Dynamic Behavior of Cell Populations Growing Under Mass Transport Limitations: Tissue growth in biomimetic scaffolds is strongly influenced by the dynamics and the heterogeneity of cell populations. A significant source of heterogeneity is the depletion of nutrients and growth factors due to transport limitations. Cells slow down, stop dividing or even die when the concentrations of key nutrients and growth factors drop below certain levels in the scaffold interior. As a result, tissue engineers have not yet been able to grow in vitro tissue samples thicker than a few millimeters for metabolically active cells.

In order to better understand these processes, my group is developing a multi-scale, hybrid framework that integrates biology with mathematical, computational, and experimental tools to study heterogeneous cell populations growing in three-dimensional scaffolds. We use a discrete, stochastic model to describe the population dynamics of migrating, interacting and proliferating cells. The diffusion and consumption of nutrients and growth factors are modeled by partial differential equations that are subject to boundary conditions appropriate for the bioreactors used in each case. These PDEs are solved numerically and the computed concentration profiles are fed to receptor-mediated binding/trafficking models or simplified kinetic expressions (i.e. Monod kinetics) to modulate cell proliferation rates and migration speeds. To meet the significant computational requirements of this model, parallel implementations of the hybrid algorithms have been developed for Linux clusters.

Finally, video microscopy and digital image analysis are used to experimentally observe the dynamic behavior of cell populations and find how cell migration and proliferation are influenced by the concentrations of nutrients and growth factors in the culture media, as well as by cell-substrate interactions.

Gas-solid and Liquid-Solid Reactions: Our research in this area focuses on the dynamic behavior of gas-solid or liquid-solid reacting systems with temporally evolving structures. Theoretical and experimental studies are carried out to determine which structural and process parameters control (a) the reactivity of porous carbonaceous materials and (b) the release rates of bioactive agents from multicomponent bioerodible systems. State-of-the-art video microscopy and digital image processing facilities support the experimental studies on coal pyrolysis and combustion. Our primary objective here is the analysis of transient phenomena such as coal particle swelling, macropore formation and heterogeneous or homogeneous ignitions. This information is crucial for the development of theoretical models that can be used for the optimal design of coal utilization processes.