Tension-compression viscoelastic behaviors of the periodontal ligament

Effect of varying auxiliaries on maxillary incisor torque control with clear aligners: A finite element analysis

INTRODUCTION

This study aimed to evaluate the effects of varying auxiliaries on tooth movement and stress distribution when maxillary central incisors were torqued 1° with a clear aligner through finite element analysis.

METHODS

Three-dimensional finite element models, including maxillary alveolar bone, periodontal ligament, dentition, and clear aligner, were constructed. According to the auxiliaries designed on the maxillary central incisor, 5 models were created: (1) without auxiliaries (control model), (2) with the power ridge, (3) with the semi-ellipsoid attachment, (4) with the horizontal rectangular attachment, and (5) with the horizontal cylinder attachment. The tooth movement and periodontal ligament stress distribution after a palatal root torque of 1° were analyzed for each of the 5 models.

RESULTS

With 1° torque predicted, the maxillary central incisor without auxiliaries showed a tendency of labial tipping, mesial tipping, and intrusion. The rotation center moved occlusally in the power ridge model. The labiolingual inclination variation increased in the semi-ellipsoid attachment model but decreased in the power ridge model. The maxillary central incisor is twisted in the distal direction in the power ridge model. The maxillary central incisor of the horizontal rectangular attachment and the horizontal cylinder attachment model behaved similarly to the control model. Periodontal stresses were concentrated in the cervical and apical areas. The maximum von Mises stresses were 11.6, 12.4, 3.81, 1.14, and 11.0 kPa in the 5 models. The semi-ellipsoid attachment model exhibited a more uniform stress distribution than the other models.

CONCLUSIONS

Semi-ellipsoid attachment performed better efficacy on labiolingual inclination, and power ridge performed better efficacy on root control. However, a distal twist of maxillary incisors could be generated by the power ridge.

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

Objectives

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

Methods

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

Results

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

Conclusion

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

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

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

The effects of aligner anchorage preparation on mandibular first molars during premolar-extraction space closure with clear aligners: A finite element study

INTRODUCTION

This study aimed to determine the effectiveness of different aligner anchorage preparations on mandibular first molars during premolar-extraction space closure with clear aligners and to assess the effects of different modes of Class II elastics on mandibular first molars.

METHODS

Finite element models were constructed on the basis of cone-beam computed tomography data from an orthodontic patient. The models comprised maxilla, mandible, maxillary and mandibular teeth without first premolars, periodontal ligaments, attachments and aligners. Tooth displacement tendencies were calculated using different aligner anchorage preparations and Class II elastics on the models from the same patient. Three group sets were designed on the basis of the positions of aligner cutouts and buttons (mesiobuccal, distobuccal and lingual). Four groups were established in each of the 3 group sets. Four groups were created: (1) no elastic traction + no anchorage preparation, (2) anchorage preparation only, (3) elastic traction only, and (4) elastic traction + anchorage preparation. Different aligner anchorage preparations (0°, 1°, 2°, 3°) were applied on mandibular second premolars and molars. The Class II traction force was set to 100 g.

RESULTS

With clear aligners, mandibular first molars were subject to mesial tipping, lingual tipping and intrusion. In the condition of no elastic traction, aligner anchorage preparation resulted in distal tipping, buccal tipping, and extrusion effect on mandibular first molars. Aligner anchorage preparation was more effective in the distal and lingual cutout groups than in the mesial cutout group. In the condition of Class II elastic traction, the bodily movement of mandibular first molars was achieved with a 3° anchorage preparation for the mesial cutout group and a 1.7° anchorage preparation for distal and lingual cutout groups. Absolute maximal anchorage was achieved with a 2° anchorage preparation for distal and lingual cutout groups.

CONCLUSIONS

Clear aligner therapy caused mesial tipping, lingual tipping and intrusion of mandibular first molars during premolar-extraction space closure. Aligner anchorage preparation effectively prevented mesial and lingual tipping of mandibular molars. Distal and lingual cutout modes were more effective than mesial cutout modes in aligner anchorage preparation. For each aligner stage (0.25 mm), 1.7° aligner anchorage preparation and Class II elastics with distal or lingual cutouts led to the bodily movement of mandibular first molars, whereas 2° anchorage preparation reached absolute maximal anchorage.

Different biomechanical effects of clear aligners in closing maxillary and mandibular extraction spaces: Finite element analysis

INTRODUCTION

Compared with fixed treatments, clear aligners (CAs) have the advantages of comfort, esthetics, and hygiene, and are popular among patients and orthodontists. However, CAs exhibit control deficiencies in extraction patients because of insufficient root control and retention effects. These deficiencies can magnify biomechanical differences in bimaxillary dentition, further causing different orthodontic requirements between maxillary and mandibular dentition. This study aimed to elaborate on the biomechanical characteristics of bimaxillary dentition in extraction space closure and provided feasible biomechanical compensation strategies for use in clinical practice.

METHODS

We constructed a 3-dimensional (3D) bimaxillary model based on patient data. Several 3D modeling-related software was used to generate a standard first premolar extraction model, CAs, and attachments. Subsequently, finite element analysis was performed to demonstrate the biomechanical effects.

RESULTS

The maxillary and mandibular dentition showed a roller coaster effect during space closure. Compared with the maxillary dentition, the mandibular posterior teeth exhibited stronger relative anchorage causing greater anterior teeth retraction. The tipping and vertical movements of the anterior teeth were related to tooth length. The longer the anterior tooth, the less tipping and greater vertical displacement occurred. Generally, when having the same retraction distance, the mandibular dentition exhibited greater retroclination and fewer extrusions. Both mechanical and retention compensations should be considered to prevent these unwanted tipping movements. Adding specific attachments to bimaxillary dentitions compensated for the retention and root control deficiencies of CAs.

CONCLUSIONS

When applying CAs to extraction patients, different biomechanical effects can present in the bimaxillary dentition because of specific dentition morphologies. To effectively treat these patients, mechanical compensation through overcorrection of the target position should be designed on the basis of bimaxillary control deficiencies, and retention compensation by adding specific attachments should also be considered according to the overcorrections.

Finite element analysis of the biomechanical effect of clear aligners in extraction space closure under different anchorage controls

INTRODUCTION

Clear aligners (CAs) have attracted increasing attention from patients and orthodontists because of their excellent esthetics and comfort. However, treating tooth extraction patients with CAs is difficult because their biomechanical effects are more complicated than those of traditional appliances. This study aimed to analyze the biomechanical effect of CAs in extraction space closure under different anchorage controls, including moderate, direct strong, and indirect strong anchorage. It could provide several new cognitions for anchorage control with CAs through finite element analysis, further directing clinical practice.

METHODS

A 3-dimensional maxillary model was generated by combining cone-beam computed tomography and intraoral scan data. Three-dimensional modeling software was used to construct a standard first premolar extraction model, temporary anchorage devices, and CAs. Subsequently, finite element analysis was performed to simulate space closure under different anchorage controls.

RESULTS

Direct strong anchorage was beneficial for reducing the clockwise occlusal plane rotation, whereas indirect anchorage was conducive for anterior teeth inclination control. In the direct strong anchorage group, an increase in the retraction force would require more specific anterior teeth overcorrection to resist the tipping movement, mainly including lingual root control of the central incisor, followed by distal root control of the canine, lingual root control of the lateral incisor, distal root control of the lateral incisor, and distal root control of the central incisor. However, the retraction force could not eliminate the mesial movement of the posterior teeth, possibly causing a reciprocating motion during treatment. In indirect strong groups, when the button was close to the center of the crown, the second premolar presented less mesial and buccal tipping but more intrusion.

CONCLUSIONS

The 3 anchorage groups showed significantly different biomechanical effects in both the anterior and posterior teeth. Specific overcorrection or compensation forces should be considered when using different anchorage types. The moderate and indirect strong anchorages have a more stable and single-force system and could be reliable models in investigating the precise control of future tooth extraction patients.

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.

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.

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

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

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.

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.

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.

Tooth Mobility Reproduction in Dental Material Research: A Scoping Review

Background:

Introducing tooth mobility simulation in laboratory studies can provide results with high accuracy and predictability.

Objectives:

This study aims to review in vitro methodologies replicating tooth mobility and provide a recommended approach for future laboratory models.

Methods:

Databases, such as PubMed, Cochrane Database of Systematic Review, BioMed Central and Chinese databases are searched, and twelve articles are included in the final review.

Results:

Simulation methods of tooth mobility involving socket enlargement, screw loosening, alveolar bone loss simulation and a combination approach are identified from the extracted data. The materials used in preparing artificial teeth, artificial sockets and periodontal ligament simulator are discussed with a focus on their limitations. The achieved degrees of mobility and the presence of the centre of rotation are also evaluated. A timeline of the review articles is constructed to understand the trend of the preferred methods in tooth mobility simulation.

Conclusion:

Future in vitro investigations can achieve clinical reliability, particularly for materials tested in the field of dental traumatology and periodontology, by recognising the importance of incorporating tooth mobility in laboratory studies. Improvised methods are proposed to ensure that potential laboratory models can resemble the actual oral environment.

Clear aligners for maxillary anterior en masse retraction: a 3D finite element study

To evaluate tooth behaviours under various maxillary incisor retraction protocols for clear aligner therapy. A three-dimensional finite element model of maxillary dentition was constructed for first premolar extraction. A loading method was developed to mimic the mode of action of clear aligners for incisor en masse retraction. Three protocols with different amounts of retraction and intrusion on incisors were designed. Initial tooth displacements and stresses on periodontal ligaments were analysed with ANSYS software. The central (U₁) and lateral (U₂) incisors exhibited uncontrolled lingual tipping and extrusion upon 0.25 mm retraction. U1 exhibited translation movement, while U₂ underwent less tipping during 0.2 mm retraction and 0.15 mm intrusion. Labial tipping and intrusion of U₁ and bodily intrusion of U₂ were observed during 0.1 mm of retraction and 0.23 mm of intrusion. With the additional intrusion on incisors, canine showed extrusion movement, and higher stresses on periodontal ligaments were shifted from U₂ to canines. Incisors also exhibited different mesial-distal angulation in the three simulations, while posterior teeth all suffered mesial inclination. Incorporating intrusion displacement in clear aligners led to a tendency of lingual root movement during incisor retraction. The complexity of tooth movement should be recognized regarding clear aligner therapy.

Numerical simulation of hydro-mechanical coupling of periodontal ligament

Orthodontic tooth movement in the alveolar bone is due to the mechanical response of periodontal ligament to applied forces. Definition of a proper constitutive model of the periodontal ligament to investigate its response to orthodontic loading is required. For this purpose, a three-dimensional finite element model of incisor tooth, periodontal ligament, and bone was built utilizing the hydro-mechanical coupling theory. Tooth displacement in response to orthodontic loading was then investigated, and the effect of different mechanical behaviors assigned to the solid phase of the periodontal ligament was compared. Results showed that where the periodontal ligament was placed in tension, pore volume was filled with fluid intake from the bone, but fluid flow direction was from the periodontal ligament toward the bone where the periodontal ligament was placed in compression. Because of the existence of interaction between solid and fluid phases of the periodontal ligament, considering biphasic material formulation was capable to address its microscopic behavior as well as time-dependent and large deformation behaviors. This article provides beneficial biomechanical data for future dental studies in determination of optimal orthodontic force.

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.

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 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.

Molecular Basis for Periodontal Ligament Adaptation to In Vivo Loading

A soft food diet leads to changes in the periodontal ligament (PDL). These changes, which have been recognized for more than a century, are ascribed to alterations in mechanical loading. While these adaptive responses have been well characterized, the molecular, cellular, and mechanical mechanisms underlying the changes have not. Here, we implicate Wnt signaling in the pathoetiology of PDL responses to underloading. We show that Wnt-responsive cells and their progeny in the PDL space exhibit a burst in proliferation in response to mastication. If an animal is fed a soft diet from the time of weaning, then this burst in Wnt-responsive cell proliferation is quelled; as a consequence, both the PDL and the surrounding alveolar bone undergo atrophy. Returning these animals to a hard food diet restores the Wnt signaling in PDL. These data provide, for the first time, a molecular mechanism underlying the adaptive response of the PDL to loading.

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.

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.

Modeling stress-relaxation behavior of the periodontal ligament during the initial phase of orthodontic treatment

The periodontal ligament is the tissue that provides early tooth motion as a result of applied forces during orthodontic treatment: a force-displacement behavior characterized by an instantaneous displacement followed by a creep phase and a stress relaxation phase. Stress relaxation behavior is that which provides the long-term loading to and causes remodelling of the alveolar bone, which is responsible for the long-term permanent displacement of the tooth. In this study, the objective was to assess six viscoelastic models to predict stress relaxation behavior of rabbit periodontal ligament (PDL). Using rabbit stress relaxation data found in the literature, it was found that the modified superposition theory (MST) model best predicts the rabbit PDL behavior as compared to nonstrain-dependent and strain-dependent versions of the Burgers four-parameter and the five-parameter viscoelastic models, as well as predictions by Schapery's viscoelastic model. Furthermore, it is established that using a quadratic form for MST strain dependency provides more stable solutions than the cubic form seen in previous studies.