a b s t r a c tAn analytical model of the fluid/cell mechanical interaction was developed. The interfacial shear stress, due to the coupling between the fluid and the cell deformation, was characterized by a new dimensionless number N fs . For N fs above a critical value, the fluid/cell interaction had a damping effect on the interfacial shear stress. Conversely, for N fs below this critical value, interfacial shear stress was amplified. As illustration, the role of the dynamic fluid/cell mechanical coupling was studied in a specific biological situation involving cells seeded in a bone scaffold. For the particular bone scaffold chosen, the dimensionless number N fs was higher than the critical value. In this case, the dynamic shear stress at the fluid/cell interface is damped for increasing excitation frequency. Interestingly, this damping effect is correlated to the pore diameter of the scaffold, furnishing thus target values in the design of the scaffold. Correspondingly, an efficient cell stimulation might be achieved with a scaffold of pore size larger than 300 mm as no dynamic damping effect is likely to take place. The analytical model proposed in this study, while being a simplification of a fluid/cell mechanical interaction, brings complementary insights to numerical studies by analyzing the effect of different physical parameters.

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. Ceramics and polymer porous structures can be produced with controlled pore size, porosity, mechanical resistance, and surface properties.1-5 Thus, novel artificial bone substitutes can be customized as to their physical properties. The question becomes which material favored best osteointegration in order to shorten the postoperative recovery phase. Much effort has been spent on searching for the optimal bone substitute architecture with regard to degradation rate and osteointegration. [6][7][8][9][10][11][12] Empirical studies show that pore interconnectivity must be >50 mm and pore diameter must be >100 mm, although this latter value is still debated. 13,14 No consensus has emerged on optimal permeability, porosity, and bulk stiffness. The need exists, therefore, to develop a synthetic approach to define target mechanical and fluid conductivity properties that likely favor osteointegration.To develop such an approach, the mechanical environment and the associated fluid motion must be considered. Many physico-chemical and biological phenomena are involved in osteointegration, but fluid motion due to mechanical loading plays a central role in bone substitute osteointegration, 15 bone mechanotransduction, 16,17 and angiogenesis. 18,19 Indeed, the transport of nutriments, wastes, biochemical signals, and cells throughout the substitute stimulates osteoblasts. 20,21 In addition, fluid motion exerts direct mechanical stress on bone cells that can stimulate 22 or damage 23 cells, depending on its magnitude. Shear stress between 0.03 and 3 Pa triggers production of essential proteins by osteobla...