Theroretical and experimental multi-scale study of an artificial bone construct: from tibial osteotomy to cell/fluid interaction

Synthetic bone substitutes are potentially the future gold standard in orthopaedic and traumatologic surgery. The availability of these bone substitutes with different biomechanical properties may well replace autografts in the future as they overcome complications associated with the graft harvesting procedure. In addition, bone substitutes have the potential to replace allografts as the risk of virus transmission may be greatly reduced. However, the biomechanical properties of the new bone substitute should be carefully analyzed to identify optimal parameters and configurations that are likely to favor an enhanced osteointegration. In this thesis, a multi-scale approach is adopted to systematically screen the impact of different mechanical parameters on the bone substitute osteointegration and to propose an optimized solution. At a large length scale (0.5 m), the impact of the bone substitute size, position and mechanical properties is studied to optimize the substitute osteointegration. In the particular case of open wedge tibial osteotomy, the development of a finite element model achieves this goal. It is found that a wedge covering one fourth of the osteotomy and placed posteriomedially together with an anteromedial supporting plate is likely to reduce the fibrous tissue ingrowth at the wedge/bone interface. In addition, the maximum stresses in the bone substitute and in the tibia are computed to be smaller for wedges with stiffness in the range of 0.5 to 3 GPa. Finally, it is suggested that patients should use crutches during the first post-operative weeks to favor the bone ingrowth at the wedge/bone interface and to limit the risk of tibial head fracture or wedge failure. At an intermediate length scale (10 mm), the bone substitute is no longer considered as a bulk material but as a construct: a porous solid material impregnated with fetal bone cells and saturated with a fluid. Such a construct is likely to be a competitive alternative to bone allografts or autografts. However, its biomechanical properties need to be adapted to each particular clinical application to favor its osteoinduction and osteointegration. Therefore, the systematic screening that was initiated at the large length scale is pursued to identify the optimal fluid conductivity and porous mechanical properties as a function of the mechanical environment. A general algorithm based on the poroelasticity theory is proposed to determine the target fluid conductivity and the mechanical properties of the construct. Maximal fluid volume exchange between the construct and its environment is researched whilst bearing in mind that the average fluid-induced shear stress will stay within a defined range for an optimal stimulation of the bone cells. In the particular case of open wedge tibial osteotomy, an optimized construct would be a porous material that has a stiffness of 0.5 GPa, a Poisson's ratio of 0.1, a porosity larger than 50% and a permeability of 1 · 10-10 m2. Poroelasticity based on mechanical and fluid conductivity tests identifies the optimal mechanical environment of PLLA-5%βTCP porous material. It appears that oscillating stresses in the range of 0-0.4 MPa are associated with optimal fluid-induced stimulation of the embedded bone cells. Finally, a constitutive viscoelastic description of the construct is proposed, which can be used to determine the mechanical environment of the PLLA-5%βTCP constructs in a given clinical application. At a small length scale (400 µm), the mechanical interaction that takes place between bone cells attached to the pore walls and the moving fluid is likely to modulate the dynamic fluid-induced shear stress. A theoretical model of this phenomenon identifies the novel dimensionless number Nf s that indicates whether the cells' mechanical stimulation might be damped or amplified. This dimensionless number highlights the central role of the pore size. It is computed that pore diameters smaller than 100 µm are likely to significantly reduce the dynamic stimulation of bone cell. On the other hand, pore diameters larger than 300 µm are found to permit an undamped mechanical stimulation. It is thus hypothesized that constructs with pore diameters larger than 300 µm would more efficiently stimulate the embedded bone cells which appear to be especially sensitive to high frequency mechanical stimulation.

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