This is a manuscript that is very different from most of my prior work. It was a unfunded project in collaboration with an associate from ISU. In many regards this is a simplistic perspective of artificial pancreas structures and their performance, but it is good scale project for an undergraduate student in engineering, an over the past several years I've had multiple undergraduate engineers work on the problem. I have ideas for how to expand upon it, but it would be helpful to first find a student that is interested.
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 142 micrometer or less and the encapsulating shell has a radius of less than approximately 283 micrometer. When the islet is on the order of 100 micrometer it is possible for the cells to remain viable in environments with as little as 4.6x102~mol/m-3 O2. These results indicate such an encapsulation scheme may be used to prepare artificial pancreas to treat diabetes.
Here I summarize the work, but the full manuscript can be found on the arXiv: https://arxiv.org/abs/1808.06766
