Modeling Mass Transfer in Hepatocyte Spheroids via Cell Viability, Spheroid Size, and Hepatocellular Functions Rachel Glicklis, 1 Jose C. Merchuk, 2 Smadar Cohen 1 1 Department of Biotechnology Engineering, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel; telephone: 972-7-646-1798; fax: 972-7-647-2915; e-mail: scohen @bgumail.bgu.ac.il 2 Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel Received 24 June 2003; accepted 2 February 2004 Published online 23 April 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.20086 Abstract: Hepatocyte aggregation into spheroids contrib- utes to their increased activity, but in the absence of a vas- cular 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 pro- ductivity. We developed a combined theoretical and exper- imental approach to define this optimal spheroid size. Hepatocyte spheroids were formed in alginate scaffolds having a pore diameter of 100 Am, in rotating T-flasks or spinners, to yield a maximal size of 100, 200, and 600 Am, 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 Am in diameter. Spheroid size affected the specific rate of albumin secretion as well; it reached a maximal level, i.e., 60 Ag/million cells/day in 100-Am diameter spheroids. This behavior was depicted in an equation relating the specific albumin secretion rate to spheroid size. The calculated results fitted with the exper- imental 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 dia- meters of 100 Am. B 2004 Wiley Periodicals, Inc. Keywords: mass transfer in spheroids; hepatocytes; al- ginate scaffolds; tissue engineering INTRODUCTION Cell aggregation leading to spheroids plays a critical role in maintaining the viability and differentiated functions of iso- lated hepatocytes in culture (Glicklis et al., 2000; Koide et al., 1990; Lazar et al., 1995; Wu et al., 1996). The cells in spheroids exhibit extensive cell–cell contacts and tight junctions, which mimic the morphology and ultrastructure of the native liver lobule (Hansen et al., 1998; Landry et al., 1985). In vitro, hepatocyte spheroids demonstrate improved liver-specific functions and prolonged differentiated state compared to hepatocytes grown as monolayers on collagen- coated dishes (Glicklis et al., 2000). Thus, cell aggregation may be an important step in the regeneration process of he- patic tissue in culture. From the perspective of mass transfer, however, cell ag- gregation in culture may have a detrimental effect on cell viability and function. The spheroids ex vivo usually lack the vascular network that exists in normal vascularized tis- sues. Thus, oxygen and nutrient supply to the cells depends merely on mass diffusion. In large spheroids, diffusional gra- dients are formed so that the cells in spheroid center do not get sufficient nutrients, the waste removal from the center is poor and thus the cells eventually die. Oxygen transport is typically considered as the main limiting factor for nutrient exchange in hepatocytes (Colton, 1995). This article presents a combined theoretical and exper- imental approach to define the optimal spheroid size, which enables maximal cell viability and albumin productivity. Hepatocyte spheroids with different particle sizes were formed in three nonadhesive cultures: 1) within alginate scaffolds having an average pore size of 100 Am in diameter; 2) rotating T-flasks; and 3) spinner flasks. Cell viability and the specific albumin secretion rate were characterized as a function of spheroid size and the relationships were ex- pressed in a series of equations based on mass balances, where it was assumed that oxygen is the main limiting factor. Solving the model equations enabled estimation of the dis- tribution profiles of dissolved oxygen as well as viable cells in spheroids with varying particle size. Furthermore, the model successfully describes that no oxygen limitation will take place in spheroids with up to 100 Am in diameter. When considering albumin secretion, it was found that the specific rate of albumin secretion depended on the number of viable cells in spheroids and it reached a maximal level in 100-Am diameter spheroids. These two results provide the incentive B 2004 Wiley Periodicals, Inc. Correspondence to: Smadar Cohen Contract grant sponsor: Israeli Ministry of Science