The cultivation of mammalian cells in aerated suspensions is a widely used practice for the production of therapeutic proteins. However, the determination of optimal cultivation parameters, such as aeration rate, stirring speed or bubble diameter is a challenge due to the complex interactions within the reactor. Up to now, the design and operation of these reactors are mainly based on trial and error methods to minimize cell death rates and increase protein productivity. A major unknown is the mechanical stress induced by the flow that affects apoptosis and protein production. This cell-fluid interaction takes place in turbulent vortices on the scale of the cells. Although significant efforts have been undertaken to clarify these interaction, a major breakthrough has not been achieved yet. This may be attributed to the inability to experimentally determine the membrane tension and energy uptake of suspended cells under turbulent flow conditions. Instead, numerical simulations can be used for the detailed analysis of cell stress.

In our work we investigated the deformation of cells and the corresponding stresses both theoretically and numerically. The flows considered were symmetric and non-symmetric Burger vortices mimicking turbulent vortices. Single cells and cell swarms have been investigated with a special focus on the interaction with the flow field and among the suspended cells. We used the method developed by Koynov et al. [1] and extended by Radl et al. [3] to viscoelastic flows on a two-dimensional grid. Thus, we are able to treat the cells as viscoelastic bodies with exact determined membrane tension. In addition to the complex hydrodynamics, we solved the species conservation equation for dissolved components responsible for cell activity. This gives us a detailed insight into the effects of mass transfer surrounding the cells. Finally, we critically analyzed the restriction to 2D simulations in comparison with a 3D setup. The results provide a promising basis for the multi-scale modeling of animal cell cultures. The connection of our simulation with experimental techniques and macro-scale simulations is discussed. Concepts for the implementation of the proposed simulations and cell growth models into macro-scale simulations are provided.

[1] A. Koynov, G. Tryggvason, J.G. Khinast, 2005, Mass Transfer and Chemical Reactions in Bubble Swarms with Dynamic Interfaces, AIChE J. 51. [2] S. Radl, J.G. Khinast, 2006, Prediction of mass transfer coefficients in non-Newtonian fermentation media using first-principles methods, Biotechnol Bioeng (online since 01/07). [3] S. Radl, G. Tryggvason, J.G. Khinast, 2007, Flow and Mass Transfer of Fully Resolved Bubbles in non-Newtonian Fluids, AIChE J. (accepted for publication).