## Abstract

We develop mathematical models to provide insights into the morphology of a tissue construct formed from a single-cell suspension in culture media, within a rotating bioreactor. The bioreactor consists of a cylindrical vessel of circular cross-section rotating about its longitudinal axis with constant angular speed. Experimental studies show that at rotation rates below a critical value, the cells 'self-assemble' to form smooth 'nodules' that are approximately cylindrical with elliptical cross-section; however, at rotation rates above a critical value, an amorphous construct forms with a highly irregular boundary. The construct is denser than the surrounding culture media and histological studies indicate that the interior of the construct, which is a mix of apoptotic cells and culture media, is surrounded by an outer rim of proliferating cells and collagen. The construct is modelled as a viscous fluid drop surrounded by an extensible membrane in a (less dense) immiscible viscous fluid within a rotating bioreactor. We consider both thin-disk and slender-pipe bioreactors for which the aspect ratio, L*/a* (where L* and a* are the bioreactor length and radius, respectively), is small and large, respectively, and obtain a series of spatially 2D problems (independent of the axial coordinate). We then examine the hypothesis that the construct morphology is a result of the mechanical forces that it experiences by considering the interfacial stability of an initially circular fluid-fluid interface to small-amplitude, oscillatory perturbations. The instability is driven by the density difference between the two fluids, and we investigate the effect of the rotation rate, the (time-dependent) gravitational field, and the material and geometrical properties of the system on the stability properties.

Original language | English (US) |
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Pages (from-to) | 311-337 |

Number of pages | 27 |

Journal | Mathematical Medicine and Biology |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2006 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Neuroscience
- Modeling and Simulation
- General Biochemistry, Genetics and Molecular Biology
- General Immunology and Microbiology
- General Environmental Science
- Pharmacology
- Applied Mathematics

## Keywords

- Linear stability
- Rotating Hele-Shaw
- Rotating Stokes flow
- Rotating bioreactor
- Tissue construct