Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport. 
Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments.  This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 microm in fibre diameter with approximately 60% porosity).  A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved.  Cell oxygen consumption, in accordance theoretically with the Michaelis-Menten law, generates non linearity in the boundary conditions of the convection diffusion equation.  Numerical solutions are obtained with a commercial code (Femlab 3.1; Comsol AB, Stockholm, Sweden).  Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant.  Results show that within a few hours of culture process and for a perfusion velocity of the order of 10(-4) m s(-1), the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism.  But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10(-3) Pa).  Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 x 10(-5) m s(-1).  But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant.  Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.