A bioartificial pancreas (BAP), in which islets of Langerhans (islets) are enclosed in a semipermeable membrane, has been developed to realize islet transplantation without the use of immunosuppressive drugs. Although recent progress in induced pluripotent stem (iPS) and embryonic stem (ES) cells has attracted attention owing to the potential applications of these cells as insulin-releasing cells, concerns about the safety of implantation of these cells remain. The use of the BAP has the advantage of easy removal if insulin-releasing cells derived from iPS/ES cells undesirably proliferate and form tumors in the BAP. Oxygen supply is a crucial issue for cell survival in BAPs as insufficient oxygen supply causes central necrosis of cell aggregates. In this study, we derived several simple equations considering oxygen supply in BAPs in order to provide insights into the rational design of three different types of BAPs (spherical microcapsules, cylindrical capsules, and planar capsules). The equations give (i) the thickness of a capsule membrane leading to no central necrosis of encapsulated cell aggregates as a function of the original size of the cell aggregate; (ii) the oxygen concentration profiles in BAPs; (iii) the effects of encapsulation of a cell aggregate on insulin release; (iv) the amount of encapsulated cells required to normalize blood glucose levels of a patient; and (v) the total volumes and sizes of BAPs. As an example, we used the equations in order to design three different types of BAPs for subcutaneous implantation.
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