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

Insights into the role of water concentrations on nanomechanical behavior of type I collagen-hyaluronan interfaces in annulus fibrosus: A molecular dynamics investigation

Multi-faceted deformation capabilities of Annulus Fibrosus (AF) results from an intricate mechanical design by nature. Wherein, organization and interactions between the constituents, collagen type I (CI), collagen type II (C2), hyaluronan, aggrecan, and water are instrumental. However, mechanisms by which such interactions influence AF mechanics at tissue-scale is not well understood. This work investigates nanoscale interfacial interactions between CI and hyaluronan (CI-H) and presents insights into their influence on tissue-scale mechanics of AF. For this, three-dimensional molecular dynamics (MD) simulations of tensile and compressive deformation are conducted on atomistic model of CI-H interface at 0%, 65%, and 75% water concentrations (WC). Results show hyaluronan lowers local hydration around CI component of interface, owing to its hydrophilic nature. Analyses show that increase in WC from 65% to 75% leads to increased interchain sliding in hyaluronan, which further lowers tensile modulus of the interface from 2.1 GPa to 660 MPa, contributing to softening observed from outer to inner AF. Furthermore, increase in WC from 65% to 75%, shifts compressive deformation from buckling-dominant to non-buckling-dominant which contributes towards lower radial bulge at inner AF. Findings provide deeper insights into mechanistic interactions and mechanisms at fundamental length-scale which influence the AF structure-mechanics at tissue-scale.

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.

Experimental and Computational Comparison of Intervertebral Disc Bulge for Specimen-Specific Model Evaluation Based on Imaging

Finite element modelling of the spinal unit is a promising preclinical tool to assess the biomechanical outcome of emerging interventions. Currently, most models are calibrated and validated against range of motion and rarely directly against soft-tissue deformation. The aim of this contribution was to develop an in vitro methodology to measure disc bulge and assess the ability of different specimen-specific modelling approaches to predict disc bulge. Bovine bone-disc-bone sections (N = 6) were prepared with 40 glass markers on the intervertebral disc surface. These were initially magnetic resonance (MR)-imaged and then sequentially imaged using peripheral-qCT under axial compression of 1 mm increments. Specimen-specific finite-element models were developed from the CT data, using three different methods to represent the nucleus pulposus geometry with and without complementary use of the MR images. Both calibrated specimen-specific and averaged compressive material properties for the disc tissues were investigated. A successful methodology was developed to quantify the disc bulge in vitro, enabling observation of surface displacement on qCT. From the finite element model results, no clear advantage was found in using geometrical information from the MR images in terms of the models' ability to predict stiffness or disc bulge for bovine intervertebral disc.

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.

Properties of PMMA end cap holders affect FE stiffness predictions of vertebral specimens

Bone cement is often used, in experimental biomechanics, as a potting agent for vertebral bodies (VB). As a consequence, it is usually included in finite element (FE) models to improve accuracy in boundary condition settings. However, bone cement material properties are typically assigned to these models based on literature data obtained from specimens created under conditions which often differ from those employed for cement end caps. These discrepancies can result in solids with different material properties from those reported. Therefore, this study aimed to analyse the effect of assigning different mechanical properties to bone cement in FE vertebral models. A porcine C2 vertebral body was potted in bone cement end caps, μCT scanned, and tested in compression. DIC was performed on the anterior surface of the specimen to monitor the displacement. Specimen stiffness was calculated from the load-displacement output of the materials testing machine and from the machine load output and average displacement measured by DIC. Fifteen bone cement cylinders with dimensions similar to the cement end caps were produced and subjected to the same compression protocol as the vertebral specimen and average stiffness and Young moduli were estimated. Two geometrically identical vertebral body FE models were created from the μCT images, the only difference residing in the values assigned to bone cement material properties: in one model these were obtained from the literature and in the other from the cylindrical cement samples previously tested. The average Youngs modulus of the bone cement cylindrical specimens was 1177 ± 3 MPa, considerably lower than the values reported in the literature. With this value, the FE model predicted a vertebral specimen stiffness 3% lower than that measured experimentally, while when using the value most commonly reported in similar studies, specimen stiffness was overestimated by 150%.

Spatiotemporal Expression of 3-B-3(-) and 7-D-4 Chondroitin Sulfation, Tissue Remodeling, and Attempted Repair in an Ovine Model of Intervertebral Disc Degeneration

OBJECTIVE

Examination of intervertebral disc (IVD) regeneration in an ovine annular lesion model.

HYPOTHESIS

Sulfation motifs are important functional determinants in glycosaminoglycans (GAGs). Previous studies have correlated 3-B-3(-) and 7-D-4 chondroitin sulfate (CS) motifs in tissues undergoing morphogenetic transition in development. We hypothesize that these motifs may also be expressed in degenerate IVDs and may represent a reparative response.

DESIGN

Induction of disc degeneration by 5 mm or 6 × 20 mm lesions in the annulus fibrosus (AF) over 6 or 3 to 6 months postoperation (PO). Tissue sections were stained with toluidine blue-fast green, 3-B-3(-) and 7-D-4 CS-sulfation motifs were immunolocalized in 3-month PO 6 × 20 mm lesion IVDs. Sulfated glycosaminoglycan (GAG), 3-B-3(-), and 7-D-4 epitopes were quantitated by ELISIA (enzyme-linked immunosorbent inhibition assay) in extracts of AF (lesion site and contralateral half) and nucleus pulposus (NP) 0, 3, and 6 months PO.

RESULTS

Collagenous overgrowth of lesions occurred in the outer AF. Chondroid metaplasia in ~20% of the 6 × 20 mm affected discs resulted in integration of an outgrowth of NP tissue with the inner AF lamellae preventing propagation of the lesion. 3-B-3(-) and 7-D-4 CS sulfation motifs were immunolocalized in this chondroid tissue. ELISIA quantified CS sulfation motifs demonstrating an increase 3 to 6 months PO in the AF lesion and a reduction in sulfated GAG not evident in the contralateral AF.

CONCLUSIONS

(1) Outer annular lesions underwent spontaneous repair. (2) Chondroid metaplasia of the inner 6 × 20 mm defect prevented its propagation suggesting an apparent reparative response.

A Systematic Review of Continuum Modeling of Skeletal Muscles: Current Trends, Limitations, and Recommendations

Finite elasticity theory has been commonly used to model skeletal muscle. A very large range of heterogeneous constitutive laws has been proposed. In this review, the most widely used continuum models of skeletal muscles were synthetized and discussed. Trends and limitations of these laws were highlighted to propose new recommendations for future researches. A systematic review process was performed using two reliable search engines as PubMed and ScienceDirect. 40 representative studies (13 passive muscle materials and 27 active muscle materials) were included into this review. Note that exclusion criteria include tendon models, analytical models, 1D geometrical models, supplement papers, and indexed conference papers. Trends of current skeletal muscle modeling relate to 3D accurate muscle representation, parameter identification in passive muscle modeling, and the integration of coupled biophysical phenomena. Parameter identification for active materials, assumed fiber distribution, data assumption, and model validation are current drawbacks. New recommendations deal with the incorporation of multimodal data derived from medical imaging, the integration of more biophysical phenomena, and model reproducibility. Accounting for data uncertainty in skeletal muscle modeling will be also a challenging issue. This review provides, for the first time, a holistic view of current continuum models of skeletal muscles to identify potential gaps of current models according to the physiology of skeletal muscle. This opens new avenues for improving skeletal muscle modeling in the framework of in silico medicine.

The Mechanical Role of the Radial Fiber Network Within the Annulus Fibrosus of the Lumbar Intervertebral Disc: A Finite Elements Study

The annulus fibrosus (AF) of the intervertebral disc (IVD) consists of a set of concentric layers composed of a primary circumferential collagen fibers arranged in an alternating oblique orientation. Moreover, there exists an additional secondary set of radial translamellar collagen fibers which connects the concentric layers, creating an interconnected fiber network. The aim of this study was to investigate the mechanical role of the radial fiber network. Toward that goal, a three-dimensional (3D) finite element model of the L3–L4 spinal segment was generated and calibrated to axial compression and pure moment loading. The AF model explicitly recognizes the two heterogeneous networks of fibers. The presence of radial fibers demonstrated a pronounced effect on the local disc responses under lateral bending, flexion, and extension modes. In these modes, the radial fibers were in a tensile state in the disc region that subjected to compression. In addition, the circumferential fibers, on the opposite side of the IVD, were also under tension. The local stress in the matrix was decreased in up to 9% in the radial fibers presence. This implies an active fiber network acting collectively to reduce the stresses and strains in the AF lamellae. Moreover, a reduction of 26.6% in the matrix sideways expansion was seen in the presence of the radial fibers near the neutral bending axis of the disc. The proposed biomechanical model provided a new insight into the mechanical role of the radial collagen fibers in the AF structure. This model can assist in the design of future IVD substitutes.

Finite element comparison between the human and the ovine lumbar intervertebral disc

Introduction

Nowadays it is still not clear which loading conditions are responsible for lumbar intervertebral disc failure. Many studies have been conducted to investigate the effect of different loading conditions on the herniation processes, and many of them were based on the ovine model. However, the biomechanical similarities between the human and the ovine lumbar disc have been demonstrated in the main planes only, whereas it is not known if they are comparable under complex loading conditions too. The aim of this study was to compare the mechanical response of the ovine and the human lumbar intervetebral disc under complex loading conditions, in order to investigate differences and similarities between the species.The loading scenarios described in a finite element study on a human lumbar segment were applied to a model of the ovine disc, and the results were then compared.It has been shown that combined loads generated highest strains in both the models, and the maximum strains had the same location in the posterior or in the postero-lateral region of the annulus, according to the loading scenario.

Conclusion

The ovine disc can be used in spinal research to investigate herniation process under any loading conditions.

Level of evidence

V.

A study of the damage behaviour of porcine intervertebral discs in a bioreactor environment

The intervertebral discs are cartilaginous, articulating structures that lie between vertebral bodies, allowing flexibility, transmission, modification, and also distribution of the forces to the spinal column. Disc degeneration is characterised by progressive loss of disc height and exaggerated radial bulging. Therefore, the spine becomes shorter, stiffer, and less mobile. In the last several decades, there is a strong need for a tissue engineering strategy that alleviates pain and restores spine function by directly addressing the underlying biological causes of disc degeneration. Numerous studies that are currently showing potential have been conducted on developing regenerative and reparative strategies for treating this condition. In this study, to numerically describe the anisotropic mechanical damage behaviour of discs, the pseudo-elastic damage model was applied. To experimentally picture the biomechanical response of discs and to study the damage mechanisms as well as the spinal disc herniation, a special bioreactor was evolved. The specimens were obtained from pigs aged six months. A total of eight functional spine units were taken from porcine lumbar spines (L1-L2). Firstly, the experiments were performed by using long-term cyclic uniaxial compression tests. Secondly, the mean value of experimental results with consideration of the different shapes and sizes of the samples was calculated. Afterwards, the experimental results were compared with outcomes of numerical simulations.

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.

Numerical Prediction of the Mechanical Failure of the Intervertebral Disc under Complex Loading Conditions

Finite element modeling has been widely used to simulate the mechanical behavior of the intervertebral disc. Previous models have been generally limited to the prediction of the disc behavior under simple loading conditions, thus neglecting its response to complex loads, which may induce its failure. The aim of this study was to generate a finite element model of the ovine lumbar intervertebral disc, in which the annulus was characterized by an anisotropic hyperelastic formulation, and to use it to define which mechanical condition was unsafe for the disc. Based on published in vitro results, numerical analyses under combined flexion, lateral bending, and axial rotation with a magnitude double that of the physiological ones were performed. The simulations showed that flexion was the most unsafe load and an axial tensile stress greater than 10 MPa can cause disc failure. The numerical model here presented can be used to predict the failure of the disc under all loading conditions, which may support indications about the degree of safety of specific motions and daily activities, such as weight lifting.

Lamellar and fibre bundle mechanics of the annulus fibrosus in bovine intervertebral disc

The intervertebral disc is a multicomposite structure, with an outer fibrous ring, the annulus fibrosus, retaining a gel-like core, the nucleus pulposus. The disc presents complex mechanical behaviour, and it is of high importance for spine biomechanics. Advances in multiscale modelling and disc repair raised a need for new quantitative data on the finest details of annulus fibrosus mechanics. In this work we explored inter-lamella and inter-bundle behaviour of the outer annulus using micromechanical testing and second harmonic generation microscopy. Twenty-one intervertebral discs were dissected from cow tails; the nucleus and inner annulus were excised to leave a ring of outer annulus, which was tested in circumferential loading while imaging the tissue's collagen fibres network with sub-micron resolution. Custom software was developed to determine local tissue strains through image analysis. Inter-bundle linear and shear strains were 5.5 and 2.8 times higher than intra-bundle strains. Bundles tended to remain parallel while rotating under loading, with large slipping between them. Inter-lamella linear strain was almost 3 times the intra-lamella one, but no slipping was observed at the junction between lamellae. This study confirms that outer annulus straining is mainly due to bundles slipping and rotating. Further development of disc multiscale modelling and repair techniques should take into account this modular behaviour of the lamella, rather than considering it as a homogeneous fibre-reinforced matrix.

STATEMENT OF SIGNIFICANCE

The intervertebral disc is an organ tucked between each couple of vertebrae in the spine. It is composed by an outer fibrous layer retaining a gel-like core. This organ undergoes severe and repeated loading during everyday life activities, since it is the compliant component that gives the spine its flexibility. Its properties are affected by pathologies such as disc degeneration, a major cause of back pain. In this article we explored the micromechanical behaviour of the disc's outer layer using second harmonic generation, a technique which allowed us to visualize, with unprecedented detail, how bundles of collagen fibres slide relative to each other when loaded. Our results will help further the development of new multiscale numerical models and repairing techniques.

Methodology based on genetic heuristics for in-vivo characterizing the patient-specific biomechanical behavior of the breast tissues

This paper presents a novel methodology to in-vivo estimate the elastic constants of a constitutive model proposed to characterize the mechanical behavior of the breast tissues. An iterative search algorithm based on genetic heuristics was constructed to in-vivo estimate these parameters using only medical images, thus avoiding invasive measurements of the mechanical response of the breast tissues. For the first time, a combination of overlap and distance coefficients were used for the evaluation of the similarity between a deformed MRI of the breast and a simulation of that deformation. The methodology was validated using breast software phantoms for virtual clinical trials, compressed to mimic MRI-guided biopsies. The biomechanical model chosen to characterize the breast tissues was an anisotropic neo-Hookean hyperelastic model. Results from this analysis showed that the algorithm is able to find the elastic constants of the constitutive equations of the proposed model with a mean relative error of about 10%. Furthermore, the overlap between the reference deformation and the simulated deformation was of around 95% showing the good performance of the proposed methodology. This methodology can be easily extended to characterize the real biomechanical behavior of the breast tissues, which means a great novelty in the field of the simulation of the breast behavior for applications such as surgical planing, surgical guidance or cancer diagnosis. This reveals the impact and relevance of the presented work.

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.

Long-Term Creep Behavior of the Intervertebral Disk: Comparison between Bioreactor Data and Numerical Results

The loaded disk culture system is an intervertebral disk (IVD)-oriented bioreactor developed by the VU Medical Center (VUmc, Amsterdam, The Netherlands), which has the capacity of maintaining up to 12 IVDs in culture, for approximately 3 weeks after extraction. Using this system, eight goat IVDs were provided with the essential nutrients and submitted to compression tests without losing their biomechanical and physiological properties, for 22 days. Based on previous reports (Paul et al., 2012, 2013; Detiger et al., 2013), four of these IVDs were kept in physiological condition (control) and the other four were previously injected with chondroitinase ABC (CABC), in order to promote degenerative disk disease (DDD). The loading profile intercalated 16 h of activity loading with 8 h of loading recovery to express the standard circadian variations. The displacement behavior of these eight IVDs along the first 2 days of the experiment was numerically reproduced, using an IVD osmo-poro-hyper-viscoelastic and fiber-reinforced finite element (FE) model. The simulations were run on a custom FE solver (Castro et al., 2014). The analysis of the experimental results allowed concluding that the effect of the CABC injection was only significant in two of the four IVDs. The four control IVDs showed no signs of degeneration, as expected. In what concerns to the numerical simulations, the IVD FE model was able to reproduce the generic behavior of the two groups of goat IVDs (control and injected). However, some discrepancies were still noticed on the comparison between the injected IVDs and the numerical simulations, namely on the recovery periods. This may be justified by the complexity of the pathways for DDD, associated with the multiplicity of physiological responses to each direct or indirect stimulus. Nevertheless, one could conclude that ligaments, muscles, and IVD covering membranes could be added to the FE model, in order to improve its accuracy and properly describe the recovery periods.

Determination of poroelastic properties of cartilage using constrained optimization coupled with finite element analysis

The feasibility of determining biphasic material properties using a finite element model of stress relaxation coupled with two types of constrained optimization to match measured data was investigated. Comparison of these two approaches, a zero-order method and a gradient-based algorithm, validated the predicted material properties. Optimizations were started from multiple different initial guesses of material properties (design variables) to establish the robustness of the optimization. Overall, the optimal values are close to those found by Cohen et al. (1998) but these small differences produced a marked improvement in the fit to the measured stress relaxation. Despite the greater deviation in the optimized values obtained from the zero-order method, both optimization procedures produced material properties that gave equally good overall fits to the measured data. Furthermore, optimized values were all within the expected range of material properties. Modeling stress relaxation using the optimized material properties showed an excellent fit to the entire time history of the measured data.