Analytically determined mechanical properties of, and models for the periodontal ligament: Critical review of literature

Inverse finite element analysis for an axisymmetric model of vertical tooth extraction

BACKGROUND AND OBJECTIVE

Tooth extraction is a common clinical procedure with biomechanical factors that can directly influence patient outcomes. Recent development in atraumatic extraction techniques have endeavoured to improve treatment outcomes, but the characterization of extraction biomechanics is sparse. An axisymmetric inverse finite element (FE) approach is presented to represent the biomechanics of vertical atraumatic tooth extraction in an ex-vivo swine model.

METHODS

Geometry and boundary conditions from the model are determined to match the extraction of swine incisors in a self-aligning ex vivo extraction experiment. Material parameters for the periodontal ligament (PDL) model are determined by solving an inverse FE problem using clusters of data obtained from 10 highly-controlled mechanical experiments. A seven-parameter visco-hyperelastic damage model, based on an Arruda-Boyce framework, is used for curve fitting. Three loading schemes were fit to obtain a common set of material parameters.

RESULTS

The inverse FE results demonstrate good predictions for overall force-time curve shape, peak force, and time to peak force. The fit model parameters are sufficiently consistent across all three cases that a coefficient-averaged model was taken that compares well to all three cases. Notably, the initial modulus ,u, converged across trials to an average value of 0.472 MPa with an average viscoelastic constant g of 0.561.

CONCLUSIONS

The presented model is found to have consistent parameters across loading cases. The capability of this model to represent the fundamental mechanical characteristics of the dental complex during vertical extraction loading is a significant advancement in the modelling of extraction procedures. Future work will focus on verifying the model as a predictive design tool for assessing new loading schemes in addition to investigating its applications to subject-specific problems.

Evaluation of the effects of semipontic design on tooth movements during mesialization of mandibular second molar performed with clear aligner treatment by finite element analysis

INTRODUCTION

Loss of the mandibular first molar is common in orthodontic patients. One treatment option is the mesialization of the second and third molars. This study aimed to investigate the displacement and type of movement in the second molar during mandibular second molar mesialization with clear aligner treatment using finite element analysis in configurations with or without pontic, semipontic, and anatomic pontic for the edentulous space.

METHODS

Mesialization of the mandibular second molar with clear aligner treatment was simulated using the AlGOR Fempro program (ALGOR, Inc, Pa) with 3 different configurations.

RESULTS

In the transverse direction, the highest rotation occurred in the anatomic pontic model, whereas the lowest rotation was in the semipontic model. In the sagittal axis, although tooth movement was realized by tipping in all scenarios, the semipontic model showed the closest movement to translation because of a higher rate of crown-root movement. In the vertical axis, although extrusion occurred in all configurations, the semipontic model showed the least extrusion forces, whereas the anatomic pontic model showed the most.

CONCLUSIONS

Mesiobuccal rotation, mesial tipping, and extrusion were observed in all models. However, the semipontic design had the closest movement to translational. Further randomized, controlled clinical trials are needed to evaluate the effects of different pontic designs on tooth movements.

A finite element analysis of periodontal ligament fluid mechanics response to occlusal loading based on hydro-mechanical coupling model

OBJECTIVE

Considering fluid stimulation is one of the essential biomechanical signals for periodontal tissues, this study aims to characterizing fluid mechanics response during occlusal loading by a hydro-mechanical coupling model for periodontal ligament.

DESIGN

Models simulating periodontium with normal bone height and with intraosseous defects were built with three mechanical modules: tooth, periodontal ligament and alveolar bone. Tooth was modeled as linear elastic, and periodontal ligament and alveolar bone as a hydro-mechanical coupling model. Transient analyses under dynamic occlusal loading were performed. Fluid dynamics within periodontal ligament space was simulated and visualized by post-processing module.

RESULTS

Reciprocating oscillatory flow occurred within the periodontal ligament under occlusal loading. Higher pore pressure and fluid velocity were observed in furcation and apical regions compared to mid-root and cervical regions. Intraosseous defects increased pore pressure and fluid velocity within the periodontal ligament, most significantly near the defect.

CONCLUSION

Based on the results of the hydro-mechanical coupling model, significant oscillatory fluid motion is observed within the periodontal ligament under occlusal loading. Particularly, higher fluid velocity is evident in the furcation and apical areas. Additionally, Intraosseous defects significantly enhance fluid motion within the periodontal ligament.

A novel method for simulating ex vivo tooth extractions under varying applied loads

BACKGROUND

Tooth extraction is a common surgical procedure where the invasiveness of the surgery can affect the nature of the dentoalveolar remodelling which follows. However, there is very little biomechanical data relating the loading applied during tooth extraction to the outcomes of the procedure. The purpose of this pilot study is to present a novel ex vivo experimental method for measuring tooth extraction mechanics and to explore preliminary metrics for predicting extraction success.

METHODS

A custom experimental apparatus was developed in-house to extract central incisors from ex vivo swine mandible samples. Twenty-five (n = 25) incisors were extracted at different rates in displacement- and force-control, along with an intermittent ramp-hold scheme for a total of five schemes. Peak forces and extraction success were recorded for each test. Video analysis assisted in determining the instantaneous stiffnesses of the dental complex during continuous extractions, which were compared using the K-means clustering algorithm.

FINDINGS

Tooth extraction forces ranged from 102 N to 309 N, with higher-rate tests tending towards higher peak forces (141 N - 308 N) than the lower-rate tests (102 N-204 N) for displacement- and force-controlled schemes. The K-means algorithm clearly identified load rates among tests, indicating that higher-rate loading increased system stiffness relative to the lower-rate tests.

INTERPRETATION

The developed experimental method demonstrated a desirable degree of control. The preliminary results suggest the influence of load rate on the mechanical response of the dental complex and extraction outcome. Future work will further investigate the biomechanics of tooth extraction and relate them to tissue damage to improve future tooth extraction procedures.

The displacement of teeth and stress distribution on periodontal ligament under different upper incisors proclination with clear aligner in cases of extraction: a finite element study

OBJECTIVES

To investigate the displacement of dentition and stress distribution on periodontal ligament (PDL) during retraction and intrusion of anterior teeth under different proclination of incisors using clear aligner (CA) in cases involving extraction of the first premolars.

METHODS

Models were constructed, consisting of the maxilla, PDLs, CA and maxillary dentition without first premolars. These models were then imported to finite element analysis (FEA) software. The incisor proclination determined the division of the models into three groups: Small torque (ST) with U1-SN = 100°, Middle torque (MT) with U1-SN = 110°, and High torque (HT) with U1-SN = 120°. Following space closure, a 200 g intrusion force was applied at angles of 60°, 70°, 80°, and 90° to the occlusal plane, respectively.

RESULTS

CA therapy caused lingual tipping and extrusion of incisors, mesial tipping and intrusion of canines, and mesial tipping of posterior teeth in each group. As the proclination of incisors increased, the incisors presented more extrusion and minor retraction, and the teeth from the canine to the second molar displayed an increased tendency of intrusion. The peak Von Mises equivalent stress (VMES) value successively decreased from the central incisor to the canine and from the second premolar to the second molar, and the VMES of the second molar was the lowest among the three groups. When the angle between the intrusion force and occlusal plane got larger, the incisors exhibited greater intrusion but minor retraction.

CONCLUSIONS

The "roller coaster effect" usually occurred in cases involving premolar extraction with CA, especially in patients with protruded incisors. The force closer to the vertical direction were more effective in achieving incisor intrusion. The stress on PDLs mainly concentrated on the cervix and apex of incisors during the retraction process, indicating a possibility of root resorption.

Construction of Human Periodontal Ligament Constitutive Model Based on Collagen Fiber Content

Periodontal ligament (PDL) is mainly composed of collagen fiber bundles, and the content of collagen fiber is an important factor affecting the mechanical properties of PDL. Based on this, the purpose of this study is to explore the effect of the PDL collagen fiber content on its viscoelastic mechanical behavior. Transverse and longitudinal samples of different regions of PDL were obtained from the human maxilla. The fiber content at different regions of human PDL was quantitatively measured using image processing software, and a new viscoelastic constitutive model was constructed based on the fiber content. The nano-indentation experiment was carried out with a loading rate of 0.5 mN·s-1, a peak load of 3 mN, and a holding time of 200 s, and the model parameters were obtained through the experiment data. The results showed that with the increase of fiber content, the deformation resistance of PDL also increased, and compared with the neck and middle region, the compressive strain in the apical region of PDL was the largest. The range of reduced elastic modulus of human PDL was calculated to be 0.39~5.08 MPa. The results of the experimental data and the viscoelastic constitutive model fit well, indicating that the model can well describe the viscoelastic behavior of human PDL.

Construction of hyperelastic model of human periodontal ligament based on collagen fibers distribution

OBJECTIVE

The human periodontal ligament (PDL) dominated by collagen fibers showed hyperelastic mechanical behavior under orthodontic force. Despite previous researches on the hyperelastic model of PDL, there were certain limitations because of the types of samples and the ignorance of distribution of collagen fibers. Therefore, the aim of this study was to quantify the effect of collagen fibers distribution of human PDL on its hyperelastic behavior.

METHODS

A total of 6 human PDL samples of root neck, root middle and root apex were cut from human maxillary central incisor and lateral incisor. The spatial angles of collagen fibers were observed by optical microscope, the hyperelastic model was constructed combined with the observation results. The quasi-static uniaxial tensile tests with displacement load 0.05 mm/min were carried out, and the test data were used to identify the parameters of model.

RESULTS

The mechanical behavior of human PDL conformed to the trend of hyperelastic materials, and greatly depended on the spatial angles of internal collagen fibers. The R² value statistical fit of the constitutive model to the data is excellent (R² > 0.98). This model could excellently describe the hyperelastic properties of human PDL.

SIGNIFICANCE

In this study, we quantitatively described the effect of spatial distribution of collagen fibers on the mechanical properties of human PDL. The accuracy of this model was verified by the uniaxial test data, and the relevant model parameters were acquired, which have certain reference value in subsequent researches on hyperelasticity of human PDL and clinical treatment.

Open-Full-Jaw: An open-access dataset and pipeline for finite element models of human jaw

BACKGROUND

State-of-the-art finite element studies on human jaws are mostly limited to the geometry of a single patient. In general, developing accurate patient-specific computational models of the human jaw acquired from cone-beam computed tomography (CBCT) scans is labor-intensive and non-trivial, which involves time-consuming human-in-the-loop procedures, such as segmentation, geometry reconstruction, and re-meshing tasks. Therefore, with the current practice, researchers need to spend considerable time and effort to produce finite element models (FEMs) to get to the point where they can use the models to answer clinically-interesting questions. Besides, any manual task involved in the process makes it difficult for the researchers to reproduce identical models generated in the literature. Hence, a quantitative comparison is not attainable due to the lack of surface/volumetric meshes and FEMs.

METHODS

We share an open-access repository composed of 17 patient-specific computational models of human jaws and the utilized pipeline for generating them for reproducibility of our work. The used pipeline minimizes the required time for processing and any potential biases in the model generation process caused by human intervention. It gets the segmented geometries with irregular and dense surface meshes and provides reduced, adaptive, watertight, and conformal surface/volumetric meshes, which can directly be used in finite element (FE) analysis.

RESULTS

We have quantified the variability of our 17 models and assessed the accuracy of the developed models from three different aspects; (1) the maximum deviations from the input meshes using the Hausdorff distance as an error measurement, (2) the quality of the developed volumetric meshes, and (3) the stability of the FE models under two different scenarios of tipping and biting.

CONCLUSIONS

The obtained results indicate that the developed computational models are precise, and they consist of quality meshes suitable for various FE scenarios. We believe the provided dataset of models including a high geometrical variation obtained from 17 different models will pave the way for population studies focusing on the biomechanical behavior of human jaws.

Intrusion of overerupted periodontally compromised posterior teeth using orthodontic mini‐implants: a mechanobiological finite element study

INTRODUCTION

The intrusion of posterior teeth had been considered challenging up to the development of orthodontic mini implants. In periodontally compromised teeth, the challenge is even greater, because of the root resorption risk due to periodontal ligament over-compression. Still, the precise strategy to determine the force reduction level remains uncertain.

OBJECTIVE

The objective of the study was to determine, by a finite element analysis (FEA), the force reduction needed to avoid root resorption and maintain the efficiency of orthodontic mechanics of periodontally compromised teeth similar to the sound one.

METHODS

An anatomical model was constructed representing a premolar inserted into a maxillary bone. Based on the initial model (R0), three bone height loss conditions were simulated (R2 = 2 mm, R4 = 4 mm, and R6 = 6 mm). Two intrusive movements were simulated: pure intrusion (bilateral mini implant) and uncontrolled-tipping intrusion (buccal mini implant). The hydrostatic stress at the periodontal ligament was used to evaluate the risk of root resorption due to over-compression.

RESULTS

For bilateral mini implant intrusion, the force had to be decreased by 16%, 32% and 48% for R2, R4 and R6, respectively. For buccal mini implant intrusion, the required reductions were higher (20%, 36% and 56%). A linear relationship between the intrusive force reduction and the alveolar bone height loss was observed in both intrusion mechanics.

CONCLUSIONS

According to the FE results, 8% or 9.3% of force reduction for each millimetre of bone height loss is suggested for intrusion with bilateral or buccal mini implant, respectively. The buccal mini implant anchorage must be associated with a supplemental strategy to avoid buccal crown tipping.

Strain Measurement within an Intact Swine Periodontal Ligament

The periodontal ligament (PDL) provides support, proprioception, nutrition, and protection within the tooth–PDL–bone complex (TPBC). While understanding the mechanical behavior of the PDL is critical, current research has inferred PDL mechanics from finite element models, from experimental measures on complete TPBCs, or through direct measurement of isolated PDL sections. Here, transducers are used in an attempt to quantify ex vivo PDL strain. In-fiber Bragg grating (FBG) sensors are small flexible sensors that can be placed within an intact TPBC and yield repeatable strain measurements from within the PDL space. The objective of this study was to determine: 1) if the FBG strain measured from the PDL space of intact swine premolars ex vivo was equivalent to physical PDL strains estimated through finite element analysis and 2) if a change in FBG strain could be linearly related to a change in finite element strain under variable tooth displacement, applied to an intact swine TPBC. Experimentally, individual TPBCs were subjected to 2 displacements (n = 14). The location of the FBG was determined from representative micro–computed tomography images. From a linear elastic finite element model of a TPBC, the strain magnitudes at the sensor locations were recorded. An experimental ratio (i.e., FBG strain at the first displacement divided by the FBG strain at the second displacement) and a finite element ratio (i.e., finite element strain at the first displacement divided by the finite element strain at the second displacement) were calculated. A linear regression model indicated a statistically significant relationship between the experimental and finite element ratio (P = 0.017) with a correlation coefficient (R²) of 0.448. It was concluded that the FBG sensor could be used as a measure for a change in strain and thus could be implemented in applications where the mechanical properties of an intact PDL are monitored over time.

A critical analysis of research methods and experimental models to study the load capacity and clinical behavior of the root filled teeth

The prognosis of root‐filled teeth depends not only on a successful root canal treatment but also on the restorative prognosis. This critical review discusses the advantages and limitations of various methodologies used to assess the load capacity or clinical survivability of root‐filled teeth and restorations. These methods include static loading, cyclic loading, finite element analysis and randomized clinical trials. In vitro research is valuable for preclinical screening of new dental materials or restorative modalities. It also can assist investigators or industry to decide whether further clinical trials are justified. It is important that these models present high precision and accuracy, be reproducible, and present adequate outcomes. Although in vitro models can reduce confounding by controlling important variables, the lack of clinical validation (accuracy) is a downside that has not been properly addressed. Most importantly, many in vitro studies did not explore the mechanisms of failure and their results are limited to rank different materials or treatment modalities according to the maximum load capacity. An extensive number of randomized clinical trials have also been published in the last years. These trials have provided valuable insight on the survivability of the root‐filled tooth answering numerous clinical questions. However, trials can also be affected by the selected outcome and by intrinsic and extrinsic biases. For example, selection bias, loss to follow‐up and confounding. In the clinical scenario, hypothesis‐based studies are preferred over observational and retrospective studies. It is recommended that hypothesis‐based studies minimize error and bias during the design phase.

Effects of masticatory loading on bone remodeling around teeth vs. implants: insights from a preclinical model

OBJECTIVES

Teeth connect to bone via a periodontal ligament whereas implants connect to bone directly. Consequently, masticatory loads are distributed differently to periodontal versus peri-implant bone. Our objective was to determine how masticatory loading of an implant versus a tooth affected peri-implant versus periodontal bone remodeling. Our hypothesis was that strains produced by functional loading of an implant would be elevated compared to the strains around teeth, and that this would stimulate a greater degree of bone turnover around implants versus in periodontal bone.

MATERIALS AND METHODS

Sixty skeletally mature mice were divided into two groups. In the Implant group, maxillary first molars (mxM1) were extracted, and after socket healing, titanium alloy implants were positioned sub-occlusally. After osseointegration, implants were exposed, resin crowns were placed, and masticatory loading was initiated. In a Control group the dentition was left intact. Responses of peri-implant and periodontal bone were measured using micro-CT, histology, bone remodeling assays, and quantitative histomorphometry while bone strains were estimated using finite element (FE) analyses.

CONCLUSIONS

When a submerged osseointegrated implant is exposed to masticatory forces peri-implant strains are elevated, and peri-implant bone undergoes significant remodeling that culminates in new bone accrual. The accumulation of new bone functions to reduce both peri-implant strains and bone remodeling activities, equivalent to those observed around the intact dentition.

Materials for Dentoalveolar Bioprinting: Current State of the Art

Although current treatments can successfully address a wide range of complications in the dentoalveolar region, they often still suffer from drawbacks and limitations, resulting in sub-optimal treatments for specific problems. In recent decades, significant progress has been made in the field of tissue engineering, aiming at restoring damaged tissues via a regenerative approach. Yet, the translation into a clinical product is still challenging. Novel technologies such as bioprinting have been developed to solve some of the shortcomings faced in traditional tissue engineering approaches. Using automated bioprinting techniques allows for precise placement of cells and biological molecules and for geometrical patient-specific design of produced biological scaffolds. Recently, bioprinting has also been introduced into the field of dentoalveolar tissue engineering. However, the choice of a suitable material to encapsulate cells in the development of so-called bioinks for bioprinting dentoalveolar tissues is still a challenge, considering the heterogeneity of these tissues and the range of properties they possess. This review, therefore, aims to provide an overview of the current state of the art by discussing the progress of the research on materials used for dentoalveolar bioprinting, highlighting the advantages and shortcomings of current approaches and considering opportunities for further research.

A multi-patient analysis of the center of rotation trajectories using finite element models of the human mandible

Studying different types of tooth movements can help us to better understand the force systems used for tooth position correction in orthodontic treatments. This study considers a more realistic force system in tooth movement modeling across different patients and investigates the effect of the couple force direction on the position of the center of rotation (CRot). The finite-element (FE) models of human mandibles from three patients are used to investigate the position of the CRots for different patients’ teeth in 3D space. The CRot is considered a single point in a 3D coordinate system and is obtained by choosing the closest point on the axis of rotation to the center of resistance (CRes). A force system, consisting of a constant load and a couple (pair of forces), is applied to each tooth, and the corresponding CRot trajectories are examined across different patients. To perform a consistent inter-patient analysis, different patients’ teeth are registered to the corresponding reference teeth using an affine transformation. The selected directions and applied points of force on the reference teeth are then transformed into the registered teeth domains. The effect of the direction of the couple on the location of the CRot is also studied by rotating the couples about the three principal axes of a patient’s premolar. Our results indicate that similar patterns can be obtained for the CRot positions of different patients and teeth if the same load conditions are used. Moreover, equally rotating the direction of the couple about the three principal axes results in different patterns for the CRot positions, especially in labiolingual direction. The CRot trajectories follow similar patterns in the corresponding teeth, but any changes in the direction of the force and couple cause misalignment of the CRot trajectories, seen as rotations about the long axis of the tooth.

Finite element and clinical analyses of effects of a new intraoral device (VomPress) combined with extraoral RAMPA on improving the overjet of craniofacial complex

This research intends to investigate the effects of a new intraoral device, VomPress, combined with a Right Angle Maxillary Protraction Appliance (RAMPA) extraoral device on the treatment of maxillary hypoplasia. To this end, finite element (FE) method has been employed and a skull model, including all sutures, has been investigated. In addition, the effects of VomPress combined with RAMPA on a seven-year-old girl with the malocclusion and other side problems were monitored. The results of both FE simulations and the clinical data revealed that VomPress combined with RAMPA effectively improved the malocclusion and straight neck problem by creating more space in the patient's mouth and anterosuperior protraction effects.

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.

Using FEM to Assess the Effect of Orthodontic Forces on Affected Periodontium

Orthodontic treatment in patients with no periodontal tissue breakdown vs. horizontal bone loss should be approached with caution even though it can bring significant benefits in terms of periodontal recovery and long-term success. We used the finite element method (FEM) to simulate various clinical scenarios regarding the periodontal involvement: healthy with no horizontal bone loss, moderate periodontal damage (33%) and severe horizontal bone loss (66%). Afterwards, forces of different magnitudes (0.25 N, 1 N, 3 N, and 5 N) were applied in order to observe the behavioral patterns. Through mathematical modeling, we recorded the maximum equivalent stresses (σ ech), the stresses on the direction of force application (σ c) and the displacements produced (f) in the whole tooth–periodontal ligament–alveolar bone complex with various degrees of periodontal damage. The magnitude of lingualization forces in the lower anterior teeth influences primarily the values of equivalent tension, then those of the tensions in the direction in which the force is applied, and lastly those of the displacement of the lower central incisor. However, in the case of the lower lateral incisor, it influences primarily the values of the tensions in the direction in which the force is applied, then those of equivalent tensions, and lastly those of displacement. Anatomical particularities should also be considered since they may contribute to increased periodontal risk in case of lingualization of the LLI compared to that of the LCI, with a potential emergence of the “wedge effect”. To minimize periodontal hazards, the orthodontic force applied on anterior teeth with affected periodontium should not exceed 1 N.

Where is the center of resistance of a maxillary first molar? A 3-dimensional finite element analysis

INTRODUCTION

The center of resistance (C_Res) is regarded as the fundamental reference point for predictable tooth movement. Accurate estimation can greatly enhance the efficiency of orthodontic tooth movement. Only a handful of studies have evaluated the C_Res of a maxillary first molar; however, most had a low sample size (in single digits), used idealized models, or involved 2-dimensional analysis. The objectives of this study were to: (1) determine the 3-dimensional (3D) location of the C_Res of maxillary first molars, (2) evaluate its variability in a large sample, and (3) investigate the effects of applying orthodontic load from 2 directions on the location of the C_Res.

METHODS

Cone-beam computed tomography scans of 50 maxillary molars from 25 patients (mean age, 20.8 ± 8.7 years) were used. The cone-beam computed tomography volume images were manipulated to extract 3D biological structures via segmentation. The segmented structures were cleaned and converted into virtual mesh models made of tetrahedral triangles having a maximum edge length of 1 mm. The block, which included the molars and periodontal ligament, consisted of a mean of 7753 ± 2748 nodes and 38,355 ± 14,910 tetrahedral elements. Specialized software was used to preprocess the models to create an assembly and assign material properties, interaction conditions, boundary conditions, and load applications. Specific loads were applied, and custom-designed algorithms were used to analyze the stress and strain to locate the C_Res. The C_Res was measured in relation to the geometric center of the buccal surface of the molar and the trifurcation of the molar roots.

RESULTS

The average location of the C_Res for the maxillary first molar was 4.94 ± 1.39 mm lingual, 2.54 ± 2.7 mm distal, and 7.86 ± 1.66 mm gingival relative to the geometric center of the buccal surface of the molar and 0.136 ± 1.51 mm lingual (P <0.01), 1.48 ± 2.26 mm distal (P <0.01), and 0.188 ± 1.75 mm gingival (P >0.01) relative to the trifurcation of the molar roots. In the anteroposterior (y-axis) and the vertical (z-axis) planes, the C_Res showed significant association with root divergence (P <0.01).

CONCLUSIONS

The C_Res of the maxillary first molar was located apical and distal to the trifurcation area. It showed significant variation in its location. The 3D location of and also varied with the force direction. In some samples, this deviation was large. For accurate and predictable movement, tooth-specific C_Res need to be calculated.

Finite element simulations of the effects of an extraoral device, RAMPA, on anterosuperior protraction of the maxilla and comparison with gHu-1 intraoral device

OBJECTIVES

To investigate the effects of an extraoral device, right-angle maxillary protraction appliance (RAMPA), combined with a semi-rapid maxillary expansion intraoral device (gHu-1) on the anterosuperior protraction of maxillary bone.

MATERIALS AND METHODS

The finite element (FE) model included craniofacial bones and all sutures. The linear assumption was assumed for the FE simulations and the material properties of bones and sutures. The gHu-1 was simulated under screw activations equal to Δx = 0.25 and 0.5 mm in the lateral direction with and without RAMPA under a set of external forces {F1 = 2.94, F2 = 1.47, F3 = 4.44} N.

RESULTS

Displacement contours, nodal displacements of 12 landmarks, and von Mises stresses were compared. Combining RAMPA and gHu-1 (with Δx = 0.25 mm) resulted in changes in the displacement of the front part of the maxilla near the mid-palatal suture from (0.02, -0.1, -0.02) mm to (0.02, 0.3, 0.8) mm. For gHu-1 with Δx = 0.5 mm, the displacement of the same part changed from (0.04, -0.04, -0.2) mm to (0.04, 0.3, 0) mm. Similar trends were found in other locations.

CONCLUSIONS

The findings are in agreement with the previous cephalometric clinical data of an 8-year-old patient and prove the positive effects of RAMPA on the anterosuperior protraction of the maxilla when it is combined with the intraoral device gHu-1. In addition, RAMPA does not interfere with the lateral expansion generated by the intraoral device.

Orthodontic Tooth Movement Studied by Finite Element Analysis: an Update. What Can We Learn from These Simulations?

PURPOSE OF REVIEW

To produce an updated overview of the use of finite element (FE) analysis for analyzing orthodontic tooth movement (OTM). Different levels of simulation complexity, including material properties and level of morphological representation of the alveolar complex, will be presented and evaluated, and the limitations will be discussed.

RECENT FINDINGS

Complex formulations of the PDL have been proposed, which might be able to correctly predict the behavior of the PDL both when chewing forces and orthodontic forces are simulated in FE models. The recent findings do not corroborate the simplified view of the classical OTM theories. The use of complex and biologically coherent FE models can help understanding the mechanisms leading to OTM as well as predicting the risk of root resorption related to specific force systems and magnitudes.

Biomechanical analysis of occlusal modes on the periodontal ligament while orthodontic force applied

OBJECTIVE

The study objective was to investigate four common occlusal modes by using the finite element (FE) method and to conduct a biomechanical analysis of the periodontal ligament (PDL) and surrounding bone when orthodontic force is applied.

MATERIALS AND METHODS

A complete mandibular FE model including teeth and the PDL was established on the basis of cone-beam computed tomography images of an artificial mandible. In the FE model, the left and right mandibular first premolars were not modeled because both canines required distal movement. In addition, four occlusal modes were simulated: incisal clench (INC), intercuspal position (ICP), right unilateral molar clench (RMOL), and right group function (RGF). The effects of these four occlusal modes on the von Mises stress and strain of the canine PDLs and bone were analyzed.

RESULTS

Occlusal mode strongly influenced the distribution and value of von Mises strain in the canine PDLs. The maximum von Mises strain values on the canine PDLs were 0.396, 1.811, 0.398, and 1.121 for INC, ICP, RMOL, and RGF, respectively. The four occlusal modes had smaller effects on strain distribution in the cortical bone, cancellous bone, and miniscrews.

CONCLUSION

Occlusal mode strongly influenced von Mises strain on the canine PDLs when orthodontic force was applied.

CLINICAL RELEVANCE

When an FE model is used to analyze the biomechanical behavior of orthodontic treatments, the effect of muscle forces caused by occlusion must be considered.

Tissue Engineering for Periodontal Ligament Regeneration: Biomechanical Specifications

The periodontal biomechanical environment is very difficult to investigate. By the complex geometry and composition of the periodontal ligament (PDL), its mechanical behavior is very dependent on the type of loading (compressive versus tensile loading; static versus cyclic loading; uniaxial versus multiaxial) and the location around the root (cervical, middle, or apical). These different aspects of the PDL make it difficult to develop a functional biomaterial to treat periodontal attachment due to periodontal diseases. This review aims to describe the structural and biomechanical properties of the PDL. Particular importance is placed in the close interrelationship that exists between structure and biomechanics: the PDL structural organization is specific to its biomechanical environment, and its biomechanical properties are specific to its structural arrangement. This balance between structure and biomechanics can be explained by a mechanosensitive periodontal cellular activity. These specifications have to be considered in the further tissue engineering strategies for the development of an efficient biomaterial for periodontal tissues regeneration.

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.

Mechanical performance of Anatomic-Functional-Geometry dental treatments: A computational study

In this paper the biomechanical response of a novel dental preparation technique, referred to as the Anatomic-Functional-Geometry treatment (AFG), is investigated through a 3D nonlinear finite-element modelling approach. A comparative investigation against a standard technique employed in dental clinical practice is carried out, by simulating typical experimental mechanical tests and physiological functional conditions. Failure mechanisms of treated tooth models are investigated through a progressive damage formulation implemented via a displacement-driven incremental approach. Computational results clearly show that AFG-treated teeth, as a consequence of a more conservative morphological preparation of the tooth, are characterized by more effective crown-dentin loading transfer mechanisms, higher fracture strength levels and more homogeneous stress patterns than the standard-treated ones, thereby opening towards widespread clinical application.

Mechanical effects of distributed fibre orientation in the periodontal ligament of an idealised geometry

In this study, we computationally assess the effects of the distributed fibre orientation in the periodontal ligament (PDL) on mechanical responses of the tooth-PDL complex. An idealised axial-symmetric geometry of a tooth-PDL complex was constructed. The fibre orientation in the PDL was modelled as a trigonometric function based on anatomical knowledge, and the PDL was modelled as a transversely isotropic hyperelastic material dependent on fibre orientations. Parametric studies of the fibre orientation on the mechanical responses of the tooth-PDL complex were conducted. Obtained results showed that the anatomically consistent fibre orientation functions as a supporting structure against not only vertical but also horizontal loads.

Parameter identification for the simulation of the periodontal ligament during the initial phase of orthodontic tooth movement

The paper is concerned with simulation of the periodontal ligament response to force in the initial phase of orthodontic tooth movement. This is based on two previous investigations, a in vitro experiment with specimens of porcine mandibular premolars and a in vivo experiment on human upper first incisors. For the curve fit of the in vitro experiment a model function, assuming viscoelasticity, was introduced. The viscoelastic model function was augmented by a ramp rise time term, to account for observed dependence of the response on actuator velocity, and a previous load history term, to account for the effect of the previous tests on the current test. The correlation coefficient of a curve fit for all tests grouped together was R2=0.98. Next, a curve fit of the in vivo experiment was done. Good correlation was found for a simplified model function, without viscoelastic term (R2=0.96). For both tests, in vitro and in vivo, the ramp rise time term improved correlation. A finite element model of the specimen of the in vitro experiment was created. For the PDL a hyperelastic constitutive model for compressible material was used and model parameters were identified. The present work indicates that the macroscopic response of the periodontal ligament to an external load can be simulated with a poro-visco-hyperelastic model. The simulation showed that poroelastic behaviour will gradually cease when viscoelastic relaxation progresses. This followed also from dimensionless analysis. As a consequence, for slow loading, or if initial response to fast loading is not of interest, a visco-hyperelastic model may suffice. To identify parameters of the finite element model several optimisation problems were solved. A model function, which can be regarded as a reduced order model, allowed a full factorial experiment (analysis) at low cost, to identify initial parameters. The thus found parameters were further refined with an optimum interpolation meta-model. That is, for limited number of parameter combinations the response was simulated with the finite element model and a refined parameter study was conducted by means of optimal interpolation. The thus found optimal parameters were verified by simulation with the finite element model. Optimal interpolation is computationally cheap, which allowed full factorial experiments at low cost.

A new perspective: Periodontal ligament is a viscoelastic fluid biomaterial as evidenced by dynamic shear creep experiment

Currently, Periodontal ligament (PDL) is considered as a viscoelastic solid biomaterial. However, we observed the steady-state rheological behavior of PDL through long time loading experiments, and suggested the theoretical definition of PDL as a viscoelastic fluid biomaterial. PDL specimens were prepared from the middle area of the mandibular central incisors in pigs. Dynamic force loading with frequencies of 0 (static load), 2, 5, and 10 Hz and amplitudes of 0.01, 0.02, and 0.03 MPa was adopted. The shear strain-time curve at the equilibrium position of PDL was obtained by a dynamic shear creep experiment. The results showed that the shear strain increased exponentially at first and then inclined toward an oblique line. The results showed that the PDL has viscoelastic fluid characteristics, independent of frequency and amplitude. The shear strain decreased with an increase in frequency and amplitude. To further analyze the viscoelastic characteristics of PDL, a 50000-s static shear creep experiment was re-designed. PDL exhibited viscoelastic fluid biomaterial characteristics according to the three aspects of the algebraic fitting, geometric characteristics, and physical results. For the first time, a viscoelastic fluid constitutive model was established to characterize the mechanical properties of PDL with high fitting accuracy. Furthermore, the shear viscosity coefficient of the dynamic load was larger than that of the static load, increasing with an increase in frequency and amplitude; compared with the static force, the dynamic force improved the viscosity of PDL, enhancing its function of fixing teeth, and introducing the new medical knowledge of "No tooth extraction after a meal."

In vitro Simulation of Periodontal Ligament in Fatigue Testing of Dental Crowns

OBJECTIVE

 Fatigue testing of restorative material has been appreciated as an appropriate method to evaluate dental restorations. This study aims to investigate the influence of periodontal ligament (PDL) simulation on fatigue and fracture tests results of zirconia crowns.

MATERIALS AND METHODS

 A standard tooth preparation for all ceramic zirconia crown was made on a typodont mandibular molar. The prepared master die was duplicated using epoxy resin to produce 40 replicas. PDL simulation was made by surrounding the root of 20 dies with a 0.3-mm thick silicon layer. The other 20 specimens had no PDL simulation. Zirconia crowns were fabricated using computer-aided design/computer-aided manufacturing technology and cemented to the epoxy resin dies. Ten crowns from each group were subject to chewing simulation with simultaneous thermocycling (5-55°C). All specimens were then loaded until failure in universal testing machine.

STATISTICAL ANALYSIS

 Statistical analysis was conducted using SPSS software. Shapiro-Wilk test confirmed the normal distribution of data. Descriptive statistic was performed and differences between the groups were analyzed using paired samples t-test.

RESULTS

 All fatigued crowns survived chewing simulation; no failure was observed after finishing simulation. The highest mean fracture load recorded was 3,987 ± 400 N for the no fatigue/no periodontal simulation group. Comparing the mean fracture load of the two groups with periodontal simulation and the two groups with no periodontal simulation showed no statistically significant difference (p > 0.5).

CONCLUSION

 Considering the testing set-up applied in this study, simulating PDL using resilient materials does not affect the in vitro survival and fracture resistance of zirconia crowns.

shRNA knockdown of integrin-linked kinase on hPDLCs migration, proliferation, and apoptosis under cyclic tensile stress

OBJECTIVE

To investigate the roles of integrin-linked kinase (ILK) in mediating the cell migration, proliferation, and apoptosis of human periodontal ligament cells (hPDLCs) in response to cyclic tensile stress.

METHODS

Primary hPDLCs were obtained through the enzyme digestion and tissue culture method. Short hairpin ILK-expressing hPDLCs were constructed using a recombinant lentiviral vector that specifically targeted ILK gene expression. The silencing of the ILK gene was identified by quantitative real-time polymerase chain reaction (qRT-PCR) and Western blot. The hPDLCs were seeded on a flexible substrate and loaded with cyclic tensile stress at 0.5 Hz for 0, 2, 4, and 8 hr, consecutively, with the Flexcell Tension System. The response of cell migration was tested by the scratch assay. Cell proliferation was characterized by optical density (OD) value of cell counting kit-8 (CCK-8) test and Ki67 mRNA expression of qRT-PCR. Cell apoptosis was determined by flow cytometry and Caspase-3 mRNA expression of qRT-PCR.

RESULTS

Knocking down ILK substantially reduces migration and proliferation as well as regulates the sensitivity of hPDLCs to apoptosis under cyclic tensile stress.

CONCLUSIONS

ILK can promote the proliferation and migration as well as inhibit apoptosis of hPDLCs under cyclic tensile stress.

Linear Momenta Transferred to the Dental Implant-Bone and Natural Tooth-PDL-Bone Constructs Under Impact Loading: A Comparative in-vitro and in-silico Study

During dental trauma, periodontal ligament (PDL) contributes to the stability of the tooth-PDL-bone structure. When a dental implant is inserted into the bone, the dental implant-bone construct will be more prone to mechanical damage, caused by impact loading, than the tooth-PDL-bone construct. In spite of the prevalence of such traumas, the behavioral differences between these two constructs have not been well-understood yet. The main goal of this study was to compare the momentum transferred to the tooth-PDL-bone and dental implant-bone constructs under impact loading. First, mechanical impact tests were performed on six canine mandibles of intact (N = 3) and implanted (N = 3) specimens using a custom-made drop tower apparatus, from release heights of 1, 2, and 3 cm. Next, computed tomography-based finite element models were developed for both constructs, and the transferred momenta were calculated. The experimental results indicated that, for the release heights of 1, 2, and 3 cm, the linear momenta transferred to the dental implant-bone construct were 33.1, 31.0, and 27.5% greater than those of the tooth-PDL-bone construct, respectively. Moreover, results of finite element simulations were in agreement with those of the experimental tests (error <7.5%). This work tried to elucidate the effects of impact loading on the dental implant-bone and tooth-PDL-bone constructs using both in-vitro tests and validated in-silico simulations. The findings can be employed to modify design of the current generation of dental implants, based on the lessons one can take from the biomechanical behavior of a natural tooth structure.

The Mechanical Effect of the Periodontal Ligament on Bone Strain Regimes in a Validated Finite Element Model of a Macaque Mandible

The primary anatomical function of the periodontal ligament (PDL) is to attach teeth to their sockets. However, theoretical and constitutive mechanical models have proposed that during mastication the PDL redistributes local occlusal loads and reduces the jaw's resistance to torsional deformations. These hypotheses imply that accurately modeling the PDL's material properties and geometry in finite element analysis (FEA) is a prerequisite to obtaining precise strain and deformation data. Yet, many finite element studies of the human and non-human primate masticatory apparatus exclude the PDL or model it with simplicity, in part due to limitations in μCT/CT scan resolution and material property assignment. Previous studies testing the sensitivity of finite element models (FEMs) to the PDL have yielded contradictory results, however a major limitation of these studies is that FEMs were not validated against in vivo bone strain data. Hence, this study uses a validated and subject specific FEM to assess the effect of the PDL on strain and deformation regimes in the lower jaw of a rhesus macaque (Macaca mulatta) during simulated unilateral post-canine chewing. Our findings demonstrate that the presence of the PDL does influence local and global surface strain magnitudes (principal and shear) in the jaw. However, the PDL's effect is limited (diff. ~200-300 με) in areas away from the alveoli. Our results also show that varying the PDL's Young's Modulus within the range of published values (0.07-1750 MPa) has very little effect on global surface strains. These findings suggest that the mechanical importance of the PDL in FEMs of the mandible during chewing is dependent on the scope of the hypotheses being tested. If researchers are comparing strain gradients across species/taxa, the PDL may be excluded with minimal effect on results, but, if researchers are concerned with absolute strain values, sensitivity analysis is required.

Mechanoadaptive Responses in the Periodontium Are Coordinated by Wnt

Despite an extensive literature documenting the adaptive changes of bones and ligaments to mechanical forces, our understanding of how tissues actually mount a coordinated response to physical loading is astonishingly inadequate. Here, using finite element (FE) modeling and an in vivo murine model, we demonstrate the stress distributions within the periodontal ligament (PDL) caused by occlusal hyperloading. In direct response, a spatially restricted pattern of apoptosis is triggered in the stressed PDL, the temporal peak of which is coordinated with a spatially restricted burst in PDL cell proliferation. This culminates in increased collagen deposition and a thicker, stiffer PDL that is adapted to its new hyperloading status. Meanwhile, in the adjacent alveolar bone, hyperloading activates bone resorption, the peak of which is followed by a bone formation phase, leading ultimately to an accelerated rate of mineral apposition and an increase in alveolar bone density. All of these adaptive responses are orchestrated by a population of Wnt-responsive stem/progenitor cells residing in the PDL and bone, whose death and revival are ultimately responsible for directly giving rise to new PDL fibers and new bone.

A porous fibrous hyperelastic damage model for human periodontal ligament: Application of a microcomputerized tomography finite element model

The periodontal ligament (PDL) is a soft biological tissue that connects the tooth with the trabecular bone of the mandible. It plays a key role in load transmission and is primarily responsible for bone resorption and most common periodontal diseases. Although several numerical studies have analysed the biomechanical response of the PDL, most did not consider its porous fibrous structure, and only a few analysed damage to the PDL. This study presents an innovative numerical formulation of a porous fibrous hyperelastic damage material model for the PDL. The model considers two separate softening phenomena: fibre alignment during loading and fibre rupture. The parameters for the material model characterization were fitted using experimental data from the literature. Furthermore, the experimental tests used for characterization were computationally modelled to verify the material parameters. A finite element model of a portion of a human mandible, obtained by microcomputerized tomography, was developed, and the proposed constitutive model was implemented for the PDL. Our results confirm that damage to the PDL may occur mainly because of overpressure of the interstitial fluid, while large forces must be applied to damage the PDL fibrous network. Moreover, this study clarifies some aspects of the relationship between PDL damage and the bone remodelling process.

An unusual disordered alveolar bone material in the upper furcation region of minipig mandibles: A 3D hierarchical structural study

Teeth are subjected to compressive loads during mastication. Under small loads the soft tissue periodontal ligament (PDL) deforms most. However when the loads increase and the PDL is highly compressed, the tooth and the alveolar bone supporting the tooth, begin to deform. Here we report on the structure of this alveolar bone in the upper furcation region of the first molars of mature minipigs. Using light microscopy and scanning electron microscopy (SEM) of bone cross-sections, we show that this bone is hypermineralized, containing abundant small pores around 1-5 μm in diameter, lacunae around 10-20 μm as well as larger spaces. This bone does not possess the typical lamellar motif or other repeating structures normally found in cortical or trabecular mammalian bone. We also use high resolution focused ion beam scanning electron microscopy (FIB-SEM) in the serial surface mode to image the 3D organization of the demineralized bone matrix. We show that the upper furcation bone matrix has a disordered isotropic structure composed mainly of individual collagen fibrils with no preferred orientation, as well as highly staining material that is probably proteoglycans. Much larger aligned arrays of collagen fibers - presumably Sharpey's fibers - are embedded in this material. This unusual furcation bone material is similar to the disordered material found in human lamellar bone. In the upper furcation region this disordered bone comprises almost all the volume excluding Sharpey's fibers. We surmise that this most unusual bone type functions to resist the repeating compressive loads incurred by molars during mastication.

Influence of substrate design for in vitro mechanical testing

Background

The goal of this study was to evaluate the influence of dental substrate simulator material, and the presence of root and periodontal ligament on the stress distribution in an adhesively-cemented monolithic crown.

Material and Methods

Five (5) 3D models according to the substrate simulator material and shape were modeled with CAD software for conducting non-linear finite element analysis (FEA): Tooth with and without periodontal ligament - subgroup "pl" (groups Tooth+pl and Tooth-pl), machined tooth in epoxy-resin with and without pulp chamber - subgroup "pc" (ER+pc and ER-pc) and simplified epoxy-resin substrate without pulp chamber and roots (SiER). Next, adhesively-cemented monolithic crowns in zirconia reinforced lithium silicate were modeled over each substrate. The solids were then imported in STEP format to the analysis software and the contact between teeth and cylinder was considered perfectly bonded; whereas, the contacts involving the resin cement were considered as non-separated. The materials were considered isotropic, linearly elastic, and homogeneous. An axial load (600 N) was applied to the occlusal surface and results of maximum principal stress (MPa) on the restoration were required.

Results

FEA revealed that all evaluated subtracts showed the crown intaglio surface as the most stressed region. The average stress and stress peaks were similar for restorations cemented onto Tooth+pl, Tooth-pl and ER+pc substrates, but, 13% higher in comparison to ER-pc and SiER substrates.

Conclusions

Simplified substrates can be used to evaluate posterior full crown behavior without periodontal ligaments and roots, since the rigidity of the specimen is taken into account. Key words:Finite element analysis, axial loading, computed assisted numerical analisys, monolithic crowns,methodological study.

Anterosuperior protraction of maxillae using the extraoral device, RAMPA; finite element method

This paper presents a boosting effect against gravity by analyzing the displacement and stress distribution of craniofacial structures due to the protraction of the extraoral device, the Right Angle Maxillary Protraction Appliance(RAMPA) system, including semi-rapid maxillary expansion (sRME) using the finite element method. In addition, a patient case was illustrated and compared with the results calculated from a simulation. The results from the finite element method were obtained for 0.5 mm activation using the screw of the intraoral device, gHu-1. This study reveals that RAMPA rotates the patient's maxilla and mandible in the forward direction and forces them to move forward and upward.

Development and Validation of 3D Finite Element Models for Prediction of Orthodontic Tooth Movement

OBJECTIVES

The aim of this study was to develop and validate three-dimensional (3D) finite element modeling for prediction of orthodontic tooth movement.

MATERIALS AND METHODS

Two orthodontic patients were enrolled in this study. Computed tomography (CT) was captured 2 times. The first time was at T0 immediately before canine retraction. The second time was at T4 precisely at 4 months after canine retraction. Alginate impressions were taken at 1 month intervals (T0-T4) and scanned using a digital scanner. CT data and scanned models were used to construct 3D models. The two measured parameters were clinical tooth movement and calculated stress at three points on the canine root. The calculated stress was determined by the finite element method (FEM). The clinical tooth movement was measured from the differences in the measurement points on the superimposed model. Data from the first patient were used to analyze the tooth movement pattern and develop a mathematical formula for the second patient. Calculated orthodontic tooth movement of the second patient was compared to the clinical outcome.

RESULTS

Differences between the calculated tooth movement and clinical tooth movement ranged from 0.003 to 0.085 mm or 0.36 to 8.96%. The calculated tooth movement and clinical tooth movement at all reference points of all time periods appeared at a similar level. Differences between the calculated and clinical tooth movements were less than 0.1 mm.

CONCLUSION

Three-dimensional FEM simulation of orthodontic tooth movement was achieved by combining data from the CT and digital model. The outcome of the tooth movement obtained from FEM was found to be similar to the actual clinical tooth movement.

Finite element investigation of human maxillary incisor under traumatic loading: Static vs dynamic analysis

BACKGROUND AND OBJECTIVE

Traumatic loading is the main form of injury sustained in dental injuries. In spite of the prevalence of dental trauma, little information is available on traumatic dental damage and the evaluation of tooth behavior under traumatic loading. Due to the short period of traumatic loading, at first sight, a dynamic analysis needs to be performed to investigate the dental trauma. However, it was hypothesized that dental traumatic loading could be regarded as quasi-static loading. Thus, the aim of the present study was to examine this hypothesis.

METHODS

Static and dynamic analyses of the human maxillary incisor were carried out under traumatic loading using a 3D finite element method. Also, modal analysis of the tooth model was performed in order to evaluate the assumption of the dental traumatic loading as a quasi-static one.

RESULTS

It was revealed that the static analysis of dental trauma is preferred to the dynamic analysis when investigating dental trauma, mainly due to its lower computational cost. In fact, it was shown that including the inertia of the tooth structure does not influence the results of the dental trauma simulation. Furthermore, according to the modal analysis of the tooth structure, it was found that the mechanical properties and geometry of the periodontal ligament play significant roles in the classification of dental traumatic loading as a quasi-static one, in addition to the time duration of the applied load.

CONCLUSIONS

This paper provides important biomechanical insights into the classification of dental loading as quasi-static, transient or impact loading in future dental studies.

Approach towards the porous fibrous structure of the periodontal ligament using micro-computerized tomography and finite element analysis

The periodontal ligament (PDL) is a porous and fibrous soft tissue situated around the tooth, which plays a key role in the transmission of loads from the tooth to the alveolar bone of the mandible. Although several studies have tried to characterize its mechanical properties, the behaviour of this tissue is not clear yet. In this study, a new simulation methodology based on a material model which considers the contribution of porous and fibrous structure with different material model formulations depending on the effort direction is proposed. The defined material model was characterized by a non-linear approximation of the porous fibrous matrix to experimental results obtained from samples of similar species and was validated by rigorous test simulations under tensile and compressive loads. The global PDL response was also validated using the parameters of the characterization in a finite element model of full human canine tooth obtained by micro-tomography. The results suggest that the porous contribution has high influence during compression because the bulk modulus of the material depends on the ability of interstitial fluid to drain. On the other hand, the collagen fibres running along the load direction are the main responsible of the ligament stiffness during tensile efforts. Thus, a material model with distinct responses depending of the load direction is proposed. Furthermore, the results suggest the importance of considering 3D finite element models based of the real morphology of human PDL for representing the irregular stress distribution caused by the coupling of complex material models and irregular morphologies.

Inclusion of periodontal ligament fibres in mandibular finite element models leads to an increase in alveolar bone strains

Alveolar bone remodelling is vital for the success of dental implants and orthodontic treatments. However, the underlying biomechanical mechanisms, in particular the function of the periodontal ligament (PDL) in bone loading and remodelling, are not well understood. The PDL is a soft fibrous connective tissue that joins the tooth root to the alveolar bone and plays a critical role in the transmission of loads from the tooth to the surrounding bone. However, due to its complex structure, small size and location within the tooth socket it is difficult to study in vivo. Finite element analysis (FEA) is an ideal tool with which to investigate the role of the PDL, however inclusion of the PDL in FE models is complex and time consuming, therefore consideration must be given to how it is included. The aim of this study was to investigate the effects of including the PDL and its fibrous structure in mandibular finite element models. A high-resolution model of a human molar region was created from micro-computed tomography scans. This is the first time that the fibrous structure of the PDL has been included in a model with realistic tooth and bone geometry. The results show that omission of the PDL creates a more rigid model, reducing the strains observed in the mandibular corpus which are of interest when considering mandibular functional morphology. How the PDL is modelled also affects the strains. The inclusion of PDL fibres alters the strains in the mandibular bone, increasing the strains in the tooth socket compared to PDL modelled without fibres. As strains in the alveolar bone are thought to play a key role in bone remodelling during orthodontic tooth movement, future FE analyses aimed at improving our understanding and management of orthodontic treatment should include the fibrous structure of the PDL.

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.

Biomechanical characteristics of self-ligating brackets in a vertically displaced canine model: a finite element analysis

OBJECTIVES

The objective of this study was to compare the biomechanical characteristics between two types of self-ligating brackets and conventional metal brackets using finite element analysis of a vertically displaced canine model focusing on the desired force on the canine and undesirable forces on adjacent teeth.

MATERIALS AND METHODS

Three-dimensional finite element models of the maxillary dentition with 1-mm, 2-mm, and 3-mm vertically displaced canines were constructed. Two different self-ligating brackets (In-Ovation C and Smart clip) and a conventional metal bracket (Micro-arch) were modeled. After a 0.016-inch NiTi (0.40 mm, round) wire was engaged, the displacement of each tooth was calculated using x-, y-, and z-coordinates, and the tensile and compressive stresses were calculated.

RESULTS

The extrusion and maximal tensile stress of the canine differed little between the three brackets, but the intrusion and minimal compressive stress values of the adjacent teeth differed considerably and were highest in the Smart clip and least in the In-Ovation C. The extrusion and maximal tensile stress of the canine in the 3-mm displacement model was less than that in the 2-mm displacement model, and the intrusion and minimal compressive stress of the adjacent teeth increased with the degree of displacement.

CONCLUSIONS

Self-ligating brackets were not superior to conventional brackets in leveling a vertically displaced canine. A continuous arch wire may not be recommended for leveling of severely displaced canines whether using self-ligating or conventional brackets.