In the first few lines of a paper with the same title [1] published in 1973, Aris warned the reader that "..it would be futile to expect a complete and comprehensive survey of all the overlapping areas and points of contact…" between biology and chemical engineering. Already, there existed a large and rapidly growing body of work on transport and reaction in biological systems, on growth and decay of heterogeneous cell populations, on chromatographic separations, enzyme technology and the development of artificial organs. So, Aris focused his review on the merits of the theoretical approach: the power of dimensionless numbers to provide unifying insights, the ability of simplified models to yield valuable information "…if used skillfully…" To further emphasize these points, he presented a detailed analysis of a problem characterized by the complex interplay of diffusion and reaction, a problem of "current interest" (as he calls it) and one that "…has engaged chemical engineers for more than thirty years…" Such problems were not new in biology. In 1952, Turing had published his landmark paper on the chemical basis of morphogenesis [2] that raised the question of whether pattern and structure could arise out of diffusion and reaction on a surface.

By the early 1990's, tissue engineering had become the hottest area at the interface of biology, medicine and chemical engineering. However, progress in this area has been relatively slow. One of the major obstacles for the successful development of bioartificial tissues has to do with mass transport limitations in the growing tissue. 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, we have not yet been able to grow in vitro tissue samples thicker than a few hundreds of microns for metabolically active cells.

To tackle this classical diffusion-reaction problem, we have developed a multi-scale, hybrid model to study how heterogeneous cell populations grow 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 simplified kinetic expressions to modulate cell proliferation rates and migration speeds.

Not surprisingly, the analysis shows that a dimensionless Thiele modulus can accurately quantify the effect of some key system parameters on the steady-state thickness of peripheral cell layers formed in the 3D scaffolds. More interesting, however, is the finding that the interplay of nutrient diffusion and cell growth can lead to spontaneous pattern formation in systems with uniform initial conditions. These results provide invaluable insights into the fundamental mechanisms governing tissue growth and offer guidelines for the design of biomimetic scaffolds, and bioreactors.

[1]. R. Aris, "Some Interactions Between Problems in Chemical Engineering and the Biological Sciences," in Environmental Engineering, G. Lindner and K. Nyberg, Eds., pp. 215-225, D. Reidel Publishing Co.,. Dordrecht, Holland (1973).

[2]. A. M. Turing, "The Chemical Basis of Morphogenesis," Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237, 37-72 (1952).