Hydro-mechanical coupling in the periodontal ligament: A porohyperelastic finite element model

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.

A novel method for simulating ex vivo tooth extractions under varying applied loads

BACKGROUND

Tooth extraction is a common surgical procedure where the invasiveness of the surgery can affect the nature of the dentoalveolar remodelling which follows. However, there is very little biomechanical data relating the loading applied during tooth extraction to the outcomes of the procedure. The purpose of this pilot study is to present a novel ex vivo experimental method for measuring tooth extraction mechanics and to explore preliminary metrics for predicting extraction success.

METHODS

A custom experimental apparatus was developed in-house to extract central incisors from ex vivo swine mandible samples. Twenty-five (n = 25) incisors were extracted at different rates in displacement- and force-control, along with an intermittent ramp-hold scheme for a total of five schemes. Peak forces and extraction success were recorded for each test. Video analysis assisted in determining the instantaneous stiffnesses of the dental complex during continuous extractions, which were compared using the K-means clustering algorithm.

FINDINGS

Tooth extraction forces ranged from 102 N to 309 N, with higher-rate tests tending towards higher peak forces (141 N - 308 N) than the lower-rate tests (102 N-204 N) for displacement- and force-controlled schemes. The K-means algorithm clearly identified load rates among tests, indicating that higher-rate loading increased system stiffness relative to the lower-rate tests.

INTERPRETATION

The developed experimental method demonstrated a desirable degree of control. The preliminary results suggest the influence of load rate on the mechanical response of the dental complex and extraction outcome. Future work will further investigate the biomechanics of tooth extraction and relate them to tissue damage to improve future tooth extraction procedures.

Functional non-uniformity of periodontal ligaments tunes mechanobiological stimuli across soft- and hard-tissue interfaces

The bone-periodontal ligament-tooth (BPT) complex is a unique mechanosensing soft-/hard-tissue interface, which governs the most rapid bony homeostasis in the body responding to external loadings. While the correlation between such loading and alveolar bone remodelling has been widely recognised, it has remained challenging to investigate the transmitted mechanobiological stimuli across such embedded soft-/hard-tissue interfaces of the BPT complex. Here, we propose a framework combining three distinct bioengineering techniques (i, ii, and iii below) to elucidate the innate functional non-uniformity of the PDL in tuning mechanical stimuli to the surrounding alveolar bone. The biphasic PDL mechanical properties measured via nanoindentation, namely the elastic moduli of fibres and ground substance at the sub-tissue level (i), were used as the input parameters in an image-based constitutive modelling framework for finite element simulation (ii). In tandem with U-net deep learning, the Gaussian mixture method enabled the comparison of 5195 possible pseudo-microstructures versus the innate non-uniformity of the PDL (iii). We found that the balance between hydrostatic pressure in PDL and the strain energy in the alveolar bone was maintained within a specific physiological range. The innate PDL microstructure ensures the transduction of favourable mechanobiological stimuli, thereby governing alveolar bone homeostasis. Our outcomes expand current knowledge of the PDL's mechanobiological roles and the proposed framework can be adopted to a broad range of similar soft-/hard- tissue interfaces, which may impact future tissue engineering, regenerative medicine, and evaluating therapeutic strategies. STATEMENT OF SIGNIFICANCE: A combination of cutting-edge technologies, including dynamic nanomechanical testing, high-resolution image-based modelling and machine learning facilitated computing, was used to elucidate the association between the microstructural non-uniformity and biomechanical competence of periodontal ligaments (PDLs). The innate PDL fibre network regulates mechanobiological stimuli, which govern alveolar bone remodelling, in different tissues across the bone-PDL-tooth (BPT) interfaces. These mechanobiological stimuli within the BPT are tuned within a physiological range by the non-uniform microstructure of PDLs, ensuring functional tissue homeostasis. The proposed framework in this study is also applicable for investigating the structure-function relationship in broader types of fibrous soft-/hard- tissue interfaces.

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.

In silico approach towards neuro-occlusal rehabilitation for the early correction of asymmetrical development in a unilateral crossbite patient

Neuro-occlusal rehabilitation (N.O.R.) is a discipline of the stomatognathic medicine that defends early treatments of functional malocclusions, such as unilateral crossbite, for the correction of craniofacial development, avoiding surgical procedures later in life. Nevertheless, N.O.R.'s advances have not been proved analytically yet due to the difficulties of evaluate the mechanical response after the treatment. This study aims to evaluate computationally the effect of N.O.R.'s treatments during childhood. Therefore, bilateral chewing and maximum intercuspation occlusion were modelled through a detailed finite element model of a paediatric craniofacial complex, before and after different selective grinding-alternatives. This model was subjected to the muscular forces derived from a musculoskeletal model and was validated by the occlusal contacts recorded experimentally. This approach yielded errors below 2% and reproduced successfully the occlusal, muscular, functional and mechanical imbalance before the therapies. Treatment strategies balanced the occlusal plane and reduced the periodontal overpressure (>4.7 kPa) and the mandibular over deformation (>0.002 ε) on the crossed side. Based on the principles of the mechanostat theory of bone remodelling and the pressure-tension theory of tooth movement, these findings could also demonstrate how N.O.R.'s treatments correct the malocclusion and the asymmetrical development of the craniofacial complex. Besides, N.O.R.'s treatments slightly modified the stress state and functions of the temporomandibular joints, facilitating the chewing by the unaccustomed side. These findings provide important biomechanical insights into the use of N.O.R.'s treatments for the correction of unilateral crossbite, but also encourage the application of computing methods in biomedical research and clinical practise.

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.

Intrusion of overerupted periodontally compromised posterior teeth using orthodontic mini‐implants: a mechanobiological finite element study

INTRODUCTION

The intrusion of posterior teeth had been considered challenging up to the development of orthodontic mini implants. In periodontally compromised teeth, the challenge is even greater, because of the root resorption risk due to periodontal ligament over-compression. Still, the precise strategy to determine the force reduction level remains uncertain.

OBJECTIVE

The objective of the study was to determine, by a finite element analysis (FEA), the force reduction needed to avoid root resorption and maintain the efficiency of orthodontic mechanics of periodontally compromised teeth similar to the sound one.

METHODS

An anatomical model was constructed representing a premolar inserted into a maxillary bone. Based on the initial model (R0), three bone height loss conditions were simulated (R2 = 2 mm, R4 = 4 mm, and R6 = 6 mm). Two intrusive movements were simulated: pure intrusion (bilateral mini implant) and uncontrolled-tipping intrusion (buccal mini implant). The hydrostatic stress at the periodontal ligament was used to evaluate the risk of root resorption due to over-compression.

RESULTS

For bilateral mini implant intrusion, the force had to be decreased by 16%, 32% and 48% for R2, R4 and R6, respectively. For buccal mini implant intrusion, the required reductions were higher (20%, 36% and 56%). A linear relationship between the intrusive force reduction and the alveolar bone height loss was observed in both intrusion mechanics.

CONCLUSIONS

According to the FE results, 8% or 9.3% of force reduction for each millimetre of bone height loss is suggested for intrusion with bilateral or buccal mini implant, respectively. The buccal mini implant anchorage must be associated with a supplemental strategy to avoid buccal crown tipping.

Biomechanical evaluation of the unilateral crossbite on the asymmetrical development of the craniofacial complex. A mechano-morphological approach

BACKGROUND AND OBJECTIVE

The occlusion effect on the craniofacial development is a controversial topic that has attracted the interest of many researchers but that remains unclear, mainly due to the difficulties on measure its mechanical response experimentally. This mechano-morphological relationship of the craniofacial growth is often explained by the periosteal and capsular matrices of the functional matrix hypothesis (FMH); however, its outcomes have not been analytically demonstrated yet. This computational study aims, therefore, to analytically demonstrate the mechano-morphological relationship in the craniofacial development of children with unilateral crossbite (UXB) using the finite element (FE) method.

METHODS

The craniofacial complex asymmetry of ten children, five of whom exhibit UXB, was 3D-analysed and compared with the biomechanical response computed from a FE analysis of each patient's occlusion. Due to the complexity of the geometry and the multitude of contacts involved, the inherent limitations of the model were evaluated by comparing computed occlusal patterns with those recorded by an occlusal analysis on 3D printed copies.

RESULTS

Comparison's outcomes proved the reliability of our models with just a deviation error below 6% between both approaches. Out of validation process, computational results showed that the significant elongation of mandibular branch in the contralateral side could be related to the mandibular shift and increase of thickness on the crossed side, and particularly of the posterior region. These morphological changes could be associated with periodontal overpressure (>4.7 kPa) and mandibular over deformation (0.002 ε) in that side, in agreement with the periosteal matrix's principles. Furthermore, the maxilla's transversal narrowing and the elevation of the maxillary and zygomatic regions on the crossed side were statistically demonstrated and seem to be related with their respective micro displacements at occlusion, as accounted by their specific capsule matrices. Our results were consistent with those reported clinically and demonstrated analytically the mechano-morphological relationship of children's craniofacial development based on the FMH's functional matrices.

CONCLUSIONS

This study is a first step in the understanding of the occlusion's effect on the craniofacial development by computational methods. Our approach could help future engineers, researchers and clinicians to understand better the aetiology of some dental malocclusions and functional disorders improve the diagnosis or even predict the craniofacial development.

Scaffolds in Periodontal Regenerative Treatment

Successful periodontal regeneration requires the hierarchical reorganization of multiple tissues including periodontal ligament, cementum, alveolar bone, and gingiva. The limitation of conventional regenerative therapies has been attracting research interest in tissue engineering-based periodontal therapies where progenitor cells, scaffolds, and bioactive molecules are delivered. Scaffolds offer not only structural support but also provide geometrical clue to guide cell fate. Additionally, functionalization improves bioactive properties to the scaffold. Various scaffold designs have been proposed for periodontal regeneration. These include the fabrication of biomimetic periodontal extracellular matrix, multiphasic scaffolds with tissue-specific layers, and personalized 3D printed scaffolds. This review summarizes the basic concept as well as the recent advancement of scaffold designing and fabrication for periodontal regeneration and provides an insight of future clinical translation.

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.

Microstructural heterogeneity of the collagenous network in the loaded and unloaded periodontal ligament and its biomechanical implications

The periodontal ligament (PDL) is a highly heterogeneous fibrous connective tissue and plays a critical role in distributing occlusal forces and regulating tissue remodeling. Its mechanical properties are largely determined by the extracellular matrix, comprising a collagenous fiber network interacting with the capillary system as well as interstitial fluid containing proteoglycans. While the phase-contrast micro-CT technique has portrayed the 3D microscopic heterogeneity of PDL, the topological parameters of its network, which is crucial to understanding the multiscale constitutive behavior of this tissue, has not been characterized quantitatively. This study aimed to provide new understanding of such microscopic heterogeneity of the PDL with quantifications at both tissue and collagen network levels in a spatial manner, by combining phase-contrast micro-CT imaging and a purpose-built image processing algorithm for fiber analysis. Both variations within a PDL and among the PDL with different shapes, i.e. round-shaped and kidney-shaped PDLs, are described in terms of tissue thickness, fiber distribution, local fiber densities, and fiber orientation (namely azimuthal and elevation angles). Furthermore, the tissue and collagen fiber network responses to mechanical loading were evaluated in a similar manner. A 3D helical alignment pattern was observed in the fiber network, which appears to regulate and adapt a screw-like tooth motion under occlusion. The microstructural heterogeneity quantified here allows development of sample-specific constitutive models to characterize the PDL's functional and pathological loading responses, thereby providing a new multiscale framework for advancing our knowledge of this complex limited mobility soft-hard tissue interface.

Biomechanical impact of the porous-fibrous tissue behaviour in the temporomandibular joint movements. An in silico approach

The movement of the temporomandibular joint (TMJ) is a function of its complex geometry and its interaction with the surrounding soft tissues. Owing to an increase in the prevalence of temporomandibular joint disorders (TMDs), many computational studies have attempted to characterize its biomechanical behaviour in the last 2 decades. However, most such studies are based on a single computational model that markedly simplifies the complex geometry and mechanical properties of the TMJ's soft tissues. The present study aims to computationally evaluate in a wider sample the importance of considering their complex anatomy and behaviour for simulating both damping and motion responses of this joint. Hence, 6 finite element models of healthy volunteers' TMJ were developed and subjected to both conditions in two different behavioural scenarios. In one, the soft tissues' behaviour was modelled by considering the porous-fibrous properties, whereas in the other case they were simplified assuming isotropic-hyperelastic response, as had been traditionally considered. The damping analysis, which mimic the conditions of an experimental test of the literature, consisted of applying two different compressive loads to the jaw. The motion analysis evaluated the condylar path during the mandible centric depression by the action of muscular forces. From the results of both analyses, the contact pressures, intra-articular fluid pressure, path features, and stress/strain values were compared using the porous-fibrous and isotropic-hyperelastic models. Besides the great differences observed between patients due patient-specific morphology, the porous-fibrous approach yielded results closer to the reference experimental values and to the outcomes of other computational studies of the literature. Our findings underscore, therefore, the importance of considering realistic joint geometries and porous-fibrous contribution in the computational modelling of the TMJ, but also in the design of further joint replacements or in the development of new biomaterials for this joint.

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.

Mechanical effects of distributed fibre orientation in the periodontal ligament of an idealised geometry

In this study, we computationally assess the effects of the distributed fibre orientation in the periodontal ligament (PDL) on mechanical responses of the tooth-PDL complex. An idealised axial-symmetric geometry of a tooth-PDL complex was constructed. The fibre orientation in the PDL was modelled as a trigonometric function based on anatomical knowledge, and the PDL was modelled as a transversely isotropic hyperelastic material dependent on fibre orientations. Parametric studies of the fibre orientation on the mechanical responses of the tooth-PDL complex were conducted. Obtained results showed that the anatomically consistent fibre orientation functions as a supporting structure against not only vertical but also horizontal loads.

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.

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.

Computational characterization of the porous-fibrous behavior of the soft tissues in the temporomandibular joint

The prevalence and severity of temporomandibular joint (TMJ) disorders have led to growing research interest in the development of new biomaterials and medical devices for TMJ implant designs. In computational designs, however, the time and stretch direction dependences of the TMJ soft tissues behavior are not considered and they are frequently based on measurements taken from non‐human species or from joints that differ markedly from the human TMJ. The aim of this study was to accurately characterize the porous‐fibrous properties of the TMJ soft tissues by simulating previously published experimental tests, to assist professionals in the design of new TMJ implants. To that end, material parameters were determined assuming a uniform fiber orientation throughout the entire sample. This assumption was then tested by comparing these results with those of considering multiple regions and distinct fiber orientations in each sample. Our findings validated the use of a transversely isotropic hyperelastic material model to characterize the direction dependent behavior of TMJ soft tissues and its combination with porous hyperfoam material models to mimic the compressive response of the TMJ disc. In conclusion, constitutive model proposed accurately reproduce the mechanical response of the TMJ soft tissues at different strain rates and stretch directions.

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.

A novel approach for early evaluation of orthodontic process by a numerical thermomechanical analysis

The main objective of this paper is to propose a novel method that provides an opportunity to evaluate an orthodontic process at early phase of the treatment. This was accomplished by finding out a correlation between the applied orthodontic force and thermal variations in the tooth structure. To this end, geometry of the human tooth surrounded by the connective soft tissue called the periodontal ligament and the bone was constructed by employing dental CT scan images of a specific case. The periodontal ligament was modeled by finite strain viscoelastic model through a nonlinear stress-strain relation (hyperelasticity) and nonlinear stress-time relation (viscoelasticity). The tooth structure was loaded by a lateral force with 15 different quantities applied to 20 different locations, along the midedge of the tooth crown. The resultant compressive stress in the periodontal ligament was considered as the cause of elevated cell activity that was modeled by a transient heat flux in the thermal analysis. The heat flux value was estimated by conducting an experiment on a pair of rats. The numerical results showed that by applying an orthodontic force to the tooth structure, a significant temperature rise was observed. By measuring the temperature rise, the orthodontic process can be evaluated.

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.

Theoretical Considerations and a Mathematical Model for the Analysis of the Biomechanical Response of Human Keratinized Oral Mucosa

Removable complete and partial dentures are supported by the residual alveolar ridges consisting of mucosa, submucosa, periosteum, and bone. An understanding of the biomechanical behavior of the oral mucosa is essential in order to improve the denture-bearing foundations for complete and partially edentulous patients. The purpose of this paper was to examine the biomechanical behavior of the soft tissues supporting a removable denture and develop a model for that reason. Keratinized oral mucosa blocks with their underlying bone were harvested from the maxillary palatal area adjacent to the edentulous ridges of a cadaver. The compressive response of the oral mucosa was tested by using atomic force microscopy. The specimens were first scanned in order their topography to be obtained. The mechanical properties of the specimens were tested using a single crystal silicon pyramidal tip, which traversed toward the keratinized oral mucosa specimens. Loading-unloading cycles were registered and four mathematical models were tested using MATLAB to note which one approximates the force-displacement curve as close as possible: a. spherical, b. conical, c. third order polynomial, d. Murphy (fourth order polynomial, non-linear Hertzian based). The third order polynomial model showed the best accuracy in representing the force-displacement data of the tested specimens. A model was developed in order to analyze the biomechanical behavior of the human oral keratinized mucosa and obtain information about its mechanical properties.

Biomechanics of oral mucosa

The prevalence of prosthodontic treatment has been well recognized, and the need is continuously increasing with the ageing population. While the oral mucosa plays a critical role in the treatment outcome, the associated biomechanics is not yet fully understood. Using the literature available, this paper provides a critical review on four aspects of mucosal biomechanics, including static, dynamic, volumetric and interactive responses, which are interpreted by its elasticity, viscosity/permeability, apparent Poisson's ratio and friction coefficient, respectively. Both empirical studies and numerical models are analysed and compared to gain anatomical and physiological insights. Furthermore, the clinical applications of such biomechanical knowledge on the mucosa are explored to address some critical concerns, including stimuli for tissue remodelling (interstitial hydrostatic pressure), pressure–pain thresholds, tissue displaceability and residual bone resorption. Through this review, the state of the art in mucosal biomechanics and their clinical implications are discussed for future research interests, including clinical applications, computational modelling, design optimization and prosthetic fabrication.

Inhibition of Histone Deacetylases Enhances the Osteogenic Differentiation of Human Periodontal Ligament Cells

One of the characteristics of periodontal ligament (PDL) cells is their plasticity. Yet, the underlying mechanisms responsible for this phenomenon are unknown. One possible mechanism might be related to epigenetics, since histone deacetylases (HDACs) have been shown to play a role in osteoblast differentiation. This study was aimed to investigate the role of HDACs in osteogenic differentiation of human PDL (hPDL) cells. HDAC inhibitor trichostatin A (TSA) had no effect on cell viability as was assessed by MTT assay. Osteogenic and adipogenic differentiation was analyzed by gene expression, ALP activity and mineral deposition. Western blotting was used to investigate the effect of TSA on histone acetylation and protein expression. In the presence of the HDAC inhibitor osteogenic differentiation was induced; osteoblast-related gene expression was increased significantly. ALP activity and mineral nodule formation were also enhanced. Inhibition of HDACs did not induce differentiation into the adipocyte lineage. hPDL highly expressed HDACs of both class I (HDAC 1, 2, 3) and class II (HDAC 4, 6). During osteogenic differentiation HDAC 3 expression gradually decreased. This was apparent in the absence and presence of the inhibitor. The level of acetylated Histone H3 was increased during osteogenic differentiation. Inhibition of HDAC activity induced hyperacetylation of Histone H3, therefore, demonstrating Histone H3 as a candidate target molecule for HDAC inhibition. In conclusion, hPDL cells express a distinguished series of HDACs and these enzymes appear to be involved in osteogenic differentiation. This finding suggests a potential application of TSA for bone regeneration therapy by hPDL cells.

Viscoelasticity of periodontal ligament: an analytical model

BACKGROUND

Understanding of viscoelastic behaviour of a periodontal membrane under physiological conditions is important for many orthodontic problems. A new analytic model of a nearly incompressible viscoelastic periodontal ligament is suggested, employing symmetrical paraboloids to describe its internal and external surfaces.

METHODS

In the model, a tooth root is assumed to be a rigid body, with perfect bonding between its external surface and an internal surface of the ligament. An assumption of almost incompressible material is used to formulate kinematic relationships for a periodontal ligament; a viscoelastic constitutive equation with a fractional exponential kernel is suggested for its description.

RESULTS

Translational and rotational equations of motion are derived for ligament's points and special cases of translational displacements of the tooth root are analysed. Material parameters of the fractional viscoelastic function are assessed on the basis of experimental data for response of the periodontal ligament to tooth translation. A character of distribution of hydrostatic stresses in the ligament caused by vertical and horizontal translations of the tooth root is defined.

CONCLUSIONS

The proposed model allows generalization of the known analytical models of the viscoelastic periodontal ligament by introduction of instantaneous and relaxed elastic moduli, as well as the fractional parameter. The latter makes it possible to take into account different behaviours of the periodontal tissue under short- and long-term loads. The obtained results can be used to determine loads required for orthodontic tooth movements corresponding to optimal stresses, as well as to simulate bone remodelling on the basis of changes in stresses and strains in the periodontal ligament caused by such movements.

In vivo measurements and numerical analysis of the biomechanical characteristics of the human periodontal ligament

The periodontal ligament is a complex tissue with respect to its biomechanical behaviour. It is important to understand the mechanical behaviour of the periodontal ligament during physiological loading in healthy patients as well as during the movement of the tooth in orthodontic treatment or in patients with periodontal disease, as these might affect the mechanical properties of the periodontal ligament (PDL). Up to now, only a limited amount of in vivo data is available concerning this issue. The aim of this study has been to determine the time dependent material properties of the PDL in an experimental in vivo study, using a novel device that is able to measure tooth displacement intraorally. Using the intraoral loading device, tooth deflections at various velocities were realised in vivo on human teeth. The in vivo investigations were performed on the upper left central incisors of five volunteers aged 21-33 years with healthy periodontal tissue. A deflection, applied at the centre of the crown, was linearly increased from 0 to 0.15mm in a loading period of between 0.1 and 5.0s. Individual numerical models were developed based on the experimental results to simulate the relationship between the applied force and tooth displacement. The numerical force/displacement curves were fitted to the experimental ones to obtain the material properties of the human PDL. For the shortest loading time of 0.1s, the experimentally determined forces were between 7.0 and 16.2N. The numerically calculated Young's modulus varied between 0.9MPa (5.0s) and 1.2MPa (0.1s). By considering the experimentally and numerically obtained force curves, forces decreased with increasing loading time. The experimental data gained in this study can be used for the further development and verification of a multiphasic constitutive law of the PDL.

Shape Optimization for Additive Manufacturing of Removable Partial Dentures--A New Paradigm for Prosthetic CAD/CAM

With ever-growing aging population and demand for denture treatments, pressure-induced mucosa lesion and residual ridge resorption remain main sources of clinical complications. Conventional denture design and fabrication are challenged for its labor and experience intensity, urgently necessitating an automatic procedure. This study aims to develop a fully automatic procedure enabling shape optimization and additive manufacturing of removable partial dentures (RPD), to maximize the uniformity of contact pressure distribution on the mucosa, thereby reducing associated clinical complications. A 3D heterogeneous finite element (FE) model was constructed from CT scan, and the critical tissue of mucosa was modeled as a hyperelastic material from in vivo clinical data. A contact shape optimization algorithm was developed based on the bi-directional evolutionary structural optimization (BESO) technique. Both initial and optimized dentures were prototyped by 3D printing technology and evaluated with in vitro tests. Through the optimization, the peak contact pressure was reduced by 70%, and the uniformity was improved by 63%. In vitro tests verified the effectiveness of this procedure, and the hydrostatic pressure induced in the mucosa is well below clinical pressure-pain thresholds (PPT), potentially lessening risk of residual ridge resorption. This proposed computational optimization and additive fabrication procedure provides a novel method for fast denture design and adjustment at low cost, with quantitative guidelines and computer aided design and manufacturing (CAD/CAM) for a specific patient. The integration of digitalized modeling, computational optimization, and free-form fabrication enables more efficient clinical adaptation. The customized optimal denture design is expected to minimize pain/discomfort and potentially reduce long-term residual ridge resorption.

Experiment and hydro-mechanical coupling simulation study on the human periodontal ligament

In this paper, a new method involving an experiment in vivo and hydro-mechanical coupling simulations was proposed to investigate the biomechanical property of human periodontal ligament (PDL). Teeth were loaded and their displacements were measured in vivo. The finite element model of the experiment was built and hydro-mechanical coupling simulations were conducted to test some PDL's constitutive models. In the simulations, the linear elastic model, the hyperfoam model, and the Ogden model were assumed for the solid phase of the PDL coupled with a model of the fluid phase of the PDL. The displacements of the teeth derived from the simulations were compared with the experimental data to validate these constitutive models. The study shows that a proposed constitutive model of the PDL can be reliably tested by this method. Furthermore, the influence of species, areas, and the fluid volume ratio on PDL's mechanical property should be considered in the modeling and simulation of the mechanical property of the PDL.

Biomechanical considerations on tooth-implant supported fixed partial dentures

This article discusses the connection of teeth to implants, in order to restore partial edentulism. The main problem arising from this connection is tooth intrusion, which can occur in up to 7.3% of the cases. The justification of this complication is being attempted through the perspective of biomechanics of the involved anatomical structures, that is, the periodontal ligament and the bone, as well as that of the teeth- and implant-supported fixed partial dentures.