On the identification of the ultra-structural organization of elastic fibers and their effects on the integrity of annulus fibrosus.

Due to the complicated structure of the elastic fiber network in annulus fibrosus, existing in-silico studies either simplified or just overlooked its distribution pattern. Nonetheless, experimental and simulation results have proven that elastic fibers are of great importance to maintaining the structural integrity of annulus fibrosus and therefore to ensuring the load-bearing ability of intervertebral discs. Such needs call for a fine model. This work aims at developing a biphasic annulus fibrosus model by incorporating the accurate distribution pattern of collagen and elastic fibers. Both the structural parameters and intrinsic mechanical parameters were successfully identified using single lamella and inter-lamella microscopy anatomy and micromechanical testing data. The proposed model was then used to implement finite element simulations on various anterior and posterolateral multi-lamellae annulus fibrosus specimens. In general, simulation results agree well with available experimental and simulation data. On this basis, the effects of elastic fibers on the integrity of annulus fibrosus were further investigated. It was found that elastic fibers significantly influence the free swelling, radial stretching and circumferential shear performances of annulus fibrosus. Nonetheless, no significant effects were found for the circumferential stretching capability. The proposed biphasic model considers for the first time the distribution characteristics of elastic fibers at two scales, including both the principal orientations of all fiber families and the detailed distribution pattern within each family. Better understandings on the functions of collagen and elastic fibers can therefore be realized. To further enhance its prediction capability, the current model can be extended in the future by taking the fiber-matrix interaction as well as progressive damages into consideration.

A Microstructure-Based Mechanistic Approach to Detect Degeneration Effects on Potential Damage Zones and Morphology of Young and Old Human Intervertebral Discs.

There is an increasing demand to develop predictive medicine through the creation of predictive models and digital twins of the different body organs. To obtain accurate predictions, real local microstructure, morphology changes and their accompanying physiological degenerative effects must be taken into account. In this article, we present a numerical model to estimate the long-term aging effect on the human intervertebral disc response by means of a microstructure-based mechanistic approach. It allows to monitor in-silico the variations in disc geometry and local mechanical fields induced by age-dependent long-term microstructure changes. Both lamellar and interlamellar zones of the disc annulus fibrosus are constitutively represented by considering the main underlying microstructure features in terms of proteoglycans network viscoelasticity, collagen network elasticity (along with content and orientation) and chemical-induced fluid transfer. With age, a noticeable increase in shear strain is especially observed in the posterior and lateral posterior regions of the annulus which is in correlation with the high vulnerability of elderly people to back problems and posterior disc hernia. Important insights about the relation between age-dependent microstructure features, disc mechanics and disc damage are revealed using the present approach. These numerical observations are hardly obtainable using current experimental technologies which makes our numerical tool useful for patient-specific long-term predictions.

Effect of overload on changes in mechanical and structural properties of the annulus fibrosus of the intervertebral disc.

The research focussed on analysing structural and mechanical properties in the intervertebral disc (IVD), caused by long-term cyclic loading. Spinal motion segments were divided into two groups: the control (C), and the group in which it was analysed the impact of posterior column in the load-bearing system of the spine-specimens with intact posterior column (IPC) and without posterior column (WPC). To evaluate the structural and mechanical changes, the specimens were tested with simulation of 100,000 compression-flexion load cycles after which it was performed macroscopic analysis. Mechanical properties of the annulus fibrosis (AF) from the anterior and posterior regions of the IVD were tested at the uniaxial tension test. The stiffness coefficient values were statistically 32% higher in the WPC group (110 N/mm) than in the IPC (79 N/mm). The dynamics of increase in this parameter does not correspond with the course of decrease in height loss. WPC segments revealed clear structural changes that mainly involve the posterior regions of the IVD (bulging and delamination with the effect of separation of collagen fibre bundles). Pathological changes also caused decreases in the value of stress in the AF. The greatest changes in the stress value about group C (7.43 ± 4.49 MPa) were observed in the front part of the fibrous ring, where this value was for IPC 4.49 ± 4.78 MPa and WPC 2.56 ± 1.01 MPa. The research indicates that the applied load model allows simulating damage that occurs in pathological IVD. And the posterior column's presence affects this change's dynamics, structural and mechanical properties of AF.

Numerical implementation of an osmo-poro-visco-hyperelastic finite element solver: application to the intervertebral disc.

This work deals with the finite element (FE) implementation of a biphasic poroelastic formulation specifically developed to address the intricate behaviour of the Intervertebral Disc (IVD) and other highly hydrated soft tissues. This formulation is implemented in custom FE solver V-Biomech, being the validation performed with a lumbar IVD model, which was compared against the analogous FE model of Williams et al. and the experiments of Tyrrell et al. Good agreement with these benchmarks was achieved, meaning that V-Biomech and its novel poroelastic formulation are a viable alternative for simulation of biphasic soft tissues.

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.

On the modeling of human intervertebral disc annulus fibrosus: Elastic, permanent deformation and failure responses.

As a primary load-resisting component, annulus fibrosus (AF) maintains structural integrity of the entire intervertebral disc. Experiments have demonstrated that permanent deformation and damage take place in the tissue under mechanical loads. Development of an accurate model to capture the complex behaviour of AF tissue is hence crucial in disc model studies. We, therefore, aimed to develop a non-homogenous model to capture elastic, inelastic and failure responses of the AF tissue and the entire disc model under axial load. Our model estimations satisfactorily agreed with results of existing uniaxial (along fiber, circumferential and axial directions) and biaxial tissue-level tests. The model accurately predicted the failure of the tissue in various directions in uniaxial extension. Collagen fiber content, type and orientation substantially altered AF tissue responses in uni- and bi-axial tests. Although collagen fiber content and type mostly affected failure stress, fiber orientation significantly influenced the tissue failure strain. The entire L2-L3 disc model accurately replicated load-displacement as well as loading-unloading responses of the disc under compression-tension forces. Preconditioning of the disc-body unit substantially stiffened response. Poisson's ratio of both AF and nucleus considerably affected compression-displacement responses of the disc (173% increase in compression at 1.49 mm displacement when it was changed from 0.499 to 0.49999). Any AF constitutive model should be calibrated under various tissue-level loads and directions as well as the entire disc model responses since using a single tissue-level loading (e.g. uniaxial) for calibration can lead to unrealistic responses in other tests (e.g., biaxial). Special attentions should be given to the choice of Poisson's ratio and the realistic consideration of preconditioning load.

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.

A growth-based model for the prediction of fiber angle distribution in the intervertebral disc annulus fibrosus.

There is a growing interest in the development of patient-specific finite element models of the human lumbar spine for both the assessment of injury risk and the development of treatment strategies. A current challenge in implementing these models is that the outer annulus fibrosus of the disc is composed of concentric sheets of aligned collagen fibers, the helical angles of which vary spatially. In finite element models, fiber angle is typically assumed to be constant, based on average experimental measurements from a small number of locations. The present study hypothesized that the full spatial distribution of fiber angles in the annulus fibrosus may be predicted for any disc geometry by assuming growth from a thin cylinder with constant fiber angle. This hypothesis was tested by developing an analytical model of disc growth and calibrating it with fiber angle measurements of adult bovine caudal discs. The calibrated model was then run on a representative human lumbar disc geometry. The model was able to accurately predict fiber angle distributions in both the experimental bovine caudal disc measurements and literature-reported human lumbar disc measurements. Despite its theoretical basis in development, the model requires only mature state geometry, making it practical for implementation in patient-specific finite element analyses, in which disc geometry is obtained from clinical imaging.

Complex Analysis of Diffusion Transport and Microstructure of an Intervertebral Disk.

We studied the relationship between diffusion transport and morphological and microstructural organization of extracellular matrix of human intervertebral disk. Specimens of the lumbar intervertebral disks without abnormalities were studied ex vivo by diffusion-weighed magnetic resonance imaging, histological and immunohistochemical methods, and electron microscopy. Distribution of the diffusion coefficient in various compartments of the intervertebral disk was studied. Significant correlations between diffusion coefficient and cell density in the nucleus pulposus, posterior aspects of annulus fibrosus, and endplate at the level of the posterior annulus fibrosus were detected for each disk. In disks with nucleus pulposus diffusion coefficient below 15×10-4 mm2/sec, collagens X and XI were detected apart from aggrecan and collagens I and II. The results supplement the concept on the relationship between the microstructure and cell composition of various compartments of the intervertebral disk and parameters of nutrient transport.

Load-induced changes in the diffusion tensor of ovine anulus fibrosus: A pilot MRI study.

PURPOSE: To assess the feasibility of diffusion tensor imaging (DTI) for evaluating changes in anulus fibrosus (AF) microstructure following uniaxial compression. MATERIALS AND METHODS: Six axially aligned samples of AF were obtained from a merino sheep disc; two each from the anterior, lateral, and posterior regions. The samples were mechanically loaded in axial compression during five cycles at a rate and maximum compressive strain that reflected physiological conditions. DTI was conducted at 7T for each sample before and after mechanical testing. RESULTS: The mechanical response of all samples in unconfined compression was nonlinear. A stiffer response during the first loading cycle, compared to the remaining cycles, was observed. Change in diffusion parameters appeared to be region-dependent. The mean fractional anisotropy increased following mechanical testing. This was smallest in the lateral (2% and 9%) and largest in the anterior and posterior samples (17-25%). The mean average diffusivity remained relatively constant (<2%) after mechanical testing in the lateral and posterior samples, but increased (by 5%) in the anterior samples. The mean angle made by the principal eigenvector with the spine axis in the lateral samples was 73° and remained relatively constant (<2%) following mechanical testing. This angle was smaller in the anterior (55°) and posterior (47°) regions and increased by 6-16° following mechanical testing. CONCLUSION: These preliminary results suggest that axial compression reorients the collagen fibers, such that they become more consistently aligned parallel to the plane of the endplates. LEVEL OF EVIDENCE: 1 Technical Efficacy: Stage 1 J. MAGN. RESON. IMAGING 2017;45:1723-1735.

Region-media coupling in characterization and modelling of the disc annulus single lamella swelling.

The annulus fibrosus (AF) swelling property, which is correlated with its rheological and viscoelastic properties, plays a significant role in disc nutrition and mechanical loading justification during daily activities as well as designing scaffolds for tissue engineering applications. The objective of this study was twofold: firstly to characterize the AF single lamella swelling kinetics in different regions and solutions at the temperature range of 35-40 °C and secondly to use the swelling results as a baseline to model (independent to swelling media and anatomic region) the AF single lamella swelling. It was found that the AF single lamella swelling kinetics (equilibrium swelling ratio and swelling rate) depends on anatomic region and swelling media; however, its trend for different swelling media (ionic and molecular solution) is similar and the majority of hydration occurs during first 20% of equilibrium swelling time (about 20 min). Change in swelling rate constant in circumferential direction depends on the solution type. It decreases from anterior to lateral regions for water, PBS and glucose solution and remains constant-or its change is negligible-from lateral to posterolateral regions. The effect of temperature (in the range of 35-40 °C) on swelling kinetics was seen to be negligible. It was also understood that it is possible to present a model (independent to swelling media type) to predict the swelling kinetics of posterior and posterolateral AF single lamella, as these locations are less sensitive to the swelling media.

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.

Lamellar and fibre bundle mechanics of the annulus fibrosus in bovine intervertebral disc.

UNLABELLED: The intervertebral disc is a multicomposite structure, with an outer fibrous ring, the annulus fibrosus, retaining a gel-like core, the nucleus pulposus. The disc presents complex mechanical behaviour, and it is of high importance for spine biomechanics. Advances in multiscale modelling and disc repair raised a need for new quantitative data on the finest details of annulus fibrosus mechanics. In this work we explored inter-lamella and inter-bundle behaviour of the outer annulus using micromechanical testing and second harmonic generation microscopy. Twenty-one intervertebral discs were dissected from cow tails; the nucleus and inner annulus were excised to leave a ring of outer annulus, which was tested in circumferential loading while imaging the tissue's collagen fibres network with sub-micron resolution. Custom software was developed to determine local tissue strains through image analysis. Inter-bundle linear and shear strains were 5.5 and 2.8 times higher than intra-bundle strains. Bundles tended to remain parallel while rotating under loading, with large slipping between them. Inter-lamella linear strain was almost 3 times the intra-lamella one, but no slipping was observed at the junction between lamellae. This study confirms that outer annulus straining is mainly due to bundles slipping and rotating. Further development of disc multiscale modelling and repair techniques should take into account this modular behaviour of the lamella, rather than considering it as a homogeneous fibre-reinforced matrix. STATEMENT OF SIGNIFICANCE: The intervertebral disc is an organ tucked between each couple of vertebrae in the spine. It is composed by an outer fibrous layer retaining a gel-like core. This organ undergoes severe and repeated loading during everyday life activities, since it is the compliant component that gives the spine its flexibility. Its properties are affected by pathologies such as disc degeneration, a major cause of back pain. In this article we explored the micromechanical behaviour of the disc's outer layer using second harmonic generation, a technique which allowed us to visualize, with unprecedented detail, how bundles of collagen fibres slide relative to each other when loaded. Our results will help further the development of new multiscale numerical models and repairing techniques.