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

Exploring the mechanical and biological interplay in the periodontal ligament

The periodontal ligament (PDL) plays a crucial role in transmitting and dispersing occlusal force, acting as mechanoreceptor for muscle activity during chewing, as well as mediating orthodontic tooth movement. It transforms mechanical stimuli into biological signals, influencing alveolar bone remodeling. Recent research has delved deeper into the biological and mechanical aspects of PDL, emphasizing the importance of understanding its structure and mechanical properties comprehensively. This review focuses on the latest findings concerning both macro- and micro- structural aspects of the PDL, highlighting its mechanical characteristics and factors that influence them. Moreover, it explores the mechanotransduction mechanisms of PDL cells under mechanical forces. Structure-mechanics-mechanotransduction interplay in PDL has been integrated ultimately. By providing an up-to-date overview of our understanding on PDL at various scales, this study lays the foundation for further exploration into PDL-related biomechanics and mechanobiology.

Formulation of Hyperelastic Constitutive Model for Human Periodontal Ligament Based on Fiber Volume Fraction

Collagen fibers of the Periodontal ligament (PDL) play a crucial role in determining its mechanical properties. Based on this premise, we investigated the effect of the volume fraction of human PDL collagen fibers on the hyperelastic mechanical behavior under transient loading. Samples were obtained from different root regions (neck, middle, and apex) of the PDL, prepared from fresh human anterior teeth. The collagen fibers volume fraction in various regions of the PDL was quantified by staining techniques combined with image processing software. The collagen fiber volume fractions were found to be 60.3% in the neck region, 63.1% in the middle region, and 52.0% in the apex region. A new hyperelastic constitutive model was constructed based on the volume fraction. A uniaxial tensile test was conducted on these samples, and the accuracy of the constitutive model was validated by fitting the test data. Also, relevant model parameters were derived. The results demonstrated that human PDL exhibited hyperelastic mechanical properties on the condition of transient loading. With an increase in the volume fraction of collagen fibers, the tensile resistance of the PDL was enhanced, demonstrating more significant hyperelastic mechanical properties. The hyperelastic constitutive model showed a good fit with the experimental results (R2 > 0.997), describing the hyperelastic mechanical properties of the human PDL effectively.

Loading rate, geometry, and damage state influence vertical extraction biomechanics in an ex vivo swine dental model

Introduction

Validated models describing the biomechanics of tooth extraction are scarce. This study seeks to perform experimental and numerical characterization of vertical tooth extraction biomechanics in swine incisors with imposed vertical extraction loads. Imaging analysis related mechanical outcomes to tooth geometry and applied loading rate. Then, the predictive capabilities of the developed finite element analysis (FEA) models were demonstrated by testing different loading scenarios and validating the results against experimental equivalents.

Methods

Simulated vertical extractions were performed on partial swine central incisors (n = 49) and studied for peak extraction force and dental complex stiffness. Post-extraction µCT images were obtained to measure root surface attachment area (RSAA) and observe patterns of periodontal ligament (PDL) rupture. Crosshead force-displacement data was used in an inverse finite element analysis (IFEA) to verify parameters for the PDL in an axisymmetric model of tooth extraction. New force-hold loading protocols were devised in silico and validated in a series of tests on swine incisors to demonstrate the predictive efficacy of the finite element model. Force-hold loading on an initially-damaged PDL was also simulated.

Results

Reductions in loading rate and RSAA were found to significantly reduce peak extraction forces by 98N-120 N. Increases in instantaneous stiffness during loading were associated with increases in loading rate. Inverse finite element solutions demonstrated consistent PDL parameters across loading cases. Force-hold loading predicted extraction behaviour with large variance in extraction time. Damage imposed in the FEA model was able to predict experimental results from experiments on similarly-damaged dental complexes.

Conclusion

This study presents a comprehensive experimental and numerical characterization of vertical tooth extraction biomechanics employing an ex vivo swine model. The results of these experiments suggest that the axisymmetric FEA model is a powerful tool for predicting a range of conditions and dental complex geometries. The predictive power of the FEA model demonstrated in this study encourages its use in pre-clinical testing and development of new vertical extraction loading schemes for improving clinical outcomes.

Inverse finite element analysis for an axisymmetric model of vertical tooth extraction

BACKGROUND AND OBJECTIVE

Tooth extraction is a common clinical procedure with biomechanical factors that can directly influence patient outcomes. Recent development in atraumatic extraction techniques have endeavoured to improve treatment outcomes, but the characterization of extraction biomechanics is sparse. An axisymmetric inverse finite element (FE) approach is presented to represent the biomechanics of vertical atraumatic tooth extraction in an ex-vivo swine model.

METHODS

Geometry and boundary conditions from the model are determined to match the extraction of swine incisors in a self-aligning ex vivo extraction experiment. Material parameters for the periodontal ligament (PDL) model are determined by solving an inverse FE problem using clusters of data obtained from 10 highly-controlled mechanical experiments. A seven-parameter visco-hyperelastic damage model, based on an Arruda-Boyce framework, is used for curve fitting. Three loading schemes were fit to obtain a common set of material parameters.

RESULTS

The inverse FE results demonstrate good predictions for overall force-time curve shape, peak force, and time to peak force. The fit model parameters are sufficiently consistent across all three cases that a coefficient-averaged model was taken that compares well to all three cases. Notably, the initial modulus ,u, converged across trials to an average value of 0.472 MPa with an average viscoelastic constant g of 0.561.

CONCLUSIONS

The presented model is found to have consistent parameters across loading cases. The capability of this model to represent the fundamental mechanical characteristics of the dental complex during vertical extraction loading is a significant advancement in the modelling of extraction procedures. Future work will focus on verifying the model as a predictive design tool for assessing new loading schemes in addition to investigating its applications to subject-specific problems.

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.

FEA Comparison of the Mechanical Behavior of Three Dental Crown Materials: Enamel, Ceramic, and Zirconia

The restoration of endodontically treated teeth is one of the main challenges of restorative dentistry. The structure of the tooth is a complex assembly in which the materials that make it up, enamel and dentin, have very different mechanical behaviors. Therefore, finding alternative replacement materials for dental crowns in the area of restorative care isa highly significant challenge, since materials such as ceramic and zirconia have very different stress load resistance values. The aim of this study is to assess which material, either ceramic or zirconia, optimizes the behavior of a restored tooth under various typical clinical conditions and the masticatory load. A finite element analysis (FEA) framework is developed for this purpose. The 3D model of the restored tooth is input into the FEA software (Ansys Workbench R23)and meshed into tetrahedral elements. The presence of masticatory forces is considered: in particular, vertical, 45° inclined, and horizontal resultant forces of 280 N are applied on five contact points of the occlusal surface. The numerical results show that the maximum stress developed in the restored tooth including a ceramic crown and subject to axial load is about 39.381 MPa, which is rather close to the 62.32 MPa stress computed for the natural tooth; stresses of about 18 MPa are localized at the roots of both crown materials. In the case of the zirconia crown, the stresses are much higher than those in the ceramic crown, except for the 45° load direction, while, for the horizontal loads, the stress peak in the zirconia crown is almost three times as large as its counterpart in the ceramic crown (i.e., 163.24 MPa vs. 56.114 MPa, respectively). Therefore, the zirconia crown exhibits higher stresses than enamel and ceramic that could increase in the case of parafunctions, such as bruxism. The clinician's choice between the two materials should be evaluated based on the patient's medical condition.

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.

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.