Experiments to determine the time dependent material properties of the periodontal ligament]

The periodontal ligament is a tissue that attaches the tooth (root) to its alveolar socket, and thus plays an important role in the regulation of tooth movements. Detailed knowledge of the material properties of the periodontal ligament is therefore essential to an understanding of tooth reaction to forces applied during orthodontic treatment. A knowledge of material parameters can also be used in simulations of long-term tooth movements with the aim of improving orthodontic treatment. To this end, this study investigated time-dependent material properties, namely the hysteresis behaviour of the periodontal ligament under constant-velocity loading, the influence of loading velocity on the hysteresis, and its failure under constant loading. Specimens obtained from pigs were used for testing purposes, and the experiments were conducted in a special test setup using a material testing device. The material behaviour of the periodontal ligament was shown to be viscoelastic, and the elastic parameters of material behaviour were also determined. Under constant-velocity loading, material behaviour showed a nonlinear course of the stress-strain curve, also known as hysteresis. When loading was repeated several times, the maximum stress of the hysteresis decreased with each cycle. Determination of the deflection of the specimen at different velocities showed maximum stress to be dependent on the loading rate. The measured stress-strain curves were approximated by bilinear behaviour, permitting the use of finite element calculations. Also investigated was the failure behaviour of the periodontal ligament, which revealed tissue rupture to be inconstant.     

The relationship of mechanical properties to morphology in patellar tendon autografts after posterior cruciate ligament replacement in sheep.

In a sheep model the posterior cruciate ligament (PCL) was replaced by a patellar tendon autograft (PTAG) using the central one-third of the ipsilateral patellar tendon (PT). The sheep were sacrificed at 16, 26, 52 and 104 weeks postoperation. The PTAG, and, as controls, the contralateral PCL and PT were harvested. These were examined using biomechanical testing as well as light and transmission electron microscopy, including immunohistological techniques. The material properties (maximum stress, elastic modulus) were compared to the morphological features. The cellular distribution, the distribution of glycosaminoglycans (GAGs), the collagen fibril diameter and the occurrence of Type III collagen were studied. Prior to transplantation, the PTAG was shown to be superior in maximum stress (57.2 +/- 5.5 MPa vs 41.3 +/- 1.9 MPa) and elastic modulus (368.8 +/- 49.3 MPa vs 172.3 +/- 14.6 MPa) to the PCL. The early decline in material properties of the PTAG (maximum stress 22% and elastic modulus 42% of the control) after free grafting paralleled a cell- and capillary-rich PTAG tissue with remnants of necrosis and a poorly organized extracellular matrix. Two years after implantation, with progressive alignment of the tissue matrix, maximum stress and elastic modulus acquired approximately 60 and 70% of the control, respectively. However, there was also an evidence of degenerative changes characterized by acellular areas, loss of the normal bundling pattern of collagen fibers and abnormal accumulation of GAGs. Ultrastructurally, there was a predominant shift to thin collagen fibrils in the PTAG compared to PCL and PT, both consisting of thick and thin collagen fibrils. Thin fibrils were demonstrated to be, in part, split thick fibrils as well as newly formed fibrils. Most of these thin fibrils revealed a positive reaction with antibodies to Type III collagen.     

The major antigen of elastin-associated microfibrils is a 31-kDa glycoprotein

The major antigen derived from elastic fiber microfibrils was identified as a Mr = 31,000 glycoprotein, using immunoblotting and immunohistochemical techniques with antisera raised to "reductive guanidine extracts" of fetal bovine nuchal ligament, and to subfractions of these. A second, elastic fiber-derived, but unidentified, antigen of large molecular size (Mr greater than 200,000) was present in these extracts. Antisera raised to the purified 31-kDa glycoprotein were shown, by immunoelectron microscopy, to localize specifically to the elastin-associated microfibrils. Thus, the macro-molecule was called "microfibril-associated glycoprotein" or MAGP. MAGP is an acidic glycoprotein with a distinctive amino acid composition, being exceptionally rich in glutamic acid, rich in cystine, and low in glycine. MAGP was extractable from tissue homogenates using NaCl, urea, or guanidine hydrochloride solutions, only if a strong reducing agent was present. Thus, disulfide bonding is important for the strong association of MAGP with elastic fibers. Immunoblotting with anti-MAGP antiserum identified two additional reactive species, of Mr = 60,000 and Mr approximately 300,000, in tissue extracts. As only the 31-kDa species was detected in fibroblast culture medium, these additional species were probably aggregates, rather than precursors. MAGP did not react with antilysyl oxidase antiserum on immunoblots or by enzyme-linked immunosorbent assay. MAGP is the first macromolecule to have been established to be a constituent of elastin-associated microfibrils in both developing and mature elastic tissues.     

Developmental expression of dermatan sulfate proteoglycans in the elastic bovine nuchal ligament.

The nuchal ligament of bovines is a useful system in which to study elastic fibre formation since it contains up to 83% elastin and undergoes a period of rapid elastinogenesis during the last trimester of fetal development and in the first four post-natal months. To identify proteoglycans (PGs) which may be involved in this process we initially investigated changes in the glycosaminoglycan (GAG) profiles during nuchal ligament development. In contrast to the collagenous Achilles tendon, nuchal ligament exhibited: (a) elevated hyaluronan (HA) levels in the peak period of elastin-associated microfibril (fibrillin) synthesis (130-200 days) which precedes elastinogenesis; and (b) markedly increased synthesis of a glucuronate-rich copolymeric form of dermatan sulfate (DS) in the period corresponding to elastin formation (200-270 days). Analysis of DSPGs isolated from 230-day nuchal ligament showed that this copolymer was predominantly associated with a glycoform of biglycan which was specifically elevated at this stage in development. This finding was consistent with Northern blot analysis which showed that steady-state biglycan mRNA levels increased significantly during the elastinogenic period. In contrast, the mRNA levels for decorin, the only other DSPG detected in this tissue, declined rapidly after 140 days of fetal development. In conclusion, the results suggest that HA may play a role in microfibril assembly and that a specific glycoform of biglycan may be associated with the elastinogenic phase of elastic fibre formation.     

Immunohistochemical characterization of elastic system fibers in rat molar periodontal ligament.

Among elastic system fibers, oxytalan fibers are known as a ubiquitous component of the periodontal ligament, but the localization and role of elastin-containing fibers, i.e., elastic and elaunin fibers, has yet to be clarified. In this study, we immunohistochemically investigated the localization of elastin and fibrillin, major proteins of elastin-containing fibers in the periodontal ligament of rat lower first molars. At the light microscope level, distribution of elastin-positive fibers was not uniform but often concentrated in the vicinity of blood vessels in the apical region of the ligament. In contrast, fibrillin-positive fibers were more widely distributed throughout the ligament, and the pattern of their distribution was comparable to the reported distribution of oxytalan fibers. At the ultrastructural level, assemblies or bundles of abundant fibrillin-containing microfibrils were intermingled with a small amount of elastin. This observation indicated that elastin-positive fibers observed under the light microscope were elaunin fibers. No mature elastic fibers, however, were found in the ligament. These results show that the major components of elastic system fibers in the periodontal ligament of the rat mandibular first molar were oxytalan and elaunin fibers, suggesting that the elastic system fibers play a role in the mechanical protection of the vascular system.     

Microstructure and crystallographic texture of Charonia lampas lampas shell

Charonia lampas lampas shell is studied using scanning electron microscopy and X-ray diffraction combined analysis of the preferred orientations and cell parameters. The Charonia shell is composed of three crossed lamellar layers of biogenic aragonite. The outer layer exhibits a 0 0 1 fibre texture, the intermediate crossed lamellar layer is radial with a split of its c-axis and single twin pattern of its a-axis, and the inner layer is comarginal with split c-axis and double twinning. A lost of texture strength is quantified from the inner layer outward. Unit-cell refinements evidence the intercrystalline organic influence on the aragonite unit-cell parameters anisotropic distortion and volume changes in the three layers. The simulation of the macroscopic elastic tensors of the mineral part of the three layers, from texture data, reveals an optimisation of the elastic coefficient to compression and shear in all directions of the shell as an overall.     

The effects of modeling simplifications on craniofacial finite element models: the alveoli (tooth sockets) and periodontal ligaments

Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Young's modulus and Poisson's ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDL's material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress-strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.     

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.

     

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.     

Elastic properties, Young's modulus determination and structural stability of the tropocollagen molecule: a computational study by steered molecular dynamics

The aim of this report is to investigate at microscopic level the elastic properties of a tropocollagen-like molecule submitted to linear traction along its longitudinal axis. For this purpose, we performed steered molecular dynamics (SMD) simulations for a wide range of spring constants in order to test the molecular response based on a two-spring model connected in series. An elastic behavior was observed in an elongation range of 2.5-4% of the molecular length, estimating an "effective molecular elastic constant" of 1.02+/-0.20 kcal/mol A2 in this region. Accordingly, a Young's modulus for the tropocollagen molecule of Y=4.8+/-1.0 GPa was calculated. The complex hydrogen bond network was traced along molecular dynamics (MD) and SMD simulations revealing a rearrangement of these interactions preserving the integrity of the molecular structure when submitted to traction. No evidence of the significant role attributed to water bridges for structural stability was detected, on the contrary facts pointed out that the hydrogen bond network might be the responsible.     

Contribution of potassium ion and split modes of G-quadruplex to the sensitivity and selectivity of label-free sensor toward DNA detection using fluorescence

In recent years, bioanalytical technology based on G-quadruplex has been paid significant attention due to its versatility and stimulus-responsive reconfiguration. Notwithstanding, several key issues for template-directed reassembly of G-quadruplex have not been resolved: what is the key factor for determining the sensitivity and selectivity of split G-quadruplex probes toward target DNA. Therefore, in this study, we designed three pairs of split G-quadruplex probes and investigated the sensitivity and selectivity of these systems in terms of potassium ion concentration and split modes of G-quadruplex. Due to its simplicity and sensitivity, N-methyl-mesoporphyrin (NMM) as fluorescence probes was used to monitor the target-directed reassembling process of G-quadruplex. A G-quadruplex sequence derived from the c-Myc promoter was split into "symmetric" probes, where each fragment contained two runs of guanine residues (2+2), or into "asymmetric" fragments each containing (3+1 or 1+3) runs of guanine residues. In all three cases, the sensitivity of target detection was highly dependent on the thermodynamic stability of the hybrid structure, which can be modulated by potassium ion concentrations. Using a combination of CD, fluorescence, and UV spectroscopy, we found that increasing potassium concentrations can increase the sensitivity of target detection, but can decrease the selectivity of discriminating cognate versus mismatched "target" DNA. The previous argument that asymmetrically split probes were always better than symmetrically split probes in terms of selectivity was not plausible anymore. These results demonstrate how the sensitivities and selectivity of split probes to mutations can be optimized by tuning the thermodynamic stability of the three-way junction complex.     

A finite element model of the L5-S1 functional spinal unit: development and comparison with biomechanical tests in vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro. Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

Do Cells Contribute to Tendon and Ligament Biomechanics?

Introduction

Acellular scaffolds are increasingly used for the surgical repair of tendon injury and ligament tears. Despite this increased use, very little data exist directly comparing acellular scaffolds and their native counterparts. Such a comparison would help establish the effectiveness of the acellularization procedure of human tissues. Furthermore, such a comparison would help estimate the influence of cells in ligament and tendon stability and give insight into the effects of acellularization on collagen.

Material and Methods

Eighteen human iliotibial tract samples were obtained from nine body donors. Nine samples were acellularized with sodium dodecyl sulphate (SDS), while nine counterparts from the same donors remained in the native condition. The ends of all samples were plastinated to minimize material slippage. Their water content was adjusted to 69%, using the osmotic stress technique to exclude water content-related alterations of the mechanical properties. Uniaxial tensile testing was performed to obtain the elastic modulus, ultimate stress and maximum strain. The effectiveness of the acellularization procedure was histologically verified by means of a DNA assay.

Results

The histology samples showed a complete removal of the cells, an extensive, yet incomplete removal of the DNA content and alterations to the extracellular collagen. Tensile properties of the tract samples such as elastic modulus and ultimate stress were unaffected by acellularization with the exception of maximum strain.

Discussion

The data indicate that cells influence the mechanical properties of ligaments and tendons in vitro to a negligible extent. Moreover, acellularization with SDS alters material properties to a minor extent, indicating that this method provides a biomechanical match in ligament and tendon reconstruction. However, the given protocol insufficiently removes DNA. This may increase the potential for transplant rejection when acellular tract scaffolds are used in soft tissue repair. Further research will help optimize the SDS-protocol for clinical application.     

Functional importance of a highly elastic ligament on the mammalian diaphragm.

The diaphragm of mammals is a musculotendinous dome separating the thoracic and abdominal cavities. With no skeletal elements to stretch it, the diaphragm has the problem of positioning its muscle fibres at a length appropriate for the onset of an inspiratory contraction. This is achieved through a negative intrapleural pressure, resulting from the opposing elastic recoil of the ribcage and lungs, which sucks the diaphragm into the thorax and extends the muscle fibres. A consequence of this negative pressure is that the diaphragm muscle is under tension when inactive during expiration. This is an unusual condition for skeletal muscles, which can suffer irreversible changes when stretched to long length, or they may respond by growing longer. We now describe a highly elastic and resilient diaphragmatic ligament which sets a sarcomere length enabling the muscle to use its full operating range, reduces stress on the diaphragm muscle fibres, and assists shortening of the diaphragm muscle at the onset of inspiration by means of elastic recoil.     

Mechanics of the anterior drawer test at the ankle: the effects of ligament viscoelasticity

The anterior drawer test at the human ankle joint is a routine clinical examination. The relationship between the mechanical response of this joint and the flexion angle was elucidated by a recent mathematical model, using purely elastic mechanical characteristics for the ligament fibres. The objective of the present work was to assess the effect of ligament viscoelasticity on the force response of the ankle joint for anterior displacements of the foot relative to the tibia, at different ankle flexion positions. A viscoelastic model of the ligaments from the literature was included in the recently proposed mathematical model. Drawer tests were simulated at several flexion angles and for increasing velocities of the imposed anterior displacement. The stiffness of the model ankle joint increased only modestly with velocity. The response force found for a 6mm displacement at 20 degrees plantarflexion increased by only 13% for a one hundred-fold increase in velocity from 0.1 to 10 mm/s. The flexion angle was confirmed as the most influential parameter in the mechanical response of the ankle to anterior drawer test.     

A Finite Element Model of the L5-S1 Functional Spinal Unit: Development and Comparison with Biomechanical Tests In Vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro . Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

Identification of glycoproteins associated with elastin-associated microfibrils

The microfibrils associated with elastic tissue have been shown to be predominantly proteinaceous. On the basis of their affinity for cationic stains, including ruthenium red, they have been assumed to be glycoprotein, but more evidence to support this claim has not been adduced. Despite repeated investigation of glycoprotein materials obtained by extraction of elastic tissues with reagents that appear to remove microfibrils, the chemical composition of elastin-associated microfibrils remains obscure. An electron microscopic study of the microfibrils in two elastin-rich tissues (bovine nuchal ligament and aorta) during their development was pursued using more specific histochemical methods. The periodic acid-alkaline bismuth stain (analogous to the periodic acid-Schiff stain for glycoproteins in light microscopy) has been adapted for this study. Specific aldehyde groups (confirmed by blocking with m-aminophenol or sodium borohydride) were identified after periodate oxidation as fine granules of bismuth stain. These were shown to localize specifically along the elastin-associated microfibrils in a finely punctate form. Staining of the amorphous elastic component did not occur except for a fine rim adjacent to the microfibrils. Lectin binding with concanavalin A (with ferritin markers) confirmed that there are glucose- or mannose-containing proteins associated with the microfibrillar component of elastic tissue. This was true of these microfibrils in all layers of the aortic wall and throughout the ligament. It was also true of mature adult tissues in which there was a lesser proportion of microfibrils. It is concluded that elastin-associated microfibrils really are associated with glycoprotein(s).     

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.