The role of the fluid phase in the viscous response of bovine periodontal ligament

The mechanical response of the periodontal ligament (PDL) is complex. This tissue responds as a hyperelastic solid when pulled in tension while demonstrating a viscous behavior under compression. This intricacy is reflected in the tissue's morphology, which comprises fibers, glycosaminoglycans, a jagged interface with the surrounding porous bone and an extensive vascular network.In the present study we offer an analysis of the viscous behavior and the interplay between the fibrous matrix and its fluid phase.Cylindrical specimens comprising layers of dentine, PDL and bone were extracted from bovine first molars and affixed to a tensile-compressive loading machine. The viscous properties of the tissue were analyzed (1) by subjecting the specimens to sinusoidal displacements at various frequencies and (2) by cycling the specimens in ‘fully saturated’ and in ‘partially dry’ conditions. Both modes assisted in determining the contribution of the fluid phase to the mechanical response.It was concluded that: (1) PDL showed pseudo-plastic viscous features for cyclic compressive loading, (2) these viscous features essentially resulted from interactions between the porous matrix and unbound fluid content of the tissue. Removing the liquid from the PDL largely eliminates its damping effect in compression.     

Tensile testing of the mechanical behavior of the human periodontal ligament

Background

The periodontal ligament (PDL) plays a key role in alveolar bone remodeling and resorption during tooth movements. The prediction of tooth mobility under functional dental loads requires a deep understanding of the mechanical behavior of the PDL, which is a critical issue in dental biomechanics. This study was aimed to examine the mechanical behavior of the PDL of the maxillary central and lateral incisors from human. The experimental results can contribute to developing an accurate constitutive model of the human PDL in orthodontics.

Methods

The samples of human incisors were cut into three slices. Uniaxial tensile tests were conducted under different loading rates. The transverse sections (cervical, middle and apex) normal to the longitudinal axis of the root of the tooth were used in the uniaxial tensile tests. Based on a bilinear simplification of the stress–strain relations, the elastic modulus of the PDL was calculated. The values of the elastic modulus in different regions were compared to explore the factors that influence the mechanical behavior of the periodontal ligament.

Results

The obtained stress–strain curves of the human PDL were characterized by a bilinear model with two moduli (E₁ and E₂) for quantifying the elastic behavior of the PDL from the central and lateral incisors. Statistically significant differences of the elastic modulus were observed in the cases of 1, 3, and 5 N loading levels for the different teeth (central and lateral incisors). The results showed that the mechanical property of the human incisors’ PDLs is dependent on the location of PDL (ANOVA, P?=?0.022, P?<?0.05). The elastic moduli at the middle planes were greater than at the cervical and apical planes. However, at the cervical, middle, and apical planes, the elastic moduli of the mesial and distal site were not significantly different (ANOVA, P?=?0.804, P?>?0.05).

Conclusions

The values of elastic modulus were determined in the range between 0.607 and 4.274 MPa under loads ranging from 1 to 5 N. The elastic behavior of the PDL is influenced by the loading rate, tooth type, root level, and individual variation.

     

Oscillatory shear loading of bovine periodontal ligament--a methodological study

This study examined the stress response of bovine periodontal ligament (PDL) under sinusoidal straining. The principle of the test consisted in subjecting transverse tooth, PDL and bone sections of known geometries to controlled oscillatory force application. The samples were secured to the actuator by support plates fabricated using a laser sintering technique to fit their contours to the tooth and the alveolar bone. The actuator was attached to the root slices located in the specimen's center. Hence the machine was able to push or pull the root relative to its surrounding alveolar bone. After determining an optimal distraction amplitude, the samples were cyclically loaded first in ramps and then in sinusoidal oscillations at frequencies ranging from 0.2 to 5 Hz. In the present study the following observations were made: (1) Imaging and the laser sintering technique can be used successfully to fabricate custom-made support plates for cross-sectional root-PDL-bone sections using a laser sintering technique, (2) the load-response curves were symmetric in the apical and the coronal directions, (3) both the stress response versus phase angle and the stress response versus. strain curves tended to "straighten" with increasing frequency, and (4) the phase lag between applied strain and resulting stress was small and did not differ in the intrusive and the extrusive directions. As no mechanical or time-dependent anisotropy was demonstrable in the intrusive and extrusive directions, such results may considerably simplify the development of constitutive laws for the PDL.     

Numerical study of tension and strain distribution around rat molars]

A knowledge of the mechanical processes triggered in the bone and periodontal ligament (PDL) by orthodontic forces applied to a tooth is of decisive importance for an understanding of the subsequent remodelling around the tooth. To investigate these mechanical relationships, three-dimensional finite element (FE) models of the first lower molar in the rat were established. On the basis of digitized serial histological sections, these FE models were generated semi-automatically. Using various simplified geometrical variations, an appropriate FE model for the analysis of the stress and strain distributions was established. The numerical analyses were carried out under a mesially directed force of 0.1 N. Stress distributions in the bone and PDL showed a similar pattern, while strains in the bone were lower than in the PDL by a factor of 10-5. The data confirm the assumption that strain patterns in the PDL may be the key stimulus of bone remodelling.     

Mechanical response of periodontal ligament: Effects of specimen geometry, preconditioning cycles and time lapse

This study was conducted as part of research line addressing the mechanical response of periodontal ligament (PDL) to tensile–compressive sinusoidal loading. The aim of the present project was to determine the effect of three potential sources of variability: (1) specimen geometry, (2) tissue preconditioning and (3) tissue structural degradation over time. For the three conditions, selected mechanical parameters were evaluated and compared.(1) Standard flat specimens (obtained by sequentially slicing portions of bone, PDL and dentin using a precision band saw) and new cylindrical specimens (extracted with a diamond-coated trephine drill) were obtained from bovine mandibular first molars and subjected to a sinusoidal load profile. (2) Specimens were loaded with up to 2000 cycles. (3) Specimens were immersed in saline and tested after 0, 30 and 60 min.From the data generated, the following was concluded: (1) specimen geometry and preparation technique do not influence the mechanical response of the PDL; (2) the mechanical response stabilizes after approximately 1000 cycles; and (3) no major structural degradation occurs when PDL is immersed in saline for a time lapse up to 60 min.     

Strain-dependent up-regulation of ephrin-B2 protein in periodontal ligament fibroblasts contributes to osteogenesis during tooth movement

During orthodontic tooth movement, the application of adequate orthodontic forces allows teeth to be moved through the alveolar bone. These forces are transmitted through the periodontal ligaments (PDL) to the supporting alveolar bone and lead to deposition or resorption of bone, depending on whether the tissues are exposed to a tensile or compressive mechanical strain. Fibroblasts within the PDL (PDLF) are considered to be mechanoresponsive. The transduction mechanisms from mechanical loading of the PDLF to the initiation of bone remodeling are not clearly understood. Recently, members of the ephrin/Eph family have been shown to be involved in the regulation of bone homeostasis. For the first time, we demonstrate that PDLF exposed to tensile strain induce the expression of ephrin-B2 via a FAK-, Ras-, ERK1/2-, and SP1-dependent pathway. Osteoblasts of the alveolar bone stimulated with ephrin-B2 increased their osteoblastogenic gene expression and showed functional signs of osteoblastic differentiation. In a physiological setting, ephrin-B2-EphB4 signaling between PDLF and osteoblasts of the alveolar bone might contribute to osteogenesis at tension sites during orthodontic tooth movement.     

The divergent expression of periostin mRNA in the periodontal ligament during experimental tooth movement

A novel 90-kDa protein named periostin, which is preferentially expressed in the periosteum and the periodontal ligament (PDL), may play a role in bone metabolism and remodeling. However, the precise role of periostin in the PDL remains unclear. Therefore, we examined the expression of periostin mRNA during experimental tooth movement. Experimental tooth movement was achieved in 7-week-old male Sprague-Dawley rats. In control specimens without tooth movement, the expression of periostin mRNA was uniformly observed in the PDL surrounding the mesial and distal roots of the upper molars and was weak in the PDL of the root furcation area. The periostin mRNA-expressing cells were mainly fibroblastic cells in the PDL and osteoblastic cells on the alveolar bone surfaces. The divergent expression of periostin mRNA in the PDL began to be observed at 3 h and continued up to 96 h after tooth movement. The maximum changes, which showed stronger staining in the pressure sites than in the tension sites, were observed at 24 h. The expression of periostin mRNA in the PDL 168 h after tooth movement exhibited a similar distribution to that of the control specimens. These results suggest that periostin is one of the local contributing factors in bone and periodontal tissue remodeling following mechanical stress during experimental tooth movement.     

Nonlinear behavior of trabecular bone at small strains

Study of the behavior of trabecular bone at strains below 0.40 percent is of clinical and biomechanical importance. The goal of this work was to characterize, with respect to anatomic site, loading mode, and apparent density, the subtle concave downward stress-strain nonlinearity, that has been observed recently for trabecular bone at these strains. Using protocols designed to minimize end-artifacts, 155 cylindrical cores from human vertebrae, proximal tibiae, proximal femora, and bovine proximal tibiae were mechanically tested to yield at 0.50 percent strain per second in tension or compression. The nonlinearity was quantified by the reduction in tangent modulus at 0.20 percent and 0.40 percent strain as compared to the initial modulus. For the pooled data, the mean +/- SD percentage reduction in tangent modulus at 0.20 percent strain was 9.07+/- 3.24 percent in compression and 13.8 +/- 4.79 percent in tension. At 0.40 percent strain, these values were 23.5 +/- 5.71 and 35.7+/- 7.10 percent, respectively. The magnitude of the nonlineari't depended on both anatomic site (p < 0.001) and loading mode (p < 0.001), and in tension was positively correlated with density. Calculated values of elastic modulus and yield properties depended on the strain range chosen to define modulus via a linear curve fit (p < 0.005). Mean percent differences in 0.20 percent offset yield strains were as large as 10.65 percent for some human sites. These results establish that trabecular bone exhibits nonlinearity at low strains, and that this behavior can confound intersite comparisons of mechanical properties. A nonlinear characterization of the small strain behavior of trabecular bone was introduced to characterize the initial stress-strain behavior more thoroughly.     

Finite element analysis of a three-dimensional open-celled model for trabecular bone

Based on a regular array of cubic unit cells, each containing a body-centered spherical void, we created an idealized three-dimensional model for both subchondral trabecular bone and a class of porous foams. By considering only face-to-face stacking of unit cells, the inherent symmetry was such that, except at the surface, the displacements and stresses within any one unit cell were representative of the entire porous structure. Using prescribed displacements the model was loaded in both uniaxial compressive strain and uniaxial shear strain. Based on the response to these loads, we found the tensor of elastic constants for an equivalent homogeneous elastic solid with cubic symmetry. We then compared the predicted modulus with our experimental values for bovine trabecular bone and literature values for an open-celled latex rubber foam.     

Variation in hominoid molar enamel thickness

Enamel thickness has figured prominently in discussions of hominid origins for nearly a century, although little is known about its intra-taxon variation. It has been suggested that enamel thickness increases from first to third molars, perhaps due to varying functional demands or developmental constraints, but this has not been tested with appropriate statistical methods. We quantified enamel cap area (c), dentine area (b), and enamel-dentine junction length (e) in coronal planes of sections through the mesial and distal cusps in 57 permanent molars of Pan and 59 of Pongo, and calculated average (c/e) and relative enamel thickness (([c/e]/ radicalb) * 100). Posteriorly increasing or decreasing trends in each variable and average (AET) and relative enamel thickness (RET) were tested among molars in the same row. Differences between maxillary and mandibular analogues and between mesial and distal sections of the same tooth were also examined. In mesial sections of both genera, enamel cap area significantly increased posteriorly, except in Pan maxillary sections. In distal sections of maxillary teeth, trends of decreasing dentine area were significant in both taxa, possibly due to hypocone reduction. Significant increases in AET and RET posteriorly were found in all comparisons, except for AET in Pongo distal maxillary sections. Several significant differences were found between maxillary and mandibular analogues in both taxa. Relative to their mesial counterparts, distal sections showed increased enamel cap area and/or decreased dentine area, and thus increased AET and RET. This study indicates that when AET and RET are calculated from samples of mixed molars, variability is exaggerated due to the lumping of tooth types. To maximize taxonomic discrimination using enamel thickness, tooth type and section plane should be taken into account. Nonetheless, previous findings that African apes have relatively thinner enamel than Pongo is supported for certain molar positions.     

Tissue changes in the rabbit periodontal ligament during orthodontic tooth movement

In this (semi) quantitative animal study the reaction of the periodontal ligament (PDL) to experimental tooth movement is described. To this end, rabbit first incisors were moved sideways with helical torsion springs for periods varying from 3-24 hours. The initial force of the springs was 50 gf. The histomorphology of the PDL was studied in 5 microns thick plastic sections. Comparison with control animals and animals wearing passive springs showed that tooth movement leads to an increased trauma in the PDL within only a few hours. This trauma is characterized by hyalinization, tears and ruptures in the fibres and blood vessels, and by the presence of extravascular erythrocytes and pyknosis. Tissue damage significantly increased with time. After 24 hours of tooth movement, the PDL fibers are compressed or stretched in 68% of the sections and the blood vessels in the PDL are compressed or stretched in 62% of the sections. Even in the controls, more than 15% of the sections displayed slightly stretched or compressed fibers, and about 10% showed slightly compressed or stretched blood vessels. This indicates that some damage is regularly present in a normally functioning PDL. Increases in the percentage of sections with blood vessel compression are found in all groups wearing passive springs, especially after 6 hours. A high concordancy in compression and tension patterns of blood vessels and fibers is present in 83% of the sections. Pyknotic cells are practically confined to areas with compressed PDL fibers in rabbits wearing active springs. Extravascular erythrocytes were found in sections with all types of fiber patterns. A significant majority of extravascular erythrocytes, however, was found in areas with compressed fibers.     

A transversely isotropic hyperelastic constitutive model of the PDL. Analytical and computational aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

Viscoelastic behaviour and failure of bovine cancellous bone under constant strain rate

A programme has been established to characterize the long-term behaviour of cancellous bone. Fresh bovine cancellous specimens of dimensions 10 x 10 x 10 mm3 and 10 x 40 x 3.6 mm3 were manufactured and used within the testing programme. Results published in the literature indicate that the long-term behaviour of cancellous bone is well described by a power law, which is a very similar response of typical polymers. So far, dynamic mechanical tests (DMA) in three-point bending, under frequencies between 0.01 and 100 Hz at room temperature, confirmed the published results in a qualitative way. Nevertheless, the measured dimensionless damping, tan delta, was slightly higher than the values reported in the literature for the compact bone. The relaxation curves were obtained from dynamic tests and confirmed that bone relaxation modulus can be described by a power law function of time. Tests under constant compression strain rate were performed at four different strain rates: 0.15/s, 0.015/s, 0.0015/s and 0.00015/s and strain rate dependent behaviour was observed. An average elastic bending modulus of 300 MPa was obtained.     

A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.     

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.     

Nano- and micromechanical properties of dentine: Investigation of differences with tooth side

The soft zone in dentine beneath the dentino-enamel junction is thought to play an important role in tooth function, strain distribution and fracture resistance during mastication. Recently reported asymmetry in mechanical properties with tooth side may point at a basic property of tooth function. The aim of our study was to test if this asymmetry was reflected in the nano- and micromechanical properties of dentine. We investigated the mechanical properties of dentine on the buccal and lingual side of nine extracted human teeth using nano- and microindentation. Properties were analysed on the natural log scale, using maximum likelihood to estimate the parameters. Two-sided 0.05-level likelihood ratio tests were used to assess the influences of surface (buccal versus lingual) and dentine depth, measured from the DEJ in crown dentine and from the CDJ in root dentine. Results showed the well known gradual increase in mechanical properties with increasing distance from the DEJ. Coronal dentine showed higher elastic modulus and hardness on the lingual side of teeth for all measurements, while root dentine was harder on the buccal side. Due to the subtlety of these effects and the small number of teeth studied, results failed to reach statistical significance. Results suggest that dentine nano- and micromechanical properties vary with tooth side in agreement with recent literature using macroscopic methods. They also reveal that buccal-lingual ratios of hardness are in opposite directions in crown and root dentine, suggesting compensatory functions.     

A biomechanical study of the human periodontal ligament

The mechanical properties of the normal human periodontal ligament (PDL) were investigated at eight different root levels. One millimetre transverse sections of teeth, PDL and alveolar bone of mandibular premolars were examined in a materials testing machine. During testing bone was supported by metal rings and teeth by metal cylinders of individually adjusted sizes. Having corrected for differences of size and width of the PDL the influence of root level was estimated using a multivariate analysis of variance. The shear strength was almost constant at the upper part of the root, diminishing in apical direction. The shear extensibility and the relative failure energy in shear were higher at the middle of the root, diminishing coronally and apically. Only the elastic stiffness did not vary significantly along the root. These results demonstrate that in order to compare the mechanical properties of PDL care should be taken to compare areas at the same root level.     

Occlusal force and craniofacial biomechanics during growth in rhesus monkeys

The masticatory muscles in 132 anesthetized male and female rhesus monkeys ranging in age from juvenile to adult were unilaterally stimulated. Muscle forces and speeds were measured with a bite force transducer positioned at the incisors, premolars, and molars during twitch and tetanic contractions. Lateral cephalographs of all animals were used to estimate the orientation and mechanical advantage of the masticatory muscles. Results showed that maximal occlusal forces increased at a greater rate than body weight during growth. However, maximal occlusal forces increased isometrically relative to mandibular length. Mean forces at the incisors ranged from 70.3 newtons (n) in juveniles up to 139.9 n in adult males. Forces at the molars were 2-2.5 times greater than at the incisors. Time-to-peak tension decreased with increasing body size from 44.1 msec in juveniles to 37.4 msec in adult females to 31.0 msec in adult males. Regression analysis showed that adult males have faster muscles than adult females or juveniles even when corrected for body size. Temporalis and masseter orientation was found to change little throughout growth. The mechanical advantage of the masseter and temporalis muscles for producing occlusal forces on the distal molars improved between juveniles and adults, which is contrary to findings of Oyen et al. (Growth 43:174-187, 1979). Among adults, females had a greater mechanical advantage of the masseter muscles than males.     

Semi-automatic generation of finite element meshes fo dental preparations]

The mechanical properties and elastic behaviour of periodontal tissue are a decisive factor in understanding initial tooth mobility and bone remodelling processes in orthodontics. An experimental set-up was designed to precisely determine a tooth's elastic response to different loading conditions. Segments of pig's maxilla bearing separated molars were used, and their mechanical response to loading was recorded. Subsequently, finite element analysis (FEA) was performed on the basis of the experimental data. The combination of experimental and numerical methods was used to determine the material properties of the periodontal ligament (PDL). The geometries of the preparations were reconstructed and FE meshes generated semi-automatically with the aid of the special computer program, CAGOG (Computer Aided Generator for Orthodontic Geometries) to optimally match the experimental geometry. Nonlinear material parameters were determined for the PDL and verified by comparing experimental and numerical results obtained in other specimens with an error of about 10%. This good correlation indicates that the selected method of mesh generation is appropriate for creating realistic FE models that can be compared with experimental results.