Modeling of human intervertebral disc annulus fibrosus with complex multi-fiber networks

Strain rate-dependent failure mechanics of the intervertebral disc under tension/compression and constitutive analysis

BACKGROUND

The intervertebral disc exhibits not only strain rate dependence (viscoelasticity), but also significant asymmetry under tensile and compressive loads, which is of great significance for understanding the mechanism of lumbar disc injury under physiological loads.

OBJECTIVE

In this study, the strain rate sensitive and tension-compression asymmetry of the intervertebral disc were analyzed by experiments and constitutive equation.

METHOD

The Sheep intervertebral disc samples were divided into three groups, in order to test the strain rate sensitive mechanical behavior, and the internal displacement as well as pressure distribution.

RESULTS

The tensile stiffness is one order of magnitude smaller than the compression stiffness, and the logarithm of the elastic modulus is approximately linear with the logarithm of the strain rate, showing obvious tension-compression asymmetry and rate-related characteristics. In addition, the sensitivity to the strain rate is the same under these two loading conditions. The stress-strain curves of unloading and loading usually do not coincide, and form a Mullins effect hysteresis loop. The radial displacement distribution is opposite between the anterior and posterior region, which is consistent with the stress distribution. By introducing the damage factor into ZWT constitutive equation, the rate-dependent viscoelastic and weakening behavior of the intervertebral disc can be well described.

Micromechanics of fibrous scaffolds and their stiffness sensing by cells

Mechanical properties of the tissue engineering scaffolds are known to play a crucial role in cell response. Therefore, an understanding of the cell-scaffold interactions is of high importance. Here, we have utilized discrete fiber network model to quantitatively study the micromechanics of fibrous scaffolds with different fiber arrangements and cross-linking densities. We observe that localized forces on the scaffold result in its anisotropic deformation even for isotropic fiber arrangements. We also see an exponential decay of the displacement field with distance from the location of applied force. This nature of the decay allows us to estimate the characteristic length for force transmission in fibrous scaffolds. Furthermore, we also looked at the stiffness sensing of fibrous scaffolds by individual cells and its dependence on the cellular sensing mechanism. For this, we considered two conditions- stress-controlled, and strain-controlled application of forces by a cell. With fixed strain, we find that the stiffness sensed by a cell is proportional to the scaffold's 'macroscopic' elastic modulus. However, under fixed stress application by the cell, the stiffness sensed by the cell also depends on the cell's own stiffness. In fact, the stiffness values for the same scaffold sensed by the stiff and soft cells can differ from each other by an order of magnitude. The insights from this work will help in designing tissue engineering scaffolds for applications where mechanical stimuli are a critical factor.

Comprehensive modeling of annulus fibrosus: From biphasic refined characterization to damage accumulation under viscous loading

The annulus fibrosus (AF), a permeable, hydrated, and fiber-reinforced soft tissue, exhibits complex responses influenced by fluid pressure, osmotic pressure, and structural mechanics. Existing models struggle to comprehensively represent these intricate interactions and the heterogeneous solid responses within the AF. Additionally, the mechanisms driving differential damage accumulation between non-degenerative and degenerative intervertebral discs remain poorly understood. In this study, we introduce a biphasic-swelling damage model for the AF. We conceptually develop and rigorously validate this model through tissue-level tests employing various loading modes, consistently aligning model predictions with experimental data. Leveraging parametric geometric algorithms and custom Python scripts, we construct models simulating both non-degenerative and degenerative discs. Following calibration, we subject these models to viscous loading protocols. Our findings reveal the posterior AF's susceptibility to damage, contingent upon loading rate and water content. We elucidate the underlying mechanisms by examining the temporal evolution of fluid pressure, osmotic pressure, and the regionally dependent fiber network. This research presents a highly accurate model of the AF, providing valuable insights into disc damage. Future research endeavors should expand this model to incorporate ionic transport and diffusion, enabling a more profound exploration of intervertebral disc mechanobiology. This comprehensive model contributes to a better understanding of AF behavior and may inform therapeutic strategies for disc-related pathologies. STATEMENT OF SIGNIFICANCE: This research presents a comprehensive model of the annulus fibrosus (AF), a crucial component of the intervertebral disc that provides structural support and resists deformation. The study introduces a biphasic-swelling damage model for the AF and validates it through tissue-level tests. The model accounts for fluid pressure, osmotic pressure, and matrix mechanics, providing a more accurate representation of the AF's behavior. The study also investigates the differential damage accumulation between non-degenerative and degenerative discs, shedding light on the mechanisms driving disc degeneration. The findings have significant implications for medical treatments and interventions, as they highlight the posterior AF's susceptibility to damage. This research is of great interest to readers interested in biomechanics, tissue engineering, and medical treatments for disc degeneration.

Failure mechanical properties of lumbar intervertebral disc under high loading rate

BACKGROUND

Lumbar disc herniation (LDH) is the main clinical cause of low back pain. The pathogenesis of lumbar disc herniation is still uncertain, while it is often accompanied by disc rupture. In order to explore relationship between loading rate and failure mechanics that may lead to lumbar disc herniation, the failure mechanical properties of the intervertebral disc under high rates of loading were analyzed.

METHOD

Bend the lumbar motion segment of a healthy sheep by 5° and compress it to the ultimate strength point at a strain rate of 0.008/s, making a damaged sample. Within the normal strain range, the sample is subjected to quasi-static loading and high loading rate at different strain rates.

RESULTS

For healthy samples, the stress-strain curve appears collapsed only at high rates of compression; for damaged samples, the stress-strain curves collapse both at quasi-static and high-rate compression. For damaged samples, the strengthening stage becomes significantly shorter as the strain rate increases, indicating that its ability to prevent the destruction is significantly reduced. For damaged intervertebral disc, when subjected to quasi-static or high rates loading until failure, the phenomenon of nucleus pulposus (NP) prolapse occurs, indicating the occurrence of herniation. When subjected to quasi-static loading, the AF moves away from the NP, and inner AF has the greatest displacement; when subjected to high rates loading, the AF moves closer to the NP, and outer AF has the greatest displacement. The Zhu-Wang-Tang (ZWT) nonlinear viscoelastic constitutive model was used to describe the mechanical behavior of the intervertebral disc, and the fitting results were in good agreement with the experimental curve.

CONCLUSION

Experimental results show that, both damage and strain rate have a significant effect on the mechanical behavior of the disc fracture. The research work in this article has important theoretical guiding significance for preventing LDH in daily life.

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.

Modelling of Intervertebral Disc (IVD) with Structured Mesh and Crosswise Collagen Fibers

The highly organized collagen network of human lumbar annulus fibrosus (AF) is fundamental to preserve the mechanical integrity of the intervertebral discs. In the healthy AF, fibers are embedded in a hydrated matrix and arranged in a crosswise fashion, giving an anisotropic structure capable to undergo large strains. For finite element analysis (FEA) of spine, modelling a realistic intervertebral disc geometry has always been a challenge. This paper proposes a simple yet efficient workflow details for generating structured mesh of the ground substance of the AF and the method for generating collagen fibers with controllable angles that are embedded in AF.Clinical Relevance- The biomechanical response of spine is usually studied by finite element analysis (FEA) of the assembly of vertebra and IVD and other components. The FEA results are always dependent on the correct generation of the geometry and the material of the components. For IVD, creating structured mesh with crosswise collagen fibers with adjustable angles will provide a better control over the anisotropic property definitions of the IVD and approaching a more realistic simulation.

Emerging tissue engineering strategies for annulus fibrosus therapy

Low back pain is a major public health concern experienced by 80% of the world's population during their lifetime, which is closely associated with intervertebral disc (IVD) herniation. IVD herniation manifests as the nucleus pulposus (NP) protruding beyond the boundaries of the intervertebral disc due to disruption of the annulus fibrosus (AF). With a deepening understanding of the importance of the AF structure in the pathogenesis of intervertebral disc degeneration, numerous advanced therapeutic strategies for AF based on tissue engineering, cellular regeneration, and gene therapy have emerged. However, there is still no consensus concerning the optimal approach for AF regeneration. In this review, we summarized strategies in the field of AF repair and highlighted ideal cell types and pro-differentiation targeting approaches for AF repair, and discussed the prospects and difficulties of implant systems combining cells and biomaterials to guide future research directions. STATEMENT OF SIGNIFICANCE: Low back pain is a major public health concern experienced by 80% of the world's population during their lifetime, which is closely associated with intervertebral disc (IVD) herniation. However, there is still no consensus concerning the optimal approach for annulus fibrosus (AF) regeneration. In this review, we summarized strategies in the field of AF repair and highlighted ideal cell types and pro-differentiation targeting approaches for AF repair, and discussed the prospects and difficulties of implant systems combining cells and biomaterials to guide future research directions.

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.

Study on swelling, compression property and degradation stability of PVA composite hydrogels for artificial nucleus pulposus

Artificial nucleus pulposus (ANP) replacement as an alternative to the treatment of cervical spondylosis aims to relieve pain and restore the normal cervical motion. In this study, the PVA/PVP and PVA/Pectin composite hydrogels (CH)s with different concentrations were prepared by the freezing-thawing process, and their performances were tested. The effect of different concentrations on both kinds of PVA CHs were evaluated and analysed. The results demonstrated that both kinds of CHs had good swelling property (¿190%), compressive stress-strain characteristic response and stable performance, and they were not easy to degrade (¡9%). The elastic modulus of the PVA/PVP CH was close to that of nucleus pulposus prosthesis, and the weight loss ratio of the PVA/PVP CH was lower than that of PVA/Pectin CH under load condition. Further, the experimental results showed that the PVA/PVP CH with 15 wt% solute and 1 wt% PVP content had the best comprehensive performance, which may provide significant advantages for use in future clinical application in replacing nucleus pulposus.

Injectable Cell-Laden Nanofibrous Matrix for Treating Annulus Fibrosus Defects in Porcine Model: An Organ Culture Study

Lower back pain commonly arises from intervertebral disc (IVD) failure, often caused by deteriorating annulus fibrosus (AF) and/or nucleus pulposus (NP) tissue. High socioeconomic cost, quality of life issues, and unsatisfactory surgical options motivate the rapid development of non-invasive, regenerative repair strategies for lower back pain. This study aims to evaluate the AF regenerative capacity of injectable matrix repair strategy in ex vivo porcine organ culturing using collagen type-I and polycaprolactone nanofibers (PNCOL) with encapsulated fibroblast cells. Upon 14 days organ culturing, the porcine IVDs were assessed using gross optical imaging, magnetic resonance imaging (MRI), histological analysis, and Reverse Transcriptase quantitative PCR (RT-qPCR) to determine the regenerative capabilities of the PNCOL matrix at the AF injury. PNCOL-treated AF defects demonstrated a full recovery with increased gene expressions of AF extracellular matrix markers, including Collagen-I, Aggrecan, Scleraxis, and Tenascin, along with anti-inflammatory markers such as CD206 and IL10. The PNCOL treatment effectively regenerates the AF tissue at the injury site contributing to decreased herniation risk and improved surgical outcomes, thus providing effective non-invasive strategies for treating IVD injuries.

Degenerative Disc Disease of the Spine: From Anatomy to Pathophysiology and Radiological Appearance, with Morphological and Functional Considerations

Degenerative disc disease is a common manifestation in routine imaging of the spine; this finding is partly attributable to physiological aging and partly to a pathological condition, and sometimes this distinction is simply not clear. In this review, we start focusing on disc anatomy and pathophysiology and try to correlate them with radiological aspects. Furthermore, there is a special focus on degenerative disc disease terminology, and, finally, some considerations regarding disc morphology and its specific function, as well as the way in which these aspects change in degenerative disease. Radiologists, clinicians and spine surgeons should be familiar with these aspects since they have an impact on everyday clinical practice.

The role of nerve fibers and their neurotransmitters in regulating intervertebral disc degeneration

Intervertebral disc degeneration (IVDD) has been the major contributor to chronic lower back pain (LBP). Abnormal apoptosis, senescence, and pyroptosis of IVD cells, extracellular matrix (ECM) degradation, and infiltration of immune cells are the major molecular alternations during IVDD. Changes at tissue level frequently occur at advanced IVD tissue. Ectopic ingrowth of nerves within inner annulus fibrosus (AF) and nucleus pulposus (NP) tissue has been considered as the primary cause for LBP. Innervation at IVD tissue mainly included sensory and sympathetic nerves, and many markers for these two types of nerves have been detected since 1940. In fact, in osteoarthritis (OA), beyond pain transmission, the direct regulation of neuropeptides on functions of chondrocytes have attracted researchers' great attention recently. Many physical and pathological similarities between joint and IVD have shed us the light on the neurogenic mechanism involved in IVDD. Here, an overview of the advances in the nervous system within IVD tissue will be performed, with a discussion on in the role of nerve fibers and their neurotransmitters in regulating IVDD. We hope this review can attract more research interest to address neuromodulation and IVDD itself, which will enhance our understanding of the contribution of neuromodulation to the structural changes within IVD tissue and inflammatory responses and will help identify novel therapeutic targets and enable the effective treatment of IVDD disease.

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.

Detailed mechanical characterization of the transition zone: New insight into the integration between the annulus and nucleus of the intervertebral disc

The Nucleus Pulposus (NP) and Annulus Fibrous (AF) are two primary regions of the intervertebral disc (IVD). The interface between the AF and NP, where the gradual transition in structure and type of fibers are observed, is known as the Transition Zone (TZ). Recent structural studies have shown that the TZ contains organized fibers that appear to connect the NP to the AF. However, the mechanical characteristics of the TZ are yet to be explored. The current study aimed to investigate the mechanical properties of the TZ at the anterolateral (AL) and posterolateral (PL) regions in both radial and circumferential directions of loading using ovine IVDs (N = 28). Young's and toe moduli, maximum stress, failure strain, strain at maximum stress, and toughness were calculated mechanical parameters. The findings from this study revealed that the mechanical properties of the TZ, including young's modulus (p = 0.001), failure strain (p < 0.001), strain at maximum stress (p = 0.002), toughness (p = 0.027), and toe modulus (p = 0.005), were significantly lower for the PL compared to the AL region. Maximum stress was not significantly different between the PL and AL regions (p = 0.164). We found that maximum stress (p = 0.002), failure strain (p < 0.001), and toughness (p = 0.001) were significantly different in different loading directions. No significant differences for modulus (young's; p = 0.169 and toe; p = 0.352) and strain at maximum stress (p = 0.727) were found between the radial and circumferential loading directions. STATEMENT OF SIGNIFICANCE: To date there has not been a study that has investigated the mechanical characterization of the annulus (AF)-nucleus (NP) interface (transition zone; TZ) in the intervertebral disc (IVD), nor is it known whether the posterolateral (PL) and anterolateral (AL) regions of the TZ exhibit different mechanical properties. Accordingly, the TZ mechanical properties have been rarely used in the development of computational IVD models and relevant tissue-engineered scaffolds. The current research reported the mechanical properties of the TZ region and revealed that its mechanical properties were significantly lower for the PL compared to the AL region. These new findings enhance our knowledge about the nature of AF-NP integration and may help to develop more realistic tissue-engineered or computational IVD models.

Regional variations in discrete collagen fibre mechanics within intact intervertebral disc resolved using synchrotron computed tomography and digital volume correlation

Many soft tissues, such as the intervertebral disc (IVD), have a hierarchical fibrous composite structure which suffers from regional damage. We hypothesise that these tissue regions have distinct, inherent fibre structure and structural response upon loading. Here we used synchrotron computed tomography (sCT) to resolve collagen fibre bundles (∼5μm width) in 3D throughout an intact native rat lumbar IVD under increasing compressive load. Using intact samples meant that tissue boundaries (such as endplate-disc or nucleus-annulus) and residual strain were preserved; this is vital for characterising both the inherent structure and structural changes upon loading in tissue regions functioning in a near-native environment. Nano-scale displacement measurements along >10,000 individual fibres were tracked, and fibre orientation, curvature and strain changes were compared between the posterior-lateral region and the anterior region. These methods can be widely applied to other soft tissues, to identify fibre structures which cause tissue regions to be more susceptible to injury and degeneration. Our results demonstrate for the first time that highly-localised changes in fibre orientation, curvature and strain indicate differences in regional strain transfer and mechanical function (e.g. tissue compliance). This included decreased fibre reorientation at higher loads, specific tissue morphology which reduced capacity for flexibility and high strain at the disc-endplate boundary.

Statement of significance

The analyses presented here are applicable to many collagenous soft tissues which suffer from regional damage. We aimed to investigate regional intervertebral disc (IVD) structural and functional differences by characterising collagen fibre architecture and linking specific fibre- and tissue-level deformation behaviours. Synchrotron CT provided the first demonstration of tracking discrete fibres in 3D within an intact IVD. Detailed analysis of regions was performed using over 200k points, spaced every 8 μm along 10k individual fibres. Such comprehensive structural characterisation is significant in informing future computational models. Morphological indicators of tissue compliance (change in fibre curvature and orientation) and fibre strain measurements revealed localised and regional differences in tissue behaviour.

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.

Modeling multiaxial damage regional variation in human annulus fibrosus

In the present article, a fully three-dimensional human annulus fibrosus model is developed by considering the regional variation of the complex structural organization of collagen network at different scales to predict the regional anisotropic multiaxial damage of the intervertebral disc. The model parameters are identified using experimental data considering as elementary structural unit, the single annulus lamellae stretched till failure along the micro-sized collagen fibers. The multi-layered lamellar/inter-lamellar annulus model is constructed by considering the effective interactions between adjacent layers and the chemical-induced volumetric strain. The regional dependent model predictions are analyzed under various loading modes and compared to experimental data when available. The stretching along the circumferential and radial directions till failure serves to check the predictive capacities of the annulus model. Model results under simple shear, biaxial stretching and plane-strain compression are further presented and discussed. Finally, a full disc model is constructed using the regional annulus model and simulations are presented to assess the most likely failed areas under disc axial compression. STATEMENT OF SIGNIFICANCE: The damage in annulus soft tissues is a complex multiscale phenomenon due to a complex structural arrangement of collagen network at different scales of hierarchical organization. A fully three-dimensional constitutive representation that considers the regional variation of the structural complexity to estimate annulus multiaxial mechanics till failure has not yet been developed. Here, a model is developed to predict deformation-induced damage and failure of annulus under multiaxial loading histories considering as time-dependent physical process both chemical-induced volumetric effects and damage accumulation. After model identification using single lamellae extracted from different disc regions, the model predictability is verified for various multiaxial elementary loading modes representative of the spine movement. The heterogeneous mechanics of a full human disc model is finally presented.

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.