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Cells Culture in Perfusion Bioreactors: Analysis and Selection of Scaffold Channelling Structure Based on Reynolds and Peclet Numbers

Francesco Coletti and Sandro Macchietto. Chemical Engineering, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom

Tissue Engineering has the goal of producing complete, functional tissue and organs starting from patients' own cells, thus avoiding the risk of tissue rejection upon implantation and the need for severe treatments with immune depressive post-surgery therapies.

The process of growing cells in a bioreactor is very challenging. Many complex phenomena occur and interact together in the bioreactor where the cells are seeded and grown on a porous support scaffold (for example, a collagen sponge). In particular, in three-dimensional cell cultures many problems are related to the transport of medium substrate to the inner regions of the scaffold. A way to overcome these difficulties is to use a perfusion bioreactor which forces the medium flow through the internal porous network of the scaffold thus mitigating internal diffusional limitations (Martin et al., 2004). A further enhancement can be achieved by building suitable geometries of the scaffold itself which incorporate, for example, channels throughout the tree-dimensional porous structure of a collagen sponge (Radisic et al., 2005).

Given consumption rates and diffusion coefficient, the steady-state substrate concentration profiles within a tissue in a scaffold of defined channel structure can be predicted (e.g. Radisic et al., 2005). However, little is known about the dynamics of cells growth in these type of scaffolds and, in particular, how the interaction between scaffold geometry, substrate transport by diffusion and convection, and kinetics of cell reaction and proliferation, affect the local and overall cell growth and cell distribution.

The purpose of this paper is to present some initial results towards the development of a systematic method for the analysis (and eventually, the design and optimisation) of a macroscopic channelling structure for such scaffolds. Here, a simple, single-layer scaffold geometry is considered, with straight passing channels. A mathematical dynamic, 3D transport-reaction model, proposed in previous work (Coletti et al.,2006), is used to describe the transport phenomena occurring and interacting in such a perfusion bioreactor with and without channelled scaffold structures. First, the roles of diffusion and convection of nutrient species (oxygen and glucose), from the channels to the growing tissue are investigated, interpreted and generalised in terms of the Reynolds and Peclet dimensionless numbers. Then, some guidelines are developed for the selection of the diameter of the channels and their spacing, so as to maximize cell growth with respect to time and the total volume of scaffold, while achieving a high-density cell distribution. Results are presented with reference to a specific application involving the culture of immortalized rat cells C2C12 on a collagen scaffold.


Coletti, F., Macchietto, S., Elvassore, N. (2006). Mathematical modelling of three-dimensional cell cultures in perfusion bioreactors. Accepted for publication.

Martin, I., Wendt, D., and Heberer, M. (2004). The role of bioreactors in tissue engineering. Trends in Biotechnology, 22(2), 80-86.

Radisic, M., Deen, W., Langer, R., and Vunjak-Novakovic, G. (2005). Mathematical model of oxygen distribution in engineered cardiac tissue with parallel channel array perfused with culture medium containing oxygen carriers. Am J Physiol Heart Circ Physiol , 288(3), H1278-1289.