Biomedical Engineering Reference
In-Depth Information
x
10
−3
8
0.025
0.02
0.5
0.5
6
0.4
0.4
0.015
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4
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0.01
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2
0
0
0.005
0
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0.6
0.8
1
0
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0.6
0.8
1
0
0
0.08
1.2
1
0.5
0.5
0.06
0.8
0.4
0.4
0.3
0.3
0.04
0.6
0.2
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0.1
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0.02
0
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0
Fig. 3 Simulation results from the model developed in Wilson et al. (
2007
) showing how cells
seeded around the periphery of a two-dimensional, rectangular porous scaffold eventually
colonise the scaffold. The pressure profiles for the quadrant are plotted at dimensionless times
t
¼
0
:
5, (top left panel), 1.0, 1.5 and 1.66 (bottom right panel), and show how the maximum
pressure within the scaffold increases as the cells colonise more of the scaffold. The origin
ð
x
;
y
Þ¼ð
0
;
0
Þ
is in the far corner so that the profiles may be easily viewed
3.2.1 Computational Approaches
When using computational fluid dynamics (CFD) approaches, the geometry of the
system is retained (i.e. no simplifying assumptions are made e.g. due to the bio-
reactor being long and thin), and the reactor geometries can be generated using
CAD packages. Such an approach was taken in Lawrence et al. (
2008
) who
considered the effect of bioreactor geometry on the fluid flow through porous
constructs. Rectangular and circular bioreactors were considered, with and without
porous scaffolds, and with different inlet and outlet patterns. The governing
equations (in this case, Navier-Stokes for the single-phase fluid, and Brinkman
equations for flow through the porous scaffold) were solved using computational
fluid dynamics software (COMSOL Multiphysics and ANSYS CFX). The authors
identified non-ideal fluid distribution profiles by looking for ''channeling'' (where
the fluid finds a short cut and leaves the reactor without dispersing through it), and
''dead zones'' which reduce the effective volume of the reactor and prolong the
residence time of some fluid elements. Such non-uniform flow patterns can lead to
poor nutrient distribution, and non-uniform shear stress distribution. The authors
focus on fluid flow only, and highlight nutrient transfer as an open problem. Many
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