Development of a subject-specific Finite Element modelling strategy for the knee joint in physiological conditions with preliminary validation against literature data.

Among synovial joints, the knee is one of the most complex, and the one most at risk of osteoarthrosis, a chronic degenerative disease that affects cartilage and subchondral bone tissue. This thesis is the starting point of a research project of the Computational Bioengineering Laboratory of Istituto Ortopedico Rizzoli in Bologna, that aims to develop a subject-specific Finite Element model of the knee joint (SSFE-K), to be prospectively applied to the understanding of the onset of joint cartilage degeneration. The aim of this thesis was to: -Replicate a gold standard modelling procedure, identified in Bolcos et al. 2018; -Address convergence problems, including sensitivity to meniscal geometry, to achieve model robustness, a major issue in SSFE-K; -Obtain cartilage stress/strain results in a physiological loading condition and indirectly validate these results against literature data. Two models were built: Model One kept the knee joint structures in the pose obtained from the magnetic resonance (MR) images (slightly flexed knee); Model Two was used to reproduce the instant corresponding to 20% of the stance phase of gait, adding a patellar-like force. The segmentation of MR images of a female subject without known articular pathology was done to identify the 3D shape of: femoral cartilage, lateral and medial meniscus, lateral and medial tibial cartilage. Bones were excluded from FE modeling, as they were considered rigid bodies. The four principal knee ligaments were modelled as non-linear springs. Hexahedral mapped FE meshes of cartilages and menisci were obtained through a MATLAB algorithm developed by Rodriguez-Vila et al., 2017. Since this alters the geometries to achieve a smooth hexahedral mesh, we conducted a sensitivity analysis related to meniscal geometry, by varying segmentation and meshing technique. Material properties were implemented: cartilages are transversely isotropic poro-elastic material, menisci are transversely isotropic elastic. The contact between soft tissues was modeled using a hard pressure-overclosure and frictionless surface-to-surface discretization. The tibial plates have been constrained in all six degrees of freedom and the menisci have been appropriately bounded. The components were initially kept separated to avoid compenetration; then brought back to contact through simulation; finally, a vertical force was added on the femoral cartilage. Some convergence issues have been encountered, mainly due to the geometry of the models, to contact non-linearities and to the crushing of the tibial cartilages caused by meniscal horns. We adopted the couple of hexahedral menisci that limited convergence problems and was at the same time similar in the results to the tetrahedral model, which is more consistent with the segmented meniscal geometry. While a direct validation for SSFE-K in intact conditions is impossible, a qualitative comparison with published studies indicated that: -The results of our model are consistent with the mechanical schematization of the problem; -We found large differences with the gold standard model in the only quantity there reported for intact knee conditions (Max. Principal Stress); -We obtained similar results for Min. Principal Stress and Contact Pressure compared to other SSFE-K. In summary, it was possible to replicate a gold standard modelling methodology with many non-linearities, obtaining a fairly stable and robust model and important indications to improve it.