Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis

J. V. Pohlmeyer, L. J. Cummings

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A simplified 2D mathematical model for tissue growth within a cyclically-loaded tissue engineering scaffold is presented and analyzed. Such cyclic loading has the potential to improve yield and functionality of tissue such as bone and cartilage when grown on a scaffold within a perfusion bioreactor. The cyclic compression affects the flow of the perfused nutrient, leading to flow properties that are inherently unsteady, though periodic, on a timescale short compared with that of tissue proliferation. A two-timescale analysis based on these well-separated timescales is exploited to derive a closed model for the tissue growth on the long timescale of proliferation. Some sample numerical results are given for the final model, and discussed. © 2013 Society for Mathematical Biology.
Original languageEnglish (US)
Pages (from-to)2450-2473
Number of pages24
JournalBulletin of Mathematical Biology
Issue number12
StatePublished - Oct 24 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Both authors acknowledge partial financial support from KAUST under Award No. KUK-C1-013-04 in the form of OCCAM Visiting Fellowships. We thank Drs Treena Arinzeh, Shahriar Afkhami, Michael Siegel (NJIT), and Sarah Waters (Oxford) for useful guidance with the development and numerical solution of the model.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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