Tensile and compressive behaviour of the bovine periodontal ligament

Direction-oriented fiber guiding with a tunable tri-layer-3D scaffold for periodontal regeneration

Multilayered scaffolds mimicking mechanical and biological host tissue architectures are the current prerequisites for successful tissue regeneration. We propose our tunable tri-layered scaffold, designed to represent the native periodontium for potential regenerative applications. The fused deposition modeling platform is used to fabricate the novel movable three-layered polylactic acid scaffold mimicking in vivo cementum, periodontal ligament, and alveolar bone layers. The scaffold is further provided with multiple angulated fibers, offering directional guidance and facilitating the anchorage dependence on cell adhesion. Additionally, surface modifications of the scaffold were made by incorporating coatings like collagen and different concentrations of gelatin methacryloyl to enrich the cell adhesion and proliferation. The surface characterization of our designed scaffolds was performed using tribological studies, atomic force microscopy, contact angle measurement, scanning electron microscopy, and micro-computed tomography. Furthermore, the material characterization of this scaffold was investigated by attenuated total reflectance-Fourier transformed infrared spectroscopy. The scaffold's mechanical characterization, such as strength and compression modulus, was demonstrated by compression testing. The L929 mouse fibroblast cells and MG63 human osteosarcoma cells have been cultured on the scaffold. The scaffold's superior biocompatibility was evaluated using fluorescence dye with fluorescence microscopy, scanning electron microscopy, in vitro wound healing assay, MTT assay, and flow cytometry. The mineralization capability of the scaffolds was also studied. In conclusion, our study demonstrated the construction of a multilayered movable scaffold, which is highly biocompatible and most suitable for various downstream applications such as periodontium and in situ tissue regeneration of complex, multilayered tissues.

Dynamic tensile viscoelastic properties of porcine periodontal ligament

The periodontal ligament plays a significant role in orthodontic and masticatory processes. To explicitly investigate the effects of dynamic force amplitude and frequency on the dynamic tensile properties of the periodontal ligament, in vitro tensile experiments were conducted using a dynamic mechanical analysis at various dynamic force amplitudes across a wide frequency range. Storage modulus, loss modulus, and loss factor values were measured. A Maxwell constitutive model based on modulus was established to describe the dynamic mechanical properties of the periodontal ligament. The results showed that the storage modulus ranged from 29.53 MPa to 158.24 MPa, the loss modulus ranged from 3.26 MPa to 76.16 MPa, and the loss factor values all increased with higher frequencies and higher dynamic force amplitudes. Based on the parameters obtained from the fitting results, it is evident that the short-term response has a more pronounced impact on the elastic response of the periodontal ligament than the long-term response. Increasing the dynamic force amplitude and its frequency amplified the viscous effects of the periodontal ligament and enhanced energy dissipation. The proposed constitutive model further demonstrated that the periodontal ligament acts as a viscoelastic biomaterial. These findings have implications for future research on the periodontal ligament.

The crucial role of periodontal ligament's Poisson's ratio and tension-compression asymmetric moduli on the evaluation of tooth displacement and stress state of periodontal ligament

The hydrostatic stress in the periodontal ligament (PDL) evaluated by finite element analysis is considered an important indicator for determining an appropriate orthodontic force. The computed result of the hydrostatic stress strongly depends on the PDL material model used in the orthodontic simulation. This study aims to investigate the effects of PDL Poisson's ratio and tension-compression asymmetric moduli on both the simulated tooth displacement and the PDL hydrostatic stress. Three tension-compression symmetric and two asymmetric PDL constitutive models were selected to simulate the tensile and compressive behavior of a PDL specimen under uniaxial loading, and the resulting numerical results were compared with the in-vitro PDL experimental results reported in the literature. Subsequently, a tooth model was established, and the selected constitutive models and parameters were employed to assess the hydrostatic stress state in the PDL under two distinct loading conditions. The simulated results indicate that PDL Poisson's ratio and tension-compression asymmetry exert substantial influences on the simulated PDL hydrostatic stress. Conversely, the elastic modulus exhibits minimal impact on the PDL stress state under the identical loading conditions. Furthermore, the PDL models with tension-compression asymmetric moduli and appropriate Poisson's ratio yield more realistic hydrostatic stress. Hence, it is imperative to employ suitable Poisson's ratio and tension-compression asymmetric moduli for the purpose of characterizing the biomechanical response of the PDL in orthodontic simulations.

Construction of Human Periodontal Ligament Constitutive Model Based on Collagen Fiber Content

Periodontal ligament (PDL) is mainly composed of collagen fiber bundles, and the content of collagen fiber is an important factor affecting the mechanical properties of PDL. Based on this, the purpose of this study is to explore the effect of the PDL collagen fiber content on its viscoelastic mechanical behavior. Transverse and longitudinal samples of different regions of PDL were obtained from the human maxilla. The fiber content at different regions of human PDL was quantitatively measured using image processing software, and a new viscoelastic constitutive model was constructed based on the fiber content. The nano-indentation experiment was carried out with a loading rate of 0.5 mN·s-1, a peak load of 3 mN, and a holding time of 200 s, and the model parameters were obtained through the experiment data. The results showed that with the increase of fiber content, the deformation resistance of PDL also increased, and compared with the neck and middle region, the compressive strain in the apical region of PDL was the largest. The range of reduced elastic modulus of human PDL was calculated to be 0.39~5.08 MPa. The results of the experimental data and the viscoelastic constitutive model fit well, indicating that the model can well describe the viscoelastic behavior of human PDL.

Effect of temperature on dynamic compressive behavior of periodontal ligament

Periodontal ligament (PDL) attaches tooth root to the surrounding bone. Its existence between tooth and jaw bone is of utmost importance due to its significant role in absorbing and distributing physiological and para-physiological loading. According to the previous studies, various mechanical tests have been performed to characterize the mechanical properties of the PDL; however, all of them have been done at room temperature. To the best of our knowledge, this is the first study in which the testing was performed at body temperature. The present research was planned to measure the dependency of PDL's viscoelastic behavior on temperature and frequency. Three different temperatures, including body and room temperature, were opted to perform the dynamic compressive tests of the bovine PDL. In addition, a Generalized Maxwell model (GMM) was presented based on empirical outcomes. At 37 °C, amounts of loss factor were found to be greater than those in 25 °C, which demonstrates that the viscous phase of the PDL in higher temperatures plays a critical role. Likewise, by raising the temperature from 25 °C to 37 °C, the model parameters show an enlargement in the viscous part and lessening in the elastic part. It was concluded that the PDL's viscosity in body temperature is much higher than that in room temperature. This model would be functional for a more accurate computational analysis of the PDL at the body temperature (37 °C) in various loading conditions such as orthodontic simulations, mastication, and impact.

3D Electrospun Polycaprolactone Scaffolds to Assess Human Periodontal Ligament Cells Mechanobiological Behaviour

While periodontal ligament cells are sensitive to their 3D biomechanical environment, only a few 3D in vitro models have been used to investigate the periodontal cells mechanobiological behavior. The objective of the current study was to assess the capability of a 3D fibrous scaffold to transmit a mechanical loading to the periodontal ligament cells. Three-dimensional fibrous polycaprolactone (PCL) scaffolds were synthetized through electrospinning. Scaffolds seeded with human periodontal cells (10³ mL^-1) were subjected to static (n = 9) or to a sinusoidal axial compressive loading in an in-house bioreactor (n = 9). At the end of the culture, the dynamic loading seemed to have an influence on the cells' morphology, with a lower number of visible cells on the scaffolds surface and a lower expression of actin filament. Furthermore, the dynamic loading presented a tendency to decrease the Alkaline Phosphatase activity and the production of Interleukin-6 while these two biomolecular markers were increased after 21 days of static culture. Together, these results showed that load transmission is occurring in the 3D electrospun PCL fibrous scaffolds, suggesting that it can be used to better understand the periodontal ligament cells mechanobiology. The current study shows a relevant way to investigate periodontal mechanobiology using 3D fibrous scaffolds.

Construction of hyperelastic model of human periodontal ligament based on collagen fibers distribution

OBJECTIVE

The human periodontal ligament (PDL) dominated by collagen fibers showed hyperelastic mechanical behavior under orthodontic force. Despite previous researches on the hyperelastic model of PDL, there were certain limitations because of the types of samples and the ignorance of distribution of collagen fibers. Therefore, the aim of this study was to quantify the effect of collagen fibers distribution of human PDL on its hyperelastic behavior.

METHODS

A total of 6 human PDL samples of root neck, root middle and root apex were cut from human maxillary central incisor and lateral incisor. The spatial angles of collagen fibers were observed by optical microscope, the hyperelastic model was constructed combined with the observation results. The quasi-static uniaxial tensile tests with displacement load 0.05 mm/min were carried out, and the test data were used to identify the parameters of model.

RESULTS

The mechanical behavior of human PDL conformed to the trend of hyperelastic materials, and greatly depended on the spatial angles of internal collagen fibers. The R² value statistical fit of the constitutive model to the data is excellent (R² > 0.98). This model could excellently describe the hyperelastic properties of human PDL.

SIGNIFICANCE

In this study, we quantitatively described the effect of spatial distribution of collagen fibers on the mechanical properties of human PDL. The accuracy of this model was verified by the uniaxial test data, and the relevant model parameters were acquired, which have certain reference value in subsequent researches on hyperelasticity of human PDL and clinical treatment.

Orthodontic Loads in Teeth after Regenerative Endodontics: A Finite Element Analysis of the Biomechanical Performance of the Periodontal Ligament

The objective of this study was to analyse the stress distribution in the periodontal ligament and tooth structure of a cementum-reinforced tooth, a dentine-reinforced tooth and an immature tooth during orthodontic loads using a finite element analysis. A finite element model of a maxillary incisor and its supporting tissues was developed. The root was segmented into two parts: a part that represented a root in an immature state and an apical part that represented the tissue formed after regenerative endodontics. The apical part was given the mechanical properties of dentine or cementum. The three models underwent simulation of mesial load, palatal inclination and rotation. The mean stress values and stress distribution patterns of the periodontal ligament of the dentine- and cementum-reinforced teeth were similar in all scenarios. The maturation of the root, with either dentine or cementum, was beneficial for all scenarios, since the periodontal ligament of the immature tooth showed the highest mean stress values. Under the condition of this computational study, orthodontic loads can be applied in teeth previously treated with regenerative endodontics, since the distribution of stress is similar to those of physiologically mature teeth. In vivo studies should be performed to validate these results.

Tensile creep mechanical behavior of periodontal ligament: A hyper-viscoelastic constitutive model

OBJECTIVE

In orthodontic treatment, the biomechanical response of periodontal ligament (PDL) induces tooth movement. Coupling modeling of PDL can effectively reflect its biomechanical response. The nonlinear creep mechanical behavior of PDL was studied by uniaxial tensile creep test and a new hyper-viscoelastic constitutive model. Two coupling modeling methods with limitations were excluded.

METHODS

PDL specimens were prepared from the central incisors of pig mandible. The theoretical step function was replaced by static loading with a total loading time of 1 s. The creep loading with the constant stresses of 0.05, 0.1, and 0.15 MPa was selected and kept unchanged for 1000 s. The instantaneous hyperelastic mechanical behavior and time-dependent nonlinear viscoelastic mechanical behavior of PDL were characterized by coupled instantaneous third-order Ogden hyperelastic and time-dependent nonlinear creep models.

RESULTS

The results showed that the instantaneous elastic curve of PDL increases in the form of hyperelastic index. The creep strain and creep compliance curves increase rapidly before 200s, and then increase slowly in steady state. The creep strain increased with an increase in the constant stress; conversely, the creep compliance decreased with an increase in the constant stress. The results showed that the experimental data were highly consistent with the hyper-viscoelastic constitutive model (R²>0.97).

SIGNIFICANCE

We normalize the framework of hyper-viscoelastic coupling modeling (Instantaneous hyperelastic model + time-dependent nonlinear viscoelastic model). Which can be extended to other nonlinear viscoelastic biomaterials.

Experimental repeatability, sensitivity, and reproducibility of force and strain measurements from within the periodontal ligament space during ex vivo swine tooth loading

The Periodontal Ligament (PDL) is a complex connective tissue that anchors a tooth to the surrounding alveolar bone. The small size and complex geometry of the PDL space within an intact tooth-PDL-bone complex (TPBC) limits strain measurements. An in-fiber Bragg grating (FBG) sensor offers potential for such measurements due to its small size. This work defines an experimental procedure where strain and force were measured during quasi-static, apically directed, displacement-controlled tests on swine premolar crowns. Specifically, the: inter-TPBC, intra-TPBC, and long-term repeatability after a preconditioned state was objectively identified; sensitivity to preload magnitude, TPBC alignment, and sensor depth; and reproducibility within a TPBC was determined. Data clustering was used to determine the appropriate number of preconditioning trials, ranging from one to seven. Strain and force measurements showed intra-TPBC repeatability with average adjusted root mean square from the median of 28.9% of the peak strain and 4.5% of the peak force measurement. A Mann-Whitney U test generally found statistically significant differences in peak strain and force measurements between the left and right sides, suggesting a lack of inter-TPBC repeatability. Using a Friedman test, it was shown that peak strain measures were sensitive to the TPBC alignment and sensor depth, while peak force measures were sensitive to the preload and TPBC alignment. A Friedman test suggested reproducible strain and force measurements when the FBG was replaced within the same TPBC and the preload, alignment, and sensor depth were controlled.

Tissue Engineering for Periodontal Ligament Regeneration: Biomechanical Specifications

The periodontal biomechanical environment is very difficult to investigate. By the complex geometry and composition of the periodontal ligament (PDL), its mechanical behavior is very dependent on the type of loading (compressive versus tensile loading; static versus cyclic loading; uniaxial versus multiaxial) and the location around the root (cervical, middle, or apical). These different aspects of the PDL make it difficult to develop a functional biomaterial to treat periodontal attachment due to periodontal diseases. This review aims to describe the structural and biomechanical properties of the PDL. Particular importance is placed in the close interrelationship that exists between structure and biomechanics: the PDL structural organization is specific to its biomechanical environment, and its biomechanical properties are specific to its structural arrangement. This balance between structure and biomechanics can be explained by a mechanosensitive periodontal cellular activity. These specifications have to be considered in the further tissue engineering strategies for the development of an efficient biomaterial for periodontal tissues regeneration.

Movement analysis of primate molar teeth under load using synchrotron X-ray microtomography

Mammalian teeth have to sustain repetitive and high chewing loads without failure. Key to this capability is the periodontal ligament (PDL), a connective tissue containing a collagenous fibre network which connects the tooth roots to the alveolar bone socket and which allows the teeth to move when loaded. It has been suggested that rodent molars under load experience a screw-like downward motion but it remains unclear whether this movement also occurs in primates. Here we use synchroton micro-computed tomography paired with an axial loading setup to investigate the form-function relationship between tooth movement and the morphology of the PDL space in a non-human primate, the mouse lemur (Microcebus murinus). The loading behavior of both mandibular and maxillary molars showed a three-dimensional movement with translational and rotational components, which pushes the tooth into the alveolar socket. Moreover, we found a non-uniform PDL thickness distribution and a gradual increase in volumetric proportion of the periodontal vasculature from cervical to apical. Our results suggest that the PDL morphology may optimize the three-dimensional tooth movement to avoid high stresses under loading.

A new perspective: Periodontal ligament is a viscoelastic fluid biomaterial as evidenced by dynamic shear creep experiment

Currently, Periodontal ligament (PDL) is considered as a viscoelastic solid biomaterial. However, we observed the steady-state rheological behavior of PDL through long time loading experiments, and suggested the theoretical definition of PDL as a viscoelastic fluid biomaterial. PDL specimens were prepared from the middle area of the mandibular central incisors in pigs. Dynamic force loading with frequencies of 0 (static load), 2, 5, and 10 Hz and amplitudes of 0.01, 0.02, and 0.03 MPa was adopted. The shear strain-time curve at the equilibrium position of PDL was obtained by a dynamic shear creep experiment. The results showed that the shear strain increased exponentially at first and then inclined toward an oblique line. The results showed that the PDL has viscoelastic fluid characteristics, independent of frequency and amplitude. The shear strain decreased with an increase in frequency and amplitude. To further analyze the viscoelastic characteristics of PDL, a 50000-s static shear creep experiment was re-designed. PDL exhibited viscoelastic fluid biomaterial characteristics according to the three aspects of the algebraic fitting, geometric characteristics, and physical results. For the first time, a viscoelastic fluid constitutive model was established to characterize the mechanical properties of PDL with high fitting accuracy. Furthermore, the shear viscosity coefficient of the dynamic load was larger than that of the static load, increasing with an increase in frequency and amplitude; compared with the static force, the dynamic force improved the viscosity of PDL, enhancing its function of fixing teeth, and introducing the new medical knowledge of "No tooth extraction after a meal."

In situ AFM-based nanoscale rheology reveals regional non-uniformity in viscoporoelastic mechanical behavior of the murine periodontal ligament

The periodontal ligament (PDL) is a critical player in the maintenance of tooth health, acting as the primary stabilizer of tooth position. Recent studies have identified two unique regions within the PDL, the 'dense collar' region and the 'furcation' region, which exhibit distinct structural and compositional differences. However, specific functional differences between these regions have yet to be investigated. We adapted an AFM-based nanoscale rheology method to regionally assess mechanical properties and poroelasticity in the mouse PDL while minimizing the disruption of the 3-dimensional native boundary conditions, and then explored tissue mechanical function in four different regions within the dense collar as well as in the furcation region. We found significant differences between the collar and furcation regions, with the collar acting as a stabilizing ligamentous structure and the furcation acting as both a compressive cushion for vertical forces and a conduit for nutrient transport. While this finding supports our hypothesis, based on previous studies investigating structural and compositional differences, we also found surprising inhomogeneity within the collar region itself. This inhomogeneity supports previous findings of a tilting movement in the buccal direction of mandibular molar teeth and the structural adaptation to prevent lingual movement. Future work will aim to understand how different regions of the PDL change functionally during biological or mechanical perturbations, such as orthodontic tooth movement, development, or aging, with the ultimate goal of better understanding the mechanobiology of the PDL function in health and disease.

Frequency-related viscoelastic properties of the human incisor periodontal ligament under dynamic compressive loading

Studies concerning the mechanical properties of the human periodontal ligament under dynamic compression are rare. This study aimed to determine the viscoelastic properties of the human periodontal ligament under dynamic compressive loading. Ten human incisor specimens containing 5 maxillary central incisors and 5 maxillary lateral incisors were used in a dynamic mechanical analysis. Frequency sweep tests were performed under the selected frequencies between 0.05 Hz and 5 Hz with a compression amplitude that was 2% of the PDL's initial width. The compressive strain varied over a range of 4%-8% of the PDL's initial width. The storage modulus, ranging from 28.61 MPa to 250.21 MPa, increased with the increase in frequency. The loss modulus (from 6.00 MPa to 49.28 MPa) also increased with frequency from 0.05 Hz- 0.5 Hz but remained constant when the frequency was higher than 0.5 Hz. The tanδ showed a negative logarithmic correlation with frequency. The dynamic moduli and the loss tangent of the central incisor were higher than those of the lateral incisor. This study concluded that the human PDL exhibits viscoelastic behavior under compressive loadings within the range of the used frequency, 0.05 Hz- 5 Hz. The tooth position and testing frequency may have effects on the viscoelastic properties of PDL.

In silico study of cuspid' periodontal ligament damage under parafunctional and traumatic conditions of whole-mouth occlusions. A patient-specific evaluation

BACKGROUND AND OBJECTIVE

Although traumatic loading has been associated with periodontal ligament (PDL) damage and therefore with several oral disorders, the damage phenomena and the traumatic loads involved are still unclear. The complex composition and extremely thin size of the PDL make experimentation difficult, requiring computational studies that consider the macroscopic loading conditions, the microscopic composition and fine detailed geometry of the tissue. In this study, a new methodology to analyse the damage phenomena in the collagen network and the extracellular matrix of the PDL caused by parafunctional and traumatic occlusal forces was proposed.

METHODS

The entire human mandible and a portion thereof containing a full cuspid tooth were separately modelled using finite element analysis based on computed tomography and micro-computed tomography images, respectively. The first model was experimentally validated by occlusion analysis and subjected to the muscle loads produced during hard and soft chewing, traumatic cuspid occlusion, grinding, clenching, and simultaneous grinding and clenching. The occlusal forces computed by the first model were subsequently applied to the single tooth model to evaluate damage to the collagen network and the extracellular matrix of the PDL.

RESULTS

Early occlusal contact on the left cuspid tooth guided the mandible to the more occluded side (16.5% greater in the right side) and absorbed most of the lateral load. The intrusive occlusal loads on the posterior teeth were 0.77-13.3% greater than those on the cuspid. According to our findings, damage to the collagen network and the extracellular matrix of the PDL could occur in traumatic and grinding conditions, mainly due to fibre overstretching (>60%) and interstitial fluid overpressure (>4.7 kPa), respectively.

CONCLUSIONS

Our findings provide important biomechanical insights into the determination of damage mechanisms which are caused by mechanical loading and the key role of the porous-fibrous behaviour of the PDL in parafunctional and traumatic loading scenarios. Besides, the 3D loading conditions computed from occlusal contacts will help future studies in the design of new orthodontics appliances and encourage the application of computing methods in medical practice.

Finite element modeling of the periodontal ligament under a realistic kinetic loading of the jaw system

Purpose

The stresses and deformations in the periodontal ligament (PDL) under the realistic kinetic loading of the jaw system, i.e., chewing, are difficult to be determined numerically as the mechanical properties of the PDL is variably present in different finite element (FE) models. This study was aimed to conduct a dynamic finite element (FE) simulation to investigate the role of the PDL (PDL) material models in the induced stresses and deformations using a simplified patient-specific FE model of a human jaw system.

Methods

To do that, a realistic kinetic loading of chewing was applied to the incisor point, contralateral, and ipsilateral condyles, through the experimentally proven trajectory approach. Three different material models, including the elasto-plastic, hyperelastic, and viscoelastic, were assigned to the PDL, and the resulted stresses of the tooth FE model were computed and compared.

Results

The results revealed the highest von Mises stress of 620.14 kPa and the lowest deformation of 0.16 mm in the PDL when using the hyperelastic model. The concentration of the stress in the elastoplastic and viscoelastic models was in the mid-root and apex of the PDL, while for the hyperelastic model, it was concentrated in the cervical margin. The highest deformation in the PDL regardless of the employed material model was located in the caudal direction of the tooth. The viscoelastic PDL absorbed the transmitted energy from the dentine and led to lower stress in the cancellous bone compared to the elastoplastic and hyperelastic material models.

Conclusion

These results have implications not only for understanding the stresses and deformations in the PDL under chewing but also for providing comprehensive information for the medical and biomechanical experts in regard of the role of the material models being used to address the mechanical behavior of the PDL in other components of the tooth.

A porous fibrous hyperelastic damage model for human periodontal ligament: Application of a microcomputerized tomography finite element model

The periodontal ligament (PDL) is a soft biological tissue that connects the tooth with the trabecular bone of the mandible. It plays a key role in load transmission and is primarily responsible for bone resorption and most common periodontal diseases. Although several numerical studies have analysed the biomechanical response of the PDL, most did not consider its porous fibrous structure, and only a few analysed damage to the PDL. This study presents an innovative numerical formulation of a porous fibrous hyperelastic damage material model for the PDL. The model considers two separate softening phenomena: fibre alignment during loading and fibre rupture. The parameters for the material model characterization were fitted using experimental data from the literature. Furthermore, the experimental tests used for characterization were computationally modelled to verify the material parameters. A finite element model of a portion of a human mandible, obtained by microcomputerized tomography, was developed, and the proposed constitutive model was implemented for the PDL. Our results confirm that damage to the PDL may occur mainly because of overpressure of the interstitial fluid, while large forces must be applied to damage the PDL fibrous network. Moreover, this study clarifies some aspects of the relationship between PDL damage and the bone remodelling process.

Viscoelastic properties of human periodontal ligament: Effects of the loading frequency and location

OBJECTIVES

To determine the viscoelastic properties of the human periodontal ligament (PDL) using dynamic mechanical analysis (DMA).

MATERIALS AND METHODS

This study was carried out on three human maxillary jaw segments containing six upper central incisors and four lateral incisors. DMA was used to investigate the mechanical response of the human PDL. Dynamic sinusoidal loading was carried out with an amplitude of 3 N and frequencies between 0.5 Hz and 10 Hz. All samples were grouped by tooth positions and longitudinal locations.

RESULTS

An increase of oscillation frequency resulted in marked changes in the storage and loss moduli of the PDL. The storage modulus ranged from 0.808 MPa to 7.274 MPa, and the loss modulus varied from 0.087 MPa to 0.891 MPa. The tanδ, representing the ratio between viscosity and elasticity, remained constant with frequency. The trends for storage and loss moduli were described by exponential fits. The dynamic moduli of the central incisor were higher than those of the lateral incisor. The PDL samples from the gingival third of the root showed lower storage and loss moduli than those from the middle third of the root.

CONCLUSIONS

Human PDL is viscoelastic through the range of frequencies tested: 0.5-10 Hz. The viscoelastic relationship changed with respect to frequency, tooth position, and root level.

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.

Approach towards the porous fibrous structure of the periodontal ligament using micro-computerized tomography and finite element analysis

The periodontal ligament (PDL) is a porous and fibrous soft tissue situated around the tooth, which plays a key role in the transmission of loads from the tooth to the alveolar bone of the mandible. Although several studies have tried to characterize its mechanical properties, the behaviour of this tissue is not clear yet. In this study, a new simulation methodology based on a material model which considers the contribution of porous and fibrous structure with different material model formulations depending on the effort direction is proposed. The defined material model was characterized by a non-linear approximation of the porous fibrous matrix to experimental results obtained from samples of similar species and was validated by rigorous test simulations under tensile and compressive loads. The global PDL response was also validated using the parameters of the characterization in a finite element model of full human canine tooth obtained by micro-tomography. The results suggest that the porous contribution has high influence during compression because the bulk modulus of the material depends on the ability of interstitial fluid to drain. On the other hand, the collagen fibres running along the load direction are the main responsible of the ligament stiffness during tensile efforts. Thus, a material model with distinct responses depending of the load direction is proposed. Furthermore, the results suggest the importance of considering 3D finite element models based of the real morphology of human PDL for representing the irregular stress distribution caused by the coupling of complex material models and irregular morphologies.

Elastic-viscoplastic modeling of soft biological tissues using a mixed finite element formulation based on the relative deformation gradient

The characteristic highly nonlinear, time-dependent, and often inelastic material response of soft biological tissues can be expressed in a set of elastic-viscoplastic constitutive equations. The specific elastic-viscoplastic model for soft tissues proposed by Rubin and Bodner (2002) is generalized with respect to the constitutive equations for the scalar quantity of the rate of inelasticity and the hardening parameter in order to represent a general framework for elastic-viscoplastic models. A strongly objective integration scheme and a new mixed finite element formulation were developed based on the introduction of the relative deformation gradient-the deformation mapping between the last converged and current configurations. The numerical implementation of both the generalized framework and the specific Rubin and Bodner model is presented. As an example of a challenging application of the new model equations, the mechanical response of facial skin tissue is characterized through an experimental campaign based on the suction method. The measurement data are used for the identification of a suitable set of model parameters that well represents the experimentally observed tissue behavior. Two different measurement protocols were defined to address specific tissue properties with respect to the instantaneous tissue response, inelasticity, and tissue recovery.

Modeling stress-relaxation behavior of the periodontal ligament during the initial phase of orthodontic treatment

The periodontal ligament is the tissue that provides early tooth motion as a result of applied forces during orthodontic treatment: a force-displacement behavior characterized by an instantaneous displacement followed by a creep phase and a stress relaxation phase. Stress relaxation behavior is that which provides the long-term loading to and causes remodelling of the alveolar bone, which is responsible for the long-term permanent displacement of the tooth. In this study, the objective was to assess six viscoelastic models to predict stress relaxation behavior of rabbit periodontal ligament (PDL). Using rabbit stress relaxation data found in the literature, it was found that the modified superposition theory (MST) model best predicts the rabbit PDL behavior as compared to nonstrain-dependent and strain-dependent versions of the Burgers four-parameter and the five-parameter viscoelastic models, as well as predictions by Schapery's viscoelastic model. Furthermore, it is established that using a quadratic form for MST strain dependency provides more stable solutions than the cubic form seen in previous studies.

Pathological cyclic strain-induced apoptosis in human periodontal ligament cells through the RhoGDIα/caspase-3/PARP pathway

AIM

Human periodontal ligament (PDL) cells incur changes in morphology and express proteins in response to cyclic strain. However, it is not clear whether cyclic strain, especially excessive cyclic strain, induces PDL cell apoptosis and if so, what mechanism(s) are responsible. The aim of the present study was to elucidate the molecular mechanisms by which pathological levels of cyclic strain induce human PDL cell apoptosis.

MATERIALS AND METHODS

Human PDL cells were obtained from healthy premolar tissue. After three to five passages in culture, the cells were subjected to 20% cyclic strain at a frequency of 0.1 Hz for 6 or 24 h using an FX-5000T system. Morphological changes of the cells were assessed by inverted phase-contrast microscopy, and apoptosis was detected by fluorescein isothiocyanate (FITC)-conjugated annexin V and propidium iodide staining followed by flow cytometry. Protein expression was evaluated by Western blot analysis.

RESULTS

The number of apoptotic human PDL cells increased in a time-dependent manner in response to pathological cyclic strain. The stretched cells were oriented parallel to each another with their long axes perpendicular to the strain force vector. Cleaved caspase-3 and poly-ADP-ribose polymerase (PARP) protein levels increased in response to pathological cyclic strain over time, while Rho GDP dissociation inhibitor alpha (RhoGDIα) decreased. Furthermore, knock-down of RhoGDIα by targeted siRNA transfection increased stretch-induced apoptosis and upregulated cleaved caspase-3 and PARP protein levels. Inhibition of caspase-3 prevented stretch-induced apoptosis, but did not change RhoGDIα protein levels.

CONCLUSION

The overall results suggest that pathological-level cyclic strain not only influenced morphology but also induced apoptosis in human PDL cells through the RhoGDIα/caspase-3/PARP pathway. Our findings provide novel insight into the mechanism of apoptosis induced by pathological cyclic strain in human PDL cells.

Alveolar ridge resorption after tooth extraction: A consequence of a fundamental principle of bone physiology

It is well established that tooth extraction is followed by a reduction of the buccolingual as well as the apicocoronal dimension of the alveolar ridge. Different measures have been taken to avoid this bone modelling process, such as immediate implant placement and bone grafting, but in most cases with disappointing results. One fundamental principle of bone physiology is the adaptation of bone mass and bone structure to the levels and frequencies of strain. In the present article, it is shown that the reduction of the alveolar ridge dimensions after tooth extraction is a natural consequence of this physiological principle.

Cyclic stretch influenced expression of membrane connexin 43 in human periodontal ligament cell

OBJECTIVE

Periodontal ligament (PDL) cells play an important role in preserving periodontal homeostasis and periodontal remodelling in response to mechanical stimulations. Gap junction intercellular communication (GJIC) is essential for homeostasis and many other biological processes of multicellular organisms. While the role of GJIC in mechanotransduction of PDL cells remains largely unknown. In the present study, we examined the influence of cyclic stretch on the expression of membrane gap junction protein connexin 43 (Cx43) in cultured human PDL cells.

DESIGN

Cultured human PDL cells were exposed to 1%, 10% and 20% stretch strains for 0.5 h, 1 h and 24 h. Then the membrane Cx43 protein expression was measured by flow cytometry and the Cx43 mRNA level was measured by real-time polymerase chain reaction.

RESULTS

Half hour and 1 h cyclic stretches with strains up to 20% did not change the expression of membrane Cx43 protein, while 24 h cyclic stretches with 10% and 20% strains down-regulated the expression of membrane Cx43 protein in a strain magnitude-dependent manner. Furthermore, cyclic stretch also changed the Cx43 mRNA level and induced realignment in cells.

CONCLUSION

The present research provide the first evidence that cyclic stretch influenced the membrane Cx43 protein expression in cultured human PDL cells.

Periodontal biomechanics: finite element simulations of closing stroke and power stroke in equine cheek teeth

Background

In equine dentistry periodontal diseases, especially periapical inflammation, are frequently occurring problems. Anachoresis is believed to be the most common cause for the development of such disorders. Nevertheless, there is still no substantiated explanation why settlement of pathogen microorganisms occurs in equine periodontal tissues. It is expected that excessive strains and stresses occurring in the periodontal ligament (PDL) during the horse’s chewing cycle might be a predisposing factor. In this study this assumption was examined by finite element (FE) analyses on virtual 3-D models of equine maxillary and mandibular cheek teeth, established on the basis of μCT datasets. Calculations were conducted both under conditions of closing and power stroke.

Results

Results showed a uniform distribution of low stresses and strain energy density (SED) during closing stroke, whereas during power stroke an occurrence of high stresses and SED could be observed in the PDL near the alveolar crest and in periapical regions.

Conclusion

The concentration of forces during power stroke in these specific areas of the PDL may cause local tissue necrosis and inflammation and thus establish a suitable environment for the settlement of microorganisms.

A continuous method to compute model parameters for soft biological materials

Developing appropriate mathematical models for biological soft tissues such as ligaments, tendons, and menisci is challenging. Stress-strain behavior of these tissues is known to be continuous and characterized by an exponential toe region followed by a linear elastic region. The conventional curve-fitting technique applies a linear curve to the elastic region followed by a separate exponential curve to the toe region. However, this technique does not enforce continuity at the transition between the two regions leading to inaccuracies in the material model. In this work, a Continuous Method is developed to fit both the exponential and linear regions simultaneously, which ensures continuity between regions. Using both methods, three cases were evaluated: idealized data generated mathematically, noisy idealized data produced by adding random noise to the idealized data, and measured data obtained experimentally. In all three cases, the Continuous Method performed superiorly to the conventional technique, producing smaller errors between the model and data and also eliminating discontinuities at the transition between regions. Improved material models may lead to better predictions of nonlinear biological tissues' behavior resulting in improved the accuracy for a large array of models and computational analyses used to predict clinical outcomes.

Tooth movements are guided by specific contact areas between the tooth root and the jaw bone: A dynamic 3D microCT study of the rat molar

Teeth sustain high loads over a lifetime and yet intact tooth failure is rare. The different structures of the tooth, jaw bone and the intervening soft periodontal ligament enable the tooth to endure repeated loading during mastication. Although mechanical and functional properties of the different components are thoroughly investigated, the manner in which the whole tooth functions under load is still enigmatic. A custom-made loading system inside a microCT scanner was used to directly visualize the root movements in relation to the jaw bone as the rat molar tooth was loaded. At low loads no contact was observed between the root surface and the bone, whereas at higher loads three specific contact areas between the root surface and the jaw bone were observed. These contact areas restrict tooth movement in the buccal-lingual direction, but enable the tooth to rock in a "seesaw" like manner in the distal-mesial direction. The contact areas appear to play a role in determining tooth motion and in turn define the manner in which the whole tooth moves when loaded. These observations are important for understanding basic structure-function relations of the tooth-PDL-bone system, and have direct implications for better understanding pathological and therapeutic processes in orthodontics, periodontics and jaw bone regeneration.

Constitutive modeling of the non-linear visco-elasticity of the periodontal ligament

A non-linear visco-elastic constitutive model is adopted to describe the relaxation phenomena of the periodontal ligament (PDL). The introduction of a non-linear formulation of visco-elasticity is necessary because experimental data from the literature referring to animal models show that the relaxation rate depends on the level of strain applied. In particular, the percentage of relaxation increases with decrease of the applied strain. The constitutive model is consistent with the non-linear elastic behavior of the PDL in the case of high rate loading and large strains attained by the tissue. A hyperelastic formulation is adopted for the elastic behavior of the PDL and this formulation is developed adopting suitable measures of stress and strain. The anisotropy of the tissue induced by specific spatial orientation of collagen fibers is included in the model. With respect to recent numerical formulation proposed to describe the non-linear visco-elasticity of the PDL, the proposed model has the advantage of being more consistent with the micro-structural configuration of the tissue and the large strains it can undergo. The results obtained show that a reasonable description of the PDL relaxation phenomena can be obtained by assuming that relaxation times are independent of strain, whereas the relative stiffness results are dependent on strain applied through an exponential function.

Apoptotic gene expression by human periodontal ligament cells following cyclic stretch

BACKGROUND AND OBJECTIVE

Periodontal ligament cells play an important role in maintaining homeostasis of periodontal tissue upon mechanical force loading caused by mastication or orthodontic force. Previous studies revealed force-driven periodontal ligament cell death via apoptosis, but the force-sensing genes assigned to the apoptotic pathway have not been fully characterized. The present study aimed to identify force-sensing genes implicated in the apoptotic pathway in periodontal ligament cells.

MATERIAL AND METHODS

Human periodontal ligament cells were exposed to 20% stretch strain for 6 or 24 h, and the differential expression of 84 genes implicated in the apoptotic pathway were quantified by real-time PCR array technology.

RESULTS

Ten and 11 genes showed upregulated expression after 6 and 24 h stretches, respectively, and there were two downregulated genes in response to both 6 and 24 h stretches. These genes included those encoding the tumor necrosis factor ligand family (TNFSF8), tumor necrosis factor receptor family (FAS, TNFRSF10B, TNFRSF11B, TNFRSF25 and CD27), the Bcl-2 family (BAG3, BAK1, BCL2L11 and BCLAF1), the caspase family (CASP5 and CASP7), the inhibitor of apoptosis proteins family (BIRC3, BIRC6 and NAIP), the caspase recruitment domain family (RIPK2 and PYCARD) and the death domain family (DAPK1), as well as an oncogene (BRAF).

CONCLUSION

This study identified several force-sensing genes implicated in the apoptotic pathway in periodontal ligament cells and should facilitate future studies on force-driven apoptosis by providing putative target genes.

Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature

Introduction. This review is intended to highlight and discuss discrepancies in the literature of the periodontal ligament's (PDL) mechanical properties and the various experimental approaches used to measure them. Methods. Searches were performed on biomechanical and orthodontic publications (in databases: Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, and Scopus). Results. The review revealed that significant variations exist, some on the order of six orders of magnitude, in the PDL's elastic constants and mechanical properties. Possible explanations may be attributable to different experimental approaches and assumptions. Conclusions. The discrepancies highlight the need for further research into PDL properties under various clinical and experimental loading conditions. Better understanding of the PDL's biomechanical behavior under physiologic and traumatic loading conditions might enhance the understanding of the PDL's biologic reaction in health and disease. Providing a greater insight into the response of the PDL would be instrumental to orthodontists and engineers for designing more predictable, and therefore more efficacious, orthodontic appliances.

Mechanical strength and viscoelastic response of the periodontal ligament in relation to structure

The mechanical strength of the periodontal ligament (PDL) was first measured as force required to extract a tooth from its socket using human specimens. Thereafter, tooth-PDL-bone preparations have extensively been used for measurement of the mechanical response of the PDL. In vitro treatments of such specimens with specific enzymes allowed one to investigate into the roles of the structural components in the mechanical support of the PDL. The viscoelastic responses of the PDL may be examined by analysis of the stress-relaxation. Video polarised microscopy suggested that the collagen molecules and fibrils in the stretched fibre bundles progressively align along the deformation direction during the relaxation. The stress-relaxation process of the PDL can be well expressed by a function with three exponential decay terms. Analysis after in vitro digestion of the collagen fibres by collagenase revealed that the collagen fibre components may play an important role in the long-term relaxation component of the stress-relaxation process of the PDL. The dynamic measurements of the viscoelastic properties of the PDL have recently suggested that the PDL can absorb more energy in compression than in shear and tension. These viscoelastic mechanisms of the PDL tissue could reduce the risk of injury to the PDL.

Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration

This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.

A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement

In this paper the mechanical response of soft collagenous tissues with regular fiber arrangement (RSCTs) is described by means of a nanoscale model and a two-step micro-macro homogenization technique. The non-linear collagen constitutive behavior is modeled at the nanoscale by a novel approach accounting for entropic mechanisms as well as stretching effects occurring in collagen molecules. Crimped fibers are reduced to equivalent straight ones at the microscale and the constitutive response of RSCTs at the macroscale is formulated by homogenizing a fiber reinforced material. This approach has been applied to different RSCTs (tendon, periodontal ligament and aortic media), resulting effective and accurate as proved by the excellent agreement with available experimental data. The model is based on few parameters, directly related to histological and morphological evidences and whose sensitivity has been widely investigated. Applications to simulation of some physiopathological mechanisms are also proposed, providing confirmation of clinical evidences and quantitative indications helpful for clinical practice.

Cyclic stretching force induces apoptosis in human periodontal ligament cells via caspase-9

The response of periodontal ligament (PDL) cells to mechanical stimulation is important in the periodontal tissue remodelling. Our previous study showed that cyclic stretching force on PDL cells induced early apoptosis. However, the mechanism of stretching force-induced cell death is unclear. In the present study, we examined whether PDL cells undergo apoptosis by stretching force using the terminal deoxynucleotidyl transferase (TdT)-mediated dUTP-biotin nick-end-labellling method (TUNEL) and investigated the mechanism by which cyclic stretching force initiated apoptosis. We found that PDL cells became aligned regularly and the number of apoptotic cells increased significantly in a time-and force-dependent manner after the application of cyclic stretching force. Caspase-3 activity increased in proportion to the magnitude of the stretching force, and this effect was reduced significantly by a caspase-9 inhibitor, whereas a caspase-8 inhibitor had no such effect. We therefore concluded that the in vitro application of cyclic stretching force can induce apoptosis in PDL cells by activating the caspase-3 via the caspase-9 signalling cascade. Our findings may provide a novel insight into the mechanism of apoptosis induced by stretching force in PDL cells.