On the collagen criss-cross angles in the annuli fibrosi of lumbar spine finite element models

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.

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.

Nucleus high intensity in the T2-weighted MRI is a potential predictor of annulus tear in cervical injured patients: a case comparative study

BACKGROUND

Segmental fusion operations assume paramount significance for individuals afflicted by full layers of annulus tears as they avert the perils of rapid disc degeneration and segmental instability. Structures with high signal intensity in the T2-weighted MRI can predict potential damage to the injured segment. Since local structures are shortly related biomechanically, this may be an effective predictor for annulus tears.

METHODS

A retrospective analysis of the clinical data of 57 patients afflicted by cervical injuries and subjected to single-segment ACDF has been performed in this study. The surgeon performed intraoperative exploration to assess the integration status of the annulus. The signal intensity of the prevertebral space, nucleus, and injured vertebral bodies were judged in the T2-weighted imaging data. Regression analyses identified independent predictors for annulus tears, and the area under the receiver operating characteristic curve (AUC) was computed to evaluate the predictive performance of potential independent predictors.

RESULTS

The occurrence of nucleus high intensity was significantly higher among individuals with annulus tears, and the nucleus high intensity was deemed an independent predictor for determining the presence of intraoperative visible annulus tears in patients with cervical injuries. AUC for nucleus high intensity was calculated as 0.717, with a corresponding p-value less than 0.05.

CONCLUSIONS

In the realm of diagnosing annulus tears in injured cervical patients, nucleus high intensity in the T2-weighted MRI emerges as a promising predictive factor. Notably, this applies specifically to patients devoid of fracture and visible annulus tears in their MRI scans. Such positive outcomes should be regarded as prospective indications for ACDF.

Evaluation of Chêneau brace in the treatment of thoracic and lumbar adolescent idiopathic scoliosis with apical vertebral rotation

BACKGROUND

Adolescent idiopathic scoliosis (AIS) is a common structural disorder of the spine in adolescents, often associated with structural deformities in both coronal and axial positions. Apical vertex rotation (AVR) is one of the main indicators of axial deformity in patients with scoliosis. Currently, there are few studies on the impact of AVR in the treatment of AIS.

OBJECTIVE

This study examined the influence of different AVR on AIS after brace treatment.

METHODS

Data were collected from 106 AIS participants aged 11-16 years from the orthopedic outpatient clinic of the Second Hospital of Lanzhou University. Two orthopaedic professionals measured the Cobb angle, AVR and spinal mid-line offset before and after brace treatment, and descriptive and linear correlation analyses were used to determine the correlation between AVR and AIS measured parameters.

RESULTS

(1) In AIS volunteers with the same AVR, the treatment effect of AIS with lumbar predominant curvature was higher than that of AIS with thoracic predominant curvature. The treatment effect tended to decrease with increasing AVR. (2) Spinal mid-line deviation was associated with AVR. For patients with AIS with I and II degrees of AVR, the treatment effect of spinal mid-line offset after bracing is better. For AIS patients with AVR III degrees and above, the degree of correction of spinal mid-line offset decreases with the continuous correction of Cobb angle.

CONCLUSIONS

The efficacy of AIS was found to be related to the severity of AVR. The efficacy of AIS with predominantly lumbar curvature was significantly higher than that of AIS with predominantly thoracic curvature. The efficacy of treatment of mid-line spinal deviation also decreased with increasing AVR.

One step further in biomechanical models in palaeontology: a nonlinear finite element analysis review

Finite element analysis (FEA) is no longer a new technique in the fields of palaeontology, anthropology, and evolutionary biology. It is nowadays a well-established technique within the virtual functional-morphology toolkit. However, almost all the works published in these fields have only applied the most basic FEA tools i.e., linear materials in static structural problems. Linear and static approximations are commonly used because they are computationally less expensive, and the error associated with these assumptions can be accepted. Nonetheless, nonlinearities are natural to be used in biomechanical models especially when modelling soft tissues, establish contacts between separated bones or the inclusion of buckling results. The aim of this review is to, firstly, highlight the usefulness of non-linearities and secondly, showcase these FEA tool to researchers that work in functional morphology and biomechanics, as non-linearities can improve their FEA models by widening the possible applications and topics that currently are not used in palaeontology and anthropology.

Radial trend in murine annulus fibrosus fiber orientation is best explained by vertebral growth

PURPOSE

The intervertebral disc (IVD) annulus fibrosus (AF) is composed of concentric lamellae with alternating right- and left-handed helically oriented collagen fiber bundles. This arrangement results in anisotropic material properties, which depend on local fiber orientations. Prior measurements of fiber inclination angles in human lumbar and bovine caudal IVDs found a significantly higher inclination angle in the inner AF than outer, though it is currently unknown if this pattern is conserved in smaller mammalian species. Additionally, the physical mechanism behind this pattern remains un-determined.

METHODS

In this study, AF fiber angles were measured histologically in murine caudal IVDs and compared to previously published values from bovine caudal IVDs. Fiber angles were also predicted using three theoretical models, including two based on adaptation to internal swelling pressure and one based on vertebral body growth.

RESULTS

Fiber angle was found to significantly decrease from 49.5 ± 3.8° in the inner AF to 34.5 ± 6.6° in the outer AF. While steeper than in bovine discs at all locations, the trend with radial position was comparable between species. This trend was best fit by growth-based model and opposite of that predicted by the pressure vessel models.

CONCLUSION

Trends in AF fiber orientation are conserved between mammalian species. Modeling results suggest that the AF tissue microstructure is more likely to be driven by adjacent vertebral body growth than adapted for optimal mechanical performance.

Calibration and validation of a novel hybrid model of the lumbosacral spine in ArtiSynth-The passive structures

In computational biomechanics, two separate types of models have been used predominantly to enhance the understanding of the mechanisms of action of the lumbosacral spine (LSS): Finite element (FE) and musculoskeletal multibody (MB) models. To combine advantages of both models, hybrid FE-MB models are an increasingly used alternative. The aim of this paper is to develop, calibrate, and validate a novel passive hybrid FE-MB open-access simulation model of a ligamentous LSS using ArtiSynth. Based on anatomical data from the Male Visible Human Project, the LSS model is constructed from the L1-S1 rigid vertebrae interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, and facet joints. A mesh convergence study, sensitivity analyses, and systematic calibration were conducted with the hybrid functional spinal unit (FSU) L4/5. The predicted mechanical responses of the FSU L4/5, the lumbar spine (L1-L5), and the LSS were validated against literature data from in vivo and in vitro measurements and in silico models. Spinal mechanical responses considered when loaded with pure moments and combined loading modes were total and intervertebral range of motions, instantaneous axes and centers of rotation, facet joint contact forces, intradiscal pressures, disc bulges, and stiffnesses. Undesirable correlations with the FE mesh were minimized, the number of crisscrossed collagen fiber rings was reduced to five, and the individual influences of specific anatomical structures were adjusted to in vitro range of motions. Including intervertebral motion couplings for axial rotation and nonlinear stiffening under increasing axial compression, the predicted kinematic and structural mechanics responses were consistent with the comparative data. The results demonstrate that the hybrid simulation model is robust and efficient in reproducing valid mechanical responses to provide a starting point for upcoming optimizations and extensions, such as with active skeletal muscles.

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.

Effect of changes in the lumbar posture in lifting on trunk muscle and spinal loads: A combined in vivo, musculoskeletal, and finite element model study

Irrespective of the lifting technique (squat or stoop), the lumbar spine posture (more kyphotic versus more lordotic) adopted during lifting activities is an important parameter affecting the active-passive spinal load distribution. The advantages in either posture while lifting remains, however, a matter of debate. To comprehensively investigate the role on the trunk biomechanics of changes in the lumbar posture (lordotic, free or kyphotic) during forward trunk flexion, validated musculoskeletal and finite element models, driven by in vivo kinematics data, were used to estimate detailed internal tissue stresses-forces in and load-sharing among various joint active-passive tissues. Findings indicated that the lordotic posture, as compared to the kyphotic one, resulted in marked increases in back global muscle activities (~14-19%), overall segmental compression (~7.5-46.1%) and shear (~5.4-47.5%) forces, and L5-S1 facet joint forces (by up to 80 N). At the L5-S1 level, the lordotic lumbar posture caused considerable decreases in the moment resisted by passive structures (spine and musculature, ~14-27%), negligible reductions in the maximum disc fiber strains (by ~0.4-4.7%) and small increases in intradiscal pressure (~1.8-3.4%). Collectively and with due consideration of the risk of fatigue and viscoelastic creep especially under repetitive lifts, current results support a free posture (in between the extreme kyphotic and lordotic postures) with moderate contributions from both active and passive structures during lifting activities involving trunk forward flexion.

Synchrotron tomography of intervertebral disc deformation quantified by digital volume correlation reveals microstructural influence on strain patterns

The intervertebral disc (IVD) has a complex and multiscale extracellular matrix structure which provides unique mechanical properties to withstand physiological loading. Low back pain has been linked to degeneration of the disc but reparative treatments are not currently available. Characterising the disc's 3D microstructure and its response in a physiologically relevant loading environment is required to improve understanding of degeneration and to develop new reparative treatments. In this study, techniques for imaging the native IVD, measuring internal deformation and mapping volumetric strain were applied to an in situ compressed ex vivo rat lumbar spine segment. Synchrotron X-ray micro-tomography (synchrotron CT) was used to resolve IVD structures at microscale resolution. These image data enabled 3D quantification of collagen bundle orientation and measurement of local displacement in the annulus fibrosus between sequential scans using digital volume correlation (DVC). The volumetric strain mapped from synchrotron CT provided a detailed insight into the micromechanics of native IVD tissue. The DVC findings showed that there was no slipping at lamella boundaries, and local strain patterns were of a similar distribution to the previously reported elastic network with some heterogeneous areas and maximum strain direction aligned with bundle orientation, suggesting bundle stretching and sliding. This method has the potential to bridge the gap between measures of macro-mechanical properties and the local 3D micro-mechanical environment experienced by cells. This is the first evaluation of strain at the micro scale level in the intact IVD and provides a quantitative framework for future IVD degeneration mechanics studies and testing of tissue engineered IVD replacements. STATEMENT OF SIGNIFICANCE: Synchrotron in-line phase contrast X-ray tomography provided the first visualisation of native intact intervertebral disc microstructural deformation in 3D. For two annulus fibrosus volumes of interest, collagen bundle orientation was quantified and local displacement mapped as strain. Direct evidence of microstructural influence on strain patterns could be seen such as no slipping at lamellae boundaries and maximum strain direction aligned with collagen bundle orientation. Although disc elastic structures were not directly observed, the strain patterns had a similar distribution to the previously reported elastic network. This study presents technical advances and is a basis for future X-ray microscopy, structural quantification and digital volume correlation strain analysis of soft tissue.

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

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

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 novel finite element model of the ovine lumbar intervertebral disc with anisotropic hyperelastic material properties

The Ovine spine is an accepted model to investigate the biomechanical behaviour of the human lumbar one. Indeed, the use of animal models for in vitro studies is necessary to investigate the mechanical behaviour of biological tissue, but needs to be reduced for ethical and social reasons. The aim of this study was to create a finite element model of the lumbar intervertebral disc of the sheep that may help to refine the understanding of parallel in vitro experiments and that can be used to predict when mechanical failure occurs. Anisotropic hyperelastic material properties were assigned to the annulus fibrosus and factorial optimization analyses were performed to find out the optimal parameters of the ground substance and of the collagen fibers. For the ground substance of the annulus fibrosus the investigation was based on experimental data taken from the literature, while for the collagen fibers tensile tests on annulus specimens were conducted. Flexibility analysis in flexion-extension, lateral bending and axial rotation were conducted. Different material properties for the anterior, lateral and posterior regions of the annulus were found. The posterior part resulted the stiffest region in compression whereas the anterior one the stiffest region in tension. Since the flexibility outcomes were in a good agreement with the literature data, we considered this model suitable to be used in conjunction with in vitro and in vivo tests to investigate the mechanical behaviour of the ovine lumbar disc.

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.

Moderately Degenerated Human Intervertebral Disks Exhibit a Less Geometrically Specific Collagen Fiber Orientation Distribution

STUDY DESIGN

Collagen fiber orientation analysis in moderately degenerated human cadaveric annulus fibrosus (AF) tissue samples.

OBJECTIVE

Little is known about the changes in tissue architecture during early degeneration of intervertebral disks (IVDs). As collagen organization strongly affects the disk function, the objective of this study was to quantify the AF collagen orientation and its spatial distribution in moderately degenerated IVDs (Pfirrmann grade III).

METHODS

AF tissue samples were dissected from four circumferential (anterior, left and right lateral, and posterior) and two radial (outer and inner) locations. Cryosections were imaged using Second Harmonic Generation microscopy, and the collagen fiber orientations per location were determined utilizing a fiber-tracking image analysis algorithm. Also, the proportionality between the fibers aligned in the primary direction versus other oriented fibers was determined.

RESULTS

Mean collagen fiber angles ranged between 21 and 31 degrees for outer and 15 to 19 degrees for inner AF samples. Mean collagen orientations at circumferential locations were only significantly different from each other at inner anterior and lateral location. Similarly, fiber angles between the outer and inner AF were not significantly different except at the posterior location. Fiber orientation proportionality did not show large variations. Except for a significant difference in outer AF proportionality between posterior and lateral positions, no other differences were observed.

CONCLUSION

The results of this study provide the first quantitative evidence that the collagen fiber orientation of moderately degenerated disks exhibits a spatial rather than homogeneous distribution and typical collagen orientation gradients characterizing healthy IVDs are only partially retained.

Anisotropic Multishell Analytical Modeling of an Intervertebral Disk Subjected to Axial Compression

Studies on intervertebral disk (IVD) response to various loads and postures are essential to understand disk's mechanical functions and to suggest preventive and corrective actions in the workplace. The experimental and finite-element (FE) approaches are well-suited for these studies, but validating their findings is difficult, partly due to the lack of alternative methods. Analytical modeling could allow methodological triangulation and help validation of FE models. This paper presents an analytical method based on thin-shell, beam-on-elastic-foundation and composite materials theories to evaluate the stresses in the anulus fibrosus (AF) of an axisymmetric disk composed of multiple thin lamellae. Large deformations of the soft tissues are accounted for using an iterative method and the anisotropic material properties are derived from a published biaxial experiment. The results are compared to those obtained by FE modeling. The results demonstrate the capability of the analytical model to evaluate the stresses at any location of the simplified AF. It also demonstrates that anisotropy reduces stresses in the lamellae. This novel model is a preliminary step in developing valuable analytical models of IVDs, and represents a distinctive groundwork that is able to sustain future refinements. This paper suggests important features that may be included to improve model realism.

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.

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.

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.

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.

Impact of hip anatomical variations on the cartilage stress: a finite element analysis towards the biomechanical exploration of the factors that may explain primary hip arthritis in morphologically normal subjects

BACKGROUND

Hip arthritis is a pathology linked to hip-cartilage degeneration. Although the etiology of this disease is not well defined, it is known that age is a determinant risk factor. However, hip arthritis in young patients could be largely promoted by biomechanical factors. The objective of this paper is to analyze the impact of some normal anatomical variations on the cartilage stress distributions numerically predicted at the hip joint during walking.

METHODS

A three-dimensional finite element model of the femur and the pelvis with the most relevant axial components of muscle forces was used to simulate normal walking activity. The hip anatomical condition was defined by: neck shaft angle, femoral anteversion angle, and acetabular anteversion angle with a range of 110-130°, 0-20°, and 0-20°, respectively. The direct boundary method was used to simulate the hip contact.

FINDINGS

The hydrostatic stress found at the cartilage and labrum showed that a ±10° variation with respect to the reference brings significant differences between the anatomic models. Acetabular anteversion angle of 0° and femoral anteversion angle of 0° were the most affected anatomical conditions with values of hydrostatic stress in the cartilage near 5MPa under compression.

INTERPRETATION

Cartilage stresses and contact areas were equivalent to the results found in literature and the most critical anatomical regions in terms of tissue loads were in a good accordance with clinical evidence. Altogether, results showed that decreasing femoral or acetabular anteversion angles isolatedly causes a dramatic increase in cartilage loads.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.

Regional annulus fibre orientations used as a tool for the calibration of lumbar intervertebral disc finite element models

The collagen network of the annulus fibrosus largely controls the functional biomechanics of the lumbar intervertebral discs (IVDs). Quantitative anatomical examinations have shown bundle orientation patterns, possibly coming from regional adaptations of the annulus mechanics. This study aimed to show that the regional differences in annulus mechanical behaviour could be reproduced by considering only fibre orientation changes. Using the finite element method, a lumbar annulus was modelled as a poro-hyperelastic material in which fibres were represented by a direction-dependent strain energy density term. Fibre orientations were calibrated to reproduce the annulus tensile behaviours measured for four different regions: posterior outer, anterior outer, posterior inner and anterior inner. The back-calculated fibre angles and regional patterns as well as the global disc behaviour were comparable with anatomical descriptions reported in the literature. It was concluded that annulus fibre variations might be an effective tool to calibrate lumbar spine IVD and segment models.

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

Osmotic phenomena influence the intervertebral disc biomechanics. Their simulation is challenging and can be undertaken at different levels of complexity. Four distinct approaches to simulate the osmotic behaviour of the intervertebral disc (a fixed boundary pore pressure model, a fixed osmotic pressure gradient model in the whole disc or only in the nucleus pulposus, and a swelling model with strain-dependent osmotic pressure) were analysed. Predictions were compared using a 3D poroelastic finite element model of a L4-L5 spinal unit under three different loading conditions: free swelling for 8 h and two daily loading cycles: (i) 200 N compression for 8 h followed by 500 N compression for 16 h; (ii) 500 N for 8 h followed by 1000 N for 16 h. Overall, all swelling models calculated comparable results, with differences decreasing under greater loads. Results predicted with the fixed boundary pore pressure and the fixed osmotic pressure in the whole disc models were nearly identical. The boundary pore pressure model, however, cannot simulate differential osmotic pressures in disc regions. The swelling model offered the best potential to provide more accurate results, conditional upon availability of reliable values for the required coefficients and material properties. Possible fields of application include mechanobiology investigations and crack opening and propagation. However, the other approaches are a good compromise between the ease of implementation and the reliability of results, especially when considering higher loads or when the focus is on global results such as spinal kinematics.

In silico evaluation of a new composite disc substitute with a L3-L5 lumbar spine finite element model

When the intervertebral disc is removed to relieve chronic pain, subsequent segment stabilization should restore the functional mechanics of the native disc. Because of partially constrained motions and the lack of intrinsic rotational stiffness ball-on-socket implants present many disadvantages. Composite disc substitutes mimicking healthy disc structures should be able to assume the role expected for a disc substitute with fewer restrictions than ball-on-socket implants. A biomimetic composite disc prototype including artificial nucleus fibre-reinforced annulus and endplates was modelled as an L4-L5 disc substitute within a L3-L5 lumbar spine finite element model. Different device updates, i.e. changes of material properties fibre distributions and volume fractions and nucleus placements were proposed. Load- and displacement-controlled rotations were simulated with and without body weight applied. The original prototype reduced greatly the flexibility of the treated segment with significant adjacent level effects under displacement-controlled or hybrid rotations. Device updates allowed restoring large part of the global axial and sagittal rotational flexibility predicted with the intact model. Material properties played a major role, but some other updates were identified to potentially tune the device behaviour against specific motions. All device versions altered the coupled intersegmental shear deformations affecting facet joint contact through contact area displacements. Loads in the bony endplates adjacent to the implants increased as the implant stiffness decreased but did not appear to be a strong limitation for the implant biomechanical and mechanobiological functionality. In conclusion, numerical results given by biomimetic composite disc substitutes were encouraging with greater potential than that offered by ball-on-socket implants.