Three-dimensional finite element analysis of the maxillary central incisor in two different situations of traumatic impact

Dental trauma is one of the most common events in dental practice. However, few studies have investigated the biomechanical characteristics of these injuries. The objective of this study was to analyse the stress distribution in the dentoalveolar structures of a maxillary central incisor subjected to two situations of impact loading. The following loading forces were applied using a 3D finite element model: a force of 2000 N acting at an angle of 90°on the buccal surface of the crown and a vertical 2000 N force acting in the cleidocranial direction on the incisal surface of the tooth. Harmful stresses were observed in both situations, causing damage to both the tooth and adjacent tissue. However, the damage found in soft tissues such as periodontal ligament and dental pulp was negligible. In conclusion, injuries resulting from the traumatic situations were more damaging to the integrity of the tooth and its associated hard-tissue structures.     

Experiments to determine the time dependent material properties of the periodontal ligament]

The periodontal ligament is a tissue that attaches the tooth (root) to its alveolar socket, and thus plays an important role in the regulation of tooth movements. Detailed knowledge of the material properties of the periodontal ligament is therefore essential to an understanding of tooth reaction to forces applied during orthodontic treatment. A knowledge of material parameters can also be used in simulations of long-term tooth movements with the aim of improving orthodontic treatment. To this end, this study investigated time-dependent material properties, namely the hysteresis behaviour of the periodontal ligament under constant-velocity loading, the influence of loading velocity on the hysteresis, and its failure under constant loading. Specimens obtained from pigs were used for testing purposes, and the experiments were conducted in a special test setup using a material testing device. The material behaviour of the periodontal ligament was shown to be viscoelastic, and the elastic parameters of material behaviour were also determined. Under constant-velocity loading, material behaviour showed a nonlinear course of the stress-strain curve, also known as hysteresis. When loading was repeated several times, the maximum stress of the hysteresis decreased with each cycle. Determination of the deflection of the specimen at different velocities showed maximum stress to be dependent on the loading rate. The measured stress-strain curves were approximated by bilinear behaviour, permitting the use of finite element calculations. Also investigated was the failure behaviour of the periodontal ligament, which revealed tissue rupture to be inconstant.     

Structure of the periodontal ligament during tooth eruption in the dog: descriptive aspects

Serially stained uncalcified sections of young dog mandibles were examined to study the structure of the periodontal ligament of the erupting first right molar. The periodontal ligament around tooth crown presents three zones. The first, near the dental follicle, is a tick layer of parallel collagen bundles with numerous flattened fibroblasts. The second, intermediate, contains a blood vessels network, particularly veins and capillaries. The third, outer, is occupied by a continuous layer of osteoclasts and osteoblasts. Also the periodontal ligament around the tooth presents three layers, the outer and the intermediate rich of cells more than the inner. Particularly, the outer layer shows numerous osteoblasts surrounding the developing trabeculae of the alveolar bone and the collagen fiber bundles of the periodontal ligament. These penetrate into the trabeculae and appear similar to the osteoid layer. These results indicate that the alveolar bone increases by ossification of the connective tissue of the periodontal ligament.     

Time-related PDL: viscoelastic response during initial orthodontic tooth movement of a tooth with functioning interproximal contact-a mathematical model

Most anteroposterior orthodontic movements of posterior teeth have to overcome the "resistance" of adjacent teeth with functioning interproximal contacts. The aim of this study was to develop a mathematical model describing initial posterior tooth movement associated with functioning interproximal contacts in relation to the viscoelastic mechanical behavior of the human periodontal ligament (PDL). A linear viscoelastic 2D mathematical model was modified to depict tipping movement around the center of rotation (C(rot)) of a premolar where tipping is restrained by adjacent teeth. Equilibrium equations were applied taking into account the sagittal moment developed around the C(rot). The constants of the model were analyzed and applied to a numerical model that can simulate short-term tooth creep movement caused by a tipping force. Changes in force magnitude (0.5-3N) and crown length (6-10mm) were analyzed until no movement was observed (steady state). Premolar displacement in contact with adjacent teeth showed a non-linear progression over time with an initial sharp tipping movement followed by a transient period of 2.6-7.1min. As tipping force increased the transient period increased. A similar but smaller effect was observed with an increase in crown length. The premolar initial displacement within the arch (3.2-19.5microm) is about seven-fold smaller than retraction/protraction movement of an incisor. These suggest reduction in tooth displacement when functioning interproximal contact is present and clinically recommend establishing a space in the direction of tooth displacement before tooth movement.     

The use of functionally graded dental crowns to improve biocompatibility: a finite element analysis

In post-core crown restorations, the significant mismatch between stiffness of artificial crowns and dental tissues leads to stress concentration at the interfaces. The aim of the present study was to reduce the destructive stresses by using a class of inhomogeneous materials called functionally graded materials (FGMs). For the purpose of the study, a 3-dimentional computer model of a premolar tooth and its surrounding tissues were generated. A post-core crown restoration with various crown materials, homogenous and FGM materials, were simulated and analyzed by finite element method. Finite element and statistical analysis showed that, in case of oblique loading, a significant difference (p < 0.05) was found at the maximum von Mises stresses of the crown margin between FGM and homogeneous crowns. The maximum von Mises stresses of the crown margin generated by FGM crowns were lower than those generated by homogenous crowns (70.8 vs. 46.3 MPa) and alumina crown resulted in the highest von Mises stress at the crown margin (77.7 MPa). Crown materials of high modulus of elasticity produced high stresses at the cervical region. FGM crowns may reduce the stress concentration at the cervical margins and consequently reduce the possibility of fracture.     

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.     

Quiescent epithelial cell rests of Malassez can differentiate into ameloblast-like cells

Epithelial cell rests of Malassez (ERM) are quiescent epithelial remnants of Hertwig's epithelial root sheath (HERS) that are involved in the formation of tooth roots. After completion of crown formation, HERS are converted from cervical loop cells, which have the potential to generate enamel for tooth crown formation. Cervical loop cells have the potential to differentiate into ameloblasts. Generally, no new ameloblasts can be generated from HERS, however this study demonstrated that subcultured ERM can differentiate into ameloblast-like cells and generate enamel-like tissues in combination with dental pulp cells at the crown formation stage. Porcine ERM were obtained from periodontal ligament tissue by explant culture and were subcultured with non-serum medium. Thereafter, subcultured ERM were expanded on 3T3-J2 feeder cell layers until the tenth passage. The in vitro mRNA expression pattern of the subcultured ERM after four passages was found to be different from that of enamel organ epithelial cells and oral gingival epithelial cells after the fourth passage using the same expansion technique. When subcultured ERM were combined with subcultured dental pulp cells, ERM expressed cytokeratin14 and amelogenin proteins in vitro. In addition, subcultured ERM combined with primary dental pulp cells seeded onto scaffolds showed enamel-like tissues at 8 weeks post-transplantation. Moreover, positive staining for amelogenin was observed in the enamel-like tissues, indicating the presence of well-developed ameloblasts in the implants. These results suggest that ERM can differentiate into ameloblast-like cells.     

The characteristics of epithelial cell rests of Malassez during tooth eruption of development mice

It has been demonstrated that Hertwig’s epithelial root sheath (HERS) has an important role in root development, closely related to development of cementum epithelial rests of Malassez (ERM) as the residuum after HERS fragment, and is the exclusive epithelial structure in the mature periodontal ligament. Some studies reported that ERM may play a role in maintaining a stable environment of periodontal, and likely to be involved in regeneration of periodontal tissue, especially of cementum. However, the function of the ERM is not well understood. In this study, we observed the morphology and biological characteristics of ERM of the maxillary 1st molar with surrounding periodontal tissues of BALB/c mice during the period of tooth cusp erupted out of the gingiva to occlusion stability. Immunohistochemistry revealed ERM predominately located at the cervical and root furcation regions of the periodontal ligament. The number of ERM cells at the cervical and root furcation regions of the post-built occlusion stage decreased compared to pre-built occlusion stage and occlusion building stage. Transmission electron microscopy analysis showed that epithelial cell nuclei with typical features of apoptosis were observed at the post-built occlusion stage, and consistent with positive bodies labeled by TUNEL(terminal deoxy-transferase (TdT)-mediated dUTP-biotin nick end labeling), while proliferating cell nuclear antigen positive bodies mainly located at occlusion built stage. It suggests that ERM may regulate in alveolar bone remodeling in association with the periodontal ligament during tooth erupting to occlusion stability and may play important roles potentially in regeneration and homeostasis of the periodontal tissues.     

牙周膜成骨分化研究进展

牙周膜是位于牙根与牙槽骨之间的结缔组织,具有自我更新和多向分化的能力。无论是在正畸治疗还是在牙周组织修复及再生过程中,牙周膜的成骨分化都是必不可少的。近年来,许多国内外学者致力于研究影响牙周膜成骨分化的因素,包括机械力,细胞因子,药物等,这些因素可以单独作用于牙周膜,也可以联合使用加快牙周膜成骨分化,可以为临床上加快牙齿移动和修复牙周组织缺损提供更多新的思路。现就影响牙周膜成骨分化的诸多因素及其主要机制作一综述。     

A micromechanically-based, three-dimensional interface finite element for the modelling of the periodontal ligament

Some ideas are presented for the implementation of an interface finite element capable to model in 3-dimensions several mechanical features of the periodontal ligament. Such an element is based on a simple 2-cable micromechanical model, able to reproduce the periodontal ligament stiffness and strength under any loading condition, including the pure torsion of a tooth. A single cable represents a sufficiently populated sample of collagen fibres, each with an initially crimped geometry; a single collagen fibre can provide a mechanical response, in tension, only when it is completely uncoiled. The macroscopic interface behaviour is obtained by statistical integrations over the uncoiled length of each collagen fibre, up to the fibre failure. Such a model can reproduce the periodontal ligament anisotropy due to the variable fibre orientation along the tooth root, its different behaviour in tension/compression/shear, its different behaviour for extrusive/intrusive loading, and so forth. Some numerical examples illustrate the potentialities of this interface element, quite simple in essence but rather complete from an engineering viewpoint.     

Determination of stress levels and profiles in the periodontal ligament by means of an improved three-dimensional finite element model for various types of orthodontic and natural force systems

This study was undertaken to investigate the stress-strain levels and distribution within the periodontal ligament for various types of physiological and orthodontic force systems, assuming that the bone resorption process, leading to tooth movements, is partly controlled by those conditions. Two finite element models were developed, simulating a full and partial mandibular morphology, respectively. Both models were based on morphology and physical parameters of human autopsy material. The effect of changing material parameters and structure, type of boundary conditions, calculation method and fineness of the model on the stress levels and profiles in the periodontal ligament was evaluated by a series of tests. A structure optimization technique was used to investigate the load bearing characteristics of the mandible and the influence of the anisotropic material properties of both the mandible and the segment. A ‘multiple modelling’ technique based on both the mandible and the segment was developed to test various types of boundary conditions in the analysis of the segment. Results presented as ‘stress profiles’ showing the correlation between the applied force system and the stress distribution in the periodontal ligament, based on the improved finite element models, were established.     

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.     

Effect of variable periodontal ligament thickness and its non-linear material properties on the location of a tooth’s centre of resistance

In orthodontics, the 3D translational and rotational movement of a tooth is determined by the force–moment system applied and the location of the tooth’s centre of resistance (CR). Because of the practical constraints of in-vivo experiments, the finite element (FE) method is commonly used to determine the CR. The objective of this study was to investigate the geometric model details required for accurate CR determination, and the effect of material non-linearity of the periodontal ligament (PDL). A FE model of a human lower canine derived from a high-resolution µCT scan (voxel size: 50 µm) was investigated by applying four different modelling approaches to the PDL. These comprised linear and non-linear material models, each with uniform and realistic PDL thickness. The CR locations determined for the four model configurations were in the range 37.2–45.3% (alveolar margin: 0%; root apex: 100%). We observed that a non-linear material model introduces load-dependent results that are dominated by the PDL regions under tension. Load variation within the range used in clinical orthodontic practice resulted in CR variations below 0.3%. Furthermore, the individualized realistic PDL geometry shifted the CR towards the alveolar margin by 2.3% and 2.8% on average for the linear and non-linear material models, respectively. We concluded that for conventional clinical therapy and the generation of representative reference data, the least sophisticated modelling approach with linear material behaviour and uniform PDL thickness appears sufficiently accurate. Research applications that require more precise treatment monitoring and planning may, however, benefit from the more accurate results obtained from the non-linear constitutive law and individualized realistic PDL geometry.     

Enlarged occlusal surfaces on first molars due to severe attrition and hypercementosis: examples from prehistoric coastal populations of Texas

During an examination of prehistoric samples from the Texas coast, individuals consistently exhibited a suite of traits on the first molars that included severe wear, hypercementosis, and resorption of the buccal margin of the alveolus. The occlusal surface of the tooth was worn below the cervical margin, with the subsequent incorporation of the buccal surface of the buccal roots into the occlusal plane. This expanded occlusal surface, which extends the buccal surface beyond the normal edge of the tooth, is composed of a combination of original enamel, secondary dentin, and cementum. There is a marked rounding of the buccal aspect of the occlusal surface. These conditions were noted in both maxillary and mandibular first molars. The resorption of alveolar bone surrounding the buccal roots resembles resorption associated with periodontal infection and is thought to be the result of severe levels of stress being applied to this portion of the dentition.     

正畸牙移动相关信号通路研究进展

<正>畸牙移动是在机械力的作用下,通过对牙周膜产生牵张或压缩的力来引起牙周组织在生理限度内的组织改建,从而达到牙齿移动、矫治畸形的目的。由于没有明显的年龄限制,正畸矫治在全球范围已变得越来越普遍。因此,相关的研究也日益增多。牙齿移动的生物学基础是正畸力作用于牙周组织激活一系列信号转导通路,进而引起牙周膜的修复改建。为指导临床、加速正畸矫治疗程提供新的思路,本文综述了近年来有关正畸牙移动相关信号通路的研究进展。发现最新的研究集中在MAPK信号通路,Wnt/β-catenin信号通路,PI3K/AKt/m TOR信号通路,BMP-2信号通路,Caspase-3介导的凋亡通路较多。但是正畸牙移动引起的牙周组织改建是一个多种生物力学信号转导通路相互调节相互作用的过程,对于上述信号通路之间的相互关系还有待于我们更进一步的探索。     

Matrix metalloproteinase 2 activity decreases in human periodontal ligament fibroblast cultures submitted to simulated orthodontic force

Orthodontic force compresses the periodontal ligament promoting the expression of pro-inflammatory mediators and matrix metalloproteinases responsible for tooth movement. The extent in time while periodontal cells are being treated and the increment in the amount of mechanical stress caused by the orthodontic force is thought to regulate the levels of metalloproteinases in the periodontal tissue. To study the possible regulation in the activity of metalloproteinases 2, 3, 7, 9, and 10 by simulated orthodontic force, human periodontal ligament fibroblast cultures were centrifuged (141×g) for 30, 60, 90, and 120 min, simulating the orthodontic force. Cell viability, protein quantification, and activity of metalloproteinases by zymography were evaluated at 24, 48, and 72 h after centrifugation in both cell lysates and growth medium. The activity of the 72-kDa matrix metalloproteinase 2 was decreased at 24 h regardless of the duration of centrifugation and at 48 h in cells centrifuged for 30 min only. Decrease in the amount of total protein in lysates was seen at 48 and 72 h with no change in cell viability. The data seem to indicate that the amount of mechanical stress regulates the levels of secreted matrix metalloproteinase 2. In addition, the centrifugation as a model for simulated orthodontic force may be used as a simple and reliable method to study the role played by matrix metalloproteinases in periodontal ligament when submitted to mechanical force as occurring during tooth movement.     

Epithelial rests of Malassez express immunoreactivity of TrkA and its distribution is regulated by sensory nerve innervation.

The periodontal ligament is the connective tissue that fills the space between the tooth and its bony socket. It is abundantly innervated by the sensory and sympathetic nerves. We first investigated the immunoreactivity of TrkA, which is a high-affinity receptor of nerve growth factor (NGF), in the periodontal ligament of rats. Immunoreactivity was observed at the epithelial cells in the cervical and furcation regions of the molars. These epithelial cells, which gather together to form clusters or networks, are known as the epithelial rests of Malassez. Immunoreactivity was not observed in other non-neuronal cells, such as osteoblasts, fibroblasts, odontoblasts, cementoblasts, endothelial cells, and/or osteoclasts. On the basis of these findings, we investigated the possible involvement of sensory nerve innervation in the immunoreactivity of the epithelial cells. Denervation of the inferior alveolar nerve resulted in a marked decrease in the distribution area and size of the clusters of immunoreactive cells compared with those of sham-operated rats. These findings suggest that sensory nerve innervation may have a regulatory role in maintenance of the epithelial rests of Malassez expressing TrkA in the periodontal ligament.     

Comparison of dental measurement systems for taxonomic assignment of first molars

Morphometrics of the molar crown is based traditionally on diameter measurements but is nowadays more often based on 2D image analysis of crown outlines. An alternative approach involves measurements at the level of the cervical line. We compare the information content of the two options in a three-dimensional (3D) digital sample of lower and upper first molars (M(1) and M(1) ) of modern human and Neanderthal teeth. The cervical outline for each tooth was created by digitizing the cervical line and then sectioning the tooth with a best fit plane. The crown outline was projected onto this same plane. The curves were analyzed by direct extraction of diameters, diagonals, and area and also by principal component analysis either of the residuals obtained by regressing out these measurements from the radii (shape information) or directly by the radii (size and shape information). For M(1) , the crown and cervical outline radii allow us to discriminate between Neanderthals and modern humans with 90% and 95% accuracy, respectively. Fairly good discrimination between the groups (80-82.5%) was also obtained using cervical measurements. With respect to M(1) , general overlap of the two groups was obtained by both crown and cervical measurements; however, the two taxa were differentiable by crown outline residuals (90-97%). Accordingly, while crown diameters or crown radii should be used for taxonomic analysis of unworn or slightly worn M(1) s, the crown outline, after regressing out size information, could be promising for taxonomic assignment of lower M1s.     

Cryopreservation induces macrophage colony stimulating factor from human periodontal ligament cells in vitro

Cryopreservation is used to protect vital periodontal ligaments during the transplantation of teeth. We investigated which gene products implicated in root resorption are upregulated in human periodontal ligament cells by cryopreservation, and whether cryopreservation affects the expression of macrophage-colony stimulating factor (M-CSF) in human periodontal ligament cells. We used customized microarrays to compare gene expression in human periodontal ligament cells cultured from teeth immediately after extraction and from cryopreserved teeth. Based on the result of these assays, we examined M-CSF expression in periodontal ligament cells from the immediately extracted tooth and cryopreserved teeth by real-time PCR, enzyme-linked immunosorbent assay (ELISA), Western blot analysis, and immunofluorescence. We also investigated whether human bone marrow cells differentiate into tartrate-resistant acid phosphatase (TRAP) positive osteoclasts when stimulated with RANKL (Receptor Activator for Nuclear Factor κ B Ligand) together with any secreted M-CSF present in the supernatants of the periodontal ligament cells cultured from the various groups of teeth. M-CSF was twofold higher in the periodontal ligament cells from the rapid freezing teeth than in those from the immediately extracted group (p < 0.05). Cryopreservation increased M-CSF expression in the periodontal ligament cells when analyzed by real time PCR, ELISA, Western blotting, and immunofluorescence (p < 0.05). TRAP positive osteoclasts were formed in response to RANKL and the secreted M-CSF present in the supernatants of all the experimental groups except negative control. These results demonstrate that cryopreservation promotes the production of M-CSF, which plays an important role in root resorption by periodontal ligament cells.     

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.