Periodontal Ligament Hydrostatic Pressure with Areas of Root Resorption after Application of a Continuous Torque Moment

Effects of Oral Appliances for Obstructive Sleep Apnoea in Reduced Periodontium: A Finite Element Analysis

BACKGROUND AND OBJECTIVE

In the literature, no studies correlate the effects of mandibular advancement devices (MADs) with different titration systems to periodontitis. Through a finite element analysis (FEA), this study investigates the effects generated on periodontal ligaments (PDLs) and teeth by four commercial MADs in periodontal health and with 15% bone resorption.

METHODS

Four MADs (Somnodent Flex™, Somnodent Avant™, Orthoapnea™, and Herbst™) were digitalised starting from the impressions of a patient's dental arches. A force of 11.18 N, representing an advancement of 9.5 mm, was applied, and a FEA was subsequently performed. After measuring the stresses and displacements on the PDLs and teeth in healthy periodontal conditions, the vertical dimension of the alveolar bone was reduced by 15%, and measurements were repeated.

RESULTS

In terms of PDL stress, Herbst™ is the device which guarantees a more uniform increment in case of the first stage of periodontitis (+7% for mandibular and maxillary PDLs compared to the healthy condition). For Somnodent™ devices, the PDLs stress increment is almost null for mandibular PDLs but much higher than Herbst™ for maxillary PDLs (+17% and +21% for Flex™ and Avant™). Orthoapnea™ determines a PDL stress augmentation between the other devices (+16% and +7%, respectively, for maxillary and mandibular PDLs). Concerning teeth movement, Herbst™ and Orthoapnea™ determine a lower and more uniform displacement than Somnodent devices.

CONCLUSIONS

The stress distribution and teeth displacement are strictly related to MAD geometry. Since its minor effects on teeth and PDLs, the Herbst™ could be more appropriate in patients with periodontitis.

The Effect of Larger Orthodontic Forces and Movement Types over a Dental Pulp and Neuro-Vascular Bundle of Lower Premolars in Intact Periodontium-A Numerical Analysis

BACKGROUND/OBJECTIVES

This numerical analysis of stress distribution in the dental pulp and neuro-vascular bundle (NVB) of lower premolars assessed the ischemic and degenerative-resorptive risks generated by 2 and 4 N during orthodontic movements (rotation, translation, tipping, intrusion and extrusion) in intact periodontium.

METHODS

The numerical analysis was performed on nine intact periodontium 3D models of the second lower premolar of nine patients totaling 90 simulations.

RESULTS

In intact periodontium, both forces displayed a similar stress distribution for all five orthodontic movements but different amounts of stress (a doubling for 4 N when compared with 2 N), with the highest values displayed in NVB. In intact periodontium, 2 N and 4 N induced stresses lower than the maximum hydrostatic pressure (MHP) with no ischemic risks for healthy intact teeth. The rotation was seen as the most stressful movement, closely followed by intrusion and extrusion. Translation was quantitatively seen as the least stressful when compared with other movements.

CONCLUSIONS

Larger orthodontic forces of 2 N and 4 N are safe (with any expected ischemic or resorptive risks) for the dental pulp and NVB of healthy intact teeth and in intact periodontium. Nevertheless, rotation and translation movements can induce localized circulatory disturbances in coronal pulp (i.e., vestibular and proximal sides) generating ischemic and resorptive risks on previously treated teeth (i.e., direct and indirect dental pulp capping). The intrusion and extrusion movements, due to the higher NVB-induced deformation when compared with the other three movements, could trigger circulatory disturbances followed by ischemia on previously traumatized teeth (i.e., occlusal trauma).

Biomechanical effects of a new crimpable gate spring combined with conventional rectangular archwires for torque adjustment of individual anterior teeth : A comparative finite element study

OBJECTIVE

Precise root torque adjustment of anterior teeth is indispensable for optimizing dental esthetics and occlusal stability in orthodontics. The efficiency of traditional rectangular archwire manipulation within bracket slots seems to be limited. The crimpable gate spring, a novel device, has emerged as a promising alternative. Yet, there is a paucity of guidelines for its optimal clinical application. This study used finite element analysis (FEA) to investigate the biomechanical impact of the gate spring on torque adjustment of individual anterior teeth and to elucidate the most effective application strategy.

METHODS

A FEA model was constructed by a maxillary central incisor affixed with an edgewise bracket featuring a 0.022 × 0.028 inch (in) slot. A range of stainless steel rectangular archwires, in conjunction with a gate spring, were modeled and simulated within the bracket slots. A control group utilized a conventional rectangular wire devoid of a gate spring. Palatal root moments were standardized to 9, 18, and 36 Nmm for both experimental and control groups.

RESULTS

The gate spring significantly amplified palatal root movement, notably with the 0.019 × 0.025 in archwire. However, this was accompanied by an increase in stress on the tooth and periodontal ligament, particularly in the cervical regions. The synergistic use of a 0.019 × 0.025 in rectangular archwire with a gate spring in a 0.022 × 0.028 in bracket slot was identified as most efficacious for torque control of individual anterior teeth.

CONCLUSIONS

The gate spring is a viable auxiliary device for enhancing torque adjustment on individual teeth. However, caution is advised as excessive initial stress may concentrate in the cervical and apical regions of the periodontal ligament and tooth.

Evaluating stress and displacement in the craniomandibular complex using Twin Block appliances at varied angles: A finite element study

OBJECTIVES

The objective of this investigation was to assess the stress and displacement pattern of the craniomandibular complex by employing finite element methodology to simulate diverse angulations of inclined planes that are incorporated in the Twin Block appliance.

METHODS

A 3D finite element representation was established by use of Cone Beam Computed Tomography (CBCT) scans. This comprehensive structure included craniofacial skeletal components, the articular disc, a posterior disc elastic layer, dental elements, periodontal ligaments, and a Twin Block appliance. This investigation is the first to incorporated inclined planes featuring three distinct angulations (45, 60, and 70°) as the study models. Mechanical impacts were evaluated within the glenoid fossa, tooth, condylar, and articular disc regions.

RESULTS

In all simulations, the stress generated by the Twin Block appliance was distributed across teeth and periodontal ligament, facilitating the anterior movement of mandibular teeth and the posterior displacement of maxillary teeth. Within the temporomandibular joint region, compressive forces on the superior and posterior facets of the condyle diminished, coinciding with the stress configuration that fosters condylar and mandibular growth. Stress dispersion homogenized in the condylar anterior facet and articular disc, with considerable tensile stress in the glenoid fossa's posterior aspect conforming to stress distribution that promote fossa reconfiguration. The 70° inclined plane exerts the highest force on the tissues. The condyle's maximum and minimum principal stresses are 0.36 MPa and -0.15 MPa, respectively, while those of the glenoid fossa are 0.54 MPa and -0.23 MPa.

CONCLUSION

Three angled appliances serve the purpose of advancing the mandible. A 45° inclined plane relative to the occlusal plane exerts balanced anteroposterior and vertical forces on the mandibular arch. Steeper angles yield greater horizontal forces, which may enhance forward growth and efficient repositioning.

Prognostic risk factors for apical root resorption in orthodontic patients - Are the Kjær's morphologic characteristics of clinical relevance?

BACKGROUND

Patients undergoing orthodontic treatment (OT) face an increased risk of developing external apical root resorption (EARR). A prognostic risk assessment prior to OT can potentially be conducted through anatomical features in panoramic radiography. This retrospective study aimed to assess the significance of Kjær's morphological characteristics in analyzing the risk of EARR.

METHODS

Panoramic radiographs of 1,156 patients (624 females, 532 males) were retrospectively analyzed. Anamnestic and treatment-related data were extracted from patient records. The mean age at the start of OT was 12.8 ± 2.2 years (min. 6.4 years, max. 22.3 years) and at the end of OT 15.9 years (min. 8.5 years, max. 24.1 years). The mean treatment duration was 3.1 ± 1.6 years. Panoramic radiographs with a minimum of two per patient were examined for the presence of Kjær's characteristics. The degree of EARR was registered defining resorption in four degrees of severity. Bivariate analysis and multivariate Poisson regression were performed to assess the association between Kjær's characteristics and EARR patient- and tooth- related (α = 0.05).

RESULTS

In total, 72.8% of the patients showed EARR at the end of OT with lateral maxillary incisors most frequently affected. Short roots (p < 0.001) were significantly associated with EARR in patients. Tooth-related microdontia (#12, #22, lower second premolars), narrow crowns (#11, #21, lower incisors), short roots (upper incisors, lower first molars) and ectopia (#11, #21, #13), such as shorter distal roots of the mandibular first molar showed a significant association with EARR depending on severity degree. The type of orthodontic appliance (fixed: p < 0.001, fixed and removeable: p = 0.008), as well as treatment duration (p < 0.001) were also identified as risk factors for EARR.

CONCLUSIONS

Although the risk assessment for EARR development through panoramic radiography analysis is limited, predisposition appears to be present in specific dental characteristics and treatment-related factors.

Effectiveness of different intrusion modes of maxillary anterior teeth with mini-implants in clear aligner treatment: a three-dimensional finite element analysis

BACKGROUND

The intrusion of maxillary anterior teeth is often required and there are various intrusion modes with mini-implants in clear aligner treatment. The objective of this study was to evaluate the effectiveness of maxillary anterior teeth intrusion with different intrusion modes, aiming to provide references for precise and safe intrusion movements in clinical practice.

METHODS

Cone-beam computed tomography and intraoral optical scanning data of a patient were collected. Finite element models of the maxilla, maxillary dentition, periodontal ligaments (PDLs), clear aligner (CA), attachments, and mini-implants were established. Different intrusion modes of the maxillary anterior teeth were simulated by changing the mini-implant site (between central incisors, between central and lateral incisor, between lateral incisor and canine), loading site (between central incisors, on central incisor, between central and lateral incisor, between lateral incisor and canine), and loading mode (labial loading and labiolingual loading). Ten conditions were generated and intrusive forces of 100 g were applied totally. Then displacement tendency of the maxillary anterior teeth and CA, and stress of the PDLs were analyzed.

RESULTS

For the central incisor under condition L14 and for the canine under conditions L11, L13, L23, and L33, the intrusion amount was negative. Under other conditions, the intrusion amount was positive. The labiolingual angulation of maxillary anterior teeth exhibited positive changes under all conditions, with greater changes under linguoincisal loading. The mesiodistal angulation of canine exhibited positive changes under labial loading, while negative changes under linguoincisal loading except for condition L14.

CONCLUSIONS

The intrusion amount, labiolingual and mesiodistal angulations of the maxillary anterior teeth were affected by the mini-implant site, loading site, and loading mode. Labial and linguoincisal loading may have opposite effects on the intrusion amount of maxillary anterior teeth and the mesiodistal angulation of canine. The labiolingual angulation of the maxillary incisors would increase under all intrusion modes, with greater increases under linguoincisal loading.

Effects of different tooth movement patterns and aligner thicknesses on maxillary arch expansion with clear aligners: a three-dimensional finite element study

Objectives

The objective of this study was to investigate the biomechanical effects of different tooth movement patterns and aligner thicknesses on teeth and periodontal tissues during maxillary arch expansion with clear aligners, to facilitate more precise and efficient clinical orthodontic treatments.

Methods

Three-dimensional models including teeth, maxilla, periodontal ligament, and aligner were constructed and subjected to finite element analysis. Tooth displacement trends and periodontal ligament stresses were measured for seven tooth displacement patterns (divided into three categories including overall movement of premolars and molars with gradually increasing molar expansion in each step; distributed movement of premolars and molars; and alternating movement between premolars and molars at intervals) and two aligner thicknesses (0.5 mm and 0.75 mm) during maxillary arch expansion with clear aligners.

Results

When expanding the maxillary arch with clear aligners, the effective expansion of the target teeth mainly showed a tilting movement trend. Increasing the amount of molar expansion increased the buccal displacement of the first molar but decreased the buccal displacement of the premolars. The mean buccal displacement of the target teeth was greater in the posterior teeth interval alternating movement group (0.026 mm) than in the premolar/molar distributed movement group (0.016 mm) and the overall movement group (0.015 mm). Increasing aligner thickness resulted in greater buccal displacement of the crowns and increased stress on the periodontal ligaments.

Conclusion

Increasing the amount of molar expansion reduces the efficiency of premolar expansion. Alternating movement of premolars and molars at intervals achieves a higher arch expansion efficiency, but attention should be paid to the anchorage of adjacent teeth. Increasing the thickness of the aligner increases the expansion efficiency but may also increase the burden on the periodontal tissues.

The Hydrostatic Pressure Distribution in the Periodontal Ligament and the Risk of Root Resorption-A Finite Element Method (FEM) Study on the Nonlinear Innovative Model

Excessive orthodontic force can induce inflammatory tooth root resorption due to sustained high stresses within the periodontal ligament (PDL). This study aimed to analyze the PDL pressures during upper incisor retraction using the en masse method with TISAD. The finite element method (FEM) ensured consistent conditions across cases. The models included bone geometry, adjacent teeth, PDL, and orthodontic hardware, analyzed with LS-Dyna. The pressure ranged from 0.37 to 2.5 kPa across the dental arch, with the central incisors bearing 55% of the load. The pressure distribution remained consistent regardless of the force or hook height. The critical pressure (4.7 kPa) was exceeded at 600-650 g force, with notable pressure (3.88 kPa) on the palatal root wall of the right central incisor. Utilizing 0.017 × 0.025 SS archwires in MBT 0.018 brackets provided good torque control and reduced the root resorption risk when forces of 180-200 g per side were applied, maintaining light to moderate stress. Triple forces may initiate resorption, highlighting the importance of nonlinear finite element analysis (FEA) for accurate oral cavity simulations.

Effectiveness of the Attachment Design and Thickness of Clear Aligners during Orthodontic Anterior Retraction: Finite Element Analysis

OBJECTIVE

Clear aligner treatment (CAT) provides orthodontic patients with a comfortable treatment alternative; however, this device has limited capacity to facilitate tooth movements. Although composite attachment has been proposed to facilitate tooth displacement, some of its aspects, such as aligner thickness, can influence CAT's precision. This work aimed to compare the stress distribution patterns produced by clear aligners with different thicknesses and composite attachment shapes during anterior retraction.

MATERIALS AND METHODS

Maxillary models consisting of clear aligners, maxillary teeth, and various attachments to the upper central incisor's labial surface were generated. Three models were built to mimic the retraction of the upper central incisors. Each had a distinct attachment design (rectangular attachment, ellipsoid attachment, and pyramidal attachment) and various aligner thicknesses (0.75, 0.85, 0.95, 1.05, and 1.15 mm). Upper central incisor retraction was accomplished using clear aligners. Finite element analysis was used to examine the built models. Stress distribution pattern was examined.

RESULTS

The greater the thickness of the aligner, the higher the stress experienced by the teeth. The 0.75 mm-thick aligner induces the lightest stress with a minimum of 0.0037623 MPa and a maximum of 0.32859 MPa. Meanwhile, the 1.5 mm-thick aligner has the highest stress with a minimum of 0.004679 MPa and a maximum of 0.43858 MPa. The force distribution on rectangular attachments appears evenly distributed. The maximum pressure force on rectangular attachments has a minimum of 0.38828 MPa, which is smaller than the maximum on ellipsoid and pyramidal attachments at 0.40933 and 0.45099 MPa, respectively.

CONCLUSION

The best aligner thickness is 0.75 to 0.85 mm for anterior retraction. An aligner with 0.95 mm thickness can still be used when a remarkable amount of tooth movement force is needed; however, this exception is only applicable to a limited number of clear aligner trays. The ellipsoid attachment is the best type of attachment because the resulting force is substantial and evenly distributed.

Mechanochemical coupling of MGF mediates periodontal regeneration

Clinical evidence shows that the mechanical stimulation obtained from occlusion could enhance periodontal ligament (PDL) remodeling. Mechano-growth factor (MGF) is a growth factor produced specifically following mechanical stimulus Here, we aim to investigate the mechanical enhancement potential and mechanism of the MGF in PDL regeneration. In vivo study found that MGF produced from the PDL under occlusion force could strongly enhance PDL remodeling. In vitro experiments and mathematical modeling further confirmed the mechanical enhancement effect of MGF for PDLSC differentiation toward fibroblasts. A mechanochemical coupling effect of MGF mediated the enhancement of mechanical effect, which was modulated by Fyn-FAK kinases signaling and subsequent MAPK pathway. Finally, enhanced PDL regeneration under the mechanochemical coupling of MGF and occlusal force was verified in vivo. There exists an additive mechanical effect of MGF mediated by Fyn-FAK crosstalk and subsequent ERK1/2 and p38 phosphorylation, which could be developed as an MGF-centered adjuvant treatment to optimize PDL remodeling, especially for patients with weakened bite force or destroyed periodontium.

The crucial role of periodontal ligament's Poisson's ratio and tension-compression asymmetric moduli on the evaluation of tooth displacement and stress state of periodontal ligament

The hydrostatic stress in the periodontal ligament (PDL) evaluated by finite element analysis is considered an important indicator for determining an appropriate orthodontic force. The computed result of the hydrostatic stress strongly depends on the PDL material model used in the orthodontic simulation. This study aims to investigate the effects of PDL Poisson's ratio and tension-compression asymmetric moduli on both the simulated tooth displacement and the PDL hydrostatic stress. Three tension-compression symmetric and two asymmetric PDL constitutive models were selected to simulate the tensile and compressive behavior of a PDL specimen under uniaxial loading, and the resulting numerical results were compared with the in-vitro PDL experimental results reported in the literature. Subsequently, a tooth model was established, and the selected constitutive models and parameters were employed to assess the hydrostatic stress state in the PDL under two distinct loading conditions. The simulated results indicate that PDL Poisson's ratio and tension-compression asymmetry exert substantial influences on the simulated PDL hydrostatic stress. Conversely, the elastic modulus exhibits minimal impact on the PDL stress state under the identical loading conditions. Furthermore, the PDL models with tension-compression asymmetric moduli and appropriate Poisson's ratio yield more realistic hydrostatic stress. Hence, it is imperative to employ suitable Poisson's ratio and tension-compression asymmetric moduli for the purpose of characterizing the biomechanical response of the PDL in orthodontic simulations.

Investigation of Forces and Moments during Orthodontic Tooth Intrusion Using Robot Orthodontic Measurement and Simulation System (ROSS)

The Robot Orthodontic Measurement and Simulation System (ROSS) is a novel biomechanical, dynamic, self-regulating setup for the simulation of tooth movement. The intrusion of the front teeth with forces greater than 0.5 N poses a risk for orthodontic-induced inflammatory root resorption (OIIRR). The aim was to investigate forces and moments during simulated tooth intrusion using ROSS. Five specimens of sixteen unmodified NiTi archwires and seven NiTi archwires with intrusion steps from different manufacturers (Forestadent, Ormco, Dentsply Sirona) with a 0.012″/0.014″/0.016″ wire dimension were tested. Overall, a higher wire dimension correlated with greater intrusive forces Fz (0.012″: 0.561-0.690 N; 0.014″: 0.996-1.321 N; 0.016″: 1.44-2.254 N) and protruding moments Mx (0.012″: -2.65 to -3.922 Nmm; 0.014″: -4.753 to -7.384 Nmm; 0.016″: -5.556 to -11.466 Nmm) during the simulated intrusion of a 1.6 mm-extruded upper incisor. However, the 'intrusion efficiency' parameter was greater for smaller wire dimensions. Modification with intrusion steps led to an overcompensation of the intrusion distance; however, it led to a severe increase in Fz and Mx, e.g., the Sentalloy 0.016″ medium (Dentsply Sirona) exerted 2.891 N and -19.437 Nmm. To reduce the risk for OIIRR, 0.014″ NiTi archwires can be applied for initial aligning (without vertical challenges), and intrusion steps for the vertical levelling of extruded teeth should be bent in the initial archwire, i.e., 0.012″ NiTi.

Effects of upper arch expansion using clear aligners on different stride and torque: a three-dimensional finite element analysis

BACKGROUND

During maxillary arch expansion with a clear aligner (CA), buccal tipping of the posterior teeth often occurs, resulting in an unsatisfactory arch expansion effect. The aim of this study was to analyze the appropriate maxillary arch expansion stride length and torque compensation angle for maxillary dentition to achieve an ideal moving state when a CA was used for upper arch expansion.

METHODS

This study established a three-dimensional (3D) finite element model including a CA, maxilla, periodontal ligament (PDL), and maxillary dentition. The stress distribution, stress situation, expansion efficiency, and movement trends of the maxillary dentition during upper arch expansion of different stride (0.1 mm, 0.2 mm, and 0.3 mm) and torque compensation (0°, 0.5°, 1°, and 1.5°) were measured.

RESULTS

Maxillary arch expansion lead to buccal tilt of the posterior teeth, lingual tilt of the anterior teeth, and extrusion of the incisors. As the angle of compensation increased, the degree of buccal tilt on the posterior teeth decreased, with this reducing the efficiency of upper arch expansion. When the stride length was 0.1 mm, the torque compensation was 1.2°, and when stride length was 0.2 mm and the torque compensation was approximately 2°, there was a tendency for the posterior teeth to move bodily. However, when the stride length was 0.3 mm, the increase in torque compensation could not significantly improve the buccal tilt phenomenon. In addition, the equivalent von-Mises stress values of the maxillary root, PDL, and alveolar bone were in the same order of magnitude.

CONCLUSIONS

This study indicated that the posterior teeth cause a degree of buccal tilt when maxillary arch expansion is ensured. The specific torque compensation angle should be determined based on the patient's situation and the desired effect.

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.

Impact of 3D collagen-based model and hydrostatic pressure on periodontal ligament fibroblast: A morpho-biochemical analysis

This study developed a customized hydrostatic pressure-based loading environment to investigate the effect of static hydrostatic pressure on the periodontal ligament fibroblasts (PDLf) in a three-dimensional (3D) collagen-based model. The cylindrical tissue constructs were comprised of PDL fibroblast cells seeded in type I collagen matrices and divided into three experimental groups: Control (no load), low-load (∼0.07 kPa), and high-load (∼60 kPa), all subjected to 24 h of experimental duration. Cells in the 3D construct were stained with fluorophore-conjugated antibodies for cytoskeletal protein F-actin and matricellular protein periostin. Cell culture supernatant was assessed for receptor activator of nuclear factor kappaB ligand (RANKL) and osteoprotegerin (OPG) expression. Transmission electron microscopy examined the contact between the cells and the collagen matrix. Ultrastructural changes in the 3D collagen matrix were also analyzed using scanning electron microscopy. Experiments were performed in triplicates, and data was analyzed using one-way ANOVA (p < 0.05). The 3D PDLf constructs from the low-load group demonstrated the highest levels of homogeneous cell distribution and higher expression of F-actin and periostin with enhanced interaction with the matrix. The collagen matrix in this group showed more closely packed fibers forming thicker bundles when compared to the control and the high-load 3D PDLf constructs. Nonuniform cell distribution with decreased expression of F-actin and periostin was observed in the control and high-load PDLf constructs. The high-load group showed the highest RANKL/OPG expression. This study demonstrated low-level hydrostatic pressure's role in regulating PDLf functions and extracellular matrix response, while excessive hydrostatic pressure may be detrimental to PDL fibroblast cell function.

Effective contribution ratio of the molar during sequential distalization using clear aligners and micro-implant anchorage: a finite element study

INTRODUCTION

This study aims to investigate the biomechanical effects of anchorage reinforcement using clear aligners (CAs) with microimplants during molar distalization. And also explores potential clinical strategies for enhancing anchorage in the sequential distalization process.

METHODS

Finite element models were established to simulate the CAs, microimplants, upper dentition, periodontal ligament (PDL), and alveolar bone. In group set I, the 2nd molars underwent a distal movement of 0.25 mm in group set II, the 1st molars were distalized by 0.25 mm after the 2nd molars had been placed to a target position. Each group set consisted of three models: Model A served as the control model, Model B simulated the use of microimplants attached to the aligner through precision cuts, and Model C simulated the use of microimplants attached by buttons. Models B and C were subjected to a series of traction forces. We analyzed the effective contribution ratios of molar distalization, PDL hydrostatic stress, and von Mises stress of alveolar bone.

RESULTS

The distalization of the 2nd molars accounted for a mere 52.86% of the 0.25-mm step distance without any reinforcement of anchorage. The remaining percentage was attributed to the mesial movement of anchorage teeth and other undesired movements. Models B and C exhibited an increased effective contribution ratio of molar distalization and a decreased loss of anchorage. However, there was a slight increase in the undesired movement of molar tipping and rotation. In group set II, the 2nd molar displayed a phenomenon of mesial relapse due to the reciprocal force produced by the 1st molar distalization. Moreover, the efficacy of molar distalization in terms of contribution ratio was found to be positively correlated with the magnitude of force applied. In cases where stronger anchorage reinforcement is required, precision cuts is the superior method.

CONCLUSIONS

The utilization of microimplants in conjunction with CAs can facilitate the effective contribution ratio of molar distalization. However, it is important to note that complete elimination of anchorage loss is not achievable. To mitigate undesired movement, careful planning of anchorage preparation and overcorrection is recommended.

The effect of space arrangement between anterior teeth on their retraction with clear aligners in first premolar extraction treatment: a finite element study

INTRODUCTION

Clear aligner therapy has become increasingly popular in recent years, although it has encountered several difficulties in premolar extraction treatment. These difficulties include anterior dentition, lingual tipping and extrusion. The design of the present clinical scheme usually set a tiny space between the anterior teeth before retraction in order to obtain an ideal outcome. The objective of our research was to analyze the effect of the existing spaces during retraction.

METHODS

Models including maxillary dentition without first premolars, maxilla, periodontal ligaments, gingiva, or aligners were constructed and imported to an ANSYS workbench. Five groups of models were created: without spaces and with 0.25, 0.50, 0.75 and 1.00 mm spaces between the anterior dentition. A 0.20 mm retraction step was applied to all the groups.

RESULTS

As the spaces between the anterior dentition increased, the bowing effect of the aligner caused by the passive forces decreased gradually. Accordingly, the degree of extrusion of the anterior dentition was alleviated significantly, while sagittal movement was reduced. However, the overall movement tended to be a bodily displacement rather than tipping. Meanwhile, maximum Von Mises stress of the periodontal ligaments (PDLs) was markedly decreased.

CONCLUSION

These analyses indicate that spaces between the anterior dentition during anterior retraction are beneficial for decreasing the tendency for extrusion of the anterior dentition and require provision of anchorage. Appropriate spaces can be designed to lest the lingual tipping and extrusion effect of the anterior teeth while simultaneously reducing the maximum stresses on PDLs.

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.

Efficacy of a four-curvature auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: a finite element analysis

BACKGROUND

Correct torque of the incisors is beneficial in the assessment of the effects of orthodontic treatment. However, evaluating this process effectively remains a challenge. Improper anterior teeth torque angle can cause bone fenestrations and exposure of the root surface.

METHODS

A three-dimensional finite element model of the maxillary incisor torque controlled by a homemade four-curvature auxiliary arch was established. The four-curvature auxiliary arch placed on the maxillary incisors was divided into four different state groups, among which 2 groups had tooth extraction space retracted traction force set to 1.15 N. Initial displacements and pressure stresses of the periodontal tissue in the maxillary incisors and molars were calculated after torque forces (0.5, 1, 1.5, and 2 N) were applied to the teeth at different stable states.

RESULTS

The effect of using the four-curvature auxiliary arch on the incisors was significant but did not affect the position of the molars. Given the absence of tooth extraction space, when the four-curvature auxiliary arch was used in conjunction with absolute anchorage, the recommended force value was < 1.5 N. In the other 3 groups (i.e., molar ligation, molar retraction, and microimplant retraction groups), the recommended force value was < 1 N. The application of a four-curvature auxiliary arch did not influence the molar periodontal and displacement.

CONCLUSION

A four-curvature auxiliary arch may treat severely upright anterior teeth and correct cortical fenestrations of the bone and root surface exposure.

Effect of thread depth and thread pitch on the primary stability of miniscrews receiving a torque load : A finite element analysis

PURPOSE

We have been developing a new type of miniscrew to specifically withstand orthodontic torque load. This study aimed to investigate the effect of thread depth and thread pitch on the primary stability of these miniscrews if stressed with torque load.

METHODS

Finite element analysis (FEA) was used to evaluate the primary stability of the miniscrews. For thread depth analysis, the thread depth was set to 0.1-0.4 mm to construct 7 models. For thread pitch analysis, the thread pitch was set to 0.4-1.0 mm to construct another 7 models. A torque load of 6 Nmm was applied to the miniscrew, and the other parameters were kept constant for the analyses. Maximum equivalent stress (Max EQV) of cortical bone and maximum displacement of the miniscrews (Max DM) were the indicators for primary stability of the miniscrew in the 14 models.

RESULTS

In the thread depth analysis, Max DM increased as the miniscrew thread depth increased, while Max EQV was smallest in model 3 (thread depth = 0.2, Max EQV = 8.91 MPa). In the pitch analysis, with an increase of the thread pitch, Max DM generally exhibited a trend to increase, while Max EQV of cortical bone showed a general trend to decrease.

CONCLUSION

Considering the data of Max DM and Max EQV, the most appropriate thread depth and thread pitch of the miniscrews in our model was 0.2 and 0.7 mm, respectively. This knowledge may effectively improve the primary stability of newly developed miniscrews.

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.

The effects of lingual buttons, precision cuts, and patient-specific attachments during maxillary molar distalization with clear aligners: Comparison of finite element analysis

INTRODUCTION

This study aimed to analyze the biomechanical effects of the combined use of clear aligners (CA) and auxiliaries (precision cuts, lingual buttons, and patient-specific attachments) on mesial tipping and extrusion of the premolars during maxillary molars distalization.

METHODS

Three-dimensional finite element method was employed to simulate clinical scenarios of CA with different auxiliaries for molar distalization. As such, 200 g of distal force was applied to the microimplants from the notches, lingual buttons, and hooks. Orthodontic tooth movement and the hydrostatic pressure in the periodontal ligament were compared.

RESULTS

Adding auxiliaries can provide the maxillary arch anchorage and promote the distal tipping of premolars and retroclination of maxillary incisors. In contrast, this effect was more pronounced in patient-specific attachment applications than in other types of auxiliaries. The independent application of the CA caused mesial tipping and extrusion of the premolar and also caused the incisor proclination.

CONCLUSIONS

The anchorage loss caused by the CA alone could be alleviated with the assistance of auxiliaries. Notably, patient-specific attachments further reinforce the anchorage of the anterior arch by incorporating anchor teeth as 1 anchorage unit.

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.

Effects of upper-molar distalization using clear aligners in combination with Class II elastics: a three-dimensional finite element analysis

INTRODUCTION

The effects of upper-molar distalization using clear aligners in combination with Class II elastics for anchorage reinforcement have not been fully investigated yet. The objective of this study is to analyze the movement and stress of the whole dentition and further explore guidelines for the selection of traction methods.

METHODS

Three-dimensional (3D) finite element models are established to simulate the sequential molar distalization process, including the initial distalization of the 2^nd molar (Set I) and the initial distalization of the 1^st molar (Set II). Each group set features three models: a control model without Class II elastics (model A), Class II elastics attached to the tooth by buttons (model B), and Class II elastics attached to the aligner by precision cutting (model C). The 3D displacements, proclination angles, periodontal ligament (PDL) hydrostatic stress and alveolar bone von Mises stress in the anterior area are recorded.

RESULTS

In all of the models, the maxillary anterior teeth are labial and mesial proclined, whereas the distal moving molars exhibit distal buccal inclination with an extrusion tendency. With the combination of Class II elastics, the anchorage was effectively reinforced; model C demonstrates superior anchorage reinforcement with lower stress distribution in comparison with model B. The upper canines in model B present an extrusion tendency. Meanwhile, the mandibular dentition in models B and C experience undesired movement tendencies with little discrepancy from each other.

CONCLUSIONS

Class II elastics are generally effective for anchorage reinforcement as the upper-molar distalization is performed with clear aligners. Class II elastics attached to an aligner by precision cutting is a superior alternative for maxillary anchorage control in cases that the proclination of upper incisors and extrusion of upper canines are unwanted.

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.

Effects of Rigid and Nonrigid Connections between the Miniscrew and Anchorage Tooth on Dynamics, Efficacy, and Adverse Effects of Maxillary Second Molar Protraction: A Finite Element Analysis

Introduction

Direct, rigid indirect, and nonrigid indirect absolute anchorages using temporary anchorage devices (TADs, mini-implants/miniscrews) can provide promising opportunities for challenging, yet common, orthodontic tooth movements such as molar protraction. Rigid rectangular wire and ligature wire are the most common methods of attaching a tooth to a miniscrew in indirect anchorages. We aimed to provide a comparison of the rigidity of the connecting wire in terms of stress on the miniscrew, the anchorage loss, and the risk of root resorption using finite element analysis (FEA).

Methods

The maxillary right second molar was protracted into the proximal space at a 150 g load (1) using direct absolute anchorage with a tapered miniscrew implanted between the premolar roots and using indirect absolute anchorage with the second premolar reinforced by the miniscrew through (2) a rigid stainless steel (SS) wire or (3) a nonrigid SS ligature wire (4) at different elastic moduli. Stresses and displacements of 4 models' elements were measured. The risk of external root resorption was evaluated.

Results

Connecting the tooth to the miniscrew using rigid full-size wire (model 2) compared to ligature (model 3) can give better control of the anchorage (using the ligature wire, the anchorage loss is 1.5 times larger than the rectangular wire) and may reduce the risk of root resorption of the anchorage unit. However, the risk of miniscrew failure increases with a rigid connection, although it is still lower than with direct anchorage. The miniscrew stress when using a ligature is approximately 30% of the rigid model using the rectangular wire. The miniscrew stress using the rectangular wire is approximately 82.4% of the miniscrew stress in the direct model. Parametric analysis shows that the higher the elastic modulus of the miniscrew-tooth connecting wire in the indirect anchorage, the less the anchorage loss/palatal rotation of the premolars/and the risk of root resorption of the anchorage teeth and instead the stress on the miniscrew increases.

Conclusions

Direct anchorage (followed by rigid indirect anchorage but not nonrigid) might be recommended when the premolars should not be moved or premolar root resorption is a concern. Miniscrew loosening risk might be the highest in direct anchorage and lowest in nonrigid indirect anchorage (which might be recommended for poor bone densities).

Dynamics, Efficacies, and Adverse Effects of Maxillary Full-Arch Intrusion Using Temporary Anchorage Devices (Miniscrews): A Finite Element Analysis

Introduction

Absolute anchorages obtained from temporary anchorage devices (TADs, miniscrews) considerably facilitate dental movements and make some very difficult movements such as full-arch intrusions possible. Despite the significance of assessing strategies to fully intrude the arch using mini-implants, there is no study in this regard except a few case reports. Therefore, we simulated/tested 4 scenarios.

Methods

Four maxilla models were created with different miniscrews/appliances: (1) two miniscrews were placed distal to laterals and one in the mid sagittal region. (2) Two mini-implants were inserted in mesial of canines and 2 others between bilateral first and second molars, plus another TAD in the midpalatal area, plus a transpalatal arch (TPA). (3) Two mini-implants were inserted between bilateral canines and first premolars and 2 others between bilateral first and second molars + TPA. (4) Two mini-implants were installed between lateral-and-canine and 2 miniscrews between second premolars and first molars + TPA. Intrusive forces (80 g anterior, 150 g posterior) were exerted using stainless-steel coil springs. Stresses/displacements were measured. Risk of external root resorption was evaluated.

Results

The highest amounts of incisor/molar intrusion were seen in model 1. Model 2 had fewer intrusions, but its control over undesired movements was greater. Model 4 drastically reduced molar intrusion and considerably increased premolar intrusion. Overall amounts of intrusion were highest in the first 2 models, marking them as proper candidates for cases needing greater intrusion extents. Model 2 may be useful when miniscrew loosening/failure is a concern, while model 1 is recommended when fewer miniscrews are allowed. Overall, the highest and lowest root resorptions might occur in models 1 and 4, respectively.

Conclusions

Each model showed certain efficacies/drawbacks and thus is recommended for a particular set of cases. Therefore, depending on the diagnosis and treatment plan, one or more of these scenarios might be desirable.

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.

[Evaluation of root resorption after surgical orthodontic treatment of skeletal Class Ⅲ malocclusion by three-dimensional volumetric measurement with cone-beam CT]

OBJECTIVE

To explore the method of measuring root volume with cone-beam computed tomography (CBCT) three-dimensional reconstruction technology, and to study root length and root volume of upper and lower central incisors in patients with skeletal Class Ⅲ malocclusion treated by surgical orthodontic treatment.

METHODS

Twenty patients with skeletal Class Ⅲ malocclusion undergoing surgical orthodontic treatment were selected. CBCT data at three time points, before decompensation treatment (T0), after decompensation treatment (before orthognathic surgery, T1), and the end of post-operative orthodontic treatment (T2) were collected. Three-dimensional reconstruction technology was used to measure the root length and root volume of the upper and lower central incisors (including total root volume, cervical root and apical root), calculate the percentage of reduction volume, and measure the distance of tooth movement after orthodontic treatment. Data were statistically analyzed by SPSS 20.0 software. Least significant difference (LSD) method was used for pair comparison between the groups subject to normal distribution, and non-parametric test was used for comparison between the groups not subject to normal distribution. The differences of root length and root volume of upper and lower incisors were compared, and the characteristics of root absorption were analyzed.

RESULTS

Root length and root volume of the upper and lower central incisors were reduced during the surgical orthodontic treatment (P < 0.05) in cases. Both the root volume of cervical root and apical root were significantly reduced (P < 0.05), the reduction of apical root was more significant. The percentage of root volume reduction of the upper central incisor was (30.51±23.23)%, and lower central incisor (23.24±11.96)%. Compared with the upper central incisor, the root volume reduction amount and percentage of the lower central incisor were smaller, and apical root volume reduction of the upper central incisor was greater than that of the lower central incisor, which was statistically significant (P < 0.05). During pre-surgical orthodontic treatment, maxillary central incisor palatal moving was in a controlled tipping manner, and the mandibular central incisor tipped labially.

CONCLUSION

In patients with skeletal Class Ⅲ malocclusion, root length and total root volume of upper and lower central incisors decreased during surgical orthodontic treatment. Root volume measurement indicated that the cervical root also had root resorption. The difference in root resorption of the upper and lower central incisors might be related to the distance and direction of teeth movement. CBCT three-dimensional reconstruction will compensate for the limitation of root length measurement in evaluating root resorption.

Optimization Analysis of Two-Factor Continuous Variable between Thread Depth and Pitch of Microimplant under Toque Force

Microimplant, an anchorage device, is widely applied in clinical orthodontic treatment. Since tooth torque is required to be controlled during orthodontic tooth movement, a novel microimplant needs to be developed to apply better torque force during orthodontic. In this study, the optimal value ranges of thread depth and pitch under toque force were studied for choosing microimplant with relevant value ranges in clinical design from biomechanical perspective. Finite element analysis (FEA) and optimization design technology were used for accessing the optimal value ranges of thread depth and pitch under toque force. Thread depth (D) (0.1 mm to 0.4 mm) and pitch (P) (0.4 mm to 1 mm) were used as continuous variables, with the other parameters as constant, and the optimal value ranges were obtained by analyzing the tangent slope and sensitivity of the response curve. When a torque force of 6 Nmm was applied on the microimplant, the maximum equivalent stress (Max EQV) of cortical bone and maximum displacements (Max DM) of microimplant were analysis indexes. When 0.55 mm ≤ P ≤ 1 mm, the Max EQV of cortical bone was relatively smaller with less variation range. When 0.1 mm ≤ D ≤ 0.35 mm, the Max DM of microimplant was relatively smaller with less variation range. So in conclusion, the initial stability of microimplants with pitch 0.55 mm ≤ P ≤ 1 mm and thread depth 0.1 mm ≤ D ≤ 0.35 mm was better with the torque force applied.

Initial Displacement and Stress Distribution of Upper Central Incisor Extrusion with Clear Aligners and Various Shapes of Composite Attachments Using the Finite Element Method

A clear aligner is an esthetic and more comfortable option for patients who need orthodontic treatment. However, some types of tooth movement, such as extrusion, are difficult with this tool. Therefore, composite attachments have been suggested to improve tooth movement. This study aims to evaluate the initial displacement and stress distribution during upper central incisor extrusion using the conventional composite attachments. Maxillary models with the upper teeth, clear aligners, and composite attachments placed on the labial surface of the upper right central incisor were constructed. Four models were created to simulate upper central incisor extrusion: (1) without any composite attachment; (2) rectangular beveled attachment; (3) ellipsoid attachment; and (4) horizontal rectangular attachment. Clear aligners were designed to perform upper central incisor extrusion. The constructed models were analyzed using the finite element method. Initial displacement and stress distribution were analyzed. Output analysis found that the upper right central incisor in the model with a horizontal rectangular attachment had the greatest extrusive movement, followed by the model with ellipsoid attachment and the model with beveled attachment. Maximum compressive stress was seen at the cervical region of the composite attachment. Composite attachments including horizontal rectangular attachment, ellipsoid attachment, and rectangular beveled attachment can be used to perform upper central incisor extrusion.

Biomechanical evaluation of the unilateral crossbite on the asymmetrical development of the craniofacial complex. A mechano-morphological approach

BACKGROUND AND OBJECTIVE

The occlusion effect on the craniofacial development is a controversial topic that has attracted the interest of many researchers but that remains unclear, mainly due to the difficulties on measure its mechanical response experimentally. This mechano-morphological relationship of the craniofacial growth is often explained by the periosteal and capsular matrices of the functional matrix hypothesis (FMH); however, its outcomes have not been analytically demonstrated yet. This computational study aims, therefore, to analytically demonstrate the mechano-morphological relationship in the craniofacial development of children with unilateral crossbite (UXB) using the finite element (FE) method.

METHODS

The craniofacial complex asymmetry of ten children, five of whom exhibit UXB, was 3D-analysed and compared with the biomechanical response computed from a FE analysis of each patient's occlusion. Due to the complexity of the geometry and the multitude of contacts involved, the inherent limitations of the model were evaluated by comparing computed occlusal patterns with those recorded by an occlusal analysis on 3D printed copies.

RESULTS

Comparison's outcomes proved the reliability of our models with just a deviation error below 6% between both approaches. Out of validation process, computational results showed that the significant elongation of mandibular branch in the contralateral side could be related to the mandibular shift and increase of thickness on the crossed side, and particularly of the posterior region. These morphological changes could be associated with periodontal overpressure (>4.7 kPa) and mandibular over deformation (0.002 ε) in that side, in agreement with the periosteal matrix's principles. Furthermore, the maxilla's transversal narrowing and the elevation of the maxillary and zygomatic regions on the crossed side were statistically demonstrated and seem to be related with their respective micro displacements at occlusion, as accounted by their specific capsule matrices. Our results were consistent with those reported clinically and demonstrated analytically the mechano-morphological relationship of children's craniofacial development based on the FMH's functional matrices.

CONCLUSIONS

This study is a first step in the understanding of the occlusion's effect on the craniofacial development by computational methods. Our approach could help future engineers, researchers and clinicians to understand better the aetiology of some dental malocclusions and functional disorders improve the diagnosis or even predict the craniofacial development.

Stress Distribution Pattern in Mini Dental Implant-Assisted RPD with Different Clasp Designs: 3D Finite Element Analysis

Introduction

The removable partial denture (RPD) components, especially the retentive arm, play a major role in the loading characteristic on supporting structures.

Objective

To evaluate and compare the effect of different clasp designs on the stress distribution pattern, maximum von Mises stress, and average hydrostatic pressure on abutment teeth, as well as edentulous ridges, mini dental implants (MDIs), and peri-implant bone between the conventional removable partial denture (CRPD) and mini dental implant-assisted distal extension removable partial denture (IARPD) using a three-dimensional finite element analysis (3D FEA).

Materials and Methods

3D FEA models of mandibular arches, with and without bilateral MDI at the second molar areas, and Kennedy class I RPD frameworks, with RPA, RPI, Akers, and no clasp component, were generated. A total of 200 N vertical load was bilaterally applied on both sides of distal extension areas, and the stress was analyzed by 3D FEA.

Results

The stress concentration of IARPD with RPI clasp design was located more lingually on abutment teeth, MDI, and peri-implant bone, while the other designs were observed distally on the supporting structures. The maximum von Mises stress on the abutment root surface was decreased when the RPDs were assisted with MDIs. The CRPD and IARPD with the Akers clasp design showed the highest von Mises stress followed by the designs with RPA and RPI clasp, respectively. The average hydrostatic pressure in each group was in approximation.

Conclusion

The placement of MDIs on distal extension ridges helps to reduce the stress concentration on denture supporting structures. The maximum von Mises stress is affected by the different designs of clasp components. The CRPD and the IARPD with RPI clasp provide the least stress on supporting structures.

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.

The effect of 12 weeks of mechanical vibration on root resorption: a micro-CT study

OBJECTIVE

The aim was to investigate the effect of mechanical vibration on root resorption with or without orthodontic force application.

MATERIAL AND METHODS

Twenty patients who required maxillary premolar extractions as part of orthodontic treatment were randomly divided into two groups of 10: no-force group and force group. Using a split-mouth procedure, each patient's maxillary first premolar teeth were randomly assigned as either vibration or control side for both groups. A buccally directed vibration of 50 Hz, with an Oral-B HummingBird device, was applied to the maxillary first premolar for 10 min/day for 12 weeks. After the force application period, the maxillary first premolars were extracted and scanned with micro-computed tomography. Fiji (ImageJ), performing slice-by-slice quantitative volumetric measurements, was used for resorption crater calculation. Total crater volumes were compared with the Wilcoxon and Mann-Whitney U tests.

RESULTS

The total crater volumes in the force and no-force groups were 0.476 mm3 and 0.017 mm3 on the vibration side and 0.462 mm3 and 0.031 mm3 on the control side, respectively. There was no statistical difference between the vibration and control sides (P > 0.05). There was more resorption by volume in the force group when compared to the no-force group (P < 0.05).

CONCLUSION

Mechanical vibration did not have a beneficial effect on reducing root resorption; however, force application caused significant root resorption.

Expression of Torque and Its Effect on Various Biological Structures Caused by Varying Archwire Material: A 3D FEM Study

Objective:

Studying torque expression and biomechanical effects of various wires on giving palatal root torque, using finite element (FE) method (FEM).

Conclusion:

TMA wires are most favourable for torquing, in terms of torque expression and susceptibility to root resorption.

Materials and Method:

Geometric model of maxillary right central incisor was developed, using computed tomography (CT) scan. 0.022" × 0.028" Standard edgewise brackets and 10-mm-long stainless steel (SS), titanium molybdenum (TMA) and titanium niobium (TiNb) archwires of dimension 0.019" × 0.025" were modeled and a palatal root torque of 25 degrees was applied on all wires. The angular displacement of the crown and root and nodal displacement at the incisal edge and root apex in y and z axis were analyzed along with stresses on periodontal ligament (PDL), bone, cementum, enamel, and bracket.

Results:

Buccal crown and palatal root movement was seen, which was maximum for SS and least for TMA. Angular displacement was also highest for SS. Compressive stresses were concentrated at the bucco-cervical and linguo-apical regions in the PDL, cementum, and bone and tensile stresses were concentrated in the linguo-cervical regions. In the enamel, the bracket attachment site showed maximum stresses, and slot base showed higher values of stresses than wings. All stress values were highest for SS and least for TMA.

Orthodontically induced root resorption: A critical analysis of finite element studies' input and output

INTRODUCTION

Orthodontically induced inflammatory root resorption (OIIRR) constitutes an undesirable risk connected to orthodontic treatment. Finite element analysis (FEA) is a powerful tool to study the risk of OIIRR. However, its efficiency in predicting OIIRR depends on the insertion of the correct inputs and the selection of an output coherent with the clinical failure mechanism.

METHODS

By combining a systematic review with a 3-dimensional FEA, this article discusses which are the implications of using certain periodontal ligament (PDL) properties (linear and nonlinear models) and failure criteria. Six orthodontic loading regimes were simulated in a maxillary premolar: pure intrusion, buccal tipping, and their combination applied with either a light (25 cN) or a heavy (225 cN) force. Three stress parameters in the PDL were compared: von Mises stress, minimum principal stress_, and hydrostatic stress (σ_H).

RESULTS

The comparison between linear and nonlinear models showed notable differences in stress distribution patterns and magnitudes. For the nonlinear PDL, none of the light-force models reached the critical compressive hydrostatic stress of 4.7 kPa, whereas all the heavy-force models reached it. In addition, the regions of critical compressive σ_H matched with the regions with resorption craters in clinical studies. In linear models, the σ_H critical value of 4.7 kPa was reached even in the light-force scenario.

CONCLUSIONS

Only compressive hydrostatic stress in PDL satisfied the requirements to be used as an FEA indicator of OIIRR. However, the requirements were satisfied only when a nonlinear PDL model was considered.

A finite element analysis for evaluating mandibular advancement devices

Obstructive sleep apnoea (OSA) is a disorder characterised by complete or partial occlusion of the upper airway during sleep. Muscles relax during sleeping and collapse into the airway, closing the throat and prohibiting air flowing into the lungs. Different solutions have been adopted to manage the pathology to improve the life quality of affected patients. Mandibular advancement devices (MADs) are proven to be a compliant and successful therapy in the forward repositioning of the mandible to increase the upper airway volume. However, this method has some long-term adverse events that may affect the teeth and periodontal ligaments. This paper presents a finite element model to evaluate the MADs effects (displacement and stress) on teeth and periodontal ligaments, by varying the design, the point of application of the force and the material. The modelled bodies have been reconstructed through a Reverse Engineering approach and computer-aided design tools starting from tomographic images of anatomic bodies and from laser scans of a physical MAD. The results suggest that a central connection mechanism could affect mostly the anterior teeth. In contrast, a lateral connection mechanism provides a more uniform distribution of the load on teeth.

Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: a case study

OBJECTIVES

The objective of this study was to investigate the optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar to determine tooth movements during orthodontic treatment using hydrostatic stress and logarithmic strain on the periodontal ligament (PDL) as indicators by numerical simulations.

MATERIAL AND METHODS

Teeth, PDL and alveolar bone numerical models were constructed as analytical objects based on computed tomography (CT) images. Teeth were assumed to be rigid bodies, and rotational moments ranging from 1.0 to 4.0 Nmm were exerted on the crowns. PDL was defined as a hyperelastic-viscoelastic material with a uniform thickness of 0.25 mm. The alveolar bone model was constructed using a non-uniform material with varied mechanical properties determined based on Hounsfield unit (HU) values calculated using CT images, and its bottom was fixed completely. The optimal range values of PDL compressive and tensile stress were set as 0.47-12.8 and 18.8-51.2 kPa, respectively, whereas that of PDL logarithmic strain was set as 0.15-0.3%.

RESULTS

The rotational tendency of PDL was around the long axis of teeth when loaded. The optimal range values of rotational moment for the mandibular lateral incisor, canine and first premolar were 2.2-2.3, 3.0-3.1 and 2.8-2.9 Nmm, respectively, referring to the biomechanical responses of loaded PDL. Primarily, the optimal range of rotational moment was quadratically dependent on the area of PDL internal surface (i.e. area of PDL internal surface was used to indicate PDL size), as described by the fitting formula.

CONCLUSIONS

Biomechanical responses of PDL can be used to estimate the optimal range of rotational moment for teeth. These rotational moments were not consistent for all teeth, as demonstrated by numerical simulations.

CLINICAL RELEVANCE

The quantitative relationship between the area of PDL internal surface and the optimal orthodontic moment can help orthodontists to determine a more reasonable moment and further optimise clinical treatment.

Dynamic measurement of orthodontic force using a tooth movement simulation system based on a wax model

BACKGROUND

Orthodontic force is often statically measured in general, and only the initial force derived from appliances can be assessed.

OBJECTIVE

We aimed to investigate a technological method for measuring dynamic force using tooth movement simulation.

METHODS

Tooth movement was simulated in a softened wax model. A canine tooth was selected for evaluation and divided into the crown and root. A force transducer was plugged in and fixed between the two parts for measuring force. Forces on this tooth were derived by ordinary nickel-titanium (Ni-Ti) wire, hyperelastic Ni-Ti wire, low-hysteresis (LH) Ti-Ni wire and self-made glass fibre-reinforced shape memory polyurethane (GFRSMPU) wire. These forces were measured after the tooth movement.

RESULTS

The canine tooth moved to the desired location, and only a 0.2 mm deviation remained. The changing trends and magnitudes of forces produced by the wires were consistent with the data reported by other studies. The tooth had a higher moving velocity with ordinary Ni-Ti wires in comparison to the other wires. Force attenuation for the GFRSMPU wire was the lowest (40.17%) at the end of the test, indicating that it provided light but continuous force.

CONCLUSIONS

Mimicked tooth movements and dynamic force measurements were successfully determined in tooth movement simulation. These findings could help with estimating treatment effects and optimising the treatment plan.

Morphologic evaluation of root resorption after miniscrew assisted en mass retraction in adult bialveolar protrusion patients

Background

Bialveolar protrusion is one of the most common chief complaints from the Asian orthodontic patients. Typical orthodontic treatment includes extraction of the bimaxillary premolars and en mass retraction of anterior tooth with maximum anchorage by placing miniscrews. However, excessive pursuit of profile improvement by retraction and intrusion of anterior teeth may result in root resorption, alveolar bone loss, even dehiscence. Thus this retrospective, analytical study was to evaluate the root resorption of anterior teeth after miniscrew assisted en mass retraction in adult bialveolar protrusion patients.

Materials and methods

Thirty six adult patients with bimaxillary protrusion had four first premolars extracted, and then miniscrews were placed to provide anchorage. CBCT scans were performed before (T1) and posttreatment (T2). A new improvement project introduced for 3D CBCT registration assessment of root morphology. The paired t-test was used to compare changes from T1 to T2. The relationship between the root resorption and the movement of anterior teeth were assessed by Pearson correlation coefficient analysis.

Results

The significant differences were only found in apical third of root and the largest resorption in apical third of the root is always noted in the palatal and distal sectors. Significant correlations were observed in the loss of root in distal and palatal sectors, the root length and volume decrease with the amount of anterior teeth retraction and intrusion.

Conclusion

The new 3D registration assessment of root morphology will be helpful for the clinicians. Pursuit of large retraction and intrusion leads to obvious anterior teeth root resorption.

Thread shape affects the stress distribution of torque force on miniscrews: a finite element analysis

This study aimed to investigate the effect of miniscrews thread shape on the stress distribution receiving a torque load. Seven thread shapes (S,V1,V2,B1,B2,R1,R2) models were constructed and a 6 Nmm-torque load was applied. The order of maximum equivalent stress (EQV) value was V1 > V2 > B1 > R1 > R2 > B2 > S. The order of maximum displacement of miniscrew (Max DM) value was S > B2 > R1 = V1 > B1 > V2 > R2. Model R2 may be the most appropriate thread shape affording a torque force.

Biomechanical influence of anchorages on orthodontic space closing mechanics by sliding method

This study aims to analyse the stress distributions and initial displacements of teeth during the space closing stage through a three-dimensional finite element method. Computed tomography images of a patient were used to reconstruct the detailed teeth and alveolar bone, and brackets with stainless steel archwire were modelled according to the orthodontic prescriptions. The second premolars and first molars were chosen as the anchorages in the model 6-force, with buccal tubes attached to the second molars in the model 6-force-7, and the second molars as additional anchorages in the model 7-force. The results indicated that a movement of lingual lateral inclination occurred on the incisors during the retraction, and the frictional force between the teeth and the archwire significantly reduced the stress on the teeth and periodontal structures. Graphical abstract Malocclusion is one of the most common issue in dentistry with high prevalence and orthodontic treatment need. The extraction of first premolar teeth was normally needed at the beginning of the treatment. And the straight wire appliance together with the sliding mechanics was used for space closure at the end of the treatment. However, side effects like root resorption also found after the surgery. Biomechanically, the stress distributions and initial displacements of teeth during space closing stage might be a crucial factor contributed to those undesirable side effects. And different selections of anchorages might alter the biomechanical environment during the treatment. Thus, the purpose of the current study was to analyse the stress distributions and initial displacements, with the different anchorage selections, of teeth during space closing stage through 3D finite element method.

In vitro digital image correlation analysis of the strain transferred by screw-retained fixed partial dentures supported by short and conventional implants

PURPOSE

This study used digital image correlation (DIC) to evaluate the strain transferred by splinted and non-splinted screw-retained fixed partial dentures (FPDs) supported by short and conventional implants.

MATERIAL AND METHODS

Four polyurethane models were fabricated to simulate half of the mandibular arch with acrylic resin replicas of the first premolar. Short (5 mm) and/or conventional (11 mm) implants replaced the second premolar and the first and second molars. Groups were: G1, two conventional (second premolar and first molar) and one short (second molar) implant; G2, one conventional (second premolar) and two short (first and second molar) implants; G3, three short implants; and G4, three conventional implants. Splinted (S) and non-splinted (NS) FPDs were screwed to the implant abutments. Occlusal load and a single point load on the second premolar, both of 250 N, were applied. Strain in the horizontal direction (Ɛ_xx) was calculated and compared using the DIC software.

RESULTS

Splinted crowns presented the highest strain magnitudes of all tested groups (p < 0.05). The strain was concentrated near the short implants and presented a higher magnitude compared to conventional implants, especially in G2S (-560.13 μS), G3S (-372.97 μS), and G4S (-356.67 μS).

CONCLUSIONS

Splinted crowns presented a higher strain concentration around the implants, particularly near the implant replacing the first molar. A combination of short and conventional implants seems to be a viable alternative for the rehabilitation of the posterior edentulous mandible with reduced bone height.

Designing a mandibular advancement device with topology optimization for a partially edentulous patient

STATEMENT OF PROBLEM

Patients with partial tooth loss treated with implant-supported fixed partial dentures (FPDs) have difficulty using conventional mandibular advancement devices (MADs) because of the risk of side effects. Also, which design factors affect biomechanical stability when designing MADs with better stability is unclear.

PURPOSE

The purpose of this finite element (FE) analysis study was to analyze the effect of the MAD design on biomechanical behavior and to propose a new design process for improving the stability of MADs.

MATERIAL AND METHODS

Each 3D model consisted of the maxillofacial bones, teeth, and implant-supported FPDs located in the left tooth loss area from the first premolar to the second molar and a MAD. Three types of custom-made MADs were considered: a complete-coverage MAD covering natural tooth-like conventional MADs, a shortened MAD excluding the coverage on the implant-supported FPD, and a newly designed MAD without anterior coverage. For the new MAD design, topology optimization was conducted to reduce the stress exerted on the teeth and to improve retention of the MAD. The new MAD design was finished by excluding the coverage of the maxillary and mandibular central incisors based on the results of the topology optimization. A mandibular posterior restorative force for a protrusion amount of 40% was used as the loading condition. The principal stress and pressure of the cancellous bone and periodontal ligaments (PDLs) were identified.

RESULTS

Considering the load concentration induced by the complete-coverage MAD, bone resorption risk and root resorption risk were observed at both ends of the mandibular teeth. The shortened MAD resulted in the highest stress concentration and pressure with the worst stability. However, in the case of the complete-coverage MAD, the pressure in the PDLs was reduced to the normal range, and the risk of root resorption was reduced.

CONCLUSIONS

For patients with implant-supported FPDs, MAD designs with different extents of coverage had an influence on biomechanical behavior in terms of stress distribution in cancellous bone and PDLs. A MAD design without anterior coverage provided improved stability compared with complete-coverage or shortened designs. The presented method for MAD design, which combined FE analysis and topology optimization, could be effectively applied in the design of such improved MADs.