common approach in tissue engineering is to fabricate
three-dimensional precursor tissue analogs from cells, scaffolds, and
signaling molecules. A critical design criterion for such tissue
engineering constructs is to support the growth of cells within the
scaffold so that the precursor analog may transform into the tissue of
interest. For relatively thin tissues such as the skin, standard
techniques are often sufficient for the in vitro cultivation of cells
grown on two-dimensional surfaces. But uniform cell growth is not
guaranteed even with thin, porous scaffolds, and heterogeneous growth
can result with a confluent layer of cells at the outer surface, and
limited nonuniform growth in the inner core. For thicker tissues
such as the bone and the liver, the standard cell culture techniques
do not work well in three-dimensional scaffolds. As the thickness of
the precursor tissue analog and the cell density increase within the
scaffold, the limitation of solute transport becomes apparent.
This effect of scaffold thickness has been observed in many three-dimensional tissue engineering systems, where the growth of cells is restricted to a few hundred microns from the fluid-tissue interface. This length scale is similar to the characteristic length for solute diffusion in tissues, where the average inter-capillary distance is on the order of a hundred microns, depending on the metabolic activity of the particular tissue6tissue. Compared to the in vivo tissues with rich capillary networks, the in vitro precursor tissue analogs lack vascularization to support the solute transport within the interior of the scaffolds. Cells located in the interior of the scaffold rely on diffusion for solute transport and are compromised by the depletion of nutrients by cells located near the outer surface.
To quantify determine the role of initial spatial distribution on the transport process quantitatively in tissue engineering systems, we developed a mathematical model to simulate the cell growth as a function of the environmental parameters. We validated the model with experimental systems with initially controlled spatial distribution of cells. In particular, the model takes into account the influence of the cell growth on the temporal and spatial variation of a proliferation-limiting critical molecule, such as oxygen, as well as the reciprocating influence of the distribution of the critical molecule on cell growth.
Reference: Analysis of cell growth in three-dimensional scaffolds, with J. Dunn, W.-Y. Chan, V. Cristini, J.-S. Kim, J.S. Lowengrub, S. Singh and B.M. Wu Tissue Eng., v12 (2006) 705-716.
We are currently developing a more sophisticated model that takes into account angiogenesis when the tissue scaffold is implanted in vivo.