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.     

Finite element analysis of stress distribution in intact and porcelain veneer restored teeth

The aim of this study was to investigate the stress distribution generated in a veneer restoration of an upper central incisor compared to intact teeth using the finite element analysis after applying a lingual buccal loading at the incisal edge. Methods: Two models were developed: one model contained enamel, dentine, cementum, periodontal ligament, cortical and trabecullar bones, and the other model was a veneer restoration; both models were developed using MSC/Nastran software (MacNeal-Schwendler Corporation, Los Angeles, CA, USA) as the pre- and post-processor. A 10-N load was applied at the incisal edge from the lingual to the buccal side to simulate oral conditions in this area (protrusion). Results: Von Mises stresses were then analysed for three different regions: A-B (enamel elements under the veneer or second enamel layer), A′-B′ (buccal enamel and/or veneer element layer) and C-D (lingual enamel elements layer). A higher stress mode was observed for both models at the lingual cervical region. Conclusions: The presence of a veneer restoration on the incisors is a good alternative to mimic the behaviour of enamel under protrusion loading conditions. The use of veneers to replace enamel during rehabilitations is recommended.     

Age-related and regional differences in the stress-strain and stress-relaxation behaviours of the rat incisor periodontal ligament

Groups of rats were killed at 2, 6, 12, and 24 months of age. From dissected left and right mandibles in each rat, three pairs of transverse sections were cut at the incisal, middle, and basal regions of the incisor. One section in each pair was loaded until failure and a stress-strain curve for the periodontal ligament (PDL) was obtained. The other section was loaded to up to 50% of the maximum shear stress as determined from the contralateral section and then kept at a constant strain for 10 min, to obtain the stress-relaxation curve at the same region of the PDL. The maximum shear stress and toughness increased with age at the incisal region and the maximum shear strain increased with age at the incisal and middle regions. The tangent modulus decreased with advancing age at the middle region. The stress-relaxation during 10 min decreased with advancing age at the incisal and basal regions, but not at the middle region. The relaxation process was well described by a sum of three exponential decay functions, reflecting the short-, medium-, and long-term relaxation components. The age-related decrease in the relaxation was mainly attributable to increases in the ratio and relaxation time of the long-term relaxation component. These results suggest that with advancing age the mechanical strength and toughness of the PDL are enhanced mostly at the incisal region and that the viscous fraction is relatively decreased at the incisal and basal regions along the long axis of the rat incisor.     

Brief communication: comparing loading scenarios in lower first molar supporting bone structure using 3D finite element analysis

Finite element analysis (FEA) is a widespread technique to evaluate the stress/strain distributions in teeth or dental supporting tissues. However, in most studies occlusal forces are usually simplified using a single vector (i.e., point load) either parallel to the long tooth axis or oblique to this axis. In this pilot study we show how lower first molar occlusal information can be used to investigate the stress distribution with 3D FEA in the supporting bone structure. The LM₁ and the LP²‐LM¹ of a dried modern human skull were scanned by μCT in maximum intercuspation contact. A kinematic analysis of the surface contacts between LM₁ and LP²‐LM¹ during the power stroke was carried out in the occlusal fingerprint analyzer (OFA) software to visualize contact areas during maximum intercuspation contact. This information was used for setting the occlusal molar loading to evaluate the stress distribution in the supporting bone structure using FEA. The output was compared to that obtained when a point force parallel to the long axis of the tooth was loaded in the occlusal basin. For the point load case, our results indicate that the buccal and lingual cortical plates do not experience notable stresses. However, when the occlusal contact areas are considered, the disto‐lingual superior third of the mandible experiences high tensile stresses, while the medio‐lingual cortical bone is subjected to high compressive stresses. Developing a more realistic loading scenario leads to better models to understand the relationship between masticatory function and mandibular shape and structures. Am J Phys Anthropol, 2012. © 2011 Wiley Periodicals, Inc.     

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.     

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.     

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).     

In situ Compressive Loading and Correlative Noninvasive Imaging of the Bone-periodontal Ligament-tooth Fibrous Joint

This study demonstrates a novel biomechanics testing protocol. The advantage of this protocol includes the use of an in situ loading device coupled to a high resolution X-ray microscope, thus enabling visualization of internal structural elements under simulated physiological loads and wet conditions. Experimental specimens will include intact bone-periodontal ligament (PDL)-tooth fibrous joints. Results will illustrate three important features of the protocol as they can be applied to organ level biomechanics: 1) reactionary force vs. displacement: tooth displacement within the alveolar socket and its reactionary response to loading, 2) three-dimensional (3D) spatial configuration and morphometrics: geometric relationship of the tooth with the alveolar socket, and 3) changes in readouts 1 and 2 due to a change in loading axis, i.e. from concentric to eccentric loads. Efficacy of the proposed protocol will be evaluated by coupling mechanical testing readouts to 3D morphometrics and overall biomechanics of the joint. In addition, this technique will emphasize on the need to equilibrate experimental conditions, specifically reactionary loads prior to acquiring tomograms of fibrous joints. It should be noted that the proposed protocol is limited to testing specimens under ex vivo conditions, and that use of contrast agents to visualize soft tissue mechanical response could lead to erroneous conclusions about tissue and organ-level biomechanics.     

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.

     

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.     

Finite element analysis of stress distribution in intact and porcelain veneer restored teeth

The aim of this study was to investigate the stress distribution generated in a veneer restoration of an upper central incisor compared to intact teeth using the finite element analysis after applying a lingual buccal loading at the incisal edge. Methods: Two models were developed: one model contained enamel, dentine, cementum, periodontal ligament, cortical and trabecullar bones, and the other model was a veneer restoration; both models were developed using MSC/Nastran software (MacNeal-Schwendler Corporation, Los Angeles, CA, USA) as the pre- and post-processor. A 10-N load was applied at the incisal edge from the lingual to the buccal side to simulate oral conditions in this area (protrusion). Results: Von Mises stresses were then analysed for three different regions: A-B (enamel elements under the veneer or second enamel layer), A'-B' (buccal enamel and/or veneer element layer) and C-D (lingual enamel elements layer). A higher stress mode was observed for both models at the lingual cervical region. Conclusions: The presence of a veneer restoration on the incisors is a good alternative to mimic the behaviour of enamel under protrusion loading conditions. The use of veneers to replace enamel during rehabilitations is recommended.     

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.     

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.     

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.     

FEA analysis of Normofunctional forces on periodontal elements in different angulations

In the literature, the periodontal tissue reaction to dissimilar occlusal stress has been described, including clinical and histologic changes caused by stresses in periodontal structures. With respect to occlusal forces, periodontal assembly demonstrates varying adaptive capacity from individual to individual and period to period within the same individual. Unfortunately, these occlusal stresses are yet to be quantified. As a result, determining the effect of normal occlusal force on periodontal elements in various angulations is of interest. Based on CBCT images, one FEA of the maxillary First molar was created, consisting of tooth pulp, periodontal ligament (PDL), and alveolar bone; the effect of normal occlusal force on the pdl in alternate angulations was assessed. Occlusion will occur at three contact areas representing the centric occlusion contact points, each of which will share a 150 N force. The analysis was performed for four force inclinations (0, 22.5°, 45°, and 90°). Maximum stresses are observed in cases of 90-degree loading. These stresses, however, are insignificant and will not cause the periodontal components to rupture. These tensile stresses, which are concentrated in the apical and cervical regions, may obstruct blood flow, resulting in tooth decay or, in some cases, periodontal breakdown in PDL. There have been attempts to express numerical data of stress to be provided for normal and hyper function loads to simulate occlusal situations at various angulations that are known to be accountable for healthy and diseased periodontium.     

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.     

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.     

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.     

Three-dimensional finite element analysis of the composite and compomer onlays in primary molars

Resin onlay restoration is an esthetic alternative technique used for restoring extensively damaged primary molars. Understanding the behavior of materials under repeated functional stress and how the stress is transmitted to the remaining tooth structure is important. The aim of this study was to compare stresses in primary molars restored with indirect composite and compomer onlay. 3D frame models of the right mandibular and maxillary primary molars and the alveolar bone were created using computerized tomography images of a six-year-old girl. The enamel and dentine layers above the cement layer were unified to generate onlay restoration, and composite and compomer were used as restorative materials. The vertical occlusal load (100?N) was applied to the teeth in the occlusal contact areas. The von Mises stress distributions and normal stress distributions of the y-axis (parallel to the long axis of tooth) were evaluated. The occlusal stress is transmitted to the cervical part of healthy teeth by spreading it through the enamel layer. The composite and compomer restorative materials exhibited similar stress distribution patterns. An indirect technique creates a structure similar to the original morphological form, and it allows restorations to distribute high occlusal stresses and to minimize possible breakages.