A computational model for biomass growth simulation in tissue engineering

This article deals with computational modeling of tissue growth under interstitial perfusion inside a polymeric scaffold-based bioreactor. The mathematical model is the result of the application of the volume averaging technique to the fluid, nutrient and cellular subsystems, and is capable to account for the temporal evolution of local matrix porosity, as the sum of a time-invariant component (the porosity of the uncellularized polymer scaffold) and a time-dependent component (due to the growing biomass). The solution algorithm is based on a block Gauss-Seidel iteration procedure that allows to reduce each time level of the simulated culture period into the successive solution of linearized subproblems, whose numerical approximation is carried out using stable and convergent finite elements. Numerical simulations are carried out to investigate the role of the design porosity of the scaffold on nutrient delivery and biomass production