Optimizing alginate tubes for cell culture

Cells can be cultured to very high densities in hollow alginate tubes ($5-10\times {10}^{8}cells/mL),$ with the provisothat their nutrient and oxygen needs are met. After the tubes have been extruded, they are suspended in growth medium. Nutrients and metabolic products pass readily through the alginate tube walls and the cells grow from small aggregates until they fill the hollow space in the tube. A mathematical model is presented of nutrient and oxygen transport between the bulk phase and the tubes. Our main result is a necessary condition for growing cells to confluency. It sets an upper limit on the inner tube diameter. This limit depends on the alginate wall thickness, transport properties and consumption rates. Experimental results are reported for l-Wnt-3a cells, which have been expanded in tubes with inner diameters of $400,500,600$and $700\mu m$. For our experimental set-up, glucose was the limiting nutrient. Cells reached confluency in $400and500\mu m$ tubes at bulk glucose concentrations of $20mM$. When the bulk glucose concentration was increased to 25, 30 and 35 mM, confluency was reached in $600\mu m$ tubes for all three cases. Confluency was not achieved in tubes with inner diameters of 700 um, even at the elevated glucose concentrations, suggesting that the dissolved oxygen concentration has become the limiting factor. These results match the model predictions well and confirms that the model can be used to select tube dimensions.