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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 $142 mu m$ or less and the encapsulating shell has a radius of less than approximately $283 mu m$. When the islet is on the order of $100 mu m$ it is possible for the cells to remain viable in environments with as little as $4.6times10^{-2} mol/m^{-3}$ $O_2$. These results indicate such an encapsulation scheme may be used to prepare artificial pancreas to treat diabetes.
Injuries to articular cartilage result in the development of lesions that form on the surface of the cartilage. Such lesions are associated with articular cartilage degeneration and osteoarthritis. The typical injury response often causes collateral
Solute transport is modeled using mixture theory, applied to the nanoparticle accumulation and concentration decay in the tissue space for different vascular configurations. A comparison of a single capillary configuration (SBC) with two parallel cyl
This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as ap
While it is well-understood what a normal human placenta should look like, a deviation from the norm can take many possible shapes. In this paper we propose a mechanism for this variability based on the change in the structure of the vascular tree.
We model shell formation of core-shell noble metal nanoparticles. A recently developed kinetic Monte Carlo approach is utilized to reproduce growth morphologies realized in recent experiments on core-shell nanoparticle synthesis, which reported smoot