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Transcript of Flow Modelling
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Journal of Biotechnology 119 (2005) 181196
Flow modelling within a scaffold under the influence ofuni-axial and bi-axial bioreactor rotation
H. Singh a,1, S.H. Teoh b,2, H.T. Low b,3, D.W. Hutmacher b,
a Tissue Engineering Laboratory E3-05-04, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singaporeb Division of Bioengineering, National University of Singapore, 9 Engineering Drive 1, EA 03-12, Singapore 117576, Singapore
Received 20 September 2004; received in revised form 17 March 2005; accepted 29 March 2005
Abstract
The problem of donor scarcity has led to the recent development of tissue engineering technologies, which aim to create
implantable tissue equivalents for clinical transplantation. These replacement tissues are being realised through the use of
biodegradable polymer scaffolds; temporary/permanent substrates, which facilitate cell attachment, proliferation, retention and
differentiated tissue function. To optimise gas transfer and nutrient delivery, as well as to mimic the fluid dynamic environment
present within the body, a dynamic system might be chosen. Experiments have shown that dynamic systems enhance tissue
growth, with the aid of scaffolds, as compared to static culture systems. Very often, tissue growth within scaffolds is only seen
to occur at the periphery. The present study utilises the Computational Fluid Dynamics package FLUENT, to provide a betterunderstanding of the flow phenomena in scaffolds, within our novel bioreactor system. The uni-axial and bi-axial rotational
schemes are studied and compared, based on a vessel rotating speed of 35 rpm. The wall shear stresses within and without the
constructs are also studied. Findings show that bi-axial rotation of the vessel results in manifold increases of fluid velocity within
the constructs, relative to uni-axial rotation about the X- and Z-axes, respectively.
2005 Elsevier B.V. All rights reserved.
Keywords: Computational fluid dynamics; Tissue engineering; Bioreactor
Corresponding author. Tel.: +65 6874 1036; fax: +65 6872 3069.
E-mail addresses: [email protected] (H. Singh),
[email protected] (S.H. Teoh), [email protected]
(H.T. Low), [email protected] (D.W. Hutmacher).1 Tel.: +65 6874 8870; fax: +65 6777 3537.2 Tel.: +65 6874 4605; fax: +65 6872 3069.3 Tel.: +65 6874 2225; fax: +65 6872 3069.
1. Introduction
In a number of long-term tissue engineering stud-
ies under static conditions (e.g. Petri dish), it has
proven extremely difficult to promote the high-density
three-dimensional in vitro growth of cells that have
been removed from the body and deprived of their
normal in vivo vascular sources of nutrients and gas
exchange. To optimise gas transfer and nutrient deliv-
0168-1656/$ see front matter 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.jbiotec.2005.03.021
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182 H. Singh et al. / Journal of Biotechnology 119 (2005) 181196
ery, as well as to mimic the fluid dynamic environment
present within the body, a dynamic system has to be
chosen. The bioreactor is one example that attempts
to fulfil these requirements, particularly in the studyof tissue engineering, by simulating the physiological
and fluidic conditions that occur in vivo (Freed and
Vunjak-Novakovic, 2002; Papoutsakis, 1991; Cherry
and Papoutsakis, 1986). Cells have often been seen to
grow well along the periphery of 3D scaffold, while
proliferation is often significantly affected at the centre
of the scaffold, where necrotic neo-tissue can some-
times be seen. This is partly dueto poor fluidictransport
of media and scaffold design, among other reasons.
Therefore, simulations that provide such flow visual-
izations could greatly assist in the design of scaffolds
as well as bioreactor.
A number of experimental studies were previously
reported by using different bioreactor systems (Freed
et al., 1994; Martin et al., 2004; Vunjak-Novakovic et
al., 1996). However, limited information has been pub-
lished on studies that attempt to simulate the dynamic
fluid environment prior to commencing experimen-
tal studies. Advantages of computational simulations
include the ability to modify and study the effects of
bioreactor design with respect to the flow analysis,
without having to develop and construct actual phys-
ical models, or to run a large number of experiments.This is coupled with the significant savings in time and
costs. Furthermore, visualisation of flow as enabled by
the simulation package is a key factor in determining
the efficacy of the system, and allows for design opti-
mization prior to bioreactor design and modifications.
NASA has taken significant strides relating to their
rotating bioreactor studies, under the influence of unit
and micro-gravity. While it is known that in the pres-
ence of body forces, density differences between the
cells attached to micro-carriers and the fluid medium,
cause relative motion resulting in mechanical shearand increased mass transport. However, in the micro-
gravity environment, buoyancy effects are greatly
reduced. The gravity of Earth is replaced by centripetal
acceleration as the dominant body force. For a typ-
ical rotation rate of 2 rpm, within a 0.05 m diameter
vessel, the magnitude of the body force is reduced
(Kleis and Pellis, 1995) to approximately 0.001 m/s2.
Kleis et al. (1996) proceeded further by carrying
out studies on mass transport, with regards to their
micro-gravity bioreactor model. Consequently Boyd
and Gonda (1990) mathematically modelledthe motion
of particles within the NASA bioreactor model at both
unit and micro-gravity. However, the effects of gravity
can be felt by almost everything on Earth, and is notignored here for practical reasons. Rotating (Bursac
et al., 2003; Martin et al., 2004) and perfusion (Martin
et al., 2004; Bancroft et al., 2003; Darling and
Athanasiou, 2003; Sodian et al., 2002) bioreactors,
each with their own flow characteristics, are currently
being utilized for studies involving the culturing of
boneand cartilage.Thesebioreactor models induce dif-
ferent normal and shear forces that act on cells, with
varying consequences.
One aspect that this paper will focus on is that of
shear stresses acting on cells and tissues. A response
of an endothelial monolayer of cells subject to steady,
laminar shear stresses is that of an alteration in mor-
phology. A typical change would occur from an ini-
tial polygonal pattern, to one, which depicts an elon-
gated profile, being aligned to the direction of fluid
flow (Levesque and Nerem, 1985; Levesque et al.,
1989; Stathopoulos and Hellums, 1985). This change
is basically accompanied by the restructuring of the
cytoskeleton, or more specifically, the alignment of
microtubules, followed by the formation of actin stress
fibres. Similar experiments were conducted on bovine
endothelial cells. It was found that the stiffness ofendothelial cells exposed to shear stresses of 2 Pa,
increased with the duration time of exposure. However,
after 24 h of exposure, the stiffness of the endothe-
lial cells was similar all around the cell, indicating
the ability of the cells to adapt to the changes in the
environment. This concept includes that of stress fibre
orientation, as mentioned in the paper by Yamada et al.
(2000).
Olivier and Truskey (1993) showed that the flow
regime itself, and not just the magnitude of shear
stress, plays a critical part. Their experiments involvedturbulent flows as generated in a cone and plate vis-
cometer, which actually resulted in the detachment of
anchorage-dependent cells at shear stresses of only
1.5 dyn/cm2.
At relatively higher levels of shear stress, rang-
ing from 26 to 54 dyn/cm2, human endothelial cells
were found to detach from its surface and correspond-
ingly exhibited reduced viability (Stathopoulos and
Hellums, 1985). In contrast to this, no cell loss was
reported for bovine aorta endothelial cells, which were
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H. Singh et al. / Journal of Biotechnology 119 (2005) 181196 183
subject to a stress level (Levesque and Nerem, 1985)
of approximately 85 dyn/cm2. Pritchard et al. (1995)
found that adhesion generally increases with decreas-
ing wall shear stress. It is also now well documentedthat cell metabolism is affected by fluid stresses. Shear
stresses, within limits, tend to stimulate the release of
specific enzymes and growth factors, thereby enhanc-
ing cellular attachment and proliferation.
Stathopoulos and Hellums (1985) found that HEK
cells release urokinase, due to variations in shear stress
levels. Furthermore, human umbilical vein endothelial
cells were found to release a five-fold amount of prosta-
cyclin at 10 dyn/cm2, as compared to near-zero stress
conditions. Similarly, Vunjak-Novakovic et al. (1996,
1998) studied the affects of dynamic seeding within
polymer scaffolds with respect to chondrocytes, and
found that these cells can be conditioned to grow
under the correct shearstress levels. Chondrocyteshave
been known to proliferate better under the influence of
shear stresses and are able to withstand higher loads as
compared to chondrocytes cultured statically (Sucosky
et al., 2003). Both Porter et al. (2005) and Raimondi
et al. (2004) utilised CFD techniques to model the
effects of perfusion, to better comprehend the influence
of perfusion and hence shear stresses, on 3D cultures.
Lappa (2005) on the other hand, developed a rigorous
set of equations to model fluid flow and algorithms toestimate soft tissuegrowth within a bioreactor. Redaelli
et al. (1997) on the other hand, attempted to model
pulsatile flow within arteries. This intriguing article
describes how a FORTRAN algorithm was interfaced
to FIDAP, a commercially available CFD package, and
then simulated.
2. Software and methodology
2.1. GAMBIT and FLUENT
GAMBIT (Fluent Inc.), being a powerful graph-
ical modeling tool, was utilised as a pre-processor
for the Computational Fluid Dynamics package, FLU-
ENT. This general-purpose CFD tool can solve many
fluid flow problems such as steady, unsteady, lami-
nar and turbulent flows, heat transfer, Newtonian and
non-Newtonian flows, among others. FLUENT also
provides excellent mesh flexibility as well, allowing
the grid to be refined or coarsened based on the require-
Fig. 2.1. Actual bioreactor prototype model.
ments of the flow solution. Flow solutions are based on
the conservation of mass, momentum and energy equa-
tions. GAMBIT and FLUENT were therefore used in
tandem, to model the flow of fluid within our prototype
bioreactor model.
2.2. The bioreactor model
A novel bi-axial bioreactor system was developed
by a team from the National University of Singaporeand the Singapore Polytechnic. The unique design of
the entire system adds some flexibility that is some-
times found to be lacking in commercially available
bioreactors. This novel design involves the bioreac-
tor being vertically upright, instead of the conven-
tional horizontal-type vessel that is so often seen (see
Fig. 2.1). However, the fact that allows this design to
particularly stand out is that it allows for rotation either
about the vertical axis (spinning), the horizontal axis
(tumbling), or even rotation simultaneously about both
axes(gyroscopic action). Ideally, the utilisationof these
features would lead to enhanced cell culture media flow
throughout the entire vessel (see Fig. 2.2and Table 2.1).
2.3. The tissue engineering scaffold
The scaffolds utilised for the simulations are rou-
tinely produced by our group (Zein et al., 2002;
Hutmacher et al., 2004). The poly()caprolactone
(PCL) scaffolds used have been studied extensively for
bone engineering applications. The scaffold fibres are
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184 H. Singh et al. / Journal of Biotechnology 119 (2005) 181196
Fig. 2.2. Profile of novel bioreactor.
300m diameter and form a 90 lay-down pattern, to
form a scaffold of regular architecture with dimensions
of approximately 5 mm 5 mm 5 mm (Fig. 2.3). As
with the bioreactor models, the point of origin of the
scaffold lies at its very centre.
2.4. Scenarios, criteria and guidelines
The following set of simulations were performed,
and are as follows:
Bioreactor: rotation about the horizontal X-axis
(with scaffold);
Bioreactor: rotation about the vertical Z-axis (with
scaffold);
Bioreactor: bi-axial rotation about the horizontal and
vertical axes (with scaffold).
Table 2.1
Bioreactor dimensions
Component Dimensions (mm)Vessel diameter 94
Vessel height 130
Inlet length 6
Inlet diameter 6
Inlet distance from centre (radially) 23.5
Outlet tube length 100
Outlet tube inner diameter 6
Outlet tube outer diameter 9
Outlet distance from centre (radially) 23.5
Outlet tube through-hole diameter (6) 3
Vertical distance between holes 16
Fig. 2.3. MicroCT of a scaffold produced by rapid-prototyping
(Hutmacher et al., 2004).
Firstly, it must be noted that simulations (without
scaffolds) were used to determine appropriate locations
for placing the scaffolds. Moreover, flow phenomena
were studied, and the locations of turbulent artifacts
such as eddies and vortices were studied. Consistency
and uniformity of flow throughout the chamber were
also criteria that were particularly sought for. Where
possible, regions of very low or stagnant fluid velocity
were also avoided, as placing scaffolds within these
regions would not possibly allow for adequate flow of
culture media within and through the scaffolds, therebypotentially reducing the flow of nutrients to cells, as
well as the ability of waste to be removed.
Secondly, only the Z-axis (vertical centre-line pass-
ing through the vessel) was utilised as a line of refer-
ence, whereby specific positions along this line were
identified for placement of scaffolds. The main reason
for this is that shear stresses tend to be minimised at
distances furthest from the walls. In this way, exces-
sive shear stresses could potentially be avoided. Addi-
tionally, points along this reference line having higher
velocities were selected for scaffold fixation. This was
done, bearing in mind that there were no eddies or tur-
bulent artifacts within close proximity to the selected
positions.
2.5. Conditions, settings and meshing
Table 2.2 indicates values and parameters that were
used for the simulations. The contour and velocity plots
were captured at equal intervals of 0.0235 m, dividing
the entire vessel into sections of four. On the whole,
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H. Singh et al. / Journal of Biotechnology 119 (2005) 181196 185
Table 2.2
Boundary conditions and settings
Culture media
Density (kg/m3) 1030
Dynamic viscosity (Pa s) 0.0025
Boundary conditions
Inlet velocity (m/s) 0.5895
Vessel rotational velocity (rpm) 35
Gravity (+Zdimension) (m/s2) 9.81
Schemes
Solver: segregated, implicit
Flow: laminar
Pressure: body-force weighted
Pressurevelocity coupling: PISO
Momentum: second order upwind
three sections were at equal intervals along the Y-axis
(Planes 13), enabling viewing from the front. Another
three equal sections were taken at the side, enabling
analysis from the transverse perspective point of view.
These transverse sections (Planes 46) were conse-
quently captured along the X-axis.
All the axial conventions must be appropriately
noted and strictly adhered to. By plotting for the X-,Y- and Z-directions, the location of the maximum
wall shear stress was determined and pinpointed. The
shear stress at this specific location would thereforebe expected to have adverse effects on cells, and very
possibly resulting in their death. Counter-measures
could therefore be devised, so as to prevent damage to
cells at such locations.
The mesh applied (Fig. 2.4) here is that of a tetrahe-
dral mesh. GAMBIT is generally capable of meshing
Fig. 2.4. Sectioned mesh of scaffold via central plane.
an entire volume at one go, by applying the same
meshing constraints throughout, such as a constant
interval count. The outlet tube, however, was meshed
individually by meshing its faces due to complexcurved surfaces. Meshing was carried out face by face,
with an interval count of 20. Each individual scaffold
fibre length was meshed with a 10-interval count. The
remaining volume was the meshed with an interval
count of 50 throughout Mesh convergence analyses
were carried out to prior to the actual simulations
to select a suitable mesh density for this study. Four
sets of 3D meshes of the bioreactor vessel alone were
generated at varying degrees of mesh refinement at
(i) 50606, (ii) 227191, (iii) 282440 and (iv) 321674
tet. elements. All meshes converged successfully with
a convergence error criterion of 0.001. Velocity pro-
files were compared in FLUENT at specific planes and
points. However, only a slight increase in accuracy was
noted (approx. 3%) despite a significant increase in the
number of elements and computational time from (iii)
to (iv). Mesh (iii) was therefore selected based on its
accuracy and its economy.
Fig. 2.5indicates the sections taken of the bioreactor
for our study. Fig. 2.6 presents a section of the scaffold
as viewed from the front (sectioned vertically), with
Points 15 labelled for our analysis. Fig. 2.7 presents
the locations of Points 610 within the scaffold, asviewed from the underside when the scaffold is sec-
tioned horizontally. Fig. 2.8depicts a single pore within
the scaffold, visually presenting us with flow parame-
ters that will be discussed throughout this article.
Fig. 2.5. Plan view of vessel and corresponding sections along XY
planes with planes spaced at equal intervals (quarter-distance) of
0.0235m.
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186 H. Singh et al. / Journal of Biotechnology 119 (2005) 181196
Fig. 2.6. Scaffold sectioned along centralXZplane (front view) with
specific points and axis labelled.
Fig. 2.7. Scaffold sectioned along central XYplane (as viewed from
underside of scaffold) with specific points and axis labelled.
Fig. 2.8. Depiction of a scaffold pore with velocityvectors and shear
stresses acting along all surfaces.
Particular attention waspaidto the flowenvironment
within the scaffolds. Prior to this (not shown here), the
most suitable locations were determined for placing the
scaffolds, for each and every rotational scheme. Thiswas done to maximise the performance of each con-
figuration. The configurations were then finally com-
pared.
3. Results and discussion
3.1. Rotation about X-axis
Fig. 3.1.1 reveals the contour plots captured at
Planes 13, while Fig. 3.1.2 depicts contour plots at
side Planes 46. The scaffold centre was positioned at
the middle of the bioreactor at coordinate (0,0,0).
Fig. 3.1.3 displays the scaffold as sectioned verti-
cally, through its centre. As with the previous scenario,
Points 15 were selected for analysis, while Fig. 3.1.4
reveals the presence of an eddy. This eddy can be
observed to exist behind the scaffold. Additionally, it
can also be seen from both figures that the vectors seem
to be of higher intensity near the front-right corner
of the scaffold. It is very likely that escalated levels of
wall shear stresses would be expected to occur along
the external surface of the scaffold at these regions.Table 3.1 displays the velocity magnitudes and u,
v and w components for locations within the scaffold,
as designated by Points 15. Points 5 and 4 experience
the highest fluid velocity magnitudes at approximately
3.52 103 and 3.01 103 m/s, respectively, while
Points 1 and 2 experience the lowest velocities, at
1.25 103 and 1.49 103 m/s. The primary flow
direction is noted to be in the Y-direction. Point 7 can be
seen to experience a relatively high velocity magnitude
with respect to the other points, at 2.81 103 m/s.
The dominant v velocity component is approximately2.6 103 m/s.
Fig. 3.1.5 depictsthe wall shear stresses actingalong
the surfaces of the scaffold fibres. The average wall
shear stresses were found to generally lie between 0.8
and 1.2 Pa, as data for a variety of locations within the
scaffoldwere extracted and counter-checked.However,
specific regions were seen to indicate high peaks in wall
shear stresses.
It can also be noticed that at the very front of the
diagram, a lighter shade of blue can be seen represent-
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H. Singh et al. / Journal of Biotechnology 119 (2005) 181196 187
Fig. 3.1.1. Velocity contour plots captured at frontal Planes 13 for bioreactor with scaffold rotating about X-axis.
Fig. 3.1.2. Velocity contour plots captured at side Planes 46 for bioreactor with scaffold rotating about X-axis.
Table 3.1
Velocities at Points 110 within scaffoldbioreactor rotation about X-axis
Points
1 2 3 4 5 6 7 8 9 10
Magnitude (103 m/s) 1.25 1.49 2.12 3.01 3.52 1.77 2.81 1.78 2.04 1.68
x (103 m/s) 0.35 0.50 0.29 0.25 0.31 0.13 0.40 0.30 0.33 0.50
y (103 m/s) 1.20 1.40 2.10 3.00 3.50 1.25 2.60 1.75 1.75 1.00
z (103 m/s) 0.04 0.12 0.08 0.04 0.14 1.25 1.00 0.05 1.00 1.25
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Fig. 3.1.3. Sectioned scaffold and velocity vector plot at y = 0 m plane within bioreactor rotating about X-axis.
ing approximately 1.2 Pa in shear stresses. This occurs
near the zones of contact between criss-crossing scaf-
fold fibres.It is also noticed that forthe externalsurface,
the colour-coded dark blue colour softens to cyan
and light green, from left to right. This implies that
the higher wall shear stresses are located towards the
right side (positive X-direction) of the scaffold. One
very likely reason for this phenomenon relates to thedesign of the bioreactor. It is suspected that the pres-
ence of the outlet tube tends to deviate and diverge the
swirling fluid, reducing fluid velocity andshear stresses
especially in areas within close proximity to the outlet
tube. The fluid then accelerates, increasing in veloc-
ity due to the rotating action of the bioreactor, thereby
resulting in higher shear stresses to the right (positive
X-direction) of the scaffold. The location of the peak
wall shear stress can be seen within Fig. 3.1.5, as theminiscule red spot (indicated by the arrow).
Fig. 3.1.4. Sectioned scaffold and velocity vector plot at z = 0 m plane within bioreactor rotating about X-axis.
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Fig. 3.1.5. Wall shear stressrange of 04Pa forscaffold withinbiore-actor rotating about X-axis.
3.2. Rotation of bioreactor with scaffold about
Z-axis
For this scenario, the scaffold was positioned at the
coordinate (0,0,0.028), 28 mm above the origin rela-
tive to our directional convention. Figs. 3.2.1 and 3.2.2
depict similarities that can be seen to occur with respect
to the Planes 2 and 5, where a central core of slow-
moving fluid is noted. This is pronounced in Fig. 3.2.2.As previously mentioned, the formation of the core
is possibly due to fluid velocity being a function of
the angular velocity and radius of the chamber. As
the angular velocity is held constant, the fluid velocity
increases proportionally as the distance from the rotat-
ing center increases. Furthermore, centrifugal forcestend to displace fluid outwards. In Fig. 3.2.2, aneddy
can be seen to have formed, as shown in Plane 5. The
location of this entity is approximately one third of
the bioreactor height from the base, directly below the
scaffold. This recirculation zone can be related to the
corresponding contour plot in Fig. 3.2.2, within the
dark-blue zone that is in the bottom half of the ves-
sel. Plane 6 also reveals another eddy, corresponding
in location to thecontour plot. This phenomenon occurs
near the base of the vessel.
Fig. 3.2.3 displays the sectioned scaffold (as viewed
from the front) where velocity vectors seem to be
deflected by the scaffold. This occurs on the right and
bottom sides of the scaffold. Additionally, a small eddy
can be seen to have formed just slightly to the left of
the scaffold (Fig. 3.2.3). The next frame depicts the
scaffold sectioned along the horizontal plane, wherez = 0 m. Again, the rear (bottom of figure) and right
faces of the scaffold experience heightened levels of
flow (Figs. 3.2.4 and 3.2.5).
Table 3.2 indicates that Points 2 and 5 experi-
ence similarly high fluid velocity magnitudes, being
approximately 3.8 10
3 and 3.76 10
3 m/s. Thisrelates well to Fig. 3.2.3, which shows that the vec-
tors approaching from the right are deflected upwards.
Fig. 3.2.1. Velocity contour plots captured at frontal Planes 13 for bioreactor with scaffold rotating about Z-axis.
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190 H. Singh et al. / Journal of Biotechnology 119 (2005) 181196
Fig. 3.2.2. Velocity contour plots captured at side Planes 46 for bioreactor with scaffold rotating about Z-axis.
Fig. 3.2.3. Sectioned scaffold and velocity vector plot at y = 0 m plane within bioreactor rotating about Z-axis.
Table 3.2
Velocities at Points 110 within scaffoldbioreactor rotation about Z-axis
Points
1 2 3 4 5 6 7 8 9 10
Magnitude (103 m/s) 0.71 3.80 2.02 1.92 3.76 0.94 5.06 2.02 1.04 4.08
x (103 m/s) 0.08 0.16 0.22 0.23 0.08 0.75 0.75 0.10 0.90 0.75
y (103 m/s) 0.65 3.80 2.00 1.80 3.75 0.50 5.00 2.00 0.40 4.00
z (103 m/s) 0.28 0.05 0.21 0.63 0.20 0.25 0.13 0.23 0.33 0.35
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Fig. 3.2.4. Sectioned scaffold and velocity vector plot at z =0.028 m plane within bioreactor rotating about Z-axis.
This is further confirmed by the v velocity compo-
nents, which prove that their major velocity contri-
butions are particularly attributed to the fluid flow in
the Y-direction. Point 1, though, experiences a lower
magnitude of velocity, at about 0.71 103 m/s. This
indicates that cells at this location may be derived of
essential nutrient transport.The wall shear stress plot for the scaffold again indi-
cates that higherstresses tend to occur at theouteredges
and faces, which are in direct contact with the mov-
ing fluid. It is within the scaffold that these stresses
Fig. 3.2.5. Wall shear stressrange of 02Pa forscaffold withinbiore-
actor rotating about Z-axis.
decrease significantly, to a value of 1 Pa and less. Upon
careful examination, it is revealed that higher stresses
here not only occur along the outer surfaces of the scaf-
fold, but especially at the areas where scaffold fibres
intersect along the outer faces of the scaffold. The aver-
age shear stresses along the scaffold fibres within the
scaffoldrangefrom 0.2to 0.6 Pa approximately. In con-trast, shear stresses at the fibre intersections range from
0.8 to 1.6 Pa. It is clear that the shear stresses acting on
and within the scaffold are not uniform throughout,
but are dependent on the direction of flow, too. This is
despite the relatively small dimensions of the scaffold
of approximately 5 mm length per side.
3.3. Bi-axial rotation of bioreactor with scaffold
This scenario involves positioning the scaffold at
z =
0.02 m, along the vertical centre-line of the ves-sel. From Fig. 3.3.1, pockets of slow-moving fluid, as
indicated by the dark-blue region captured at Planes 1
and 3. However, for Plane 2, a significant portion of this
dark-blue contour seems to have filled up a large por-
tion of the chamber, primarilyat the bottom-half region.
Closer examination of the corresponding velocity vec-
tor plot reveals the presence of an eddy at the bottom
of the vessel, as indicated by the recirculating vectors.
This small recirculation body corresponds in location
to the small extension, as can be seen in Plane 2 of
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192 H. Singh et al. / Journal of Biotechnology 119 (2005) 181196
Fig. 3.3.1. Velocity contour plots captured at frontal Planes 13 for bioreactor with scaffold rotating bi-axially.
Fig. 3.3.1, to be extending downwards to the bottom-
right of the chamber (Fig. 3.3.2).
Fig. 3.3.3 depicts velocity vectors being deflected
upwards and to the left by the scaffold. This vector
plot also suggests that the top-right corner would espe-
cially experience relatively higher wall stresses, due to
the intensity of the arrows at that location. A small
eddy can also be seen slightly to the left of the scaf-fold. The next vector plot reveals an eddy to the left
of the scaffold. Here, the faster-moving fluid flowing
along the rear of the scaffold can be seen entering the
scaffold and exiting from the front face of the scaffold,
along the positive Y direction. It is of interest to note
that from Table 3.3, all 10 locations experience sim-
ilar magnitudes of velocity, ranging from 23 103
to 29 103 m/s. This indicates that improved flow
and mixing can potentially be achieved by adopting
this scheme. We also see that the magnitudes haveincreased by 1 order, indicating that this rotational
scheme improves fluid flow significantly. The data fur-
Fig. 3.3.2. Velocity contour plots captured at side Planes 46 for bioreactor with scaffold rotating bi-axially.
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Fig. 3.3.3. Sectioned scaffold and velocity vector plot at y = 0 m plane within bioreactor rotating bi-axially.
Table 3.3
Velocities at Points 110 within scaffoldbioreactor rotation about bi-axial XZ-axes
Points
1 2 3 4 5 6 7 8 9 10
Magnitude (103 m/s) 28.51 28.01 28.31 26.00 24.01 27.72 28.01 27.53 27.55 23.14
x (103 m/s) 0.20 0.05 0.60 0.40 0.05 0.75 0.50 1.25 2.50 2.50
y (
10
3
m/s) 28.50 28.00 28.30 26.00 24.00 27.70 28.00 27.50 27.40 23.00z (103 m/s) 0.50 0.75 0.38 0.05 0.50 0.55 0.40 0.10 1.35 0.10
Fig. 3.3.4. Sectioned scaffold and velocity vector plot at z =0.02 m plane within bioreactor rotating bi-axially.
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194 H. Singh et al. / Journal of Biotechnology 119 (2005) 181196
Fig. 3.3.5. Wall shearstress rangeof 08Pa forscaffold withinbiore-
actor rotating bi-axially.
ther indicates that the X-velocities generally do not
seem to be major constituents of the respective magni-
tudes, unlike the v or Y-velocities (Fig. 3.3.4).
Fig. 3.3.5 displays the shear stresses along surfaces
as well as within the scaffold. It is noted that shear
stresses seem to increase in the positive X direction,
indicating that the maximum wall shear stresses occurs
at the right side of the scaffold. This is verified by
Fig. 3.3.5, which isolates wall shear stresses within
the range of 08 Pa. It can be seen that the intersect-ing fibres tend to experience higher stresses at points
of intersection, as highlighted by the green-coloured
streaks. The nominal shear stresses within the scaffold,
however, seem to be generally lower, at approximately
1.62 Pa, as indicated by the lighter-blue colour. This
is in contrast to the stresses experienced at the fibre
intersections, which fall within the range of 2.44.8 Pa
approximately.
In summary, the most outstanding differences relate
to the bi-axial or gyroscopically rotating bioreactor.
The velocity magnitudes at each of the locations fromPoints 1 to 10 have increased significantly by manifold,
and up to one order of calculation in some cases. The
data clearly prove that bi-axial rotationof thebioreactor
results in the increase of fluid flow within the scaffold
under the studied conditions. At point 1, a 22.79 ratio
of fluid velocities is noted; by comparing the velocities
generated by the bi-axial andXrotational schemes (see
Table 3.1 and Fig. 3.4). Consequently, a ratio of 40.02
for Point 1 was also noted, by comparing the veloci-
ties due to the bi-axial and Z rotational schemes (see
Fig. 3.4. Fluid velocity magnitudes at Points 15 within scaffold
subjected to rotation about respective axes.
Table 3.2 and Fig. 3.5). The above results indicate a
significant enhancement of fluid velocity and mixing,
due to the bi-axial mode of bioreactor rotation. Bi-axialrotation clearly enhances mixing of the fluid, as fluid
particles rotate under the influence of two axes. This
increases the penetrability of particles into the scaffold,
as they can enter the pores of the scaffold from more
than one direction. It is also noted that fluid mixing has
improved due to the bi-axial rotation, as compared to
uni-axial rotation. This is indicated by breaking up of
contours, contrary to the uniform contours as noted
for the uni-axial rotation cases. It must be mentioned
that bi-axial rotation, however, may result in a slight
increase of turbulent artifacts such as eddies.The shear stresses within the scaffolds do not vary
greatly for both uni-axially rotating cases. These gen-
erally values range from 0.4 to 0.6 Pa for the proto-
type model. However, bi-axial rotation of the prototype
model reports an average shear stress value of 1.8 Pa
withinthe scaffold. This valueof shear stressrepresents
those that occur within the scaffold. Findings also show
that the wall shear stresses acting along the external
Fig. 3.5. Fluid velocity magnitudes at Points 610 within scaffold
subjected to rotation about respective axes.
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H. Singh et al. / Journal of Biotechnology 119 (2005) 181196 195
edges of the scaffolds tend to be approximately three
to four times more than the internal shear stresses as
indicated. This is notedto particularlyoccurat theinter-
sections of scaffold struts/bars and at the circular edgesof thefibre end-faces. Onereason for this is that stresses
tend to be concentrated at the edges, which are directly
exposed to the dynamic fluid.
The Reynolds number is a commonly applied non-
dimensional parameter that is applied to assess the state
of a system, where
Re =Vd
or Re =
r2
(3.1)
whereby V is the fluid velocity, d the diameter, r the
radius and is the rotational velocity. The Reynoldsnumber represents a ratio of inertial to viscous effects
and indicates laminar, transient or turbulent flow. For
example, a flow scheme would tend towards the lam-
inar scheme due to a higher fluid viscosity, reducing
the Reynolds number of a fluid. The Reynolds num-
ber is of interest in many bioreactor systems as laminar
flow regimes are often employed. However, our sys-
tem is more complex because bi-axial rotation within
our asymmetric vessel is coupled with inlet and out-
let flows. Hence, we did not attempt to calculate Re.
The gravity and buoyancy effects are of less signifi-cance with respect to our bioreactor system, and were
therefore neglected in our simulations.
4. Conclusions
1. Three different flow configurations were discussed
with respect to our prototype bioreactor design, pri-
marily rotation about the X (tumble), Z (spin) and
XZ(bi-axial) axes.
2. Fluid velocities and shear stresses within the scaf-folds were studied and compared, and proved that
bi-axial rotation results in significant improvements
in terms of fluid transport through the scaffolds.
This is due to the combined effects of the rota-
tional velocity vectors about both axes, which
when combined, would almost certainly result in a
higher rotational velocity component, as compared
to rotation about a single axis. However, a rise in
shear forces was also reported. Greater transport
within scaffolds for example, would therefore result
in most cases (and not just ours) as a result of bi-
axial rotation.
3. These simulations assist in identifying critical
issues and problems, for example, in approximat-ing the locations of recirculation zones. These
zones may potentially damage cells and inhibit
growth. Furthermore, these recirculating bodies
may impede the flow of fluid into and out of the
scaffold. The choice of flow regime is therefore of
great importance.
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