Mechanics of the maxillary central incisor. Influence of the periodontal ligament represented by beam elements

This study aimed to evaluate the influence of loading on a maxillary central incisor with the periodontal ligament (PDL) represented by 2D elastic beam elements using a 2D finite element analysis. Two models (M) were built varying the PDL representation: Mh (homogeneous PDL) and Mht (heterogeneous PDL with beam3 elements). Stress and displacements were determined for three loading conditions (L): Ll, lingual face loading at 45° with the tooth long axis; Li, perpendicular to the incisal edge; and Lip, on the incisal edge, parallel to the tooth long axis. Evaluation was performed on ANSYS software. Lip provided lower stress variation on the tooth and support structures when compared to Ll and Li. PDL's influence on stress values was lower for Lip. Oblique loading showed stress and displacement not observed in parallel loading condition through PDL's heterogeneous representation and it is probably incompatible with the in vivo condition.     

Investigation of effective intrusion and extrusion force for maxillary canine using finite element analysis

Abstract

Orthodontic tooth movement is mainly regulated by the biomechanical responses of loaded periodontal ligament (PDL). We investigated the effective intervals of orthodontic force in pure maxillary canine intrusion and extrusion referring to PDL hydrostatic stress and logarithmic strain. Finite element analysis (FEA) models, including a maxillary canine, PDL and alveolar bone, were constructed based on computed tomography (CT) images of a patient. The material properties of alveolar bone were non-uniformly defined using HU values of CT images; PDL was assumed to be a hyperelastic–viscoelastic material. The compressive stress and tensile stress ranging from 0.47 to 12.8?kPa and 18.8 to 51.2?kPa, respectively, were identified as effective for tooth movement; a strain 0.24% was identified as the lower limit of effective strain. The stress/strain distributions within PDL were acquired in canine intrusion and extrusion using FEA; root apex was the main force-bearing area in intrusion–extrusion movements and was more prone to resorption. Owing to the distinction of PDL biomechanical responses to compression and tension, the effective interval of orthodontic force was substantially lower in canine intrusion (80–90?g) than in canine extrusion (230–260?g). A larger magnitude of force remained applicable in canine extrusion. This study revised and complemented orthodontic biomechanical behaviours of tooth movement with intrusive–extrusive force and could further help optimize orthodontic treatment.     

A periodontal ligament driven remodeling algorithm for orthodontic tooth movement

While orthodontic tooth movement (OTM) gains considerable popularity and clinical success, the roles played by relevant tissues involved, particularly periodontal ligament (PDL), remain an open question in biomechanics. This paper develops a soft-tissue induced external (surface) remodeling procedure in a form of power law formulation by correlating time-dependent simulation in silico with clinical data in vivo (p<0.05), thereby providing a systematic approach for further understanding and prediction of OTM. The biomechanical stimuli, namely hydrostatic stress and displacement vectors experienced in PDL, are proposed to drive tooth movement through an iterative hyperelastic finite element analysis (FEA) procedure. This algorithm was found rather indicative and effective to simulate OTM under different loading conditions, which is of considerable potential to predict therapeutical outcomes and develop a surgical plan for sophisticated orthodontic treatment.     

Experimental model of tooth mobility in the human "in vivo"]

The aim of the present study was to investigate experimentally the mechanical properties of tooth deflection under external loading. These properties have a significant impact on tooth movement during orthodontic treatment. The stresses and strains caused by tooth movement influence bone remodelling, which is the basis of orthodontic treatment. The movement of a tooth as a direct reaction to the forces acting on it is termed "initial" movement. It is nonlinear and has a clearly time-dependent component. While the initial tooth movement represents the totality of the reaction mechanisms of all the tissues of the tooth unit, it is determined primarily by the mechanical properties of the periodontal ligament (PDL). The PDL is the softest tissue of the tooth unit and is therefore subject to the largest deformations when forces act on the crown of the tooth. The objective of orthodontic treatment is to achieve as precise and rapid tooth movement as possible, without provoking such undesired effects as bone and root resorption. To enable the implementation of an optimal orthodontic force system that meets these requirements, a thorough knowledge of the biomechanics of tooth movement is a must.     

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.     

A visco-elastic model for the prediction of orthodontic tooth movement

This study presents a biomechanical model of orthodontic tooth movement. Although such models have already been presented in the literature, most of them incorporate computationally expensive finite elements (FE) methods to determine the strain distribution in the periodontal ligament (PDL). In contrast, the biomechanical model presented in this work avoids the use of FE methods. The elastic deformation of the PDL is modelled using an analytical approach, which does not require setting up a 3D model of the tooth. The duration of the lag phase is estimated using the calculated hydrostatic stresses, and bone remodelling is predicted by modelling the alveolar bone as a viscous material. To evaluate the model, some typically used motion patterns were simulated and a sensitivity analysis was carried out on the parameters. Results show that despite some shortcomings, the model is able to describe commonly used motion patterns in orthodontic tooth movement, in both single- and multi-rooted teeth.     

Focal adhesion kinase mediates β-catenin signaling in periodontal ligament cells

Periodontal ligament (PDL) cells convert the orthodontic forces into biological responses by secreting signaling molecules to induce modeling of alveolar bone and tooth movement. Beta-catenin pathway is activated in response to mechanical loading in PDL cells. The upstream signaling pathways activated by mechanical loading resulting in the activation of β-catenin pathway through Wnt-independent mechanism remains to be characterized. We hypothesized that mechanical loading induces activation of β-catenin signaling by mechanisms that dependent on focal adhesion kinase (FAK) and nitric oxide (NO). We found that mechanical or pharmacological activation of β-catenin signaling in PDL cells upregulated the expression of β-catenin target genes. Pre-treatment of PDL cells with FAK inhibitor-14 prior to mechanical loading abolished the mechanical loading-induced phosphorylation of Akt and dephosphorylation of β-catenin. PDL cells pre-treated with NO donor or NO inhibitor and subjected to mechanical loading. Western blot analysis showed that the mechanical loading or pre-treatment with NO donor increased the levels of dephosphorylated β-catenin, pAkt, and pGSK-3β. Pre-treatment with NO inhibitor blocked the mechanical loading-induced phosphorylation of Akt and dephosphorylation of β-catenin. These data indicate that mechanical loading-induced β-catenin stabilization in PDL cells involves phosphorylation of Akt by two parallel pathways requiring FAK and NO.     

Mechanical stress alters protein O‐GlcNAc in human periodontal ligament cells

Protein O‐linked N‐acetylglucosamine (O‐GlcNAc) is a post‐translational modification of intracellular proteins that regulates several physiological and pathophysiological process, including response to various stressors. However, O‐GlcNAc's response to mechanical stress has not been investigated yet. As human periodontal ligament (PDL) cells are stimulated by compression force during orthodontic tooth movement that results in structural remodelling, in this study we investigated whether mechanical stress induces any alteration in protein O‐GlcNAc in PDL cells. In this study, PDL cells isolated from premolars extracted for orthodontic indications were exposed to 0, 1.5, 3, 7 and 14 g/cm² compression forces for 12 hours. Cell viability was measured by flow cytometry, and protein O‐GlcNAc was analysed by Western blot. Cellular structure and intracellular distribution of O‐GlcNAc was studied by immunofluorescence microscopy. We found that between 1.5 and 3 g/cm² mechanical compression, O‐GlcNAc significantly elevated; however, at higher forces O‐GlcNAc level was not increased. We also found that intracellular localization of O‐GlcNAc proteins became more centralized under 2 g/cm² compression force. Our results suggest that structural changes stimulated by compression forces have a significant effect on the regulation of O‐GlcNAc; thus, it might play a role in the mechanical stress adaptation of PDL cells.     

Strain-dependent up-regulation of ephrin-B2 protein in periodontal ligament fibroblasts contributes to osteogenesis during tooth movement

During orthodontic tooth movement, the application of adequate orthodontic forces allows teeth to be moved through the alveolar bone. These forces are transmitted through the periodontal ligaments (PDL) to the supporting alveolar bone and lead to deposition or resorption of bone, depending on whether the tissues are exposed to a tensile or compressive mechanical strain. Fibroblasts within the PDL (PDLF) are considered to be mechanoresponsive. The transduction mechanisms from mechanical loading of the PDLF to the initiation of bone remodeling are not clearly understood. Recently, members of the ephrin/Eph family have been shown to be involved in the regulation of bone homeostasis. For the first time, we demonstrate that PDLF exposed to tensile strain induce the expression of ephrin-B2 via a FAK-, Ras-, ERK1/2-, and SP1-dependent pathway. Osteoblasts of the alveolar bone stimulated with ephrin-B2 increased their osteoblastogenic gene expression and showed functional signs of osteoblastic differentiation. In a physiological setting, ephrin-B2-EphB4 signaling between PDLF and osteoblasts of the alveolar bone might contribute to osteogenesis at tension sites during orthodontic tooth movement.     

Development of a novel intraoral measurement device to determine the biomechanical characteristics of the human periodontal ligament

Periodontal diseases like gingivitis and periodontitis have damaging effects on the periodontium and commonly affect the mechanical properties of the periodontal ligament (PDL), which in the end might lead to loss of teeth. Monitoring tooth mobility and changes of the material properties of the PDL might help in early diagnosis of periodontal diseases and improve their prognosis. It was the aim of this study to develop a novel intraoral device to determine the biomechanical characteristics of the periodontal ligament. This includes the measurement of applied forces and resulting tooth displacement in order to investigate the biomechanical behaviour of the periodontium with varying loading protocols with respect to velocity and tooth displacement. The developed device uses a piezoelectric actuator to apply a displacement to a tooth's crown, and the resulting force is measured by an integrated force sensor. To measure the tooth displacement independently and non-invasively, two magnets are fixed on the teeth. The change in the magnetic field caused by the movement of the magnets is measured by a total of 16 Hall sensors. The displacement of the tooth is calculated from the movement of the magnets. The device was tested in vitro on premolars of four porcine mandibular segments and in vivo on two volunteers. The teeth were loaded with varying activation curves. Comparing the force progression of different activation velocities, the forces decreased with decreasing velocity. Intensive testing demonstrated that the device fulfils all requirements. After acceptance of the ethical committee, further testing in clinical measurements is planned.     

Mechanical responses of the periodontal ligament based on an exponential hyperelastic model: a combined experimental and finite element method

The V–W exponential hyperelastic model is adopted to describe the instantaneous elastic response of the periodontal ligament (PDL). The general theoretical framework of constitutive modeling is described based on nonlinear continuum mechanics, and the elasticity tensor used to develop UMAT subroutine is formulated. Nanoindentation experiment is performed to characterize mechanical properties of an adult pig PDL specimen. Then the experiment is simulated by using the finite element (FE) analysis. Meanwhile, the optimized material parameters are identified by the inverse FE method. The good agreement between the simulated results and experimental data demonstrates that the V–W model is capable of describing the mechanical behavior of the PDL. Therefore, the model and its implementation into FE code are validated. By using the model, we simulate the tooth movement under orthodontic loading to predict the mechanical responses of the PDL. The results show that local concentrations of stress and strain in the PDL are found.     

Expression of UNCL during development of periodontal tissue and response of periodontal ligament fibroblasts to mechanical stress in vivo and in vitro

Mutations in two genes, uncoordinated (unc) and uncoordinated-like (uncl), lead to a failure of mechanotransduction in Drosophila. UNCL, the human homolog of unc and uncl, is preferentially expressed in periodontal ligament (PDL) fibroblasts compared with gingival fibroblasts. However, the precise role of UNCL in the PDL remains unclear. The aim of the present study has been to examine whether mechanical stimuli modulate the expression of UNCL in the human PDL in vivo and in vitro and to examine the roles of UNCL in the development, regeneration, and repair of the PDL. We have investigated the expression pattern of UNCL during the development of periodontal tissue and the response of PDL fibroblasts to mechanical stress in vivo and in vitro. The expression of UNCL mRNA and protein increases with PDL fibroblast differentiation from the confluent to multilayer stage but slightly decreases on mineralized nodule formation. UNCL has also been localized in ameloblasts and adjacent cells, differentiating cementoblasts, and osteoblasts of the developing tooth. Strong distinct UNCL expression has further been observed in the differentiating cementoblasts of the tooth periodontium at the site of tension after orthodontic tooth movement. Application of cyclic mechanical stress on PDL fibroblasts increases the expression of UNCL mRNA. These results indicate that UNCL plays important roles in the development, differentiation, and maintenance of periodontal tissues and also suggest a potential role of UNCL in the mechanotransduction of PDL fibroblasts.This work was supported by a grant from the Korea Health 21R&D Project, Ministry of Health & Welfare, Republic of Korea (03-PJ1-PG1-CH08-0001).     

Role of Mechanical Stress-induced Glutamate Signaling-associated Molecules in Cytodifferentiation of Periodontal Ligament Cells

In this study, we analyzed the effects of tensile mechanical stress on the gene expression profile of in vitro-maintained human periodontal ligament (PDL) cells. A DNA chip analysis identified 17 up-regulated genes in human PDL cells under the mechanical stress, including HOMER1 (homer homolog 1) and GRIN3A (glutamate receptor ionotropic N-methyl-d-aspartate 3A), which are related to glutamate signaling. RT-PCR and real-time PCR analyses revealed that human PDL cells constitutively expressed glutamate signaling-associated genes and that mechanical stress increased the expression of these mRNAs, leading to release of glutamate from human PDL cells and intracellular glutamate signal transduction. Interestingly, exogenous glutamate increased the mRNAs of cytodifferentiation and mineralization-related genes as well as the ALP (alkaline phosphatase) activities during the cytodifferentiation of the PDL cells. On the other hand, the glutamate signaling inhibitors riluzole and (+)-MK801 maleate suppressed the alkaline phosphatase activities and mineralized nodule formation during the cytodifferentiation and mineralization. Riluzole inhibited the mechanical stress-induced glutamate signaling-associated gene expressions in human PDL cells. Moreover, in situ hybridization analyses showed up-regulation of glutamate signaling-associated gene expressions at tension sites in the PDL under orthodontic tooth movement in a mouse model. The present data demonstrate that the glutamate signaling induced by mechanical stress positively regulates the cytodifferentiation and mineralization of PDL cells.     

Experimental-numerical analysis of minipig's multi-rooted teeth

The paper pertains to the analysis of the biomechanical behaviour of the periodontal ligament (PDL) by using a combined experimental and numerical approach. Experimental analysis provides information about a two-rooted pig premolar tooth in its socket with regard to morphological configuration and deformational response. The numerical analysis developed for the present investigation adopts a specific anisotropic hyperelastic formulation, accounting for tissue structural arrangement. The parameters to be adopted for the PDL constitutive model are evaluated with reference to data deducted from experimental in vitro tests on different specimens taken from literature. According to morphometric data relieved, solid models are provided as basis for the development of numerical models that adopt the constitutive formulation proposed. A reciprocal validation of experimental and numerical data allows for the evaluation of reliability of results obtained. The work is intended as preliminary investigation to study the correlation between mechanical status of PDL and induction to cellular activity in orthodontic treatments.     

Histochemical examination of cathepsin K,MMP1 and MMP2 in compressed periodontal ligament during orthodontic tooth movement in periostin deficient mice

The purpose of this study was to investigate immunolocalization of collagenolytic enzymes including cathepsin K, matrix metalloproteinase (MMP) 1 and 2 in the compressed periodontal ligament (PDL) during orthodontic tooth movement using a periostin deficient (Pn-/-) mouse model. Twelve-week-old male mice homozygous for the disrupted periostin gene and their wild type (WT) littermates were used in these experiments. The tooth movement was performed according to Waldo’s method, in which elastic bands of 0.5 mm thickness were inserted between the first and second upper molars of mice under anesthesia. At 1 and 3 days after orthodontic force application, mice were fixed with transcardial perfusion of 4 % paraformaldehyde in 0.1 M phosphate buffer (pH 7.4), and the first molars and peripheral alveolar bones were extracted for histochemical analyses. Compared with WT mice, immunolocalization of cathepsin K, MMP1 and MMP2 was significantly decreased at 1 and 3 days after orthodontic tooth movement in the compressed PDL of Pn-/- mice, although MMP1-reactivity and MMP2-reactivity decreased at different amounts. Very little cathepsin K-immunoreactivity was observed in the assessed regions of Pn-/- mice, both before and after orthodontic force application. Furthermore, Pn-/- mice showed a much wider residual PDL than WT mice. Taken together, we concluded that periostin plays an essential role in the function of collagenolytic enzymes like cathepsin K, MMP1 and MMP2 in the compressed PDL after orthodontic force application.     

HSPA1A is upregulated in periodontal ligament at early stage of tooth movement in rats

Heat shock proteins (HSPs) are molecular chaperones that maintain intracellular protein homeostasis and ensure survival of cells. Continuous orthodontic force on the tooth is considered to be a type of physical stress loaded to the periodontal ligament (PDL). However, little is known about the role of HSPs during tooth movement. This study was performed to examine the expression of HSPs in the PDL during tooth movement using laser microdissection, microarray analysis, real-time RT-PCR and immunohistochemistry. Gene expression of HSPA1A in the pressure zone of the PDL was higher during 6 h of tooth movement than in the control group. Expression of HSPA1A decreased with time. HSPA1A was also detected in the pressure zone of the PDL at the protein level 24 h after the initial tissue change. These results strongly suggest that expression of HSPA1A in the PDL during early stages of tooth movement is a critical factor for tissue reaction.     

A mechanobiological model of orthodontic tooth movement

Orthodontic tooth movement is achieved by the process of repeated alveolar bone resorption on the pressure side and new bone formation on the tension side. In order to optimize orthodontic treatment, it is important to identify and study the biological processes involved. This article presents a mechanobiological model using partial differential equations to describe cell densities, growth factor concentrations, and matrix densities occurring during orthodontic tooth movement. We hypothesize that such a model can predict tooth movement based on the mechanobiological activity of cells in the PDL. The developed model consists of nine coupled non-linear partial differential equations, and two distinct signaling pathways were modeled: the RANKL–RANK–OPG pathway regulating the communication between osteoblasts and osteoclasts and the TGF-β pathway mediating the differentiation of mesenchymal stem cells into osteoblasts. The predicted concentrations and densities were qualitatively validated by comparing the results to experiments reported in the literature. In the current form, the model supports our hypothesis, as it is capable of conceptually simulating important features of the biological interactions in the alveolar bone—PDL complex during orthodontic tooth movement.     

Mechanical stress regulates osteogenic differentiation and RANKL/OPG ratio in periodontal ligament stem cells by the Wnt/β-catenin pathway

BackgroundThe balance between osteoblastic and osteoclastic activity is critical in orthodontic tooth movement (OTM). Mesenchymal stem cells (MSCs) play an important role in maintaining bone homeostasis, and periodontal ligament stem cells (PDLSCs) are tissue-specific MSCs in the periodontal ligament. However, whether PDLSCs are required for periodontal tissue remodeling during OTM is not fully understood.MethodsHere, we used PDGFRα and Nestin to trace PDLSCs during OTM in rats. We treat human PDLSCs with 100 kpa static pressure for 1 h or 12 h in vitro, and examined the phenotypic changes and expression of RANKL and OPG in these cells.ResultsIn vivo, we found that positive signals of PDGFRα and Nestin in the PDL gradually increased and then decreased on the pressure side to which pressure was applied. In vitro, the osteogenic differentiation of PDLSCs was significantly increased after force treatment for 1 h relative to 12 h. In contrast, the expression ratio of RANKL/OPG was reduced at 1 h and significantly increased at 12 h. Furthermore, we found that the Wnt/β-catenin pathway was dynamically activated in the PDL and in PDLSCs after mechanical stimulation. Importantly, the canonical Wnt pathway inhibitor DKK1 blocked the osteogenesis effect and rescued the ratio of RANKL/OPG in PDLSCs under force treatment for 1 h.ConclusionsOur findings reveal that PDLSCs participate in OTM and that the Wnt/β-catenin pathway maintains bone homeostasis during tooth movement by regulating the balance between osteoblastic and osteoclastic activity.General significanceWe describe a novel potential mechanism related to tooth movement.     

Differential expression of osteoblast and osteoclast chemmoatractants in compression and tension sides during orthodontic movement

Orthodontic tooth movement is achieved by the remodeling of alveolar bone in response to mechanical loading, and is supposed to be mediated by several host mediators, such as chemokines. In this study we investigated the pattern of mRNAs expression encoding for osteoblast and osteoclast related chemokines, and further correlated them with the profile of bone remodeling markers in palatal and buccal sides of tooth under orthodontic force, where tensile (T) and compressive (C) forces, respectively, predominate. Real-time PCR was performed with periodontal ligament mRNA from samples of T and C sides of human teeth submitted to rapid maxillary expansion, while periodontal ligament of normal teeth were used as controls. Results showed that both T and C sides exhibited significant higher expression of all targets when compared to controls. Comparing C and T sides, C side exhibited higher expression of MCP-1/CCL2, MIP-1α/CCL3 and RANKL, while T side presented higher expression of OCN. The expression of RANTES/CCL5 and SDF-1/CXCL12 was similar in C and T sides. Our data demonstrate a differential expression of chemokines in compressed and stretched PDL during orthodontic tooth movement, suggesting that chemokines pattern may contribute to the differential bone remodeling in response to orthodontic force through the establishment of distinct microenvironments in compression and tension sides.