models of maxilla-tooth-periodontal ligament clear aligner of the right upper central incisors with five different steps of 0.1, 0.125, 0.15, 0.165, 0.25 mm and three different alveolar bone heights were established via finite element analysis. We analysed the changing trends in initial displacement, the periodontal ligament, the alveolar bone, and apical stress of right upper central incisor. In the process of retraction, the right upper central incisor a movement trend of the crown deviating from the distal root to the mesial, and with the decrease of the height of the alveolar bone and the increase of the displacement, the crown would appear distal labial torsion with a deepening trend of vertical overlay.The maximum stress distribution of the periodontal ligament and alveolar bone showed a positive correlation. The overall stress distribution of the periodontal ligament and apical stress increased with decrease of alveolar bone height and the increase of alveolar bone displacement. In patients with mild, moderate, and severe pathological displacement of the right upper central incisor, the best step distance of anterior tooth retraction is 0.165, 0.15, and 0.125 mm, respectively.

Effects of Increasing the Orthodontic Forces over Cortical and Trabecular Bone during Periodontal Breakdown-A Finite Elements Analysis

Background and Objectives: Herein we used numerical analysis to study different biomechanical behaviors of mandibular bone subjected to 0.6 N, 1.2 N, and 2.4 N orthodontic loads during 0-8 mm periodontal breakdown using the Tresca failure criterion. Additionally, correlations with earlier FEA reports found potential ischemic and resorptive risks. Materials and Methods: Eighty-one models (nine patients) and 243 simulations (intrusion, extrusion, rotation, tipping, and translation) were analyzed. Results: Intrusion and extrusion displayed after 4 mm bone loss showed extended stress display in the apical and middle third alveolar sockets, showing higher ischemic and resorptive risks for 0.6 N. Rotation, translation, and tipping displayed the highest stress amounts, and cervical-third stress with higher ischemic and resorptive risks after 4 mm loss for 0.6 N. Conclusions: Quantitatively, rotation, translation, and tipping are the most stressful movements. All three applied forces produced similar stress-display areas for all movements and bone levels. The stress doubled for 1.2 N and quadrupled for 2.4 N when compared with 0.6 N. The differences between the three loads consisted of the stress amounts displayed in color-coded areas, while their location and extension remained constant. Since the MHP was exceeded, a reduction in the applied force to under 0.6 N (after 4 mm of bone loss) is recommended for reducing ischemic and resorptive risks. The stress-display pattern correlated with horizontal periodontal-breakdown simulations.

Orthodontic Internal Resorption Assessment in Periodontal Breakdown-A Finite Elements Analysis (Part II)

This finite elements analysis (FEA) assessed the accuracy of maximum shear stress criteria (Tresca) in the study of orthodontic internal surface resorption and the absorption-dissipation ability of dental tissues. The present study was conducted over eighty-one models totaling 324 simulations with various bone loss levels (0-8 mm), where 0.6 N and 1.2 N were applied in the intrusion, extrusion, rotation, tipping, and translation movements. Tresca criteria displayed localized high-stress areas prone to resorption for all situations, better visible in the dentine component. The internal resorptive risks are less than external ones, seeming to increase with the progression of the periodontal breakdown, especially after 4 mm. The internal and external surface high-stress areas are strictly correlated. The qualitative stress display for both forces was almost similar. The rotation and tipping displayed the highest resorptive risks for the pulp chamber, decreasing with bone loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same applied force is kept. The dentine resemblance to ductile based on its high absorption-dissipation ability seems correct. Tresca seems to supply a better predictability of the prone-to-resorption areas than the other failure criteria.

Cortical and Trabecular Bone Stress Assessment during Periodontal Breakdown-A Comparative Finite Element Analysis of Multiple Failure Criteria

Background and Objectives: This numerical analysis investigated the biomechanical behavior of the mandibular bone as a structure subjected to 0.5 N of orthodontic force during periodontal breakdown. Additionally, the suitability of the five most used failure criteria (Von Mises (VM), Tresca (T), maximum principal (S1), minimum principal (S3), and hydrostatic pressure (HP)) for the study of bone was assessed, and a single criterion was identified for the study of teeth and the surrounding periodontium (by performing correlations with other FEA studies). Materials and Methods: The finite element analysis (FEA) employed 405 simulations over eighty-one mandibular models with variable levels of bone loss (0-8 mm) and five orthodontic movements (intrusion, extrusion, tipping, rotation, and translation). For the numerical analysis of bone, the ductile failure criteria are suitable (T and VM are adequate for the study of bone), with Tresca being more suited. S1, S3, and HP criteria, due to their distinctive design dedicated to brittle materials and liquids/gas, only occasionally correctly described the bone stress distribution. Results: Only T and VM displayed a coherent and correlated gradual stress increase pattern for all five movements and levels of the periodontal breakdown. The quantitative values provided by T and VM were the highest (for each movement and level of bone loss) among all five criteria. The MHP (maximum physiological hydrostatic pressure) was exceeded in all simulations since the mandibular bone is anatomically less vascularized, and the ischemic risks are reduced. Only T and VM displayed a correlated (both qualitative and quantitative) stress increase for all five movements. Both T and VM displayed rotation and translation, closely followed by tipping, as stressful movements, while intrusion and extrusion were less stressful for the mandibular bone. Conclusions: Based on correlations with earlier numerical studies on the same models and boundary conditions, T seems better suited as a single unitary failure criterion for the study of teeth and the surrounding periodontium.

Assessment of the Orthodontic External Resorption in Periodontal Breakdown-A Finite Elements Analysis (Part I)

This Finite Elements Analysis (FEA) assessed the accuracy of Tresca failure criteria (maximum shear stress) for the study of external root resorption. Additionally, the tooth absorption-dissipation ability was assessed. Overall, 81 models of the second mandibular premolar, out of a total of 324 simulations, were involved. Five orthodontic movements (intrusion, extrusion, rotation, translation, and tipping) were simulated under 0.6 N and 1.2 N in a horizontal progressive periodontal breakdown simulation of 0-8 mm. In all simulations, Tresca criteria accurately displayed the localized areas of maximum stress prone to external resorption risks, seeming to be adequate for the study of the resorptive process. The localized areas were better displayed in the radicular dentine-cementum component than in the entire tooth structure. The rotation and translation seem prone to a higher risk of external root resorption after 4 mm of loss. The resorptive risks seem to increase along with the progression of periodontal breakdown if the same amount of applied force is guarded. The localized resorption-prone areas follow the progression of bone loss. The two light forces displayed similar extensions of maximum stress areas. The stress displayed in the coronal dentine decreases along with the progression of bone loss. The absorption-dissipation ability of the tooth is about 87.99-97.99% of the stress.

Finite Elements Analysis of Tooth-A Comparative Analysis of Multiple Failure Criteria

Herein Finite elements analysis (FEA) study assesses the adequacy and accuracy of five failure criteria (Von Mises (VM), Tresca, maximum principal (S1), minimum principal (S3), and Hydrostatic pressure) for the study of tooth as a structure (made of enamel, dentin, and cement), along with its stress absorption-dissipation ability. Eighty-one 3D models of the second lower premolar (with intact and 1-8 mm reduced periodontium) were subjected to five orthodontic forces (intrusion, extrusion, tipping, rotation, and translation) of 0.5 N (approx. 50 gf) (in a total of 405 FEA simulations). Only the Tresca and VM criteria showed biomechanically correct stress display during the 0-8 mm periodontal breakdown simulation, while the other three showed various unusual biomechanical stress display. All five failure criteria displayed comparable quantitative stress results (with Tresca and VM producing the highest of all), showing the rotational and translational movements to produce the highest amount of stress, while intrusion and extrusion, the lowest. The tooth structure absorbed and dissipated most of the stress produced by the orthodontic loads (from a total of 0.5 N/50 gf only 0.125 N/12.5 gf reached PDL and 0.01 N/1 gf the pulp and NVB). The Tresca criterion seems to be more accurate than Von Mises for the study of tooth as structure.

Assessment of the Maximum Amount of Orthodontic Force for PDL in Intact and Reduced Periodontium (Part I)

This study examines 0.6 N and 1.2 N as the maximum orthodontic force for periodontal ligament (PDL) at multiple levels of periodontal breakdown, and the relationships with the ischemic, necrotic, and resorptive risks. Additionally, this study evaluates if Tresca failure criteria is more adequate for the PDL study. Eighty-one 3D models (from nine patients; nine models/patients) with the 2nd lower premolar and different degrees of bone loss (0-8 mm) where subjected to intrusion, extrusion, rotation, translation, and tipping movements. Tresca shear stress was assessed individually for each movement and bone loss level. Rotation and translation produced the highest PDL stresses, while intrusion and extrusion determined the lowest. Apical and middle third PDL stresses were lower than the cervical stress. In intact periodontium, the amount of shear stress produced by the two investigated forces was lower than the 16 KPa of the maximum physiological hydrostatic pressure (MHP). In reduced periodontium (1-8 mm tissue loss), the apical amount of PDL shear stress was lower than MHP for both applied forces, while cervically for rotation, translation and tipping movements exceeded 16 KPa. Additionally, 1.2 N could be used in intact periodontium (i.e., without risks) and for the reduced periodontium only in the apical and middle third of PDL up to 8 mm of bone loss. However, for avoiding any resorptive risks, in the cervical third of PDL, the rotation, translation, and tipping movements require less than 0.2-0.4 N of force after 4 mm of loss. Tresca seems to be more adequate for the study of PDL than other criteria.

Assessment of the Maximum Amount of Orthodontic Force for Dental Pulp and Apical Neuro-Vascular Bundle in Intact and Reduced Periodontium on Bicuspids (Part II)

This study examines 0.6 N-4.8 N as the maximum orthodontic force to be applied to dental pulp and apical NVB on intact and 1-8 mm reduced periodontal-ligament (PDL), in connection with movement and ischemic, necrotic and resorptive risk. In addition, it examines whether the Tresca finite-element-analysis (FEA) criterion is more adequate for the examination of dental pulp and its apical NVB. Eighty-one (nine patients, with nine models for each patient) anatomically correct models of the periodontium, with the second lower-premolar reconstructed with its apical NVB and dental pulp were assembled, based on X-ray CBCT (cone-beam-computed-tomography) examinations and subjected to 0.6 N, 1.2 N, 2.4 N and 4.8 N of intrusion, extrusion, translation, rotation, and tipping. The Tresca failure criterion was applied, and the shear stress was assessed. Forces of 0.6 N, 1.2 N, and 2.4 N had negligible effects on apical NVB and dental pulp up to 8 mm of periodontal breakdown. A force of 4.8 N was safely applied to apical NVB on the intact periodontium only. Rotation and tipping seemed to be the most invasive movements for the apical NVB. For the dental pulp, only the translation and rotation movements seemed to display a particular risk of ischemia, necrosis, and internal orthodontic-resorption for both coronal (0-8 mm of loss) and radicular pulp (4-8 mm of loss), despite the amount of stress being lower than the MHP. The Tresca failure criterion seems more suitable than other criteria for apical NVB and dental pulp.

Quantification of orthodontic loads on teeth in the correction of canine overeruption using different archwire designs

INTRODUCTION

This study quantifies the effects of material, size of the continuous archwires, and level of overeruption on the loads on teeth in the correction of overerupted canines.

METHODS

An orthodontic force test (OFT) was used to measure the 3-dimensional loads delivered by the archwires to the brackets attached to the maxillary right incisors, canine, and premolars. Dentoforms simulating canine overeruptions at the 0.5 mm and 1 mm levels were made from computerized tomography scans. Archwires with 2 types of material (stainless steel [SS] and nickel-titanium [NiTi]) and 2 sizes (0.014-in and 0.016-in) were tested, respectively, on the 0.022 × 0.028-in brackets through elastomeric ligatures.

RESULTS

The forces were dominantly intrusive on the canines and extrusive on the first premolars and lateral incisors. The magnitudes of the extrusive forces were about 74% and 52% that of intrusive force on the canines, which range from -0.48 ± 0.01 N to -5.70 ± 0.14 N depending on the wire material, size, and severity of overeruption (P <0.01). The canine intrusive forces created by SS wires were about 3 times higher than that of NiTi wires with the same sizes, 0.016-in archwires were about twice higher than that of 0.014-in with the same materials, and 1 mm overeruption level doubled with respect to 0.5 mm. Significant second-order moment as coupled with the intrusive or extrusive forces.

CONCLUSIONS

The intrusive and extrusive forces on teeth in the correction of canine overeruption can be quantified by the in vitro orthodontic force test, and the effects of the 3 factors significantly affect the loads on the teeth.

The effects of different types of periodontal ligament material models on stresses computed using finite element models

INTRODUCTION

Finite element (FE) method has been used to calculate stress in the periodontal ligament (PDL), which is crucial in orthodontic tooth movement. The stress depends on the PDL material property, which varies significantly in previous studies. This study aimed to determine the effects of different PDL properties on stress in PDL using FE analysis.

METHODS

A 3-dimensional FE model was created consisting of a maxillary canine, its surrounding PDL, and alveolar bone obtained from cone-beam computed tomography scans. One Newton of intrusion force was applied vertically to the crown. Then, the hydrostatic stress and the von Mises stress in the PDL were computed using different PDL material properties, including linear elastic, viscoelastic, hyperelastic, and fiber matrix. Young's modulus (E), used previously from 0.01 to 1000 MPa, and 3 Poisson's ratios, 0.28, 0.45, and 0.49, were simulated for the linear elastic model.

RESULTS

The FE analyses showed consistent patterns of stress distribution. The high stresses are mostly concentrated at the apical area, except for the linear elastic models with high E (E >15 MPa). However, the magnitude varied significantly from -14.77 to -127.58 kPa among the analyzed patients. The E-stress relationship was not linear. The Poisson's ratio did not affect the stress distribution but significantly influenced the stress value. The hydrostatic stress varied from -14.61 to -95.48 kPa.

CONCLUSIONS

Different PDL material properties in the FE modeling of dentition do not alter the stress distributions. However, the magnitudes of the stress significantly differ among the patients with the tested material properties.

Assessment of the Best FEA Failure Criteria (Part II): Investigation of the Biomechanical Behavior of Dental Pulp and Apical-Neuro-Vascular Bundle in Intact and Reduced Periodontium

The aim of this study was to biomechanically assess the behavior of apical neuro-vascular bundles (NVB) and dental pulp employing Tresca, Von Mises, Pressure, S1 and S3 failure criterions in a gradual periodontal breakdown under orthodontic movements. Additionally, it was to assess the accuracy of failure criteria, correlation with the maximum hydrostatic pressure (MHP), and the amount of force safe for reduced periodontium. Based on cone-beam computed tomography, 81 3D models of the second lower premolar were subjected to 0.5 N of intrusion, extrusion, rotation, tipping, and translation. A Finite Elements Analysis (FEA) was performed. In intact and reduced periodontium apical NVB, stress (predominant in all criteria) was significantly higher than dental pulp stress, but lower than MHP. VM and Tresca displayed identical results, with added pulpal stress in translation and rotation. S1, S3 and Pressure showed stress in the apical NVB area. 0.5 N seems safe up to 8 mm periodontal breakdown. A clear difference between failure criteria for dental pulp and apical NVB cannot be proved based only on the correlation quantitative results-MHP. Tresca and VM (adequate for ductile materials) showed equivalent results with the lowest amounts of stress. The employed failure criteria must be selected based on the type of material to be analyzed.

The three-dimensional displacement tendency of teeth depending on incisor torque compensation with clear aligners of different thicknesses in cases of extraction: a finite element study

Background

Despite the popularity of clear aligner treatment, the effect of the thickness of these aligners has not been fully investigated. The objective of this study was to assess the effects of incisor torque compensation with different thicknesses of clear aligner on the three-dimensional displacement tendency of teeth in cases of extraction.

Methods

Three-dimensional finite element models of the maxillary dentition with extracted first premolars, maxilla, periodontal ligaments, attachments, and aligners were constructed and subject to Finite Element Analysis (FEA). Two groups of models were created: (1) with 0.75 mm-thick aligners and (2) with 0.5 mm-thick aligners. A loading method was developed to simulate the action of clear aligners for the en masse retraction of the incisors. Power ridges of different heights were applied to both groups to mimic torque control, and the power ridges favoring the translation of the central incisors were selected. Then, we used ANSYS software to analyze the initial displacement of teeth and the principle stress on the PDL.

Results

Distal tipping, lingual tipping and extrusion of the incisors, distal tipping and extrusion of the canines, and mesial tipping and intrusion of the posterior teeth were all generated by clear aligner therapy. With the 0.5 mm-thick aligner, a power ridge of 0.7 mm could cause bodily retraction of the central incisors. With the 0.75 mm-thick aligner, a power ridge of 0.25 mm could cause translation of the central incisors. Aligner torque compensation created by the power ridges generated palatal root torque and intrusion of the incisors, intrusion of the canines, mesial tipping and the intrusion of the second premolar; these effects were more significant with a 0.75 mm-thick aligner. After torque compensation, the stress placed on the periodontal ligament of the incisors was distributed more evenly with the 0.75 mm-thick aligner.

Conclusions

The torque compensation caused by power ridges can achieve incisor intrusion and palatal root torque. Appropriate torque compensation with thicker aligners should be designed to ensure bodily retraction of anterior teeth and minimize root resorption, although more attention should be paid to the anchorage control of posterior teeth in cases of extraction.

Assessment of the Best FEA Failure Criteria (Part I): Investigation of the Biomechanical Behavior of PDL in Intact and Reduced Periodontium

The accuracy of five failure criterions employed in the study of periodontal ligaments (PDL) during periodontal breakdown under orthodontic movements was assessed. Based on cone-beam computed tomography (CBCT) examinations, nine 3D models of the second lower premolar with intact periodontium were created and individually subjected to various levels of horizontal bone loss. 0.5 N of intrusion, extrusion, rotation, tipping, and translation was applied. A finite Elements Analysis (FEA) was performed, and stresses were quantitatively and qualitatively analyzed. In intact periodontium, Tresca and Von Mises (VM) stresses were lower than maximum physiological hydrostatic pressure (MHP), while maximum principal stress S1, minimum principal stress S3, and pressure were higher. In reduced periodontium, Tresca and VM stresses were lower than MHP for intrusion, extrusion, and the apical third of the periodontal ligament for the other movements. 0.5 N of rotation, translation and tipping induced cervical third stress exceeding MHP. Only Tresca (quantitatively more accurate) and VM are adequate for the study of PDL (resemblance to ductile), being qualitatively similar. A 0.5 N force seems safe in the intact periodontium, and for intrusion and extrusion up to 8 mm bone loss. The amount of force should be reduced to 0.1-0.2 N for rotation, 0.15-0.3 N for translation and 0.2-0.4 N for tipping in 4-8 mm periodontal breakdown. S1, S3, and pressure criteria provided only qualitative results.

An analysis of the optimal intrusion force of the maxillary central incisor with root horizontal resorption using the finite element method and curve fitting

There are no studies on the optimal intrusion force in orthodontic patients with the existing root resorption (RR). The study aimed to analyze the optimal intrusion force for central incisors with existing horizontal root resorption using the finite element method (FEM). We calculated the optimal intrusion force using the finite element method and curve fitting. We found that with the increase of the maxillary central incisor's root horizontal resorption length, the optimal intrusion force interval's median gradually increases. If the resorption length is more significant than 1/2 of the root length, it is not recommended to use intrusion force theoretically.

Development and verification of a constitutive model for human periodontal ligament based on finite element analysis

This study aimed to develop a constitutive model for human periodontal ligament (PDL) by combining the hyperelastic and viscosity models. We performed the finite element analysis (FEA) to simulate the experimental processes of the PDL in vitro and in vivo tests to verify the developed model. The FEA results indicated that the simulative curves were consistent with the experimental curves in the PDL in vitro tests. Moreover, for the in vivo measurements, the simulative result of 0.6258 N was similar to the experimental value of 0.65 N. The study results can help orthodontists better understand the biomechanical characteristics of PDL.

Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations

This scoping review is intended to synthesize the techniques proposed to model the tooth-periodontal ligament-bone complex (TPBC), while also evaluating the suggested periodontal ligament (PDL) material properties. It is concentrated on the recent advancements on the PDL and TPBC models, while identifying the advantages and limitations of the proposed approaches. Systematic searches were conducted up to December 2020 for articles that proposed PDL models to assess orthodontic tooth movement in Compendex, Web of Science, EMBASE, MEDLINE, PubMed, ScienceDirect, Google Scholar and Scopus databases. Although there have been many studies focused on the evaluation of PDL material properties through numerous modelling approaches, only a handful of approaches have been identified to investigate the interface properties of the PDL as a complete dynamical system (TPBC models). Past reviews on the analytical and experimental determination of the PDL properties already show a concerning range in reported output values-some nearly six orders of magnitude in difference-that strongly suggested the need for further investigation. Surprisingly, it has not yet been possible to determine a narrower range of values for the PDL material properties. Moreover, very few scientific approaches address the TPBC as an integrated complex system model. In consequence, current methods for capturing the PDL material behaviour in a clinical setting are limited and inconclusive. This synthesis encourages more systematic, pragmatic and phenomenological research in this area.

Stress evaluation of different implant lengths on atrophic edentulous mandibles with fixed full-arch implant-supported prosthesis: a finite element analysis

Finite element analysis was used to compare the effect of different implant lengths on atrophic mandible with full-arch fixed prostheses. Four models were constructed with different implant lengths: 4, 6, 8 and 10 mm. A 100-N occlusal load was applied. The stress at the bone level, implant, and prosthetic components were obtained. Similar behavior was observed for all groups, except for 4 mm, which showed more discrepant values ​​for all prosthetic components. Although longer implants presented better biomechanical behavior, the 4 mm implant seems to be a viable alternative for severely atrophic mandibles, however, further studies need to be carried out.