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Miniaturized culture systems of hepatic cells are emerging as a strong tool facilitating studies related to liver diseases and drug discovery. However, the experimental optimization of various parameters involved in the operation of these systems is time-consuming and expensive. Hence, developing numerical tools predicting the function of such systems can significantly reduce the associated cost. In this paper, a perfusion-based three dimensional (3D) bioreactor comprising encapsulated human liver hepatocellular carcinoma (HepG2) spheroids are analyzed. The flow and mass transfer equations for oxygen as well as different metabolites such as albumin, glucose, glutamine, ammonia, and urea were solved in three different domains, i.e., free flow, hydrogel, and spheroid porous media sections. Since the spheroids were encapsulated inside the hydrogel, shear stress imposed on them were found to be less than tolerable thresholds. The predicted cumulative albumin concentration over the 7 days of culture period showed a good agreement with the experimental data. Based on the critical role of oxygen supply to the hepatocytes, a parametric study was performed and the effect of various parameters was investigated. Results illustrated that convection mechanism was the dominant transport mechanism in the main-stream section contrary to the intra spheroids parts where the diffusion was the prevailing transport mechanism. In the hydrogel parts, the rate of diffusion and convection mechanisms were almost identical. As expected, higher perfusion rate would provide high oxygen level for the cells and, smaller spheroids with a diameter of 100 μm were at the low risk of hypoxic conditions due to short diffusive oxygen penetration depth. Numerical results evidenced that spheroids with diameter size >200 μm at low porosities (ε = 0.2–0.3) were at risk of oxygen depletion, especially at locations near the core center. Therefore, these results could be beneficial in preventing hypoxic conditions during  in vitro  experiments. The presented numerical model provides a numerical platform which can help researchers to design and optimize complex bioreactors and obtain numerical indexes of the main metabolites in a very short time prior to any fabrications. Such numerical indexes can be helpful in certifying the outcomes of forensic investigations.

Numerical Investigations of Hepatic Spheroids Metabolic Reactions in a Perfusion Bioreactor