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.

Original languageEnglish (US)
Pages (from-to)2450-2473
Number of pages24
JournalBulletin of Mathematical Biology
Issue number12
StatePublished - Dec 2013

All Science Journal Classification (ASJC) codes

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


  • Mathematical model
  • Tissue engineering


Dive into the research topics of 'Cyclic Loading of Growing Tissue in a Bioreactor: Mathematical Model and Asymptotic Analysis'. Together they form a unique fingerprint.

Cite this