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.     

Hyperelastic anisotropic microplane constitutive model for annulus fibrosus

In a recent paper, Peng et al. (2006, "An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Interaction for the Human Annulus Fibrosis," ASME J. Appl. Mech., 73(5), pp. 815-824) developed an anisotropic hyperelastic constitutive model for the human annulus fibrosus in which fiber-matrix interaction plays a crucial role in simulating experimental observations reported in the literature. Later, Guo et al. (2006, "A Composites-Based Hyperelastic Constitutive Model for Soft Tissue With Application to the Human Fibrosis," J. Mech. Phys. Solids, 54(9), pp. 1952-1971) used fiber reinforced continuum mechanics theory to formulate a model in which the fiber-matrix interaction was simulated using only composite effect. It was shown in these studies that the classical anisotropic hyperelastic constitutive models for soft tissue, which do not account for this shear interaction, cannot accurately simulate the test data on human annulus fibrosus. In this study, we show that the microplane model for soft tissue developed by Caner and Carol (2006, "Microplane Constitutive Model and Computational Framework for Blood Vessel Tissue," ASME J. Biomech. Eng., 128(3), pp. 419-427) can be adjusted for human annulus fibrosus and the resulting model can accurately simulate the experimental observations without explicit fiber-matrix interaction because, in microplane model, the shear interaction between the individual fibers distributed in the tissue provides the required additional rigidity to explain these experimental facts. The intensity of the shear interaction between the fibers can be adjusted by adjusting the spread in the distribution while keeping the total amount of the fiber constant. A comparison of results obtained from (i) a fiber-matrix parallel coupling model, which does not account for the fiber-matrix interaction, (ii) the same model but enriched with fiber-matrix interaction, and (iii) microplane model for soft tissue adapted to annulus fibrosus with two families of fiber distributions is presented. The conclusions are (i) that varying degrees of fiber-fiber and fiber-matrix shear interaction must be taking place in the human annulus fibrosus, (ii) that this shear interaction is essential to be able to explain the mechanical behavior of human annulus fibrosus, and (iii) that microplane model can be fortified with fiber-matrix interaction in a straightforward manner provided that there are new experimental data on distribution of fibers, which indicate a spread so small that it requires an explicit fiber-matrix interaction to be able to simulate the experimental data.     

Influence of experimental protocols on the mechanical properties of the intervertebral disc in unconfined compression

The lack of standardization in experimental protocols for unconfined compression tests of intervertebral discs (IVD) tissues is a major issue in the quantification of their mechanical properties. Our hypothesis is that the experimental protocols influence the mechanical properties of both annulus fibrosus and nucleus pulposus. IVD extracted from bovine tails were tested in unconfined compression stress-relaxation experiments according to six different protocols, where for each protocol, the initial swelling of the samples and the applied preload were different. The Young's modulus was calculated from a viscoelastic model, and the permeability from a linear biphasic poroviscoelastic model. Important differences were observed in the prediction of the mechanical properties of the IVD according to the initial experimental conditions, in agreement with our hypothesis. The protocol including an initial swelling, a 5% strain preload, and a 5% strain ramp is the most relevant protocol to test the annulus fibrosus in unconfined compression, and provides a permeability of 5.0 ± 4.2e(-14)m(4)/N[middle dot]s and a Young's modulus of 7.6 ± 4.7 kPa. The protocol with semi confined swelling and a 5% strain ramp is the most relevant protocol for the nucleus pulposus and provides a permeability of 10.7 ± 3.1 e(-14)m(4)/N[middle dot]s and a Young's modulus of 6.0 ± 2.5 kPa.     

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.     

The chemokine,CXCL16, and its receptor,CXCR6, are constitutively expressed in human annulus fibrosus and expression of CXCL16 is up-regulated by exposure to IL-1ß in vitro

Chemokines are an important group of soluble molecules with specialized functions in inflammation. The roles of many specialized chemokines and their receptors remain poorly understood in the human intervertebral disc. We investigated CXCL16 and its receptor, CXCR6, to determine their immunolocalization in disc tissue and their presence following exposure of cultured human annulus fibrosus cells to proinflammatory cytokines. CXCL16 is a marker for inflammation; it also can induce hypoxia-inducible factor 1α (HIF-1α), which is a phenotypic marker of heathy nucleus pulposus tissue. We found CXCL16 and CXCR6 immunostaining in many cells of the annulus portion of the disc. Molecular studies showed that annulus fibrosus cells exposed to IL-1ß, but not TNF-α, exhibited significant up-regulation of CXCL16 expression vs. control cells. There was no significant difference in the percentage of annulus cells that exhibited immunolocalization of CXCL16 in grade I/II, grade III or grade IV/V specimens. The presence of CXCL16 and its receptor, CXCR6, in the annulus in vivo suggests the need for future research concerning the role of this chemokine in proinflammatory functions, HIF-1α expression and disc vascularization.     

Penetrating annulus fibrosus injuries affect dynamic compressive behaviors of the intervertebral disc via altered fluid flow: an analytical interpretation

Extensive experimental work on the effects of penetrating annular injuries indicated that large injuries impact axial compressive properties of small animal intervertebral discs, yet there is some disagreement regarding the sensitivity of mechanical tests to small injury sizes. In order to understand the mechanism of injury size sensitivity, this study proposed a simple one dimensional model coupling elastic deformations in the annulus with fluid flow into and out of the nucleus through both porous boundaries and through a penetrating annular injury. The model was evaluated numerically in dynamic compression with parameters obtained by fitting the solution to experimental stress-relaxation data. The model predicted low sensitivity of mechanical changes to injury diameter at both small and large sizes (as measured by low and high ratios of injury diameter to annulus thickness), with a narrow range of high sensitivity in between. The size at which axial mechanics were most sensitive to injury size (i.e., critical injury size) increased with loading frequency. This study provides a quantitative hypothetical model of how penetrating annulus fibrosus injuries in discs with a gelatinous nucleus pulposus may alter disc mechanics by changing nucleus pulposus fluid pressurization through introduction of a new fluid transport pathway though the annulus. This model also explains how puncture-induced biomechanical changes depend on both injury size and test protocol.     

Disc mechanics with trans-endplate partial nucleotomy are not fully restored following cyclic compressive loading and unloaded recovery

Mechanical function of the intervertebral disc is maintained through the interaction between the hydrated nucleus pulposus, the surrounding annulus fibrosus, and the superior and inferior endplates. In disc degeneration the normal transfer of load between disc substructures is compromised. The objective of this study was to explore the mechanical role of the nucleus pulposus in support of axial compressive loads over time. This was achieved by measuring the elastic slow ramp and viscoelastic stress-relaxation mechanical behaviors of cadaveric sheep motion segments before and after partial nucleotomy through the endplate (keeping the annulus fibrosus intact). Mechanics were evaluated at five conditions: Intact, intact after 10,000 cycles of compression, acutely after nucleotomy, following nucleotomy and 10,000 cycles of compression, and following unloaded recovery. Radiographs and magnetic resonance images were obtained to examine structure. Only the short time constant of the stress relaxation was altered due to nucleotomy. In contrast, cyclic loading resulted in significant and large changes to both the stiffness and stress relaxation behaviors. Moreover, the nucleotomy had little to no effect on the disc mechanics after cyclic loading, as there were no significant differences comparing mechanics after cyclic loading with or without the nucleotomy. Following unloaded recovery the mechanical changes that had occurred as a consequence of cyclic loading were restored, leaving only a sustained change in the short time constant due to the trans-endplate nucleotomy. Thus the swelling and redistribution of the remaining nucleus pulposus was not able to fully restore mechanical behaviors. This study reveals insights into the role of the nucleus pulposus in disc function, and provides new information toward the potential role of altered nucleus pulpous function in the degenerative cascade.     

A simple model for the function of proteoglycans and collagen in the response to compression of the intervertebral disc.

The nucleus pulposus of the intervertebral disc exerts a pressure which enables it to support axial compression when contained by the annulus fibrosus. The disc was modelled as a thick-walled cylindrical pressure vessel in which the nucleus was contained radially by the annulus. As a result, the stress in the annulus had radial (compressive) as well as tangential (tensile) components. The radial stress at a given point in the annulus was considered to be balanced by the internal pressure which is expected to arise from the attraction of water by proteoglycans. There was a reasonable agreement between the calculated radial stress distribution and published results on the distribution of water within the annulus. As the internal pressure is expected to be isotropic, the annulus was expected to contribute to the axial resistance to compression of the disc; this contribution would be equal, in magnitude, to the radial stress. Predictions of the pressure distribution within the annulus were similar to published experimental measurements made in the radial and axial directions. The tangential stress within the annulus was considered to arise from the restoring stress in its strained collagen fibrils.     

Heat-induced changes in porcine annulus fibrosus biomechanics

The intervertebral disc is implicated as the source of low-back pain in a substantial number of patients. Because thermal therapy has been thought to have a therapeutic effect on collagenous tissues, this technique has recently been incorporated into several minimally invasive back pain treatments. However, patient selection criteria and precise definition of optimum dose are hindered by uncertainty of treatment mechanisms. The purpose of this study was to quantify acute changes in annulus fibrosus biomechanics after a range of thermal exposures, and to correlate these results with tissue denaturation. Intact annulus fibrosus (attached to adjacent vertebrae) from porcine lumbar spines was tested ex vivo. Biomechanical behavior, microstructure, peak of denaturation endotherm, and enthalpy of denaturation (mDSC) were determined before and after hydrothermal heat treatment at 37 degrees C, 50 degrees C, 60 degrees C, 65 degrees C, 70 degrees C, 75 degrees C, 80 degrees C, and 85 degrees C. Shrinkage of excised annular tissue (removed from adjacent vertebrae) was also measured after treatment at 85 degrees C. Significant differences in intact annulus biomechanics were observed after treatment, but the effects were much smaller in magnitude than those observed in excised annulus and those reported previously for other tissues. Consistent with this, intact tissue was only minimally denatured by treatment at 85 degrees C for 15 min, whereas excised tissue was completely denatured by this protocol. Our data suggest that in situ constraint imposed by the joint structure significantly retards annular thermal denaturation. These findings should aid the interpretation of clinical outcomes and provide a basis for the future design of optimum dosing regimens.     

Cells scaffold complex for Intervertebral disc Anulus Fibrosus tissue engineering: in vitro culture and product analysis

The study was designed to investigate feasibility of tissue culture in vitro utilizing static culture method. Annulus fibrosus cells obtained from spine of rabbits were cultured. Results showed that fibrous tissue infiltration could be detected in shallow layer. With extended time, tissue infiltration depth increased, but there were still a large amount of holes in central part. Fibrous tissue infiltration was detected in the control side products and inner infiltration wasn't obvious. Hydroxyproline content of the control side products gradually increased with extended culture time. Hydroxyproline content of the control side products in the third and fourth month was significantly higher than that in the first month, but lower than those of the experimental side products and normal annulus fibrosus cells. DNA content of the control side products in the third and fourth month was significantly increased compared to the first month. DNA content of the control side products at each phase point was significantly lower than that of the experimental side and normal annulus fibrosus cells. Furthermore, there was lower expression levels of the type I, II collagen mRNA and protein in the experimental side scaffolds compared to the control side product. This study demonstrates the successful formation of Intervertebral disc Anulus Fibrosus in vitro by static culture method.     

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.     

Preservation of the chondrocyte's pericellular matrix improves cell‐induced cartilage formation

The extracellular matrix surrounding chondrocytes within a chondron is likely to affect the metabolic activity of these cells. In this study we investigated this by analyzing protein synthesis by intact chondrons obtained from different types of cartilage and compared this with chondrocytes. Chondrons and chondrocytes from goats from different cartilage sources (articular cartilage, nucleus pulposus, and annulus fibrosus) were cultured for 0, 7, 18, and 25 days in alginate beads. Real‐time polymerase chain reaction analyses indicated that the gene expression of Col2a1 was consistently higher by the chondrons compared with the chondrocytes and the Col1a1 gene expression was consistently lower. Western blotting revealed that Type II collagen extracted from the chondrons was cross‐linked. No Type I collagen could be extracted. The amount of proteoglycans was higher for the chondrons from articular cartilage and nucleus pulposus compared with the chondrocytes, but no differences were found between chondrons and chondrocytes from annulus fibrosus. The expression of both Mmp2 and Mmp9 was higher by the chondrocytes from articular cartilage and nucleus pulposus compared with the chondrons, whereas no differences were found with the annulus fibrosus cells. Gene expression of Mmp13 increased strongly by the chondrocytes (>50‐fold), but not by the chondrons. Taken together, our data suggest that preserving the pericellular matrix has a positive effect on cell‐induced cartilage production. J. Cell. Biochem. 110: 260–271, 2010. © 2010 Wiley‐Liss, Inc.     

Mechanical damage to the intervertebral disc annulus fibrosus subjected to tensile loading

Damage of the annulus fibrosus is implicated in common spinal pathologies. The objective of this study was to obtain a quantitative relationship between both the number of cycles and the magnitude of tensile strain resulting in damage to the annulus fibrosus. Four rectangular tensile specimens oriented in the circumferential direction were harvested from the outer annulus of 8 bovine caudal discs (n = 32) and subjected to one of four tensile testing protocols: (i) ultimate tensile strain (UTS) test; (ii) baseline cyclic test with 4 series of 400 cycles of baseline cyclic loading (peak strain = 20% UTS); (iii & iv) acute and fatigue damage cyclic tests consisting of 4 x 400 cycles of baseline cyclic loading with intermittent loading to 1 and 100 cycles, respectively, with peak tensile strain of 40%, 60%, and 80% UTS. Normalized peak stress for all mechanically loaded specimens was reduced from 0.89 to 0.11 of the baseline control levels, and depended on the magnitude of damaging strain and number of cycles at that damaging strain. Baseline, acute, and fatigue protocols resulted in permanent deformation of 3.5%, 6.7% and 9.6% elongation, respectively. Damage to the laminate structure of the annulus in the absence of biochemical activity in this study was assessed using histology, transmission electron microscopy, and biochemical measurements and was most likely a result of separation of annulus layers (i.e., delamination). Permanent elongation and stress reduction in the annulus may manifest in the motion segment as sub-catastrophic damage including increased neutral zone, disc bulging, and loss of nucleus pulposus pressure. The preparation of rectangular tensile strip specimens required cutting of collagen fibers and may influence absolute values of results, however, it is not expected to affect the comparisons between loading groups or dose-response reported.     

Collagen fibre orientation in the annulus fibrosus of intervertebral disc during bending and torsion measured by x-ray diffraction

X-ray diffraction has been used to measure the orientation of the collagen fibres in the ventral annulus fibrosus of intact L1/2 rabbit intervertebral disc during in vitro bending and torsion. Fibres are tilted with respect to the axis of the spine. As predicted by theory, fibre tilt decreases in those regions of the annulus which are stretched by bending but increases in the slackened regions. Good agreement with the quantitative predictions of bending theory was obtained in three of the six series of experiments, the predicted trend being found in all six. Tilt direction alternates in successive lamellae of the annulus. When discs were subjected to both clockwise and anticlockwise torsion of 5°, the two families of titled fibres reoriented in the expected directions.     

Material constants for a finite element model of the intervertebral disk with a fiber composite annulus

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disk was constructed. The model incorporated four substructures: one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when nonaxisymmetric loads were imposed on the model. The annulus material was represented as a layered fiber-reinforced composite. This paper describes the selection of material constants to represent the anisotropic layers of the annulus. It shows that a single set of material constants can be chosen so that model predictions of gross disk behavior under compression, torsion, shear, and moment loading are in reasonable agreement with the mean and range of experimentally measured disk behaviors. It also examines the effects of varying annular material properties.     

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.     

Temporal changes of mechanical signals and extracellular composition in human intervertebral disc during degenerative progression

In this study, a three-dimensional finite element model was used to investigate the changes in tissue composition and mechanical signals within human lumbar intervertebral disc during the degenerative progression. This model was developed based on the cell-activity coupled mechano-electrochemical mixture theory. The disc degeneration was simulated by lowering nutrition levels at disc boundaries, and the temporal and spatial distributions of the fixed charge density, water content, fluid pressure, Von Mises stress, and disc deformation were analyzed. Results showed that fixed charge density, fluid pressure, and water content decreased significantly in the nucleus pulposus (NP) and the inner to middle annulus fibrosus (AF) regions of the degenerative disc. It was found that, with degenerative progression, the Von Mises stress (relative to that at healthy state) increased within the disc, with a larger increase in the outer AF region. Both the disc volume and height decreased with the degenerative progression. The predicted results of fluid pressure change in the NP were consistent with experimental findings in the literature. The knowledge of the variations of temporal and spatial distributions of composition and mechanical signals within the human IVDs provide a better understanding of the progression of disc degeneration.     

No Effects of Psychosocial Stress on Intertemporal Choice

Intertemporal choices - involving decisions which trade off instant and delayed outcomes - are often made under stress. It remains unknown, however, whether and how stress affects intertemporal choice. We subjected 142 healthy male subjects to a laboratory stress or control protocol, and asked them to make a series of intertemporal choices either directly after stress, or 20 minutes later (resulting in four experimental groups). Based on theory and evidence from behavioral economics and cellular neuroscience, we predicted a bidirectional effect of stress on intertemporal choice, with increases in impatience or present bias immediately after stress, but decreases in present bias or impatience when subjects are tested 20 minutes later. However, our results show no effects of stress on intertemporal choice at either time point, and individual differences in stress reactivity (changes in stress hormone levels over time) are not related to individual differences in intertemporal choice. Together, we did not find support for the hypothesis that psychosocial laboratory stressors affect intertemporal choice.     

Glycation increases human annulus fibrosus stiffness in both experimental measurements and theoretical predictions

One of the primary age-related changes to collagenous tissues is the increased concentration of advanced glycation endproducts (AGEs). Although AGEs have been shown to increase the mechanical stiffness of many tissues, their influence on the mechanical properties of the annulus fibrosus has not been measured experimentally. In previous theoretical work, we hypothesized that the mechanical influence of AGEs on the annulus could be represented in an additive strain energy function with a separate crosslinking term, but the material coefficients associated with this term were not correlated with AGE concentration. In the current study, we measured the tensile stress-strain response of the human annulus in the axial direction both before and after glycation with methylglyoxal. Using nonlinear regression, the strain energy function was simultaneously applied to these new data and to data from a wide range of experimental protocols reported in the literature to determine values for the material coefficients appearing in the constitutive equation. Nonenzymatic collagen crosslinking induced a statistically significant change in annular material properties. Furthermore, the concentration of AGEs correlated positively with the material coefficients found in the terms of the strain energy function that we associate with collagen crosslinking. These data suggest that AGEs contribute to age-related disc stiffening as well as validate the hypothesis that biochemical constituents can be related mathematically to tissue behavior. In the future, this structurally guided constitutive relationship may provide further insight into the structure-function relationships of the annulus fibrosus.