Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis

A simplified 2D mathematical model for tissue growth within a cyclically-loaded tissue engineering scaffold is presented and analyzed. Such cyclic loading has the potential to improve yield and functionality of tissue such as bone and cartilage when grown on a scaffold within a perfusion bioreactor. The cyclic compression affects the flow of the perfused nutrient, leading to flow properties that are inherently unsteady, though periodic, on a timescale short compared with that of tissue proliferation. A two-timescale analysis based on these well-separated timescales is exploited to derive a closed model for the tissue growth on the long timescale of proliferation. Some sample numerical results are given for the final model, and discussed.