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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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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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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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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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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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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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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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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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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