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

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Abstract

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.

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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.

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  1. Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA

    J. V. Pohlmeyer & L. J. Cummings

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  1. J. V. Pohlmeyer
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  2. L. J. Cummings
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Correspondence to L. J. Cummings.

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Pohlmeyer, J.V., Cummings, L.J. Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis. Bull Math Biol 75, 2450–2473 (2013). https://doi.org/10.1007/s11538-013-9902-x

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  • DOI: https://doi.org/10.1007/s11538-013-9902-x

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