Optimisation of fluid distribution inside a porous construct

A problem presented at the UK MMSG Nottingham 2006.

Presented by:
Dr Sarah Cartmell (Institute of Science and Technology in Medicine, University of Keele)
Mr Vipin Michael (Institute of Science and Technology in Medicine, University of Keele)
C Bailey, R Booth, S Cartmell, L Cummings, R Dyson, V Michael, S Naire, L Parsons Chini, S Payvandi, Z Rong, S Waters, RJ Whittaker, H Woollard

Problem Description

Orthopaedic disease or trauma can lead to substantial loss of tissue significantly affecting the patient's quality of life. Tissues such as bone and cartilage can be grown outside the body. To do this, the cartilage cells (chondrocytes) or bone cells (osteoblasts) are taken from a small piece of cartilage or bone tissue from the patient and grown up in a dish in the laboratory. These cells are then placed onto a porous biodegradable scaffold. This cell/scaffold sample can then be cultivated in an environment called a 'bioreactor'.

To overcome some of the problems associated with larger bioreactors, it is proposed to incorporate hollow porous-walled fibres within the scaffold and allow additional media perfusion through them. This will potentially increase the availability of oxygen at closer proximity to the cells and overcome some of the limits to oxygen diffusion. The study group was asked to simulate the perfusion conditions in this system and obtain velocity, pressure, and shear stress field throughout the scaffold. Additionally we would like to obtain an oxygen profile through the construct generated by the tube flow.

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Study Group Report

Mathematical modelling was used to investigate various features of the flow, nutrient delivery, and waste product removal, within the bioreactor system. We first formulated a Darcy flow model in which the interior of the bioreactor was modelled as a porous medium, and flow in the porous fibres considered separately. Numerical solutions to this system were found, as were solutions to full Stokes equations within an idealised scaffold.

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Follow-Up Activities

The following publications have been written as a result of this problem:

Mathematical modelling of fibre-enhanced perfusion inside a tissue-engineering bioreactor
RJ Whittaker, R Booth, R Dyson et. al. (2009)
Journal of Theoretical Biology 256 (4), 533–546.