Breakthroughs in computational modeling of cartilage regeneration in perfused bioreactors

We report about two specific breakthroughs, relevant to the mathematical modeling and numerical simulation of tissue growth in the context of cartilage tissue engineering in vitro. The proposed models are intended to form the building blocks of a bottom-up multiscale analysis of tissue growth, the idea being that a full microscale analysis of the construct, a 3-D partial differential equation (PDE) problem with internal moving boundaries, is computationally unaffordable. We propose to couple a PDE microscale model of a single functional tissue subunit with the information computed at the macroscale by 2-D-0-D models of reduced computational cost. Preliminary results demonstrate the effectiveness of the proposed models in describing the interplay among interstitial perfusion flow, nutrient delivery, and consumption and tissue growth in realistic scaffold geometries.