DESIGN OF A PERCOLATION REACTOR
by
Perla Issa
B. Eng. Mechanical Engineering (1997)
McGill University
Submitted to the Department of Mechanical Engineering
In Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
February 2000
©2000 Massachusetts Institute of Technology
All rights reserved
Signature of Author...................................
Department of Mechanical Engineering
December 17, 1999
C ertified by..................................
Mehmet Toner
Associate Professor Harvard-MIT Division of Health Science and Technology
Thesis Supervisor
Accepted by ..........................................................................................
Ain A. Sonin
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
1
SEP 2 0 2000
LIBRARIES
n
DESIGN OF A PERCOLATION REACTOR
by
Perla Issa
Submitted to the Department of Mechanical Engineering
on December 17, 1999 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Mechanical Engineering
ABSTRACT
Liver failure is a major cause of mortality. A Bioartificial Liver (BAL) device
employing isolated hepatocytes can potentially provide temporary support for liver
failure patients. We have designed and manufactured a small-scale BAL device that
attempts to mimic some of the elements of the flow conditions observed in the liver by
creating a well-defined 3D porous matrix. The proposed reactor consists of perforated
discs stacked on top of each other. The holes of two consecutive discs are misaligned in a
specific manner to create a similar fluid flow configuration as the one seen in the liver.
The advantages of such a design are numerous: high flow rates can be achieved while
still minimizing the local shear stress levels, cells are cultured on a flat-plate as seen in
the liver, and all cells are directly exposed to flow in order to supply oxygen and
nutrients. Two prototypes of the proposed reactor were manufactured with two different
disc spacing: 565 gm and 127 pm. The perforated discs were produced by injectionmolding and their biocompatibility demonstrated using hepatocyte cultures under static
conditions (i.e. no flow). A theoretical analysis of the fluid flow conditions was
developed using porous media theory. The reactors (without cells) were then operated
over a wide range of flow rates to experimentally characterize the fluid flow conditions.
The flow was shown to be uniformly distributed across the reactor and the shear stress
values were minimal (0.028 dyne/cm 2 to 0.18 dyne/cm 2 for flow rates ranging from 2
ml/min to 12 ml/min). The reactor was also tested with hepatocytes for two different flow
rates: 0.2 ml/min and 0.5 ml/min. The final percentage of attached cells ranged from 98%
to 76% and their associated viability ranged between 87% and 78%. The results indicate
that the cells adequately sustain attachment and viability in the percolation reactor under
the flow conditions tested in this study. Finally, it is worth noting that further
optimization of the percolation structure is needed to increase the performance of the
reactor substantially.
Thesis Supervisor: Mehmet Toner
Title:
Associate Professor
Center for Engineering in Medicine
Massachusetts General Hospital and Harvard Medical School
Affiliated faculty: Harvard-MIT Division of Health Science and Technology
2
ACKNOWLEDGEMENTS
I would like to express my gratitude to Professor Mehmet Toner for his expert
guidance and insightful discussions. As well, I am grateful for his continued
encouragement throughout the course of this project. Furthermore, I would like to thank
Albert Folch for his knowledgeable advice and assistance.
Special thanks is extended to Arno Tilles, Junji Washizu, George Pins, and Ul
Balis for their most valuable help, time and suggestions.
The completion of this project would not have been possible without the patience
and attention I received from certain people. I would like to offer special thanks to
everyone in the lab that has helped me in some way: Pat Walton and Kyongbun Lee for
their patience and assistance in the computer lab, Octavio Hurtado for his help in the
microfabrication facility, Jeanne Classen, Bharath Dwarakanath, William Jastromb,
Annette McDonald, and Molly Williams for their support of the tissue culture facility,
Bob Crowther and Ali Eroglu for their help in microscopy, and finally Linda Huffer and
Lynne Stubblefield for handling all administrative issues. What I came to find in Boston
extended beyond any of my expectations. I developed friendships that will last a lifetime.
Thank you all for making this experience such a memorable one.
Finally I would like to thank my family for their constant encouragement, support
and understanding throughout my graduate years.
Financial support was provided by the Harvard-MIT Division of Health Science
and Technology, Shriners Hospital for Children, Fonds pour la Formation des Chercheur
et l'Aide a la Recherche (FCAR) of the government of Quebec, and finally Mom and
Dad.
3
ABSTRACT
ACKNOWLEDGMENTS
TABLE OF CONTENT
LIST OF FIGURES
LIST OF TABLES
NOMENCLATURE
2
3
4
6
8
9
CHAPTER 1
INTRODUCTION
11
1.1. LIVER FAILURE AND BIOARTIFICIAL LIVER DEVICES
1.2. LIVER GEOMETRY
1.2.1. Organization of the liver
1.2.2. Blood supply
1.2.3. The liver acinus as a porous bed of hepatocytes
1.3. THE OVERALL GOAL OF THIS STUDY
REFERENCES
11
12
12
15
15
16
19
CHAPTER 2
DESIGN AND MANUFACTURE OF THE
PERCOLATION REACTOR
20
2.1. INJECTION-MOLDING
2.2. MOLD MAKING
2.3. DESIGN OF THE REACTOR BODY
20
21
25
CHAPTER 3
MATERIALS AND METHODS
28
3.1. BIOCOMPATIBILITY STUDIES
3.1.1. Cell culture
3.1.2. Attachment experiments
3.1.3. Functional assay
3.2. EXPERIMENTAL FLOW CHARACTERIZATION OF THE REACTOR
3.2.1. Flow circuit
3.2.2. Fluid flow characterization
Fluid flow uniformity across the reactor
Velocity profile and shear stress experiments
3.2.3. Experimental characterization of the reactor with cells
REFERENCES
28
28
28
30
30
30
31
31
33
34
35
CHAPTER 4
FLUID FLOW ANALYSIS
36
4.1. PERCOLATION REACTOR PROPERTIES
4.1.1. Porosity
36
36
4
4.1.2. Specific surface
4.1.3 Tortuosity
4.1.4 Permeability
4.2. FLUID FLOW ANALYSIS
4.2.1. Flow conditions
4.2.2. Pressure drop estimation: Navier Stokes equation
4.2.3. Pressure drop estimation: Darcy's Law
4.2.4. Shear stress estimation
REFERENCES
37
37
38
38
38
39
41
42
43
CHAPTER 5
MODEL PREDICTIONS AND EXPERIMENTAL
CHARACTERIZATION
44
5.1. BIOCOMPATIBILITY STUDIES UNDER STATIC CULTURES
5.1.1. Cell attachment studies
5.1.2. Albumin secretion
5.2. THEORETICAL FLUID FLOW ANALYSIS
5.2.1. Percolation reactor properties
5.2.2. Flow conditions
5.2.3.Pressure drop estimation: Navier Stokes equation
5.2.4. Pressure drop estimation: Darcy's law
5.2.5. Shear stress estimation
5.3. EXPERIMENTAL CHARACTERIZATION OF THE FLUID FLOW
5.3.1. Fluid flow uniformity across the reactor
5.3.2. Velocity profile and shear stress experiments
5.3.3. Experimental characterization of the reactor with cells
REFERENCES
44
44
46
47
47
48
48
49
50
52
52
55
62
64
CHAPTER 6
DISCUSSION AND OUTLOOK
65
CONCLUSION AND OUTLOOK
REFERENCES
69
70
5
LIST OF FIGURES
Figure 1.1: Portion of a histological section showing the radiating cell plates in
two classical lobules and the portal areas.
13
Figure 1.2: Schematic depiction of the portal area and the cell plates. Blood
flows from branches of the portal vein and the hepatic artery through the
sinusoids into the central vein (hepatic vein).
14
Figure 1.3: Schematic representation of the classical lobule and the ellipsoidal
acinus. At the left the three zones of the hepatic acinus are designated.
14
Figure 1.4: Hole pattern on perforated discs. Solid lines represent holes on the
upper disc while dashed lines represent holes on the lower disc.
17
Figure 2.1: Mold template. Dark area indicates posts. Scale 1:0.73
22
Figure 2.2: Picture of the aluminum mold producing the perforated discs.
Rhomboidal posts can be seen in the middle as well as the polished surface
underneath. Scale 1:1.2
23
Figure 2.3: Picture of the aluminum ring lifting a transparent perforated disc,
as a result of tightening four screws. Scale 1:0.93
24
Figure 2.4: Picture of five different perforated discs. Scale 1:1.5
24
Figure 2.5: Picture of assembled percolation reactor. Scale 1:1.125
27
Figure 2.6: Picture depicting the bottom of the reactor. Scale 1:1.8
27
Figure 2.7: Picture depicting the top of the reactor. Scale 1:1.8
27
Figure 3.1: Microscope view at 4x magnification. A portion of a hole in the
upper disc (A) and a portion of another hole (B) on a disc 565 pm below are
shown.
32
Figure 4.1: Flow regions in porous medium characterized by the modified
Reynolds number, Rem. Remc is the critical value at which the flow transits
from Darcy's regime to Forcheimer's.
41
Figure 5.1: Kinetics of hepatocyte attachment. Comparison between tissue culture
polystyrene dishes (TCPS) with plasma-treated and untreated discs. Error bars
represent the standard deviation of five different measurements.
45
Figure 5.2: Albumin production of hepatocytes cultured with fibroblasts using
a ratio of 1 hepatocyte for 6 fibroblasts.
6
46
Figure 5.3: Schematic representation of an outlet hole with three corresponding
inlet holes. Solid lines represent holes on the upper disc while dashed lines
represent holes on the lower disc.
52
Figure 5.4: Average velocity per outlet as a function of radial position for
the reactor with 565gm disc spacing. A) Qtotai = 8.8ml/min,
B) Qtot ai = 13ml/min, C) Qtotail=16.1ml/min
54
Figure 5.5: Average velocity per outlet as a function of radial position for the
reactor with 127gm disc spacing. Qtotai = 2ml/min,.
55
Figure 5.6: Fluid velocity profile between two percolating discs separated
by a spacing of 565 gm with a total fluid flow rate of
A) 7.8ml/min, V(y) = -13.2y 3 + 0.6y 2 + 4y + 0.04,
B) 12.5 ml/min V(y) = 82.6y 3 - 101.7y 2 + 34.4y - 1.6. Error bars represent
the standard deviation of five different measurements.
56
Figure 5.7: Comparison between theoretical and experimental fluid flow rates
for a disc spacing of 565 gm.
58
Figure 5.8: Fluid velocity profile between two percolating discs separated
by 127 pm. A) Qtotai = 6.82ml/min, V(y) = -19252y 3 + 2804.8y 2 - 45.7y +
0.3, B) Qt otai = 2.3ml/min, V(y) = 5876.3y 3 + 811.2y 2 - 7.7y + 0.08.
Error bars represent the standard deviation of five different measurements.
59
Figure 5.9: Comparison between theoretical and experimental fluid flow rates for
a disc spacing of 127 pm.
60
Figure 5.10: Experimental and theoretical wall shear stress as function of
flow rate for both reactors.
7
61
LIST OF TABLES
Table 1.1: Physiological parameters of the liver.
16
Table 5.1: Percolation reactor properties.
47
Table 5.2: Estimated pressure drop and Rem for the percolation reactor.
49
Table 5.3: Pressure drop according to Darcy's law for different flow rates.
50
Table 5.4: Shear stress estimations for different flow rates.
51
Table 5.5: Comparison between the parallel-plate reactor and the percolation
reactor when subjected to a flow rate of 0.2 ml/min and 0.5 ml/min. The
percentage of the remaining attached cells at the end of the experiment and
their viability is shown with their corresponding standard deviation.
62
8
NOMENCLATURE
a: hole side length (1.154x 1 0 3 m)
Ahole:
hole cross-sectional area (1.154x10- m2)
Adisc:
disc cross-sectional area (2027x10-6m2)
Di,: horizontal distance between an outlet and an inlet hole on two consecutive discs
(2.66x 10-3 m)
Hs: Spacer height (565gm, 127gm)
ISAP: Interstitial surface area of pores
(M2 )
K: permeability (m2 )
if: flow path length (m)
lu: unit length (m)
nh: number of holes per disc (50 holes)
qtotal: cross-sectional
qest:
average, axial velocity (m/sec)
pump flow rate divided the number of holes (mm 3/sec)
qmeas:
experimentally measured flow rate through one hole (mm 3/sec)
Q: fluid flow rate (m3 /sec)
R: disc radius (25.4x10 3 im)
Sd:
surface area of disc (m2 )
Sh:
surface area of holes
(M2)
S,: surface area of spacer (m2 )
td:
disc thickness (I.1x10-3 )
T: tortuosity
THA: Terminal hepatic arteriole
TPV: terminal portal venule
V(y): best curve-fit to the velocity profile obtained experimentally
Vp: Volume of pores
(M3 )
V: Total volume of unit (m3)
y: vertical distance starting from the bottom disc in the reactor
E: porosity
y: kinematic viscosity (10-6 m2/sec)
9
g: dynamic fluid viscosity (10-3kg/msec)
p: fluid density (10
3
kg/m 3)
10
CHAPTER 1
INTRODUCTION
1.1. LIVER FAILURE AND BIOARTIFICIAL LIVER DEVICES
Each year approximately 30,000 individuals develop severe hepatic failure. Less
than 3,000 of these patients will undergo orthotopic liver transplantation, the only
available method for the clinical management of severe hepatic failure13. For the patients
who are not selected for transplantation there is no adequate treatment available and it is
estimated that 375 prospective recipients die each year while waiting for a transplant.
Those suffering from cirrhosis fight the seventh leading cause of death in the USA and
those suffering from acute liver failure face a mortality greater than 80% 1. The livers of
acute liver failure patients undergo a regenerative process. Stabilization of these patients
during this regenerative period with an extracorporeal device, would allow liver
regeneration and circumvent the need for transplantation. An extracorporeal device
consists of an enclosed casing containing functioning mammalian hepatocytes subjected
to fluid flow. The fluid is either culture medium, blood or plasma. An extracorporeal
device could also be used as a useful bridge-to-transplantation for potential transplant
recipients. Furthermore, 25% of liver transplant recipients undergo post-surgical
complications and require a second surgical procedure, these patients are also candidates
for an extracorporeal device.
Presently Bioartificial Liver assist (BAL) devices used in clinical trials are based
on hollow-fiber designs. These bioreactors contain bundles of small-diameter fibers
enclosed in a rigid housing. The fibers are porous allowing the passage of molecules.
11
Cells are inoculated in the extrafiber space while the appropriate fluid is pumped through
the fiber lumen 7 . There are two important shortcomings to hollow-fiber based liver
devices. In hollow fiber reactors only a small fraction of packed multilayered cells are in
direct contact with fibers, thereby the majority of cells experience oxygen limitation. It is
also noteworthy that hepatocytes in liver are organized in a planar like geometry in
sinusoids, and not as packed cylinders as in the hollow fiber devices. This issue is further
described in the next section.
1.2. LIVER GEOMETRY
The liver is the largest gland in the body and is situated in the upper abdominal
cavity. The liver has multiple functions essential to maintain life including carbohydrate
metabolism, synthesis of proteins, amino acid metabolism, urea synthesis, lipid
metabolism, drug biotransformation, and waste removal.
1.2.1. Organization of the liver
The internal architecture of the liver consists of repeating pattern of hexagonal
areas in which plates of cells are arranged radially around a central vein (see figure 1.1).
At three corners of these polygonal areas there is a small triangular area of connective
tissue enclosing a small bile duct, a branch of the hepatic artery (the terminal hepatic
arteriole, THA), and a branch of the portal vein (the terminal portal venule, TPV). This
complex is referred to as the portal area (see figure 1.2). Blood enters the unit via the
THA and the TPV, exchanges solutes with the cells and exits via the Terminal Hepatic
12
Venule (THV) into the central vein. This polygonal unit, about 700 pm in diameter and
2mm long, is called the classical lobule 2(see figure 1.3).
More recent investigations defined the hepatic acinus as the structural and
functional unit of the liver . It is irregular in size and shape and lies between two central
veins (see figure 1.3). Blood enters the unit through lateral branches of the portal vein
and the hepatic artery and exits via the central vein. The liver acinus is divided into zone
1, 2 and 3 according to the quality of portal blood 4 (see figure 1.3). The cells in zone 1
have first access to the incoming oxygen and nutrients. The cells of zone 2 receive
processed blood from zone 1 and those of zone 3 receive blood after being processed in
zone 1 and 2.
Central vein
Bile
Interlobular
ducts
vein
Central
vein
Bile
ducts
Branch of
hepatic artery
nter-
t4
A
Bile ducts
r
W ie
%,6 OIA
t
q
Inter-
jl
vein
0.4,
/,
-; ,
3'
lobular
lobular
41
k-4
Oft
j
veins
4.
A
; 7\
or
-Z
t
7
Bile
ducts
Branches of
hepatic-
artery
U
I I
r
Interlobular
vein
IP-:J
Artery
Bile
ducts
Interlobular
connective tissue
Liver cell plates
Bile ducts
iillfi
Interlobular veins
Figure 1.1: Portion of a histological section showing the radiating cell plates in two classical
lobules and the portal areas ".
13
Sinusoids
HenaticuAe
00
3ile Duct
0~
arto
0
0
Figure 1.2: Schematic depiction of the portal
area and the cell plates. Blood flows from
branches of the portal vein and the hepatic
artery through the sinusoids into the central
vein (hepatic vein) 2
Vein
-rOnch
Hepatic Artery
Classical
lobule
Zones
of-
acinus--
Hepatic acinus
Figure 1.3: Schematic representation of the classical lobule and the ellipsoidal acinus. At the left
the three zones of the hepatic acinus are designated 2.
14
1.2.2. Blood supply
The liver is situated between the portal vascular system and the general
circulation. It receives well-oxygenated blood (13-14ml/dl during the fasting state)' from
the general circulation via the hepatic artery, which represents 25% of the total liver flow.
The remaining 75% is supplied by the portal vein which carries poorly oxygenated blood
(4-5ml/dl during the fasting state)' that has already circulated through the intestines, the
pancreas and the spleen 1. Blood from these two sources mix in the hepatic sinusoids
which form an elaborate three-dimensional network, presenting an enormous surface area
(550cm 2 /cm 3) 7 for exchange of metabolite between the blood and the cells. Most cells in
the radially-arranged cellular plates are exposed on both sides to blood flowing through
the sinusoids. Finally the blood leaves the sinusoids through numerous openings in the
thin wall of the central vein.
1.2.3. The liver acinus as a porous bed of hepatocytes
In order to create a structure which properly imitates liver conditions, we need a
more quantitative description of the liver acinus and its flow conditions. The fluid flow
through the hepatic acinus is quite complex. From a global view, flow appears to be
unidirectional occurring from the TPV and the THA through the sinusoids to the central
vein. However, this is not the case at the microcirculatory level. Numerous branches and
interconnections between sinusoids coupled with the irregular geometry of the acinus
increases the complexity of the flow. Studies have also shown that richly interconnected
channels form the sinusoids', indicating that fluid flow through the acinus traverses a
tortuous path. From these observations, the liver acinus is often characterized as a porous
15
bed of hepatocytes 7 for analytical studies. Characteristic parameters of porous medium
are obtained from previous investigations and their values are shown in table 1.1.
Table 1.1: Physiological parameters of the liver.
Name
Symbol
Porosit y
Value
Units
References
3
0.11
Length of sinusoids
Ls
350
gm
2
Diamel er of sinusoids
Ds
7
gm
3
Surface area/volume of tissue
Sa/Vt
550
cm-1
8
Permea bility
KL
4.3X10-12
m2
9
Charac teristic velocity
VL
3x10-3
m/sec
9
Pressur e portal vein (inlet)
Pp
588
Pa
7
Pressur e hepatic vein (outlet)
Ph
196
Pa
7
Shear stress in the sinusoids
t
20
dyne/cm 2
6
Major differences are found between the hollow-fiber geometry and the liver. In
in-vivo conditions hepatocytes are in a plate arrangement and not packed in layers inside
fibers. The liver also possess multiple inlets and outlets which minimizes local shear
stress while providing adequate oxygen and nutrient supply. Our goal is to create a new
reactor to address some of these issues.
1.3. THE OVERALL GOAL OF THIS STUDY
The present study is an attempt to mimic some of the elements of the flow
conditions observed in the liver by creating a well-defined 3D porous matrix. The
proposed device consists of perforated circular discs stacked on top of each other. The
16
discs contain an array of holes in a hexagonal pattern. The holes of two consecutive discs
are misaligned in a specific manner to create a percolating flow. A hexagonal pattern is
chosen so that every outlet is supplied by three inlets and every inlet supplies three
outlets (figure 1.4.). This geometry is selected to create a similar configuration seen in the
liver: the central vein (the outlet) is supplied through the sinusoid by three portal areas
(the inlets), and every portal area supplies three central veins. The hole size, the spacing
between two holes and the spacing between two discs alter the flow of fluid through the
device.
o
o
O
0
0
0
Figure 1.4: Hole pattern on perforated discs. Solid lines represent holes on the upper disc while
dashed lines represent holes on the lower disc.
The present study consists of designing, manufacturing and optimizing the
percolation reactor. Chapter 2 describes the design and manufacture of the percolation
reactor. The production of the perforated discs by injection molding and the manufacture
of the outside casing are described in detail. Chapter 3 goes through the materials and
methods of 1) the biocompatibility tests performed on the injected-molded surfaces using
static cell cultures, 2) the experimental characterization of the fluid flow as well as the
experimental comparison with a parallel-plate reactor. In chapter 4 the theoretical fluid
17
flow analysis using porous media theory is described, the percolation reactor properties,
the flow regime, the pressure drop, and the shear stress are defined. Chapter 5 presents
the model predictions and the experimental characterization. The biocompatibility studies
results, the theoretical fluid flow predictions, and the experimental characterization of the
bioreactor (with and without cells) are reported. Finally chapter 6 discusses the findings
and gives an outlook on the future.
18
REFERENCES
1. Arias, H. Popper, D. Schachter and D.A. Shafritz (Editors), The liver: Biology and
Pathobiology,pp 916-920, Raven Press, New York (1983).
2. Fawcett, A textbook of Histology. 12 th Edition, pp 652-657, Chapman & Hall, New
York (1994).
3. Goresky, and B.E. Nadeau, Uptake of materials by the intact liver: the exchange of
glucose across the cell membranes, J. Clin. Invest. 53, pp 634-646 (1974).
4. Gumucio, Functional and anatomic heterogeneity in the liver acinus: impact on
transport, Am. J. Physiol. 244, pp G578-G582 (1983).
5. A. Kamlot, J. Roozga, F.D. Watanabe and A.A. Demetriou, Review: Artificial liver
support systems, Biotechnol. Bioeng. 50, pp 382-391 (1996).
6. Kan, H. Miyoshi, K. Yanagi, and N. Ohshima, Effects of shear stress on metabolic
function of the co-culture system of hepatocyte/nonparenchymal cells for a
bioartificial liver, ASAIO J. 44, pp M441-M444 (1998).
7. Lee and B. Rubinsky, A multi-dimensional model of momentum and mass transfer in
the liver, Int. J.Heat & Mass Transfer, 32, pp 2421-2434 (1989).
8. Miller, C.S. Zanolli and J.J. Gumucio, Quantitative morphology of the hepatic acinus,
Gastroent.76, pp 965-969 (1979).
9. Nakata, C.F. Leong and R.W. Brauer, Direct measurement of blood pressures in
minute vessels of the liver, Am. J. Physiol. 199, pp 1181-1188 (1960).
10. Popper, C.S. Davidson, C.M. Leevey and F. Schaffner, The social impact of the liver
disease, N. Eng. J. Med. 281, pp 1455 (1969).
11. Rappaport, The microcirculatory hepatic unit, Microvasc. Res. 6, pp 212-228 (1973).
12. Sobotta, Atlas of Human Anatomy VOL II, G.E. Stechert & Co. New York (1936)
13. Trey, D.G. Burns and S.J. Saunders, Treatment of hepatic coma by exchange blood
transfusion, N. Eng. J. Med. 274, pp 473 (1966).
19
CHAPTER 2
DESIGN AND MANUFACTURE OF THE
PERCOLATION REACTOR
The percolation reactor consists of perforated discs which are stacked on top of
each other and enclosed in a casing. A hexagonal hole pattern is chosen so that every
outlet is supplied by three inlets and every inlet is supplied by three outlets, as seen in the
liver. The discs are produced by injection molding.
2.1. INJECTION MOLDING
The production of discs perforated by an array of holes presents a number of
challenges. Reproducibility is essential, scaling-up should be straightforward and
production time must be reasonable. Manually drilling holes was rejected because
replication is difficult and time-consuming; instead, the injection molding option is
selected. Injection molding is a process in which plastic is melted and injected at high
pressure into a cavity. This cavity molds and contains the plastic until it solidifies into the
desired shape. The injection molding machine used in the present study is a MorganPress G-IOOT (Morgan Industry, Long Beach, California), it is equipped with a preheatplate, an injection speed controller and an anti-drool nozzle. The chosen material is
polystyrene due to its widespread use in cell culture, excellent molding characteristics
(high melt flow rate 13.3g/10min and low burn rate) and its transparent appearance.
Polystyrene beads (Styron 615) are purchased from the Dow Chemical Company
20
(Cranbury, New Jersey). Drying the beads is essential, because any residual moisture
absorbed by the beads causes the material to foam and affects part quality. To ensure
complete drying, the material is spread in one inch layers in trays and placed in a vacuum
oven for at least two hours at 80'C. Once ready, the material is fed into the top of the
melt cylinder heated to 200'C, followed by a three-minute hold. The melted material is
injected at a pressure of 7000 psi into a cold mold. Finally, the part is removed using an
ejection system described in the next section.
2.2. MOLD MAKING
For our device, we found the fabrication of the mold to be the most challenging
part of the manufacturing step. The mold consists of "posts" whose height and diameter
respectively correspond to the thickness of the disc and the diameter of the holes. Several
techniques are considered such as 1) nickel plating, 2) chemical etching of metal and 3)
conventional machining.
1) The first option is photolithography followed by nickel plating. The process
consists of depositing a layer of photoresist on a silicon wafer, with a thickness equal to
the desired disc thickness, exposing it to UV light through a mask, developing it, plating
the exposed areas with nickel and finally removing the rest of the photoresist.
Unfortunately, this process had to be abandoned due to technical difficulties encountered
while electroplating nickel.
2) The second alternative consists of chemically etching metal. In this process a
sheet of metal is coated with photoresist, exposed to UV light with a mask and
developed, leaving a pattern of "bare" metal ready to be etched. Working in collaboration
21
with Fotofabrication (Chicago, Illinois) a stainless steel template is created by isotropic
etching. Unfortunately, the etching process produces a rough surface which replicates
into a rough translucent plastic surface unsuitable for microscopic phase-contrast
examination
3) Finally, the molds were manufactured by conventional machining. First a twoinch aluminum cylinder is cut, then 1 mm deep and 4 mm wide straight cuts are made
with a 1 mm spacing. The cylinder is then rotated by 60 degrees and the same cuts are
made (see figure 2.1).
46.0 mmD
1.0 MM
(1.812" DIA)
4.0 mm
60'
V %
50.8 mmD-/ '\
(2.00" DIA.)
Figure 2.1: Mold template. Dark area indicates posts. Scale: 1:0.73
This process creates an array of 1 mm high rhomboidal posts with a 4 mm
spacing. The mold is then manually polished with a lot of attention to the posts to create a
mirror-finish surface (figure 2.2). The last step of mold making consists of integrating an
ejection system that will release the plastic part from the mold. A removable aluminum
22
ring surrounds the cavity where the plastic part is situated. The inner side is underneath
the part while the outer area has threaded holes in which screws are tightened allowing
the ring to lift with the plastic part on top of it (see figure 2.3). A groove is created on the
edge of the ring, which once filled with plastic creates a spacer integrated with the disc.
Grooves of 565 pm deep and 127 pm deep and 500 pm wide are made. Figure 2.4
displays a series of perforated discs made with the above mold. As can be seen in the
picture perfect reproducibility is achieved. Another observation is the presence of cracks.
After being injected the material cools down and shrinks in the mold, inducing internal
stress that are relieved by the creation of cracks. These cracks are only partial, they do not
extend from one hole to the other. They do not decrease the structural integrity of the
discs.
Figure 2.2: Picture of the aluminum mold producing the perforated discs. Rhomboidal posts can be seen in
the middle as well as the polished surface underneath. Scale 1:1.2
23
Figure 2.3: Picture of the aluminum ring lifting a transparent perforated disc , as a result of tightening four
screws. Scale 1:0.93
Figure 2.4: Picture of five different perforated discs. Scale 1:1.5
24
2.3. DESIGN OF THE REACTOR BODY
The next step in the production of the percolation reactor is the design of the
reactor body. The percolating discs must be held in a jacket that would encapsulate flow.
This jacket has to meet a number of requirements:
1.
The fluid flow conditions must be uniform across the perforated discs.
2. It needs to be leak-proof.
3. Inlet and outlet tubing should not obstruct the field of view.
4. Axial transparency is necessary to be able to see through from top to bottom.
5. The lower disc needs to be positioned at 2.5 mm or less from the microscope
platform to ensure proper focus of the microscope on the lower disc with
magnifications of 4x, lOx and 20x. This feature is essential for proper bead
observation.
A picture of the reactor is shown in figure 2.5. The bottom of the reactor consists of
three parts: the bottom disc, the ring and the cylinder (figure 2.6), while the top part
includes two units: the cover and the disc holder (figure 2.7). Everything, except the
bottom disc, is made of polymethylmethacrylate (PMMA) and the bottom disc is made of
polystyrene. The percolating discs fit into the cylinder and sit on top of a step, which is
supported by three feet (1mm high). These feet create three grooves underneath the discs
allowing the fluid to exit radially. This fluid is then collected in the ring where the outlet
tubing is located. Finally, the ring and the cylinder are sealed at the bottom by a 1mm
thick transparent polystyrene disc. The three parts are glued together for proper sealing
with methylchloride. The top of the reactor consists of a perfectly transparent PMMA
disc glued with a PMMA cylinder. The bottom of the cylinder sits on the edges of the
25
disc keeping pressure on them, preventing any motion. The fluid is brought into the
reactor through a groove in the PMMA disc, going from the edge to the center of the
reactor. Finally, three thumbscrews are used to fasten the top and the bottom reactor
together.
1) To comply with the first requirement a 2 cm gap is inserted between the
percolating discs and the fluid inlet. The fluid has a chance to maintain a
uniform inlet velocity across the discs, which will be verified experimentally.
2) To comply with the second requirement all the parts are glued together while
an O-ring is inserted into a slot situated on the outer edge of the cylinder to
properly seal the reactor once the top and bottom parts are brought together.
3) To comply with the third requirement the inlet and outlet tubing are situated
on the side of the reactor.
4) To meet with the fourth requirement the top and the bottom discs are made of
perfectly transparent plastics.
5) The fifth requirement is meet as a result of this design. The lower perforated
disc is at 2.5mm from the ground: the polystyrene disc is 1 mm thick, the feet
are 1 mm high and the step is 0.5 mm thick, totaling 2.5 mm.
26
Figure 2.5: Picture of assembled percolation reactor. Scale 1:1.125
Figure 2.6: Picture depicting the bottom of the reactor. Scale 1:1.8
Figure 2.7: Picture depicting the top of the reactor. Scale 1:1.8
27
CHAPTER 3
MATERIALS AND METHODS
3.1. BIOCOMPATIBILITY STUDIES
The biocompatibility of the injected molded is tested by measuring attachment and
function of hepatocytes under static culture conditions.
3.1.1. Cell culture
Hepatocytes were isolated from 2 to 3-month old adult Lewis rats (Charles River,
Cambridge) by a modified procedure of Seglen 4 . Detailed procedures for isolation and
purification of hepatocytes were previously described by Dunn et a12 . Routinely, 200-300
million cells were isolated with viability between 85% and 95%, as judged by Trypan
blue exclusion. Culture medium was Dulbecco's modified Eagle's Medium (DMEM,
Gibco) supplemented with 10% fetal bovine serum (FBS, JR Scientific), 0.5 U/ml insulin,
7 ng/ml glucagon, 20 ng/ml epidermal growth factor, 7.5 pg/ml hydrocortisone, 200 U/ml
penicillin, 200gg/ml streptomycin and 50gg/ml gentamycin' . 3T3 fibroblast culture
medium consisted of DMEM (Gibco) with high glucose, supplemented with 10% bovine
calf serum (BCS , JRH Biosciences) and 200 U/ml penicillin and 200gg/ml
streptomycin'.
3.1.2. Attachment experiments
The kinetics of hepatocyte attachment on PSD is compared to that on ordinary tissue
culture polystyrene dishes (TCPS). Three-inch diameter solid PSD are made by injection
28
molding, they are then manually washed in a Sparkleen detergent solution (Fisher
Scientific Co, Pennsylvania), air-dried and separated into two groups. The first group is
treated by 0 2-plasma exposure for 5 minutes at 200 W (PX250 Plasma etcher, March,
Concord, California) while the second is left untreated. They are then rinsed with 70%
ethanol, placed in P100 tissue culture dishes (Corning, New York) and left overnight
under UV light for sterilization. Prior to use, the PSD and the TCPS are coated with type
I collagen solution prepared from rat tail tendoms 2. The procedure consists of:
1) mixing four parts of distilled water with one part of collagen prepared from rat tail
tendons.
2) adding ten milliliters of this solution into the P100 tissue culture dishes.
3) incubating at 37'C for 30 minutes.
4) the solution is then removed and the dishes are rinsed twice with media.
Approximately six million freshly isolated hepatocytes are seeded in 10 ml of media per
dish. A shaker is placed in the tissue culture hood to prevent attachment prior to
completion of the seeding procedure. Time zero begins when shaking is stopped. All
dishes are placed in an incubator at 37'C and six time points are studied: 10, 20, 30, 45,
60 and 90 minutes. At each of these time points, unattached cells are removed by
immersing (once) and shaking the PSD and the TCPS in a phosphate buffered saline
(PBS) solution at 37oC and pictures are taken of the remaining attached cells. The number
of cells in each picture is counted and the viewing area is measured. Cell density is
therefore obtained at each time point and for each condition. The measured cell density is
normalized to the seeding density leading to a percentage of attached cells.
29
3.1.3. Functional assay
Albumin is used to assess the functionality of hepatocytes on various surfaces.
We used hepatocyte co-cultures with 3T3 fibroblasts as a standard methodology for long
term culture of hepatocytes'. In the present study two ratios of hepatocyte to fibroblast
(H:F) are tested: 2:1 and 1:6. Both plasma treated and collagen coated PSD are used,
while the control consists of standard P100 TCPS coated with collagen. When H:F = 2:1,
4.5 million hepatocytes and 2.25 million fibroblasts are seeded, whereas in the case of
H:F = 1:6, 0.75 million hepatocytes and 4.5 million fibroblasts are seeded. The seeding
procedure is the same in both cases; it consists of first coating the surface with collagen
as described previously. Thereafter, on day 0, freshly isolated rat hepatocytes are seeded
in 10 ml of their proper media and incubated at 37'C to allow proper attachment and
spreading. The media is removed twenty-four hours later (day one) and fibroblasts are
seeded in 10 ml of medium containing 10% BCS (see above) to increase attachment. On
day 2, the fibroblast medium is replaced by hepatocyte medium and is changed every 24
hours. Samples of 1 ml are taken every other day starting on day 3 and kept at 4'C.
Albumin content is measured by enzyme linked immunosorbent assays (ELISA) 3 .
3.2. EXPERIMENTAL CHARACTERIZATION OF THE REACTORS
3.2.1 Flow circuit
The percolation reactor is subjected to flow and observed under the microscope
for the next experiments. A peristaltic pump (Masterflex® LIS@ from Cole-Parmer
Instruments Co, Illinois) and Masterflex® Silicone tubing US® 16 are used in all
30
experiments. Nylon tube connectors are purchased from Small Parts Inc, Florida, to join
the tubing to the reactor. Finally the fluid reservoir consists of two 50ml Falcon conical
tubes (Becton Dickinson Labware. New Jersey). A Nikon Diaphot microscope (Nikon)
equipped with a Hg lamp and power supply (Nikon) is used in all experiments. It is
equipped with a CCD camera (optitronics CCD V 1470). Metamorph Image Analysis
System (Universal Imaging) is used for digital image acquisition and a Panasonic AG6730 video cassette recorder (Panasonic) is used for video recording.
3.2.2. Fluid flow characterization
The bioreactor is first tested for the uniformity of the fluid flow across the discs.
The second series of experiments consists of obtaining the velocity profiles across two
discs and the wall shear stress. The fluid flow experiments are based on a two disc
reactor, which is observed under the microscope.
Fluid flow uniformity across the reactor
The aim of this series of experiments is to check the uniformity of the flow across
the perforated discs by studying the displacement of beads within the reactor. Polystyrene
blue dyed microspheres (Polysciences, Pennsylvania) are used as beads. For the discs
with a 565 gm spacing 10 pm beads are used, while for the discs with a 127 pm spacing
3 gm beads are used. The polystyrene beads have a density of 1.05g/cm 3, very close to
that of water. The fluid flow conditions can be inferred from the motion of the beads.
Their inertia can be neglected, due to their small size, and no buoyancy or sinking effects
is present since their density is equal to that of water.
31
The first series of experiments are performed with a disc spacing of 565 Rm.
Using a magnification of 4x, one is able to look at a hole on the upper disc and at a hole
on the lower disc at the same time (figure 3.1). Indeed, at 4x the depth of focus is large
enough to include both discs at a spacing of 565 gm. Thus 10 gm beads can be visualized
leaving a hole on the upper disc and going into a hole on the lower disc. Their trajectory
can therefore be studied. For the uniformity studies several units are video recorded all
across the disc. The video recording is then replayed and five random beads are timed as
they leave the upper disc and go into the lower hole. Every unit therefore has five
different measurements to average. The horizontal distance is measured by taking
pictures of the unit and the vertical distance is known to be 565 Rm. An average velocity
is therefore obtained and compared with others across the reactor. This experiment is
performed for a range of flow rates going from 8.8ml/min to 16. 1ml/min.
,3A
Figure 3.1: Microscope view at 4x magnification. A portion of a hole in the upper disc (A) and a
portion of another hole (B) on a disc 565 pm below are shown.
32
The experimental set-up is slightly altered with a disc spacing of 127 pm. A
magnification of lOx is used to properly see 3 ptm beads. The inlet and the corresponding
outlet hole can no longer be seen on the same viewing area. Instead a region in between
the inlet and the outlet hole is observed and again five random beads in focus are timed.
The distance crossed by the beads is assumed horizontal since only beads that stay in
focus from the beginning to the end of the viewing area are timed. It is easily measured
by taking pictures of the unit.
Velocity profile and shear stress experiments
The goal is to obtain the velocity profile between the two discs. Thus, local velocities
at various vertical distances need to be obtained. This can be achieved by inferring
vertical distances from the degrees of angular rotation of the focus knob on the
microscope. The experiment consists of focusing on a given plane, knowing the vertical
distance from the lower disc, and timing five different beads that are in focus.
Magnifications of lOx and 20x are used to decrease the depth of focus, which increases
the sensitivity in the height measurements. The distance crossed by the beads is assumed
horizontal since the beads stay in focus from beginning to end, and is easily measured by
taking pictures. The local velocity at a certain vertical distance is therefore obtained. The
wall shear stress is calculated by multiplying the fluid viscosity by the velocity difference
of the first two data points and dividing them by the difference of their corresponding
vertical distances.
=Y 2 -(1)
Y2
-11
33
where V, and V2 are the first and the second velocities obtained experimentally and yi
and Y2 are the corresponding vertical distance. These experiments are performed for a
number of flow rates and both disc spacing.
3.2.3. Experimental characterization of the reactor with cells
Experiments are also performed to test the percolation reactor with hepatocytes subjected
to flow. The percolation reactor with 127 ptm disc spacing was selected for these studies.
The reactor consisted of two perforated discs with the lower disc collagen coated and
seeded with hepatocytes. The perforated disc to be seeded was placed in a P60 tissue
culture dish (Falcon, Lincoln Park, New Jersey), collagen coated as previously described
and seeded with 2x10 6 hepatocytes in 3 ml of medium. The culture was incubated at
37'C and allowed to stabilize for 24 hours prior to its use in the experiment. A
comparison was also made with a parallel-plate reactor with the same surface area (same
number of cells) and the same channel height. The parallel-plate reactor was described
elswhere 4. The experiments consisted of running the two reactors simultaneously at a
given flow rate for six hours. Cell density before and after was measured by taking
picture, at a 20x magnification, of each seeded plate at different random locations.
Finally the overall cell viability was determined by Calcein AM/Ethidium homodimer- 1
assay (Viability/Cytotoxicity Kit, Molecular Probes L-3224, Eugene, Oregon)
Experiments were ran at two different flow rates 0.2 ml/min and 0.5 ml/min. Each
experiment was repeated twice.
34
REFERENCES
1- S.N. Bhatia, U.J. Balis, M.L. Yarmush, and M. Toner, Effect of cell-cell interactions
in preservation of cellular phenotype: cocultivation of hepatocytes and
nonparenchymal cells, FASEB J. 13, pp 1883-1899 (1999).
2- J.C.Y. Dunn, M.L. Yarmush, H.G. Koebe, R.G. Tompkins, Hepatocyte function and
extracellular matrix geometry: long-term culture in a sandwich configuration, FASEB
J. 3, pp 174-177 (1989).
2- J.C.Y. Dunn, R.G. Tompkins and M.L. Yarmush, Long term in vitro function of adult
hepatocytes in a collagen sandwich configuration, Biothechnol. Prog. 7, pp 237-245
(1991).
3- P.O. Seglen, Preparation of isolated rat liver cells, Methods Biol, 13 pp 29-83 (1976).
4- A.W. Tilles, U.J. Balis, Y. Choi, H. Baskaran, M.L. Yarmush, and M. Toner, Internal
membrane oxygenation removes substrate oxygen limitations in a small-scale
hepatocyte bioreactor, (in preparation).
35
CHAPTER 4
FLUID FLOW ANALYSIS
A detailed understanding of the flow conditions acting on hepatocytes in the
percolation reactor is necessary for proper functioning of the device. Given that a porous
material is defined as a solid containing holes or voids, either connected or nonconnected, dispersed within it in either a regular or random manner 3 , the percolation
reactor used in this study is modeled using the porous media theory.
4.1. PERCOLATION REACTOR PROPERTIES
Macroscopic properties of the percolation reactors which are important in the
study of the fluid flow through porous materials are defined in the following section.
4.1.1. Porosity E
Porosity is the fraction of the total volume of the unit that is occupied by void. It
.3
is equal to the void volume divided by the total volume of the unit
=
VP
(2)
Vt
where V is the pore volume and Vt is the total volume of the unit.
The void volume and the total volume are calculated for the present reactors as follows.
Vp
Aholetdfln + AdiscHs
Vt= Adisc(t + Hs)
36
(3)
(4)
where Ahole is the hole cross-sectional area, Adic is the disc cross-sectional area, td the disc
thickness, nh the number of holes and H, the spacer height.
4.1.2. Specific surface I
The specific surface of a porous material is defined as the interstitial surface area
of the pores per unit of total volume
3
ISAP
Vt
where ISAP is the interstitial surface area of pores.
ISAP
(5)
= Sh +Sd + S,
= 4 tdanh + 2 (Ad-nhAh) + 27rRH,
(6)
where Sh is the holes surface area, Sd the disc surface area, S, the spacer surface area, a
the hole side length and R the disc radius.
4.1.3. Tortuosity T
Tortuosity accounts for the fact that the path length of the flow is greater than the
length of the sample of porous material. It is equal to the flow path length divided by the
unit length 3
(7)
T =L
Lu
where Lf is the flow path length and Lu the unit length.
Lf
td +(HS2 +
Dio2pm
LU= td + Hs
(8)
(9)
where Dio is the horizontal distance between an outlet hole and an inlet hole on two
consecutive discs.
37
4.1.4. Permeability K
The definition of permeability of a porous medium is the volume of a fluid of unit
viscosity passing through a unit cross-section of the medium per unit time under the
action of a unit pressure drop
".
It quantifies the ease with which a fluid flows though the
material due to an applied pressure gradient. In other words, permeability is the "fluid
conductivity" of the porous material 3. The permeability must be determined by the
geometry of the porous material and must be entirely independent of the nature of the
fluid. Many theories were developed to link the porous structure to permeability. The
theory that best applies to our structure is the Kozeny theory 3. It treats the porous
medium as a bundle of capillary tubes of equal length. These tubes are not necessarily of
circular cross-section. A modification of the Kozeny theory was proposed to account for
the fact that the tubes of flow are not straight, and hence the path length of flow is greater
than the length of the unit. The modified Kozeny equation is 3
K =
(10)
2TX 2
4.2. FLUID FLOW ANALYSIS
4.2.1. Flow conditions
The first step in the analysis of the reactor's fluid flow consists of determining the
flow conditions, mainly whether the flow is laminar or turbulent. Laminar flow of a fluid
is characterized by stationary streamlines
6.In
other words a fluid element which at one
point is traversing the same path as another element must follow the path of this element
throughout its course. The flow regime in a porous material may be characterized by the
Reynolds number as defined below
1,2:
38
Re = uK
(11)
2
where u is the area average fluid velocity through a column of porous material and y is
the kinematic viscosity. Experimental evidence
0
has shown that laminar flow in porous
media is characterized by a Reynolds number of less than 10. The critical velocity U,
below which the flow would be laminar may be expressed as:
e
Ucr
102
(12)
K1/
K=
This critical velocity can be used to obtain a critical flow rate Qc, that can be compared to
the flow rates used in the experiments:
(13)
Qcr=UcrAdisc
4.2.2. Pressure drop estimation: Navier-Stokes equation
Of importance also in the analysis of the reactor's fluid flow is the pressure drop
between inlet and outlet. Steady incompressible laminar flow in porous media was
studied by Liu et al
8,9
and DuPlessis et al 5. Using the volume averaging technique on the
Navier-Stokes equation and the Kozeny-Carman theory, they developed equations to
predict the pressure drop for flow through porous media taking viscous and inertial
effects into account. These equations assume that the fluid is incompressible and that the
solid matrix is incompressible, immobile and not supported by the fluid 9. These
assumptions are all met in our study. The proposed equations by Liu et al
DuPlessis et al 5 are
8,9
and
8:
AP
L
=
fvpq(1-)
13
ds2E"I
39
2
(14)
where d, is the equivalent spherical diameter of the particles forming the porous structure,
q the axial velocity andf, the normalized pressure drop. They are defined below.
d
q =
6Vp(1- E)
(15)
ISAP x E
Q
(16)
Adisc
fv =85.2+0.69 Re m X
Re
2
r22
2
162+ Rem2
(17)
where Re..is the modified Reynolds number as defined by:
Re m=
+ (1-
E 2271(2dspq
(1 -
e'o
(18)
Figure 4.1 shows the variation of the normalized pressure drop as a function of the
modified Reynolds number. Two flow regimes are depicted in the graph: Darcy's regime
and Forcheimer's regime. Darcy's regime is characterized by low flow rates in which
viscous and inertial effects are negligible. Forcheimer flow regime is characterized by
higher flow rates in which viscous effects and inertial effects are no longer negligible.
The above equations are valid for both Darcy and Forcheimer flow regimes. Liu et al 9
estimated the critical value for the flow to transit from Darcy's regime to Frocheimer's
regime to be Rem,= 7.2, and from Forcheimer's regime to the turbulent regime to be Rem
=1600.
40
a
E
E
Darcy's flow
Forchheimer flow region
Ree
Figure 4.1: Flow regions in porous medium characterized by the modified Reynolds number, Rem.
Rem is the critical value at which the flow transits from Darcy's regime to Forcheimer's 9 .
4.2.3. Pressure drop estimation: Darcy's Law
In the case where viscous and inertial effects are not important we can obtain
pressure drop values using Darcy's law. A one-dimensional model in porous media was
introduced by Darcy (1856)7 with a simple linear relationship between pressure gradient
and flow rate. Darcy's law is expressed as:
Qtotal
Adisc
KAP
(19)
11
where Qotai is the total fluid flow rate, y the dynamic fluid viscosity, Adise the disc area, K
the permeability and AP the pressure drop. Darcy's law was empirically derived and does
not take viscous and inertial effects into account. The pressure drop AP across the reactor
can be calculated with the following formula:
Al
L
-
1l
(20)
KAdsc
41
4.2.4. Shear stress estimation
Low shear stress in a bioreactor is of paramount importance since hepatocytes in
vivo are not exposed directly to flow. By increasing the number of holes in a disc the
local flow rate in each hole decreases which in turn decreases the shear stress. When
looking at one unit consisting of one outlet hole and three inlet holes (see figure 1.4) the
flow can be modeled as radial flow between two parallel discs. The associated wall shear
stress for this type of flow is expressed as 4 :
= 3pqWhle
(21)
7(Hs2 r
where r is the horizontal distance from the center of the outlet hole to the point of interest
and
qhole
is the local flow rate going through one hole. In the present study the shear stress
will be evaluated midway between the outlet and the corresponding inlet hole; r=0.5Di0
where Dio is the horizontal distance between an outlet hole and an inlet hole on two
consecutive discs. Therefore r = 1.33 mm. The local flow rate qhole is equal to the total
flow rate divided by the number of holes:
qhole
-=
(22)
Qtotal
nh
This concludes the theoretical fluid flow analysis. The next section will present
both experimental and theoretical characterization studies.
42
REFERENCES
1- A. Bejan and D.A. Nield, Convection in porous media, Springer, New York,
(1999).
2nd
pp 9
2- A. Bejan, Convection heat transfer,John Wiley & Sons Inc., New York, pp 521
(1995).
3- R.E. Collins, Flow offluid through porous media, Reinhold chemical engineering
series, Reinhold publishing corporation, New York (1961).
4- G.A. Ledezma, A. Folch, S.N. Bhatia, U.J. Balis, M.L. Yarmush, and M. Toner,
Numerical model of fluid flow and oxygen transport in a Radial-Flow Microchannel
containing hepatocytes, J. Biomech. Eng., 121, pp 58-64 (1999).
5- J.P. DuPlessis, J.H. Masliyah, Flow through isotropic granular porous media, Transp.
Porous Media,6, pp 207-221 (1991).
6- F. James, Introductionto fluid mechanics, MIT Press, Cambridge, MA (1994).
7- M. Muskat, Flow of homogenousfluids through porous media, McGraw Hill, New
York (1937).
8- S. Liu, J.H. Masliyah, Principles of single-phase flow through porous media,
Advances in chemistry series, n 251, American Chemical Society, Washington D.C,
pp 227 (1996).
9- S. Liu, J.H. Masliyah, Steady incompressible laminar flow in porous media, Elsevier
Science Ltd, pp 3565-3586 (1994).
10- J.C. Ward, Turbulent flow in porous media, J.Hydraul. Div. Am. Soc. Civ. Eng. 90,
pp 1-12 (1964).
43
CHAPTER 5
MODEL PREDICTIONS AND EXPERIMENTAL
CHARACTERIZATION
5.1. BIOCOMPATIBILITY STUDIES UNDER STATIC CULTURES
In this section, we summarize a series of studies performed to evaluate the
effectiveness of the injection molded surfaces for cell culture. Primary rat hepatocyte
were used in the studies due to their relevance to the development of a bioartificial liver
device. Cell attachment and long-term function are used to assess the biocompatibility of
injection molded surfaces as described next.
5.1.1. Cell attachment studies
Among the key steps in determining the interaction of cells seeded on a given
surface is the kinetics of cell attachment onto the surface of interest. We chose to study
the kinetics of attachment on injection molded polystyrene surfaces as compared to
standard tissue culture polystyrene dishes (TCPD). The polystyrene discs made in-house
are divided into plasma treated and non-treated groups. The remainder of the preparation
parameters are identical among the two groups of surfaces. Figure 5.1, shows the
percentage of attached cells as a function of time during the initial 90 minutes.
44
10090 80 -1
0
1age
70
50
4)
V
_
_- Plasma
treated discs coated with
ca
o. 204) 30-
10-
0
10
20
30
40
50
60
70
80
90
Time [minutes]
Figure 5.1: Kinetics of hepatocyte attachment. Comparison between tissue culture polystyrene
dishes (TCPS) with plasma treated and untreated discs. Error bars represent. the standard deviation
of five different measurements.
For the TCPD coated with collagen, the percentage of attached cells reaches 90%
within 10 minutes and remains constant at that level for the remainder of the experiment.
The plasma treated discs coated with collagen start with a lower percentage of attached
cells, only 58% of the cells are attached after 10 minutes, however the number of
attached cells reaches that of the control after 60 minutes. The untreated discs coated with
collagen start at much lower percentages; they reach 29% after 10 minutes and it is only
after 90 minutes that 75% of cells attach and thus approach the control and plasma treated
cells. These studies indicate that the injection molded surfaces do provide an adequate
surface for cell attachment. Given that the plasma treated surfaces performed slightly
better than the non treated surfaces, we used plasma treated and collagen coated surfaces
for the remainder of the study.
45
5.1.2. Albumin secretion
To determine the long-term function of hepatocytes on a given surface, we
measured albumin secretion in co-cultures. Figure 5.2 shows albumin production levels
when the hepatocyte to fibroblast ratio H:F = 1:6 and the culture length is 25 days.
240
200
0
160
-- w- Control TCPS with
collagen
120
-
Plasma treated discs
with collagen
4)
cc
--
S 8040
40
07
5
9
13
17
21
25
Days
Figure 5.2: Albumin production of hepatocytes cultured with fibroblast using a ratio of
fibroblasts.
1 hepatocyte for 6
It is evident by examining the graph that the production of albumin by
hepatocytes cultured on TCPS or on plasma treated discs is equivalent. Similar results
were found in co-cultures where the ratio of hepatocytes to fibroblast H:F = 2:1 (data not
shown). These results clearly suggest that the injection molding approach used to create
polystyrene dishes for hepatocyte culture is compatible with long-term functioning of
hepatocytes on these surfaces.
46
5.2. THEORETICAL FLUID FLOW ANALYSIS
In this section we will describe results from the theoretical fluid flow modeling. First
the porous media properties of the percolation reactors are conveyed. Second, the flow
conditions, the pressure drop values, and the shear stress levels are estimated.
5.2.1. Percolation reactor properties
Porosity, specific surface, tortuosity and permeability are macroscopic properties
which characterize the structure of the percolation reactors. They are defined in section
4.1. and their values are given below.
Table 5.1 : Percolation reactors properties
Properties
Units
Porosity
Specific surface
m1
Tortuosity
Permeability
m2
565 gm disc spacing
127 gm disc spacing
36%
13%
1270
1691
2.3
3.1
6.29x10-9
1.24x1010
Decreasing the spacer height by a factor of five affects the properties of the
percolation reactor. Porosity and permeability values decrease while tortuosity and
specific surface values increase. A lower porosity results in a smaller fluid volume since
porosity is the ratio of the void volume (fluid volume) to the total volume. The reactor
therefore maintains the same number of cells with less fluid which increases its
efficiency. A higher value for the specific surface improves the performance of the
reactor since it implies that there is more surface area available per unit volume. There is
therefore more space for cells. A lower permeability and a higher tortuosity value depict
a more intricate structure. The fluid would require higher pressures to flow through a
47
reactor with a higher tortuosity. By creating a structure with a higher specific surface
value we require larger pressure drops which may adversely affect cells.
5.2.2. Flow conditions
Determining whether the flow regime is laminar or turbulent is important. A critical
flow rate (Qcr) can be calculated representing the transition from laminar to turbulent
flow (see section 4.2.1. equation (12) and (13)). For the reactor with 565 gm disc spacing
the critical flow rate equals 1581 ml/min, while for the reactor with a disc spacing of 127
gm the critical flow rate equals 10945 ml/min. The critical flow rates are extremely high
compared to the flow rates encountered in this experimental study (2ml/min to
20ml/min). Therefore the flow regime in the present study is laminar.
5.2.3. Pressure drop estimation: Navier-Stokes equation
The pressure drop across the reactor can be obtained by the Navier-Stokes equation
where viscous and inertial effects are taken into account. A series of equations to predict
the pressure drop for flow through porous media is presented in section 4.2.2. Table 5.2
shows the modified Reynolds number (Rem) and the pressure drop across the percolation
reactor for different flow rates. These flow rates are within the range used in the
experiments.
48
Table 5.2: Estimated pressure drop and Rem for the percolation reactor.
Fluid flow rate
[ml/min]
2
0.15
4
0.3
401
5.3
8
0.7
802
10.7
12
0.9
1204
16
Rem
Pressure drop [Pa/m]
127 gm disc spacing
565 gm disc spacing
200
2.7
As expected the pressure drop values increase with increasing flow rates. The
estimated pressure drops required for the reactor with a disc spacing of 127 pm are one to
two order of magnitude higher than those required for the reactor with a disc spacing of
565 gm. A smaller disc spacing reduces the fluid area which makes it harder for the fluid
to flow. This more intricate structure will therefore result in larger pressure drop. When
Rem is smaller than 7.2, the flow is considered to be in Darcy's regime and when Rem is
larger than 7.2 the flow is in Forchheimer's flow region. In all of our experiments the
modified Reynolds number is below 7.2 which would imply that Darcy's law is valid
throughout our experiments.
5.2.4. Pressure drop estimation: Darcy's Law
According to Darcy's law the pressure drop across porous media can be calculated by
equation (20) section 4.2.3. Pressure drop values for various flow rates are shown in table
5.3. These flow rates correspond to the conditions used in our experimental studies.
49
Table 5.3: Pressure drop according to Darcy's law for different flow rates
Fluid flow rate
[ml/min]
2
Pressure drop [Pa/m]
127 gm disc spacing
565 pm disc spacing
132
2.6
4
265
5.2
8
530
10.4
12
795
15.7
When the disc spacing equals 565 gm Darcy's law and Navier-Stokes equation
produce very similar results. On the other hand when the disc spacing equals 127 gm, a
difference of 34% is observed between the two models. Knowing that Darcy's law does
not take viscous and inertial effects into account while the Navier-Stokes equation does
may explain the discrepancy encountered. One would expect the viscous effect to be
much more predominant with a disc spacing of 127 gm as compared to a disc spacing of
565 pm.
5.2.5. Shear stress estimation
Estimating the shear stress across the bottom disc is important because it can
potentially affect cell viability and function. In section 4.2.4 equation (21) theoretically
predicts the shear stress levels in the reactors. Table 5.4 shows the shear stress values for
various flow rates. These flow rates fall within the range used in the experimental studies.
50
Table 5.4: Shear stress estimations for different flow rates.
Fluid flow rate
[ml/min]
2
Shear stress [dyne/cm]
127 gm disc spacing
565 gm disc spacing
0.3
0.015
4
0.6
0.03
8
1.2
0.06
12
1.8
0.09
As expected the shear stress increases with increasing flow rates. The shear stress
values for the reactor with a disc spacing of 127 gm are 20 times higher than those for a
reactor with a 565 gm disc spacing. This can be explained qualitatively since a smaller
disc spacing would decrease the fluid cross-sectional area which would increase the
fluid's velocity leading to higher shear stress. In a more quantitative manner, equation
(20) shows us that the shear stress is proportional to 11H,2 . Therefore decreasing H, by a
factor of approximately 5 would increase the shear stress by a factor of about 25. These
results demonstrate that the percolating flow reactor result in shear stresses that are
reasonably low (less than 10 dyne/cm 2) for cell culture.
51
5.3. EXPERIMENTAL CHARACTERIZATION OF THE FLUID
FLOW
In this section results from experimental studies are presented. We will begin with
the study of the flow uniformity across the reactor, then the velocity profile and the shear
stress are presented and finally the cell behavior under flow in the percolation reactor is
given.
5.3.1. Fluid flow uniformity across the reactor:
To determine the uniformity of the flow across the perforated discs, the average
velocity per outlet is plotted versus the radial distance. The average velocity per outlet
refers to the average of the three velocity measurements between an outlet hole and each
of the three corresponding inlet holes on the lower disc, (figure 5.3).
Va9IV +
V
21
+I31()
=(23)
V,
Figure 5.3: Schematic of an outlet hole with three corresponding inlet holes. Solid lines represent
holes on the upper disc while dashed lines represent holes on the lower disc.
52
The radial distance refers to the distance from the center of the reactor to the
center of the outlet hole under observation. Figure 5.4A-C and figure 5.5 display the
average velocity per outlet (defined above) versus the radial distance for both disc
spacing. For a 565 gm disc spacing three different flow rates are examined: 8.8, 13 and
16. 1ml/min. The average of all velocities, in each experiment, is obtained as well as the
standard deviation. When the total flow rate is 8.8ml/min, the average velocity found is
1.13 ± 0.18 mm/sec (figure 5.4A). When the total flow rate is 13ml/min, the average
velocity is equal to 1.56 ± 0.24 mm/sec (figure 5.4B). Finally when the total flow rate is
equal to 16. 1ml/min the average velocity equals 2.1 ± 0.38 mm/sec (figure 5.4C). We
also ran an experiment with a disc spacing of 127gm and a fluid flow rate of 2ml/min.
The average velocity found is 0.73 ± 0.08 mm/sec (figure 5.5). The standard deviation in
all experiments represent only an 11% to 18% variation with respect to the average
velocity. These results indicate that the flow is uniform across the perforated discs. The
study of the fluid flow of one unit consisting of one outlet hole and one inlet hole can
therefore be assumed to be an appropriate representation of the flow in all the different
units across the disc
53
''2.5
A
-~
E
2 -
0
a.
-W
U
11
0
0
4)
CD
z0
5
0
10
15
20
N.5
25
E
2
0
CL
0
4)
C)
0
e
5
10
15
20
25
15
20
25
1
3
0
2.5
0
E 1.5c) s=
00
5
10
Radial distance [mm ]
Figure 5.4: Average velocity per outlet as a function of radial position for the reactor with
disc spacing. A) Qt0w 8.8 mllmin, B) Q ,wl3mLd/min, C) Qt0w 16m1/min.
54
56
5km
1.41.2
3
0
0.. 0.8
5 E 0.61
S 0.41! 0.2
S
0
0
5
10
15
20
Radial distance [m m]
Figure 5.5: Average velocity as a function of radial position for the reactor with 127 pm disc
spacing. Qto0 = 2ml/min.
5.3.2. Velocity profile and shear stress experiments:
The fluid velocity profile between two percolating discs is obtained by the
microscopic observation of polystyrene beads while they flow pass the percolation
reactor with a disc spacing of 565 pm and 127 gm.
Two samples of velocity profiles with a 565 pm disc spacing are shown in figure
5.6A-B. In figure 5.6A a total flow rate of 7.8 ml/min is used, while in figure 5.6B the
total flow rate equals 12.5 ml/min. A fitted curve through the data points provides a best
curve-fit to the velocity profile using a third-order polynomial. In figure 5.6 the vertical
distance represent the spacing between two perforated discs from 0 at the bottom of the
disc to 565 gm at the top of the disc.
55
0.60.50.40.3
2 0.20.1
0
0.2
0.4
0.6
0.8
1.2
1.4
Velocity [mm/se c]
0
0.60.50.4C
Ln
0.30.20. 1
0
0
0.5
1
1.5
2
2.5
Velocity [mm/sec]
Figure 5.6: Fluid velocity profile between two percolating discs separated by a spacing of 565pm
with a total fluid flow rate of A) 7.8ml/min, V(y)=-13.2y 3 + 0.6y2 + 4y + 0.04, B) 12.46 ml/min,
V(y) = 82.6y 3 - 101.7y 2 + 34.4y - 1.6. Error bars represent the standard deviation of five different
measurements.
By examining the velocity profiles we notice that the maximum velocities occur
around the mid portion of the spacer. We are unable to rigorously prove the no-slip
condition (v=0 mm/sec) at the boundaries (y=0 prm and y=565 Rm). This is due to the
fact that the polystyrene beads used are of a finite size (10 prm in diameter), thus we can
not measure velocities at vertical distances of exactly 0 gm and 565 gm. Nevertheless the
56
flow velocity decreases and approaches zero as one gets closer to the top and the bottom
discs.
The measured velocity profiles are used to calculate the fluid flow rate through a
given hole using the following formula:
565pm
qmeas
= 27crJV(y)dy
(24)
where V(y) is the equation of the best curve-fit to the velocity profile, y is the vertical
distance starting from the bottom disc and r is the distance from the center of the outlet
hole to the center of the view in focus. The value of r is easily determined by taking
pictures of the unit on the microscope. Inherent to this calculation is an assumption that
the fluid flow velocity profile is uniform across the fluid flow cross section 27rrHs since
we are integrating along y and not r. The values obtained from the above method are
compared to the estimated average fluid flow rate which is defined below:
qest
=
(25)
Qtota
nh
where Qtotai is the pump flow rate and nh in the number of holes on a disc. Figure 5.7
shows the result of the above calculations for three experiments. In the first experiment
the pump flow rate is equal to 12.5 ml/min, divided by 50 holes we obtain a flow rate of
4.15 mm 3/sec per hole, while the flow rate obtained from the velocity profile equals 4.77
mm 3 /sec. In the second experiment the pump flow rate equals 7.8 ml/min leading to a
flow rate of 2.6 mm 3 /sec per hole which is in agreement with the experimental flow of
2.8 mm 3/sec. Finally, the third experiment has a pump flow rate of 3.2 ml/min, the
equivalent of 1.07 mm3 /sec per hole, and the experimental flow rate is 0.87 mm 3/sec.
57
These results support that the measured velocity profiles do represent the actual behavior
of the fluid flow in the percolation reactor.
0
4
o
a)
3
EQ-7
0)
'al
0
eX
1
Ont/nin
o--a7,8rnTrr
0
2
4
6
Estimated single hole flow rate [mm 3/sec]
Figure 5.7: Comparison between theoretical and experimental fluid flow rates for a disc spacing of
565 pm.
Fluid velocity profiles between two percolating discs with a disc spacing of 127 j
m are also obtained. Two samples are shown in figure 5.8. The corresponding flow rates
are 6.8ml/min and 2.3m1/min. The general shape of the velocity profiles is the same as
before. The maximum velocities occur relatively in the middle of the spacing and the
boundaries exhibit lower velocities that tend to zero. The maximum velocities with a disc
spacing of 127 pim are higher than those encountered with a disc spacing of 565 jm.
From figure 5.6A, we have that a reactor with a disc spacing of 565 jm , subjected to a
flow rate of 7.8 ml/min, exhibits a maximum velocity of 1 mm/sec. While from figure
5.8A we have that a reactor with a disc spacing of 127 jim, subjected to a flow rate of 6.7
ml/min, exhibits a maximum velocity of 5 mm/sec. For approximately the same flow rate
the velocity is increased by 5 folds as the disc spacing is decreased by 5. The
conservation of mass well explains this phenomena: as the fluid area decreases the
58
velocity has to increase by the same amount so that within a certain time the same
amount of mass circulates.
0.14
0.12
E
E
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
5
4
6
7
Velocity [mm/sec]
(D
:a
lU
.t
0.14
0.12
E
E
0.1
0.08
0.06
0.04
0.02
0
0
0.5
1.5
1
2
Velocity [mm/sec]
Figure 5.8: Fluid velocity profile between two percolating discs separated by 127pm.
A) Qt0s = 6.82ml/min, V(y) = -19252y 3 + 2804.8y 2 - 45.7y + 0.3, B) Qt 0 , = 2.3ml/min, V(y) =
5876.3y 3 + 811.24y 2 - 7.7y + 0.08. Error bars represent the standard deviation of five different
measurements.
The velocity profile equations are again integrated using equation (23) to obtain
the measured single hole flow rate (qeas). The estimated single hole flow rate (q,,t) is
also obtained using equation (24). The values are compared in figure 5.9. In the first
experiment the pump flow rate is equal to 6.82ml/min divided by 50 holes we obtain an
estimated fluid flow rate of 2.27mm 3/sec, while the fluid flow rate obtained from the
59
-
velocity profile equals 1.36mm 3/sec. In the second experiment the pump flow rate equals
5.55ml/min, leading to an estimated flow of 1.85mm 3/sec per hole while the velocity
profile yields a flow of 1.24mm 3 /sec. The third experiment has a pump flow rate of
3.3ml/min, 1. 1mm 3 /sec per hole while the experimental flow rate equals 0.821 mm 3/sec.
Finally the pump flow rate for the fourth experiment equals 2.3ml/min, leading to a flow
rate of 0.766mm 3/sec per hole, the experimental flow rate obtained equals 0.5mm 3/sec.
For 127 pm disc spacing a larger discrepancy is found between estimated and measured
flow rates compared with a disc spacing of 565 pm. This may be due to the fact that the
determination of the focal level of 3 gm beads within a spacing of 127 gm is much harder
than the determination of the focal level of 10 gm beads within a spacing of 565 pm.
3
2.5-
a)-
1.5
E
Q=$5mrrin
-
aIR
S0.51
a
(5=2.3m~min
0
0
1
2
3
Estimated single hole flow rate [mm 3/sec]
Figure 5.9: Comparison between theoretical and experimental fluid flow rates for a disc spacing of
127 m.
Finally the shear stress acting on the bottom disc is obtained for both reactors. It is
calculated using equation (1) from section 3.2.2.:
V -V
v2-
y2
60
-
(1)
1
where V1 and V2 are the first and the second velocities obtained experimentally and yi
and Y2 are the corresponding vertical distances. Figure 5.10 shows the experimental and
theoretical shear stress versus the pump flow rate for both disc spacing. The theoretical
shear stress predictions are obtained from equation (20) in section 4.3.4.
0.24
0.20
$
0.16-
-
0.12 -
*0.127 mm disc spacing
. 0.565 mm disc spacing
_____________
'~0.08
U) 0.04
-
0.00-.
0
2
4
6
8
10
12
14
Flow rate [ml/min]
Figure 5.10: Experimental and theoretical wall shear stress as a function of flow rate for both
reactors.
The experimental shear stress values for the reactor with a disc spacing of 565 pm
agrees very closely to the theoretical predictions. As for the reactor with a disc spacing of
127 gm the experimental shear stress values differ from the those predicted by theory.
This may again be due to the difficulties encountered while manipulating 3 pim beads
within a 127 prm spacing. For all the flow rates with a disc spacing of 127 gm the
experimental shear stress underestimates the theoretical shear stress which may lead us to
conclude that we were unsuccessful in timing the fastest beads flowing through the
reactor.
61
5.3.3. Experimental characterization of the reactor with cells
The final tests performed on the percolation reactor consisted of characterizing
the cell behavior under different flow rates. The percolation reactor with two perforated
discs with a spacing of 127 pm is selected and is compared to a parallel-plate bioreactor.
The beginning and the ending cell number are obtained for both reactors, as well as the
cell viability. The results are shown for two flow rates in table 5.5.
Table 5.5: Comparison between the parallel-plate reactor and the percolation reactor when subjected to a
flow rate of 0.2ml/min and 0.5ml/min. The percentage of the remaining attached cells at the end of the
experiment and their viability is shown with their corresponding standard deviations.
% attachment
% viability
Flow rate
[ml/min]
0.2
Parallel-plate
Inlet
56% 25
0.5
55%
0.2
67% ± 16
0.5
22%
2
5
bioreactor
Outlet
19% ± 15
Percolating
bioreactor
98% ± 5
6% ± 8
76%
19
22% ± 21
87%
8
0%±0
78%
11
A significant difference is seen between the inlet and the outlet regions of the
parallel-plate reactor. Based on the prior study performed in our laboratory, we showed
that the oxygen in medium is utilized by the cells at the entrance region under slow flow
conditions encountered in this study and thus results in very low oxygen tension at the
exit region. As a result, hepatocytes deprived of oxygen may detach from the surface and
also die due to necrosis'. This phenomena was not observed in the percolation reactor
where the percentage of the remaining cells and their viability are high and uniform
across the reactor. A decrease in the performance of both reactors, albeit much less for
the percolation reactor, was seen when the flow rate was increased from 0.2 ml/min to 0.5
62
ml/min. Shear forces at the cell level are now more significant (1.4 dyne/cm 2 for the
parallel-plate, 0.075 dyne/cm 2 for the percolation reactor) and may play a larger role in
the detachment of cells. Nevertheless the performance of the percolation reactor was
significantly better than that of the parallel-pate, and proved to be adequate to sustain
reasonable cell attachment and viability under flow conditions. Further studies are now
underway to evaluate the long-term functionality of hepatocytes in the percolation
bioreactor.
63
REFERENCES
1- A.W. Tilles, U.J. Balis, Y. Choi, H. Baskaran, M.L. Yarmush, and M. Toner, Internal
membrane oxygenation removes substrate oxygen limitations in a small-scale
hepatocyte bioreactor, (in preparation).
64
CHAPTER 6
DISCUSSION AND OUTLOOK
The overall goal of this study is to develop a bioreactor which mimics some of the
characteristics of liver's fluid flow conditions. Looking at cell arrangement and blood
flow in the liver allows us to create a better environment for hepatocytes for the potential
design of a BAL device. From a global point of view flow in the liver is unidirectional.
Blood enters the liver acinus through three portal areas (the inlets), traverses the sinusoids
where hepatocytes are located and finally exits through the central vein (the outlet). In
addition every portal area supplies three central veins. Our design consists of perforated
discs stacked on top of each other. A hexagonal hole pattern is chosen so that every inlet
hole supplies three outlet holes and every outlet hole is supplied by three inlet holes.
Current BAL devices mainly consist of hollow fibers. Such designs have an
advantage in that fibers provide a physical barrier to the shear stress caused by high flow
rates. Consequently, oxygen supply can be improved by increasing the perfusion flow
rate through the fibers. However, these designs have important limitations. In the hollow
fiber design cells are packed inside fibers and not organized in a planar geometry as seen
in the liver. In the percolation reactor cells are cultured on flat surfaces. The flat plate
geometry is also the conventional tissue culture environment in which hepatocyte
function is known to be adequate and sustainable. Another implication of the hollow fiber
geometry is that the number of cells that are in direct contact with the fiber (consequently
65
with the fluid) is low, it ranges from as few as 1/14 of the total cell number 2 to at most
1/7 of the total cell number'5,6 . This is not the case with the percolation reactor where
100% of the cells are directly exposed to the fluid in order to maximize oxygen and
nutrient supply. The liver also exhibits a flat-plate geometry where most cells are exposed
to flow on two sides.
A comparison of the percolation reactor to a conventional parallel-plate reactor is
salient in the present study since both designs exhibit a flat-plate geometry and that all
cells are in contact with the flow. An experimental side-by-side comparison (for the same
surface area and thus the cell number) was performed and results showed that the
percentage of attached cells and their corresponding viability were two to three folds
higher for the percolation reactor compared to those of the parallel-plate bioreactor. The
conventional parallel-plate reactor has several limitations. The cells situated near the exit
of the reactor experience oxygen and nutrient limitations since cells near the inlet deplete
the medium of its nutrients and oxygen. Increasing the flow rate to improve the supply of
oxygen and nutrients leads to higher shear stress that causes mechanical damage to the
cells. The percolation reactor alleviates this dilemma by incorporating many inlets and
outlets, allowing higher flow rates with lower shear stress at a given local point.
Cells cultured on the surfaces used in the present study performed well compared
to other studies. The function level of hepatocytes on the injected molded surfaces, as
indicated by albumin production levels, reached a steady-state value of approximately 5.6
gg/106 hepatocytes/h. This value is even higher than typical values seen in other studies'
66
consisting of approximately 4 gg/10 6 hepatocytes/h. Therefore, there is no apparent
toxicity to the surfaces we manufactured for cell culture.
An understanding of the flow conditions acting on hepatocytes in the percolation
reactor is vital for a proper BAL device design. It is known that the contact of
hepatocytes with high shear stress is harmful 4 but the exact threshold and the functional
behavior are unclear. For the purpose of this study, the shear stress in normal hepatic
sinusoids will be considered as the maximum value above which cell integrity is
compromised. The shear stress in the sinusoids approaches 20 dyne /cm 2 4 . The shear
stress acting in the percolation reactors are very small compared to those in the liver,
ranging from 0.02 dyne/cm 2 to 0.1 dyne/cm 2 for flow rates ranging from 2 ml/min to 12
ml/min. Hepatocytes cultured in the percolation reactors may therefore not be exposed to
deleteriously high levels of shear stress.
Nevertheless, the percolation reactors manufactured in this study present a
number of limitations. Cell densities encountered in both of our reactors are of the order
of 106 cells/ml, while typical hollow fiber density ranges in the order of 107 cells/ml and
liver tissue approximately 108 cells/ml. This would lead to a larger reactor volume if
scaled-up. Decreasing the disc spacing and/or the disc thickness would lead to higher cell
density values. A simple decrease of the disc spacing to 70 pm would increase cell
density to 107 cell/ml. Other limitations arise from the comparison of the characteristic
properties of the percolation reactors with those of the liver. Porosity values approached
the liver's (36%-13% for the percolation reactors as compared to 11% for the liver) while
67
specific surface (1,270 m-1-1,691 m 1 for the percolation reactors compared to 55,000 m-1
for the liver) and permeability (6.29x1O-9 m2
-
1.24x 1040 m2 for the percolation reactors
as compared to 4.3x10- 2 m 2 for the liver) were poorly matched. These limitations are
again due to the characteristic dimensions of the present reactors. An optimization of the
geometry could lead to a closer match with the liver. For example if the hole radius is
decreased to 10 gm, the hole spacing reduced to 40 pim, the disc thickness decreased to
500 gm and finally the spacer thickness reduced to 15 gm, we obtain a porosity value of
25%, while the specific surface is increased to 47,030 m-1 and the permeability is raised
to 3.35x 10-42 M 2 , approaching the liver values. Optimizing the geometry of the
percolation reactor would lead to numerous advantages but unfortunately could not be
executed with the bulk manufacturing techniques used in the present study.
68
CONCLUSION AND OUTLOOK
In the present study we designed and manufactured a percolation reactor based on
liver flow. The biocompatibility of the surfaces was demonstrated, the bioreactor's fluid
flow was theoretically modeled and experimentally characterized (with and without
cells). Further optimization of the percolation structure is needed to increase the
performance of the reactor. Foremost the spacer thickness should be decreased, and then
the hole size and the hole spacing should be reduced leading to a much greater number of
holes. Future work to be performed on the percolation reactor consists of: evaluating of
the long-term functionality of hepatocytes in the reactor, scaling-up to perform small
animal studies (approximately 20 x 106 cells for rat animal models) and testing the
reactor in-vitro, and finally testing the reactor in-vivo with various animal models. In
summary, the advantages of the percolation reactor are numerous: high bulk flow rates
are achieved while still minimizing the local shear stress level, cells are cultured as a
monolayer mimicking the flat-plate geometry of the liver and all cells are exposed to flow
maximizing the supply of oxygen and nutrients.
69
REFERENCES
1.
S.N. Bhatia, U.J. Balis, M.L. Yarmush, and M. Toner, Effect of cell-cell interactions
in preservation of cellular phenotype: cocultivation of hepatocytes and
nonparenchymal cells, FASEB J., 13, pp 1883-1899 (1999).
2. A.A. Demetriou, J. Rozga, L. Podesta, E. Lepage, E. Morsiani, A.D. Moscioni, A.
Hoffman, M. McGrath, L. Kong, H. Rosen, Early clinical experience with a hybrid
bioartificial liver, Scandinav. J. Gastroent.Suppl. 208, pp 111-117 (1995).
3. A. Kamlot, J. Roozga, F.D. Watanabe and A.A. Demetriou, Review: Artificial liver
support systems, Biotechnol. Bioeng. 50, pp 382-391 (1996).
4. Kan, H. Miyoshi, K. Yanagi, and N. Ohshima, Effects of shear stress on metabolic
function of the co-culture system of hepatocyte/nonparenchymal cells for a
bioartificial liver, ASAIO J. 44, pp M44 1 -M444 (1998).
5. N.L. Sussman and J.H. Kelly, Improved liver function following treatment with an
extracorporeal liver assist device, Artif Organs, 17, pp 27-30 (1993).
6. F.D. Watanabe, C.J. Mullon, W.R. Hewitt, N. Arkadopoulos, E. Kahaku, S. Eguchi,
T. Khalili, W. Arnaout, C.R. Shackleton, J. Rozga, B. Solomon, and A.A. Demetriou,
Clinical experience with a bioartificial liver in the treatment of severe liver failure. A
phase I clinical trial, Ann. Surg. 225, pp 484-494 (1997).
70