Development and parameter identification of a visco-hyperelastic model for the periodontal ligament

A finite element analysis of periodontal ligament fluid mechanics response to occlusal loading based on hydro-mechanical coupling model

OBJECTIVE

Considering fluid stimulation is one of the essential biomechanical signals for periodontal tissues, this study aims to characterizing fluid mechanics response during occlusal loading by a hydro-mechanical coupling model for periodontal ligament.

DESIGN

Models simulating periodontium with normal bone height and with intraosseous defects were built with three mechanical modules: tooth, periodontal ligament and alveolar bone. Tooth was modeled as linear elastic, and periodontal ligament and alveolar bone as a hydro-mechanical coupling model. Transient analyses under dynamic occlusal loading were performed. Fluid dynamics within periodontal ligament space was simulated and visualized by post-processing module.

RESULTS

Reciprocating oscillatory flow occurred within the periodontal ligament under occlusal loading. Higher pore pressure and fluid velocity were observed in furcation and apical regions compared to mid-root and cervical regions. Intraosseous defects increased pore pressure and fluid velocity within the periodontal ligament, most significantly near the defect.

CONCLUSION

Based on the results of the hydro-mechanical coupling model, significant oscillatory fluid motion is observed within the periodontal ligament under occlusal loading. Particularly, higher fluid velocity is evident in the furcation and apical areas. Additionally, Intraosseous defects significantly enhance fluid motion within the periodontal ligament.

Minimum residual root dentin thickness of mandibular premolars restored with a post: A finite element analysis study

STATEMENT OF PROBLEM

Thin root dentin after post space preparation will increase the risk of root fracture. However, the minimum residual root dentin thickness to be preserved after post space preparation is unclear.

PURPOSE

The purpose of this finite element analysis (FEA) study was to measure the residual root dentin thicknesses and analyze the stress distributions of post-restored mandibular premolars.

MATERIAL AND METHODS

The cone beam computed tomography (CBCT) data of 90 first and second mandibular premolars from Chinese participants (44 men, 46 women; aged between 20 and 79 years) were analyzed. Cross-sections 5 to 9 mm from the radiologic apex were used to measure the buccolingual and mesiodistal root diameters. The probability that the residual thickness of the buccolingual and mesiodistal root walls would be no less than 0.5, 0.6, 0.7, 0.8, 0.9, and 1 mm after post space preparation with a #2 Peeso reamer was calculated. Six 3-dimensional finite element models of cast post-restored mandibular premolars with 0.5, 0.6, 0.7, 0.8, 0.9, and 1 mm mesial and distal root dentin thicknesses were established. A static force of 100 N was applied to the buccal cusp tip at 45, 60, 75, and 90 degrees to the long axis of the tooth, and the maximum tensile stress and von Mises stress were analyzed. The Bonferroni post hoc test (αcorrected=.003) was used for multiple comparisons.

RESULTS

The buccolingual root diameter of mandibular premolars was wider than the mesiodistal root diameter. The probabilities that the mesiodistal residual root dentin thickness of mandibular first and second premolars at 5 mm from the apex would be no less than 1 mm after post space preparation with a #2 Peeso reamer were only 10% and 28%, respectively. The maximum tensile stress was at a minimum when the mesial and distal residual root dentin thickness was 0.6 mm in the external cervical dentin adjacent to the crestal bone and 1 mm in the apical dentin corresponding to the apex of the post. The maximum tensile stress of the mandibular premolar model with 0.6-mm mesial and distal residual root dentin thicknesses was lower than that with 0.9 mm and 1.0 mm thicknesses (Pcorrected<.001).

CONCLUSIONS

Short posts or smaller instruments for post space preparation are recommended to obtain a 1-mm residual root dentin thickness in the mesiodistal direction of mandibular premolars. If a 1-mm thickness cannot be preserved, a minimum residual root dentin thickness of 0.6 to 0.9 mm in the mesiodistal direction should be retained.

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.

The effects of material and structural properties of the periodontal ligament in mechanical function of tooth-PDL-bone complex in dental trauma: A sensitivity study using finiteelement analysis

Periodontal ligament (PDL) plays a crucial role in transferring load from tooth to its adjacent bone, and its role is more pronounced in case of trauma, due to its shock-absorbing character, which has not been fully understood yet. Different constitutive models have correlated mechanical function of PDL with its anisotropic, inhomogeneous, non-linear elastic nature, and it was variably modeled using Finite Element (FE) simulations of dental trauma. Furthermore, since capturing accurate dimension of PDL is difficult, various thicknesses were considered for PDL in FE reconstruction process. In this study, the sensitivity of FE analyses to variation in mechanical properties, including a large range of elastic properties for a linear elastic model, also a hyper-elastic material model, and various thicknesses of PDL was investigated by developing a CT-based FE model of tooth-PDL-bone complex. Results of this study highlighted the crucial role of PDL in absorption and dissipation of energy, as well as in stress distribution within alveolar bone during dental trauma. It was observed that as Young's modulus of PDL decreases and its thickness increases, its shock-absorbing capacity would be escalated. Moreover, it was found that inclusion of PDL reduces the maximum von Mises stress exerted on the alveolar bone by about 60% in some areas, compared to the case in which the PDL is absent. Results of this work underscore the need of presenting comprehensive constitutive models to describe mechanical behavior of PDL, with the goal of understanding the behavior of a tooth-PDL-bone complex in pathological conditions, such as trauma.

Determination of the compressive modulus of elasticity of periodontal ligament derived from human first premolars

Purpose

There are two commonly cited modulus of elasticity of the human periodontal ligament (EPDL), i.e., 6.89 ✕ 10-5 GPa (E1) and 6.89 ✕ 10-2 GPa (E2), which are exactly 1000-fold different from each other. This study aims to clarify the ambiguity of the two EPDL used for simulations and determine a more accurate EPDL value of human first premolars using experimental and simulation approaches.

Methods

Numerical simulations using finite element analysis were performed to analyze PDL deformation under an average Asian occlusal force. To confirm the results, simple and multi-component, true-scale 3D models of a human first premolar were used in the simulations. Finally, a compression test using a universal testing machine on PDL specimens was conducted to identify the compressive EPDL of human first premolars.

Results

The simulation results from both models revealed that E1 was inaccurate, because it resulted in excessive PDL deformation under the average occlusal force, which should not occur during mastication. Although the E2 did not lead to excessive PDL deformation, it was obtained by an error in unit conversion with no scientific backing. In contrast, the compression test results indicated that the compressive EPDL was 9.64 ✕ 10-4 GPa (E3). In the simulation, E3 did not cause excessive PDL deformation.

Conclusion

The simulation results demonstrated that both commonly cited EPDL values (E1 and E2) were incorrect. Based on the experimental and simulation results, the average compressive EPDL of 9.64 ✕ 10-4 GPa is proposed as a more accurate value for human first premolars.

Clinical significance

The proposed more accurate EPDL would contribute to more precise and reliable FEA simulation results and provide a better understanding of the stress distribution and deformation of dental materials, which will be beneficial to precision dentistry, orthodontics and restoration designs.

One step further in biomechanical models in palaeontology: a nonlinear finite element analysis review

Finite element analysis (FEA) is no longer a new technique in the fields of palaeontology, anthropology, and evolutionary biology. It is nowadays a well-established technique within the virtual functional-morphology toolkit. However, almost all the works published in these fields have only applied the most basic FEA tools i.e., linear materials in static structural problems. Linear and static approximations are commonly used because they are computationally less expensive, and the error associated with these assumptions can be accepted. Nonetheless, nonlinearities are natural to be used in biomechanical models especially when modelling soft tissues, establish contacts between separated bones or the inclusion of buckling results. The aim of this review is to, firstly, highlight the usefulness of non-linearities and secondly, showcase these FEA tool to researchers that work in functional morphology and biomechanics, as non-linearities can improve their FEA models by widening the possible applications and topics that currently are not used in palaeontology and anthropology.

Effect of the Maxillary Sinus on Tooth Movement during Orthodontics Based on Biomechanical Responses of Periodontal Ligaments

The maxillary sinus is a common anatomic limitation for orthodontic tooth movement. The effect of orthodontic forces on a particular anatomy can be studied using finite element analysis (FEA). Our study aimed to determine the effect of different tooth penetration depths into the maxillary sinus floor (MSF) on the orthodontic force system for bodily tooth movement. Using the cone-beam computed tomography of a patient with low MSF, we modeled the geometry of canine, premolar, and molar teeth with their periodontal ligaments and the alveolar bone surrounding them. The models were manually modified to simulate different root penetration depths. Thereafter, the center of resistance and stress distributions for teeth penetrating into the MS were determined using FEA. Moreover, the force systems for teeth with a low MSF to varying degree were evaluated based on the FEA results. During orthodontic tooth movement, the individual differences in the periodontal anatomy should be considered. The CR position decreases with the penetration depth, while the average hydrostatic stress in the PDL increases rapidly. In this paper, we present the correction coefficients of the orthodontic force and moment for a tooth penetrating into the MSF, which is necessary for personalized treatment planning.

Exploring the Biomechanical Properties of the Human Cornea In Vivo Based on Corvis ST

Purpose: The aim of this study was to provide a method to determine corneal nonlinear viscoelastic properties based on the output data of corneal visualization Scheimpflug technology (Corvis ST).

Methods: The Corvis ST data from 18 eyes of 12 healthy humans were collected. Based on the air-puff pressure and the corneal displacement from the Corvis ST test of normal human eyes, the work done by the air-puff attaining the whole corneal displacement was obtained. By applying a visco-hyperelastic strain energy density function of the cornea, in which the first-order Prony relaxation function and the first-order Ogden strain energy were employed, the corneal strain energy during the Corvis ST test was calculated. Then the work done by the air-puff attaining the whole corneal displacement was completely regarded as the strain energy of the cornea. The identification of the nonlinear viscoelastic parameters was carried out by optimizing the sum of difference squares of the work and the strain energy using the genetic algorithm.

Results: The visco-hyperelastic model gave a good fit to the data of corneal strain energy with time during the Corvis ST test (R² > 0.95). The determined Ogden model parameter μ ranged from 0.42 to 0.74 MPa, and α ranged from 32.76 to 55.63. The parameters A and τ in the first-order Prony function were 0.09–0.36 and 1.21–1.95 ms, respectively.

Conclusion: It is feasible to determine the corneal nonlinear viscoelastic properties based on the corneal contour information and air-puff pressure of the Corvis ST test.

Development and verification of a constitutive model for human periodontal ligament based on finite element analysis

This study aimed to develop a constitutive model for human periodontal ligament (PDL) by combining the hyperelastic and viscosity models. We performed the finite element analysis (FEA) to simulate the experimental processes of the PDL in vitro and in vivo tests to verify the developed model. The FEA results indicated that the simulative curves were consistent with the experimental curves in the PDL in vitro tests. Moreover, for the in vivo measurements, the simulative result of 0.6258 N was similar to the experimental value of 0.65 N. The study results can help orthodontists better understand the biomechanical characteristics of PDL.

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.

OpenMandible: An open-source framework for highly realistic numerical modelling of lower mandible physiology

OBJECTIVE

Computer modeling of lower mandible physiology remains challenging because prescribing realistic material characteristics and boundary conditions from medical scans requires advanced equipment and skill sets. The objective of this study is to provide a framework that could reduce simplifications made and inconsistency (in terms of geometry, materials, and boundary conditions) among further studies on the topic.

METHODS

The OpenMandible framework offers: 1) the first publicly available multiscale model of the mandible developed by combining cone beam computerized tomography (CBCT) and μCT imaging modalities, and 2) a C++ software tool for the generation of simulation-ready models (tet4 and hex8 elements). In addition to the application of conventional (Neumann and Dirichlet) boundary conditions, OpenMandible introduces a novel geodesic wave propagation - based approach for incorporating orthotropic micromechanical characteristics of cortical bone, and a unique algorithm for modeling muscles as uniformly directed vectors. The base intact model includes the mandible (spongy and compact bone), 14 teeth (comprising dentin, enamel, periodontal ligament, and pulp), simplified temporomandibular joints, and masticatory muscles (masseter, temporalis, medial, and lateral pterygoid).

RESULTS

The complete source code, executables, showcases, and sample data are freely available on the public repository: https://github.com/ArsoVukicevic/OpenMandible. It has been demonstrated that by slightly editing the baseline model, one can study different "virtual" treatments or diseases, including tooth restoration, placement of implants, mandible bone degradation, and others.

SIGNIFICANCE

OpenMandible eases the community to undertake a broad range of studies on the topic, while increasing their consistency and reproducibility. At the same time, the needs for dedicated equipment and skills for developing realistic simulation models are significantly reduced.

Parameter identification for the simulation of the periodontal ligament during the initial phase of orthodontic tooth movement

The paper is concerned with simulation of the periodontal ligament response to force in the initial phase of orthodontic tooth movement. This is based on two previous investigations, a in vitro experiment with specimens of porcine mandibular premolars and a in vivo experiment on human upper first incisors. For the curve fit of the in vitro experiment a model function, assuming viscoelasticity, was introduced. The viscoelastic model function was augmented by a ramp rise time term, to account for observed dependence of the response on actuator velocity, and a previous load history term, to account for the effect of the previous tests on the current test. The correlation coefficient of a curve fit for all tests grouped together was R2=0.98. Next, a curve fit of the in vivo experiment was done. Good correlation was found for a simplified model function, without viscoelastic term (R2=0.96). For both tests, in vitro and in vivo, the ramp rise time term improved correlation. A finite element model of the specimen of the in vitro experiment was created. For the PDL a hyperelastic constitutive model for compressible material was used and model parameters were identified. The present work indicates that the macroscopic response of the periodontal ligament to an external load can be simulated with a poro-visco-hyperelastic model. The simulation showed that poroelastic behaviour will gradually cease when viscoelastic relaxation progresses. This followed also from dimensionless analysis. As a consequence, for slow loading, or if initial response to fast loading is not of interest, a visco-hyperelastic model may suffice. To identify parameters of the finite element model several optimisation problems were solved. A model function, which can be regarded as a reduced order model, allowed a full factorial experiment (analysis) at low cost, to identify initial parameters. The thus found parameters were further refined with an optimum interpolation meta-model. That is, for limited number of parameter combinations the response was simulated with the finite element model and a refined parameter study was conducted by means of optimal interpolation. The thus found optimal parameters were verified by simulation with the finite element model. Optimal interpolation is computationally cheap, which allowed full factorial experiments at low cost.

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.

Linear Momenta Transferred to the Dental Implant-Bone and Natural Tooth-PDL-Bone Constructs Under Impact Loading: A Comparative in-vitro and in-silico Study

During dental trauma, periodontal ligament (PDL) contributes to the stability of the tooth-PDL-bone structure. When a dental implant is inserted into the bone, the dental implant-bone construct will be more prone to mechanical damage, caused by impact loading, than the tooth-PDL-bone construct. In spite of the prevalence of such traumas, the behavioral differences between these two constructs have not been well-understood yet. The main goal of this study was to compare the momentum transferred to the tooth-PDL-bone and dental implant-bone constructs under impact loading. First, mechanical impact tests were performed on six canine mandibles of intact (N = 3) and implanted (N = 3) specimens using a custom-made drop tower apparatus, from release heights of 1, 2, and 3 cm. Next, computed tomography-based finite element models were developed for both constructs, and the transferred momenta were calculated. The experimental results indicated that, for the release heights of 1, 2, and 3 cm, the linear momenta transferred to the dental implant-bone construct were 33.1, 31.0, and 27.5% greater than those of the tooth-PDL-bone construct, respectively. Moreover, results of finite element simulations were in agreement with those of the experimental tests (error <7.5%). This work tried to elucidate the effects of impact loading on the dental implant-bone and tooth-PDL-bone constructs using both in-vitro tests and validated in-silico simulations. The findings can be employed to modify design of the current generation of dental implants, based on the lessons one can take from the biomechanical behavior of a natural tooth structure.

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.

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.

Generalization of exponential based hyperelastic to hyper-viscoelastic model for investigation of mechanical behavior of rate dependent materials

In this research, the exponential stretched based hyperelastic strain energy was generalized to the hyper-viscoelastic model using the heredity integral of deformation history to take into account the strain rate effects on the mechanical behavior of materials. The heredity integral was approximated by the approach of Goh et al. to determine the model parameters and the same estimation was used for constitutive modeling. To present the ability of the proposed hyper-viscoelastic model, the stress-strain response of the thermoplastic elastomer gel tissue at different strain rates from 0.001 to 100/s was studied. In addition to better agreement between the current model and experimental data in comparison to the extended Mooney-Rivlin hyper-viscoelastic model, a stable material behavior was predicted for pure shear and balance biaxial deformation modes. To present the engineering application of current model, the Kolsky bars impact test of gel tissue was simulated and the effects of specimen size and inertia on the uniform deformation were investigated. As the mechanical response of polyurea was provided over wide strain rates of 0.0016-6500/s, the current model was applied to fit the experimental data. The results were shown more accuracy could be expected from the current research than the extended Ogden hyper-viscoelastic model. In the final verification example, the pig skin experimental data was used to determine parameters of the hyper-viscoelastic model. Subsequently, a specimen of pig skin at different strain rates was loaded to a fixed strain and the change of stress with time (stress relaxation) was obtained. The stress relaxation results were revealed the peak stress increases by applied strain rate until the saturated loading rate and the equilibrium stress with magnitude of 0.281MPa could be reached.

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.