|Abstract:|| Articular cartilage is a connective tissue consisting of a relatively few number of cells, the chondrocytes (CCs), that are immersed in an extensive hydrated matrix, composed primarily of proteoglycans and collagens.
In vitro tissue engineering has been investigated as a potential source of functional tissue constructs for cartilage repair, as well as a model system for controlled studies of cartilage development and function. Among the different kinds of devices for the cultivation of 3D cartilage cell colonies, we consider here polymeric scaffold-based perfusion bioreactors. The perfusion fluid supplies nutrients and oxygen to the growing biomass. At the same time, the fluid-induced shear acts as a physiologically relevant stimulus for the metabolic activity of CCs, because it may enhance cell proliferation and
metabolism, provided that the shear stress level is moderate. In this complex environment, mathematical and computational modeling may help in the optimal design of the bioreactor configuration. In this perspective, we propose a computational model for the simulation of the biomass growth, under given inlet and geometrical conditions. Precisely, we consider a two-step approach. First, we perform a simplified short term analysis in which only biomass growth is taken into account, the nutrient concentration and
the fluid-induced shear stress being assumed constant in time and uniform in space. This allows us to calibrate the biomass growth model with respect to the shear stress dependence on experimental data. Then, we carry out a full analysis where the nutrient concentration and perfusion velocity change in time and space and the growing biomass modifies the porosity
of the scaffold matrix, altering the fluid flow. The model parameters are consistently derived from volume averaging techniques that allow us to upscale the microscopic structural properties to the macroscopic level. The predictions we obtain in this way are significant for long times of culture.|