Diffusion of biologically relevant molecules through gel-like tissue scaffolds.

Encapsulation of living cells into gel-like matrices that are capable of maintaining their viability over an extended time period is starting to play a major role in medicine in applications such as, cell-based sensors, cellular therapy, and tissue engineering. The permeability of nutrients and waste products through these matrices is critical to their performance. In this article, we report a methodology for selecting scaffolds with different permeabilities and surface area/volume ratios that can be used to house a 3D cell aggregate. Such a system can be modeled if the consumption or production rates for metabolites and waste products, respectively and the diffusion coefficients of these solutes in culture medium and the encapsulating gel matrix are known. A transient finite volume mass diffusion model, based on Fick's law, is derived where the consumption of a solute by the cells is modeled through a source term. The results show that the "performance" of cell-doped gel is critically dependent on the rate at which cells consume key molecules e.g., glucose. Pragmatically, the model also provides insight as to how many cells a given gel geometry and structure can support. The approach used applies to any porous structure where mass transport occurs through diffusion.