A computational model to describe the regional interlamellar shear of the annulus fibrosus

Elastic Fibers in the Intervertebral Disc: From Form to Function and toward Regeneration

Despite extensive efforts over the past 40 years, there is still a significant gap in knowledge of the characteristics of elastic fibers in the intervertebral disc (IVD). More studies are required to clarify the potential contribution of elastic fibers to the IVD (healthy and diseased) function and recommend critical areas for future investigations. On the other hand, current IVD in-vitro models are not true reflections of the complex biological IVD tissue and the role of elastic fibers has often been ignored in developing relevant tissue-engineered scaffolds and realistic computational models. This has affected the progress of IVD studies (tissue engineering solutions, biomechanics, fundamental biology) and translation into clinical practice. Motivated by the current gap, the current review paper presents a comprehensive study (from the early 1980s to 2022) that explores the current understanding of structural (multi-scale hierarchy), biological (development and aging, elastin content, and cell-fiber interaction), and biomechanical properties of the IVD elastic fibers, and provides new insights into future investigations in this domain.

Sensitivity of Intervertebral Disc Finite Element Models to Internal Geometric and Non-geometric Parameters

Finite element models are useful for investigating internal intervertebral disc (IVD) behaviours without using disruptive experimental techniques. Simplified geometries are commonly used to reduce computational time or because internal geometries cannot be acquired from CT scans. This study aimed to (1) investigate the effect of altered geometries both at endplates and the nucleus-anulus boundary on model response, and (2) to investigate model sensitivity to material and geometric inputs, and different modelling approaches (graduated or consistent fibre bundle angles and glued or cohesive inter-lamellar contact). Six models were developed from 9.4 T MRIs of bovine IVDs. Models had two variations of endplate geometry (a simple curved profile from the centre of the disc to the periphery, and precise geometry segmented from MRIs), and three variations of NP-AF boundary (linear, curved, and segmented). Models were subjected to axial compressive loading (to 0.86 mm at a strain rate of 0.1/s) and the effect on stiffness and strain distributions, and the sensitivity to modelling approaches was investigated. The model with the most complex geometry (segmented endplates, curved NP-AF boundary) was 3.1 times stiffer than the model with the simplest geometry (curved endplates, linear NP-AF boundary), although this difference may be exaggerated since segmenting the endplates in the complex geometry models resulted in a shorter average disc height. Peak strains were close to the endplates at locations of high curvature in the segmented endplate models which were not captured in the curved endplate models. Differences were also seen in sensitivity to material properties, graduated fibre angles, cohesive rather than glued inter-lamellar contact, and NP:AF ratios. These results show that FE modellers must take care to ensure geometries are realistic so that load is distributed and passes through IVDs accurately.

Interlamellar matrix governs human annulus fibrosus multiaxial behavior

Establishing accurate structure–property relationships for intervertebral disc annulus fibrosus tissue is a fundamental task for a reliable computer simulation of the human spine but needs excessive theoretical-numerical-experimental works. The difficulty emanates from multiaxiality and anisotropy of the tissue response along with regional dependency of a complex hierarchic structure interacting with the surrounding environment. We present a new and simple hybrid microstructure-based experimental/modeling strategy allowing adaptation of animal disc model to human one. The trans-species strategy requires solely the basic knowledge of the uniaxial circumferential response of two different animal disc regions to predict the multiaxial response of any human disc region. This work demonstrates for the first time the determining role of the interlamellar matrix connecting the fibers-reinforced lamellae in the disc multiaxial response. Our approach shows encouraging multiaxial predictive capabilities making it a promising tool for human spine long-term prediction.

Interlamellar-induced time-dependent response of intervertebral disc annulus: A microstructure-based chemo-viscoelastic model

The annulus fibrosus of the intervertebral disc exhibits an unusual transversal behavior for which a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency has not yet been developed, and it is hence the aim of the present contribution. A physically-based model is proposed by introducing a free energy function that takes into account the actual disc annulus structure in relation with the surrounding biochemical environment. The response is assumed to be dominated by the viscoelastic contribution of the extracellular matrix, the elastic contribution of the oriented collagen fibers and the osmo-induced volumetric contribution of the internal fluid content variation. The regional dependence of the disc annulus response due to variation in fibers content/orientation allows a micromechanical treatment of the soft tissue. A finite element model of the annulus specimen is designed while taking into consideration the 'interlamellar' ground substance zone between lamellae of the layered soft tissue. The kinetics is designed using full-field strain measurements performed on specimens extracted from two disc annulus regions and tested under different osmotic conditions. The time-dependency of the tissue response is reported on stress-free volumetric changes, on hysteretic stress and transversal strains during quasi-static stretching at different strain-rates and on their temporal changes during an interrupted stretching. Considering the effective contributions of the internal fluid transfer and the extracellular matrix viscosity, the microstructure-based chemo-mechanical model is found able to successfully reproduce the significant features of the macro-response and the unusual transversal behavior including the strong regional dependency from inner to outer parts of the disc: Poisson's ratio lesser than 0 (auxetic) in lamellae plane, higher than 0.5 in fibers plane, and their temporal changes towards usual values (between 0 and 0.5) at chemo-mechanical equilibrium. The underlying time-dependent mechanisms occurring in the tissue are analyzed via the local numerical fields and important insights about the effective role of the interlamellar zone are revealed for the different disc localizations. STATEMENT OF SIGNIFICANCE: The structural complexity of the annulus fibrosus has only been appreciated through recent experimental contributions and a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency of the unusual transversal behavior has not yet been developed. Here, a microstructure-based chemo-viscoelastic model is developed to highlight the interlamellar-induced time-dependent response by means of a two-scale strategy. The model provides important insights about the origin of the time-dependent phenomena in disc annulus along with regional dependency, essential for understanding disc functionality.

The Mechanical Role of the Radial Fiber Network Within the Annulus Fibrosus of the Lumbar Intervertebral Disc: A Finite Elements Study

The annulus fibrosus (AF) of the intervertebral disc (IVD) consists of a set of concentric layers composed of a primary circumferential collagen fibers arranged in an alternating oblique orientation. Moreover, there exists an additional secondary set of radial translamellar collagen fibers which connects the concentric layers, creating an interconnected fiber network. The aim of this study was to investigate the mechanical role of the radial fiber network. Toward that goal, a three-dimensional (3D) finite element model of the L3–L4 spinal segment was generated and calibrated to axial compression and pure moment loading. The AF model explicitly recognizes the two heterogeneous networks of fibers. The presence of radial fibers demonstrated a pronounced effect on the local disc responses under lateral bending, flexion, and extension modes. In these modes, the radial fibers were in a tensile state in the disc region that subjected to compression. In addition, the circumferential fibers, on the opposite side of the IVD, were also under tension. The local stress in the matrix was decreased in up to 9% in the radial fibers presence. This implies an active fiber network acting collectively to reduce the stresses and strains in the AF lamellae. Moreover, a reduction of 26.6% in the matrix sideways expansion was seen in the presence of the radial fibers near the neutral bending axis of the disc. The proposed biomechanical model provided a new insight into the mechanical role of the radial collagen fibers in the AF structure. This model can assist in the design of future IVD substitutes.

New findings confirm the viscoelastic behaviour of the inter-lamellar matrix of the disc annulus fibrosus in radial and circumferential directions of loading

While few studies have improved our understanding of composition and organization of elastic fibres in the inter-lamellar matrix (ILM), its clinical relevance is not fully understood. Moreover, no studies have measured the direct tensile and shear failure and viscoelastic properties of the ILM. Therefore, the aim of this study was, for the first time, to measure the viscoelastic and failure properties of the ILM in both the tension and shear directions of loading. Using an ovine model, isolated ILM samples were stretched to 40% of their initial length at three strain rates of 0.1%s^-1 (slow), 1%s^-1 (medium) and 10%s^-1 (fast) and a ramp test to failure was performed at a strain rate of 10%s^-1. The findings from this study identified that the stiffness of the ILM was significantly larger at faster strain rates, and energy absorption significantly smaller, compared to slower strain rates, and the viscoelastic and failure properties were not significantly different under tension and shear loading. We found a strain rate dependent response of the ILM during dynamic loading, particularly at the fastest rate. The ILM demonstrated a significantly higher capability for energy absorption at slow strain rates compared to medium and fast strain rates. A significant increase in modulus was found in both loading directions and all strain rates, having a trend of larger modulus in tension and at faster strain rates. The finding of no significant difference in failure properties in both loading directions, was consistent with our previous ultra-structural studies that revealed a well-organized (±45°) elastic fibre orientation in the ILM. The results from this study can be used to develop and validate finite element models of the AF at the tissue scale, as well as providing new strategies for fabricating tissue engineered scaffolds.

STATEMENT OF SIGNIFICANCE

While few studies have improved our understanding of composition and organization of elastic fibres in the inter-lamellar matrix (ILM) of the annulus in the disc no studies have measured the direct mechanical failure and viscoelastic properties of the ILM. The findings from this study identified that the stiffness of the ILM was significantly larger at faster strain rates, and energy absorption significantly smaller, compared to slower strain rates. The failure properties of the ILM were not significantly different under tension and shear.

Structure and mechanical function of the inter-lamellar matrix of the annulus fibrosus in the disc

The inter-lamellar matrix (ILM) has an average thickness of less than 30 µm and lies between adjacent lamellae in the annulus fibrosus (AF). The microstructure and composition of the ILM have been studied in various anatomic regions of the disc; however, their contribution to AF mechanical properties and structural integrity is unknown. It was suggested that the ILM components, mainly elastic fibers and cross-bridges, play a role in providing mechanical integrity of the AF. Therefore, the manner in which they respond to different loadings and stabilize adjacent lamellae structure will influence AF tear formation and subsequent herniation. This review paper summarizes the composition, microstructure, and potential role of the ILM in the progression of disc herniation, clarifies the micromechanical properties of the ILM, and proposes critical areas for future studies. There are a number of unknown characteristics of the ILM, such as its mechanical role, impact on AF integrity, and ultrastructure of elastic fibers at the ILM-lamella boundary. Determining these characteristics will provide important information for tissue engineering, repair strategies, and the development of more-physiological computational models to study the initiation and propagation of AF tears that lead to herniation and degeneration. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1307-1315, 2016.

Optical Coherence Tomographic Elastography Reveals Mesoscale Shear Strain Inhomogeneities in the Annulus Fibrosus

STUDY DESIGN

Basic science study using in vitro tissue testing and imaging to characterize local strains in annulus fibrosus (AF) tissue.

OBJECTIVE

To characterize mesoscale strain inhomogeneities between lamellar and inter-/translamellar (ITL) matrix compartments during tissue shear loading.

SUMMARY OF BACKGROUND DATA

The intervertebral disc is characterized by significant heterogeneities in tissue structure and plays a critical role in load distribution and force transmission in the spine. In particular, the AF possesses a lamellar architecture interdigitated by a complex network of extracellular matrix components that form a distinct ITL compartment. Currently, there is not a firm understanding of how the lamellar and ITL matrix coordinately support tissue loading.

METHODS

AF tissue samples were prepared from frozen porcine lumbar spines and mounted onto custom fixtures of a materials testing system that incorporates optical coherence tomography (OCT) imaging to perform tissue elastography. Tissues were subjected to 20 and 40% nominal shear strain, and OCT images were captured and segmented to identify regions of interest corresponding to lamellar and ITL compartments. Images were analyzed using an optical flow algorithm to quantify local shear strains within each compartment.

RESULTS

Using histology and OCT, we first verified our ability to visualize and discriminate the ITL matrix from the lamellar matrix in porcine AF tissues. Local AF strains in the ITL compartment (22.0 ± 13.8, 31.1 ± 16.9 at 20% and 40% applied shear, respectively) were significantly higher than corresponding strains in the surrounding lamellar compartment (12.1 ± 5.6, 15.3 ± 5.2) for all tissue samples (P < 0.05).

CONCLUSION

Results from this study demonstrate that the lamellar and ITL compartments of the AF distribute strain unevenly during tissue loading. Specifically, shear strain is significantly higher in the ITL matrix, suggesting that these regions may be more susceptible to tissue damage and more mechanobiologically active.

LEVEL OF EVIDENCE

N/A.

Derivation of inter-lamellar behaviour of the intervertebral disc annulus

The inter-lamellar connectivity of the annulus fibrosus in the intervertebral disc has been shown to affect the prediction of the overall disc behaviour in computational models. Using a combined experimental and computational approach, the inter-lamellar mechanical behaviour of the disc annulus was investigated under conditions of radial loading.

Twenty-seven specimens of anterior annulus fibrosus were dissected from 12 discs taken from four frozen ovine thoracolumbar spines. Specimens were grouped depending on their radial provenance within the annulus fibrosus. Standard tensile tests were performed. In addition, micro-tensile tests under microscopy were used to observe the displacement of the lamellae and inter-lamellar connections. Finite elements models matching the experimental protocols were developed with specimen-specific geometries and boundary conditions assuming a known lamellar behaviour. An optimisation process was used to derive the interface stiffness values for each group. The assumption of a linear cohesive interface was used to model the behaviour of the inter-lamellar connectivity.

The interface stiffness values derived from the optimisation process were consistently higher than the corresponding lamellar values. The interface stiffness values of the outer annulus were from 43% to 75% higher than those of the inner annulus. Tangential stiffness values for the interface were from 6% to 39% higher than normal stiffness values within each group and similar to values reported by other investigators. These results reflect the intricate fibrous nature of the inter-lamellar connectivity and provide values for the representation of the inter-lamellar behaviour at a continuum level.