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Chemical and Biological Engineering, Materials Science and Engineering, Ames Laboratory

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Fickian diffusion into a core-shell geometry is modeled. The interior core mimics pancreatic Langerhan islets and the exterior shell acts as inert protection. The consumption of oxygen diffusing into the cells is approximated using Michaelis-Menten kinetics. The problem is transformed to dimensionless units and solved numerically. Two regimes are identified, one that is diffusion limited and the other consumption limited. A regression is fit that describes the concentration at the center of the cells as a function of the relevant physical parameters. It is determined that, in a cell culture environment, the cells will remain viable as long as the islet has a radius of around 142μm or less and the encapsulating shell has a radius of less than approximately 283μm. When the islet is on the order of 100μm it is possible for the cells to remain viable in environments with as little as 4.6×10−2mol/m−3 O2. These results indicate such an encapsulation scheme may be used to prepare artificial pancreas to treat diabetes.


This is a pre-print of the article King, Clarence C., Amelia Ann Brown, Irmak Sargin, Kaitlin M. Bratlie, and Scott P. Beckman. "Modeling of reaction-diffusion transport into a core-shell geometry." arXiv preprint arXiv:1808.06766v1 (2018). Posted with permission.

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