Multiscale modelling of bioreactors for growing bone tissue

A problem presented at the UK MMSG Loughborough 2008.

Presented by:
Mr Norazharuddin Abdullah (Engineering Science, University of Oxford)
Dr Diganta Das (Chemical Engineering, Loughborough University)
SB Abdullah, CL Bailey, CJW Breward, IL Chernyavsky, DB Das, JA Fozard, I Halliday, IJ Hewitt, JR King, AM Middleton, CP Please, JP Ward

Problem Description

Failure to grow thick (3D) implantable bone tissue is partly due to the lack of tissue vascularisation resulting from a fall in nutrient supply to the cells as the distance between the cells and nutrient sources increases. Previous attempts that used porous scaffold without hollow fibre (HF) produced tissues of less than 0.5mm thickness which are of limited clinical use. Recent studies suggest that HF membrane bioreactor (HFMB) may be used to grow bone tissues for implanting into patients with skeletal defects. The HFMBs mimic the capillary network that exists in bones and are effective in supplying nutrients to cells and removing waste products.

The problem proposed involves developing further existing models or developing new mathematical models to describe the important mass transport, flow dynamics and the key kinetics of a HFMB bioreactor. Another aim is to produce an accurate model that will be considerably less computationally expensive than existing approaches (e.g. CFD simulations in 3D).

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Study Group Report

The study-group report presents and analyses a model that describes the transport and kinetics of nutrients within hollow fibre membrane bioreactors (HFMBs). The HFMB is a assumed to be a cylinder with small radius tubes passing axially through the structure in which there is fluid flow carrying nutrient which can diffuse into the structure containing the bone cells. Using scaling arguments the model is reduced to a simple system of PDEs that are computationally inexpensive. A number of results from simulations are presented and, in particular, nutrient penetration was investigated in terms of the systems Péclet and Damköhler's number.

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