Time-dependent mechanical behaviour of the periodontal ligament

Engineered 3D Periodontal Ligament Model with Magnetic Tensile Loading

In vitro models are invaluable tools for deconstructing the biological complexity of the periodontal ligament (PDL). Model systems that closely reproduce the 3-dimensional (3D) configuration of cell-cell and cell-matrix interactions in native tissue can deliver physiologically relevant insights. However, 3D models of the PDL that incorporate mechanical loading are currently lacking. Hence, we developed a model where periodontal tissue constructs (PTCs) are made by casting PDL cells in a collagen gel suspended between a pair of slender, silicone posts for magnetic tensile loading. Specifically, one of the posts was rigid and the other was flexible with a magnet embedded in its tip so that PTCs could be subjected to tensile loading with an external magnet. Additionally, the deflection of the flexible post could be used to measure the contractile force of PDL cells in the PTCs. Prior to tensile loading, second harmonics generation analysis of collagen fibers in PTCs revealed that incorporation of PDL cells resulted in collagen remodeling. Biomechanical testing of PTCs by tensile loading revealed an elastic response at 4 h, permanent deformation by 1 d, and creep elongation by 1 wk. Subsequently, contractile forces of PDL cells were substantially lower for PTCs under tensile loading. Immunofluorescence analysis revealed that tensile loading caused PDL cells to increase in number, express higher levels of F-actin and α-smooth muscle actin, and become aligned to the tensile axis. Second harmonics generation analysis indicated that collagen fibers in PTCs progressively remodeled over time with tensile loading. Gene expression analysis also confirmed tension-mediated upregulation of the F-actin/Rho pathway and osteogenic genes. Our model is novel in demonstrating the mechanobiological behavior that results in cell-mediated remodeling of the PDL tissue in a 3D context. Hence, it can be a valuable tool to develop therapeutics for periodontitis, periodontal regeneration, and orthodontics.

Exploring biological mechanisms in orthodontic tooth movement: Bridging the gap between basic research experiments and clinical applications - A comprehensive review

OBJECTIVES

The molecular mechanisms behind orthodontic tooth movements (OTM) were investigated by clarifying the role of chemical messengers released by cells.

METHODS

Using the Cochrane library, Google scholar, and PubMed databases, a literature search was conducted, and studies published from 1984 to 2024 were considered.

RESULTS

Both bone growth and remodeling may occur when a tooth is subjected to mechanical stress. These chemicals have a significant effect on the stimulation and regulation of osteoblasts, osteoclasts, and osteocytes during alveolar bone remodeling. This regulation can take place in pathological conditions, such as periodontal diseases, or during OTM alone. This comprehensive review outlines key molecular mechanisms underlying OTM and explores various clinical assumptions associated with specific molecules and their functional domains during this process. Furthermore, clinical applications of certain molecules such as relaxin, prostaglandin E (PGE), and interleukin-1β (IL-1β) in accelerating OTM have been reported. Our findings underscore the existing gap between OTM clinical applications and basic research investigations.

CONCLUSION

A comprehensive understanding of orthodontic treatment is enriched by insights into biological systems. We reported the activation of osteoblasts, osteoclast precursor cells, osteoclasts, and osteocytes in response to mechanical stress, leading to targeted cellular and molecular interventions and facilitating rapid and regulated alveolar bone remodeling during tooth movement. Despite the shortcomings of clinical studies in accelerating OTM, this review highlights the crucial role of biological agents in this process and advocates for prioritizing high-quality human studies in future research to gain further insights from clinical trials.

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.

Rational design of viscoelastic hydrogels for periodontal ligament remodeling and repair

The periodontal ligament (PDL) is a distinctive yet critical connective tissue vital for maintaining the integrity and functionality of tooth-supporting structures. However, PDL repair poses significant challenges due to the complexity of its mechanical microenvironment encompassing hard-soft-hard tissues, with the viscoelastic properties of the PDL being of particular interest. This review delves into the significant role of viscoelastic hydrogels in PDL regeneration, underscoring their utility in simulating biomimetic three-dimensional microenvironments. We review the intricate relationship between PDL and viscoelastic mechanical properties, emphasizing the role of tissue viscoelasticity in maintaining mechanical functionality. Moreover, we summarize the techniques for characterizing PDL's viscoelastic behavior. From a chemical bonding perspective, we explore various crosslinking methods and characteristics of viscoelastic hydrogels, along with engineering strategies to construct viscoelastic cell microenvironments. We present a detailed analysis of the influence of the viscoelastic microenvironment on cellular mechanobiological behavior and fate. Furthermore, we review the applications of diverse viscoelastic hydrogels in PDL repair and address current challenges in the field of viscoelastic tissue repair. Lastly, we propose future directions for the development of innovative hydrogels that will facilitate not only PDL but also systemic ligament tissue repair. STATEMENT OF SIGNIFICANCE.

Mechanobiology of orthodontic tooth movement: An update

The purpose of this review is to provide an update on the changes at the cellular and tissue level occurring during orthodontic force application. For the understanding of this process, knowledge of the mechanobiology of the periodontal ligament and the alveolar bone are essential. The periodontal ligament and alveolar bone make up a functional unit that undergoes robust changes during orthodontic tooth movement. Complex molecular signaling is responsible for converting mechanical stresses into biochemical events with a net result of bone apposition and/or bone resorption. Despite an improved understanding of mechanical and biochemical signaling mechanisms, it is largely unknown how mechanical stresses regulate the differentiation of stem/progenitor cells into osteoblast and osteoclast lineages. To advance orthodontics, it is crucial to gain a better understanding of osteoblast differentiation from mesenchymal stem/progenitor cells and osteoclastogenesis from the hematopoietic/monocyte lineage.

The optimal activation of plastic aligner for canine distal movement: a three-dimensional finite element analysis

This study aimed to investigate the optimal activation of plastic aligner for the canine distal movement by combining the stress and strain of periodontal ligament. Computer-aided design models of the upper canine, periodontal ligament, alveolar bone, and plastic aligner were constructed. The stresses and strains of periodontal ligament were acquired by fitting plastic aligner on the canine, which will cause the canine distal-direction movement. The activation of plastic aligner was set into 12 groups, including 0.050, 0.100, 0.125, 0.150, 0.175, 0.200, 0.225, 0.250, 0.275, 0.300, 0.350, and 0.400 mm. Assuming the volume-averaged hydrostatic stress (VAHS) ranging from 4.7 to 16 kPa to be the optimal stress, and an average strain no less than 0.3 to be the optimal strain. The optimal activation of plastic aligner was acquired based on the optimal stress and average strain. As the activation increased, the stress and strain of periodontal ligament increased visibly. The degree of activation of plastic aligner was nonlinearly and positively related to VAHS and average strain. According to the fitted curves, the activation corresponding to the optimal stress was 0.07-0.24 mm and the activation was not less than 0.21 mm based on the optimal strain. The optimal activation of plastic aligner for the canine distal movement was 0.21-0.24 mm in this study. The degree of activation affects the force system of orthodontic tooth movement, and it should be taken into consideration to obtain healthy and efficient tooth movement. The activation with 0.21-0.24 mm seems optimal for orthodontic tooth movement in the plastic aligner system in this study.

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.

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

INTRODUCTION

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

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.

In situ AFM-based nanoscale rheology reveals regional non-uniformity in viscoporoelastic mechanical behavior of the murine periodontal ligament

The periodontal ligament (PDL) is a critical player in the maintenance of tooth health, acting as the primary stabilizer of tooth position. Recent studies have identified two unique regions within the PDL, the 'dense collar' region and the 'furcation' region, which exhibit distinct structural and compositional differences. However, specific functional differences between these regions have yet to be investigated. We adapted an AFM-based nanoscale rheology method to regionally assess mechanical properties and poroelasticity in the mouse PDL while minimizing the disruption of the 3-dimensional native boundary conditions, and then explored tissue mechanical function in four different regions within the dense collar as well as in the furcation region. We found significant differences between the collar and furcation regions, with the collar acting as a stabilizing ligamentous structure and the furcation acting as both a compressive cushion for vertical forces and a conduit for nutrient transport. While this finding supports our hypothesis, based on previous studies investigating structural and compositional differences, we also found surprising inhomogeneity within the collar region itself. This inhomogeneity supports previous findings of a tilting movement in the buccal direction of mandibular molar teeth and the structural adaptation to prevent lingual movement. Future work will aim to understand how different regions of the PDL change functionally during biological or mechanical perturbations, such as orthodontic tooth movement, development, or aging, with the ultimate goal of better understanding the mechanobiology of the PDL function in health and disease.

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.

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.

The impact of digging on the evolution of the rodent mandible

There are two main (but not mutually exclusive) methods by which subterranean rodents construct burrows: chisel-tooth digging, where large incisors are used to dig through soil; and scratch digging, where forelimbs and claws are used to dig instead of incisors. A previous study by the authors showed that upper incisors of chisel-tooth diggers were better adapted to dig but the overall cranial morphology within the rodent sample was not significantly different. This study analyzed the lower incisors and mandibles of the specimens used in the previous study to show the impact of chisel-tooth digging on the rodent mandible. We compared lower incisors and mandibular shape of chisel-tooth digging rodents with nonchisel-tooth digging rodents to see if there were morphological differences between the two groups. The shape of incisors was quantified using incisor radius of curvature and second moment of area (SMA). Mandibular shape was quantified using landmark based geometric morphometrics. We found that lower incisor shape was strongly influenced by digging group using a Generalized Phylogenetic ancova (analysis of covariance). A phylogenetic Procrustes anova (analysis of variance) showed that mandibular shape of chisel-tooth digging rodents was also significantly different from nonchisel-tooth digging rodents. The phylogenetic signal of incisor radius of curvature was weak, whereas that of incisor SMA and mandibular shape was significant. This is despite the analyses revealing significant differences in the shape of both mandibles and incisors between digging groups. In conclusion, we showed that although the mandible and incisor of rodents are influenced by function, there is also a degree of phylogenetic affinity that shapes the rodent mandibular apparatus.

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.

New finite element study protocol: Clinical simulation of orthodontic tooth movement

The aim of this work was to model tooth movement in a more clinically-exact fashion, thanks to the use of new IT tools and imaging systems (cone-beam). Image segmentation and 3D reconstruction now enable us to model the anatomy realistically, while finite element (FE) analysis makes it possible to evaluate stresses and their distribution on the level of the tooth, the periodontal ligament (PDL) and the alveolar bone when a force is applied. The principle is to monitor tooth movement by obtaining optical impressions at each stage of treatment. The model corresponds to a genuine clinical situation. FE analysis is correlated with the clinically-observed displacement. The protocol remains long and complex. It nevertheless makes it possible to obtain, throughout the duration of treatment, patient-specific models that can be exploited using finite element methods. It requires further validation in more thorough studies but offers interesting prospects: precise study of induced tooth movement, distribution of stresses in the PDL, and development of a customized previsualization tool.

Restorative material and loading type influence on the biomechanical behavior of wedge shaped cervical lesions

OBJECTIVES

To evaluate the influence of restorative materials used on the rehabilitation of MOD cavities and loading type, on biomechanical behavior of wedge-shaped (WS) lesions in endodontically treated maxillary premolars. The investigation was conducted by 3D finite element analysis (FEA) and strain gauge test.

MATERIALS AND METHODS

Six models were generated, with MOD cavities and endodontic treatment: A (MOD amalgam restoration), R (MOD composite restoration), AL (A + cervical lesion (L)), RL, ALR (A + cervical lesion restored with composite (LR)), and RLR. Each model underwent two compressive loading (100N): axial and oblique-45° angle to the long axis on the buccal cusp. The models were analyzed by von Mises criteria. For strain gauge test, 14 standardized maxillary premolars were treated according to the groups described for FEA. Two strain gauges were bonded on each sample submitted to compressive loading in a mechanical testing machine.

RESULTS

A presented higher stress concentration and strain values than R. Oblique loading promoted highest stress concentration and strain rates for all groups. ALR and RLR presented similar stress-strain distribution pattern when compared to A and R.

CONCLUSION

The interaction between MOD cavity restored with amalgam and oblique loading propitiated the highest stress concentration and strain values on cervical region and WS lesion.

CLINICAL RELEVANCE

The MOD cavity restored with composite resin is a better option than amalgam to improve the biomechanical behavior of wedge-shaped lesion, avoiding dental failure. In addition, the occlusal interferences must be removed, allowing homogeneous contact distribution and preventing WS lesion progression.

Predicting the holistic force-displacement relation of the periodontal ligament: in-vitro experiments and finite element analysis

BACKGROUND

The biomechanical property of the periodontal ligament (PDL) is important in orthodontics and prosthodontics. The objective of this study was to evaluate the feasibility of measuring the biomechanical behavior of the periodontal ligament using micro-computed tomography (micro-CT).

METHODS

A custom-made apparatus measured the force and displacement of a porcine PDL specimen within the micro-CT environment. Synchronized computed tomography (CT) images were used to obtain the deformation and displacement of the entire specimen and to reconstruct the three-dimensional mesh model. To match the experimental results, finite element analysis was then applied to simulate the biomechanical response of the PDL. The mechanical model of the PDL was assumed as the hyperelastic material in this study.

RESULTS

The volume variations of the tooth and the alveolar bone were less than 1%, which implies that tooth displacement was caused mostly by displacement of the PDL. Only translational displacement was observed with each load step because the transformation matrix acquired from the CT image registration was identical. The force-displacement curve revealed the nonlinear behavior of the PDL. There was a high correlation between the experimental displacement results and the simulation displacement results. The numerical results (based on the assumption that the PDL is the hyperelastic material) showed good agreement with the experimental results.

CONCLUSIONS

Nondestructive measurements by micro-CT obtained the biomechanical behavior of the PDL. Using the hyperelastic characteristic as the constitutive model can properly predict the force-displacement relation of the PDL after loading. This study provided a feasible approach for measuring the biomechanical behavior of the PDL for further dental application.

The biomechanical function of periodontal ligament fibres in orthodontic tooth movement

Orthodontic tooth movement occurs as a result of resorption and formation of the alveolar bone due to an applied load, but the stimulus responsible for triggering orthodontic tooth movement remains the subject of debate. It has been suggested that the periodontal ligament (PDL) plays a key role. However, the mechanical function of the PDL in orthodontic tooth movement is not well understood as most mechanical models of the PDL to date have ignored the fibrous structure of the PDL. In this study we use finite element (FE) analysis to investigate the strains in the alveolar bone due to occlusal and orthodontic loads when PDL is modelled as a fibrous structure as compared to modelling PDL as a layer of solid material. The results show that the tension-only nature of the fibres essentially suspends the tooth in the tooth socket and their inclusion in FE models makes a significant difference to both the magnitude and distribution of strains produced in the surrounding bone. The results indicate that the PDL fibres have a very important role in load transfer between the teeth and alveolar bone and should be considered in FE studies investigating the biomechanics of orthodontic tooth movement.

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.

Estimation of periodontal ligament's equivalent mechanical parameters for finite element modeling

INTRODUCTION

Young's modulus (E) and Poisson's ratio (v) of the periodontal ligament are needed in a finite element analysis for investigating the biomechanical behavior of a tooth, periodontal ligament, and bone complex. However, large discrepancies in E (0.01-1,750 MPa) and v (0.28-0.49) were reported previously. The objective of this study was to narrow the ranges and to provide equivalent E and v pairs suitable for finite element modeling of a tooth, periodontal ligament, and bone complex by using a reported crown load-displacement relationship as the criterion.

METHODS

A 3-dimensional finite element model of a 3-tooth, periodontal ligament, and bone complex, consisting of a maxillary central incisor with 2 adjacent teeth, from a cone-beam computed tomography scan was created. The dimensions, constraints, and loading condition were kept similar to those reported in the human study. With the load applied to the crown, both v and E were adjusted independently, and the corresponding crown displacements were calculated. The resulting load-displacement curves were compared with those reported in the human study. The mean absolute displacement difference method was used to find the best fit. The E and v pairs that generated the minimum mean absolute displacement difference were identified.

RESULTS

The finite element model with 1 of the 3 E and v pairs (v = 0.35, E = 0.87 MPa; v = 0.4, E = 0.71 MPa; and v = 0.45, E = 0.47 MPa) simulated the tooth, periodontal ligament, and bone complex well. The mean absolute displacement differences were 0.0135, 0.0138, and 0.0138 mm, respectively; these are less than 8% of 0.175 mm, which was the crown displacement of the tooth, periodontal ligament, and bone complex under the load of 500 cN.

CONCLUSIONS

The E and v values close to the 3 pairs might be used for finite element modeling of the tooth, periodontal ligament, and bone complex.

The oxytalan fibre network in the periodontium and its possible mechanical function

The biomechanical character of the periodontal ligament (PDL) is crucial in its response to functional and orthodontic forces. Collagen has been the primary subject of investigations in this field. Several studies, however, indicate that oxytalan fibres, which belong to the elastic fibre family, also contribute to the biomechanical character and behaviour of the PDL. In order to elucidate this, we have evaluated the available literature on the oxytalan fibre network within the PDL and supra-alveolar tissues with respect to development, morphology and distribution, and response to mechanical stimulation. To this end, we have combined the classical histological studies with more recent in vitro studies. Oxytalan fibres develop simultaneously with the root and the vascular system within the PDL. A close association between oxytalan fibres and the vascular system also remains later in life, suggesting a role in vascular support. Mechanical loading of the PDL, through orthodontic force application, appears to induce an increase in the number, size, and length of oxytalan fibres. In line with this, in vitro stretching of PDL fibroblasts (PDLFs) results in an increased production of fibrillin, a major structural component of the microfibrils that make up oxytalan fibres. The available data suggest a mechanical function for oxytalan, but to date experimental data are limited. Further research is required to clarify their exact mechanical function and possible role in orthodontic tooth movement.

Appropriateness of viscoelastic soft materials as in vitro simulators of the periodontal ligament

The periodontal ligament is a viscoelastic soft tissue that connects the tooth to the alveolar bone. This tissue should be simulated in numerical as well as in laboratory models. The mechanical properties of this tissue were previously determined ex vivo and in vivo. The aim of the study was to analyse the appropriateness of impression and reline materials used in dentistry to simulate viscoelastic behaviour of the periodontal ligament. Two reline [Durabase (Reliance Dental MFG, Co.) and Soft Liner (GC Corporation)] and two impression [President Plus (Coltene) and Prestige L (Vanini Dental Industry)] materials were examined in recovery and tensile relaxation tests. Recovery: This experiment simulated in vivo test. Roots of a pair of plastic maxillary premolar teeth were covered with each test material and embedded in acryl while maintaining the contact point. A 0·1-mm stainless steel strip, inserted at the contact point and maintained for 10 s, was used to tip the teeth. After removal, the tightness of dental contact point was measured over 30 min by determining the force needed to insert a 0·05-mm metal strip. Tensile relaxation: strips were elongated to 120%, 140% and 160% of their initial length and maintained at that length for 30 min. Two-phase decay function was applied. The results showed that elastic modulus and relaxation behaviour were significantly different between materials. Elastic modulus values were in the same range of those reported in the literature. However, the recovery values and behaviour showed that impression materials, especially President, are the materials of choice for this purpose because they simulated better the in vivo test.

Mechanism of action and morphologic changes in the alveolar bone in response to selective alveolar decortication-facilitated tooth movement

BACKGROUND AND PURPOSE

The aim of this study was to test if corticotomy-induced osteoclastogenesis and bone remodeling underlie orthodontic tooth movement and how selective alveolar decortication enhances the rate of tooth movement.

MATERIALS AND METHODS

A total of 114 Sprague-Dawley rats were included in 3 treatment groups: selective alveolar decortication alone (SADc); tooth movement alone (TM); and "combined" therapy (SADc + TM). Surgery was performed around the buccal and palatal aspects of the left maxillary first molar tooth and included 5 decortication dots on each side. Tooth movement was performed on the first molar using a 25-g Sentalloy spring. Measurements were done at baseline (day 0: no treatment rendered) and on days 3, 7, 14, 21, 28 and 42. Microcomputed tomography, Faxitron analyses, and quantitative real-time polymerase chain reaction (q-PCR) of expressed mRNAs were used to assess changes.

RESULTS

The combined group showed increased tooth movement (P = 0.04) at 7 days compared with the tooth movement group with significantly decreased bone volume (62%; P = 0.016) and bone mineral content (63%; P = 0.015). RNA markers of osteoclastic cells and key osteoclastic regulators (M-CSF [macrophage colony-stimulating factor], RANKL [receptor activator of nuclear factor kappa-B ligand], OPG [osteoprotegerin], calcitonin receptor [CTR], TRACP-5b [tartrate-resistant acid phosphatase 5b], cathepsin K [Ctsk]) all showed expression indicating increased osteoclastogenesis in the combined group. RNA markers of osteoblastic cells (OPN [osteopontin], BSP [bone sialoprotein], OCN [osteocalcin]) also showed increased anabolic activity in response to the combination of alveolar decortication and tooth movement.

CONCLUSIONS

The data suggest that the alveolar decortication enhances the rate of tooth movement during the initial tooth displacement phase; this results in a coupled mechanism of bone resorption and bone formation during the earlier stages of treatment, and this mechanism underlies the rapid orthodontic tooth movement.

Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature

Introduction. This review is intended to highlight and discuss discrepancies in the literature of the periodontal ligament's (PDL) mechanical properties and the various experimental approaches used to measure them. Methods. Searches were performed on biomechanical and orthodontic publications (in databases: Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, and Scopus). Results. The review revealed that significant variations exist, some on the order of six orders of magnitude, in the PDL's elastic constants and mechanical properties. Possible explanations may be attributable to different experimental approaches and assumptions. Conclusions. The discrepancies highlight the need for further research into PDL properties under various clinical and experimental loading conditions. Better understanding of the PDL's biomechanical behavior under physiologic and traumatic loading conditions might enhance the understanding of the PDL's biologic reaction in health and disease. Providing a greater insight into the response of the PDL would be instrumental to orthodontists and engineers for designing more predictable, and therefore more efficacious, orthodontic appliances.

The mechanical function of the periodontal ligament in the macaque mandible: a validation and sensitivity study using finite element analysis

Whilst the periodontal ligament (PDL) acts as an attachment tissue between bone and tooth, hypotheses regarding the role of the PDL as a hydrodynamic damping mechanism during intraoral food processing have highlighted its potential importance in finite element (FE) analysis. Although experimental and constitutive models have correlated the mechanical function of the PDL tissue with its anisotropic, heterogeneous, viscoelastic and non-linear elastic nature, in many FE simulations the PDL is either present or absent, and when present is variably modelled. In addition, the small space the PDL occupies and the inability to visualize the PDL tissue using μCT scans poses issues during FE model construction and so protocols for the PDL thickness also vary. In this paper we initially test and validate the sensitivity of an FE model of a macaque mandible to variations in the Young's modulus and the thickness of the PDL tissue. We then tested the validity of the FE models by carrying out experimental strain measurements on the same mandible in the laboratory using laser speckle interferometry. These strain measurements matched the FE predictions very closely, providing confidence that material properties and PDL thickness were suitably defined. The FE strain results across the mandible are generally insensitive to the absence and variably modelled PDL tissue. Differences are only found in the alveolar region adjacent to the socket of the loaded tooth. The results indicate that the effect of the PDL on strain distribution and/or absorption is restricted locally to the alveolar bone surrounding the teeth and does not affect other regions of the mandible.

Three-dimensional morphometry of strained bovine periodontal ligament using synchrotron radiation-based tomography

The periodontal ligament (PDL) is a highly vascularized soft connective tissue. Previous studies suggest that the viscous component of the mechanical response may be explained by the deformation-induced collapse and expansion of internal voids (i.e. chiefly blood vessels) interacting with liquids (i.e. blood and interstitial fluids) flowing through the pores. In the present work we propose a methodology by means of which the morphology of the PDL vascular plexus can be monitored at different levels of compressive and tensile strains. To this end, 4-mm-diameter cylindrical specimens, comprising layers of bone, PDL and dentin covered by cementum, were strained at stretch ratios ranging from lambda = 0.6 to lambda = 1.4 and scanned using synchrotron radiation-based computer tomography. It was concluded that: (1) the PDL vascular network is layered in two distinct planes of blood vessels (BVs): an inner layer (close to the tooth), in which the BVs run in apico-coronal direction, and an outer layer (close to the alveolar bone), in which the BVs distribution is more diffuse; (2) during tension and compression, the porosity tissue is kept fairly constant; (3) mechanical straining induces important changes in BV diameters, possibly modifying the permeability of the PDL and thus contributing to the viscous component of the viscoelastic response observed under compressive forces.

Effect of sulfated glycosaminoglycan digestion on the transverse permeability of medial collateral ligament

Dermatan and chondroitin sulfate glycosaminoglycans (GAGs) comprise over 90% of the GAG content in ligament. Studies of their mechanical contribution to soft tissues have reported conflicting results. Measuring the transient compressive response and biphasic material parameters of the tissue may elucidate the contributions of GAGs to the viscoelastic response to deformation. The hypotheses of the current study were that digestion of sulfated GAGs would decrease compressive stress and aggregate modulus while increasing the permeability of porcine medial collateral ligament (MCL). Confined compression stress relaxation experiments were carried out on porcine MCL and tissue treated with chondroitinase ABC (ChABC). Results were fit to a biphasic constitutive model to derive permeability and aggregate modulus. Bovine articular cartilage was used as a benchmark tissue to verify that the apparatus provided reliable results. GAG digestion removed up to 88% of sulfated GAGs from the ligament. Removal of sulfated GAGs increased the permeability of porcine MCL nearly 6-fold versus control tissues. Peak stress decreased significantly. Bovine articular cartilage exhibited the typical reduction of GAG content and resultant decreases in stress and modulus and increases in permeability with ChABC digestion. Given the relatively small amount of GAG in ligament (<1% of tissue dry weight) and the significant change in peak stress and permeability upon removal of GAGs, sulfated GAGs may play a significant role in maintaining the apposition of collagen fibrils in the transverse direction, thus supporting dynamic compressive loads experienced by the ligament during complex joint motion.

Functional cues in the development of osseous tooth support in the pig, Sus scrofa

Alveolar bone supports teeth during chewing through a ligamentous interface with tooth roots. Although tooth loads are presumed to direct the development and adaptation of these tissues, strain distribution in the alveolar bone at different stages of tooth eruption and periodontal development is unknown. This study investigates the biomechanical effects of tooth loading on developing alveolar bone as a tooth erupts into occlusion. Mandibular segments from miniature pigs, Sus scrofa, containing M(1) either erupting or in functional occlusion, were loaded in compression. Simultaneous recordings were made from rosette strain gages affixed to the lingual alveolar bone and the M(2) crypt. Overall, specimens with erupting M(1)s were more deformable than specimens with occluding M(1)s (mean stiffness of 246 vs. 944 MPa, respectively, p=0.004). The major difference in alveolar strain between the two stages was in orientation. The vertically applied compressive loads were more directly reflected in the alveolar bone strains of erupting M(1)s, than those of occluding M(1)s, presumably because of the mediation of a more mature periodontal ligament (PDL) in the latter. The PDL interface between occluding teeth and alveolar bone is likely to stiffen the system, allowing transmission of occlusal loads. Alveolar strains may provide a stimulus for bone growth in the alveolar process and crest.

Mechanisms of tooth eruption and orthodontic tooth movement

Teeth move through alveolar bone, whether through the normal process of tooth eruption or by strains generated by orthodontic appliances. Both eruption and orthodontics accomplish this feat through similar fundamental biological processes, osteoclastogenesis and osteogenesis, but there are differences that make their mechanisms unique. A better appreciation of the molecular and cellular events that regulate osteoclastogenesis and osteogenesis in eruption and orthodontics is not only central to our understanding of how these processes occur, but also is needed for ultimate development of the means to control them. Possible future studies in these areas are also discussed, with particular emphasis on translation of fundamental knowledge to improve dental treatments.

Acceleration of orthodontic tooth movement by alveolar corticotomy in the dog

INTRODUCTION

Tooth movement and alveolar bone reaction after corticotomies have not been thoroughly examined. In this study, the effects of corticotomies on orthodontic tooth movement and alveolar bone reaction were investigated in dogs.

METHODS

Corticotomies were performed on the cortical bone of the mandibular left third premolar region in 12 male adult beagles. The third premolars on the left experimental side and on the right sham side were moved mesially with a continuous force of 0.5 N.

RESULTS

Tooth movement velocities from 0 to 1 week and from 1 to 2 weeks after the corticotomies were significantly faster on the experimental side than on the sham side. Hyalinization of the periodontal ligament appeared only at 1 week after the corticotomies on the experimental sides, whereas it was observed from 1 to 4 weeks after the corticotomies on the sham sides. Tartrate-resistant-acid-phosphatase positive cells of the experimental side tended to work vigorously at an early time on the alveolar wall and in the bone marrow cavities.

CONCLUSIONS

Orthodontic tooth movement increased for at least 2 weeks after the corticotomies. This might be brought about by rapid alveolar bone reaction in the bone marrow cavities, which leads to less hyalinization of the periodontal ligament on the alveolar wall.

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.