Dynamic shear properties of the porcine molar periodontal ligament

Dynamic tensile viscoelastic properties of porcine periodontal ligament

The periodontal ligament plays a significant role in orthodontic and masticatory processes. To explicitly investigate the effects of dynamic force amplitude and frequency on the dynamic tensile properties of the periodontal ligament, in vitro tensile experiments were conducted using a dynamic mechanical analysis at various dynamic force amplitudes across a wide frequency range. Storage modulus, loss modulus, and loss factor values were measured. A Maxwell constitutive model based on modulus was established to describe the dynamic mechanical properties of the periodontal ligament. The results showed that the storage modulus ranged from 29.53 MPa to 158.24 MPa, the loss modulus ranged from 3.26 MPa to 76.16 MPa, and the loss factor values all increased with higher frequencies and higher dynamic force amplitudes. Based on the parameters obtained from the fitting results, it is evident that the short-term response has a more pronounced impact on the elastic response of the periodontal ligament than the long-term response. Increasing the dynamic force amplitude and its frequency amplified the viscous effects of the periodontal ligament and enhanced energy dissipation. The proposed constitutive model further demonstrated that the periodontal ligament acts as a viscoelastic biomaterial. These findings have implications for future research on the periodontal ligament.

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-fiber Bragg sensor measurements assess fluid effects on strain in the periodontal space of an ex-vivo swine incisor complex under mechanical loading

The purpose of this study is to determine whether in-fiber Bragg grating (FBG) sensors detect changes within the periodontal ligament (PDL) of ex-vivo swine tooth-PDL-bone complex (TPBC) when manipulating fluid content. Recording strain will allow for a better understanding of the biomechanics of viscoelastic load transfer from the tooth to the PDL during chewing and/or orthodontic tooth movement, as well as replication of these dynamics in regenerated PDL tissues. FBG sensors placed within the PDL of swine incisor teeth were used to measure strain resulting from an intrusive load. Specimens were mounted in a custom platform within an MTS machine and a compressive load was applied at 0.3 mm/s to a depth of 0.5 mm and held for 10 s. Median peak strain and load and median absolute deviation (MAD) were compared: dry vs. saline (n = 19) with bias-corrected bootstrap 95% CI. Dry vs. saline conditions did not statistically differ (median peaks of 5με, 103-105 N) and recorded strains showed high repeatability (MAD of 0.82με, 0.72με, respectively). FBG sensors did not detect the fluid changes in this study, suggesting that the deformation of tissues in the PDL space collectively determine FBG strain in response to tooth loading. The repeatability of measurements demonstrates the potential for FBG sensors to assess the strain in the PDL space of an in vivo swine model.

Effect of temperature on dynamic compressive behavior of periodontal ligament

Periodontal ligament (PDL) attaches tooth root to the surrounding bone. Its existence between tooth and jaw bone is of utmost importance due to its significant role in absorbing and distributing physiological and para-physiological loading. According to the previous studies, various mechanical tests have been performed to characterize the mechanical properties of the PDL; however, all of them have been done at room temperature. To the best of our knowledge, this is the first study in which the testing was performed at body temperature. The present research was planned to measure the dependency of PDL's viscoelastic behavior on temperature and frequency. Three different temperatures, including body and room temperature, were opted to perform the dynamic compressive tests of the bovine PDL. In addition, a Generalized Maxwell model (GMM) was presented based on empirical outcomes. At 37 °C, amounts of loss factor were found to be greater than those in 25 °C, which demonstrates that the viscous phase of the PDL in higher temperatures plays a critical role. Likewise, by raising the temperature from 25 °C to 37 °C, the model parameters show an enlargement in the viscous part and lessening in the elastic part. It was concluded that the PDL's viscosity in body temperature is much higher than that in room temperature. This model would be functional for a more accurate computational analysis of the PDL at the body temperature (37 °C) in various loading conditions such as orthodontic simulations, mastication, and impact.

Sensitivity of the shear wave speed-stress relationship to soft tissue material properties and fiber alignment

The use of shear wave propagation to noninvasively measure material properties and loading in tendons and ligaments is a growing area of interest in biomechanics. Prior models and experiments suggest that shear wave speed primarily depends on the apparent shear modulus (i.e., shear modulus accounting for contributions from all constituents) at low loads, and then increases with axial stress when axially loaded. However, differences in the magnitudes of shear wave speeds between ligaments and tendons, which have different substructures, suggest that the tissue's composition and fiber alignment may also affect shear wave propagation. Accordingly, the objectives of this study were to (1) characterize changes in the apparent shear modulus induced by variations in constitutive properties and fiber alignment, and (2) determine the sensitivity of the shear wave speed-stress relationship to variations in constitutive properties and fiber alignment. To enable systematic variations of both constitutive properties and fiber alignment, we developed a finite element model that represented an isotropic ground matrix with an embedded fiber distribution. Using this model, we performed dynamic simulations of shear wave propagation at axial strains from 0% to 10%. We characterized the shear wave speed-stress relationship using a simple linear regression between shear wave speed squared and axial stress, which is based on an analytical relationship derived from a tensioned beam model. We found that predicted shear wave speeds were both in-range with shear wave speeds in previous in vivo and ex vivo studies, and strongly correlated with the axial stress (R² = 0.99). The slope of the squared shear wave speed-axial stress relationship was highly sensitive to changes in tissue density. Both the intercept of this relationship and the apparent shear modulus were sensitive to both the shear modulus of the ground matrix and the stiffness of the fibers' toe-region when the fibers were less well-aligned to the loading direction. We also determined that the tensioned beam model overpredicted the axial tissue stress with increasing load when the model had less well-aligned fibers. This indicates that the shear wave speed increases likely in response to a load-dependent increase in the apparent shear modulus. Our findings suggest that researchers may need to consider both the material and structural properties (i.e., fiber alignment) of tendon and ligament when measuring shear wave speeds in pathological tissues or tissues with less well-aligned fibers.

Experimental repeatability, sensitivity, and reproducibility of force and strain measurements from within the periodontal ligament space during ex vivo swine tooth loading

The Periodontal Ligament (PDL) is a complex connective tissue that anchors a tooth to the surrounding alveolar bone. The small size and complex geometry of the PDL space within an intact tooth-PDL-bone complex (TPBC) limits strain measurements. An in-fiber Bragg grating (FBG) sensor offers potential for such measurements due to its small size. This work defines an experimental procedure where strain and force were measured during quasi-static, apically directed, displacement-controlled tests on swine premolar crowns. Specifically, the: inter-TPBC, intra-TPBC, and long-term repeatability after a preconditioned state was objectively identified; sensitivity to preload magnitude, TPBC alignment, and sensor depth; and reproducibility within a TPBC was determined. Data clustering was used to determine the appropriate number of preconditioning trials, ranging from one to seven. Strain and force measurements showed intra-TPBC repeatability with average adjusted root mean square from the median of 28.9% of the peak strain and 4.5% of the peak force measurement. A Mann-Whitney U test generally found statistically significant differences in peak strain and force measurements between the left and right sides, suggesting a lack of inter-TPBC repeatability. Using a Friedman test, it was shown that peak strain measures were sensitive to the TPBC alignment and sensor depth, while peak force measures were sensitive to the preload and TPBC alignment. A Friedman test suggested reproducible strain and force measurements when the FBG was replaced within the same TPBC and the preload, alignment, and sensor depth were controlled.

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."

Effects of extracellular matrix viscoelasticity on cellular behaviour

Substantial research over the past two decades has established that extracellular matrix (ECM) elasticity, or stiffness, affects fundamental cellular processes, including spreading, growth, proliferation, migration, differentiation and organoid formation. Linearly elastic polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers coated with ECM proteins are widely used to assess the role of stiffness, and results from such experiments are often assumed to reproduce the effect of the mechanical environment experienced by cells in vivo. However, tissues and ECMs are not linearly elastic materials-they exhibit far more complex mechanical behaviours, including viscoelasticity (a time-dependent response to loading or deformation), as well as mechanical plasticity and nonlinear elasticity. Here we review the complex mechanical behaviours of tissues and ECMs, discuss the effect of ECM viscoelasticity on cells, and describe the potential use of viscoelastic biomaterials in regenerative medicine. Recent work has revealed that matrix viscoelasticity regulates these same fundamental cell processes, and can promote behaviours that are not observed with elastic hydrogels in both two- and three-dimensional culture microenvironments. These findings have provided insights into cell-matrix interactions and how these interactions differentially modulate mechano-sensitive molecular pathways in cells. Moreover, these results suggest design guidelines for the next generation of biomaterials, with the goal of matching tissue and ECM mechanics for in vitro tissue models and applications in regenerative medicine.

Shear wave speeds track axial stress in porcine collateral ligaments

Ligament tension is an important factor that can affect the success of total knee arthroplasty (TKA) procedures. However, surgeons currently lack objective approaches for assessing tension in a particular ligament intraoperatively. The purpose of this study was to investigate the use of noninvasive shear wave tensiometry to characterize stress in medial and lateral collateral ligaments (MCLs and LCLs) ex vivo and evaluate the capacity of shear wave speed to predict axial load. Nine porcine MCL and LCL specimens were subjected to cyclic axial loading while shear wave speeds were measured using laser vibrometry. We found that squared shear wave speed increased linearly with stress in both the MCL (r²_avg = 0.94) and LCL (r²_avg = 0.98). Shear wave speeds were slightly lower in the MCL than the LCL when subjected to a comparable axial stress (p < 0.001). Specimen-specific calibrations predicted tension within 13.0 N, or 5.2% of the maximum load. A leave-one-out analysis was also performed and showed that calibrated relationships based on ligament type could predict axial tension within 15% of the maximum load. These observations suggest it may be feasible to use noninvasive shear wave speed measures as a proxy of ligament loading, which in the future might enhance decision making during orthopedic procedures such as TKA.

Viscoelastic properties of human periodontal ligament: Effects of the loading frequency and location

OBJECTIVES

To determine the viscoelastic properties of the human periodontal ligament (PDL) using dynamic mechanical analysis (DMA).

MATERIALS AND METHODS

This study was carried out on three human maxillary jaw segments containing six upper central incisors and four lateral incisors. DMA was used to investigate the mechanical response of the human PDL. Dynamic sinusoidal loading was carried out with an amplitude of 3 N and frequencies between 0.5 Hz and 10 Hz. All samples were grouped by tooth positions and longitudinal locations.

RESULTS

An increase of oscillation frequency resulted in marked changes in the storage and loss moduli of the PDL. The storage modulus ranged from 0.808 MPa to 7.274 MPa, and the loss modulus varied from 0.087 MPa to 0.891 MPa. The tanδ, representing the ratio between viscosity and elasticity, remained constant with frequency. The trends for storage and loss moduli were described by exponential fits. The dynamic moduli of the central incisor were higher than those of the lateral incisor. The PDL samples from the gingival third of the root showed lower storage and loss moduli than those from the middle third of the root.

CONCLUSIONS

Human PDL is viscoelastic through the range of frequencies tested: 0.5-10 Hz. The viscoelastic relationship changed with respect to frequency, tooth position, and root level.

Gauging force by tapping tendons

Muscles are the actuators that drive human movement. However, despite many decades of work, we still cannot readily assess the forces that muscles transmit during human movement. Direct measurements of muscle-tendon loads are invasive and modeling approaches require many assumptions. Here, we introduce a non-invasive approach to assess tendon loads by tracking vibrational behavior. We first show that the speed of shear wave propagation in tendon increases with the square root of axial stress. We then introduce a remarkably simple shear wave tensiometer that uses micron-scale taps and skin-mounted accelerometers to track tendon wave speeds in vivo. Tendon wave speeds are shown to modulate in phase with active joint torques during isometric exertions, walking, and running. The capacity to non-invasively assess muscle-tendon loading can provide new insights into the motor control and biomechanics underlying movement, and could lead to enhanced clinical treatment of musculoskeletal injuries and diseases.

DETERMINATION OF VISCOELASTIC PROPERTIES OF THE PERIODONTAL LIGAMENT USING NANOINDENTATION TESTING AND NUMERICAL MODELING

Viscoelasticity of the periodontal ligament (PDL) plays an important role in load transmission between tooth and alveolar bone, as well as tooth movement. This paper provides a novel nanoindentation experiment in combination with a rheological model to characterize the viscoelastic mechanical properties of the PDL. Two creep models of the indentation experiments with a Berkovich and a spherical indenter based on Zener model were developed. The hardness and reduced modulus were determined by using the Berkovich indenter. The parameters were identified through curve fittings. The fitting results show that the creep models are both in good agreement with the experimental data. Meanwhile, the models were both validated by comparing the numerical curves for load–depth relationship in loading segment with the corresponding experimental data. It is found that the spherical indenter is more suitable for testing the viscoelastic mechanical properties of the PDL than Berkovich indenter. Hence, the nanoindentation experiment with spherical indenter was simulated to further evaluate the Zener model by finite element analysis. The good agreement between the simulated results and experimental data demonstrates that the Zener model is capable of describing the viscoelastic mechanical behavior of the PDL.

Collagen cross-linking treatment effects on corneal dynamic biomechanical properties

Cornea is a soft tissue with the principal function of transmitting and refracting light rays. The objective of the current study was to characterize possible effects of the riboflavin/UVA collagen cross-linking on corneal dynamic properties. The original corneal cross-linking protocol was used to induce cross-links in the anterior portion of the bovine cornea. A DMA machine was used to conduct mechanical tensile experiments at different levels of tensile strains. The samples were divided into a control group (n = 5) and a treated group (n = 5). All specimens were first stretched to a strain of 5% and allowed to relax for twenty minutes. After completion of the stress-relaxation experiment, a frequency sweep test with oscillations ranging from 0.01 to 10 Hz was performed. The same procedure was repeated to obtain the stress-relaxation and dynamic properties at 10% strain. It was observed that the collagen cross-linking therapy significantly increased the immediate and equilibrium tensile behavior of the bovine cornea (P < 0.05). Furthermore, for all samples in control and treated groups and throughout the whole range of frequencies, a significantly larger tensile storage modulus was measured at an axial strain of 10% compared to what was obtained at a tensile strain of 5%. Finally, it was noted that although this treatment procedure resulted in a significant increase in the storage and loss modulus at any axial strain and frequency (P < 0.05), it significantly reduced the ratio of the dissipated and stored energy during a single cycle of deformation. Therefore, it was concluded that while the riboflavin/UVA collagen cross-linking increased significantly corneal stiffness, it decreased significantly its damping capability and deformability. This reduced damping ability might adversely interfere with corneal mechanical performance.

Dynamic testing of regional viscoelastic behavior of canine sclera

Intraocular pressure (IOP) fluctuations have gained recent clinical interest and thus warrant an understanding of how the sclera responds to dynamic mechanical insults. The objective of this study was to characterize the regional dynamic viscoelastic properties of canine sclera under physiological cyclic loadings. Scleral strips were excised from the anterior, equatorial, and posterior sclera in ten canine eyes. The dimensions of each strip were measured using a high resolution ultrasound imaging system. The strips were tested in a humidity chamber at approximately 37 °C using a Rheometrics Systems Analyzer. A cyclic strain input (0.25%, 1 Hz) was applied to the strips, superimposed upon pre-stresses corresponding to an IOP of 15, 25, and 45 mmHg. The cyclic stress output was recorded and the dynamic properties were calculated based on linear viscoelasticity. Uni-axial tensile tests were also performed on the same samples and the results were compared to those reported for human eyes. The results showed that the sclera's resistance to dynamic loading increased significantly while the damping capability decreased significantly with increasing pre-stresses for all regions of sclera (P < 0.001). Anterior sclera appeared to have a significantly higher damping capability than equatorial and posterior sclera (P = 0.003 and 0.018, respectively). The secant modulus from uni-axial tensile tests showed a decreasing trend from anterior to posterior sclera, displaying a similar pattern as in the human eye. In conclusion, all scleral regions in the canine eyes exhibited an increased ability to resist and a decreased ability to dampen cyclic stress insults at increasing pre-stress (i.e., increasing steady-state IOP). The regional variation of the dynamic properties differed from those of uni-axial tensile tests. Dynamic testing may provide useful information to better understand the mechanical behavior of the sclera in response to dynamic IOP.

Experimentally determined mechanical properties of, and models for, the periodontal ligament: critical review of current literature

Introduction. This review is intended to highlight and discuss discrepancies in the literature of the periodontal ligament's (PDL) mechanical properties and the various experimental approaches used to measure them. Methods. Searches were performed on biomechanical and orthodontic publications (in databases: Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, and Scopus). Results. The review revealed that significant variations exist, some on the order of six orders of magnitude, in the PDL's elastic constants and mechanical properties. Possible explanations may be attributable to different experimental approaches and assumptions. Conclusions. The discrepancies highlight the need for further research into PDL properties under various clinical and experimental loading conditions. Better understanding of the PDL's biomechanical behavior under physiologic and traumatic loading conditions might enhance the understanding of the PDL's biologic reaction in health and disease. Providing a greater insight into the response of the PDL would be instrumental to orthodontists and engineers for designing more predictable, and therefore more efficacious, orthodontic appliances.

Mechanical strength and viscoelastic response of the periodontal ligament in relation to structure

The mechanical strength of the periodontal ligament (PDL) was first measured as force required to extract a tooth from its socket using human specimens. Thereafter, tooth-PDL-bone preparations have extensively been used for measurement of the mechanical response of the PDL. In vitro treatments of such specimens with specific enzymes allowed one to investigate into the roles of the structural components in the mechanical support of the PDL. The viscoelastic responses of the PDL may be examined by analysis of the stress-relaxation. Video polarised microscopy suggested that the collagen molecules and fibrils in the stretched fibre bundles progressively align along the deformation direction during the relaxation. The stress-relaxation process of the PDL can be well expressed by a function with three exponential decay terms. Analysis after in vitro digestion of the collagen fibres by collagenase revealed that the collagen fibre components may play an important role in the long-term relaxation component of the stress-relaxation process of the PDL. The dynamic measurements of the viscoelastic properties of the PDL have recently suggested that the PDL can absorb more energy in compression than in shear and tension. These viscoelastic mechanisms of the PDL tissue could reduce the risk of injury to the PDL.

Analysis of gene expression profiles in human periodontal ligament cells under hypoxia: the protective effect of CC chemokine ligand 2 to oxygen shortage

Periodontal ligament (PDL) cells appear to play important functional roles in response to mechanical stress. We hypothesized that hypoxia caused by a deformation of blood vessels and the following ischaemia may play a crucial role in differential gene expression in PDL cells affected by mechanical stress. Gene induction in cultured human PDL cells by hypoxia was analyzed using cDNA array, followed by RT-PCR analysis. Eleven hypoxia-responsive genes were found differentially expressed under low-oxygen conditions in PDL cells. Among them, CCR2, CC chemokine ligand 2 (CCL2) receptor was studied in more detail since little information is available on the role of chemokines in adaptive responses of PDL cells under hypoxia. Here we investigate whether CCR2 mediates the signalling to maintain the homeostasis of PDL cells. We found that cell death of PDL cells was induced under hypoxia with down-regulation of CCL2 mRNA expression. However, the exogenous CCL2 prevented PDL cell death under oxygen shortage with the increment of cellular inhibitor of apoptosis (cIAP) mRNA expression. The present study demonstrated substantial effects of hypoxia on gene expression of CCL2 and CCR2 in PDL cells, indicating that mechanical loading accompanied with mild hypoxia allows PDL cells to elicit adaptive responses with up-regulation of CCR2.

Comparison of dynamic shear properties of the porcine molar and incisor periodontal ligament

The role of the periodontal ligament (PDL) is to support the tooth during function and resist external forces applied to it. The dominant vertical component of these forces is associated with shear in the PDL. The mechanical response to vertical force may, however, be different between the molar and incisor as their loading regimen is different. The present study was designed to determine the viscoelastic behavior in shear of the PDL of the porcine molar and incisor (n = 10 for each). From dissected mandibles transverse sections including the mesial root of first molar and the incisal root were obtained and used for dynamic shear tests. Shear strain of 1.0% was applied in superoinferior direction parallel to the root axis with a wide range of frequencies (0.01-100 Hz). The viscoelastic behavior was characterized by the storage and loss modulus and loss tangent as a function of the frequency. For the incisor and molar, the complex and storage moduli increased significantly with the frequency. For the incisor, the loss modulus also increased with the frequency. The loss modulus and loss tangent were significantly (p < 0.05) larger in the incisor than in the molar. The present results suggest that the incisal PDL revealed more viscous behavior during dynamic shear than the molar one, which might have important implications for the principal role of the anterior teeth such as PDL sensation.