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.     

Finite element simulation of the behavior of the periodontal ligament: A validated nonlinear contact model

Due to its significance in tooth movement, the stress/deformation field of periodontium and the alveolar bone remodeling process, periodontal ligament (PDL) cannot be excluded from the studies investigating dental biomechanics regarding its excessive deformability. Therefore, many analytical and numerical researches are carried out to simulate its response and to create a constitutive model via experiments intending to discover the material properties of PDL. The aim of this study is to formulate a user specified contact model that can be used in conjunction with finite element (FE) software and reflects PDL’s influence on neighboring structures based on the currently available information, without requiring an actual volumetric finite element mesh of ligament. The results show good agreement with available experimental tooth mobility data. Smooth stress fields are obtained on the tooth root and alveolar bone, which is a significant aspect in bone-remodeling studies. The advantage of simulating PDL as a contact model at the interface of tooth root and the alveolar process instead of a solid-meshed FE model with poor geometric morphology and/or very dense mesh is expected to save pre/post-processing workforce, to increase the accuracy and to contribute to the smoothness of interface stress distributions.     

Response of the tooth-periodontal ligament-bone complex to load: A microCT study of the minipig molar

One strategy evolved by teeth to avoid irreversible damage is to move and deform under the loads incurred during mastication. A key component in this regard is the periodontal ligament (PDL). The role of the bone underlying the PDL is less well defined. We study the interplay between the PDL and the underlying alveolar bone when loaded in the minipig. Using an Instron loading device we confirmed that the force-displacement curves of the molars and premolars of relatively fresh minipig intact mandibles are similar to those obtained for humans and other animals. We then used this information to obtain 3D images of the teeth before and after loading the tooth in a microCT such that the load applied is in the third linear part of the force displacement curve. We observed that at many locations there is a complimentary topography of the cementum and alveolar bone surface, strongly suggesting an active interplay between the tooth and the bone during mastication. We also observed that the loaded tooth does not come into direct contact with the underlying bone surface. A highly compressed layer of PDL is present between the tooth and the bone. The structure of the bone in the upper furcation region has a unique appearance with little obvious microstructure, abundant pores that have a large size range and at many locations the bone at the PDL interface has a needle-like shape. We conclude that there is a close interaction between the tooth, the PDL and the underlying alveolar bone during mastication. The highly compressed PDL layer that separates the tooth from the bone may fulfill a key shock absorbing function.     

The divergent expression of periostin mRNA in the periodontal ligament during experimental tooth movement

A novel 90-kDa protein named periostin, which is preferentially expressed in the periosteum and the periodontal ligament (PDL), may play a role in bone metabolism and remodeling. However, the precise role of periostin in the PDL remains unclear. Therefore, we examined the expression of periostin mRNA during experimental tooth movement. Experimental tooth movement was achieved in 7-week-old male Sprague-Dawley rats. In control specimens without tooth movement, the expression of periostin mRNA was uniformly observed in the PDL surrounding the mesial and distal roots of the upper molars and was weak in the PDL of the root furcation area. The periostin mRNA-expressing cells were mainly fibroblastic cells in the PDL and osteoblastic cells on the alveolar bone surfaces. The divergent expression of periostin mRNA in the PDL began to be observed at 3 h and continued up to 96 h after tooth movement. The maximum changes, which showed stronger staining in the pressure sites than in the tension sites, were observed at 24 h. The expression of periostin mRNA in the PDL 168 h after tooth movement exhibited a similar distribution to that of the control specimens. These results suggest that periostin is one of the local contributing factors in bone and periodontal tissue remodeling following mechanical stress during experimental tooth movement.     

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.     

Tensile and compressive behaviour of the bovine periodontal ligament

The mechanical response of the bovine periodontal ligament (PDL) subjected to uniaxial tension and compression is reported. Several sections normal to the longitudinal axis of bovine incisors and molars were extracted from different depths. Specimens with dimensions 10 x 5 x 2 mm including dentine, PDL and alveolar bone were obtained from these sections. Scanning electron microscopy suggested a strong similarity between the bovine PDL and the human PDL microstructure described in the literature. The prepared specimens were tested in a custom made uniaxial testing machine. They were clamped on their bone and dentine extremities and immersed in a saline solution at 37 degrees C. Stress-strain curves indicated that the PDL is characterized by a non-linear and time-dependent mechanical behaviour with the typical features of collagenous soft tissues. The curves exhibited hysteresis and preconditioning effects. The mechanical parameters evaluated in tension were maximum tangent modulus, strength, maximizer strain and strain energy density. For the molars, all these parameters increased with depth except for the apical region. For the incisors, all parameters increased with depth except ultimate strain which decreased. It was assumed that collagen fibre density and orientation were responsible for these findings.     

A biomechanical study of the human periodontal ligament

The mechanical properties of the normal human periodontal ligament (PDL) were investigated at eight different root levels. One millimetre transverse sections of teeth, PDL and alveolar bone of mandibular premolars were examined in a materials testing machine. During testing bone was supported by metal rings and teeth by metal cylinders of individually adjusted sizes. Having corrected for differences of size and width of the PDL the influence of root level was estimated using a multivariate analysis of variance. The shear strength was almost constant at the upper part of the root, diminishing in apical direction. The shear extensibility and the relative failure energy in shear were higher at the middle of the root, diminishing coronally and apically. Only the elastic stiffness did not vary significantly along the root. These results demonstrate that in order to compare the mechanical properties of PDL care should be taken to compare areas at the same root level.     

Mass acquisition of human periodontal ligament stem cells

The periodontal ligament (PDL) is an essential fibrous tissue for tooth retention in the alveolar bone socket. PDL tissue further functions to cushion occlusal force, maintain alveolar bone height, allow orthodontic tooth movement, and connect tooth roots with bone. Severe periodontitis, deep caries, and trauma cause irreversible damage to this tissue, eventually leading to tooth loss through the destruction of tooth retention. Many patients suffer from these diseases worldwide, and its prevalence increases with age. To address this issue, regenerative medicine for damaged PDL tissue as well as the surrounding tissues has been extensively investigated regarding the potential and effectiveness of stem cells, scaffolds, and cytokines as well as their combined applications. In particular, PDL stem cells (PDLSCs) have been well studied. In this review, I discuss comprehensive studies on PDLSCs performed in vivo and contemporary reports focusing on the acquisition of large numbers of PDLSCs for therapeutic applications because of the very small number of PDLSCs available in vivo.     

Numerical study of tension and strain distribution around rat molars]

A knowledge of the mechanical processes triggered in the bone and periodontal ligament (PDL) by orthodontic forces applied to a tooth is of decisive importance for an understanding of the subsequent remodelling around the tooth. To investigate these mechanical relationships, three-dimensional finite element (FE) models of the first lower molar in the rat were established. On the basis of digitized serial histological sections, these FE models were generated semi-automatically. Using various simplified geometrical variations, an appropriate FE model for the analysis of the stress and strain distributions was established. The numerical analyses were carried out under a mesially directed force of 0.1 N. Stress distributions in the bone and PDL showed a similar pattern, while strains in the bone were lower than in the PDL by a factor of 10-5. The data confirm the assumption that strain patterns in the PDL may be the key stimulus of bone remodelling.     

Tooth periodontal ligament: Direct 3D microCT visualization of the collagen network and how the network changes when the tooth is loaded

The periodontal ligament (PDL), a soft tissue connecting the tooth and the bone, is essential for tooth movement, bone remodeling and force dissipation. A collagenous network that connects the tooth root surface to the alveolar jaw bone is one of the major components of the PDL. The organization of the collagenous component and how it changes under load is still poorly understood. Here using a state-of-the-art custom-made loading apparatus and a humidified environment inside a microCT, we visualize the PDL collagenous network of a fresh rat molar in 3D at 1 μm voxel size without any fixation or contrasting agents. We demonstrate that the PDL collagen network is organized in sheets. The spaces between sheets vary thus creating dense and sparse networks. Upon vertical loading, the sheets in both networks are stretched into well aligned arrays. The sparse network is located mainly in areas which undergo compressive loading as the tooth moves towards the bone, whereas the dense network functions mostly in tension as the tooth moves further from the bone. This new visualization method can be used to study other non-mineralized or partially mineralized tissues, and in particular those that are subjected to mechanical loads. The method will also be valuable for characterizing diseased tissues, as well as better understanding the phenotypic expressions of genetic mutants.     

The effects of the periodontal ligament on mandibular stiffness: a study combining finite element analysis and geometric morphometrics

It is generally accepted that the periodontal ligament (PDL) plays a crucial role in transferring occlusal forces from the teeth to the alveolar bone. Studies using finite element analysis (FEA) have helped to better understand this role and show that the stresses and strains in the alveolar bone are influenced by whether and how PDL is included in FE models. However, when the overall distribution of stresses and strains in crania and mandibles are of interest, PDL is often not included in FE models, although little is known about how this affects the results. Here we study the effect of representing PDL as a layer of solid material with isotropic homogeneous properties in an FE model of a human mandible using a novel application of geometric morphometrics. The results show that the modelling of the PDL affects the deformation and thus strain magnitudes not only of the alveolar bone around the biting tooth, but that the whole mandible deforms differently under load. As a result, the strain in the mandibular corpus is significantly increased when PDL is included, while the strain in the bone beneath the biting tooth is reduced. These results indicate the importance of the PDL in FE studies. Thus we recommend that the PDL should be included in FE models of the masticatory apparatus, with tests to assess the sensitivity of the results to changes in the Young's modulus of the PDL material.     

The effects of modeling simplifications on craniofacial finite element models: the alveoli (tooth sockets) and periodontal ligaments

Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Young's modulus and Poisson's ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDL's material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress-strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.     

Tensile testing of the mechanical behavior of the human periodontal ligament

Background

The periodontal ligament (PDL) plays a key role in alveolar bone remodeling and resorption during tooth movements. The prediction of tooth mobility under functional dental loads requires a deep understanding of the mechanical behavior of the PDL, which is a critical issue in dental biomechanics. This study was aimed to examine the mechanical behavior of the PDL of the maxillary central and lateral incisors from human. The experimental results can contribute to developing an accurate constitutive model of the human PDL in orthodontics.

Methods

The samples of human incisors were cut into three slices. Uniaxial tensile tests were conducted under different loading rates. The transverse sections (cervical, middle and apex) normal to the longitudinal axis of the root of the tooth were used in the uniaxial tensile tests. Based on a bilinear simplification of the stress–strain relations, the elastic modulus of the PDL was calculated. The values of the elastic modulus in different regions were compared to explore the factors that influence the mechanical behavior of the periodontal ligament.

Results

The obtained stress–strain curves of the human PDL were characterized by a bilinear model with two moduli (E₁ and E₂) for quantifying the elastic behavior of the PDL from the central and lateral incisors. Statistically significant differences of the elastic modulus were observed in the cases of 1, 3, and 5 N loading levels for the different teeth (central and lateral incisors). The results showed that the mechanical property of the human incisors’ PDLs is dependent on the location of PDL (ANOVA, P?=?0.022, P?<?0.05). The elastic moduli at the middle planes were greater than at the cervical and apical planes. However, at the cervical, middle, and apical planes, the elastic moduli of the mesial and distal site were not significantly different (ANOVA, P?=?0.804, P?>?0.05).

Conclusions

The values of elastic modulus were determined in the range between 0.607 and 4.274 MPa under loads ranging from 1 to 5 N. The elastic behavior of the PDL is influenced by the loading rate, tooth type, root level, and individual variation.

     

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 M₁ 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 M₂ crypt. Overall, specimens with erupting M₁s were more deformable than specimens with occluding M₁s (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 M₁s, than those of occluding M₁s, 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.     

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 multipotent clonal human periodontal ligament cell line

Abstract The periodontal ligament (PDL) that anchors the tooth root to the alveolar bone influences the lifespan of the tooth, and PDL lost through periodontitis is difficult to regenerate. The development of new PDL-regenerative therapies requires the isolation of PDL stem cells. However, their characteristics are unclear due to the absence of somatic PDL stem cell lines and because PDL is composed of heterogeneous cell populations. Recently, we succeeded in immortalizing human PDL fibroblasts that retained the properties of the primary cells. Therefore, we aimed to establish a human PDL-committed stem cell line and investigate the effects of basic fibroblast growth factor (bFGF) on the osteoblastic differentiation of the cells. Here, we report the development of cell line 1–17, a multipotent clonal human PDL cell line that expresses the embryonic stem cell-related pluripotency genes Oct3/4 and Nanog , as well as the PDL-related molecules periostin and scleraxis. Continuous treatment of cell line 1–17 with bFGF in osteoblastic induction medium inhibited its calcification, with down-regulated expression of FGF-Receptor 1 ( FGF-R1 ), whereas later addition of bFGF potentiated its calcification. Furthermore, bFGF induced calcification of cell line 1–17 when it was co-cultured with osteoblastic cells. These results suggest that cell line 1–17 is a PDL-committed stem cell line and that bFGF exerts dualistic (i.e., promoting and inhibitory) effects on the osteoblastic differentiation of cell line 1–17 based on its differentiation stage.     

Dynamic shear properties of the porcine molar periodontal ligament

The role of the periodontal ligament (PDL) is to support the tooth during function and resist external forces applied to it. The dominant vertical component of these forces is associated with shear in the PDL. Little information, however, is available on the dynamic behavior of the PDL in shear. Therefore, the present study was designed to determine the dynamic shear properties of the PDL in the porcine molar (n=10). From dissected mandibles transverse sections of the mesial root of the first molar were obtained at the apical and coronal levels and used for dynamic shear tests. Shear strain (0.5%, 1.0%, and 1.5%) was applied in superoinferior direction parallel to the root axis with a wide range of frequencies (0.01-100 Hz). The dynamic complex and storage moduli increased significantly with the loading frequency, the dynamic loss modulus showed only a small increase. The dynamic elasticity was significantly larger in the coronal region than in the apical region although the dynamic viscosity was similar in both regions. The present results suggest that non-linearities, compression/shear coupling, and intrinsic viscoelasticity affect the shear material behavior of the PDL, which might have important implications for load transmission from tooth to bone and vice versa.     

Mechanical Response of Bone under Short-term Loading of a Dental Implant with an Internal Layer Simulating the Nonlinear Behaviour of the Periodontal Ligament

We consider a non-standard design for a fixed dental implant, incorporating a soft layer which simulates the presence of the periodontal ligament (PDL). Instead of being aimed at causing an a priori defined stress/strain field within the surrounding bone, upon loading, such a design simply tries to better reproduce the natural tooth–PDL configuration. To do this, the mechanical properties of the internal layer match those of the PDL, determined experimentally to be strongly nonlinear. Three-dimensional finite element analyses show that the presence of such a layer produces (i) a prosthesis mobility very similar to that of a healthy tooth, for several loading conditions, and (ii) a stress/strain distribution substantially different from that arising, upon loading, around a conventional implant. The lack of knowledge of the real mechanical fields existing, under loading, in the bone around a healthy tooth makes it very difficult to state that the stress distribution produced by the modified implant is “better” than that produced by the standard one. Nevertheless, the comparison of the results obtained here, with those of previous refined analyses of the tooth–PDL–bone system, indicates that the modified implant tends to produce a stress distribution in the bone, upon loading, closer to “natural” than that given by the standard one, within the limits imposed by the presence of threads coupling the implant with the bone.