bioengineering thesis
DESCRIPTION
Bioreactor designTRANSCRIPT
THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE
DEPARTMENT OF BIOENGINEERING
THE NOVEL DESIGN OF A BIOREACTOR FOR IN VITRO PROLIFERATION AND DIFFERENTIATION OF HUMAN MESENCHYMAL STEM CELLS
JOSHUA D. SALVI
Spring 2009
A thesis submitted in partial fulfillment
of the requirements for a baccalaureate degree
in Bioengineering with honors in Bioengineering
Reviewed and approved* by the following: Henry J. Donahue Baker Professor of Cellular and Molecular Physiology Thesis Co-Supervisor Peter J. Butler Associate Professor of Bioengineering Thesis Co-Supervisor William O. Hancock Associate Professor of Bioengineering Honors Adviser * Signatures are on file in the Schreyer Honors College.
We approve the thesis of Joshua D. Salvi: Date of Signature _____________________________________ ______________ Henry J. Donahue Baker Professor of Cellular and Molecular Physiology Thesis Co-Supervisor _____________________________________ ______________ Peter J. Butler Associate Professor of Bioengineering Thesis Co-Supervisor _____________________________________ ______________ William O. Hancock Associate Professor of Bioengineering Honors Adviser
9-6939-2728
ABSTRACT
Continued use of autografts and allografts for bone-tissue therapy has serious
implications, including the decreased strength of such grafts in vivo over time [2]. A
novel solution to this problem is the use of tissue-engineered implants from the patient’s
bone marrow. Numerous techniques have already been used to build either two- or three-
dimensional scaffolds. Additionally, previous studies have demonstrated that oscillating
fluid flow-induced shear stresses will aid in the chemotransport among osteoblastic
lineages. In an exploratory series of studies, two-dimensional nanoscale substrates have
been analyzed with their flat counterparts under both static and flow conditions.
Furthermore, these protocols have been simulated through finite element analysis in
COMSOL by solving for various stresses encountered by cells under oscillating fluid
flow. Expanding these two-dimensional substrata to three-dimensional scaffolds,
progenitor cells, including human mesenchymal stem cells (hMSCs) and human bone
marrow stromal cells (hBMSCs), have been proliferated while maintaining their
differentiation potential into the osteoblastic lineage in vitro. These studies culminated in
the design of a three-dimensional bioreactor in which finite element analysis was used to
optimize the stress distribution and perfusion throughout the volume of a scaffold. The
purpose of these experiments was to explore the field of tissue engineering as it applies to
the musculoskeletal sciences. This reductionist approach to tissue engineering resulted in
the proposal of a new in silico method and an analysis of key parameters for successful in
vitro stem cell tissue culture.
TABLE OF CONTENTS ABSTRACT .................................................................................................................................... 3 INTRODUCTION ......................................................................................................................... 6
Background .............................................................................................................................. 6 Bone Grafts ....................................................................................................................... 6 Skeletal Tissue Engineering Approaches .......................................................................... 7 Progenitor Cell Lines ...................................................................................................... 12 Finite Element Analysis ................................................................................................... 15 Substrates and Scaffolds.................................................................................................. 16 Bioreactors ...................................................................................................................... 18
Literature Review .................................................................................................................. 21 Two-Dimensional Substrata ............................................................................................ 21 Three-Dimensional Scaffolds .......................................................................................... 25 Bioreactor Designs .......................................................................................................... 30 Finite Element Analyses .................................................................................................. 34 Literature Review Summary ............................................................................................ 36
Proposal ................................................................................................................................. 39 Two-Dimensional Substrata ............................................................................................ 39 Three-Dimensional Scaffolds .......................................................................................... 39 Biophysical Stimuli .......................................................................................................... 40 Bioreactor Design ........................................................................................................... 40 Finite Element Analyses .................................................................................................. 41 Thesis Statement and Hypotheses ................................................................................... 43
MATERIALS AND METHODS ................................................................................................ 44 Nanoscale Substrate Fabrication ............................................................................................ 44 Salt Leaching and 3D Scaffolds ............................................................................................. 45 Cell Harvesting ...................................................................................................................... 46 Cell Culture ............................................................................................................................ 47 Oscillating Fluid Flow ........................................................................................................... 48 Fluorescent Markers .............................................................................................................. 49 Alkaline Phosphatase Assay .................................................................................................. 51 Substrate Characterization ..................................................................................................... 52 Simulation of the 2D Microenvironment ............................................................................... 53 Bioreactor Design .................................................................................................................. 55 Statistics ................................................................................................................................. 56
RESULTS ..................................................................................................................................... 57 2D Substrate Characterization ............................................................................................... 57 3D Scaffold Characterization ................................................................................................. 60 Mechanosensitivity of Stem Cells on Substrates ................................................................... 63 FACS Analysis ...................................................................................................................... 66 AP Activity ............................................................................................................................ 71 Finite Element Analysis of Cell Confluence ......................................................................... 74 Finite Element Analysis of Cell Height ................................................................................. 78 FEA of Cells Cultured on Various Nanotopographies .......................................................... 85 3D Bioreactor Design by the Finite Element Method ........................................................... 89
DISCUSSION ............................................................................................................................... 96 Two-Dimensional Substrata Characterization ....................................................................... 96
Findings from AFM Imaging ........................................................................................... 96 Drawbacks of Cell Height Estimates .............................................................................. 97
Three-Dimensional Scaffold Characterization ...................................................................... 98 Findings from SEM Imaging ........................................................................................... 98 Drawbacks of Porosity Calculations ............................................................................... 99
Stem Cell Growth on 2D Substrates .................................................................................... 101 Mechanosensitivity of Stem Cells .................................................................................. 101 Proliferation and Differentiation Potentials ................................................................. 102 Alkaline Phosphatase Activity ....................................................................................... 103
Stem Cell Growth on 3D Scaffolds ..................................................................................... 105 Alkaline Phosphatase Activity ....................................................................................... 105 Comparison with 2D Substrata ..................................................................................... 106
Finite Element Analysis ....................................................................................................... 107 Discussions of Cell Confluence and Hydrophobicity .................................................... 107 Benefits over Empirical Data Collection ...................................................................... 109 Benefits of Oscillating Fluid Flow ................................................................................ 109 Summary of FEM as a Tool in Cell Culture .................................................................. 110
Bioreactor Design ................................................................................................................ 111 Satisfaction of Design Criteria and Specifications ....................................................... 111 Comparison of Two Models .......................................................................................... 113 Analysis of Design ......................................................................................................... 114
CONCLUSIONS ........................................................................................................................ 116 Methods of Biomaterial Characterization ............................................................................ 116 Ability of Substrates and Scaffolds to Regulate Stem Cell Activity ................................... 118 Finite Element Method as a Novel Tool in Tissue Engineering .......................................... 120 Summary of Bioreactor Properties Key for Success ............................................................ 122 Closing Remarks .................................................................................................................. 124
REFERENCES ........................................................................................................................... 127 APPENDICES ............................................................................................................................ 132
Appendix A: Acknowledgments .......................................................................................... 132 Appendix B: Health Insurance Portability and Accountability Act (HIPAA) ..................... 133 Appendix C: Funding Sources ............................................................................................. 134 Appendix D: Supplemental Sketches .................................................................................. 135 Appendix E: Summary of Common Tissue Engineering Growth Factors ........................... 137 Appendix F: COMSOL Model Reports ............................................................................... 138 Appendix G: Academic Vita ................................................................................................ 208
INTRODUCTION Background:
Bone Grafts:
Ten years ago, there were 650,000 reported cases of bone allograft transplantation
[9]. Bone transplantation is key in rebuilding diseased tissues. These include the hips,
shoulders, knees, and spine. Grafts are also key in the repair of bone loss from fractures
or cancers [10]. Allografts are tissue transplantations between individuals of the same
species. In this case, bone is grafted from one human being to another. Autografts, on the
other hand, are grafts of tissue from one location on an individual to another location of
that same individual. Autografts are far less common than allografts, due mainly to the
constraints of individual patients. For example, osteoporotic bone is virtually useless in
autograft transplantation, and allografts are thus necessary. Xenografts, methods rarely
used in orthopedic surgery, involve tissue grafts from one species to another. Bone
allografts are the most common due to their osteoconductive properties and the inclusion
of osteogenic factors that induce bone tissue growth [9]. These factors include bone tissue
progenitors (such as mesenchymal stem cells), osteoblasts, and osteocytes.
Allografts are harvested either from a living donor or cadaveric sources within 24
hours of death [9]. Key components of this harvesting include the maintenance of cell
viability and prevention of allograft infection. This is not to say that current methods are
perfect, but they have been successful nonetheless. Risk of HIV infection is very low, at a
rate of 1 in 150,471. If lymph nodes are tested prior to transplantation, this rate has been
reduced to as low as 1 in 1.67 million [9]. There have also been cases of HCV
transmission, though these were rare. Though current sterilization methods are not
6
perfect, grafts rarely lead to disease transmission. Nonetheless, a viable alternative
without such transmission, similar to the functionality of autografts, would be preferred.
Other factors affect allograft performance. With continued use in vivo, allografts
lead to mechanical failure of bone. Using human models, it has recently been
demonstrated that a decreased bone mineral density, degradation of material properties
(such as elasticity), and increased numbers of micro-fissures resulted with time. These
data were correlated to the 60% failure rate of allografts within 10 years after
transplantation [2].
These structural anomalies are a function of age. The donor must be 45 or
younger in order to decrease failure rates. Furthermore, additional tissue processing for
sterility (e.g. freeze-thaw cycles) increase failure rates [9]. These data can be correlated to
a trade-off between preventing transmission of disease and preventing mechanical failure.
Thus, current bone graft methods are limited by the lack of donors, possible
disease transmission, and known mechanical failure with time. A tissue engineering
method incorporating autograft principles but assuring the osteogenic potential would act
as one viable solution.
Skeletal Tissue Engineering Approaches:
When considering the potential for tissue regeneration by tissue engineering, a
unique example can be found in nature. Amphibian limb models are classic in that they
demonstrate that a limb can be naturally regenerated after injury. The unique factor in
these regeneration models is the initial development of a regeneration blastema prior to
continued development of the limb. After inducing injury in a number of amphibians,
7
ectopic blastemas followed by ectopic limbs were witnessed within 60 days post-wound.
Furthermore, if a skin graft was added to the wound location, amphibians demonstrated a
73% rate of limb regeneration [11]. One model is illustrated in Figure 1.
Figure 1. The Stepwise Model for Limb Regeneration [11].
Shown in Figure 1 is a stepwise model for limb regeneration in amphibians. After
the injury, the key factors in limb regeneration (as opposed to skin regeneration alone or
blastema regression) include continued proliferation as signals from nerves and
fibroblasts are prevalent. The three pathways include wound healing (as seen in humans),
bump formation, and complete limb regeneration. Note that dedifferentiation to
progenitor cell lines was required in order to form the regeneration blastema. These
phenomena in limb regeneration remain mysterious by mechanism, but the key factor of
utilizing one’s own cells to regenerate tissue becomes the focal point of skeletal tissue
engineering [11].
In response to the phenomena, orthopedists have developed a number of methods
in skeletal tissue engineering, specifically to combat current issues with bone grafts [9].
8
Among the many strategies in skeletal tissue engineering, there are three basic
approaches to tissue engineering [12]:
1. In situ Regeneration of Skeletal Tissue
2. Isolation and Culture of Cells, Followed by Reimplantation
3. Combination of Cells and Scaffolds to Implant a Bone-Like or Cartilage-Like
Construct
The in situ regeneration is similar to that encountered in amphibian limb models,
where a graft or scaffold will stimulate the growth of skeletal tissue. The second method,
however, involves in vitro culture of progenitor cells, typically harvested from human
bone marrow. These aggregates are then injected into the patient without an
accompanying scaffold. Finally, the third and most popular approach uses a complete
three-dimensional model of bone or cartilage. However, the cells within the scaffold must
have reached maturity prior to implantation [12, 13].
Considering two-dimensional and three-dimensional biomaterials specifically,
there are numerous biomaterial factors that can influence cell-surface interactions. Within
seconds to minutes, cellular fluid adhesion is affected by surface wettability, and protein
adhesion can be affected by local pH, ionic composition, and temperature. Cell
attachment is then influenced by van der Waal’s forces. Finally, hours later, cell adhesion
and spreading are affected by matrix proteins and cytoskeleton proteins [12]. Two key
factors in cell-surface interactions include surface topography and surface chemistry.
Surface chemistry is quantified through wettability, zeta potential, and elemental
composition (i.e. ESCA). However, the focus of the following studies is surface
topography. Osteoblastic cells significantly respond to surface morphology, and surface
9
roughness studies result in controversial conclusions. Lithographic methods and
numerous microscale substrates resulted in conflicting results, and further data are
required in order to obtain meaningful conclusions [12-14].
Similar methods and progenitor cells from bone marrow have been involved in
myocardial regeneration. These approaches have also taken advantage of scaffold
structures similar to chondrocyte repair. Though the final product may vary greatly, it
was demonstrated that the same progenitor cell lines can be used for numerous
applications [15].
The coupling of these approaches can be found in the development of bioreactors
for skeletal tissue engineering. Prior to developing a bioreactor, multiple cell lines,
substrates, and growth factors must be analyzed for potential differentiation and
proliferation in vitro. Furthermore, the bioreactor design is not the end result. Bone tissue
constructs must then be analyzed through implantation studies prior to the development
of a final product [16]. These approaches are summarized in Figure 2.
Figure 2. Outline of the Tissue Engineering Process [16].
10
When designing a bioreactor, one must consider how nutrients and growth factors
will be supplied to cells in culture. Furthermore, perfusion seeding of scaffolds may be
required if a three-dimensional scaffold is involved. An analysis of intercellular and
intracellular interaction of cells cultured in these scaffolds is also required. Nonetheless,
the bioreactor system must account for multiple scaffold types, cell types, and scaffold
dimensions. These reactors have included tissue culture flasks, agitated vessels, packed
beds, fluidized beds, and membrane bioreactors [9, 12, 13, 16-18]. A systems view of
bioreactor designs can be found in Figure 3.
Figure 3. A Systems View of the Ideal Bioreactor in Tissue Engineering. Note the number
of factors that must be considered in the design of these systems [16].
11
Progenitor Cell Lines:
Stem cells are unique in that they can continue to proliferate for long periods of
times, are unspecialized, and can differentiate into multiple lineages. Human embryonic
stem cells (hESCs) are harvested from a blastocyst initiated by in vitro fertilization [19].
The focus of this study, however, is on adult stem cells. Specifically, human
mesenchymal stem cells (hMSCs) are harvested from umbilical cord blood, bone
marrow, or fat in somatic tissue. There are two types of adult stem cells. Hematopoietic
stem cells give rise to erythrocytes, leukocytes, and platelets in the blood. However,
human bone marrow stromal cells (hBMSCs) are non-hematopoietic, meaning that they
do not give rise to blood cells. Instead, stromal cells differentiate into osteoblasts,
chondrocytes, adipocytes, and other connective tissue. Plasticity is the phenomenon by
which stromal cells harvested from one tissue type can differentiate into the lineage of
another phenotype. For example, bone marrow stromal cells can differentiate into bone,
cardiac muscle, and skeletal muscle lineages [20]. The differentiation pathways
illustrating such transdifferentiation are illustrated in Figure 4.
12
Figure 4. Comparison of hematopoietic (Top) and stromal (Bottom) stem cell
differentiation [20].
Considering the construction of filaments in the extracellular matrix, the common
pattern witnessed is that of branching morphogenesis. Compare this to the branching of a
tree, where continued growth leads to a fairly complex matrix of numerous branches.
This morphogenesis becomes key in the differentiation of progenitor cells, whereby the
intercellular space becomes complex in a three-dimensional matrix. In skeletal tissue
engineering, mimicking this branching morphogenesis in vitro through the creation of a
three-dimensional scaffold on which progenitor cells are cultured is key.
In bone, the branching of tissue by the dynamic nature of osteoblastic growth and
osteoclastic decay leads to a lighter and more structurally sound system. In fact, such
properties also lead to improved diffusion across the mesenchyme [21, 22]. However,
another strong consideration is the method by which differentiation occurs.
13
Initially, pluripotent stem cells can differentiate to the myoblast, fibroblast,
chondrocyte, adipocyte, or osteoblastic lineages. Initially, however, these cells must
commit as a progenitor cell that can then differentiate to all but the myoblastic and
fibroblastic lineages. After the addition of osteogenic media with synthetic
gluococorticoid, dexamethasone, and bone morphogenic protein (BMP-2) enhances
differentiation potential to the osteoblastic lineage. These osteoblasts can then further
mature to bone lining cells or osteocytes [23]. The aforementioned differentiation
pathways are illustrated in Figure 5.
The major issue with tissue engineering, however, has been that continued
expansion of progenitor cells in vitro significantly reduces their differentiation potential.
Tissue engineering techniques thus attempt to mimic the in vivo environment of bone in
order to maximize this differentiation [21, 24, 25]. This technique typically requires some
combination of growth factors, biomaterials, and biophysical signals witnessed in vivo.
Figure 5. The Multiple Differentiation Pathways for Osteoblasts [22].
14
Finite Element Analysis:
When considering the biomechanics of bone, orthopedists and biomedical
engineers often turn to structural analyses by the finite element method (or finite element
analysis, FEA). FEA allows for the discretization of complex geometries, granting much
greater flexibility in the study of mechanics than finite volume methods (FVM). The key
difference between FEA and FVM is the analysis by nodes or volumes, respectively.
Typically, finite element analyses require the use of computer technology for discrete
approximations [26].
FEA is useful in solving complex differential equations by first denoting a
number of finite elements or nodes and then approximating between them. First, consider
any differential equation. For our purposes, let this be a second-order differential
equation in one dimension. This equation can be generalized to a decomposition of
, where L is some linear operator. Using dot products, we can then state the
function · 2 · , and I(u) is the minimum of . The next
phase then uses an arbitrary variable in order to determine that · · . We can
then solve for this equation instead of solving for . This equation is known as
the Galerkin form, and it now requires that L only be a stationary point as opposed to a
linear operator. This method for solving equations by nodal approximations becomes key
when solving for complex geometries [26, 27].
As mentioned previously, finite element analysis requires the use of
computational methods. In this particular study, COMSOL Multiphysics (formerly
FEMLAB) has been used. COMSOL is unique in that it can not only analyze complex
geometries by finite element analysis, but it can also couple multiple physics modules
15
into a single geometry. The program was initially developed by Germund Dahlquist at the
Royal Institute of Technology in Stockholm, Sweden [28]. This created the ability to
couple structure stress-strain analyses with the fluid mechanics of a geometry as
implemented by steady-state Navier-Stokes equations [29].
A sample application of finite element analyses to studies of skeletal tissue
engineering is that of bone remodeling. In the morphogenesis of skeletal tissue, bone
undergoes changes of mechanical properties and changes of relaxed lengths. These are
typically studied independently, but FEMLAB (the predecessor to COMSOL) allowed
the use of multiphysics to study them simultaneously. By using microspin velocity as the
rate by which bone remodeling occurs, and noting both the current state and relaxed state
of each element, constitutive equations could then be coupled. Finally, these models were
able to find the anisotropic elasticity with respect to time. Though not described in detail
here, this simulation exemplifies an excellent application of the finite element method to
studies of skeletal tissue remodeling [30].
Substrates and Scaffolds:
As mentioned previously, the key issue in the continued expansion of progenitor
cells in vitro is mimicking the in vivo environment. Typically, cells are often cultured on
flat surfaces, such as plasma-cleaned glass, polystyrene, or quartz slides. Not
surprisingly, cells cultured on these substrates lose their differentiation potential with
continued expansion.
To combat this issue, biomedical engineers have fabricated a number of two-
dimensional substrates that mimic the in vivo environment. The first method, the one
16
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17
Though demineralization improves allografts and autografts after implantation,
mineralization becomes key when analyzing three-dimensional scaffolds. As mentioned
previously, these scaffolds provide a matrix upon which progenitor cells can grow into
mature bone. This construct is then re-implanted into the patient from whom bone
marrow is derived. Electro-spun nanofibers, hydrogels, carbon nanotubes, and a
multitude of other materials and approaches have been used in the development of
scaffolds. However, it has been demonstrated recently that mineralization by calcium and
phosphorous-containing materials provide additional support to the scaffold and induce
further growth of osteoblasts [33]. These properties thus become key in the development
of scaffolds.
Bioreactors:
The bioreactor provides a sterile environment for in vitro cell culture. The goal of
the design is to mimic in vivo conditions, thus improving proliferation and differentiation
of mesenchymal stem cells. Skeletal tissue engineering bioreactors include those with
fluid flow or mechanical stretching [34-37]. These provide dynamic mechanisms for the
differentiation into numerous lineages.
In a myriad of past studies, static cultures were involved. Though static cultures
have been simple to implement, these cultures result in non-homogeneous cell
distributions. Additionally, extracellular matrix proteins are not deposited uniformly,
adversely affecting the biomechanical properties of cells cultured in three-dimensional
scaffolds. This phenomenon is expected, since cells in vivo are grown under mechanical
18
loads by interstitial fluid flow [34]. As a result, implementation of biophysical signals
will be integral in this study.
Spinner flask bioreactors, on the other hand, use a magnetic stir bar to thoroughly
mix the media. Cells cultured in these bioreactors demonstrated increased proliferation
and uniformity of distribution. However, the spinner flask bioreactor was not the optimal
device for in vitro osteogenesis due to decreased cell adhesion under turbulent flow
patterns [34].
Originally developed by NASA, the rotating wall vessel (RWV) bioreactor
implements two concentric cylinders, with the outer cylinder rotating. Scaffolds then
float in the annular space after centrifugal forces and gravitational forces are balanced.
Therefore, the culture conditions are microgravity-like. This bioreactor system is
excellent for inducing chondrogenesis, so it is widely involved in cartilage tissue
engineering. However, the rotating wall vessel bioreactor does not significantly induce
osteogenesis. One factor discovered by NASA, though, was that turbulence in bioreactors
is unfavorable. Though turbulence increases mixing in bioreactors, such fluid flow
properties significantly reduce cell activity. Thus, this bioreactor functions through
laminar flow profiles [34, 38].
Flow perfusion bioreactors are models very similar to the one developed in this
study. These devices perfuse media through scaffolds with a pump mechanism and can be
used for uniform seeding of cells in three-dimensional scaffolds. Additionally, flow
perfusion bioreactors improve mass transport throughout the interior of the scaffold,
unlike the spinner flask and rotating wall vessel models. Furthermore, fluid shear stress
has been demonstrated to induce osteogenesis in vitro. Studies comparing static and
19
perfused scaffolds in a flow perfusion bioreactor found that calcium deposition
significantly improved in these devices. Since interstitial fluid flow is a key component of
in vivo bone growth, this bioreactor acts as a significant improvement over the
aforementioned models [16, 34, 39].
Finally, continued mechanical loading of cells is believed to significantly improve
mass transports of nutrients throughout the interstitial space of the scaffold. For example,
bioreactors have induced mechanical loading by oscillating fluid flow, substrate bending,
longitudinal stretching, and compressive loading [34, 40].
20
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22
Upon using the polymer demixing method, it was found that various
weight/weight ratios would result in very different topographical features. When poly(L-
lactic acid)/polystyrene demixing was performed, increased ratios of polystyrene would
result in a topography more similar to nanopits rather than nanoislands (Figure 8). After
demixing, poly(L-lactic acid) would segregate to the upper surface of the polymer film,
mimicking similar culture dishes. After analysis by XPS and contact angle (wettability),
it was found that the PLLA/PS 70/30 w/w resulted in the most in vivo like conditions [1].
When human fetal osteoblastic cells (hFOB) were cultured on each of these
surfaces, both cell morphology and adhesion were measured. Additionally, these
substrata were compared with both flat poly(L-lactic acid) and polystyrene surfaces. In
doing so, it was thus determined that cell area was significantly greater (p < 0.01) on both
the poly(L-lactic acid)/polystyrene 70/30 and 90/10 w/w substrata when compared with
the flat controls. Furthermore, cell adhesion was also significantly greater (p < 0.01) on
these same substrata when compared with the flat controls. These demixed films
correspond to nanoislands as opposed to the nanopits illustrated in Figure 9.b. These data
demonstrate that osteoblastic cells will preferentially grow and adhere to various surfaces
based upon surface topography alone. This conclusion corresponds well with tissue
engineering concepts described previously in the background [1].
Nanoscale surface characteristics were further characterized by integrin
expression and osteopontin regulation in hFOBs cultured on nanoscale substrata [47]. It
was discovered that surface topography and wettability influence osteoblastic
extracellular matrix protein expression [47]. Furthermore, additional studies confirmed
that nanoscale surface topography positively influences cell morphology and adhesion
23
when other biomaterials were used [1, 45, 47-52]. The key issue, however, was that cell
activity and both proliferation and differentiation potentials were not measured in these
experiments. Though adhesion may be increase significantly, proliferation and the
maintenance of differentiation potential in vitro are the true keys to skeletal tissue
engineering. Without such data acquisition, it cannot yet be concluded that these substrata
are in fact beneficial to osteoblastic differentiation of human bone marrow stromal cells
and other mesenchymal progenitors.
However, other studies have demonstrated that inducing biophysical signals via
oscillating fluid flow may increase proliferation and possibly differentiation potential.
The data in support of this theory simply used flat substrates as opposed to the
aforementioned nanoscale topographies. It was demonstrated that calcium signaling and
upregulation of the MAP kinases ERK 1/2 result from oscillating fluid flow-induced
shear stresses [8, 39, 53-56]. Again, polymer demixed films were not involved in these
experiments. It should also be noted that a similar study analyzed the elastic moduli of
hFOBs cultured on numerous nanoscale substrata using contact-mode atomic force
microcopy (AFM). It was concluded that cells cultured on 11-38 nm nanoislands
displayed significantly greater elastic moduli when compared with those on flat
polystyrene or plasma-cleaned glass surfaces [57]. Intuition would then beg the
hypothesis that some combination of induced biophysical signals and surface topography
would result in increased apparent shear stresses due to the increased elastic moduli of
cells cultured on these substrata. Thus, such a combination may in fact provide a more
versatile and adept method for maintenance of stem cell differentiation potential with
continued expansion in vitro.
24
Three-Dimensional Scaffolds:
Though it has been previously demonstrated that two-dimensional nanoscale
topographies increase focal adhesion and expression of extracellular matrix proteins, it
has been widely disputed that three-dimensional scaffolds provide a more adept
microenvironment due to increased surface area and a better matrix for bone growth in
skeletal tissue engineering. Numerous studies have analyzed such scaffolds, but none of
the scaffolds to be mentioned involve a nanotopographic substrate as a comparative
measure along with induced biophysical signals to promote progenitor cell activity [4].
Figure 10. Structures of PEG4600DM (A), PEG526MMA-nLA-fluvastatin (B), acrylated-
PEG3400-RGDS (C), and methacrylated heparin (D) used for hydrogel fabrication [4].
As mentioned previously, bone morphogenic protein-2 (BMP2) becomes
necessary in the commitment of progenitor cells to the osteoblastic lineages (Figure 5).
Recent studies in multiple laboratories have used PEG hydrogels to create a scaffold via
25
copolymerization (Figure 10). Note that the structures of these polymers have a high
molecular weight and a high density of ester functional groups. These become key in the
interaction with BMP2. The PEG and heparin copolymers noncovalently bonded to the
BMP2, resulting in a more adept method for controlling a sustained level of osteogenic
growth factors within the scaffold [4]. As a result, these data were correlated to increased
differentiation potential of progenitor cells into the osteoblastic lineage in vitro on these
three-dimensional hydrogels.
However, hydrogels can be expensive to fabricate and maintain, and other simpler
scaffolds have also been thoroughly explored. Another example was the development of
collagen and collagen-hydroxyapatite scaffolds. The key concept in the development of
these three-dimensional structures was the utilization of biomaterials inherent in the
extracellular matrix of bone. Scanning electron microscopy images and pore sizes of
these two scaffolds are depicted in Figure 11.
Figure 11. Collagen (A) and Collagen-Hydroxyapatite (ColHA; B) scaffolds. ColHA
frozen at -30°C (C) and -80°C (D), along with porosities (E).
26
Note that most pores were on the order of 50 to 200 microns, near the range of
marrow stromal cells (approximately 20-40 microns). After culturing osteoblastic cells on
these scaffolds, it was discovered that the collagen-hydroxyapatite scaffolds promoted
osteoconduction both in vitro and in vivo [5]. However, these scaffolds must be stored at
-30°C or -80°C, significantly decreasing their versatility in tissue engineering. The
concept of utilizing physiologic biomaterials will be applied in this study, but a scaffold
with more versatile properties would act as an improvement to the aforementioned
scaffolds.
A novel method for development used peptide-amphiphile (PA) molecules to
create a self-assembled network of nanofibers. The concept of electrospun nanofibers has
been popular recently, but these scaffolds tend to have very little three-dimensional
depth; in fact, it is argued by this investigator that these fiber networks resemble more of
a two-dimensional sheet rather than a three-dimensional scaffold. However, cells cultured
on these nanofiber networks displayed a significantly greater level of mesenchymal
progenitor cell proliferation when compared with two-dimensional tissue culture plates.
Furthermore alkaline phosphatase activity was also significantly increased on these
networks when compared with the two-dimensional plates. Again, note that these plates
were basic tissue culture substrates, and the networks were not compared with other
scaffolds nor with multiple surface topographies. Finally, osteocalcin was significantly
increased on these networks [58-64]. Osteocalcin is a key hormone in the development of
the extracellular matrix in skeletal tissue engineering. Though the nanofiber networks
provide a significant improvement over tissue culture plates, it must be noted again that
27
these networks are not truly three-dimensional scaffolds when compared with the other
aforementioned scaffolds.
Some studies delve into comparisons between scaffolds, but these comparisons
typically only involve commercially-available scaffolds. For example, one study
compared a β-tricalcium phosphate ceramic with an open-celled poly(lactic acid) foam.
Poly(lactic acid) has been approved by the Food and Drug Administration for therapeutic
use due to its biodegradability. Typical quantification methods in these studies analyzed
alkaline phosphatase, osteopontin, and osteocalcin through assays [65]. However, all of
these were in static culture, and there was only comparison between commercially-
available three-dimensional scaffolds. None of the studies compared these scaffolds with
unapproved biomaterials or two-dimensional substrata. This study will attempt to
compare multiple scaffolds and substrata.
Many tissue engineers are now beginning to grasp the concept that cell seeding is
enhanced through the application of a bioreactor. One example is the use of poly(DL-
lactic-co-glycolic acid) porous scaffolds to enhance osteoblastic proliferation in vitro.
Cell seeding was significantly enhanced by the utilization of a spinner flask bioreactor
[3]. As mentioned previously, however, these bioreactors do not provide optimal fluid
flow patterns. Poly(DL-lactic-co-glycolic acid) scaffolds also demonstrate yet another
opportunity to use porous polymers in a three-dimensional scaffold as opposed to
physiologic biomaterials such as collagen or collagen-hydroxyapatite. Furthermore, the
polymer used in this method was also approved by the FDA, so a similar biomaterial
would thus be preferred in the development of the scaffold in this particular study.
28
Putting biomaterial properties aside, a key component in the fabrication of
optimal three-dimensional scaffolds is the mesh size preferred by osteoblastic cells and
their progenitors. Using a titanium fiber mesh, it was determined that mesh size and
porosity does, in fact, affect cell responses to growth on the scaffolds. Under both static
and flow conditions, alkaline phosphatase activity was significantly altered between 20
micron and 40 micron average pore sizes. Furthermore, mineralization and osteopontin
secretion were also significantly affected by mesh sizes in the corresponding scaffolds.
Figure 12.A depicts the titanium mesh after four days of culture. By day 8 in culture
(Figure 12.B), mesenchymal stem cell concentration began to increase. Finally, day 16
(Figure 12.C) of culture demonstrates a confluence of cells and mineralization within the
construct [66].
Figure 12. Titanium/MSC constructs after static culture.
The three-dimensional scaffolds described here demonstrate that numerous
methods were used analyzing various biomaterials and porosities. However, studies have
29
yet to compare many types of scaffolds with their two-dimensional counterparts while
inducing biophysical signals in vitro.
Bioreactor Designs:
One of the most common methods for seeding cells in three-dimensional scaffolds
is by the use of flow perfusion bioreactors. Each of these reactors are key for initial
scaffold seeding, but a bioreactor with oscillating fluid flow has yet to be devised.
Detailed below are a few of these bioreactor designs and their respective qualities.
A flow perfusion bioreactor typically involves some flow chamber with
unidirectional flow from a pump that will perfuse media with cells through the path of
least resistance. An example of this bioreactor is detailed in Figure 13 below [3].
Figure 13. Schematic of a standard flow perfusion bioreactor. Note that no flow occurs around the outer perimeter.
The bioreactor detailed above simply involved the basic design of the reactor
system and peristaltic flow loop [3]. However, the seeding efficiency was not analyzed,
begging the question as to whether or not the aforementioned system was truly
advantageous over other similar bioreactor systems. Does the flow and seeding in a
perfusion bioreactor provide uniform seeding density? Does the modification of scaffold
30
porosity affect the perfusion or shear stresses throughout the scaffold while perfusing
media through the scaffold? These questions have not yet been answered by Bancroft in
his preliminary design studies.
Years prior to the design of the bioreactor by Bancroft, many tissue engineers
developed small flow chambers for two-dimensional substrata. In essence, these were
also similar in that they perfused media through the system. Furthermore, the study also
analyzed continuous unidirectional flow over bone marrow stromal cells in culture. Note
that this flow is not oscillatory as occurs in vivo, but the use of continuous flow in vitro
still provides some mechanism for improvement over static culture. Many flow loops
have a tendency to simply used peristaltic pumps in a unidirectional fashion, but
oscillatory fluid flow was rarely used in these studies [3, 67].
Using highly porous collagen microspheres for long term in vitro culture of bone
marrow cells in an arguably two-dimensional bioreactor system, biophysical stimuli were
maintained in the bioreactor system under unidirectional peristaltic flow. In this particular
case, “long term” flow referred to culture of murine bone marrow cells over a four month
period. The bioreactor system provided a significantly beneficial environment over
traditional static culture in flasks. The authors of the study pointed out, however, that
maintenance of biophysical and biochemical stimuli was not as successful as would be
preferred. Future bioreactors should incorporate such maintenance, and other possibilities
also include an improvement of culture media or the growth factors involved in the
experiments [67].
Additional studies then analyzed the seeding and differentiation of human
mesenchymal stem cells (hMSCs) in unidirectional peristaltic flow systems with a
31
chamber similar to that constructed in the previous study. The goal was to analyze the
effects of flow rates and then the capability for differentiation with time in vitro [7].
The scaffolds analyzed in these studies were PET matrices, which were in fact
two-dimensional meshes as opposed to three-dimensional scaffolds. Most perfusion
bioreactor systems, aside from being peristaltic unidirectional as opposed to continuous
oscillatory flow, have typically involved near-two-dimensional matrices instead of three-
dimensional alternatives. After setting up the flow loop, it was determined that there
exists an inverse relationship between flow rate and seeding density. This is to say that
lower flow rates result in much greater seeding densities. However, cells did not begin to
proliferate significantly until after the first four weeks had passed, as depicted in Figure
14 below [7].
Figure 14. Cell density seeded on three PET scaffolds with time in a peristaltic flow chamber [7].
The bioreactor studies with PET meshes demonstrated that faster seeding kinetics
resulted in perfusion systems as opposed to static culture. Furthermore, differentiation
32
into the osteoblastic lineage was significantly enhanced in these two-dimensional
systems. Please note that nanoscale topographies, oscillating fluid flow-induced
biophysical signals, and primary donor cells were not used in these experiments. Such a
lack of analysis leaves a large gap open for study when compared with numerous studies
[7, 66, 68-78]. As a result, we must consider alternative bioreactor systems.
Nonetheless, this perfusion bioreactor system was quite successful in its attempt
to culture cells to confluence and induce differentiation into the osteoblastic lineage. An
example of the PET mesh after culture in the perfusion bioreactor is detailed in Figure 15
below. After 40 days of culture, a dense cellular mass was witnessed under scanning
electron microscopy. It can thus be determined that bioreactor systems provide numerous
advantages over classic static culture in flasks [7].
Figure 15. SEM image of PET scaffold with hMSCs cultured for 40 days [7].
As can be seen, numerous flow perfusion bioreactor systems have been
developed. However, these systems involved unidirectional flow as opposed to the
oscillatory flow occurring in vivo. Additionally, many bioreactors tend to implement two-
dimensional scaffolds as opposed to true three-dimensional constructs. By maintaining
33
biophysical and biochemical signals in vitro, a novel bioreactor design would better
mimic the in vivo environment through oscillatory flow and three-dimensional constructs.
Finite Element Analyses:
Mentioned before, finite element analyses are integral in the estimation of
physical properties in more complex geometries. In tissue engineering, these analyses are
more common in the simulation of numerous bioreactor systems, specifically spinning
flask bioreactors and perfusion flow bioreactors. However, fluid flow over cells cultured
on nanoscale topographies has yet to be analyzed through finite element methods.
Regarding the simulation of flow perfusion bioreactors, the most common method
used is the Lattice-Boltzmann method, where physical three-dimensional space is broken
into a number of nodes. The Lattice-Boltzmann method is very similar to the method
described previously. The important factor to consider, however, is that fluid flow
simulations with the Lattice-Boltzmann method simplify the Navier-Stokes equations to a
second-order set of equations and assume that all fluids are Newtonian fluids. As a result,
the calculations with these methods are very rough estimates of the reality at hand [79].
The methods used in literature were successful in the simulations of velocity
fields through bioreactors, and shear stresses were coupled with velocities at the solid-
fluid interface. In coupling empirical data regarding scaffold properties and then
analyzing flow fields, the flow field properties existing within the flow perfusion
bioreactors could thus be estimated. An example simulation is detailed in Figure 16
below. The upper image depicts the transverse velocity field through a three-dimensional
scaffold in mm/s. The simulation image on the bottom of Figure 16 displays the same
34
three-dimensional scaffold, but with a top view [79]. Note, again, that the velocity
gradients can then be correlated to shear stresses.
Figure 16. Velocity fields in a flow perfusion bioreactor as estimated by the LB method. The upper image depicts transverse flow through a scaffold from a side view, and the
bottom image depicts the same flow from a top view [79].
Finite element analyses become key in the design of an optimal bioreactor system.
Many tissue engineers have failed to perform these simulations prior to bioreactor design,
much unlike the approach taken in this study. Furthermore, simulations have been limited
to bioreactors in the literature. One possibility would be to examine the biophysical
signals experienced by cells on multiple nanoscale substrata.
35
Literature Review Summary:
The table below is meant to compare many of the current techniques used in bone-tissue engineering. Notice that a single study
does not use both 2D and 3D substrates while coupling these with biophysical signals. Additionally, the use of computer simulations
(finite element analysis) is unique to this study. The proposal listed on this table will be described in the next section.
Author Biomaterial 2D/3D Cell Line Desired Lineage
Biophysical Signals Quantification Novel Aspects
Wang, ‘99 [67]
Bovine Collagen Scaffolds 2D
Murine Bone
Marrow (C57BL/6J)
Expansion No CFU-GM
Assay, Hemacytometry
Porous Microspheres
Bancroft, ‘03 [3]
poly(DL-lactic-co-glycolic acid) Scaffolds 3D Rat Marrow
Stromal Osteogenic No Hemacytometry, PCR 3D Bioreactor
Holtorf, ‘05 [66] Titanium Fiber Mesh 3D hBMSC Osteogenic Yes
ALP, Osteopontin,
Ca2+ Deposition
Mesh Variability, Constant Porosity
Lim, ‘05 [1], [45]
poly(L-lactic acid)/polystyrene
Demixed Substrata 2D hFOB
Adhesion and
Expansion No
Adhesion, ALP, SIMS,
Hemacytometry
Nanoscale Substrata
Porter, ‘05 [79] N/A 3D N/A N/A N/A Lattice-
Boltzman Computational
Modeling
36
Trojani, ‘05 [6] (Si-HPMC)-based Hydrogel 3D Osteosarcoma Osteogenic No
ALP, Mineralization,
RT-PCR (TGFβ,
Interleukin, etc.)
Injectable Hydrogel, pH Maintenance
Zhao, ‘05 [7]
poly(ethylene terepthalate) Mesh 3D hMSC Osteogenic No Cell Density Perfusion Bioreactor
Hee, ‘06 [65]
poly(lactic acid) Foam, Beta TCP Scaffolds 3D
Human Dermal
Fibroblasts Osteogenic No
Scaffold Dry Weight, ALP,
Histology, Osteopontin
Comparison of Commercially
Available Scaffolds
Hosseinkhani, ‘06 [61]
Peptide-Amphiphile Nanofibers “3D” hMSC Osteogenic No ALP,
Osteocalcin “Three-Dimensional”
Nanofibers
Riddle, ‘06 [55] Glass Slides 2D hMSC Expansion Yes Intracellular
Calcium Application of
Mechanical Loading
Benoit, ‘07 [4]
poly(ethylene glycol) Hydrogels 3D hMSC Osteogenic No BMP2, ALP
Bidirectional Interaction between Cells and Hydrogel
Hansen, ‘07 [57]
polystyrene/polybromostyreneDemixed Substrata 2D MC3T3-E1 Expansion No Cellular
Modulus
Cell Stiffness correlated with
Nanoscale Substrata
Lim, ‘07 [50]
poly(L-lactic acid)/polystyrene
Demixed Substrata 2D hFOB
Adhesion and
Expansion No FAK, pY397,
Integrin Adhesion on
Nanoscale Substrata
Riddle, ‘07 [56] Glass Slides 2D hBMSC Expansion Yes
ATP, Western Blot,
Intracellular Calcium,
Calcineurin
Fluid Flow-Induced Proliferation
37
38
Dawson, ‘08 [5] Type I Collagen Scaffolds 3D hBMSC Osteogenic,
Chondrogenic No Histology, micro-CT,
ALP
Microchannels Promote Osteogenesis
PROPOSED
1. PLLA/PS Demixed Substrata
2. PS/PBrS Demixed Substrata
3. Calcium Phosphate Scaffolds
4. PLLA Salt Leached Scaffolds
5. Simulated Bioreactor
2D 3D
hMSC hBMSC Osteogenic
Yes (Empirical
and Simulated)
AFM, SEM, ALP, Flow Cytometry, Intracellular
Calcium, Finite Element
Analysis
1. Comparison of 2D and 3D Protocols
2. Design of a 3D Perfusion
Bioreactor with Biophysical
Signals 3. Simulations of
Oscillating Fluid Flow
Proposal:
Two-Dimensional Substrata:
This study will involve the fabrication and analysis of two-dimensional nanoscale
substrates with variations in surface topography. Specifically, the goal will be to analyze
the responses of progenitor cell lines on randomly distributed nanoislands as opposed to
nanopits or uniform topographies as fabricated by photolithographic methods.
To accomplish this polymer demixing will be used with the following immiscible
polymers:
1. Poly(L-lactic acid)/Polystyrene (PLLA/PS) 70/30 w/w
2. Polystyrene/Polybromostyrene (PS/PBrS) 60/40 w/w
Finally, the surface chemistry will be maintained among these substrates. These
will then be compared with flat controls of the same chemistry. In this case, either
poly(L-lactic acid) or polystyrene will be analyzed as the negative control.
Three-Dimensional Scaffolds:
Multiple scaffold variations will then be analyzed and compared with the results
of two-dimensional substrata. The scaffolds will be compared by relative porosities, and
progenitor cell activity will be compared both between the scaffolds and the
aforementioned two-dimensional substrata.
The scaffolds to be analyzed in this study include the following:
1. FDA-Approved BD© Calcium Phosphate Scaffold
2. BoneMedik© Calcium Phosphate Coral Scaffold
39
3. Salt-Leached Poly(L-lactic acid) polymer scaffolds (150-710 micron NaCl
crystals)
It should be noted that the wide range of salt crystals will be further divided into
relative sizes to obtain hypothetical variations in porosities. These scaffolds will vary
greatly in surface chemistry, surface topography, and relative porosities. For this reason,
a direct comparison or causal effects between scaffold features will be difficult to
ascertain. Nonetheless, these three-dimensional scaffolds will later be used in a fabricated
bioreactor.
Biophysical Stimuli:
Bone in vivo undergoes biophysical stimuli by oscillating fluid flow through the
insterstitial space. Thus, an important factor will be the addition of these stimuli to the
tissue engineering protocol.
Using oscillating fluid flow, shear stresses will be induced within the physiologic
range. Specifically, stresses will be induced at 5, 10, and 20 dyne/cm2. This flow will be
coupled with the two dimensional substrata only due to the lack of a current bioreactor
system for such flow. However, simulations of the bioreactor system being developed
will determine flow rates necessary to induce such shear stresses throughout the volume
of each scaffold.
Bioreactor Design:
A bioreactor will not be fabricated in this study, but a design will be created for
potential fabrication at a later date. Such a design involves certain criteria to be met. The
40
bioreactor system will be used for long-term culture of human bone marrow stromal cells
for differentiation into the osteoblastic lineage in vitro. All of the prior studies eventually
lead up to the design of such a bioreactor, so these criteria cannot be taken lightly. The
design criteria and specifications have been tabulated below:
Design Criteria Design Specifications
The bioreactor must maintain physiologic shear stresses as witnessed in
vivo.
Maintain a uniform shear stress throughout the volume of the scaffold at 5, 10, and 20
dynes/cm2.
Standard scaffolds must fit within the bioreactor volume.
Ensure the bioreactor has a variable diameter between 2 and 10 mm.
The bioreactor must withstand oscillating fluid flow conditions.
Determine a symmetrical geometry capable of withstanding 1 Hz oscillations.
Flow must be uniform throughout the scaffold volume.
Simulate the flow profiles throughout the volume of the scaffold to ensure all are
greater than zero.
The bioreactor must work for all scaffolds.
After determining the relative porosities of each scaffold, repeat the above analyses
with each porosity value.
Finite Element Analyses:
COMSOL Multiphysics will be used extensively in the design of the
aforementioned bioreactor. The above specifications must be met, and finite element
analyses will determine the optimal geometry, flow rates, and scaffold properties key in
the meeting of these specifications before a final design is reached.
Additionally, this study will simulate fluid flow of media over cells cultured on
the nanoscale substrata described previously. The goal will be to analyze the biophysical
stimuli experienced by cells under oscillating fluid flow. It will be interesting to
41
determine where turbulence may result and what these flow patterns look like. In essence,
these simulations will be used solely for exploratory purposes.
42
Thesis Statement and Hypotheses:
Thesis Statement:
Through a number of experimental protocols, skeletal tissue engineering methods will be modified and made optimal (i.e., increased growth and differentiation) for maintenance of stem cell proliferation and differentiation in vitro by mimicking the in vivo extracellular milieu of bone and induced biophysical signals.
Hypothesis 1:
Nanoscale substrates select for subpopulations of progenitor cells through differentiation into the osteoblastic lineage, as influenced by surface characteristics, including chemistry and topography
Hypothesis 2:
Hypothesis 3:
A bioreactor designed with finite element methods will satisfy all the criteria needed for long‐term culture on three‐dimensional scaffolds with induced biophysical signals.
The same progenitor cell lines cultured on three‐dimensional calcium phosphate scaffolds will display significantly maintained differentiation potential with continued expansion in vitro compared with two‐dimensional substrata and flat controls.
43
MATERIALS AND METHODS
Nanoscale Substrate Fabrication:
Two methods for polymer demixing have been demonstrated to result in the same
surface chemistry and similar surface topography characteristics. Polybromostyrene
(PBrS), with a molecular weight of 65x103 amu, and polystyrene (PS), with a molecular
weight of 289x103 amu, blend solutions were involved in one method. Another blend
solution included polystyrene (PS, MW = 289x103) and poly(L-lactic acid) (PLLA). In
order to assure nanoisland topography, PS/PBrS was blended in 60/40 w/w, and
PLLA/PS blended in 70/30 w/w. The blended, immiscible polymers were then dissolved
in chloroform in concentrations of 0.5%, 1.0%, 2.0%, and 3.0%. The varying
concentrations would hypothetically increase the scale of the nanoislands as
concentration was increased.
Once blended, the polymer solutions were then dispensed onto quartz slides or
glass cover slips depending upon the particular protocol. Quartz slides were used for flow
experiments, and cover slips were involved in numerous assays, including alkaline
phosphatase assays. These were then spin casted at 4000 rpm for 30 seconds. In doing so,
the volatile chloroform rapidly evaporated, allowing segregation of the two blended
polymers. The films were sealed and allowed to dry for 24 hours.
For the PS/PBrS polymer films, an annealing process was required to assure
uniform surface chemistry. The spin-cast films were heated to the glass transition
temperature (Tg) of PS but below the Tg of PBrS. Film concentrations of 0.5% and 1.0%
were annealed for 1 hour, and spin-cast films of 2.0% and 3.0% were annealed for 2
44
hours. The annealing process allowed the PS composition of the films to segregate to the
air-film interface.
After the fabrication process was complete, substrates were sealed and allowed to
cool for 24 hours if annealing was performed. Annealing was not required for PLLA/PS
spin-cast films. In preparation for cell culture, all substrates were exposed to UV
radiation for 60 minutes prior to seeding.
Salt Leaching and 3D Scaffolds:
Poly(L-lactic acid) was initially dissolved in chloroform with NaCl crystals of
various diameters. The diameters were divided into three categories: 150-300 μm, 300-
500 μm, and 500-710 μm. The mixture was poured into a Petri dish such that the liquid
was approximately 3-5 mm deep. It was then sealed and allowed to dry for 48 hours.
The solid PLLA/NaCl scaffold was then leached three times with ddH2O in order
to dissolve and thus remove all NaCl crystals from the PLLA scaffold interface.
Hypothetically, crystals of increased diameters would result in pore sizes of increased
diameters. These diameters would then be correlated to an increase in porosity between
the scaffolds. The salt-leached PLLA scaffolds were then cut into cylindrical scaffolds
approximately 3-5 mm thick and 6 mm in diameter.
The additional three-dimensional scaffolds included a coral scaffold as
manufactured by BoneMedik© and a calcium phosphate scaffold as manufactured by
Becton-Dickson©. These scaffolds were then cut into cylinders that were 4 mm thick and
6 mm in diameter to remain uniform with the salt-leached PLLA scaffolds.
45
To prepare the scaffolds for cell culture, all scaffolds were immersed in 100%
EtOH for 24 hours. The ethanol was then aspirated and all scaffolds were exposed to UV
radiation for 60 minutes. This process was repeated three times to ensure complete
sterilization of all scaffolds prior to seeding.
Cell Harvesting:
Human mesenchymal stem cells (hMSCs) were obtained from Cambrex©. These
cells were from a distributer, so a primary donor was preferable.
Another cell line included primary human bone marrow stromal cells (hBMSCs),
another type of progenitor stem cell. To harvest these cells, human bone marrow was first
obtained from a patient at the Milton S. Hershey Medical Center through a protocol
defined by the Internal Review Board (IRB). The marrow was harvested from the rimings
of the femoral head of a 43 year old male patient undergoing hip surgery. Cells were then
washed and separated using ficoll gradient (1.077 g/ml). Cells located at the interphase of
this gradient were collected. They were then plated at a density of 2x105 cells/cm2 in
growth medium composed of low glucose Dulbecco’s Modified Eagle Medium
(DMEM), 10% fetal bovine serum (FBS), 1% Penn/Strep, and 1% L-glutamine. After
four days of incubation, non-adherent cells were removed and adherent cells maintained
in growth medium with media changes every two to three days.
46
Cell Culture:
hMSCs and hBMSCs were maintained in low glucose DMEM, 10% FBS, 1%
FBS, 1% P/S, and 1% L-glutamine until required for experimental protocols, with media
changes every 2-3 days. When cells reached a confluence of 70-90%, they were then
trypsinized and passed to prevent the natural differentiation that occurs when progenitor
cells reach confluence. The hMSCs were used up to a passage of 7-8, and the hBMSCs
were viable up to a passage of 4-5. When ready for data acquisition, cells were then
seeded onto the corresponding substrates or scaffolds with either growth or osteogenic
media used. Osteogenic differentiation media consisted of low glucose DMEM, 50 µg/ml
ascorbic acid phosphate, 10 nM dexamethasone, and 10 nM β-glycerol phosphate.
Cells were then seeded onto two dimensional nanoscale substrates at a density of
4x103 cells/cm2. For three dimensional scaffolds, cells were seeded at 5x106 cells/cm3.
This seeding would occur after sterilization of the appropriate substrates or scaffolds.
Scaffold seeding was performed via the vacuum filtration method. Substrate seeding was
performed with a pipette.
Cells were then allowed to expand, proliferate, and differentiate for a period
defined by the particular protocol. Media changes took place every 2-3 days, and cells
were incubated at 37°C up to 12-14 days.
47
Oscillating Fluid Flow:
After hMSCs were cultured on various nanoscale substrata, they were then
cleaned with PBS three times and loaded onto a vacuum flow chamber (Figure 17). Clear
flow media was perfused through the chamber, and all were attached to the pneumatic
pump depicted in Figure 17..
Figure 17. Pneumatic pump (A) and flow chamber (B).
The pneumatic pump induced oscillating fluid flow. This flow rate could then be
correlated to shear stresses acting upon the substrata by the following equation:
, where τw is the shear stress at the wall, μ is the dynamic viscosity of the flow
media, Q is the amplitude of the sinusoidal flow rate, W is the width of the flow chamber,
and H is the height of the flow chamber. Since the dynamic viscosity, width of the
chamber, and height of the chamber were constant, the shear stress at the wall could then
48
be controlled by adjusting the amplitude of the sinusoidal flow rate. This is assuming
Poiseuille, laminar flow rates in a Newtonian fluid. In doing so, the pneumatic pump was
then used to induce shear stresses by oscillating fluid flow at 5, 10, and 20 dyne/cm2.
The fluid flow protocol called for the flow chamber to be coupled with a
fluorescent microscope calibrated for Fura-2 fluorescent markers. The first 180 seconds
were under static conditions, followed by 180 seconds of fluid flow. The entire period of
360 seconds was then recorded temporally by absolute changes in fluorescence.
Fluorescent Markers:
For short-term oscillating fluid flow experiments, Fura Red fluorescent dyes were
loaded for 30 minutes prior to data collection. Fura 2 was not involved due to the fact that
it would adsorb to the polystyrene or poly(L-lactic acid) substrata. The fluorescent
marker acted as a measurement of intracellular calcium concentrations ([Ca2+]i). After the
absolute fluorescence was recorded for 360 seconds, the data was outputted to a PC. Cells
were manually selected, and each experiment included 15-40 cells within the data range.
Data processing included an initial average (μ) of absolute fluorescence during the
static period (0-180 s). During the flow period, the peak fluorescence was then
determined. If the peak fluorescence surpassed the average plus four times the standard
deviation of static fluorescence (μ+4σ), the cell was considered to have responded. This
same analysis was performed for each manually selected cell within each short-term
oscillating fluid flow experiment to determine the mechanosensitivity of cells as
determined by [Ca2+]i response.
49
hBMSCs cultured for either 7 or 12 days in both growth medium and osteogenic
differentiation media were harvested and then tagged with SSEA-4, CD73 (SH3/4),
CD90 (Thy-1), or CD105 (SH2, Endoglin) primary antibodies. hBMSCs without
antibodies served as negative controls. We chose to examine these markers because
SSEA-4, an embryonic antigen previously believed to be specifically expressed by
human embryonic stem cells has been shown to identify stem cells that are osteogenic in
vivo [80]; CD73 and CD105 react with bone progenitor cells, but not with osteoblasts or
osteocytes; and expression of CD90 in hBMSC is correlated with osteogenic potential.
These cells were then washed three times with PBS and suspended for
fluorescence-activated cell sorting (FACS) analysis. This analysis first uses flow
cytometry to sort cells by size and complexity. After sorting, the fluorescence of cells
was then measured and correlated with each of the antibodies. Each experiment analyzed
10,000 counts, which resulted in 7,000-9,500 cells per experiment on average. Controls
were used to determine the fluorescence of nonresponding cells, and a threshold was
determined for each experimental protocol in order to determine the percentage of cells
responding to the corresponding antibodies.
50
Alkaline Phosphatase Assay:
Alkaline phosphatase is a hydrolase enzyme key in the dephosphorylation of
numerous molecules in the intracellular environment of cells. The alkaline phosphatase
(ALP) assay is key in measuring the activity of this enzyme, which can then be correlated
to the overall activity of cells.
An alkaline phosphatase assay kit was involved in this protocol. Two previously
prepared standards with 0.9% NaCl and blanks were first created to develop a standard
calibration curve for optical density and absorbance. Human mesenchymal stem cells
cultured for 12 days on two dimensional substrata and three dimensional scaffolds were
then lysed. The cell lysate was added to 65 mM phenolphthalein monophosphate in 7.8 M
2-amino-2-methyl-1-propanol with a pH of 10.5. It should be noted that ALP requires an
alkaline environment for optimal activity, as indicated by its name.
To this mixture, 0.1 M phosphate buffer with a pH of 11.2 was added. The
mixture was diluted progressively in order to create a curve for each of the cell lysates.
The phosphate buffer acts as a color stabilizer when measuring the alkaline phosphatase
activity for the cells cultured on each of the substrates. These assays were then automated
in order to measure absorbance relative to blank samples and calibration curves. The
absorbance is directly correlated to cell ALP activity.
51
Substrate Characterization:
After fabrication of the two dimensional nanoscale substrata, the samples were
dried and prepared for atomic force microscopy (AFM). AFM was key in the analysis of
the nanoscale topography of these nanoislands. Specifically, the method allowed for
characterization of the scales and random distribution of the rough surfaces of these
nanoscale substrata. All AFM was performed under dry conditions.
The three dimensional scaffolds were not characterized utilizing AFM. Instead,
scanning electron microscopy (SEM) was used to characterize the three dimensional
characteristics and pore sizes among each of the scaffolds. SEM required that all
scaffolds were dried and coated with gold (Au) prior to analysis. Scanning electron
microscopy images were then outputted to ImageJ in order to determine the relative
porosities between the scaffold types. The software considered the relative white-to-black
balance along each of the upper surfaces of the scaffolds. This balance was then
correlated with the relative pore sizes along the scaffold. Porosity is normally defined by
the following equation: , where Vv is the volume of the void space, VT is the total
volume of the bulk material, and the porosity is the ratio between the two. Since SEM
simply characterizes a two-dimensional image of a three-dimensional material, porosity
is redefined by the following equation: , where Av is the area of the void
space, AT is the total area of the surface, and estimated porosity is the ratio between these
two. In terms of imaging, Av is redefined by , which is the total number of black
pixels after the image undergoes a threshold algorithm, and AT is redefined by , which
is the total number of pixels in the image. This definition of porosity acts as a very rough
estimate and should only be considered as a relative porosity measure used to compare
52
scaffolds. The absolute value is, in essence, inaccurate due to the assumption that these
pores remain continuous throughout the bulk of the material, which is not true in reality.
Nevertheless, these relative values play key roles in the comparison between scaffolds.
Wettability was previously determined in order to compare the relative
hydrophobicities among different substrata. The measure of hydrophobicity on the
surfaces of biomaterials plays a key role in cell adhesion and morphology. Decreased
hydrophobicity, or increased hydrophilicity, leads to better adhesion and a wider spread
of cells when analyzing their morphologies or histologies. Again, these data were
previously determined, and the measure of wettability simply ensured uniform surface
chemistry among substrata.
Simulation of the 2D Microenvironment:
COMSOL Multiphysics was used to simulate the two-dimensional
microenvironment of cells cultured on nanoscale topographies. Included in the
comparison were different levels of cell confluence, differing elastic moduli of cells
cultured on numerous substrata, and an analysis of the flow patterns over a cell cultured
on a hydrophobic substrate.
When comparing the cells cultured on multiple substrata, data from a contact-
mode atomic force microscopy (AFM) study by Joshua Hansen were used as inputs for
the moduli of cells on these surfaces. Cells cultured on plasma-cleaned glass had an
average modulus of 7000 Pa, those on flat polystyrene had a modulus of approximately
4000 Pa, cells on 11 nm nanoislands (PS/PBrS 40/60 w/w) displayed an elastic modulus
of 9000 Pa, and those cultured on 38 nm nanoislands had an approximate modulus of
53
12000 Pa. Incompressible Navier-Stokes fluid flow was coupled with a stress-strain
analysis to determine the apparent shear stresses induced on the surfaces of these cells.
When analyzing oscillatory fluid flow, one must ensure that the flow remains
laminar if assumptions and equations are to hold. The maximum Reynolds number was
16.302 using the follow ng ci riteria:
• Inlet Pressure: 0.5 cos
• Outlet Pres .5sure: 0 cos
• Constants: 2 / ; 131 ; 4000 /
The incompressible Navier-Stokes equations and the assumptions following
include:
•
•
•
These equations for fluid flow analyses can then be coupled with a stress-strain
analysis to determine shear stresses throughout the two-dimensional microenvironment.
In the analysis of shear stresses, the normalized von Mises stress was used:
1√2
6 6 6
All of these data were then analyzed to determine flow patterns, values of shear
stresses at multiple locations, and the absolute flow rates in various geometries.
Note: COMSOL model reports detailing the inputs and outputs from the
simulations can be found in Appendix F.
54
Bioreactor Design:
In the design of the bioreactor, COMSOL Multiphysics was also used to create
various geometries and alter the flow rates. Porosity values previously determined were
used as inputs, with a permeability of zero, when simulating the insertion of a scaffold in
each bioreactor geometry. Furthermore, the previous equations and assumptions as
involved in the two-dimensional microenvironment were also used in the three-
dimensional analysis of various bioreactors. However, to conserve computing power, the
three-dimensional geometry was simplified to a cylindrical coordinate system with axial
symmetry. In turn, this allowed the three-dimensional system to be analyzed through two-
dimensional simulations.
To satisfy the aforementioned design criteria for a bioreactor, multiple geometries
were first used as inputs in the bioreactor. Specifically, two geometries, one with a
confluence with the scaffold and another with a gap, were used. The next variable altered
was the porosity of the scaffold from the relative values determined with SEM and
ImageJ. The simulation then displayed various flow profiles through the bioreactor and
the corresponding scaffold. Additionally, the incompressible Navier-Stokes equations
were coupled with a stress-strain analysis of the scaffold, and the von Mises stresses
throughout the volume of the scaffold were determined.
Design criteria were met if the bioreactor and corresponding scaffold displayed
uniform flow profiles and consistent von Mises stresses throughout the scaffold volume.
This criterion should remain true for all relative porosity values, indicating that the same
bioreactor could hypothetically be used under multiple conditions.
55
Once the geometry was determined, multiple flow rates were used in order to
determine the flow rate or pressure value necessary to ensure von Mises stress of 5, 10,
and 20 dyne/cm2 throughout the volume of the scaffold. Analysis was simply performed
through an iterative design process until the optimal flow rates were determined.
Again, the final geometry was the key component of this analysis. No physical
bioreactor was fabricated in this study. The purpose was simply to optimize the system
and demonstrate that FEA can be used as an excellent design tool in bioreactor
fabrication for tissue engineering.
Note: COMSOL model reports detailing the inputs and outputs from the
simulations can be found in Appendix F.
Statistics:
All numerical data were analyzed with one-way analysis of variance (ANOVA).
Significance was then determined with the Tukey Post Hoc Test. These methods assumed
a normal distribution of data, independent samples of data, equal variances of the
populations, and Simple Random Samples (SRS). Furthermore, values were considered
significant if p<0.05 and very significant if p<0.01.
56
RESULTS
2D Substrate Characterization:
Polystyrene/Polybromostyrene (PS/PBrS 40/60 w/w) demixed substrata were
dried and subsequently characterized with atomic force microscopy (AFM). AFM images
of these surfaces are depicted in Figure 18 below.
Figure 18. AFM Images of PS/PBrS 40/60 w/w polymer demixed substrata.
The figure above depicts PS/PBrS 40/60 w/w demixed substrata from
concentrations of 0.5%, 1.0%, and 2.0% after dissolution in chloroform. The 0.5%
PS/PBrS 40/60 w/w resulted in nanoislands of approximately 11 nm in height, 1.0% in
nanoislands of approximately 38 nm height, and 2.0% in nanoislands of approximately 85
nm in height. Note that the diameters of these nanoislands are random, and the
distribution of the surface topography is also random. Compare these substrata with those
resulting from UV photolithography, which results in uniform distribution of nanoscale
or microscale topographies. It should be noted that the average diameters of the 11 nm
nanoislands are 0.5 to 0.9 μm, 38 nm nanoislands with diameters of 0.7 to 1.0 μm, and 85
nm nanoislands with diameters from as small as 0.5 μm on average to as great as 1.7 μm
57
on average. This variation could thus correspond to a difference in overall surface area
between the nanoscale topographies.
Poly(L-lactic acid)/Polystyrene (PLLA/PS 70/30 w/w) demixed substrata were
also fabricated, dried, and analyzed with AFM. The AFM images from these analyses are
depicted in Figure 19 below. Titles listed above each figure are average island heights.
Figure 19. AFM Images of PLLA/PS 70/30 w/w polymer demixed substrata.
The image above depicts the substrata fabricated from 0.5%, 1.0%, 2.0%, and
3.0% PLLA/PS 70/30 w/w polymer demixing. Note that the corresponding nanoisland
heights were on the same order as the PS/PBrS 40/60 w/w demixed films; however, the
topographical characterization was much different than the other polymers. The
nanoscale for 0.5% films was approximately 12 nm in height, 1.0% films were around 21
nm in height, 2.0% films were approximately 45 nm, and the 3.0% demixed substrata
were around 80 nm in height. These substrata were even less uniform than their PS/PBrS
counterparts. The diameters also significantly changed from the 12-21 nm nanoislands to
the 45-80 nm nanoislands. Diameters for the 12-21 nm nanoislands were approximately
0.1-0.3 μm, and the diameters for the 45-80 nm nanoislands were approximately 0.5-1.0
58
μm. As before, this variation could hypothetically correspond to a variation in the surface
area among the different nanoscale substrata.
59
3D Scaffold Characterization:
Each of the three
imensional scaffolds was
The BD© scaffold is
d
analyzed with scanning
electron microscopy (SEM).
The SEM images for these
scaffolds are shown in Figure
20.
shown in Figure 20.A and 20.B
at different scales. Note that
the pore sizes may be very
large in this particular scaffold,
but the continuous porosity of
the BD© calcium phosphate
scaffold is very low. The
BoneMedik© coral scaffold is
shown in Figure 20.C and 20.D
at different scales. Note that
although the pore sizes appear
much smaller, the depth of
pores appear to be much
greater in these coral scaffolds.
60
Figure 20. SEM Images of scaffolds(A/B-BD©; C/D-Coral; E/F-PLLA(150 μm); G/H-PLLA(300 μm); I/J-PLLA(500 μm).
Furthermore, there is much greater uniformity of pores in the coral scaffold as opposed to
its calcium phosphate counterpart. The salt-leached PLLA scaffolds are shown in Figures
20.(E-J). Figures 20.E and 20.F depict the scaffolds with leached NaCl crystals ranging in
diameter from 150 to 300 μm at two different scales, 20.G and 20.H depict those from
leached salt crystals of 300 to 500 μm, and 20.I and 20.J depict PLLA scaffolds whose
leached crystals ranged in diameter from 500 to 710 μm. Note that the pore sizes
increased with the size of the NaCl crystals, but not by much. Furthermore, it appeared
that “pits” were actually leached from the PLLA polymer as opposed to true pores. It
would thus be hypothesized that proper cell seeding would not be possible in such
scaffolds when compared with the coral or calcium phosphate scaffolds.
Using these SEM images, the relative porosities were then determined with
ageJ
Figure 21. Estimated porosities calculated in ImageJ from SEM images of 3D scaffolds. (*p<0.05 w/ PLLA(300-500); **p<0.01 w/ PLLA(300-500); ***p<0.001 w/ PLLA(300-500); +++p<0.001 w/ PLLA(500-710) N=10)
Im through the protocol in Materials and Methods – Substrate Characterization.
Figure 21 shows the results from these porosity calculations.
61
The “gel” as shown in this graph was another scaffold fabricated from ground
calcium phosphate, fibrin, and thrombin. The process was similar to the formation of a
blood clot in vivo. However, these scaffolds were not properly analyzed due to a
breakdown of the fibrin/thrombin composite upon drying.
Note that the salt-leached PLLA scaffolds with 300-500 μm diameters displayed
porosities significantly greater than the BD© calcium phosphate scaffolds and the
BoneMedik© coral scaffolds. Furthermore, the PLLA scaffolds with NaCl crystals
ranging from 500-710 μm diameters displayed significantly (p<0.001) greater porosities
than all other scaffolds, including the salt-leached PLLA scaffolds with 150-300 μm
diameter crystals. These data demonstrate a significant variation among estimated
porosities between the num
scaffolds shown previously have demonstrated that the coral and calcium phosphate
scaffolds actually have true, continuous pores when compared with the PLLA scaffolds.
Thus, it could be argued that these porosity estimates are not true indicators of cell
performance on each of the three dimensional scaffolds. Instead, these data will be
involved in the simulations of multiple scaffolds in each of the bioreactor geometries
with finite element analysis.
erous scaffolds. However, note that the morphology of the
62
Mechanosensitivity of Stem Cells on Substrates:
Human mesenchymal stem cells were cultured in Dulbecco’s Modified Eagle
Medium (DMEM) with 10% fetal bovine serum (FBS), 1% penicillin-streptomycin, and
1% L-glutamine. Randomly distributed nanoisland textures with varying heights (12, 21,
5, and 80 nm) were fabricated using poly(L-lactic acid)/polystyrene (70/30 w/w)
emixing techniques in concentrations of 0.5%, 1%, 2%, and 3% w/w. The solutions
ere spin-casted on quartz slides at 4000 rpm for 30 s, completing substrate fabrication.
lat PLLA surfaces were also created using this process.
Oscillating fluid flow has been demonstrated to induce an increase in intracellular
alcium ([Ca2+]i). Increased [Ca2+]i activates MAP kinases ERK1/2, resulting in increased
or mechanosensitivity. hMSCs
h of the nanotopographies.
4
d
w
F
c
cellular proliferation. Thus, [Ca2+]i acts as a marker f
cultured on the nanotopographical substrates were placed on a vacuum-sealed oscillating
fluid flow chamber. Shear stresses of 5, 10, and 20 dyne/cm2 were induced by this
oscillating fluid flow. Fura Red AM stain was used to measure [Ca2+]i over time within
the cells through fluorescence microscopy. The initial 180s were static, and the final 180s
included oscillating fluid flow-induced shear stresses.
Figure 22 depicts the percentage of cells responding under static and fluid flow
conditions at each of the shear stresses after culture on eac
63
Figure 22. % Cell Response on various nanotopographies under different shear stresses
after 180 s. (*p<0.05 w/ Flat; N=3)
At 5 dyne/cm2, the cells cultured on the 12 nm nanoislands displayed significantly
greater [Ca2+]i response compared with the flat control. Furthermore, shear stresses
differences were noted b of 10 dyne/cm2 and 20
yne/cm2.
Figure 23. Absolute increase in fluorescence under fluid flow. (*p<0.05 w/ Flat;
#p<0.05 w/ 12 nm; ##p<0.01 w/ 12 nm; N=3)
continued to increase with corresponding shear stresses. Due to this increase, no
etween substrates under conditions
d
Depicted in Figure 23 are the absolute cellular response results, measured as a
change in fluorescence from the static baseline.
64
Cells on 12 nm nanoisland topographies demonstrated significantly greater
mechanosensitivity than cells on 45 nm and 80 nm nanoislands at 5 dyne/cm2.
Additionally, significant differences occurred between the 45-80 nm nanoislands and the
12 nm nanoislands along with the flat PLLA surfaces at 10 dyne/cm2.
Finally, Figure 24 depicts the percent increase in fluorescence from a baseline set
to 1
er fluid flow. (*p<0.05 w/ Flat; #p<0.05
w/ 12 nm; N=3)
There were no significant differences in percent increase among the substrates
under shear stresses of 5 dyne/cm2 and 20 dyne/cm2. However, the cells cultured on 80
nm nanoislands under oscillating fluid flow-induced shear stresses of 10 dyne/cm2
displayed a significantly lower percent increase when compared with both the flat PLLA
00% for each of the shear stress conditions.
Figure 24. Percent increase in fluorescence und
control and the cells cultured on 12 nm nanoislands.
65
FACS Analysis:
Multiple stem cell markers were used to determine whether substrate nanoscale
topographies affect stem cell differentiation behavior in vitro by using fluorescence-
PS/PBrS 40/60 w/w demixed films at varying spin-casting concentrations
displayed randomly distributed nanoisland textures with varying island heights (11, 38,
and 85 nm). After annealing, PS segments segregate to the film surface, and hBMSCs
responses to nanotopographic scale could be assessed under the same surface chemistry
of polystyrene. hBMSCs cultured on 11 nm substrates for 7 days displayed a significantly
lower SSEA-4, CD73, and CD105 positive cell percentage relative to flat control and
larger nanoisland surfaces (Figure 26). After 12 days of culture, cells cultured in
osteogenic differentiation media resulted in lower positive percentages relative to cells in
growth media, regardless of textured or flat surfaces (Figure 27). Cell response to CD90
after 7 days of culture displayed similar trends but did not demonstrate significant results.
Figure 25 depicts a sample output from FACS analysis.
activated cell sorting (FACS) analysis.
66
SSEA-4 (Osteogenic)SSEA-4 (Growth)
Control
11 nm
38 nm
85 nm
Flat
Control
11 nm
38 nm
85 nm
Flat
Figure 25. FACS Output for SSEA‐4 fluorescent markers.
The curves in Figure 25 display the fluorescence of a total of 10,000 counts.
level, and the percentage of counts beyond the
esho
Figures 26/27. hBMSC response to SSEA-4, CD73, CD90, and CD 105 in growth and osteogenic media after and 12 days of cultur m; N=3)
Greater fluorescence would be shifted to the right. In each experiment, the fluorescent
counts were compared with the same control. A threshold was set for each experiment
based upon the control’s fluorescence
thr ld (minus the artifacts in the control) allowed for a comparison in the percentage
of cells responding to each marker utilizing a FACS analysis. These data are displayed in
Figures 26 and 27 below.
7e. (*p<0.05 w/ Flat; **p<0.01 w/ Flat; ##p<0.01 w/ 85 n
67
The above data depict the responses of hBMSCs cultured on 11 nm, 38 nm, and
85 nm nanoislands. hBMSCs cultured on flat polystyrene surfaces were used as a control.
Cells were cultured for either 7 or 12 days in growth or osteogenic differentiation media
and then tagged with either SSEA-4, CD73, CD90, or CD105 antibodies. Outputs similar
to the data shown previously were collected for each of these experiments, and the
percentage of cells responding was thus calculated.
First, note the general differences between all cells cultured in growth versus
osteogenic media on both Day 7 and Day 12. The general trend was a decrease in percent
response to antibodies, or an increase in differentiation, from growth to osteogenic media.
Such a decrease was an expected result, and it demonstrated success in data collection.
Next, look at the data for cells cultured for 7 days in growth media. There were no
significant differences among the substrates for SSEA-4, CD90, or CD105 antibodies.
However, cells cultured on the 11 nm substrata displayed significantly lower antibody
response to CD73 when compared with both the flat control and those cultured on 85 nm
nanoislands. Though this was significant, the response was still greater than 80%. Thus,
this unexpected result in significance was attributed more to significance by statistics
than by biological means since most cells remained undifferentiated.
Analyzing data from Day 7 in osteogenic differentiation media yields much
different results. First, note that significant differentiation of cells tagged with CD90
antibody diminished any significance among the substrata. However, cells cultured on 11
nm nanoislands displayed significantly lower responses to SSEA-4, CD73, and CD105
antibodies when compared with both the flat control and 85 nm nanoislands. This
decrease in response is correlated to an increased osteogenic potential and thus
68
differentiation of cells cultured on the 11 nm nanoislands. Again, this agrees with the data
found for mechanosensitivity of stem cells cultured on 12 nm nanoislands as shown in
Figure 22. Thus, we have an increased osteogenic potential and increased
mechanosensitivity of hMSCs on 11-12 nm nanoislands, and these data are significant
when compared with other scales of topographies and flat controls. Again, surface
chemistry remained consistent among the substrata.
Focusing now on the cells cultured for 12 days in growth media, significant
results have also occurred. First, note that the overall cell responses to different
antibodies in growth media after 12 days were generally lower than those cultured for 7
days. Such differences could have been due to some natural differentiation occurring as
s cultured on 11 nm
hBMSCs reached confluence. However, stem cells cultured on 38 nm nanoislands for 12
days in growth media displayed a significantly greater response to the CD90 antibody
when compared with the flat control. Furthermore, progenitor cells cultured on the 11 nm
nanoislands for 12 days in growth media also displayed a significantly greater fluorescent
response to SSEA-4 antibody when compared with the flat control. These increases could
be attributed a significantly increased rate of progenitor cell proliferation on these
substrata. However, this hypothesis conflicts with the response of cell
nanoislands for 7 days in growth media and tagged with CD73.
Finally, progenitor cells cultured in osteogenic differentiation media for 12 days
demonstrated a generally lower response to all antibodies when compared with those
cultured in growth media. However, cells cultured on 11 nm nanoislands and tagged with
CD105 antibody displayed significantly decreased fluorescent response compared with
the flat control. These data are again correlated to an increased osteogenic potential, and
69
these data are once again coupled with the increased mechanosensitivity of stem cells on
12 nm nanoisland topographies. All other cells tagged with SSEA-4, CD73, and CD90
antibodies displayed such a low response that no significant differences were noted
among the substrata.
70
AP Activity:
Human mesenchymal stem cells (hMSCs) were cultured on the BD© calcium
phosphate scaffolds, BoneMedik© coral scaffolds, flat polystyrene surfaces, and 11 nm
nanoislands topographies fabri PS/PBrS 40/60 w/w polymer demixing. The
rogenitor cells were cultured in osteogenic differentiation media for 12 days. Cells were
med for each of the scaffolds
and substrates (N=6). The AP activity was normalized by the number of proteins in the
lysate, resulting in units of Sigma Units (arbitrary units) per protein.
Depicted in Figure 28 below is the AP activity for cells cultured on flat
polystyrene and 11 nm nanoislands.
Figure 28. AP Activity for cells cultured on flat PS and 11 nm nanoislands. (***p<0.001
w/ 11 nm; N=6)
As expected, hMSCs cultured on the 11 nm nanoisland substrata displayed
significantly greater AP activity when compared with the flat substrate. These data are
further coupled with the data stating that progenitor cells cultured on 11-12 nm
cated from
p
lysed, and an alkaline phosphatase activity assay was perfor
***
71
72
splay significantly increased mechanosensitivity, osteogenic potential, and
Figure 29. AP Activity for cells cultured on BD© calcium phosphate scaffolds and
BoneMedik© coral scaffolds. (**p<0.01 w/ coral; N=6)
The progenitor cells cultured on the BoneMedik© coral scaffolds displayed
significantly greater alkaline phosphatase activity when compared with the BD© calcium
BD© scaffold is currently undergoi l, but the BoneMedik© scaffold is
ot. However, the analysis of the morphology of these scaffolds demonstrated previously
nanoislands di
now AP activity when compared with flat controls of the same surface chemistry (i.e.
PLLA or PS).
Depicted in Figure 29 below is the AP activity for each of the three dimensional
scaffolds in this experiment.
**
phosphate scaffolds. In one sense, such a result is unexpected, due to the fact that the
ng FDA approva
n
that cell seeding may be more efficient on the coral scaffold than on the calcium
phosphate scaffold due to increased continuity of more continuous pores on the coral
72
scaffold. Furthermore, the relative porosity of the BoneMedik© scaffold was also greater
than the estimated porosity of the BD© scaffold.
73
Finite Element Analysis of Cell Confluence:
Numerous studies thus far have involved oscillatory fluid flow to induce shear
tresses on the surfaces of progenitor cells. However, the microscale and macroscale
element analysis (FEA) was
therefore employed to simulate fluid flow over these cells. In doing so, the data can then
predict both flow patterns and possibly cell responses to such flow. Cell biologists
typically do not employ such methods, making this particular study novel in its bio-
computational aspects.
The initial simulation in COMSOL Multiphysics attempted to analyze the effects
of cell confluence on fluid flow patterns. As opposed to oscillatory fluid flow,
unidirectional flow of media was employed. The pressure difference, as opposed to being
sinusoidal in nature, was now a constant at ∆ , where ∆P is the pressure
difference across the bioreactor, ρ is the density of the fluid in kg/m3 (in this case, water
was used with ρ = 1000 kg/m3), g is the acceleration due to gravity (g = 9.81 m/s2), and L
is the length of the bioreactor being simulated in meters. Figure 30 below depicts the
macroscopic view of flow over cells cultured on less hydrophilic surfaces with varying
levels of confluence. Note that there were very little differences in flow patterns within
the bioreactor.
s
patterns of flow have yet to be analyzed in detail. Finite
74
75
Analysis of cell confluence; macroscopic view. Incompressible Navier-
Stokes with a Newtonian fluid was assumed.
Although there were minor disturbances in the flow profiles, most notably with
50% and 100% confluence at the upper boundary of the bioreactor, significant
differences in flow patterns were not noted. Thus, it was recommended that a
Figure 30. FEA
75
microscopic view of flow over cells be analyzed due to the inconclusive results from this
preliminary study.
Figure 31 below depicts the microscopic view of flow over cells with various
confluence. Note the velocity field contour lines in addition to the color surface.
Figure 31. FEA of cell confluence; microscopic view. (A) 50% confluence with cell at
entrance to flow field; (B) 100% confluence with cell at entrance to flow field; (C) 100%
confluence with high hydrophobicity; (D) 50% confluence without cell at entrance.
Figures 31.A and 31.B depict unidirectional fluid flow of cells with 50%
confluence and 100% confluence, respectively. In both cases, a cell was located at the
e
the flow patterns, such es of following cells.
hus, it could be argued that the shear stresses along the surfaces of these cells would
ntrance to the flow region. In doing so, this initial bump in the flow significantly altered
that flow was at or near zero along the surfac
T
also be significantly lower.
When increasing hydrophobicity significantly and ignoring entrance region
effects, Figure 31.C depicts the flow along cells in such a bioreactor at the microscopic
76
level. Note that the flow is nonzero along the upper region of the cells, but the space
between cells exhibited flow rates at or near zero. Thus, this unidirectional flow
mulat
rfaces of
such cells are non-uniform in nature.
Finally, Figure 31.D depicts the culture of cells on hydrophilic surfaces at 50%
confluence beyond the entrance region. In this case, the lack of flow initially witnessed in
Figures 31.A and 31.B becomes minimal. Furthermore, some flow occurs over a greater
surface area of the cells, and the shear stresses become more uniform when compared
with those in Figure 31.C. Therefore, these data suggest that cells with a lower
confluence and on hydrophilic surfaces will have more uniform shear stresses under
os
si ion suggests that the shear stresses between cells in extremely hydrophobic
conditions are also at or near zero. Furthermore, the shear stresses along the su
cillating fluid flow than their hydrophobic counterparts at a higher confluence.
77
Finite Element Analysis of Cell Height:
The next study attempted to examine the various effects of culture of cells on
surfaces differing in hydrophobicity under fluid flow conditions, using cell height as the
independent variable. Though the core of this thesis analyzes surface morphology under
constant surface chemistry, such chemistry should still be considered when developing a
Figure 32. Cell with a very high contact angle with respect to the surface under constant,
unidirectional flow.
bioreactor. Considering that cell morphology is controlled by the hydrophobicity of
substrata, it would be predicted that the apparent shear stresses would also vary as surface
chemistry is altered if cell height were to increase with hydrophobicity. First, consider the
extreme case of a cell with a very high contact angle with respect to the culture surface
under unidirectional flow, as shown in Figure 32.
78
This study demonstrates a few important characteristics of such extreme
ypothetically fabricate negative effects
on cell adhesion, distribution of shear stresses, and conservation of energy. In other
words, the assumptions necessary for reproducibility in experimental protocols would
break down if such turbulence were to occur.
As a result, this extreme condition predicts that oscillatory fluid flow provides a
more consistent and beneficial experimental condition than protocols utilizing
unidirectional constant or unidirectional peristaltic fluid flow of media over cells extreme
increases in cell height.
The study then continues by examining oscillatory fluid flow and altering the cell
height among the simulations. The purpose was to determine the general differences
between relative shear stresses induced by oscillating fluid flow on cells cultured on
substrata with varying levels of hydrophobicity. It was hypothesized that cells with lower
height would exhibit greater shear stresses, but those with greater cell height would have
shear stresses concentrated near the center of the cell. This hypothesis stemmed from the
conditions. First, the high cell height may lead to a lack of flow at edge of the cell on
both sides of flow. Such height change leads to a concentration of higher shear stresses at
the upper surface of the cell. It would thus be predicted that cell shear stresses with
increased cell height would be non-uniform in nature. As a result, oscillatory fluid flow
would be more beneficial than unidirectional flow in distributing the shear stresses along
the surface of this cell with increased height.
Furthermore, note that eddies begin to form in the distal region of flow, just
beyond the right side of the cell in the flow field. These eddies can lead to turbulence if
velocity is increased, and such turbulence could h
79
pr nary simulation shown in Figure 32. The results of these simulations are displayed
in Figure 33.
elimi
cell height. Oscillatory fluid flow of media was used, and these data depict the simulation
depicts the von Mises stress distribution in the various simulations.
Figure 33. Shear stresses along the surfaces of cells cultured on substrata with varying
at t = 3.0 seconds. Red arrows depict the velocity field, and the grayscale gradient
80
Note that the flow profiles were similar among the various conditions, except at
the cell surfaces. As cell height was increased, the fluid flow profile was further
disturbed. It is very difficult to quantify the von Mises stresses from these simulation
outputs, but the purpose is to depict and define the various levels of cell height involved
in this protocol. Figure 34 demonstrates the first quantification of these data in terms of
relative shear stresses at the center of each cell in the experiments.
Figure 34. Shear stresses at the cell center over 3.0 seconds, along with the
corresponding averages for each variance in cell height.
First, note the wide variation in von Mises stresses from t = 0.0 s to t = 3.0 s
between cells cultured on various substrata. As can easily be seen, the amplitudes of these
sinusoidal patterns vary greatly, with those for the 7.5 µm-high cells having the greatest
peak amplitudes at nearly 120 dyn/cm2. The flat control was generally the lowest in its
How ater shear
stresses would be concentrated at the cell center on cells of greater height was nearly
time-dependent shear stresses at the cell center.
ever, upon averaging these data, the hypothesized trend that gre
81
observed. The flat control expectedly exhibited the lowest average shear stress at the cell
center, followed by the 1.5 µm- and 3 µm-high cells. Additionally, the very 7.5 µm-high
cells exhibited the greatest average shear stress at this location. However, the 5 µm-high
cells did not follow this trend. Such results could have been due to an error in the
simulation or some unpredicted factor in shear stress versus cell height. Nonetheless, all
other substrata followed predicted trends.
Figure 35 depicts the same data for various substrata at the left adhesion point
between the cell and the surface under oscillating fluid flow for 3.0 seconds.
Figure 35. Shear stresses at the leftmost point on the cell over 3.0 seconds, along with
the corresponding averages for each variance in cell height.
es very difficult to analyze these time-
Unlike the previous location, the von Mises stresses at the leftmost point on each
cell from t = 0.0 s to t = 3.0 s was very similar in its sinusoidal pattern among cells
cultured on various substrata. In fact, it becom
dependent data at this location. Nevertheless, one can easily locate very high peaks for
the flat control and 1.5 µm-high cells.
82
Upon averaging these time-dependent shear stresses, one finds a trend very much
unlike that found at the center of the cell. The flat control exhibited the greatest average
shear stress over this period of 3.0 seconds. Furthermore, the trend demonstrated that
shear stress at this adhesion point decreased with increasing cell height. This trend was
hypothesized from the preliminary cell height data, predicting that most shear stresses
would be concentrated away from this point under conditions where height is greatest.
F
Finally, these data were again analyzed at the rightmost point on each cell over a
period of 3.0 seconds for each substrate in Figure 36.
igure 36. Shear stresses at the rightmost point on the cell over 3.0 seconds, along with
the corresponding averages for each variance in cell height.
Considering that oscillatory fluid flow was used, similar trends in data were
displayed at the distal location in the flow field. These data further demonstrate the
benefit of oscillatory fluid flow over unidirectional flow, where such consistency would
not be exhibited as demonstrated previously for the cell with increased height. The trend
83
depicting decreasing shear stress with increasing cell height was once again noted at this
location.
Thus, these data demonstrate the benefits of decreased cell height and the use of
oscillatory fluid flow in the distribution of more uniform shear stresses across the surface
of cells.
84
FEA of Cells Cultured on Various Nanotopographies:
All of the previous simulations lead up to this series of experiments. Finite
lemen
lass, flat polystyrene, and two polystyrene/polybromostyrene (PS/PBrS 40/60
/w) demixed substrates. The nanoislands simulated were 11 nm and 38 nm high
[57], cells cultured on these
surfaces exhibited the following approximate elastic moduli:
• Plasma-Cleaned Glass: Ecell ≈ 7000 Pa
• Flat Polystyrene: Ecell ≈ 4000 Pa
• 11 nm Nanoislands (PS/PBrS 40/60 w/w): Ecell ≈ 9000 Pa
• 38 nm Nanoislands (PS/PBrS 40/60 w/w): Ecell ≈ 12000 Pa
The purpose of these experiments was thus to analyze the differences in apparent
von Mises stresses under the same flow conditions. In order to do so, all cells were
simulated as 3 µm-high cells with consistency among the aforementioned oscillatory
fluid flow conditions. Additionally, the velocity fields were analyzed in order to
determine whether these conditions were upheld. As shown previously, velocity fields
should not be significantly altered when flow occurs over various nanoscale substrata
(Figure 30). Furthermore, hydrophilic surfaces and oscillatory fluid flow have been
demonstrated to exhibit the greatest level of shear stress distribution according to prior
experimentation (Figures 33-36).
Although it would be predicted that these assumptions will hold true, it is still
helpful to verify these assumptions by initially analyzing the velocity fields and von
e t analysis with COMSOL Multiphysics was employed to analyze oscillatory fluid
flow over cells cultured on nanoscale substrates. These substrates included plasma-
cleaned g
w
topographies. According to past analyses of these substrates
85
Mises stress gradients at various time points and on the various substrata. These data
have been depicted in Figure 37.
Figure 37. FEA simulation of oscillatory fluid flow on various substrata at t = 0.5 s, t =
2.3 s, and t = 3.0 s. Red arrows depict the velocity field, and the grayscale gradient
depicts the von Mises stress distribution in the various simulations.
Though the size of the image makes it difficult to completely analyze these
simulations in detail, it is helpful to analyze each of the columns to compare among the
86
four substrata (Figure 37.a-d) at each time point. Notice that there are no significant
differences in the velocity field as demonstrated by the grayscale streamlines and the red
arrows. The middle column, at t = 2.3 seconds, depicts the peak velocity in the sinusoidal
fluid flow simulation. Again, even at the peak flow, there is no significant difference in
velocity field and von Mises stress distribution among the various surfaces. This analysis
allows for a consistent examination of the apparent shear stresses along the cell surface.
In order to analyze the average shear stresses along the cell surface, the von Mises
stress was quantified for each element along the arc length of the cell surface. Each of
these elements was then averaged with the others to find this apparent shear stress at the
cell surface. These average shear stresses at t = 0.5 s, t = 2.3 s, and t = 3.0 s are depicted
in Figure 38 below.
Figure 38. Average shear stresses in the FEA of oscillatory fluid flow over various
substrata at t = 0.5 s, t = 2.3 s, and t = 3.0 s. (*p<0.05; **p<0.01; ***p<0.001)
At t = 0.5 s, there were significant differences in apparent shear stresses among
multiple surfaces. Cells cultured on 38 nm nanoislands displayed significantly greater
shear stresses than both the cells cultured on plasma-cleaned glass and those cells
cultured on flat polystyrene. Furthermore, cells cultured on 11 nm nanoislands were also
87
significantly greater in apparent shear stresses than those cultured on flat polystyrene.
Thus, the apparent shear stresses exhibited under oscillatory fluid flow was always
significantly greater on the various nanoscale topographies than their flat counterparts at
this time point.
At t = 2.3 s, there was no significance for those cells cultured on 11 nm
nanoislands. However, cells cultured on 38 nm nanoisland topographies were once again
red on 38 nm nanoisland substrates were once again significantly
greater in apparent shear stresses than their flat counterparts. Furthermore, those cultured
on 11 nm nanoislands exhibited significantly greater apparent shear stresses than the cells
cultured on flat polystyrene.
The key result of this study was the finding that cells cultured on 11 and 38 nm
nanoisland topographies exhibited significantly greater apparent shear stresses under the
same oscillatory flow conditions than their flat counterparts. This increase in apparent
she of
cells
significantly greater than those cultured on plasma-cleaned glass and flat polystyrene.
These data suggest that the significant increase in apparent shear stresses is upheld under
peak flow conditions.
Finally, at 3.0 s, the significance in data similar to the t = 0.5 s time point
returned. Cells cultu
ar stress could thus be correlated to other findings of increased mechanosensitivity
cultured on these nanoscale substrata when compared with flat controls.
88
3D Bioreactor Design by the Finite Element Method:
As previously described, the ultimate purpose of these preliminary studies is to
design a novel bioreactor capable of maintaining many of the aforementioned optimal
properties. The design of such a two-dimensional bioreactor has been analyzed above, but
roughout the scaffold volume, (2) ensuring the bioreactor diameter
t symmetrical bioreactor geometries, both satisfying the 2 to
the utilization of three-dimensional scaffolds in a bioreactor where oscillating fluid flow
is induced must now be developed with the five design criteria set forth in the project
proposal located in the Introduction.
The bioreactor design must satisfy the design criteria by (1) maintaining a
uniform shear stress th
is between 2 and 10 mm, (3) allowing for 1 Hz oscillations of fluid flow over time
through a symmetrical geometry, (4) ensuring all velocities are greater than zero in the
scaffold volume, and (5) repeating the optimal geometry simulation for each previously
analyzed scaffold by comparing simulations with the relative porosities calculated earlier.
To do so, two differen
10 mm diameter requirement, were first created with COMSOL Multiphysics. The first
geometry suspended the scaffold in the center of the bioreactor, and the second geometry
tightly held the scaffold against the bioreactor walls. First, however, the general geometry
satisfying the Criteria 2 and 3 are depicted in Figure 39.
89
Figure 39. Initial geometry with FEA setup for analysis of scaffolds. This geometry has a
Scaffold
diam
e upper-right image depicts the
volume scale factor. As can be seen, fluid flow will occur more easily throughout the
length of the bioreactor, but shear stresses will be very high where the volume scale
factor is very low (at the two flow ports and the center of the bioreactor). This
symmetrical design was then simplified to a 2D axisymmetrical simulation. Symmetry
significantly decreases required computing power for FEA. The bottom-right image then
eter between 2 and 10 mm, and it is symmetrical for use with 1 Hz oscillations of
fluid flow.
The upper-left image in Figure 39 depicts the general geometry. Note that it is
symmetrical for use with 1 Hz oscillatory fluid flow. Th
90
depicts the area of interest, where the scaffold will be placed. The numerical values in
this design were arbitrary at this point in order to show general geometry and design
setup.
The next phase of the design process then compared the tight and loose scaffold
geometries. The purpose was to determine which geometry would better satisfy Criterion
1, which states that the bioreactor must exhibit uniform shear stresses throughout the
volume of the scaffold. A simulation of the BD© scaffold using the Brinkman model for
porous media in both tight and loose geometries is shown in Figure 40.
Figures 40.A and 40.B compare the stresses between both loose and tight
geometries for the BD© scaffold as shown by the color gradient. Note that the tight
Figure 40. Bioreactor simulations of the BD© scaffold in tight and loose geometries.
91
geometry (Figure 40.B) has a high concentration of shear stress near the axis of
symmetry, with very little von Mises stresses near the outer perimeter of the scaffold. On
the other hand, the loose geometry exhibited von Mises stresses with a more uniform
concentrated near
the center of the scaffold with very little flow near the outer perimeter. Thus, perfusion of
media throughout the scaffolds followed nearly the same pattern between the two
geometries.
Therefore, the loose geometry was considered the better choice due to its
satisfaction of Criterion 1. The shear stresses were more uniformly distributed throughout
the volume of the BD© calcium phosphate scaffold in this particular geometry, providing
a better level of mechanotransduction as shown by previous experiments. Perfusion was
nearly the same between the two bioreactor geometries, so the key factor was simply the
distribution of von Mises stress.
With the optimal bioreactor geometry chosen, the next phase was to ensure that
velocity throughout the volume of the scaffold remained greater than zero for each of the
aforementioned scaffolds. To do so, each scaffold was simulated in the loose geometry
bi e
rc length of the scaffold from the axis of symmetry (r = 0) to the outer edge of the
distribution throughout the volume of the scaffold. The uniformity was far from perfect,
but this novel design demonstrates a benefit to loose-fitting bioreactors with their
scaffolds.
Figures 40.C and 40.D compare the velocity fields between the loose and tight
geometries for the BD© scaffold. In both cases, most of the flow was
oreactor, and the velocity field was quantified. The velocity of each element along th
a
scaffold (r = R) was determined, and these were than averaged along the z-axis of the
92
scaffold. Provided was an average velocity gradient from r = 0 to r = R for each scaffold
under the same conditions. The output of these analyses is depicted in Figure 41 below.
Figure 41. Average velocities from r = 0 to r = R in the loose bioreactor geometry for
each of the scaffolds. These data were then averaged again along the arc length to
produce the graph on the right.
e velocity gradients appear very similar among all the
ensure that the same bioreactor could hypothetically be used for numerous scaffolds
First, note that the prediction of a greater velocity near the center (r = 0) and a
diminishing velocity near the outer perimeter (r = R) was verified according to the graph
on the left in Figure 41. Furthermore, Criterion 4 was satisfied by demonstrating that the
velocity did not drop below zero on average throughout the arc length of each scaffold. It
is very interesting to note that th
scaffolds. Upon averaging these data along the arc length of the scaffold, the graph on the
right in Figure 41 further demonstrates that these velocities do not significantly change as
porosity is significantly altered (Figure 21). Thus, this same bioreactor geometry could be
used for numerous scaffolds with significantly different porosities.
The final criterion, Criterion 5, required that all the scaffolds be analyzed and
their shear stresses (in this case, von Mises stresses) be compared. The purpose is to
93
under the same protocol. Using the same method as in Figure 41, von Mises stresses were
now calculated along the arc length of each scaffold in the loose bioreactor geometry
from r = 0 to r = R. These data are depicted in Figure 42 below.
Fig h
of the previously quantified scaffolds.
ure 42. FEA simulation of von Mises stress in the loose bioreactor geometry for eac
Note once again that all of the scaffolds displayed very similar distribution of
shear stresses along the arc length of the scaffolds from r = 0 to r = R. These data were
then averaged once again, and the graph on the right of Figure 42 depicts the average
shear stresses in each of the scaffolds. As hypothesized, there was no significant
difference in average shear stress among the various scaffolds. However, the patterns
mimicked the porosities of each scaffold (Figure 21). Nonetheless, this lack of
significance demonstrates that the bioreactor could be used for numerous scaffolds with
significantly different porosities under the same protocol. As a result, Criterion 5 was
thus satisfied.
As a result, this novel three-dimensional bioreactor design satisfied all of the
aforementioned criteria. Furthermore, the benefits of fluid flow previously demonstrated
on two-dimensional substrata could now be examined in three-dimensional scaffolds.
94
Thus, the results come full-circle from the simplification of a three-dimensional in vivo
environment to two-dimensional in vitro studies of biophysical signals and then the
expansion of this two-dimensional study into a three-dimensional in vivo bioreactor based
upon such prior data regarding the benefits and analyses of two-dimensional culture in
bioreactors in vitro.
95
DISCUSSION Two-Dimensional Substrata Characterization:
Findings from AFM Imaging:
Previous studies have successfully involved methods to determine the three-
dimensional topographic characteristics of two-dimensional substrata at an order of
agnitude equivalent to nanometer [1, 48]. The images from atomic force microscopy
racteristics at the nanoscale.
By increasing the concentration of polymer in chloroform solvent, the nanoscale was thus
increased. PS/PBrS 40/60 w/w films were found to elicit nanoislands increasing from 11
nm to 85 nm, while the solute (i.e. polymer) concentration was increased from 0.5% to
2.0%. PLLA/PS 70/30 w/w films elicited similar nanotopographical characteristics,
increasing from 12 nm to 80 nm in nanoisland height, while the solute concentration was
increased from 0.5% to 3.0% in chloroform.
The extracellular milieu of bone in vivo is characterized by nanotopographies of
the same order of magnitude [13]. Though the number varies, it is widely believed that
such nanoislands would be approximately 10-30 nm in height. Thus, it was demonstrated
that these polymer demixing techniques successfully mimicked the nanoscale of in vivo
bone tissue.
Another finding was the contrast with lithographic methods. Typically,
lithography results in an ordered patterning of topographical features [31]. The problem
with such a method is that it does not successfully mimic the in vivo environment, due to
the fact that the extracellular milieu of bone is in fact very disordered. In contrast with
lithographic methods which could already successfully create the same nanoscale as
m
(AFM) demonstrated the presence of three-dimensional cha
96
previously mentioned, this stu e a disordered patterning of
FM, one can easily witness a random
e height varies greatly among the islands, along with the
lity.
rther varied. Though variation is not necessarily problematic, such a
dy wished to provid
nanoislands. When analyzing the images from A
assortment of nanoislands. Th
width of each nanoisland. Furthermore, the nanotopography is randomly dispersed along
the surface of the film. Such random distribution demonstrated success of these polymer
films in improving upon current lithographic methods in mimicking the extracellular
milieu of in vivo bone tissue through both scale and disorder.
Drawbacks of Cell Height Estimates:
A skilled technician in atomic force microscopy understands issues resulting from
the cantilever. Even with a sharp cantilever, AFM images depict rounded surfaces where
surfaces are instead sharp. Thus, it should be noted that the round nature of these islands
may not be accurate when compared with rea
Another issue results from the random character of the nanoscale topographies.
For example, larger (80-85 nm; Figures 18 and 19) topographies demonstrate an
exaggeration of this phenomenon. Though the nanoscale is labeled as 80 nm or 85 nm,
islands actually vary in height to an extreme degree. Furthermore, the width of these
islands is fu
phenomenon must be recognized throughout further discussion of results.
97
Three-Dimensional Scaffold Characterization:
Findings from SEM Imaging:
Scanning electron microscopy (SEM) allowed for microscopic analysis of five
different three-dimensional scaffolds. In doing so, numerous differences between the
various scaffolds were revealed. Firstly, the BD© calcium phosphate scaffolds (Figures
20A and 20B) demonstrated similar textures and topographies when compared with the
BoneMedik© coral scaffolds (Figures 20C and 20D). However, the calcium phosphate
caffolds did not appear to have deep pores, and the scaffold instead illustrated a series of
ding from a seemingly solid calcium phosphate
ts.
could then be compared with
other scaffolds found in previous studies. Collagen and collagen-hydroxyapatite
constructs were illustrated with a rough texture similar to that of the scaffolds found in
the poly(L-lactic acid) constructs [5]. When compared with scaffolds created from
s
three-dimensional topographies exten
construct. The coral scaffolds, on the other hand, demonstrated pores with much deeper
topographies, leading to better perfusion throughout the scaffold. Furthermore, the
calcium phosphate scaffold images depicted much larger topographies when compared
with the smaller pores of the coral scaffolds.
The three poly(L-lactic acid) polymer scaffolds demonstrated a very different
texture than both the coral and calcium phosphate scaffolds. As the NaCl salt crystals
were increased in diameter, polymer “shells” became larger accordingly. However, the
pores in these scaffolds were not true pores; instead, the topographies demonstrated
microscale pits as opposed to true microscale pores. These images became integral in
understand the differences in cell and media perfusion among the construc
Textures depicted from SEM images of the scaffolds
98
nanofibers, the coral and calcium phosphate scaffolds demonstrated the deep pores found
. Such deep pores became useful in the perfusion of media
ading
imation of porosity is the concept that three-
mens
in these constructs [66, 71-73]
le to efficient cell seeding. Thus, these data provided beneficial insights into the
drawbacks of collagen scaffolds through analyses of pore depth and construct texture and
benefits of coral scaffolds by comparison with nanofibrous scaffolds in previous studies.
The estimates of porosity were then calculated from these SEM images utilizing
contrast comparison techniques in ImageJ. As mentioned before, these data demonstrated
increased estimated porosities in the polymer scaffolds. However, such findings must be
met with a skeptical attitude, especially due to the aforementioned lack of pore depth in
such poly(L-lactic acid) constructs.
Drawbacks of Porosity Calculations:
One of the greatest issues with the est
di ional constructs are simplified to two-dimensional images. In doing so, the
representation severely loses its accuracy. A mock scaffold is depicted in Figure 43.
Figure 43. A comparison of the 2D representation of a 3D construct (A) with the actual 3D construct. Notice the loss of depicted pores in these representations.
A B
99
In Figure 43, notice that the two-dimensional image in Figure 43A depicts only
five pores. ImageJ would then be used to calculate the porosity, estimating that these five
pores are continuous throughout the volume of the construct. Thus, it would be estimated
that the porosity would be approximately 20-25% according to the two-dimensional
representation. However, the reality is much different. The three-dimensional image in
Figure 43B depicts pores lost in the two-dimensional image. As can be imagined, the
actual porosity may thus be much greater than the estimate due to the loss of pores by
two-dimensional simplification. Therefore, estimated porosities are inaccurate and may in
fact be much lower than reality.
100
Stem Cell Growth on 2D Substrates:
Mechanosensitivity of Stem Cells:
As depicted in Figures 22-24, the mechanosensitivity of mesenchymal stem cells
(hMSCs) cultured on PLLA/PS 70/30 w/w demixed films was studied by analyzing the
relative fluorescence of Fura Red stain. When analyzing the percentage of cells
responding in Figure 22, one finds that, at a shear stress of 5 dyne/cm2, hMSCs cultured
on 12 nm nanoislands displayed a significantly greater response when compared with
cells cultured on 21 nm nanoislands, 45 nm nanoislands, 80 nm nanoislands, and flat
PLLA controls. At greater stresses (10 and 20 dyne/cm2), the responses were too great to
tion that mechanosensitivity
of stem cells cultured on nanoscale topographies is significantly greater than cells
cultured on flat controls while the surface chemistry is held constant.
Figure 24, as opposed to illustrating the percentage of cells responding, showed
the absolute fluorescent response above the average baseline during static conditions. It
was observed that cells cultured on larger (45 nm and 80 nm) nanoislands displayed
significantly lower absolute fluorescent responses than hMSCs cultured on 12 nm
nanoislands. This difference demonstrated a variance among sizes of nanotopographies in
the mechanosensitivity. Thus, it was observed that cells not only preferred nanoscale
topographies, but a preference existed for certain scales (i.e. 12 nm) over others (45 and
80 nm).
Finally, Figure 25 depicted the percent increase in fluorescence above the baseline
during static conditions. Similar to the data in Figure 24, hMSCs were observed to exhibit
some preference among the substrates. These data thus became critical in the
determine any significance. Such data illustrate the observa
101
development of a bioreactor. If cells exhibit preferences in mechanosensitivity at
ear stresses and also among varying nanoscale
these substrates for
slands.
different fluid flow induced sh
topographies, such conditions should be implemented in the bioreactor. As a result, the
bioreactor design used oscillatory fluid flow, along with varying three-dimensional
porosities based upon these two-dimensional data.
Proliferation and Differentiation Potentials:
Utilizing data from fluorescence activated cell sorting (FACS) analysis (Figure
25) led to an analysis of proliferation and differentiation potentials of human bone
marrow stromal cells (hBMSCs) cultured on PS/PBrS 40/60 w/w demixed films.
Specifically, these films displayed nanoscales of 11 nm, 38 nm, and 85 nm. A flat
polystyrene control was also analyzed. hBMSCs were cultured on
either 7 or 12 days, and harvested cells were tagged with SSEA-4, CD73, CD90, or
CD105 primary antibodies with a fluorescent secondary antibody.
After seven days, the cells were harvested from culture in either growth or
osteogenic media. It was observed that cells cultured on 11 nm nanoislands in osteogenic
media displayed significantly lower SSEA-4, CD73, and CD105 reactivity compared
with the flat control and 85 nm nanoisland substrates. This decrease in reactivity was
directly correlated with an increase in differentiation potential of hBMSCs cultured on 11
nm nanoi
After twelve days, the cells were harvested from culture in either growth or
osteogenic media. hBMSCs cultured on 11 nm nanoislands in growth media displayed
significantly greater reactivity to SSEA-4 compared with the flat control. Such reactivity
102
was directly correlated with an increase in proliferation potential for cells cultured on
these substrata. Additionally, hBMSCs cultured on these same 11 nm substrates
displayed significantly lower CD105 reactivity when compared with flat controls. These
data further verified the observation that cell differentiation potential was increased on
these substrata.
Thus, proliferation and differentiation potentials were also found to have
aphies when compared with their flat
parison of the two samples, it was observed that cells cultured on 11 nm
increased on specific nanoisland topogr
counterparts. Combined with previous data, we can now infer that substrate topography
regulates progenitor cell mechanosensitivity, proliferation, and differentiation potentials.
Previous studies have also verified that focal adhesions also increase on the same
substrata [1]. Combining all of these data allows for the observation that nanoscale
substrata of 10-40 nm height provide an excellent alternative to flat counterparts
commonly used in tissue culture protocols.
Alkaline Phosphatase Activity:
Human mesenchymal stem cells (hMSCs) cultured on 11 nm nanoislands from
PS/PBrS 40/60 w/w demixed films and flat polystyrene substrata were harvested after 12
days of culture in osteogenic media. Alkaline phosphatase assays were performed on
each of the samples (Figure 28).
After com
nanoislands displayed significantly greater alkaline phosphatase (AP) activity than
hMSCs cultured on flat polystyrene controls. Thus, cells have been demonstrated to
display increased intracellular activity based solely upon surface morphology.
103
When these data are compared with previous studies, the data demonstrate a
consistent observation that progenitor cells cultured on 11-12 nm nanoislands display
significantly greater cell alkaline phosphatase activity, mechanosensitivity, proliferation
potential, and differentiation potential. Thus, surface morphology alone can regulate stem
cell activity.
104
Stem Cell Growth on 3D Scaffolds:
Alkaline Phosphatase Activity:
Similar to the aforementioned studies of cells cultured on two-dimensional
substrates, human mesenchymal stem cells (hMSCs) were also studied on three-
dimensional scaffolds. hMSCs were cultured on either BD© calcium phosphate or
samples were then analyzed for alkaline phosphatase (AP) activity, normalized by the
number of total proteins in the sample (Figure 29).
After analysis of these data, it was observed that progenitor cells cultured on the
BoneMedik© coral scaffolds displayed significantly greater AP activity than those cells
cultured on the BD© calcium phosphate scaffolds.
This observation was expected when considering the differences in porosities and
surface morphologies (Figures 20, 21). The coral scaffold was observed to have a greater
porosity value than the calcium phosphate scaffold. Additionally, the morphology of the
coral scaffolds were observed to have deeper and more uniform pores than the BD©
calcium phosphate scaffold samples after examination by scanning electron microscopy.
Thus, it could be argued that increased perfusion and deeper pores allowed for better flow
of osteogenic media throughout the volume of the scaffolds. Such flow, in turn, would
lead to greater alkaline phosphatase activity in cells.
BoneMedik© coral scaffolds for 12 days in osteogenic media prior to harvesting. These
105
Comparison with 2D Substrata:
One will notice that the alkaline phosphatase activities were not directly
mpar
tes ranged from 125-250 sigma units
e.
co ed statistically. No analysis was performed due to major differences in seeding
density and differences in protocols between the two-dimensional and three-dimensional
samples.
However, the number of sigma units per protein was on average greater among
two-dimensional samples (Figure 28) than on three-dimensional samples (Figure 29).
Specifically, averages for two-dimensional substra
per protein, whereas those for three-dimensional scaffolds ranged from 10-70 sigma units
per protein. When comparing the calcium phosphate scaffolds with the two-dimensional
substrata, there was an order of magnitude differenc
These observations should be taken with a grain of salt, due the aforementioned
differences in protocol and lack of statistical analyses between two- and three-
dimensional substrates and scaffolds.
106
Finite Element Analysis:
Discussions of Cell Confluence and Hydrophobicity:
FEM simulations were used in this study in order to analyze fluid flow patterns
inside a cell cultured flow chamber. Firstly, we examined the variability of fluid flow
patterns among various levels of cell confluence. At the macroscopic level, no significant
ls of confluence, 50% confluent or
r stresses. However, we suspect that the lower
tory effects from cell-to-cell
communication. Thus, there may be an optimal cell confluence level that allows both
uniform, positive fluid flow effects and cell-to-cell communication effects.
As regards cell height effects, FEM demonstrated a lack of flow in the distal
region of cells when the cell height is greater. Furthermore, these data suggest that
oscillating fluid flow used in some bioreactor systems [8, 39, 40] would be more
beneficial than constant or peristaltic unidirectional fluid flow found in similar
bioreactors due to a more uniform distribution of shear stresses along cell surfaces [7, 35,
74, 76, 77, 81]. In analyses using oscillating fluid flow conditions, cells with larger
differences were noted. Thus, cell confluence was concluded to have no major effect on
the flow profiles in bioreactors. However, microscopic analyses demonstrated that little
to no flow would occur between highly confluent cells. When cell confluence was
decreased, fluid flow could more easily occur between cells. Furthermore, cells in the
entrance region of flow in the bioreactor would alter the patterns of flow over cells
downstream. It would thus be assumed that lower leve
less, would be optimal in the design of bioreactors utilizing such fluid flow. This lower
confluence allows for a better distribution of fluid flow across cell surfaces and thus a
more even distribution of wall shea
confluence may be a trade-off considering potential stimula
107
heights lead to more concentrated shear stresses near the center of the cell. With
reading), the shear stresses at the
ith a greater
decreasing cell height (relevant to increased cell sp
center of the cells decreased on average and the shear stresses at the left and right of the
cell increased. These relative changes imply a more efficient distribution of shear stresses
with decreasing cell height. Taken together, these data suggest that bioreactors should use
oscillating fluid flow in combination with substrates that stimulate cell spreading for a
better distribution of wall shear stresses in the cell culture system.
Our previous studies demonstrated that cells cultured on various nanoscale
topographies will exhibit different biophysical properties, including varying elastic
moduli, cell adhesion, and morphology [1, 45, 57]. Continuing with finite element
analyses utilizing oscillating fluid flow, data from these studies was implemented to
determine any potential differences in the apparent shear stresses of cells cultured on
these various substrates. It was demonstrated in this study that cells cultured on 11 and 38
nm nanoislands exhibited a significantly greater apparent shear stress than cells on flat
surface. Such shear stress variation was due to an increased elastic modulus present in the
cells cultured on these surfaces. Increased cell stiffness is correlated with an increased
apparent shear stress, and these data support the hypothesis that cells w
elastic modulus will exhibit increased apparent shear stresses under oscillating fluid flow
conditions.
108
Benefits over Empirical Data Collection:
The success of finite element analyses was witnessed in the examination of
factors not easily determined empirically through the demonstration that cells cultured on
nanotopographic substrata exhibited increased apparent shear stresses relative to cells on
flat surfaces. Furthermore, FEM was used in such a way that an experiment could be set
up to empirically validate these results through parallel analyses. Thus, these methods
provide an excellent segue into exploring future routes of study.
Benefits of Oscillating Fluid Flow:
A key element of the data presented was the demonstrated benefit of oscillating
fluid flow as a superior method to its unidirectional counterpart. Flow is more evenly
distributed in the bioreactor system over time, leading to a more even distribution of von
Mises stresses across cell membranes. This distribution allows such systems to be more
predictive due to a better estimate of the flow rates and shear stresses at the walls of a
bioreactor. Thus, it can be concluded that oscillating fluid flow provides greater benefits
than constant or peristaltic unidirectional fluid flow systems.
109
Summary of FEM as a Tool in Cell Culture
actor systems, this same
ethod could provide insight not easily acquired through empirical methods.
FEM was successfully used to analyze flow patterns over cells, as demonstrated
by the data previously presented. FEM provides an excellent tool in the prediction of
experimental protocols and the design of bioreactor systems. Though the bioreactor
system presented here was simulated as a two-dimensional substrate simplified to a single
plane, FEM can easily be expanded to analyze more complex geometries. When
discussing the difference in perfusion of three-dimensional biore
m
110
Bioreactor Design:
Satisfaction of Design Criteria and Specifications:
This particular design specification was accomplished in two manners. First,
uniform shear stresses were witnessed in the loose variation of the bioreactor design, as
depicted in Figure 40.A. The shear stresses throughout this particular design’s volume
were uniform.
Additionally, it was specified that the design must satisfy physiologically correct
shear stresses. The target ranges were 5, 10, and 20 dyne/cm2. By altering input
velocities, the shear stresses could be adequately controlled. Average shear stresses were
shown to be 5.36, 10.54, and 21.88 dyne/cm2 in this particular model. Figure 44 depicts
the changes in shear stress along the r=0 to r=R arc length of the scaffold.
Figure 44. Average shear stresses along the arc length of the loose scaffold model were successfully maintained at approximately 21.88, 10.54, and 5.36 dyne/cm2.
Criterion/Specification 1: The bioreactor must maintain physiologic shear stresses as witnessed in vivo. It must maintain uniform shear stresses throughout the volume of the scaffold at 5, 10, and 20 dyne/cm2.
111
e
h 3 mm (loose) or 4 mm (tight). In both cases, the
Though the bioreactors simulated in Figure 39 and Figure 40 did not undergo
oscillating fluid flow, the benefits of 1 Hz oscillations were previously determined in the
finite element analyses of oscillating fluid flow over two-dimensional substrata.
However, the symmetrical nature about the r-plane should lead to the capability of
withstanding oscillatory fluid flow without harm to the scaffold.
Flow profiles were depicted in Figure 40 and Figure 41. Figure 40 demonstrated
through a surface map of both tight (Figure 40.D) and loose (Figure 40.C) scaffolds that
the loose bioreactor design led to a more uniform distribution of velocity through the
volume of the scaffold.
Additionally, velocities along the arc length of the loose scaffold was simulated
f
Criterion/Specification 2: Standard scaffolds must fit within the bioreactor volume. ing somewhere between 2.0 and The bioreactor must have a variable diameter rang
10.0 mm.
The bioreactor is depicted in Figure 39. Though it may be difficult to witness, th
eight of the scaffolds were set to either
bioreactor was modeled such that it could support scaffolds ranging in diameter from 5
mm to 8 mm. This value was well within the range specified previously.
Criterion/Specification 3: The bioreactor must withstand oscillating fluid flow conditions. A oscillations.
symmetrical geometry must be determined which can withstand 1 Hz
Criterion/Specification 4: Flow must be uniform throughout the scaffold volume. Flow profiles must be simulated throughout the volume of the scaffold to ensure that all are greater than zero.
or different types of scaffolds. In all cases, a parabolic velocity profile was maintained,
112
w ns
a
osity values as
d in shear
st and
Figure 42 depict these differences. It was observed that scaffold porosity changes did not
correlate to significant changes in velocity profiles or shear stress profiles along the arc
length of each scaffold. According to these FEM simulations, the bioreactor should
perform equally well for all porosities examined in this study.
Comparison of Two Models:
el
in city profiles and shear stresses throughout the volumes of
ease in the scaffold’s perfusion ratio compared with that of the
of the scaffold within the bioreactor. This particular model assumed that the scaffold
here velocity was greatest at r=0 and smallest at r=R. Even with no-slip conditio
ssumed, the velocity never dropped below zero.
The loose bioreactor design (Figures 40.A and 40.C) was chosen as the optimal
bioreactor design. This bioreactor was simulated with various por
Criteriondeter
/Specification 5: The bioreactor must work for all scaffolds. After mining the relative porosities of each scaffold, these values must then be inserted
into iterative simulations of the bioreactor of choice.
etermined from SEM characterization of scaffolds. In doing so, the changes
ress and velocity along the arc length of each scaffold was determined. Figure 41
The tight bioreactor model was far less successful than the loose bioreactor mod
exhibiting uniform velo
scaffolds. This comparison of success was observed in finite element simulations as
depicted in Figure 40. Notice that the loose bioreactor is more capable of exhibiting
uniform shear stresses throughout scaffold volumes. Such stress distribution would thus
be correlated to an incr
tight bioreactor.
The only issue with the loose bioreactor model is the need for secured suspension
113
simply floated in the volume of the bioreactor, which could potentially cause harm to
both the cells and scaffolds alike. To prevent this issue, it would be beneficial to include
so magnitude
sm n
disruption of fluid flow. Empirical data must then be collected after fabrication of the
scaffold with the securing mechanism in place. Such a design is depicted in Figure 45.
igur
success, however, perfusion studies must
me type of securing mechanism with adjustable supports one order of
aller than the bioreactor diameter. This difference in size should prevent issues i
Scaffold
z r
Supports with Screws for Adjustment
Flow
F e 45. Loose scaffold with six tight cables to suspend the scaffold within the volume of the bioreactor.
Analysis of Design:
This bioreactor design satisfied all of the design criteria and specifications set
forth previously. Additionally, further design components have been prepared in order to
increase the likelihood of success for such a bioreactor.
Before the design can be considered a
be performed whereby a prototype is first manufactured and then set up with a
114
un
sc
un
S
o
4
nidirectiona
caffold with
The n
nidirectiona
pecifically,
f fluid flow
l or oscillato
the bioreact
next phase
l fluid flow
the initial te
and with dif
ory pump. C
tor in order t
would the
on cells cult
est would be
fferent shear
Cells of any
to verify the
en be to a
tured in each
e an alkaline
r stresses. Th
y type will t
data from fi
analyze the
h scaffold w
phosphatas
his design sc
then be perfu
inite elemen
effects of
with this part
e assay after
chematic is o
fused throug
nt analyses.
oscillatory
ticular biorea
r varying pe
outlined in F
gh the
and
actor.
eriods
Figure
6.
Figur
Fabricatbioreactfrom CAmodel.
re 46. Future
tion of tor AD
A
tf
e directions f
Analysis ofperfusion capabilitiecells in varscaffolds wthe newly‐fabricated bioreactor
for bioreacto
f
es of rious with ‐
r.
or design.
Analysis olong‐termfluid flowprogenitocells in thvolume ovarious scaffolds within thibioreacto
of m of or e f
is or.
115
CONCLUSIONS Methods of Biomaterial Characterization:
Numerous methods can be used to characterize biomaterial properties. Surface
chemistry properties can be analyzed with X-ray photoelectron spectroscopy (XPS), and
tensiometry can be analyzed with contact angle measurements, for example. However,
the key analysis in this study was surface morphology. In order to do so, both atomic
force microscopy (AFM) and scanning electron microscopy (SEM) were involved.
After characterization of two different two-dimensional substrata, it was
discovered that AFM was very successful in predicting surface morphology. The method
not only provided useful data, but it was simple to employ. The significant drawback to
data from AFM was that it will oftentimes depict rough surfaces with rounded edges.
Such an artifact is due to the nature of the cantilever and was not corrected in the
previous data presented in this work.
SEM was used in order to characterize the morphology of three-dimensional
scaffolds. It was very useful in estimating the pore sizes and thus the relative porosities of
numerous scaffolds. However, these relative porosities varied significantly from the true
porosity values, as illustrated previously. Thus, other methods than electron microscopy
would be beneficial to determine the total available void volume relative to the total
scaffold volume (i.e. the porosity).
Therefore, the methods involved in this study were successful in that they
adequately described the morphology of various two-dimensional substrata and three-
dimensional scaffolds. However, these morphologies had their flaws, though the most
significant flaws resulted from estimates of three-dimensional porosity values from the
116
twwo-dimensioonal surfacee images inn the SEM characterization of thhe various tthree-
dimensional sscaffolds.
th
m
It wou
hese biomate
methods have
uld be benef
erials, along
e been illustr
ficial in futu
with other c
rated in Figu
ure studies to
characteristi
ure 47.
o further cha
ics, through
aracterize th
additional m
he morpholog
methods. Pos
gy of
ssible
Figu
Mic
Surfac
StrA
OSpec
Chemi
PhysicDete
re 47. Addit
croscopy
ce and TFilm
ructuralnalysis
Optical ctroscop
cal Ana
cal Properminati
tional metho
•En•Fo•Ne•Tra
y
•Co•X‐•Se•Au
Thin
•Sm•X‐
•Ult•Fopy
•IndSp•Ind•Ion
lysis
•Po•Co•Dif•Ac
erty on
ods for 2D an
nergy Dispersiocused Ion Beear‐Field Scanansmission El
onfocal RamaRay Photoeleecondary Ion Muger Electron
mall Angle X‐RRay Diffractio
traviolet‐Visibourier Transfo
ductively Couectroscopyductively Coun Chromatog
olarization andontact Angle Mfferential Scaccelerated Su
nd 3D mater
ive X‐Ray Speamnning Optical lectron Micro
n Spectroscoectron SpectroMass SpectroSpectroscopy
Ray Scatteringon
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upled Plasma‐
upled Plasma‐raphy
d Strain MeasMeasuremennning Calorimrface Area an
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ectroscopy
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pyoscopyoscopyy
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erization.
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117
A
ch
re
sc
M
in
co
sc
ph
d
n
sp
co
Ability of Su
Surfac
hanges in po
esponse of st
The p
cales in the
Mechanosens
ncreased on
ompared wit
cales. Simil
hosphatase
ifferentiation
anoscale su
pecific (11-3
onclusions h
Figure 48
Increasemechanosens
among 12 nanoscale sub
ubstrates an
ce morpholo
orosity amon
tem cells cul
reviously pr
stem cell r
sitivity, as
these surfa
th flat surfac
lar results
(AP) activi
n. The key
ubstrates com
38 nm) nan
have been su
. Summary o
Two
d sitivitynm bstrata
Incactivnms
d Scaffolds
ogy changes,
ng scaffolds,
ltured on the
resented data
response for
determined
aces. Sensiti
ces and also
also result
ty, increase
was that th
mpared with
noscale subst
ummarized in
of human me
sur
Stem Co‐Dimens
creased AP vity among 11 m nanoscale substrata
to Regulate
, including in
were used a
ese surfaces.
a have demo
r those cells
through in
ivity signific
o among the
ted from th
ed stem cell
hese data ill
h flat surfa
trata over th
n Figure 48.
esenchymal s
rface morph
ell Resposional Su
Increased stproliferation11‐38 nm na
substra
e Stem Cell
ncreased nan
as independe
.
onstrated the
cultured on
ntracellular
cantly incre
12 nm nano
he data de
l proliferatio
lustrated a p
aces. Additio
hose substra
stem cell res
hology.
onsivenerface Mo
tem cell n among anoscale ata
Incrdam
nano
Activity:
noscale subs
ent variables
utility of sp
n two-dimen
calcium ([C
ased on nan
oislands com
escribing in
on, and inc
preference f
onally, spec
ates of a lar
sponse to two
ss to orpholog
reased stem ceifferentiation
mong 11‐38 nmoscale substrat
strata and rel
s to determin
pecific nanoi
nsional subs
Ca2+]i) resp
noscale subs
mpared with
ncreased alk
reased stem
for stem cel
cificity aros
rger scale. T
o-dimension
gy
ell
m ta
Preferenc38 nm nasubstrat
larger na
118
lative
ne the
sland
strata.
ponse,
strata
other
kaline
m cell
ls on
e for
These
nal
ce for 11‐anoscaleta over noscales
It should also be noted that increased responsiveness has been correlated with
rther studies.
urements, and antibody studies through
fluorescence-activated cell sorting (FACS). These studies would thus parallel those
previously completed for two-dimensional substrata.
previous studies of increased elastic moduli among cells cultured on these specific two-
dimensional nanoscale substrata. This relationship between cell stiffness and biological
response to materials could be explored through fu
The biological response of stem cells cultured on three-dimensional scaffolds was
also briefly analyzed. Unlike the studies of two-dimensional substrata, only alkaline
phosphatase activity was assayed. After analysis, the data illustrated that the
BoneMedik© coral scaffolds displayed significantly greater AP activity compared with
the BD© calcium phosphate scaffold. This variance could have been a result of
differences in porosity as previously discussed. However, the key finding was that not all
scaffolds are created equal. Whether this is a function of surface chemistry, surface,
morphology, or some combination of biomaterial properties is yet to be discovered.
Future studies analyzing the biological response to three-dimensional scaffolds
could include studies of AP activity under oscillating fluid flow conditions, analyses of
mechanosensitivity by intracellular calcium meas
119
F
H
n
Finite Eleme
Typic
However, flu
ot analyzed
ent Method
cally, biolog
uid flow prof
in detail. In
as a Novel T
gical respon
files and the
nstead, these
Tool in Tiss
nses are p
e affects of b
variables w
sue Enginee
predicted ba
biophysical s
were simply c
ering:
ased upon
stimuli on c
cont
empirical
ell surfaces
data.
were
rolled byy total flow
or
th
fl
in
un
an
ef
o
ce
pr
sh
ac
p
r some simil
hese variable
As de
low patterns
n vitro, and
nknown dat
nalyses affo
ffects of the
f t oftwahe s r
ells under os
The o
redicting mi
hear stresses
cquired emp
ossible uses
Figure
M
• Aver• Aver
lar macrosco
es to be stud
emonstrated
over cells o
thus the in
ta. When co
orded by mu
se biophysic
re in predict
scillating flu
other factor
icroscopic p
s at various
pirically, an
of FEM in c
e 49. Demons
Macroscopic
rage flow prorage shear st
opic paramet
ied in great
previously,
or substrates
silico meth
oupling fluid
ultiphysics, o
cal stimuli ca
ting relative
uid flow cond
that can b
parameters. T
locations alo
nd FEM thu
cell culture h
strated exam
c Functions
ofilestresses
ter. Finite el
detail.
the finite e
in cell cultu
hod provides
d flow patte
or finite elem
an be predic
shear stresse
ditions.
be useful is
This was de
ong the surf
us provides
have been ill
mples novel F
••
lement analy
element met
ure. These da
s a novel tec
rns of cells
ment analysi
cted. Previou
es (i.e. von M
the use of
emonstrated
faces of cells
an excellen
lustrated in F
FEM applica
Micros
• Flow along• Surface sh
yses, on the o
thod can be
ata can be di
chnique to e
in culture w
is, software,
usly illustrate
other hand, a
e used to pr
ifficult to ac
extract other
with stress-s
, the downst
ed was the u
Mises stresse
f finite elem
through the
s. Such data
nt alternativ
Figure 49.
ations in tiss
scopic Funct
g surfacesear stresses
es) imposed
ment analys
e data descr
a cannot be e
120
rates
allow
redict
cquire
rwise
strain
tream
utility
upon
es in
ribing
e
ve. Some o
sue culture.
tions
asily
f the
The applications in Figure 49 have been divided in macroscopic and microscopic
with various geometries and inputs for
tro can be coupled with physical outputs
eterm
utilities. It should be noted, however, that these were simply the uses demonstrated in this
paper. Thus, the applications illustrated in Figure 49 are not all-inclusive.
Another novel application of the finite element method in tissue engineering was
found in the design of bioreactors. FEM provides the ability to predict perfusion, flow
properties, deformation, stresses, and more
various bioreactors. For example, it may be useful to determine whether eddies or
turbulence result in a mixing chamber. FEM can predict this through both velocity
profiles and Reynolds number calculations. The utility of FEM as a design tool in tissue
engineering was illustrated in the bioreactor designed in this paper.
Thus, the finite element method acts as an excellent tool for predictive studies in
tissue engineering. It is recommended that FEM be coupled with future studies as a
preliminary method when designing experiments. In doing so, biological responses to
materials and bioreactors determined in vi
d ined in silico.
121
S
F
ummary of
Finite
rom the mod
f Bioreactor
e element an
del, numerou
r Properties
nalyses were
us properties
Key for Su
e used to de
s were deem
uccess:
esign a com
med beneficia
mputational b
al over other
bioreactor m
rs
model.
in the desiign of
a successful bbioreactor. TThese properrties have been summarizzed in Figure 50.
This
sa
d
b
m
ad
cr
re
w
Figure
The p
atisfying all
irection) is r
een demons
more benefic
dvantage of
Addit
riterion requ
emaining fas
was the key
oscillat
Tperfusihe opt
othe volu
e 50. Summa
parameters ou
design crite
required for
strated throu
cial than un
such a param
ionally, the
uires that flow
stened to the
y parameter
R‐ and Z‐s
s allows for thing fluid flow
Increased
imal bioreacton of media aume of the sc
ary of proper
utlined in Fi
eria. Symme
the utilizatio
ugh two-dim
nidirectional
meter.
scaffold mu
w exist arou
e inner walls
r when com
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he utilization w during cell c
Perfusion
tor should maand cells throucaffold under
of ulture.
sa
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igure 50 dep
etry both rad
on of oscillat
mensional as
l flow. Thu
ust both be
und all outer
s of the bior
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aximize ughout study.
am
Key BioreacPropertie
ary to optimi
pict those co
dially (r-dire
ting fluid flo
ssays and fi
us, the opti
loose and s
surfaces of t
reactor by sm
o major bi
Loose/Sec
Media must caffold, but tadversely affe
the scaffo
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Turbulent floadhesion, andmust thus be
any eddie
ctor es
ize bioreacto
ommon amo
ection) and l
ow. Oscillati
inite elemen
imal biorea
secure. This
the scaffold
mall cables (
oreactor ge
cure Scaffold
flow even arhe fluid flow ect cell growthold from its po
aminar Flow
ow leads to lod the Reynoldless than 230es in the flow
or designs.
ng the biore
longitudinall
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nt analyses t
ctor would
s counterintu
(i.e. loose) w
(i.e. secure).
eometries. T
Fitting
round the should not h by jarring osition.
oss of cell ds number 00, without w field.
eactor
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w has
to be
take
uitive
while
This
Those
122
bioreactors with a loose fitting illustrated better distribution of flow rates and shear
rrelates to
increased seeding efficiencies, increased biomechanical stimuli by fluid flow over
adhered cells, and thus more efficient tissue growth in the scaffold. As a result, the key
parameter for any bioreactor must be its perfusion efficiency.
Finally, laminar flow must be maintained in all bioreactor designs. Turbulence
has been demonstrated to break down focal adhesions and shear cells off surfaces. Such
flow would lead to a degradation of tissue growth efficiency in the scaffold. If the
Reynolds number is kept below 2300 and eddies do not appear in the current, it can be
assumed that laminar flow is maintained in the device. Such a parameter must be
analyzed by the finite element method.
ity of
is me
stresses throughout the volume of the scaffold under consideration.
Future bioreactors must be compared by their relative levels of perfusion
throughout the volume of the scaffold being studied. Increased perfusion co
Bioreactor designs in the future should use FEM as a design tool. The util
th thod in tissue engineering has been adequately demonstrated in this paper through
a preliminary design. The purpose of this study was to demonstrate key parameters for
bioreactors and introduce a new method for bioreactor design. With these goals in mind,
the design was a success.
123
Closing Remarks:
The field of skeletal tissue engineering is interdisciplinary in nature. This study
ion of tissue engineering,
umero
ing laws have not yet been confirmed. With so
any p
t method was introduced as a novel technique for tissue
s were successfully analyzed.
Additionally, various bioreactor geometries were considered. As a result, key properties
required for bioreactor optimization were determined. It was determined that FEM would
be best-suited as a preliminary mechanism to be coupled with tissue engineering studies.
alone involved skills from cell biology, bioengineering, computer science, and
biochemistry. Such a diverse field requires numerous approaches, and a new method has
been introduced here. Furthermore, the changing landscape of tissue engineering is
dependent upon legislation over cell line restrictions, support through funding sources,
and the capability of in vivo studies. Through an explorat
n us abilities and limitations present in the field have hopefully been illuminated.
Taking a reductionist approach to bioreactor design, individual properties have
been analyzed in lieu of the design of an entire system. Both two-dimensional and three-
dimensional biomaterials were characterized. Biological responses on these materials
were then analyzed and compared. The field of biomaterials is yet another discipline to
be added to the list, one whose govern
m ossible biological responses to materials, a myriad of assays and microscopic
techniques was required. In the end, only the cellular response could be analyzed. This
provided an optimal set of materials with specific parameters upon which cells will
proliferate and differentiate preferentially.
The finite elemen
engineering design purposes. Two-dimensional flow profile
124
As a result, a new approach to tissue engineering is proposed. This process is illustrated
Figure 51. An iterative design process for design of “in vitro” bioreactors, including a
As depicted in Figure 51, the process will begin the computational modeling of
in silico to a bioreactor during fabrication. As before,
stem cells will be harvested and cultured in the in vitro bioreactor. After the study is
These will then be modeled by FEM once again for re-optimization, and the process will
This study was thus successful in demonstrating the complete process as depicted
in Figure 51. All of the specific aims set forth in the Introduction have been
in Figure 51.
Preliminary
Modeling (FEM, in silico)
Computational
Bioreactor
vitro)
Assessment of
or FailureBioreactor Success Fabrication (in
preliminary computational modeling step.
some bioreactor or specific properties to be assessed in a bioreactor. The optimal design
as determined will then be applied
Cell Culture in Stem Cell Bioreactor (in vitro) Harvesting (in vivo)
complete, data will be analyzed to determine successes and/or failures in the design.
continue. Such an approach deviates slightly from the traditional approach to skeletal
tissue engineering.
125
accomplished, and this study has thus been a success. The field of tissue engineering is a
vast terrain waiting to be explored. These pages have only delved into the outer perimeter
of the field, hopefully whetting one’s appetite for further exploration. It is the hope of this
investigator that such exploration will not only be considered but also pursued.
126
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131
APPENDIX A
ACKNOWLEDGMENTS
• Dr. Henry Donahue - I began working with Dr. Donahue in 2007, and I am very grateful for all he has provided me as I completed this thesis. Previous work in his lab led to the insights in oscillating fluid flow that became the cornerstone of this thesis. Without Dr.
• Donahue, this thesis would not be possible. Dr. Peter Butler – My work with Dr. Butler spanned two summers of the Biomaterials and Bionanotechnology Summer Institute (BBSI) and two years in the Department of Bioengineering. He has provided me with training in COMSOL for the finite element analyses in this thesis, and I cannot thank him enough for all he has done. Dr. Jung Yul Lim• – I worked with Dr. Lim under the guidance of Dr. Donahue to develop the nanoscale substrates in this thesis. Training me at first with a high level of guidance and later without, he was instrumental in the development of my work in cell culture and polymer science.
• Dianne McDonald – Mrs. McDonald was the acting administrator of the BBSI program, and I worked very closely with her to develop myself during those two summers.
• Drs. Yue Zhang and Christopher Niyibizi, Jacqueline Yanoso – These two brilliant investigators and graduate student assisted me in the flow cytometry studies of stem cells on 2D substrates.
Govey• Dr. Ryan Riddle, Amanda Taylor, Peter – These students, among others in the d me heavily in my studies.
• Dr. William HancockDepartment of Musculoskeletal Sciences, assiste
– Dr. Hancock provided insights into writing techniques and presentations necessary for the completion and defense of this thesis.
• Dr. Margaret Slattery – Dr. Slattery was instrumental in gin the Department of Bioengineering.
uiding me during my education
• Carol Boring – Without Carol, I would never have graduated in time, and this thesis would not be complete.
• Bioengineering Faculty – All of the bioengineering faculty provided me with the skills necessary to complete this work. Dr. Keefe Manning provided a strong foundation in biofluid mechanics, Dr. Andrew Webb provided a background in statistics, Dr. Ryan Clement granted me training in MATLAB, and all of the other faculty/staff should be acknowledged equally.
• SURIP, Step-Up, BBSI Students – These students, some of whom will one day be colleagues, motivated me and kept me sane when experiments failed. They deserve more credit than these lines deserve.
• Students of Bioengineering – My fellow students in Bioengineering at Penn State assisted me in statistical analyses and revising this work. They were also integral in providing positive feedback throughout the years.
• My Family – This is self-explanatory, but my family provided the most support, a level of support that I find to be a diamond in the rough.
• All other acquaintances – Those that I met along the way, Students with whom I interacted, Friends I have made – All of them deserve my eternal thanks for both this thesis and a wonderful college experience.
132
APPENDIX B
HEALTH INSURANCE PORTABILITY AND ACCOUNTABILITY ACT (HIPAA)
All materials and information contained in this thesis are believed to be accurate and
nd distributed without alteration.
under
ials should consult professional legal counsel.
reliable; however, the Schreyer Honors College, the Department of Bioengineering, and The Pennsylvania State University assume no responsibility for the use of the materials and information.
Unless otherwise noted on an individual document, the Schreyer Honors College grants permission to copy and distribute files, documents, and information for non-commercial use provided they are copied a
All human subjects and cell lines have been approved by the IRB at Penn Statecompliance with HIPAA.
Parties using these mater
Please , 2002. All materials dated prior to August 14, 2002 should be reviewed in conjunction with the
note: The Final HIPAA Privacy Rule was published in August 14
Final Privacy Rule published in the federal register on August 14, 2002.
133
APPENDIX C
FUNDING SOURCES
hese studies have been funded jointly by the National Science Foundation (NSF) and the National Institutes of Health (NIH). The grants established the BBSI, and research
• NSF
T
funds from the BBSI grants were used in the completion of these studies
: EEC-0234026 • NIH: AG13087
Additionally, funding has been provided from the following sources for travel and
• Department of Bioengineering
research:
• Schreyer Honors College • The Pennsylvania State University • Pennsylvania Tobacco Fund
134
APPENDIX D
SUPPLEMENTAL SKETCHES
Figure A1. Anatomy of the long bone [82].
135
Figure A2. Pathways for stem cell harvesting and differentiation [83].
136
APPENDIX E
COMMON GROWTH FACTORS
Factor Class/Family Known Types/Examples Applications
BMP1, BMP2, BMP3, BMP4, Bone Morphogenic Proteins
(BMPs) BMP5, BMP6, BMP7, BMP8a, Formation of bone and cartilage
BMP8b, BMP10, BMP15 Epidermal Growth Factor
(EGF) EGF, HB-EGF, Epigen
Regulation of cell growth, proliferation, and differentiation
Erythropoietin (EPO) EPO, Epogen, Betapoietin Control of erythropoeisis
Fibroblast Growth Factor (FGF)
FGF1-10, FHF1-4 Angiogenesis, wound healing,
embryonic development
Granulocyte-Colony Stimulating Factor (G-CSF)
Stimulation of bone marrow to GCSF/CSF3 produce granulocytes and stem
cells Granulocyte-Macrophage Colony Stimulating Factor
(GM-CSF) Same as above Same as above
Growth Differentiation Factor 9 (GDF9)
Development of the primary GDF9
follicles in the ovary Hepatocyte Growth Factor
(HGF) HGF/SF
Regulation of cell growth, cell motility and morphogenesis
Insulin-Like Growth Factor (IGF)
IGF1R, IGF2R, IGF-1, IGF-2, Communication with physiologic IGFP1-6 environment
Myostatin (GDF-8) GDF-8 Limit of muscle tissue growth
Nerve Growth Factor (NGF) Differentiation and survival of
NGF, Neutrotrophins target neurons
Platelet-Derived Growth Factor (PDGF)
PDGFA, PDGFB, PDGFC, PDGFD, PDGFAB
Cell growth and division, Angiogenesis
Thrombopoeitin (TPO) Production of platelets by the
TPO/THPO bone marrow
Transforming Growth Factor Alpha (TGF-α)
TGF-α Epithelial development, Neural
cell proliferation, Upregulated in cancer
Transforming Growth Factor Beta (TGF-β)
Proliferation, Cellular Differentiation, Immunity,
TGF-β Cancer, Heart Disease, Diabetes,
Marfan Syndrome
Vascular Endothelial Growth Factor (VEGF)
VEGF-A, VEGF-B, VEGF-C, VEGF-D, PIGF
Angiogenesis, Vasculogenesis, Vasodilation, Lymphangiogenesis,
Inflammation, Wound healing, Cancer
137
APPENDIX F
COMSOL MODEL REPORTS
COMSOL Model Report – Cell Height Study
1 ents odel Rep
• Table of Contents
• Constants
• Ge
• Postprocessing •
2. Model Properties Property Value
. Table of Cont• Title - COMSOL M ort
• Model Properties
• Geometry om1
• Solver Settings
Variables
Model name Author Company Department Reference URL Saved date Jun 19, 2008 2:00:43 PM C 20reation date Jun 12, 08 10:36:24 AMCOMS OMSOL 3.4.0OL version C .248
File name: G:\COMSOL\1.mph
138
Application modes and modules :
• Geom1 (2Do Incoo Plane Stress (Structural Mechanics Module)
Name Expression Value Description
used in this model
) mpressible Navier-Stokes
3. Constants
w 2*pi[rad/s] frequency Patm 0[Pa] k 40[Pa/m]
4. Geometry Number of geometries: 1
4.1. Geom1
139
4.1.1. Point mode
140
4.1.2. Boundary mode
141
4.1.3. Subdomain mode
5. Geom1 Space dimensions: 2D
Independent variables: x, y, z
5.1. Mesh 5.1.1. Mesh Statistics
Number of degrees of freedom 3584
Number of mesh points 224 Number of elements 393 Triangular 393 Quadrilateral 0 Number of boundary elements 53 Number of vertex elements 7 Minimum element quality 0.751Element area ratio 0.027
142
5.2. Application Mode: Incompressible Navier-)
mpressible Navier-Stokes
ion Mode Properties
Property Value
Stokes (nsApplication mode type: Inco
Application mode name: ns
5.2.1. Applicat
Default element type Lagrange - P2 P1
Analysis type Transient Corner smoothing Off Frame Fram f) e (reWeak constraints Off Constraint type Ideal
143
5.2.2. Variables
Dependent variables: u, v, p, nxw, nyw
Shape functions: shlag(2,'u'), shlag(2,'v'), shlag(1,'p')
Interior boundaries not active
5.2.3. Boundary Settings
Boundary 1 2, 4, 6-7 3 Type Inlet Wall Wallintype p uv uv walltype noslip noslip slipPressure (p0) Pa 0.5*k*cos(w*t)+Patm 0 0 Boundary 5 Type Outlet intype uv walltype noslip Pressure (p0) Pa -0.5*k*cos(w*t)+Patm
5.2.4. Subdomain Settings
Subdomain 1 Integration order (gporder) 4 4 2Constraint order (cporder) 2 2 1
5.3. Application Mode: Plane Stress (smps) tural Mechanics Module)
mode nam s
e Unit Description
Application mode type: Plane Stress (Struc
Application e: smp
5.3.1. Scalar Variables
Name Variable Valut_old_ini t_old_ini_sm Initial condition previous time step (contact
with dynamic friction) ps -1 s
144
5.3.2. Application Mode Properties
Property Value Default element type Lagrange - QuadraticAnalysis type Static Large deformation On Specify eigenvalues using Eigenfrequency Create frame On Deform frame Frame (deform) Frame Frame (ref) Weak constrai s Off ntConstraint typ Ideal e
5.3.3. Variables
Dependent variables: u2, v2, p2
functions: shlag(2,'u2'), shlag(2,'v2')
2 6-7 1, 5
Shape
Interior boundaries not active
5.3.4. Boundary Settings
Boundary -4 Follower pressure (P) Pa 0 p 0 loadcond distr_force follower_press distr_force constrcond free free fixed
5.3.5. Subdomain Settings
The subdomain settings only contain default values.
6. Solver Settings Solve using a script: off
Analysis type TransientAuto select solver On Solver Time dependentSolution form Automatic Symmetric Off Adaption Off
145
6.1. Direct (PARDISO)
Solver type: Linear system
Va
solver
Parameter lue Preordering algorithm Nested dissectionRow preordering On Pivoting perturbation 1.0E-8 Relative tolerance 1.0E-6 Factor in error estimate 400.0 Check tolerances On
6.2. Time Stepping Value Parameter
Times 0:0.1:3 Relative tolerance 0.01 Absolute tolerance 0.0010 Times to store in output Specified times Time steps taken by solver Free Manual tuning of step size Off Initial time step E-6 1Maximum time step 1.0 Maximum BDF order 5 Singular mass matrix Maybe Consistent initialization of DAE systems ackward EuB ler Error estimation strategy Exclude algebraicAllow complex numbers Off
6.3. Advanced Parameter Value Constraint handling method EliminationNull-space function AutomaticAssembly block siz 1000 e Use Hermitian transpose of constraint matrix and in symmetry
n Off
detectioUse complex funct al input Off ions with reStop if error due to efined operation On undStore solution on f Off ile
146
Type of scaling AutomaticManual scaling Row equilibration On Manual control of reassembly Off Load constant On Constraint constant On Mass constant On Damping (mass) consta On nt Jacobian constant On Constraint Jacobian constant On
7. Postprocessing
147
8. Variables
ion Unit Expression
8.1. Point Name DescriptFxg_smps Point load in global x dir. N 0 Fyg_smps Point load in global y dir. N 0 disp_smps Total displacement m sqrt(real(u2)^2+real(v2)^2)
8.2. Boundary 8.2.1. Boundary 1-5
Name Description Unit Expression K_x_ns Viscous force per
area, x component
Pa eta_ns * (2 * nx_ns * ux+ny_ns * (uy+vx))
T_x_ns Total force per area, x component
Pa -nx_ns * p+2 * nx_ns * eta_ns * ux+ny_ns * eta_ns * (uy+vx)
K_y_ns Viscous force per area, y component
Pa eta_ns * (nx_ns * (vx+uy)+2 * ny_ns * vy)
T_y_ns Total force per area, y component
Pa -ny_ns * p+nx_ns * eta_ns * (vx+uy)+2 * ny_ns * eta_ns * vy
Fxg_smps Edge load in global x-dir.
N/m 0
Fyg_smps Edge load in global y-dir.
N/m 0
disp_smps Total displacement
m sqrt(real(u2)^2+real(v2)^2)
Tax_smps Surface traction (force/area) in x dir.
Pa (F11_smps * Sx_smps+F12_smps * Sxy_smps) * nx_smps+(F11_smps * Sxy_smps+F12_smps * Sy_smps) * ny_smps
Tay_smps Surface traction Pa (F21_smps * Sx_smps+F22_smps * (force/area) in y dir.
Sxy_smps) * nx_smps+(F21_smps * Sxy_smps+F22_smps * Sy_smps) * ny_smps
148
8.2.2. Boundary 6-7
ription Unit Expression Name DescK_x_ns Viscous force per
area, x Pa eta_ns * (2 * nx_ns * ux+ny_ns * (uy+vx))
component T_x_ns Total force per Pa -
area, x ecomponent
nx_ns p+2 * nx_ns * eta_ns * ux+ny_ns * ns (uy+vx)
* ta_ *
K_y_ns Viscous force per Pa eta_ns * (nx_ns * (vx+uy)+2 * ny_ns * vy) area, y component
T_y_ns Total force pearea, y
r
component
Pa -ny_ns * p+nx_ns * eta_ns * (vx+uy)+2 * ny_ns * eta_ns * vy
Fxg_smps P_smps * dvol_deform * Edge load in global x-dir.
N/m -nx2_smps * (1+wz_smps) * thickness_smps/dvol
Fyg_smps N/m -ny2_smps * P_smps * dvol_deform * Edge load inglobal y-dir. (1+wz_smps) * thickness_smps/dvol
disp_smps t
Total displacemen
m sqrt(real(u2)^2+real(v2)^2)
Tax_smps
Sxy_smps+F12_smps * Sy_smps) * ny_smps
Surface traction (force/area) in x dir.
Pa (F11_smps * Sx_smps+F12_smps * Sxy_smps) * nx_smps+(F11_smps *
Tay_smps s+(F21_smps *
_smps+F22_smps * Sy_smps) * _smps
Surface traction(force/area) in y dir.
Pa (F21_smps * Sx_smps+F22_smps * Sxy_smps) * nx_smpSxyny
8.3. Subdomain Unit Name Description Expression
U_ns Velocity field m/s sqrt(u^2+v^2) V_ns Vorticity 1/s vx-uy divU_ns Divergence of
velocity field 1/s ux+vy
cellRe_ns Cell Reynolds number
1 rho_ns * U_ns * h/eta_ns
res_u_ns Equation residual for u
N/m^3 _x_ns-s * (2 * uxx+uyy+vxy)
rho_ns * (ut+u * ux+v * uy)+px-Feta_n
res_sc_u_ns Shock capturing
N/m^3 rho_ns * (ut+u * ux+v * uy)+px-F_x_ns
149
residual for u res_v_ns Equation
v N/m^3 rho_ns * (vt+u * vx+v * vy)+py-F_y_ns-
(vxx+uyx+2 * vyy) residual for eta_ns *res_sc_v_n
ing r v
3 s Shock capturresidual fo
N/m^ rho_ns * (vt+u * vx+v * vy)+py-F_y_ns
beta_x_ns Convective
t
k ^field, xcomponen
g/(m 2*s) rho_ns * u
beta_y_ns
t
^Convective field, ycomponen
kg/(m 2*s) rho_ns * v
Dm_ns Mean diffusiocoefficient
n
Pa*s eta_ns
da_ns Total time scale factor
k 3g/m^ rho_ns
taum_ns GLS time-scale
mh)))
^3*s/kg nojac(min(timestep/rho_ns,0.5 * h/max(rho_ns * U_ns,6 * eta_ns/
tauc_ns GLSscale
time- m^2/s in(1,rho_ns * U_ns * h/eta_ns)) nojac(0.5 * U_ns * h * m
Fxg_smps Body load in global x-dir.
N 2/m^ 0
Fyg_smps dy load in global y-dir.
N/m^2Bo 0
disp_smps Total displacement
m sqrt(real(u2)^2+real(v2)^2)
sx_smps sx normal stress global
Pa smps+Sxy_smps *
F12_smps)+F12_smps * (Sxy_smps * F11_smps+Sy_smps * F12_smps))/J_smps
(F11_smps * (Sx_smps * F11_
sys.
sy_smps (Sx_smps * y_smps * 2_smps * (Sxy_smps *
ps+Sy_smps * ps))/J_smps
sy normal stress global sys.
Pa (F21_smps * F21_smps+Sx
ps)+F2F22_smF21_smF22_sm
sxy_smps sxy shear stress global sys.
Pa (F11_smps * (Sx_smps * F21_smps+Sxy_smps * F22_smps)+F12_smps * (Sxy_smps * F21_smps+Sy_smps * F22_smps))/J_smps
ex_smps ex normstrain glob
al al
1 u2x+0.5 * (u2x^2+v2x^2)
150
sys. ey_smps ey normal
strain global
sys.
1 v2y+0.5 * (u2y^2+v2y^2)
ez_smps 1 -nu_smps * (ex_smps/((1+nu_smps) * (1-2 *
ey_smps/((1+nu_smps) * (1-2 * nu_smps))) * (1+nu_smps) * (1-2 * nu_smps)/(1-nu_smps)
ez normal strain
nu_smps))+
exy_smps exy shear strain glsys.
obal 2x+u2x * u2y+v2x * v2y) 1 0.5 * (u2y+v
Sx_smps ond * ((1-nu_smps) * ex_smps/((1+nu_smps) * (1-2 * nu_smps))+nu_smps *
s/((1+nu_smps) * (1-2 *
Sx SecPiola-Kirchhoff global sys.
Pa E_smps
ey_smpnu_smps))+nu_smps * ez_smps/((1+nu_smps) * (1-2 * nu_smps)))
Sy_smps
mps) * _smps/((1+nu_smps) * (1-2 *
nu_smps))+nu_smps * _smps/((1+nu_smps) * (1-2 *
nu_smps)))
Sy SecondPiola-Kirchhoff global sys.
Pa E_smps * (nu_smps * ex_smps/((1+nu_smps) * (1-2 * nu_smps))+(1-nu_sey
ez
Sz_smps Sz SePiola-
cond
Kirchhoff global sys.
Pa 0
Sxy_smps Sxy econd Piola-Kirchhoff
Pa S
global sys.
E_smps * exy_smps/(1+nu_smps)
wz_smps tive of
out-of-plane displacement
1 sqrt(1+2 * Out of plane deriva
if(1+2 * ez_smps<0,-1,-1+ez_smps))
K_smps Bulk modulus s)) Pa E_smps/(3 * (1-2 * nu_smpG_smps
lus Pa Shear
modu0.5 * E_smps/(1+nu_smps)
mises_smps von Mises Pa sqrt(sx_smps^2+sy_smps^2-sx_smps * ) stress sy_smps+3 * sxy_smps^2
Ws_smps Strain energy ^2 _smps * J/m 0.5 * thickness_smps * (ex
151
density sx_smps+ey_smps * sy_smps+2 * exy_smps * sxy_smps)
evol_smps 1 -1+Jel_smps Volumetric strainF11_smps Deformation 1 1+u2x
gradient 11 comp.
F12_smps Deformation gradient 12 comp.
1 u2y
F21_smps Deformation 1 gradient 21 comp.
v2x
F22_smps Deformation nt 22
1 1+v2y gradiecomp.
F33_smps Deformation 1 gradient 33 comp.
1+wz_smps
detF_smps Determinadeformation gradient
1 12_smps nt of F33_smps * (F11_smps * F22_smps-F* F21_smps)
J_smps Volume ratio 1 detF_smps Jel_smps Elastic volume
ratio 1 J_smps
invF11_smps
comp.
1 ps Inverse of deformation gradient 11
F22_smps * F33_smps/detF_sm
invF12_smps Inverse of 1 deformation gradient 12 comp.
-F12_smps * F33_smps/detF_smps
invF21_smps 1 -F21_smps * F33_smps/detF_smps Inverse of deformation gradient 21 comp.
invF22_smps Inverse
1 F11_smps * F33_smps/detF_smps of deformationgradient 22 comp.
invF33_smps tF_smps
Inverse of deformation gradient 33 comp.
1 (F11_smps * F22_smps-F21_smps * F12_smps)/de
sz_smps sz normal stress s. global sy
Pa 0
tresca_smps s s2_smps),abs(s2_smps-
Tresca stres Pa max(max(abs(s1_smps-
s3_smps)),abs(s1_smps-s3_smps))
152
COMSOL el Report – C
1. Table of Contents e - ode eport
• Table of Contents el
• Geome• Geom1
olverstpr
• Variab
2. Model Properties
Mod ell Confluence Study
• Titl COMSOL M l R
• Mod Properties try
• S Settings • Po ocessing
les
Property ValueModel name Author Company Department Reference URL Saved date 2008 2:06:39 PMJun 6,Creation date un 6, 2008 1:31:37 PM JCOMSOL ver OL .0.248 sion COMS 3.4
File name: G:\COMSOL\10%-Confluency.mph
Application modes and modules used in this model:
• Geom1 (2D) o Plane Strain (Structural Meo Incompressible Navier-Stokes
chanics Module)
153
3. Geometry Number of geometries: 1
3.1. Geom1
154
3.1.1. Point mode
155
3.1.2. Boundary mode
156
3.1.3. Subdomain mode
4. Geom1 Space dimensions: 2D
Independent variables: x, y, z
4.1. Mesh 4.1.1. Mesh Statistics
Number of degrees of freedom 28861
Number of mesh points 1757 Number of elements 3263 Triangular 3263 Quadrilateral 0 Number of boundary elements 249 Number of vertex elements 28 Minimum element quality 0.691Element area ratio 0
157
4.2. Application Mode: Plane Strain (smpn) type: Plane Strain (Structural Mechanics Module)
: smpn
Value Unit Description
Application mode
Application mode name
4.2.1. Scalar Variables
Name Variablet_old_ini t_old_ini_smpn -1 s Initial condition previous time step (contact
with dynamic friction)
4.2.2. Application Mode Properties
Property Value Default element type ange - QuadraticLagrAnalysis type tatic SLarge deformation On Specify eigenvalues using nfrequency EigeCreate frame Off
158
Deform frame Frame (ref) Frame Frame (ref) Weak constraints Off Constraint type Ideal
4.2.3. Variables
Dependent variables: u2, v2, p2
Shape functions: shlag(2,'u2'), shlag(2,'v2')
Interior boundaries not active
4.2.4. Subdomain Settings
Subdomain 1name Solid domain
4.3. Application Mode: Incompressible Navier-Stokes (ns) Application mode type: Incompressible Navier-Stokes
Application mode name: ns
4.3.1. Application Mode Properties
Property Value Default element type Lagrange - P2 P1
Analysis type Stationary Corner s Off moothing Frame Frame (ref) Weak constraints Off Constraint type Ideal
4.3.2. Variables
u, v,
lag(2,'u lag(2,'v'), shlag(1,'p')
Dependent variables: p, nxw, nyw
Shape functions: sh '), sh
Interior boundaries not active
159
4.3.3. Boundary Settin
1 2-11, 13-28 12
gs
Boundary Type Inlet Wall Open boundaryNormal inflow velocity (U0in) m/s 0.38095238 1 1
4.3.4. Subdomain Settings
Subdomain 1 Integration order (gporder) 4 4 2Constraint order (cporder) 2 2 1
5. Solver Settings Solve using a script: off
is type Analys Static Auto select solver On Solver StationarySolution form AutomaticSymmetric auto Adaption Off
5.1. Direct (PARDISO) Solver type: Linear system solver
Parameter Value Preordering algorithm issection Nested dRow preordering On Pivoting perturbation 1.0E-8 Relative tolerance 1.0E-6 Factor in error estima .0 te 400Check tolerances On
160
5.2. Stationary Parameter Value Linearity utomaA ticRelative tolerance 1.0E-6 Maximum number of iterations 25 Manual tuning of damping parameters Off Highly nonlinear problem On Initial damping factor 1.0 Minimum damping factor 1.0E-4 Restriction for step size upd 10.0 ate
5.3. Advanced Parameter Value Constraint handlin d Eliminationg methoNull-space function AutomaticAssembly block siz 1000 e Use Hermitian tran onstraint matrix and in symmetry Off spose of cdetection Use complex funct ith real input Off ions wStop if error due to undefined operation On Store solution on file Off Type of scaling None Manual scaling Row equilibration On Manual control of reasse Off mbly Load constant On Constraint constant On Mass constant On Damping (mass) consta On nt Jacobian constant On Constraint Jacobian con t On stan
161
6. Postprocessing
s
ion Unit Expression
7. Variable
7.1. Point Name DescriptFxg_smpn Point load in global x dir. N 0 Fyg_smpn Point load in global y dir. N 0 disp_smpn Total displacement m sqrt(real(u2)^2+real(v2)^2)
7.2. Boundary Name Description Unit Expression Fxg_smpn Edge load in
global x-dir. N/m 0
Fyg_smpn Edge load in global y-dir.
N/m 0
162
disp_smpn Total displacement
m sqrt(real(u2)^2+real(v2)^2)
Tax_smpn Surface traction (force/area) in x dir.
Pa (F11_smpn * Sx_smpn+F12_smpn * Sxy_smpn) * nx_smpn+(F11_smpn * Sxy_smpn+F12_smpn * Sy_smpn) * ny_smpn
Tay_smpn Surface traction (force/area) in y dir.
Pa (F21_smpn * Sx_smpn+F22_smpn * Sxy_smpn) * nx_smpn+(F21_smpn * Sxy_smpn+F22_smpn * Sy_smpn) * ny_smpn
K_x_ns Viscous force per area, x component
Pa eta_ns * (2 * nx_ns * ux+ny_ns * (uy+vx))
T_x_ns Total force per area, x component
Pa -nx_ns * p+2 * nx_ns * eta_ns * ux+ny_ns * eta_ns * (uy+vx)
K_y_ns Viscous force per area, y component
Pa eta_ns * (nx_ns * (vx+uy)+2 * ny_ns * vy)
T_y_ns Total force per area, y component
Pa -ny_ns * p+nx_ns * eta_ns * (vx+uy)+2 * ny_ns * eta_ns * vy
7.3. Subdomain iption Unit Expression Name Descr
Fxg_smpn Body load in bal x-dir.
N/m^2 0 glo
Fyg_smpn Body load in global y-dir.
N/m^2 0
disp_smpn m sqrt(real(u2)^2+real(v2)^2) Total displacement
sx_smpn sx normal Pa stress global
FF11_smpn+Sxy_smpn * F12_smpn)+F12_smpn * (Sxy_smpn * F11_smpn+Sy_smpn * F12_smpn))/J_smpn
( 11_smpn * (Sx_smpn *
sys.
sy_smpn l
Pa n * (Sx_smpn * F21_smpn+Sxy_smpn * F22_smpn)+F22_smpn * (Sxy_smpn * F21_smpn+Sy_smpn * F22_smpn))/J_smpn
sy normal stress globasys.
(F21_smp
sz_smpn sz normal Pa Sz_smpn * F33_smpn^2/J_smpn
163
stresys.
ss global
sxy_smpn sxy shear stress global sy
P
s.
a
pn * mpn+Sy_smpn *
(F11_smpn * (Sx_smpn * F21_smpn+Sxy_smpn * F22_smpn)+F12_smpn * (Sxy_smF21_sF22_smpn))/J_smpn
ex_smpn rain global
sys.
ex normal st
1 u2x+0.5 * (u2x^2+v2x^2)
ey_smpn global
ey normal strainsys.
1 v2y+0.5 * (u2y^2+v2y^2)
exy_smpn global
1 exy shear strainsys.
0.5 * (u2y+v2x+u2x * u2y+v2x * v2y)
Sx_smpn ex_smpn/((1+nu_smpn) * (1-2 * nu_smpn))+nu_smpn *
Sx Second Piola-Kirchhoff
Pa
global sys.
E_smpn * ((1-nu_smpn) *
ey_smpn/((1+nu_smpn) * (1-2 * nu_smpn)))
Sy_smpn d Piola-
Pa E_smpn * (nu_smpn * ex_smpn/((1+nu_smpn) * (1-2 * nu_smpn))+(1-nu_smpn) * ey_smpn/((1+nu_smpn) * (1-2 *
Sy Secon
Kirchhoff global sys.
nu_smpn))) Sz_smpn Sz Second
Piola-Kirchhoff global sys.
Pa E_smpn * nu_smpn * _smpn/((1+nu_smpn) * (1-2 *
nu_smpn))+ey_smpn/((1+nu_smpn) * (1- nu_smpn)))
(ex
2 *Sxy_smpn
obal sys.
Pa E_smpn * exy_smpn/(1+nu_smpn) Sxy Second Piola-Kirchhoff gl
K_smpn Bulk modulus
Pa E_smpn/(3 * (1-2 * nu_smpn))
G_smpn Shear modulus
Pa 0.5 * E_smpn/(1+nu_smpn)
mises_smpn von Mises stress
Pa sqrt(sx_smpn^2+sy_smpn^2+sz_smpn^2-sx_smpn * sy_smpn-sy_ssz_smpn-sx_smpn * sz_smpn+3 * sxy_smpn^2)
mpn *
Ws_smpn Strain energy
J/m^2 ex_smpn * sy_smpn+2 *
0.5 * thickness_smpn * (sx_smpn+ey_smpn *
164
density exy_smpn * sxy_smpn) evol_smpn Volumetric 1 -1+Jel_smpn
strain ez_smpn
global sys.
1 ez normal strain
0
F11_smpn Deformation
1 gradient 11comp.
1+u2x
F12_smpn Deformation
1 u2y gradient 12comp.
F21_smpn Deformation
1 v2x gradient 21comp.
F22_smpn Deformation
1 1+v2y gradient 22 comp.
F33_smpn Deformation
comp.
1 gradient 33
1+ez_smpn
detF_smpn
mpn-Determinantof deformationgradient
1 F33_smpn * (F11_smpn * F22_sF12_smpn * F21_smpn)
J_smpn Volume ratio 1 detF_smpn Jel_smpn Elastic
volume ratio1 J_smpn
invF11_smp 1 n
Inverse of deformation gradient 11 comp.
F22_smpn * F33_smpn/detF_smpn
invF12_smp
2
1 -F12_smpn * F33_smpn/detF_smpn n
Inverse of ationdeform
gradient 1comp.
invF21_smp
_smpn n
Inverse ofdeformationgradient 21comp.
1 -F21_smpn * F33_smpn/detF
invF22_smp Inverse of
t 22
1 n deformation
gradiencomp.
F11_smpn * F33_smpn/detF_smpn
165
invF33_smp f
t 33
1 F21_smpn * tF_smpn n
Inverse odeformationgradiencomp.
(F11_smpn * F22_smpn-F12_smpn)/de
tresca_smpn
Pa max(max(abs(s1_smpn-s2_smpn),abs(s2_smpn-
n)),abs(s1_smpn-s3_smpn))
Tresca stress
s3_smpU_ns Velocity m/s sqrt(u^2+v^2) fieldV_ns Vorticity 1/s vx-uy divU_ns Divergence
of velocity field
1/s y ux+v
cellRe_ns Cell Reynolds number
ns * U_ns * h/eta_ns 1 rho_
res_u_ns Equation residual for u
N/m^3 * (u * ux+v * uy)+px-F_x_ns-eta_ns * (2 * uxx+uyy+vxy) rho_ns
res_sc_u_ns Shock N/m^3 rho_ns * (u * ux+v * uy)+px-F_x_ns capturing residual for u
res_v_ns Equation N/m^3 rho_ns * (u * vx+v * vy)+py-F_y_ns-residual for v eta_ns * (vxx+uyx+2 * vyy)
res_sc_v_ns Shock
or v
N/m^3 y-F_y_ns capturing residual f
rho_ns * (u * vx+v * vy)+p
beta_x_ns /(m^2*sConvective field, x component
kg)
rho_ns * u
beta_y_ns Convectivefield, y component
/(m^2*s) kg rho_ns * v
Dm_ns Mean Pa*s eta_ns diffusion coefficient
da_ns Total ctor
kg/m^3 rho_ns time scale fa
taum_ns GLS time-scale
m^3*s/kg eta_ns/h)) nojac(0.5 * h/max(rho_ns * U_ns,6 *
tauc_ns m^2/s nojac(0.5 * U_ns * h * min(1,rho_ns * U_ns * h/eta_ns))
GLS time-scale
166
COMSOL R ort –
1. Table of Contents • Title - COMSOL Model Report • Table of Contents
el • Consta
• Geom1• Solver
tpro• Variabl
2. Model Properties
Model ep Young’s Modulus Study
• Mod Properties nts
• Geometry Settings
• Pos cessing es
Property Value Model name Author Company Department Reference URL Saved date 008 1:32:46 PM Jul 9, 2Creation date , 2 6:2Jun 12 008 10:3 4 AMCOMSOL ver L 3.4.0.248 sion COMSO
File name: G:\COMSOL\11 nm.mph
Application m d modules used in
• Geom1 (2D)
o Plane Stress (Structural Mechanics Module)
odes an this model:
o Incompressible Navier-Stokes
167
3. Constants Name Expression Value Descriptionw 2*pi[rad/s] frequency Patm 0[Pa] k 40[Pa/m]
4. Geometry Number of geometries: 1
4.1. Geom1
168
4.1.1. Point mode
169
4.1.2. Boundary mode
170
4.1.3. Subdomain mode
5. Geom1 Space dimensions: 2D
Independent variables: x, y, z
5.1. Mesh 5.1.1. Mesh Statistics
Number of degrees of freedom 2451
Number of mesh points 155 Number of elements 265 Triangular 265 Quadrilateral 0 Number of boundary elements 43 Number of vertex elements 7 Minimum element quality 0.741Element area ratio 0.077
171
5.2. Application Mode: Incompressible Navier-)
mpressible Navier-Stokes
ion Mode Properties
Property Value
Stokes (nsApplication mode type: Inco
Application mode name: ns
5.2.1. Applicat
Default element type Lagrange - P2 P1
Analysis type Transient Corner smoothing Off Frame Fram f) e (reWeak constraints Off Constraint type Ideal
172
5.2.2. Variables
Dependent variables: u, v, p, nxw, nyw
Shape functions: shlag(2,'u'), shlag(2,'v'), shlag(1,'p')
Interior boundaries not active
5.2.3. Boundary Settings
Boundary 1 2, 4, 6-7 3 Type Inlet Wall Wallintype p uv uv walltype noslip noslip slipPressure (p0) Pa 0.5*k*cos(w*t)+Patm 0 0 Boundary 5 Type Outlet intype uv walltype noslip Pressure (p0) Pa -0.5*k*cos(w*t)+Patm
5.2.4. Subdomain Settings
Subdomain 1 Integration order (gporder) 4 4 2Constraint order (cporder) 2 2 1
5.3. Application Mode: Plane Stress (smps) tural Mechanics Module)
mode nam s
e Unit Description
Application mode type: Plane Stress (Struc
Application e: smp
5.3.1. Scalar Variables
Name Variable Valut_old_ini t_old_ini_sm Initial condition previous time step (contact
with dynamic friction) ps -1 s
5.3.2. Application Mode Properties
Property Value
173
Default element type Lagrange - QuadraticAnalysis type Static Large deformation On Specify eigenvalues using Eigenfrequency Create frame On Deform frame Frame (deform) Frame Frame (ref) Weak constraints Off Constraint type Ideal
5.3.3. Variab s
nt variables: u2, v2, p2
r bound e tive
und r ngs
Boundary 2-4 6-7 1, 5
le
Depende
Shape functions: shlag(2,'u2'), shlag(2,'v2')
Interio ari s not ac
5.3.4. Bo a y Setti
Follower pressure (P) Pa 0 p 0 loadcond distr_force follower_press distr_force constrcond free free fixed
5.3.5. Subdomain Settings
Subdomain 1 Young's modulus (E) Pa 9000
6. Solver Settings
Analysis type Transient
Solve using a script: off
Auto sele On ct solver Solver Time depend tenSolution form Automatic Symmetric Off Adaption Off
174
175
6.1. Direct (PARDISO) Solver type: Linear system solver
Parameter Value Preordering algorithm Nested dissectionRow preordering On Pivoting perturbation 1.0E-8 Relative tolerance 1.0E-6 Factor in error estimate 400.0 Check tolerances On
6.2. Time Stepping Parameter Value Times 0:0.1:3 Relative tolerance 0.01 Absolute tolerance 0.0010 Times to store in output Specified times Time steps taken by solver Free Manual tuning of step size Off Initial time step 1E-6 Maximum time step 1.0 Maximum BDF order 5 Singular mass matrix Maybe Consistent initialization of DAE systems Backward Euler Error estimation strategy Exclude algebraicAllow complex numbers Off
6.3. Advanced Parameter Value Constraint handling method EliminationNull-space function AutomaticAssembly block size 1000 Use Hermitian transpose of constraint matrix and in symmetry detection
Off
Use complex functions with real input Off Stop if error due to undefined operation On Store solution on file Off
176
Type of scaling AutomaticManual scaling Row equilibration On Manual control of reassembly Off Load constant On Constraint constant On Mass constant On Damping (mass) consta On nt Jacobian constant On Constraint Jacobian constant On
7. Postprocessing
177
8. Variables
ion Unit Expression
8.1. Point Name DescriptFxg_smps Point load in global x dir. N 0 Fyg_smps Point load in global y dir. N 0 disp_smps Total displacement m sqrt(real(u2)^2+real(v2)^2)
8.2. Boundary 8.2.1. Boundary 1-5
Name Description Unit Expression K_x_ns Viscous force per
area, x component
Pa eta_ns * (2 * nx_ns * ux+ny_ns * (uy+vx))
T_x_ns Total force per area, x component
Pa -nx_ns * p+2 * nx_ns * eta_ns * ux+ny_ns * eta_ns * (uy+vx)
K_y_ns Viscous force per area, y component
Pa eta_ns * (nx_ns * (vx+uy)+2 * ny_ns * vy)
T_y_ns Total force per area, y component
Pa -ny_ns * p+nx_ns * eta_ns * (vx+uy)+2 * ny_ns * eta_ns * vy
Fxg_smps Edge load in global x-dir.
N/m 0
Fyg_smps Edge load in global y-dir.
N/m 0
disp_smps Total displacement
m sqrt(real(u2)^2+real(v2)^2)
Tax_smps Surface traction (force/area) in x dir.
Pa (F11_smps * Sx_smps+F12_smps * Sxy_smps) * nx_smps+(F11_smps * Sxy_smps+F12_smps * Sy_smps) * ny_smps
Tay_smps Surface traction Pa (F21_smps * Sx_smps+F22_smps * (force/area) in y dir.
Sxy_smps) * nx_smps+(F21_smps * Sxy_smps+F22_smps * Sy_smps) * ny_smps
178
8.2.2. Boundary 6-7
ription Unit Expression Name DescK_x_ns Viscous force per
area, x Pa eta_ns * (2 * nx_ns * ux+ny_ns * (uy+vx))
component T_x_ns Total force per Pa -
area, x ecomponent
nx_ns p+2 * nx_ns * eta_ns * ux+ny_ns * ns (uy+vx)
* ta_ *
K_y_ns Viscous force per Pa eta_ns * (nx_ns * (vx+uy)+2 * ny_ns * vy) area, y component
T_y_ns Total force pearea, y
r
component
Pa -ny_ns * p+nx_ns * eta_ns * (vx+uy)+2 * ny_ns * eta_ns * vy
Fxg_smps P_smps * dvol_deform * Edge load in global x-dir.
N/m -nx2_smps * (1+wz_smps) * thickness_smps/dvol
Fyg_smps N/m -ny2_smps * P_smps * dvol_deform * Edge load inglobal y-dir. (1+wz_smps) * thickness_smps/dvol
disp_smps t
Total displacemen
m sqrt(real(u2)^2+real(v2)^2)
Tax_smps
Sxy_smps+F12_smps * Sy_smps) * ny_smps
Surface traction (force/area) in x dir.
Pa (F11_smps * Sx_smps+F12_smps * Sxy_smps) * nx_smps+(F11_smps *
Tay_smps s+(F21_smps *
_smps+F22_smps * Sy_smps) * _smps
Surface traction(force/area) in y dir.
Pa (F21_smps * Sx_smps+F22_smps * Sxy_smps) * nx_smpSxyny
8.3. Subdomain Unit Name Description Expression
U_ns Velocity field m/s sqrt(u^2+v^2) V_ns Vorticity 1/s vx-uy divU_ns Divergence of
velocity field 1/s ux+vy
cellRe_ns Cell Reynolds number
1 rho_ns * U_ns * h/eta_ns
res_u_ns Equation residual for u
N/m^3 _x_ns-s * (2 * uxx+uyy+vxy)
rho_ns * (ut+u * ux+v * uy)+px-Feta_n
res_sc_u_ns Shock capturing
N/m^3 rho_ns * (ut+u * ux+v * uy)+px-F_x_ns
179
residual for u res_v_ns Equation
v N/m^3 rho_ns * (vt+u * vx+v * vy)+py-F_y_ns-
(vxx+uyx+2 * vyy) residual for eta_ns *res_sc_v_n
ing r v
3 s s Shock capturresidual fo
N/m^ rho_ns * (vt+u * vx+v * vy)+py-F_y_n
beta_x_ns Convective
t
kfield, xcomponen
g/(m^2*s) rho_ns * u
beta_y_ns
t
Convective field, ycomponen
kg/(m^2*s) rho_ns * v
Dm_ns Mean diffusioncoeffic
ient
P a*s eta_ns
da_ns Total
kg/m^3 rho_ns time scale factor
taum_ns m^3*s/kg nojac(min(timestep/rho_ns,0.5 )))
GLS time-scale
* h/max(rho_ns * U_ns,6 * eta_ns/h
tauc_ns e
m^2/s ns * GLS time-scal
nojac(0.5 * U_ns * h * min(1,rho_U_ns * h/eta_ns))
Fxg_smps N/m^2 0 Body load inglobal x-dir.
Fyg_smps bal y-dir.
N/m^2Body load in glo
0
disp_smps Total displacement
m sqrt(real(u2)^2+real(v2)^2)
sx_smps ess global
sys.
Pa
smps)+F12_smps * (Sxy_smps * F11_smps+Sy_smps * F12_smps))/J_smps
sx normal str
(F11_smps * (Sx_smps * F11_smps+Sxy_smps * F12_
sy_smps sy normal Pa (F21_smps * (Sx_smps * xy_smps *
2_smps * (Sxy_smps *
ps))/J_smps
stress global sys.
F21_smps+SF22_smps)+F2
ps+Sy_smps * F21_smF22_sm
sxy_smps ps * (Sx_smps *
y_smps * F21_smps+Sy_smps *
sxy shear stressglobal sys.
Pa (F11_smF21_smps+Sxy_smps * F22_smps)+F12_smps * (Sx
F22_smps))/J_smps ex_smps
s. 1 ex normal strain
global syu2x+0.5 * (u2x^2+v2x^2)
ey_smps train 1 v2y+0.5 * (u2y^2+v2y^2) ey normal s
180
global sys. ez_smps ez normal strain
smps) * (1-2 1 -nu_smps * (ex_smps/((1+nu_smps) * (1-2
* nu_smps))+ey_smps/((1+nu_* nu_smps))) * (1+nu_smps) * (1-2 * nu_smps)/(1-nu_smps)
exy_smps 1 0.5 * (u2y+v2x+u2x * u2y+v2x * v2y) exy shear strainglobal sys.
Sx_smps Sx Second Piola-Kirchhoff global sys.
Pa E_smps * ((1-nu_smps) * ex_smps/((1+nu_smps) * (1-2 * nu_smps))+nu_smps *
+nu_smps) * (1-2 * nu_smps))+nu_smps * ez_smps/((1+nu_smps) * (1-2 * nu_smps)))
ey_smps/((1
Sy_smps * (nu_smps * +nu_smps) * (1-2 *
/((1+nu_smps) * (1-2 * nu_smps))+nu_smps *
mps)))
Sy Second Piola-Kirchhoff global sys.
Pa E_smps ex_smps/((1nu_smps))+(1-nu_smps) * ey_smps
ez_smps/((1+nu_smps) * (1-2 * nu_sSz_smps Sz ond
off Pa Sec
Piola-Kirchhglobal sys.
0
Sxy_smps Sxy Second Piola-Kirchhoffglobal sys.
smps * exy_smps/(1+nu_smps) Pa E_
wz_smps Out of plane derivative of out-of-displacement
plane
+2 * ez_smps<0,-1,-1+sqrt(1+2 * ez_smps))
1 if(1
K_smps Bulk modulus ) Pa E_smps/(3 * (1-2 * nu_smps)G_smps Pa Shear modulus 0.5 * E_smps/(1+nu_smps)mises_smps ises
stress Pa
) von M sqrt(sx_smps^2+sy_smps^2-sx_smps *
sy_smps+3 * sxy_smps^2Ws_smps Strain energy J/m^2 (ex_smps *
density 0.5 * thickness_smps * sx_smps+ey_smps * sy_smps+2 * exy_smps * sxy_smps)
evol_smps Volumetric
1 strain
-1+Jel_smps
F11_smps Deformation 1 gradient 11 comp.
1+u2x
F12_smps Deformation gradient 12 comp.
1 u2y
F21_smps Deformation gradient 21 comp.
1 v2x
F22_smps Deformation 1 1+v2y
181
gradient 22 comp.
F33_smps Deformation gradient 33 comp.
1 1+wz_smps
detF_smps F12_smps * F21_smps)
Determinant of deformationgradient
1 F33_smps * (F11_smps * F22_smps-
J_smps 1 Volume ratio detF_smps Jel_smps Elastic e
ratio 1 volum J_smps
invF11_smps Inverse of deformation
1
gradient 11 comp.
F22_smps * F33_smps/detF_smps
invF12_smps deformation gradient 12 comp.
1 ps Inverse of -F12_smps * F33_smps/detF_sm
invF21_smps 1_smps * F33_smps/detF_smps Inverse of deformation gradient 21 comp.
1 -F2
invF22_smps
1 F11_smps * F33_smps/detF_smps Inverse of deformationgradient 22 comp.
invF33_smps 1 (F11_smps * F22_smps-F21_smps * F12_smps)/detF_smps
Inverse of deformation gradient 33 comp.
sz_smps sz normal sglobal s
tress ys.
Pa 0
tresca_smps
-s3_smps))
Tresca stress Pa max(max(abs(s1_smps-s2_smps),abs(s2_smps-s3_smps)),abs(s1_smps
182
COMSOL Model Report – Bioreactor Design
1. Table of Contents
• Model • Consta
• Geom2• Materials/Coefficients Library
• Postpr• Variab
rtieProperty lue
• Title - COMSOL Model Report • Table of Contents
Properties nts
• Geome• Geom1
try
• Solver Settings ocessing les
2. Model PropeVa
s
Model name Author Company Department Reference URL Saved date Jun 24, 2008 2:22:41 PMCreation date Jun 9, 2008 1:27:09 PM COMSOL version COMSOL 3.4.0.248
File name: G:\COMSOL\Bioreactor-2D-BD.mph
183
Application modes and modules used in this model:
• Geom1 (Axial symmetry (2D)) o Axial Symmetry, Stress-Strain (Structural Mechanics Module) o Incompressible Navier-Stokes (Chemical Engineering Module)
• Geom2 (3D)
3. Constants Name Expression Value DescriptionT 273[K] temperature
4. Geometry Number of geometries: 2
4.1. Geom1
184
4.1.1. Point mode
185
4.1.2. Boundary mode
186
4.1.3. Subdomain mode
187
4.2. Geom2
188
4.2.1. Point mode
189
4.2.2. Edge mode
190
4.2.3. Boundary mode
191
4.2.4. Subdomain mode
5. Geom1 Space dimensions: Axial symmetry (2D)
Independent variables: R, PHI, Z
5.1. Mesh 5.1.1. Mesh Statistics
Number of degrees of freedom 3498
Number of mesh points 230 Number of elements 358 Triangular 358 Quadrilateral 0 Number of boundary elements 127 Number of vertex elements 20 Minimum element quality 0.646Element area ratio 0.02
192
5.2. Application Mode: Axial Symmetry, Stress-axi)
ariables
alue Unit Description
Strain (smApplication mode type: Axial Symmetry, Stress-Strain (Structural Mechanics Module)
Application mode name: smaxi
5.2.1. Scalar V
Name Variable Vt_old_ini t_old_ini_smaxi -1 s Initial condition previous time step (contact
with dynamic friction)
193
5.2.2. Application Mode Properties
Property Value Default element type Lagrange - QuadraticAnalysis type Static Large deformation On Specify eigenvalues using Eigenfrequency Create frame Off Deform frame Frame (ref) Frame Frame (ref) Weak constraints Off Constraint type Ideal
5.2.3. Variables
Dependent variables: uor, w, p
Shape functions: shlag(2,'uor'), shlag(2,'w')
Interior boundaries active
5.2.4. Boundary Settings
25 13 Boundary 4, 6, 8, 12, 14, 16- 1, 3, 5, 7, 9, 11, 2, 15
2Edge load (force/area) Z-dir. N/m(Fz)
0 0 0
constrcond free sym fixedBoundary 10 Edge load (force/area) Z-dir. (Fz 2) N/m p4 constrcond free
5.2.5. S in Set
, 5
ubdoma tings
Subdomain 1-2 -6 3 4 Young's modulus (E) Pa 1e9[Pa]
(Polyethylene) (Polyethylene) 2.4e9 1e9[Pa]
Density (rho) kg/m3 930[kg/m^3] 930[kg/m^3] ylene)
1190[kg/m^3](Polyethylene) (Polyeth
Thermal expansion 1/K 150e-6[1/K] 150e-6[1coeff. (alpha) (Polyethylene)
/K] (Polyethylene)
70e-6[1/K]
Poisson's ratio (nu) 1 0.33 0.40 0.40
194
5.3. Application Mode: Incompressible Navier- (chns)
: Inc okes (Chemical Engineering
ation Mod s
e
StokesApplication moModule)
de type ompressible Navier-St
Application mode name: chns
5.3.1. Applic e Propertie
Property ValuDefault element type ge - P2 P1LagranAnalysis type Stationary Corner smoothing Off Weakly compressible flow Off Turbulence model None Realizability Off Non-Newtonian flow Off Brinkman on by default Off Two-phase flow Single-phase flowSwirl velocity Off Frame Frame (ref) Weak constraints Off Constraint type Ideal
5.3.2. Variables
variables: u4, v4, w2, , lo logd2, logw2, phi2, nrw2, nzw2
y S ttings
7, 9,
Dependent p4 gk2,
Shape functions: shlag(2,'u4'), shlag(2,'v4'), shlag(1,'p4')
Interior boundaries not active
5.3.3. Boundar e
Boundary 1, 3, 5, 11, 13 2 15Type Symmetry b boundoundary Open ary Inlet Normal inflow velocity (U0 0.03in) m/s 1 1 Volume per time uni ) t (V0 m3/s 0 0 0.016 flowtype velocity volumevelocityBoundary 16-23, 25
195
Type Wall Normal inflow velocity (U0in) m/s 1 Volume per time unit (V0) m3/s 0 flowtype velocity
5.3.4. Subdomain Settings
Subdomain 1-3, 5-6 4 Integration order (gporder) 4 4 2 4 4 2 Constraint order (cporder) 2 2 1 2 2 1
3Density (rho) kg/m 1040 1040 Dynamic viscosity (eta) Pa s 0.00078 0.00078 Porosity (epsilonp) 1 1 0.119375Permeability (k) 2m 1 0.119375Flow in porous media (Brinkman equations) 0 1 (brinkmaneqns)
6. Geom2 Space dimensions: 3D
dent variables: x, y
stics
Indepen , z
6.1. Mesh 6.1.1. Mesh Stati
Number of degrees of freedom 3498Number of mesh points 2010Number of elements 7709Tetrahedral 7709Prism 0 Hexahedral 0 Number of boundary elements 3066Triangular 3066Quadrilateral 0 Number of edge elements 544 Number of vertex elements 56 Minimum element quality 0.279Element volume ratio 0.008
196
7. Materials/Coefficients Library
7.1. PMMA Parameter Value Heat capacity at constant pressure (C) 1420[J/(kg*K)]Young's modulus (E) 3e9[Pa] Thermal expansion coeff. (alph 70e-6[1/K] a) Relative permittivity (epsilonr) 3.0 Thermal conductivity (k) 0.19[W/(m*K)]Poisson's ratio (nu) 0.40 Density (rho) 1190[kg/m^3]
7.2. Polyethylene Value Parameter
Heat capacity at constant pressure (C) 1900[J/(kg*K)]Young's modulus (E) 1e9[Pa]
197
Thermal expansion coeff. (alpha) 150e-6[1/K] Relative permittivity (epsilonr) 2.3 Thermal conductivity (k) 0.38[W/(m*K)]Density (rho) 930[kg/m^3]
7.3. Ethanol, liquid Parameter Value Heat capacity at constant pressure (C) Cp(T[1/K])[J/(kg*K)]Dynamic viscosity (eta) eta(T[1/K])[Pa*s] Thermal conductivity (k) k(T[1/K])[W/(m*K)] Kinematic viscosity (nu0) nu0(T[1/K])[m^2/s] Density (rho) rho(T[1/K])[kg/m^3]
7.3.1. Functions
Function Expression Derivatives Complex output
nu0(T) (10^(1.16E-05*T^2-1.54e-2*T+0.608))/(-1.426e-3*T^2-0.1167*T+948.62)
diff((10^(1.16E-05*T^2-1.54e-2*T+0.608))/(-1.426e-3*T^2-0.1167*T+948.62),T)
false
Cp(T) 20.7*T-3840 diff(20.7*T-3840,T) false rho(T) -1.426e-3*T^2- diff(-1.426e-3*
0.1167*T+948.62 T^2-
0.1167*T+948.62,T) false
eta(T) 10^(1.162*T+0.6
E-05*T^2-1.54e-08)
diff(10^(1.16E-05*T^2-1.54e-2*T+0.608),T)
false
k(T) -1.03e-3*T+0.4848 d 3e-3*T+0.4848,T) false iff(-1.0
8. Solver Settings Solve using a script: off
Analysis type Static Auto select solver On Solver StationarySolution form AutomaticSymmetric auto Adaption Off
198
8.1. Direct (UMFPACK)
solver
Parameter Value
Solver type: Linear system
Pivot threshold 0.1 Memory allocation factor 0.7
8.2. Stationary Parameter Value Linearity AutomaticRelative tolerance 1.0E-6 Maximum number of iterations 25 Manual tuning of damping parameters Off Highly nonlinear problem Off Initial damping factor 1.0 Minimum damping factor 1.0E-4 Restriction for step size update 10.0
8.3. AdParamete Value
vanced r
Constraint imhandling method El inationNull-space Automatic function Assembly b 100lock size 0 Use Hermitian transpose of constraint matrix and in symmetry detection Off Use complex functions with real input Off Stop if error due to undefined operation On Store solution on file Off Type of scaling None Manual scaling Row equilibration On Manual control of reassembly Off Load constant On Constraint constant On Mass constant On Damping (mass) con t On stanJacobian constant On Constraint Jacobian constant On
199
9. Postprocessing
200
10. Variables
10.1. Point Name Description Unit Expression FRg_smaxi Point load in global R dir. N 0 FZg_smaxi Point load in global Z dir. N 0 disp_smaxi Total displacement m sqrt(real(uaxi_smaxi)^2+real(w)^2)uaxi_smaxi R-displacement m uor * R uaxiR_smaxi R derivative of R-
displacement 1 uorR * R+uor
uaxiZ_smaxi Z derivative of R displacement
1 uorZ * R
uaxi_t_smaxi R-velocity m/s diff(uaxi_smaxi,t)
201
10.2. Boundary 10.2.1. Boundary 1-9, 11-25
Name Description Unit Expression FRg_smaxi Edge load in
global R-dir. N/m^2 0
FZg_smaxi Edge load in global Z-dir.
N/m^2 0
disp_smaxi Total displacement
m sqrt(real(uaxi_smaxi)^2+real(w)^2)
uaxi_smaxi R-displacement
m uor * R
uaxiR_smaxi R derivative of R-displacement
1 uorR * R+uor
uaxiZ_smaxi Z derivative of R displacement
1 uorZ * R
uaxi_t_smaxi R-velocity m/s diff(uaxi_smaxi,t) TaR_smaxi Surface
traction (force/area) in
Pa (F11_smaxi * SR_smaxi+F13_smaxi * SRZ_smaxi) * nR_smaxi+(F11_smaxi * SRZ_smaxi+F13_smaxi * SZ_smaxi) * nZ_smaxi R dir.
TaZ_smaxi Surface traction
e/area) in .
Pa (F31_smaxi * SR_smaxi+F33_smaxi * SRZ_smaxi) * nR_smaxi+(F31_smaxi * SRZ_smaxi+F33_smaxi * SZ_smaxi) * nZ_smaxi
(forcZ dir
K_R_chns Pa eta_chns * (2 * nR_chns * u4R+nZ_chns * Viscous forceper area, R component
(u4Z+v4R))
T_R_chns Total force per Pa -nRarea, R component
_chnu4R Z_
s * p4+2 * nR_chns * eta_chns * chns * eta_chns * (u4Z+v4R) +n
K_Z_chns Viscous force per area, Z
P
component
a eta_chns * (nR_chns * (v4R+u4Z)+2 * nZ_chns * v4Z)
T_Z_chns
component
Pa -nZ_chns * p4+nR_chns * eta_chns * (v4R+u4Z)+2 * nZ_chns * eta_chns * v4Z
Total force perarea, Z
202
10.2.2. Boundary 10
Name Description Unit Expression FRg_smaxi Edge load in N/m^2
global R-dir. 0
FZg_smaxi Edge load in global Z-dir.
N/m^2 FZ_smaxi
disp_smaxi Total displacement
rt(real(uaxi_smaxi)^2+real(w)^2) m sq
uaxi_smaxi R-displacement
m uor * R
uaxiR_smaxi erivative of +uor R dR-displacement
1 uorR * R
uaxiZ_smaxi Z derivative of R displacement
1 uorZ * R
uaxi_t_smaxi R-velocity m/s maxi,t) diff(uaxi_sTaR_smaxi
) in
Pa (F11_smaxi * SR_smaxi+F13_smaxi * smaxi+(F11_smaxi *
Surface traction
a(force/areR dir.
SRZ_smaxi) * nR_SRZ_smaxi+F13_smaxi * SZ_smaxi) * nZ_smaxi
TaZ_smaxi
a) in
Pa Surface traction (force/areZ dir.
(F31_smaxi * SR_smaxi+F33_smaxi * SRZ_smaxi) * nR_smaxi+(F31_smaxi * SRZ_smaxi+F33_smaxi * SZ_smaxi) * nZ_smaxi
K_R_chns Pa * Viscous force per area, R component
eta_chns * (2 * nR_chns * u4R+nZ_chns(u4Z+v4R))
T_R_chns Total force perarea, R
component
Pa -nR_chns * p4+2 * nR_chns * eta_chns * u4R+nZ_chns * eta_chns * (u4Z+v4R)
K_Z_chns Viscous force per area, Z component
Pa eta_chns * (nR_chns * (v4R+u4Z)+2 * nZ_chns * v4Z)
T_Z_chns Total force perarea, Z
component
Pa -nZ_chns * p4+nR_chns * eta_chns * (v4R+u4Z)+2 * nZ_chns * eta_chns * v4Z
203
10.3. Subdomain UName Descriptio
n nit Expression
FRg_smaxi Body load in global R-dir.
N/m^3 0
FZg_smaxi Bodin global Z-
y load
ir.
N ^3
d
/m 0
disp_smaxi
t
m sqrt(real(uaxi_smaxi)^2+real(w)^2) Total displacemen
uaxi_smaxi m uor * R R-displacement
uaxiR_smaxi R derivative
eme
1of R-displacnt
uorR * R+uor
uaxiZ_smaxi Z rivative
eme
1 deof R displacnt
uorZ * R
uaxi_t_smaxi R-velocity m/s axi,t) diff(uaxi_smsR_smaxi sR normal
stress global sys.
PSRZ_smaxi *
F13_smaxi)+F13_smaxi * (SRZ_smaxi *
a (F11_smaxi * (SR_smaxi * F11_smaxi+
F11_smaxi+SZ_smaxi * F13_smaxi))/J_smaxi
sZ_smaxi
.
Pa (F31_smaxi * (SR_smaxi *
_smaxi * (SRZ_smaxi * F31_smaxi+SZ_smaxi *
sZ normalstress global sys
F31_smaxi+SRZ_smaxi * F33_smaxi)+F33
F33_smaxi))/J_smaxi sPHI_smaxi sPHI
stress
Pa normal
SPHI_smaxi * F22_smaxi^2/J_smaxi
sRZ_smaxi sRZ shear stress
Pa (F11_smaxi * (SR_smaxi * F31_smaxi+SRZ_smaxi *
_smaxi * (SRZ_smaxi * smaxi *
global sys. F33_smaxi)+F13F31_smaxi+SZ_F33_smaxi))/J_smaxi
eR_smaxi eR normal 1 uorR * R+uor+0.5 * ((uorR *
204
strain globalsys.
R+uor)^2+wR^2)
eZ_smaxi l
rZ * R)^2+wZ^2) eZ normal strain globasys.
1 wZ+0.5 * ((uo
ePHI_smaxi ePHI normal strain
1 uor+0.5 * uor^2
eRZ_smaxi eRZ shear strain global
uorR * R+uor) * uorZ * R+wR * wZ)
sys.
1 0.5 * (uorZ * R+wR+(
SR_smaxi SR Second Piola-Kirglobal sys.
chhoff eR_smaxi/((1+nu_smaxi) * (1-2 *
xi))+nu_smaxi * axi/((1+nu_smaxi) * (1-2 *
nu_smaxi))+nu_smaxi *
Pa E_smaxi * ((1-nu_smaxi) *
nu_smaePHI_sm
eZ_smaxi/((1+nu_smaxi) * (1-2 * nu_smaxi)))
SZ_smaxi Pa E_smaxi * (nu_smaxi * eR_smaxi/((1+nu_smaxi) * (1-2 *
xi/((1+nu_smaxi) * (1-2 * nu_smaxi))+(1-nu_smaxi) * eZ_smaxi/((1+nu_smaxi) * (1-2 * nu_smaxi)))
SZ Second Piola-Kirchhoff global sys.
nu_smaxi))+nu_smaxi * ePHI_sma
SPHI_smaxi SPHI Second Piola-Kirchhoff
Pa E_smaxi * (nu_smaxi * 1-2 *
xi) * (1-2 *
eR_smaxi/((1+nu_smaxi) * (nu_smaxi))+(1-nu_smaxi) *ePHI_smaxi/((1+nu_smaxi) * (1-2 * nu_smaxi))+nu_smaxi * eZ_smaxi/((1+nu_smanu_smaxi)))
SRZ_smaxi SRZ
Piola-Kirchhoff
sys.
Pa u_smaxi) Second
global
E_smaxi * eRZ_smaxi/(1+n
K_smaxi Bulk s
Pa E_smaxi/(3 * (1-2 * nu_smaxi)) modulu
G_smaxi Shear modulus
) Pa 0.5 * E_smaxi/(1+nu_smaxi
mises_smaxi stress
Pa xxi-sPHI_smaxi *
sZ_smaxi+3 *
von Mises sqrt(sR_smaxi^2+sPHI_smaxi^2+sZ_smai^2-sR_smaxi * sPHI_smasZ_smaxi-sR_smaxi * sRZ_smaxi^2)
205
Ws_smaxi y
J/m^3 sR_smaxi+ePHI_smaxi * sPHI_smaxi+eZ_smaxi * sZ_smaxi+2 *
Strain energdensity
0.5 * (eR_smaxi *
eRZ_smaxi * sRZ_smaxi) evol_smaxi Volumetric
1 -1+Jel_smaxi
strainF11_smaxi Deform
gradientcomp.
ation 11
1 1+uaxiR_smaxi
F13_smaxi Deformationgradient 13 comp
.
1 uaxiZ_smaxi
F22_smaxi Deformationgradiecomp.
nt 22
1 1+uor
F31_smaxi Deformation gradient 31 comp.
1 wR
F33_smaxi Deformation
1 gradient 33 comp.
1+wZ
detF_smaxi Determinant
deformation gradient
1 xi-of
F22_smaxi * (F11_smaxi * F33_smaF13_smaxi * F31_smaxi)
J_smaxi Volume ratio
1 detF_smaxi
Jel_smaxi Elastic tio
1 volume ra
J_smaxi
invF11_smaxi Inverse deformation gradient 11
.
1 of
comp
F22_smaxi * F33_smaxi/detF_smaxi
invF13_smaxi Inverse tion
3
of deformagradient 1comp.
1 -F13_smaxi * F22_smaxi/detF_smaxi
invF22_smaxi Inverse of n 2
maxi * deformatio
t 2gradiencomp.
1 (F11_smaxi * F33_smaxi-F31_sF13_smaxi)/detF_smaxi
invF31_smaxi
t 31 comp.
Inverse of deformationgradien
1 -F31_smaxi * F22_smaxi/detF_smaxi
206
invF33_smaxi Inverse of tion 33
deformagradientcomp.
1 F11_smaxi * F22_smaxi/detF_smaxi
tresca_smaxi Tresca Pa max(max(abs(s1_smaxi-_smaxi-
s3_smaxi)),abs(s1_smaxi-s3_smaxi)) stress s2_smaxi),abs(s2
U_chns m/s sqrt(u4^2+v4^2) Velocityfield
V_chns Vorticity 1/s u4Z-v4R divU_chns Divergence 1/s u4R+v4Z+u4/R
of velocity field
cellRe_chns Cell 1 rho_chns * U_chns * h/eta_chns Reynolds number
res_u4_chns Equation Pa R * (rho_chns * (u4 * u4R+v4 * u4Z)+p4R-ns)+2 * eta_chns * (u4/R-u4R)-
eta_chns * R * (2 * u4RR+u4ZZ+v4RZ) residual for u4
F_r_ch
res_sc_u4_ch
idual for
Pa R * (rho_chns * (u4 * u4R+v4 * u4Z)+p4R-ns
Shock capturing resu4
F_r_chns)+2 * eta_chns * (u4/R-u4R)
res_v4_chns Equation for
Pa R * (rho_chns * (u4 * v4R+v4 * v4Z)+p4Z-ta_chns * (R *
(v4RR+u4ZR)+2 * R * v4ZZ+u4Z+v4R) residual v4
F_z_chns)-e
res_sc_v4_chns hns * (u4 * v4R+v4 * v4Z)+p4Z-F_z_chns)
Shock capturing residual for v4
Pa R * (rho_c
beta_R_chns Convective Pa*s R * rho_chns * u4 field, R component
beta_Z_chns Convective field, Z component
Pa*s R * rho_chns * v4
Dm_chns Mean kg/s R * eta_chns diffusion coefficient
da_chns Total ctor
kg/m^2 R * rho_chns time scale fa
taum_chns GLS time-scale
m^3*s/kg eta_chns/h))
nojac(0.5 * h/max(rho_chns * U_chns,6 *
tauc_chns m^2/s nojac(0.5 * U_chns * h * min(1,rho_chns * U_chns * h/eta_chns))
GLS time-scale
207
APPE
NDIX G
Schreyer Honors College A DE
dem ta o alvi
CA MIC VITA
Aca ic Vi f Joshua Damian S
ical InfBiograph ormation Name: Joshua Salvi
601 King n Roa
5
Damian
Address: York,
3PA
sto17402
d
E-Mail ID:
jds519
Education Major: eering, opHonors: eering
ove sign iation of H ls
Thesis Advisors: Henry J. Donahue (er J. B (Uni
Honors Advisor: O. Hancock
Work Experienc
BioenginBioengin
tion in Chemical Engineering
Thesis Title: The NDifferent
l De of a Bioreactor for in vitro Proliferation and uman Mesenchymal Stem CelHershey, PA)
Pet
William
utler versity Park, PA)
e
08/2007-05/2009 a art ering aduate Researcher
at ul es at University Park rviso er J.
5/2009 ta e
t ohe D ion;
teer iso y
Penn StUndergr
vestig
te Dep ment of Bioengine
InSupe
or in mr: Pet
tiple laboratori Butler
05/2007-0
Penn SInvestiga
c
te Collegor and V
of Medicine lunteer
ResearVolun
d in the ed in the
epartment of Orthopaedics and RehabilitatHershey Medical Center
Superv r: Henr J. Donahue
208
01/2006-05/2009 Penn State SI Leader, T Assisted students in CHEM 110(12), BIOE 201, PHYS 211, and
MATH Superv wsky, William Hancock 07/2002-05/2005 Circuit City Stores, Inc. S t
F hnology repair visor: Varied
Learning Center utor, Teaching Assistant
140 isor: Janice Smith, Herbert Lipo
ales Counselor, Customer Service Assistanocused on sales in home electronics and tec
Super Awards and Leadership Academic Awards: Bioengineering Student M John W. White Graduate
arshal Fellowship
Moffitt Scholarship in Engineering Presidential Volunteer Service Award America’s Scholar of Promise Award
wards:
eadership:
tary
Evan Pugh Scholar, Junior and Senior Awards Vaun A. Other A Eagle Scout Memberships: Tau Beta Pi Sigma Xi Golden Key International Honour Society
Biomedical Engineering Society (BMES) L
BMES Chapter President Debate Team Captain
Student Council Secre Research Publications: Jung Yul Lim, Joshua D. Salvi, Ryan C. Riddle, Henry J.
ent s in Cell Culture.
Conferences: ture on specific
for subpopulations of stem cells
Donahue. Nanotopography regulation of stem cell mechanosensitivity.
Joshua D. Salvi, Jung Yul Lim, Henry J. Donahue. Finite Elem
Analyses of Fluid Flow Condition
Joshua D. Salvi, Jung Yul Lim, Yue Zhang, Jacqueline Yanoso, Donahue, CulChristopher Niyibizi, Henry J.
nanoscale topographies selects
209
210
tial. 55th Orthopaedic Research Las Vegas, Nevada, USA.
specific nanoscale topographies selects for subpopulations of stem enic potential. 2008 Biomedical
8, St. Louis, MO,
Jung Yul Lim, Joshua D. Salvi, Ryan C. Riddle, Henry J. Donahue, Nanoscale substrate topography regulates stem cell
anosensitivity. 54th Orthopaedic Research Society (ORS), #22, March 2-5, 2008, San Francisco, CA, USA.
y J. Donahue, Substrate s to fluid flow.
), September 26-29,
with increased osteogenic potenSociety (ORS), February 22-25, 2009,
Joshua D. Salvi, Jung Yul Lim, Henry J. Donahue, Culture on
cells with increased osteogEngineering Society (BMES) October 2-4, 200USA.
mech
Joshua D. Salvi, Jung Yul Lim, Henr
nanotopography affects stem cell responsivenes2007 Biomedical Engineering Society (BMES2007, Los Angeles, CA, USA.
Extracurricular Involvement Department: Bioengineering Curriculum Committee
Representative
ommunity Service: Circle K International
PA
ills
Biomedical Engineering Society Faculty Senate Liaison C Shaver’s Creek Volunteer Boy Scouts of America High School Tutor in York, Related Sk
MATLAB
ab Techniques:
Fluorescence Microscopy, Confocal Microscopy
Distillation, Organic Synthesis
Programming: C++/C#
JavaScript, HTML
L Cell Culture, Light Microscopy
Atomic Force Microscopy, Electron Microscopy Fluorescence-Activated Cell Sorting, Cytometry
AP Assays, Western Blot, PCR Polymer Demixing