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.     

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.     

Constitutive expression of IL-22 in the human intervertebral disc and its reduction by exposure to pro-inflammatory cytokines in vitro

The importance of cytokines in disc degeneration is well recognized. Little is known about IL-22 expression in the human intervertebral disc. We investigated IL-22 immuno-localization in disc tissue, and molecular expression and production of IL-22 by annulus cells cultured in three-dimensional (3D) culture. We examined human disc tissue using immunohistochemistry and we cultured isolated annulus cells in 3D to analyze IL-22 expression and production, and its receptor, IL-22R, in conditioned media. Ingenuity pathway analysis (IPA) also was used to identify significant gene expression networks within the molecular data. IL-22 and IL-22R were immunolocalized in many cells in the human outer and inner annulus; fewer cells exhibited localization in the nucleus. Three-dimensional culture of annulus cells demonstrated production of IL-22 in conditioned media; exposure to IL-1ß or TNF-α significantly reduced IL-22 levels. Significant decreases also were identified in conditioned media assayed for IL-22R in TNF-α treated cells. IPA analysis showed that IL-22 ranked among the top canonical pathways. We found constitutive expression and production of IL-22 and IL-22R in the disc, which expands our understanding of the effect of pro-inflammatory cytokines on IL-22 expression and production. Three-dimensional cultured annulus cells exposed to IL-1ß or TNF produced significantly lower levels of IL-22 into their conditioned media compared to levels produced by control cells. Our findings have clinical relevance because of the elevated pro-inflammatory milieu within the degenerating human disc.     

A Structurally and Functionally Biomimetic Biphasic Scaffold for Intervertebral Disc Tissue Engineering

Tissue engineering offers high hopes for the treatment of intervertebral disc (IVD) degeneration. Whereas scaffolds of the disc nucleus and annulus have been extensively studied, a truly biomimetic and mechanically functional biphasic scaffold using naturally occurring extracellular matrix is yet to be developed. Here, a biphasic scaffold was fabricated with collagen and glycosaminoglycans (GAGs), two of the most abundant extracellular matrix components in the IVD. Following fabrication, the scaffold was characterized and benchmarked against native disc. The biphasic scaffold was composed of a collagen-GAG co-precipitate making up the nucleus pulposus-like core, and this was encapsulated in multiple lamellae of photochemically crosslinked collagen membranes comprising the annulus fibrosus-like lamellae. On mechanical testing, the height of our engineered disc recovered by ~82-89% in an annulus-independent manner, when compared with the 99% recovery exhibited by native disc. The annulus-independent nature of disc height recovery suggests that the fluid replacement function of the engineered nucleus pulposus core might mimic this hitherto unique feature of native disc. Biphasic scaffolds comprised of 10 annulus fibrosus-like lamellae had the best overall mechanical performance among the various designs owing to their similarity to native disc in most aspects, including elastic compliance during creep and recovery, and viscous compliance during recovery. However, the dynamic mechanical performance (including dynamic stiffness and damping factor) of all the biphasic scaffolds was similar to that of the native discs. This study contributes to the rationalized design and development of a biomimetic and mechanically viable biphasic scaffold for IVD tissue engineering.     

The mechanical behaviour of bony endplate and annulus in prolapsed disc configuration

The mechanical response of intervertebral joints is deeply influenced by disc degeneration. The phenomenon is expressed in terms of variations in the biomechanical properties of the material, whose compressibility characteristics change because of the liquid content loss in the tissue and, what is even more important, to prolapse. In this work, the problem is investigated by means of a computational mechanics approach; a coupled material and geometric non-linear model is developed, representing vertebra, annulus and nucleus submitted to an axial load. A transversely isotropic law is assumed for cortical bone in the vertebral body and an isotropic law for the cancellous portion; a hyperelastic formulation is assumed for the disc, allowing effective interpretation of the mechanical characteristics of degeneration. The results obtained are reported with regard to bony endplate and annulus behaviour; interaction phenomena between bony endplate and nucleus are emphasized.     

Changes in the interfacial shear resistance of disc annulus fibrosus from genipin crosslinking

Crosslinking soft tissue has become more common in tissue engineering applications, and recent studies have demonstrated that soft tissue mechanical behavior can be directly altered through crosslinking. Using a recently reported test method that shears adjacent disc lamella, the effect of genipin crosslinking on interlamellar shear resistance was studied using in vitro bovine disc annulus.     

Inclusion of regional poroelastic material properties better predicts biomechanical behavior of lumbar discs subjected to dynamic loading

Understanding the relationship between repetitive lifting and the breakdown of disc tissue over several years of exposure is difficult to study in vivo and in vitro. The aim of this investigation was to develop a three-dimensional poroelastic finite element model of a lumbar motion segment that reflects the biological properties and behaviors of in vivo disc tissues including swelling pressure due to the proteoglycans and strain-dependent permeability and porosity. It was hypothesized that when modeling the annulus, prescribing tissue specific material properties will not be adequate for studying the in vivo loading and unloading behavior of the disc. Rather, regional variations of these properties, which are known to exist within the annulus, must also be included. Finite element predictions were compared to in vivo measurements published by Tyrrell et al. (1985) of percent change in total stature for two loading protocols, short-term creep loading and standing recovery and short-term cyclic loading with standing recovery. The model in which the regional variations of material properties in the annulus had been included provided an overall better prediction of the in vivo behavior as compared to the model in which the annulus properties were assumed to be homogenous. This model will now be used to study the relationship between repetitive lifting and disc degeneration.     

Dependence of mechanical behavior of the murine tail disc on regional material properties: a parametric finite element study

In vivo rodent tail models are becoming more widely used for exploring the role of mechanical loading on the initiation and progression of intervertebral disc degeneration. Historically, finite element models (FEMs) have been useful for predicting disc mechanics in humans. However, differences in geometry and tissue properties may limit the predictive utility of these models for rodent discs. Clearly, models that are specific for rodent tail discs and accurately simulate the disc's transient mechanical behavior would serve as important tools for clarifying disc mechanics in these animal models. An FEM was developed based on the structure, geometry, and scale of the mouse tail disc. Importantly, two sources of time-dependent mechanical behavior were incorporated: viscoelasticity of the matrix, and fluid permeation. In addition, a novel strain-dependent swelling pressure was implemented through the introduction of a dilatational stress in nuclear elements. The model was then validated against data from quasi-static tension-compression and compressive creep experiments performed previously using mouse tail discs. Finally, sensitivity analyses were performed in which material parameters of each disc subregion were individually varied. During disc compression, matrix consolidation was observed to occur preferentially at the periphery of the nucleus pulposus. Sensitivity analyses revealed that disc mechanics was greatly influenced by changes in nucleus pulposus material properties, but rather insensitive to variations in any of the endplate properties. Moreover, three key features of the model-nuclear swelling pressure, lamellar collagen viscoelasticity, and interstitial fluid permeation-were found to be critical for accurate simulation of disc mechanics. In particular, collagen viscoelasticity dominated the transient behavior of the disc during the initial 2200 s of creep loading, while fluid permeation governed disc deformation thereafter. The FEM developed in this study exhibited excellent agreement with transient creep behavior of intact mouse tail motion segments. Notably, the model was able to produce spatial variations in nucleus pulposus matrix consolidation that are consistent with previous observations in nuclear cell morphology made in mouse discs using confocal microscopy. Results of this study emphasize the need for including nucleus swelling pressure, collagen viscoelasticity, and fluid permeation when simulating transient changes in matrix and fluid stress/strain. Sensitivity analyses suggest that further characterization of nucleus pulposus material properties should be pursued, due to its significance in steady-state and transient disc mechanical response.     

Physical signals and solute transport in human intervertebral disc during compressive stress relaxation: 3D finite element analysis

A 3D finite element model for charged hydrated soft tissues containing charged/uncharged solutes was developed based on the multi-phasic mechano-electrochemical mixture theory (Lai et al., J. Biomech. Eng. 113 (1991), 245-258; Gu et al., J. Biomech. Eng. 120 (1998), 169-180). This model was applied to analyze the mechanical, chemical and electrical signals within the human intervertebral disc during an unconfined compressive stress relaxation test. The effects of tissue composition [e.g., water content and fixed charge density (FCD)] on the physical signals and the transport rate of fluid, ions and nutrients were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization was more pronounced at the center (nucleus) region of the disc while the effective (von Mises) stress was higher at the outer (annulus) region. Parametric analyses revealed that the decrease in initial tissue water content (0.7-0.8) increased the peak stress and relaxation time due to the reduction of permeability, causing greater fluid pressurization effect. The electrical signals within the disc were more sensitive to FCD than tissue porosity, and mechanical loading affected the large solute (e.g., growth factor) transport significantly, but not for small solute (e.g., glucose). Moreover, this study confirmed that the interstitial fluid pressurization plays an important role in the load support mechanism of IVD by sharing more than 40% of the total load during disc compression. This study is important for understanding disc biomechanics, disc nutrition and disc mechanobiology.     

The influence of exogenous cross-linking and compressive creep loading on intradiscal pressure

This study involves a biomechanical evaluation of a prospective injectable treatment for degenerative discs. The high osmolarity of the non-degenerated nucleus pulposus attracts water contributing to the hydrostatic behavior of the tissue. This intradiscal pressure is known to drop as fluid is exuded from the matrix due to compressive loading. The objective of this study was to compare the changes in intradiscal pressure in control and genipin cross-linked intervertebral discs. Thirty bovine lumbar motion segments were randomly divided into a phosphate-buffered saline control group and a 0.33% genipin group and soaked at room temperature for 2 days. A needle pressure sensor was held in the center of the disc while short-term and static creep compressive loads were applied. The control group demonstrated a 25% higher average intradiscal pressure compared to genipin-treated discs under 750 N compressive load (p=0.029). Depressurization during static compressive creep was 56% higher in the control than in the genipin group (p=0.014). These results suggest cross-linking induced changes in the poroelastic properties of the involved tissues affected the mechanics of compressive load support in the disc with lower levels of nucleus pressure, a corresponding decrease in the elastic expansion of the annulus, and an increased axial compressive loading of the inner and outer annulus tissues. It is possible that concurrent changes in hydraulic permeability and proteoglycan retention known to be associated with genipin cross-linking were also contributors to poroelastic changes. Reduction of peak pressures and moderation of pressure fluctuations could be beneficial relative to discogenic pain.     

Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus

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

Moderately degenerated lumbar motion segments: Are they truly unstable?

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

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.     

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.     

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.     

Numerical exploration of the combined effect of nutrient supply,tissue condition and deformation in the intervertebral disc

Novel strategies to heal discogenic low back pain could highly benefit from comprehensive biophysical studies that consider both mechanical and biological factors involved in intervertebral disc degeneration. A decrease in nutrient availability at the bone–disc interface has been indicated as a relevant risk factor and as a possible initiator of cell death processes. Mechanical behaviour of both healthy and degenerated discs could highly interact with cell death in these compromised situations. In the present study, a mechano-transport finite element model was used to investigate the nature of mechanical effects on cell death processes via load-induced metabolic transport variations. Cycles of static sustained compression were chosen to simulate daily human activity. Healthy and degenerated cases were simulated as well as a reduced supply of solutes and an increase in solute exchange area at the bone–disc interface. Results showed that a reduction in metabolite concentrations at the bone–disc boundaries induced cell death, even when the increased exchange area was simulated. Slight local mechanical enhancements of glucose in the disc centre were capable of decelerating cell death but occurred only with healthy mechanical properties. However, mechanical deformations were responsible for a worsening in terms of cell death in the inner annulus, a disadvantaged zone far from the boundary supply with both an increased cell demand and a strain-dependent decrease of diffusivity. Such adverse mechanical effects were more accentuated when degenerative properties were simulated. Overall, this study paves the way for the use of biophysical models for a more integrated understanding of intervertebral disc pathophysiology.     

Contribution of vertebral [corrected] bodies, endplates, and intervertebral discs to the compression creep of spinal motion segments

Spinal segments show non-linear behavior under axial compression. It is unclear to what extent this behavior is attributable to the different components of the segment. In this study, we quantified the separate contributions of vertebral bodies and intervertebral discs to creep of a segment. Secondly, we investigated the contribution of bone and osteochondral endplate (endplates including cartilage) to the deformation of the vertebral body. From eight porcine spines a motion segment, a disc and a vertebral body were dissected and subjected to mechanical testing. In an additional test, cylindrical samples, machined from the lowest thoracic vertebrae of 11 porcine spines, were used to compare the deformation of vertebral bone and endplate. All specimens were subjected to three loading cycles, each comprising a loading phase (2.0 MPa, 15 min) and a recovery phase (0.001 MPa, 30 min). All specimens displayed substantial time-dependent height changes. Average creep was the largest in motion segments and smallest in vertebral bodies. Bone samples with endplates displayed substantially more creep than samples without. In the early phase, behavior of the vertebra was similar to that of the disc. Visco-elastic deformation of the endplate therefore appeared dominant. In the late creep phase, behavior of the segment was similar to that of isolated discs, suggesting that in this phase the disc dominated creep behavior, possibly by fluid flow from the nucleus. We conclude that creep deformation of vertebral bodies contributes substantially to creep of motion segments and that within a vertebral body endplates play a major role.     

Barriers to mesenchymal stromal cells for low back pain

Intervertebral disc degeneration is the main cause of low back pain. In the past 20 years, the injection of mesenchymal stromal cells (MSCs) into the nucleus pulposus of the degenerative disc has become the main approach for the treatment of low back pain. Despite the progress made in this field, there are still many barriers to overcome. First, intervertebral disc is a highly complex load-bearing composite tissue composed of annulus fibrosus, nucleus pulposus and cartilaginous endplates. Any structural damage will change its overall biomechanical function, thereby causing progressive degeneration of the entire intervertebral disc. Therefore, MSC-based treatment strategies should not only target the degenerated nucleus pulposus but also include degenerated annulus fibrosus or cartilaginous endplates. Second, to date, there has been relatively little research on the basic biology of annulus fibrosus and cartilaginous endplates, although their pathological changes such as annular tears or fissures, Modic changes, or Schmorl's nodes are more commonly associated with low back pain. Given the high complexity of the structure and composition of the annulus fibrosus and cartilaginous endplates, it remains an open question whether any regeneration techniques are available to achieve their restorative regeneration. Finally, due to the harsh microenvironment of the degenerated intervertebral disc, the delivered MSCs die quickly. Taken together, current MSC-based regenerative medicine therapies to regenerate the entire disc complex by targeting the degenerated nucleus pulposus alone are unlikely to be successful.     

3D finite element analysis of nutrient distributions and cell viability in the intervertebral disc: effects of deformation and degeneration

The intervertebral disc (IVD) receives important nutrients, such as glucose, from surrounding blood vessels. Poor nutritional supply is believed to play a key role in disc degeneration. Several investigators have presented finite element models of the IVD to investigate disc nutrition; however, none has predicted nutrient levels and cell viability in the disc with a realistic 3D geometry and tissue properties coupled to mechanical deformation. Understanding how degeneration and loading affect nutrition and cell viability is necessary for elucidating the mechanisms of disc degeneration and low back pain. The objective of this study was to analyze the effects of disc degeneration and static deformation on glucose distributions and cell viability in the IVD using finite element analysis. A realistic 3D finite element model of the IVD was developed based on mechano-electrochemical mixture theory. In the model, the cellular metabolic activities and viability were related to nutrient concentrations, and transport properties of nutrients were dependent on tissue deformation. The effects of disc degeneration and mechanical compression on glucose concentrations and cell density distributions in the IVD were investigated. To examine effects of disc degeneration, tissue properties were altered to reflect those of degenerated tissue, including reduced water content, fixed charge density, height, and endplate permeability. Two mechanical loading conditions were also investigated: a reference (undeformed) case and a 10% static deformation case. In general, nutrient levels decreased moving away from the nutritional supply at the disc periphery. Minimum glucose levels were at the interface between the nucleus and annulus regions of the disc. Deformation caused a 6.2% decrease in the minimum glucose concentration in the normal IVD, while degeneration resulted in an 80% decrease. Although cell density was not affected in the undeformed normal disc, there was a decrease in cell viability in the degenerated case, in which averaged cell density fell 11% compared with the normal case. This effect was further exacerbated by deformation of the degenerated IVD. Both deformation and disc degeneration altered the glucose distribution in the IVD. For the degenerated case, glucose levels fell below levels necessary for maintaining cell viability, and cell density decreased. This study provides important insight into nutrition-related mechanisms of disc degeneration. Moreover, our model may serve as a powerful tool in the development of new treatments for low back pain.