Pascale Royer

CHEMO-HYDRO-MECHANICAL COUPLING IN ANNULUS FIBROSUS TISSUE

The study focus on biomechanical annulus fibrosus behaviour. On one hand, cyclic tensile tests are performed on annulus samples and bring out a non-linear behaviour with an important hysteresis on each cycle. On the other hand, digital image correlation allows to obtain surfacic strain fields in both anisotropic planes. Finally, a poro-elastic model in large strain is used to understand these observations.

Experimental analysis of the transverse mechanical behaviour of annulus fibrosus tissue

Uniaxial tensile and relaxation tests were carried out on annulus fibrosus samples carved out in the circumferential direction. Images were shot perpendicularly to the loading direction. Digital image correlation techniques accurately measured the evolution of full displacement fields in both transverse directions: plane of fibres and plane of lamellae. In the fibre plane, strains were governed by the reorientation of fibres along the loading direction. This implies strong transverse shrinkage with quasi-linear behaviour. Conversely, a wide range of behaviour was observed in the lamella plane: from shrinkage to swelling. Strong nonlinear evolutions were generally obtained. The strain field in the lamella plane generally presented a central strip section with more pronounced swelling. Our physical interpretation relies on the porous nature of annulus tissue and its anisotropic stiffness. Indeed, the liquid over-pressure generated inside the sample by the strong shrinkage in the fibre plane discharges in the perpendicular direction since rigidity is lower in the lamella plane. Regarding the strain field measured in the lamella plane, this interpretation agrees with (a) symmetric strain distribution with respect to the longitudinal axis of samples, (b) the reversal in behaviour from shrinkage to swelling and (c) the decrease in strain during relaxation tests associated with outward flows. The variety of transverse behaviours observed experimentally could result from uncertainties regarding the initial reference state of tissue samples. Since the mechanical behaviour is highly nonlinear, experimental results underline that a slight uncertainty concerning the pre-stress applied to samples can lead to wide variability in the mechanical properties identified.

Time Analysis of the Three Characteristic Behaviours of Dual-Porosity Media. I: Fluid Flow and Solute Transport

Homogenisation of consolidation and compressible fluid flow in dual-porosity media has highlighted the existence of three characteristic macroscopic behaviours. These three behaviours are, namely, a dual-porosity description which includes memory effects, a single-porosity description with which the microporosity is simply ignored and an intermediate behaviour which we refer as behaviour with reservoir effect. With this latter, the whole dual-porosity medium is represented by an equivalent single-porosity medium. In contrast with a single-porosity behaviour, the porosity of the entire dual-porosity medium is accounted for. During solute transport in dual-porosity media, while memory effects are most often experimentally observed, the homogenised model obtained for the most general values of the involved parameters leads to a model with reservoir effect. Therefore, the observed memory effects are not reproduced by this model and a clear interpretation of the origins of these effects remains an unresolved issue. The study is presented in two complementary articles. The objective of this article is, first, to determine a physical interpretation of the existence of the three characteristic behaviours of dual-porosity media. This is performed by exploring the homogenised models and their domains of validity for the analogy of heat conduction in a dual-conductivity composite. This leads to the original result that consists to relate each type of behaviour to a specific relationship between two characteristic times. This is then used for interpreting the results obtained for compressible flow in dual-porosity media. Finally, it allows to elucidate the conditions under which memory effects may occur during solute transport in dual-porosity media.

Annulus fibrosus microstructure: an explanation to local heterogeneities

Annulus fibrosus (AF) is the outer tissue of nintervertebral discs (IVD). Its peculiar nmicrostructure and biphasic composition define by nan oriented fibre network embedded in a highly nhydrated matrix (60−70%) is usually assimilated to nporous composite material. It confers to AF a nonlinear, nviscous and anisotropic behaviour. nMany experimental and numerical studies nunderlined the anisotropic and non-linear nmechanical behaviours on averaged values n[Ambard and Cherblanc, 2009; Malandrino et al, n2011] but fail to represent the experimental strain nheterogeneities [Baldit et al, 2013a; Michalek et al, n2010], that would be related to the microstructure nand the biphasic constitution. On the other hand, ncharacterization rarely relies on volumic behavior nbut it’s relevant when models deal with soft porous nmedia [Baldit et al, 2013b]. nThis work aims to couple a poro-hyper-elastic nmodel identification with homogenized and ndiscretized geometries highlighting model nsensitivity and limits regarding experimental ntransverse strains measurements.

Mechanical behaviour of annulus fibrosus tissue: identification of a poro-hyper-elastic model from experimental measurements

Annulus fibrosus (AF) is the outer tissue of intervertebral disc (IVD) which is a highly specialized element of the spine that provides flexibility and dissipative capacities. When mechanical loads are transmitted along the spine, IVD mainly supports compression and bending stresses. This results in a hydrostatic excessive pressure in the central nucleus pulposus and generates circumferential tensile stresses in the surrounding AF. To hold these large circumferential strains, AF tissue is assimilated to a composite material made of oriented structures of collagen fibers embedded in a highly hydrated (60−70%) matrix [6]. This particular microstructure and biphasic composition confers to AF a non-linear and anisotropic behavior. Many experimental studies have underlined the anisotropic and non-linear mechanical behavior of AF using uniaxial tensile tests [5-7]. However, few authors have experimentally investigated the biaxial behavior [8].