computational fluid dynamics modeling of scalable stirred
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2016-02-03
Computational Fluid Dynamics Modeling of Scalable
Stirred Suspension Bioreactors for Pluripotent Stem
Cell Expansion
Le, An
Le, A. (2016). Computational Fluid Dynamics Modeling of Scalable Stirred Suspension Bioreactors
for Pluripotent Stem Cell Expansion (Unpublished master's thesis). University of Calgary, Calgary,
AB. doi:10.11575/PRISM/25392
http://hdl.handle.net/11023/2831
master thesis
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UNIVERSITY OF CALGARY
Computational Fluid Dynamics Modeling of Scalable Stirred Suspension Bioreactors for
Pluripotent Stem Cell Expansion
by
An Thuy Dang Le
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
GRADUATE PROGRAM IN BIOMEDICAL ENGINEERING
CALGARY, ALBERTA
JANUARY, 2016
© An Thuy Dang Le 2016
ii
Abstract
Pluripotent stem cells (PSCs) including embryonic and induced pluripotent stem cells are known
for their potential use in cell-based therapy, disease model study, and drug screening. One of the
key challenges in pluripotent stem cell research is to establish scalable bioprocesses that reliably
produce cells with high quality at any desired quantity. Stirred suspension bioreactors (SSBs) are
known to provide a controlled and well-mixed environment for aggregate-forming cells, such as
murine and human PSCs. Hydrodynamic environment of SSBs, particularly shear stress and small
eddies, have been shown to have a significant impact on the expansion and pluripotency of
pluripotent stem cells. However, the exact mechanism has not been fully understood. In this
project, computational fluid dynamic (CFD) simulation was employed to model the hydrodynamic
environment within SSBs with various configurations and physical conditions. Understanding the
hydrodynamics is one of the first key steps in bioprocess development of PSCs using SSBs.
iii
Acknowledgements
I would like to express my gratefulness to my supervisors, Dr. Michael Kallos and Dr. Ian Gates,
for their guidance and support through this project. They have provided me the best environment
for doing research, given me the opportunities to be creative, and motivated me to become a good
biomedical engineer.
I would like to thank Dr. Derrick Rancourt for giving me the opportunity to work on this exciting
project. Additionally, I would like to acknowledge Dr. Guoliang Meng for his in-depth training on
pluripotent stem cells culture and Dr. Charlie Hsu for his help with cell aggregate sizing using
Multisizer III in Krawetz’s Lab.
I would like to thank all PPRF lab members for their help and support. Every day at the lab is a
joyful day for me. Specially, I would like to acknowledge Breanna Borys for her help on the 10
ml bioreactor biological experiment and analysis.
Last but not least, I would like to thank my family for their unconditional love and care. Their trust
and understanding have given me strength to follow my dreams.
Thank you.
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Table of Contents
Abstract ............................................................................................................................... ii Acknowledgements ............................................................................................................ iii Table of Contents ............................................................................................................... iv List of Tables ..................................................................................................................... vi List of Figures and Illustrations ........................................................................................ vii List of Symbols, Abbreviations and Nomenclature .............................................................x
CHAPTER ONE: INTRODUCTION ..................................................................................1 Motivation ........................................................................................................................1 1.1 Research Aims ...........................................................................................................2
CHAPTER TWO: LITERATURE REVIEW ......................................................................4 2.1 Pluripotent Stem Cells ...............................................................................................4
2.1.1 Stem Cells and Regenerative Medicine Overview ............................................4 2.1.2 Controversial Issues Related to ESCs ...............................................................5 2.1.3 Induced-pluripotent Stem Cell Discovery and Its Significance ........................6 2.1.4 The Needs and Current Status of PSC Expansion .............................................7 2.1.5 Expansion of PSCs in Stirred Suspension Bioreactors ......................................8 2.1.6 Differentiation of PSCs in Stirred Suspension Bioreactors ...............................9 2.1.7 Challenges in PSC Bioprocess Development ..................................................10 2.1.8 The Significance of Controlling Aggregate Size .............................................12
2.2 Computational Fluid Dynamics (CFD) ....................................................................13 2.2.1 The role of CFD Modeling in Bioprocess Development .................................13 2.2.2 Turbulent Flow ................................................................................................15 2.2.3 Governing Equations in CFD Modeling of SSBs ............................................16 2.2.4 Finite Element Method ....................................................................................17
2.3 Conclusions ..............................................................................................................18
CHAPTER THREE: HYDRODYNAMICS OF STANDARD LAB-SCALE 100 ML SPINNER FLASK BIOREACTOR ..........................................................................19
3.1 Introduction ..............................................................................................................19 3.2 Materials and Methods .............................................................................................21
3.2.1 Cell culture and Cell Aggregate Measurements ..............................................21 3.2.2 Calculations .....................................................................................................22
3.2.2.1 Maximum Shear Stress Calculation .......................................................22 3.2.3 Computational Fluid Dynamics Modeling ......................................................23
3.2.3.1 Geometry ...............................................................................................23 3.2.3.2 Model Physics and Grid Generation ......................................................24
3.3 Results and Discussion ............................................................................................26 3.3.1 Grid Dependence and Model Validation .........................................................26 3.3.2 Base Case: Standard 100 ml Spinner Flask Bioreactor ...................................28 3.3.3 Hydrodynamics of 100ml Bioreactor at Different Agitation Rates .................34 3.3.4 Relationships between Hydrodynamic Parameters and Aggregate size ..........36
3.3.4.1 Effects of shear rate on aggregate size ...................................................36 3.4 Conclusions ..............................................................................................................40
v
CHAPTER FOUR: COMPUTATIONAL FLUID DYNAMIC MODELING OF SCALED-DOWN 10 ML STIRRED SUSPENSION BIOREACTORS WITH DIFFERENT IMPELLER DESIGNS .............................................................................................42
4.1 Introduction ..............................................................................................................42 4.2 Materials and Methods .............................................................................................44
4.2.1 Cell Culture .....................................................................................................44 4.2.2 Computational Fluid Dynamics Modeling ......................................................45
4.2.2.1 Geometry ...............................................................................................45 4.2.2.2 Model Physics ........................................................................................46
4.3 Results and Discussions ...........................................................................................47 4.3.1 Base Case: Hydrodynamics of 10 ml Bioreactor at 100 rpm ..........................47 4.3.2 Comparison of 100 ml and 10 ml Bioreactor Models at 100 rpm ...................49 4.3.3 Effects of Agitation Rates ...............................................................................52
4.3.3.1 Hydrodynamic Effects ...........................................................................52 4.3.3.2 Biological Effects ..................................................................................54
4.3.4 Effects of Impeller Geometry ..........................................................................59 4.3.4.1 Hydrodynamic Effects ...........................................................................59 4.3.4.2 Biological Effects ..................................................................................64
4.3.5 Effects of Shear Rate and Eddy Size on Aggregate Size ................................69 4.4 Conclusions ..............................................................................................................71
CHAPTER FIVE: DISCUSSIONS OF LIMITATIONS, RECOMMENDATIONS, AND CONCLUSIONS.......................................................................................................73
5.1 Discussions of Limitations and Recommendations .................................................73 5.1.1 CFD Modeling .................................................................................................73 5.1.2 Biological Experiments ...................................................................................74
5.2 Conclusions ..............................................................................................................74
REFERENCES ..................................................................................................................77
APPENDIX A: CELL CULTURE ....................................................................................86 A.1. Static cell culture ....................................................................................................86
A.1.1. Gelatin coating ...............................................................................................86 A.1.2. Static Passaging .............................................................................................86
A.2. Standard 100 ml Spinner Flask Bioreactor ............................................................87 A.2.1. Preparation of 100 ml Bioreactor ..................................................................87 A.2.2. Bioreactor Inoculation and Feeding Regime .................................................88 A.2.3. Aggregate Size Measurement using Particle Sizer ........................................88
APPENDIX B: HYDRODYNAMICS ..............................................................................90 B.1. Calculation Results .................................................................................................90 B.2. Quasi-steady state approximation ..........................................................................90
vi
List of Tables
Table 3–1: Dimensions of 100 ml model ...................................................................................... 24
Table 3–2: Average velocity, shear rate, and energy dissipation rate at different fluid heights ... 34
Table 3–3: Volume average velocity, shear rate, and energy dissipation rate at different agitation rates ........................................................................................................................ 36
Table 4–1: Dimensions of 10 ml bioreactor models ..................................................................... 46
Table 4–2: Comparisons of volume-averaged velocity, shear rate, and turbulent dissipation rate at different agitation rates in 10 ml bioreactor with cylinder impeller .......................... 52
Table 4–3: Comparison of volume-averaged velocity, shear rate, and turbulent dissipation rate between bioreactor with paddle impeller and bioreactor with cylinder impeller at 150 rpm ................................................................................................................................. 60
Table 5–1: Results from maximum shear stress calculation for 100 ml bioreactor ...................... 90
Table 5–2: Results from Reynolds number calculation for 10 ml bioreactor ............................... 90
vii
List of Figures and Illustrations
Figure 3–1: Model geometry built in COMSOL Multiphysics. A) 3D view of fluid occupied region in 100ml bioreactor; B) Top view of model geometry .............................................. 24
Figure 3–2: 100 ml bioreactor model grids created in COMSOL Multiphysics. A) Finer grid (948,668 tetrahedral finite elements); B) normal grid (278,951 tetrahedral elements) ........ 26
Figure 3–3: Comparison of results of fine grid (948,668 tetrahedral finite elements) and normal grid (278,951 tetrahedral elements). ......................................................................... 27
Figure 3–4: Maximum shear stress calculated from equation 1 and simulated using CFD ......... 28
Figure 3–5: Results of basics hydrodynamic variables obtained from CFD simulation. A) Pressure profile; B) Velocity and streamlines; C) Shear rate; D) Energy dissipation rate ... 31
Figure 3–6: Velocity on cut plane yz (x=0) plane. A) At t=0s, the impeller is perpendicular to the cut plane, velocity =0; B) At t=10s, the impeller is perpendicular to the cut plane, maximum velocity =0.119 m/s; B) At t=11s, the impeller is 300 from entering the cut plane, maximum velocity=0.129 m/s; D) At t=12s, the impeller is 300 leaving the cut plane, maximum velocity =0.232 m/s ................................................................................... 32
Figure 3–7: Velocity (A), shear rate (B), and energy dissipation rate (D) at different fluid heights in 100 ml bioreactor model. Cut plane 1 (z=0.03 m) on the left side is the horizontal plane above the impeller. Cut plane 2 (z=0.02 m) in the middle is the horizontal plane through the center of the impeller. Cut plane 3 (z=0.01 m) on the right is the horizontal plane below the impeller ............................................................................ 33
Figure 3–8: Velocity (A), shear rate (B), and energy dissipation rate (C) at different agitation rates (80 rpm, 100 rpm, and 120 rpm from left to right). All surfaces were plot at 12s of simulation .............................................................................................................................. 35
Figure 3–9: Cell aggregate distribution (D) at 80 rpm (A), 100 rpm (B), and 120 rpm (C)......... 38
Figure 3–10: Shear rate and mean average size. A) Volume average shear rate; B) Maximum shear rate ............................................................................................................................... 39
Figure 3–11: Relationship between eddy size and cell aggregate size. The average eddy size was calculated from volume-average energy dissipation rate obtained by CFD simulation, and the cell aggregate size was obtained from biological experiment. .............. 40
Figure 4–1: Model geometry built in COMSOL Multiphysics. A) 3D view of fluid occupied region in 10 ml cylindrical impeller bioreactor; B) 3D view of fluid occupied region in 10 ml paddle impeller bioreactor .......................................................................................... 45
Figure 4–2: Basic hydrodynamics of 10 ml cylindrical impeller bioreactor at 100 rpm .............. 48
viii
Figure 4–3: Comparison of shear rate distribution in 100 ml bioreactor and 10 ml bioreactor at 100 rpm. The data was extracted from quasi-steady sate state (after 3s) of agitation. The area under the curve was normalized to unity. .............................................................. 50
Figure 4–4: Comparison of turbulent dissipation distribution in 100 ml and 10 ml bioreactors at 100 rpm. The volume fraction of shear rate above 150 s-1 is insignificant so that the lines representing the cumulative volume of 10 ml and 100 ml bioreactor at 100 rpm no longer increase on the y-axis. The area under the curve was normalized to unity. .............. 51
Figure 4–5: Comparison of shear rate distribution between different agitation rates in 10 ml bioreactor. The volume fraction of shear rate above 150 s-1 is insignificant so that the lines representing the cumulative volume of different agitation rates no longer increase on the y-axis. The area under the curve was normalized to unity. ........................................ 53
Figure 4–6: Comparison of turbulent dissipation between different shear rates in 10 ml bioreactor. The volume fraction of turbulent dissipation at rates higher than 0.02 m2/s3 is insignificant so that the lines representing the cumulative volume of different agitation rates no longer increase on the y-axis. The area under the curve was normalized to unity. . 54
Figure 4–7: Comparison of biological responses in cylindrical impeller 10 ml bioreactors at different agitation rates and in static culture. ........................................................................ 59
Figure 4–8: Velocity vector field in 10 ml bioreactor with cylinder impeller and in 10 ml bioreactor with paddle impeller at 150 rpm. Longer and thicker arrows indicate velocity vectors with high magnitude, and the arrows point toward the direction of the velocity vectors. .................................................................................................................................. 61
Figure 4–9: Comparison of shear rate distribution between the 10 ml bioreactor with cylinder impeller and 10 ml bioreactor with paddle impeller at 150 rpm. The area under the curve was normalized to unity. ....................................................................................................... 62
Figure 4–10: Comparison of turbulent energy dissipation rate between 10 ml bioreactor with cylinder impeller and 10 ml bioreactor with paddle impeller at 150 rpm. The area under the curve was normalized to unity. ....................................................................................... 63
Figure 4–11: Comparison of biological responses in 10 bioreactors with cylinder impeller and in 10 ml bioreactor with paddle impeller at 150 rpm. .................................................... 68
Figure 4–12: Effects of shear rate on murine ESC aggregate size in 10 ml bioreactor with cylinder impeller. The error bars are standard deviations in aggregate size. ........................ 70
Figure 4–13: Similarity in average aggregate size and eddy size at different turbulent dissipation rates in 10 ml bioreactor. .................................................................................... 71
Figure 5–1: Shear rate distribution from 0s-12s in 100 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 3s ...................................................................................... 91
ix
Figure 5–2: Turbulent dissipation rate distribution from 0s-12s in 100 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 3s. ........................................................... 92
Figure 5–3: Shear rate distribution from 0s-10s in 10 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 4 s. .................................................................................... 93
Figure 5–4: Turbulent dissipation rate distribution from 0s-10s in 10 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 4 s. .......................................................... 94
x
List of Symbols, Abbreviations and Nomenclature
List of Abbreviations CFD Computational Fluid Dynamics c-Myc c-Myc proto-oncogene; Transcription factor DMEM Dulbecco's Modified Eagle's Medium EBs Embryoid Bodies ESC Embryonic Stem Cells FBS Fetal Bonvine Serum iPSC Induced Pluripotent Stem Cells Klf4 Kruppel-like factor 4; Transcription factor LIF Leukemia Inhibitory Factor Octr4 Pluripotency transcription factor PIV Particle Image Velocimetry Sox 2 Pluripotency transcription factor List of Symbols and Nomenclature Di Impeller diameter (m) Dt Vessel diameter (m) k Turbulent kinetic energy (m2/s2) k Turbulent kinetic energy (m2/s2) N Agitation rate (rpm) NP Power number P Power input (W) p Pressure (Pa) Pk Production of kinetic energy Re Reynolds number u Velocity (m/s) VL Working volume (m3) W Impeller width (m) γ Shear rate (1/s) ε Dissipation rate (m2/s3) η Eddy scale (m) μ Dynamic viscosity (Pa.s) ν Kinematic viscosity (m2/s) ρ Density (kg/m3) τ Shear stress (Pa) υT Turbulent eddy viscosity (m2/s)
1
Chapter One: Introduction
Motivation
Pluripotent stem cells (PSCs) play a key role in regenerative medicine due to their ability to
differentiate into different cell types in the three germ layers (1). Recently, the new induced
pluripotent stem cell (iPSC) derivation breakthrough has made these cells even more attractive to
modern medicine, especially cell-based organ transplantation field. However, transplantation
using PSC derived cells is still remained a challenge. One of the most important reasons is that the
bioprocess for producing large quantity of PSCs has not been well defined (2, 3). It has been
estimated that each cell-based transplantation case needs at least a lot size of a billion cells per
dose to be effective (4, 5). It is nearly impossible to obtain as many cells using conventional static
culture system due to high labor and material cost, time consuming, and large incubator space
requirement (2). Stirred suspension bioreactors (SSBs) have been selected as a preferred method
for expanding PSCs largely due to its well-mixing environment, controllability, and scalability (6).
The stirring mechanism in SSBs not only helps enhance mass transport, but also helps control PSC
aggregate size (7, 8). Besides mixing and aggregate size control, important environmental aspects
such as pH and dissolved oxygen can also be controlled in SSBs as in the DASGIP system (9).
SSB scaling-up bioprocess is very popular in protein production industry (10). Therefore, there is
an extensive amount of published work including simulation and experimental data on scaling
criteria of SSB in the literature (11–13).
Despite these advantages, there are still many challenges regarding the use of SSBs for
PSC expansion and differentiation. It has been shown that the hydrodynamic environment in
SSBs, particularly high shear stress and small turbulent eddies, can cause damage to the cell
membrane and alterations in gene expression (2, 14). Furthermore, reported differentiation
2
efficiency in SSBs is much lower compared to differentiation efficiency in static culture system
(14, 15). PSCs tend to stay undifferentiated in fluid shear environment even in the absence of
leukemia inhibitory factor (16, 17). However, the detailed mechanisms of these effects have not
been clear.
One of the most important steps in PSC bioprocess development using SSBs is to understand
the actual hydrodynamic environment inside a particular stirring vessel (2). This can be done
efficiently using computational fluid dynamics (CFD) modeling. CFD modeling has been used
extensively in bioprocess development and design of various bioreactor configurations (18–20).
In this project, CFD is to model the hydrodynamics of standard 100 ml and scaled-down 10 ml
spinner flask bioreactors for PSC expansion. The final goal of this project was to understand the
hydrodynamic environment of SSBs at various scales and conditions as well as the effects of
impeller geometry. Biological experiments in this project focuses on cell expansion and cell
aggregate size at various conditions. It has been shown that 3D aggregate structure and size can
affect cell growth, proliferation, and cell differentiation of PSCs (21–23). Therefore, with the
information obtained from CFD simulation and biological experiment, this project will be a
valuable contribution to bioprocess development of PSCs.
1.1 Research Aims
This project was divided into the following specific aims:
Specific aim 1: “Modeling of standard lab- scale spinner flask bioreactor” is described in
Chapter 3 of this thesis. In this chapter, the hydrodynamics of 100 ml bioreactor at various agitation
rates was revealed using CFD simulation. In addition, cell aggregate size distribution data of
3
murine embryonic stem cells matched with the expectations from shear stress and energy
dissipation rate profiles.
Specific aim 2: “Modeling of scaled-down 10 ml bioreactors” is described in Chapter 4 of
this thesis. The hydrodynamics environment in 10 ml bioreactors obtained from CFD modeling
was compared with standard 100 ml bioreactor. The magnitude of volume average shear stress and
energy dissipation rate can be matched to the larger scale by increasing the impeller speed in the
10 ml bioreactor. The speed increment was determined based on CFD modeling. In addition, the
effects of impeller geometry are also described in this chapter.
Specific aim 3: Based on simulation data and biological responses, the effects of shear stress
and eddy sizes on cell expansion and aggregate size were clarified. The biological data is described
in each of chapter 3 and 4 for predefined conditions. Based on the results from 100 ml and 10 ml
bioreactors, optimal expansion condition for murine PSCs and bioreactor scaling criteria were
justified.
4
Chapter Two: Literature Review
2.1 Pluripotent Stem Cells
2.1.1 Stem Cells and Regenerative Medicine Overview
Discovery of stem cells by James Till and Ernest McCulloch in 1963 is one of the most
remarkable medical research achievements of the 20th century (24). The two most important
characteristics that define stem cells are cell renewal, while keeping unspecialized state, and the
ability to differentiate into different cell types (25). In stem cell biology, proliferation is the ability
of stem cells to replicate themselves multiple times, and pluripotency refers to a stem cell that has
the potential to differentiate into any of the three germ layers including ectoderm, endoderm, and
mesoderm (26). Stem cells play a significant role in wound healing and organ repair processes. In
some organs, such as the gut and bone marrow, stem cells regularly divide. However, in some
organs, such as the pancreas and the heart, stem cells only divide under certain conditions (27).
Until recently, two types of stem cells that scientists have mainly focused on are embryonic stem
cells (ESCs) and somatic or adult stem cells (ASCs).
ESCs are pluripotent stem cells derived from the inner cell mass of an early-stage embryo
called the blastocyst (28). The inner cell mass containing ESCs gives rise to the entire body of an
organism including all of the specialized cell types and organs such as the heart, lung, skin, sperm,
egg, and many other tissues. Many published research findings have shown that ESCs can be
directed to differentiate into a target cell type by controlling the microenvironment of the cells and
using suitable growth factors (27). Current advanced biomaterials and medium development,
controlling cell differentiation or maintaining their pluripotency with high efficiency are possible.
Therefore, ESCs are ideal candidates for many disease treatments as well as drug testing models.
5
On the other hand, ASCs are found among specialized tissues or organs, and those cells
have the ability to differentiate into multiple but limited number of cell types (1). The main roles
of ASCs are to maintain and repair the tissue or organ in which they reside. For instance, ASCs
from the kidneys normally differentiate into the cells found in the kidneys. The use of ASCs and
their derived tissues might help minimize or eliminate rejection after transplantation. ASCs have
a great potential in specific organ repair and regeneration, but compared to ESCs, they are limited
in their differentiation potential and replicative capacity (29).
2.1.2 Controversial Issues Related to ESCs
Though offering great promise for understanding human development and hope for new
disease treatments, human ESC research has also raised numerous ethical and political
controversies. The first reason is that human ESCs involves the destruction of a human embryo.
Many people believe that an embryo is a person, and therefore, an embryo also has interests and
rights that must be respected. Based on this perspective, isolating the human ESCs from the inner
call mass of a blastocyst is undistinguishable from murder (1). Many countries including the
United States, United Kingdom, and Japan have restricted human ESC research. In 2001, President
G.W Bush allowed federal funding for stem cell research using human ESC lines that had already
existed, while prohibiting the federal funding for the derivation and use of additional ESC lines
(30).
Another important issue associated with using human ESC therapy is patient safety. Unless
the transplanted cells are derived from the patient or autologous, they will be rejected by the hostile
immune system. It has been demonstrated that ESCs up-regulate histocompatibility antigen type I
and type II when they differentiate thus triggering the immune rejection responds (29). Although
6
human ESCs have been accepted for use for drug screening purposes, it is difficult to obtain these
cells from the patients. Due to these limitations, human ESC-based therapies have faced numerous
challenges in getting clinical trials and FDA approval.
2.1.3 Induced-pluripotent Stem Cell Discovery and Its Significance
Scientists have continuously tried to find alternative cell sources that have similar functions
to human ESCs, but safer and does not involve the destruction of human embryos. In 2006, Dr.
Yamanaka’s research group in Japan identified four major transcription factors that regulate
pluripotency including Klf-4, Sox-2, Oct-4, and c-Myc (31). Their study shows that by over
expressing the genes encoding those four transcriptional factors, the mouse fibroblasts can be
reprogrammed to become pluripotent stem cells. Since somatic cells become pluripotent, they can
generate any tissue in the mouse.
In 2007, the same research group showed that the same four transcription factors could also
generate induced pluripotent stem cells (iPSCs) in human (25). The generated iPSCs are
genetically and functionally similar to ESCs. This research finding has a significant impact in stem
cell research and regenerative medicine. The research trend is currently shifting toward iPSCs
generation and differentiation rather than ESCs. Recognizing the remarkable discovery of iPSCs,
the Nobel Prize in Medicine or Physiology was awarded jointly to Dr. Shinya Yamanaka and Sir
John B. Gurdon in 2012 (29).
The generation of human iPSCs has overcome major limitations in ESCs. Since iPSCs
developed from a patient’s own somatic cells, they are more accessible than ESCs and can be
easily isolated from patient skin, blood samples, and tissues of interest without the destruction of
7
human embryos (28). Therefore, unlike human ESCs, human iPSCs do not raise moral and ethical
controversies.
Because somatic cells from any individual can be reprogrammed into iPSCs, it is possible
to make disease-specific cell lines from patients. Hence, besides stem cell-based therapy, one of
the most important applications of human iPSCs is specific disease model study. Additionally,
iPSCs can be used for drug screening, which is a great deal for many pharmaceutical companies
(29). Traditionally, before introduced to the market, a drug has to pass intensive animal studies
and many phases of clinical trials. Those testing processes are complicated and costly. Depending
on the patient’s age, gender, and genetic background, the drug can have different effects. One of
the best way for drug screening is probably through using patient’s specific iPSCs rather than
animal models or traditional drug testing methods. Using iPSCs can help reduce testing duration,
simplify patient selection process, and possibly reduce the pre-market cost.
2.1.4 The Needs and Current Status of PSC Expansion
One of the main goals of generating iPSCs is to use them for clinical applications such as
heart repair after myocardial infarction or B-cell transplantation in diabetic patients. The number
of cells required for each cell-based therapy ranges from few tens of millions to few billions (5).
For instance, at least 109 cardiomyocytes are needed to replace damaged cardiac tissue after
myocardial infarction (MI) (32). Furthermore, about 1.3x109 insulin producing β cells per 70-kg
patient are required for insulin independence after islet transplantation (5). Therefore, it is
necessary to design a good process for reproducible large scale production of human iPSCs before
moving toward to clinical applications.
8
Currently, human iPSCs are commonly derived and expanded in static T-flasks or tissue
culture dishes with the use of fibroblast feeder cells or matrix as supporting system. Static 2-D
culture systems do not adequately represent the in vivo environment of the cells. Although matrix
and feeders offer a great support for cell growth in static cultures, they often contain animal
components and some other factors that might have negative effects on the phenotype and
genotype of the cells as well as their environment. Static culture has high variability due to the
lack of automated control system. Besides, static culture is time-consuming due to feeder cell
separation, serial cell passaging, and handling requirements (33). In order to achieve 109 cells for
transplantation, about 500 of 10-cm tissue culture dishes are need (28). Therefore, expanding
iPSCs in 2-D static culture is highly inefficient and unfeasible.
2.1.5 Expansion of PSCs in Stirred Suspension Bioreactors
Suspension bioreactors (SSBs) that have been used for animal cell cultures and protein
productions can be adapted to produce the required number of iPSCs for clinical application.
Suspension system has many advantages compared to static culture. First, this is a 3-D feeder-free
culture system which can produce comparable or even higher cell expansion but less labor
intensive than static culture system (7, 9). Second, the system can be scaled-up to meet clinical
application needs (32). Third, SSB is a well-mixed system which allows the nutrients and oxygen
to be evenly distributed in the entire culture vessel (15). This is a great system for cells grown as
aggregates, like PSCs, since while the mass transfer is much more limited in static culture when
the aggregate size gets bigger. Fourth, the system can be automatically controlled so that the
variability is very low compared to manual static culture system (33). For instance, the DASGIP
bioreactors used in many cell culture laboratories and protein production facilities come with
9
different vessel sizes as well as a temperature, dissolved oxygen, and pH control system. Based on
these advantages, SSB is currently one of the most feasible and practical system for human iPSC
expansion.
Recent study of Chen at al. (32) shows that human ESCs can be grown in spinner flask
culture system for over 20 passages without loss of cell viability and growth kinetic. Based on
flow cytometry, a biomarker detection assay, the study demonstrates that those cells remain
pluripotency and normal karyotype. The resulted cumulative fold expansion after 21 passages is
about 1013. Since the culture system used is a robust scalable system for human ESC production
under GMP conditions, it has a great potential for future clinical application. Although the study
describes the production of human ESCs, the system would also be suitable for production of
human iPSC since both cell types have similar genotype, phenotype, and usually identical growth
conditions.
2.1.6 Differentiation of PSCs in Stirred Suspension Bioreactors
Differentiation is one of the most critical steps of cell production for transplantation. In
fact, the cells used for transplantation are preferably differentiated cells. For instant, iPSCs need
to be differentiated to cardiomyocytes before injecting to an MI patient. The ability to differentiate
to different cell types is a great advantage but also a problem when dealing with human ESCs and
iPSCs. For a single cell transplantation, only a single cell type is needed for a target tissue or organ.
However, it is very difficult to differentiate all the pluripotent cells into one single specific cell
type. Therefore, differentiation efficiency is normally low (34).
Many previous studies were successful in expanding human ESCs and iPSCs in suspension
bioreactors while maintaining the pluripotency of the cells. However, differentiation of the cells
10
into a specific cell type in suspension culture has not been successful or very inefficient (15). One
study suggested that bioreactor culture many induce pluripotency and reduce the differentiation
efficiency through fluid shear stress (14). This can be an example of mechanotransduction
phenomenon which is the conversion of mechanical signals that the cell senses from its
environment to internal biochemical signals (35). Mechanical cures can change the cell phenotype,
proliferation, and differentiation. Therefore, in addition to biochemical factors, mechanical forces
or stresses can be used to direct the cells to differentiate into a specific cell type (8) .
Recently, due to the development of special reagents and media as well as differentiation
techniques, the efficiency of tuning cell fate in suspension bioreactor has improved. Chen et al.
(2012) also show that cardiomyocytes can be directly from pluripotent cell aggregates in SSBs.
The cell aggregates were differentiated on day 3 and the contracting differentiated cells were
observed on day 9. They did cell specific marker staining and found that about 27% percent of the
cell population was differentiated to cardiomyocytes.
2.1.7 Challenges in PSC Bioprocess Development
Human ESCs and iPSCs grow as adherent cells in static culture (34). Since these cells are
highly sensitive, they often need a support system which can be mouse fibroblast feeder cells or
extra cellular matrix components. Before transferring them to suspension culture, the cells need to
be expanded to a desirable cell quantity in static culture first. Moving the cells from static culture
with the support system to suspension culture system without the support system can be
problematic. Changes in surrounding environment can cause changes to cell growth kinetics as
well as cell phenotype (2).
11
One special biological aspect that need to be taken into account while culturing human
iPSCs is that these cell survive and grow as aggregates (9). Forcing them to grow as single cells
after traditional cell passaging often result in significant cell death as well as a reduction in growth
rate (32). Due to this reason, many current techniques suggest to break the cells into small
aggregates from the big aggregates rather than into single cells. However, it is difficult to control
the new cell seeding density since the number of cells in each small aggregate can only be
estimated based on the size, and counting the number of seeding aggregates is also difficult.
Expanding iPSCs while maintaining their normal karyotype is challenging. It is difficult and
almost impossible to achieve homogeneous cell population since some of the cells may go under
spontaneous differentiation while some of the cells in the same culture environment try to maintain
their pluripotency (33). There are many methods to help isolate the differentiated from pluripotent
cells, but the separation process is time-consuming, especially in larger scale like suspension
bioreactor.
One of a major concern when culturing animal cells especially human ESCs and iPSCs in
suspension bioreactor is the level of shear stress. Shear stress level can be adjusted by changing
the agitation rate. It is important to run the bioreactor at an optimal speed that does not cause
damages to shear-stress sensitive cells while maintaining good mixing (15). The optimal shear
stress level is different for each suspension bioreactor system with different geometry, cell density,
and culture media viscosity (34). The most common method has been used to prevent the cells
from shear damage is by trial and error. For instance, the optimal shear stress is determined by
observing the growth kinetics of the cells at different speeds. However, this method can only give
the maximum or the minimum optimal shear stress level, but does not give the full shear stress
profile that represent the actual system. Shear stress has been found to play a role in endothelial
12
cell formation and proliferation. The effects of shear stress in iPSC pluripotency and their
differentiation capability are not yet clear and need to be investigated.
It is important to have an automated system that not only monitors but also control pH,
dissolved oxygen, and agitation rate. The quantity of the cells has to come side-by-side with the
quality. Designing a good cell manufacturing process is one of the key step for human iPSCs to
get closer to cell-therapy clinical application. The quality of the iPSCs is not only dependent on
the cell source and reprogramming methods but also the expanding and differentiating process.
There have been GMP qualified suspension bioreactor system for other cell types and protein
productions, but not yet for human iPSCs (32).
2.1.8 The Significance of Controlling Aggregate Size
Aggregate size is one of the key biological parameters that needs to be controlled in
bioprocess development of PSCs (23, 36). The transport of oxygen and nutrient within the cell
aggregates is significantly influenced by the size and structure of these aggregates and the effects
of hypoxia have found to be noticeable for aggregates larger than 300 μm (37) . As the aggregate
size exceeds the tolerance limit, the diffusion process of nutrients into the core of the aggregate
becomes limited, leading to various problems such as decrease in cell proliferation and possible
necrosis toward the center of the aggregates (38, 39). For instance, study by Ungrin et al. (21) has
shown that optimal size of aggregates can enhance the expansion of human PSC in suspension
culture and the cell growth declines in excessively large aggregates.
Furthermore, aggregate size also plays an important role in PSC differentiation. One of the
most popular methods for differentiating PSCs is through the generation of heterogeneous 3-D
embryoid bodies (EBs) (40). An aggregate of PSCs in suspension culture that has the ability to
13
from different cell types of all three germ lineages is considered as an EB (41). There are different
methods for generating EBs. Standard methods such as hanging drops, liquid suspension, and
methylcellulose culture have limited scalability and are difficult to control (42). On the other hand,
EB generation in SSBs is a highly scalable process and is capable of regulating the EB size (41).
It has been found that the EB size greatly influences PSC differentiation via impacting the
environmental factors that affect the stem cell differentiation such as the diffusion of soluble
molecules and cell adhesions (41). Therefore, understanding the effects of hydrodynamic
environment of SSBs on aggregate size is an essential step in bioprocess development of PSC
expansion and differentiation.
2.2 Computational Fluid Dynamics (CFD)
2.2.1 The role of CFD Modeling in Bioprocess Development
CFD has been used extensively in modeling various bioprocesses and hydrodynamics of
various bioreactor types (18). Stirring in a bioreactor is needed in order to achieve good mixing
within bioreactor vessels, but it can also cause some potential damage to the cells if the level of
shear forces caused stirring goes beyond the cells’ tolerance limit (43). The cells are dispersed
throughout the entire bioreactor system so that the level of shear stress needs to be calculated
locally and globally, not just at the tip of the impeller. Specific local hydrodynamics is difficult
and almost impossible to measure experimentally. Therefore, CFD has become an important tool
for modeling the hydrodynamic environment of bioreactor with various configurations (18, 44).
In bioreactor design, selecting a suitable impeller is one of the key steps. However,
redesigning and experimentally testing the impeller performance can be time consuming and
costly. Fortunately, CFD modeling can help in choosing the right impeller and rotating speed and
14
the performance of the impeller can be directly simulated in CFD modeling within a relatively
short period of time with minimal labor cost (10).
Scaling-up and scaling-down are very important and popular in bioprocess development.
Before building production scale bioreactors, extensive rounds of testing and screening need to be
done at a small economical scale (45, 46). However, maintaining the same hydrodynamic
environment between small and large scale is challenging. There are different criteria using in
scaling of bioreactors. These include maintaining of tip speed, Reynolds number, and specific
power input (47). In order to verify the validity of these criteria, CFD modeling is needed.
The majority of work on CFD modeling of SSBs is from bioprocess development of
monoclonal antibodies (12). The main focus of these studies is to find the optimal mixing
environment to achieve highest protein production (11, 13, 18). The production scale of the
bioreactors used in protein production can go up to 25,000 L (13). Large scale bioreactors for
protein production often contain many problems such as mass transfer limitation and high shear
stress near the tip of the impeller (48). Since the final desired product is protein, the optimal
conditions are often tailored to specific production rate rather than maintaining the consistency of
the cell phenotype and genotype (49). However, this is not the case for bioprocess development of
PSCs. Since the final goal is to obtain qualified cells for transplantation, the effects of
hydrodynamics on the cell phenotype and genotype need to be carefully evaluated. Unlike CHO
cells which are grown as single cell suspension in SSBs, PSCs are grown as 3-D aggregates so that
the effects of hydrodynamics on the cells are different. Although it has been known that the size
of the cell aggregates can be altered by changing the agitation rate, the exact mechanism has not
been cleared (2). Modeling the hydrodynamic environment using CFD simulation and
15
experimentally testing the growth of PSCs in small lab-scale SSBs can help clarify indicated
aggregate size control process.
2.2.2 Turbulent Flow
Flow in SSBs has often been characterized as turbulent flow. There exist different types of
flows in nature. For instant blood flow through capillaries is laminar, and air flow near the jet is
considered turbulent. There is no definite definition for turbulent flow. However, there are some
key characteristics that help define turbulent flow (50). These include:
Large Reynolds number: Reynolds number is a dimensionless number, defined as the
ratio of momentum force to viscous forces. The flow is turbulent when Reynolds number
is large and dominated by inertia forces.
Irregularity: The flow is random and chaotic, consisting of different scales of eddies. The
largest eddies are of the order of flow geometry such as boundary layer thickness, and the
smallest eddies are formed by viscous stresses dissipated into internal energy.
Dissipation: In turbulent flow, kinetic energy in the small eddies are transformed into
internal energy. The small eddies receive the kinetic energy from slightly larger eddies
and these slightly larger eddies receive energy from larger eddies and so on. This process
of multiscale eddy energy transfer is called cascade process. The largest possible eddies
are those that extend across the entire system. The smallest eddies are set by viscosity,
and smaller eddies, the stronger the velocity gradient and the more important the effect of
viscosity. Therefore, smallest eddy scale (Kolmogorov length scale) can be defined as:
η=ν3/4ε-1/4, where ν is fluid kinematic viscosity (m2/s) and ε is volume average rate of
turbulent energy dissipation (m2/s3).
16
Diffusivity: The diffusivity in turbulent flow is high and mixing increases. The
turbulence escalates the exchange of momentum in boundary layers and lessens the
delays thus separation at bluff bodies such as cylinders.
Continuum: Although there are eddies in the flow, they are much larger than molecular
scales and therefore, the flow is treated as continuum.
2.2.3 Governing Equations in CFD Modeling of SSBs
Most CFD simulations are based on the governing equations of motions for a continuous
viscous fluid: Navier-Stokes equations. The key principles behind these equations are conservation
of mass, conservation of momentum, and conservation of energy (51). The hydrodynamic
properties of turbulent incompressible fluid can be described in Reynolds-Averaged Navier Stokes
equations (52) (see List of Symbols at beginning of thesis):
∂∂t
. . , . 0 2.1
Where dynamic viscosity depends only on the physical properties of fluid, and turbulent eddy
viscosity is affected by velocity fluctuation ′.
One of the most common used turbulent model in CFD is two equation k-ε model. The two
equation model relates how the energy is transferred from the larger to smaller eddies, and it can
predict the behaviors of a turbulent flow without previous knowledge of turbulent structure (53).
Equation 2.1 is complemented by two additional convection-diffusion-reaction equations in k-ε
model (54):
. k 2.2
17
. 2.3
Where and the production of turbulent kinetic energy due to the mean velocity
gradient | | . The default values for model constants are: 0.09,
1.44, 1.92, 1.0, 1.3.
The k-equation (2.2) is a transport equation for turbulent kinetic energy k (m2/s2), and the ε-
equation (2.3) is an equation for the dissipation rate of turbulent kinetic energy ε (m2/s3). This
model has been proven to give reasonably good results for free-shear-layer flow with relatively
small pressure gradient (52). The k-ε model is also the most widely used in simulating the
hydrodynamic environment in SSBs (18, 19, 55), and has been validated with particle image
velocimetry (56).
2.2.4 Finite Element Method
The finite element method is one of the methods used in CFD to solve complex system of
partial differential equations from Navier-Stokes equations. Finite element method is preferred in
solving systems with complex and irregular geometries (57). Essentially, each continuous
geometry is meshed into discrete domain or grid with finite small elements, and the number of
nodes are the numbers of degrees of freedom needed to be solved. There are various finite element
shapes, and the choice of a finite element depends on the shape of original geometry, physics of
the problem, and the level of accuracy required in the final solution (58). In finite element method,
the global functional representation of a variable consist of an assembly of local functional
representations so that the global boundary conditions can be applied at local finite elements by
modification of a system of algebraic equations (58). This process of forming global representation
18
from local representations is known as interpolation. It is important to carefully choose an
appropriate interpolation method conserve the continuity between adjacent elements and to
enhance the accuracy of the solution (59).
2.3 Conclusions
It has been shown that hydrodynamic environment in SSBs affects PSC expansion and
differentiation (2, 14). The first key step in PSC bioprocess development is to understand the
hydrodynamics within the bioreactor from CFD simulation. The k-ε model in CFD can be used to
predict the behaviors of a turbulent flow without previous knowledge of turbulent structure (53) .
The next step is to apply CFD results for scaling-up and scaling-down bioprocesses, for example,
selecting the right impeller design and speed to produce optimal cell expansion and aggregate size.
19
Chapter Three: Hydrodynamics of Standard Lab-scale 100 ml Spinner Flask Bioreactor
3.1 Introduction
Pluripotent stem cells (PSCs) play a key role in regenerative medicine due to their self-
renewal and capability to differentiate into multiple lineages (2). Recently, with the discovery of
induced pluripotent stem cells (iPSCs), it may be possible for these cells to be used in clinical
applications such as cell-based transplantation. However, in order for cell-based transplantation to
be widely used, robust cell manufacturing processes that produce large quantity of cells with high
quality are needed. The average number of cells required per dose of transplantation is of the order
of billions (5) which is equivalent to the total number of cells harvested from more than 500
conventional static T75 tissue culture flasks. Therefore, using static culture to generate PSCs for
transplantation are impractical, costly, and labor intensive.
Stirred suspension bioreactors (SSBs) have been used to expand variety of cell types
including both anchorage dependent cells and anchorage independent cells on micro-carriers (7,
60). This system offers many advantages including scalability, a well-controlled environment,
good mixing to enhance mass transport, and less labour and material cost compared to static culture
(5). Both mouse and human PSCs have been successfully expanded in SSBs in many laboratories
without using micro-carriers (7, 61) even though the cells are anchorage dependent in static culture.
It has been shown that PSCs can be expanded in SSBs by using multiple passages while
maintaining high pluripotency (28, 62). However, differentiation in SSBs has remained a challenge
(2, 14, 15). Taiani et al. (14) showed that in bioreactor-differentiated cultures, a subpopulation of
cells in aggregates expressed the pluripotency marker Oct-4 in cell nuclei. Furthermore, Oct-4
expression still remained even after 30 days of SSB culture without leukemia inhibitory factor
20
(LIF). This phenomenon raised questions about the effects of hydrodynamic environment on the
pluripotency and differentiation ability of PSCs. Study of Lara et al. (2013) demonstrated that
multiple aspects of hydrodynamic environment, such as shear stress and flow regime, affect
pluripotency marker expression. Specifically, flow exposure not only helped to maintain Oct 4
expression but also increased Oct-4 expression after 36 hours in the absence of LIF. The gene
expressions for Oct-4 and other pluripotency markers such as Nanog and Rex1 were also
significantly higher than those in static culture for the same culture duration, seeding density, and
media components (17).
The effects of hydrodynamic environment on PSCs have been shown in numerous studies
(2), but the exact mechanisms of these effects have not been fully discovered. The first step in SSB
bioprocess development is to have a good understanding of hydrodynamics within the bioreactor
and how it can affect quantifiable biological properties such as cell aggregate size and expansion.
Computational fluid dynamics (CFD) modeling is a powerful tool to investigate the
hydrodynamics inside SBBs. CFD enables one to obtain important information about the fluid
environment such as local shear stress level and energy dissipation rate that are nearly impossible
to be obtained experimentally (19). Based on many existing studies, the total shear stress acting
on the cells and aggregates comes from two main sources which are the local fluid velocity gradient
and cell interaction with turbulence eddies (19, 43). The magnitude of fluid velocity gradient is
given by:
| | (3.1)
Shear stress can be calculated from velocity gradient as:
21
(3.2)
where τ (Pa) is the shear stress; γ (s-1) is shear rate or velocity gradient; u, v, and w (m/s) are the
velocity in x, y, and z direction; and μ (Pa*s) is the fluid viscosity. For Newtonian fluids such as
water, the viscosity is constant. For non-Newtonian fluids, the viscosity is a function of shear rate,
temperature, and exposure time.
Aggregates can also be sheared from the eddies with similar size or smaller (19, 43). The
size of the small eddies, η, depends on the energy dissipation rate, є, and kinematic viscosity ν,
specifically η=(ν3/є)1/4 (43). Cell aggregates have been found to be controlled by hydrodynamics
in SSBs (2), but exact mechanisms have not been cleared. Moreover, aggregate sizes are often
mentioned in the context of agitation rate which is not suitable representation of actual
hydrodynamic environment in bioreactors with different vessel and impeller geometries. The goal
of this study was to investigate the hydrodynamic environment inside a standard lab-scale 100 ml
spinner flask by using CFD simulation and determine how certain hydrodynamic variables such
as shear rate and turbulent eddies can affect aggregate forming cells such as PSCs.
3.2 Materials and Methods
3.2.1 Cell culture and Cell Aggregate Measurements
The D3 cell line of murine ESCs (provided by Dr. Rancourt, University of Calgary) were
grown on murine embryonic fibroblasts for one passage upon thawing and then were routinely
passaged twice into gelatin-coated petri dish (BD BioSciences, Bedford, MA, USA). The
expansion medium for murine ESCs consisted of 15% fetal bovine serum (Gibco, Grand Island,
NY), 1% non-essential amino acids (Gibco), 1% penicillin and streptomycin (Gibco), 0.1 mM β-
Mercaptoethanol (Sigma, St.Louis, MO), high glucose DMEM (Gibco), and 1,000U/ml leukemia
22
inhibitory factor (EMD Millipore, Billerica, MA, USA). In suspension cultures, murine ESCs were
inoculated as single cells into duplicate 100ml spinner flasks (NDS Technologies, Vineland, NJ,
USA). Spinner plate speeds at 80, 100, and 120 rpm were calibrated by using a Touchless Digital
Tachometer (VWR). All cell cultures were maintained at 370C and 5% CO2. The size distribution
of murine ESCs aggregates were measured on the fifth day of suspension culture using Beckman
Coulter Multisizer III (Miami, FL, USA). For each run, murine ESC aggregates were diluted such
that the coincident counting rate was between 3-10%. Samples were counted for 20 seconds per
run, which returns about an average of 3000 events. An average of 3 runs were collected per
sample. After collection, the data were analyzed using the complementary Multisizer 3.53
software. Background signal from debris and single cells were gated out of the data range by
excluding particles smaller than 40 μm in diameter.
3.2.2 Calculations
3.2.2.1 Maximum Shear Stress Calculation
The maximum shear stress in SSB can be calculated from (63):
τMax 5.33ρ єν (3.3 )
where τMax (Pa) is the maximum shear stress, ρ (kg/m3) is the fluid density, ν (m2/s) is the kinematic
viscosity, and ε (m2/s3) is energy dissipation rate which relates to vessel geometry, impeller
geometry and properties of fluid via (63):
(3.3 a)
where VL (m3) is the fluid volume and P (W) is the power input which is estimated from:
23
P NP N3 Di5 ρ (3.3 b)
where N (rotation per second) is the agitation rate, Di (m) is the impeller diameter, and NP is the
power number that is defined by:
(3.3 c)
NP can be estimated according to Nagata (63) s follows:
. .
. . (3.3 d)
. (3.3 e)
(3.3 f)
. . . (3.3 g)
. . . . (3.3 k)
3.2.3 Computational Fluid Dynamics Modeling
3.2.3.1 Geometry
Standard lab-scale 100 ml bioreactor have been used extensively in expansion of both
murine and human PSCs (7, 61, 62). The bioreactor consists of a glass vessel and a top mounted
magnetic based impeller. In addition, there is a small indentation (9 mm) at the center bottom of
the flask which helps reduce the dead space right below the impeller. The geometry built in
COMSOL Multiphysics is only up to the level of fluid height (Figure 3-1).
24
Figure 3–1: Model geometry built in COMSOL Multiphysics. A) 3D view of fluid occupied region in 100ml bioreactor; B) Top view of model geometry
Table 3–1: Dimensions of 100 ml model
Dimension Scale and unit Vessel inner diameter 0.064 (m) Fluid height 0.034 (m) Impeller shaft diameter 0.0159 (m) Impeller shaft length (height) 0.019 (m) Impeller diameter (horizontal length) 0.051 (m) Impeller width (thickness) 0.012 (m) Indentation height from the bottom vessel 0.009 (m)
3.2.3.2 Model Physics and Grid Generation
The flow is considered to be fully turbulent when the Reynolds’ number, defined by
Re=N(Di2)/υ, is greater than 20,000 and fully laminar when it is less than 10 (55). The type of flow
in between fully laminar and fully turbulent is transition flow which is difficult to characterize. In
this study, Re ranges from 4.2x103 to 6.4x103 which is closer to the turbulent regime. As a
consequence, in the CFD model, the Reynolds Averaged Navier-Stokes (RANS) k-ε technique
was chosen to model the flow in 100 ml at operated agitation rates from 80 rpm to 120 rpm. The
25
k-ε model is very popular for industrial applications due to its good convergence rate and relatively
low memory requirements compared to other turbulent models (64). All the solid walls are
presented by non-slip conditions and the free surface is specified with an open boundary
(atmospheric pressure) condition; the effect of capillary effects are not taken into account. The
model assumed that the fluid properties are as same as water as the majority of cell culture medium
is made up of water.
The commercial finite element multiphysics software package COMSOL Multiphysics
Version 4.4 (COMSOL, Inc. California, USA) was used to model the hydrodynamics of 100 ml
bioreactor. The simulations were run on Intel dual core Xeon 3.30 GHz with 24 GB RAM. All
cores were under load during each simulation and about 8 Gb out of 24 Gb of memory was
allocated for COMSOL Multiphysics.
The finite element grid was created by using the physics-controlled mesh generation option
in COMSOL. The finer grid (Figure 3-2A) consists of 1,117,436 finite elements whereas the
normal grid (Figure 3-2B) consists of 350,161 finite elements. All simulations at different agitation
rates were run using fine grid with 1,629,259 degrees of freedom. Each speed was simulated for
12s duration with average CPU run time of 96 hours. Data from the simulation were then exported
into Excel spreadsheet for further analysis. Most flow visualizations were performed by using
built-in post-processing tools within the COMSOL Multiphysics package.
26
Figure 3–2: 100 ml bioreactor model grids created in COMSOL Multiphysics. A) Finer grid (948,668 tetrahedral finite elements); B) normal grid (278,951 tetrahedral elements)
3.3 Results and Discussion
3.3.1 Grid Dependence and Model Validation
In CFD modeling, grid generation is a crucial step that affects the convergence, solution
accuracy, and CPU time (53). Due to the strong interaction of the mean flow and turbulence,
turbulent flow numerical solutions and results are more susceptible to grid dependency than
laminar flow (65, 66). In this study, 100 ml model at 100 rpm were solved using two different grid
sizes: normal grid consists of 278,951 tetrahedral finite elements and fine grid consists of 948,668
tetrahedral finite elements. The results from two grids sizes were compared and plotted on Figure
3–3 . The average pressure was the same in both, and the difference in average velocity and shear
stress are less than 2.5%. The difference in average energy dissipation rate was 8%, but the
difference in average eddy scale was only 2%. Since the differences in solutions between two grid
sizes were relatively small, no further grid refinements were carried out. Figure 3–4 shows
A B
27
maximum shear stress results obtained from equation 1 and CFD simulation. The difference was
2% at 120 rpm, 4.5% at 100 rpm, and 9.5% at 80 rpm. As expected, higher agitation rate results in
larger Reynolds number and greater maximum shear stress. In this study, the flow at 120 rpm is
closest to fully turbulent which the CFD model and equation 1 calculation precisely described.
Figure 3–3: Comparison of results of fine grid (948,668 tetrahedral finite elements) and normal grid (278,951 tetrahedral elements).
0
0.2
0.4
0.6
0.8
1
1.2
Avg Pressure Avg Velocity Avg Shear Rate Avg EnergyDissipation rate
Avg Eddy Size
Rel
ativ
e R
atio
Model Results
Relative Results from Fine Grid and Normal Grid
Fine Grid Normal Grid
28
Figure 3–4: Maximum shear stress calculated from equation 1 and simulated using CFD
3.3.2 Base Case: Standard 100 ml Spinner Flask Bioreactor
Previous studies in the same bioreactor system have shown that murine and human ESCs
grew best at 100 rpm (7, 61) which was chosen as the base case for this study. In this study, the
CFD simulations give constant profiles of velocity, shear rate, and energy dissipation rate after
0.000
0.200
0.400
0.600
0.800
80 rpm 100 rpm 120 rpm
Max
imu
m S
hea
r S
tres
s (P
a)
Agitation rate in 100 ml Bioreactor (rpm)
Maximum Shear Stress
Calculated Max Shear Simulated Max Shear
29
about 3s (see Appendix B for detailed profiles). All results in this study were extracted from 10s
or beyond
Figure 3-5 shows distributions of the pressure, velocity, shear stress, and energy dissipation
rate. Both pressure and shear stress can exert forces to the cells but with different magnitude and
direction. The pressure in the bioreactor was essentially hydrostatic pressure which depended on
fluid height and gravity. Many studies showed that the effects due to hydrostatic pressure are
minimal compared to the effects due to shear stress (67). Therefore, in a small biological system
like 100 ml spinner flask, the effects of hydrostatic pressure on the cells are often neglected.
The velocity magnitude of velocity is highest at the tip of the impeller as expected. Below
the impeller, the flow is less turbulent and the mixing is not as active as in the region near the tip
of the impeller. The dimple-like indentation on the center bottom of the flask was designed to
prevent the stagnation of the fluid in that area. Without this indentation, the cells in this region
would grow into large cell aggregates and cell death would occur due to mass transfer limitation.
Figure 3-5B showed strong flow separation near the tip of the impeller. This suggests not only
good mixing around the tip of the impeller but also high shear stress (Figure 3–5C) and energy
dissipation rate (Figure 3–5D). High shear stress and small eddy due to high energy dissipation
rates at this region have been reported as the sources of cell damage and cell behavior changes in
SSBs (63). However, the significantly high shear stress region only occupies a small fraction of
the bioreactor volume. More than 95% of bioreactor volume produced shear rate level less than 50
s-1 which was too low to cause cell damage. However, small level shear stress levels might cause
some changes in genetic construction of the cells which needs further investigation from
mechanotransduction studies.
30
Figure 3–6 showed how the velocity profile on yz (x=0) plane changed over time. Initially,
the impeller is perpendicular to the cut plane with 0 velocity. The impeller rotates counter
clockwise at the rate of 100 rotations per minute, and the velocity profile is plotted at 10s, 11s, and
12s. The results show that the velocity magnitude is highest and flow separation is strongest at 12s
when the impellers has just passed the plane. When the tip of the impeller moves further away
from the cut plane as in 10s, the velocity decreases and weaker radial flow is observed. At 11s, the
impeller is moving closer to the cut plane, the velocity started to increase to slightly higher than
the velocity obtained at 10s, but much lower than on obtained at 12s.
Figure 3-7 shows the changes in velocity, shear rate, and energy dissipation rate at different
horizontal or z- planes. At the middle of the impeller, z=0.02m, the velocity was highest. It is
consistent with Figure 3-6 that the velocity is higher in the wake region side of the impeller. Shear
stress and energy dissipation rate are also highest near the tip of the impeller. Velocity, shear rate,
and energy dissipation rate reduced significantly as the cut plane is further away from the impellers
(Table 3-2).
These results suggested that impeller speed and position play an important role in
magnitude and distribution of velocity, shear rate, and energy dissipation rate in the bioreactor.
Furthermore, strongest mixing happens near the tip of the impeller, but potential damages to the
cells are also highest around this region. In actual practice of bioreactor culture, the height of the
impeller was adjusted to a consistent level to obtain good mixing and low variability between runs.
31
Figure 3–5: Results of basics hydrodynamic variables obtained from CFD simulation. A) Pressure profile; B) Velocity and streamlines; C) Shear rate; D) Energy dissipation rate
A) Pressure B) Velocity and Streamline
C) Shear Rate D) Energy Dissipation
32
Figure 3–6: Velocity on cut plane yz (x=0) plane. A) At t=0s, the impeller is perpendicular to the cut plane, velocity =0; B) At t=10s, the impeller is perpendicular to the cut plane, maximum velocity =0.119 m/s; B) At t=11s, the impeller is 300 from entering the cut plane, maximum velocity=0.129 m/s; D) At t=12s, the impeller is 300 leaving the cut plane, maximum velocity =0.232 m/s
A B
C D
33
Figure 3–7: Velocity (A), shear rate (B), and energy dissipation rate (D) at different fluid heights in 100 ml bioreactor model. Cut plane 1 (z=0.03 m) on the left side is the horizontal plane above the impeller. Cut plane 2 (z=0.02 m) in the middle is the horizontal plane through the center of the impeller. Cut plane 3 (z=0.01 m) on the right is the horizontal plane below the impeller
A) Velocity (m/s)
C) Shear Rate (s-1)
B) Energy Dissipation rate (m2/s3)
34
Table 3–2: Average velocity, shear rate, and energy dissipation rate at different fluid heights
Above the impeller (z=0.03 m)
Middle of Impeller (z=0.2 m)
Below the Impeller (z=0.01 m)
Velocity 0.047 (m/s) 0.096 (m/s) 0.051 (m/s)
Shear rate 12.04 (s-1) 30.6(s-1) 7.47 (s-1)
Energy Dissipation rate 1.19E-3(m2/s3) 1.09E-2(m2/s3) 7.48E-4 (m2/s3)
3.3.3 Hydrodynamics of 100ml Bioreactor at Different Agitation Rates
Agitation rate is meaningless alone without considering vessel dimensions, impeller
geometry, and fluid properties. Instead of agitation rate, other characteristic flow parameters such
as velocity, shear rate, and eddy scale should be used for each particular bioreactor system.
Figure 3-8 shows distributions of the velocity, shear rate, and energy dissipation rate on
middle horizontal cut plane (z=0.02m) at 12s. On this plane, the effects of changing agitation rate
are strong compared to other horizontal distances in the entire bioreactor volume. At 12s, the
impeller position is at different locations with different velocity magnitudes depending on the
agitation rate. As expected, increase in agitation rate leads to increase in maximum and volume
averaged velocity magnitude, shear rate, and energy dissipation rate (Figure 3-8 and Table 3-3). If
20% increase in agitation rate from 100 rpm to 120 rpm gives a rise to about 20% increase in shear
rate, the increase in energy dissipations rate went up by 60%. Significant increase in energy
dissipation rate is expected based on the relationship between dissipation rate є and agitation rate
N described in equation 3.3. Besides, 25% increase in agitation rate from 80 rpm to 100 rpm led
to 25% increase in shear rate and 76% increase in energy dissipation rate. Therefore, it was
35
expected that the difference in cell aggregate size between 80 rpm and 100 rpm would be larger
than between 100 rpm and 120 rpm.
Figure 3–8: Velocity (A), shear rate (B), and energy dissipation rate (C) at different agitation rates (80 rpm, 100 rpm, and 120 rpm from left to right). All surfaces were plot at 12s of simulation
A) Velocity
B) Shear Rate
C) Energy Dissipation Rate
36
Table 3–3: Volume average velocity, shear rate, and energy dissipation rate at different agitation rates
80 rpm 100 rpm 120 rpm
Velocity 0.048 (m/s) 0.0586 (m/s) 0.0690 (m/s)
Shear rate 11.27 (s-1) 14.1 (s-1) 16.9 (s-1)
Energy Dissipation rate 1.79E-3 (m2/s3) 3.15E-3 (m2/s3) 5.04E-3 (m2/s3)
3.3.4 Relationships between Hydrodynamic Parameters and Aggregate size
3.3.4.1 Effects of shear rate on aggregate size
The biological results of cell aggregate size distribution shown in Figure 3-9 agreeably
reflected the CFD results above. The average aggregate diameter from Multisize measurement at
100 rpm and 80 rpm were similar to the average aggregate diameters at the same agitation rates in
previous study by Comier et al. (7) demonstrating the consistency of cell aggregate generation in
used bioreactor system. The difference in cell aggregate size between 80 rpm and 100 rpm (33%)
was indeed larger than between 100 rpm and 120 rpm (13.7%). When mode of aggregate size from
100 rpm sample (152 μm) and 120 rpm sample (130 μm) almost overlapped, the mode size
distribution from 80 rpm sample distinctly shifted to the right (236 μm) Therefore, larger change
in shear rate and energy dissipation rate indeed lead to larger change in cell aggregate size.
Figure 3-10 shows the relationship between shear rate and cell aggregate size. Higher
maximum shear rate and average shear rate leads to smaller average cell aggregate size. The error
bars in the graphs are the standard deviations which indicated how wide the aggregate size spreads
throughout the bioreactor volume. The number of small aggregates in 120 rpm sample is highest
37
due to highest shear and energy dissipation rate. Although volume-averaged shear rate and energy
dissipation rate at 80 rpm are low and most of the aggregates were large, some of the aggregates
might be broken up near the tip of the impeller. Hence, the 80 rpm sample has largest standard
deviation among three tested agitation rates. The aggregate size at 100 rpm is most uniformly
distributed with less small aggregates (less than 70 μm) compared to other two agitation rates.
Therefore, 100 rpm has been reported to be the most optimal agitation rate for growing murine
ESCs in the same bioreactor system (7).
The relationship between eddy size and cell damage have been a topic of debate in
bioreactor bioprocess development for many years. It was found that the relationship between cell
aggregate size and energy dissipation rate was similar to the relationship between eddy size and
energy dissipation rate (63). Therefore, cell aggregates would have similar size as eddy size.
Before CFD simulation was used popularly in modeling hydrodynamics of SBBs, only minimum
Komogorov length scale was calculated based on maximum energy dissipation rate near the tip of
the impeller and known kinematic viscosity. It was hypothesized that potential cell damages occur
when eddy scale was smaller or equal to the size of single cell or cell aggregate (43). However,
the details of this relationship has not been clear. In addition, the hydrodynamic environment of
SSB is not uniform, and there is a distribution of velocity, shear rate, and energy dissipation rate.
Therefore, one single calculated maximum shear or Komogorov scale are not enough to explain
the potential damages as well as variation in aggregate size within the bioreactor.
In this study, with the help of CFD modeling, not only distribution of shear rate, but also
distribution of energy dissipation rate and eddy scale can be obtained. Figure 3-11 shows that the
volume average eddy size from CFD simulation is actually similar to average aggregate size. This
finding helped explain how the aggregate size is possibly controlled in the bioreactor. Because of
38
the forces exerted by turbulent eddies on the aggregates varies with size, the number of cells on an
aggregate being sheared off from cell aggregate-eddy interaction would also differ. Therefore,
resulted aggregates would have different sizes. Unlike cell damage which was difficult to predict
and quantify, cell aggregate size can be accurately measured using large sample size as in this
study. Additional CFD simulations at different agitation rates and corresponding biological
experiments can be done to reconfirm the similarity between cell aggregate distribution and eddy
size distribution in 100 ml spinner flask.
Figure 3–9: Cell aggregate distribution (D) at 80 rpm (A), 100 rpm (B), and 120 rpm (C)
39
Figure 3–10: Shear rate and mean average size. A) Volume average shear rate; B) Maximum shear rate
40
80
120
160
200
240
280
400 450 500 550 600 650 700 750
Ave
rage
Agg
rega
te S
ize
(µm
)
Maximum Shear Rate (s-1)
A) Maximum Shear Rate and Mean Aggregate Size
40
90
140
190
240
290
12 13 14 15 16 17
Ave
rage
Agg
rega
te S
ize
(µm
)
Shear Rate (s-1)
B) Volume Average Shear Rate and Aggregate Size
40
Figure 3–11: Relationship between eddy size and cell aggregate size. The average eddy size was calculated from volume-average energy dissipation rate obtained by CFD simulation, and the cell aggregate size was obtained from biological experiment.
3.4 Conclusions
In this study, the hydrodynamics of standard lab-scale 100ml bioreactor spinner flask was
characterized. The maximum shear stress levels obtained from CFD simulations were similar to
the results obtained from calculation described by Nagata (63). The impeller plays a significant
role on shear stress and energy dissipation rate distribution inside the bioreactors. Specifically,
closer to the tip of the impeller, the flow was more turbulent with higher velocity, shear rate, and
energy dissipation rate. Significant high shear and small eddy region only occupied a small volume
fraction within the bioreactor. Therefore, the maximum shear rate was about 40 times greater than
volume average shear rate. Near the impeller, the shear stress applied on the cells is larger than at
other region so that the cell membrane can get damaged and the aggregates can be broken up
0
50
100
150
200
0 0.001 0.002 0.003 0.004 0.005 0.006
Siz
e (µ
m)
Volume -averaged є (m/s3)
CFD Average Eddy Size and Average Aggregate Size at Different Turbulent Dissipation Rates
CFD Average Eddy Size Average Aggregate Size
41
easier. Although the volume fraction of high shear region is low, there are still chances that the
cell and aggregates travel through this region. Therefore, there are always small aggregates in the
bioreactor despite of low agitation rates.
Cell aggregate size was measured by using an automatic particle sizer Multisizer III. The
aggregate size agreed with CFD results in many aspects. Larger increase in shear rate and energy
dissipation rate led to larger decrease in cell aggregate size. In addition, average aggregate size
was also similar to volume-averaged eddy size obtained from CFD simulation. The results
suggested that aggregate size distribution was possibly controlled by shear rate and eddy size
distribution inside the bioreactor. Increase in agitation rate with a consistent increment of 20 rpm
did not bring the same level increment in shear aggregate size. This is important information for
bioprocess development of aggregate forming cells like PSCs. For bioreactor scaling up, it would
be ideal to keep shear rate and energy dissipation rate consistent. The effect of changes certain
physical parameters such as impeller geometry, vessel dimensions, fluid viscosity, and agitation
rate on hydrodynamic environment also need to be carefully evaluated in order to design a good
bioprocess for PSC expansion. It is important to keep the cell aggregate size consistent since large
aggregate might increase mass transfer limitation and cell loss (34, 63).
42
Chapter Four: Computational Fluid Dynamic Modeling of Scaled-Down 10 mL Stirred Suspension Bioreactors with Different Impeller Designs
4.1 Introduction
Stirred suspension bioreactors (SSBs) have been used widely for various purposes including
protein production, cell expansion, and cell differentiation. Recently, it has been reported that
induced pluripotent stem cells (PSCs) can also be derived in SSBs (15). There are many great
advantages that make SSBs an ideal choice for bioprocess development of mammalian cells in
general and stem cells in particular. These include creating well-mixing environment (7, 19),
reducing labor cost from conventional static culture (5), and having great scalability (9, 32, 46).
Before executing the main production plan in large scale bioreactors, extensive rounds of screening
and testing at smaller scale bioreactor needs to be done to select the optimal condition for cell
growth or protein production (68). The smallest scale that represents the bigger system would be
the most ideal choice for screening purposes.
Pluripotent stem cells have been commonly cultured in the laboratory using 100 ml spinner
flask bioreactors (5, 7, 69) . In many cases, 100 ml bioreactors are used for screening purposes to
determine optimal seeding density, feeding regime, effects of growth factors, effects of agitation
rates, and expansion of different cell lines (7, 61, 62). Each screening might need multiple
bioreactors in order to have a good sample size for final analysis. Using 100 ml bioreactor for
screening and factorial design experiments can be time consuming and costly due to large number
of cells required for seeding and amount of culture media needed for initial inoculation and
feeding. Therefore, scale-down version of 100 ml bioreactor is needed for high throughput
screening.
43
Developing small scaled SSBs has been a new trend in bioprocess development (55). One
of the newest and most advanced small scale SSB system is the ambr from TAP Biosystem, UK.
This system uses 24 disposable bioreactors controlled by an automated work station. Each
bioreactor has 10 to 15 ml of working volume and its contents are stirred by an internal impeller.
Hydrodynamic environment of single ambr vessel was characterized using computational fluid
dynamics (CFD) modeling and mixing time measurement (13). Although a large part of
hydrodynamics in ambr system was revealed in this study, some aspects of bioreactor scaling-
down has not been clear. For instance, the effects of rectangular shape of the ambr vessel was not
investigated. The similarity between ambr and 5 L bioreactor was just based on the tip speed and
dissipation rate with no information on shear stress. The cells chosen for this study were CHO
cells which respond to shear stress differently than stem cells. Therefore, ambr system might not
be an ideal choice for growing shear sensitive cells such as PSCs until the effects of hydrodynamic
environment in amber system on the cells have been fully characterized.
Here, we use 10 ml bioreactors (HexaScreen, Barcelona, Spain) for PSC culture. These
bioreactors closely resemble the standard lab-scale 100 ml spinner flasks with cylindrical vessels
and top mounted rotating system. Unlike the ambr vessels, these 10 ml HexaScreen bioreactors
are reusable that allows the researchers to run multiple experiments with relatively low cost. Each
small vessel can be treated as a single T-25 flask or 10 cm2 petri dish for daily sampling and
multipurpose screening without concerning about contamination or hydrodynamic changes as in
100 ml bioreactor way of sampling.
In this study, we used computational fluid dynamic (CFD) to model the hydrodynamic
environment of 10 ml bioreactor to test whether it can be used as a scaled-down model of standard
100 ml spinner flask. Besides, biological experiments with pluripotent stem cells were conducted
44
to verify that the hydrodynamic environment in 10 ml bioreactor is suitable for shear-sensitive and
aggregate forming cell culture.
4.2 Materials and Methods
4.2.1 Cell Culture
The D3 cell line of murine ESCs (provided by Dr. Rancourt, University of Calgary) were
grown on murine embryonic fibroblasts for one passage upon thawing and then were routinely
passaged twice into gelatin-coated petri dish (BD BioSciences, Bedford, MA, USA). The
expansion medium for murine ESCs consisted of 15% fetal bovine serum (Gibco, Grand Island,
NY), 1% non-essential amino acids (Gibco), 1% penicillin and streptomycin (Gibco), 0.1 mM β-
Mercaptoethanol (Sigma, St.Louis, MO), high glucose DMEM (Gibco), and 1,000U/ml leukemia
inhibitory factor (EMD Millipore, Billerica, MA, USA). In suspension cultures, murine ESCs were
inoculated as single cells into duplicate 10 ml spinner flasks (HexaScreen, Barcelona, Spain) at
density of 33, 000 cells/ml. BioWiggler (Global Cell Solutions, Charlottesville, VA, USA) stir
plate with 8 programmed stirring positions was used to agitate 10 ml bioreactors. The accuracy
and precision of bioreactor agitation rates at 100, 120, and 150 rpm were tested by using a
Touchless Digital Tachometer (VWR). All cell cultures were maintained at 370 and 5% CO2.
Duplicate of the whole 10 ml bioreactor was taken for daily examining of cell aggregate size,
growth, and metabolites. Cell aggregate size was measured based on photographs taken on Zeiss
microscope and built in size measurement tool (AnxioVision 4). Cell count and cell viability
assessment were performed using standard hemocytometer, and cell metabolites were measured
using a Bio-profile 100 Plus (NOVA Biomedical, Waltham, MA, USA).
45
4.2.2 Computational Fluid Dynamics Modeling
4.2.2.1 Geometry
In this study, 10 ml bioreactors with two different impeller design were modelled. The
vessel diameter for both models stayed the same. One model has simple cylinder impeller (Figure
4–1A) and another one with overall paddle-shape impeller (Figure 4–1B). Similar to 100 ml
bioreactors, 10 ml bioreactors also had a small indentation on the center bottom of the vessel to
reduce the dead space. The dimensions of the 10 ml bioreactor models were listed on Table 4–1.
Figure 4–1: Model geometry built in COMSOL Multiphysics. A) 3D view of fluid occupied region in 10 ml cylindrical impeller bioreactor; B) 3D view of fluid occupied region in 10 ml paddle impeller bioreactor
46
Table 4–1: Dimensions of 10 ml bioreactor models
Dimension Cylinder Impeller Paddle Impeller
Vessel inner diameter 0.032 (m) 0.032 (m)
Fluid height 0.0145(m) 0.015 (m)
Impeller diameter (horizontal length) 0.0254 (m) 0.0274 (m)
Impeller width (vertical length) 0.0054 (m) 0.0074 (m)
Indentation height from the bottom vessel 0.005 (m) 0.005 (m)
4.2.2.2 Model Physics
The flow in stirred vessel is considered to be fully laminar when the Reynolds number is
less than 10 and fully turbulent number is greater than 20,000 (13). The transition region is where
the Reynolds number falls between this range. Transition flow is difficult to characterize and there
has been yet a commercially available CFD program that can fully solve this flow behavior. In this
study, Reynolds number from 1,031 to 1,858 which is closer to the turbulent regime. Therefore, in
the CFD model, Reynolds Averaged Navier-Stokes (RANS) k-ε technique was chosen to model
the flow in 10 ml bioreactor at 100, 120, and 150 rpm. The k-є model is very popular for industrial
applications due to its good convergence rate and relatively low memory requirements compared
to other turbulent models (18). All the solid walls are presented by non-slip conditions and the free
surface is specified with an open boundary (atmospheric pressure) condition; the effects of
capillary effects are not taken into account. The model assumed that the fluid properties are as
same as water.
47
The commercial finite element Multiphysics software package COMSOL Multiphysics
Version 4.4 (COMSOL, Inc. California, USA) was used to model the hydrodynamics of 10 ml
bioreactor. The simulations were run on Intel dual core Xeon 3.30 GHz with 24 GB RAM. All
cores were under load during each simulation and about 8 Gb out of 24 Gb of memory was
allocated for COMSOL Multiphysics.
The finite element grid was created using physics-controlled mesh generation option in
COMSOL. The grid consisted of 534,346 finite elements which was comparable with the fine grid
generated for 100 ml bioreactor in previous study. Each agitation rate was simulated for 12s
duration and 826,993 degree of freedom was solved with average CPU run time of 70 hours. Data
from the simulations were then exported into Excel spreadsheet for further analysis. Flow
visualizations were performed by using built-in port-processing tools within COMSOL
Multiphysics package.
4.3 Results and Discussions
4.3.1 Base Case: Hydrodynamics of 10 ml Bioreactor at 100 rpm
Figure 4–2 shows the distributions of the pressure, velocity, shear stress, and energy
dissipation rate at 100 rpm. Similar to 100 ml model (refer to Chapter 3), the pressure in 10 ml
model is basically hydrostatic pressure that has no significant effect on the cells at resulted level
(67). The velocity is highest at the tip of the impeller, toward the wake region. Due to non-slip
condition, the velocity magnitude increases in region that is closer to the rotating impeller. Shear
rate and turbulent dissipation rate are also highest near the tip of the impeller. The region with
relatively high shear rate (greater than 100 s-1) and high turbulent dissipation rate (greater than
0.03 m2/s-3) only occupies a small volume fraction of the entire bioreactor.
48
Figure 4–2: Basic hydrodynamics of 10 ml cylindrical impeller bioreactor at 100 rpm
49
4.3.2 Comparison of 100 ml and 10 ml Bioreactor Models at 100 rpm
As previously discussed in 100 ml models (refer to Chapter 3), higher volume averaged
shear rates and energy dissipation rates led to smaller aggregate sizes. Figure 4–3 shows that shear
rate distribution in 100 ml and 10 ml bioreactors at 100 rpm are similar. Cumulative volume
fraction is the sum of volume fractions for all shear rate levels up to the current one, and it equals
to 1 for the entire graph from 0 s-1 to 150 s-1. Al though the maximum shear rate is much higher
than 150 s-1, the volume fraction for shear stress level higher than 150 s-1 is very small so that the
graphs no longer increases vertically. There is steep increase from lowest shear rate of about 5 s-1
up to shear rate of 60 s-1, indicating that shear rate of this range occupies the most volume fraction
of both 10 ml and 100 ml bioreactors. The line graph representing10 ml bioreactor is above the
line graph representing 100 ml bioreactor for shear rate under 60 s-1, but the order is reversed for
shear rate above 60s-1. Therefore, the overall volume- averaged mean shear rate in 100 ml
bioreactor is higher than in 10 ml bioreactor. In fact, the different in volume- averaged shear rate
of the two bioreactor scales is about 14% (Table 4–2).
Figure 4–4 shows the comparison of turbulent dissipation rate between two bioreactor
scales. The volume fraction in 10 ml bioreactor stops increasing after its turbulent dissipation rate
reaches 0.01m2/s3. However, the volume fraction of higher dissipation rate (above 0.01 m2/s3) is
still continuing to increase. In fact, the volume averaged turbulent dissipation rate in 100 ml model
is significantly higher than in 10 ml model (about 158% higher, Table 4–2). In addition, the volume
average velocity in 100 ml bioreactor is also higher than in 10 ml bioreactor (Table 4–2). In order
to match up the shear rate and energy dissipation profiles between the two bioreactor scales,
agitation rate increase in 10 ml bioreactor is needed. The level of increase is predicted by CFD
simulation and verified by biological experiments.
50
Figure 4–3: Comparison of shear rate distribution in 100 ml bioreactor and 10 ml bioreactor at 100 rpm. The data was extracted from quasi-steady sate state (after 3s) of agitation. The area under the curve was normalized to unity.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 20 40 60 80 100 120 140 160
Cu
mu
lati
ve V
olu
me
Fra
ctio
n
Shear Rate (1/s)
Shear Rate Distribution in 10 ml and 100 ml Bioreactors at 100 RPM
10 ml-100 rpm 100 ml-100 rpm
51
Figure 4–4: Comparison of turbulent dissipation distribution in 100 ml and 10 ml bioreactors at 100 rpm. The volume fraction of shear rate above 150 s-1 is insignificant so that the lines representing the cumulative volume of 10 ml and 100 ml bioreactor at 100 rpm no longer increase on the y-axis. The area under the curve was normalized to unity.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 0.005 0.01 0.015 0.02
Cu
mu
lati
ve V
olu
me
Fra
ctio
n
Turbulent Dissipation Rate (m2/s3)
Turbulent Dissipation Rate in 10 ml and 100 ml Bioreactors at 100 RPM
10 ml-100 rpm 100 ml-100 rpm
52
4.3.3 Effects of Agitation Rates
4.3.3.1 Hydrodynamic Effects
At lower range of shear rate (less than 50 s-1), the volume fraction for this range is highest
at 100 rpm and lowest at 150 rpm (Figure 4–5). The order is reversed for shear rate greater than
50 s-1. Overall, it shows that the shear rate is higher at higher agitation rate and greater increase in
agitation rate leads to greater increase in shear rate. For instance, 20% increase in agitation rate
from 100 rpm to 120 rpm gives 21% increase in volume averaged shear rate, and 25% increase in
agitation rate from 120 rpm to 150 rpm gives 25.5% increase in volume averaged shear rate in 10
ml bioreactor (Table 4–2). These results are consistent with previous 100 ml model.
The turbulent dissipation rate in Figure 4–6 shows similar trend to Figure 4-5. Overall, the
turbulent dissipation rate is highest at 150 rpm and lowest at 100 rpm in 10 ml bioreactor. However,
the level of difference in turbulent dissipation rate is more dramatic than in shear rate. Specifically,
20% increase in agitation rate leads to 56% increase in volume averaged turbulent dissipation rate,
and 25% increase in agitation rate leads to 66% increase in volume averaged turbulent dissipation
rate. Interestingly, volume averaged turbulent dissipation rate (0.003 m2/s3) in 10 ml bioreactor at
150 rpm matches with 100 ml bioreactor at 100 rpm.
Table 4–2: Comparisons of volume-averaged velocity, shear rate, and turbulent dissipation rate at different agitation rates in 10 ml bioreactor with cylinder impeller
100 rpm 120 rpm 150 rpm Velocity (m/s) 0.028 0.033 0.040 Shear Rate (s-1) 12.34 14.95 18.76 Energy Dissipation Rate (m2/s3) 1.16E-3 1.81E-3 3.0E-3
53
Figure 4–5: Comparison of shear rate distribution between different agitation rates in 10 ml bioreactor. The volume fraction of shear rate above 150 s-1 is insignificant so that the lines representing the cumulative volume of different agitation rates no longer increase on the y-axis. The area under the curve was normalized to unity.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 30 60 90 120 150
Cu
mu
lati
ve V
olu
me
Fra
ctio
n
Shear Rate (s-1)
Shear Rate at Different Agitation Rates
100 rpm 120 rpm 150 rpm
54
Figure 4–6: Comparison of turbulent dissipation between different shear rates in 10 ml bioreactor. The volume fraction of turbulent dissipation at rates higher than 0.02 m2/s3 is insignificant so that the lines representing the cumulative volume of different agitation rates no longer increase on the y-axis. The area under the curve was normalized to unity.
4.3.3.2 Biological Effects
As mentioned previously, the volume averaged turbulent dissipation rate in 10 ml at 150
rpm matches with the optimal value in 100 ml bioreactor at 100 rpm. Therefore, it is expected that
150 rpm in 10 ml bioreactor would give the best cell expansion out of three tested agitation rates.
Indeed, the results show that the 10 ml bioreactor culture achieves highest cell expansion at 150
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0 0.005 0.01 0.015 0.02
Cu
mu
lati
ve V
olu
me
Fra
ctio
n
Dissipation Rate (m2/s3)
Turbulent Dissipation Rate at Different Agitation Rates
100 rpm 120 rpm 150 rpm
55
rpm (Figure 4-7A). Due to lower shear rate and low energy dissipation rate, the aggregate size in
bioreactors agitated at 100 rpm are large (Figure 4-7B) leading to possible mass transfer limitation
that affects cell proliferation (2, 23, 70). Therefore, the cells expansion at 100 rpm in 10 ml
bioreactor is very low and seems to have decreased after the third day. The cell aggregate size at
150 rpm in 10 ml bioreactor is smallest among tested agitation rates and is similar to the aggregate
size at 100 rpm in 100 ml bioreactor. The viability of the cells in 10 ml bioreactors operated at 150
rpm remained above 95% even at day 4. The viability at other agitation rates was slightly lower
but was still higher than 90%. Based on hydrodynamic and biological response similarities, 10 ml
bioreactor at 150 rpm can be considered to be the scaled-down model of 100 ml bioreactor at 100
rpm.
The media properties of murine ESCs were examined by measuring the pH, nutrient
concentration (glucose), and waste products (lactate and ammonia) daily for both experiments
throughout the culture period. The glucose concentration in the media for the mESCs that were
expanded at different agitation rates in the stirred suspension and in the static cultures decreased
steadily over the course of the culture periods (Figure 4-7D). However, the glucose concentration
after four days remained above zero for all conditions, indicating that nutrient concentration is not
limiting cell proliferation after four days.
The pH of the media dropped over the culture period for all conditions (Figure 4-7C). By
the fourth day of culture, the pH of the static condition was significantly lower than all bioreactor
conditions. Although the final cell multiplication ratio was greater in the 150 rpm mini bioreactor
compared to static culture, it is possible that the pH in the static condition is lower due to a
difference in growth conditions of the suspended spheres and adherent monolayers. There is a
limited growth surface area in the static culture compared to the stirred suspension bioreactors
56
causing increased cell death and release of lactic acid into the culture media. Low dissolved oxygen
concentration and the absence of agitation could attribute to the decrease in expansion of mESC
cells in static condition. It has been reported that a pH below 7.1 reduces cell proliferation in stem
cells (32). Figure 4-7G shows that pH remains in healthy range for all bioreactor conditions, but
high acidic for static condition as a result of high lactic acid concentration. Although ammonia
level increased (Figure 4-7F), the concentration of ammonia on day 4 for all culture conditions
was below 1.5 mml/L which is not considered to be inhibitory to mammalian cell growth (7). Since
the difference in metabolites is small and the concentrations of glucose, lactate, and ammonia are
within the safe limit, the differences in cell expansion and aggregate size between three agitation
rates are mainly due to hydrodynamic environment.
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4
Mu
ltip
lica
tion
Rat
io
Time (days)
A) Multiplication Ratios at Different Agitation Rates
100rpm 120rpm 150rpm Static
57
0
50
100
150
200
250
300
350
400
100 120 150
Agg
rega
te D
iam
eter
(μ
m)
Agitation Rate (rpm)
B) Mean Aggregate Diameters at Different Agitation Rates
6.5
6.7
6.9
7.1
7.3
7.5
7.7
7.9
0 1 2 3 4
pH
Time (days)
C) Change in pH of Culture Media
100rpm 120rpm 150rpm Static
58
0.0
1.0
2.0
3.0
4.0
1 2 3 4
g/L
Time (days)
D) Glucose Concentration in the Media
100rpm 120rpm 150rpm Static
0.0
1.0
2.0
3.0
4.0
1 2 3 4
g/L
Time (days)
E) Lactate Concentration in the Media
100rpm 120rpm 150rpm Static
59
Figure 4–7: Comparison of biological responses in cylindrical impeller 10 ml bioreactors at different agitation rates and in static culture.
4.3.4 Effects of Impeller Geometry
4.3.4.1 Hydrodynamic Effects
Figure 4–8 shows the velocity field of 10 ml bioreactor with paddle impeller and 10 ml
bioreactor with cylinder impeller at 150 rpm. The impellers rotate counter clockwise as shown by
the directions of small arrows. Near the bottom of the bioreactor vessel, the velocities are more
uniform with regular axial direction. Closer to the impeller at the middle of the bioreactor height,
the velocity increases and radial flow is very strong. At this region, the flow is highly turbulent
with strong flow separation shown by the arrows. Visually, the radial flow is stronger and velocity
magnitude is higher in the bioreactor with paddle impeller. In fact, the volume averaged velocity
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3 4
mm
ol/L
Time (days)
F) Ammonia Concentration in the Media
100rpm 120rpm 150rpm Static
60
in the paddle impeller model is about 85% greater than in cylinder impeller model at the same
agitation rate (Table 4–3).
Figure 4–9 shows that shear rate in paddle impeller model is higher than in cylinder
impeller. Due to the rectangular shape with relatively small corners, shear rate near the tip of
paddle impeller is much higher than maximum shear rate in cylinder impeller model. In the entire
bioreactor volume, the average shear rate in paddle impeller model is 74% greater than in cylinder
impeller model (Table 4–3). The impeller geometry also strongly affects the turbulent dissipation
rate in 10 ml bioreactors (Figure 4–10). The volume average turbulent dissipation rate in paddle
impeller model is about 3.2 times greater than in cylinder impeller model (Table 4–3). Hence, with
higher shear rate and turbulent dissipation rate, the 10 ml bioreactor with paddle impeller is
expected to produce smaller cell aggregates.
Table 4–3: Comparison of volume-averaged velocity, shear rate, and turbulent dissipation rate between bioreactor with paddle impeller and bioreactor with cylinder impeller at 150 rpm
Cylinder Impeller (150 rpm) Paddle Impeller (150 rpm)
Velocity (m/s) 0.040 0.075
Shear Rate (s-1) 18.76 32.8
Energy Dissipation Rate (m2/s3) 3.0E-3 9.7E-3
61
Figure 4–8: Velocity vector field in 10 ml bioreactor with cylinder impeller and in 10 ml bioreactor with paddle impeller at 150 rpm. Longer and thicker arrows indicate velocity vectors with high magnitude, and the arrows point toward the direction of the velocity vectors.
Paddle Impeller
Cylinder Impeller
62
Figure 4–9: Comparison of shear rate distribution between the 10 ml bioreactor with cylinder impeller and 10 ml bioreactor with paddle impeller at 150 rpm. The area under the curve was normalized to unity.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 30 60 90 120 150
Cu
mu
lati
ve V
olu
me
Fra
ctio
n
Shear Rate (s-1)
Effects of Impeller Geometry on Shear Rate
Cylinder Impeller (150 rpm) Paddle Impeller (150 rpm)
63
Figure 4–10: Comparison of turbulent energy dissipation rate between 10 ml bioreactor with cylinder impeller and 10 ml bioreactor with paddle impeller at 150 rpm. The area under the curve was normalized to unity.
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
0 0.005 0.01 0.015 0.02
Cu
mu
lati
ve V
olu
me
Fra
ctio
n
Turbulent Dissipation Rate (m2/s3)
Effects of Impeller Geometry on Turbulent Dissipation Rate
Cylinder Impeller (150rpm) Paddle Impeller (150rpm)
64
4.3.4.2 Biological Effects
Cell growth in 10 ml bioreactor with paddle impeller and in 10 ml bioreactor with cylinder
impeller at 150 rpm are shown on Figure 4-11A. The cell density in bioreactor with cylinder
impeller is higher than in bioreactor with paddle impeller. However, the difference is less
significant compared to the cell growth at lower agitation rates. Changes in pH (Figure 4-11B),
glucose concentration (Figure 4-11E), lactate concentration (Figure 4-11F), and ammonia
concentration (Figure 4-11G) are also similar for both bioreactor systems with different impeller
geometries. As expected, the cell aggregate size in 10 ml bioreactor with paddle impeller (Figure
4-11C) is smaller than the aggregate size in 10 ml bioreactor with cylinder impeller (Figure 4-11D)
at the same agitation rate. Due to stronger shear rate and turbulent dissipation rate, there are more
small aggregates in bioreactor with paddle impeller giving the mean aggregate diameter of 114 μm
which is smaller than aggregate dimeter in 10 ml bioreactor with cylinder impeller (150 μm).
Relatively smaller aggregate below 250 μm are not affected by mass transfer limitation and are
easier to split into single cells than bigger aggregates. Therefore, resulted cell density in bioreactor
at 150 rpm with both impeller geometries was much higher than the viable cell density produced
at lower agitation rates. Furthermore, the viability of both culture conditions were always above
95% in 4 days of culture duration. Although high shear rate and energy dissipation rate might cause
some damages to the cells, these hydrodynamic ingredients are necessary to maintain the healthy
cell aggregate size as well as cell growth in suspension culture.
65
0.0E+00
2.0E+05
4.0E+05
6.0E+05
8.0E+05
1.0E+06
1.2E+06
1.4E+06
1 2 3 4
Via
ble
Cel
l Con
cen
trat
ion
(ce
lls/
mL
)
Time (days)
A) Cell growth
150 rpm, Cylinder 150rpm, Paddle
66
6.0
6.5
7.0
7.5
8.0
1 2 3 4
pH
Time (days)
B) Change in pH of Media
150 rpm, Cylinder 150 rpm, Paddle
0.E+00
5.E-02
1.E-01
2.E-01
2.E-01
60 80 100 120 140 160 180 200 210 220 240
Tot
al N
um
ber
Fra
ctio
n
Aggregate Diameter (µm)
C) Cylinder Impeller at 150 RPMAggregate Size Distribution
67
0.E+00
5.E-02
1.E-01
2.E-01
2.E-01
3.E-01
60 80 100 120 140 160 180 200 220
Tot
al N
um
ber
Fra
ctio
n
Aggregate Diameter (μm)
D) Paddle Impeller at 150 RPMAggregate Size Distribution
0.0
1.0
2.0
3.0
4.0
1 2 3 4
g/L
Time (days)
E) Glucose Concentration in Media
150 rpm, Cylinder 150 rpm, Paddle
68
Figure 4–11: Comparison of biological responses in 10 bioreactors with cylinder impeller and in 10 ml bioreactor with paddle impeller at 150 rpm.
0.0
1.0
2.0
3.0
4.0
1 2 3 4
g/L
Time (days)
F) Lactate Concentration in Media
150 rpm, Cylinder 150 rpm, Paddle
0
0.5
1
1.5
2
1 2 3 4
mm
ol/L
Time (days)
G) Ammonia Concentration in Media
150 rpm, Cylinder 150 rpm, Paddle
69
4.3.5 Effects of Shear Rate and Eddy Size on Aggregate Size
Figure 4–12 shows the relationship between shear rate and cell aggregate size in 10 ml
bioreactor. The results are very similar to 100 ml model described in previous chapter. Higher
shear leads to smaller aggregate, and the level of difference in aggregate size is dependent on the
level of difference in shear rate. For instance, 25% increase in shear rate from 100 rpm to 120 rpm
leads to 13% decrease in aggregate size, and 74% increase in shear rate from 120 rpm to 150 rpm
leads to 31% decrease in aggregate size. At low shear level as in 10 bioreactors being agitated at
100 rpm, majority of the cell aggregates stay in low shear region so that the overall aggregate size
is very large. However, despite of the agitation rates, aggregate breakup near the tip of rotating
impeller is always possible. Therefore, there are always small aggregates present in stirred
suspension culture, and higher shear would produce higher number of small aggregates.
Figure 4–13 shows the similarity of average eddy size and average cell aggregate size in
10 ml bioreactor at different turbulent dissipation rates. As turbulent dissipation rate increases, the
eddy size decreases (71). Results from previous 100 ml model in previous chapter showed that
average cell aggregate have similar size as average eddy size at different agitation rates. In fact,
the average aggregate size and average eddy size in 10 ml bioreactor are also similar. The
difference is only 15 µm or less which is about size of a single murine ESC. Therefore, once again,
the results show that CFD modeling can be used to predict hydrodynamics and cell aggregate size
in stirred suspension bioreactor.
70
Figure 4–12: Effects of shear rate on murine ESC aggregate size in 10 ml bioreactor with cylinder impeller. The error bars are standard deviations in aggregate size.
0
50
100
150
200
250
0 5 10 15 20 25 30 35
Agg
rega
te S
ize
(µm
)
Volume Averaged Shear Rate (s-1)
Effects of Shear Rate on Aggregate Size in 10 ml Bioreactors
71
Figure 4–13: Similarity in average aggregate size and eddy size at different turbulent dissipation rates in 10 ml bioreactor.
4.4 Conclusions
Hydrodynamics of 10 ml bioreactor at different agitation and with different impeller
geometries were modeled using COMSOL Multiphysics. Velocity, pressure, shear rate, and energy
dissipation rate profiles in 10 ml bioreactor were similar to 100 ml bioreactor. However, the
magnitude of these hydrodynamic values were smaller in 10 ml bioreactor than in 100 ml
bioreactor at the same agitation rate. This can be adjusted by increase the agitation rate in 10 ml
bioreactor. It was found in this study that, 150 rpm in 10 ml bioreactor has similar hydrodynamics
and biological responses as 100 rpm in 100 ml bioreactor. Therefore, 10 ml bioreactor can be used
as a scaled down model of 100 ml bioreactor with a predefined adjustment in impeller speed. CFD
0
20
40
60
80
100
120
140
160
180
0 0.002 0.004 0.006 0.008 0.01 0.012
Siz
e (µ
m)
Turbulent Dissipation Rate (m2/s3)
Aggregate Size and Eddy Size at Different Turbulent Dissipation Rates
Mean Eddy Size Mean Aggregate Size
72
modeling is a great tool to help determine the impeller speed and predict the hydrodynamic change
in scaling down bioprocess.
In this study, over 4-day culture period, the cell aggregate size and cell expansion were found
to be highly dependent on hydrodynamic environment. The metabolites of the cells in 10 ml
bioreactors were found to be in a healthy range. Extended culture duration can be done in the future
to further investigate the effects of metabolites on the cells.
The effects of shear rate and eddy size on cell aggregate size was reconfirmed in this study.
Similar to 100 ml bioreactor, the level of effects was dependent on the level of changes in
hydrodynamics, mainly shear rate and energy dissipation rate. Once again, it was shown that the
average aggregate sizes are similar to average eddy sizes at corresponding turbulent dissipation
rates. Therefore, CFD can be used to not only predict the hydrodynamics, but also the performance
of the bioreactor on producing the optimal cell expansion and cell aggregate size.
73
Chapter Five: Discussions of Limitations, Recommendations, and Conclusions
5.1 Discussions of Limitations and Recommendations
5.1.1 CFD Modeling
Although CFD simulation used in this project has captured many important information on
hydrodynamic environment inside the bioreactors with various configurations, there are several
limitations that need further investigations. In order to accurately apply k-є model, the flow has to
be fully turbulent. However, based on the calculated Reynolds number, the flow is actually in the
transition zone which is not yet fully turbulent (13). The turbulent flow assumption is needed not
only in this studies but other similar studies because the transition flow is difficult to characterize
and current CFD packages are not fully capable of modeling this type of flow (18). The k-є has
shown good agreement with experimental results for small pressure gradient, but less accurate for
adverse pressure gradients (52). Moving forward from this project, experimental validation of CFD
simulation can be done using PIV (72). The velocity field obtained from PIV can be used to derive
shear stress and energy dissipation rate as in CFD modeling.
The fluid used in all simulations was assumed to be as same as water. Although this
assumption is widely used in many CFD modeling studies (13, 18, 19, 73), the exact fluid property,
particularly cell culture medium with presence of cells, is needed in order to obtain the accurate
model outputs. The viscosity of fluid can be measured experimentally using rheometer. However,
depending on protein and cell concentration, the fluid mixture can behave differently (74).
Therefore, measuring the viscosity of cell culture medium at various shear rate and cell density is
necessary in order to accurately determine fluid properties of cell culture medium. This can be a
constant number for Newtonian fluid or a function of shear rate for non-Newtonian fluid (43, 75).
74
The grid generations were performed without taking into account the size of the aggregates.
The model assumed one-phase turbulent flow and the cell aggregate size and mass were neglected
to simplify the numerical complexity and to save computational cost. However, as the exact level
of forces acting on the cells of the aggregates is needed for other studies such as
mechanotransduction study, the size and the mass of the aggregates should be incorporated into
the CFD model and the mesh size should be adaptive to the size of the aggregates. In this case,
two-phase flow can be employed to model the fluid and solid cell aggregate interaction which may
involve more complex numerical solutions and higher computation cost (76).
5.1.2 Biological Experiments
The main focus of this project is to model the fluid environment and correlate the
simulation data with cell expansion and aggregate size. The next step would be staining for
pluripotency markers and testing differentiation capability of resulted cell aggregates to clarify
the different effects of hydrodynamics on cell behaviors.
Although the results show good agreements between 100 ml and 10 ml bioreactors on the
relationship between small eddy size and aggregate size, additional data at different agitation
rates are needed to further support this finding. In addition, it is worth testing similar conditions
using different aggregate-forming cells such as human ESCs and iPSCs.
5.2 Conclusions
CFD simulation is a powerful tool for modeling the hydrodynamics of SSBs. Using CFD
simulation, important hydrodynamic variables such as fluid velocity, shear rate, and energy
dissipation rates can be obtain locally and globally. These are difficult to get experimentally, even
75
with the most used velocity imaging technique like PIV (77). In Chapter 3, standard lab-scale 100
ml spinner flask was simulated using RANS k-ε model in COMSOL Multiphysics. As expected
the shear rate and energy dissipation rate were highest near the tip of the impeller. The significant
difference in volume-averaged and maximum values of shear rate (~40 times) and energy
dissipation rates (~100 times) suggesting that the “possible cell damage” region only occupied a
small volume fraction of the bioreactor. However, more or less, the cell and aggregates could travel
through this region and experience high shear. Even though the aggregate size increased as shear
rate end energy dissipation rate decreased, small aggregate sizes always presented in all stirring
conditions.
In Chapter 4, the same method was used to model the hydrodynamics of 10 ml bioreactor.
The velocity, shear rate, and energy dissipation rate profiles were similar to 100 ml model in
Chapter 3. The magnitude of the two bioreactor scales could be matched up by increasing the
agitation rate in 10 ml bioreactor. It was shown in Chapter 4 that, 150 rpm in 10 ml bioreactors
gave similar volume-averaged turbulent dissipation rate as 100 rpm in 100 ml bioreactor described
in Chapter 4. Therefore, based on hydrodynamic profile, 10 ml bioreactor at 150 rpm could be
considered as a scaled-down model of 100 ml bioreactor at 100 rpm.
In addition to effects of scaling-down, the effects of impeller geometry were also described
in Chapter 4. The 10 ml bioreactor with paddle impeller produced higher shear than 10 ml
bioreactor with cylinder impeller at the same agitation rate. The paddle impeller provided more
sweeping area than cylinder impeller due to 7.8% difference in length and width. The relatively
thin and small corner led to high local shear rate and high energy dissipation rate near the tip of
the impeller. Overall volume-average shear rate in 10 ml bioreactor with paddle impeller was 75%
higher than the 10 ml bioreactor with cylinder impeller, at 150 rpm.
76
Biological results in Chapters 3 and 4 agreed with the expectations based on hydrodynamic
profiles. In higher shear environment, the cells aggregates were less likely to be broken up so that
the mean aggregate size was higher at lower shear rate. The same observations in aggregate size
were obtained in 10 ml bioreactors. Furthermore, biological results also showed that the average
aggregate size obtained from 10 ml bioreactor at 150 rpm (150 μm) was similar to the average
aggregate size in 100 ml bioreactor at 100 rpm (135 μm). The difference was very small and is
about the size of a single ES cell (78).Therefore, high through put screenings and experimental
testing could be done using 10 ml scaled-down bioreactors instead of using 100 ml bioreactors.
Another useful of information for cell aggregate control and bioreactor scaling was the
relationship between average eddy size and average aggregate diameter. The average small eddy
sizes in Chapters 3 and 4 were calculated from volume-averaged turbulent dissipation rate (12).
The results in 100 ml model (chapter 3) and 10 ml model (chapter 4) showed that the average cell
aggregate size was similar to the average eddy size obtained from CFD modeling. Interestingly,
this result also imply that the volume-averaged turbulent dissipation rate can be considered as a
scale-up and scale-down criterion in bioreactor design for expanding aggregate-forming cells such
as PSCs. Using turbulent energy dissipation rate as a scaling criterion is in fact very popular in
bioprocess development (12, 79). However, the volume-averaged energy dissipation rate here can
only be obtained from CFD simulation.
Overall, CFD simulation results and biological results showed good agreements. The results
from this work can be applied into bioprocess design and development of aggregate-forming cells.
Furthermore, the information on hydrodynamics of 100 ml and 10 ml bioreactors can be used in
mechanotransduction studies to investigate the effects of shear stress on gene expressions of the
cells.
77
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APPENDIX A: CELL CULTURE
A.1. Static cell culture
A.1.1. Gelatin coating
Each 100 ml of 0.1% gelatin solution was made by adding 0.1 gram of gelatin type B into
100ml sterile double distilled water. The solution was autoclaved, cooled down, and then stored at
40C for future use.
About 3ml of gelatin solution was added to fully cover the surface of a 10 cm2 tissue culture
dish. The tissue culture dish was let sit in the sterile laminar flow hood at room temperature for 20
minutes. The gelatin solution was then removed from the tissue culture dish and discarded. The
dish was let dry in the hood with the lid slightly opened for about 15 to 20 minutes. The gelatin-
coated tissue culture dish could be used instantly, or be wrapped with aluminum foil and stored in
4C fridge, for up to three days.
A.1.2. Static Passaging
Before passaging the cells, 10 ml of murine ESC culture medium was added to each gelatin-
coated tissue culture dish and then pre-incubated at 37C and 5% CO2.
Murine ESCs of D3 cell line were passaged every two days when the cultured reached
70% confluency. At this state the cells were in exponential growth phase and were healthy.
Overgrown culture could promote cell differentiation where the cells lost the ability to form well
defined colonies.
In the beginning of passaging, the consumed culture media was straightforwardly removed
from the tissue culture since murine ESCs adhered well to the bottom surface of the dish. The dish
was rinsed with 8ml DPBS 1X buffer solution. For cell detachment, 3ml of 0.25% trypsin-EDTA
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was added to the entire bottom surface of each 10 cm2 tissue culture dish and then incubated at
37C for 3-5 minutes until the cells have detached and lift off from the cell culture surface. After
the incubation, the cells were not completely dissociated, but remained as suspended colonies.
These colonies were broken up into single cells by pipetting the cell suspension up and down for
about 10 times until the single cells suspension had achieved. At least 3 ml of murine ESC culture
medium was added to the cell suspension in each culture dish to block the Trypsin from damaging
the cell membrane. The whole solution was then transferred to 15 ml sterile conical tube. The tube
was then centrifuged at 300 *g for 5 minutes. The supernatant was removed and 2 ml murine ESC
culture medium was added to each conical to suspend the single cells contained in the pellet. Two
50µm of homogenous cell suspension solution were taken for cell counting. Cell count was done
by using hemocytometer. Based on the information from the cell count, appropriate cell suspension
volume was added to each of the new 10cm^2 tissue culture dish to reach the inoculation density
of 40,000 cells/ml. The culture dishes were then incubated at 37C and 5% CO2.
A.2. Standard 100 ml Spinner Flask Bioreactor
A.2.1. Preparation of 100 ml Bioreactor
Six 100 ml spinner flask bioreactors were siliconized with Sigmacoat in order to prevent
the cells from sticking to the wall of the bioreactors. After siliconization process, the bioreactors
were then soaked with DPBS 1X solution for one day and after that, they were washed and soaked
with double distilled water for another day. The bioreactors were then let dry to be autoclaved for
cell culture use.
Agitation rate of three spinner plates was calibrated using Touchless Digital Tachometer.
The speed of the impeller corresponded with the frequency of the beam of light reflected off self-
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adhesive tabs. The speed was measured twice to ensure its accuracy and precision. The agitation
rates used in this experiment were 80, 100, and 120 rpm.
A.2.2. Bioreactor Inoculation and Feeding Regime
The cells were first expanded in static culture to in order to have a total of 3.5 x106 cells
for each 100 ml bioreactor. Before bioreactor inoculation, the required amount of murine ESC
culture media was calculated and pre-warmed in the incubator for about 2 hours. The first part of
bioreactor inoculation is basically static culture passing. After counting the cells, appropriate
volume of cell suspension solution was added to each bioreactor to achieve an inoculation density
of 3.5 x104 cells/ml. Three pairs of bioreactors (80, 100, and 120rpm) were agitated using
calibrated spinner plates inside the incubators at 37C and 5% CO2.
Media change took place on day 3 and day 4 of bioreactor cell culture. A pair of bioreactors
was taken out of the incubator and let sit in the laminar flow hood for one minute. Because of
gravity, the cell aggregates will settle at the bottom of the bioreactor, leaving the top part of the
bioreactor clear. Top 50 ml of spent media was removed from each bioreactor and replaced by 50
ml fresh media that had had been pre-warmed in the incubator.
A.2.3. Aggregate Size Measurement using Particle Sizer
The size distribution of murine ESC aggregates was measured using a Beckman Coulter
Multisizer III (Miami, FL, USA) with a 1000-um aperture, which has an effective particle-size
range of 20 µm to 600 µm. Murine ESC aggregate were collected from the bioreactor by gravity
sedimentation; supernatant was aspirated and aggregates were then re-suspended in 60:40 isoton
II (Beckman Coulter, Mississauga, ON) and glycerol (Fischer Scientific, Ottawa, ON). The
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instrument was set to apply a current of 800 uA, with a preamp gain of 4, and a maximum cell
volume of 25 µm3. Diluent resistivity and baseline noise were re-calculated prior to each session
by measuring noise level to determine the lower size threshold. The average noise level range
between 2.9 - 3.1% of the aperture diameter, which equate to a lower size limit of 29.8 µm to 34
µm. The amplitude of the voltage pulse associated with each particle was converted to a particle
size based on calibration coefficient using a L90 Latex Particle Standard with a nominal size of 90
µm with the bin size set to 128 and bin spacing on log diameter. For each run, murine ESC
aggregates were diluted such that the coincident counting rate was between 3-10%. Samples were
counted for 20 seconds per run, which returns about an average of 3000 events. An average of 3
runs were collected per sample. After collection, the data were analyzed using the Multisizer 3.53
software with counts plotted against diameters as a histogram using linear bins and a linear scale
for the x-axis. Background signal from debris and single cells were gated out of the data range by
excluding particles smaller than 40 μm in diameter.
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APPENDIX B: HYDRODYNAMICS
B.1. Calculation Results
Reynolds number can be calculated as: Re=N(Di)2/υ
The maximum shear stress in SSB was calculated from (63) described in Chapter 3.
Table 5–1: Results from maximum shear stress calculation for 100 ml bioreactor
Agitation rate (rpm)
Reynolds number Power number
Maximum Shear stress (Pa)
80 3570 0.611 0.408
100 4463 0.579 0.556
120 5356 0.554 0.715
Table 5–2: Results from Reynolds number calculation for 10 ml bioreactor
Agitation rate (rpm) Reynolds number
100 1064
120 1277
150 1597
B.2. Quasi-steady state approximation
Below graphs were taken from CFD solutions. Quasi-steady state solution is achieved
when the color lines representing the volumetric shear rate profile at each time point are aligned.
In this case, the quasi-steady state is about 3 s. The cumulative relative volume refers to the sum
of volume fraction up to the current bin. For example, in figure 5-1, above 3 s, the volume fraction
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for shear rate values that are below 300 s-1 is large (steep increase in the color lines). After this
range (0-250 s-1), the increase in cumulative volume fraction is insignificant so that the color lines
stay at the same y value. In other words, the volume fraction of shear rate below 400 s-1 is
essentially the same as the volume fraction of shear rate below 300 s-1 because the volume fraction
between 300 s-1 and 400 s-1 is very small and almost equals to zero.
Figure 5–1: Shear rate distribution from 0s-12s in 100 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 3s
Shear Rate Distribution in 100 ml Bioreactor at 100 rpm
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Figure 5–2: Turbulent dissipation rate distribution from 0s-12s in 100 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 3s.
Turbulent Dissipation Rate Distribution in
100 ml Bioreactor at 100 rpm
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Figure 5–3: Shear rate distribution from 0s-10s in 10 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 4 s.
Shear Rate Distribution in 10 ml Bioreactor at 100 rpm
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Figure 5–4: Turbulent dissipation rate distribution from 0s-10s in 10 ml Bioreactor at 100 rpm. The quasi-steady state is achieved by about 4 s.
Turbulent Dissipation Rate Distribution in
10 ml Bioreactor at 100 rpm