Mechanical behaviour of biological tissue - Anisotropy, non-linearity and fluid flow in annulus fibrosus
Résumé
The intervertebral disc is a highly-specialized element of the spine that provides flexibility and dissipative capacities. When mechanical loads are transmitted along the spine, the intervertebral disc 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 annulus fibrosus. To hold these large circumferential strains, the annulus tissue is a composite material made of oriented structures of collagen fibres embedded in a highly hydrated matrix. These tissues can be assimilated to porous media where liquid flows play a major role in the macroscopic mechanical behaviour. These coupling effects are of major importance when dealing with cell nutrition issues. Indeed, the alternating fluid flows resulting from loading cycles can increase mass exchanges between inner and outer tissues. Annulus samples (2×2×10 mm) were carved out from porcine lumbar discs and subjected to loading cycles with a maximum longitudinal strain of 10%. Two optical microscopes equipped with digital video cameras were positioned perpendicularly to the tensile direction. Specific images analysis procedures allow identifying the transverse thicknesses and the surface strain field. Strong non-linear behaviours were systematically observed corresponding to the stiffening of tissue for large strains. Under loading cycles, a significant hysteresis was observed, in agreement with the essential dissipative function of intervertebral discs. In the plan of fibres, linear reversible responses were consistently observed with Poisson's ratios computed about 0.9. In the plan of lamellae, the linear swelling leads to negative values of Poisson's ratios. Indeed, the transverse behaviour in the plan of fibres is governed by the reorientation of fibres along the loading direction. This strong transverse shrinkage generates a fluid over-pressure inside the porous matrix that discharges in the perpendicular direction. Based on these observations, a FEM was proposed. It integrates lengthy elastic cables embedded in a poro-elastic matrix. With few physical parameters, this model recovers the main features of annulus mechanical behaviour: non-linear stiffness, hysteresis, fibres reorientation, transverse strains. It also underlines the strong influence of the initial fibres angle.