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In Europe, low back pain (LBP) affects the quality of life of up to 30% of the active population. Although the origin of LBP is not well identified and is probably not unique, epidemiological studies suggest that the severity of the disease is correlated with mechanical factors. The lumbar spine is a complex structure where bone, cartilage, ligaments, and muscles have specific and functional mechanical interactions that depend on the shape and structure of each tissue. Thus, any local tissue abnormality may generate non-physiological loadings on surrounding tissues, extending or catalysing a pre-existing degenerative process. To date, lumbar spine finite element modelling is one of the most promising methods to thoroughly investigate functional load transfers between the different spine tissues. However, many geometrical or mechanical parameters used for tissue modelling are still not quantified and need to be assumed. Previous computational studies demonstrated that the intervertebral disc (IVD) plays a key role in distributing the internal forces across the lumbar spine structure. Within the IVD, together with the nucleus pulposus (NP) pressure, the annulus fibrosus (AF) collagen organization is one of the most influential parameter for the disc stabilization. However, AF collagen organization is not unique and seems to depend on the particularity of spine morphologies. Therefore, any lumbar spine model based on particular geometrical data would require specific definitions of fibre-induced AF anisotropy. Unfortunately, particular AF anisotropies are hardly measurable. Thus, the present project aims to investigate the stabilization of a L4-L5 lumbar spine bi-segment finite element model as a function of the AF fibre orientations. For this, a mathematical function, based on local AF matrix shear strains, fibre stresses and fibre stress distribution has been proposed. In this function was implemented and was partially validated on smaller AF model. Enhancements could be proposed and be applied to the L4-L5 model. Methods and procedure to optimize annulus AF orientations could be validated. The proposed evaluation function had to be changed. It was found that an optimal orientation depends mainly on fibre stress and matrix shear stress. The optimizations converged to average angles between 32 and 68 and radial gradients between 10 and 17 degree. Tangential gradients could not be found. Moreover a critical fibre angle could be determined where fibre under uni-axial load are not loaded any more. Using literature data it was possible to solve one of the main issues of collagen fibre orientations in the AF and to bring together the two hypothesis of either a only radial or only a tangential gradient. Moreover it was concluded that pre-stress respectively hoop stress is an nonnegligible factor which has to be accounted for in IVD finite element models.