Modeling viscoelastic behavior of periodontal ligament with nonlinear finite element analysis

Advancements in Methods of Classification and Measurement Used to Assess Tooth Mobility: A Narrative Review

Evaluating tooth mobility is clinically significant, not only for diagnosing periodontal tissues but also in determining the overall periodontal treatment plan. Numerous studies related to tooth mobility have been conducted over the years, including the proposal of various classifications as well as the development of electronic devices for objective measurement. However, there is still no consensus on the measurement methods and criteria for assessing tooth mobility. In this study, we provide a comprehensive review of past and current tooth mobility classification and measurement methods. In order to propose a new method to intuitively evaluate tooth mobility based on previous studies, a digital approach capable of recording tooth micromovements induced by dynamic load should be considered.

Biomechanical Behavior Evaluation of Resin Cement with Different Elastic Modulus on Porcelain Laminate Veneer Restorations Using Micro-CT-Based Finite Element Analysis

The aim of this study is to evaluate the biomechanical behavior of the porcelain laminate veneer restorations (PLV) of the maxillary central incisor luted with two types of resin cements having different incisal preparations: butt joint and palatal chamfer. Biomechanical analyses were performed using the micro-CT-based finite element models, and von Mises stress and strain values of the PLV, resin cement, adhesive layer, and tooth structure were computed. The PLV with butt joint preparation showed larger stress values than those of restored with palatal chamfer preparation, regardless of the elasticity of the cement and loading conditions. An increase in the elasticity modulus of the resin cement induced slightly larger stresses on the adhesive layer, tooth tissues, and restorative materials. Overall, this study demonstrates the role of the preparation design and luting materials on the mechanical behavior of the PLV restorations and discusses the potential failure mechanisms of the PLV restorations under different loading mechanisms.

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.

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.

Biomechanical Modelling for Tooth Survival Studies: Mechanical Properties, Loads and Boundary Conditions-A Narrative Review

Recent biomechanical studies have focused on studying the response of teeth before and after different treatments under functional and parafunctional loads. These studies often involve experimental and/or finite element analysis (FEA). Current loading and boundary conditions may not entirely represent the real condition of the tooth in clinical situations. The importance of homogenizing both sample characterization and boundary conditions definition for future dental biomechanical studies is highlighted. The mechanical properties of dental structural tissues are presented, along with the effect of functional and parafunctional loads and other environmental and biological parameters that may influence tooth survival. A range of values for Young's modulus, Poisson ratio, compressive strength, threshold stress intensity factor and fracture toughness are provided for enamel and dentin; as well as Young's modulus and Poisson ratio for the PDL, trabecular and cortical bone. Angles, loading magnitude and frequency are provided for functional and parafunctional loads. The environmental and physiological conditions (age, gender, tooth, humidity, etc.), that may influence tooth survival are also discussed. Oversimplifications of biomechanical models could end up in results that divert from the natural behavior of teeth. Experimental validation models with close-to-reality boundary conditions should be developed to compare the validity of simplified models.

Investigation of the biomechanical stability of Cfr-PEEK in the treatment of mandibular angulus fractures by finite element analysis

The purpose of this study is to explore the effectiveness of Cfr-PEEK, in the fixation of unfavorable fractures of mandibular angulus by comparing it with the titanium and resorbable biomaterials. 8 different fixation models were created. In the first 4 groups, a single mini plate was applied to the upper edge of the fracture line by the Champy method. In the other 4 groups, an additional plate was placed on the lower edge of the fracture line. In these models, titanium, resorbable and Cfr-PEEK plate/screw systems were investigated by the finite element analysis method. The highest Von Mises stress was observed on the upper plate in the group 5 while the lowest was seen in the lower plate in the group 7. The highest stress values on the screws were observed on the screws placed closer to the fracture line. Considering the stresses on the bone around the screws, the highest Pmax and Pmin values were seen in group 5, and the lowest values were seen in the group 7. The highest displacement was observed in the group 3, while the lowest was observed in the group 5. According to the results it can be said that Cfr-PEEK plate/screw systems may provide advantages by decreasing the stresses on the fixation systems over the titanium plates and providing more stable fixation over the resorbable systems. Cfr-PEEK plates of 2 mm thickness seems to be a potential alternative to 1 mm thick titanium plates.

Torque movement of the upper anterior teeth using a clear aligner in cases of extraction: a finite element study

Background

Clear aligner treatment has become popular over recent years. It is necessary to identify methods by which we could avoid the bowing effect in extractions with clear aligner. The present study was to identify the appropriate method to design torque movement involving the upper anterior teeth of extraction cases, in order to maintain or improve the axis and torque of the upper anterior teeth with a clear aligner during movement and closure of the extraction space.

Results

As the height of the power ridge increased, the rotation angle of the upper central incisor in the sagittal direction decreased gradually and the location of the rotation center changed significantly; the rotation center moved in the apical direction and then changed to the crown side. The highest von-Mises stress of the upper central incisor root, periodontal ligaments, and alveolar bone, showed little change as the power ridge height increased. When the axial inclination of the upper central incisor was normal (U1-SN = 105°), the tendency of movement for the upper central incisor approached translation with a power ridge height of 0.7 mm (corresponding distorted angle: 5.8415). When the axial inclination of the upper central incisor was oversized (U1-SN = 110°), the axial inclination of the upper central incisor reduced to normal following completion of the anterior segment retraction with a power ridge of 0.4 mm (corresponding distorted angle: 3.4265).

Conclusion

Analysis indicates that pure palatal tipping movement of the upper anterior teeth is generated without torque control, thus resulting in the bowing effect. The required torque control of the upper anterior teeth with oversize axial inclination is weaker than that of the upper anterior teeth with normal axial inclination because limited torque loss is expected for oversize axial inclination teeth. Variation sensitivity of the rotation center should be considered carefully due to biological problems when designing translation of the upper anterior teeth with normal axial inclination.

Finite Element Study of Periodontal Ligament Properties for a Maxillary Central Incisor and a Mandibular Second Molar Under Percussion Conditions

Purpose

The quantitative percussion diagnostics (QPD) response of a mandibular second molar and a maxillary central incisor including their supporting ligament/bone structure was simulated using dynamic 3D finite element analysis (FEA). The focus of the work was on the role of the periodontal ligament (PDL) which acts as a damper in the dental structure and dissipates occlusal forces transmitted from the tooth surface to the surrounding bone.

Methods

Several FEA models were developed to examine the effects of mechanical characteristics that have been reported for the PDL. Specifically, the effects of changing the PDL’s quasi-static elastic modulus and Rayleigh damping properties were predicted.

Results

The present FEA simulations indicate that the PDL can significantly reduce forces for both the incisor and the molar compared to when there is no PDL (i.e. ankylosed tooth) as long as the quasi-static elastic modulus of the PDL is among the lowest reported (~ 0.1 MPa). In addition, the FEA simulations for both the incisor and molar with this lower value of the PDL quasi-static elastic modulus are also in reasonably good agreement with experimental percussion data. A simple approximation for partitioning Rayleigh damping properties between the hard and soft tissues was also found to provide reasonable values of overall damping that are consistent with experimental data.

Conclusion

The overall findings indicate that using a quasi-static elastic modulus of approximately 0.1 MPa for the PDL in combination with Rayleigh damping gives realistic predictions of the mechanical response of a tooth under QPD loading conditions.

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.

OpenMandible: An open-source framework for highly realistic numerical modelling of lower mandible physiology

OBJECTIVE

Computer modeling of lower mandible physiology remains challenging because prescribing realistic material characteristics and boundary conditions from medical scans requires advanced equipment and skill sets. The objective of this study is to provide a framework that could reduce simplifications made and inconsistency (in terms of geometry, materials, and boundary conditions) among further studies on the topic.

METHODS

The OpenMandible framework offers: 1) the first publicly available multiscale model of the mandible developed by combining cone beam computerized tomography (CBCT) and μCT imaging modalities, and 2) a C++ software tool for the generation of simulation-ready models (tet4 and hex8 elements). In addition to the application of conventional (Neumann and Dirichlet) boundary conditions, OpenMandible introduces a novel geodesic wave propagation - based approach for incorporating orthotropic micromechanical characteristics of cortical bone, and a unique algorithm for modeling muscles as uniformly directed vectors. The base intact model includes the mandible (spongy and compact bone), 14 teeth (comprising dentin, enamel, periodontal ligament, and pulp), simplified temporomandibular joints, and masticatory muscles (masseter, temporalis, medial, and lateral pterygoid).

RESULTS

The complete source code, executables, showcases, and sample data are freely available on the public repository: https://github.com/ArsoVukicevic/OpenMandible. It has been demonstrated that by slightly editing the baseline model, one can study different "virtual" treatments or diseases, including tooth restoration, placement of implants, mandible bone degradation, and others.

SIGNIFICANCE

OpenMandible eases the community to undertake a broad range of studies on the topic, while increasing their consistency and reproducibility. At the same time, the needs for dedicated equipment and skills for developing realistic simulation models are significantly reduced.

Upper Second Molar Distalization with Clear Aligners: A Finite Element Study

Among orthodontists and scientists, in the last years, upper molar distalization has been a debated topic in the orthodontic aligner field. However, despite that few clinical studies have been published, no insights on aligners’ biomechanics regarding this movement are available. The aim of this study was to assess, through finite element analysis, the force system resulting in the upper arch during second maxillary molar distalization with clear aligners and variable attachments settings. The average tooth distalization was found to be 0.029, with buccal flaring of the upper incisors in all attachment configurations. The mesial deformation of the aligner was registered to be 0.2 mm on average. Different pressure areas on the interface between aligners and upper molars were registered, with the mesial attachment surface to be directly involved when present. Periodontal ligament pressure was reported to range between 67 g/cm2 and 132 g/cm2. Configurations with rectangular attachments from second molar-to-canine and from first molar-to-canine present, in an in silico environment, almost equal efficiency in distalizing the upper second molar. However, attachments from the second molar to the canine are suggested to be adopted in clinical environments due to greater feasibility in everyday practice.

Determination of stress distribution on periodontal ligament and alveolar bone by various tooth movements - A 3D FEM study

Aim

The purpose of this study was to evaluate the stress distribution on the maxillary central incisors by various tooth movements using three-dimensional finite element modeling with varying periodontal ligament (PDL) thickness and different alveolar bone height (at the apex and alveolar crest).

Material and methods

A Finite Element Modeling model was created using surface data of the tooth using SolidWorks Software. Different types of force (intrusion, extrusion, tipping, and bodily movement) were applied on the maxillary central incisor, with two different periodontal ligament thickness (0.15 mm and 0.24 mm) and alveolar bone height (at the apex and alveolar crest). Stress generated due to force applied due to different types of tooth movement was calculated and compared.

Results

Maximum stresses generated under intrusion, extrusion, tipping, bodily movement were 9.0421 E^-003 N/mm² for 0.15 mm pdl at alveolar bone, 7.2833 E^-5 N/mm²for 0.24 mm pdl labio-lingually, 9.1792 E^-002 N/mm² at 0.15 mm pdl at alveolar bone height and 6.2208 E^-6 N/mm² for 0.24 mm pdl at alveolar crest respectively.

Conclusion

The stress pattern seen was nearly the same in all the cases in both PDL thickness. The maximum stress pattern was found to be at the apex of the central incisor, reducing from apex to the cervical region. Intrusion, extrusion, and tipping movement showed the greatest amount of relative stress at the apex of the maxillary central incisor. The bodily movement produced forces at root apex and distributed it all over.

Displacement and stress distribution of Kilroy spring and nickel-titanium closed-coil spring during traction of palatally impacted canine: A 3-dimensional finite element analysis

OBJECTIVE

To compare the stress distribution and initial displacements during traction of palatally impacted canine between Kilroy and nickel-titanium (NiTi) closed-coil springs by means of the finite element analysis.

SETTING AND SAMPLE POPULATION

A finite element method analysis of two traction methods for a maxillary impacted canine.

MATERIALS AND METHODS

The corresponding periodontal ligaments (PDLs), brackets, molar tubes and a 0.019 × 0.025-in base stainless-steel (SS) wire were modelled and imported to ANSYS SpaceClaim version 2020 R1. Traction was simulated under two different set-ups with equal force magnitude (60 g); (1) the Kilroy spring, which is made of 0.016-inch SS, and (2) the NiTi closed -coil spring. Von Mises stress distributions and initial displacements of the maxillary teeth were analysed.

RESULTS

In both mechanics, while the highest stress was seen on the impacted canine (Kilroy, 10.41 kPa; NiTi closed-coil, 5.27 kPa), the stress distribution decreased as the distance from the impacted canine increased. The Kilroy spring showed a greater total displacement (465.60 μm) on the impacted canine. The higher stresses on the adjacent lateral (5.29 kPa) and premolar (6.41 kPa) occurred with the Kilroy spring.

CONCLUSIONS

The Kilroy spring yielded higher stresses than the NiTi closed-coil spring on the impacted canine and the adjacent teeth. The difference between distribution of the stresses over the impacted canine induced greater displacement with the Kilroy spring, particularly in the vertical direction.

Numerical Simulation of Mandible Bone Remodeling under Tooth Loading: A Parametric Study

Bone adapts to the change of mechanical stimulus by bone remodeling activities. A number of numerical algorithms have been developed to model the adaptive bone remodeling under mechanical loads for orthopedic and dental applications. This paper examines the effects of several model parameters on the computed apparent bone density in mandible under normal chewing and biting forces. The density change rate was based on the strain energy density per unit mass. The algorithms used in this study containing an equilibrium zone (lazy zone) and saturated values of density change rate provides certain stability to result in convergence without discontinuous checkerboard patterns. The parametric study shows that when different boundary conditions were applied, the bone density distributions at convergence were very different, except in the vicinity of the applied loads. Compared with the effects of boundary conditions, the models are less sensitive to the choice of initial density values. Several models starting from different initial density values resulted in similar but not exactly the same bone density distribution at convergence. The results also show that higher reference value of mechanical stimulus resulted in lower average bone density at convergence. Moreover, the width of equilibrium zone did not substantially affect the average density at convergence. However, with increasing width, the areas with the highest and the lowest bone density areas were all reduced. The limitations of the models and challenges for future work were discussed for the better agreement between the computed results and the in vivo data.

Clear aligner orthodontic therapy of rotated mandibular round-shaped teeth: A finite element study

OBJECTIVE

To evaluate, using the finite element method, the orthodontic rotational movement of a lower second premolar obtained with clear aligners, analyzing different staging and attachment configurations.

MATERIALS AND METHODS

A CAD model including a complete lower dental arch (with element 4.5 mesially rotated 30°) and the corresponding periodontal ligaments, attachments, and aligner was designed and imported to finite element software. Starting from the CAD model, six projects were created to simulate the following therapeutic combinations for correcting element 4.5 position: (1) without attachments, (2) single attachment placed on the buccal surface of element 4.5, (3) three attachments placed on the buccal surfaces of teeth 4.4 to 4.6. For each project, both 1.2° and 3° of aligner activation were considered.

RESULTS

All the analyzed configurations revealed a clockwise rotation movement of element 4.5 on the horizontal plane. Models with attachments showed a greater tooth displacement pattern than models without attachments. Simulations with attachments and 3° of aligner activation exhibited the best performance concerning tooth movement but registered high stresses in the periodontal ligaments, far from the ideal stress levels able to produce tooth rotational movement.

CONCLUSIONS

The model with a single attachment and 1.2° of aligner activation was the most efficient, followed by the three attachment model with the same degree of activation. Aligner activation should not exceed 1.2° to achieve better control of movement and reasonable stress in periodontal structures.

A numerical-experimental study on thermal evaluation of orthodontic tooth movement during initial phase of treatment

The most desired target of orthodontic treatment is tooth movement as a result of application of efficient force system. In this study, effect of tooth loading is studied on temperature profile around the tooth at early stages of treatment. The basis of temperature variation is increase of cell number and activities in periodontium as a result of compression and tension of this layer. Highest cellular activities occur in the beginning of loading procedure and aim to reduce mechanical stress in the periodontium which finally ends up with orthodontic tooth movement during couple of years. To find out the correlation between temperature variation and the applied force, in vivo experiments are conducted on ten rats and temperature is measured in specific time periods. It is observed that temperature is higher in direction of the net force about 0.3℃. Next, numerical finite element analysis is carried out on the rat tooth model. Mechanical stress results show that regions with compressive stress have rather high temperature in the experiments. Mechanical stress on periodontium-bone interface is multiplied by a coefficient to simulate cellular activities on this boundary as a heat source and thermal analysis is carried out to obtain temperature profile. The thermo-mechanical coefficient is identified for each rat by imposing the experimental temperatures on numerical outputs. For assessment of a treatment efficiency and deduction of the applied force, temperatures could be measured experimentally and compared with the corresponding numerical analysis temperature result obtained by employing the thermo-mechanical coefficient found earlier for each rat.

Nonlinear Biomechanical Characteristics of the Schneiderian Membrane: Experimental Study and Numerical Modeling

Objective

The aim of this study is to quantify the nonlinear mechanical behavior of the Schneiderian membrane.

Methods

Thirty cadaveric maxillary sinus membrane specimens were divided into the elongation testing group and the perforation testing group. Mechanical experimental measurements were taken via ex vivo experiments. Theoretical curves were compared with experimental findings to assess the effectiveness of the nonlinear mechanical properties. The FE model with nonlinear mechanical properties was used to simulate the detachment of the Schneiderian membrane under loading.

Results

The mean thickness of the membrane samples was 1.005 mm. The mean tensile strength obtained by testing was 6.81 N/mm². In membrane perforation testing, the mean tensile strength and the linear elastic modulus were significantly higher than those in membrane elongation testing (P < 0.05). The mean adhesion force between the Schneiderian membrane and the bone was 0.052 N/mm. By FE modeling, the squared correlation coefficients of theoretical stress-strain curves for the nonlinear and linear models were 0.99065 and 0.94656 compared with the experimental data.

Conclusions

The biomechanical properties of the Schneiderian membrane were implemented into the FE model, which was applied to simulate the mechanical responses of the Schneiderian membrane in sinus floor elevation.

A novel approach for early evaluation of orthodontic process by a numerical thermomechanical analysis

The main objective of this paper is to propose a novel method that provides an opportunity to evaluate an orthodontic process at early phase of the treatment. This was accomplished by finding out a correlation between the applied orthodontic force and thermal variations in the tooth structure. To this end, geometry of the human tooth surrounded by the connective soft tissue called the periodontal ligament and the bone was constructed by employing dental CT scan images of a specific case. The periodontal ligament was modeled by finite strain viscoelastic model through a nonlinear stress-strain relation (hyperelasticity) and nonlinear stress-time relation (viscoelasticity). The tooth structure was loaded by a lateral force with 15 different quantities applied to 20 different locations, along the midedge of the tooth crown. The resultant compressive stress in the periodontal ligament was considered as the cause of elevated cell activity that was modeled by a transient heat flux in the thermal analysis. The heat flux value was estimated by conducting an experiment on a pair of rats. The numerical results showed that by applying an orthodontic force to the tooth structure, a significant temperature rise was observed. By measuring the temperature rise, the orthodontic process can be evaluated.

Computational design and engineering of polymeric orthodontic aligners

Transparent and removable aligners represent an effective solution to correct various orthodontic malocclusions through minimally invasive procedures. An aligner-based treatment requires patients to sequentially wear dentition-mating shells obtained by thermoforming polymeric disks on reference dental models. An aligner is shaped introducing a geometrical mismatch with respect to the actual tooth positions to induce a loading system, which moves the target teeth toward the correct positions. The common practice is based on selecting the aligner features (material, thickness, and auxiliary elements) by only considering clinician's subjective assessments. In this article, a computational design and engineering methodology has been developed to reconstruct anatomical tissues, to model parametric aligner shapes, to simulate orthodontic movements, and to enhance the aligner design. The proposed approach integrates computer-aided technologies, from tomographic imaging to optical scanning, from parametric modeling to finite element analyses, within a 3-dimensional digital framework. The anatomical modeling provides anatomies, including teeth (roots and crowns), jaw bones, and periodontal ligaments, which are the references for the down streaming parametric aligner shaping. The biomechanical interactions between anatomical models and aligner geometries are virtually reproduced using a finite element analysis software. The methodology allows numerical simulations of patient-specific conditions and the comparative analyses of different aligner configurations. In this article, the digital framework has been used to study the influence of various auxiliary elements on the loading system delivered to a maxillary and a mandibular central incisor during an orthodontic tipping movement. Numerical simulations have shown a high dependency of the orthodontic tooth movement on the auxiliary element configuration, which should then be accurately selected to maximize the aligner's effectiveness.

Finite element analysis: A boon to dentistry

The finite element analysis (FEA) is an upcoming and significant research tool for biomechanical analyses in biological research. It is an ultimate method for modeling complex structures and analyzing their mechanical properties. In Implantology, FEA has been used to study the stress patterns in various implant components and also in the peri-implant bone. It is also useful for studying the biomechanical properties of implants as well as for predicting the success of implants in clinical condition. FEA of simulated traumatic loads can be used to understand the biomechanics of fracture. FEA has various advantages compared with studies on real models. The experiments are repeatable, there are no ethical considerations and the study designs may be modified and changed as per the requirement. There are certain limitations of FEA too. It is a computerized in vitro study in which clinical condition may not be completely replicated. So, further FEA research should be supplemented with clinical evaluation.