Targeted mechanical properties for optimal fluid motion inside artificial bone substitutes

Our goal was to develop a method to identify the optimal elastic modulus, Poisson's ratio, porosity, and permeability values for a mechanically stressed bone substitute. We hypothesized that a porous bone substitute that favors the transport of nutriments, wastes, biochemical signals, and cells, while keeping the fluid-induced shear stress within a range that stimulates osteoblasts, would likely promote osteointegration. Two optimization criteria were used: (i) the fluid volume exchange between the artificial bone substitute and its environment must be maximal and (ii) the fluid-induced shear stress must be between 0.03 and 3 Pa. Biot's poroelastic theory was used to compute the fluid motion due to mechanical stresses. The impact of the elastic modulus, Poisson's ratio, porosity, and permeability on the fluid motion were determined in general and for three different bone substitute sizes used in high tibial osteotomy. We found that fluid motion was optimized in two independent steps. First, fluid transport was maximized by minimizing the elastic modulus, Poisson's ratio, and porosity. Second, the fluid-induced shear stress could be adjusted by tuning the bone substitute permeability so that it stayed within the favorable range of 0.03 to 3 Pa. Such method provides clear guidelines to bone substitute developers and to orthopedic surgeons for using bone substitute materials according to their mechanical environment.