Suffocating On a Plastic Bag? Modeling Hypoxia In Porous Polymer-Cell Constructs

This talk will describe modeling  the simultaneous reaction (consumption) and diffusion of oxygen through porous polymer-cell constructs (encapsulated cells), based on reaction-diffusion models first used in the context of chemical reaction engineering. Encapsulated cells are used for xenotransplantation in the context of diabetes treatment; they allow for the transport of chemicals into and out of the construct while maintaining surface properties that prevent the foreign body response from the host’s immune system. We will discuss under what conditions hypoxia-defined as a region of tissue which is deprived of oxygen-could occur in these constructs. We will elucidate the oxygen concentration profile for the zeroth and first order reaction kinetics in slabs, cylinders and spheres, using the Robin set of boundary conditions, which take external resistance to diffusion into account. The concentration profiles require two parameters: the Thiele Modulus, which is analogous to a ratio of a reaction rate to a diffusion rate, and the Biot number for mass transfer, which is analogous the ratio of mass transfer limitations inside of the cells to the mass transfer limitations outside of the cells (i.e. the polymer). We find that under certain sets of conditions, “dead zones” or hypoxic regions can be formed. We will conclude by making recommendations on the prevention of hypoxia in these constructs.