Comparison of four methods to simulate swelling in poroelastic finite element models of intervertebral discs

Unveiling interactions between intervertebral disc morphologies and mechanical behavior through personalized finite element modeling

Introduction: Intervertebral Disc (IVD) Degeneration (IDD) is a significant health concern, potentially influenced by mechanotransduction. However, the relationship between the IVD phenotypes and mechanical behavior has not been thoroughly explored in local morphologies where IDD originates. This work unveils the interplays among morphological and mechanical features potentially relevant to IDD through Abaqus UMAT simulations. Methods: A groundbreaking automated method is introduced to transform a calibrated, structured IVD finite element (FE) model into 169 patient-personalized (PP) models through a mesh morphing process. Our approach accurately replicates the real shapes of the patient's Annulus Fibrosus (AF) and Nucleus Pulposus (NP) while maintaining the same topology for all models. Using segmented magnetic resonance images from the former project MySpine, 169 models with structured hexahedral meshes were created employing the Bayesian Coherent Point Drift++ technique, generating a unique cohort of PP FE models under the Disc4All initiative. Machine learning methods, including Linear Regression, Support Vector Regression, and eXtreme Gradient Boosting Regression, were used to explore correlations between IVD morphology and mechanics. Results: We achieved PP models with AF and NP similarity scores of 92.06\% and 92.10\% compared to the segmented images. The models maintained good quality and integrity of the mesh. The cartilage endplate (CEP) shape was represented at the IVD-vertebra interfaces, ensuring personalized meshes. Validation of the constitutive model against literature data showed a minor relative error of 5.20%. Discussion: Analysis revealed the influential impact of local morphologies on indirect mechanotransduction responses, highlighting the roles of heights, sagittal areas, and volumes. While the maximum principal stress was influenced by morphologies such as heights, the disc's ellipticity influenced the minimum principal stress. Results suggest the CEPs are not influenced by their local morphologies but by those of the AF and NP. The generated free-access repository of individual disc characteristics is anticipated to be a valuable resource for the scientific community with a broad application spectrum.

Comparative FEM study on intervertebral disc modeling: Holzapfel-Gasser-Ogden vs. structural rebars

Introduction: Numerical modeling of the intervertebral disc (IVD) is challenging due to its complex and heterogeneous structure, requiring careful selection of constitutive models and material properties. A critical aspect of such modeling is the representation of annulus fibers, which significantly impact IVD biomechanics. This study presents a comparative analysis of different methods for fiber reinforcement in the annulus fibrosus of a finite element (FE) model of the human IVD. Methods: We utilized a reconstructed L4-L5 IVD geometry to compare three fiber modeling approaches: the anisotropic Holzapfel-Gasser-Ogden (HGO) model (HGO fiber model) and two sets of structural rebar elements with linear-elastic (linear rebar model) and hyperelastic (nonlinear rebar model) material definitions, respectively. Prior to calibration, we conducted a sensitivity analysis to identify the most important model parameters to be calibrated and improve the efficiency of the calibration. Calibration was performed using a genetic algorithm and in vitro range of motion (RoM) data from a published study with eight specimens tested under four loading scenarios. For validation, intradiscal pressure (IDP) measurements from the same study were used, along with additional RoM data from a separate publication involving five specimens subjected to four different loading conditions. Results: The sensitivity analysis revealed that most parameters, except for the Poisson ratio of the annulus fibers and C01 from the nucleus, significantly affected the RoM and IDP outcomes. Upon calibration, the HGO fiber model demonstrated the highest accuracy (R2 = 0.95), followed by the linear (R2 = 0.89) and nonlinear rebar models (R2 = 0.87). During the validation phase, the HGO fiber model maintained its high accuracy (RoM R2 = 0.85; IDP R2 = 0.87), while the linear and nonlinear rebar models had lower validation scores (RoM R2 = 0.71 and 0.69; IDP R2 = 0.86 and 0.8, respectively). Discussion: The results of the study demonstrate a successful calibration process that established good agreement with experimental data. Based on our findings, the HGO fiber model appears to be a more suitable option for accurate IVD FE modeling considering its higher fidelity in simulation results and computational efficiency.

Enzymatic denaturation versus excessive fatigue loading degeneration: Effects on the time-dependent response of the intervertebral disc

Degenerative disc disease (DDD), regardless of its phenotype and clinical grade, is widely associated with low back pain (LBP), which remains the single leading cause of disability worldwide. This work provides a quantitative methodology for comparatively investigating artificial IVD degeneration via two popular approaches: enzymatic denaturation and fatigue loading. An in-vitro animal study was used to study the time-dependent responses of forty fresh juvenile porcine thoracic IVDs in conjunction with inverse and forward finite element (FE) simulations. The IVDs were dissected from 6-month-old-juvenile pigs and equally assigned to 5 groups (intact, denatured, low-level, medium-level, high-level fatigue loading). Upon preloading, a sinusoid cyclic load (Peak-to-peak/0.1-to-0.8 MPa) was applied (0.01-10 Hz), and dynamic-mechanical-analyses (DMA) was performed. The DMA outcomes were integrated with a robust meta-model analysis to quantify the poroelastic IVD characteristics, while specimen-specific FE models were developed to study the detailed responses. The results demonstrated that enzymatic denaturation had a more significantly pronounced effect on the resistive strength and shock attenuation capabilities of the intervertebral discs. This can be attributed to the simultaneous disruption of the collagen fibers and water-proteoglycan bonds induced by trypsin digestion. Fatigue loading, on the other hand, primarily influenced the disc's resistance to deformation in a frequency-dependent pattern, where alterations were most noticeable at low loading frequencies. This study confirms the intricate interplay between the biochemical changes induced by enzymatic processes and the mechanical behavior stemming from fatigue loading, suggesting the need for a comprehensive approach to closely mimic the interrelated multifaceted processes of human disc degeneration.

Dataset of Finite Element Models of Normal and Deformed Thoracolumbar Spine

Adult spine deformity (ASD) is prevalent and leads to a sagittal misalignment in the vertebral column. Computational methods, including Finite Element (FE) Models, have emerged as valuable tools for investigating the causes and treatment of ASD through biomechanical simulations. However, the process of generating personalised FE models is often complex and time-consuming. To address this challenge, we present a dataset of FE models with diverse spine morphologies that statistically represent real geometries from a cohort of patients. These models are generated using EOS images, which are utilized to reconstruct 3D surface spine models. Subsequently, a Statistical Shape Model (SSM) is constructed, enabling the adaptation of a FE hexahedral mesh template for both the bone and soft tissues of the spine through mesh morphing. The SSM deformation fields facilitate the personalization of the mean hexahedral FE model based on sagittal balance measurements. Ultimately, this new hexahedral SSM tool offers a means to generate a virtual cohort of 16807 thoracolumbar FE spine models, which are openly shared in a public repository.

Impact of osteoporosis and Cement-Augmented fusion on adjacent spinal levels Post-Fusion Surgery: Patient-Specific finite element analysis

Cement-augmentation is a technique commonly used during posterior lumbar instrumented fusion (PLIF) to reinforce compromised osteoporotic vertebral bone, minimize the risk of loosening screws, enhance stability, and improve overall surgical outcomes. In this study, we introduce a novel segmented vertebral body regional modeling approach to investigate the effects of osteoporosis and cement-augmented lumbar fusion on disc biomechanics at spinal levels adjacent to the fused vertebrae. Using our previously validated personalized-poroelastic-osteoligamentous FE model of the spine, fusion was simulated at L4-L5, and the biomechanics of adjacent levels were studied for 30 patients (non-osteoporotic patients (N = 15), osteoporotic patients (N = 15)). PLIF models, with and without cement-augmentation, were developed and compared after an 8 h-rest period (200 N), following a 16 h-cyclic compressive loading of 500-1000 N (40 and 20 min, respectively). Movement in different directions (flexion/ extension/ lateral bending/ axial rotation) was simulated using 10Nm moment before and after cyclic loading. The material mapping algorithm was validated by comparing the results of voxel-based and parametric models. The FE cement-augmented models, subject to daily activity loading, demonstrated significant differences in disc height loss and fluid loss as compared to non-cemented models. The calculated axial stress and fiber strain values were also significantly higher for these models. This work demonstrates that although osteoporosis does not significantly alter the time-dependent characteristics of adjacent IVDs post-surgery, cement-augmentation increases the risk of adjacent segment disease (ASD) incidence. A holistic understanding of the trade-offs and long-term complex interplay between structural reinforcement modalities, including cement augmentation, and altered biomechanics warrants further investigation.

Biomechanical response of lumbar intervertebral disc in daily sitting postures: a poroelastic finite element analysis

This study aims to establish and validate a poroelastic L4-L5 finite element model to evaluate the effect of different sitting postures and their durations on the mechanical responses of the disc. During the sustained loading conditions, the height loss, fluid loss and von-Mises stress gradually increased, but the intradiscal pressure decreased. The varying rates of aforementioned parameters were more significant at the initial loading stage and less so at the end. The predicted values in the flexed sitting posture were significantly greater than other postures. The extended sitting posture caused an obvious von-Mises stress concentration in the posterior region of the inter-lamellar matrix. From the biomechanical perspective, prolonged sitting may pose a high risk of lumbar disc degeneration, and therefore adjusting the posture properly in the early stage of sitting time may be useful to mitigate that. Additionally, upright sitting is a safer posture, while flexed sitting posture is more harmful.

The influence of over-distraction on biomechanical response of cervical spine post anterior interbody fusion: a comprehensive finite element study

Introduction: Anterior cervical discectomy and fusion (ACDF) has been considered as the gold standard surgical treatment for cervical degenerative pathologies. Some surgeons tend to use larger-sized interbody cages during ACDF to restore the index intervertebral disc height, hence, this study evaluated the effect of larger-sized interbody cages on the cervical spine with ACDF under both static and cyclic loading. Method: Twenty pre-operative personalized poro-hyperelastic finite element (FE) models were developed. ACDF post-operative models were then constructed and four clinical scenarios (i.e., 1) No-distraction; 2) 1 mm distraction; 3) 2 mm distraction; and 4) 3 mm distraction) were predicted for each patient. The biomechanical responses at adjacent spinal levels were studied subject to static and cyclic loading. Non-parametric Friedman statistical comparative tests were performed and the p values less than 0.05 were reflected as significant. Results: The calculated intersegmental range of motion (ROM) and intradiscal pressure (IDP) from 20 pre-operative FE models were within the overall ranges compared to the available data from literature. Under static loading, greater ROM, IDP, facet joint force (FJF) values were detected post ACDF, as compared with pre-op. Over-distraction induced significantly higher IDP and FJF in both upper and lower adjacent levels in extension. Higher annulus fibrosus stress and strain values, and increased disc height and fluid loss at the adjacent levels were observed in ACDF group which significantly increased for over-distraction groups. Discussion: it was concluded that using larger-sized interbody cages (the height of ≥2 mm of the index disc height) can result in remarkable variations in biomechanical responses of adjacent levels, which may indicate as risk factor for adjacent segment disease. The results of this comprehensive FE investigation using personalized modeling technique highlight the importance of selecting the appropriate height of interbody cage in ACDF surgery.

Is the fluid volume fraction equal to the water content in tendons? Insights on biphasic modeling

The mass density of highly hydrated soft tissues is generally assumed to be very close to that of the water, resulting that the fluid mass fraction (water content) being equal to the fluid volume fraction. Within this context, the present study aims to investigate whether such an assumption actually holds for tendon tissues and to what extent it may affect the constitutive characterizations based on biphasic (poroelastic) models. Once the water content was assessed by a classical drying assay, the fluid volume fraction was obtained based on an image segmentation approach. The main achieved results point out that the fluid volume fraction is ∼20% higher than the water content in the studied tendons (flexor digitorum profundus bovine tendons). Based on this, it is shown that the use of the water content instead of the fluid volume fraction may considerably bias the results drawn by biphasic modeling of tendons. Accordingly, a proper measurement of the fluid volume fraction is then required.

Biomechanical consequences of the intervertebral disc centre of rotation kinematics during lateral bending and axial rotation

The location of the instantaneous centre of rotation (ICR) of a lumbar unit has a considerable clinical importance as a spinal health estimator. Consequently, many studies have been conducted to measure or estimate the ICR during rotations in the three anatomical planes; however the results reported are widely scattered. Even if some inter-subjects variability is to be expected, such inconsistencies are likely explained by the differences in methods and experiments. Therefore, in this paper we seek to model three behaviours of the ICR during lateral bending and axial rotation based on results published in the literature. In order to assess the metabolic and mechanical sensibility to the assumption made on the ICR kinematics, we used a previously validated three dimensional non-linear poroelastic model of a porcine intervertebral disc to simulate physiological lateral and axial rotations. The impact of the geometry was also briefly investigated by considering a 11[Formula: see text] wedge angle. From our simulations, it appears that the hypothesis made on the ICR location does not significantly affect the critical nutrients concentrations but gives disparate predictions of the intradiscal pressure at the centre of the disc (variation up to 0.7 MPa) and of the displacement fields (variation up to 0.4 mm). On the contrary, the wedge angle does not influence the estimated intradiscal pressure but leads to minimal oxygen concentration decreased up to 33% and increased maximal lactate concentration up to 13%. While we can not settle on which definition of the ICR is more accurate, this work suggests that patient-specific modeling of the ICR is required and brings new insights that can be useful for the development of new tools or the design of surgical material such as total lumbar disc prostheses.

Anatomical parameters alter the biomechanical responses of adjacent segments following lumbar fusion surgery: Personalized poroelastic finite element modelling investigations

Introduction: While the short-term post-operative outcome of lumbar fusion is satisfying for most patients, adjacent segment disease (ASD) can be prevalent in long-term clinical observations. It might be valuable to investigate if inherent geometrical differences among patients can significantly alter the biomechanics of adjacent levels post-surgery. This study aimed to utilize a validated geometrically personalized poroelastic finite element (FE) modeling technique to evaluate the alteration of biomechanical response in adjacent segments post-fusion. Methods: Thirty patients were categorized for evaluation in this study into two distinct groups [i.e., 1) non-ASD and 2) ASD patients] based on other long-term clinical follow-up investigations. To evaluate the time-dependent responses of the models subjected to cyclic loading, a daily cyclic loading scenario was applied to the FE models. Different rotational movements in different planes were superimposed using a 10 Nm moment after daily loading to compare the rotational motions with those at the beginning of cyclic loading. The biomechanical responses of the lumbosacral FE spine models in both groups were analyzed and compared before and after daily loading. Results: The achieved comparative errors between the FE results and clinical images were on average below 20% and 25% for pre-op and post-op models, respectively, which confirms the applicability of this predictive algorithm for rough pre-planning estimations. The results showed that the disc height loss and fluid loss were increased for the adjacent discs in post-op models after 16 h of cyclic loading. In addition, significant differences in disc height loss and fluid loss were observed between the patients who were in the non-ASD and ASD groups. Similarly, the increased stress and fiber strain in the annulus fibrosus (AF) was higher in the adjacent level of post-op models. However, the calculated stress and fiber strain values were significantly higher for patients with ASD. Discussion: Evaluating the biomechanical response of pre-op and post-op modeling in the non-ASD and ASD groups showed that the inherent geometric differences among patients cause significant variations in the estimated mechanical response. In conclusion, the results of the current study highlighted the effect of geometrical parameters (which may refer to the anatomical conditions or the induced modifications regarding surgical techniques) on time-dependent responses of lumbar spine biomechanics.

Spinal Cord Stress After Anterior Cervical Diskectomy and Fusion: Results from a Patient-Specific Finite Element Model

Degenerative cervical myelopathy (DCM) is the commonest cause of cervical spinal cord dysfunction in older adults and is characterized by spinal cord compression and stress during neck motion. Although surgical decompression eliminates static spinal cord compression, cord stress resulting from flexion-extension motion of the spinal column has not been determined for single and multi-level surgical interventions. The effect of surgery on spinal cord stress is expected to change with the number of surgical levels as well as patient-specific anatomy. Using a MRI-derived patient-specific finite element model, we simulated 1-, 2- and 3-level anterior cervical diskectomy and fusion (ACDF) surgery for DCM. A substantial decrease in spinal cord stress at the level of spinal cord decompression was noted in all simulations. This was associated with a considerable increase in spinal cord stress rostral to the surgical level, and the magnitude of stress was higher in multi-level surgery. Increased spinal cord stress at the rostral adjacent segment correlated with increased segmental range of motion (r = 0.69, p = 0.002) and disk pressure (r = 0.57, p = 0.05). Together, these results indicate that ACDF for DCM is associated with adverse spinal cord stress patterns adjacent to the fusion construct, and further research is needed to determine if the altered stress is associated with clinical outcomes after surgery for DCM.

Impact of extracellular matrix and collagen network properties on the cervical intervertebral disc response to physiological loads: A parametric study

Current intervertebral disc finite element models are hard to validate since they describe multi-physical phenomena and contain a huge number of material properties. This work aims to simplify numerical validation/identification studies by prioritizing the sensitivity of intervertebral disc behavior to mechanical properties. A 3D fiber-reinforced hyperelastic model of a C6-C7 intervertebral disc is used to carry out the parametric study. 10 parameters describing the extracellular matrix and the collagen network behaviors are included in the parametric study. The influence of varying these parameters on the disc response is estimated during physiological movements of the head, including compression, lateral bending, flexion, and axial rotation. The obtained results highlight the high sensitivity of the disc behavior to the stiffness of the annulus fibrosus extracellular matrix for all the studied loads with a relative increase in the disc apparent stiffness by 67% for compression and by 57% for axial rotation when the annulus stiffness increases from 0.4 to 2 MPa. It is also shown that varying collagen network orientation, stiffness, and stiffening in the studied configuration range have a noticeable effect on rotational motions with a relative apparent stiffness difference reaching 6.8%, 10%, and 22%, respectively, in lateral bending. However, the collagen orientation does not affect disc response to axial load.

Comparative biomechanical analyses of lower cervical spine post anterior fusion versus intervertebral disc arthroplasty: A geometrically patient-specific poroelastic finite element investigation

Background/Objective

The optimal surgical technique for the treatment of cervical degenerative disc disease (CDDD) towards decreasing the risk of adjacent segment disease (ASD) remains elusive. This study aimed to comparatively investigate the biomechanics of the lower cervical spine following fusion (ACDF) and artificial disc arthroplasty (Bryan® and Prestige LP®) using a validated geometrically patient-specific poroelastic finite element modeling (FEM) approach.

Methods

Ten subject-specific pre-operative models were developed and validated based on a FEM approach. Poroelastic models were then constructed using post-operation images for three different treatment scenarios: ACDF; Prestige LP® and Bryan® artificial discs at the C5-C6 level. The biomechanical responses at both surgical and adjacent spinal levels were studied subject to static and cyclic loading.

Results

Postoperatively, greater range of motion (ROM), higher annulus fibrosus stress and strain values, and increased disc height and fluid loss at the adjacent levels were detected post ACDF, as compared with pre-op as well as artificial disc arthroplasty. The facet joint forces were larger for the Prestige LP® disc, particularly during extension. The lowest values in disc height and fluid exchange were observed in the Bryan® artificial disc arthroplasty models.

Conclusion

Biomechanical analyses revealed that ACDF poses the highest potential risk for adjacent disc degeneration. The artificial discs investigated here (Prestige LP® and Bryan®) not only preserved motion at the instrumented level, but also sustained the pre-op ROM and decreased the intradiscal pressure (IDP) and facet joint forces (FJFs) at adjacent levels, particularly during flexion/extension. The Bryan® artificial disc demonstrated the most efficacy in maintaining the natural poroelastic characteristics of adjacent discs.

The translational potential of this article

This study provided a technique for clinicians to use quantitative data towards subject-specific evaluation to comparatively evaluate the impact of ACDF and disc arthroplasty using two types of artificial discs on the biomechanics of the cervical spine. It confirms differences in the poroelastic characteristics of adjacent discs for different fixation techniques, and reveals the advantage of artificial discs with a flexible core for decreasing the risk of ASD.

Immuno-Modulatory Effects of Intervertebral Disc Cells

Low back pain is a highly prevalent, chronic, and costly medical condition predominantly triggered by intervertebral disc degeneration (IDD). IDD is often caused by structural and biochemical changes in intervertebral discs (IVD) that prompt a pathologic shift from an anabolic to catabolic state, affecting extracellular matrix (ECM) production, enzyme generation, cytokine and chemokine production, neurotrophic and angiogenic factor production. The IVD is an immune-privileged organ. However, during degeneration immune cells and inflammatory factors can infiltrate through defects in the cartilage endplate and annulus fibrosus fissures, further accelerating the catabolic environment. Remarkably, though, catabolic ECM disruption also occurs in the absence of immune cell infiltration, largely due to native disc cell production of catabolic enzymes and cytokines. An unbalanced metabolism could be induced by many different factors, including a harsh microenvironment, biomechanical cues, genetics, and infection. The complex, multifactorial nature of IDD brings the challenge of identifying key factors which initiate the degenerative cascade, eventually leading to back pain. These factors are often investigated through methods including animal models, 3D cell culture, bioreactors, and computational models. However, the crosstalk between the IVD, immune system, and shifted metabolism is frequently misconstrued, often with the assumption that the presence of cytokines and chemokines is synonymous to inflammation or an immune response, which is not true for the intact disc. Therefore, this review will tackle immunomodulatory and IVD cell roles in IDD, clarifying the differences between cellular involvements and implications for therapeutic development and assessing models used to explore inflammatory or catabolic IVD environments.

From Mechanobiology to Mechanical Repair Strategies: A Bibliometric Analysis of Biomechanical Studies of Intervertebral Discs

Neck pain and low back pain are major challenges in public health, and intervertebral disc (IVD) biomechanics is an important multidisciplinary field. To date, no bibliometric literature review of the relevant literature has been performed, so we explored the emerging trends, landmark studies, and major contributors to IVD biomechanics research. We searched the Web of Science core collection (1900–2022) using keywords mainly composed of “biomechanics” and “intervertebral disc” to conduct a bibliometric analysis of original papers and their references, focusing on citations, authors, journals, and countries/regions. A co-citation analysis and clustering of the references were also completed. A total of 3189 records met the inclusion criteria. In the co-citation network, cluster #0, labeled as “annulus fibrosus tissue engineering”, and cluster #1, labeled as “micromechanical environment”, were the biggest clusters. References by MacLean et al and Holzapfel et al were positioned exactly between them and had high betweenness centrality. There existed a research topic evolution between mechanobiology and mechanical repair strategies of IVDs, and the latter had been identified as an emerging trend in IVD biomechanics. Numerous landmark studies had contributed to several fields, including mechanical testing of normal and pathological IVDs, mechanical evaluation of new repair strategies and development of finite element model. Adams MA was the author most cited by IVD biomechanics papers. Spine, the European Spine Journal, and the Journal of Biomechanics were the three journals where the most original articles and their references have been published. The United States has contributed most to the literature (n = 1277 papers); however, the research output of China is increasing. In conclusion, the present study suggests that IVD repair is an emerging trend in IVD biomechanics.

Comparative biomechanical analysis of rigid vs. flexible fixation devices for the lumbar spine: A geometrically patient-specific poroelastic finite element study

BACKGROUND AND OBJECTIVE

Lumbar spinal stenosis (LSS), or the narrowing of the spinal canal, continues to be the leading preoperative diagnosis for adults older than 65 years who undergo spine surgery. Although the treatment of LSS depends on its severity, the optimal surgical technique towards decreasing the risk of adjacent segment disease (ASD) remains elusive. This study aimed to comparatively analyze spinal biomechanics with rigid and flexible fixation devices (i.e., rigid and dynamic posterolateral fusion (PLF) and interspinous process (ISP) devices) during daily activities.

METHODS

Using a validated parametric poroelastic finite element modeling approach, 8 subject-specific pre-operative models were developed, and their validity was evaluated. Parametric FE models of the lumbar spines were then regenerated based on post-operation images for (A) rigid PLF (B) dynamic PLF (C) rigid ISP device (Coflex) and (D) flexible ISP device (DIAM) at L4-L5 level. Biomechanical responses for instrumented and adjacent intervertebral discs (IVDs) were analyzed and compared subject to static and cyclic loading.

RESULTS

The preoperative models were well comparable with previous works in literature. The postoperative results for the PLF and Coflex rigid systems, demonstrated greater ROM; higher values of stress and strain in the AF region; and increased disc height and fluid loss at the adjacent levels, as compared with the pre-op models and the post-op results of the flexible systems (i.e., dynamic PLF and DIAM). The calculated forces on the facet joint were of smaller magnitude for the ISP devices as compared to the PLF, particularly during extension.

CONCLUSIONS

This study demonstrates that the dynamic PLF construct and DIAM implants could be effective to maintain the natural poroelastic characteristics of adjacent IVDs, which could be beneficial for enhancing long-term clinical outcomes. FEM provides clinicians with an invaluable patient-specific quantitative tool for informed surgical planning and discerning follow-up management.

Influence of structural and material property uncertainties on biomechanics of intervertebral discs - Implications for disc tissue engineering

This study investigated how variations of structural and material properties of human intervertebral discs (IVDs) affect the biomechanical responses of the IVDs under simulated physiological loading conditions using a stochastic finite element (SFE) model. An SFE method, which combined an anatomic FE model of human lumbar L3-4 segment and probabilistic analysis of its structural and material properties, was used to generate a dataset of 500 random disc samples with varying structural and material properties. The sensitivity of the biomechanical responses, including intervertebral displacements/rotations, intradiscal pressures (IDP), fiber stresses and matrix strains of annulus fibrosus (AF), were systematically quantified under various physiological loading conditions, including a 500N compression and 7.5Nm moments in the 3 primary rotations. Significant variations of the IDPs, IVD displacements/rotations, and stress/strain distributions were found using the dataset of 500 ramdom disc samples. Under all the loading conditions, the IDPs were positively correlated with the Poisson's ratio of the NP (r = 0.46 to 0.75, p = 0.004-0.001) and negatively with the Young's modulus of the annulus matrix (r = -0.48 to -0.65, p = 0.003-0.001). The primary intervertebral rotations were significantly affected by the Young's modulus of the annulus matrix (r = -0.44 to -0.71, p = 0.001-0.032) and the orientations of the annular fibers (r = -0.45 to -0.69, p = 0.001-0.029). The heterogeneity of structures and material properties of the IVD had distinct effects on the biomechanical performances of the IVD. These data could help improve our understanding of the intrinsic biomechanics of the IVD and provide references for optimal design of tissue engineered discs by controlling structural and material properties of the disc components.

Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

Penguin Suit and Fetal Position Finite Element Model to Prevent Low Back Pain in Spaceflight

BACKGROUND: This study aimed to investigate the biomechanical effects of different interventions on astronauts lumbar intervertebral discs in a microgravity environment during spaceflight and in a gravity environment when the astronaut returns.METHODS: A finite element model of the L4L5 lumbar segment was developed with eight loading schemes representing different interventions. The loading schemes included no intervention, wearing a penguin suit, sleeping in a fetal position, wearing a penguin suit combined with sleeping in the fetal position, reclining for 4 or 16 h/d, and maintaining upright posture for 4 or 16 h/d.RESULTS: Without intervention, the microgravity environment led to increased central pore pressure, radial displacement, and water content in the lumbar intervertebral disc. Wearing a penguin suit combined with sleeping in the fetal position can reduce disc pore pressure, axial stress, radial displacement, and water content to 0.156 MPa, 11.50 kPa, 0.538 mm, and 1.390%, respectively. When astronauts return to the gravity environment, staying upright for 4 h can reduce the pore pressure, axial stress, radial displacement, and water content of the intervertebral disc to 0.222 MPa, 10.72 kPa, 0.373 mm, and 0.219%, respectively.CONCLUSION: This study showed that wearing a penguin suit and sleeping in the fetal position both have the potential to protect the lumbar intervertebral disc from the negative effects caused by microgravity. Remaining in the upright posture for 4 h per day may help squeeze out the water in the intervertebral disc safely when astronauts return to the gravity environment.Zhang S, Wang K, Zhu R, Jiang C, Niu W. Penguin suit and fetal position finite element model to prevent low back pain in spaceflight. Aerosp Med Hum Perform. 2021; 92(5):312318.

The importance of intervertebral disc material model on the prediction of mechanical function of the cervical spine

BACKGROUND

Linear elastic, hyperelastic, and multiphasic material constitutive models are frequently used for spinal intervertebral disc simulations. While the characteristics of each model are known, their effect on spine mechanical response requires a careful investigation. The use of advanced material models may not be applicable when material constants are not available, model convergence is unlikely, and computational time is a concern. On the other hand, poor estimations of tissue's mechanical response are likely if the spine model is oversimplified. In this study, discrepancies in load response introduced by material models will be investigated.

METHODS

Three fiber-reinforced C2-C3 disc models were developed with linear elastic, hyperelastic, and biphasic behaviors. Three different loading modes were investigated: compression, flexion and extension in quasi-static and dynamic conditions. The deformed disc height, disc fluid pressure, range of motion, and stresses were compared.

RESULTS

Results indicated that the intervertebral disc material model has a strong effect on load-sharing and disc height change when compression and flexion were applied. The predicted mechanical response of three models under extension had less discrepancy than its counterparts under flexion and compression. The fluid-solid interaction showed more relevance in dynamic than quasi-static loading conditions. The fiber-reinforced linear elastic and hyperelastic material models underestimated the load-sharing of the intervertebral disc annular collagen fibers.

CONCLUSION

This study confirmed the central role of the disc fluid pressure in spinal load-sharing and highlighted loading conditions where linear elastic and hyperelastic models predicted energy distribution different than that of the biphasic model.

Biomechanical Investigation Between Rigid and Semirigid Posterolateral Fixation During Daily Activities: Geometrically Parametric Poroelastic Finite Element Analyses

While spinal fusion using rigid rods remains the gold standard treatment modality for various lumbar degenerative conditions, its adverse effects, including accelerated adjacent segment disease (ASD), are well known. In order to better understand the performance of semirigid constructs using polyetheretherketone (PEEK) in fixation surgeries, the objective of this study was to analyze the biomechanical performance of PEEK versus Ti rods using a geometrically patient-specific poroelastic finite element (FE) analyses. Ten subject-specific preoperative models were developed, and the validity of the models was evaluated with previous studies. Furthermore, FE models of those lumbar spines were regenerated based on postoperation images for posterolateral fixation at the L4–L5 level. Biomechanical responses for instrumented and adjacent intervertebral discs (IVDs) were analyzed and compared subjected to static and cyclic loading. The preoperative model results were well comparable with previous FE studies. The PEEK construct demonstrated a slightly increased range of motion (ROM) at the instrumented level, but decreased ROM at adjacent levels, as compared with the Ti. However, no significant changes were detected during axial rotation. During cyclic loading, disc height loss, fluid loss, axial stress, and collagen fiber strain in the adjacent IVDs were higher for the Ti construct when compared with the intact and PEEK models. Increased ROM, experienced stress in AF, and fiber strain at adjacent levels were observed for the Ti rod group compared with the intact and PEEK rod group, which can indicate the risk of ASD for rigid fixation. Similar to the aforementioned pattern, disc height loss and fluid loss were significantly higher at adjacent levels in the Ti rod group after cycling loading which alter the fluid–solid interaction of the adjacent IVDs. This phenomenon debilitates the damping quality, which results in disc disability in absorbing stress. Such finding may suggest the advantage of using a semirigid fixation system to decrease the chance of ASD.

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.

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.

The response surface method-genetic algorithm for identification of the lumbar intervertebral disc material parameters

Long-term compressive load on the lumbar intervertebral disc (IVD) might lead to lumbar IVD herniation. Exploring the material parameters of normal and degenerative enucleated IVDs is the basis for studying their mechanical behavior. According to the inverse analysis principle of the parameter estimation, an optimization method was proposed to identify the parameters of the porous material of the lumbar IVD based on finite element inverse analysis. The poroelastic finite element models were established in line with the compression creep experiment. The material parameters were combined by Box-Behnken design (BBD), and the response surface (RS) models were constructed using a quadratic polynomial with cross terms and optimized by genetic algorithm (GA). The results showed that the simulation result of the best material parameter combination had a good agreement with the experiment. Compared with the normal lumbar IVD, the elastic modulus and permeability decreased, and Poisson's ratio increased for the enucleated disk, resulting in a significant difference in mechanical properties. The algorithm used in this study can reduce the parameter identification error compared with only the RS method, and decrease the number of finite element simulations compared with only the GA.

Is there any advantage of using stand-alone cages? A numerical approach

Background

Segment fusion using interbody cages supplemented with pedicle screw fixation is the most common surgery for the treatment of low back pain. However, there is still much controversy regarding the use of cages in a stand-alone fashion. The goal of this work is to numerically compare the influence that each surgery has on lumbar biomechanics.

Methods

A non-linear FE model of the whole lumbar spine was developed to compare between two types of cages (OLYS and NEOLIF) with and without supplementary fixation. The motion of the whole spine was analysed and the biomechanical environment of the adjacent segments to the operated one was studied. Moreover, the risk of subsidence of the cages was qualitatively evaluated.

Results

A great ROM reduction occurred when supplementary fixation was used. This stiffening increased the stresses at the adjacent levels. It might be hypothesised that the overloading of these segments could be related with the clinically observed adjacent disc degeneration. Meanwhile, the stand-alone cages allowed for a wider movement, and therefore, the influence of the surgery on adjacent discs was much lower. Regarding the risk of subsidence, the contact pressure magnitude was similar for both intervertebral cage designs and near the value of the maximum tolerable pressure of the endplates.

Conclusions

A minimally invasive posterior insertion of an intervertebral cage (OLYS or NEOLIF) was compared using a stand-alone design or adding supplementary fixation. The outcomes of these two techniques were compared, and although stand-alone cage may diminish the risk of disease progression to the adjacent discs, the spinal movement in this case could compromise the vertebral fusion and might present a higher risk of cage subsidence.

Electronic supplementary material

The online version of this article (10.1186/s12938-019-0684-8) contains supplementary material, which is available to authorized users.

Presentation of an Approach on Determination of the Natural Frequency of Human Lumbar Spine Using Dynamic Finite Element Analysis

Occurring resonance may negatively affect the health of the human lumbar spine. Hence, vibration generated in working and living environments should be optimized to avoid resonance when identifying the natural frequency of the human lumbar spine. The range of the natural frequency of the human lumbar spine has been investigated, but its specific numerical value has not been determined yet. This study aimed at presenting an approach based on resonance for predicting the specific numerical value of the natural frequency of the human lumbar spine. The changes in the numerical fluctuation amplitudes and the cycles of lumbar mechanical parameters during resonance are greater than those during nonresonant vibration. Given that the range of the natural frequency has been identified, vibrations at different excitation frequencies within this range can be applied in a human lumbar finite element model for dynamic finite element analysis. When the excitation frequency is close to the natural frequency, resonance occurs, causing great changes in the numerical fluctuation amplitudes and the cycles of lumbar mechanical parameters. Therefore, the natural frequency of the lumbar finite element model could be back-calculated. Results showed that the natural frequency of the established model was 3.5 Hz. Meanwhile, the closer the excitation frequency was to the natural frequency, the greater the changes in the numerical fluctuation amplitudes and cycles in the parameters would be. This study presented an approach for predicting the specific numerical value of the natural frequency of the human lumbar spine. Identifying the natural frequency assists in finding preventive measures for lumbar injury caused by vibration and in designing the vibration source in working and living environments to avoid approximating to the natural frequency of the human lumbar spine.

Finite Element Investigation of the Effects of the Low-Frequency Vibration Generated by Vehicle Driving on the Human Lumbar Mechanical Properties

Long-term exposure to low-frequency vibration generated by vehicle driving impairs human lumbar spine health. However, few studies have investigated how low-frequency vibration affects human lumbar mechanical properties. This study established a poroelastic finite element model of human lumbar spinal segments L2–L3 to perform time-dependent vibrational simulation analysis and investigated the effects of different vibrational frequencies generated by normal vehicle driving on the lumbar mechanical properties in one hour. Analysis results showed that vibrational load caused more injury to lumbar health than static load, and vibration at the resonant frequency generated the most serious injury. The axial effective stress and the radial displacement in the intervertebral disc, as well as the fluid loss in the nucleus pulposus, increased, whereas the pore pressure in the nucleus pulposus decreased with increased vibrational frequency under the same vibrational time, which may aggravate the injury degree of human lumbar spine. Therefore, long-term driving on a well-paved road also induces negative effects on human lumbar spine health. When driving on a nonpaved road or operating engineering machinery under poor navigating condition, the auto seat transmits relatively high vibrational frequency, which is highly detrimental to the lumbar spine health of a driver.

COMPUTATION OF THE DYNAMIC COMPRESSION EFFECTS IN SPINE DISCS USING INTEGRAL METHODS

The computational modeling using integral methods of dynamic loading and its effects on the nutrients transport in spine discs is addressed in this work. The numerical simulation and analysis was carried out using the Boundary Element Method (BEM) and a 3D model (axisymmetric) of the disc. The boundary model was discretized using linear interpolated elements and a multi-region approach. Concentration and production of three nutrients as lactate, oxygen and glucose were obtained. The maximum lactate concentration was observed very close to the interface between the nucleus and the inner annulus. A relatively simple model discretized with 130 boundary elements yielded very similar results to these coming from more complex FEM-based models. The numerical efforts in the domain and boundary discretizations were optimized using the BEM. Our results are in good agreement with those obtained using with finite element-based models. As expected, the dynamic loading increased the oxygen–glucose consumption and the lactate production, thus leading to a poor oxygen–glucose concentration at the nucleus of the disc. All of that is a favorable environment for a disc degeneration mechanism to be developed.

Annulus fibrosus functional extrafibrillar and fibrous mechanical behaviour: experimental and computational characterisation

The development of current surgical treatments for intervertebral disc damage could benefit from virtual environment accounting for population variations. For such models to be reliable, a relevant description of the mechanical properties of the different tissues and their role in the functional mechanics of the disc is of major importance. The aims of this work were first to assess the physiological hoop strain in the annulus fibrosus in fresh conditions (n = 5) in order to extract a functional behaviour of the extrafibrillar matrix; then to reverse-engineer the annulus fibrosus fibrillar behaviour (n = 6). This was achieved by performing both direct and global controlled calibration of material parameters, accounting for the whole process of experimental design and in silico model methodology. Direct-controlled models are specimen-specific models representing controlled experimental conditions that can be replicated and directly comparing measurements. Validation was performed on another six specimens and a sensitivity study was performed. Hoop strains were measured as 17 ± 3% after 10 min relaxation and 21 ± 4% after 20-25 min relaxation, with no significant difference between the two measurements. The extrafibrillar matrix functional moduli were measured as 1.5 ± 0.7 MPa. Fibre-related material parameters showed large variability, with a variance above 0.28. Direct-controlled calibration and validation provides confidence that the model development methodology can capture the measurable variation within the population of tested specimens.

A stabilized finite element method for finite-strain three-field poroelasticity

We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.

Effect of Hydration on Healthy Intervertebral Disk Mechanical Stiffness

The intervertebral disk has an excellent swelling capacity to absorb water, which is thought to be largely due to the high proteoglycan composition. Injury, aging, degeneration, and diurnal loading are all noted by a significant decrease in water content and tissue hydration. The objective of this study was to evaluate the effect of hydration, through osmotic loading, on tissue swelling and compressive stiffness of healthy intervertebral disks. The wet weight of nucleus pulposus (NP) and annulus fibrosus (AF) explants following swelling was 50% or greater, demonstrating significant ability to absorb water under all osmotic loading conditions (0.015 M-3.0 M phosphate buffered saline (PBS)). Estimated NP residual strains, calculated from the swelling ratio, were approximately 1.5 × greater than AF residual strains. Compressive stiffness increased with hyperosmotic loading, which is thought to be due to material compaction from osmotic-loading and the nonlinear mechanical behavior. Importantly, this study demonstrated that residual strains and material properties are greatly dependent on osmotic loading. The findings of this study support the notion that swelling properties from osmotic loading will be important for accurately describing the effect of degeneration and injury on disk mechanics. Furthermore, the tissue swelling will be an important consideration for developing biological repair strategies aimed at restoring mechanical behavior toward a healthy disk.

A database of lumbar spinal mechanical behavior for validation of spinal analytical models

Data from two experimental studies with eight specimens each of spinal motion segments and/or intervertebral discs are presented in a form that can be used for comparison with finite element model predictions. The data include the effect of compressive preload (0, 250 and 500N) with quasistatic cyclic loading (0.0115Hz) and the effect of loading frequency (1, 0.1, 0.01 and 0.001Hz) with a physiological compressive preload (mean 642N). Specimens were tested with displacements in each of six degrees of freedom (three translations and three rotations) about defined anatomical axes. The three forces and three moments in the corresponding axis system were recorded during each test. Linearized stiffness matrices were calculated that could be used in multi-segmental biomechanical models of the spine and these matrices were analyzed to determine whether off-diagonal terms and symmetry assumptions should be included. These databases of lumbar spinal mechanical behavior under physiological conditions quantify behaviors that should be present in finite element model simulations. The addition of more specimens to identify sources of variability associated with physical dimensions, degeneration, and other variables would be beneficial. Supplementary data provide the recorded data and Matlab® codes for reading files. Linearized stiffness matrices derived from the tests at different preloads revealed few significant unexpected off-diagonal terms and little evidence of significant matrix asymmetry.

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

A computational spinal motion segment model incorporating a matrix composition-based model of the intervertebral disc

The extracellular matrix of the intervertebral disc is subjected to changes with age and degeneration, affecting the biomechanical behaviour of the spine. In this study, a finite element model of a generic spinal motion segment that links spinal biomechanics and intervertebral disc biochemical composition was developed. The local mechanical properties of the tissue were described by the local matrix composition, i.e. fixed charge density, amount of water and collagen and their organisation. The constitutive properties of the biochemical constituents were determined by fitting numerical responses to experimental measurements derived from literature. This general multi-scale model of the disc provides the possibility to evaluate the relation between local disc biochemical composition and spinal biomechanics.

Effects of resting modes on human lumbar spines with different levels of degenerated intervertebral discs: a finite element investigation

BACKGROUND

The negative effect of long-term working load on lumbar is widely known. However, insertion of different resting modes on long-term working load, and its effects on the lumbar spine is rarely studied. The purpose of this study was to investigate the biomechanical responses of lumbar spine with different levels of degenerated intervertebral discs under different working-resting modes.

METHODS

Four poroelastic finite element models of lumbar spinal segments L2-L3 with different grades of disc degeneration were developed. Four different loading conditions represented four different resting frequencies, namely, no rest, one-time long rest, three-time moderate rests, and five-time short rests, on the condition that the total resting time was the same except in the no rest mode. Loading amplitudes of diurnal activities included 100 N, 300 N, and 500 N.

RESULTS

With increasing resting frequency, the axial effective stress and fluid loss decreased, whereas the pore pressure and radial displacement increased. Under different resting frequencies, the changing rate of each biomechanical parameter was different.

CONCLUSIONS

Under a situation of fixed total resting time, high resting frequency was advisable. If sufficient resting frequency was unavailable for healthy people as well as patients with mildly and moderately degenerated intervertebral discs, they could similarly benefit from relatively less resting frequencies. However, one-time rest will not be useful in cases where intervertebral discs were seriously degenerated. Reasonable working-resting modes for different degrees of disc degeneration, which could assist patients achieve a better restoration, were provided in this study.

On the Use of Biaxial Properties in Modeling Annulus as a Holzapfel-Gasser-Ogden Material

Besides the biology, stresses and strains within the tissue greatly influence the location of damage initiation and mode of failure in an intervertebral disk. Finite element models of a functional spinal unit (FSU) that incorporate reasonably accurate geometry and appropriate material properties are suitable to investigate such issues. Different material models and techniques have been used to model the anisotropic annulus fibrosus, but the abilities of these models to predict damage initiation in the annulus and to explain clinically observed phenomena are unclear. In this study, a hyperelastic anisotropic material model for the annulus with two different sets of material constants, experimentally determined using uniaxial and biaxial loading conditions, were incorporated in a 3D finite element model of a ligamentous FSU. The purpose of the study was to highlight the biomechanical differences (e.g., intradiscal pressure, motion, forces, stresses, strains, etc.) due to the dissimilarity between the two sets of material properties (uniaxial and biaxial). Based on the analyses, the biaxial constants simulations resulted in better agreements with the in vitro and in vivo data, and thus are more suitable for future damage analysis and failure prediction of the annulus under complex multiaxial loading conditions.

Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Vertebral compression fractures are becoming increasingly common. Patient-specific nonlinear finite element (FE) models have shown promise in predicting yield strength and damage pattern but have not been experimentally validated for clinically relevant vertebral fractures, which involve loading through intervertebral discs with varying degrees of degeneration up to large compressive strains. Therefore, stepwise axial compression was applied in vitro on segments and performed in silico on their FE equivalents using a nonlocal damage-plastic model including densification at large compression for bone and a time-independent hyperelastic model for the disc. The ability of the nonlinear FE models to predict the failure pattern in large compression was evaluated for three boundary conditions: healthy and degenerated intervertebral discs and embedded endplates. Bone compaction and fracture patterns were predicted using the local volume change as an indicator and the best correspondence was obtained for the healthy intervertebral discs. These preliminary results show that nonlinear finite element models enable prediction of bone localisation and compaction. To the best of our knowledge, this is the first study to predict the collapse of osteoporotic vertebral bodies up to large compression using realistic loading via the intervertebral discs.

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.

Effect of Degeneration on Fluid-Solid Interaction within Intervertebral Disk Under Cyclic Loading - A Meta-Model Analysis of Finite Element Simulations

The risk of low back pain resulted from cyclic loadings is greater than that resulted from prolonged static postures. Disk degeneration results in degradation of disk solid structures and decrease of water contents, which is caused by activation of matrix digestive enzymes. The mechanical responses resulted from internal solid-fluid interactions of degenerative disks to cyclic loadings are not well studied yet. The fluid-solid interactions in disks can be evaluated by mathematical models, especially the poroelastic finite element (FE) models. We developed a robust disk poroelastic FE model to analyze the effect of degeneration on solid-fluid interactions within disk subjected to cyclic loadings at different loading frequencies. A backward analysis combined with in vitro experiments was used to find the elastic modulus and hydraulic permeability of intact and enzyme-induced degenerated porcine disks. The results showed that the averaged peak-to-peak disk deformations during the in vitro cyclic tests were well fitted with limited FE simulations and a quadratic response surface regression for both disk groups. The results showed that higher loading frequency increased the intradiscal pressure, decreased the total fluid loss, and slightly increased the maximum axial stress within solid matrix. Enzyme-induced degeneration decreased the intradiscal pressure and total fluid loss, and barely changed the maximum axial stress within solid matrix. The increase of intradiscal pressure and total fluid loss with loading frequency was less sensitive after the frequency elevated to 0.1 Hz for the enzyme-induced degenerated disk. Based on this study, it is found that enzyme-induced degeneration decreases energy attenuation capability of disk, but less change the strength of disk.

On the relative relevance of subject-specific geometries and degeneration-specific mechanical properties for the study of cell death in human intervertebral disk models

Capturing patient- or condition-specific intervertebral disk (IVD) properties in finite element models is outmost important in order to explore how biomechanical and biophysical processes may interact in spine diseases. However, disk degenerative changes are often modeled through equations similar to those employed for healthy organs, which might not be valid. As for the simulated effects of degenerative changes, they likely depend on specific disk geometries. Accordingly, we explored the ability of continuum tissue models to simulate disk degenerative changes. We further used the results in order to assess the interplay between these simulated changes and particular IVD morphologies, in relation to disk cell nutrition, a potentially important factor in disk tissue regulation. A protocol to derive patient-specific computational models from clinical images was applied to different spine specimens. In vitro, IVD creep tests were used to optimize poro-hyperelastic input material parameters in these models, in function of the IVD degeneration grade. The use of condition-specific tissue model parameters in the specimen-specific geometrical models was validated against independent kinematic measurements in vitro. Then, models were coupled to a transport-cell viability model in order to assess the respective effects of tissue degeneration and disk geometry on cell viability. While classic disk poro-mechanical models failed in representing known degenerative changes, additional simulation of tissue damage allowed model validation and gave degeneration-dependent material properties related to osmotic pressure and water loss, and to increased fibrosis. Surprisingly, nutrition-induced cell death was independent of the grade-dependent material properties, but was favored by increased diffusion distances in large IVDs. Our results suggest that in situ geometrical screening of IVD morphology might help to anticipate particular mechanisms of disk degeneration.