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Mathematical Medicine and Biology Advance Access originally published online on October 16, 2006
Mathematical Medicine and Biology 2007 24(2):169-208; doi:10.1093/imammb/dql024
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Tissue growth in a rotating bioreactor. Part II: fluid flow and nutrient transport problems

L. J. Cummings** and S. L. Waters

School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK

** Email: linda.cummings{at}nottingham.ac.uk


  Abstract

Fluid flow and nutrient transport around a growing tissue construct within a cylindrical bioreactor of circular cross-section are considered. The bioreactor is filled with nutrient-rich culture medium, and the growing tissue construct is modelled as a cylindrical obstacle, also of circular cross-section, at a given (moving) position within the nutrient solution. The bioreactor rotates about its cylindrical axis, and its axial length is small relative to its radius (the high-aspect ratio vessel bioreactor). This small-aspect ratio means that a simple idealized model may be considered, in which (leading order) quantities are averaged across the axial direction. The leading-order fluid flow is then of Hele–Shaw type, and may be solved for explicitly. The trajectory of the tissue construct within the rotating bioreactor is determined by analysis of the various forces acting on it. Several different modes of motion are found to be possible, depending on the experimental conditions, and examples of each type of motion are presented. Additionally, we solve the problem for the nutrient transport around the tissue construct in the special case in which the construct remains fixed in the laboratory frame, and (as the cells proliferate in response to the nutrient available locally) deduce growth rates for the construct. Finally, we discuss our results in the light of possible experimental bioreactor set-ups. We note the present model's limitations, and consider how our work could be extended and improved to inform experimental protocols in future.

Keywords: rotating bioreactor; tissue construct; rotating Hele-Shaw; tissue engineering

Received on 16 June 2005. Revised on 23 May 2006. Accepted on 29 August 2006.


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