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

J. V. Pohlmeyer; L. J. Cummings

doi:10.1007/s11538-013-9902-x

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

J. V. Pohlmeyer, L. J. Cummings

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2450-2473
Number of pages	24
Journal	Bulletin of Mathematical Biology
Volume	75
Issue number	12
DOIs	https://doi.org/10.1007/s11538-013-9902-x
State	Published - Dec 2013

All Science Journal Classification (ASJC) codes

Neuroscience(all)
Immunology
Mathematics(all)
Biochemistry, Genetics and Molecular Biology(all)
Environmental Science(all)
Pharmacology
Agricultural and Biological Sciences(all)
Computational Theory and Mathematics

Keywords

Mathematical model
Tissue engineering

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10.1007/s11538-013-9902-x

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title = "Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis",

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.",

keywords = "Mathematical model, Tissue engineering",

author = "Pohlmeyer, {J. V.} and Cummings, {L. J.}",

note = "Funding Information: 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.",

year = "2013",

month = dec,

doi = "10.1007/s11538-013-9902-x",

language = "English (US)",

volume = "75",

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journal = "Bulletin of Mathematical Biology",

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AU - Pohlmeyer, J. V.

AU - Cummings, L. J.

N1 - Funding Information: 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.

PY - 2013/12

Y1 - 2013/12

N2 - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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