Publications

by Keyword: Elasticity


By year:[ 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 ]

Asadipour, N., Trepat, X., Muñoz, J. J., (2016). Porous-based rheological model for tissue fluidisation Journal of the Mechanics and Physics of Solids , 96, 535-549

It has been experimentally observed that cells exhibit a fluidisation process when subjected to a transient stretch, with an eventual recovery of the mechanical properties upon removal of the applied deformation. This fluidisation process is characterised by a decrease of the storage modulus and an increase of the phase angle. We propose a rheological model which is able to reproduce this combined mechanical response. The model is described in the context of continua and adapted to a cell-centred particle system that simulates cell–cell interactions. Mechanical equilibrium is coupled with two evolution laws: (i) one for the reference configuration, and (ii) another for the porosity or polymer density. The first law depends on the actual strain of the tissue, while the second assumes different remodelling rates during porosity increase and decrease. The theory is implemented on a particle based model and tested on a stretching experiment. The numerical results agree with the experimental measurements for different stretching magnitudes.

Keywords: Cell remodelling, Cell rheology, Fluidisation, Softening, Viscoelasticity


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


Andreu, I., Luque, T., Sancho, A., Pelacho, B., Iglesias-García, O., Melo, E., Farré, R., Prósper, F., Elizalde, M. R., Navajas, D., (2014). Heterogeneous micromechanical properties of the extracellular matrix in healthy and infarcted hearts Acta Biomaterialia 10, (7), 3235-3242

Infarcted hearts are macroscopically stiffer than healthy organs. Nevertheless, although cell behavior is mediated by the physical features of the cell niche, the intrinsic micromechanical properties of healthy and infarcted heart extracellular matrix (ECM) remain poorly characterized. Using atomic force microscopy, we studied ECM micromechanics of different histological regions of the left ventricle wall of healthy and infarcted mice. Hearts excised from healthy (n = 8) and infarcted mice (n = 8) were decellularized with sodium dodecyl sulfate and cut into 12 μm thick slices. Healthy ventricular ECM revealed marked mechanical heterogeneity across histological regions of the ventricular wall with the effective Young's modulus ranging from 30.2 ± 2.8 to 74.5 ± 8.7 kPa in collagen- and elastin-rich regions of the myocardium, respectively. Infarcted ECM showed a predominant collagen composition and was 3-fold stiffer than collagen-rich regions of the healthy myocardium. ECM of both healthy and infarcted hearts exhibited a solid-like viscoelastic behavior that conforms to two power-law rheology. Knowledge of intrinsic micromechanical properties of the ECM at the length scale at which cells sense their environment will provide further insight into the cell-scaffold interplay in healthy and infarcted hearts.

Keywords: Atomic force microscopy, Extracellular matrix, Heart scaffold, Nanoindentation, Viscoelasticity


Muñoz, J. J., Conte, V., Asadipour, N., Miodownik, M., (2013). A truss element for modelling reversible softening in living tissues Mechanics Research Communications , 49, 44-49

We resort to non-linear viscoelasticity to develop a truss element able to model reversible softening in lung epithelial tissues undergoing transient stretch. Such a Maxwell truss element is built by resorting to a three-noded element whose mid-node is kinematically constrained to remain on the line connecting the end-nodes. The whole mechanical system undergoes an additive decomposition of the strains along the truss direction where the total contribution of the mid-node is accounted for by using a null-space projection and static condensation techniques. Assembling of such line-elements in 3D networks allows us to model extended regions of living tissues as well as their anisotropies.

Keywords: Maxwell, Null-space, Reversible softening, Truss, Viscoelasticity


Redondo-Morata, L., Giannotti, M. I., Sanz, F., (2012). AFM-based force-clamp monitors lipid bilayer failure kinetics Langmuir , 28, (15), 6403-6410

The lipid bilayer rupture phenomenon is here explored by means of atomic force microscopy (AFM)-based force clamp, for the first time to our knowledge, to evaluate how lipid membranes respond when compressed under an external constant force, in the range of nanonewtons. Using this method, we were able to directly quantify the kinetics of the membrane rupture event and the associated energy barriers, for both single supported bilayers and multibilayers, in contradistinction to the classic studies performed at constant velocity. Moreover, the affected area of the membrane during the rupture process was calculated using an elastic deformation model. The elucidated information not only contributes to a better understanding of such relevant process, but also proves the suitability of AFM-based force clamp to study model structures as lipid bilayers. These findings on the kinetics of lipid bilayers rupture could be extended and applied to the study of other molecular thin films. Furthermore, systems of higher complexity such as models mimicking cell membranes could be studied by means of AFM-based force-clamp technique.

Keywords: Chain-Length, Spectroscopy, Nanomechanics, Microscopy, Elasticity, Stability, Membranes, Reveals, Fusion, Ions


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


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


Gavara, N., Roca-Cusachs, P., Sunyer, R., Farre, R., Navajas, D., (2008). Mapping cell-matrix stresses during stretch reveals inelastic reorganization of the cytoskeleton Biophysical Journal , 95, (1), 464-471

The mechanical properties of the living cell are intimately related to cell signaling biology through cytoskeletal tension. The tension borne by the cytoskeleton (CSK) is in part generated internally by the actomyosin machinery and externally by stretch. Here we studied how cytoskeletal tension is modified during stretch and the tensional changes undergone by the sites of cell-matrix interaction. To this end we developed a novel technique to map cell-matrix stresses during application of stretch. We found that cell-matrix stresses increased with imposition of stretch but dropped below baseline levels on stretch release. Inhibition of the actomyosin machinery resulted in a larger relative increase in CSK tension with stretch and in a smaller drop in tension after stretch release. Cell-matrix stress maps showed that the loci of cell adhesion initially bearing greater stress also exhibited larger drops in traction forces after stretch removal. Our results suggest that stretch partially disrupts the actin-myosin apparatus and the cytoskeletal structures that support the largest CSK tension. These findings indicate that cells use the mechanical energy injected by stretch to rapidly reorganize their structure and redistribute tension.

Keywords: Cell Line, Computer Simulation, Cytoskeleton/ physiology, Elasticity, Epithelial Cells/ physiology, Extracellular Matrix/ physiology, Humans, Mechanotransduction, Cellular/ physiology, Models, Biological, Stress, Mechanical