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

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.

Biomechanics of soft biological tissues and organs, mechanobiology, homeostasis and modelling

The human body consists of many different soft biological tissues that exhibit diverse microstructures and functions and experience diverse loading conditions. Yet, under many conditions, the mechanical behaviour of these tissues can be described well with similar nonlinearly elastic or inelastic constitutive relations, both in health and some diseases. Such constitutive relations are essential for performing nonlinear stress analyses, which in turn are critical for understanding physiology, pathophysiology and even clinical interventions, including surgery. Indeed, most cells within load-bearing soft tissues are highly sensitive to their local mechanical environment, which can typically be quantified using methods of continuum mechanics only after the constitutive relations are determined from appropriate data, often multi-axial. In this review, we discuss some of the many experimental findings of the structure and the mechanical response, as well as constitutive formulations for 10 representative soft tissues or organs, and present basic concepts of mechanobiology to support continuum biomechanical studies. We conclude by encouraging similar research along these lines, but also the need for models that can describe and predict evolving tissue properties under many conditions, ranging from normal development to disease progression and wound healing. An important foundation for biomechanics and mechanobiology now exists and methods for collecting detailed multi-scale data continue to progress. There is, thus, considerable opportunity for continued advancement of mechanobiology and biomechanics.

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.

Tensile forces in the neurovascular bundle: A contributor to orthodontic relapse?

OBJECTIVES

The aim of this study is to investigate the neurovascular bundle (NVB) as a potential orthodontic relapse factor. The mechanical properties and the forces generated in the NVB after orthodontic extrusion are explored.

MATERIALS AND METHODS

Six NVBs branching from the inferior alveolar nerve to the apices of the mandibular canines and premolars of mature pigs were harvested. Stress relaxation tests were conducted. A standard linear solid model (SLS) was utilized to simulate the orthodontic extrusion of a single rooted tooth with NVB length and cross-sectional diameter of 3.6 and 0.5 mm, respectively, so the NVB was stretched 10% and 20% of its original length. The maximum force within the NVB was then calculated.

RESULTS

Based on our data, the average Young's modulus before relaxation (E 0 ), after relaxation (E P ) and the difference between Young's moduli before and after relaxation (E S ) were 324 ± 123, 173 ± 73 and 151 ± 52 kPa, respectively. The theoretical force within the NVB stretched to 10% and 20% strain was 3 and 5 mN, respectively.

CONCLUSION

The data from our study indicate that the NVB exhibits stress relaxation, a characteristic trait of viscoelastic materials. SLS model simulation predicted residual forces around 5 mN for elongation up to 20%. We observed strain hardening with additional elongation, which has the potential to cause forces to increase exponentially. Therefore, tensile forces in the NVB should not be ruled out as a contributor to orthodontic relapse, especially in adult patients who may have decreased adaptability of their NVB. Further preclinical and clinical models should be developed to further clarify what is the contribution of the NVB to orthodontic relapse.

Rational design of viscoelastic hydrogels for periodontal ligament remodeling and repair

The periodontal ligament (PDL) is a distinctive yet critical connective tissue vital for maintaining the integrity and functionality of tooth-supporting structures. However, PDL repair poses significant challenges due to the complexity of its mechanical microenvironment encompassing hard-soft-hard tissues, with the viscoelastic properties of the PDL being of particular interest. This review delves into the significant role of viscoelastic hydrogels in PDL regeneration, underscoring their utility in simulating biomimetic three-dimensional microenvironments. We review the intricate relationship between PDL and viscoelastic mechanical properties, emphasizing the role of tissue viscoelasticity in maintaining mechanical functionality. Moreover, we summarize the techniques for characterizing PDL's viscoelastic behavior. From a chemical bonding perspective, we explore various crosslinking methods and characteristics of viscoelastic hydrogels, along with engineering strategies to construct viscoelastic cell microenvironments. We present a detailed analysis of the influence of the viscoelastic microenvironment on cellular mechanobiological behavior and fate. Furthermore, we review the applications of diverse viscoelastic hydrogels in PDL repair and address current challenges in the field of viscoelastic tissue repair. Lastly, we propose future directions for the development of innovative hydrogels that will facilitate not only PDL but also systemic ligament tissue repair. STATEMENT OF SIGNIFICANCE.

An in vivo evaluation of clear aligners for optimal orthodontic force and movement to determine high-efficacy and periodontal-friendly aligner staging

Objectives

To investigate the effect of aligner displacement on tooth movement and periodontal health to improve the efficiency of aligner treatment and explore the mechanism in vivo.

Methods

A two-tooth site was established by a finite element (FE) model to virtually evaluate aligner staging. A randomized controlled experiment was conducted when the tooth sites in beagles were treated with fixed or aligner appliances with different movement and force, and tooth movement and internal structure were recorded during the alignment. After sacrificing five dogs, bone-periodontal ligament (PDL)-tooth specimens were removed and processed to conduct uniaxial compression and tensile tests as well as micro-CT imaging and histological analysis.

Results

Three displacements of 0.25, 0.35 and 0.45 mm were obtained from FE analysis and applied in beagles. In general, aligners had poorer performance on movement compared to fixed systems in vivo, but the aligner with a staging of 0.35 mm had the highest accuracy (67.46%) (P < 0.01). Loaded with severe force, fixed sites exhibited tissue damage due to excess force and rapid movement, while aligners showed better safety. The PDL under a 0.35-mm aligner treatment had the highest elastic modulus in the biomechanical test (551.4275 and 1298.305 kPa) (P < 0.05).

Conclusions

Compared to fixed appliances, aligners achieve slightly slower movement but better periodontal condition. Aligners with an interval of 0.35 mm have the highest accuracy and best PDL biomechanical and biological capacities, achieving the most effective and safest movement. Even with complexity of oral cavity and lack of evaluation of other factors, these results provide insight into faster displacement as a method to improve the efficacy of aligners.

Identification of the periodontal ligament material parameters using response surface method

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

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.

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.