HYDRODYNAMIC EFFECTS ON ANIMAL CELLS
IN MICROCARRIER BIOREACTORS
BY
MATTHEW SHANE CROUGHAN
B.S. Chemical Engineering
University of California at Berkeley
(June, 1983)
in
Submitted to the Department of Chemical Engineering
Partial Fulfillment of the Requirements for the Degree of
DOCTOR OF PHILOSOPHY IN CHEMICAL ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June, 1988
Massachusetts Institute of Technology
Signature of Author:
Department of ChemicallEngineering
February 23, 1988
Certified by:
Daniel I.C. Wang
Professor of Chemical and Biochemical Engineering
Thesis Supervisor
Accepted by:
Robert C. Armstrong
Professor of Chemical Engineering
Chairman of the Committee for Graduate Students
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1
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A
HYDRODYNAMIC EFFECTS ON ANIMAL CELLS
IN
MICROCARRIER BIOREACTORS
BY
MATTHEW SHANE CROUGHAN
in
Submitted to the Department of Chemical Engineering
Massachusetts Institute of Technology
on February 23, 1988
partial fulfillment of the requirements for the Degree of
Doctor of Philosophy in Chemical Engineering
ABSTRACT
In this thesis, a fundamental approach was initiated toward the
design of microcarrier bioreactors for industrial animal cell culture.
Cell damage from hydrodynamic forces was considered along with the
Hydrodynamic effects on the
agitation requirements for mass transfer.
growth and death of FS-4 cells on microcarriers were studied in small
stirred-tank bioreactors. With mild agitation, growth was not affected
by changes in fluid viscosity, microcarrier concentration, or level of
appeared to unaffected by the hydrodynamic
agitation, and thus
With high agitation, a reduction in net growth was
environment.
observed and was found to be entirely due to cell death and removal and
not growth inhibition.
The mechanisms of hydrodynamic death were investigated through
experiments on the effects of fluid viscosity, microcarrier concentraCell death in microcarrier bioreactors was
tion, and agitation power.
found to occur through microcarrier-eddy interactions, microcarrier
collisions, and, in unusual circumstances, time-average flow fields.
Microcarrier-eddy interactions led to cell death when the turbulence
For dilute
generated eddies which were smaller than the microcarriers.
to the
proportional
be
to
cultures, the specific death rate was found
both
For
regime.
concentration of eddies in the viscous dissipation
with
increase
to
dilute and concentrated cultures, cell death was found
agitation power and decrease with fluid viscosity.
A quantitative expression was derived which related the cell
microcarrier concentration, kinematic
to the
population kinetics
the
included
expression
The
agitation power.
and
viscosity,
hydrodynamic
of
function
a
contributions from cell growth, which was not
environment, and cell death from both microcarrier-eddy interactions and
microcarrier collisions. The expression was used to quantify the tradeoff between hydrodynamic cell death and oxygen transfer upon scale-up.
An illustration was presented to show how bioreactor design can be
approached as an optimization problem involving quantitative rate
expressions.
Thesis supervisor:
Title:
Dr. Daniel I.C. Wang
Professor of Chemical and Biochemical Engineering
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS .....................................................
LIST OF FIGURES.....................................................
.
LIST OF TABLES.......................................................
INTRODUCTION.........................................................
LITERATURE REVIEW AND THESIS FORMULATION
Hydrodynamic effects on cell growth................................
The cell cycle and DNA replication.................................
Assessment of cell death through DNA release measurements..........
Hydrodynamic effects on cell metabolism............................
Microscopic flow fields and cell deformation mechanics.............
Effects of microcarrier and cell concentration.....................
Hydrodynamic damage in microcarrier cultures.......................
Cell-liquid transport in microcarrier cultures.....................
Fluid-lift, airlift, and stirred-tank bioreactors..................
Cell damage from turbulence........................................
Protective polymers................................................
Cell damage from time-average flow fields..........................
MATERIALS AND METHODS
Cell types.........................................................
Cell culture reagents and procedures...............................
Culture aeration and effect of dissolved oxygen on cell growth.
Agitation power determinations.....................................
Cell concentration determinations..................................
DNA assay..........................................................
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Specific fluorescence of FS-4 cellular DNA........................... 59
Effect of cell concentration in T-flasks............................. 63
Selection, use, and characterization of inert microcarriers........ 64
Viscosity and density measurements.................................
66
Selection and use of thickening agent.............................. 68
Rheological evaluation of dextran solutions......................... 73
Cell damage from direct sparging................................... 76
RESULTS AND DISCUSSION............................................... 78
CHAPTER 1.
HYDRODYNAMIC EFFECTS ON FS-4 CELLS WITH MILD AGITATION
1A. Effect of fluid viscosity with mild agitation................... 79
1B. Growth at different microcarrier concentrations................. 81
1C. Growth in stagnant T-flasks.................................... 87
1D. Effect of cell concentration on growth in T-flasks.............. 89
1E. Effect of inert microcarriers with mild agitation.............. 91
1F. Cell growth with mild agitation................................ 93
CHAPTER 2.
2A.
HYDRODYNAMIC EFFECTS ON FS-4 CELLS WITH HIGH AGITATION
Growth reduction and cell removal under high agitation........
95
2B. Random cell removal through normal forces......................100
2C. DNA release under high agitation...............................104
2D. Growth and death under high agitation...........................106
2E. Hydrodynamic regulation of cell growth..........................113
2F. No secondary growth after cell removal..........................114
2G. Hydrodynamic effects on glucose consumption....................117
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CHAPTER 3.
HYDRODYNAMIC PHENOMENA IN y-CHO CULTURES
3A. Growth, reversible cell removal, and secondary growth..........121
3B. Hydrodynamic resistance through secondary growth...............125
3C. Selection of model cell line...................................129
CHAPTER 4.
MECHANISMS OF HYDRODYNAMIC DEATH IN DILUTE CULTURES
4A. First, second, and higher order mechanisms of death........... .131
4B. Effects of power and viscosity in dilute cultures............. .132
4C. Cell death through microcarrier-eddy interactions............. .136
4D. Hydrodynamic forces in microcarrier-eddy interactions......... .143
4E. Kinetics of cell growth and death in dilute cultures.......... .146
4F. Cell damage from time-average flow fields..................... .153
4G. Effects of cavitation......................................... .155
CHAPTER 5.
5A.
MECHANISMS OF HYDRODYNAMIC DEATH IN CONCENTRATED CULTURES
Effect of microcarrier concentration with high agitation......
159
5B. Cell death through microcarrier collisions..................... 161
5C. Effects of agitation power on cell death from collisions....... 167
5D. Effects of fluid viscosity on cell death from collisions....... 171
CHAPTER 6.
CELL DAMAGE FROM DIRECT SPARGING
6A. Effect of antifoam addition and direct sparging on growth......178
6B. Mechanisms of cell damage from direct sparging.................181
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CHAPTER 7.
BIOREACTOR DESIGN AND OPTIMIZATION
7A. Mass transfer requirements...............................
.185
7B. Basic principles in bioreactor design and optimization...
.192
7C. Illustration of optimization calculations................
.196
206
7D. Protection through polymer absorption and viscoelasticity
....
-..
SUMMARY AND CONCLUSIONS................... .....................-
210
RECOMMENDATIONS FOR FUTURE RESEARCH....... ....... ................
212
....
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..- ..NOMENCLATURE.............................. . ....... - .-
217
- ...........
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REFERENCES................................ . . . -.. . . . - -.
224
APPENDIX 1:
Calculation of the relative DNA release under high agitation .......
234
APPENDIX 2:
Estimation of the yield and maintenance coefficient for oxygen.....240
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ACKNOWLEDGEMENTS
The
author wishes
to
acknowledge
the
following organizations
for
financial support:
National Science Foundation of the United States of America
for supporting much of this research through the Engineering Research
Center
Initiative
to
the M.I.T.
Biotechnology
Process
Engineering
Center under the cooperative agreement CDR 8500003
Biogen, Inc.
for supporting the initial phases of this research
Exxon Corporation and E.I. Dupont Denemours Corporation
for fellowship support during my coursework
The author also wishes to acknowledge the following individuals and
greater beings who have contributed to this thesis:
God
for creating the earth,
the universe,
and M.I.T.,
and for serving as
the ultimate reviewer of this research
Claire Malloy Croughan and Mabel Wilson Croughan
for creating me, and for their continuous support of my education
Kathryn Colleen Kidd, soon to be Kathryn Kidd Croughan
for her joy when the experiments were successful and her support when
they were unsuccessful
Professors C.K. Colton, T.A. Hatton, C.L. Cooney, and A.J. Sinskey
for serving as members of my
thesis committee, for their review of
this research, and for their insightful comments
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Jean-FrancoisHamel, Elizabeth Sayre, Jeff Bigler, and Bruce Woodson
for their participation in this research
Don Giard and the staff
for
their
sharing
of the Cell Culture Center at M.I.T.
knowledge
of
animal
cell
for
culture,
their
services and help, and for Don's advice regarding my golf swing
Professor Preetinder S. Virk
for his useful and stimulating suggestions, and for his good wit
John Aunins,
Steve Lee,
Adema,
Steve Perry, Jono Goldstein, Mark Applegate,
Marc Davidson, Dave Robbins, Linda Cima,
Brian Kell,
Mike Glacken, Enno
Chris Hwang, Dawn Orton, Shiping Wang, and many others
for their suggestions and help, and for the good times in the lab
Professors Harvey Blanch and Frances Arnold, and Robert Lesch
for spawning my interest in biotechnology at U.C. Berkeley
Ruth Ayers, Diana Kenney, Marguerite Walsh, and Lynne Comeau
for their services and good humor
Professor Daniel I.C. Wang (last
but not least)
Professor Wang has been an outstanding research advisor.
He exhibits
a tremendous commitment to the training of his students and to the
advance of scientific knowledge.
For Professor Wang, who reminds me
of a wise and dexterous owl, the following poem was written:
An owl can see in the dark
and find lost coins
An owl can soar above the trees
and view the entire forest
An owl can build a nest
and raise more owls
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LIST OF FIGURES
Figure 1.
Growth of Vero cells at different
stirring speeds (Hirtenstein and Clark, 1980)....................... 29
Figure 2.
Relative growth extent of FS-4 cells
versus integrated shear factor (Hu, 1983)........................... 31
Figure 3.
Schematic of a sphere
caught in a simple shear field..................................... 43
Figure 4.
Relative growth extent of FS-4 cells
versus impeller tip speed (Hu, 1983)................................ 45
Figure 5.
Effect of dissolved oxygen
on growth of FS-4 cells.............................................. 52
Figure 6.
Increase in fluorescence
versus concentration of calf-thymus DNA.............................. 58
Figure 7.
Growth of FS-4 cells
in stagnant T-flasks................................................. 61
Figure 8.
Specific fluorescence of FS-4 cells
taken from T-flasks during exponential growth....................... 62
Figure 9.
Shear stress versus shear rate
for various medium solutions......................................... 67
Figure 10. Chemical effects of dextran on
growth of FS-4 cells with mild agitation............................. 72
Figure 11. Effect of 20 g/L dextran (78,500 MW)
on growth of FS-4 cells with mild agitation......................... 80
Figure 12. Growth of FS-4 cells at various
microcarrier concentrations with mild agitation..................... 83
Figure 13. Maximum surface coverage of FS-4 cells
versus microcarrier concentration.................................. 84
Figure 14. Average specific growth rate of FS-4 cells
versus microcarrier concentration..................................
86
Figure 15. Growth of FS-4 cells
in stagnant T-flasks................................................. 88
Figure 16. Effect of cell concentration
on growth of FS-4 cells in T-flasks................................. 90
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Figure 17.
Effect of inert microcarriers
on growth of FS-4 cells with mild agitation......................... 92
Figure 18. Attached cell concentrations for FS-4
microcarrier cultures at different stirring speeds................. 96
Figure 19.
Removal of whole FS-4 cells
from microcarriers at different stirring speeds.................... 97
Figure 20. Specific rate of whole cell removal
versus estimated mitotic index for FS-4 microcarrier cultures......102
Figure 21. Growth of FS-4 cells on microcarriers followed
agitation at different stirring speeds after concentration.........105
Figure 22. Cumulative release of DNA into suspension
for 15 g/L FS-4 microcarrier culture at 150 RPM....................107
Figure 23. Measured DNA release for 15 g/L culture at 150 RPM
versus release expected under three different scenarios............112
Figure 24. Attached cell concentrations for FS-4 cultures
grown at different stirring speeds.................................115
Figure 25. Glucose concentrations profiles
for 15 g/L FS-4 microcarrier cultures..............................118
Figure 26. Suspended and attached cell concentrations for
y-CHO microcarrier cultures at different stirring speeds...........122
Figure 27. Attachment and growth on new microcarriers for
y-CHO cells taken from suspension of microcarrier culture..........126
Figure 28. Viable cells produced per microcarrier
for y-CHO cultures at different stirring speeds....................128
Figure 29. Effect of 20 g/L dextran (78,500 MW)
on net growth of FS-4 cells at different stirring speeds...........133
Figure 30. Effect of 50 g/L dextran (78,500 MW)
on net growth of FS-4 cells at different stirring speeds...........135
Figure 31. Relative growth rate vs. Kolmogorov eddy length scale
for FS-4 cultures with 0.2 g/L microcarriers.......................138
Figure 32. Relative growth rate vs. Kolmogorov eddy length scale
for FS-4 cultures with 5 g/L microcarriers (data from Hu,1983).....140
Figure 33. Maximum cell concentration versus Kolmogorov eddy
length for chicken embryo fibroblasts on 5 g/L microcarriers
(data from Sinskey et al., 1981)...................................142
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10
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Figure 34. Specific death rate in dilute FS-4 cultures vs.
the concentration of eddies in the viscous dissipation regime......149
Figure 35. Specific death rate versus average power input
per unit mass for cultures of Vero cells on microcarriers,
FS-4 cells on microcarriers, and freely-suspended protozoa.........152
Figure 36. Effect of dextran (78,500 MW) on net growth of
FS-4 cells in a reactor with strong time-average shear fields......154
Figure 37. Specific death rate versus eddy concentration for
dilute FS-4 cultures with different levels of maximum shear
stress from time-average flow fields...............................156
Figure 38. Effect of inert microcarriers on
net growth of FS-4 cells with high agitation.......................160
Figure 39. Net growth rate under high agitation for FS-4 cultures
with different concentrations of inert microcarriers...............165
Figure 40. Net growth at different stirring speeds
for FS-4 cultures with 15 g/L inert microcarriers..................168
Figure 41. Second-order death rate constant q2 versus
average power input per unit mass for FS-4 cultures................170
Figure 42. Effect of dextran (78,500 MW) on net growth
of FS-4 cells at different stirring speeds
with 15 g/L inert microcarriers....................................172
Figure 43. Normalized second-order death rate constant
versus kinematic fluid viscosity for FS-4 cultures.................174
Figure 44. Second-order death rate constant versus the ratio of
average power input per unit mass to kinematic fluid viscosity
for FS-4 cultures...................................................176
Figure 45. Effect of antifoam addition and direct sparging
on net growth of FS-4 cells on microcarriers.......................180
Figure 46. 100-liter reactor with 4-bladed flat-blade turbine
and 4-bladed pitched-blade turbine.................................198
Figure 47. Estimated maximum concentration of FS-4 cells
vs. average power input per unit mass
at different fluid viscosities in 100-liter reactor................205
Figure 48. Cumulative change in Hoechst-dye fluorescence
for culture fluid from 15 g/L FS-4 cultures........................235
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11
Figure 49. Cumulative release of DNA into suspension for 15 g/L
FS-4 culture at 150 RPM. Data is shown for three different
methods of calculation.............................................239
LIST OF TABLES
Viscosity and density measurements
Table 1.
for various medium solutions............................. ..........
69
Table 2. Glucose uptake by FS-4 cells in
15 g/L microcarrier cultures at different stirring speeds..........119
Geometry of 100-liter bioreactor
Table 3.
for optimization illustration............................ ..........
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12
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199
INTRODUCTION
Large-scale animal cell culture is currently being developed for the
cells
that will adhere
riers appears
van Wezel
with high
separation (Nahapetian,
noted its advantages.
and
densities
cell
medium/cell
simple
1986).
technique and have
the microcarrier
have employed
Many researchers
First developed by
technique can provide a homogeneous
the microcarrier
environment
culture
growth on the surface of microcar-
to surfaces,
promising for industrial operations.
(1967),
culture of
For the
industrial production of many valuable proteins.
improvements
Nonetheless,
of the technique have
and
improved
microcarriers, media formulations, and inoculation procedures.
Although
primarily
been
reactors
limited
have been
no
cultures,
to
developed
thorough
study
the
development
of
new
and
successfully used
has
been
published
for microcarrier
which
compares
and
determines the best reactor designs and agitation procedures.
It
widely accepted but not well documented that animal cells on
is
microcarriers are especially susceptible to damage from fluid-mechanical
forces.
wall,
This susceptibility results from the lack of a protective cell
the
dividual
translate;
relatively large size of animal cells, and the lack of incell
mobility.
they therefore
Anchored
cells
can not reduce
can
the
not
net
experienced upon exposure to fluid-mechanical forces.
-
13
-
freely
forces
rotate
and
or
torques
In microcarrier cultures, agitation is required for cell-liquid mass
growth,
cell
maximum
For
mixing.
adequate
liquid-phase
and
(oxygenation),
transport
mass
gas-liquid
transport,
transfer
mass
be
must
achieved with little or no detrimental effects from hydrodynamic forces.
Although
condition
this
cultures,
laboratory
densities
culture
or
it
can
becomes
are
volumes
more
increased.
attain
to
difficult
low-density
in
attained
readily
be
as
cell
scale-up
Successful
to
large-volume cultures will require a thorough understand-
high-density,
ing of the hydrodynamic and mass transport phenomena.
Accordingly,
fundamental
the overall
to
approach
microcarrier bioreactors.
objective of this work is
the
design,
operation,
to formulate
a
scale-up
of
and
The general approach will be to:
1) determine the effects of momentum transfer on cell growth,
independent of the effects of heat and mass transfer,
2) perform experimental investigations on the mechanisms of cell damage
from fluid-mechanical forces,
3) develop theoretical models to describe the mechanisms of cell
damage,
4) use the verified models of hydrodynamic damage,
models
of
mass
transport,
to
develop
along with published
engineering
a quantitative
approach to the design of microcarrier bioreactors.
The knowledge generated by this research will be useful in
microcarrier bioreactors
the design of
and will add to the general understanding of
hydrodynamic phenomena.
-
14
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LITERATURE REVIEW AND THESIS FORMULATION
Hydrodynamic Effects on Cell Growth
of well-defined hydrodynamic forces on cell growth have
The effects
No investigations have been performed
not been thoroughly investigated.
to normal
with regard
forces
and only a few have been performed with
regard to shear stresses.
Under flow conditions which do not lead to substantial
cells from their growth surface,
removal
of
cell growth appears to be unaffected by
fluid shear stresses. For endothelial cells growing on glass coverslips,
(1981)
Dewey
et al
shear
stresses
up
endothelial
cells
found that
cell
dyne/cm
affected by fluid
found that cell growth was not
to
8 dyne/cm 2 .
In more
recent
growing on plastic coverslips,
growth was
affected by
not
experiments
Sprague
et al
shear stresses up
with
(1987)
to
30
2
For moderate
to high levels of shear stresses,
a few quantitative
studies have been performed regarding removal of cells from their growth
surface.
(1986) observed extensive cell removal
Viggers
et al
surface
for shear stresses of 128 dyne/cm2 .
Vero,
and MRC-5
cells
grown on plastic or
observed extensive cell removal
of 30
dyne/cm2 or higher. In experiments
(1985)
Stathopoulos and Hellums
-
15
-
from the growth
In experiments with BHK,
glass slides,
Crouch et al
for shear stresses in
(1985)
slides,
coverslips,
In experiments with endothelial cells on glass
the range
with kidney cells on glass
observed cell removal for shear
stresses of 6.5 dyne/cm2 or greater.
flow conditions which result in
Under
growth surface,
their
from
attached
1985;
is
generally
Stathopoulos
measured
in terms
of
the viability
reported
and Hellums,
to be greater
of trypan blue
ability to reproduce and grow.
which
remain
than 90% (Crouch
et al,
the
However,
1985).
of cells
substantial removal
exclusion and
cells
these viabilities
are
of
the
in terms
not
The hydrodynamic effects on cell growth
are unknown for flow conditions which can cause extensive cell removal
or death.
When animal
frequently
is
growth
net
cells are
not been investigated.
or
death,
objective
inhibited,
in the
increase
observed with an
level
of
The biological basis behind this reduction in net growth has
agitation.
cell
a reduction in
an agitated vessel,
grown in
of
a
this
The reduction could be due to growth inhibition,
combination
thesis
unchanged,
microcarrier cultures.
or
is
of
to
death
and growth
investigate
by
enhanced
the
inhibition.
whether
cell
hydrodynamic
One
growth
is
forces
in
The primary thrust will be to determine whether
growth inhibition and/or cell death account for the reduced net growth
in
overagitated microcarrier cultures.
The Cell Cycle and DNA Replication
To understand the potential hydrodynamic effects on cell growth, one
must first understand the growth cycle of animal cells.
their DNA and pass it
on to their progeny,
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16
-
cells pass
To replicate
through a cycle
with four
biosynthesis
General
the
DNA
synthesis during
the G2 phase,
and actual
For almost all animal cells growing
the M phase.
during
during
for mitosis
1983).
and M (Alberts et al,
during the G1 phase,
occurs
preparation
S phase,
mitosis
G1 , S, G2,
sequential phases:
in
culture, the duration of the S, G2, and M phase is roughly constant at 7
hours,
3
hours,
Alberts et al,
1-2
and
(Darnell
respectively
hours,
et
al,
1986;
A change in the average doubling time of a cell
1983).
population will occur because of a change in the duration of G,
and/or
because some fraction of the cell population enters or exits an out-ofcycle, non-growing state termed Go.
There
some debate whether a Go state actually exists or whether
is
all differences in doubling time are due to differences in the duration
of the Gl phase
the
et al,
At the restriction point,
or at the passage between Go and G.
G
decision is made whether a given cell will replicate.
behind
decision
this
Independent
of the
will
irrespective
pass
is
not
basis behind
through
the
although
understood,
fully
factors
environmental
several
on
depends
divide
Clearly,
Darnell et al, 1986).
1978;
a restriction point for cell growth exists at some point late
however,
in
(Pardee
(Darnell
the
decision,
S,
G2,
and
of the "post-decision" environment.
a
M
cell
et
The basis
it
clearly
al,
1986).
stimulated
phases
to
essentially
Non-growing cells are
almost always held up in the Gl or Go phase.
There
inhibit
in
are at least two ways
cell
growth.
The
which high levels of agitation may
hydrodynamic
-
17
-
environment
may
affect
the
may affect the
or it
capability required for cell growth,
biosynthetic
These effects would be uncoupled
cell's decision whether to replicate.
with changes in cell metabolism which are not involved with growth.
If
growth,
cells rather than just inhibit
hydrodynamic stresses actual kill
it
would be interesting to know if
only at certain positions in
cells are killed at random or
the cell cycle.
When anchorage-dependent
animal cells grow on a surface, cells in mitosis generally round-up and
assume a less flattened morphology than the interphase cells (Alberts et
mitotic cells can be selectively and
For some cell lines,
al, 1983).
viably removed by applying mild shear
growth
to the
stresses
surface
This procedure does not
(Prescott, 1976; Pardee, 1978; Terasima, 1962).
Cell
work for many cell lines and growth surfaces (Freshney, 1983).
removal
is
frequently not selective for mitotic cells if
the agitation
is excessive (Terasima, 1962) or if the cells are grown on microcarriers
and have not been pretreated with colcemid (Ng et al, 1980; Mitchell and
Wray, 1979).
If
anchored cells are killed by hydrodynamic
forces,
it
is
unclear
whether death occurs before, during, or after removal of the cells from
the microcarriers.
result
in
cell
It is also unclear whether
lysis
and
disintegration.
If
death will
removal,
eventually
lysis,
and
disintegration occur, counting whole cells in suspension will not fully
Accordingly,
one may wish to
component which is
released by the
account for the number of cells killed.
analyze for
a stable
disintegrated cells.
intracellular
It is then important
-
18
-
to know how much of this
component was originally contained by each cell.
Assessment of Cell Death through DNA Release Measurements
quantitatively
To
assess
one could analyze for DNA release
forces,
lysis
and
death
cell
from hydrodynamic
into the culture fluid.
For
normal diploid cells, the DNA content of each cell is solely a function
of the cell's position in the growth cycle and should not depend on the
hydrodynamic
populations
environment
per
well-defined
is
se.
The
specific
and
thus
DNA
DNA
release
content
can
be
cell
of
directly
correlated to the number of cells killed.
The amount
If
lysed.
of DNA release will depend upon what type of cells are
Go or G
in
cells
diploid equivalent per cell.
release
two
will be
are lysed,
cells in
If
diploid equivalents
the DNA release will be one
G2
per
or M are lysed,
cells.
the DNA
If cells
are
removed randomly throughout the cell cycle, the average DNA release will
depend upon the distribution of the cell population among the phases of
For a cell population growing exponentially through
the growth cycle.
binary fission,
the distribution function,
f(t),
of cell ages is
given
by (Johnson, 1961)
f(t)
is
where
t
times
dt is
=
the time
t/Td)
(ln 2) 2(1 td
(Eq. 1)
since mitosis,
Td is
the doubling time,
and f(t)
the fraction of the cell population with an age between t
and t + dt.
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19
-
There
average
least
at
are
two
to
approaches
reasonable
determine
the
For the first approach, one
DNA content of a cell population.
can assume that a distinct Go phase does not exist and that all cells
are
going
the
through
cell
All
cycle.
changes
therefore due to changes in the duration of Gi.
Sa
The average DNA content
then given by
is
Sa,
per cell,
rate are
in growth
f
=
(Eq. 2)
f(t) S(t) dt
where S(t) is the DNA content per cell in diploid equivalents at a given
time t since mitosis.
throughout
constant
If one assumes that the rate of DNA synthesis is
the S period,
the integral
above can be solved to
yield
2 (TM + TG2 + TS)/Td
Sa
+
2
(TM + TG2)/Td
(Eq. 3)
=
2
where TS,
TG2,
and TM are the respective durations of the S, G2 , and M
phases.
For a second approach to determine
the average DNA content of cell
populations, one can assume that a separate, out-of-cycle Go phase does
exist and that the duration of the G1 phase is
specific
growth
rate
will
then
depend
population, IGo, which resides in Go.
-
20
-
upon
actually constant.
the
fraction
of
The
the
The average DNA content of the
population is
Sa
then given by
Td - Tc(l -
=
0
.5 (2 (TM + TG2 + Ts)/Tc +
2
(Eq. 4)
(TM + TG2)/Tc )
Td
where Td is
the observed doubling time and Tc is
the total cycle time
(TGl + TS + TG2 + TM).
this
In
quantitatively
is
death
cell
thesis,
measurements of the DNA content of culture fluids.
are related
the models
through
to cell numbers
assessed
through
The DNA measurements
presented above.
For
conditions of excessive agitation, the amount of cell death is compared
The comparisons are used to determine
growth.
to the net reduction in
whether cell growth is affected by hydrodynamic forces under conditions
of excessive agitation.
The
assessed
effects
However,
with
monitoring
through
precursors,
such
the
is
on cell growth
incorporation
of
different
levels
at
thymidine,
as
when there
excessive
forces
of hydrodynamic
extensive cell lysis,
agitation,
unresolved complications
radioactive
the
and difficulties
be
could also
radioactive
of
DNA
agitation.
such as that which occurs
precursor
technique
(Aherne et al,
has
1977).
The
radioactive precursor technique is therefore not used in this thesis.
Hydrodynamic Effects on Cell Metabolism
Hydrodynamic
forces may not only lead to cell death and lysis but
could also lead to significant changes in cell metabolism.
-
21
-
Many of the
metabolic events that occur in animal cells are not directly related to
forces,
or not cell growth
Whether
growth.
cell
not
are
which
events
metabolic
is
inhibited by hydrodynamic
associated
growth
could
be
influenced by agitation.
metabolism,
studies have shown that cell shape,
several
cells,
For endothelial
and endocytotic activity can be strongly affected by fluid
flow. The results are summarized as follows:
1) the cells align and elongate in the direction of flow over 1-2 days
exposure
to
shear stresses above
5 dyne/cm 2
(Dewey et al,
1981;
Levesque and Nerem, 1985)
2)
the
histadine
activity
decarboxylase
of
cells
the
increases
linearly with shear stress for 1-2 hour exposures to shear stresses
above 2.8 dyne/cm 2 (DeForrest and Hollis, 1980; Hollis and Ferrone,
1974; Rosen et al, 1974)
3)
cell
to
permeability
increases
proteins
for
1-hour
2
exposures to shear stresses above 7 dyne/cm (Fry,
or
longer
1968; DeForrest
and Hollis, 1980)
4) prostacyclin
production increases
6-fold upon exposure
2
and increases
shear stress of 10 dyne/cm
to a mean
16-fold upon a pulsed
exposure at 1 Hz between 8 and 12 dyne/cm2 (Frangos et al, 1985)
5)
exposure
to a shear
stress of 30 dyne/cm2
significantly enhances
receptor-mediated binding, internalization, and degradation of
low-density lipoproteins (Sprague et al, 1987)
These results are due,
at least in
part,
to the natural adaptation of
endothelial cells to fluid flow in blood vessels.
-
22
-
For cell lines other than endothelial, there has been a very limited
number
direct
of
on how cell metabolism is
studies
(1986)
and Hu
Dodge
cells,
For hybridoma
environment.
hydrodynamic
affected by the
found that net cell growth was slightly reduced, but volumetric glucose
consumption was unchanged, by high levels of agitation.
be
to lactic acid by dead or
in part, to conversion of glucose
due,
This result may
It may also indicate that the specific glucose uptake rate
lysed cells.
of the cells was slightly increased by agitation.
epithelial
For
kidney
glass
on
cells
exposure
shear
to
stress
between
levels
of
agitation on specific
direct
13
dyne/cm 2 .
P-interferon productivity.
Besides
reports
in
differences
of
Giard et
al,
It
1979).
cell
cultures
metabolism between agitated and stagnant (or nearly stagnant)
(Bryant, 1969;
For
found no
are
there
studies,
and
6.5
Schulz et al (1986)
recombinant mouse-L cells on microcarriers,
these
and
(1985) found that post-shear urokinase release was increased by
Hellums
effects
Stathopoulos
slides,
is unclear, however, whether
these differences are due to mass or momentum transfer.
this
thesis,
a
thorough
hydrodynamic
effects
on
cell
In
investigation
growth,
while
is
only
made
a
into
very
the
limited
investigation is made into the hydrodynamic effects on cell metabolism.
Before any reactor design can be fully optimized,
hydrodynamic
effects
on both cell growth and metabolism will have to be fully understood.
-
23
-
Microscopic Flow Fields and Cell Deformation Mechanics
When shear flow occurs over a cell anchored to a surface, the microaffected by the protusion of the cell.
scopic flow field is
a net torque created by the flow around its
experiences
The cell
circumference.
This torque is countered by the adhesive force between the substrate and
the front of the cell.
(1972a) attempted to
Hyman
for
solve
the
microscopic
From a literature
(1972b).
that his published solution was incorrect
survey, the problem appears to remain unsolved.
field
He later admitted
a cell protuding into a linear shear field.
around
flow
The relevant Reynold's
number is given by
Re
=
the undisturbed shear rate,
where Y is
rical shape assumed),
range
(Eq. 5)
Y h2/v
around the
For the
interest in cell culture,
the flow
cell will be creeping with a Reynold's
currently
Because
are of
the cell height (hemisphefluid viscosity.
the kinematic
and v is
of parameters which
h is
available
visualization
flow
number below 0.5.
techniques
not
can
resolve to better than 20-30 microns, any theoretical solution to the
microscopic
flow field can not be experimentally
verified with actual
cells.
Because there is no available solution to the microscopic flow field
around
a
cell
protuding
into
a
shear
field,
have been correlated with the
anchored
cells
stress.
This approach
is
all
shear
24
-
on
undisturbed wall
shear
is
known
taken not only because very little
-
effects
also because
but
fluid mechanics,
detailed
the
about
the microscopic
flow field is coupled to the cell shape and cell deformation mechanics.
at least in
The cell shape will be determined,
field
and hydrodynamic
local
flow
field, one
To determine
forces.
simultaneously
must
part, by the local flow
the
the cell shape and
solve
for
both
the
fluid
motion and the cell deformation mechanics.
The deformation mechanics of red blood cells have been successfully
from
described
Evans, 1983).
purely
1972,
(Hochmuth et al,
models
physical
The deformation mechanics
of nucleated cells are only
In contrast
currently being elucidated (Sato et al, 1987; Cheng, 1987).
to a red blood cell,
a nucleated cell with dynamic internal structures
can not be modelled as a Newtonian
will
cells
in
Furthermore,
membrane.
actively
1973;
solution surrounded by an elastic
response to fluid shear stresses,
shape by
adjust their
lengthening and
nucleated
shortening
Purely physical models for nucleated cells would
cytoskeleton fibers.
be successful only for time scales which are shorter than the response
time of the cell.
It will clearly be a challenging problem to solve for
the deformation mechanics of nucleated cells.
the
In most microcarrier cultures,
cells
The
are exposed not only to shear forces,
effects
of normal
forces
forces
effects
may
account
for
in
laminar
flow
the
but also to normal forces.
on animal cells have,
never been quantitatively investigated.
typically
fields
-
and
25
-
The
flow field is turbulent.
to my knowledge,
The undiscovered role of normal
poor
global
agreement
between
hydrodynamic
shear
effects
in
stirred
tanks,
(1987).
as reported by Rosenberg et al
such
The poor
agreement may also arise due to the limited understanding of turbulence.
For microcarrier cultures in turbulent bioreactors, one can only roughly
estimate the magnitude and direction of the hydrodynamic
forces on the
cells.
investigate
To
damage in turbulent
information should be obtained both through direct experiments
reactors,
with
the mechanisms of hydrodynamic
turbulent
reactors
and
experiments with well-defined hydrodynamic forces.
mechanisms
of
cell
damage
in
of
translation
through
turbulent
In
forces.
from
this thesis,
reactors
investigated through experiments with turbulent reactors.
attempt is
results
are
the
directly
A reasonable
terms of normal forces and shear
made to present results in
Further elucidation of the effects of well-defined forces, inc-
luding the incorporation of cell deformation mechanics and the solution
of microscopic flow fields, are left for future research.
Effects of Microcarrier and Cell Concentration
For
industrial
cell
high
culture,
cell
concentrations
can
potentially reduce production costs through four different means:
1) increased volumetric productivities and thus reduced capital and
overhead costs,
2) decreased labor required per cell and thus reduced labor costs,
3)
increased concentrations of the desired product and thus reduced
purification costs, and
4)
increased
concentration
other
of
-
26
-
cell-derived
products
(growth
factors,
accelerated growth,
which may result in
etc..)
accelerated
product formation, or reduced serum requirements.
For a specific cell line, the maximum number of cells per microcarAccordingly,
rier is approximately constant.
one wishes to
if
obtain
It
high cell densities, microcarrier concentrations must be increased.
is
therefore
important
to understand how an increase in microcarrier
concentration will affect the hydrodynamic environment near the cells.
concentra-
of microcarrier
data on the effects
Currently-available
tion is limited and frequently contradictory.
In small spinner flasks,
Hu et al (1985) found no decrease in growth rate when bare microcarriers
were added to cultures,
or when cultures with 5 g/l microcarriers were
concentrated to 15 g/l.
In contrast, however, Feder and Tolbert (1983)
report
that
cell damage
increased
above
decreased
growth
12
g/l.
rates
when microcarrier
occurs
as
et
concentrations
al
Furthermore,
Mered
microcarrier
concentrations
(1980)
were
are
observed
increased
from 1 to 5 g/l.
If there is no detrimental effect of microcarrier concentration, and
if
similar
microcarrier
chemical
environments
concentration should lead to
cell concentration.
often attributed,
microcarrier
an
increase
in
a proportional
increase
in
maintained,
When this proportionality
without apparent proof,
microcarrier collisions.
of
can be
is
not observed,
it
is
to a detrimental effect from
However, in most studies, the physical effects
concentration
are
not
-
-
27
clearly
separated
from
the
of
effects
chemical
effects
detrimental
The
concentration.
cell
attributed to collisions may actually be due to nutrient limitations or
other
some
effect
from high
experiments
previous
were
Furthermore,
concentrations.
cell
conducted with various
culture
The role of collisions,
different levels of agitation.
vessels
vessel
the
geometry,
impeller
configuration,
at
along with any
other hydrodynamic effects of microcarrier concentration, may
upon
the
and
depend
level
of
agitation.
Accordingly,
the bioreactor design engineer now faces the following
unanswered questions:
1) What are the physical effects associated with microcarrier
concentration?
2) How do these effects vary with the level of agitation?
3) Do collisions between microcarriers lead to cell damage?
If so, at
what level of agitation, and at what rate of damage?
In
this thesis, results are presented which address these questions.
Hydrodynamic Damage in Microcarrier Cultures
Hirtenstein and Clark
in microcarrier cultures.
there is
in
Their data, shown in Figure 1, indicate that
an optimal stirring speed near 60 rpm for growth of Vero cells
a 250-ml traditional
speeds was
by
have studied the effects of agitation
(1980)
spinner vessel.
The poorer growth at the slow
likely due to transport limitations,
probably brought about
either inadequate surface aeration or incomplete suspension of the
beads.
The poorer growth at the high speeds was likely due to
-
28
-
107
60 rpm
1-
6
10-
z
0
0-J
0
O-
90 rpm
U
zIUiJ
U
10
5
30 rpm
120 rpm
4
101
2
3
4
5
6
7
TIME (DAYS)
Growth of Vero cells at different
stirring speeds (Hirtenstein and Clark, 19 80)
Figure
the
show
clearly
The results
from excessive agitation.
detrimental effects
between mass
trade-off
transport
and
in
Figure 1
hydrodynamic
Nonetheless, these results can not be
damage in microcarrier cultures.
readily translated into the design of an industrial-scale reactor.
Sinskey
et
(1981)
al
agitation on microcarrier
by the
and Hu
cultures
studied
effects
the
small stirred vessels.
in
of
As shown
relative cell growth can be correlated
Figure 2,
data of Hu in
(1983) have
as given by
with an integrated shear factor (ISF),
2 wrN Di
ISF
(Eq. 6)
=
(Dt - Di)
where N is the impeller rotation rate, Dt is the vessel diameter, and Di
is
the impeller diameter.
The integrated shear factor is
a measure of
the strength of the shear field between the impeller and vessel wall.
Although the correlation of net growth with integrated shear factor
is
useful,
it
is
not readily
incorporated
into a mechanistic model of
hydrodynamic effects on cells attached to microcarriers.
must be
analyzed in
mechanics.
must
be
terms of the more
fundamental parameters
The response of the cells to the hydrodynamic
clearly
elucidated.
The problem
The effects
of mass
of fluid
environment
transport must
be
included in a more thorough quantitative analysis.
Cell-liquid Transport in Microcarrier Cultures
When investigating
the effects
of hydrodynamic forces,
or momentum
transfer, one must eliminate any other effects due to mass and heat
-
30
-
Impeller
Diam. (cm)
100
75
Vessel
Vol. (ml)
3.2
250
4.1
250
5.1
250
7.5
2000
8.5
2000
50
25
0
10
20
30
INTEGRATED SHEAR FACTOR (SEC~ 1 )
Figure 2.
Relative
growth extent vs. integrated shear factor (Hu,
1983)
transfer.
growth
cell
induce
may
it
cultures,
microcarrier
through
simply
is
the subsequent mixing
chemical
of
elimination
the
and
Dunn
1974;
1973,
(Stoker,
gradients
shaken,
a stagnant cell culture is
If
1984).
Ireland,
For
important to understand whether there are
any transport limitations between the cells and medium.
such as a microcarrier,
When a sphere,
is
suspended in
a turbulent
vessel, mass transport between the sphere surface and bulk medium can be
described by (Sano et al, 1974; Chaudhari and Ramachandran,
Sh
where Sh is
unit
mass,
coefficient
cultures,
2 + 0.4(F d
=
4
dp
is
for
the
the
the
the average power dissipation per
i is
diameter,
sphere
under
chemical
Sherwood
(Eq. 7)
/Df V2 1/3
the Sherwood number,
and
Df
by
equation
Sherwood number for cell-liquid mass transport, Shc.
species which
normalized
the
is
diffusion
For microcarrier
consideration.
given
number
1980)
represents
7
For each chemical
is consumed or produced by cells on microcarriers,
gradient
between
chemical
the
the
concentration
in
the
the
bulk
medium, Xb, and the concentration at the cell surface, Xc, is given by
where
if is
Xb - Xc
i Rc dp
T
Xb
Df Xb Shc
the surface
(Eq. 8)
in
coverage
cells per unit area,
uptake rate per cell for a given chemical species.
are produced by the cells, Rc will be negative.
-
32
-
and Rc is
the
For chemicals which
Substituting typical values for the parameters in equations 7 and 8,
one
unity,
on
values
with
the cell surface are
at
concentrations
of
order
the
the concentrations in the bulk medium.
that
a
conclusion
parallel
Furthermore,
gradients.
be
can
the
The
0.1.
to
0.001
less
far
are
the normalized gradients
that
finds
generally
than
chemical
essentially equal
therefore
to
A Nusselt number analysis shows
made
temperature
to
with
regard
and
chemical
temperature
are
gradients
insignificant even if the microcarriers are suspended in a stagnant flow
2
field (Shc = 2, Nuc =
).
Thus, it appears that mere suspension of microcarriers provides for
adequate
mass and heat transport between the
supported by the results
conclusion is
(1983);
uniform growth is
levels
of
agitation
of Sinskey et al
are
concentrations
are
and Hu
(1981)
observed over a wide range of nondetrimental
that
sufficiently
are
suspended,
and
maintained
at
as
long
suitable
as
the
levels,
the
suspend
to
strong
microcarriers and provide for adequate surface aeration.
microcarriers
This
cells and medium.
As long as the
bulk
the
chemical
effects
of
agitation will come solely through momentum transfer.
Fluid-lift, Airlift, and Stirred-tank Bioreactors
The vast majority of microcarrier cultures are conducted in
Such vessels provide a relatively homogeneous culture
tank bioreactors.
environment
almost
all
which
can be
readily
assessed
currently-available microcarriers
such equipment.
stirred-
and
controlled.
are designed
In
fact,
for use
in
Most microcarriers have a specific density in the range
-
33
-
Neutrally buoyant microcarriers are generally not used
mild agitation.
as
through
gravity
for microcarrier
cultures
medium
the
from
separated
be
not
could
they
for complete suspension with relatively
allows
This
to 1.04.
of 1.03
sedimentation.
Fluid-lift
reactors have
been employed
reactors
When fluid-lift
1981).
(Clark and Hirtenstein,
are used with
microcarriers that have a specific density of 1.04 and a diameter of 185
microns, the maximum linear velocity through the bed is on the order of
The cells are exposed only to very weak hydrodynamic forces
5 cm/min.
(less than 1 dyne/cm2 ).
The cell density and reactor height, however,
are limited by the uptake of oxygen from the medium as it flows past the
densities
wishes
one
If
cells.
to
a
operate
fluidized
fluid forces,
and
high
cell
microcarriers with a specific density
on a industrial scale,
The energy dissipation
more comparable to glass will have to be used.
rates,
bed with
will then be
comparable to
the values
in a
stirred-tank reactor with microcarriers of a specific density near 1.04.
reactors
Airlift
animal
Handa
et
their
use
direct
1981;
insect
and
cells
1987).
al,
for
sparging
Spier
have been used for
cultures.
damage
and Griffiths,
to
cells
is
freely-suspended
1984;
found which document
frequently
on microcarriers
stated
that
(Pharmacia,
Nonetheless, no published reports
1984).
were found which document such damage.
-
It
of
Boraston et al,
1986;
No published reports were
microcarrier
causes
al,
(Tramper et
cultures
34
-
One
of this
purpose
to
is
thesis
and
investigate
experimentally
document whether cell damage occurs from direct sparging of microcarrier
Cell damage is known to occur from direct sparging of suspen-
cultures.
sion cultures
that damage
fact,
(Tramper
al,
et
1987).
Handa et al,
1986;
likely
is
It
In
occurs from direct sparging in microcarrier cultures.
given
microcarrier cultures,
the damage may be more extensive in
that the cells are immobilized and are more susceptible to mechanical
If
forces.
generated,
foam is
into the
transfer of the microcarriers
foam phase (Fleischaker, 1982) may cause further problems.
are
Independent of whether microcarriers
mass
transfer
reactor
types,
high-density,
airlift,
there will be a trade-off between
or stirred-tank reactor,
fluid-lift,
in a
suspended
three
all
For
and hydrodynamic damage upon scale-up.
the fluid-mechanical environment will be comparable
this
In
cultures.
large-scale
in
hydrodynamic
thesis,
phenomena in the stirred-tank design are investigated.
Cell Damage from Turbulence
agitated with a rotating impeller,
When a vessel is
the Reynold's
number for the bulk flow is given by (Nagata, 1975)
Re
where vb is
=
N Di2 vb
the kinematic viscosity of the bulk suspension,
impeller
rotation
rate,
Reynold's
number
exceeds
turbulent
(Eq. 9)
(Nagata,
and
1975).
Di
the
is
approximately
For
-
impeller
1000,
complete
35
-
the
N is
diameter.
flow
off-bottom
the
If
this
field becomes
suspension
of
microcarriers,
virtually all stirred-tank bioreactors must be operated
in the turbulent regime.
In the turbulent
flow field of a microcarrier culture, short-term
hydrodynamic forces arise through the motion of turbulent eddies.
with
conjunction
exists
there
the
transfer
of energy
a spectrum of eddy sizes
eddies,
small
to
from large
In
down to the viscous dissipation
For sufficiently high bulk flow Reynold's numbers, the smallest
regime.
eddies exist in a state of isotropic, statistical equilibrium and can be
described by the Kolmogorov scales for eddy length and viscosity (Hinze,
1975).
stirred-tank, the
In a
large energy-containing eddies
nonisotropic and nonhomogeneous
(Nagata, 1975).
are
highly
Nonetheless, isotropic
equilibrium at the Kolmogorov scale will exist if the eddies in the
viscous dissipation regime are much smaller than the energy-containing
eddies
(Hinze,
isotropic
1975).
equilibrium
exists
at
the
viscous
indicate
which
results
several
are
There
dissipation
scale
in
stirred-tank microcarrier bioreactors:
1) For
stirred
containing
tanks,
eddies,
Komasawa et al
(1974) found
or turbulent macroscales,
given by one-fifth the impeller width.
that the
have
sizes
energy
roughly
Translating these results
to most microcarrier cultures, one can estimate that the energycontaining eddies are more than an order of magnitude larger than
eddies in the viscous dissipation regime.
2) For stirred tanks, Nagata (1975) found that the lateral and
-
36
-
This
numbers.
wave
indicates
at high
nearly superimposable
energy spectra became
longitudinal
that
local
isotropy
at
exists
the
viscous dissipation scale.
3) In analyzing several sets of results, including those of Sato
et
(1967)
al
spectra in
for
that
found
(1975)
tanks, Wadia
stirred
energy
the viscous dissipation regime followed the prediction
of Heisenberg (1948) for isotropic turbulence in statistical equilibrium.
The
agitation
for
observation held
unbaffled
in an
stirred tank with an impeller Reynold's number of 8400, typical of
the conditions in a stirred-tank microcarrier reactor.
studies of Komasawa et al (1974),
4) As shown by the tracer-particle
the presence of particles
the turbulent flow of a stirred tank
in
does not preclude the existence of isotropic equilibrium.
are nearly
the particles
if
are high,
bulk-flow Reynold's numbers
If the
neutrally-buoyant, and if the particles are comparable in size to
the
Kolmogorov
eddy
length
isotropic
scale,
exist in the viscous dissipation regime.
equilibrium
should
Microcarriers are nearly
neutrally-buoyant and are comparable in size to the Kolmogorov eddy
length scale.
In
light
of
approaching
the
evidence
isotropic
presented,
equilibrium
it
exists
appears
that
the
viscous
in
condition
a
dissipation
regime for many microcarrier cultures.
With the belief that Kolmogorov's theories of isotropic equilibrium
can be applied to microcarrier cultures,
-
37
-
one might first
consider
the
of
role
occupied by
If a relatively
size.
eddy
a microcarrier,
eddy formed
large
microcarrier would be
the
in a region
entrained
and
would rotate and translate in a manner that would reduce the net torques
and forces
If a relatively small eddy formed adjacent
on its surface.
to a microcarrier, the motion of the microcarrier would be more limited,
as
results of Kuboi
shown by the
microcarrier would have
eddy.
Accordingly,
small
intense
et al
(1974),
to experience more
cells on microcarriers
eddies
of
of
and the cells on the
the full force of
the
will be the most damaged by
a size and velocity large
enough
affect
to
individual cells, but too small to readily entrain entire microcarriers.
In
eddies
turbulent
cultures,
microcarrier
in
viscous
the
dissipation regime are often intermediate in size between the cells and
Because
microcarriers.
isotropic
equilibrium,
these
they
eddies
are
appear
described
to
by
exist
the
in a state
Kolmogorov
of
scales
(Tennekes and Lumley, 1985)
where L is
scale
for
(Eq. 10)
1/4
L
=
(v3
v
=
(ve) 1/4
(Eq. 11)
9
=
(v/e)1/2
(Eq. 12)
the length scale, v is
the eddies.
the velocity scale,
are
These scales
functions
and 0 is
of only
the time
the power
dissipation per unit mass, e, and the kinematic fluid viscosity, v.
The size of the smallest eddies decreases with an increase
-
38
-
in power
or
For
in kinematic viscosity.
a decrease
power
sufficiently high
inputs at a given viscosity, the turbulence should generate eddies which
are smaller than microcarriers.
Cell damage from turbulence should then
become evident, if the proposed role of eddy length is correct.
the effects of both power input and viscosity are
this thesis,
In
to
investigated
determine
performed
are
investigations
the
damage
regard
power
average
the
to
the
Experimental
eddies.
smallest
with
correlates with
Although the role of local power dissipation rates
dissipation rates.
is
for
scale
length
Kolmogorov
if hydrodynamic
partially investigated and discussed, more thorough investigations
are left for future work.
In dilute cultures, cell damage should occur
and concentrated cultures.
primarily
through
cultures,
cell
interactions,
are performed for both dilute
separate experiments
thesis,
this
In
damage
may
In
interactions.
microcarrier-eddy
occur not
only
through
concentrated
microcarrier-eddy
but also through microcarrier-microcarrier
interactions.
To provide clear and unique information with regard to each mechanism,
microcarrier-eddy and microcarrier-microcarrier
damage mechanisms
are
studied separately.
Protective Polymers
To
eliminate or
reduce
cell
damage
from
fluid-mechanical
their
medium.
have
added polymers
to
commonly used polymer is
methylcellulose
(Kuchler et al,
many
investigators
-
39
-
forces,
The
1960;
most
Bryant,
Holmstrom,
1969;
1966,
1986).
1968;
Pluronic polyols have
and Pirt,
Birch
also been used (Swim and Parker, 1960;
Runyan and Geyer, 1963; Kilburn and Webb, 1968; Mizrahi, 1984),
along
polysucrose
1984),
(Mizrahi,
carboxymethylcellulose
sodium
with
al,
et
Tramper
1969;
(Pharmacia, 1981), dextran (Schulz et al, 1986), and hydroxyethyl starch
In general, metabolic uptake
(Mizrahi, 1984).
insignificant (Mizrahi, 1984).
value
(Bryant, 1966,
trace
metals
1969;
these polymers
of
is
The polymers appear to have no nutritive
Mizrahi,
they can provide
although
1984),
(Thomas and Johnson,
in deficient medium
1967)
eliminate protein precipitation from medium with poor serum
and can
(Swim and
Parker, 1960).
It is widely believed that these polymers protect animal cells from
mechanical damage.
observed if
In
agitated systems,
the medium is
these protective polymers
Runyan
and
Geyer,
1963;
cell disruption is
frequently
not supplemented with either serum or one of
(Swim and Parker,
Bryant,
1966;
1960; Kuchler et al,
1960;
Johnson,
1967;
Thomas
and
Holmstrom, 1968; Kilburn and Webb, 1968; Birch and Pirt, 1969; Mizrahi,
1984).
for
Because
the known protective polymers
and serum can substitute
each other with regard to mechanical protection, it appears
serum
contains
a
protective
polymer,
although
it
has
not
that
been
identified.
The mechanism of the protective effect of these polymers has not
been determined.
The mechanism may involve a reduction of turbulent
damage through an increase in viscosity.
-
40
-
Addition of the polymers would
of
size
the
and
viscosity
medium
the
increase
likely
smallest
the
This hypothesis
eddies, and thus reduce cell damage from turbulence.
this thesis.
will be investigated in
Cell Damage from Time-Average Flow Fields
are both time-average and time-
In a turbulent flow field, there
flucuating
and
pressure
over small
change greatly
components
velocity
the
time-average
intervals
in position,
If
components.
velocity
strong hydrodynamic forces could arise and damage cells.
the
evaluate
To
fashion,
thorough
one
profile
average
flow
various
time-average
very
is
approach
role
determine
might
as
around a microcarrier
flow
difficult,
a
in
fields
it
circulates
through
this
Because
tank.
stirred
currently
not
if
time-
position-dependent
the
impossible,
a
in
components
velocity
time-average
of
one might
instead employ a simplified approach and ignore the dynamic effects due
into
down
ignored,
3.
Figure
small
small
problem
the
This
region
velocity
regions,
in
and
velocity
turbulent
if
can be simplified
schematic of a sphere
the
flow field is
the time-average
If
circulation.
to microcarrier
reactor where
the
to
in
the
gradient
field is approximately constant.
flucuations
situation
a shear
broken
are
depicted
field represents
in
the
in
a
time-average
Such gradients will
subse-
quently be referred to as time-average shear rates.
Lin
et al
(1970)
developed an analytical
steady-state
solution to
the flow profile near a neutrally-buoyant sphere, as depicted in Figure
-
41
-
3.
The relevant Reynold's number is given by
Re
Y rm2 /V
=
(Eq. 13)
where rm is the microcarrier radius and Y is the undisturbed shear rate.
For
equation 13 are generally below 1,
calculated
from
and the flow can be approximated as
r,
The maximum shear stress,
creeping.
numbers
Reynold's
the
bioreactors,
microcarrier
on the sphere surface is
then
given by
r=
As shown in
time-average
speed,
(Eq. 14)
n Y
the fluid viscosity.
where n is
maximum
3
shear
rate
time-average
ITS,
the maximum shear stress depends upon the
equation 14,
and is
and
is
shear rate
given,
in
In most
fluid viscosity.
proportional
the reference
to
the
frame of the
vessels,
the
impeller tip
rotating
im-
peller, by (Oldshue, 1983):
Y = K1 ITS
and where K1
maximum
shear
is
=
If
a constant.
rate
occurs
(Eq. 15)
K 1 grN Di
a radial
radial
the
in
flow impeller
jet
from
is
the
used,
the
impeller.
Analyzing the flow profiles developed by Nagata (1975), one can estimate
that K1 takes on a value near 0.4 cm-1 for a typical paddle impeller.
-
42
-
Ux
U00+Y(z-z
V,7
0
)
z
Ox
Figure 3. Schematic of a sphere
caught in a simple shear field
-
43
-
Both Hu (1983) and Sinskey et al (1981) found that cell growth does
As shown by the data of Hu (1983) in
not correlate with impeller tip.
Figure 4,
maximum growth or zero growth can be observed at the same tip
As originally concluded by
speed, depending on the size of the vessel.
Hu,
the impeller tip speed, or the maximum time-average
determining whether there are
role in
not appear to play a fundamental
shear rate, does
detrimental hydrodynamic effects.
In the experiments of Hu (1983), the maximum time-average shear rate
was approximately 16 sec~ 1 , as calculated from equation 15.
The maximum
shear stress was approximately 0.4 dyne/cm2, as22calculated from equation
2
This maximum shear stress is much less than 7 dyne/cm , the minimum
14.
value
Hellums,
shear
Thus,
1985).
fields
cause
to
reported
was
not
(Stathopoulos
removal
or
damage
cell
it appears that cell damage
in
occurring
the
experiments
and
from time-average
performed
Hu
by
(1983). This probably accounts for the lack of correlation between cell
damage and maximum time-average shear rate.
To determine whether cell damage from time-average shear fields can
occur,
one can not only calculate and compare
can also
flow fields is
time-average
increase
the
investigate
the
stresses.
viscosity
turbulence.
If
amount
occurring,
an increase
since this will
of damage,
reduce
the
If cell
effects of viscosity.
cell damage from turbulence
will
shear stresses,
amount
is
in
as
damage from
viscosity should
lead to higher shear
occurring,
of damage,
but one
it
in
an increase
will
dampen
the
Viscosity can be used to distinguish between damage from
-
44
-
Symbol
1 0M0 --
I-
z
W
75
Impeller
Diam. (cm)
Vessel
Vol. (m 1)
3.2
250
0
4.1
250
0
5.1
250
0
7.5
2000
8.5
2000
X
500
cc
-
ULU
-
25-
-
0-
0)
10
20
30
40
IMPELLER TIP SPEED (CM/SEC)
Figure 4.
Relative growth extent vs. impeller tip speed (Hu, 1983)
turbulence and damage from time-average flow fields.
viscosity will cause cell damage
in
An increase
has sufficiently high time-average
As was mentioned, the
shear rate for most reactors occurs in
maximum time-average
the impeller.
shear rates.
a reactor
only if
off
the jet
In some reactors, the maximum time-average shear rate may
occur in a region of close clearance between the rotating impeller and a
stationary
clearance
profile
in
vessel
between
the
impeller
instance,
For
component.
if
and vessel wall,
there
the
close
a
tangential
this region may periodically assume a character
the flow between concentric rotating cylinders.
is
flow
similar
to
The maximum tangential
shear rate may then be estimated from the solution of Lee (1966)
for the
flow profile between concentric rotating cylinders, and is thus given by
Y =
4 r N Dt2
2(Eq.
16)
2
Dt 2 - D,
where Dt is the vessel diameter, N is the impeller rotation rate, and Di
is the impeller diameter.
In this thesis, a vessel with a close clearance between the impeller
and vessel wall
is used to investigate the onset of cell damage from
time-average flow fields.
The effects of viscosity are investigated for
shear stresses below and above 7 dyne/cm2 , as calculated from equations
14-16.
Criteria are developed to predict the onset of cell damage from
time-average flow fields.
These criteria are used to purposefully avoid
-
46
-
cell
damage
from
time-average
flow
fields
turbulence.
-
47
-
during
the
experiments
on
MATERIALS AND METHODS
Cell Types
cells were used in
Two types of representative
foreskin fibroblasts
engineered to produce
and
fully
fully
suspension
y-interferon (7-CHO).
cells were
y-CHO
The
Jan
850-cm 2
roller
School
from Biogen
obtained
of Medicine.
the FS-4 cells were propagated
bottles
in
grow
The FS-4 cells were obtained from
Vilcek, New York University
experimental use,
to
difficult
are
anchorage-dependent,
(Perry, 1987).
The FS-4 cells are diploid
y-CHO cells are aneuploid and,
The
Research Corporation, Cambridge, MA.
Dr.
human
(FS-4) and recombinant Chinese hamster ovary cells
anchorage-dependent.
not
although
this thesis:
to doubling 14-22
in
Corning, NY).
No
Products,
(Corning Science
to
Prior
deterioration of the cell line was detected prior to doubling 32.
Cell Culture Reagents and Procedures
nearly
In
microcarriers
with cells
glass
petri
Uppsala,
(Pharmacia Inc.,
grown on
dishes
cultures
experiments,
roller bottles
or
flasks
all
were
grown
Sweden) or
on
in polystyrene
(Corning). A few experiments were
Cytodex 2 and 3 microcarriers
Unless
(Corning).
otherwise
Cytodex
1
T-
conducted
(Pharmacia) or in
noted,
the
term
"microcarrier" refers to Cytodex 1 microcarriers.
All cultures were grown in Dulbecco's Modification of Eagle's Medium
(DMEM;
(Gibco),
Gibco,
Grand Island, NY)
50 mg/l streptomycin
supplemented with 50 U/ml
(Gibco),
-
48
-
penicillin
and either 5 or 10% (v/v) fetal
a single
For the FS-4 cultures,
serum.
calf
lot of fetal calf serum
For
(Hazelton Dutchland Inc., Denver, PA) was used for all experiments.
the
McLean,
Laboratories,
was
additionally
supplemented with 0.25 pM methotrexate
Milwaukee,
and mycoplasma contamination.
for viral
WI).
(Flow
and the medium
was used for all experiments,
VA)
Aldrich Chemical Co.,
pterin,
calf serum
lot of dialyzed fetal
a single
cultures,
-y-CHO
(L- + ametho-
All serum was
screened
The serum lots used in
these
experiments were originally tested against several other lots; they were
chosen for their ability to promote superior cell growth and attachment.
The microcarrier cultures were grown in 125 or 500-ml Corning SlowSpeed
spinner vessels
30
NY).
Corning,
These
are specially designed for gentle agitation and can suspend up
vessels
to
(Corning Science Products,
g/l
impeller
of
microcarriers
diameter
of
5.3
35 RPM.
at
cm,
an
The
125-ml vessels have
an
and
an
impeller width
of
1.9
cm,
The 500-ml vessels have an impeller
internal vessel diameter of 6.3 cm.
diameter of 7.8 cm, an impeller width of 2.5 cm, and an internal vessel
diameter
of 9.6 cm.
each impeller
was
In
nearly
all of the experiments,
positioned at approximately half
the
the liquid height.
the 500-ml vessels,
When the 5.3 cm impeller was used in
the middle of
the middle of
impeller was positioned at one-third of the liquid height.
Prior
to use, the glass components of the vessel were siliconized with Prosil
28 (SCM
Specialty Chemicals,
Gainesville,
of the microcarriers.
-
49
-
Florida)
to prevent adherence
For each experiment, all cultures were grown at the same time from a
This
inoculum.
single
numerous
of
use
the
through
achieved
was
(Bellco Biotechnology,
stirrers
all cultures
vessels
spinner
microcarrier
cultures
(Corning) and
magnetic
the
for
The stirring speed for
NJ).
Vineland,
determined with a stroboscope
was
(Pioneer Model DS303,
Cole Parmer, Chicago, IL) and was verified, if possible, through direct
The stirring speeds were found to
visual observations with a stopwatch.
vary less than 5% from setpoint.
inoculated from roller bottles according
to the
(1985).
They
cultures were
All
procedures
developed by Giard et al
(1979)
and Hu et al
were grown at 37*C in a humidified incubator with 10% carbon dioxide in
air.
The cultures were fed by replacing 60-80% of the culture medium
For each culture,
with fresh medium at predetermined intervals.
length between medium exchanges, IL,
interval
was
the
determined in hours
from the equations
180
I
=
LC
--
(for FS-4 cultures)
(Eq. 17)
(for -y-CHO cultures)
(Eq. 18)
m
44
I
where
Cm
is
L
values
-
C
m
the microcarrier
These interval
and 4.5
=
g/l.
between
concentration
7.2
and
dry grams
per
liter.
maintained glucose levels between 1.0
feeding schedules
They also
in
limited lactic
7.45,
and
limitations.
-
50
-
acid build-up, maintained pH
hopefully
eliminated
nutrient
Culture Aeration and Effect of Dissolved Oxygen on Cell Growth
Oxygen was supplied to all cultures through surface aeration.
preliminary control
the effect of dissolved oxygen on cell
experiment,
in microcarrier
growth
In a
cultures was
Two
investigated.
FS-4 cultures
were grown at different levels of dissolved oxygen in the 125-ml vessels
In
at 35 RPM.
between 85
culture,
the dissolved oxygen level was maintained
one culture,
and 90%
of saturation with respect to air.
In the other
85%
60 and
the dissolved oxygen level was maintained between
saturation with respect to air.
5 shows
Figure
the growth of the FS-4 cells
in the two
cultures.
Growth at 60-85% dissolved oxygen was nearly identical to growth at 8590%
dissolved oxygen.
essentially
dissolved oxygen
oxygen were
it appears
that growth of FS-4 cells
is
uniform over a dissolved oxygen range of 60-90% saturation
with respect to air.
this
Thus,
expected
Accordingly,
Because
range.
for the
all FS-4 cultures were grown within
similar effects
y-CHO cultures,
all
of
dissolved
y-CHO cultures
were
also grown in this dissolved oxygen range.
For nearly all cultures,
90:10 air-CO2
sidearms.
provided
For
the
the headspace gas was equilibrated with the
incubator atmosphere
through loosened caps on the vessel
This maintained adequate oxygen levels in
the headspace
oxygenation through surface aeration.
for sufficient culture
high density cultures, however,
oxygen transfer
from surface
aeration required elevated levels of oxygen in the headspace.
the high density cultures,
and
Thus, for
the headspace was continuously exchanged with
-
51
-
+*-
60-85% sat.
85-90%
----
sat.
with air
with air
106
CO
1-
Z
zZ
0
O
1Cz
10
50
150
100
200
250
TIME (HRS)
Effect of dissolved
Figure i.
oxygen on growth of FS-4 cells
52
-
300
The flow rates
a humidified mixture of air, carbon dioxide, and oxygen.
of the three gases were controlled with variable-area flowmeters (Models
The
FMO42-07, FM042-15, and FM062-01, Aalborg Instruments, Monsey, NY).
oxygen content of the headspace was adjusted so as to control the oxygen
level in the culture between 60-90% of saturation with air.
The carbon
dioxide content of the headspace was maintained at 10% so as to control
the culture pH between 7.2 and 7.45.
Agitation Power Determinations
For
mass,
e,
each microcarrier
the
culture,
average power
input per unit
was determined from the standard power-number correlation:
=
7
N
p
N3 D.5/
i
(Eq. 19)
c
where Np is the power number, N is the impeller rotation rate, Di is the
impeller diameter, and Vc is the average culture volume.
were
determined from the
flat-blade
paddles
in
Power numbers
correlations presented in Nagata
unbaffled
vessels.
These
(1975)
correlations
for
are
described by the following equations:
N
=
p
A
Re
Re
)
B (103 + 1.2 Re
+3(Eq.
(10 3 + 3.2 Re 0.66 )p
20)
where A, B, and p are empirical constants given by the equations:
A
=
14 + (w/Dt)[670(Di/Dt - 0.6)2 + 185]
B
=
10[1.3 - 4(w/Dt - 0.5)
p
=
-
1.14(Di/Dt)]
1.1 + 4(w/Dt) - 2.5(Di/Dt
-
53
(Eq. 21)
-
-
0.5)2
-
7(Di/Dt)
(Eq. 22)
(Eq. 23)
the
where w is
impeller width,
Dt is
the impeller diameter,
Di is
the
tank diameter, and Re is the impeller Reynold's number given by equation
of a microcarier suspension was
9. The bulk kinematic viscosity, vb,
estimated by the ratio of suspension viscosity (Hiemenz, 1977) to
volume-average density:
r;(l + 2.54 + 1042)
(1- 0) +
=
b
the fluid viscosity,
where r; is
the fluid density, pm is
is
p
4
hydrated microcarrier density, and
(Eq. 24)
the
is the volume fraction of solids.
Cell Concentration Determinations
For all microcarrier cultures, supernatant and microcarrier samples
Glucose concentrations were determined
were taken at least once a day.
through the hexokinase method (Sigma Chemical Co.,
concentration
of
cells
microcarriers
to
attached
St. Louis, MO).
was
measured
The
in
duplicate with a modification of the nuclei counting technique described
by Hu et al
soon
Samples from 1 to 15-ml were withdrawn from the
spinner vessels and placed in
well-mixed
As
(1985).
as
polystyrene
centrifuge tubes.
the microcarriers settled to the bottom of the
tube, the
supernatant was removed and the microcarriers were resuspended in 0.15 M
citric
acid with 0.5 g/l crystal violet.
After incubation for 2 hours
at 370 C, the samples were sheared with a Pasteur pipette.
nuclei
were
then
magnification with
Complete
nuclei
counted
phase-contrast
release
hemacytometer
a
in
or
always
was
examination of the microcarriers.
-
under
The released
120-200
fold
Hoffmann modulation microscopy.
verified
through
microscopic
For the samples with high concentra54
-
of inert microcarriers,
tions
citric
which will be susequently described,
the
acid concentration was increased to 0.3 M so as to overcome the
dilution effect from the extra bead volume.
In this thesis, results for microcarrier cultures will frequently be
expressed in terms of cell concentration, or the number of cells per ml
of
volume,
culture
including
solids
especially
volume,
for
counts are
nuclei
necessary to correct for the
is
it
performed on a liquid volume basis,
the
Because
solids.
high
with
cultures
of
concentrations
Accordingly, cell concentrations were determined from
microcarriers.
the equation
104 ((/E)
C
(Eq. 25)
=
4)
F (1 + F
(
where C is the cell concentration in cells/ml,
counted,
E
number of hemacytometer
the
is
volume
fraction of solids
volume
divided
the
by
in
final
the culture,
is the number of nuclei
squares scored,
and F is
the initial
To
minimize
volume.
sample
4
the
is
sample
any
bias
associated with the frequency of nuclei observation in the hemacytometer
field,
were
samples
generally in
sampling,
the
diluted
or
concentrated
such
that
the
C/E
was
To provide an adequate volume for
the range of 30 to 80.
cultures with only 0.05
g/l microcarriers
were
grown in
500-ml vessels.
Samples
from
all
cultures
were
frequently
microscope after being fixed with crystal violet.
-
55
-
observed
under
a
The morphology of the
cells
qualitatively
was
recorded along
average
approximate
the
with
These direct microscopic counts were
number of cells per microcarrier.
used, along with glucose and oxygen uptake data, as a redundant check on
the nuclei counts.
No discrepancies were found in the results presented
in this thesis.
For the T-flask cultures,
cell concentrations were also determined
by counting the number of nuclei released after treatment with crystal
the cells were first
release,
in
the
In order to
citric acid (0.3 M).
violet and
obtain complete nuclei
washed twice with PBS and then incubated
After the flasks were
counting solution for 48 hours at 37*C.
vigorously slapped and shaken, the released nuclei were counted.
DNA Assay
DNA
The
fluorometric
technique
complete
of
culture
the
(Brunk et al,
Instruments,
Scientic
(Hoefer
fluid,
content
1979)
determined
employing Hoechst
San Francisco,
with suspended
was
fluid
CA).
with
a
33258 dye
Samples of culture
cells but void of microcarriers, were
taken before and after each interval feeding. The samples were placed in
15-ml polystyrene centrifuge
were later thawed,
two minutes
tubes and stored at
mixed for 10 seconds on a vibromixer,
in a sonication bath (Model 8850,
The samples
-20*C.
sonicated for
Cole-Parmer Inst. Co.,
Chicago, IL) with intermitant mixing, and then centrifuged for 5 minutes
at 300g.
From the sample supernatant, 0.8 mls were taken and then added
to a UV-fluorometric cuvette
(Spectrocell Inc.,
2.7 mls of phosphate buffered saline (PBS)
-
56
-
Oreland,
PA)
containing
with 1 pg/ml Hoechst dye and
no calcium or magnesium.
The content of each cuvette was mixed and the
pH was adjusted to 7.60 + 0.01 with 10 pl aliquots of dilute NaOH.
Elmer, Norwalk, CT).
wavelength was 458 nm,
control
Several
and the band widths were 3 nm.
were
experiments
concentration was determined through
(Sigma
Chemical
Figure
antibiotics.
calf-thymus
Co.,
Perkin-
The excitation wavelength was 365 nm, the emission
procedures listed above for the DNA assay.
DNA
(Model LS-5,
was then measured with a fluorimeter
fluorescence
The
St.
Louis,
6 shows
MO)
the
DNA concentration.
to
performed
validate
the
The response of the assay to
the
use of
dissolved in
calf thymus
DNA
DMEM with 5% FCS and
increase in fluorescence versus
The increase
in
fluorescence
the
represents
the fluorescence of the sample minus the fluorescence of a control with
As shown in Figure 6, the fluorescence was found to
no calf thymus DNA.
plateau
when
the
approximately 20.
(1979)
for
ratio
to
of DNA
dye
concentration
(w/w) exceeded
Similar behavior has been observed for by Brunk et al
the fluorescent DNA assay with DAPI dye.
In Figure 6, the
regressed lines through the data in the non-plateau regions have slopes
of 1.04 and 0.96,
respectively,
a good linear correlation
Brunk et al (1979).
on log-log coordinates.
over a wide dynamic range,
This indicates
as also
found by
For DNA concentrations below 2 pg/ml, the standard
deviation of the assay was 0.06 pg DNA/ml.
For a given DNA concentration in
the cuvettes,
the fluorescence was
found to increase with pH and decrease with the relative proportion of
DMEM to PBS.
The pH of all samples was adjusted using small aliquots
-
57
-
A
,ug/mL
0.08
*
2.0 Ag/mL
dye
dye
1000
Slope
=
0.96
100
A
A
A
A
10
Slope
0.1
0.01
I
I
I
I
I I I I I
I
I
I
f
0.1
I I I
=
tI
1.04
I
t
I
I
I
I I I I
10
CALF THYMUS DNA CONC. (gG/ML)
Increase in fluorescence
Figure 6.
vs. calf thy mus DNA concentration
-
58
-
100
as described
of dilute NaOH
above.
Minor corrections
then had to be
made for sample dilution and the change in the proportion of DMEM.
The
fluorescence
of a cell suspension,
and
subsequent to freezing
thawing, was found to only be a weak function of sonication time with a
The fluorescence of the calf thymus
maximum at approximately 2 minutes.
standards
was
of sonication or any of the
not effected by 2 minutes
other sample processing procedures.
The fluorescence
DNA
content
approximately
of
of medium with serum was unexpectedly high.
serum
was
subsequently
measured
and
found
The
be
to
the
The source of this DNA was not determined;
20 pg/ml.
serum was not contaminated with viable microorganisms.
The DNA content,
however, does correspond to a lysed cell concentration of approximately
107 cells/ml, a typical white blood cell count.
Thus, the DNA in serum
could have come from white blood cell lysis during blood centrifugation
or
processing.
It
could
psychrophilic microbes
also
have
come
from
contamination
with
during serum storage prior to sterilization,
as
observed by Shiigi and Mishell (1975).
Specific Fluorescence of FS-4 Cellular DNA
The specific fluorescence of the DNA from FS-4 cells was determined
Thirty identical
through the use of T-flask cultures.
cultures were
started in 75-cm 2 T-flasks containing 12.5 mls of medium and an initial
2
attached cell concentration of 2.2 x 103 cells/cm .
flasks
were
sacrificed
in
duplicate
-
59
At daily intervals,
and the concentration of attached
-
The growth curve is
cells was measured.
Figure 7.
shown in
The growth
curve was used, in part, to determine the growth rate of the cells taken
for the DNA assay calibration.
for
cells
obtain
To
the
DNA
assay
sacrificed at 60 hours after inoculation.
were
flasks
two
calibration,
The cells were in exponential
1
growth at a specific growth rate of 0.023 hr- .
The culture fluid was
removed through
discarded and the attached cells were washed with PBS,
trypsinization, centrifuged for 5 minutes at 150 x g, and resuspended in
One-third of
3 mls of medium containing 5% (v/v) FCS and antibiotics.
this standard cell suspension was removed and diluted 1:6.25 in the same
Both
medium.
the
normal
and
diluted
cell
samples
were
and
stored
processed as previously described for the DNA assay.
Figure 8
shows fluorescence versus cell concentration for the FS-4
As found by other researchers
cell samples.
(Brunk et al,
fluorescence increases linearly with cell concentration.
is high due to the DNA from the serum supplement.
30 hours,
and one can reasonably assume that TS
the
1979),
The intercept
For these cells, Td =
is
TG2 is 4
7 hours,
hours, and TM is 1.5 hours (Baserga, 1976; Darnell et al, 1986; Alberts
et al,
then
An average DNA content of 1.24 diploid equivalents
1983).
be
calculated
from
equation
3.
The
value
of
1.25
can
diploid
equivalents is obtained if the calculation is performed with equation 4,
and if
one assumes a G1 duration of 6 hours,
fibroblasts
(Defendi
and
Mason,
1963;
Baserga, 1976).
-
60
-
typical for human diploid
Macieira-Coelho
et
al,
1966;
U
U)
-J
-J
w
C)
10
10
i
i
60
i
120
i
i
180
240
TIME
I
300
(HRS)
Growth of FS-4
Figure
cells in stagnant T-flasks
-
61
-
360
40
38
36
34
32
30
4
2
6
LYSED CELL CONC.
Figure 8.
8
10
(10 5 CELLS/ML)
Specific fluorescence of FS-4 cells
-
62
-
There
is
difference between the results obtained with equa-
little
For the purposes of this paper, equation 3 will always be
tion 3 or 4.
The DNA assay calibration is thus 6.3 fluorescence units/(million
used.
FS-4 diploid equivalents/ml).
population is
Sa =
The average DNA content of an FS-4 cell
therefore estimated by
+
0.5 ( 218.04p
27.940
)
(Eq. 26)
where p is given in hr-1.
Effect of Cell Concentration in T-flasks
For FS-4 microcarrier cultures under mild agitation, the growth rate
was found to decrease with the microcarrier and cell concentration.
One
could not clearly distinguish, however, whether the observed effect was
due
to
high cell
or high microcarrier
concentrations
concentrations.
New experiments had to be designed so that the effects of microcarrier
concentration and cell concentration could be studied separately.
Experiments in
the
effects
of
T-flasks were performed to
cell
microcarrier concentration.
cm 2 and 25-cm 2 T-flasks.
growth
surface
separate
concentration
independently determine
from
the
effects
of
Various volumes of media were added to 75-
This procedure allows one to vary the ratio of
to medium
volume
(S/V),
or
stagnant environment free of microcarriers.
cell
concentration,
in a
To insure that the oxygen
level was at least 60% of saturation with air at the cell surface,
the
This depth was calculated from a
maximum medium depth used was 2.0 cm.
stagnant diffusion model with a specific oxygen uptake rate of 5 x 10-11
mmole/cell-hr
(Fleischaker,
1981,
-
1982)
63
-
and a maximum surface coverage
of
5 x
104
surface was
cm.
All
cell/cm 2
(Hu et
To
1985).
al,
that
insure
the
culture
completely wetted, the minimum medium depth used was 0.16
T-flasks
850 cells/cm 2 .
contained DMEM with 5% serum and were inoculated at
The cultures
250 hours.
were sacrificed after
Growth
was measured using triplicate flasks for each surface/volume ratio.
Selection, Use, and Characterization of Inert Microcarriers
Cell
strongly
growth in microcarrier and T-flask cultures was
affected
by
cell
Thus,
concentration.
to
found to be
investigate
the
effects of microcarrier concentration, one would ideally want to use an
"inert microcarrier".
An inert microcarrier would have
and density as a normal microcarrier,
the same size
but would be chemically inert and
incapable of supporting cell growth or attachment.
could be used to change the solids concentration,
Inert microcarriers
even during inocula-
tion, without affecting the chemical environment or the number of cells
inoculated per "active" microcarrier.
G-50
Sephadex
requirements
of an
beads
(Pharmacia)
were
inert microcarrier.
These beads
to
fulfill
have
the
negligible
Control experiments showed that they
charge and ion exchange capacity.
do not support cell growth or attachment.
between 90-106
found
The beads with dry diameters
microns have a size distribution,
to that of Cytodex 1 microcarriers.
upon hydration,
close
In subsequent paragraphs, the term
"inert microcarrier" will refer to this size fraction of Sephadex beads.
-
64
-
A
reticule was
microscopic
Cytodex 1
to
used
a
of
have a diameter of 178 + 23 micrometers;
Cytodex 1 microcarriers
have
size
the
of
diameter
both
Hydrated in DMEM with 5% serum,
and inert microcarriers.
microcarriers
determine
162
+
Direct
micrometers.
18
inert
microscopic counts were used to determine the number of microcarriers
per gram.
1;
there
There are 3.8 million microcarriers per gram of dry Cytodex
are
3.3
million
microcarriers
per
gram
of
dry
inert
microcarriers.
To determine
the density and specific volume of hydrated microcar-
riers,
microcarrier suspensions were vacuum filtered for 2 minutes
remove
unbound
The
medium.
filtered
The change in
graduated cylinder containing medium.
were used to calculate
space)
appears
is
then
is 1.03
the density
g/ml,
added
to
a
weight and volume
the specific volume and density.
Cytodex 1 microcarriers,
volume is
were
beads
to
For hydrated
the hydrated bead
10.2 ml/g,
and the gravity-settled bed volume (including void
18 ml/g.
In
the Pharmacia literature
(1981),
the bed volume
to have been accidently substituted for the bead volume,
and
thus the specific surface area, bead volume, and number per gram are all
in error by a factor of 1.76.
3440 cm2 /g, not 6000 cm2 /g.
For example, the specific surface area is
For the inert microcarriers, the hydrated
density is 1.03 g/ml, and the hydrated bead volume is 7.6 ml/g.
Inert microcarriers were used to independently determine the effect
of bead concentration in the microcarrier cultures.
In one experiment,
inert microcarriers were added to four identical vessels
-
65
-
at different
All four cultures had 1.5
concentrations: 0, 8.5, 18.5, and 28.5 g/l.
g/l Cytodex 1 microcarriers,
agitated at
35 RPM.
contained medium with 5% serum,
To determine how the results of this experiment
would vary with the level
of agitation,
was repeated at a stirring
it
the
inert microcarriers
speed of 150 RPM.
At the higher speed,
added to levels of
0, 5, 10, 15, 20, 25, and 30 g/l.
effect
and were
of adding inert microcarriers
were
Eventually, the
investigated for a number of
was
stirring speeds and fluid viscosities.
Viscosity and Density Measurements
The density of various medium solutions was measured at 37*C with a
Viscosities were measured at 37*C with a
balance and volumetric flasks.
concentric-cylinder
viscometer
LVT with UL adaptor,
(Model
Stoughton, MA) for shear rates between 7 sec-l and 74
surface
at the
rate
of the inner cylinder,
r,
Brookfield,
sec- 1 .
The shear
was calculated from the
equation (Lee, 1966)
r
where N
cylinder
is
=
41r N ro2
2(Eq.
r2 -r2
the rotation rate
(1.258
cm),
and ro
27)
(sec- 1 ), ri
is
is
the radius of the inner
the inner radius of the outer cylinder
(1.381 cm).
Figure
results
rate.
are
Data
shows
9
the
plotted as
is
of
results
the
viscosity measurements.
The
versus
shear
percent of maximum shear
shown for water as the calibration
stress
standard.
Data is
also shown for Dulbecco's Modification of Eagle's Medium (DMEM), fetal
-
66
-
30
25
_-
DMEM,
5%
FCS
50 g/L dextran
S--Fetal
20
calf
serum (FCS)
DMEM,
15
5%
*-DMEM
10
-+-
0
10
20
30
40
50
60
70
Water
80
SHEAR RATE (1/SEC)
Figure 9.
Shear stress vs. shear rate for various medium solutions
FCS
calf serum (FCS), DMEM with 5% (v/v) FCS, and DMEM with 5% (v/v) FCS and
50 g/L dextran of 78,500 average molecular weight.
various
the
as
solutions,
determined
by
the
The viscosities of
are
slopes,
regressed
tabulated in Table 1 along with the measured densities.
All solutions exhibited a constant viscosity except fetal calf serum
which
(FCS),
a
exhibited
slight
very
behavior.
pseudo-plastic
The
viscosity and density of DMEM were only scarcely greater than the values
Supplementation of DMEM with fetal calf
for pure water.
and density.
slightly increased the viscosity
with dextran greatly
density.
For
Further supplementation
dextran concentration,
a given
Methocel
the
raised
A15LV
Supplementation
increase.
viscosity
in
increased viscosity with only slight increases
supplementation with
a
increase but
a
higher molecular weight allowed for a similar density
greater
serum only
viscosity
by
of
medium
approximately
with
18%
1
with
g/l
no
significant change in density.
At
the beginning
and end of several
density of the culture fluid were measured.
cultures,
the viscosity
and
No significant changes in
culture fluid viscosity or density were observed.
Selection and Use of Thickening agent
The
mechanisms
investigated,
Such
of
cell
in part, with
experiments
are
in
damage
microcarrier
experiments on the effects
best performed with Newtonian
cultures
of viscosity.
solutions,
solutions with constant viscosity and no viscoelastic interactions.
-
68
-
were
i.e.,
TABLE 1. VISCOSITY AND DENSITY MEASUREMENTS
Solution
Density (g/ml)
Viscosity (g/cm-sec)
DMEM
1.003
0.0071
Fetal Calf Serum
1.015
0.0088
5% (v/v) FCS
1.004
0.0074
DMEM, 25% (v/v) FCS
1.006
0.0078
20 g/L Dextran, 78,500 MW
1.008
0.0104
35 g/L Dextran, 78,500 MW
1.013
0.0135
50 g/L Dextran, 78,500 MW
1.018
0.0185
60 g/L Dextran, 78,500 MW
1.022
0.0227
80 g/L Dextran, 39,000 MW
1.030
0.0275
1.069
0.0275
DMEM,
DMEM,
5% (v/v) FCS, with
180 g/L Dextran, 9,000 MW
-
69
-
Viscous
effects
independent
then be uniquely determined,
can
the
of
For Newtonian solutions, the viscosity is a
effects of viscoelasticity.
single physical constant that can be easily measured with a viscometer.
medium,
culture
could
and
significantly
or no toxic
little
a Newtonian fashion with
in
the viscosity
increase
Several thickening agents with very low molecular
effect on the cells.
weights
cell
in
soluble
completely
agent which was
conducted for a thickening
A search was therefore
were tested, including sucrose,
and
1,3-butanediol,
glycerol,
These substances are known to form Newtonian solutions
1,7-heptanediol.
At concentrations sufficiently high to give a
when dissolved in water.
2-fold or higher increase
in
viscosity,
all of these substances either
killed the cells or severely inhibited growth.
(A15-LV,
Methylcellulose
carboxymethylcellulose
Sigma Chemical
(LV grade,
were also investigated as thickening agents.
to
be
nontoxic,
essentially
completely clear solution.
the
but
did
Small,
of 10-100 microns, would
order
Midland,
Dow Chemical Co.,
not
Co.,
MI)
and sodium
St.
Louis,
MO)
Methylcellulose was found
dissolve
readily
clear particles,
gradually form
into
with diameters
in the
a
on
methylcel-
lulose-medium solutions even after filtering through 0.2 micron filters.
Sodium carboxymethylcellulose
gave similar problems with solubility,
and
was found to be toxic when positive growth surfaces were used, such as
Cytodex
1,
2,
and
boxymethycellulose
Nakamura,
1973,
3
microcarriers.
Both
methylcellulose
are known to be viscoelastic
1974)
(Hoyt,
and
car-
1985; Amari and
and frequently give solutions with pseudoplastic
-
70
-
(Nicodemo
rheology
relatively
al,
et
1974;
1985),
Dow,
although
viscosities
independent of shear rate can probably be obtained with the
lowest molecular weight methylcellulose (Dow, 1985).
The
search
finding
a
for
aqueous solutions.
promising candidates.
nontoxic.
nonionic
low-molecular-weight,
Newtonian rheology in
as
For
eventually directed toward
a thickening agent was
aqueous
of
which
exhibited
Dextrans were soon identified
are
generally
low-molecular-weight
dextrans,
Dextran polymers
solutions
polymer
are nonionic
Newtonian rheology can be expected, as will be subsequently shown.
(Sigma Chemical Co.,
Low-molecular-weight dextrans
St. Louis, MO)
were tested for their effects on cell growth with mild agitation.
The
dextran polymers were dissolved directly in DMEM to give entirely clear
solutions.
filter
were
Three
39,400,
sterilized
different
average
and 78,500
weights were
the DMEM-dextran solutions
Prior to use in cell cultures,
and
molecular
daltons
tested in
supplemented with
weights
were
(clinical grade).
order to determine
5% FCS
and antibiotics.
investigated:
9,000,
The different molecular
the lowest molecular weight
which was suitable as a thickening agent.
Figure 10 shows the effect of various dextran supplements on growth
Specific
in FS-4 microcarrier cultures at 35 RPM in the 125-ml vessels.
growth rate,
relative to a control culture with no dextran,
against dextran concentration.
is
plotted
Data is included for three different
-
71
-
A
78,500
A
39,000
*
MW
MW
9,000
MW
1.20
0.90
F-
0.60
0
0.30
0</)
0.00
I..J
Lu
-0.30
-0.60
40
DEXTRAN
80
120
CONCENTRATION
160
(G/L)
Chemical effects
Figure 10.
of dextran on cell growth
72 -
200
molecular weights:
and 9,000 daltons.
39,000,
78,500,
was collected under conditions of mild agitation.
in
dynamic damage
All of the data
There was no hydro-
as will be shown in
any of the cultures,
the Results
and Discussion section.
The data in Figure 10 illustrates the chemical effects of dextran on
For an average molecular weight of 78,500 daltons, dextran
cell growth.
g/l have
below 25
concentrations
effect on
no
concentration of 60 g/l reduces the growth rate by 12%.
to
a
If one wishes
3-fold, use
the viscosity by approximately
increase
while
cell growth,
of 78,500
MW
dextran will lead to a 12% reduction in growth rate, 39,000 MW will lead
to a 25% reduction,
78,500
was
MW
and 9,000 MW will lead to cell death.
moderate
within
nontoxic
acceptably
Dextran of
increases
in
This substance was therefore suitable as a thickening agent
viscosity.
as long as it exhibited Newtonian rheology.
Rheological Evaluation of Dextran Solutions
In
the measurements with
covered shear
the concentric-cylinder
rates between 7 and 74 sec-1,
molecular-weight
dextrans
to
found
were
viscometer,
which
aqueous solutions of low-
have
constant
viscosities.
Typical results were shown in Figure 9 for medium with 50 g/L dextran of
to
176,800,
solutions
and
for
for molecular weights up
general,
In
78,500 average molecular weight.
up
concentrations
to
280
of
aqueous
dextran
are known to have constant viscosities for shear rates up to
an over 1000 sec- 1 (Margaritas and Pace, 1985).
range
g/l,
shear
rates
observed
-
agitated
in
73
-
This is well beyond the
microcarrier
cultures.
Newtonian rheology can thus be expected as long as the dextran polymers
do not exhibit viscoelastic interactions with the turbulence.
Through macromolecular extension, many polymers exhibit viscoelastic
interactions
with
turbulent
the
bursting
viscoelastic
A
process.
interaction occurs when a polymer molecule has a relaxation time which
is near the duration time of a turbulent burst (Virk, 1975; Denn, 1980).
The relaxation time, A, of a polymer molecule can be estimated from the
results of Zimm (1956):
A
=
(Eq. 28)
0.42 Mw [rq] rs/ R T
the molecular weight of the polymer,
where Mw is
[r;]
the intrinsic
is
viscosity, ns is the solvent viscosity, R is the ideal gas constant, the
T is
the temperature.
can
be
estimated
The minimum duration of a turbulent burst,
from
the
time
Kolmogorov
for
scale
the
9
mini
highest
frequency eddies in the viscous dissipation regime:
6
min
=
(v/E
0.01 and 0.001 seconds.
be
no
typical values of
cell culture vessels,
In animal
which is
(Eq. 29)
)1/2
If
a polymer molecule has
0
min range between
a relaxation
orders of magnitude less than these values of 0min,
viscoelastic
interaction
between
the
polymer
time
there will
molecules
and
turbulence.
To determine whether such viscoelastic
dextran
solutions,
the
characteristic
-
74
-
interactions
relaxation
time
could occur in
of
72,000
MW
water at
dextran in
The
1979).
al,
(Wolf et
calculated from published viscosity data
20*C was
1982)
through standard methods (Rodriquez,
nsp
=
viscosity,
intrinsic
[q],
calculated
was
from the equation:
[1] + k'[1]2 x
(Eq. 30)
x
where x
3
The intrinsic viscosity was thus determined to be 24 cm /g.
viscosity.
This
corresponds
over
seconds,
to
three
relaxation
characteristic
a
orders
magnitude
of
should
interactions
not
between
occur
than
smaller
the
x
3
10-7
minimum
the
Thus, viscoelastic
turbulence
Other
of molecular weight near 78,500 daltons.
have noted that low-molecular-weight
of
time
turbulent burst durations in microcarrier reactors.
polymers
the specific
g/cm3 and 77sp is
in
the polymer concentration
is
dextran
and
researchers
dextrans generally do not exhibit
viscoelastic behavior in most turbulent flows (Hoyt, 1985).
For a typical commercial mixture of dextran polymers with an average
molecular weight near 78,500, such as Dextran T70 (Pharmacia), the ratio
of weight-average
Mw to number-average Mw is
approximately
1.6.
This
degree of polydispersity should not lead to non-Newtonian behavior.
In
78,500
of
dextran polymers
summary,
exhibit all of the desired properties
solubility,
polymers
relative
were
therefore
used
in
the
viscosity.
-
of a thickening agent:
and
nontoxicity,
75
-
molecular weight
average
Newtonian
experiments
rheology.
on
the
complete
These
effects
of
Cell Damage from Direct Sparging
of
effect
The
sparging
Two experimental
microcarrier cultures.
was
growth
cell
on
examined
FS-4
for
cultures were grown in
500-ml
Bellco spinner flasks (Model 1965-00500, Bellco Biotechnology, Vineland,
cell damage
from time-average
To
diameter of 10.2 cm.
flasks have an internal
The
NJ).
flow fields,
eliminate
in
the Teflon impeller
each
flask was cut to a diameter of 5.4 cm and a width of 2.7 cm.
A filter
placed
through a
stick
was
Vineland, NJ)
(Ace Glass,
porosity C
of
The filter sticks were
rubber cork stuck in the sidearm of each flask.
modified such that the solid tubular sections ran down the side of each
flask
then curved radially inward near
and
each
the bottom of
on
layed almost horizontally
regions
the bottom.
The fritted
this
flask;
allowed for free bubble rise without interference from the filter stick.
experimental
One
culture was sparged at a superficial
Foaming was essentially
cm/sec with a 90:10 air-CO2 mixture.
of 0.01
gas velocity
eliminated through the daily addition of 20-40 ppm Medical Emulsion AF
antifoam
(v/v) solution
and
was
ultraviolet radiation.
tifoam in
sparging.
filter
were
through
sterilized
6
hours
of
exposure
to
A second experimental culture was grown with an-
an identical vessel,
complete with filter
stick, but with no
A third experimental culture was grown with no antifoam,
stick,
impeller.
FCS,
The antifoam was added as a 1%
(Dow Corning, Midland, MI).
no
a 500-ml Corning vessel with a 7.8 cm
and no sparging in
All cultures contained 2.0 g/l microcarriers in DMEM with 5%
identically
inoculated
from
the
same
inoculum,
and
replenished with nutrients on the normal interval feeding basis.
-
76
-
were
Due to
the low cell concentrations, dissolved oxygen levels were essentially at
saturation with 90:10 air-CO 2 gas mixtures.
The stirring speeds were
set at the minimum levels to provide microcarrier suspension: 50 RPM in
the Bellco flasks and 35 RPM in
changes
in
the Corning flask.
Net cell growth,
were used to assess the effects
viable cell concentrations,
of sparging, antifoam addition, and filter stick presence.
-
77
or
-
RESULTS AND DISCUSSION
As mentioned in
the Introduction,
the objective of this thesis is
to
formulate a fundamental approach to the design, operation, and scale-up
of microcarrier bioreactors.
This objective was fulfilled by a series
of experiments on the following topics:
1)
hydrodynamic effects on growth of FS-4 cells with mild agitation,
2)
hydrodynamic effects on growth of FS-4 cells with high agitation,
3)
hydrodynamic phenomena in y-CHO cultures,
4)
mechanisms of hydrodynamic death in dilute cultures,
5)
mechanisms of hydrodynamic death in concentrated cultures,
6)
cell damage from direct sparging
The topics listed above constitute the first six chapters of the Results
and Discussion section.
the
seventh chapter
The results from these chapters
are used in
a quantitative approach to bioreactor
to develop
design and optimization.
-
78
-
CHAPTER 1.
lA.
HYDRODYNAMIC EFFECTS ON FS-4 CELLS WITH MILD AGITATION
Effect of Fluid Viscosity with Mild Agitation
The
hydrodynamic
investigated under
effects
on
growth
of
FS-4
cells
conditions of mild agitation.
were
first
This established a
baseline for the subsequent analysis for conditions of high agitation.
Hydrodynamic effects on growth with mild agitation were investigated
with experiments on the effect of fluid viscosity.
growth with and without a 20 g/l
mild agitation in
Figure 11 shows cell
dextran supplement
the 500-ml vessels.
(78,500 MW)
under
The cultures were agitated with
5.3 cm impellers at 60 RPM, slightly above the minimum speed of 45 RPM
for complete microcarrier
g/l microcarriers,
dilute.
suspension.
or 0.002 volume fraction solids,
the
microcarriers
concentrations
dextran.
and were thus very
The cells exhibited the normal growth observed in FS-4 microca-
rrier cultures with mild agitation.
to
The cultures contained only 0.2
were
and
Over 95% of the cells were attached
excluded
essentially
Supplementation with
trypan
blue.
with
identical
20
g/l
The
or
attached
without
dextran did not
cell
20
lead to
g/l
toxic
chemical effects or mass transfer limitations.
At 60 RPM,
input of approximately 10 cm2 /sec3,
or an average power
there appeared to be no cell death from time-average shear fields
microcarrier-eddy
interactions
was
If cell death from microcarrier-eddy
interactions.
occurring,
or
an
increase
in
viscosity
should
have
increased the minimum eddy size, reduced the death rate, and increased
-
79
-
+
20 g/L
Dextran
No
Dextran
106
0
10
10
30
60
90
120
150
180
TIME (HRS)
Effect of 20 g/L dextran
Figure 11.
(78,500 MW) on growth with mild agitation
-
80
-
If cell death from time-average
cell concentrations.
the viable
flow
fields was occurring, an increase in viscosity should have increased the
maximum shear stress,
increased the death rate,
cell concentrations.
Because an increase
no
on the viable
effect
significant cell
cell
in
concentrations,
death from hydrodynamic
and reduced the viable
viscosity had essentially
there
forces
appeared
to be no
in these dilute
cul-
tures.
Growth at Different Microcarrier Concentrations
1B.
With mild agitation, microcarrier-eddy interactions and time-average
for the dilute
data
lead to
fields apparently did not
shear
significant cell death.
cultures, however, did not
The
indicate whether cell
death can occur through hydrodynamic interactions between microcarriers.
even
though
the
be referred to as collisions,
will be subsequently
interactions
These
interactions
primarily
may
involve
fluid
the
flow
between microcarriers which come in close but not actual contact.
To
determine
whether
death
cell
occurs
through
microcarrier
collisions with mild agitation, the hydrodynamic effects of microcarrier
Cultures of FS-4 cells were grown over
concentration were investigated.
a range
of microcarrier concentrations between 0.05
and 15 g/l.
The
cultures were fed according to the interval feeding schedules and were
inoculated with 17
minimum
inoculation
to
microcarrier,
per
cells
requirement
identified by Hu et al
nutrients,
23
6
of
cells
per
clearly
above
microcarrier,
the
as
Through provision of excess defined
(1985).
and through prevention of the build-up of toxic metabolites,
-
81
-
it was
that
hoped
could be
the physical effects of microcarrier concentration
investigated without being strongly influenced by differences
The experiments were first performed with
environments.
in chemical
by
medium supplemented
To
(v/v) serum.
5%
if
determine
there were
nutrient limitations associated with the 5% serum level, the experiments
were repeated with a serum level of 10%.
Figure 12 shows the growth of FS-4 cells at different microcarrier
was
microcarriers
grown
a
in
35
at
5% serum
concentrations with
RPM.
500-mi
g/l
culture with 0.05
The
to
vessel
Corning
an
provide
All other cultures were grown in 125-ml
adequate volume for sampling.
Corning vessels.
At all microcarrier concentrations, at least a four-fold increase in
was
concentration
cell
for microcarrier
performance
This
observed.
good
1985).
(Hu et al,
of FS-4 cells
cultures
relatively
represents
Nonetheless, the cultures with high cell or microcarrier concentrations
showed very
long
multiplication
concentration).
lag
ratios
phases,
decreased
(final
cell
13
the
cultures.
and
decreased
initial
cell
The cells in the high density cultures also appeared to
shows
maximum
the low density cultures.
the maximum surface coverage
microcarrier concentration.
that
over
concentration
be much more "spread out" than the cells in
Figure
rates,
growth
surface
These normalized
coverage
was
(cells/cm 2 ) at each
results
lower
for
clearly indicate
the
high
density
However, the detrimental effect of increased microcarrier or
-
82
-
10
5% FCS
.
15 g/I
-&-A~ 5 g/
6
10
-Ar
+
.-----
-
+--O
10
--
1.5 g/I
0.5 g/l
5
0.1 5 g/I
0-
0.05 g/1
10
10
4
3
0
50
150
100
200
250
300
TIME, (HRS)
Growth at various microcarrier
Figure 12.
concentrations with mild agitation
-
83
-
350
6
10
10% FCS
0
Avg. slope = -0.16
0
wU
10
5% FCS
w0
0
w
10
4
I I I I IIIII
I
-2
10
11111111
i
i
j
! ! ! ! 1
i
!
!
! t 1 111
-1
10
10
MICROCARRIER CONCENTRATION (G/L)
Maximum surface coverage
Figure 1 3.
vs. microcarrier concentration
-
84
-
2
cell
concentrations
dependency
was
very
on microcarrier
weak
and
had
an
average
exponential
of
only
-0.16.
A
concentration
two-fold
increase in microcarrier concentration resulted in only a 10% reduction
in
maximum surface coverage.
present
with
approximately
both
5
and
Nonetheless,
10%
serum.
the weak effect was clearly
Furthermore,
the same at both serum levels.
the
slope
is
Even though the cells in
10% FCS generally grew to 50% higher concentrations than the cells in 5%
FCS,
the
additional
did
serum
not
eliminate
or
even
reduce
the
detrimental effect of higher microcarrier or cell concentrations.
Figure 14
microcarrier
maximum
at
shows
the average
concentration.
approximately
specific growth rate
With 5% FCS,
0.2
g/l
a
at
maximum
growth
microcarriers,
concentration of 1.5 x 104 cells/ml.
reaches
the
approximately
With 10%
0.15
concentration of 1.1 x 104 cells/ml.
g/l,
as a function of
or
FCS,
or
rate reaches
an
the
an
initial
a
cell
growth rate
initial
cell
The existence of these maxima
indicates that the growth rate was influenced by at least two competing
factors.
As the microcarrier or cell concentrations were increased, at
least one factor exerted a positive influence on the growth rate while
at least one other factor exerted a negative influence.
It
is
well-documented
promoting factors
on
many
animal
cells
secrete
growth-
As microcarrier or cell concentra-
(Butler, 1986).
tions are increased,
influence
that
cell-derived growth factors could exert a positive
the growth
It
rate.
is also well-documented that many
animal cells secrete growth-inhibiting factors (Stoker and Piggott,
-
85
-
10
1LU
0
10% FCS
0
-2
10
0
5% FCS
0
C,,
w
10
-3
II
I
I
I I
I I I I I IIIII
till,,
I I I
-1
I
I
I
10
I
I. I
1
MICROCARRIER CONCENTRATION (G/L)
Average specific growth
Figure 14.
rate vs. microcarrier concentration
-
86 -
2
1974; McMahon et al, 1982; Bohmer et al, 1985; Hsu and Wang, 1986).
or
microcarrier
cell
concentrations
could exert a negative
inhibitors
increased,
are
cell-derived
on the growth
influence
As
rate.
The
Figure 14 could result from competition between cell-derived
maxima in
growth promotors and inhibitors.
Cell damage from microcarrier collisions could also exert a negative
influence on the observed growth rates.
or net
observed
growth
which represent
rates,
growth and
death.
damage
concentrated microcarrier
in
As will be
shown in
14 actually presents
Figure
the
the difference
section
cultures,
a
between
on hydrodynamic
collision
mechanism
should decrease the observed growth rate in direct proportion to the
however,
For the high-density cultures,
microcarrier concentration.
a
two-fold increase in microcarrier concentration resulted in less than a
25%
reduction
clearly
did
in
not
concentration.
observed
decrease
This is
growth
rate.
direct
in
the first
The
observed
proportion
indication
to
the
growth
rates
microcarrier
that the slower growth in
the high density cultures was not due to microcarrier collisions.
1C.
Growth in Stagnant T-flasks
To further investigate whether cell damage from collisions occurred
in
the
microcarrier
cultures
at
cultures was compared to growth in
the
growth curve
RPM, growth
35
stagnant T-flasks.
grown in
for FS-4 cells
in
the
microcarrier
Figure 15 shows
stagnant T-flasks.
The data
show the concentration of attached cells and was previously presented in
Figure 7.
The cells exhibited a period of rapid exponential growth
-
87
-
10
U
Cl)
-J
-J
ul
C)
10
10
3
I
60
120
I
180
I
I
240
I
I
300
TIME (HRS)
Figure 15.
Growth of FS-4
cells in stagnant T-flasks
-
88
-
I
360
followed by a period of constantly-decreasing growth rate. In comparison
to
the
microcarrier
cultures,
the
T-flask
cultures
showed
initial growth rate but lower subsequent growth rate.
the T-flasks may have been accelerated by the
derived growth promotors at the cell surface.
a higher
Initial growth in
local build-up
of cell-
Subsequent growth may
have been inhibited by the build-up of growth inhibitors.
the T-flask cultures had an average
Over the entire growth period,
growth rate of 0.0085 hr-1.
For an FS-4 microcarrier culture at 35 RPM
with the same ratio of growth surface area to medium volume (6.0 cm-1),
one would expect an average growth rate of 0.009 hr- 1 .
in
mildly-agitated
average,
rate
in
mixing,
as
cells
cultures grow just as
microcarrier
Although the
in stagnant T-flasks.
Thus, FS-4 cells
on the
quickly,
average
growth
T-flasks may have been somewhat affected by the lack of
the
it appears
that
or no hydrodynamic
little
reduction of
cell
growth occurred through microcarrier collisions at 35 RPM.
ID.
Effect of Cell Concentration on Growth in T-flasks
If
cultures
decreased
the
was
not
due
growth
to
rate
of
collisions,
the
but
high-density
was
rather
microcarrier
due
to
growth
inhibitors or other chemical effects, a similar trend should be observed
for
cultures
grown in T-flasks.
The
growth rate
in T-flasks
should
decrease with increased surface/volume ratios, or cell concentrations.
Figure
16
shows
the
effect
of
surface/volume
ratio,
or
cell
concentration, on the average growth rate in stagnant T-flask cultures.
-
89
-
0.020
wr
H
0
Avg. slope = -0.40
0.015
0
0
a
wf
T-Flasks, 5% FCS
0.010
i
I
1
0
1
GROWTH SURFACE AREA/MEDIA VOLUME, (CMl\)
Effect of cell density
Figure 16.
on growth in stagnant T-flasks
-
90
-
10
As
fact,
the average
same
as
that
surface/volume
cell
lower
a
at
occurs
ratio
approximately
is
in
decrease
the
cultures,
T-flasks
for
However,
ratio.
growth
In
the
cultures.
microcarrier
high-density
the
for
observed
in surface/volume
dependency of -0.40
exponential
average
the
cultures,
microcarrier
increase
decreases with an
rate
growth
the
with
observed
previously
rate
than
concentration
with
for
This difference may be due to inhibitor build-up
microcarrier cultures.
at the cell surface in stagnant T-flasks.
Although no conclusive evidence has been shown, it appears that the
decreased performance of the high density microcarrier cultures may have
experiments
microcarrier
chemical
However, the results from the
cell damage from microcarrier collisions.
inert
or other
There was no indication of significant
of cell concentration.
effects
inhibitors
growth
to
in part,
least
at
due,
been
further
will
indicate
whether
microcarrier collisions had any effect.
lE.
Effect of Inert Microcarriers with Mild Agitation
To
investigate
from the effects
at various
cultures
proximately
of cell concentration,
levels
were
the effects of microcarrier concentration separate
microcarrier
to
agitated
7 cm2 /sec
3
at
, and
35
inert microcarriers
cultures
or
RPM,
contained
in
average
1.5
125-ml
power
were added
vessels.
inputs
g/l microcarriers
of
All
ap-
with 5%
(v/v) serum.
Figure 17 shows the attached, or viable, cell concentrations for the
-
91
-
106
Symbol
C. (g/l)
A
0
A
8.5
o
18.5
*
28.5
5% FCS
1.5 g/I Cytodex 1
35 rpm
100
50
150
TIME, (HRS)
Effect of inert microcarriers
Figure 17.
on growth with mild agitation
-
92
-
200
cultures with
growth was nearly identical in all of the cultures.
Cell
Ci.
inert microcarrier concentrations,
different
If cell death from
microcarrier collisions was occurring, an increase in inert microcarrier
concentration
should have
the death rate,
increased
increased the collision frequency,
cell concentrations.
and reduced the viable
However,
the viable cell concentrations were clearly not effected from increases
in
even up to 28 g/l.
the inert microcarrier concentration
microcarrier
from
cultures
at
35
RPM.
therefore
was
collisions
For the
not
Cell death
significant
the
in
cultures grown with high microcarrier
concentrations at 35 RPM, the decreases in surface coverage (Figure 13)
and observed
growth rate
were
(Figure 14)
due to the effects
of cell
concentration and not microcarrier concentration.
Cell Growth with Mild Agitation
lF.
With mild agitation,
increase
also
not
in
viscosity or inert microcarrier concentration.
affected by
small
to
culture
volume,
the
in
increases
previously observed by Hu (1983).
area
cells was not affected by an
growth of FS-4
the
Growth was
level of agitation,
as
For a given ratio of growth surface
in
cells
mildly
agitated
microcarrier
cultures grew just as quickly, on the average, as cells in stagnant Tflasks.
All of this evidence
indicates that little
or no hydrodynamic
death occurs in FS-4 microcarrier cultures with mild agitation.
In general, if cell growth or death was influenced from any type of
hydrodynamic mechanism,
in
net cell growth should be affected by a change
a fundamental hydrodynanic variable,
-
93
-
such as agitation power,
fluid
viscosity, or microcarrier concentration.
Because changes
in these
three variables had no effect on net cell growth with mild agitation, it
appears that cell growth and death were not significantly influenced by
hydrodynamic
forces with mild agitation.
This conclusion is
in line
with the published results which show that growth of attached cells is
not affected by mild shear stresses (Dewey et al, 1981; Sprague et al,
1987).
This conclusion is also in line with the results of Dodge and Hu
(1986),
which show that growth of freely-suspended
the agitation.
affected by moderate increases in
-
94
-
animal cells is
not
CHAPTER 2.
2A.
HYDRODYNAMIC EFFECTS ON FS-4 CELLS WITH HIGH AGITATION
Growth Reduction and Cell Removal under High Agitation
microcarrier
cultures.
hydrodynamic
forces.
or no hydrodynamic damage in
there was little
With mild agitation,
Cell
These
growth
was
not
apparently
conclusions
provide
a
affected by
baseline
for
the
analysis of cell growth with high agitation.
Numerous
were performed
experiments
to
high agitation on cell growth and death.
cell
concentrations
for
FS-4
cultures
at
microcarrriers
The data was determined at
An actual
at 60 RPM.
35 RPM and was slightly decreased
reduction in
indicates
on
grown
Net growth of attached cells was
each speed from duplicate cultures.
at
of
Figure 18 shows the attached
different stirring speeds in 125-ml vessels.
highest
the effects
investigate
attached cell concentration was observed at 150 RPM;
this
from
the
there
microcarriers.
was
hydrodynamic
In general, as
of
removal
the
cells
increased, the
the stirring speed was
cells were either removed from the microcarriers
and/or inhibited from
growing at their maximum rate.
Because
FS-4 cells are completely anchorage-dependent,
any cells
in
suspension must have come either through incomplete attachment during
inoculation,
to
subsequent
or through cell removal from the microcarriers
attachment.
Figure
19
the removal
shows
microcarriers at different stirring speeds.
from measured concentrations
of whole
cells
The results were calculated
of whole cells in
suspension.
No correc-
tion was made for incomplete attachment of the inoculum; such a
-
95
-
from the
+
35
rpm
60
-A-
rpm
--- A--- 150
rpm
10
10
6
10
40
120
80
160
200
240
TIME (HRS)
Attached cell concentrations
Figure 18.
at different stirring speeds
-
96
-
A
35
rpm ..
60
-- +--
rpm
150
rpm
12
-e0
,---------0'
10
,0'
/
40
120
80
160
200
TIME (HRS)
Removal of whole
Figure 19.
cells from microcarriers
-
97
-
240
Cell fragments were observed in the
correction would have been minor.
However, these fragments
from the cultures at 60 and 150 RPM.
samples
could not be accurately counted and were not included in the whole-cell
counts.
Figure 19 shows that removal of whole cells from the microcarriers
at all
occurred
stirring speeds,
and
throughout the
duration of
all
At 35 RPM, the whole cells removed generally represented less
cultures.
than 5% of the total observable cells (whole cells on microcarriers and
in suspension).
cells
At 60 RPM, cell removal increased slightly; the whole
observable
removed generally represented about 9% of the total
cells.
150 RPM,
At
greatly increased;
cell removal
cells
the whole
removed eventually represented nearly 60% of the total observable cells.
The
cells
whole
disintegrate
suspension were
counts below
of the cells removed.
cell fragments
fragments
suspension,
1-2
over a period between
suspension cell
all
in
were
days.
to
generally
lyse
and
This lysis reduced the
the values which would fully account
for
The lysis also resulted in the release of
was unclear,
It
into suspension.
generated
found
solely
through
lysis
however,
of
whether the
whole
cells
in
or whether the fragments were also generated through lysis
of attached cells.
Whole animal cells
shape,
due
in
suspension will generally assume a spherical
to the high surface
energy of the cell membrane
-
98
-
in
aqueous
To maintain a flattened morphology with a high
solutions (Evans, 1983).
membrane surface area, cells must generally exert mechanical forces with
Upon removal from the growth surface, most cells
their cytoskeleton.
will
develop
mechanical
cells exposed
Animal
become spherical.
stiffness
and may have
to
shear, however, can
a non-spherical
shape
for
several hours after removal from the growth surface (Sato et al, 1987).
of
absence
the
in
Nonetheless,
fixing
animal
dead
agents,
cells
generally do not remain attached and flattened on a growth surface in an
agitated environment.
At
all
stirring speeds,
cells attached
the
to
the microcarriers
exhibited flattened morphologies and did not uptake trypan blue.
in
Thus,
terms of the ability to exclude trypan blue and remain attached with
a flattened morphology,
the cells on the microcarriers
always appeared
to be viable.
In
contrast,
the
cells
suspension
in
always
appeared
to
be
nonviable. Generally over 90% took up observable amounts of trypan blue
stain.
Most
suspension
of
cells
them
over
lysed
had extensive
a
surface
period
trypan blue,
In terms
the cells in
that the cells
in
1-2
days.
The
irregularities and roughness.
They did not attach and grow upon inoculation
T-flask cultures.
between
into new microcarrier or
the ability to reproduce and exclude
of
suspension were always nonviable.
It appears
suspension were essentially killed upon removal from
the microcarriers.
-
99
-
Random Cell Removal Through Normal Forces
2B.
The removal of cells from the microcarriers increased with the level
of
agitation and
been
have
of
action
the
to
due
this removal was selective for mitotic cells,
If
hydrodynamic forces.
to
appeared
thus
which tend to be more rounded, the specific rates of removal should have
increased with mitotic index.
To investigate whether cell removal was
selective for mitotic cells, the rates of whole cell removal presented
in Figure 19 were analyzed on an interval basis.
For the
culture
concentrations
cell
presented
in
insignificant hydrodynamic death.
interval
time
to
t1
t2
can
The attached
the agitation was mild.
35 RPM,
at
18
Figure
The mitotic
thus
be
cell growth with
reflect
index,
determined
IM,
from
during
the
each
equation
presented in Johnson (1961):
IM=
TM y
1n 2
where TM is
the
ti
and
and C1
t2 ,
(Eq. 31)
TM ln(C 2 /C 1 )
(t2 - ti) ln 2
the duration of mitosis,
interval,
times
-
and C2
are
yu is
the specific growth rate in
the attached cell concentrations
at
can
be
The
respectively.
duration
of
mitosis
reasonably estimated as 1.5 hours (Alberts et al, 1983).
In
the culture at 35 RPM,
there was a small but measurable removal
For each time interval,
of cells from the microcarriers.
-
100
-
the specific
can be estimated from the equation:
rate of whole cell removal, Jw
Jw
W2
=
(t2 -
-
32)
(Eq.
W1
ti) (C2 + Cl)/2
where Wi and W 2 are the suspended whole cell concentrations at times ti
and t2 , respectively, and Cl and C2 are the attached cell concentrations
at times ti and t2 , respectively.
For
culture at
the
35 RPM, Figure 20
the
shows
whole cell removal versus the estimated mitotic index.
was
selective
for
mitotic
cells,
the
increase linearly with mitotic index.
scatter with a linear
appears
cells.
culture
that
cell
removal was
rate
should
the data exhibits random
However,
random
If cell removal
removal
specific
correlation coefficient
specific rate of
of only 0.16.
and not
Thus, it
for mitotic
selective
The same conclusion can be drawn from a similar analysis for the
at
60 RPM,
introduces
although the minor hydrodynamic damage
some error in the calculation of the mitotic index from equation 31.
to indicate
These results are not the first
hydrodynamic forces in microcarrier cultures.
on DEAE-dextran microcarriers,
random cell removal by
When CHO cells are grown
cell removal from excessive agitation is
apparently random unless the cells are pretreated with colcemid
al, 1980).
These results are
surprising if
one believes
(Ng
et
cell removal
occurs primarily through shear stresses. In response to a shear field at
the
growth
surface,
distracting torque
a rounded mitotic
cell will
experience
than a flattened interphase cell.
a higher
Furthermore,
rounded mitotic cell will probably have fewer attachment sites and a
-
101
-
a
2.00
I
1.50
0
12
1.00
Lu
Hr
0.50
0.00
-0.50
-1.00
-
0.00
0.02
0.01
0.03
MITOTIC INDEX
ESTIMATED
Specific rate of whole cell
removal vs. estimated mitotic index
Figure 20.
-
102
-
0.04
weaker
attachment
cell.
If cell
to
growth
the
removal
occurs
surface
through the
in mitotis should be more
rounded cells
interphase
than a flattened
action of shear
susceptible
to
stresses,
removal
than
flattened cells in interphase.
However,
also from normal forces.
In microcarrier cultures,
in the
generated by pressure fluctuations
normal forces can be
In
turbulent flow fields.
response to a pressure fluctuation near a microrcarrier surface,
may be
but
cell removal can occur not only from shear stresses,
subjected to a distractive normal force.
a cell
Because the pressure
fluctuation will occur on the length scale of a turbulent eddy, which is
much larger than a cell, the magnitude of the distractive force will be
roughly proportional to cross-sectional
surface.
area of the cell on the growth
If the cell has a constant number of attachment sites
per
also
be
area,
cross-sectional
the
total
attachment
proportional to the cross-sectional area.
force
will
Overall, both the attachment
and distractive forces will be proportional to cross-sectional area of
the cell.
The cross-sectional area, or shape,
cancel out as a factor.
rounded up
removal
cell
than
a
If
in mitosis
flattened
of the cell will then
cell removal occurs through normal forces,
should roughly be no more
cell
in
interphase.
For
susceptible
a
to
microcarrier
cultures, the observed lack of selectivity for removal of mitotic cells
may indicate that cell removal occurs primarily through normal forces.
-
103
-
2C.
DNA Release Under High Agitation
When FS-4 cultures are exposed
the microcarriers.
cell
the
to
of cells from
growth along with random and lethal removal
reduction in
part,
to high agitation, there is a net
in
The net reductions
forces.
from hydrodynamic
death and removal
at least in
growth are due,
The
question remains, however, whether this was the sole effect of agitation
on net cell
growth, or whether growth inhibition occurred along with
lethal cell removal.
account
of
the
To answer this question, one needs a very accurate
number
of cells
killed
and
removed by
hydrodynamic
This was achieved by monitoring the DNA
forces, both whole and lysed.
release into suspension from a high-density microcarrier culture.
To investigate the release of DNA into the culture fluid under high
agitation,
The cultures were operated at 45 RPM to
vessels with 7.8 cm impellers.
eliminate
microcarrier
agglomeration.
When
nearly
microcarriers were pooled, concentrated to 15 g/l,
two identical 125-ml vessels.
two 500-mi
in
FS-4 cells were grown on 5 g/l microcarriers
the
confluent,
and transferred to
One of these 15 g/l cultures was agitated
at 35 RPM while the other was agitated at 150 RPM.
Figure 21 shows the growth of the cells in
the cultures with 5 g/l
microcarriers.
The data show the concentration of cells attached to the
microcarriers;
it
conditions
of
represents
typical
Figure
mild agitation.
growth
21
for
also
FS-4
shows
cells
the
under
subsequent
performance of the nearly-confluent cultures with 15 g/l microcarriers.
The nearly-confluent culture at 35 RPM showed minor growth with a 25%
-
104
-
-
5 g/L
45 rpm
15
35
A
g/L --rpm
- 15
g/L
150 rpm
10
A
A
\A
10
0~
10
60
180
120
240
300
360
TIME (HRS)
Growth followed by agitation
Figure 21.
at different speeds after concentration
-
105
-
at
The nearly-confluent culture
attached cell concentration.
in
increase
a 15%
150 RPM exhibited
decrease
in attached cell concentration.
Cell death and removal clearly occurred in the nearly-confluent culture
at 150 RPM.
into suspension from
Figure 22 shows the cumulative release of DNA
The data are plotted in terms
culture agitated at 150 RPM.
the 15 g/l
of FS-4 diploid equivalents and were calculated relative to the control
culture at 35 RPM.
The error bars represent the combined uncertainty in
both the DNA measurements and in the correction for the control culture,
as more thoroughly described in Appendix 1.
there was
extensive
In the culture at
suspension.
from both the lysed and whole cells in
150 RPM,
The data include the DNA
release of DNA into
the culture
fluid.
This provides further evidence of significant cell death and removal.
2D.
Growth and Death Under High Agitation
In
overagitated
an
occurring
if
increasing.
rate q,
culture,
microcarrier
the total number of cells,
cell
growth
must
both attached and removed,
be
is
If cell death and removal are occurring at a specific death
the DNA concentration,
D,
in
the culture fluid should increase
according to the relation
dD
dD
=
Sr q C
(Eq. 33)
dt
where C is
the cell concentration and Sr is
the cells removed.
The DNA concentration,
-
106
-
the average DNA content of
D, includes the DNA for both
1.80
1.50
1.20
0.90
0.60
0.30
0.00
40
20
TIME SINCE TRANSFER
60
(HRS)
Cumulative release of DNA into
Figure 22.
suspension for 15 g/L culture at 150 RPM
-
107
-
80
the lysed and whole cells in
there
the
is
random cell removal,
average
DNA
average
DNA
content
is
content
content
given
the
as measured by our assay.
If
such as for FS-4 cells on microcarriers,
of the
of
by
suspension,
cells
cell population,
equation 26
as
Sr,
removed,
Sa.
presented
is
equal
to
the
average
DNA
Materials
and
This
in
the
Methods section.
In
FS-4 cultures with high agitation,
and removal.
there is
extensive cell death
The specific growth rate will then be strongly dependent
Secondary growth, as referred to
on whether secondary growth can occur.
in this thesis, represents cell growth over areas from which other cells
previously
were
removed
through
hydrodynamic
forces.
In
a
manner
analogous to the stimulation of growth through direct mechanical removal
of
cells,
as
in Alberts
described
might
culture
contact-inhibited
through hydrodynamic removal.
at
high
agitation
may
be
et
al
(1983),
stimulated
if
cell
areas
growth
are
in a
opened
up
If secondary growth can occur, a culture
actually
grow
faster
than
a
culture
at
low
agitation which is more confluent and contact-inhibited.
To investigate the nature of cell growth in
the 15 g/l cultures
at
35 and 150 RPM, the DNA release data were compared to the predictions of
three mechanistic models.
both cultures were growing at the same rate at any given time
cells
in
since
inoculation.
agitation,
model,
For the first model, it was assumed that the
nor
Cell
stimulated by
which represents
was
growth
cell
neither
removal.
inhibited
According
by excessive
to
the
growth and death with no secondary growth,
-
108
-
first
the
specific
growth rate,
p, in
each time interval was calculated from the
equation:
ln(C2, 3 5 /G1 ,3 5 )
(Eq. 34)
(t2 - ti)
where C 1 ,3 5 and C 2 ,3 5 are the attached cell concentrations at 35 RPM for
The apparent specific death rate, q, at
times ti and t2 , respectively.
150 RPM was then calculated from the equation:
ln(C 2 ,1 50 /C1 ,150)
(t
where p is
cell
-
2
for
the
35)
t1 )
and C1 , 1 5 0 and C2 , 1 5 0 are the attached
given by equation 34,
concentrations
(Eq.
RPM
150
culture
at
times
t1
and
t2 ,
Assuming there was only cell death and removal with no
respectively.
growth inhibition or secondary growth at 150 RPM, one can calculate the
expected change in DNA concentration from the equations:
D 2 - Di
=
- Di
=
D2
Sa q
p - q
-
C
for C1 + C 2
(Eq. 36)
- C2
(Eq. 37)
for C1
Sa q C 1 ,1 5 0 (t2 -ti)
where y and q are given by equations 34 and 35,
respectively,
Sa is
the
average DNA content per cell and is given by equation 26, and Dl and D2
represent the DNA for both the lysed and whole cells in
suspension at
150 RPM, as measured by our assay, for times t1 and t2 , respectively.
For the second model, it was assumed that secondary growth occurred,
and that growth in the overagitated cultures was fully corrected for the
-
109
-
reduced contact inhibition due to cell removal.
had been removed,
For areas where cells
secondary growth was assumed to occur at the same rate
as the normal initial
growth, with all growth regulated through contact
inhibition.
effect
The
of
contact
inhibition
on
growth
incorporated with the following empirical equations which fit
was
the data
presented in Hu et al (1985) for FS-4 cells:
where
Z
P
=
ymax (100 - Z)/60
for Z > 40
(Eq. 38)
y
=
ymax
for Z < 40
(Eq. 39)
is
the
percent
confluence.
For
the
culture
with
15
g/l
microcarriers at 35 RPM, the best fit to equation 38 is given with pmax
0.024 hr-l and full confluence at 4.0 x 106 cells/ml.
For
the
secondary
second
model,
represents
growth
growth, the specific growth rate for the
agitation was calculated
average
which
percent
in
each time
interval
death
confluence was used along with the
and full confluence at 4 x 106 cells/ml.
rate,
expected change
with
culture with high
from equation 38.
0.024 hr-1
and
and
The
estimated pmax of
The specific death
in DNA concentration, were calculated from
equations 35-37.
For the third model,
it
was assumed the reduced net growth at high
agitation arose solely through growth inhibition and not cell death and
removal.
clearly not realistic in
Although this model is
light of the
data presented in this thesis, the predictions of the model are included
for the sake of comparison and completeness.
-
110
-
For the third model, the
DNA in the culture fluid should not increase at 150 RPM relative to the
control at 35 RPM.
Figure
23
shows
the
predictions
of
the
three mechanistic models
along with the measured cumulative release of DNA.
The predictions of
the two growth and death models scatter because the data was analyzed on
an
interval
basis and because the
which are somewhat imprecise
predictions
(±10%).
rely
on nuclei
counts
The measured DNA release clearly
does not match the expected release for growth inhibition without cell
death and removal,
measured
or for growth and death with secondary growth.
data does,
release
however,
match
the
expected release
The
for
growth and death without secondary growth.
To the degree that cell removal was random,
cells
on microcarriers,
cells
in
the
data in Figure
23
as indicated for FS-4
demonstrates
that
the
the 150 RPM culture were essentially growing at the same rate
as the cells
different
in
the 35 RPM culture.
at 35 RPM, the
than the growth rate
would not have matched
If the growth rate at 150 RPM was
the expectation
for
amount of DNA release
growth
and death without
secondary growth.
Thus, the data strongly indicate that there is a situation of growth
and death with no secondary growth.
The reduction in net growth at 150
RPM appears to have been due entirely to cell death and removal, and not
growth
inhibition.
Even though there was extensive cell removal and
death, growth appears to have been unaffected by hydrodynamic forces.
-
111
-
3.50
- -90
3.00
2.50
+
2.00
-----
Measured
G
& D with
2nd growth
1.50
-- G & D without
2nd growth
1.00
--
--
A
- A
-
Growth inhib.
with no death
0.50
0.001
-0.50
I
20
TIME SINCE
40
I
60
80
TRANSFER (HRS)
Figure 23.
Measured DNA release vs. release
expected under three different scenarios
At both 35 and 150 RPM, the attached cells exhibited the normal ability
These findings
to reproduce, and thus appear to have been truly viable.
are
the
first
published
results
which
response of cells under high agitation.
document
a
growth
and
death
A growth and death response was
originally proposed in 1984 as published in Croughan et al (1987).
2E.
Hydrodynamic Regulation of Cell Growth
For FS-4 cultures exposed to mild agitation, growth is unaffected by
hydrodynamic forces.
shear forces
unaffected by hydrodynamic
growth is
Sprague
For endothelial cells exposed to mild fluid flow,
et
al,
1987).
cells under high
For FS-4
et al,
(Dewey
1981;
agitation, growth
appears to also be unaffected by hydrodynamic forces.
The apparent
not
surprising.
lack of growth regulation from hydrodynamic
The
decision
to
replicate
depends
to environmental
genetically-programmed response
on
factors.
forces
the
is
cell's
For normal
cells, such as FS-4, this genetic programming has come through years of
It primarily depends upon the cell's role in
evolution and adaptation.
the original animal donor.
exposed to
response
fluid flow in
If a particular cell type was not normally
vivo,
it
to hydrodynamic forces.
will have no genetically-programmed
Unless fluid flow can influence
the
normal growth regulation processes, the decision to replicate should not
depend on the hydrodynamic environment.
for most
animal
cells,
the
For FS-4 cells,
decision to replicate does
depend on the hydrodynamic environment,
to influence normal growth regulation.
-
113
-
and probably
not appear to
and fluid flow does not appear
Lack of Secondary Growth After Cell Removal
2F.
The data in Figure 23 indicates that there is no secondary growth in
To further investigate this
FS-4 cultures exposed to high agitation.
observation, FS-4 cultures were grown at different stirring speeds from
the point of inoculation.
stirring speeds
The cultures were held at their respective
as the culture under mild agitation reached confluence
and stopped growing.
If there was secondary growth in the overagitated
The
cultures, a clear and very strong trend should have been observed.
observed
the
growth rate at high agitation
observed
growth
rate
confluent
agitation became
at
low
agitation
stopped
and
should have increased relative
the
as
growing.
culture
The
have been constant throughout the duration of all cultures,
been
greatly
culture
reduced
as
the
shows
the
results
under
low
in
difference
or the observed specific death rate,
observed growth rates,
low
at
should not
but should
agitation
became
confluent.
Figure
24
of
experiment.
Attached
concentrations are shown throughout the duration of the experiment.
cell
The
cultures contained 3 g/l microcarriers and were grown in 100-ml spinner
vessels
as
with 3.8 cm impellers,
described in Groughan et al, 1987.
The straight lines through the data represent
which assumes that all
the best fit
to a model
cultures were growing at the same rate at
any
inoculation, and that the specific
death rates were
constant in each culture throughout all time periods.
The data follows
given time since
these assumptions, which represent growth and death with no secondary
growth.
Furthermore,
the data clearly indicates that the specific death
-
114
-
10
6
10
10
4
0
100
50
TIME (HRS)
Figure 24.
Attached cell concentrations for
cultures grown at different stirring speeds
-
115
-
150
2G.
Hydrodynamic Effects on Glucose Consumption
Growth of FS-4 cells appears to be neither inhibited nor enhanced by
hydrodynamic
forces.
therefore
not
metabolic
events
The metabolic
significantly
which
are
events
required
altered by
agitation.
not
associated
growth
for
growth
are
Nonetheless,
all
could be
strongly
influenced by agitation.
For the cultures with 15 g/l microcarriers
glucose
concentration profiles are
taken just before and just after
data
in each
time interval ti
shown in
given in Figure 25.
each medium exchange.
to t2 , one
Figure 21,
the
Samples were
Analyzing the
can calculate the
specific
glucose uptake rate, Rg, from the equation
(G2 - Gl) ln(C 2 /C1 )
(t2 - ti)(C 2 - Ci)
Rg
(Eq.
40)
where Gl and G 2 represent the glucose concentrations at times ti and t ,
2
respectively, and
C1
and C2
represent
the attached, or viable,
cell
concentration at times ti and t2 , respectively.
For each time interval,
rates.
RPM.
It
Table 2 gives the specific
glucose uptake
also gives the specific growth rates for the culture at 35
There is
glucose uptake
no correlation between specific growth rate and specific
rate
(correlation coefficient = 0.18).
In all of our
experiments with FS-4 cells, no correlation has ever been found between
specific growth rate and specific glucose uptake rate.
glucose uptake is not growth associated for FS-4 cells.
-
117
-
It appears that
rates did not significantly decrease when the culture at low agitation
This is further indication that there is no secondary
became confluent.
growth in
FS-4 microcarrier cultures exposed to high agitation.
lack of secondary growth may be due to the nature of
The apparent
cell removal by hydrodynamic forces.
adherent,
Cell
hydrodynamic
remnants
may
secondary growth.
For FS-4 cells, which are strongly
forces may not generally
leave
might
remain which
remove complete
the
area
cells.
unsuitable
for
The previous attachment and removal of a cell from a
given position may preclude future growth over that position.
There is
secondary growth and lack of growth
a clear
analogy between lack of
through
contact inhibition, wherein cells can grow over areas already
occupied by other cells.
If cells can not grow over areas previously occupied by other cells,
growth would not be stimulated as areas were opened up by hydrodynamic
cell removal.
The cultures with signficant cell removal would exhibit
growth regulation as
contained a
if they
greater number of
cells, as if they were more contact inhibited.
in
part,
for
the
similarity
This effect may account,
growth rates between cultures
in
attached
agitation and more confluent cultures at low agitation.
at high
The similarity
may also arise through an unidentified mechanism of growth regulation.
Cell growth is
controlled not only by contact
many other poorly-understood mechanisms
-
116
-
inhibition,
(Darnell et al,
but also by
1986).
+
35
---+- 35--150
rpm
rpm
_1
z
0
F-
z
Z
z
O
0
0
LU
0
D
IJ
09
40
20
TIME SINCE TRANSFER
60
(HRS)
Figure 25.
Glucose concentration
profiles for the 15 g/L cultures
-
118
-
80
TABLE 2.
GLUCOSE UPTAKE BY FS-4 CELLS IN MICROCARRIER CULTURES
Specific glucose uptake rate
(1/hr)
(10-12 gm/cell-hr)
Interval
35 RPM
Specific growth rate
35 RPM
150 RPM
46
0.0106
48
-0.0069
3
52
0.0073
4
40
0.0013
5
44
0.0018
Avg.
46
0.0028
-
119
-
The data
Within a 99%
gm/cell-hr, or only 76% of the value
1 0-12
on
the average
At 150 RPM, the average uptake
uptake rate was 46 x 10-12 gm/cell-hr.
35 x
35 RPM,
For the culture at
the hydrodynamic environment.
rate was
dependent
2 show that glucose consumption is
Table
in
at 35 RPM.
confidence limit, the difference in average uptake rates
significant.
was statistically
one accounted for glucose uptake by
If
the whole or lysed cells in suspension, the difference in average rates
would
even greater.
be
agitation reduces
that high
It appears
the
glucose uptake rate of FS-4 cells.
For FS-4 cells, glucose uptake is not growth associated and is significantly
For hybridoma cells,
reduced by high levels of agitation.
Dodge and Hu (1986) found that net cell growth was slightly reduced, but
volumetric
glucose
agitation.
This
glucose
result may have been due,
in
specific
glucose
uptake
rate
of
by
part,
to lactic acid by dead or lysed cells.
the
that
unchanged,
was
consumption
the
high
levels
of
to conversion of
It may also
hybridoma
indicate
cells
was
slightly increased by agitation.
this
In
have
been
Review
thesis,
the effects of hydrodynamic
extensively
section,
there
investigated.
are
limited
As
but
hydrodynamic effects on cell metabolism.
be
fully
optimized,
hydrodynamic
discussed
interesting
effects
120 -
in
on cell growth
the
results
Literature
regarding
Before any reactor design can
metabolism will have to be fully understood.
-
forces
on
both
cell
growth
and
HYDRODYNAMIC PHENOMENA IN
CHAPTER 3.
3A.
y-CHO CULTURES
Growth, Reversible Cell Removal, and Secondary Growth
Nearly all of the results for this thesis were derived from experi-
experiments were performed with
a few
for the purposes of comparison,
However,
ments with FS-4 cells.
y-CHO cells.
y-
Figure 26 presents limited results on the effects of agitation in
CHO
microcarrier
concentrations
shown
are
for
and 5% dialyzed FCS
microcarriers
and
attached
Both
cultures.
grown
two
cultures
in
the 125-ml
cell
suspended
with
1.0
Corning vessels.
g/l
One
culture was agitated at 35 RPM; the other at 100 RPM.
In contrast with the FS-4 cells, the
monolayer.
surface
However,
coverage.
cell
growth
y-CHO cells grew to more than a
still
appeared to
Growth plateaued after
the
be
regulated
cells were
2-3
by
layers
thick on the microcarriers.
In parallel with FS-4 cells on microcarriers, the y-CHO cells on the
microcarriers
of agitation.
excluded trypan blue and appeared healthy at both levels
However, in somewhat of a contrast with the results from
the FS-4 cultures,
the
y-CHO culture at 100 RPM exhibited essentially
identical attached cell concentrations as the
For an FS-4 culture,
the same
increase in
reduction in average observed growth rate.
-CHO
culture at 35 RPM.
agitation would bring a 50%
Microcarrier cultures of
y-
CHO cells are less sensitive to agitation than microcarrier cultures of
-
121
-
w
R
10
10
Attached
35 rpm
o
5'4\
10
Attached
100 rpm
- "-Suspended
100 rpm
A-
Suspended
35 rpm
10
10
I
0
40
80
I
I
120
I
160
I
200
I
I
240
TIME (HRS)
Figure 26.
Suspended and attached
cell concentrations for -y-CHO cultures
I
280
FS-4 cells.
In
time
each
occurred
a
26,
Figure
drop
vertical
was
medium
spent
rapid
very
0.04 hr- 1 or greater.
pre-exchange
their
values.
on the
The
order of
1
These rates are much higher than 0.004 hr- , the
growth
specific
medium.
suspended cell concentrations
rates associated with these recoveries were
specific
maximum
to
recoveries
concentration
fresh
with
exchanged
Subsequent to each medium exchange, the
exhibited
cell
suspended
in
y-CHO
of
rate
parable medium (Perry, 1987).
Thus,
cells
suspension with com-
in
the rapid
increases in suspended
cell concentrations were not due to cell growth, but were rather due to
cell removal from the microcarriers.
Prior
each medium exchange,
to
the
cell concentrations
suspended
were essentially independent of the time since the last medium exchange.
The suspended cell concentrations were therefore not steadily increasing
in
each feeding interval,
between the
data points
concentrations
were
as improperly indicated by the straight lines
in
Figure
26.
Instead,
re-established
apparently
constant soon after each medium exchange,
as
if
suspended
the
and
held
cell
relatively
a sort of equilibrium
existed between the cells on the microcarriers and those in suspension.
In Figure 26, the suspended cell concentrations represent the whole
cells
higher
in suspension, both viable and dead.
level
concentrations
of
agitation
than the
The
y-CHO culture at
(100 RPM) exhibited higher
culture
-
at the
123
-
lower level
the
suspended cell
of agitation
(35
Thus,
RPM).
y-CHO cells, removal of cell from the
for both FS-4 and
increased with the level of agitation,
microcarriers
and thus appeared
to come about, at least in part, through hydrodynamic forces.
The culture at 100 RPM exhibited much more extensive
cell removal
and yet had essentially the same attached cell concentrations
Even though significant cell removal occurred after
culture at 35 RPM.
medium
each
exchange,
cell concentrations
the attached
recovered
their pre-exchange values or greater by the next medium exchange.
indicates
that
the
as
to
This
y-CHO cells exhibited secondary growth over areas
the
where cells had been previously removed through hydrodynamic forces.
The
cells
y-CHO cells
suspension
in
in suspension.
In
the
appeared much
y-CHO cultures,
different
than FS-4
70-90% of the suspended
cells appeared healthy and excluded trypan blue.
In the FS-4 cultures,
none of the suspended cells appeared healthy and less than 10% excluded
trypan blue.
To truly measure viability, however, one must determine the ability
of
the
cells
For
reproduce.
to
the
FS-4
cultures,
the
cells
in
suspension did not viably attach and multiply on fresh growth surfaces.
To investigate the reproductive capability of
a new microcarrier
the
culture was inoculated
y-CHO culture at 100 RPM.
y-CHO cells in suspension,
from the suspended
cells in
The cells were removed during the medium
exchange at 237 hours, centrifuged for 5 minutes at 150 x g, resuspended
in
fresh medium,
and then used to inoculate a new culture with 1.0 g/l
-
124
-
microcarriers
at 35 RPM in
a 125-ml vessel.
In
terms
of trypan blue
exclusion, the cells had a viability of 80%.
The concentration of suspended cells which excluded trypan blue was
used to
determine
concentration.
"TPB
viable"
microcarrier
the
trypan blue
viable,
or
"TPB
viable",
inoculum
Figure 27 shows the attached cell concentrations and the
inoculum
concentration.
cultures,
it
Given the
appears
that
most,
normal
if
not
lag phase
all,
suspended cells which excluded trypan blue were actually viable.
29
hours,
essentially
all
of
"TPB
viable"
attached
the
Within
to
the
The culture subsequently grew at
microcarriers and started to multiply.
virtually the same rate as the cultures
shown in Figure 26.
cells
of
of
inoculated from roller bottles
Thus, in striking contrast to FS-4 cells, many y-
CHO cells in suspension are viable.
3B.
Hydrodynamic Resistance through Secondary Growth
In FS-4 microcarrier cultures, cell removal from excessive agitation
is irreversible and lethal.
Secondary growth does not occur over areas
where removal has occured.
The cultures under high agitation exhibit
growth regulation
as
if
they were
just
will
permanently
and
inhibited
as more
An FS-4 culture exposed to high
confluent cultures under low agitation.
agitation
as contact
irreversibly
deviate
from
a
control
culture with low agitition, as shown by Figure 24 in Chapter 2.
In
y-CHO
cultures,
removal
cell
125
excessive
agitation
is
Secondary growth will occur over
frequently reversible and not lethal.
-
from
-
+
"fTPB viable"
Attached
cells
-+-
inoculum
106
Z
-
0
Z
Z
z
F-
10
I
IIIII
60
40
20
I
I
80
TIME (HRS)
Attachment and growth
Figure 27.
7-CHO cells taken from suspension
-
126
-
I
100
Although the cells grow to more than
areas where removal has occurred.
a monolayer,
coverage.
Thus,
to be
appears
still
growth
regulated by maximum surface
cell growth should be stimulated if
areas are opened up
When cultures
are at or near the
through hydrodynamic
cell removal.
maximum surface coverage,
the cultures with a high degree
of removal
should exhibit higher total growth rates than cultures with a low degree
of removal.
Figure 28 shows the viable cells produced per microcarrier over the
time course of the
per
microcarrier
cells
subsequent
y-CHO cultures at 35 and 100 RPM.
cumulative increase
represents the
to
in the
number of
Data are presented for both attached
inoculation.
and total viable cells.
The cells produced
The number of total viable cells was calculated
including those
as the sum of the attached and viable suspended cells,
As the suspension cell concentrations
removed through medium exchange.
prior to 117 hours were very low and were not measured,
they were not
included in the calculations.
The number of attached cells produced per microcarrier was nearly
identical at 35 and 100 RPM.
However, the total number of viable cells
produced per microcarrier was
30% higher at 100 RPM.
Total cell growth
was clearly higher at 100 RPM.
Cell removal was also higher at 100 RPM.
As discussed, the cells in
suspension did not primarily arise through growth
in suspension, but
rather through cell removal from the microcarriers.
At 100 RPM,
-
127
-
the
vw
400
350
300
A
A
Total
100 rpm
250
0 .- Total
35
200
-----
rpm
Attached
35 rpm
150
A-
Attached
100 rpm
100
50
I
I
40
I
I
i
I
I
80
I
I
S
120
I
I
I
160
I
II
200
I
II
I
240
TIME (HRS)
Figure 28.
Viable cells produced per
microcarrier for y-CHO cultures
II
280
produced
cells
suspension
viable
of
number
microcarrier,
per
which
roughly represents the number of viable cells removed per microcarrier,
was 3-fold higher than at 35 RPM.
Thus,
as
went
removal
one
total
increased
hand-in-hand with
increased cell
secondary growth,
expect with
might
Growth
growth.
was
Even
stimulated as areas were left void through hydrodynamic removal.
though cell removal was much more extensive at 100 RPM, the culture was
able to maintain comparable attached cell concentrations to the culture
at
RPM.
35
hydrodynamic
growth
Secondary
damage.
fast
was
growth
Secondary
can
to
enough
overcome
lead
clearly
to
any
reduced
hydrodynamic sensitivity.
It is likely that secondary growth accounts for the difference in
hydrodynamic
It
also
is
because
the
y-CHO microcarrier cultures.
growth can occur
likely
that
secondary
cells
are
frequently
reversible removal may leave
growth.
FS-4 and
sensitivity between
removed
whole
in
and
y-CHO cultures
viable.
few remnants to hinder future
Such reversible removal may come about because
secondary
y-CHO cells are
aneuploid and do not exhibit the same attachment properties
cells, such as FS-4 cells.
Such
as diploid
Future research should be performed to more
thoroughly elucidate the nature of cell removal and secondary growth.
3C.
Selection of Model Cell Line
The viability
of
study of hydrodynamic
y-CHO cells in suspension greatly complicates the
phenomena in
-
these
129
-
cultures.
Because the cells
can reattach
after they have been removed from the microcarriers,
rate of removal
is not easily measured and does not simply correlate
A form of equilibrium exists between the cells
with the rate of death.
in
suspension and
the
and
removal
the
those
reverse
The
the microcarriers.
on
rate
reattachment
of
forward
must
rate of
measured
be
simultaneously.
In an FS-4 culture, all of the viable cells are on the microcarriers
and all of the dead cells are
in
The rate of hydrodynamic
suspension.
Hydrodynamic cell
correlates directly with the rate of death.
removal
removal is not reversible;
there is no equilbrium.
The forward rate of
death and removal can be measured and modelled directly with no required
correction for the reverse rate of reattachment.
cultures
were
chosen
as
the
simpler
extend the
cells,
system,
model
experiments were performed with FS-4 cells.
For this reason, FS-4
and
nearly
Future work will hopefully
analysis based on irreversible removal, suitable
to an analysis based on reversible removal,
-
130
-
all
suitable for
for FS-4
y-CHO cells.
MECHANISMS OF HYDRODYNAMIC DEATH IN DILUTE CULTURES
CHAPTER 4.
First, Second, and Higher Order Mechanisms of Hydrodynamic Death
4A.
Cell death and removal have been identified as the primary response
It
of FS-4 cells to excessive agitation.
type
hydrodynamic
of
this
cause
forces
is
For
removal.
and
death
what
however,
not clear,
microcarrier cultures with high agitation, cell death may arise through
turbulent
microcarriers,
no
Papoutsakis,
and
the
1986b).
fields,
collisions
and
microcarriers
between
solid
the
From the data currently available, it appears
arises
damage
significant
microcarriers
between
collisions
or
components of the vessel.
that
flow
time-average
eddies,
solid
through
of
components
Because microcarriers
the
collisions
vessel
between
(Cherry
and
are very small and almost
neutrally buoyant, they should not rapidly penetrate the boundary layers
surrounding the solid vessel components.
In general, the mechanisms of hydrodynamic death can be grouped into
The first order mechanisms
first, second, and higher order mechanisms.
represent the interaction of a single microcarrier with the surrounding
field.
flow
The
second
mechanisms
the
represent
simultaneous
interaction of two microcarriers with the surrounding flow field.
higher
order
mechanisms
represent
the
simulateneous
interaction
The
of
multiple microcarriers with the surrounding flow field.
The first
The
second
order mechanisms should be predominant in
order
mechanisms
become
should
-
131
-
more
dilute cultures.
significant
as
the
microcarrier
The higher order mechanisms
concentration is increased.
only in
should be predominant
very concentrated cultures.
The higher
order mechanisms will not be investigated in this thesis.
To provide
clear
and unique information
regarding
the first
mechanism, experiments were first performed with dilute cultures.
order
These
experiments elucidated the nature of the first-order mechanisms without
interference
from the second-order mechanisms.
were performed with concentrated cultures.
Subsequent experiments
The higher rates of damage
in the concentrated cultures were analyzed to investigate the nature of
the second order mechanisms.
4B.
Effects of Power and Viscosity in Dilute Cultures
For dilute microcarrier cultures, the mechanisms of cell death from
turbulence were investigated through experiments on the effects of power
and viscosity.
through
Cell damage from time-average flow fields was avoided
average shear rate and fluid
limitations on the maximum time
viscosity. The maximum shear stress from time-average flow fields was
than 5 dyne/cm2.
less
riers,
The cultures
contained
or 0.002 volume fraction solids,
only 0.2 g/l microcar-
and were therefore
not subject
to significant damage from microcarrier collisions.
Figure 29 shows the effect of 20 g/L dextran supplement (78,500 MW)
on cell growth in
The
cell
the dilute cultures at different levels of agitation.
concentrations
the
represent
viable,
or
attached,
cell
To eliminate cell damage from time-
concentrations for the cultures.
-
132
-
106
-N
60
rpm
No dextran
10
0
--- A
77----a
e
rpm
20 g/L dextran
220 rpm
20 g/L dextran
.....
..
..
...
.........
10
60
220 rpm
No dextran
10
3
30
60
90
I
I
I
I
120
150
I
180
TIME (HRS)
Figure 29.
Effect of 20 g/L dextran (78,500 MW)
on net growth at different stirring speeds
the cultures were grown in the 500-ml vessels with
average flow fields,
5.3
power
and
The data for the control
cm impellers.
or a
at 60 RPM,
cultures
2
input of approximately 10 dyne/cm , has already been illustrated
discussed
in Figure
11
1.
of Chapter
It
for
repeated here
is
reference.
At 60 RPM,
there was no significant hydrodynamic
cell
in
viscosity and
death and removal.
At 230 RPM,
there was no effect from an increase
death and removal from hydrodynamic forces were strongly evident.
For the cultures with and without dextran at 230 RPM,
concentrations
were
however,
indicate,
lower than
that
in the
controls at 60 RPM.
cell
hydrodynamic
the viable cell
death
and
The data
removal
can be
At
reduced with a viscosity increase through dextran supplementation.
the
230 RPM,
culture with 20
g/L dextran exhibited much higher viable
cell concentrations than the culture with no dextran.
Figure 30 shows the effect of a 50 g/L dextran supplement (78500 MW)
on cell growth in the dilute cultures at different levels of agitation.
Again, to
eliminate
cell
damage
from
time-average
shear fields,
cultures were grown in the 500-mL vessels with 5.3 cm impellers.
RPM, supplementation with 50 g/L dextan
cell concentrations.
dextran led to an increase in
due
to viscous
At 60
led to a reduction in viable
This reduction was due to the mild toxic effect of
50 g/L dextran on cell growth.
was
the
At 185 RPM, supplementation with 50 g/l
viable cell concentration.
This increase
reduction of cell death and removal. With
50 g/L
dextran, the viable cell concentrations in the culture at 185 RPM were
-
134
-
106
-- - -
10
60 rpm
No dextran
60 rpm
50 g/L dextran
,.0
185
----
rpm
50 g/L dextran
10
- 185 rpm
No dextran
10
30
60
90
120
150
180
TIME (HRS)
Effect of 50 g/L dextran (78,500 MW)
Figure 30.
on net growth at different stirring speeds
Supplemen-
nearly equal to the concentrations in the culture at 60 RPM.
completely
g/L dextran almost
50
tation with
eliminated hydrodynamic
death and removal at 185 RPM.
Numerous other experiments, similar to the one described above, were
the
on
performed
dextran
employed
experiments
The
fields.
flow
collisions
from microcarrier
to cell damage
were not subject
at different
dextran supplements
All cultures contained 0.2 g/l microcarriers
levels of agitation.
average
various
effect of
and
time-
or
supplements
between 20 and 50 g/L (78,500 MW) and were performed over a wide range
of
of
levels
results
The
agitation.
the
followed
trends
shown
in
Figures 29 and 30 and are included in the subsequent data analysis.
4C.
Cell Death Through Microcarrier-Eddy Interactions
As
discussed
section,
the
riers.
death from turbulence
hydrodynamic
turbulence
and
Thesis
should become evident when
isotropic
regime,
the
equilbrium appears
of
size
average
to exist in the viscous
the
estimated by the average Kolmogorov length scale,
3
-
1/4
The size
in power or
can be
L:
(Eq. 41)
the average power input per unit mass and v is
fluid viscosity.
increase
eddies
smallest
L = (v / i)
where F is
Formulation
generates eddies which are smaller than the microcar-
Because
dissipation
Review
Literature
the
in
the smallest eddies
of
a decrease
the kinematic
decreases with an
in kinematic viscosity.
For suffi-
ciently high power inputs at a given viscosity, the turbulence
generate eddies which are smaller than microcarriers.
-
136
-
should
Cell damage from
turbulence should then become evident.
To investigate whether the proposed role of eddy length is correct,
For each
the experimental data for the dilute cultures was analyzed.
culture,
the relative observed growth rate,
pr, was calculated from the
equation
(Eq. 42)
Ar -= Pobs//d
where pobs was the average observed growth rate of the culture,
was the
mild
average observed growth rate of a control
agitation
the
with
culture grown under
average
The
concentration.
dextran
same
and pd
observed growth rates, which represent the difference between the actual
growth rates and death rates, were calculated through linear regressions
on
the
attached cell
growth rates
use
The
concentrations.
relative
of
observed
corrects for the mild effects of dextran toxicity which
were observed with dextran supplements greater than 25 g/l.
Figure
average
31
eddy
Kolmogorov
viscosities.
decrease
shows the plot of relative observed growth rate versus
length
number
a
for
different
of
Cell death through hydrodynamic forces,
as indicated by a
growth rate, becomes
apparent when the
in relative
specific
average Kolmogorov length scale falls below about 130 microns,
2/3
of
the
fluid
microcarrier
diameter
of
185
microns.
As
or about
expected,
hydrodynamic death occurs when the turbulence generates eddies which are
smaller
than
the
For
microcarriers.
a
number
of
different
fluid
viscosities, hydrodynamic death in dilute cultures correlates well with
Kolmogorov length scale.
The correlation describes the effect of both
-
137
-
*
0.74
cp
1.04
cp
A
1.10
1.35
cp
+
cp
*
1.79
A
1.85
cp
cp
1.20
0.90
0.60
0.30
0.00
-0.30
-0.60
I
I
50
I
100
KOLMOGOROV
,
I
,
150
,
,,
I
200
I
,
,
250
LENGTH SCALE (MICRONS)
Figure 31.
Relative growth rate vs. Kolmogorov eddy
length scale for FS-4 cultures with 0.2 g/L microcarriers
i
300
viscosity
and power
The
(v3/f)1/4.
isotropic
that
as
combined
in
the
unique
length
correlation provides
existence of
this
equilibrium
exists
at
scale
more evidence
Kolmogorov
the
group,
scale
in
overagitated microcarrier cultures.
The results in Figure 31 are not the only data which illustrates the
correlation
length scale.
of hydrodynamic death with Kolmogorov
Prior
to the experimental work in this thesis, the data presented in Hu (1983)
and Sinskey
effects
et al (1981)
were analyzed.
Both researchers studied the
of agitation on net growth of cells
cultures.
microcarrier
in
Experiments were performed on the effect of vessel geometry but not on
the effect of fluid viscosity.
Figure 32 shows
cells.
the correlation of the data of Hu
for FS-4
(1983)
Relative growth extent, or relative net positive growth after
inoculation, is compared to average Kolmogorov eddy length scale.
death is
the relative growth extent,
indicated by a decrease in
proportional
Cell
which is
to relative observed growth rate for positive net growth.
Figure 31.
The data show a similar trend to the results in
Cell death
from turbulence becomes evident when the average Kolmogorov length scale
Further decreases in
falls below about 130 microns.
scale lead to a sharper decline than observed in
be
expected
with
the
This would
and
the
The plateau at very small eddy lengths
corresponding collision damage.
indicates no net positive
Figure 31.
concentrations
microcarrier
higher
Kolmogorov length
growth occurred.
negative growth might have occured.
-
139
-
It
is
unclear whether net
10080-
60-
Symbol
40-
Impeller
Diam. (cm)
A
20-
0-
50
100
150
KOLMOGOROV EDDY LENGTH SCALE
Vessel
Vol. (ml)
3.2
250
4.1
250
5.1
250
7.5
2000
8.5
2000
200
(MICRONS)
Figure 3 2. Relative growth rate vs. Kolmogorov eddy length scale
for FS-4 cultures with 5 g/L microcarriers (data from Hu, 1983)
In
well
Figure
for
32,
a single correlation describes the
a number
that
indication
of different vessel
cell
regime.
dissipation
death
Such
arises
geometries.
eddies
through
eddies
exist
in
a
data reasonably
This
in
state
is
further
the
of
viscous
isotropic
equilibrium which depends only on the local power dissipation rate and
kinematic viscosity, and not on the vessel geometry.
eddies,
in
contrast,
Energy containing
are highly dependent on reactor geometry.
If cell
death arose through the action of the energy-containing eddies, a strong
effect of geometry should be observed.
Figure 33 shows the correlation of the data of Sinskey et al (1981)
Maximum cell concentration is
for chicken embryo fibroblasts.
compared
As observed in Figure 32, a single
to average Kolmogorov length scale.
correlation fits the data for a number of different vessel geometries.
Hydrodynamic
death,
concentration,
is
as
indicated by
evidenced
when
decrease
a
the
length
in
scale
the
maximum
falls
cell
below
100
The microcarrier diameter was not reported and may have been
microns.
Cell growth drops very sharply for
slightly smaller than 185 microns.
eddies smaller than 100 microns; this may indicate a difference between
FS-4 cells
and chicken embryo fibroblasts.
The plateau at very small
eddy lengths does not indicate whether net negative growth occurred.
For a number of different
microcarrier
scale.
cultures
data sets,
correlates
well
hydrodynamic death in
with average Kolmogorov length
As expected, cell death occurs when the turbulence
eddies that are smaller than the microcarriers.
-
141
-
dilute
generates
In parallel research
6A
w
U
5-
(0
0
4-
0
A
A
U
Symbol
z
0
3.3
4.4
0
7.5
A
U
2 -
Impeller
Diam. (cm)
Vessel
Vol. (ml)
250
250
1000
-J
------- 0o-QA
100
KOLMOGOROV
200
300
EDDY LENGTH SCALE (MICRONS)
Figure 3 3. Maximum cell concentration vs.
Kolmogorov eddy length scale for chicken
embryo fibroblasts on 5 g/L microcarriers
(data taken from Sinskey et al., 1981)
-
142
-
with cultures
observed
a
of freely-suspended animal cells,
similar
correlation
of cell
McQueen et al
death with Kolmogorov length
eddies smaller
Cell death occurs when the turbulence generates
scale.
than about 3.5 microns,
(1987)
or about 1/3 to 1/2 the cell diameter.
Hydrodynamic Forces in Microcarrier-Eddy Interactions
4D.
To determine whether the correlation of cell death with eddy length
has
a fundamental basis,
produce
hydrodynamic
Currently,
however,
hydrodynamics
one
forces
there
is
near a particle
eddies
should determine whether the
sufficiently
no
in
thorough
strong
to
can
damage
cells.
the
complex
description of
a turbulent flow field.
Accordingly,
only very rough estimates of the forces can be made.
If
Matsuo and Unno
forces predominate,
viscous
(1981)
suggest that
the shear stress on the surface of a sphere in a turbulent flow field is
given by
r
where
r; is
=
the
2rq(2/15)1/2
(Eq. 43)
1/2
fluid viscosity.
If
Reynold's stresses are
important,
Matsuo and Unno (1981) suggest that
r
=
0. 3 7p f(e/v)d
(Eq. 44)
where pf is the fluid density and dp is the microcarrier diameter.
For the conditions under which cell death was observed,
the average
power input per unit mass was first used to estimate the shear stresses
from equations 43 and 44.
From equation 43, shear stress estimates in
-
143
-
the range of 1-3 dyne/cm 2 were obtained.
These values are somewhat less
than 7 dyne/cm2 , the minimum shear stress for which significant cell
damage
has
been
equation 44,
obtained.
reported
(Stathopoulos
shear stress estimates
and
Hellums,
1985).
From
the range of 2-16 dyne/cm2 were
in
The upper range of these values are in the range known to
cause cell damage.
The shear stress estimates can alternatively be performed with local
instead
power dissipation
of average
In a stirred tank, the
rates.
power dissipation rates in the impeller discharge stream are much higher
than the average dissipation rate.
(1981)
and
Placek
dissipation rates
in
and
For Rushton turbines, Okamoto et al
(1985)
Tavlarides
that
report
the
power
the impeller discharge stream are approximately
fold higher than the average dissipation rates.
6
This ratio was used to
estimate
the maximum local power dissipation rate and the corresponding
maximum
shear
From
equation
43,
the
maximum
are
in
the range of 2-6 dyne/cm2 , again still
known
to
cause
estimates
values
stress.
From equation
damage.
44,
stress estimates were in the range of 10-100 dyne/cm2.
shear
stress
less than the
the maximum
shear
These values are
all within the range known to cause cell death and removal
(Crouch
et
al, 1985; Stathopoulos and Hellums, 1985).
As
cells
already mentioned with regard to
selectivity of cell removal,
could be damaged
or killed not only by shear
on microcarriers
stresses, but also by normal forces.
Normal forces will be generated by
velocity and pressure fluctuations in
the turbulent flow field of a
-
144
-
microcarrier culture. In terms of cell death, the critical fluctuations
occur on a scale which
those which
will be
in the viscous dissipation regime.
eddies
unit area on the microcarrier
magnitude
in size
intermediate
These flucuations will involve
and microcarriers.
between cells
is
Thus,
the normal
the
force per
Fn, might be estimated from the
surface,
fluctuations which occur on the scale of the
of the pressure
viscous dissipation regime:
F
P
-
n
(Eq. 45)
vdr
where P'vdr represents root mean square turbulent pressure
or pressure
intensity, due
to
the
eddies
in the
fluctuation,
viscous
dissipation
regime.
in
Turbulence
isotropic
viscous
dissipation
regime
is
essentially
and has a characteristic Reynold's number near unity (Hinze,
The pressure fluctuations due to the viscous dissipation eddies
1975).
might
the
thus be estimated
Hinze (1975)
P'
where u'
from an extension
of the result presented
in
for isotropic turbulence of low Reynold's number:
=
(Eq. 46)
Pf u2
and P' represent the velocity and pressure intensity,
respec-
tively.
In
terms
fluctuations
The effective
of
are
cell
relevant
the
death,
pressure
and
velocity
dissipation scale.
those which occur on the viscous
velocity intensity might thus be estimated by Kolmogorov
velocity scale for the viscous dissipation eddies.
-
145
-
The normal force per
unit area on the microcarrier surface, Fn, is then given by
F
pf (EV)1/ 2
=
(Eq. 47)
where pf is the fluid density.
Using
estimate
power
average
normal forces
rates
dissipation
equation
on the order of 1-4 dyne/cm 2
which
exhibited hydrodynamic
rates
in
If the
death.
increased to 2-10 dyne/cm2 .
47,
one
can
for the cultures
local power
dissipation
the normal forces estimates are
the impeller stream are used,
strength can damage
in
It is unknown whether normal forces of this
or remove cells from a growth surface.
In fact, a
literature review indicates no published data with regard to the effects
of normal forces on animal cells.
performed in
4E.
Future research will hopefully be
this area.
Kinetics of Cell Growth and Death in Dilute Cultures
Although
the
investigated more
thoroughly,
a
near
hydrodynamics
surface
must
be
the comparison of experimental data with
simplified models can help to elucidate
excessive agitation.
microcarrier
the mechanisms of death from
The data in Figures 31-33 indicate that cell death
occurs when the turbulence generates eddies which are smaller than the
microcarriers.
length
scale,
Based upon the correlation of cell death with Kolmogorov
a
model
was
developed
to
describe
hydrodynamic damage in dilute microcarrier cultures.
the
kinetics
This "eddy-length"
model is based upon the following assumptions:
1) hydrodynamic damage occurs through microcarrier-eddy encounters
-
146
-
of
2) damage will occur only if a microcarrier encounters an eddy smaller
than a critical length, Lc,
assumption is
based upon the correlations
This
130 microns.
of approximately
Figures
shown in
31 and
32.
growth inhibition, are the only
death and removal, and not
3) cell
forms
This assumption is based upon the
damage.
of hydrodynamic
experimental results previously presented and discussed.
4) a constant fraction of the culture volume is
appearing eddies
regime.
Kolmogorov
the
in
filled with randomly
This
assumption is
implicit in the derivation of the Kolmogorov scales from an energy
balance.
Under the fourth assumption, the effective eddy concentration in the
proportional to the inverse of the eddy volume,
Kolmogorov regime is
or
(E/V3)3/4.
Because cell death occurs through cell-eddy encounters, the
total rate
of cell death is proportional
concentration times the eddy concentration.
proportional
therefore
to
the
Expressed in mathematical form,
dC
--
eddy
dt
q
where p is
-
pC
=
Ke(/v3)3/4
of the
cell
The specific death rate is
concentration,
or
(i/v3)3/4.
the kinetic "eddy-length" model becomes
=PC
=
to the product
qjC
L > Lc
(Eq. 48)
L < Lc
(Eq. 49)
(Eq. 50)
the intrinsic specific growth rate and is
-
147
-
independent of the
level of agitation,
qi is
the specific death rate due to microcarrier-
eddy interactions, 7 is the average power input per unit mass, v is the
fluid
kinematic
viscosity,
a
is
Ke
and
function
of
the
cell
and
microcarrier properties, and possibly the reactor geometry.
To test the kinetic model presented above,
microcarrier
the data for the dilute
culture,
For each
cultures were analyzed.
the
average
specific death rate was calculated from the equation:
q
=
(Eq. 51)
Ad - Mobs
where pobs and pd have been defined with equation 42.
Figure 34 shows a
plot of specific death rate versus eddy concentration group, (e/V
for
two
different vessels with the
same
impeller.
Each set of data
shows a linear correlation, as predicted by the eddy length model.
The
intercept values near zero follow the assumption of insignificant cell
death with mild agitation.
For the data from the 500-ml
cm) vessel,
(9.6
the value of Ke from
linear regression is 6.9 x 10-13 cm3 /sec with a 95% confidence interval
10-13 cm3 /sec.
of ± 1.7 x
value
two
interval
values
confidence
of ± 1.3 x 10-13 cm3 /sec.
of Ke
interval,
is not
as
statistically
from
determined
presented in Kleinbaum and Kupper (1985).
not
125-ml vessel,
the
of Ke from linear regression is 5.4 x 10-13 cm 3 /sec with a 95%
confidence
the
For the data from the
indicate
a clear effect of vessel
The difference between
significant within a
the
statistical
148
-
methods
The limited data therefore do
geometry.
In fact, a
correlation fits both vessel geometries reasonably well.
-
95%
single
A
= 5.3
cm
Dt = 6.3
cm
Di
*
Di
Dt
=
5.3
cm
=
9.6
cm
60
50
Cl)
40
w
I
30
20
U
U]
n~
Cl)
10
0
0
2
8
6
4
EDDY CONC. (ES/V
3 3/4
)
10
(10 6/ML)
Specific death rate vs. eddy
Figure 34.
concentration for dilute FS-4 cultures
149
12
The data in Figures 31-34 all indicate reasonably good correlations
power
with average
dissipation regime,
viscous
strong effects of vessel
Because cell death is probabilistic and involve eddies in the
geometry.
expect
input and do not indicate
which are also probabilistic,
one would not
In this thesis, the average value
a strong effect of geometry.
of 6.2 x 10-13 cm3 /sec will be used for Ke in the kinetic expression for
cell death
from microcarrier-eddy
interactions.
Future research will
hopefully determine and incorporate any effects of vessel geometry in
more advanced kinetic expressions.
hydrodynamic
The
predictions
the
model,
in
effects
dilute
predictions
the
of
the
To further test the validity of
of the eddy-length model.
the
followed
cultures
FS-4
model
were
also
compared
to
the
following sets of results:
1) the effects of agitation on net growth of Vero cells on Cytodex 1
microcarriers,
as determined by Hirtenstein and Clark (1981)
and
shown in Figure 1 of this thesis,
2) the effects of agitation on net growth of FS-4 cells on Cytodex 1
microcarriers, as shown in Figure 24 of this thesis,
the effects
3)
of agitation on secondary disruption of protozoa in
baffled stirred tanks, as determined by Midler and Finn (1966)
For
both
the
Vero
and
FS-4
cells,
the
cultures
were
grown
in
unbaffled spinner vessels, and the specific death rates were determined
from equation 51.
The microcarrier concentrations were 3 g/l,
or 3%
solids by volume, and thus were slightly out of the dilute regime.
-
150
-
For
protozoa,
the
which
are
and about half
sensitive
shear
size
the
of
microcarriers, the specific death rates were calculated from the slopes
of secondary disruption data.
correlations
The power inputs were determined from the
Rushton et al
presented in
(1950)
and Bates et al
(1963)
with the corrections presented in Bujalski et al (1987).
Figure
35
shows
a log-log plot
of specific
power input per unit mass for the Vero cells,
and protozoa.
The data indicate that Vero
linear correlation with a slope near 0.75.
are
FS-4 cells,
average
the eddy-length model, all three sets of data show a
As predicted by
cells
death versus
considerably more
sensitive
agitation than FS-4
to
cells.
However, the power input calculations for the Vero cells were rough and
may have been in error with regard to absolute values.
The data for the
protozoa was taken over a wide range of tank geometries.
The ratios of
impeller to tank diameter were varied between 0.24 and 0.71.
wide
range
of geometries,
the data
can be reasonably
single correlation based on average power input.
that there
are
strong effects
no
Over this
described by
a
This is more evidence
of geometry when cell death arises
through eddies in the viscous dissipation regime.
a number
For
describes
cultures.
random
of sets
that kinetics
Thus,
of
dissipation regime.
eddy-length model
the
death
of cell
it appears
interactions
data,
in
accurately
dilute or reasonably
dilute
that cell death truly does arise through
between microcarriers
and
eddies
in the
viscous
Such interactions will not lead to cell death,
however, if the eddy is larger than the microcarrier.
-
151
-
10
Slope= 0.82
Protozoa
IU
Cw
1-
10
Slope=0.76
Vero cells
Slope =0.72
FS-4 cells
10
10
II
I
10
AVERAGE
10
I
I
I
I
4
Protozoa
I~
102
10
10 3
Animal
cells
POWER PER UNIT MASS (CM 2/S EC3
35.
Specific death rate vs. power input
per mass for Vero cells, FS-4 cells, and protozoa
Figure
-
152
Cell Damage from Time-Average Flow Fields
4F.
the conditions
To investigate
fields
shear
there is
these vessels,
time-average
a clearance
with
are
rates
shear
equation 16.
is
rate
In the
of impeller rotation, strong
in
generated
region
the
the
between
For operation at 220 RPM, the maximum time-
impeller tip and tank wall.
shear
dilute
of only 5 mm between the impeller
Under high rates
and vessel wall.
average
performed
were
in the 125-ml vessels with high viscosity increases.
cultures
tip
experiments
occur,
might
under which damage from time-average
approximately
160
estimated
as
sec-l,
from
A viscosity increase to 1.5 cp or higher might therefore
will lead to shear
as it
induce damage from time-average shear fields,
stresses greater than 7 dyne/cm 2 (equation 14).
Shear stresses of this
value are the minimum reported to cause cell damage (Stathopoulos and
Hellums,
shear
Accordingly,
1985).
fields was
onset of damage
the
investigated by increasing
from
time-average
the fluid viscosity above
1.5 cp in the 125-ml vessels at 220 RPM.
Figure 36
shows the results of this investigation.
are presented for four conditions
the 125-mL vessels.
in
Growth curves
Because many
of the conditions were investigated with duplicate cultures, and because
different
inocula were used for
each set of duplicates, viable
concentrations are reported relative to initial
The
cultures
at
35
insignificant hydrodynamic
the
exhibited
RPM
The
death.
dextran had very low viable cell
degree of hydrodynamic death.
cell
values at inoculation.
cell
normal
cultures
concentrations
at
220
growth
with
RPM with
no
and exhibited a great
When the viscosity was increased to 1.04
-
153
-
10
A
I
~--------------
LG ~
------
rpm
No dextran
220 rpm
20 g/L dextran
-
e0
~
35
- 220 rpm
50 g/L
0
0
0.1
I
30
I
60
I
90
I
120
*
I
150
TIME (HRS)
Figure 36.
Effect of dextran on net growth in
a reactor with strong time-average shear fields
dextran
220 rpm
No dextran
cp with 20 g/l
cell
dextran,
death and removal were strongly reduced.
When the viscosity was further increased to 1.85 cp with 50 g/l dextran,
cell death was more pronounced than in the 20 g/1 cultures.
stress
from
this
flow
time-average
fields,
Tmax,
or
cell death from time-average
If
dyne/cm2.
dextran,
at 220 RPM with 50 g/l
culture
the
In
the maximum shear
was
9
approximately
flow fields was occuring in
culture, but not in the other cultures, the specific death rate
should be higher
power.
expected
than would be
for the
given viscosity
Figure 37 shows that this hypothesis is correct.
death rates
from Figure
34, and
and
The specific
the best-fit linear correlation, are
2
shown for the cultures with Tmax < 5 dyne/cm .
The specific death rate
2
for the culture with Tmax = 9 dyne/cm is far above the correlation for
the other cultures.
a 99% confidence
average
shear
The difference is statistically significant within
interval
fields.
and is
Thus,
that
appears
it
of cell damage from time-
indicative
cell
damage
from
time-
The onset of such damage can be roughly
average shear fields can occur.
predicted through fluid-mechanical modelling and through knowledge of a
critical shear stress for cell damage.
The predictions can be used to
purposely avoid cell damage from time-average
in many of the experiments in this thesis.
flow fields,
as was done
The predictions can also be
used to develop criteria for reactor design and scale-up.
4G.
Effects of Cavitation
In the turbulent flow field of a stirred tank, dynamic reductions in
pressure will occur as the fluid flows around the impeller.
-
155
-
For
*
Max time-avg
IT < 5
*
Max time-avg
- = 9 dyne/cm 2
dyne/cm2
60
a
w
Co
50
N
0
1~
40
Lu
I-
30
I
FLu
0
20
10
2
4
6
EDDY CONG.
(EIV
8
3 3/4
)
10
12
I (10 6/ML)
Specific death rat e vs. eddy
Figure 37.
concentration at different levels of maximum
shear stress from time-average shear fields
156 -
sufficiently strong agitation, the reduction in pressure may lead to the
formation of vapor cavities, an explosive phenomena known as cavitation.
the local pressure falls below the fluid
Cavitation will arise only if
If cavitation were
vapor pressure at the given operating temperature.
to occur in
likely would result in
it
a microcarrier bioreactor,
cell
damage or lysis.
The
existence
generally
can
cavitation
of
cavitation number (Daily and Harleman,
correlated with
be
The cavitation number,
1966).
a
a,
is given by (Boucher and Alves, 1973)
P
a
=
-
Py
(Eq. 52)
2
Pg U /2
where P is the static pressure in the undisturbed flow, Pv is the fluid
vapor pressure, pf is the fluid density, and U is the free-stream fluid
Cavitation will occur only if
velocity.
the cavitation number
below a critical value characteristic of the
critical values
These
given geometry.
are gnerally in the range of 0.2 to
2.5
falls
(Boucher and
Alves, 1973).
For
a
stirred
tank,
minimum
the
cavitation
number
might
be
reasonably estimated from the maximum fluid velocity, including both the
For a radial flow impeller, both
time-average and turbulent components.
the
maximum
time-average
generally occur in
fluid
the radial jet
average radial velocity,
Umax,
is
-
velocity
and
off the impeller.
turbulent
intensity
The maximum time-
proportional to the tip speed of the
157
-
impeller, as given by the data presented in Oldshue (1983):
ii
0.7
=
max
(Eq. 53)
r N D.
1
In reference to this velocity, the maximum values of relative turbulent
an upper
Thus,
1985).
limit on the total
Tavlarides,
(Placek and
of 60%
order
generally on the
intensity are
fluid velocity Umax can be
estimated by
U
max
u'max
where
U
=
is
max
the
+
u'
max
maximum
(0.7 w N D.)
-
(Eq. 54)
1.6
turbulent
mean
square
which
exhibited
root
velocity
fluctuation.
For
the
cultures
microcarrier
removal, the maximum total
less
than 72 cm/sec.
maximum
This is
values
and
death
fluid velocities given by equation 54 were
Thus, with P = 760 mm Hg and Pv = 47.1 mm Hg
one can estimate a minimum cavitation number
(Liley and Gambill, 1973),
of 370.
cell
over two orders of magnitude greater than the typical
for
which
occurs.
cavitation
Thus,
it
appears
that
cavitation did not occur in the experiments performed in this thesis.
In
general,
for
the
levels of agitation employed
cultures, cavitation should not present a problem.
in microcarrier
Nonetheless, for any
given design and set of operating conditions, the cavitation number can
be calculated.
as
one
of
the
A minimum value for the cavitation number might be set
The critical
design criteria.
incipient cavitation, however, appears
equipment (Boucher and Alves,
1973).
-
158
-
to
cavitation number
depend on the
for
scale of the
MECHANISMS OF HYDRODYNAMIC DEATH IN CONCENTRATED CULTURES
CHAPTER 5.
5A.
Effect of Microcarrier Concentration with High Agitation
primarily
through
circumstances,
unusual
concentrated
cultures
encounters
For
fields.
flow
time-average
cell
and,
cell death might also occur through hydrodynamic
As
between microcarriers.
discussed
previously,
collisions, even though
these
they may
flow between microcarriers which come
fluid
the
involve
in
microcarrier-eddy
under
interactions will be referred to as
primarily
occurs
agitation,
under high agitation,
interactions
death
high
cultures
dilute
For
in
close but not actual contact.
To
with
collisions
microcarrier
cultures
The
whether
determine
contained
occurs
inert
microcarriers
agitated at 150 RPM in
1.5 g/l Cytodex 1,
inert microcarriers were
through
death
agitation,
high
cultures
cell
microcarrier
were
added
the 125-ml vessels.
5% (v/v) serum,
added to levels of 0,
5,
to
All
and no dextran.
10,
15,
20,
25,
A control culture at 35 RPM without inert microcarriers was
and 30 g/l.
grown for reference purposes.
Figure 38 shows the attached cell concentrations
microcarrier
concentrations.
culture
The
at
150
for various inert
RPM without
inert
microcarriers exhibited a moderate amount of cell death and removal.
the
inert
microcarrier
concentration
was
increased,
concentrations were progressively reduced.
As
the attached cell
A detrimental effect from
adding inert microcarriers was especially apparent during the attachment
-
159
-
Speed
106
35 rpm
150 rpm
150 rpm
z-
5
10
..J
0-J
150 rpm
0
150 rpm
z
0
4
10
60
120
180
240
TIME, (HRS)
Effect of inert microcarriers
on net growth with high agitation
Figure
38.
-
160
-
300
With high inert microcarrier concentrations, cell concentrations
stage.
At 30 g/l,
12 hours.
dropped precipitously during the first
only 54% of
The debri from the unattached cells
the inoculum was viably attached.
was clearly evident for up to 30 hours past inoculation.
A detrimental effect of adding inert microcarriers was also apparent
inert microcarriers,
the
culture
at 150 RPM grew to 45% of the maximum density observed in
the
control
culture
growth stage.
during the
absence
In the
of
As inert microcarriers were added,
at 35 RPM.
growth
progressively decreased until the culture with 30 g/l exhibited only 8%
of the maximum density of the control.
At high levels of agitation, the
observed growth rates were clearly reduced through the addition of inert
microcarriers.
5B.
Cell Death through Microcarrier Collisions
microcarriers
Because
they
primarily
will
small and nearly neutrally buoyant,
are very
follow
streamlines.
fluid
Almost
all
relative
motion between two neighboring microcarriers will arise from the action
of turbulent eddies.
might
The viscous forces or pressure fluctuations from a
throw
two neighboring
microcarriers
single
eddy
other.
The volumetric frequency of such collisions, fe,
order in
microcarrier concentration,
f
where K2
is
c
=
K
against
each
would be second
Cm, and would thus be given by:
(Eq. 55)
C
2 m
a collision frequency constant.
The amount of cell death
from each collision will be proportional to the cells per unit surface
-
161
-
area,
If
and the effective surface area exposed to each collision, K 3 -
T,
a cell
in
an exposed area had a probability K4
of
rate
volumetric
the
collision,
death
cell
of death from each
from
collisions,
(dC/dt)coll. , would be then be given by
(dC/dt) Coll.
where C is
q2,
K 3K 4)
-
2
i m
volumetric cell concentration.
represents
-
q
C
C
(Eq. 56)
The specific death constant,
the combined product of the parameters K 2 , K 3 , and K4
divided by the total surface area per microcarrier, K 5 , or 4nrrp 2 ,
As all three parameters K2 , K3 , and K4 will vary with the level of
agitation and the strength of the hydrodynamic forces involved with the
collision,
the combined
term q2 should be a function of the
of
For mild agitation, there was no effect
agitation and fluid viscosity.
of adding
level
and thus the value of q2 was zero.
inert microcarriers,
In
general, the value of q2 will depend not only on hydrodynamic variables,
but also on the cell and microcarrier properties.
If
the eddy-length model is
microcarrier collisions,
the
now extended to include cell death from
(or viable)
attached
cell concentrations
should follow the equations
pC
1
with mild agitation
(Eq. 57)
with strong agitation
(Eq. 58)
dt
dC
C
=
pC - q 1 C -
q 2CC
dt
where
the criteria for cell death involves
-
162
-
the level of agitation and
may not be a simple function of Kolmogorov eddy length.
If
cell damage
occurred from a microcarrier collision, and if one of the microcarriers
the resulting damage should be,
was an inert microcarrier with no cells,
half of that which would
on average,
cells.
Thus,
are
microcarriers
inert
if
occur if
had
both microcarriers
added
at
high
levels
of
agitation, equation 58 should be extended to
dC
=pC
-
-
qlC
-
q2 C
(Eq. 59)
(q2 /2)C C
-
dt
where Ci is the concentration of inert microcarriers.
To evaluate whether microcarrier collisions
levels
are
important at high
one can analyze the data shown in
of agitation,
the model presented in
equation 59 is
correct,
Figure 38.
If
the data should follow
the relation
obs =
(Eq. 60)
b - (q2 /2 )C.
where
1
Mobs
=
C
dC
(Eq. 61)
avg
-
dt
and with constant q1 , Cm, and average y
b = constant
If
there is
=
(Eq. 62)
p - ql- q 2 Cm
a second order damage mechanism,
and if
all first
order
mechanisms are relatively independent of microcarrier concentration, the
observed growth rate should decrease in a linear fashion with the inert
microcarrier concentration.
The rate of damage
-
163
-
from the second
order
(involving the inert microcarriers) should be proportional
mechanism(s)
to
of damage from the first order mechanism(s)
The rate
slope.
the
should be proportional to the difference between the intercept,
b,
and
the value of (p - q2Cm)-
Figure
the average growth rate observed after attachment
inert microcarrier
the
versus
shows
39
of equations
predictions
concentration.
60-62 and clearly
The
follows
the
that there are at
collisions.
involves microcarrier
concentration and thus
in microcarrier concentration and
first order
mechanism is
other
indicates
data
One mechanism is second order in
least two distinct death mechanisms.
microcarrier
The
involves microcarrier-eddy encounters.
the
For
cultures
at
150
bulk
the
RPM,
increased through the addition of inert microcarriers.
power
number
correlations
in
presented
the
viscosity
kinematic
was
According to the
Materials
Methods
and
section, the culture with 30 g/l inert microcarriers should have had an
average
power
input
25%
microcarriers at 150 RPM.
than
higher
the
culture
with
no
inert
This would have apparently resulted in a 18%
increase in qi and an (as yet) undetermined increase in q2.
in
may have introduced minor errors
the calculations
This effect
of qi and q2 from
equations 60-62.
The linearity of the data in Figure 39 does not strictly prove that
the first order mechanism was independent of microcarrier concentration.
Nonetheless, the data follows a model which assumes this independence
-
164
-
-. 4
10
Co
C
1~
x
35 rpm
=
150 rpm
-2
0
12
6
18
24
INERT MICROCARRIER CONCENTRATION, (GM/LITER)
Observed specific growth rate
Figure 39.
vs. inert microcarrier concentration
-
165
-
30
is
on the microcarrier
of energy dissipation
rate
the
The pertinent criteria
range of concentrations investigated.
over the
If
the power draw will go up,
are added at constant speed,
microcarriers
surface.
The
but so will the amount of energy dissipated by other microcarriers.
average
Thus,
relatively unchanged.
be
may
solids
offset
increased
the
on
dissipation
increased
remain
may
increased power draw from
the
the
by
microcarrier
each
on
rate
dissipation
energy
other
This effect may account for the linearity of the data in
microcarriers.
Figure 39.
For
cultures
the
at
spacing
average
the
surfaces ranged from 50 to 380 microns,
microcarrier
length scales
Kolmogorov
RPM,
150
microcarrier
was
spacing
greater
than the
average
the
while the average
60 microns.
to
ranged from 50
between
The average
Kolmogorov length
scale for all but the most concentrated culture.
an eddy-microcarrier mechanism to be
for
In order
independent of
microcarrier concentration, one might think that average spacing between
the microcarrier surfaces would have to be greater than the
eddy
diameter,
somewhat
or
the
loosely,
Kolmogorov
length
smallest
scale.
Strictly, however, the Kolmogorov length scale is not defined as an eddy
but
diameter,
dissipation
does
not
rather
occurs
in
invalidate
as
the
typical
the absence
the
of
distance
solids.
the
logic behind
over
This
which
subtle
eddy-length
viscous
difference
model,
but
it
should make one wary of comparing eddy lengths with the distance between
microcarriers.
For microcarrier-eddy interactions to be independent of
-
166
-
microcarrier concentration,
it
is not
required that
the
microcarrier
spacing is greater than the Kolmogorov length scale, but rather that the
microcarrier
spacing
is greater
than the
dissipation occurs when an eddy interacts
distance
distance over which viscous
with a microcarrier.
should be somewhat less than the Kolmogorov
This
length scale,
as
the presence of solids is known to increase power dissipation (Hiemenz,
1977; Monin and Yaglom, 1971).
5C.
Effects of Agitation Power on Cell Death from Collisions
To investigate
the effects of agitation power on collision damage,
cultures with inert microcarriers were grown in the 125-ml vessels.
cultures
contained
3
g/1
Cytodex
1
g/l
inert
All cultures were agitated at 35
microcarriers, 5% FCS, and no dextran.
RPM for a 44 hour
15
microcarriers,
All
The cultures were subsequently
attachment period.
agitated at various speeds during the growth period.
The results of the experiment are shown in Figure 40.
at
the higher
lower viable
Extensive
stirring speeds,
especially
cell death from hydrodynamic
stirring speeds.
140 and 200 RPM,
than the control culture
cell concentrations
The cultures
exhibited
at 35 RPM.
occurred at the higher
forces
The amount of death increased sharply with stirring
speed; the culture at 200 RPM exhibited a strong and continual decrease
in
attached
cell
shown
As
concentration.
by
a
comparison
between
Figures 29 and 40, the rate of death for the concentrated culture at 200
RPM far
exceeded
that
for
a dilute culture
at 220
RPM in
the
same
vessel. The difference was due to death from microcarrier collisions.
-
167
-
10
6
-3-35
rpm
-----
70
rpm
e--- 100
rpm
*-
150
rpm
-
-
200
rpm
10
30
60
90
120
TIME SINCE ATTACHMENT
150
(HRS)
Figure 40. Net growth at different stirring
speeds with 15 g/L ine rt microcarriers
168 -
the
between
per unit
pobs,
rate,
attached cell
was
constant,
q2,
For each culture,
the
specific
order
second
agitation power
growth
to determine the relationship
Figure 40 were analyzed
The data in
mass.
death
from
calculated
a
linear
at
For the cultures
concntrtins.
and
average
observed net
regression
on
the
the
high agitation,
total specific death rate q was calculated from the equation:
q
=
p - pobs
(Eq. 63)
where p was the observed growth rate for the control culture at 35 RPM
with no hydrodynamic death.
specific death
The
rate due to microcar-
rier-eddy interactions, qi, was calculated from the correlation derived
for
the
dilute cultures
Figure 34.
(6.3 cm) vessels,
in the 125-ml
The collision death rate constant,
q2,
shown in
as
was then calculated
from the equation
q
-
g
(Eq. 64)
q2
C + C./2
m
i
where
the
factor
microcarriers.
of
for
2 accounts
For each value of
the
lack of
q2, a 95%
on
cells
the
inert
confidence interval was
calculated according to the statistical methods presented in Walpole and
Myers
(1972).
Because
uncertainty in the
value
of q2
arises
from
uncertainity in the values of both q and qi, the total interval for each
q2 was estimated as the sum of the intervals for each qt and qi.
Figure 41 shows the collision death rate constant, q2, versus
The data scatters somewhat but
average agitation power per unit mass.
indicates that q2 increases with the level of agitation.
-
169
the
-
The intercept
A
Di
=5.3
cm
Dt
=
6.3
cm
0.14
0.12
0.10
0.08
0.07
0.05
0.03
0.01
-0.01
200
400
600
800
1000
AVG. POWER PER MASS (CM 2/SEC3 )
Second order death rate constant
q2 vs. average power input per unit mass
Figure 41.
-
170 -
further verifying the observation of
falls close to the value of zero,
The error bars
insignificant hydrodynamic death with mild agitation.
represent
the
in
relationship
which
increase between
an
shows
been
graphed
determined
As
correlation.
mathematical
drawn
e can be
and
with
coordinates
arithmetic
on
q2
any
For purposes of simplicity, the data
through the confidence intervals.
has
Almost
q2.
of
calculation
the
uncertainty
The
point.
lead to tremendous
of q and q
the calculation
combined uncertainty in
data
each
for
intervals
confidence
95%
regression,
through
simple
a
the
line
linear
has
a
correlation coefficient of 0.85.
5D.
Effects of Fluid Viscosity on Cell Death from Collisions
To investigate
cultures
inert
with
supplements.
the effects of fluid viscosity on collision damage,
microcarriers
To avoid cell damage
were
grown
with
from time-average
500-ml vessels were used with the 5.3 cm impellers.
various
dextran
flow fields,
the
All five cultures
contained 3 g/l Cytodex 1 microcarriers, 15 g/l inert microcarriers, and
5%
FCS.
All
five
cultures
were
grown
at
supplement for a 33 hour attachment period.
60
RPM with
no
dextran
Four of the cultures were
subsequently agitated at 190 RPM while one control culture continued to
be agitated at 60 RPM.
The four cultures at 190 RPM were supplemented
with various levels of 78,500 MW dextran.
The
results
of the experiment are shown in Figure 42.
All
four
cultures at 190 RPM exhibited lower viable cell concentrations than the
control culture at 60 RPM.
Extensive hydrodynamic death and removal
-
171
-
106
60 rpm
0m
No dextran
A1S------- AA
...
10
190 rpm
44 g/L dextran
.
-----
5
190 rpm
59 g/L dextran
0 -190
rpm
3 1 g/L dextran
-A-
190
rpm
No dextran
10
4
0
30
60
90
TIME SINCE ATTACHMENT
120
150
(HRS)
Effect of dextran (78,500 MW) on net growth
Figure 42.
at different stirring speeds with 15 g/L inert microcarriers
occurred at 190 RPM.
The total rate of death was the greatest
in
the
culture with no dextran but was moderately reduced with 31 g/l dextran
and
strongly
reduced with
44
and
59
g/l
dextran.
As
shown
by
a
comparison between Figure 30 and Figure 42, the rate of death in the
concentrated culture
with no dextran at 190 RPM far exceeded that for
the dilute culture with no dextran at 185 RPM in
the same vessel.
The
difference was again due to cell death from microcarrier collisions.
The data in
between
Figure
analyzed to determine
42 were
the collision death rate constant,
For
viscosity.
microcarrier-eddy
each
culture,
the
qi,
interactions,
q2,
the relationship
and the kinematic fluid
specific
death
rate
due
to
was calculated from the correlation
derived for the dilute cultures in the 500-ml (9.6 cm) vessels, as shown
in
The collision death rate constant, q2, was calculated
Figure 34.
section 5C.
from the methods presented in
inputs,
the
collision
rate
death
Due to differences in power
constants
were
normalized
by
the
average agitation power per unit mass.
Figure 43 shows the normalized collision death rate constant, q2/E,
versus
kinematic
The
fluid viscosity.
data
scatters
somewhat but
clearly indicates that q2 decreases with the kinematic fluid viscosity.
The error
point.
q2,
bars
represent
the
95% confidence
intervals
for
each
data
Again, there was tremendous uncertainty in the calculation of
and almost any mathematical
confidence
intervals.
For
relationship
purpose
the
of
can be drawn through the
simplicity,
the
data
graphed on arithmetic coordinates with a simple linear regression.
-
173
-
was
As
*
Di =5.3
cm
Dt =9.6 cm
0.40
1(0
C~J
0.30
0.20
q
4p
0.10
I
4I
0.00
p
-0.10
0.00
I
I
1.00
0.50
KINEMATIC
1.50
I
2.00
2.50
FLUID VISC. (10- 2 CM 2/SEC)
Normalized second-order death
Figure 43.
rate constant vs. kinematic fluid viscosity
-
174
determined through regression, the line has a correlation coefficient of
0.84.
Figure 44 shows the collision death rate constant, q2, as a function
of
E/v
for both the 125 and 500-ml vessels with the same impeller.
The
e/v.
The
scatters
data
q2
that
shows
clearly
but
with
increases
The data do
regressed line has a correlation coefficient of 0.84/1.0.
The regressed
indicate a significant effect of vessel geometry.
not
through
line
data
observation
the
verifying
the
of
all
of
has
an
insignificant
cell
further
zero,
near
intercept
mild
with
death
agitation.
The collision death rate constant increased with the power input and
collisions
This indicates that microcarrier
the fluid viscosity.
decreased with
fluid.
arise through the action of turbulence in the
The
collisions may occur primarily through turbulent eddies which are of a
size
comparable
to
spacing
Cherry and Papoutsakis
velocities and
In
viscous
between microcarriers.
(1986a),
As
discussed
such eddies may lead to high relative
collisions between neighboring microcarriers.
microcarrier
dissipation
cultures,
regime
the
eddies
typically
are
spacing between microcarriers.
This hypothesis is
near
the
to
the
are
in
or
comparable
in
size
which
It is likely that such high wave number
eddies account for most of the cell death from microcarrier
in Figure 44.
in
collisions.
supported by the lack of geometric effects observed
High wave number eddies exist in
-
175
-
states of equilbrium
A
Di =5.3 cm
Dt
6.3 cm
0
Di = 5.3 cm
Dt = 9.6 cm
0.16
0.12
0.08
0.04
0.00
-0.04
20
40
60
POWER PER MASS/KIN.
80
100
VISC. (10 3/SEC 2
Figure 44. Second-order death
rate constant vs. (E/v)
-
176
-
120
which are not strongly dependent on reactor geometry. Low wave number
eddies
and time-average flow fields are strongly influenced by reactor
geometry.
-
177
-
CELL DAMAGE FROM DIRECT SPARGING
CHAPTER 6.
Effect of antifoam addition and direct sparging on cell growth
6A.
It is frequently stated that direct sparging causes damage to cells
1981;
(Pharmacia,
microcarriers
on
and
Spier
1984).
Griffiths,
Nonetheless, no published reports were found which document such damage.
damage
Cell
is
known
to
damage occurs from direct sparging in
the damage may be more
in
extensive
sparging
direct
Handa et al,
(Tramper et al, 1986;
cultures
from
occur
of
suspension
It is likely that
1987).
microcarrier cultures.
given that
cultures,
microcarrier
In fact,
the cells are immobilized and are more susceptible to mechanical forces.
effect
The
of
sparging
As
cultures.
microcarrier
two experimental
section,
on
cell
described
growth
in
was
the
examined
FS-4
and
Methods
500-ml Bellco
spinner
Materials
cultures were grown in
for
flasks equipped with filter sticks for direct sparging. One experimental
culture was sparged at a superficial gas velocity of 0.01 cm/sec with a
Foaming was essentially eliminated through the
90:10 air-CO 2 mixture.
daily addition of 20-40 ppm Medical
Midland, MI).
stick,
and
impeller.
FCS,
were
basis,
no
stick, but with no sparging.
complete with filter
experimental
third
Corning,
A second experimental culture was grown with antifoam in
an identical vessel,
A
Emulsion AF antifoam (Dow
culture was
sparging
in
grown with no
500-ml
a
Corning
antifoam, no
vessel
with
a
filter
7.8
cm
All cultures contained 2.0 g/l microcarriers in DMEM with 5%
replenished
with nutrients
on
the normal
interval
feeding
and were essentially at saturation with the 90:10 air CO2 gas
-
178
-
mixtures.
Cell growth in the
the results of the experiment.
Figure 45 shows
modified Bellco vessel with antifoam was essentially identical
to cell
This indicates that the
growth in the Corning vessel with no antifoam.
modifications to the Bellco vessel, including the presence of the filter
It also indicates that antifoam
growth.
on cell
had no effect
stick,
AF, at levels between 40 and 180 ppm, had no effect on cell growth.
Aunins et al
on microcarriers,
tPA-CHO cells
For
similarly found no
(1986)
effect on cell growth from antifoam AF at 100 ppm.
For
culture
the
which
directly
was
sparged,
from
cell damage
sparging.
the
viable
cell
This is evidence of
concentrations were lower than in the controls.
significant
the
damage was
The
clearly
evident even though the superficial gas velocity was only 0.01 cm/sec
and there was no significant
the
first
published
foam formation.
of
evidence
cell
To my knowledge, this is
from
damage
sparging
in
covered
the
microcarrier cultures.
Subsequent
to
the
described
experiment
above,
growth period up to 180 hours after inoculation,
added to the sparged culture.
approximately
0.5
cm/day.
which
antifoam was no longer
A foam layer began to form at a rate of
After
four
days,
nearly
microcarriers had collected on the vessel wall above the
Many microcarriers
were spattered
regions of the vessel.
If
through bubble
bursts
all
179
-
the
foam layer.
into
one wishes to keep the microcarriers
-
of
distant
in the
5x10
4
4
A
No antifoam
No sparging
*
Antifoam
w/o sparging
*
Antifoam
w/ sparging
4
10.
0
40
80
120
160
TIME (HRS)
Figure 45.
Effect of antifoam and
sparging on net cell growth
-
180
-
200
liquid phase, foam formation must be strictly avoided.
Mechanisms of Cell Damage from Sparging in Microcarrier Cultures
6B.
For
on
cultures,
there has been little
cultures
In the absence of foam
investigation.
microcarrier
in
from sparging
The possible mechanisms are listed below along
not clear.
is
of
microcarrier
For
sparging.
of cell damage
the mechanism
amount
considerable
been
has
direct
from
damage
cell
research
formation,
there
cultures,
suspension
with a review of the results for suspension cells:
1)
Nutrient
such as
onto
depletion.
Required nutrients which are surface active,
denatured or
deactivated
bubble burst
at
fluid phase
out of the
These substances could be concurrently
the bubble interface.
the
adsorbed
could be
many proteins,
rose with the bubble or as
as they
culture
Aunins
surface.
the
(1986) have
et al
shown that significant medium degradation can occur through direct
sparging
a
over
week
long
period.
Such
degradation may
arise
through protein denaturation at the liquid-gas interface.
2)
Interfacial
interface,
forces.
Upon
cell
contact
with
the cell membrane could spread and lyse,
moving
a
bubble
or non-integral
membrane proteins, such as fibronectin, could be removed.
If cell
lysis did not occur upon initial contact, the cell may still adhere
to the bubble and then lyse when the bubble bursts at the culture
surface.
that
and Handa et al (1987)
Kilburn and Webb (1968)
damage
of
cells
suspension
from
reduced by adding surface active agents,
general,
sparging
is
have found
significantly
such as Pluronic F-68.
In
surface active agents may form a shield between the cell
-
181
-
or
lysis
comes only
that protection
however,
appears,
cell
eliminate
thus
and bubble, and
It
entrainment.
from surface-active
agents which are high in molecular weight (Kilburn and Webb, 1968).
3)
directly
the
to
exposed
killed
could be
Cells
Bubble bursts.
bursts
bubble
at
they
damaged if
or
the
culture
are
surface.
Evidence for this mechanism has been given by Tramper et al (1986)
and Handa et al (1987) for suspension cells.
Tramper et al (1986)
showed that cells caught in a bubble burst at the end of a pipette
were
columns, both Handa et al
For bubble
damaged.
Tramper and Vlak
the volumetric
found that
(1987)
(1987)
and
rate of damage
from sparging of suspension cells decreased with an increase in the
bubble
Tramper
indicative
This is
height-to-diameter ratio.
disengagement at
the
culture surface
1987)
or
at
and Vlak,
injector
the
of cell damage from
(Handa et al,
1987;
(Tramper
nozzle
and
Vlak, 1987).
4) Hydrodynamic
hydrodynamic forces
bubble.
could
Cells
forces.
be
killed
or
damaged
by
the fluid adjacent to a rising or bursting
in
This effect should increase with volumetric gas flow rate,
but should decrease with fluid viscosity.
An increase in viscosity
should slow the bubble rise and dampen the turbulence in the fluid
adjacent to the bubble.
For
suspension
cells,
essentially unaffected by
cell
damage
increase
from
sparging
fluid viscosity
in
appears
to
be
through dextran
Although the data is limited and
supplementation (Handa et al, 1987).
not conclusive, it appears that damage of suspension cells from sparging
-
182
-
in
hydrodynamic
be
not
may
This
nature.
is
as
surprising,
not
suspension cells are more than two orders of magnitude smaller than most
bubbles and are relatively resistant to damage from hydrodynamic forces
(Augenstein et al, 1972; Dodge and Hu, 1986; McQueen et al, 1987; Smith
et al, 1987).
Cells
A simple calculation readily illustrates that
from hydrodynamic forces.
the
from
observed
damage
hydrodynamic in nature.
which
column
discussed
in
occupied
Aunins
are much more sensitive to damage
however,
on microcarriers,
Figure
in
sparging
45
could
have
been
In the sparged culture, the bubbles rose in a
10%
approximately
et al
of
the power
(1986),
the
volume.
culture
input to
As
the liquid near
bubbles may be approximated by the power required to match the buoyancy
Thus,
forces.
for the sparged column region, the power
sparging per unit mass of fluid, es,
Q ( Pf -
may be roughly calculated by:
pb ) g H
-
Pf ( H (7rDt 2/4) 0.1
g===
Es
the gas density,
where Pb is
input from
Q
is
(Eq.
H0)
the volumetric
65)
flow rate of gas in
ml/sec, g is the gravitational acceleration, H is the reactor height,
and H0
is
the gas hold-up in
the sparged region.
The gas hold-up was
estimated to be 20 ml from the increase in culture volume upon sparging.
Equation
local power
into
the
a value
65 was used to estimate
input per unit mass
in
of 100 cm2 /sec
the sparged region.
3
for the
This is
well
range for which death occurs from impeller-generated power,
-
183
-
even with
the mild viscosity
in
bubbles.
part,
antifoam
about by the
Thus, the damage from sparging could have been due, at
supplementation.
least
increase brought
to
Future
power
dissipation
in
the
fluid adjacent
research will hopefully elucidate
to
the mechanisms
kinetics of cell damage from sparging in microcarrier cultures.
-
184
-
rising
and
BIOREACTOR DESIGN AND OPTIMIZATION
CHAPTER 7.
7A.
Mass Transfer Requirements
In microcarrier cultures, agitation is required for cell-liquid mass
transfer
mass
transfer,
gas-liquid
mixing.
As previously
(oxygenation),
phase
liquid
and
transfer can be
discussed, cell-liquid mass
For each chemical species
approached with a Sherwood number analysis.
which is consumed or produced by cells on microcarriers, the normalized
gradient between the chemical concentration in the bulk medium, Xb, and
the concentration at the cell surface, Xc, is given by
Xb - Xc
T
the
is
(Eq. 66)
Df Xb Shc
Xb
where
Re dp
I
diffusion coefficient
per
coverage
surface
for the
cell
rate
number
for cell-liquid mass
per
unit area,
The
chemical species.
given
transport,
Shc,
is
Df
and Rc
species,
given chemical
the
for
uptake
cells
in
given by
(Sano
is
the
is
the
Sherwood
et al,
1974; Chaudhari and Ramachandran, 1980)
Sh
i
where
is
c
=
the
(Eq. 67)
2 + 0.4(F d 4/D V )1/3
pD f
per
input
power
average
unit
mass
and
dp
is
the
microcarrier diameter.
In
the
design
of
a
reactor,
one
might
specify
the
chemical
concentrations at the cell surface, or the acceptable gradients between
the
cell
surface
and
bulk
In
media.
-
185
-
general,
as
long
as
the
are
microcarriers
and the viscosity has not been
= 2)
(She
suspended
the gradients will be negligible.
greatly increased,
Given negligible
the cells and bulk fluid, one
gradients between
should also consider the requirements for adequate mixing in the liquid
transferred
are
chemicals
in the
liquid phase
the
throughout
tions
the
into
In regions where
reactor.
liquid
mixing
phase,
should
be
to to eliminate cell damage from locally high concentrations.
adequate
If
required to maintain appropriate chemical concentra-
Mixing is
phase.
are directly added for pH control,
acid or bases
mixing should be
adequate to minimize the pH excursion and any corresponding cell damage.
If
oxygen
pure
is
used for oxygenation,
mixing should be adequate
to
as dissolved oxygen
limit the local concentration of dissolved oxygen,
levels in excess of normal air saturation are frequently toxic (Kilburn
and Webb, 1968; Balin et al, 1976).
In
general,
in
to
only
added,
fluid should be
supply and nutrient uptake.
nutrient
not
the
minimize
the
transients
circulated among
the
regions
of
Adequate circulation is required
in regions
where
chemicals
are
but also to ensure that adequate nutrient levels are maintained
distant
susceptible
Oxygen is
regions of the reactor.
to
depletion.
As
oxygen
is
often the nutrient most
toxic
in
excess
of
air
saturation, which represents a very low molar concentration, the oxygen
content
of
supplied.
the medium must be
For
sufficiently
limited in the
region where
high cell concentrations
and
oxygen
is
low mixing
rates, the limited oxygen content may be completely consumed before the
-
186
-
medium recirculates back to the region of oxygen supply.
Liquid phase mixing requirements are frequently analyzed in terms of
Mt,
the mixing time,
a
For many reactors in the
after it has been added at a single position.
fully-turbulent regime,
for
the reactor
concentration throughout
reach a homogeneous
to
chemical
required
time
the
represents
time
mixing
The
times.
mixing
for the fluid phase can be
estimated from (McCabe et al, 1985):
M
al (H/D .)
=
(Eq. 68)
/N
(Dt/D)
where H is the liquid height, N is the impeller rotation rate, and al is
a constant which is characteristic of the reactor and impeller geometry.
The mixing time generally
estimated as
be
can
equation
(McCabe
et al,
1985).
time required for fluid element to circulate once around a
the
reactor
required for about
time
circulations of the tank contents
five complete
Thus,
represents the
From
68.
consumption rate,
oxygen supply
this
of
the
mixing
time
and
the
one-fifth
circulation
the variation in
given by
volumetric
oxygen
dissolved oxygen level between the
of the
and uptake regions
time
reactor,
ADO,
can be roughly
estimated
R
0
AD
where Mt is
CM
t
(Eq. 69)
=
the mixing time given by equation 68, C is the viable cell
concentration, and R0 is the specific oxygen uptake rate per cell.
-
187
-
In
the design of a microcarrier reactor, one might specify the maximum AD0
between
agitation
The
local medium.
and
cells
the
oxygen concentration
in
based on the cell metabolism and any gradients
should
then be
sufficient to provide a AD0 less than the specified maximum.
Given adequate cell-liquid transport and liquid-phase mixing, one
consider
also
should
into and out of the bulk fluid.
products
to supply,
difficult nutrient
only sparingly soluble in
by the cells and yet is
all
Nearly
and waste
other nutrients
perfusion (Nahapetian, 1986)
products
can
levels
adequate
solution;
aqueous
Oxygen is
also
be
cell culture medium.
soluble
easily maintained
or medium exchange.
in
through
Oxygen can also be
through an external
this technique requires high recirculation rates and
immobilization.
cell
generally the most
are highly
supplied through continuous perfusion and recycle
oxygenator,
waste
consumed at a considerable rate
is
as it
and
nutrients
of
transfer
overall
the
microcarrier cultures
For normal
in a stirred
tank, the perfusion techique is not a viable means of supplying oxygen.
through
supplied
generally
is
Oxygen
between the bulk fluid and a gas phase.
transfer,
*
where
KL
o
is
transfer
mass
The volumetric rate of oxygen
generally described by an equation of the form:
NO, is
N
continuous
=
K a (D
the
L
o
-
overall
(Eq. 70)
D )
o
oxygen
transfer
coefficient,
a
is
the
interfacial gas-liquid surface area per unit culture volume, Do * is the
dissolved oxygen concentration in equilibrium with the gas phase, and Do
-
188
-
is
the
steady
average
dissolved
state,
the
in
oxygen concentration
transfer
oxygen
volumetric
At
the bulk media.
rate
the
equal
will
volumetric oxygen consumption rate, and thus
*
R
C
o
K a
=
(D
(Eq. 71)
D )
-
o
L
o
where R0 is the specific oxygen uptake rate per cell and C is the viable
cell concentration.
In
design of a microcarrier bioreactor,
the
in the
oxygen
pressure of
maximum partial
pressure of oxygen in
average
The
partial
will specify the equilibrium
Po,
the gas phase,
the
gas phase and the
bulk medium.
in the
of dissolved oxygen
concentration
one might specify
value Do* in the liquid from the typical Henry's Law relation
*
D
where
#
is
P
=
o
the
0
(Eq. 72)
#
Henry's
Law coefficient.
levels
above
the
gas phase and
air saturation.
the
gas
the toxic effects of dissolved oxygen
In setting the average concentration of
dissolved oxygen
in the bulk medium, one should consider the
concentration at
the cell
between
different
regions
surface,
of
phase
one should consider the level of
composition or equilbrium value Do*,
mixing near
In setting
the
desired
the variation in dissolved oxygen
vessel,
and
gradient
in dissolved
oxygen between the cells and local fluid.
Specification
transfer.
of
Do
and
The maximum cell
Do*
sets
the
concentration
-
189
-
driving
is
force
for
oxygen
then determined by
the
If surface aeration is employed, the value of KLa
values of R0 and KLa.
is
of
equations
by
given
generally
the
form
(Aunins et
al,
1987;
Oldshue, 1983):
-K
KL a
=
a2 (Re) 6 (Sc)
Re
=
N D. /v
Sc
=
v/Df
Fr
=
N
Sh
where
s
i
(Eq. 75)
(Eq. 76)
0
(Eq. 77)
and 63 are empirical constants,
surface aeration, as
as
(Eq. 74)
(Fr)
b
number for surface aeration,
volume
(Eq. 73)
/D )(1/H)
D./g
i
61, 62,
where a2,
(ShS Df 0
=
Ks is
the oxygen transfer coefficient
is the gas-liquid surface
given by the reciprocal
the Sherwood
Shs is
for
area per unit culture
of the liquid height H for surface
aeration, Re is the impeller Reynold's number, Sc is the Schmidt number,
the Froude number,
Di is
the impeller diameter,
rotation rate,
v is
the diffusion coefficient
Dfo is
Fr is
Dt is
the tank diameter,
the kinematic fluid viscosity,
N is
vb is
for oxygen,
the impeller
the kinematic
suspension viscosity, and g is the acceleration due to gravity.
tank is
fully baffled,
the effect
If the
of Froude number becomes negligible
and 63 is essentially zero.
Aunins
et
al
(1986)
have investigated surface
aeration in
baffled
cell culture reactors containing medium with 10% serum and no thickening
-
190
-
agents. From their results, one can determine a value of 0.61 for a2 and
The value of 62 is generally considered to be 0.33 (Aunins
0.73 for 61.
et al, 1986).
is
oxygen
If
tubing
surface
and
the value of KLa is determined by the sum:
aeration,
=
K La
K
a
K
a
(Eq. 78)
from surface aeration,
as given
the contribution from silicone
and Ktat represents
73-77,
equation
+
the contribution
where Ksas represents
by
silicone
both
supplied through
tubing aeration, as determined by the tubing mass transfer coefficient,
Kt,
baffled
tubing surface
the
and
culture
cell
tubing mass
transfer
area
unit
per
reactors
which
coefficient
is
are
volume,
culture
geometrically
given by
For
at.
similar,
the
an equation of the form
(Aunins et al,1986):
1/Kt
where a3,
=
a3 (dt/D
+
c
64, 65,
) (Re)-64 (dt/D
-65 (Sc)-66
and 66 are empirical constants,
c is
(Eq. 79)
the conduction
resistance through the tubing wall, dt is the tubing diameter, Dt is the
tank
diameter,
Df,o
is
the
coefficient
diffusion
for
oxygen
in
the
medium, Re is the impeller Reynold's number as given by equation 75, and
the Schmidt number as given by equation 76.
Sc is
have
found values
values
of 0.055 for a3 and 0.69 for 64,
Aunins et al (1986)
and have estimated
For 0.03 cm silastic silicone
of 0.53 for 65 and 0.33 for 66.
tubing, the value of c was estimated to be 140 sec/cm.
-
191
-
7B.
Basic Principles in Bioreactor Design and Optimization
design
The
of
is
bioreactors
maximum cell concentration
the
Upon scale-up,
optimization problem.
engineering
chemical
classic
a
will be determined by the effects of several independent variables, such
fluid viscosity,
as the microcarrier concentration,
and
sparging
rate.
increase
An
in
microcarrier
cell death from collisions.
concentration will
may also lead to more
it
provide more surface area for growth; however,
level of agitation,
An increase in fluid viscosity will reduce
An increase in
hydrodynamic death, but will also reduce mass transfer.
will
agitation
hydrodynamic death.
transfer,
mass
increase
may
but
also
increase
An increase in sparging rate will increase mass
transfer, but may also lead to more cell death.
In general, there will
be a trade-off between mass transfer and hydrodynamic death.
To accurately incorporate these trade-offs in bioreactor design, one
needs
quantitative
death.
hydrodynamic
quantitative
In
this
death
expressions
thesis,
for
expressions
In
the
previous
the
rates
section
for the rates of mass
quantitative expressions
of
transfer
mass
of
this
and
chapter,
transfer were reviewed.
for the rates of hydrodynamic
in microcarrier cultures have been derived for the
first time.
The cell population kinetics have been found to follow the expression:
dC_
=
-
C - qC -
(Eq. 80)
q2 mC
dt
6.2 x 10-13
q=
q
=
(Eq. 81)
3 3/4
(Eq. 82)
7.6 x 10-16 (T/V)
-
192
-
where p is
independent of the level of
the inherent growth rate and is
agitation, qi is the first-order specific death rate in sec-1, and q2 is
For low levels of
the collision death rate constant in micro/ml-sec.
agitation,
insignificant,
essentially
is
death
hydrodynamic
the
and
values of qi and q2 are generally negligible.
Equations
81
microcarrier-eddy
processes
relatively
kinetics
the
describe
interactions
appear to
and
microcarrier
flow fields is
appears
damage
to
cell
from
death
These
collisions.
2
approximately 5-9 dyne/cm .
In contrast, cell damage
highly dependent on reactor geometry.
occur when
from
surface
microcarrier
of
involve high wave number eddies and appear to be
independent of reactor geometry.
from time-average
Such
82
and
the
time-average
maximum
shear
fields,
flow
the
stress
on
Tmax,
exceeds
This fact can be used as a criterion for
the avoidence of cell damage from time-average flow fields.
Kinetic expressions for the rates of mass transfer and hydrodynamic
death can be used to optimize the reactor performance according to many
different
death,
objectives.
The
the
yield
maximize
nutrients,
or maximize
productivity.
to
minimize
generally
be
objective may be
of
a
given
to minimize hydrodynamic
product
the cell concentration
on
a
given
and volumetric
set
of
reactor
In the most general sense, the overall objective will be
the
cost
As
of production.
significant,
kinetic
the
economies
expressions
greatest use in the design of large scale units.
-
193
-
of
may
scale
find
will
their
one might consider
To illustrate the use of the kinetic expressions,
problem
the
scale
concentration
the maximum cell
bioreactors,
In such
bioreactor.
in a large
cell concentration
the
of maximizing
is
frequently limited by the rate of oxygen transfer (Aunins et al, 1986).
The
oxygen limitation will occur as
oxygen
level
of
Specification
Do,min,
value,
minimum
this
or minimally
a critical
below
drops
the cells grow and the dissolved
acceptable
value.
gas
phase
and
the
composition will specify the maximum driving force for oxygen transfer.
Specification of the reactor geometry, agitation power input, and fluid
At the point of maximum oxygen
viscosity will specify the value of KLa.
transfer,
an oxygen balance gives:
*
R
o
C
max
K a (D
=
L
-
o
D
.
o,min
(Eq. 83)
)
where R. is the specific oxygen uptake rate and Cmax is the maximum cell
concentration which can be adequately supplied with oxygen.
For
many
associated
cells,
uptake
oxygen
(Tyo and Wang,
1980;
is
both
Goldstein,
growth
1986).
and
maintenance
The specific oxygen
uptake rate can generally be described by an equation of the form (Pirt,
1975):
R
0
where Yn/o
is
+
=
(Eq. 84)
M
n/o0
the growth yield of cells on oxygen and Mo is
maintainence coefficient, or the specific oxygen uptake
growth.
-
194
-
the oxygen
rate under no
to
are utilized
given
concentration
cell
maximum
the
extent,
fullest
their
of a reactor
transfer capabilites
oxygen
If the
by
the
limitations of oxygen transfer will equal the maximum cell concentration
contact
maximum
cell
and
specific growth rate drops to
When the
inhibited.
This
grow toward confluence
the cells
concentration will be reached as
become
death.
of hydrodynamic
limitations
the
given by
a
value equal to the total specific death rate, the rate of change in cell
concentration will be zero, and the cells will have reached the maximum
cell concentration:
dC
dt
or
=
0
=
q, +
=
pC - q1 C -
(Eq. 85)
(Eq. 86)
q2 m
between
Substituting
q 2 GmG
84,
83,
equations
and
86,
one
arrives
at
the
result:
*
K
Y
C
max
n/o
-
where Cmax is
Yn/o
M
a
L
-
(D
+
D
.
)
o,min
q2 Cm
o
q, +
(Eq. 87)
the maximum cell concentration as determined by the rate
of oxygen transfer and hydrodynamic death.
Equation 87 quantitatively
transfer
and hydrodynamic
sets
forth the trade-off between oxygen
specifies a quantitative relation
It
death.
for maximixing cell concentration.
Through information on the rates of
oxygen transfer and hydrodynamic cell death, equation 87 can be used to
determine
which
reactor
fluid
geometry,
-
195
-
viscosity,
microcarrier
and
concentration,
These
concentration.
for the other mass transfer requirements.
consideration
must be
sufficient
suspend the microcarriers
to
cell
maximum
performed, however, with
must be
calculations
the
to
lead
agitation
of
level
The agitation
adequate
and provide
liquid-phase mixing.
in
As shown
Equation 87,
oxygen transfer without a
in
an increase
concurrent increase in hydrodynamic death will lead to a higher maximum
cell
appears
involve only the
to
cultures,
microcarrier
For
concentration.
smallest eddies,
In contrast, mass
dependent on geometry.
damage
hydrodynamic
strongly
which are not
transfer involves not only
small eddies, but also large eddies, which are strongly dependent on
By manipulating the effects of geometry on the large eddies,
geometry.
significant
increases
in mass
attainable
should be
transfer
without
concurrent increases in hydrodynamic damage.
7C.
Illustration of Optimization Calculations
design can be approached
To fully illustrate how bioreactor
optimization
optimization calculations
The
culture.
rate
quantitative
involving
problem
as an
expressions,
are described below for an FS-4 microcarrier
optimum
combination
of
agitation,
microcarrier
concentration, and fluid viscosity were determined for a given reactor.
The
objective
general,
such
was
an
to
maximize
optimization
different reactor geometries.
maximum
the
be
might
cell
concentration.
performed
for
a
number
In
of
The geometry which leads to the highest
maximum cell concentration would be chosen as the best.
-
196
-
The geometry of the reactor for this optimization is shown in Figure
46 and in Table 3.
The reactor has a liquid volume of 100-liters and is
a pitched-blade
equipped with baffles,
The
(FBT).
turbine
is
reactor
turbine
reactors
the
to
similar
geometrically
which have been extensively studied by Aunins et al
(1986).
For this
it was assumed that oxygen transfer came solely through
optimization,
The oxygen transfer coefficient
aeration.
surface
and a flat-blade
(PBT),
equations 73-77 with a2 = 0.61, 61 = 0.73, 62
=
then given by
is
0.33, and 63 = 0 (Aunins
et al, 1986).
From the results of Bates et al (1963) and Rushton et al (1950), one
can estimate
a power
turbine and a
number of 1 for the pitched-blade
power number of 4 for the flat-blade turbine, with both turbines in
The spacing between the turbines
fully-turbulent regime.
60%
of
their
independently.
that
such,
the
Thus,
operation in the
for
required for microcarrier
E,
was estimated by:
e
=
where N
impellers
may
less than
not
operate
From the results in Richards (1963), one could estimate
the power draw would be only 80%
operation.
mass,
As
diameter.
is
the
0.8 N
p
N3 D.5/
i
suspension,
of the
value
for
independent
complete turbulent regime, as
the average power input per unit
(Eq. 88)
V
c
is the combined power number with an estimated value of five,
Vc is the culture volume, and N is the impeller rotation rate, with all
terms in cgs units.
-
197
-
Baffles
D.O. Probe
4-FBT
Figure 46. 100-Liter reactor with
4-bladed flat-blade turbine (4-FBT)
and pitched-blade turbine (4-PBT)
-
198
-
TABLE 3.
GEOMETRY OF 100-LITER BIOREACTOR
Dimension
Size (cm)
Tank diameter
53.3
Liquid height
44.8
Impeller diameter
26.7
Baffle width
6.1
Radius to baffle inner edge
15.6
Impeller blade width
8.0
Height of center of pitched-blade turbine
15.0
Height of center of flat-blade turbine
30.0
-
199
-
10-liter reactor
For the
al
investigated by Aunins et
(1986),
the
minimum speed for complete microcarrier suspension was approximately 30
RPM
1986)
(Goldstein,
This correponds to an estimated value of 16
and no thickening agents.
Upon scale up to
for the average power input per unit mass.
cm2/sec3
the
10 g/l microcarriers,
for medium with 10% serum,
agitation power
per
required for suspension should be reduced according to
the
100-liter
geometrically-similar
unit mass
the
reactor,
equation (Nienow, 1985):
1
sl
where
average
the
is
(Eq. 89)
0.28
i,
/ Di2
2
unit
per
input
power
mass
required
for
microcarrier suspension in the 10-liter reactor, T2 is the average power
per
mass
unit
reactor, Di,1
Di,2 is
89,
required
is the
suspension
for microcarrier
the
impeller diameter for
in the
100-liter
10-liter reactor, and
From equation
the impeller diameter for the 100-liter reactor.
one can estimate a minimum power per unit mass of 13 cm2/sec3 for
microcarrier
complete
unthickened
medium.
incorporate
the minor
in
suspension
From the
the
100-liter
of Zweitering
results
with
vessel
(1958),
effects of fluid viscosity and volume
one
can
fraction
solids on the power required for microcarrier suspension.
optimization
This
liquid-phase
was
performed
The
criteria
200
-
adequate
dissolved oxygen
was less than 2% of saturation
cell-liquid transport was
-
of
The liquid phase mixing
the estimated variation in
as determined from equation 69,
air.
the
under
mixing and cell-liquid transport.
considered adequate if
content,
with
was
considered
adequate
if
the
fluid,
determined
as
increase
viscosity
from
was
as
so
limited
to
than
less
was
66,
equation
and
local
0.10.
The
the cells
between
in oxygen
gradient
estimated normalized
introduce
not
cell-mass
transport limitations at a Sherwood number of two, or the minimum value
for complete suspension.
Cell
damage
the viscosity
limiting
flow
from time-average
fields
was
easily avoided by
For all conditions investigated, the
increase.
maximum shear stress on the microcarrier surface from time-average flow
fields was less than 1 dyne/cm
2
This optimization requires knowledge of the mathematical dependence
of specific growth rate on cell and microcarrier concentration.
4
the
cells,
mathematical
inhibition and
contact
inhibition
contact
on
cell-derived growth
growth
was
inhibitors.
with
incorporated
of
effects
the
both
involves
dependence
For FS-
The effect of
the
following
empirical equations which fit the data presented in Hu et al (1985) for
FS-4 cells:
where Z
p
=
ymax (100 - Z)/60
for Z > 40
(Eq. 90)
A
=
Amax
for Z < 40
(Eq. 91)
The growth rate free of contact
the percent confluence.
is
inhibition, pmax, and the maximum surface coverage depend weakly on the
volumetric
cells
are
cell concentration, as
inoculated
microcarrier,
at
a
shown in Chapter
constant
roughly
the weak dependence
-
on volumetric
201
-
1.
number
Because
of
cells
FS-4
per
cell concentration can
microcarrier
is
concentrations
dependence
optimization,
this
For
concentration.
empirical
a
by
described
roughly
be
microcarrier
on
range
relevant
the
between 5 and 15 g/l.
of
For this range,
the data in Figures 12-14 for 5% serum can be described by the empirical
relations:
pmax
=
Z
=
4.3 x 10
5
/C
0 26 2
(Eq. 92)
100 C
0.80
500 (Cm )
(Eq. 93)
where Cm is the microcarrier concentration in microcarriers/ml, C is the
cell concentration in cells/ml, pmax is the maximum growth rate in
sec- , and Z is the percent confluence.
This optimization was performed under the following assumptions:
1) the headspace gas contained a 90:10 air-CO 2 mixture,
2) the medium was supplemented with 5% (v/v) fetal calf serum
3)
the diffusion coefficient for oxygen in unthickened medium with 5%
serum was 2.5 x 10-5 cm2 /sec,
oxygen
diffusion
in
as given in
and
water
corrected
(1977)
Reid et al
for
minor
for
temperature
effects from the correlation of Wilke and Chang (1955)
4) the diffusion coefficent for oxygen was inversely proportional
to
fluid viscosity, as given by Wilke and Chang (1955)
5)
the
Henry's
law
coefficient
for
oxygen
was
0.86
mM/L-atm
(Fleischaker and Sinskey, 1981)
6) the minimum acceptable level of average
-
202
-
dissolved oxygen in the
Below this value, oxygen can
fluid was 10% of saturation with air.
become growth-limiting (Miller et al, 1987; Balin et al, 1976).
The
mmole/cell-hr.
10-11
x
1.3
maintenance
the
and
cells/mmole
Yn/o,
oxygen,
on
cells
of
yield
growth
the
7)
3.8
was
x
108
was
coefficient
on
oxygen, Mo,
estimation
of
these
values
is
described in Appendix 2.
making
After
of
number
power
the
independent
to
variables
fluid viscosity
two:
reduced
and
calculation
optimization involves
The
input per unit.
one has
above,
listed
assumptions
the
average
of the
concentration for each combination of fluid viscosity and
maximum cell
average power input.
The
combination which gives the highest
maximum
cell concentration would be chosen as the optimum.
For
combination
each
of
calculation
microcarrier
concentration
and
concentration and
cell
the maximum
viscosity
fluid
of
involved
an
iterative
agitation
the
power,
corresponding
procedure.
At
the
maximum cell concentration, the specific growth rate, p, should equal
the
total
viscosity and agitation power,
from
qi
specific death rate,
equations
microcarrier
81
and
the values of qi and q2 were calculated
If
82.
then
one
maximum
the
concentration,
For each value of fluid
+ q2Cm.
guesses
cell
a
value
concentration
for
can
the
be
determined from equation 87, and the corresponding specific growth rate
This procedure can be repeated
can be determined from equations 90-93.
until the specific growth rate given by equations 90-93 is equal to the
total specific
death rate,
q
The corresponding maximum cell
+ q2Cm.
-
203
-
concentration represents the solution to the iteration.
they
concentration
cell
liquid mixing and cell-liquid transport were
were
and
concentration, one can determine whether the criteria of
microcarrier
adequate
maximum
the
calculated
having
After
the
not,
power
agitation
criteria are fulfilled.
should
be
fulfilled.
If
until
the
increased
For this optimization, the calculations were
extended into a range of power levels
far above the minimum values
for
adequate liquid mixing and cell-liquid transport.
Figure
47
shows
the
of
results
the
calculations.
optimization
Maximum cell concentration is plotted against power input per unit mass.
are shown for three different viscosities:
Calculations
(0.74 cp),
and medium slightly thickened
cell concentrations
normal medium
and 1.09 cp).
(0.92
Maximum
are shown only for power levels which are equal to
or greater than the minimum power for complete microcarrier suspension.
For
particular
this
the
optimization,
required
agitation
for
microcarrier suspension more than fulfilled the requirements for liquid
mixing and cell-liquid transport.
The results
show some
in Figure 47
For all
interesting trends.
three viscosities, the maximum cell concentration initially rises as the
agitation
is
suspension.
capabilities.
increased
These
The
increases
highest
minimum
the
above
are
cell
due
to
increased
concentration
is
microcarrier
for
level
oxygen
obtained with
lowest viscosity, again due to oxygen transfer capabilities.
-
204
-
transfer
If the
the
2.25
0.74
cp
2.00
0.9 2 cp
1.09 cp
1.75
N
1.50
1.25
IIIL-I
I
40
80
I
120
AVG. POWER PER MASS (CM
I_
160
2
_
200
/SEC 3 )
Estimated maximum cell concentration
vs. average power input per unit mass
at different fluid viscosities
Figure 47.
-
205
-
agitation is increased above the optimum at the lowest viscosity, the
maximum cell concentrations drop sharply.
Eventually, at a power input of approximately
from excessive agitation.
125 cm2 /sec
3
is due to cell death
This
death rate is
of 0.74 cp, the specific
for the viscosity
The attached cell
greater than the maximum growth rate of the cells.
concentrations will decrease from the time of inoculation.
If
the
flatter and less
increased
is
viscosity
above
sensitive to agitation.
the
cp,
0.74
curves
become
In general, an increase in
viscosity leads to a reduction in both oxygen transfer and hydrodynamic
death.
For
optimum viscosity.
increases.
input in a given
any given power
As the power input increases,
for
allow
Higher viscosities
reactor,
is an
there
the optimum viscosity
operation
at higher power
inputs.
For this particular optimization, the highest cell concentration was
If this optimization was performed for
obtained with lowest viscosity.
a
different
reactor,
concentration might be
The trends shown in
or
a
cell
different
line,
obtained with a slightly
Figure 47,
would still
however,
the
highest
cell
increased viscosity.
be present.
There
would still be a trade-off between mass transfer and hydrodynamic death.
Protection through Polymer Adsorption and Viscoelasticity
As
previously
discussed
the
in
Literature
Review
section,
many
investigators have used polymers to protect cells from fluid-mechanical
disruption.
The mechanism of this protective effect was not previously
-
206
-
in
this
thesis,
it
from turbulent damage by
Although
viscosity.
medium
the
increasing
presented
results
the polymers may protect cells
that
appears
the
of
light
In
identified.
viscous
reduction
of
turbulent damage most likely does account for some of the protection, it
does not appear
for all the results presented in
to fully account
the
literature.
In
instances,
many
with
qualitatively,
great
of protection
deal
percent.
very
low
of
degree
great
polymer
is
observed,
or
viscosity
protection
concentrations
instance, serum supplementation apparently provides a
For
increases.
a
and yet
increases
the viscosity only a few
Methylcellulose supplementation, at a typical concentration of
approximately 1 g/l and with a typical molecular weight of approximately
15000,
al,
also apparently provides a great deal of protection
1960;
leads
Bryant,
1966; Holmstrom,
to a viscosity
1968; Birch and Pirt,
increase of only 18%.
(Kuchler et
1969)
and yet
For a dilute microcarrier
culture, an 18% viscosity increase would provide only a 31% reduction in
hydrodynamic
death.
accurately represents
ture.
It
polymers is
appears,
It
to say whether a 31% reduction
is difficult
results presented in
the qualitative
however,
that
the
protection
the litera-
provided
by
some
more than would be expected through only viscous reduction
of turbulent damage.
The mechanism of the protective effect is therefore open to more
investigation.
Kuchler et al (1960), Bryant (1966), and Mizrahi (1984)
have hypothesized that the polymers adsorb onto the cells and form a
-
207
-
This adsorption would occur along with a concurrent
protective shell.
the
in
concentration
in polymer
reduction
For
supernatant.
culture
methylcellulose, Bryant (1966) observed a steady decrease in the culture
viscosity,
indicating polymer
potentially
and pluronic
cells.
polyols,
found a clear protective effect even though over 99% of
(1984)
Mizrahi
starch,
hydroxyethyl
For carboxymethylcellulose,
the
onto
attachment
the added polymer remained in the supernatant.
there
has directly measured whether
To my knowledge, no one
any adsorption of the polymers
is
From the data currently available, the protective shell
onto the cells.
hypothesis is neither directly supported nor refuted.
protection
of
mechanism
Another
interactions
between the polymers and the
discussed in
the Materials and Methods
occur
flow fields.
As
these interactions
can
turbulent
section,
viscoelastic
involve
may
even with very low polymer concentrations.
In the
experiments
presented in this thesis, low molecular weight dextrans were used as the
Viscoelastic interactions were purposefully avoided
thickening agents.
to
effects
the
isolate
such
polymers,
as
of
For
viscosity.
methylcellulose
and
some
of
the
protective
carboxymethylcellulose,
viscoelastic behavior has been reported (Amari and Nakamura, 1973, 1974;
Hoyt, 1985).
There
protect
cells
hydrodynamic
mass
great
is
from
damage
potential
turbulent
appears
the
behind
damage.
use
For
of
viscoelasticity
microcarrier
to
cultures,
to involve only the smallest eddies while
transfer involves both small
-
and large eddies.
208
-
If viscoelastic
polymers
are
added that
the
the small eddies but not
interfere with
large eddies, a strong decrease in hydrodynamic damage may be attainable
without
concurrently
a
viscoelastic
polymers
should
in
decrease
strong
a
have
characteristic
relaxation
equivalent to the burst duration for the smallest eddies.
might
not
strongly
indicated by the
should
be
interfere
results
performed
to
with
the
of Quraishi
et al
investigate
the
protecting cells from turbulent damage.
-
209
-
transfer
mass
(1977).
use
of
The
transfer.
mass
time
Such polymers
processes,
as
New experiments
viscoelasticity
in
SUMMARY AND CONCLUSIONS
approach has been
fundamental and quantitative
thesis, a
this
In
The effects of
initiated toward the design of microcarrier bioreactors.
forces
hydrodynamic
on
growth
cell
death
and
death.
significant hydrodynamic
no
Growth was
inert microcarrier
fluid viscosity,
in
changes
under
studied
With mild agitation, there
conditions of both mild and high agitation.
was
were
not
affected by
concentration,
or level
of agitation, and thus appeared to be unaffected by the hydrodynamic
environment per se.
With high agitation,
a reduction in net growth was
observed and was found to be entirely due to cell death and removal and
not
inhibition.
growth
Cell
was
growth
still
by
the
agitation
was
unaffected
hydrodynamic enviroment per se.
For
FS-4
cultures,
irreversible and lethal.
which
lethal.
from
excessive
from
removal
excessive
Secondary growth did not occur over areas from
had been previously
cells
removal
cell
agitation
removed.
In
frequently
was
-CHO
cultures,
reversible
cell
and
not
Secondary growth readily occurred over areas from which cells
had been previously removed.
cell
In fact,
growth was
areas were left void through hydrodynamic cell removal.
stimulated
as
For a moderate
level of agitation, the secondary growth was fast enough to overcome any
reduction in attached cell
removal.
Secondary
growth
concentrations from hydrodynamic
can clearly lead
sensitivity.
-
210
-
to
death or
reduced hydrodynamic
Through
cultures.
microcarrier
found to occur
fluid
power,
cell
viscosity,
in
death
through microcarrier-eddy
in unusual
Microcarrier-eddy
fields.
flow
time-average
and,
collisions,
of
effects
agitation
and
microcarrier bioreactors was
interactions,
the
on
experiments
concentration,
microcarrier
investigated with FS-4
of hydrodynamic damage were
The mechanisms
circumstances,
were
interactions
predominant in dilute cultures and led to cell death when the turbulence
For dilute
generated eddies which were smaller than the microcarriers.
to the
death rate was found to be proportional
the specific
cultures,
concentration of eddies
For both
dissipation regime.
in the viscous
cell death was found to increase with
dilute and concentrated cultures,
agitation power and decrease with fluid viscosity.
A
population
kinetics
viscosity,
and
the
to
and
and cell death
microcarrier
trade-off
the
transfer
upon scale-up.
The
kinematic
included
the
which was not a function of hydrodynamic
microcarrier-eddy interactions
from both
The
kinetic
expression
hydrodynamic
between
An
expression
cell
the
related
concentration,
microcarrier
collisions.
quantify
which
derived
power.
agitation
contributions from cell growth,
environment,
was
expression
quantitative
illustration was
cell
was
death
presented
used
and
to
to
oxygen
show how
bioreactor design can be approached as an optimization problem involving
quantitative rate expressions.
-
211
-
RECOMMENDATIONS FOR FUTURE RESEARCH
The results in this thesis point to several interesting areas
for
The topics have been discussed throughout the thesis
future research.
and include:
1)
Effects of normal forces on animal cells.
In many cell culture bioreactors, the flow field is turbulent.
cells are exposed not only to shear forces,
To
bioreactor
optimize
is
it
designs,
effects of normal forces on cells.
The
but also to normal forces.
important
understand
to
the
A literature survey indicates that
the effects of well-defined normal forces on animal cells have not been
investigated.
the
typically
The undiscovered role of normal forces may account for
poor
agreement
shear
between
effects
in
laminar
flow
fields and global hydrodynamic effects in turbulent stirred tanks, such
as
by
reported
microcarriers,
Rosenberg
et
al
For
(1987).
cell
removal
from
the observed lack of selectivity for mitotic cells may
indicate that cell removal occurs primarily through normal forces.
2)
Effects of reactor geometry on the kinetics of hydrodynamic death.
In
this thesis, hydrodynamic phenomena were correlated with average
power input per unit mass.
The results did not indicate a strong effect
of reactor geometry on the kinetics of hydrodynamic cell death, although
a
limited
number
of
reactor
geometries
-
212
-
was
investigated.
Future
should
dissipation.
with
of
rates
and
power
to involve only the smallest eddies, which
In constrast, mass
strongly dependent on geometry.
small
only
eddies,
involves
not
strongly
dependent on geometry.
involves
large
eddies
geometry (Nienow, 1985).
are
local
geometries
manipulated,
For microcarrier cultures,
of hydrodynamic death.
hydrodynamic death appears
are not
on
reactor
The kinetics of mass transfer should be considered along
kinetics
the
information
quantitative
incorporate
range of
a wider
investigate
should
research
high
and
also
but
large
transfer
which
eddies,
are
Suspension of the microcarrier also
strongly
again
is
dependent
on
reactor
If the effects of geometry on the large eddies
transfer
mass
of
rates
should be
obtainable
without high rates of hydrodynamic death.
3)
Microscopic fluid flow fields.
In
microcarrier
Future
the hydrodynamic forces experienced by the cells in
this thesis,
research
direction of the
extensive
in only an
cultures were calculated
should
determine
forces experienced by the cells.
modelling
microcarrier-eddy
precisely
more
of
the
microscopic
interactions
flow
approximate manner.
the
magnitude
and
This will require
fields
which
and microcarrier collisions.
thorough models might incorporate the protrusion of the cells
flow field along with the mechanics of cell deformation.
arise
in
The most
into the
The results of
these models will allow for more a more precise and thorough approach to
bioreactor design and optimization.
-
213
-
4)
Reversible cell removal and secondary growth.
y-CHO
For
from which
areas
in contrast,
cultures,
had been previously
cells
cell removal was
secondary growth did not occur.
For FS-4
removed.
irreversible
and lethal, and
At a moderate level of agitation, the
y-CHO cultures was fast enough to overcome any
secondary growth in the
from hydrodynamic death and
reduction in attached cell concentrations
Secondary growth thus led to reduced hydrodynamic sensitivity
removal.
and
was
agitation
excessive
Secondary growth readily occurred
frequently reversible and non-lethal.
over
from
removal
cell
cultures,
were
cells
the
occured because
have
may
Such
removed whole.
reversible removal may have been related to the attachment properties of
thoroughly
Future research should be performed to more
y-CHO cells.
the aneuploid
elucidate
removal and
of cell
the nature
its
relation
to
secondary growth.
5)
Hydrodynamic effects on cell metabolism.
cell
animal
Industrial
culture
frequently
will
be
used
for
the
The performance of these industrial processes
production of proteins.
will depend not only on the cell concentration and growth rate, but also
on the
cell metabolism.
hydrodynamic
It is therefore
important to understand the
effects on both cell metabolism and cell growth.
In
thesis, the hydrodynamic effects on cell growth were investigated.
growth of the cells
hydrodynamic
therefore
not
forces.
appeared
The
to be neither inhibited nor enhanced by
The metabolic
significantly
this
events required
altered by
-
214
-
agitation.
for growth were
Nonetheless,
all
events
metabolic
influenced by agitation.
growth
not
were
which
associated
In fact, the specific glucose uptake rate was
significantly reduced at high levels of
not growth associated and was
There are numerous other limited but
agitation.
effects on cell metabolism,
regarding hydrodynamic
been
have
could
Literature Review section.
interesting results
as discussed in
the
Future research will hopefully extend the
current information on the hydrodynamic effects of cell metabolism.
6)
Mechanisms of cell damage from direct sparging.
often lead
sparging
can
however,
prematurely
sparging.
Direct
and for many suspension cultures,
cultures,
For microcarrier
rule
damage.
extensive cell
to
the
out
sparging
One
represents
potentially
should not,
of
usefulness
potential
a
direct
direct
simple
and
inexpensive method for oxygenation of large-scale cell culture reactors.
If the mechanisms of cell damage from sparging are elucidated, a viable
In general, the use of sparging
sparging technique may become apparent.
should be considered in
and cell
The kinetics
death.
quantitatively
light of the trade-off between oxygen transfer
of cell damage
described along the kinetics
from sparging
should be
of oxygen transfer.
The
kinetic expressions can be used to determine the sparging conditions and
reactor
bubbles
design which lead to optimum performance.
involves
turbulence,
the
use
of
If cell damage from
thickening
viscoelastic polymers may reduce the amount of damage.
-
215
-
agents
or
7)
Viscoelastic reduction of hydrodynamic death.
Polymers
are
frequently
added
to
cell culture medium to
The mechanism of protection may
cells from fluid-mechanical disruption.
involve
viscoelastic
In
flow fields.
between
interactions
general,
for
is
there
the
protect
the
polymers
and turbulent
great potential behind the use
reduction
of
hydrodynamic
death
of
from
viscoelastic
agents
turbulence.
Hydrodynamic damage appears to involve only the smallest
turbulent eddies, while mass transfer involves both the small and large
eddies.
added that
If viscoelastic polymers are
interfere with
the
small eddies but not the large eddies, a strong decrease in hydrodynamic
death should be
attainable without a concurrently strong
mass transfer.
-
216
-
decrease in
NOMENCLATURE
Roman
a
gas-liquid interfacial area per unit culture volume, cm-1
as
culture surface area per unit culture volume, cm-1
at
silicone tubing surface area per unit culture volume, cm-1
A
parameter in power number correlation, dimensionless
b
intercept value in equation 60, sec-'
B
parameter in power number correlation, dimensionless
c
conduction resistance through silicone tubing, sec/cm
C
3
volumetric concentration of attached cells, cells/cm
Cmax
3
maximum volumetric concentration of attached cells, cells/cm
Ci
3
vol. concentration of attached cells at time ti, cells/cm
Cl, 3 5
3
C1 for culture at 35 RPM, cells/cm
Cl, 1 5 0
3
C1 for culture at 150 RPM, cells/cm
C2
3
vol. concentration of attached cells at time t2 , cells/cm
C 2 ,3 5
3
C2 for culture at 35 RPM, cells/cm
C 2 ,1 5 0
3
C2 for culture at 150 RPM, cells/cm
Ci
3
inert microcarrier concentration, microcarriers/cm
Cm
3
microcarrier concentration, microcarriers/cm
D
3
concentration of DNA in culture fluid, diploid equiv./cm
DI
3
D at time t1 in 150 RPM culture, diploid equivalents/cm
D2
3
D at time t2 in 150 RPM culture, diploid equivalents/cm
Df
diffusion coefficient, cm2 /sec
Df, o
2
diffusion coefficient for oxygen in culture medium, cm /sec
Di
impeller diameter, cm
-
217
-
Di, i
impeller diameter for reactor one, cm
Di, 2
impeller diameter for reactor two, cm
Dt
inner diameter of vessel, cm
Do
3
dissolved oxygen concentration in liquid, mmoles/cm
Do,min
3
minimum acceptable DO, mmoles/cm
Do*
D
dp
microcarrier diameter, cm
dt
silicone tubing diameter, cm
E
number of hemacytometer squares scored
fe
frequency of microcarrier collisions, #collision/cm3-sec
f(t)
distribution function of cell age, t, since mitosis
F
ratio of initial to final sample volume for nuclei counts
Fn
2
normal force per unit area on microcarrier surface, dyne/cm
Fr
Froude number, dimensionless
g
2
acceleration due to gravity, 980 cm/sec
G
glucose concentration, g/liter
Gi
glucose concentration at time ti, g/liter
G2
glucose concentration at time t2 , g/liter
h
cell height above growth surface, cm
H
liquid height in reactor, cm
Ho
3
gas hold-up in reactor, cm
IL
interval length between exchanges of medium, sec
IGo
fraction of cell population in Go resting state, dmsnless.
IM
fraction of cell population in mitotic phase, dimensionless
ISF
integrated shear factor, sec
ITS
impeller tip speed, cm/sec
3
at saturation with gas phase, mmoles/cm
-
218
-
1
Jw
specific rate of whole cell removal, sec-l
K1
ratio of time-average shear rate to impeller tip speed, cm-1
K2
3
collision frequency constant, #collisions-cm /micro.2-sec
K3
2
average effective surface area exposed to each collision, cm
K4
probability of death for a cell in the collision-exposed area
K5
total surface area per microcarrier (- 4wrrp2), cm2/micro.
K6
specific fluorescence of FS-4 DNA, fluor./(dip. equiv./cm3)
Ke
3
first-order specific death rate constant, cm /sec
KL
overall oxygen transfer coefficient, cm/sec
Ks
oxygen transfer coefficient for surface aeration, cm/sec
Kt
oxygen transfer coefficient for tubing aeration, cm/sec
L
length scale for eddies in viscous dissipation regime, cm
Lc
critical eddy length scale for cell death, cm
Mo
specific oxygen uptake rate with no growth, mmoles/cell-sec
Mt
mixing time for fluid phase in reactor, sec
Mw
molecular weight of polymer, daltons
N
rotation rate of impeller or viscometer, rotations/sec
No
volumetric rate of oxygen transfer into liquid, mmole/cm3-sec
Ngppower
number for impeller, dimensionless
Nu
Nusselt number for cell-liquid heat transport, dimensionless
p
parameter in power number correlation, dimensionless
P
2
static pressure in undisturbed flow, dyne/cm
Pv
vapor pressure of fluid, dyne/cm 2
P'
2
intensity of turbulent pressure fluctuation, dyne/cm
P'vdr
2
P' due solely to eddies in viscous diss. regime, dyne/cm
q
1
total specific death rate, sec-
-
219
-
qi
specific death rate due to micro.-eddy interactions, sec-'
q2
3
second-order death rate constant, cm /microcarrier-sec
Q
3
flow rate of gas for sparging, cm /sec
ri
radius of inner viscometer cylinder, cm
ro
radius of outer viscometer cylinder, cm
rp
microcarrier radius, cm
R
2
ideal gas constant, 8.31 x 107 g-cm 2 /mole-*K-sec
Rc
specific uptake rate of a given chemical, mmole/cell-sec
Re
Reynolds number for flow, dimensionless
Rg
specific glucose uptake rate, g/cell-sec
RO
specific oxygen uptake rate, mmole/cell-sec
Sa
average DNA content of cell population,
Sr
average DNA content of cells removed, diploid equiv./cell
Sc
Schmidt number, dimensionless
Shc
Sherwood number for cell-liquid mass transport, dimensionless
Shs
Sherwood number for surface aeration, dimensionless
T
temperature, degrees Kelvin
ti
time at beginning of interval, sec
t2
time at end of interval, sec
Tc
total time of cell cycle with constant TG1, sec
Td
doubling time of cell population, sec
TG2
duration of G2 phase, sec
TM
duration of mitotic phase, sec
TS
duration of DNA synthesis (S) phase, sec
Sa
average DNA content per cell,
u'
root mean square turbulent velocity component, cm/sec
-
220
-
diploid equiv./cell
diploid equivalents/cell
u'max
maximum root mean square turbulent velocity component, cm/sec
U
time-average fluid velocity component, cm/sec
U
total fluid velocity component, cm/sec
Umax
maximum total fluid velocity component, cm/sec
Umax
maximum time-average fluid velocity component, cm/sec
v
velocity scale for eddies in viscous diss. regime, cm/sec
Vc
3
average culture volume, cm
w
impeller width, cm
W
3
volumetric concentration of unattached whole cells, cells/cm
x
3
polymer concentration, g/cm
Xb
3
concentration of given nutrient in bulk liquid, mmole/cm
Xc
3
concentration of given nutrient at cell surface, mmole/cm
Y
shear rate in flow field undisturbed by microcarrier, sec-1
Yn/o
growth yield of cells on oxygen, cells/mmole oxygen
Z
percent confluence, dimensionless
Greek
al
parameter in fluid mixing-time relation, dimensionless
a2
parameter in gas-liquid mass transfer relation, dimsnlss.
a3
parameter in tubing-liquid mass transfer relation, dimsnlss.
Henry's law coefficient for oxygen solubility, mmole/cm3-atm
F
shear rate at surface of inner viscometer cylinder, sec-l
61
exponent on Reynolds number for surface aeration, dimsnlss.
52
exponent on Schmidt number for surface aeration, dimsnlss.
63
exponent on Froude number for surface aeration, dimsnlss.
64
exponent on Reynolds number for tubing aeration, dimsnlss.
-
221
-
65
exponent on diameter ratio for tubing aeration, dimensionless
66
exponent on Schmidt number for tubing aeration, dimensionless
ADO
3
spatial variation in dissolved oxygen level, mmole/cm
power input or dissipation per unit mass,
cm2/sec3
3
2
average power input or dissipation per unit mass, cm /sec
El
2
average power input per unit mass in reactor 1, cm /sec
3
e2
2
average power input per unit mass in reactor 2, cm /sec
3
emax
2
maximum local power dissipation per unit mass, cm /sec
Es
3
2
power input from sparging per unit mass of fluid, cm /sec
A
response time of polymer molecule, sec
77
viscosity of fluid, gm/cm-sec
A
Hoechst-dye fluorescence of culture fluid, fluor. units
Al, 3 5
A for 35 RPM culture at time ti, fluorescence units
A1 ,1 5 0
A for 150 RPM culture at time ti, fluorescence units
A2 ,3 5
A for 35 RPM culture at time t
A2 ,1 5 0
A for 150 RPM culture at time t
77S
viscosity of solvent, gm/cm-sec
?7sp
specific viscosity, dimensionless
[?7]
3
intrinsic viscosity, cm /gm
0
time scale for eddies in viscous dissipation regime, sec
p
1
specific growth rate, sec-
Ad
p under mild agitation for a given dextran conc., sec-1
pmax
maximum growth rate with no contact inhibition, sec-1
pobs
difference between actual growth rate and death rate, sec-1
Pr
relative observed specific growth rate, dimensionless
V
2
kinematic viscosity of fluid, cm /sec
-
222
-
2
3
, fluorescence units
2
, fluorescence units
L/b
2
kinematic viscosity of suspension, cm /sec
number of nuclei counted in hemacytometer
Pb
3
density of bubbles, gm/cm
pf
3
density of fluid, gm/cm
Pm
density of hydrated microcarriers, gm/cm 3
a-
cavitation number, dimensionless
r
shear stress on microcarrier surface, dyne/cm 2
Tmax
2
maximum shear stress from time-average flow fields, dyne/cm
volume fraction of solids, dimensionless
2
surface coverage of microcarriers or T-flasks, cell/cm
correction factor for DNA release calculations, dimsnlss.
2
correction factor for DNA release calculations, dimsnlss.
-
223
-
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liquid by
APPENDIX 1
CALCULATION OF THE RELATIVE DNA RELEASE UNDER HIGH AGITATION
in
described
As
release
the
into
DNA
of
high
under
fluid
culture
to
performed
was
experiment
an
2,
Chapter
investigate
the
agitation.
Cultures of FS-4 cells were grown on 5 g/l microcarriers in
two 500-ml vessels with 7.8 cm impellers.
The cultures were operated at
45 RPM to eliminate microcarrier agglomeration.
were pooled,
the microcarriers
to
two
agitated
concentrated
One of
identical 125-ml vessels.
at
35
RPM while
other was
the
When nearly confluent,
and transferred
to 15 g/l,
these
g/l
15
agitated
at
cultures
was
RPM.
The
150
attached cell concentrations were shown in Figure 21.
Figure 48 shows
the cumulative change in Hoechst-dye fluorescence
for samples taken from the culture fluid of the 15 g/L cultures.
culture at 150 RPM,
into
suspension.
fluorescence,
In the
there was extensive cell death and removal of cells
The
data
or DNA content,
show
strong
a
increase
the culture fluid.
in
35 RPM, there was very little removal of cells into
in
Hoechst-dye
In the culture at
suspension.
The
data show a moderate decrease in Hoechst-dye fluorescence.
The cause of the decrease in fluorescence for the 35 RPM culture was
not determined.
The culture medium contained approximately 1 pg/ml DNA
The background fluorescence from
from the 5% (v/v) serum supplement.
This decrease could have come
this DNA may have decreased over time.
-
234
-
+
35
-----
rpm
---150
rpm
-2
-4
20
40
60
TIME SINCE TRANSFER (HRS)
Figure 48. Cumulative chang e in
Hoechst-dye fluorescence for culture
fluid from 15 g/L cultures
-
235
-
80
about through:
1) cellular uptake of DNA polymers (unlikely)
a substance which
production of
2) cellular
specific
reduced the
fluorescence of the DNA-Hoechst dye complexes
3)
of
uptake
cellular
substance
a
which
otherwise
enhanced
the
specific fluorescence of the DNA-Hoechst dye complexes
4) degradation of the DNA into smaller molecules or single chains
with a concurrent reduction of the specific fluorescence
To calculate the absolute release of DNA into the culture fluid at
one must correct
150 RPM,
for the decrease
in
the control
at 35 RPM.
There are at least three reasonable methods to perform this correction:
the simplest correction.
This represents
Absolute correction.
1)
The
change in fluorescence at 35 RPM is simply subtraced from the change in
fluorescence at 150 RPM.
For each time interval ti to t
2
, the absolute
release of DNA into the culture fluid at 150 RPM, D 2 - Dl, is given by:
(\ 2 ,1
150
D
-
where
,
1
K6
2
K6
represents
the
fluorescence of
specific
, 1 5 0 and A2 , 1 5 0 represent the fluorescence in
RPM
culture
represent the
A1 ,3 5 )
,3 5
(Eq. 94)
=
D
1
2
(
150)
at
times
t1
and
t
2
,
fluorescence in the
DNA,
the samples from the 150
respectively,
and
Al,
35
and
A2 , 3 5
samples from the 35 RPM culture at
times ti and t2 , respectively.
-
FS-4 cellular
236
-
2)
Correction
proportional
to
volumetric
method of correction would be appropriate
at
35
RPM was
reduced
which
the
due
specific
otherwise
uptake of DNA.
one
to:
of these
a) cellular
if
concentration.
the fluorescence
production of
fluorescence, b)
increased the
cell
a
decrease
substance which
cellular uptake
specific
This
subtance
or c)
cellular
fluorescence,
of a
If one corrects for the decrease in fluorescence due to
cellular
processes,
the absolute release
of DNA into the
culture fluid at 150 RPM, D2 - D1 , is given by:
(-X2,150 ~
D
-
D
gi
~
A1 ,3 5 )
(Eq. 95)
1
K6
is a correction factor roughly given by:
C1,150
1,35
C1 ,1 5 0
and
+
ft
C
where
1 (A2 ,3 5
=
2
where
A1 ,1 5 0 )
+
C2,150
C2 ,1 5 0
(Eq. 96)
=
C
2,35
represent
the
attached,
or
concentrations in the 150 RPM culture at times t1 and t
and C1 , 3 5 and C2 , 3 5 represent the attached,
or viable,
2
viable,
cell
, respectively,
cell concentra-
tions in the 35 RPM culture at times ti and t2 , respectively.
3)
Correction
proportional
to
DNA
if
correction would be appropriate
concentration.
the fluorescence
was due to degradation and breakdown of the DNA.
first order process.
This
method
of
decrease at 35 RPM
This would likely be a
The amount of DNA breakdown would be proportional
to the amount of DNA present.
If one corrects for this breakdown, the
-
237
-
absolute release of DNA into the culture fluid at 150 RPM,
D2 - Dl,
is
given by:
~
2 1, 5 0
D
where
-
~ A1 ,3 5 )
2 (X 2 , 3 5
,1 5 0
(Eq. 97)
=
D
(2 is
1
a correction factor roughly given by:
1,150
+
2,150
(Eq. 98)
-
g
2,35
P1,35
Figure 49 shows the cumulative release of DNA into the culture fluid
at
150
Data
RPM.
calculation.
is
the
for
shown
three
different
correction proportional to DNA
concentration (Method 3) gives the highest release.
not
a
large
difference
of three methods
Chapter
2.
The
the
in
results
from
Nonetheless, there
the
three
different
For the purposes of this thesis, the average
methods of calculation.
value
of
The correction proportional to cell concentration (Method
2) gives the lowest release while the
is
methods
is
plotted in
used and is
error bars
in Figures 22
Figures 22 and 23 in
and 23 cover the
results from the three different methods of calculation.
range of
The error bars
are given by the range of results plus twice the standard deviation of
the assay.
-
238
-
+-Method
-
one
Method
Method
-
two
three
1.80
1.50 W7
1.20
LU
/7,
ZA
W/
U
0.90
---
z
/
(I ~
/,'
-
O.30
0.60
/
0.30
0.00.
1
0
20
1
40
TIME SINCE
TRANSFER
60
80
(HRS)
Cumulative release of DNA into
Figure 49.
suspension for 15 g/L culture at 150 RPM.
Data is shown for 3 different methods of
calculation.
-
239
APPENDIX 2.
ESTIMATION OF THE GROWTH YIELD AND MAINTENANCE COEFFICIENT FOR OXYGEN
For FS-4 cells,
the growth yield of cells
on oxygen was estimated
from the results of Balin et al (1976) for oxygen-limited growth of WI38 cells.
These cells are human diploid fibroblasts and are similar to
FS-4 cells.
At a dissolved oxygen level equivalent to 7.8 mm Hg 02, the
WI-38
had
cells
specific
a
specific
growth
rate, y,
0.032 hr-1 , a total
of
oxygen uptake rate, Ro, of 1.3 x 10-10 mmole/cell-hr, and a
maintenance-associated
oxygen
uptake
rate,
Mo,
mmole/cell-hr, as estimated through interpolation.
of
2.8
x
10-11
The growth yield of
cells on oxygen, Yn/o, was then calculated from the equation
Y
and was
n/o
p /
=
(R
o
-
M )
(Eq. 99)
o
thus estimated to be 3 x 108 cell/mmole.
This yield was used
for the optimization calculations in Chapter 7.
The
results
from
Fleischaker
and
Sinskey
(1981)
were
used
to
estimate the maintainence coefficient on oxygen, Mo, for FS-4 cells.
At
a specific growth rate of approximately 0.011 hr-1, the FS-4 cells had a
specific
oxygen uptake rate,
of 5 x 10-11 mmole/cell-hr.
Ro,
Using
equation 99 and the yield of 3 x 108 cells/mmole estimate above, one can
calculate
coefficient
a value
of
on oxygen,
1.3 x
Mo.
10-11
mmole/cell-hr
for
the
maintenance
This maintenance coefficient was used for
the optimization calculations in Chapter 7.
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240
-