Viscoelastic Response of the Periodontal Ligament: An Experimental–Numerical Analysis

A viscoelastic constitutive model for the periodontal ligament (PDL) capable of accounting for large strains, anisotropy, and inelastic time-dependent effects was developed. Anisotropy characteristics are determined by the composite nature of the tissue and, in particular, by the distribution of collagen fibres. Time-dependent viscous phenomena are due to microstructural modifications during loading, such as fluid fluxes moving through the solid matrix and the internal rearrangement of fibers and constitutive adaptation. The viscoelastic model presented here was implemented in a general purpose finite element code. In vitro experimental tests were carried out on the PDL specimens of adult pigs to obtain stress-relaxation and cyclic stress-strain curves. The comparison of experimental and numerical results revealed good correspondence and confirmed the capability of the formulation assumed to properly interpret the viscoelastic behavior of the PDL.     

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

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

基于超黏弹性的牙周膜本构模型构建及模拟

为了准确描述牙周膜的生物力学行为,基于大变形连续介质力学理论及不可压缩各向同性假设,以人体牙周膜平面剪切和应力松弛实验数据为基础,利用有限元软件ABAQUS的数据拟合功能,构建牙周膜的超黏弹性本构模型及参数。随后,通过对5组牙周膜平面剪切实验过程的模拟,验证牙周膜超黏弹性模型的正确性。最后,通过有限元计算对比分析牙周膜线弹性模型与超黏弹性模型对载荷的力学响应。结果表明在牙根位移量为0～0.06 mm时,牙周膜可近似用线弹性模型表示;当位移量大于0.06 mm,两种模型的差异显著,超黏弹性模型更加符合牙周膜的材料特性。研究结果为牙周膜提供一种实用性强的超黏弹性模型,为牙齿正畸的生物力学研究和治疗方案的精确设计提供理论依据。     

Comparison of Dynamic Shear Properties of the Porcine Molar and Incisor 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. The mechanical response to vertical force may, however, be different between the molar and incisor as their loading regimen is different. The present study was designed to determine the viscoelastic behavior in shear of the PDL of the porcine molar and incisor (n = 10 for each). From dissected mandibles transverse sections including the mesial root of first molar and the incisal root were obtained and used for dynamic shear tests. Shear strain of 1.0% was applied in superoinferior direction parallel to the root axis with a wide range of frequencies (0.01–100 Hz). The viscoelastic behavior was characterized by the storage and loss modulus and loss tangent as a function of the frequency. For the incisor and molar, the complex and storage moduli increased significantly with the frequency. For the incisor, the loss modulus also increased with the frequency. The loss modulus and loss tangent were significantly (p < 0.05) larger in the incisor than in the molar. The present results suggest that the incisal PDL revealed more viscous behavior during dynamic shear than the molar one, which might have important implications for the principal role of the anterior teeth such as PDL sensation.     

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

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

Frequency dependence of complex moduli of brain tissue using a fractional Zener model

Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests are not sufficient to determine the complete viscoelastic behaviour of the material, and dynamic test methods are more appropriate. The concept of complex modulus of elasticity is a powerful tool for characterizing the frequency domain behaviour of viscoelastic materials. On the other hand, it is well known that classical viscoelastic models can be generalized by means of fractional calculus to describe more complex viscoelastic behaviour of materials. In this paper, the fractional Zener model is investigated in order to describe the dynamic behaviour of brain tissue. The model is fitted to experimental data of oscillatory shear tests of bovine brain tissue to verify its behaviour and to obtain the material parameters.     

Hyaluronic acid-poly-D-lysine-based three-dimensional hydrogel for traumatic brain injury

Brain tissue engineering in the postinjury brain represents a promising option for cellular replacement and rescue, providing a cell scaffold for either transplanted or resident cells. In this article, a hyaluronic acid (HA)-poly-D-lysine (PDL) copolymer hydrogel with an open porous structure and viscoelastic properties similar to neural tissue has been developed for brain tissue engineering. The chemicophysical properties of the hydrogel with HA:PDL ratios of 10:1, 5:1, and 4:1 were investigated by scanning electron microscopy (SEM) and X-ray photoelectron spectrometry. Neural cells cultured in the hydrogel were studied by phase-contrast microscope and SEM. The incorporation of PDL peptides into the HA-PDL hydrogel allowed for the modulation of neuronal cell adhesion and neural network formation. Macrophages and multinucleated foreign body giant cells found at the site of implantation of the hydrogel in the rat brain within the first weeks postimplantation decreased in numbers after 6 weeks, consistent with the host response to inert implants in numerous tissues. Of importance was the infiltration of the hydrogel by glial fibrillary acidic protein-positive cells-reactive astrocytes-by immunohistochemistry and the contiguity between the hydrogel and the surrounding tissue demonstrated by SEM. These findings indicated the compatibility of this hydrogel with brain tissue. Collectively, the results demonstrate the promise of an HA-PDL hydrogel as a scaffold material for the repair of defects in the brain.     

Oral biofilm challenge regulates the RANKL-OPG system in periodontal ligament and dental pulp cells

Inflammatory bone destruction triggered by oral bacteria is a hallmark of chronic and apical periodontitis. Receptor activator of NF-κB ligand (RANKL) activates bone resorption, whereas osteoprotegerin (OPG) blocks its action. These are members of the tumor necrosis factor ligand and receptor families, respectively. Although individual oral pathogens are known to regulate RANKL and OPG expression in cells of relevance to the respective diseases, such as periodontal ligament (PDL) and dental pulp (DP) cells, the effect of polymicrobial oral biofilms is not known. This study aimed to investigate the effect of the Zürich in vitro supragingival biofilm model on RANKL and OPG gene expression, in human PDL and DP cell cultures, by quantitative real-time polymerase chain reaction. RANKL expression was more pronouncedly up-regulated in DP than PDL cells (4-fold greater), whereas OPG was up-regulated to a similar extent. The RANKL/OPG ratio was increased only in DP cells, indicating an enhanced capacity for inducing bone resorption. The expression of pro-inflammatory cytokine interleukin-1β was also increased in DP, but not PDL cells. Collectively, the high responsiveness of DP, but not PDL cells to the supragingival biofilm challenge could constitute a putative pathogenic mechanism for apical periodontitis, which may not crucial for chronic periodontitis.     

Mechanical impedance of the canine diaphragm

In the paper the equation of motion of the small amplitude transverse forced vibration of a radially prestressed and circularly clamped thin membrane has been developed. The material of the membrane is considered to be homogeneous, isotropic, incompressible and viscoelastic. From the analytical solution of this equation the incremental mechanical impedance of the membrane was derived as a function of frequency, geometrical parameters and incremental viscoelastic coefficients of the material. The parameters of the model were fitted to experimental impedance data using a global optimisation procedure to obtain the incremental viscoelastic moduli of the canine diaphragm. The estimated quasi-static behaviour of the model is shown to be consistent with the results of experimental quasi-static measurements. It is concluded that the incremental viscoelastic moduli of a soft tissue and the stress dependence of these material coefficients can be determined by fitting the parameters of the model to the impedance data of that particular tissue.     

Modeling of viscoelastic behavior of dental chemically activated resin composites during curing

Shrinkage stresses generated in dental resin composites during curing are among the major problems in adhesive dentistry, because they interfere with the integrity of the restored tooth. The aim of this study was to find a mechanical model to describe the viscoelastic behavior of a two-paste resin composite during curing, to aid our understanding of the process of shrinkage stress development. In this study, stress-strain data on Clearfil F2 during curing were obtained by a dynamic test method and analyzed using three mechanical models (Maxwell, Kelvin, and the Standard Linear Solid model). With a modeling procedure, the model's stress response was compared with the experimental stress data, and the material parameters were calculated. On the basis of the modeling and evaluation results, a model for describing the viscoelastic behavior of the shrinking resin composite was selected. The validation results showed that the modeling procedure is free of error, and that it was capable of finding material parameters associated with a two-parametric model with a high degree of accuracy. The viscoelastic behavior of the shrinking resin composite, as excited by the conditions of the test method, cannot be described by a single mechanical model. In the early stage of curing, the most accurate prediction was achieved by the Maxwell model, while during the remainder of the curing process the Kelvin model can be used to describe the viscoelastic behavior of the two-paste resin composite.     

Immunolocalization of lubricin in the rat periodontal ligament during experimental tooth movement

Lubricin is a protein which contributes to the boundary lubrication, facilitating low friction levels at the interfacing surfaces of joints. In tendons and ligaments it facilitates the relative movement of collagen bundles. Its expression is affected by mechanical signals and cytokines. During application of orthodontic forces to teeth, there is a transduction of mechanical forces to the cells of the periodontal ligament (PDL), which triggers several biological reactions causing the synthesis of prostaglandins, cytokines and growth factors. The aim of the present study was to examine the immunolocalization of lubricin and to evaluate if it is time-dependently and differentially detected within the PDL following the application of orthodontic forces to create areas of compression and tension. This was achieved by placing elastic bands between the maxillary first and second molars of 16 male Sprague-Dawley rats (each weighing 120-200 g) for 12 and 24 h. The molar-bearing segments were dissected and processed for histological and immunohistochemical examination. Binding of a monoclonal antibody was used to evaluate lubricin localization using an indirect streptavidin/biotin immunperoxidase technique. Lubricin, was constitutively expressed in the PDL of rat molars. After the experimental force was applied to the tooth, lubricin was down-regulated, on both sides (compression and tension) of the PDL, in a time-dependent fashion, although to a different extent, being at any time more expressed on the tension side. Furthermore, in every sample, almost all PDL cells in the adjacent tooth cementum and alveolar bone, were more heavily immunolabeled by lubricin antibody, contrary to those located in the central portion of the PDL. Lubricin expression therefore seems related to PDL remodeling and tooth displacement following the application of an orthodontic force, and it appears that lubricin may play an important role during tooth movement.     

Increased unscheduled DNA synthesis in aged human diploid fibroblasts

Using Hayflick's model, ultraviolet (UV) induced unscheduled DNA synthesis was compared in cells at a low, middle and high population doubling level (PDL). Concomitant DNA replication was prevented by arresting all cultures in the G₁ phase by lowering the serum concentration. After UV-irradiation cells at a high PDL incorporated 1.5–2 times more [³H] thymidine into DNA than cells at a low and middle PDL. These findings seem to indicate that the repair capacity of cells at a high PDL is more than those of cells at low and middle PDL. Alternatively, the higher incorporation might be explained by a difference in the pool sizes of precursors of cells at different PDL. These possibilities were examined by adding fluorodeoxyuridine to the system to reduce de novo synthesis of deoxythymidine triphosphate (dTTP), and measuring the pool size of dTTP and the specific activity of [³H] dTTP in cells at different PDL. The results indicated that the increased incorporation in fact reflects increased unscheduled DNA synthesis in cells at a high PDL.     

Application of a vibration measuring technique to evaluate the dynamic stiffness of porcine periodontal ligament.

The performance of a tooth replacement by using a dental implant relies on the mechanical and biological capability of the anatomical substitute to restore lost physiological functions. The design of an implant device able to properly replace the physiological tooth requires the study of the load transfer mechanism at the implant-bone interface and the understanding of the relevance of the periodontal ligament (PDL) in this mechanism. The PDL is a connective soft tissue that provides the fixation of the tooth in its bone-socket and the attenuation of occlusal loads. It also provides the ground cells that are involved in the remodelling process, induced by a change in the stress-strain pattern of the alveolar bone and also in the cementum of the tooth root. The purpose of this study was to determine the PDL effects on the dynamic load transfer mechanism, from the tooth to the alveolar bone, evaluating the equivalent dynamic stiffness of the ligament structure. A porcine fresh mandible with a tooth was used within the study, applying an experimental procedure to identify the dynamic transmissibility of the entire system. The transmissibility function provided information about the stiffness and damping of the PDL, information that can assist the design of an improved dental implant system.     

Late passage cells display an increase in contractile behavior

During aging, alterations in the extracellular matrix and cytoskeleton have been noted. Aging affects both the structure and the biological activity of fibronectin as well as the cellular content and organization of f-actin. The purpose of this study was to examine the functional significance of such alterations. Assays for cell migration, cell spreading, collagen gel contraction, and f-actin organization were conducted using diploid cells strains of high and low population doubling level (PDL). First, an assessment of cell spreading behavior revealed that high PDL cells spread more than low PDL cells. Second, analyses performed with a modified phagokinetic track assay indicate that high PDL cells migrate (phagocytize) faster than low PDL cells. Lastly, it was found that high PDL cells contract collagen gels faster than low PDL cells. Therefore, high PDL cells are capable of exerting more force upon their extracellular matrix than low PDL cells. In agreement with previous observations, we found by phalloidin staining that the f-actin content of high PDL cells was substantially greater than that of low PDL cells. The elevated f-actin content of high PDL cells could promote increased cellular contractility thereby leading to the increase in cell spreading, migration, and collagen gel contraction observed here.     

A comparative FEM-study of tooth mobility using isotropic and anisotropic models of the periodontal ligament. Finite Element Method

Orthodontic tooth movement is usually characterized by two centres: the centre of resistance and the centre of rotation. A literature survey shows that both centres vary to a significant extent in both clinical and computational experiments. This paper reports on studies upon five different hypothetical mechanical representations of the periodontal ligament (PDL) which plays the most significant role in tooth mobility. The first model considers the PDL as an isotropic and linear-elastic continuum without fibres; it also discusses some preliminary visco-elastic aspects. The next three models assume a nonlinear and anisotropic material composed of fibres only that are arranged in three different orientations, two hypothetical that have appeared previously in the literature and one more consistent with actual morphological data. The fifth model considers the PDL as an orthotropic material consisting of both a continuum and of fibres. Results were obtained by applying the Finite Element Method (FEM) on a maxillary central incisor. It was found that the isotropic linear-elastic PDL leads to occlusal positions of both centres in comparison with those obtained through the well-known Burstone's theoretical formula, while histological anisotropic fibres locate them apically and eccentrically.     

Nonlinear finite element analysis of the vibration characteristics of the maxillary central incisor related to periodontal attachment

The vibration characteristics of a maxillary central incisor were investigated by using the finite element method (FEM) according to nonlinear behavior of the human periodontal ligament (PDL). The effect of alveolar bone loss was also studied to obtain the relationship between the vibration property of the tooth in the periodontal system and the level of periodontal attachment for assessing the condition of periodontium. Three-dimensional (3D) finite element model of the tooth was constructed using CT image-reconstruction, and the elastic face foundation constraint was applied to the surface of the tooth root where the PDL was attached to. Modal analysis was performed by using FEM. The nonlinear behavior of the PDL was assigned and approached by the piecewise linearized method. The results indicated that the vibration of the maxillary central incisor in the periodontal system could be described by several modal frequencies and modes. The first four modes were dominant, which varied with the deformation of the PDL or the force applied on the tooth. The vibration frequency of the maxillary central incisor decreased with the losing of the alveolar bone, but the ratio of decrease had no significant correlation with the nonlinear behavior of the human PDL. The vibration frequency of the maxillary central incisor can be used to describe the loss of the alveolar bone and the level of periodontal attachment, under physiological short-term loading.     

A constitutive model for protein-based materials

Protein-based materials are critical to the construction of tissue substitutes that exhibit precisely defined mechanical properties. Under physiologically relevant conditions, materials derived from natural or synthetic structural proteins are characterized by nonlinear elastic responses at medium and large deformations, time-dependent or viscoelastic behavior, and display the effects of strain-induced structural changes. Although a constitutive model that accurately describes mechanical behavior is essential for the rational design of tissue constructs, few models account for all of these characteristics. In this report, we present a new constitutive model for protein based materials, in which nonlinear elasticity is captured by the Arruda-Boyce eight-chain model, time dependant viscoelasticity is described by a generalized Maxwell model, and the effect of strain-induced structural change is incorporated using a network alteration theory originally proposed by Tobolsky. The model was applied to a number of protein-based materials and cell containing constructs, including recombinant elastin-mimetic protein polymers and fibroblast populated collagen gel matrices. Significantly, numerical implementation of this model is straightforward and mechanical behavior accurately described under a variety of loading conditions. Moreover, when calibrated using stress relaxation data alone, the model accurately predicted cyclic loading responses. Although limitations exist, this model provides a convenient tool to correlate viscoelastic data obtained by different testing modes and may assist in reducing the number of experimental tests required to fully capture the range of viscoelastic responses of protein-based materials.     

The constitutive properties of the brain paraenchyma Part 2. Fractional derivative approach

Fractional models have proven to be very useful for studying viscoelastic materials. We consider the fractional Zener model (also called four-parameter model) to study both the relaxation function and creep compliance. The analytical results are compared with the known experimental results of the human brain tissue to obtain the best fit and brain mechanical parameters. The results are also compared to the non-fractional Zener model and four-parameter Burgers model, indicating that the four-parameter fractional model gives a substantially better fit for the all experimental data.     

Fibroblast growth factor 2 inhibits the expression of stromal cell-derived factor 1α in periodontal ligament cells derived from human permanent teeth in vitro

Although cells derived from periodontal ligament (PDL) tissue are reported to have stem cell-like activity and are speculated to play a crucial role for tissue healing and regeneration after injury or orthodontic treatment, mechanisms regulating their recruitment and activation remain unknown. Recently, stromal cell-derived factor 1α (SDF-1α) has been reported to be important for stem cell homing and recruitment to injured sites. The aim of this study was to evaluate whether fibroblast growth factor 2 (FGF-2) affects the expression of SDF-1α in PDL cells derived from human permanent teeth in vitro. Using real-time PCR, the expression of SDF-1α mRNA in PDL cells was inhibited by treatment with 10 ng/ml FGF-2. When PDL cells were treated with SU5402 (an inhibitor of FGF receptor 1) in combination with FGF-2, the FGF-2-reduced expression of SDF-1α was inhibited. In the presence of the JNK inhibitor SP600125, SDF-1α mRNA in PDL cells was not suppressed by the FGF-2 treatment. Western blot analysis also showed that SDF-1α production was suppressed by treatment with FGF-2, but it recovered with treatment by FGF-2 + SU5402. These findings suggest that SDF-1α from PDL cells plays an important role in the regeneration and homeostasis of periodontal tissues via the recruitment of stem cells.