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Math Med Biol. 2014 Dec;31(4):393-430. doi: 10.1093/imammb/dqt015. Epub 2013 Sep 13.

# Multiphase modelling of the influence of fluid flow and chemical concentration on tissue growth in a hollow fibre membrane bioreactor.

### Author information

1
OCIAM, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK pearsonn@maths.ox.ac.uk.
2
Biomechanical Engineering Group, Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, UK.
3
OCIAM, Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.

### Abstract

A 2D model is developed for fluid flow, mass transport and cell distribution in a hollow fibre membrane bioreactor. The geometry of the modelling region is simplified by excluding the exit ports at either end and focusing on the upper half of the central section of the bioreactor. Cells are seeded on a porous scaffold throughout the extracapillary space (ECS), and fluid pumped through the bioreactor via the lumen inlet and/or exit ports. In the fibre lumen and porous fibre wall, flow is described using Stokes and Darcy governing equations, respectively, while in the ECS porous mixture theory is used to model the cells, culture medium and scaffold. Reaction-advection-diffusion equations govern the concentration of a solute of interest in each region. The governing equations are reduced by exploiting the small aspect ratio of the bioreactor. This yields a coupled system for the cell volume fraction, solute concentration and ECS water pressure which is solved numerically for a variety of experimentally relevant case studies. The model is used to identify different regimes of cell behaviour, and results indicate how the flow rate can be controlled experimentally to generate a uniform cell distribution under regimes relevant to nutrient- and/or chemotactic-driven behaviours.

#### KEYWORDS:

asymptotic reduction; multi-phase flow; tissue engineering

PMID:
24036069
DOI:
10.1093/imammb/dqt015
[Indexed for MEDLINE]