Our research in biofluids focuses mainly on applications arising in tissue engineering. A common experimental protocol in tissue engineering involves seeding cells (e.g. osteocytes or chondrocytes) onto a porous biodegradable scaffold, which can then be placed into a chamber (a "bioreactor") and perfused with nutrient-rich culture medium. The nutrient, together with the shear stress imparted by the flow to the cell surface, stimulates cell proliferation.
We propose and solve mathematical models describing the growth of tissue within such porous scaffolds. Recent work (described in the publications below) has focused on how the scaffold can be manipulated, both chemically and mechanically, in order to provide improved net tissue yield. Current work is concerned with tissue growth within individual scaffold pores, in particular, how the internal pore geometry can affect the final tissue distribution and total yield.
Another current project concerns mathematical modeling of Ischemia-Reperfusion Injury (IRI), the paradoxical further injury that can result to tissue when blood flow is restored after a period of ischemia. A complicated sequence of biochemical reactions, triggered by the reintroduction of shear stress at the endothelial wall when flow is restored, and by the reintroduction of oxygen, can lead to the production of Reactive Oxygen Species (ROS) which can cause cell damage and possibly death. We are studying the potential of so-called "postconditioning therapy", in which the blood flow is restored gradually, rather than abruptly, to the ischemic organ. Our model investigates the efficacy of various postconditioning therapies in an attempt to determine optimal (injury minimizing) scenarios.
Motivated by experimental work (Miller et al. in Biomaterials 27(10):2213 –2221, 2006, 32(11):2775–2785, 2011) we investigate the effect of growth factor driven haptotaxis and proliferation in a perfusion tissue engineering bioreactor, in which nutrient-rich culture medium is perfused through a 2D porous scaffold impregnated with growth factor and seeded with cells. We model these processes on the timescale of cell proliferation, which typically is of the order of days. While a quantitative representation of these phenomena requires more experimental data than is yet available, qualitative agreement with preliminary experimental studies (Miller et al. in Biomaterials 27(10):2213–2221, 2006) is obtained, and appears promising. The ultimate goal of such modeling is to ascertain initial conditions (growth factor distribution, initial cell seeding, etc.) that will lead to a final desired outcome.
A simplified 2D mathematical model for tissue growth within a cyclicallyloaded 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.