Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus.

Accurate tissue stress predictions for the annulus fibrosus are essential for understanding the factors that cause or contribute to disc degeneration and mechanical failure. Current computational models used to predict in vivo disc stresses utilize material laws for annular tissue that are not rigorously validated against experimental data. Consequently, predictions of disc stress resulting from physical activities may be inaccurate and therefore unreliable as a basis for defining mechanical-biologic injury criteria. To address this need we present a model for the annulus as an isotropic ground substance reinforced with two families of collagen fibers, and an approach for determining the material constants by simultaneous consideration of multiple experimental data sets. Two strain energy functions for the annulus are proposed and used in the theory to derive the constitutive equations relating the stress to pure stretch deformations. These equations are applied to four distinct experimental protocols and the material constants are determined from a simultaneous, nonlinear regression analysis. Good agreement between theory and experiment is achieved when the invariants are included within multiple, separate exponentials in the strain energy function.     

Modeling interlamellar interactions in angle-ply biologic laminates for annulus fibrosus tissue engineering

Mechanical function of the annulus fibrosus of the intervertebral disc is dictated by the composition and microstructure of its highly ordered extracellular matrix. Recent work on engineered angle-ply laminates formed from mesenchymal stem cell (MSC)-seeded nanofibrous scaffolds indicates that the organization of collagen fibers into planes of alternating alignment may play an important role in annulus fibrosus tissue function. Specifically, these engineered tissues can resist tensile deformation through shearing of the interlamellar matrix as layers of collagen differentially reorient under load. In the present work, a hyperelastic constitutive model was developed to describe the role of interlamellar shearing in reinforcing the tensile response of biologic laminates, and was applied to experimental results from engineered annulus constructs formed from MSC-seeded nanofibrous scaffolds. By applying the constitutive model to uniaxial tensile stress–strain data for bilayers with three different fiber orientations, material parameters were generated that characterize the contributions of extrafibrillar matrix, fibers, and interlamellar shearing interactions. By 10 weeks of in vitro culture, interlamellar shearing accounted for nearly 50% of the total stress associated with uniaxial extension in the anatomic range of ply angle. The model successfully captured changes in function with extracellular matrix deposition through variations in the magnitude of model parameters with culture duration. This work illustrates the value of engineered tissues as tools to further our understanding of structure–function relations in native tissues and as a test-bed for the development of constitutive models to describe them.     

Advanced Glycation End-Products Reduce Collagen Molecular Sliding to Affect Collagen Fibril Damage Mechanisms but Not Stiffness

Advanced glycation end-products (AGE) contribute to age-related connective tissue damage and functional deficit. The documented association between AGE formation on collagens and the correlated progressive stiffening of tissues has widely been presumed causative, despite the lack of mechanistic understanding. The present study investigates precisely how AGEs affect mechanical function of the collagen fibril – the supramolecular functional load-bearing unit within most tissues. We employed synchrotron small-angle X-ray scattering (SAXS) and carefully controlled mechanical testing after introducing AGEs in explants of rat-tail tendon using the metabolite methylglyoxal (MGO). Mass spectrometry and collagen fluorescence verified substantial formation of AGEs by the treatment. Associated mechanical changes of the tissue (increased stiffness and failure strength, decreased stress relaxation) were consistent with reports from the literature. SAXS analysis revealed clear changes in molecular deformation within MGO treated fibrils. Underlying the associated increase in tissue strength, we infer from the data that MGO modified collagen fibrils supported higher loads to failure by maintaining an intact quarter-staggered conformation to nearly twice the level of fibril strain in controls. This apparent increase in fibril failure resistance was characterized by reduced side-by-side sliding of collagen molecules within fibrils, reflecting lateral molecular interconnectivity by AGEs. Surprisingly, no change in maximum fibril modulus (2.5 GPa) accompanied the changes in fibril failure behavior, strongly contradicting the widespread assumption that tissue stiffening in ageing and diabetes is directly related to AGE increased fibril stiffness. We conclude that AGEs can alter physiologically relevant failure behavior of collagen fibrils, but that tissue level changes in stiffness likely occur at higher levels of tissue architecture.     

Ageing of the human corneal stroma: structural and biochemical changes

High and low angle X-ray diffraction patterns from the corneal stroma give information about the mean intermolecular spacing of the collagen molecules and the mean interfibrillar spacing of the collagen fibrils, respectively. X-ray data were collected, using a high intensity synchrotron source, from human corneas and sclera at approximately physiological hydration. The spacings were measured as a function of tissue age. Between birth and 90 years there is an increase in the cross-sectional area associated with each molecule in corneal collagen from approx. 3.04 nm² to 3.46 nm², and an increase in scleral collagen from approx. 2.65 nm² to 3.19 nm². These changes may be due to an increase in the extent of non-enzymatic cross-linking between collagen molecules over the age range. We have investigated this possibility by measuring collagen glycation using the thiobarbituric acid assay and the subsequent advanced glycation end-products (AGEs) using fluorescence emission. The results obtained have shown an age-related increase in glycation and AGEs in both tissues. We have also demonstrated a decrease in the interfibrillar spacing of corneal collagen with increasing age which may be related to changes in the proteoglycan composition of the interfibrillar matrix.     

Advanced Glycation Endproducts Interfere with Adhesion and Neurite Outgrowth

Advanced glycation endproducts (AGEs) represent a non-enzymatic posttranslational protein modification. AGEs are generated by a series of chemical reactions of free reducing monosaccharides, such as glucose, fructose or metabolites of the monosaccharide metabolism with amino groups of proteins. After oxidation, dehydration and condensation, stable AGE-modifications are formed. AGE-modified proteins accumulate in all cells and tissues as a normal feature of ageing and correlate with the glucose concentration in the blood. AGEs are increased in diabetic patients and play a significant role in the pathogenesis of most age-related neural disorders, such as Alzheimer’s disease. We examined the role of AGEs on neurite outgrowth of PC12 cells. We induced the formation of AGEs using the reactive carbonyl compound methylglyoxal (MGO) as a physiological metabolite of glucose. We found that AGE-modification of laminin or collagen interfered with adhesion but not with neurite outgrowth of PC12 cells. Furthermore, the AGE-modification of PC12 cell proteins reduced NGF-induced neurite outgrowth. In conclusion, our data show that AGEs negatively influence neural plasticity.     

The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine

To date, studies that have investigated the kinematics of spinal motion segments have largely focused on the contributions that the spinal ligaments play in the resultant motion patterns. However, the specific roles played by intervertebral disk components, in particular the annulus fibrosus, with respect to global motion is not well understood in spite of the relatively large literature base with respect to the local ex vivo mechanical properties of the tissue. The primary objective of this study was to implement the nonlinear and orthotropic mechanical behavior of the annulus fibrosus in a finite element model of an L4/L5 functional spinal unit in the form of a strain energy potential where the individual mechanical contributions of the ground substance and fibers were explicitly defined. The model was validated biomechanically under pure moment loading to ensure that the individual role of each soft tissue structure during load bearing was consistent throughout the physiologically relevant loading range. The fibrous network of the annulus was found to play critical roles in limiting the magnitude of the neutral zone and determining the stiffness of the elastic zone. Under flexion, lateral bending, and axial rotation, the collagen fibers were observed to bear the majority of the load applied to the annulus fibrosus, especially in radially peripheral regions where disk bulging occurred. For the first time, our data explicitly demonstrate that the exact fiber recruitment sequence is critically important for establishing the range of motion and neutral zone magnitudes of lumbar spinal motion segments.     

Ultrastructural observations on collagen and proteoglycans in the annulus fibrosus of the intervertebral disc

Replicas of freeze-fractured collagen fibrils of peripheral and central parts of the annulus fibrosus of bovine intervertebral discs show microfibrils which run either arranged in parallel or in a helix with an inclination-angle ranging from 4 degrees to 8 degrees. According to results of freeze-fracutred tissues, thin sections of specimens treated with 4M guanidinium chloride show collagen fibrils with a parallel or a slightly wavy microfibrillar packing. Thin sections of specimens treated with alcian blue diluted in MgCl2 critical electrolyte solutions reveal interfibrillar proteoglycan particles with a filamentous shape in the peripheral zones of the annulus fibrosus and a predominant leaf-like appearance in the inner ones. These observations are discussed with reference to previous data concerning the variation in composition from the peripheral to the inner parts of the annulus fibrosus.     

N-Phenacylthiazolium Bromide Reduces Bone Fragility Induced by Nonenzymatic Glycation

Nonenzymatic glycation (NEG) describes a series of post-translational modifications in the collagenous matrices of human tissues. These modifications, known as advanced glycation end-products (AGEs), result in an altered collagen crosslink profile which impacts the mechanical behavior of their constituent tissues. Bone, which has an organic phase consisting primarily of type I collagen, is significantly affected by NEG. Through constant remodeling by chemical resorption, deposition and mineralization, healthy bone naturally eliminates these impurities. Because bone remodeling slows with age, AGEs accumulate at a greater rate. An inverse correlation between AGE content and material-level properties, particularly in the post-yield region of deformation, has been observed and verified. Interested in reversing the negative effects of NEG, here we evaluate the ability of n-phenacylthiazolium bromide (PTB) to cleave AGE crosslinks in human cancellous bone. Cancellous bone cylinders were obtained from nine male donors, ages nineteen to eighty, and subjected to one of six PTB treatments. Following treatment, each specimen was mechanically tested under physiological conditions to failure and AGEs were quantified by fluorescence. Treatment with PTB showed a significant decrease in AGE content versus control NEG groups as well as a significant rebound in the post-yield material level properties (p<0.05). The data suggest that treatment with PTB could be an effective means to reduce AGE content and decrease bone fragility caused by NEG in human bone.     

Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load

The angled, lamellar structure of the annulus fibrosus is integral to its load-bearing function. Reorientation of this fiber structure with applied load may contribute to nonlinear mechanical behavior and to large increases in tensile modulus. Fiber reorientation has not yet been quantified for loaded non-degenerated and degenerated annulus fibrosus tissue. The objective of this study was to measure fiber reorientation and mechanical properties (toe- and linear-region modulus, transition strain, and Poisson's ratio) of loaded outer annulus fibrosus tissue using a new application of FFT image processing techniques. This method was validated for quantification of annulus fiber reorientation during loading in this study. We hypothesized that annulus fibrosus fibers would reorient under circumferential tensile load, and that fiber reorientation would be affine. Additionally, we hypothesized that degeneration would affect fiber reorientation, toe-region modulus and Poisson's ratio. Annulus fibrosus fibers were found to reorient toward the loading direction, and degeneration significantly decreased fiber reorientation (the fiber reorientation parameter, m(FFT)=-1.70 degrees /% strain for non-degenerated and -0.95 degrees /% strain for degenerated tissue). Toe-region modulus was significantly correlated with age (r=0.6). Paired t-tests showed no significant difference in the fiber reorientation parameter calculated experimentally with that calculated using an affine prediction. Thus, an affine prediction is a good approximation of fiber reorientation. The findings of this study add to the understanding of overall disc mechanical behavior and degeneration.     

Ageing of the human corneal stroma: structural and biochemical changes.

High and low angle X-ray diffraction patterns from the corneal stroma give information about the mean intermolecular spacing of the collagen molecules and the mean interfibrillar spacing of the collagen fibrils, respectively. X-ray data were collected, using a high intensity synchrotron source, from human corneas and sclera at approximately physiological hydration. The spacings were measured as a function of tissue age. Between birth and 90 years there is an increase in the cross-sectional area associated with each molecule in corneal collagen from approx. 3.04 nm2 to 3.46 nm2, and an increase in scleral collagen from approx. 2.65 nm2 to 3.19 nm2. These changes may be due to an increase in the extent of non-enzymic cross-linking between collagen molecules over the age range. We have investigated this possibility by measuring collagen glycation using the thiobarbituric acid assay and the subsequent advanced glycation end-products (AGEs) using fluorescence emission. The results obtained have shown an age-related increase in glycation and AGEs in both tissues. We have also demonstrated a decrease in the interfibrillar spacing of corneal collagen with increasing age which may be related to changes in the proteoglycan composition of the interfibrillar matrix.     

A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage

Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric tensile–compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic materials that allows the mechanical properties of the tissue to differ in tension and compression. In this paper, we derive an orthotropic stress constitutive equation that is second-order in terms of the Biot strain tensor as an alternative to traditional exponential type equations. Several reduced forms of the bimodular second-order equation, with six to nine parameters, and a bimodular exponential equation, with seven parameters, were fit to an experimental dataset that captures the highly asymmetric and orthotropic mechanical response of cartilage. The results suggest that the bimodular second-order models may be appealing for some applications with cartilaginous tissues.     

Preferential sites for intramolecular glucosepane cross-link formation in type I collagen: A thermodynamic study

The extracellular matrix (ECM) undergoes progressive age-related stiffening and loss of proteolytic digestibility due to an increase in concentration of advanced glycation end products (AGEs). The most abundant AGE, glucosepane, accumulates in collagen with concentrations over 100 times greater than all other AGEs. Detrimental collagen stiffening properties are believed to play a significant role in several age-related diseases such as osteoporosis and cardiovascular disease. Currently little is known of the potential location of covalently cross-linked glucosepane formation within collagen molecules; neither are there reports on how the respective cross-link sites affect the physical and biochemical properties of collagen. Using fully atomistic molecular dynamics simulations (MD) we have identified six sites where the formation of a covalent intra-molecular glucosepane cross-link within a single collagen molecule in a fibrillar environment is energetically favourable. Identification of these favourable sites enables us to align collagen cross-linking with experimentally observed changes to the ECM. For example, formation of glucosepane was found to be energetically favourable within close proximity of the Matrix Metalloproteinase-1 (MMP1) binding site, which could potentially disrupt collagen degradation.     

A special theory of biphasic mixtures and experimental results for human annulus fibrosus tested in confined compression

A finite deformation mixture theory is used to quantify the mechanical properties of the annulus fibrosus using experimental data obtained from a confined compression protocol. Certain constitutive assumptions are introduced to derive a special mixture of an elastic solid and an inviscid fluid, and the constraint of intrinsic incompressibility is introduced in a manner that is consistent with results obtained for the special theory. Thirty-two annulus fibrosus specimens oriented in axial (n = 16) and radial (n = 16) directions were obtained from the middle-lateral portion of intact intervertebral discs from human lumbar spines and tested in a stress-relaxation protocol. Material constants are determined by fitting the theory to experimental data representing the equilibrium stress versus stretch and the surface stress time history curves. No significant differences in material constants due to orientation existed, but significant differences existed due to the choice of theory used to fit the data. In comparison with earlier studies with healthy annular tissue, we report a lower aggregate modulus and a higher initial permeability constant. These differences are explained by the choice of reference configuration for the experimental studies.     

Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus

Intervertebral disc degeneration results in disorganization of the laminate structure of the annulus that may arise from mechanical microfailure. Failure mechanisms in the annulus were investigated using composite lamination theory and other analyses to calculate stresses in annulus layers, interlaminar shear stress, and the region of stress concentration around a fiber break. Scanning electron microscopy (SEM) was used to evaluate failure patterns in the annulus and evaluate novel structural features of the disc tissue. Stress concentrations in the annulus due to an isolated fiber break were localized to approximately 5 microm away from the break, and only considered a likely cause of annulus fibrosus failure (i.e., radial tears in the annulus) under extreme loading conditions or when collagen damage occurs over a relatively large region. Interlaminar shear stresses were calculated to be relatively large, to increase with layer thickness (as reported with degeneration), and were considered to be associated with propagation of circumferential tears in the annulus. SEM analysis of intervertebral disc annulus fibrosus tissue demonstrated a clear laminate structure, delamination, matrix cracking, and fiber failure. Novel structural features noted with SEM also included the presence of small tubules that appear to run along the length of collagen fibers in the annulus and a distinct collagenous structure representative of a pericellular matrix in the nucleus region.     

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.     

Contribution of collagen fibers to the compressive stiffness of cartilaginous tissues

Cartilaginous tissues such as the intervertebral disk are predominantly loaded under compression. Yet, they contain abundant collagen fibers, which are generally assumed to contribute to tensile loading only. Fiber tension is thought to originate from swelling of the proteoglycan-rich nucleus. However, in aged or degenerate disk, proteoglycans are depleted, whereas collagen content changes little. The question then rises to which extend the collagen may contribute to the compressive stiffness of the tissue. We hypothesized that this contribution is significant at high strain magnitudes and that the effect depends on fiber orientation. In addition, we aimed to determine the compression of the matrix. Bovine inner and outer annulus fibrosus specimens were subjected to incremental confined compression tests up to 60 % strain in radial and circumferential direction. The compressive aggregate modulus was determined per 10 % strain increment. The biochemical composition of the compressed specimens and uncompressed adjacent tissue was determined to compute solid matrix compression. The stiffness of all specimens increased nonlinearly with strain. The collagen-rich outer annulus was significantly stiffer than the inner annulus above 20 % compressive strain. Orientation influenced the modulus in the collagen-rich outer annulus. Finally, it was shown that the solid matrix was significantly compressed above 30 % strain. Therefore, we concluded that collagen fibers significantly contribute to the compressive stiffness of the intervertebral disk at high strains. This is valuable for understanding the compressive behavior of collagen-reinforced tissues in general, and may be particularly relevant for aging or degenerate disks, which become more fibrous and less hydrated.     

The micromechanical environment of intervertebral disc cells determined by a finite deformation,anisotropic, and biphasic finite element model

Cellular response to mechanical loading varies between the anatomic zones of the intervertebral disc. This difference may be related to differences in the structure and mechanics of both cells and extracellular matrix, which are expected to cause differences in the physical stimuli (such as pressure, stress, and strain) in the cellular micromechanical environment. In this study, a finite element model was developed that was capable of describing the cell micromechanical environment in the intervertebral disc. The model was capable of describing a number of important mechanical phenomena: flow-dependent viscoelasticity using the biphasic theory for soft tissues; finite deformation effects using a hyperelastic constitutive law for the solid phase; and material anisotropy by including a fiber-reinforced continuum law in the hyperelastic strain energy function. To construct accurate finite element meshes, the in situ geometry of IVD cells were measured experimentally using laser scanning confocal microscopy and three-dimensional reconstruction techniques. The model predicted that the cellular micromechanical environment varies dramatically between the anatomic zones, with larger cellular strains predicted in the anisotropic anulus fibrosus and transition zone compared to the isotropic nucleus pulposus. These results suggest that deformation related stimuli may dominate for anulus fibrosus and transition zone cells, while hydrostatic pressurization may dominate in the nucleus pulposus. Furthermore, the model predicted that micromechanical environment is strongly influenced by cell geometry, suggesting that the geometry of IVD cells in situ may be an adaptation to reduce cellular strains during tissue loading.     

An ionised/non-ionised dual porosity model of intervertebral disc tissue

The volume of the intrafibrillar water space – i.e. the water contained inside the collagen fibres – is a key parameter that is relevant to concepts of connective tissue structure and function. Confined compression and swelling experiments on annulus fibrosus samples are interpreted in terms of a dual porosity model that distinguishes between a non-ionised intrafibrillar porosity and an ionised extrafibrillar porosity. Both porosities intercommunicate and are saturated with a monovalent ionic solution, i.c. NaCl. The extrafibrillar fixed charge density of the samples is assessed using radiotracer techniques and the collagen content is evaluated by measurement of hydroxyproline concentration. The interpretation of the experimental data yields values for the intrafibrillar water content, the average activity coefficient of the ions, the Donnan osmotic coefficient, the fraction of intrafibrillar water, the stress-free deformation state, and an effective stress–strain relationship as a function of the radial position in the disc. A linear fit between the second Piola–Kirchhoff effective stress and Green–Lagrange strain yielded an effective stiffness: H_e=1.087 ± 0.657 MPa. The average fraction of intrafibrillar water was 1.16 g/g collagen. The results were sensitive to changes in the activity and osmotic coefficients and the fraction of intrafibrillar water. The fixed charge density increased with distance from the outer edge of the annulus, whereas the hydroxyproline decreased.The authors wish to thank Dr. Jill Urban for her advice concerning fixed charge density measurements, and Ing. Paul Willems for his assistance with the experiments. The research of Dr. J. M. Huyghe has been made possible through a fellowship of the Royal Netherlands Academy of Arts and Sciences.