A significant challenge in 3D tissue culture is providing localized microscale flow in a physiologically relevant manner through tissue, especially tissue that is highly metabolically active such as liver. We have developed a microfluidic reactor system that fosters 3D tissue formation on the length scale of a capillary bed, and have demonstrated that cells retain enhanced liver-specific function in this system [1]. We have recently extended these design principles to a microfluidic 12-well plate format to accommodate a broader range of applications including high information content assays [2]. In this paper, we focus on simulation and modeling of the mass transfer and reaction in this new microfluidic system, with an emphasis on predicting the operating regimes that control local oxygen concentration both within the tissue and within the entire system as a whole. We also describe how the model can be extended to the analysis of drug metabolism for applications in the pharmaceutical industry.

One critical issue we address is the coupling of mass transfer and mechanical stresses arising from fluid flow in the tissue. Fluid flow forces are desirable from a physiological perspective, but excessive local forces, such as those that might ensue from flow rates designed to provide maximal mass transfer, might adversely affect tissue function by washing out autocrine factors, stimulating growth of connective tissue, or even compromising survival of parenchymal cells. As such, careful consideration of the coupling between mechanical and chemical gradients is crucial in the design of bioreactors as well as in optimizing of the conditions under which they operate [3]. In this regard, computational methods have been proven as invaluable tools as these relationships and the way they affect each other are mathematically complex.

In our previous bioreactor designs, we have also employed computational methods to solve for both bulk fluid flow and mass transport within the tissue [4]. However, integrating solutions across these two length scales and studying the impact of bulk flow (~ 10 mm) on the perfusion through the filter and the tissue (~ 10 µm) have proven very challenging because of computational limitations due to prohibitively large mesh sizes. Previously, we circumvented this by addressing the two different length scales separately: we simulated bulk flow in the reactors by using ADINA and the oxygen transport and shear forces within a single channel of tissue using FEMLAB.

Here, we present a model of our current multiwell microfluidic bioreactor in which we have been able to couple the fluid flow to convection-diffusion equations across both length scales allowing us to study the physiological regimes of mechanical stress arising from the bulk fluid flow and the impact that it has on oxygen mass transport to the cells. In addition to this, we show how our model can be used to simulate drug metabolism in our bioreactor.

We experimentally validate our model with dissolved oxygen measurements and drug metabolism studies and present data to show reactor performance under different flow conditions. We also show how this model can be used to optimize the operating parameters of this reactor enabling us to objectively select flow rates, cell to media ratios and cell-seeding densities.

Although these studies have been demonstrated on our microfluidic bioreactor system, the modeling methodologies applied here to comprehensively describe a tissue engineering bioreactor are more generic. Though the physical properties of the fluids and tissue may change, the coupling of the fundamental equations are still equally applicable. Likewise, although we have performed our experiments primarily on liver cells, there is no reason why our system is not adaptable for other cells if we are able to recreate the physiological environments necessary for them to maintain their function.

References

1. Sivaraman A, Leach JK, Townsend S, et al. A microscale in vitro physiological model of the liver: Predictive screens for drug metabolism and enzyme induction. Current Drug Metabolism. Dec 2005;6(6):569-591. 2. Domansky K, Inman W, Serdy J, Griffith LG. 3D Perfused liver microreactor array in the multiwell cell culture plate format. Paper presented at: 9th International Conference on Miniaturized Systems for Chemistry and Life Sciences; October 9-13, 2005, 2005; Boston, Massachusetts, USA. 3. Griffith LG, Swartz MA. Capturing complex 3D tissue physiology in vitro. Nature Reviews Molecular Cell Biology. Mar 2006;7(3):211-224. 4. Powers MJ, Janigian DM, Wack KE, Baker CS, Stolz DB, Griffith LG. Functional behavior of primary rat liver cells in a three-dimensional perfused microarray bioreactor. Tissue Engineering. Jun 2002;8(3):499-513.