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The architecture of load-bearing fibrous tissues is optimized to enable a specific set of mechanical functions. This organization arises from a complex process of cell patterning, matrix deposition, and functional maturation [1]. In their mature state, these tissues span multiple length scales, encompassing nanoscale interactions of cells with extracellular matrix to the centimeter length scales of the anatomic tissue volume and shape. Two structures that typify dense fibrous tissues are the meniscus of the knee and the annulus fibrosus (AF) of the intervertebral disc (IVD). The mechanical function of the wedge-shaped knee meniscus is based on its stiff prevailing circumferential collagen architecture that resists tensile deformation [2,3]. Adding to its complexity, radial tie fibers and sheets are interwoven amongst these fibers, increasing stiffness in the transverse direction and binding the tissue together [4]. In the annulus fibrosus, multiple anisotropic lamellae are stacked in concentric rings with their prevailing fiber directions alternating above and below the horizontal axis in adjacent layers [5]. The high circumferential tensile properties of this laminate structure allow it to resist bulging of the nucleus pulposus with compressive loading of the spine. Given their structural properties, unique form, and demanding mechanical environments, the knee meniscus and the AF region of the IVD represent two of the most challenging tissues to consider for functional tissue engineering.Copyright © 2007 by ASME

Engineering a functional replacement for the annulus fibrosus (AF) of the intervertebral disc is contingent upon recapitulation of AF structure, composition, and mechanical properties. In this study, we propose a new paradigm for AF tissue engineering that focuses on the reconstitution of anatomic fiber architecture and uses constitutive modeling to evaluate construct function. A modified electrospinning technique was utilized to generate aligned nanofibrous polymer scaffolds for engineering the basic functional unit of the AF, a single lamella. Scaffolds were tested in uniaxial tension at multiple fiber orientations, demonstrating a nonlinear dependence of modulus on fiber angle that mimicked the nonlinearity and anisotropy of native AF. A homogenization model previously applied to native AF successfully described scaffold mechanical response, and parametric studies demonstrated that nonfibrillar matrix, along with fiber connectivity, are key contributors to tensile mechanics for engineered AF. We demonstrated that AF cells orient themselves along the aligned scaffolds and deposit matrix that contributes to construct mechanics under loading conditions relevant to the in vivo environment. The homogenization model was applied to cell-seeded constructs and provided quantitative measures for the evolution of matrix and interfibrillar interactions. Finally, the model demonstrated that at fiber angles of the AF (28 degrees -44 degrees ), engineered material behaved much like native tissue, suggesting that engineered constructs replicate the physiologic behavior of the single AF lamella. Constitutive modeling provides a powerful tool for analysis of engineered AF neo-tissue and native AF tissue alike, highlighting key mechanical design criteria for functional AF tissue engineering.

Study design Measurement and normalization of disc geometry parameters for several animal models used in disc research. Objectives To compare normalized values of disc geometry to the human disc geometry to aid in the selection and interpretation of animal model studies. Summary of background data Animal models are widely used to study intervertebral disc degeneration and to evaluate disc treatment methods because of the availability of the tissue, the decreased variability between subjects compared with humans, and the feasibility to perform in vivo experiments. There is a general lack of comparative data with respect to the human disc analog for animal models. Methods The disc height, lateral width, AP width, area, and the nucleus pulposus lateral width, AP width, area, and centroid offset were all measured and normalized by 2 scaling factors, lateral width and disc area, for comparison to human. Results The species studied were ranked according to the average percent deviation of the normalized disc height, AP width and nucleus pulposus area from human geometry as: mouse lumbar (12%), rat lumbar (15%), mouse tail (18%), baboon (19%), bovine tail (22%), rabbit (26%), sheep (31%), and rat tail (46%). Conclusions This paper provides a reference to compare disc geometries of experimental animal models to the human lumbar disc, to aid both in interpretation of and in planning for experimental disc research, and to provide normalized disc geometry parameters for computational models.

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 10,000cycles of compression, acutely after nucleotomy, following nucleotomy and 10,000cycles 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.

The annulus fibrosus of the intervertebral disc is comprised of concentric lamella of oriented collagen fibers embedded in a hydrated proteoglycan matrix with smaller amounts of minor collagens, elastin, and small proteoglycans. Its structure and composition enable the disc to withstand complex loads and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of the annulus fibrosus constituent structures to mechanical function remain unclear. Therefore, the objective of this study was to use a structurally motivated, anisotropic, nonlinear strain energy model of annulus fibrosus to determine the relative contributions of its structural components to tissue mechanical behavior. A nonlinear, orthotropic hyperelastic model was developed for the annulus fibrosus. Terms to describe fibers, matrix, and interactions between annulus fibrosus structures (shear and normal to the fiber directions) were explicitly included. The contributions of these structures were analyzed by including or removing terms and determining the effect on the fit to multidimensional experimental data. Correlation between experimental and model-predicted stress, a Bland-Altman analysis of bias and standard deviation of residuals, and the contribution of structural terms to overall tissue stress were calculated. Both shear and normal interaction terms were necessary to accurately model multidimensional behavior. Inclusion of shear interactions more accurately described annulus fibrosus nonlinearity. Fiber stretch and shear interactions dominated contributions to circumferential direction stress, while normal and shear interactions dominated axial stress. The results suggest that interactions between fibers and matrix, perhaps facilitated by crosslinks, elastin, or minor collagens, augment traditional (i.e., fiber-uncrimping) models of nonlinearity.

The repair of dense fiber-reinforced tissues poses a significant challenge for the tissue engineering community. The function of these structures is largely dependent on their architectural form, and as such, scaffold organization is an important design parameter in generating tissue analogues. To address this issue, we have recently utilized electrospinning to instill controllable fiber anisotropy in nanofibrous scaffolds. This abstract details the mechanical characterization of the bulk and local properties of these scaffolds, and points to their potential application in the repair and/or generation of fiber- reinforced tissues that recapitulate the native form.

The unique biochemical composition and structure of the intervertebral disc allow it to support load, permit motion, and dissipate energy. With degeneration, both the biochemical composition and mechanical behavior of the disc are drastically altered, yet quantitative relationships between the biochemical changes and overall motion segment mechanics are lacking. The objective of this study was to determine the contribution of nucleus pulposus glycosaminoglycan content, which decreases with degeneration, to mechanical function of a rat lumbar spine motion segment in axial loading. Motion segments were treated with varying doses of Chondroitinase-ABC (to degrade glycosaminoglycans) and loaded in axial cyclic compression-tension, followed by compressive creep. Nucleus glycosaminoglycan content was significantly correlated (p < 0.05) with neutral zone mechanical behavior, which occurs in low load transition between tension and compression (stiffness: r = 0.59; displacement: r = -0.59), and with creep behavior (viscous parameter eta(1): r = 0.34; short time constant tau(1): r = 0.46). These results indicate that moderate decreases in nucleus glycosaminoglycan content consistent with early human degeneration affect overall mechanical function of the disc. These decreases may expose the disc to altered internal stress and strain patterns, thus contributing through mechanical or biological mechanisms to the degenerative cascade.

This chapter studies the soft tissues of the spine and outlines the structure, composition, and mechanical function of each of the soft tissues of the spine: the inter-vertebral discs, the ligaments, and the spinal cord. The structure of spine tissue includes the inter-vertebral discs that is situated between each of the rigid vertebrae of the spine, the ligaments which connects the vertebrae at various points, and the spinal cord. The entire spinal column provides structural support for the trunk of the body and protects the spinal cord. The inter-vertebral discs and spinal ligaments impart flexibility and mobility to the spine, allowing motions of the body such as twisting and bending forward, backward, and side to side. Moreover, to provide support, the inter-vertebral discs and ligaments must be stiff enough to maintain stability under large spinal loads. To provide flexibility, the soft tissues of the spine must be soft enough to allow motion in many directions, which can subject these tissues to loading in bending, torsion, tension, compression, and shear. The spinal cord does not support mechanical loads, but must be flexible enough to deform along with the spine during motion without damage. The spinal cord provides motor control and sensory perception to the rest of the body.

The aim of this study is to develop T1rho as an MR marker of the compositional and functional condition of cartilage. Specifically, we investigate the correlation of changes in cartilage biomechanical and biochemical properties with T1rho relaxation rate in a cytokine-induced model of degeneration. Bovine cartilage explants were cultured with 30 ng/mL of interleukin-1beta to mimic the cartilage degradation of early osteoarthritis. The average rate of T1rho relaxation was calculated from T(1rho) maps acquired on a 4.7 T research scanner. Stress-relaxation biomechanical tests were conducted with a confined compression apparatus to measure uniaxial aggregate modulus (HA) and hydraulic permeability (k0) using linear biphasic theory. Proteoglycan, collagen, and water content were measured via biochemical assays. Average T(1rho) relaxation rate was strongly correlated with proteoglycan content (R2 = 0.926), HA (R2 = 0.828), and log10 k0 (R2 = 0.862). Results of this study demonstrate that T1rho MRI can detect changes in proteoglycan content and biomechanical properties of cartilage in a physiologically relevant model of cartilage degeneration. The T1rho technique can potentially be used to noninvasively and quantitatively assess the biochemical and biomechanical characteristics of articular cartilage in humans during the progression of osteoarthritis.

The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R 2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (R 2 T o e =0.88, R 2 L i n =0.94) over models that only included isotropic matrix and fiber stretch terms (R 2 T o e = 0.36, R 2 L i n =0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior. The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.

Knowledge of the functional role of the nucleus pulposus is critical for the development and evaluation of disc treatment strategies to restore mechanical function. While previous motion segment studies have shown that nucleotomy alters disc mechanics, disruption of the annulus fibrosus may have influenced these experiments. The objective of this study was to determine the mechanical role of the nucleus pulposus in support of axial loads via a trans-endplate nucleotomy procedure. Sheep motion segments were randomly assigned to three groups: control, limited nucleotomy, and radical nucleotomy. Mechanical testing consisted of 20 cycles of compression–tension, a 1-h creep, and a slow constant-rate compressive ramp test. Nucleotomy led to increased axial deformations, in particular an elongated neutral zone, a greater range of motion, and altered creep behavior. In general, the elastic properties exhibited a graded response with respect to the amount of nucleus material removed. This graded effect can be attributed to swelling of the nucleus pulposus in the limited nucleotomy group, whereas little swelling was observed in the radical group. The findings of the present study indicate that functional evaluation of nucleus pulposus replacements and disc implants should include range of motion measures (including neutral zone) and viscoelastic creep experiments in addition to considering compressive stiffness.

Altered mechanical loading, secondary to biochemical changes in the nucleus pulposus, is a potential mechanism in disc degeneration. An understanding of the role of this altered mechanical loading is only possible by separating the mechanical and biological effects of early nucleus pulposus changes. The objective of this study was to quantify the mechanical effect of decreased glycosaminoglycans (GAG) and increased crosslinking in the nucleus pulposus using in vitro rat lumbar discs. Following initial mechanical testing the discs were injected according to the four treatment groups: PBS control, chondroitinase-ABC (ChABC) for GAG degradation, genipin (Gen) for crosslinking, or a combination of chondroitinase and genipin (ChABC+Gen). After treatment the discs were again mechanically tested, followed by histology or biochemistry. Neutral zone mechanical properties were changed by approximately 20% for PBS, ChABC, and ChABC+Gen treatments (significant only for PBS in a paired comparison). These trends were reversed with genipin crosslinking alone. With ChABC treatment the effective compressive modulus increased and the GAG content decreased; with the combination of ChABC+Gen the mechanics and GAG content were unchanged. Degradation of nucleus pulposus GAG alters disc axial mechanics, potentially contributing to the degenerative cascade. Crosslinking is unlikely to contribute to degeneration, but may be a potential avenue of treatment.

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.

STUDY DESIGN Mechanically test lumbar discs of transgenic mice in compression-tension and torsion. OBJECTIVES Determine if a reduction in type I collagen results in decreased disc mechanics. SUMMARY OF BACKGROUND DATA Quantitative relationships between disc structure and function would improve the understanding of disc generation and are essential relationships for functional tissue engineering. The reduced type I collagen transgenic mouse has been used in structure-function studies of bone and tendon, but not intervertebral discs. Methods for testing mouse discs have recently been developed, making disc structure-function studies possible. METHODS Microradiographed and mechanically tested lumbar discs from control and collagen-reduced mice in both compression-tension and torsion were used. Disc area and polar moment of inertia were determined from radiographic data, stiffness from mechanical data, and apparent modulus from geometric and mechanical data. RESULTS Collagen-reduced discs had a larger area and polar moment of inertia compared to controls. The linear and torsional stiffness of collagen-reduced and control discs were not significantly different. Finally, the apparent modulus of collagen-reduced discs was significantly less than controls in compression (73% of control) and torsion (50%). CONCLUSIONS Compared to controls, collagen-reduced discs had reduced apparent modulus in both loading directions, suggesting that the transgenic disc tissue was mechanically inferior to controls. These results are consistent with the widely accepted functional role of type I collagen in disc mechanics, and therefore supports the use of transgenic mice to study structure-function relationships of the disc. Future work will focus on quantifying structure-function relationships related to degeneration, as well as those relevant to the design of tissue-engineered disc replacements.

The objectives of this study were (1) to quantify changes in the mechanical behavior of the intervertebral disc in response to cyclic compressive loading and (2) to determine whether mechanical behavior would be restored following a period of unloading. The elastic and viscoelastic compressive mechanical behaviors of adult sheep motion segments were assessed. Ten thousand cycles of compressive loading resulted in increased elastic stiffness and decreased stress-relaxation. After 18 h of unloading in a PBS bath stiffness and relaxation were fully restored. Cyclic loading did not cause structural damage as determined by radiographs and magnetic resonance images. After cyclic loading, average stiffness increased from 603 to 800 N/mm (p = 0.015) and returned to initial levels after the recovery period. Cyclic loading caused a decrease in total relaxation (from 92 to 38 N, p < 0.001) that also returned to initial levels after recovery. The reversible, repeatable effects of cyclic loading and recovery demonstrated in this in vitro study may be attributed to fluid flow. Intervertebral disc fluid transport during the diurnal recovery cycle may be key to understanding intervertebral disc degeneration, as fluid exudation and recovery may be integral to maintaining adequate disc nutrition.

The objective of this study was to use a homogenization model of the anisotropic mechanical behavior of annulus fibrosus (AF) to address some of the issues raised in structural finite element and fiber-reinforced strain energy models. Homogenization theory describes the effect of microstructure on macroscopic material properties by assuming the material is composed of repeating representative volume elements. We first developed the general homogenization model and then specifically prescribed the model to in-plane single lamella and multi-lamellae AF properties. We compared model predictions to experimentally measured AF properties and performed parametric studies. The predicted tensile moduli ( E θ and Ez) and their dependence on fiber volume fraction and fiber angle were consistent with measured values. However, the model prediction for shear modulus ( G θ z ) was two orders of magnitude larger than directly measured values. The values of E θ and Ez were strongly dependent on the model input for matrix modulus, much more so than the fiber modulus. These parametric analyses demonstrated the contribution of the matrix in AF load support, which may play a role when protoeglycans are decreased in disc degeneration, and will also be an important design factor in tissue engineering. We next compared the homogenization model to a 3-D structural finite element model and fiber-reinforced energy models. Similarities between the three model types provided confidence in the ability of these models to predict AF tissue mechanics. This study provides a direct comparison between the several types of AF models and will be useful for interpreting previous studies and elucidating AF structure–function relationships in disc degeneration and for functional tissue engineering.

In previous studies mouse lumbar spines have been used to model the human lumbar spine in order to investigate disc degeneration. While disc stiffness has been know to increase with age in humans, how mouse mechanical properties change with respect to age has not been examined. Uniaxial mechanical testing was performed utilizing motion segments that were harvested from lumbar spines representing two age groups. Force and displacement data were normalized using disc geometry and used to calculate neutral zone and stiffness. Results showed a significant difference between the neutral zones of the two age groups and trends were found in normalized stiffness. Studies in human disc mechanics use stiffness as a measure of change in disc mechanics, but our testing methods have allowed us to generate a stress/strain curve that utilizes three parameters for measuring change in disc mechanics instead of one.

In this study uniaxial tensile testing of rabbit patellar tendon was used to determine whether constant strain rate ramp testing approximates equilibrium tendon behavior. Modulus and Poisson's ratio calculated from constant strain-rate ramp tests were compared with modulus and Poisson's ratio calculated from incremental stress-relaxation tests, which allow viscoelastic behaviors to dissipate. Samples were tested along the fiber direction and perpendicular to the fiber direction.

The assessment of bone health in children requires strategies to minimize the confounding effects of bone size on dual energy X-ray absorptiometry (DXA) areal bone mineral density (BMD) results. Cortical bone composes 80% of the total skeletal bone mass. The objective of this study was to develop analytic strategies for the assessment of whole body DXA that describe the biomechanical characteristics of cortical bone across a wide range of body sizes using peripheral quantitative computed tomography (pQCT) measures of cortical geometry, density (mg/mm(3)), and strength as the gold standard. Whole body DXA (Hologic QDR 4500) and pQCT (Stratec XCT-2000) of the tibia diaphysis were completed in 150 healthy children 6-21 years of age. To assess DXA and pQCT measures relative to age, body size, and bone size, gender-specific regression models were used to establish z scores for DXA bone mineral content (BMC) for age, areal BMD for age, bone area for height, bone area for lean mass, BMC for height, BMC for lean mass, and BMC for bone area; and for pQCT, bone cross-sectional area (CSA) for tibia length and bone strength (stress-strain index, SSI) for tibia length. DXA bone area for height and BMC for height were both strongly and positively associated with pQCT CSA for length and with SSI for length (all P0.0001), suggesting that decreases in DXA bone area for height or DXA BMC for height represent narrower bones with less resistance to bending. DXA BMC for age (P0.01) and areal BMD (P0.05) for age were moderately correlated with strength. Neither DXA bone area for lean mass nor BMC for lean mass correlated with pQCT CSA for length or SSI for length. DXA BMC for bone area was weakly associated with pQCT SSI for length, in females only. Therefore, normalizing whole body DXA bone area for height and BMC for height provided the best measures of bone dimensions and strength. DXA BMC normalized for bone area and lean mass were poor indicators of bone strength.

In-vitro mechanical testing of spinal motion segments has the potential to provide insight into mechanisms of intervertebral disc degeneration as well as a means for evaluating treatments. We describe a novel tri-linear method for quantifying the non-linear load-displacement behavior which is robust across different spinal levels, and quantifies stiffness at low-loads, which has not been included by previous threshold based methods. Mechanical data from in-vitro compression/tension testing of rodent motion segments is used to compare our tri-linear method with a threshold based method, and demonstrates that our method is insensitive to spinal level as well as provides constitutive information for low-load behavior.Copyright © 2003 by ASME

A three dimensional anisotropic model for tendon behavior was used to fit experimental stress-strain data. This model was motivated by tendon microstructure and included the contributions of fibers, matrix, and fiber-matrix interactions. Our results suggest that fiber-matrix interactions contribute to tendon mechanical behavior.Copyright © 2003 by ASME

A primary goal in considering treatment for meniscal injuries is the preservation of the health of the articular cartilage. However, the chondroprotective effects of various techniques for meniscal injury treatments are unknown. We used a canine model to quantify articular cartilage degeneration in the medial compartment of the canine knee, resulting from a surgically created tear or a partial meniscectomy (PM) of the posterior region of the medial meniscus (each group, n = 10). After sacrifice at 12 weeks, the development of gross chondropathy and the changes in cartilage tensile stiffness were quantified, and correlations between these measurements were examined. Both treatment surgical treatment groups caused significantly greater gross chondropathy as compared to the unoperated contralateral controls. Cartilage tensile stiffness was significantly lower than unoperated controls by nearly 28% in both experimental groups. However, there were no significant differences observed between the gross chondropathy or the cartilage mechanical property changes between the experimental groups. Importantly, the severity of gross chondropathy was found to significantly correlate with the decrement in tensile stiffness properties of the articular cartilage. These findings indicate that significant degeneration of canine articular cartilage develops to a similar degree in the presence of a partially healed meniscus tear or a PM of the knee.

Articular cartilage has been shown to exhibit large transverse contractions when loaded in tension, suggesting the existence of large values for the Poisson’s ratio. Previous studies have suggested that this effect is dependent on amplitude of applied strain, so that a single Poisson’s ratio may not be sufficient to describe cartilage behavior. In this study, the Poisson’s ratio (ν), toe region modulus Eo, and linear region modulus E of human patellar articular cartilage were calculated in simple tension tests from optical analysis of the two-dimensional strain fields at equilibrium. The Poisson’s ratio was found to be independent of strain due to the absence of viscoelastic effects during testing. The Poisson’s ratio was found to be significantly higher in the surface zone (1.87±1.11, p

The anulus fibrosus (AF) of the intervertebral disc exhibits spatial variations in structure and composition that give rise to both anisotropy and inhomogeneity in its material behaviors in tension. In this study, the tensile moduli and Poisson’s ratios were measured in samples of human AF along circumferential, axial, and radial directions at inner and outer sites. There was evidence of significant inhomogeneity in the linear-region circumferential tensile modulus (17.4±14.3 MPa versus 5.6±4.7 MPa, outer versus inner sites) and the Poisson’s ratio ν21 (0.67±0.22 versus 1.6±0.7, outer versus inner), but not in the axial modulus (0.8±0.9 MPa) or the Poisson’s ratios ν12 (1.8±1.4) or ν13 (0.6±0.7). These properties were implemented in a linear anisotropic material model of the AF to determine a complete set of model properties and to predict material behaviors for the AF under idealized kinematic states. These predictions demonstrate that interactions between fiber populations in the multilamellae AF significantly contribute to the material behavior, suggesting that a model for the AF as concentric and physically isolated lamellae may not be appropriate.

The anulus fibrosus (AF) is a lamellar, fibrocartilaginous component of the intervertebral disc, which exhibits highly anisotropic behaviors in tension. These behaviors arise from the material’s unique collagen structure. We have investigated the use of a linear, fiber-induced anisotropic model for the AF using a quadratic strain energy density formulation with an explicit representation of the collagen fiber populations. We have proposed a representative set of intrinsic material properties using independent datasets of the AF from the literature and appropriate thermodynamic constraints. The model was validated by comparing predictions with previous experimental data for AF behavior and its dependence on fiber angle. The model predicts that compressible effects may exist for the AF, and suggests that physical effects of the equivalent “matrix,” “fiber,” “fiber–matrix,” and “fiber–fiber,” interactions may be important contributors to the mechanical behavior of the AF. [S0148-0731(00)00802-5]

The anulus fibrosus (AF) of the intervertebral disc is a highly structured material made up of alternating tissue layers (lamella) with collagen fibers oriented +30° and −30° to the circumferential axis (Figure 1). Collagen confers a high tensile stiffness to the AF which contributes to the load-bearing function of the intervertebral disc in vivo. In addition, the specialized organization of the AF gives rise to strongly anisotropic behaviors which may contribute to its mechanical function. Numerous models have been proposed for the material behavior of the AF including a fiber-reinforced composite or membrane, a layered transversely isotropic material, an orthotropic material, and a poroelastic isotropic material [6,8,9,12]. Fiber-reinforced models are complicated by the need to quantify the collagen content, the collagen and ground substance material properties, and associated fiber-matrix interactions. Continuum models of the AF are complicated by the need to determine a unique set of material properties which can require as many as 9 independent constants for a linear orthotropic material.

Introduction While IVD strain can be measured, the stress distribution within the disk is dependent on the IVD's material properties and its geometry and must be calculated. The IVD geometry remains incompletely characterized. Prior whole-disk models have been constructed from single IVDs. While this approach ensures that the geometry has a physiological basis, the degree to which results from a single IVD shape can be generalized to the entire population is uncertain. The primary objective of this study, therefore, was to develop a quantitative representation of IVD shape for the population. The approach incorporates a representative average IVD shape from multiple individuals and uses principal components analysis (PCA) to partition the variability of IVD shape into a small number of orthogonal modes of variation. These modes of variation can be adjusted parametrically. Since IVD shape is expected to change with degeneration, each mode of variation was correlated with degeneration grade to isolate degeneration-related shape variability from normal variability between individuals. Materials and Methods Magnetic Resonance Imaging Total 14 postmortem, agarose embedded L3-L4 motion segments (13 M, 1 F - age 69 ± 12 years - Pfirrmann grade 3.3 ± 0.8) underwent MRI (7T Siemens scanner - custom RF coil) using a 3D FLASH sequence (TE/TR = 3.7/9 ms) with ∼200 mm isotropic resolution.1 Image SegmentationBefore segmentation, the MRI images underwent intensity inhomogeneity correction, 50% downsampling, and Gaussian smoothing. Segmentation of the intervertebral disk was done in SNAP.2 The intensity-based region competition active contour tool was used to provide an initial segmentation. Errors in the automatic result were corrected by manual slice-by-slice segmentation. Shape Quantification The shape model was created by PCA of the disk segmentations.3 To make the images amenable to PCA, they were embedded as signed distance functions.3 The mean of the signed distance functions represents the average disk shape, with the residual shape variability captured as offsets from the mean signed distance function. These residuals were analyzed by PCA to produce a new 13-dimensional orthonormal basis for IVD shape. Each basis vector represents a different mode of shape variation. The basis vectors were ordered by the amount of variability that they capture from the original dataset. Following PCA, each disk in the dataset was projected into the new basis as a linear combination of the mean shape and the shape variation basis vectors. To determine which basis vectors represented degeneration-related shape variation, the projection coefficients were then correlated to Pfirrmann grade. Finally, to supplement the PCA-derived representation, the disk shapes were summarized by geometric measures: width, (left to right), depth (anterior-posterior distance at the mid-sagittal plane), height (averaged over the entire IVD), and axial-plane area. Results The first basis vector M1 represented an order of magnitude more variance than any other basis vector. Relative to M1, the second basis vector M2 captured 11% as much variance; M3, 9%; M4, 7%; M5, 5%; M6, 3%. Basis vectors 7 to 13 captured less than 2% as much variance as basis vector M1. Given the low variances associated with basis vectors M2 to M13 relative to basis vector M1, it is possible to represent IVD shape by the basis vector M1 coefficient w1 alone and still capture the majority of the population's IVD shape variation. Examination of the shapes produced by adding and subtracting one standard deviation of basis vector M1 from the mean shape reveals that basis vector M1 primarily controls lateral disk bulging, with little change in disk height. The basis vector M1 was also the only basis vector to show a significant correlation to degeneration as measured by Pfirrmann grade. None of the basis vectors were significantly correlated with age. Conclusion The objective of obtaining a low-dimensional representation of IVD shape was met. IVD shape variation was dominated by a single lateral bulging-related component, which was also correlated to degeneration grade. The low dimensionality of the shape representation makes it amenable to human manipulation, permitting straightforward modeling of a representative sampling of IVD shapes for example, for finite element analysis. The shape representation can also be used directly as a shape before Bayesian image segmentation of low-detail IVD images, for example, in vivo MRI. Further work is required to establish causation between degeneration and shape changes. Acknowledgment NIH grant R01 AR05005. I confirm having declared any potential conflict of interest for all authors listed on this abstract Yes Disclosure of Interest None declared Pfirrmann CW, et al. Spine 2001;26:1873 Yushkevich PA, et al. NeuroImage 2006;31:1116 Tsai A, et al. IEEE Transaction Medical Imaging 2003;22:137

Introduction The IVD cartilaginous endplate (CEP) is a 450 mm to 800 mm thick layer of hyaline cartilage,2 which functions as a mechanical barrier between the pressurized nucleus pulposus and the vertebral endplate, and as a gateway for nutrient diffusion to the avascular disk.1–3 With age and degeneration, the CEP becomes thinner, calcifies, and may have reduced porosity,4 and it has been implicated as a contributor to degeneration.1–3 As the CEP is not well imaged on MRI, key geometric parameters of the CEP have not been obtained noninvasively. Thus, the objective of this study was to measure geometric properties of the CEP with MRI. Materials and Methods Lumbar motion segments ( n = 24), from 11 human cadavers (age 64.9 ± 10.0 years) were imaged on a Siemens 7T MRI scanner using a custom RF coil. Disk degeneration was graded via mid-sagittal T2 mapping. Full volume imaging of each disk at 200 mm isotropic resolution was achieved via 3D FLASH (TR/TE = 9/3.7 ms) in 6 minutes (Fig. 1). Geometric parameters (area, circumference, anterior-posterior width, lateral width) were measured in the axial and mid-sagittal planes for both the CEP and the entire disk using OsiriX software. Disk height was measured using custom-written Matlab code.5 Evaluation of CEP thickness was done on a mid-sagittal image of each disc. Semiautomated image analysis was conducted using custom-written Matlab code in which signal intensity profiles across the CEP thickness were captured at the center of the CEP and at ± ¼ and ± ¾ of its A-P length. Comparisons between superior and inferior CEP geometry were established using paired, two-tailed t-tests ( p Results Directly measured whole disk and CEP geometry for each level are provided in the Table. The mean CEP thickness in the mid-sagittal plane across all disk levels and locations was 0.50 ± 0.20 mm. No significant differences were found in CEP thickness with respect to the superior or inferior endplate or disk level ( p > 0.2). There was no significant difference in CEP A-P width, lateral width, or circumference area with respect to superior/inferior location ( p > 0.7) or disk level ( p > 0.6) except between L1-L2 and L4-L5 ( p Conclusion This study noninvasively visualized the CEP morphology and quantified CEP circumference, area, A-P width, lateral width, and thickness using an MRI 3D FLASH sequence. The measured disk geometries in this study agree well with previous literature.5,6 CEP geometries were not linearly correlated with age or T2 mapping, which is correlated with disk degenerative grade. The lack of correlation between CEP geometries and either age or T2 mapping as a marker of degeneration was not completely expected, since it has been discussed that CEP thickness decreases with degeneration.1–3 Additional data and increased sample size may provide more insight into the potential role of the CEP in the degenerative cascade. Acknowledgment NIH grant R01 AR050052. I confirm having declared any potential conflict of interest for all authors listed on this abstract Yes Disclosure of Interest None declared Urban JPG. Arthritis Research Therapy 2003;5:120 Roberts S. Spine 1989;14:166 Moore RJ. European Spine Journal 2000;9:92 Bernick S, Spine 1982;7:97 O'Connell GD. Spine 2007:32:328 Elliott DM. Spine 2004;29:713

detach by the high fluid flow during arthroscopic implantation. Results: Cells were alive throughout the cell culture procedure. Consistency of the polymer was ideal for implantation between 7 and 9 days. The cell-encapsulated polymer was recovered after implantation and viability of cells and attachment to the co-polymer was demonstrated. Good attachment was observed by ESEM before and after implantation. Discussion: Fluid flow during arthroscopic implantation affects the attachment of chondrocytes to the copolymer. Previous attempts to deliver chondrocyte-constructs were performed and no cells attached to the polymer were observed. The encapsulation technique appears to help maintain cells within the construct, an important consideration for arthroscopic implantation.

Loss of or damage to the meniscus alters the pattern of loading in the knee joint and frequently leads to cartilage degeneration and osteoarthritis. The mechanical properties of articular cartilage have been shown to reflect the extent of cartilage degeneration in human osteoarthritis and in experimental models of joint disease, but there is little experimental data documenting changes in cartilage mechanics following meniscectomy. We hypothesized that the tensile properties of the surface zone of articular cartilage are altered following total medial meniscectomy. Twelve mongrel dogs underwent complete resection of the medial meniscus in the right knee, and the femoral cartilage was studied 12 weeks after the operation. We performed uniaxial, tensile stress-relaxation tests to determine the equilibrium tensile modulus of surface-zone cartilage. Water and glycosaminoglycan content were also measured at site-matched locations. The tensile moduli of the cartilage decreased significantly following meniscectomy. The linear region modulus decreased by 40%, from 25.5 +/- 7.7 to 15.3 +/- 7.2 MPa. There was a weak (r = -0.45), but significant, correlation between the linear region modulus and the gross morphological grade for cartilage damage. Water and glycosaminoglycan content did not change following meniscectomy. Composition was not correlated with mechanical properties or morphological grade, suggesting that cartilage structure may play a more important role than composition in determining the mechanical properties. The observed decrease in cartilage material properties provides a quantitative measure of the loss of cartilage function following meniscectomy and reflects a pattern of change that is consistent with damage to the collagen-proteoglycan solid network.