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

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.

Movement examination of the lumbar spine using a developed wearable motion sensor

A system for monitoring spinal movements based on wearable motion sensors is proposed here. For this purpose, a hardware system is first developed that measures data of linear acceleration, angular velocity, and the magnetic field of the spine. Then, the obtained data from these sensors are combined in a proposed complementary filter, and their angular variations are estimated. The obtained results of angular variation of this system in comparison with an accurate reference illustrate that the root mean squared error is less than 1.61 degrees for three angles of ϕ r , θ r and ψ r for this system that proves this system can accurately estimate the angular variation of the spine. Then, the system is mounted on the lumbar spine of several volunteers, and the obtained angles from the patients' spine are compared with some healthy volunteers' spine, and the performance of their spine improves over time. The results show that this system can be very effective for patients who suffer from back problems and help in their recovery process a lot.

Annulus Calibration Increases the Computational Accuracy of the Lumbar Finite Element Model

STUDY DESIGN

Mechanical simulations.

OBJECTIVE

Inadequate calibration of annuli negatively affects the computational accuracy of finite element (FE) models. Specifically, the definition of annulus average radius (AR) does not have uniformity standards. Differences between the elastic moduli in the different layers and parts of the annulus were not fully calibrated when a linear elastic material is used to define its material properties. This study aims to optimize the computational accuracy of the FE model by calibrating the annulus.

METHODS

We calibrated the annulus AR and elastic modulus in our anterior-constructed lumbar model by eliminating the difference between the computed range of motion and that measured by in vitro studies under a flexion-extension loading condition. Multi-indicator validation was performed by comparing the computed indicators with those measured in in vitro studies. The computation time required for the different models has also been recorded to evaluate the computational efficiency.

RESULTS

The difference between computed and measured ROMs was less than 1% when the annulus AR and elastic modulus were calibrated. In the model validation process, all the indicators computed by the calibrated FE model were within ±1 standard deviation of the average values obtained from in vitro studies. The maximum difference between the computed and measured values was less than 10% under nearly all loading conditions. There is no apparent variation tendency for the computational time associated with different models.

CONCLUSION

The FE model with calibrated annulus AR and regional elastic modulus has higher computational accuracy and can be used in subsequent mechanical studies.

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.

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

BACKGROUND AND OBJECTIVE

The degeneration of intervertebral discs is significantly dependent of the changes in tissue composition ratio and tissue structure. Up to the present, the effects of degeneration on the quasi-static biomechanical responses of discs have not been well understood. The goal of this study is to quantitatively analyze the quasi-static responses of healthy and degenerative discs.

METHODS

Four biphasic swelling-based finite element models are developed and quantitatively validated. Four quasi-static test protocols, including the free-swelling, slow-ramp, creep and stress-relaxation, are implemented. The double Voigt and double Maxwell models are further used to extract the immediate (or residual), short-term and long-term responses of these tests.

RESULTS

Simulation results show that both the swelling-induced pressure in the nucleus pulposus and the initial modulus decrease with degeneration. In the free-swelling test of discs possessing healthy cartilage endplates, simulation results show that over 80% of the total strain is contributed by the short-term response. The long-term response is dominant for discs with degenerated permeability in cartilage endplates. For the creep test, over 50% of the deformation is contributed by the long-term response. In the stress-relaxation test, the long-term stress contribution occupies approximately 31% of total response and is independent of degeneration. Both the residual and short-term responses vary monotonically with degeneration. In addition, both the glycosaminoglycan content and permeability affect the engineering equilibrium time constants of the rheologic models, in which the determining factor is the permeability.

CONCLUSIONS

The content of glycosaminoglycan in intervertebral soft tissues and the permeability of cartilage endplates are two critical factors that affect the fluid-dependent viscoelastic responses of intervertebral discs. The component proportions of the fluid-dependent viscoelastic responses depend also strongly on test protocols. In the slow-ramp test, the glycosaminoglycan content is responsible for the changes of the initial modulus. Since existing computational models simulate disc degenerations only by altering disc height, boundary conditions and material stiffness, the current work highlights the significance of biochemical composition and cartilage endplates permeability in the biomechanical behaviors of degenerated discs.

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.

Adjacent segments biomechanics following lumbar fusion surgery: a musculoskeletal finite element model study

PURPOSE

This study exploits a novel musculoskeletal finite element (MS-FE) spine model to evaluate the post-fusion (L4-L5) alterations in adjacent segment kinetics.

METHODS

Unlike the existing MS models with idealized representation of spinal joints, this model predicts stress/strain distributions in all passive tissues while organically coupled to a MS model. This generic (in terms of musculature and material properties) model uses population-based in vivo vertebral sagittal rotations, gravity loads, and an optimization algorithm to calculate muscle forces. Simulations represent individuals with an intact L4-L5, a preoperative severely degenerated L4-L5 (by reducing the disc height by ~ 60% and removing the nucleus incompressibility), and a postoperative fused L4-L5 segment with either a fixed or an altered lumbopelvic rhythm with respect to the intact condition (based on clinical observations). Changes in spine kinematics and back muscle cross-sectional areas (due to intraoperative injuries) are considered based on in vivo data while simulating three activities in upright/flexed postures.

RESULTS

Postoperative changes in some adjacent segment kinetics were found considerable (i.e., larger than 25%) that depended on the postoperative lumbopelvic kinematics and preoperative L4-L5 disc condition. Postoperative alterations in adjacent disc shear, facet/ligament forces, and annulus stresses/strains were greater (> 25%) than those found in intradiscal pressure and compression (< 25%). Kinetics of the lower (L5-S1) and upper (L3-L4) adjacent segments were altered to different degrees.

CONCLUSION

Alterations in segmental rotations mainly affected adjacent disc shear forces, facet/ligament forces, and annulus/collagen fibers stresses/strains. An altered lumbopelvic rhythm (increased pelvis rotation) tends to mitigate some of these surgically induced changes.

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.

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

Collagen fibers within the annulus fibrosus (AF) lamellae are unidirectionally aligned with alternating orientations between adjacent layers. AF constitutive models often combine two adjacent lamellae into a single equivalent layer containing two fiber networks with a crisscross pattern. Additionally, AF models overlook the inter-lamellar matrix (ILM) as well as elastic fiber networks in between lamellae. We developed a nonhomogenous micromechanical model as well as two coarser homogenous hyperelastic and microplane models of the human AF, and compared their performances against measurements (tissue level uniaxial and biaxial tests as well as whole disc experiments) and seven published hyperelastic models. The micromechanical model had a realistic non-homogenous distribution of collagen fiber networks within each lamella and elastic fiber network in the ILM. For small matrix linear moduli (<0.2 MPa), the ILM showed substantial anisotropy (>10%) due to the elastic fiber network. However, at moduli >0.2 MPa, the effects of the elastic fiber network on differences in stress-strain responses at different directions disappeared (<10%). Variations in sample geometry and boundary conditions (due to uncertainty) markedly affected stress-strain responses of the tissue in uniaxial and biaxial tests (up to 16 times). In tissue level tests, therefore, simulations should represent testing conditions (e.g., boundary conditions, specimen geometry, preloads) as closely as possible. Stress/strain fields estimated from the single equivalent layer approach (conventional method) yielded different results from those predicted by the anatomically more accurate apparoach (i.e., layerwise). In addition, in a disc under a compressive force (symmetric loading), asymmetric stress-strain distributions were computed when using a layerwise simulation. Although all developed and selected published AF models predicted gross compression-displacement responses of the whole disc within the range of measured data, some showed excessively stiff or compliant responses under tissue-level uniaxial/biaxial tests. This study emphasizes, when constructing and validating constitutive models of AF, the importance of the proper simulation of individual lamellae as distinct layers, and testing parameters (sample geometric dimensions/loading/boundary conditions).

Computational Challenges in Tissue Engineering for the Spine

This paper deals with a brief review of the recent developments in computational modelling applied to innovative treatments of spine diseases. Additionally, it provides a perspective on the research directions expected for the forthcoming years. The spine is composed of distinct and complex tissues that require specific modelling approaches. With the advent of additive manufacturing and increasing computational power, patient-specific treatments have moved from being a research trend to a reality in clinical practice, but there are many issues to be addressed before such approaches become universal. Here, it is identified that the major setback resides in validation of these computational techniques prior to approval by regulatory agencies. Nevertheless, there are very promising indicators in terms of optimised scaffold modelling for both disc arthroplasty and vertebroplasty, powered by a decisive contribution from imaging methods.

Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand

Quantification of lumbar spine load transfer is important for understanding low back pain, especially among persons with a lower limb amputation. Computational modeling provides a helpful solution for obtaining estimates of in vivo loads. A multiscale model was constructed by combining musculoskeletal and finite element (FE) models of the lumbar spine to determine tissue loading during daily activities. Three-dimensional kinematic and ground reaction force data were collected from participants with ([Formula: see text]) and without ([Formula: see text]) a unilateral transtibial amputation (TTA) during 5 sit-to-stand trials. We estimated tissue-level load transfer from the multiscale model by controlling the FE model with intervertebral kinematics and muscle forces predicted by the musculoskeletal model. Annulus fibrosis stress, intradiscal pressure (IDP), and facet contact forces were calculated using the FE model. Differences in whole-body kinematics, muscle forces, and tissue-level loads were found between participant groups. Notably, participants with TTA had greater axial rotation toward their intact limb ([Formula: see text]), greater abdominal muscle activity ([Formula: see text]), and greater overall tissue loading throughout sit-to-stand ([Formula: see text]) compared to able-bodied participants. Both normalized (to upright standing) and absolute estimates of L4-L5 IDP were close to in vivo values reported in the literature. The multiscale model can be used to estimate the distribution of loads within different lumbar spine tissue structures and can be adapted for use with different activities, populations, and spinal geometries.