Effects of age on the stress–strain and stress–relaxation properties of the rat molar periodontal ligament

Uniaxial mechanical stretch properties correlated with three-dimensional microstructure of human dermal skin

The intact and healthy skin forms a barrier to the outside world and protects the body from mechanical impact. The skin is a complex structure with unique mechano-elastic properties. To better direct the design of biomimetic materials and induce skin regeneration in wounds with optimal outcome, more insight is required in how the mechano-elastic properties emerge from the skin's main constituents, collagen and elastin fibers. Here, we employed two-photon excited autofluorescence and second harmonic generation microscopy to characterize collagen and elastin fibers in 3D in 24 human dermis skin samples. Through uniaxial stretching experiments, we derive uni-directional mechanical properties from resultant stress-strain curves, including the initial Young's modulus, elastic Young's modulus, maximal stress, and maximal and mid-strain values. The stress-strain curves show a large variation, with an average Young's modules in the toe and linear regions of 0.1 MPa and 21 MPa. We performed a comprehensive analysis of the correlation between the key mechanical properties with age and with microstructural parameters, e.g., fiber density, thickness, and orientation. Age was found to correlate negatively with Young's modulus and collagen density. Moreover, real-time monitoring during uniaxial stretching allowed us to observe changes in collagen and elastin alignment. Elastin fibers aligned significantly in both the heel and linear regions, and the collagen bundles engaged and oriented mainly in the linear region. This research advances our understanding of skin biomechanics and yields input for future first principles full modeling of skin tissue.

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.

Mathematical Modeling and Simulations for Large-Strain J-Shaped Diagrams of Soft Biological Materials

Herein, we study stress⁻strain diagrams of soft biological materials such as animal skin, muscles, and arteries by Finsler geometry (FG) modeling. The stress⁻strain diagram of these biological materials is always J-shaped and is composed of toe, heel, linear, and failure regions. In the toe region, the stress is almost zero, and the length of this zero-stress region becomes very large (≃150%) in, for example, certain arteries. In this paper, we study long-toe diagrams using two-dimensional (2D) and 3D FG modeling techniques and Monte Carlo (MC) simulations. We find that, except for the failure region, large-strain J-shaped diagrams are successfully reproduced by the FG models. This implies that the complex J-shaped curves originate from the interaction between the directional and positional degrees of freedom of polymeric molecules, as implemented in the FG model.

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.

Biomechanical adaptation of the bone-periodontal ligament (PDL)-tooth fibrous joint as a consequence of disease

In this study, an in vivo ligature-induced periodontitis rat model was used to investigate temporal changes to the solid and fluid phases of the joint by correlating shifts in joint biomechanics to adaptive changes in soft and hard tissue morphology and functional space. After 6 and 12 weeks of ligation, coronal regions showed a significant decrease in alveolar crest height, increased expression of TNF-α, and degradation of attachment fibers as indicated by decreased collagen birefringence. Cyclical compression to peak loads of 5-15N at speeds of 0.2-2.0mm/min followed by load relaxation tests showed decreased stiffness and reactionary load rate values, load relaxation, and load recoverability, of ligated joints. Shifts in joint stiffness and reactionary load rate increased with time while shifts in joint relaxation and recoverability decreased between control and ligated groups, complementing measurements of increased tooth displacement as evaluated through digital image correlation. Shifts in functional space between control and ligated joints were significantly increased at the interradicular (Δ10-25μm) and distal coronal (Δ20-45μm) regions. Histology revealed time-dependent increases in nuclei elongation within PDL cells and collagen fiber alignment, uncrimping, and directionality, in 12-week ligated joints compared to random orientation in 6-week ligated joints and to controls. We propose that altered strains from tooth hypermobility could cause varying degrees of solid-to-fluid compaction, alter dampening characteristics of the joint, and potentiate increased adaptation at the risk of joint failure.

Biomechanics of a bone-periodontal ligament-tooth fibrous joint

This study investigates bone-tooth association under compression to identify strain amplified sites within the bone-periodontal ligament (PDL)-tooth fibrous joint. Our results indicate that the biomechanical response of the joint is due to a combinatorial response of the constitutive properties of organic, inorganic, and fluid components. Second maxillary molars within intact maxillae (N=8) of 5-month-old rats were loaded with a μ-XCT-compatible in situ loading device at various permutations of displacement rates (0.2, 0.5, 1.0, 1.5, 2.0 mm/min) and peak reactionary load responses (5, 10, 15, 20 N). Results indicated a nonlinear biomechanical response of the joint, in which the observed reactionary load rates were directly proportional to displacement rates (velocities). No significant differences in peak reactionary load rates at a displacement rate of 0.2mm/min were observed. However, for displacement rates greater than 0.2mm/min, an increasing trend in reactionary rate was observed for every peak reactionary load with significant increases at 2.0mm/min. Regardless of displacement rates, two distinct behaviors were identified with stiffness (S) and reactionary load rate (LR) values at a peak load of 5 N (S(5 N)=290-523 N/mm) being significantly lower than those at 10 N (LR(5 N)=1-10 N/s) and higher (S(10 N-20 N)=380-684 N/mm; LR(10 N-20 N)=1-19 N/s). Digital image correlation revealed the possibility of a screw-like motion of the tooth into the PDL-space, i.e., predominant vertical displacement of 35 μm at 5 N, followed by a slight increase to 40 μm at 10 N and 50 μm at 20 N of the tooth and potential tooth rotation at loads above 10 N. Narrowed and widened PDL spaces as a result of tooth displacement indicated areas of increased apparent strains within the complex. We propose that such highly strained regions are "hot spots" that can potentiate local tissue adaptation under physiological loading and adverse tissue adaptation under pathological loading conditions.

Age-related adaptation of bone-PDL-tooth complex: Rattus-Norvegicus as a model system

Functional loads on an organ induce tissue adaptations by converting mechanical energy into chemical energy at a cell-level. The transducing capacity of cells alters physico-chemical properties of tissues, developing a positive feedback commonly recognized as the form-function relationship. In this study, organ and tissue adaptations were mapped in the bone-tooth complex by identifying and correlating biomolecular expressions to physico-chemical properties in rats from 1.5 to 15 months. However, future research using hard and soft chow over relevant age groups would decouple the function related effects from aging affects. Progressive curvature in the distal root with increased root resorption was observed using micro X-ray computed tomography. Resorption was correlated to the increased activity of multinucleated osteoclasts on the distal side of the molars until 6 months using tartrate resistant acid phosphatase (TRAP). Interestingly, mononucleated TRAP positive cells within PDL vasculature were observed in older rats. Higher levels of glycosaminoglycans were identified at PDL-bone and PDL-cementum entheses using alcian blue stain. Decreasing biochemical gradients from coronal to apical zones, specifically biomolecules that can induce osteogenic (biglycan) and fibrogenic (fibromodulin, decorin) phenotypes, and PDL-specific negative regulator of mineralization (asporin) were observed using immunohistochemistry. Heterogeneous distribution of Ca and P in alveolar bone, and relatively lower contents at the entheses, were observed using energy dispersive X-ray analysis. No correlation between age and microhardness of alveolar bone (0.7 ± 0.1 to 0.9 ± 0.2 GPa) and cementum (0.6 ± 0.1 to 0.8 ± 0.3 GPa) was observed using a microindenter. However, hardness of cementum and alveolar bone at any given age were significantly different (P<0.05). These observations should be taken into account as baseline parameters, during development (1.5 to 4 months), growth (4 to 10 months), followed by a senescent phase (10 to 15 months), from which deviations due to experimentally induced perturbations can be effectively investigated.

Micromechanical analysis of native and cross-linked collagen type I fibrils supports the existence of microfibrils

The mechanical properties of individual collagen fibrils of approximately 200 nm in diameter were determined using a slightly adapted AFM system. Single collagen fibrils immersed in PBS buffer were attached between an AFM cantilever and a glass surface to perform tensile tests at different strain rates and stress relaxation measurements. The stress-strain behavior of collagen fibrils immersed in PBS buffer comprises a toe region up to a stress of 5 MPa, followed by the heel and linear region at higher stresses. Hysteresis and strain-rate dependent stress-strain behavior of collagen fibrils were observed, which suggest that single collagen fibrils have viscoelastic properties. The stress relaxation process of individual collagen fibrils could be best fitted using a two-term Prony series. Furthermore, the influence of different cross-linking agents on the mechanical properties of single collagen fibrils was investigated. Based on these results, we propose that sliding of microfibrils with respect to each other plays a role in the viscoelastic behavior of collagen fibrils in addition to the sliding of collagen molecules with respect to each other. Our finding provides a better insight into the relationship between the structure and mechanical properties of collagen and the micro-mechanical behavior of tissues.

Appropriateness of viscoelastic soft materials as in vitro simulators of the periodontal ligament

The periodontal ligament is a viscoelastic soft tissue that connects the tooth to the alveolar bone. This tissue should be simulated in numerical as well as in laboratory models. The mechanical properties of this tissue were previously determined ex vivo and in vivo. The aim of the study was to analyse the appropriateness of impression and reline materials used in dentistry to simulate viscoelastic behaviour of the periodontal ligament. Two reline [Durabase (Reliance Dental MFG, Co.) and Soft Liner (GC Corporation)] and two impression [President Plus (Coltene) and Prestige L (Vanini Dental Industry)] materials were examined in recovery and tensile relaxation tests. Recovery: This experiment simulated in vivo test. Roots of a pair of plastic maxillary premolar teeth were covered with each test material and embedded in acryl while maintaining the contact point. A 0·1-mm stainless steel strip, inserted at the contact point and maintained for 10 s, was used to tip the teeth. After removal, the tightness of dental contact point was measured over 30 min by determining the force needed to insert a 0·05-mm metal strip. Tensile relaxation: strips were elongated to 120%, 140% and 160% of their initial length and maintained at that length for 30 min. Two-phase decay function was applied. The results showed that elastic modulus and relaxation behaviour were significantly different between materials. Elastic modulus values were in the same range of those reported in the literature. However, the recovery values and behaviour showed that impression materials, especially President, are the materials of choice for this purpose because they simulated better the in vivo test.

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.

Age-Related Changes of Periodontal Ligament Surface Areas during Force Application

Objective: To investigate the age-dependent morphology of the periodontal ligament (PDL) tissue and changes in its surface area (SA) during force application provided with a standardized orthodontic setup for a period of 12 weeks in young and adult rats.

Methods: Two groups of 30 rats, age 6 weeks and 9 to 12 months, were used. Orthodontic appliances were placed to move the maxillary molars mesially with the contralateral sides used as controls. At 1, 2, 4, 8, and 12 weeks, groups of animals were killed. The PDL SA and the PDL SA ratio between pressure and tension regions were determined.

Results: An age-related decrease in the PDL SA was noted at control sides. Significant changes during the experimental period occurred only at experimental sides: The PDL SA was smaller at pressure than at tension regions only at week 1 in young rats; in adult rats, the difference between the two regions was significant at week 8. These changes were confirmed by the morphologic disorganization of the PDL and alterations in the PDL SA ratio.

Conclusions: During force application, the PDL at the pressure regions became disorganized and subsequently was reorganized, as is shown by the histologic changes and SA of the PDL over time. This process occurred earlier and was more prominent in young rats; it occurred later and was more prolonged in adult animals.

Analysis of contribution of collagen fibre component in viscoelastic behaviour of periodontal ligament using enzyme probe

The aims of this study are to observe microscopic changes in the periodontal ligament (PDL) collagen fibres after collagenase treatment, to analyse stress-relaxation behaviour of PDL specimens treated with collagenase, and to elucidate the contribution of the collagen component to the viscoelastic behaviour of the PDL. Transverse sections of rat mandibular first molars (n=24) were treated in vitro with 0, 8, 16, or 24 units of bacterial collagenase for 4h at 37 degrees C. Histological specimens were then prepared, and image analyses were done for polarised light microscopic appearances of collagen fibres. Further, stress-relaxation tests were performed for PDL specimens treated with 8 units of collagenase (n=7) and control specimens (n=7). Image analysis showed that higher concentrations of collagenase reduced greater area occupied by the PDL collagen fibres and birefringent retardation of the fibres. The amount of stress-relaxation during 600 s was 1.37 times greater in the collagenase-treated specimens than in the controls. The observed values of the stress-relaxation process were well described by a function with three exponential decay terms. The relaxation parameters of the first and second terms did not show significant differences, but those of the third term did so between the collagenase-treated and control specimens. The ratio and relaxation time of the third term for the collagenase-treated specimens were significantly less than those for the controls. These findings suggest that in the long-term relaxation component of the stress-relaxation process of the PDL the viscoelastic properties of the collagen fibres may play an important role.

Dynamic shear properties of the porcine molar 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. Little information, however, is available on the dynamic behavior of the PDL in shear. Therefore, the present study was designed to determine the dynamic shear properties of the PDL in the porcine molar (n=10). From dissected mandibles transverse sections of the mesial root of the first molar were obtained at the apical and coronal levels and used for dynamic shear tests. Shear strain (0.5%, 1.0%, and 1.5%) was applied in superoinferior direction parallel to the root axis with a wide range of frequencies (0.01-100 Hz). The dynamic complex and storage moduli increased significantly with the loading frequency, the dynamic loss modulus showed only a small increase. The dynamic elasticity was significantly larger in the coronal region than in the apical region although the dynamic viscosity was similar in both regions. The present results suggest that non-linearities, compression/shear coupling, and intrinsic viscoelasticity affect the shear material behavior of the PDL, which might have important implications for load transmission from tooth to bone and vice versa.

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.

Stress-relaxation and microscopic dynamics of rabbit periodontal ligament

The aim of the present study was to examine the structural basis for the stress-relaxation behaviour of the periodontal ligament (PDL). Seventeen 4-month-old rabbits were used. A tooth-PDL-bone segment was cut in a rectangular prism from the incisor of a dissected mandible. The specimen was mounted in a testing machine built on a video stereomicroscope. Following preconditioning, each specimen was stretched to a deformation of 35 microm and then the deformation was kept constant for 300 s to obtain a stress-relaxation curve. Thereafter, stress-relaxation tests were repeated sequentially at deformations of 55, 75, and 95 microm. Polarised-light video-stereomicroscopic images of the specimens were simultaneously recorded and analysed with the stress-relaxation curves. The image analysis revealed that during stress-relaxation, the brightness of the birefringent fibres tended to initially increase rapidly and then do so gradually. There were negative correlations between the brightness and relaxation modulus at the four deformations. The decreases of normalised relaxation modulus for 300 s were less at greater deformation levels. The stress-relaxation process was well described by a function with three exponential decay terms and a constant. These findings suggest that during stress-relaxation of the PDL, the alignment of the collagen molecules and fibrils within the stretched fibres may occur, which could be driven by the strain energy imparted to the specimen on initial stretching.

Mechanical behavior of bovine periodontal ligament under tension-compression cyclic displacements

In the present study, the mechanical response of bovine periodontal ligament (PDL) subjected to displacement-controlled tension-compression harmonic oscillations and subsequent rupture was examined. Specimens including dentine, cementum, PDL, and alveolar bone were extracted from different depths and locations of bovine first molars. They were immersed in a saline solution at room temperature and clamped on their bone and dentine extremities. The samples were tested at +/-35% of the PDL's width, with a frequency of 1 Hz. The mechanical parameters evaluated were hysteresis, phase lag, and the modulus of the stress-stretch ratio curves in tension and compression. The tensile strength and the corresponding stretch ratio were also recorded. Stress-stretch ratio curves indicated a non-linear, time-dependent response with hysteresis and preconditioning effects. The hysteresis and phase lag in compression were much higher than in tension, suggesting that the dissipated energy was higher in compression than in tension. The root depth and location did not play essential roles for the tension or compression data, with the exception of limited statistical differences for tensile strength and corresponding stretch ratio. Thus, biological variability in the specimens, as a result of different bone contours, PDL width, and fiber orientation, did not affect the energy-absorbing capacity of the PDL. The evolution of the stress rate with stress demonstrated a constant increase of stiffness with stress. The stiffness values were twofold higher in tension than in compression. The data also showed that the stiffness of the PDL was comparable with data reported for other soft tissues.

In vitro time-dependent response of periodontal ligament to mechanical loading

This study examined the time-dependent response of bovine periodontal ligament (PDL). Applying linear viscoelastic theory, the objective was 1) to examine the linearity of the PDL's response in terms of its scaling and superposition property and 2) to generate the phase lag-vs.-frequency spectrum graph. PDL specimens were tested under three separate straining conditions: 1) tension ramp tests conducted at different strain rates, 2) pulling step-straining to 0.3 in discrete tests and to 0.3 and 0.6 in one continuous run, and 3) tension-compression sinusoidal oscillations. To this effect, bar-shaped specimens of bovine roots that comprised portions of dentin, PDL tissue, and alveolar bone were produced and strained in a microtensile machine. The experimental data demonstrated that neither the scaling nor the superposition properties were verified and that the viscoelastic response of the PDL was nonlinear. The PDL's elastic response was essentially stiffening, and its viscous component was pseudoplastic. The tangent of the PDL's strain-stress phase lag was in the 0-0.1 range in the tensile direction and in the 0.35-0.45 range in the compressive direction. In line with other biological tissues, the phase lag was largely independent of frequency. By use of the data generated, a mathematical model is outlined that reproduces both the elastic stiffening and viscous thinning of the PDL's response.