The role of fiber-matrix interactions in a nonlinear fiber-reinforced strain energy model of tendon

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 R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (R2(toe) = 0.88, R2(Lin) = 0.94) over models that only included isotropic matrix and fiber stretch terms (R2(Toe) = 0.36, R2(Lin) = 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.     

Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc

Degenerate intervertebral discs exhibit both material and structural changes. Structural defects (lesions) develop in the anulus fibrosus with age. While degeneration has been simulated in numerous previous studies, the effects of structural lesions on disc mechanics are not well known. In this study, a finite element model (FEM) of the L4/5 intervertebral disc was developed in order to study the effects of anular lesions and loss of hydrostatic pressure in the nucleus pulposus on the disc mechanics. Models were developed to simulate both healthy and degenerate discs. Degeneration was simulated with either rim, radial or circumferential anular lesions and by equating nucleus pressure to zero. The anulus fibrosus ground substance was represented as a nonlinear incompressible material using a second-order polynomial, hyperelastic strain energy equation. Hyperelastic material parameters were derived from experimentation on sheep discs. Endplates were assumed to be rigid, and annulus lamellae were assumed to be vertical in the unloaded state. Loading conditions corresponding to physiological ranges of rotational motion were applied to the models and peak rotation moments compared between models. Loss of nucleus pulposus pressure had a much greater effect on the disc mechanics than the presence of anular lesions. This indicated that the development of anular lesions alone (prior to degeneration of the nucleus) has minimal effect on disc mechanics, but that disc stiffness is significantly reduced by the loss of hydrostatic pressure in the nucleus. With the degeneration of the nucleus, the outer innervated anulus or surrounding osteo-ligamentous anatomy may therefore experience increased strains.     

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential–axial and the radial–axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber–matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure–function, and to quantify the effect of degeneration. The biaxial stress–strain response was described well by the model (R ²?>?0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young’s modulus, provided an explanation for the low values in previously published axial direction Young’s modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.     

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.     

A linear material model for fiber-induced anisotropy of the anulus fibrosus

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.     

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.     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

Elastic fibers in the anulus fibrosus of the dog intervertebral disc

A light microscopic investigation of the anulus fibrosus in cervical intervertebral discs of the dog was conducted to ascertain the arrangement and distribution of elastic fibers. Elastic fibers were observed in all lamellae of the anulus fibrosus. However, collagenous fibers were the predominant type of connective tissue fiber, and elastic fibers were randomly dispersed among them. Intralamellar (collagenous and elastic) fibers were vertically and obliquely oriented in both superficial and deep lamellae of the anulus fibrosus. All intralamellar fibers were densely and regularly arranged in superficial lamellae, but they were more loosely organized in deep lamellae. A narrow border of interlamellar, elastic fibers was observed between broader, contiguous lamellae in the superficial zone of the anulus fibrosus. Interlamellar elastic fibers wer vertically and obliquely arranged in superficial lamellae; however, they were radially oriented in deep lamellae. The deepest lamella of the anulus fibrosus consisted of a loose, three-dimensional network of intermeshing collagenous and elastic fibers. These observations suggest that elastic fibers are integral components of the articular and shock absorption mechanisms of the anulus fibrosus, and the cervical intervertebral disc of the dog is a suitable model for experimental investigation of the role of elastic fibers in intervertebral disc herniation.     

Mechanical characterization of electrospun polycaprolactone (PCL): a potential scaffold for tissue engineering

This paper investigates the mechanical behavior of electrospun polycaprolactone (PCL) under tensile loading. PCL in bulk form degrades slowly and is biocompatible, two properties that make it a viable option for tissue engineering applications in biomedicine. Of particular interest is the use of electrospun PCL tubes as scaffolds for tissue engineered blood vessel implants. Stress relaxation and tensile tests have been conducted with specimens at room temperature (21 degrees C) and 37 degrees C. Additionally, to probe the effects of moisture on mechanical behavior, specimens were tested either dry (in air) or submerged in water. In general, the electrospun PCL was found to exhibit rate dependence, as well as some dependence on the test temperature and on whether the sample was wet or dry. Two different models were investigated to describe the experimentally observed material behavior. The models used were Fung's theory of quasilinear viscoelasticity (QLV) and the eight-chain model developed for rubber elastomers by Arruda and Boyce (1993, "A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials," J. Mech. Phys. Solids, 41(2), pp. 389-412). The implementation and fitting results, as well as the advantages and disadvantages of each model, are presented. In general, it was found that the QLV theory provided a better fit.     

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.     

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.     

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.     

Strain transfer in the annulus fibrosus under applied flexion

A detailed understanding of the anatomical and mechanical environment in the intervertebral disc at the scale of the cell is necessary for the design of tissue engineering repair strategies and to elucidate the role of mechanical factors in pathology. The objective of this study was to measure and compare the macroscale to microscale strains in the outer annulus fibrosus in various cellular regions of intact discs over a range of applied flexion. Macroscale strains were measured on the annulus fibrosus surface, and contrasted to in situ microscale strains using novel confocal microscopy techniques for dual labeling of the cell and the extracellular matrix. Fiber oriented surface strains were significantly higher than in situ fiber strains, which implies a mechanism of load redistribution that minimizes strain along the fibers. Non-uniformity of the strains and matrix distortion occurred immediately and most interestingly varied little with increase in flexion (3–16°), suggesting that inter-fiber shear is important in the initial stages of strain redistribution. Fiber oriented intercellular strains were significantly larger and compressive compared to in situ strains in other regions of the extracellular matrix indicating that the mechanical environment in this region may be unique. Further examination of the structural morphology in this pericellular region is needed to fully understand the pathway of strain transfer from the tissue to the cell. This study provides new knowledge on the complex in situ micro-mechanical environment of the annulus fibrosus that is essential to understanding the mechanobiological behavior of this tissue.     

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.     

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.     

Hyaluronan distribution in the human and canine intervertebral disc and cartilage endplate

A biotinylated complex of aggrecan G1-domain and link protein was used to characterize the distribution of hyaluronan in paraffin-embedded sections of adult human and canine intervertebral disc and cartilage endplate. Limited chondroitinase ABC and trypsin digestions of the sections before staining was utilized to expose hyaluronan potentially masked by aggrecan. Hyaluronan concentration and hyaluronan to uronic acid ratio in different parts of the discs were measured as a background for the histological analysis.Hyaluronan staining was strong in the nucleus pulposus and inner parts of annulus fibrosus of both species, corroborated by biochemical assays of the same compartments. Particularly in human samples, hyaluronan in the interterritorial matrix of nucleus pulposus and annulus fibrosus was readily accessible to the probe without enzyme treatments. In contrast, the cell-associated hyaluronan signal was enhanced after trypsin or limited chondroitinase ABC-treatment of the sections, suggesting that pericellular hyaluronan was more masked by aggrecan than in the distant matrix. A puzzling feature of canine cartilage endplate cells was their intensive cell-associated hyaluronan signal, part of which appeared intracellular. Hyaluronan was abundant between the collagenous lamellae in annulus fibrosus, perhaps important in the plasticity of this tissue.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.     

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.