Staff member


Andrea Malandrino

Postdoctoral Researcher
Integrative Cell and Tissue Dynamics
amalandrino@ibecbarcelona.eu
+34 934 037 068
Staff member publications

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


Blanchard, R., Morin, C., Malandrino, A., Vella, A., Sant, Z., Hellmich, C., (2016). Patient-specific fracture risk assessment of vertebrae: A multiscale approach coupling X-ray physics and continuum micromechanics International Journal for Numerical Methods in Biomedical Engineering 32, (9), e02760

Summary: While in clinical settings, bone mineral density measured by computed tomography (CT) remains the key indicator for bone fracture risk, there is an ongoing quest for more engineering mechanics-based approaches for safety analyses of the skeleton. This calls for determination of suitable material properties from respective CT data, where the traditional approach consists of regression analyses between attenuation-related grey values and mechanical properties. We here present a physics-oriented approach, considering that elasticity and strength of bone tissue originate from the material microstructure and the mechanical properties of its elementary components. Firstly, we reconstruct the linear relation between the clinically accessible grey values making up a CT, and the X-ray attenuation coefficients quantifying the intensity losses from which the image is actually reconstructed. Therefore, we combine X-ray attenuation averaging at different length scales and over different tissues, with recently identified 'universal' composition characteristics of the latter. This gives access to both the normally non-disclosed X-ray energy employed in the CT-device and to in vivo patient-specific and location-specific bone composition variables, such as voxel-specific mass density, as well as collagen and mineral contents. The latter feed an experimentally validated multiscale elastoplastic model based on the hierarchical organization of bone. Corresponding elasticity maps across the organ enter a finite element simulation of a typical load case, and the resulting stress states are increased in a proportional fashion, so as to check the safety against ultimate material failure. In the young patient investigated, even normal physiological loading is probable to already imply plastic events associated with the hydrated mineral crystals in the bone ultrastructure, while the safety factor against failure is still as high as five.

Keywords: Bone, Bone mass density, Continuum micromechanics, Elastoplasticity, Spine, Strength, X-ray physics


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

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


Malandrino, A., Noailly, J., Lacroix, D., (2014). Numerical exploration of the combined effect of nutrient supply, tissue condition and deformation in the intervertebral disc Journal of Biomechanics 47, (6), 1520-1525

Novel strategies to heal discogenic low back pain could highly benefit from comprehensive biophysical studies that consider both mechanical and biological factors involved in intervertebral disc degeneration. A decrease in nutrient availability at the bone-disc interface has been indicated as a relevant risk factor and as a possible initiator of cell death processes. Mechanical behaviour of both healthy and degenerated discs could highly interact with cell death in these compromised situations. In the present study, a mechano-transport finite element model was used to investigate the nature of mechanical effects on cell death processes via load-induced metabolic transport variations. Cycles of static sustained compression were chosen to simulate daily human activity. Healthy and degenerated cases were simulated as well as a reduced supply of solutes and an increase in solute exchange area at the bone-disc interface. Results showed that a reduction in metabolite concentrations at the bone-disc boundaries induced cell death, even when the increased exchange area was simulated. Slight local mechanical enhancements of glucose in the disc centre were capable of decelerating cell death but occurred only with healthy mechanical properties. However, mechanical deformations were responsible for a worsening in terms of cell death in the inner annulus, a disadvantaged zone far from the boundary supply with both an increased cell demand and a strain-dependent decrease of diffusivity. Such adverse mechanical effects were more accentuated when degenerative properties were simulated. Overall, this study paves the way for the use of biophysical models for a more integrated understanding of intervertebral disc pathophysiology.

Keywords: Boundary conditions, Cell nutrition, Cell viability, Computational analysis, Intervertebraldisc, Softtissuebiomechanics


Malandrino, A., Lacroix, D., Noailly, J., (2014). Exploring the link between mechanical load and cell death in the invertebral disc: A theoretical study of mechno-regulated hypermetabolism and metabolic transport Bone & Joint Journal Orthopaedic Proceedings Supplement 8th Combined Meeting Of Orthopaedic Research Societies (CORS) , The British Editorial Society of Bone & Joint Surgery (Venice, Italy) 96-B, (Supp. 11), 18

Summary Statement An organ culture experiment was simulated to explore the mechanisms that can link cell death to mechanical overload in the intervertebral disc. Coupling cell nutrition and tissue deformations led to altered metabolic transport that largely explained cell viability measurements.Introduction Part of intervertebral disc (IVD) maintenance relies on limited nutrient availability to the cells and on mechanical loads, but effective implication of these two factors is difficult to quantify. Theoretical models have helped to understand the link between solute transport and cell nutrition in deforming IVD, but omitted the direct link between tissue mechanics and cell metabolism. Hence, we explored numerically the relation between disc mechanics and cell death in relation to an organ culture experiment.Methods A finite element model of a caudal bovine IVD was created to reproduce an organ culture experiment. All subtissues were modelled, and coupled to cell metabolism in two ways: (i) mechanical strains and metabolic reactions were simply coupled to the diffusions of oxygen, lactate and glucose through a mechano-transport algorithm (IND model). (ii), a hypermetabolism model based on in vitro data involved a 30% increase in glucose consumption by the cells, activated either as a Step or as a Gaussian function over 15% strain (DIR model). Exponential decays of cell density occurred below 0.5 mM of glucose and/or below pH 6.78. Concentrations of 21 kPa oxygen and 4.5 mM glucose were imposed at the boundary, and a combination of 0.2 MPa compression and 10° bending was applied over 7 days.Results The highest hypermetabolic response was given by the Step activation. For all models, cell death mostly occurred in the compressed area of the flexed IVD, and steady-state cell viability was reached in about two days of load. In the outer annulus fibrosus (AF), the DIR model with Step activation led to increased cell death, in line with the cell viability measured in vitro. In the inner AF, all cell viability results matched the reported measurements.Discussion/Conclusion This study focused on elucidating the links between mechanical stimulation and cell survival in the IVD, and simulation of nutrition issues allowed reproducing the results of an organ culture experiment. Results suggest that mechano-regulated metabolism can play a significant role in the nutrition-related cell death. Truly, the IND model gave both low glucose and low pH, and altered metabolic transport represented the main cell death mechanism. Yet, the role of hypermetabolism was increased nearby the nutrient supply at the outer AF, meaning that cell death could occur, even in regions where nutrient supply seems ensured by short diffusion distances. Though further mechanistic developments must be considered, this novel mechano-regulated metabolism model permits mechano-transport models to be used to explore important interactions between tissue biophysics and multiphysics. In particular, the extracellular matrix degradation along degeneration and cell death can be coupled to the poromechanical parameters introduced, e.g. initial porosity and osmotic pressure values that largely depend on the proteoglycan concentration.


Noailly, J., Malandrino, A., Galbusera, F., Jin, Zhongmin, (2014). Computational modelling of spinal implants Computational Modelling of Biomechanics and Biotribology in the Musculoskeletal System (ed. Jin, Z.), Woodhead Publishing (Cambridge, UK) Biomaterials and Tissues, 447-484

This chapter focuses on the use of the finite element method in the design and exploration of spinal implants. Following an introduction to biomechanical alterations of the spine in disease and to spine finite element modelling, focus is placed on different models developed for spine treatment simulations. Despite the hindrance of working thorough representations of in vivo situations, predictions of load transfer within both the implants and the tissues simulated allow improved interpretations of known clinical outcomes, and permit the educated design of new implants. The potential of probabilistic modelling is also discussed in relation to model validation and patient-specific analyses. Finally, the latest developments in the multiphysical modelling of intervertebral discs are presented, revealing a strong potential for the study of implant-based strategies that aim to restore the functional biophysics of the spine.

Keywords: Spinal implant, Finite element modelling, Spine surgery, Spine biomechanics, Tissue mechanobiology


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


Malandrino, A., Lacroix, D., Noailly, J., (2013). Intervertebral disc cell death explained by metabolism-deformation couplings in a porohyperelastic finite element model Poromechanics V 5th Biot Conference on Poromechanics , American Society of Civil Engineers (Vienna, Austria) , 2193-2201

Comprehensive understanding of disc degeneration and low back pain requires knowledge about both the mechanical and the biological factors that may affect tissue maintenance. In the present study, a coupled intervertebral disc model with a porohyperelastic formulation (mechanics) and a glycolitic metabolic transport and cell viability (biology) were used. Mechanotransduction phenomena were investigated. Boundary conditions and disc model characteristics, both inspired from an organ culture experiment, were introduced. The model predicted cell death in the most compressed region of the intervertebral disc, in agreement with the simulated experiment. Such result was attributed to a local effect of reduced metabolites diffusion when coupled to local mechanics in the porohyperelastic disc. Direct force sensing by the cells was explored and was shown to potentially extend the risk area in terms of cell death. The study contributes to the elucidation of mechanotransduction phenomena in the spine, and paves the way to biophysical developments, highly relevant to mechanobiology-inspired treatments of low-back pain.


Malandrino, A., Fritsch, A., Lahayne, O., Kropik, K., Redl, H., Noailly, J., Lacroix, D., Hellmich, C., (2012). Anisotropic tissue elasticity in human lumbar vertebra, by means of a coupled ultrasound-micromechanics approach Materials Letters 78, 154-158

The extremely fine structure of vertebral cortex challenges reliable determination of the tissue's anisotropic elasticity, which is important for the spine's load carrying patterns often causing pain in patients. As a potential remedy, we here propose a combined experimental (ultrasonic) and modeling (micromechanics) approach. Longitudinal acoustic waves are sent in longitudinal (superior-inferior, axial) as well as transverse (circumferential) direction through millimeter-sized samples containing this vertebral cortex, and corresponding wave velocities agree very well with recently identified 'universal' compositional and acoustic characteristics (J Theor Biol 287:115, 2011), which are valid for a large data base comprising different bones from different species and different organs. This provides evidence that the 'universal' organization patterns inherent to all the bone tissues of the aforementioned data base also hold for vertebral bone. Consequently, an experimentally validated model covering the mechanical effects of this organization patterns (J Theor Biol 244:597, 2007, J Theor Biol 260:230, 2009) gives access to the complete elasticity tensor of human lumbar vertebral bone tissue, as a valuable input for structural analyses aiming at patient-specific fracture risk assessment, e.g. based on the Finite Element Method.

Keywords: Human vertebra, Micromechanics, Tissue elasticity, Ultrasonics


Malandrino, A., Noailly, J., Lacroix, D., (2012). Mechanical effect on metabolic transport and cell viability in the intervertebral disc The Proceedings of the 10th International Symposium on CMBBE 10th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering , ARUP (Berlin, Germany) SS12: In silico modelling of the spinal disc degeneration, 248-253

The degeneration process in the intervertebral disc (IVD) is linked to progressive cell death and to mechanical factors. Therefore, the inclusion of cell viability criteria coupled with disc mechanics in a computational model would enable to get a better understanding of the degeneration process in IVD. A recently developed finite element (FE) model of the L4-L5 IVD based on poromechanics and IVD metabolism (Malandrino et al., 2011) was modified to include an exponential decay of cells over time below critical glucose and pH levels. The implementation was verified against in vitro literature data on cell viability. Viability criteria were used in the IVD model where diffusions of glucose, oxygen and lactate accounted for predicted porosity and volume changes. Subtissue-specific mechanical properties and cell concentrations were modelled. Daily compressive phases (standing and resting) were applied. Metabolite boundary concentrations were reduced at the endplates to induce critical conditions within the IVD. Solutions with and without mechanical coupling were compared. Critical glucose rather than pH levels were relevant to cell viability far away from the solute supply. Deformation couplings increased glucose in the disc centre so that cells stopped dying up to 10 hours earlier over two days simulated when mechanical deformations were considered. These results can help in the understanding of coupled mechanical and biological factors. If metabolite supply is disturbed, as it could happen during endplate calcification or circulatory diseases, a local accelerated cell death in the disc centre may occur in absence of tissue compliance. This study highlights the need to restore both nutritional and mechanical factors in order to favour cell viability along regenerative treatments.


Malandrino, Andrea, Noailly, Jerome, Lacroix, Damien, (2011). The effect of sustained compression on oxygen metabolic transport in the intervertebral disc decreases with degenerative changes Plos Computational Biology 7, (8), 1-12

Intervertebral disc metabolic transport is essential to the functional spine and provides the cells with the nutrients necessary to tissue maintenance. Disc degenerative changes alter the tissue mechanics, but interactions between mechanical loading and disc transport are still an open issue. A poromechanical finite element model of the human disc was coupled with oxygen and lactate transport models. Deformations and fluid flow were linked to transport predictions by including strain-dependent diffusion and advection. The two solute transport models were also coupled to account for cell metabolism. With this approach, the relevance of metabolic and mechano-transport couplings were assessed in the healthy disc under loading-recovery daily compression. Disc height, cell density and material degenerative changes were parametrically simulated to study their influence on the calculated solute concentrations. The effects of load frequency and amplitude were also studied in the healthy disc by considering short periods of cyclic compression. Results indicate that external loads influence the oxygen and lactate regional distributions within the disc when large volume changes modify diffusion distances and diffusivities, especially when healthy disc properties are simulated. Advection was negligible under both sustained and cyclic compression. Simulating degeneration, mechanical changes inhibited the mechanical effect on transport while disc height, fluid content, nucleus pressure and overall cell density reductions affected significantly transport predictions. For the healthy disc, nutrient concentration patterns depended mostly on the time of sustained compression and recovery. The relevant effect of cell density on the metabolic transport indicates the disturbance of cell number as a possible onset for disc degeneration via alteration of the metabolic balance. Results also suggest that healthy disc properties have a positive effect of loading on metabolic transport. Such relation, relevant to the maintenance of the tissue functional composition, would therefore link disc function with disc nutrition.

Keywords: Bovine nucleus pulposus, Human anulus fibrosus, Finite-element, Fluid-flow, Hydraulic permeability, Confined compression, Coupled diffusion, Solute transport, Water-content, Lumbar spine


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


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