A swelling-based biphasic analysis on the quasi-static biomechanical behaviors of healthy and degenerative intervertebral discs

The effect of failure mechanics on the fatigue responses of lumbar intervertebral disc

Lumbar disc herniation is usually caused by the accumulation of long-term mechanical loads and sudden overload damage. Therefore, this study aims to illustrate how fatigue failure in lumbar spine segments is influenced by both cyclic loading magnitude and pre-existing damage. Eighty-six sheep intervertebral disc samples were divided into four groups to test the fatigue responses in healthy and damaged intervertebral discs. Both before and after fatigue loading, the specimens were performed on loading-unloading tests to analyze the viscoelasticity changes, while the specimens were performed on MRI examination to analyze the geometric and morphological changes. The Stress-Failure curve (SN curve) was examined, while the number of cycles to failure of damaged specimens was much smaller than that of healthy specimens at the same stress level during cyclic loading, and the relationship was approximately linear on a logarithmic scale. In addition, the healthy specimens will not accumulate fatigue failure if the compression force remains below 50% of the ultimate compressive tolerance (UTC). Before and after fatigue loading, the loading-unloading curves do not coincide and show obvious strain-rate-dependent viscoelastic characteristics, while the elastic modulus of the damaged specimen is significantly smaller. For magnetic resonance imaging, morphological changes included the changes of nucleus pulposus (NP) shape and area, while fatigue has a more significant effect on ruptured and herniated disc specimens. The dissipated energy of the intervertebral discs under cyclic loading was then calculated based on viscoelastic constitutive equations, which show that the load and preexisting damage both have significant effects on the dissipation rate.

Finite element model reveals the involvement of cartilage endplate in quasi-static biomechanics of intervertebral disc degeneration

Background and objective

The intrinsic link between the compositional and structural attributes and the biomechanical functionality is evident in intervertebral discs. However, it remains unclear from a biomechanical perspective whether cartilage endplate (CEP) degeneration exacerbates intervertebral disc degeneration.

Methods

This study developed and quantitatively validated four biphasic swelling-based finite element models. We then applied four quasi-static tests and simulated daily loading scenarios to examine the effects of CEP degradation.

Results

Under free-swelling conditions, short-term responses were prevalent, with CEP performance changes not significantly impacting response proportionality. The creep test results showed the more than 50 % of the strain was attributed to long-term responses. Stress-relaxation testing indicated that all responses increased with disc degeneration, yet CEP degeneration's impact was minimal. Daily load analyses revealed that disc degeneration significantly reduces nucleus pulposus pressure and disc height, whereas CEP degeneration marginally increases nucleus pressure and slightly decreases disc height.

Conclusions

Glycosaminoglycan content and CEP permeability are critical to the fluid-dependent viscoelastic response of intervertebral discs. Our findings suggest that CEP contributes to disc degeneration under daily loading conditions.

Biomechanics of annulus fibrosus: Elastic fiber simplification and degenerative impact on damage initiation and propagation

This study addresses three primary objectives related to lumbar intervertebral disc (IVD) biomechanics under ramping quasi-static loading conditions. First, we explore the conditions justifying the simplification of axisymmetric elastic fiber families into single fiber bundles through discretized strain energy functions. Simulations reveal that a concentration factor exceeding 10 allows for a consistent deviation below 10% between simplified and non-simplified responses. Second, we investigate the impact of elastic fibers on the physiological stiffness in IVDs, revealing minimal influence on biological motions but significant effects on degeneration. Lastly, we examine the initiation and progression of annulus fibrosus (AF) damage. Our findings confirm the validity of simplifying elastic fiber families and underscore the necessity of considering elastic fiber damage in biomechanical studies of AF tissues. Elastic fibers contribute to increased biaxial stretch stiffness, and their damage significantly affects the loading capacity of the inner AF. Additionally, degeneration significantly alters the susceptibility to damage in the AF, with specific regions exhibiting higher vulnerability. Damage tends to extend circumferentially and radially, emphasizing the regional variations in collagen and elastic fiber properties. This study offers useful insights for refining biomechanical models, paving the way for a more comprehensive understanding of IVD responses and potential clinical implications.

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.

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.