Biomechanical behavior of bovine periodontal ligament: Experimental tests and constitutive model

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.

Mechanical properties of animal ligaments: a review and comparative study for the identification of the most suitable human ligament surrogates

The interest in the properties of animal soft tissues is often related to the desire to find an animal model to replace human counterparts due to the unsteady availability of human tissues for experimental purposes. Once the most appropriate animal model is identified, it is possible to carry out ex-vivo and in-vivo studies for the repair of ligamentous tissues and performance testing of replacement and support healing devices. This work aims to present a systematic review of the mechanical properties of ligaments reported in the scientific literature by considering different anatomical regions in humans and several animal species. This study was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) method. Moreover, considering the lack of a standard protocol for preconditioning of tissues, this aspect is also addressed. Ninety-six studies were selected for the systematic review and analysed. The mechanical properties of different animal species are reported and summarised in tables. Only results from studies reporting the strain rate parameter were considered for comparison with human ligaments, as they were deemed more reliable. Elastic modulus, ultimate tensile stress, and ultimate strain properties are graphically reported identifying the range of values for each animal species and to facilitate comparison between values reported in the scientific literature in animal and human ligaments. Useful similarities between the mechanical properties of swine, cow, and rat and human ligaments have been found.

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.

Identification of the periodontal ligament material parameters using response surface method

The orthodontic treatment can be guided by the finite element (FE) simulation of periodontal ligament (PDL) mechanical properties, and the biomimetic degree of FE simulation can be primarily affected by the material properties of the PDL. According to the principle of parameter inverse, a method: response surface (RS) method and FE inverse method were proposed to identify the material parameters of PDL. The Prony series viscoelastic FE model was established based on the relaxation experiment. With root mean square error of simulation results and experimental results as the objective function, the optimal parameter combination was obtained by RS method, and the FE simulation result were compared with the experimental result. The result showed that the optimal parameters of the PDL were elastic modulus: 3.791 MPa, Poisson's ratio: 0.42, temperature: 29.294°C separately, and the simulation result of optimal combination maintained consistency with experiment with the correlation coefficient of 0.97258, indicating that the method proposed in this paper could well identify of PDL material parameters. The parameter identification method used in this paper can significantly improve the calculation efficiency, and reduce the parameter identification error compared with the simple FE inverse method, which has scientific significance and theoretical value.

Biomechanical Modelling for Tooth Survival Studies: Mechanical Properties, Loads and Boundary Conditions-A Narrative Review

Recent biomechanical studies have focused on studying the response of teeth before and after different treatments under functional and parafunctional loads. These studies often involve experimental and/or finite element analysis (FEA). Current loading and boundary conditions may not entirely represent the real condition of the tooth in clinical situations. The importance of homogenizing both sample characterization and boundary conditions definition for future dental biomechanical studies is highlighted. The mechanical properties of dental structural tissues are presented, along with the effect of functional and parafunctional loads and other environmental and biological parameters that may influence tooth survival. A range of values for Young's modulus, Poisson ratio, compressive strength, threshold stress intensity factor and fracture toughness are provided for enamel and dentin; as well as Young's modulus and Poisson ratio for the PDL, trabecular and cortical bone. Angles, loading magnitude and frequency are provided for functional and parafunctional loads. The environmental and physiological conditions (age, gender, tooth, humidity, etc.), that may influence tooth survival are also discussed. Oversimplifications of biomechanical models could end up in results that divert from the natural behavior of teeth. Experimental validation models with close-to-reality boundary conditions should be developed to compare the validity of simplified models.

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.

Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations

This scoping review is intended to synthesize the techniques proposed to model the tooth-periodontal ligament-bone complex (TPBC), while also evaluating the suggested periodontal ligament (PDL) material properties. It is concentrated on the recent advancements on the PDL and TPBC models, while identifying the advantages and limitations of the proposed approaches. Systematic searches were conducted up to December 2020 for articles that proposed PDL models to assess orthodontic tooth movement in Compendex, Web of Science, EMBASE, MEDLINE, PubMed, ScienceDirect, Google Scholar and Scopus databases. Although there have been many studies focused on the evaluation of PDL material properties through numerous modelling approaches, only a handful of approaches have been identified to investigate the interface properties of the PDL as a complete dynamical system (TPBC models). Past reviews on the analytical and experimental determination of the PDL properties already show a concerning range in reported output values-some nearly six orders of magnitude in difference-that strongly suggested the need for further investigation. Surprisingly, it has not yet been possible to determine a narrower range of values for the PDL material properties. Moreover, very few scientific approaches address the TPBC as an integrated complex system model. In consequence, current methods for capturing the PDL material behaviour in a clinical setting are limited and inconclusive. This synthesis encourages more systematic, pragmatic and phenomenological research in this area.

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 RESEARCH ON VISCOELASTICITY PROPERTY OF DIFFERENT LAYERS PERIODONTAL LIGAMENT UNDER COMPRESSION

The periodontal ligament (PDL) exhibits different material mechanical properties along the long axis of the teeth. To explore the creep and the relaxation effects of dissimilar layers of PDL, this paper took the central incisors of porcine mandibular as experimental subjects and divided them perpendicular to the teeth axis into five layers. Creep experiments and relaxation experiments on five layers were conducted to obtain the creep compliance and relaxation modulus at different layers. Linear elastic model, generalized Kelvin model, and generalized Maxwell model were used to describe the major characteristics of the PDL: Instantaneous elasticity, creep and relaxation. Fitting accuracy of three-parameter, five-parameter, and seven-parameter of the model was compared, and the constitutive equations of different layers were established by the least square method.

The results presented that the creep strain and the relaxation stress of PDL were exponentially correlated with time under different loading conditions. Different layers showed a significant effect on the creep strain and relaxation stress of PDL. Along the long axis of the teeth, the changing rule of the creep compliance and relaxation modulus of each layer showed quite the contrary, and the instantaneous elastic modulus first decreased to the minimum, then increased to the maximum. Higher instantaneous elastic modulus led to lower creep compliance and higher relaxation modulus. The generalized Kelvin model and the generalized Maxwell model well characterized the creep and relaxation properties of PDL. Fitting accuracy increased with the number of model parameters. The relaxation time of PDL was about one order of magnitude shorter than the creep retardation time, which indicated that the relaxation effect lasted shorter than the creep effect.

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."

Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: a case study

OBJECTIVES

The objective of this study was to investigate the optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar to determine tooth movements during orthodontic treatment using hydrostatic stress and logarithmic strain on the periodontal ligament (PDL) as indicators by numerical simulations.

MATERIAL AND METHODS

Teeth, PDL and alveolar bone numerical models were constructed as analytical objects based on computed tomography (CT) images. Teeth were assumed to be rigid bodies, and rotational moments ranging from 1.0 to 4.0 Nmm were exerted on the crowns. PDL was defined as a hyperelastic-viscoelastic material with a uniform thickness of 0.25 mm. The alveolar bone model was constructed using a non-uniform material with varied mechanical properties determined based on Hounsfield unit (HU) values calculated using CT images, and its bottom was fixed completely. The optimal range values of PDL compressive and tensile stress were set as 0.47-12.8 and 18.8-51.2 kPa, respectively, whereas that of PDL logarithmic strain was set as 0.15-0.3%.

RESULTS

The rotational tendency of PDL was around the long axis of teeth when loaded. The optimal range values of rotational moment for the mandibular lateral incisor, canine and first premolar were 2.2-2.3, 3.0-3.1 and 2.8-2.9 Nmm, respectively, referring to the biomechanical responses of loaded PDL. Primarily, the optimal range of rotational moment was quadratically dependent on the area of PDL internal surface (i.e. area of PDL internal surface was used to indicate PDL size), as described by the fitting formula.

CONCLUSIONS

Biomechanical responses of PDL can be used to estimate the optimal range of rotational moment for teeth. These rotational moments were not consistent for all teeth, as demonstrated by numerical simulations.

CLINICAL RELEVANCE

The quantitative relationship between the area of PDL internal surface and the optimal orthodontic moment can help orthodontists to determine a more reasonable moment and further optimise clinical treatment.

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.

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.

Numerical simulation of hydro-mechanical coupling of periodontal ligament

Orthodontic tooth movement in the alveolar bone is due to the mechanical response of periodontal ligament to applied forces. Definition of a proper constitutive model of the periodontal ligament to investigate its response to orthodontic loading is required. For this purpose, a three-dimensional finite element model of incisor tooth, periodontal ligament, and bone was built utilizing the hydro-mechanical coupling theory. Tooth displacement in response to orthodontic loading was then investigated, and the effect of different mechanical behaviors assigned to the solid phase of the periodontal ligament was compared. Results showed that where the periodontal ligament was placed in tension, pore volume was filled with fluid intake from the bone, but fluid flow direction was from the periodontal ligament toward the bone where the periodontal ligament was placed in compression. Because of the existence of interaction between solid and fluid phases of the periodontal ligament, considering biphasic material formulation was capable to address its microscopic behavior as well as time-dependent and large deformation behaviors. This article provides beneficial biomechanical data for future dental studies in determination of optimal orthodontic force.

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.

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.

A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis

Excessive forces may cause root resorption and insufficient forces would introduce no effect in orthodontics. The objective of this study was to investigate the optimal orthodontic forces on a maxillary canine, using hydrostatic stress and logarithmic strain of the periodontal ligament (PDL) as indicators. Finite element models of a maxillary canine and surrounding tissues were developed. Distal translation/tipping forces, labial translation/tipping forces, and extrusion forces ranging from 0 to 300 g (100 g=0.98 N) were applied to the canine, as well as the force moment around the canine long axis ranging from 0 to 300 g·mm. The stress/strain of the PDL was quantified by nonlinear finite element analysis, and an absolute stress range between 0.47 kPa (capillary pressure) and 12.8 kPa (80% of human systolic blood pressure) was considered to be optimal, whereas an absolute strain exceeding 0.24% (80% of peak strain during canine maximal moving velocity) was considered optimal strain. The stress/strain distributions within the PDL were acquired for various canine movements, and the optimal orthodontic forces were calculated. As a result the optimal tipping forces (40-44 g for distal-direction and 28-32 g for labial-direction) were smaller than the translation forces (130-137 g for distal-direction and 110-124 g for labial-direction). In addition, the optimal forces for labial-direction motion (110-124 g for translation and 28-32 g for tipping) were smaller than those for distal-direction motion (130-137 g for translation and 40-44 g for tipping). Compared with previous results, the force interval was smaller than before and was therefore more conducive to the guidance of clinical treatment. The finite element analysis results provide new insights into orthodontic biomechanics and could help to optimize orthodontic treatment plans.

Finite element investigation of human maxillary incisor under traumatic loading: Static vs dynamic analysis

BACKGROUND AND OBJECTIVE

Traumatic loading is the main form of injury sustained in dental injuries. In spite of the prevalence of dental trauma, little information is available on traumatic dental damage and the evaluation of tooth behavior under traumatic loading. Due to the short period of traumatic loading, at first sight, a dynamic analysis needs to be performed to investigate the dental trauma. However, it was hypothesized that dental traumatic loading could be regarded as quasi-static loading. Thus, the aim of the present study was to examine this hypothesis.

METHODS

Static and dynamic analyses of the human maxillary incisor were carried out under traumatic loading using a 3D finite element method. Also, modal analysis of the tooth model was performed in order to evaluate the assumption of the dental traumatic loading as a quasi-static one.

RESULTS

It was revealed that the static analysis of dental trauma is preferred to the dynamic analysis when investigating dental trauma, mainly due to its lower computational cost. In fact, it was shown that including the inertia of the tooth structure does not influence the results of the dental trauma simulation. Furthermore, according to the modal analysis of the tooth structure, it was found that the mechanical properties and geometry of the periodontal ligament play significant roles in the classification of dental traumatic loading as a quasi-static one, in addition to the time duration of the applied load.

CONCLUSIONS

This paper provides important biomechanical insights into the classification of dental loading as quasi-static, transient or impact loading in future dental studies.

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.

RESEARCH OF MAXILLARY IMPACTED CANINE IN ORTHODONTIC TREATMENT BASED ON NANOINDENTATION EXPERIMENTS

This study selected the maxillary labial impacted canine as the research object to build the model of periodontal ligament (PDL) and simulate the process of orthodontic treatment. This paper obtained stress–strain curve by calculating and analyzing the data of nanoindentation experiments. The parameters were identified through curve fittings by ABAQUS. The fitting results show that the third-order Ogden model is in good agreement with the experimental data which demonstrate that the third-order Ogden model is able to reflect the material properties of the PDL. In this paper, orthodontic process of the maxillary labial impacted canine was simulated. The results show that inside and outside surfaces of PDL all have stress variation, the stress on the root apex and dental cervix of PDL is relatively large, the maximum appears at dental cervix and the minimum appears close to tooth impedance center.