Computational simulation modelling of bioreactor configurations for regenerating human bladder.

Abstract

The objective of this study was to investigate a bioreactor suitable for human bladder regeneration. Simulations were performed using the computational fluid dynamic tools. The thickness of the bladder scaffold was 3 mm, similar to the human bladder, and overall hold-up volume within the spherical shape scaffold was 755 ml. All simulations were performed using (i) Brinkman equation on porous regions using the properties of 1% chitosan-1% gelatin structures, (ii) Michaelis-Menten type rate law nutrient consumption for smooth muscle cells (SMCs) and (iii) Mackie-Meares relationship for determining effective diffusivities. Steady state simulations were performed using flow rates from 0.5 to 5 ml/min. Two different inlet shapes: (i) straight entry at the centre (Design 1) and (ii) entry with an expansion (Design 2) were simulated to evaluate shear stress distribution. Also, mimicking bladder shape of two inlets (Design 3) was tested. Design 2 provided the uniform shear stress at the inlet and nutrient distribution, which was further investigated for the effect of scaffold locations within the reactor: (i) attached with a 3-mm open channel (Design 2-A), (ii) flow through with no open channel (Design 2-B) and (iii) porous structure suspended in the middle with 1.5-mm open channel on either side (Design 2-C). In Design 2-A and 2-C, fluid flow occurred by diffusion dominant mechanisms. Furthermore, the designed bioreactor is suitable for increased cell density of SMCs. These results showed that increasing the flow rate is necessary due to the decreased permeability at cell densities similar to the human bladder.

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Seokwon Pok a , Dhananj ay V. Dhane a & Sundar ar aj an V. Madi hal l y a
a School of Chem i cal Engi neer i ng, Okl ahom a St at e Uni ver si t y , 423 Engi neer i ng Nor t h,
St i l l wat er , OK, 74078, USA
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To ci t e t hi s art i cl e: Seokwon Pok, Dhananj ay V. Dhane & Sundar ar aj an V. Madi hal l y ( 2012) : Com put at i onal si m ul at i on
m odel l i ng of bi or eact or conf i gur at i ons f or r egener at i ng hum an bl adder , Com put er Met hods i n Bi om echani cs and Bi om edi cal
Engi neer i ng, DOI : 10. 1080/10255842. 2011. 641177
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Computational simulation modelling of bioreactor configurations for regenerating
human bladder
Seokwon Pok, Dhananjay V. Dhane and Sundararajan V. Madihally*
School of Chemical Engineering, Oklahoma State University, 423 Engineering North, Stillwater, OK 74078, USA
(Received 31 March 2011; final version received 12 November 2011)
The objective of this study was to investigate a bioreactor suitable for human bladder regeneration. Simulations were
performed using the computational fluid dynamic tools. The thickness of the bladder scaffold was 3mm, similar to the
human bladder, and overall hold-up volume within the spherical shape scaffold was 755ml. All simulations were performed
using (i) Brinkman equation on porous regions using the properties of 1% chitosan–1% gelatin structures, (ii) Michaelis–
Menten type rate law nutrient consumption for smooth muscle cells (SMCs) and (iii) Mackie–Meares relationship for
determining effective diffusivities. Steady state simulations were performed using flow rates from 0.5 to 5ml/min. Two
different inlet shapes: (i) straight entry at the centre (Design 1) and (ii) entry with an expansion (Design 2) were simulated to
evaluate shear stress distribution. Also, mimicking bladder shape of two inlets (Design 3) was tested. Design 2 provided the
uniform shear stress at the inlet and nutrient distribution, which was further investigated for the effect of scaffold locations
within the reactor: (i) attached with a 3-mm open channel (Design 2-A), (ii) flow through with no open channel (Design 2-B)
and (iii) porous structure suspended in the middle with 1.5-mm open channel on either side (Design 2-C). In Design 2-A and
2-C, fluid flow occurred by diffusion dominant mechanisms. Furthermore, the designed bioreactor is suitable for increased
cell density of SMCs. These results showed that increasing the flow rate is necessary due to the decreased permeability at
cell densities similar to the human bladder.
Keywords: tissue engineering; CFD; SMC
1. Introduction
Several approaches have been explored to colonise cells
within a porous scaffold necessary for in vitro tissue
regeneration. Using traditional tissue culture plastic,
porous templates are inserted into wells and cells are
seeded in a growth medium. However, adapting the
technique to thicker structures is limited by the diffusion of
nutrientsastheprimarymodeofnutrientdistributionwithin
the porous structure is dictated by Fick’s first law. The
thickness of the tissue grown in static cultures is not
comparable to that necessary for transplantation. Bio-
reactorshavebeenwidelyutilisedtocontinuouslyreplenish
the nutrients by convective flow (Gray et al. 1988; Gooch
et al. 2001; Huang et al. 2005; Martin and Vermette 2005).
Inadditiontoimprovingthenutrientdistribution,fluidflow
can also introduce shear force on the cells. This shear
force stimulates cells and alters the secretion character-
istics, which could affect the quality of the regenerated
tissue. Cells respond to stresses by altering their
extracellular matrix (ECM) biosynthesis (Gooch et al.
2001) and change the tissue composition (Chatzizisis et al.
2007;Cooperetal.2007).Usingvariousbioreactordesigns,
some studies reported an improvement in the quality of the
regenerated tissue (Niklason et al. 1999). However, other
studies have reported deterioration in the quality (Heydar-
khan-Hagvall et al. 2006). The overall outcome of
regenerated tissue using bioreactors is of poor quality
(Niklason et al. 1999; Martin et al. 2004; Chen and Hu
2006).Thiscouldbeattributedtoincompleteconsideration
of reactor design.
A number of studies have been carried out to model
fluid dynamics (Williams et al. 2002; Sander and Nauman
2003; Porter et al. 2005; Cioffi et al. 2006; Brown and
Meenan 2007; Hutmacher and Singh 2008) in bioreactors.
Simulations have used simplified mathematical models
and reduced scaffold size due to increased computational
demand in simulating reactors suitable for clinical
transplantation. Furthermore, tissue regeneration is a
dynamic process where the porous characteristics change
due to matrix deposition and tissue maturation. Assembly
and maturation of ECM elements in tissue regeneration
play a significant role in determining the quality of the
regenerated tissue. These changes affect the transport
characteristics and nutrient distribution. In addition,
in vitro regeneration strategies are not characterised for
high aspect ratio tissues, which have large surface area
relative to the thickness (Heydarkhan-Hagvall et al. 2006).
Among different reactor configurations, the flow through
reactor is better suited for regenerating high aspect ratio
ISSN 1025-5842 print/ISSN 1476-8259 online
q 2011 Taylor & Francis
http://dx.doi.org/10.1080/10255842.2011.641177
http://www.tandfonline.com
*Corresponding author. Email: sundar.madihally@okstate.edu
Computer Methods in Biomechanics and Biomedical Engineering
iFirst article, 2011, 1–12
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tissues due to the following advantages (Lawrence et al.
2009): (i) uniformly supports or constrains the scaffold to
prevent deformation, (ii) continuous flow replenishes the
nutrients while providing better control on hydrodynamic
shear stress induced by the fluid flow and (iii) easy scaled-
up to clinical requirement.
Increasing computational capabilities and advances in
the application of numerical techniques has made it
possible to include complex transport steps in modelling.
We previously reported on the analysis of fluid flow
characteristics along with nutrient distribution in growing
tissues in 2-mm thick and 100-mm diameter circular
scaffolds (Devarapalli et al. 2009; Lawrence et al. 2009).
We evaluated the effect of various factors including (i)
reactor shapes (rectangular and circular), (ii) flow rate,
(iii) inlet–outlet location, (iv) inlet–outlet size that
regulates velocities, (v) changing pore architecture, (vi)
nutrient consumption (particularly oxygen and glucose)
characteristics and (vii) different types of cells [smooth
muscle cells (SMCs), chondrocytes and hepatocytes] in
flat bioreactor configurations. The bioreactor shape and
position of inlets and outlets affected the fluid distribution
and shear stress in high aspect ratio reactors containing
porous structures.
Many tissues in the body are three dimensional in
nature. Hence, evaluating bioreactors for tissue-specific
shapes suitable for regenerating clinically required
dimensions is important. In this study, we aimed to
evaluatebioreactorconfigurationssuitableforregenerating
a human bladder by selecting appropriatedimensions. Two
different shapes of inlets were simulated to minimise shear
stress at the bioreactor inlet. Mimicking bladder shape of
inlet was also tested. Within the reactor, the importance of
locating the porous structure was also evaluated in
conditions mimicking tissue regeneration, i.e. changes in
cell number and permeability. These results show a
possibility of building a reactor that could support bladder
regeneration.
2. Materials and methods
2.1 Preparation of porous scaffolds
For simulation, obtaining the scaffold characteristics was
necessary. For this purpose, 1–1% (w/v) chitosan–gelatin,
chitosan with 190–310kDa MW and gelatin Type-A (300
Bloom) were obtained from Sigma Aldrich Chemical Co.
(St Louis, MO, USA); solutions were prepared in 0.1M
acetic acid using deionised water. A well of 10-cm
diameter was prepared on Teflon dishes using silicon glue,
and 25ml of respective solutions was poured in the well
and frozen overnight at 2808C. The frozen solution was
lyophilised overnight (Virtis, Gardiner, NY, USA). When
porous scaffolds are formed by lyophilisation technique a
thin non-porous film forms at the surface. This skinny
layer hinders access to the underlying porous structure if
not removed. For removing the skinny layer from scaffolds
of 1–1% (w/v), a wet paper was placed on the top of the
solution once it was poured inside the well and frozen
along with the solution. After lyophilising, the paper was
peeled off to generate scaffold without the skinny
layer. Since acetic acid remaining in the scaffold has to
be removed, dried samples were first incubated with
pure ethanol for 10min and washed four times with
phosphate-buffered saline. Wet samples were analysed
using an inverted microscope outfitted with a CCD
camera. Obtained digital micrographs were analysed using
Sigma Scan Pro software (Systat Software, Inc., Point
Richmond, CA, USA) for pore size and number of pores.
These numbers were utilised in the computational
simulation.
2.2Bioreactor designs
The computational package used in this work was the
commercially available code COMSOL 3.5a Multiphysics
(COMSOL, Inc., Burlington, MA, USA). The spherical3D
bioreactor geometry was created by drawing spheres of
different radii in 3D (Geom1) and then using the
‘difference’ tab in COMSOL for getting the desired
annular region. To add inlet and the outlet to this annular
region, a rectangular shape was drawn in 2D (Geom2) and
then revolving it 3608 along the axis. Based on the human
bladder size, the volume of the reactor was set to 820ml.
The volume of scaffold was chosen to be 755ml with a
thickness of 3mm, similar to the human bladder.
Different inlet shapes: Geometries were created with three
different shapes of inlets to assess shear stress distribution
(Figure 1(a)–(c)):
Design 1: Single cylindrical inlet and outlet with
28-mm height and 6-mm diameter at the centre of the
top and bottom of the reactor.
Design 2: Funnel-shaped inlet and outlet with 28-mm
height, 6-mm diameter at the centre of the top and
bottom of the reactor.
Design 3: Double cylindrical inlet and single outlet
with the same size of Design 1.
Different locations of scaffolds: since funnel-shaped inlet
(Design 2) showed minimal shear stress at the inlet area
and uniform oxygen distribution throughout the reactor,
Design 2 was selected for further analysis. Three different
locations of the scaffold within the reactor were
investigated using Design 2 (Figure 2(a)–(c)):
Design 2-A: A 3-mm thick porous scaffold attached to
the interior wall of the spherical reactor. There was an
additional 3-mm open channel above the porous
structure which did not have any porous structure.
Design 2-B: A 3-mm thick porous structure was the
annular region through which medium was circulated.
S. Pok et al.2
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Design 2-C: A 3-mm thick scaffold was suspended
in the middlewith 1.5-mm open channel on either side.
The sub-domain and boundary conditions were set in the
Physics tab. The geometry was meshed one-by-one on
all the edges using the constrained edge element
distribution in the free mesh parameters tab. Subsequently,
the surfaces and the sub-domains were meshed using
the triangular method and keeping the maximum
elemental size as 0.005. The number of mesh points
was 12,099–15,673, and the number of elements was
51,417,68,479.
(a)
3
6
28
3
110110 110
Design 2-ADesign 2-BDesign 2-C
6
28
6
28
3
3 mm thick
open channel
3 mm thick
porous
structure
(b)(c)
Figure 2.
scaffold and (c) open flow area on either side.
Designs of bioreactors with different locations of scaffold: (a) open flow channel, (b) no open flow between bioreactor and
(a)(b) (c)
(d)
z
x
Design 1 Design 2Design 3
0.04 mol/m3
0.08
0.12
0.16
0.2
0
0.5
1.0
1.5
2.0
2.5
3.0 mPa
y
(e) (f)
Figure1.
outlet, (b and e) funnel-shaped inlet and outlet and (c and f) two cylindrical inlets and single outlet. Volumetric flow rate was 1ml/min.
Effectsofdifferentshapesofinletonshearstressandoxygendistributionthroughthereactor(aandd)singlecylindricalinletand
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2.3Fluid flow simulation
The flow rate was set at 0.5ml/min initially. Then, the
flow rate was increased to 1ml/min and then to 5ml/min
to determine the minimum flow rate at which the nutrients
were consumed fully. The simulation was performed
using the previously described procedure with minor
modifications (Devarapalli et al. 2009) such as accounting
for the effective diffusivity using Mackie–Meares
relationship (Mackie and Meares 1955a, 1955b; Sengers
et al. 2005b). In brief, fluid flow characteristics in the
porous sections were determined by solving the Brinkman
equation given by
m72us2m
kus¼ 7p;
ð1Þ
and the continuity equation given by
7·us¼ 0;
ð2Þ
where k is the permeability of the porous medium (m2), us
denotes the fluid superficial velocity vector in 3D (m/s), p
is the fluid pressure (Pa) and m is the effective viscosity in
the porous medium (kg/ms). The permeability (k) of the
porous medium is a geometric characteristic of the porous
structure, depending on the pore size and number of pores.
Based on the pore architecture of chitosan–gelatin porous
structures, the permeability was calculated using an
average pore size of 80mm and 140pores/mm2in the
equation (Truskey et al. 2004)
k ¼
p
128nAd4;
ð3Þ
where nAis the number of pores per unit area and d is the
average pore diameter. Both the permeability (k, m2) and
void fraction (f, dimensionless) were incorporated into
Equation (1) in order to account for the porous
characteristics of the matrix, yielding another form of
the Brinkman equation. The fluid flow characteristics in
the non-porous sections of the reactor were modelled
solving the incompressible Navier–Stokes equation in 3D
flow field which is given by
rðu·7Þu ¼ 27·½2t þ pdij?;
7·u ¼ 0;
ð4Þ
ð5Þ
where u is the 3D flow velocity (m/s), r is the fluid’s
density (kg/m3), p is the pressure (Pa) and dij is the
Kronecker delta function
?
h
ku ¼ 27·2t
1p
þ pdij
?
;
ð6Þ
where 1pis the porosity of the porous media, taken as 85%
based on the chitosan porous structure characteristics. The
shear stress tensor is an integral part of the Navier–Stokes
equations describing the flow in a free channel. The shear
stress was visualised as the viscous force per unit area in
the z direction, as calculated by
t·n:
ð7Þ
Maximum shear stress ranges through the porous structure
were evaluated using ‘Domain Plot Parameters’ and
‘Surface’ function. While solving the incompressible
Navier–Stokes equations, the perpendicular flow was
designated as 5ml/min and the outlet pressure was set to
atmospheric pressure.
Since the nutrient consumption is governed by
diffusion rather than convection, it is important to
accommodate the diffusive characteristics of nutrients
through the porous structure. The change in effective
diffusivity (Deffin m2/s) due to altered void fraction in the
porous structure was calculated using Mackie–Meares
relationship (Mackie and Meares 1955a, 1955b; Sengers
et al. 2005b).
Deff¼ D1
1p
2 2 1p
??2
;
ð8Þ
whereD1isthediffusioncoefficientfromStokes–Einstein
equation. Velocity profiles within the scaffold thickness
were obtained using ‘Cross-Section Plot Parameters’ in the
software, and Peclet number was calculated using the
equation,
Pe ¼Vr
DO2
;
ð9Þ
where Vis the velocity, r is a radius of the scaffold and DO2
is the diffusion coefficient of oxygen.
2.4Reactions in the porous structure
Reactions in the porous region were simulated by the
method previously described (Devarapalli et al. 2009).
The physical characteristics of chitosan–gelatin scaffold
were used for porous structure with SMCs. Oxygen and
glucose consumptions were simulated independently for
the reason that glucose concentration (5.5mol/m3) in the
growth medium is in large excess relative to oxygen
(0.2mol/m3) concentration (determined using the Henry’s
law constant at 378C). The rate constants were obtained for
SMCs based on the reaction rates reported in the literature
(Motterlini et al. 1998; Alpert et al. 2002; Sengers et al.
2005a; Fogler 2006). It was assumed that SMCs are
uniformly distributed in the entire scaffold. Using the
steady state velocity profiles, the steady state concen-
tration profiles of oxygen and glucose were obtained by
solving the equation of continuity using the chemical
reaction engineering moduleinCOMSOL3.5a
S. Pok et al.4
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Multiphysics. The nutrient consumption was included in
the simulation via the rate law. The convective diffusion
equation was used to obtain the concentration at varying
position along the cross-section of the reaction:
7·ð2D7CAÞ þ u·7CA¼ rA;
ð10Þ
where cAis the concentration of the species (mol/m3), rAis
the rate of reaction of the species under consideration
(mol/m3s),Disthediffusivityofthespecies(m2/s)anduis
the velocity vector (m/s). The physical properties of water
were used as it constitutes the bulk of the growth medium.
The flow properties (i.e. viscosity and density) of the
nutrient stream depend on the properties of the bulk fluid.
Since the cells are present only in the porous scaffolds, the
nutrient consumption rate law was defined only in the
porousregion,thereactiontermwaszerointhenon-porous
regions. It is a typical practice to decouple oxygen and
glucose consumptions for the primary reason that glucose
concentration in the growth medium is in large excess
relative to oxygen concentration (the initial concentration
of oxygen in the growth medium was determined using
the Henry’s law constant at 378C for each cell type).
In addition, for every mole of glucose consumed, 6mol of
oxygen is consumed according to the stoichiometry of
aerobic metabolism. The rate constants were obtained for
SMCs using Michaelis–Menten type rate law based on the
reaction rates reported in the literature (Motterlini et al.
1998; Alpert et al. 2002; Sengers et al. 2005a; Fogler
2006). The rate law is given by the expression
2rAðmol=m3sÞ ¼
VmCA
Kmþ CA;
ð11Þ
where rAis the reaction rate, Vmis the maximum reaction
rate and Kmis the Michaelis constant. CAwas replaced by
c1for the oxygen concentration, and CAwas replaced by c2
for the glucose concentration. Both the rate laws were
defined in the COMSOL to enable the visualisation of both
the oxygen and glucose profiles within the porous
structure. The nutrient concentration profiles were
obtained using ‘Slice Plot Parameter’, and the minimum
values were found using ‘Cross-Section Plot Parameters’.
3.Results
3.1Effect of inlet shape on shear stress
To minimise the shear stress at the inlet area, three
different shapes of inlets were simulated. First, two
different inlet shapes were simulated to evaluate the shear
stress distribution at the inlet area of the porous structure.
To mimic physiological bladder configuration, two inlets
instead of one were also simulated. Based on our previous
work (Devarapalli et al. 2009), the minimum volumetric
flow rate of 0.5ml/min was selected using the relation
2rO2jinlet¼ yDCO2=VR, where VRis the volume of the
reactor and DCO2is the medium concentration change at
the outlet of the reactor. In Design 3, the total volumetric
flow rate is the same as the other two designs. In other
words,eachinlethadhalfthetotalflowrate.Pressuredrops
through the reactor were simulated using the Brinkman
equation.Theseresults(Table1)showedthatnosignificant
difference was observed in pressure drop with different
inlet shapes. Even though Design 3 had a half flow rate in
each inlet, its pressure drop was similar to Design 1. The
maximum shear stress at the inlet area of the scaffold was
also evaluated. The maximum shear stresses of three
designs increased constantly with increasing flow rate.
However, Design 2 showed less increase in shear stress by
increasing the flow rate compared to Designs 1 and 3. The
maximum shear stress of Design 2 was ,161mPa at
5ml/min of flow rate, whereas the shear stress in Design 1
was 1160mPa. Design 2 provided uniform shear stress at
the inlet while uniformly distributing sufficient amount of
nutrients. This resulted in reduction of the shear stress at
the wider inlet of Design 2 (Figure 1(a)–(c)). As the flow
rate in each inlet of Design 3 was half of that in Design 1,
the maximum shear stress and pressure drop of Design 3
decreased to the levels of Design 2 (Table 1).
The effect of different inlet shapes on nutrient distri-
bution was also evaluated. These results (Figure 1(d)–(f))
showed that Designs 1 and 2 had uniform distribution of
oxygen through the entire bioreactor. However, Design 3
had reduced oxygen concentration near the outlet area,
attributed to the reduced fluid flow between the two inlets.
Since the results of the pressure drop, shear stress and
nutrient distribution analysis showed that Design 2 had the
most favourable configurations, Design 2 was selected for
further analysis in the presence of porous structure.
Table 1. Effects of inlet shapes and flow rate on pressure drop through the reactor and shear stress at the inlet area.
Design 1Design 2Design 3
Flow rate
(ml/min)
Dp
(mPa)
Max. shear stress
(mPa)
Dp
(mPa)
Max. shear stress
(mPa)
Dp
(mPa)
Max. shear stress
(mPa)
0.5
1
5
12.07
24.19
127.55
44
99
8.32
16.73
90.56
17
35
161
8.22
16.56
88.85
31
64
1160405
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3.2Effect of location of the scaffold on velocity profile
Next, the nutrient distribution can occur by two
mechanisms: diffusion and convective flow (Martin and
Vermette 2005). To understand the effect of placement of
the scaffold in the flow field, three scaffold locations within
the reactor wereinvestigated using Design2 (Figure2). The
velocity profiles with 5ml/min of the flow rate showed
(Figure 3) that the reduced channel size with the same
volumetric flow rate increases the velocity. Design 2-B that
had no open channel between the reactor and the porous
structure had a higher average velocity (69,000mm/s) than
Design 2-A (38mm/s) and Design 2-C (82mm/s).
Furthermore, the velocity profile indicated that Design 2-
C was the most favourable configuration with very low
velocitiesacrossthescaffold.However,Design2-Ashowed
that the velocity reduced by reaching the inside wall of the
scaffold,andthevelocitywaszeroattheendofthescaffold.
In addition, the average Pe ´clet number was calculated
in the porous area using Equation (9). The velocity at the
centre of the scaffold was used to calculate the Pe ´clet
number with 1.1937 £ 1029m2/s of diffusivity of oxygen.
These results showed that Design 2-A and Design 2-C had
Pe ´clet number of ,1, whereas Design 2-B had ,170 of
dimensionless Pe ´clet number (data not shown). This
suggested that Design 2-A and Design 2-C had diffusion
dominant characteristics, whereas Design 2-B was
convectiveflow dominant. The overall nutrient distribution
within the scaffold (i) in Design 2-A occurred by diffusion,
(ii) in Design 2-B occurred by convection and (iii) in
Design 2-C occurred both by diffusion and convection.
3.3
pressure drop and shear stress
Effect of location of the scaffold and flow rate on
Pressuredropthroughthebioreactorandshearstresswithin
thescaffoldwereanalysedwith different scaffoldlocations
and flow rates. Since pressure drop and shear stress were
calculated by conservation of momentum equations, these
values were not a function of the rate constants of SMCs.
Results showed (Table 2) that the pressure drop increased
withtheflowratefrom0.5to5ml/min,andDesign2-Bhad
the highest pressure drop compared to others.
Since shear stresses at the inlet area were minimised
from earlier simulation results, shear stresses at the inlet
area were neglected. The maximum shear stresses showed
a linear increase with increasing flow rate (Table 2).
Design 2-C showed a higher shear stress range relative to
other designs. The maximum shear stress range in Design
2-A was 45–58mPa, in Design 2-B was 90–200mPa and
in Design 2-C was 150–230mPa. However, these values
were not significantly different between the designs.
3.4
steady state
Oxygen and glucose concentration profile at the
To evaluate the effect of location of scaffold on nutrient
consumptions of oxygen and glucose, simulations were
performed with defined rate laws for SMCs. Initial
simulations were performed at the same cell density
(1.2 £ 1012cells/m3). These results showed (Figure 4 and
Table 2) that the location of the scaffold did not
significantly affect both the minimum oxygen concen-
tration and outlet oxygen concentration at 0.5ml/min flow
rate. The minimum oxygen concentration was found near
the outlet area of the bioreactor. Design 2-A showed a
higher concentrationwith 0.5ml/min flowratethan Design
2-B and Design 2-C. However, Design 2-B and Design 2-C
had higher minimum oxygen concentration at higher flow
rates than Design 2-A. In other words, Design 2-B and
Design 2-C showed a rapid increase in minimum oxygen
concentration with the flowrate, whereasDesign2-A had a
gradual increase. In addition, there was no significant
difference in glucose consumption for three designs with
lower flow rate. Along with a result of oxygen
concentration, Design 2-B and Design 2-C had a higher
glucose concentration than Design 2-A. However, no
significantdifferencewasobservedinglucoseconsumption
by varying the flow rate and the location of the scaffold.
To understand the variation in the nutrients in different
locations and across the thickness (Figure 5), ‘Cross-
Section Plot Parameters’ analysis was carried out. These
results confirmed that oxygen distribution for three designs
did not indicate significant differences at lower flow rates.
Furthermore, in Design 2-B and Design 2-C the porous
structureswerefullysaturatedwithoxygenat5ml/minflow
rate. Glucose was also in copious amounts in every design.
3.5
consumption
Effect of cell density and permeability on nutrients
During the process of tissue regeneration, structural
permeability changes due to ECM deposition, cell growth
120000
100000
80000
300
250
200
150
100
50
0
0.00.51.0 1.52.0 2.53.0
Thickness (mm)
Design_2_A
Design_2_B
Design_2_C
Velocity (nm/s)
Figure 3.
the scaffold thickness when the volumetric flow rate is 5ml/min.
Changes in the velocity of the growth medium across
S. Pok et al.6
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Page 8

and scaffold degradation. To understand the effect of
varying cell density and permeability on nutrient
consumption, pressure drop and shear stress, simulations
were performed by decreasing the permeability while
maintaining constant cell density. The flow rate was fixed
at 5ml/min. These results showed reduction in velocity
within the porous structure as the permeability approached
that of healed tissue. Concurrently, the minimum oxygen
concentration (Table 3) reduced significantly with
decreasing permeability at the constant cell number. Slice
plot results for Design 2-C (Figure 6) also showed some
locations with insufficient oxygen concentration regions
within the porous structure, particularly with a per-
meability of 4.7mm2. This result suggested that increasing
the flow rate is necessary to adjust requirements to the cell
proliferation. In addition, pressure drop in Design 2-A and
Design 2-C increased slightly due to reduced permeability
whereas Design 2-B showed an increase in pressure
drop. However, shear stress was not affected significantly
by reducing the permeability (data not shown). This
suggested that pressure and flow rate should be adjusted by
decreasing the permeability.
To account for changes in cell number, the number of
cells was varied to evaluate the effect of cell density,
neglecting changes in permeability. These results showed
(Table 3) that the minimum oxygen concentration and the
outlet oxygen concentration decreased by increasing the
cell density of SMCs. Shear stresses were not altered
significantly by increasing the cell density at the constant
permeability. Furthermore, optimum flow rates for Design
2-C were evaluated to maintain the minimum oxygen
concentration of 0.05mol/m3followed by increasing the
cell density (Figure 7). The SMC density in the human
bladder was calculated to be 1.3 £ 1013cells/m2using
histological micrographs reported in the literature review
(Baumert et al. 2007). Hence, simulations were performed
for each doubling of the initial cell density up to 16
doublings which exceed SMC density of 1.3 £
1013cells/m3. While performing the simulation, desirable
minimum oxygen concentration was set to 0.05mM
(based on typical oxygen tension of 40mmHg in healthy
tissues) and the flow rate was progressively increased.
These results showed a need to adjust the flow rate to
account for increasing the cell number during tissue
regeneration.
4.Discussion
BladdercontainsalargenumberofSMCsandfewlayersof
urothelial cells (UCs). Static cultures relying on Fickian
diffusion for distribution of nutrients cannot support the
growth of thicker (.0.5–1.0mm) tissues. Fluid is
constantly replenished by recirculating in the porous
structures to improve the nutrient distribution by convec-
tion. Bioreactors of different configurations have been
Table 2.
Effects of location of scaffold and flow rate on pressure drop through the reactor, shear stress through the scaffold and nutrient distributions.
Design 2-A
Design 2-B
Design 2-C
Flow
rate(ml/min)
Dp
(mPa)
Max.
shear
stress
(mPa)
Min.
Coxygen
(mol/m3)
Outlet
Coxygen
(mol/m3)
Min.
Cglucose
(mol/m3)
Dp
(mPa)
Max.
shear
stress
(mPa)
Min.
Coxygen
(mol/m3)
Outlet
Coxygen
(mol/m3)
Min.
Cglucose
(mol/m3)
Dp
(mPa)
Max.
shear
stress
(mPa)
Min.
Coxygen
(mol/m3)
Outlet
Coxygen
(mol/m3)
Min.
Cglucose
(mol/m3)
0.5
8.32
4.5,6
0.0352
0.0696
4.362
10,622
9,20
0.0274
0.0449
4.628
20.72
15,23
0.0262
0.0557
4.379
1
16.73
9,12
0.0666
0.1220
4.640
21,249
18,40
0.0745
0.1035
4.997
41.54
30,46
0.0590
0.1118
4.811
5
90.56
45,58
0.1076
0.1828
4.868
106,255
90,200
0.1553
0.1770
5.227
214.15
150,230
0.1314
0.1819
5.224
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Page 9

explored for in vitro bladder regeneration (Wallis et al.
2008; Davis et al. 2011; Bouhout et al. 2011), although the
bioreactor design features are not well characterised for
regenerating human bladder. Since hydrodynamic shear
force influences cellular alignment (Huang et al. 2005;
Waters et al. 2006) in the flow direction (Gray et al. 1988;
Takahashi and Berk 1996; Huang et al. 2005), fluid path
helpsalignthecellinthe requireddirection.Thebioreactor
is known to differentially affect SMCs and UCs on the
secretionofmatrixelements (Farhatand Yeger2008).Also
increasedorganisationofmatrixelementsisobservedwhen
the bioreactors are operated under cyclical mechanical
stimulation.SMCspresentonasubstratesubjectedtostrain
orient themselves perpendicular to the applied strain
(Kim and Mooney 2000). This in turn leads to oriented
packingofsynthesisedmatrixandsignificantimprovement
in the quality and mechanical property of the regenerated
tissue (Isenberg and Tranquillo 2004).
Flow rate
0.2
0.16
0.12
0.08
0.04
mol/m3
(b)
(a)
(c)
0.5 mL/min1 mL/min 5 mL/min
Figure 5.
open flow channel, (b) no open flow between bioreactor and scaffold and (c) open flow area on either side.
Sliced plots foroxygen concentration through the reactor containing scaffolds in differentpositions with various flow rates: (a)
Flow rate (mL/min)
02468 100246810
Minimum oxygen concentration (mol/m3)
0.00
0.04
0.08
0.12
0.16
0.20
Design 2-A
Design 2-B
Design 2-C
Flow rate (mL/min)
Minimum glucose concentration (mol/m3)
4.2
4.4
4.6
4.8
5.0
5.2
5.4
(a)
(b)
Figure 4.Effects of location of the scaffold and flow rate on (a) oxygen concentration profile and (b) glucose concentration profile.
S. Pok et al.8
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Page 10

This study focussed on understanding the shapes of
inlets, the location of the scaffold and what controls the
nutrient distribution with different conditions for regen-
eration of human bladder. Chitosan–gelatin system was
selected as the model system due to extensive existing
knowledge in our laboratory related to (i) favourable
chemistry, degradation and SMC cell growth, (ii) scaffold
characteristics (porosity and pore size distribution) and
mechanical properties in hydrated condition (Huang et al.
2005, 2006; Tillman et al. 2006) and (iii) favourable host
tissue response than most other materials. Since scaffold
degradation is enzyme-mediated, the dynamic changes in
the porous scaffold due to degradation can be ignored in
the absence of enzymes during the initial study period.
Furthermore, one could systematically study the role of
degradation by adding enzymes and their reaction kinetics.
This combination promotes cell adhesion and increased
secretion of ECM components in static cultures with very
slow cell growth. Hence, one could assess the effect of
ECM maturation without considering dynamic changes in
cell number.
Since it is widely known that SMCs respond to
hydrodynamic shear stress (Shi et al. 2009), evaluation of
optimised shear stress is essential for the design of
bioreactors. In this study, shear stress at the inlet area was
minimised by increasing the size of connected area at inlet.
Funnel-shaped entrance (Design 2) provided a smooth
expansion instead of sudden expansion of the fluid at the
inlet, minimising significant variation in shear stress
throughout the scaffold. The maximum shear stress of
Design2wassignificantlylowerthanthatinDesign1.This
could be attributed to the funnel shaped entrance guiding
the fluid through the expansion. Reduced shear stress
provides an opportunity to increase the flow rate without
significant concerns of excessive shear stress that could be
detrimental to the cells. Nevertheless, current simulations
assumednodeformation intheporousstructureduetofluid
flow. We need to extend these results to include the
structural changes via incorporation of mechanical
characteristics. The compressive force due to fluid flow
could alter the observed shear stress levels.
Since nutrient transfer can be explained with diffusion
and convective flow and their dominants can be changed
by the location of scaffold and channel size in the reactor,
three different types of designs were simulated to evaluate
the effects on flow mechanism, pressure drop, shear stress
and nutrient distribution. Diffusion or convection
dominants were assessed by determining the Peclet
number. Design 2-A and Design 2-C had Peclet number
of ,1, whereas Design 2-B had a Peclet number .1.
In particular, nutrient distribution occurred in Design 2-C
both by diffusion and convection. This provides an
opportunity to increase the nutrient amount by increasing
the flow rate when diffusion is limited by decreased
porosity.
Table 3.
Effects of varying cell density and changes in permeability on oxygen consumption rate.
Design 2-A
Design 2-B
Design 2-C
Cell number
Pore size
(mm)
k
(mm2)
Dp
(mPa)
Min. Coxygen
(mol/m3)
Outlet Coxygen
(mol/m3)
Dp (mPa)
Min. Coxygen
(mol/m3)
Outlet Coxygen
(mol/m3)
Dp
(mPa)
Min. Coxygen
(mol/m3)
Outlet Coxygen
(mol/m3)
1 £
85
154
90.56
0.1076
0.1828
106,255
0.1553
0.1770
214.15
0.1314
0.1819
1 £
50
18
90.57
0.0398
0.1875
886,240
0.1100
0.1773
229.74
0.0369
0.1861
1 £
20
4.7
90.58
0
0.1944
34,611,082
0
0.1782
232.85
0
0.1939
2 £
85
154
90.56
0.0595
0.1698
106,255
0.1179
0.1565
214.15
0.1243
0.1610
4 £
85
154
90.56
0.0226
0.1550
106,255
0.0622
0.1198
214.15
0.0759
0.1368
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To consider the changes in effective diffusivity with
permeability, it was calculated for various void fractions
using Mackie–Meares model (Mackie and Meares 1955a,
1955b; Sengers et al. 2005b), which describes the
diffusion of electrolytes in a resin membrane. Mackie–
Meares model is based on the lattice model for liquids and
assumes that the polymer fibres are of the same size as the
solutes and the polymer network only blocks the pathway
of solutes without affecting their mobility. Although
Mackie–Meares model is shown to agree with a variety of
conditions, it underestimates diffusivities with higher
solute concentrations (based on water as the solvent) (Lai
et al. 2009). Mackie–Meares model ignores polymer–
solute interactions such as adsorption effects. Thus,
obtaining a better estimation of diffusivities and validating
the Mackie–Meares model predictions are important for
biomedical applications. Further, structural changes due to
fluid flow alter the nutrient distribution due to altered local
convective flow and diffusivity.
The inner wall of the bladder is made up of 150–200-
mm thick UCs (Khandelwal et al. 2009). Bioreactor should
allow regeneration of UCs for successful regeneration of
bladdertissue.Design2-Cisideallysuitedforthispurpose.
We could extend the current simulation results to include a
with UC consumption kinetics. The flow through the UC
layer should not be a significant factor as free diffusion is
sufficient to distribute the nutrients without the need of
convectiveflow.Althoughabioreactorwiththedimensions
suitable for bladder regeneration is not constructed
according to the optimised design, we have validated the
simulations and governing equations in a 100-mm circular
reactor with 2-mm thick chitosan scaffolds. In particular,
we measured the pressure drop across the bioreactor
constructed in-house and an in-line physiological pressure
transducer. Results obtained with and without chitosan
porous structures agreed with the simulation results,
suggesting validity of the used governing equations.
Recently, others have evaluated the utilisation and
operation of bioreactors of different dimensions to
regenerate bladder (Wallis et al. 2008; Davis et al. 2011;
Bouhout et al. 2011). Nevertheless, the described flow
conditions need to be validated experimentally in the
presenceofcellstodeterminewhetherthoseminimumflow
rates are sufficient to ensure nutrient distribution. To
perform experiments, one has to generate 3D porous
Cell density (1X = 1.2*1012 cells/m3)
1X 2X 4X8X16X
Flow rate (mL/min)
0
20
40
60
80
Pressure drop (Pa)
0
1
2
3
4
5
6
7
Flow rate
Pressure drop
Figure 7.
minimum oxygen concentration of 0.05mol/m3with increasing
cell density.
Optimal flow rate and pressure drop to maintain
Permeability (µm2)
154184.7
3 110Design 2-ADesign 2-B
Design 2-C
Scaffold
Figure 6. Effects of permeability change on oxygen distribution for Design 2-C at 5ml/min flow rate.
S. Pok et al.10
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Page 12

structuresofrequireddimensionsmimickingbladdershape
(Atala et al. 2006). In addition, one has to determine the
effect of flow rate on the quality of the regenerated tissue.
Nevertheless, we need to understand whether the
regenerated tissue in the bioreactor at the suggested flow
rate is healthy or shows altered phenotypic characteristics
(Lai et al. 2002). The assembly and maturation of matrix
elements play a significant role in determining the
biomechanics of bladder tissue (Korossis et al. 2009).
Since matrix composition imbalance leads to several
disorders (Lemack et al. 1999; Wognum et al. 2009), one
has to assess the quality of the regenerated bladder.
To summarize, this computational simulation study
evaluated design features required in a bioreactor to
regenerate human bladder. New funnel-shaped inlet
decreased the shear stress at the inlet area, and it showed
uniform distribution of the shear stress through the porous
structure. The location of the porous structure within the
reactor affected the hydrodynamic forces and nutrient
distributions significantly. Bioreactor with suspended
porous structure in the middle with open flow area on
either side had less pressure drop and shear stress
distribution with retaining sufficient nutrient distributions.
In addition, it is necessary for altering the volumetric flow
rate and pressure to maintain constant nutrient distribution
followed by cell proliferation and matrix deposition.
References
Alpert E, Gruzman A, Totary H, Kaiser N, Reich R, Sasson S.
2002. A natural protective mechanism against hyperglycae-
mia in vascular endothelial and smooth-muscle cells: role of
glucose and 12-hydroxyeicosatetraenoic acid. Biochem
J. 362:413–422.
Atala A, Bauer SB, Soker S, Yoo JJ, Retik AB. 2006. Tissue-
engineered autologous bladders for patients needing
cystoplasty. Lancet. 367:1241–1246.
Baumert H, Simon P, Hekmati M, Fromont G, Levy M, Andr B,
et al. 2007. Development of a seeded scaffold in the great
omentum: feasibility of an in vivo bioreactor for bladder
tissue engineering. Eur Urol. 52:884–892.
Bouhout S, Gauvin R, Gibot L, Aube D, Bolduc S. 2011. Bladder
substitute reconstructed in a physiological pressure environ-
ment. J Pediatr Urol. 7:276–282.
Brown A, Meenan BJ. 2007. Investigating the effects of fluid
shear forces on cellular responses to profiled surfaces in-
vitro: a computational and experimental investigation. Conf
Proc IEEE Eng Med Biol Soc. 2007:5387–5390.
Chatzizisis YS, Coskun AU, Jonas M, Edelman ER, Feldman CL,
Stone PH. 2007. Role of endothelial shear stress in the
natural history of coronary atherosclerosis and vascular
remodeling: molecular, cellular, and vascular behavior. J Am
Coll Cardiol. 49:2379–2393.
Chen H-C, Hu Y-C. 2006. Bioreactors for tissue engineering.
Biotechnol Lett. 28:1415–1423.
Cioffi M, Boschetti F, Raimondi MT, Dubini G. 2006. Modeling
evaluation of the fluid-dynamic microenvironment in tissue-
engineered constructs: a micro-CT based model. Biotechnol
Bioeng. 93:500–510.
Cooper JA, Jr, Li WJ, Bailey LO, Hudson SD, Lin-Gibson S,
Anseth KS, Tuan RS, Washburn NR. 2007. Encapsulated
chondrocyte response in a pulsatile flow bioreactor.
Acta Biomater. 3(1):13–21.
Davis NF, Mooney R, Piterina AV, Callanan A, McGuire BB,
Flood HD, McGloughlin TM. 2011. Construction and
evaluation of urinary bladder bioreactor for urologic tissue-
engineering purposes. Urology. 78(4):954–960.
Devarapalli M, Lawrence BJ, Madihally SV. 2009. Modeling
nutrient consumptions in large flow-through bioreactors for
tissue engineering. Biotechnol Bioeng. 103:1003–1015.
Farhat WA, Yeger H. 2008. Does mechanical stimulation have
any role in urinary bladder tissue engineering? World J Urol.
26:301–305.
Fogler HS. 2006. Elements of chemical reactor engineering.
4th ed. Upper Saddle River, NJ: Prentice Hall.
Gooch KJ, Kwon JH, Blunk T, Langer R, Freed L, Vunjak-
Novakovic EG. 2001. Effects of mixing intensity on tissue-
engineered cartilage. Biotechnol Bioeng. 72:402–407.
Gray ML, Pizzanelli AM, Grodzinsky AJ, Lee RC. 1988.
Mechanical and physicochemical determinants of the
chondrocytebiosyntheticresponse.JOrthopRes.6:777–792.
Heydarkhan-Hagvall S, Esguerra M, Helenius G, Sapderberg R,
Johansson BR, Risberg B. 2006. Production of extracellular
matrix components in tissue-engineered blood vessels.
Tissue Eng. 12:831–842.
Huang Y, Onyeri S, Siewe M, Moshfeghian A, Madihally SV.
2005. In vitro characterization of chitosan-gelatin scaffolds
for tissue engineering. Biomaterials. 26:7616–7627.
Huang Y, Siewe M, Madihally SV. 2006. Effect of spatial
architecture on cellular colonization. Biotechnol Bioeng.
93:64–75.
Hutmacher DW, Singh H. 2008. Computational fluid dynamics
for improved bioreactor design and 3D culture. Trends
Biotechnol. 26:166–172.
Isenberg BC, Tranquillo RT. 2003. Long-term cyclic distention
enhances the mechanical properties of collagen-based media-
equivalents. Ann Biomed Eng. 31:937–949.
Khandelwal P, Abraham SN, Apodaca G. 2009. Cell biology and
physiology of the uroepithelium. Am J Physiol Renal
Physiol. 297:F1477–F1501.
Kim BS, Mooney DJ. 2000. Scaffolds for engineering smooth
muscle under cyclic mechanical strain conditions. J Biomech
Eng. 122:210–215.
Korossis S, Bolland F, Southgate J, Ingham E, Fisher J. 2009.
Regional biomechanical and histological characterisation of
the passive porcine urinary bladder: implications for
augmentation and tissue engineering strategies. Biomater-
ials. 30:266–275.
Lai CZ, Koseoglu SS, Lugert EC, Boswell PG, Rabai J, Lodge
TP, Buhlmann P. 2009. Fluorous polymeric membranes for
ionophore-based ion-selective potentiometry: how inert is
Teflon AF? J Am Chem Soc. 131(4):1598–1606.
Lai JY, YoonCY, Yoo JJ, Wulf T,Atala A. 2002. Phenotypic and
functional characterization of in vivo tissue engineered
smooth muscle from normal and pathological bladders.
J Urol. 168:1853–1857; discussion 8.
Lawrence BJ, Devarapalli M, Madihally SV. 2009. Flow
dynamics in bioreactors containing tissue engineering
scaffolds. Biotechnol Bioeng. 102:935–947.
Lemack GE, Szabo Z, Urban Z, Boyd CD, Csiszar K,
Vaughan ED, Jr, Felsen D. 1999. Altered bladder function
in transgenic mice expressing rat elastin. Neurourol Urodyn.
18(1):55–68.
Computer Methods in Biomechanics and Biomedical Engineering 11
Downloaded by [Fondren Library, Rice University ] at 12:13 30 January 2012

Page 13

Mackie JS, Meares P. 1955a. Diffusion in a cation exchanger
resin I. Proc R Soc. 232:448–495.
Mackie JS, Meares P. 1955b. Diffusion in a cation exchanger
resin II. Proc R Soc. 232:495–505.
Martin Y, Vermette P. 2005. Bioreactors for tissue mass culture:
design, characterization, and recent advances. Biomaterials.
26:7481–7503.
Martin I, Wendt D, Heberer M. 2004. The role of bioreactors in
tissue engineering. Trends in Biotechnol. 22:80–86.
Motterlini R, Kerger H, Green CJ, Winslow RM, Intaglietta M.
1998. Depression of endothelial and smooth muscle cell
oxygen consumption by endotoxin. Am J Physiol Heart Circ
Physiol. 275:H776–H782.
Niklason LE, Gao J, Abbott WM, Hirschi KK, Houser S,
Marini R, Langer R. 1999. Functional arteries grown invitro.
Science. 284(5413):489–493.
Porter B, Zauel R, Stockman H, Guldberg R, Fyhrie D. 2005. 3-D
computational modeling of media flow through scaffolds in a
perfusion bioreactor. J Biomech. 38:543–549.
Sander EA, Nauman EA. 2003. Permeability of musculoskeletal
tissues and scaffolding materials: experimental results and
theoretical predictions. Crit Rev Biomed Eng. 31:1–26.
Sengers BG, Heywood HK, Lee DA, Oomens CWJ, Bader DL.
2005. Nutrient utilization by bovine articular chondrocytes: a
combined experimental and theoretical approach. J Biomech
Eng. 127:758–766.
Sengers BG, van Donkelaar CC, Oomens CW, Baaijens FP.
2005. Computational study of culture conditions and nutrient
supply in cartilage tissue engineering. Biotechnol Prog. 21:
1252–1261.
Shi ZD, Ji XY, Qazi H, Tarbell JM. 2009. Interstitial flow
promotes vascular fibroblast, myofibroblast, and smooth
muscle cell motility in 3-D collagen I via upregulation
of MMP-1. Am J Physiol Heart Circ Physiol. 297:
H1225–H1234.
Takahashi M, Berk BC. 1996. Mitogen-activated protein kinase
(ERK1/2) activation by shear stress and adhesion in
endothelial cells. Essential role for a herbimycin-sensitive
kinase. J Clin Invest. 98:2623–2631.
Tillman J, Ullm A, Madihally SV. 2006. Three-dimensional cell
colonization in a sulfate rich environment. Biomaterials.
27:5618–5626.
Truskey GA, Yuan F, Katz DF. 2004. Transport phenomena in
biological systems. Upper Saddle River, NJ: Pearson
Prentice Hall. p. 317–321.
Wallis MC, Yeger H, Cartwright L, Shou Z, Radisic M, Haig J,
Suoub M, Antoon R, Farhat WA. 2008. Feasibility study of a
novel urinary bladder bioreactor. Tissue Eng Part A.
14:339–348.
Waters SL, Cummings LJ, Shakesheff KM, Rose FR. 2006.
Tissue growth in a rotating bioreactor. Part I: mechanical
stability. Math Med Biol. 23:311–337.
Williams KA, Saini S, Wick TM. 2002. Computational fluid
dynamics modeling of steady-state momentum and mass
transport in a bioreactor for cartilage tissue engineering.
Biotechnol Prog. 18:951–963.
Wognum S, Schmidt DE, Sacks MS. 2009. On the mechanical
role of de novo synthesized elastin in the urinary bladder
wall. J Biomech Eng. 131:101018.
S. Pok et al. 12
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