Skip Navigation



Mathematical Medicine and Biology Advance Access published online on October 16, 2006
Mathematical Medicine and Biology, doi:10.1093/imammb/dql024
This Article
Right arrow Full Text (Rapid PDF)
Right arrow All Versions of this Article:
24/2/169    most recent
dql024v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Cummings, L. J.
Right arrow Articles by Waters, S. L.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Cummings, L. J.
Right arrow Articles by Waters, S. L.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received June 16, 2005
Revised May 23, 2006
Accepted August 29, 2006

Article

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

L. J. Cummings 1 * and S. L. Waters 1

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

* To whom correspondence should be addressed.
L. J. Cummings, E-mail: 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.
Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.