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by Keyword: Intervertebral disc


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Wills, C. R., Malandrino, A., Van Rijsbergen, M., Lacroix, D., Ito, K., Noailly, J., (2016). Simulating the sensitivity of cell nutritive environment to composition changes within the intervertebral disc Journal of the Mechanics and Physics of Solids , 90, 108-123

Altered nutrition in the intervertebral disc affects cell viability and can generate catabolic cascades contributing to extracellular matrix (ECM) degradation. Such degradation is expected to affect couplings between disc mechanics and nutrition, contributing to accelerate degenerative processes. However, the relation of ECM changes to major biophysical events within the loaded disc remains unclear. A L4-L5 disc finite element model including the nucleus (NP), annulus (AF) and endplates was used and coupled to a transport-cell viability model. Solute concentrations and cell viability were evaluated along the mid-sagittal plane path. A design of experiment (DOE) was performed. DOE parameters corresponded to AF and NP biochemical tissue measurements in discs with different degeneration grades. Cell viability was not affected by any parameter combinations defined. Nonetheless, the initial water content was the parameter that affected the most the solute contents, especially glucose. Calculations showed that altered NP composition could negatively affect AF cell nutrition. Results suggested that AF and NP tissue degeneration are not critical to nutrition-related cell viability at early-stage of disc degeneration. However, small ECM degenerative changes may alter significantly disc nutrition under mechanical loads. Coupling disc mechano-transport simulations and enzyme expression studies could allow identifying spatiotemporal sequences related to tissue catabolism.

Keywords: Cell nutrition, Finite element analysis, Intervertebral disc degeneration, Multiphysics, Tissue composition


Malandrino, Andrea, Pozo, Jose Maria, Castro-Mateos, Isaac, Frangi, Alejandro F., van Rijsbergen, Marc M., Ito, Keita, Wilke, Hans-Joachim, Dao, Tien Tuan, Ho Ba Tho, Marie-Christine, Noailly, Jerome, (2015). On the relative relevance of subject-specific geometries and degeneration-specific mechanical properties for the study of cell death in human intervertebral disc models Frontiers in Bioengineering and Biotechnology 3, (Article 5), 1-15

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.

Keywords: Intervertebral Disc Degeneration, Finite element modelling, Lumbar spine, Poroelasticity, Damage model, Subject-specific modelling, Disc cell nutrition


Malandrino, Andrea, Lacroix, Damien, Hellmich, Christian, Ito, Keita, Ferguson, Stephen J., Noailly, J., (2014). The role of endplate poromechanical properties on the nutrient availability in the intervertebral disc Osteoarthritis and Cartilage , 22, (7), 1053-1060

Objective To investigate the relevance of the human vertebral endplate poromechanics on the fluid and metabolic transport from and to the intervertebral disc (IVD) based on educated estimations of the poromechanical parameter values of the bony endplate (BEP). Methods 50 micro-models of different BEP samples were generated from μCTs of lumbar vertebrae and allowed direct determination of porosity values. Permeability values were calculated by using the micro-models, through the simulation of permeation via computational fluid dynamics. These educated ranges of porosity and permeability values were used as inputs for mechano-transport simulations to assess their effect on both the distributions of metabolites within an IVD model and the poromechanical calculations within the cartilaginous part of the endplate i.e., the cartilage endplate (CEP). Results BEP effective permeability was highly correlated to local variations of porosity (R2 ≈ 0.88). Universal patterns between bone volume fraction and permeability arose from these results and from other experimental data in the literature. These variations in BEP permeability and porosity had negligible effects on the distributions of metabolites within the disc. In the CEP, the variability of the poromechanical properties of the BEP did not affect the predicted consolidation but induced higher fluid velocities. Conclusions The present paper provides the first sets of thoroughly identified BEP parameter values that can be further used in patient-specific poromechanical studies. Representing BEP structural changes through variations in poromechanical properties did not affect the diffusion of metabolites. However, attention might be paid to alterations in fluid velocities and cell mechano-sensing within the CEP.

Keywords: Bony endplate, Spine mechanobiology, Intervertebral disc metabolites, Hydraulic Permeability, Bone Porosity, Poromechanics


Ruiz, C., Noailly, J., Lacroix, D., (2013). Material property discontinuities in intervertebral disc porohyperelastic finite element models generate numerical instabilities due to volumetric strain variations Journal of the Mechanical Behavior of Biomedical Materials , 26, 1-10

Numerical studies of the intervertebral disc (IVD) are important to better understand the load transfer and the mechanobiological processes within the disc. Among the relevant calculations, fluid-related outputs are critical to describe and explore accurately the tissue properties. Porohyperelastic finite element models of IVD can describe accurately the disc behaviour at the organ level and allow the inclusion of fluid effects. However, results may be affected by numerical instabilities when fast load rates are applied. We hypothesized that such instabilities would appear preferentially at material discontinuities such as the annulus-nucleus boundary and should be considered when testing mesh convergence. A L4-L5 IVD model including the nucleus, annulus and cartilage endplates were tested under pure rotational loads, with different levels of mesh refinement. The effect of load relaxation and swelling were also studied. Simulations indicated that fluid velocity oscillations appeared due to numerical instability of the pore pressure spatial derivative at material discontinuities. Applying local refinement only was not enough to eliminate these oscillations. In fact, mesh refinements had to be local, material-dependent, and supplemented by the creation of a material transition zone, including interpolated material properties. Results also indicated that oscillations vanished along load relaxation, and faster attenuation occurred with the incorporation of the osmotic pressure. We concluded that material discontinuities are a major cause of instability for poromechanical calculations in multi-tissue models when load velocities are simulated. A strategy was presented to address these instabilities and recommendations on the use of IVD porohyperelastic models were given.

Keywords: Fast loads, Intervertebral disc, Numerical instabilities, Poroelastic model


Malandrino, Andrea, Noailly, J., Lacroix, Damien, (2013). Regional annulus fibre orientations used as a tool for the calibration of lumbar intervertebral disc finite element models Computer Methods in Biomechanics and Biomedical Engineering , 16, (9), 923-928

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.

Keywords: Intervertebral disc, Annulus fibrosus, Model calibration, Fibre orientation


Galbusera, F., Schmidt, H., Noailly, J., Malandrino, A., Lacroix, D., Wilke, H.J, Shirazi-Adl, A., (2011). Comparison of four methods to simulate swelling in poroelastic finite element models of intervertebral discs Journal of the Mechanical Behavior of Biomedical Materials , 4, (7), 1234-1241

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.

Keywords: Intervertebral disc, Boundary pore pressure, Osmotic pressure, Swelling, Finite element, Poroelasticity


Malandrino, A., Planell, J. A., Lacroix, D., (2009). Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation Journal of Biomechanics 42, (16), 2780-2788

A statistical factorial analysis approach was conducted on a poroelastic finite element model of a lumbar intervertebral disc to analyse the influence of six material parameters (permeabilities of annulus, nucleus, trabecular vertebral bone, cartilage endplate and Young's moduli of annulus and nucleus) on the displacement, fluid pore pressure and velocity fields. Three different loading modes were investigated: compression, flexion and axial rotation. Parameters were varied considering low and high levels in agreement with values found in the literature for both healthy and degenerated lumbar discs. Results indicated that annulus stiffness and cartilage endplate permeability have a strong effect on the overall fluid- and solid-phase responses in all loading conditions studied. Nucleus stiffness showed its main relevance in compression while annulus permeability influenced mainly the annular pressure field. This study confirms the permeability's central role in biphasic modelling and highlights for the lumbar disc which experiments of material property characterization should be performed. Moreover, such sensitivity study gives important guidelines in poroelastic material modelling and finite element disc validation.

Keywords: Intervertebral disc, Permeability, Fractional factorial design, Design of experiments, Finite element analysis