Finite element modeling of the periodontal ligament under a realistic kinetic loading of the jaw system

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.

The Effects of Different Attachment Types and Positions on Rotation Movement in Clear Aligner Treatments: A Finite Element Analysis

Aim Rotation of the mandibular premolars during aligner treatment is a difficult movement to achieve accurately. The purpose of this study is to compare the effects of different attachment types and positions used in clear aligner treatments on the rotation movement and retention of clear aligners in the rotated first premolar teeth. The study also addressed the stress values in periodontal ligaments (PDLs) with finite element analysis. Materials and methods For purposes of this research, we created a mandibular tooth model and modeled the premolar tooth with a 30° rotation. Twelve separate groups were created by attaching horizontal rectangular, vertical rectangular, ellipsoid, and semi-ellipsoid attachments to the premolar tooth in buccal, lingual, and combined buccal and lingual ways. A model without attachments was created to be used as the control group. An activation movement of 0.25 mm was applied to the first premolar tooth in all 12 models. The study evaluated clear aligner displacement, von Misses stress on the PDL, and tooth displacements using the finite element stress analysis method. Results It was found that the group with horizontal rectangular attachments placed on both the buccal and lingual sides had the highest stress value in the PDL (0.1971 MPa) and the highest displacement in the tooth (0.1267 mm). Conversely, the group with semi-ellipsoid attachments placed both buccally and lingually had the least displacement movement in clear aligners (0.1441 mm). Conclusion The results indicate that groups with attachments provided better retention than groups without attachments. Models with horizontal, rectangular attachments showed significantly more tooth displacement compared to other models. Horizontal rectangular attachments placed buccally and lingually combined to provide tooth movement in rotated mandibular first premolars can be recommended for clinical use.

FEA Comparison of the Mechanical Behavior of Three Dental Crown Materials: Enamel, Ceramic, and Zirconia

The restoration of endodontically treated teeth is one of the main challenges of restorative dentistry. The structure of the tooth is a complex assembly in which the materials that make it up, enamel and dentin, have very different mechanical behaviors. Therefore, finding alternative replacement materials for dental crowns in the area of restorative care isa highly significant challenge, since materials such as ceramic and zirconia have very different stress load resistance values. The aim of this study is to assess which material, either ceramic or zirconia, optimizes the behavior of a restored tooth under various typical clinical conditions and the masticatory load. A finite element analysis (FEA) framework is developed for this purpose. The 3D model of the restored tooth is input into the FEA software (Ansys Workbench R23)and meshed into tetrahedral elements. The presence of masticatory forces is considered: in particular, vertical, 45° inclined, and horizontal resultant forces of 280 N are applied on five contact points of the occlusal surface. The numerical results show that the maximum stress developed in the restored tooth including a ceramic crown and subject to axial load is about 39.381 MPa, which is rather close to the 62.32 MPa stress computed for the natural tooth; stresses of about 18 MPa are localized at the roots of both crown materials. In the case of the zirconia crown, the stresses are much higher than those in the ceramic crown, except for the 45° load direction, while, for the horizontal loads, the stress peak in the zirconia crown is almost three times as large as its counterpart in the ceramic crown (i.e., 163.24 MPa vs. 56.114 MPa, respectively). Therefore, the zirconia crown exhibits higher stresses than enamel and ceramic that could increase in the case of parafunctions, such as bruxism. The clinician's choice between the two materials should be evaluated based on the patient's medical condition.

Identification of the periodontal ligament material parameters using response surface method

The orthodontic treatment can be guided by the finite element (FE) simulation of periodontal ligament (PDL) mechanical properties, and the biomimetic degree of FE simulation can be primarily affected by the material properties of the PDL. According to the principle of parameter inverse, a method: response surface (RS) method and FE inverse method were proposed to identify the material parameters of PDL. The Prony series viscoelastic FE model was established based on the relaxation experiment. With root mean square error of simulation results and experimental results as the objective function, the optimal parameter combination was obtained by RS method, and the FE simulation result were compared with the experimental result. The result showed that the optimal parameters of the PDL were elastic modulus: 3.791 MPa, Poisson's ratio: 0.42, temperature: 29.294°C separately, and the simulation result of optimal combination maintained consistency with experiment with the correlation coefficient of 0.97258, indicating that the method proposed in this paper could well identify of PDL material parameters. The parameter identification method used in this paper can significantly improve the calculation efficiency, and reduce the parameter identification error compared with the simple FE inverse method, which has scientific significance and theoretical value.

Anchorage effects of ligation and direct occlusion in orthodontics: A finite element analysis

BACKGROUND AND OBJECTIVE

During orthodontic treatment, the figure-of-eight ligature and the physiological occlusion play an important role in providing anchorage effects. However, their effects on reaction forces of tooth and stress state in periodontal ligament (PDL) have not been quantitatively evaluated yet. In this study, we presented a finite element analysis process for simulating posterior molar ligature and direct occlusion during orthodontics in order to quantitatively assess their anchorage effects.

METHODS

A high precision 3D biomechanical model containing upper and lower teeth, PDL, brackets and archwire was generated from the images of computed tomographic scan and sophisticated modelling procedures. The orthodontic treatment of closing the extraction gap was simulated via the finite element method to evaluate the biomechanical response of the molars under the conditions with or without ligation. The simulations were divided into experimental and control groups. In the experimental group, orthodontic force of 1 N was first applied, then direct occlusal forces of 3 and 10 N were applied on each opposite tooth. While in the control group, occlusal forces were applied without orthodontic treatment. The tooth displacement, the stress state in the PDL and the directions of the resultant forces on each tooth were evaluated.

RESULTS

In the case of molars ligated, the maximum hydrostatic stress in the molars' PDL decreases by 60%. When an initial tooth displacement of several microns occurs in response to an orthodontic force, the direction of the occlusal force changes simultaneously. Even a moderate occlusal force (3 N per tooth) can almost completely offset the mesial forces on the maxillary teeth, thus to provide effective anchorage effect for the orthodontics.

CONCLUSIONS

The proposed method is effective for simulating ligation and direct occlusion. Figure-of-eight ligature can effectively disperse orthodontic forces on the posterior teeth, while a good original occlusal relationship provides considerable anchorage effects in orthodontics.

Timing selection for loosened tooth fixation based on degree of alveolar bone resorption: a finite element analysis

Objective

This study aimed to evaluate timing of fixation to retard bone absorption using finite element analysis(FEA).

Methods

Volunteer CT images were used to construct four models of mandibles with varying degrees of alveolar bone resorption. By simulating occlusal force loading, biomechanical analysis was made on the periodontal membrane, tooth root and surrounding bone (both cancellous and cortical) of mandibular dentition.

Results

The von Mises stress value of the periodontal structures was positively related with the degree of alveolar bone resorption, and the von Mises stress at the interface between the periodontal membrane and tooth root was increased significantly in moderate to severe periodontitis models. The von Mises stress at the interface between the periodontal cortical bone and cancellous bone was increased significantly in the severe periodontitis model. And the von Mises stress value with oblique loading showed significantly higher than vertical loading.

Conclusion

Teeth with moderate to severe periodontitis, loosened tooth fixation can be used to retard bone absorption.

Pathophysiology of Demineralization, Part I: Attrition, Erosion, Abfraction, and Noncarious Cervical Lesions

PURPOSE OF THE REVIEW

Compare pathophysiology for infectious and noninfectious demineralization disease relative to mineral maintenance, physiologic fluoride levels, and mechanical degradation.

RECENT FINDINGS

Environmental acidity, biomechanics, and intercrystalline percolation of endemic fluoride regulate resistance to demineralization relative to osteopenia, noncarious cervical lesions, and dental caries. Demineralization is the most prevalent chronic disease in the world: osteoporosis (OP) >10%, dental caries ~100%. OP is severely debilitating while caries is potentially fatal. Mineralized tissues have a common physiology: cell-mediated apposition, protein matrix, fluid logistics (blood, saliva), intercrystalline ion percolation, cyclic demineralization/remineralization, and acid-based degradation (microbes, clastic cells). Etiology of demineralization involves fluid percolation, metabolism, homeostasis, biomechanics, mechanical wear (attrition or abrasion), and biofilm-related infections. Bone mineral density measurement assesses skeletal mass. Attrition, abrasion, erosion, and abfraction are diagnosed visually, but invisible subsurface caries <400μm cannot be detected. Controlling demineralization at all levels is an important horizon for cost-effective wellness worldwide.

Modeling tooth enamel in FEA comparisons of skulls: Comparing common simplifications with biologically realistic models

Palaeontologists often use finite element analyses, in which forces propagate through objects with specific material properties, to investigate feeding biomechanics. Teeth are usually modeled with uniform properties (all bone or all enamel). In reality, most teeth are composed of pulp, dentine, and enamel. We tested how simplified teeth compare to more realistic models using mandible models of three reptiles. For each, we created models representing enamel thicknesses found in extant taxa, as well as simplified models (bone, dentine or enamel). Our results suggest that general comparisons of stress distribution among distantly related taxa do not require representation of dental tissues, as there was no noticeable effect on heatmap representations of stress. However, we find that representation of dental tissues impacts bite force estimates, although magnitude of these effects may differ depending on constraints. Thus, as others have shown, the detail necessary in a biomechanical model relates to the questions being examined.

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

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

Efficient Design of a Clear Aligner Attachment to Induce Bodily Tooth Movement in Orthodontic Treatment Using Finite Element Analysis

Clear aligner technology has become the preferred choice of orthodontic treatment for malocclusions for most adult patients due to their esthetic appeal and comfortability. However, limitations exist for aligner technology, such as corrections involving complex force systems. Composite attachments on the tooth surface are intended to enable active control of tooth movements. However, unintended tooth movements still occur. In this study, we present an effective attachment design of an attachment that can efficiently induce tooth movement by comparing and analyzing the movement and rotation of teeth between a general attachment and an overhanging attachment. The 3D finite element modes were constructed from CBCT data and used to analyze the distal displacement of the central incisor using 0.5- and 0.75-mm-thick aligners without an attachment, and with general and overhanging attachments. The results show that the aligner with the overhanging attachment can effectively reduce crown tipping and prevent axial rotation for an intended distal displacement of the central incisor. In all models, an aligner with or without attachments was not capable of preventing the lingual inclination of the tooth.

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.