Modeling Mass Transfer in Hepatocyte Spheroids Via Cell Viability, Spheroid Size, and Hepatocellular Functions

Hepatocyte aggregation into spheroids attributes to their increased activity, but in the absence of a vascular network the cells in large spheroids experience mass transfer limitations. Thus, there is a need to define the spheroid size which enables maximal cell viability and productivity. We developed a combined theoretical and experimental approach to define this optimal spheroid size. Hepatocyte spheroids were formed in alginate scaffolds having a pore diameter of 100 microm, in rotating T-flasks or spinners, to yield a maximal size of 100, 200, and 600 microm, respectively. Cell viability was found to decrease with increasing spheroid size. A mathematical model was constructed to describe the relationship between spheroid size and cell viability via the oxygen mass balance equation. This enabled the prediction of oxygen distribution profiles and distribution of viable cells in spheroids with varying size. The model describes that no oxygen limitation will take place in spheroids up to 100 microm in diameter. Spheroid size affected the specific rate of albumin secretion as well; it reached a maximal level, i.e., 60 microg/million cells/day in 100-microm diameter spheroids. This behavior was depicted in an equation relating the specific albumin secretion rate to spheroid size. The calculated results fitted with the experimental data, predicting the need for a critical number of viable hepatocytes to gain a maximal albumin secretion. Taken together, the results on mass transport in spheroids and its effects on cell viability and productivity provide a useful tool for the design of 3D scaffolds with pore diameters of 100 microm.