fluid flow effects on nanoparticle localization in
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University of Calgary
PRISM: University of Calgary's Digital Repository
Graduate Studies The Vault: Electronic Theses and Dissertations
2017
Fluid flow effects on nanoparticle localization in
zebrafish vessels and cultured human endothelial
cells
Gomez, Maria Juliana
Gomez, M. J. (2017). Fluid flow effects on nanoparticle localization in zebrafish vessels and
cultured human endothelial cells (Unpublished master's thesis). University of Calgary, Calgary,
AB. doi:10.11575/PRISM/26195
http://hdl.handle.net/11023/3572
master thesis
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UNIVERSITY OF CALGARY
Fluid Flow Effects on Nanoparticle Localization in Zebrafish Vessels and Cultured Human
Endothelial Cells
by
Maria Juliana Gomez
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFULMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
GRADUATE PROGRAM IN BIOMEDICAL ENGINEERING
CALGARY, ALBERTA
JANUARY 2017
© Maria Juliana Gomez 2017
i
Abstract
Assessment of nanoparticle distribution in the vasculature is important for determining drug
delivery, molecular imaging efficacy, and risk profiles. Even though most medical nanoparticle
applications require a vascular administration, factors affecting nanoparticle association with
vessel walls in the presence of fluid forces are poorly understood. We evaluated the effect of fluid
flow on the distribution of 200 nm carboxylate-coated polystyrene nanoparticles in flow-exposed
endothelial cell cultures and zebrafish embryos. We combined confocal imaging of nanoparticle
injected transgenic zebrafish, 3D modeling, and computational fluid dynamics to assess
nanoparticle distribution under flow. Highest nanoparticle localization occurred in regions of
disturbed flow and low shear stress found at branch points and downstream of bumps and curves
in the zebrafish vasculature. Similar findings were obtained in human endothelial cells in vitro.
Overall, fluid shear stress magnitude, flow disturbances, and flow-induced changes in endothelial
physiology contribute to the vascular localization of nanoparticles.
ii
Acknowledgments
First and foremost, I would like to thank my supervisor Dr. Kristina Rinker for giving me the
opportunity to be a part of her lab and believing in me. Tina thank you very much for your kindness
and support throughout these years.
To the members of my committee Dr. Sarah Childs, Dr. David Cramb and Dr. Elena Di Martino,
for being so approachable and generous with their knowledge and time. I can’t imagine completing
this research without your guidance, help, and support, thank you. I am especially grateful to Sarah
for all her work handling the zebrafish, as well as for teaching me how to use the confocal
microscope.
I would also like to thank Arianna Forneris for her unconditional help and generosity throughout
this project. Dr. Amber Doiron and Dr. Bahareh Vafadar for their hard work obtaining key results
that help build the story of this thesis, and Dr. Ian Gates for his input on the paper and for patiently
teaching me new CFD tricks.
I would like to thank the members of the CMBRL lab: Nick, Debbie, Ken, Chris, and Bob, for
making these years so much fun! As well as my friends in Canada who made moving to a new
country easier than planned. The greatest part of this experience was getting to know all of you.
Hagar and Linda: you are family. I feel so lucky to have such beautiful people in my life. I love
you.
A mi familia por su amor incondicional y por todo lo que soy. Todo esto es gracias a ustedes. A ti
Bellis por ser la persona más espectacular que existe, siempre serás lo mejor de mi vida. A ti Lolsi
por ser mi cómplice, cada día que pasa me siento más orgullosa de ti. A ti Nico por toda tu
paciencia y por apoyarme, porque tú siempre me apoyas. Gracias por hacerme tan feliz. Y
finalmente, a ti papi, fuiste tú quien me inculcó el amor hacia la investigación y el aprendizaje,
siempre me has motivado a ser mejor y a llegar más lejos, y es por eso que eres tú el verdadero
motivo por el cual existe esta tesis. Siempre serás mi modelo a seguir.
Los amo infinitamente.
iii
Table of contents
Abstract ............................................................................................................................................ i
Acknowledgments........................................................................................................................... ii
Table of contents ............................................................................................................................ iii
List of Tables ................................................................................................................................. vi
List of Figures ............................................................................................................................... vii
List of Appendices .......................................................................................................................... x
Abbreviations ................................................................................................................................. xi
Contributions................................................................................................................................. xii
Chapter 1: Introduction ............................................................................................................... 1
Chapter 2: Literature Review ...................................................................................................... 3
2.1. Endothelial cells ............................................................................................................... 3
2.1.1. Endothelial cell heterogeneity................................................................................... 5
2.1.2. Endothelial cell mechanotransduction ...................................................................... 8
2.2. Physiological vs. pathological vasculature..................................................................... 10
2.3. Hemodynamics ............................................................................................................... 18
2.4. Nanoparticles for biomedical applications ..................................................................... 22
2.5. Flow effects on nanoparticle localization....................................................................... 24
2.5.1. Effect of flow magnitude: shear stress, shear rate, and velocity ............................. 25
2.5.2. Effect of flow pattern: disturbed and undisturbed laminar flow ............................. 29
2.6. Zebrafish embryo model for nanoparticle research........................................................ 30
Chapter 3: Hypothesis and objectives ....................................................................................... 32
Chapter 4: Methods and Materials ........................................................................................... 34
4.1. In vivo zebrafish model .................................................................................................. 34
4.2. Calculation of blood flow in the zebrafish embryo vasculature ..................................... 35
4.3. Computational fluid dynamics of zebrafish vein ........................................................... 36
4.3.1. Pre-processing: Surface model construction and computational mesh generation . 36
4.3.2. Flow simulation in the vein segment ...................................................................... 39
4.3.3. Post-processing simulation results .......................................................................... 43
4.4. Quantification of nanoparticles in zebrafish vasculature ............................................... 44
iv
4.4.1. Quantification of nanoparticles in each wall shear stress region ............................ 45
4.4.2. Quantification of nanoparticles in each flow region ............................................... 52
4.5. In vitro cell culture ......................................................................................................... 54
4.5.1. Nanoparticle size and zeta potential measurements ................................................ 54
4.5.2. Cell culture and parallel plate flow chamber .......................................................... 55
4.5.3. Computational fluid dynamics sudden expansion flow chamber ........................... 56
4.6. Nanoparticle flow exposure assay .................................................................................. 58
4.6.1. Flow pre-conditioning of endothelial cells ............................................................. 59
4.7. In vitro image acquisition and analysis .......................................................................... 59
Chapter 5: Results....................................................................................................................... 60
5.1. Nanoparticle localization in zebrafish embryo vasculature ........................................... 60
5.2. Blood flow velocity and waveform in the zebrafish embryo ......................................... 64
5.3. Zebrafish embryo vein segment surface model construction and computational mesh
generation .................................................................................................................................. 72
5.4. Zebrafish embryo vein segment computational fluid dynamics results for steady state
simulation .................................................................................................................................. 78
5.5. Nanoparticle quantification in regions with different wall shear stresses ...................... 84
5.6. Nanoparticle quantification in regions with different dispersion factors as a measure of
flow disturbances ...................................................................................................................... 93
5.7. Nanoparticle characterization for in vitro experiments .................................................. 97
5.8. Flow profiles in the sudden expansion parallel plate flow chamber .............................. 98
5.9. Nanoparticle accumulation in endothelial cells in vitro ............................................... 100
5.10. Flow preconditioned nanoparticle accumulation in endothelial cells ...................... 103
Chapter 6: Discussion ............................................................................................................... 105
6.1. Polystyrene nanoparticle as model particles for biomedical applications .................... 105
6.2. Quantification of nanoparticle accumulation using 3D modelling .............................. 107
6.3. Blood flow velocity quantification and effect on nanoparticle accumulation on the
zebrafish embryo vasculature ................................................................................................. 108
6.4. Nanoparticle accumulation to regions of lower wall shear stress ................................ 111
6.5. Nanoparticle accumulation to regions of disturbed flow ............................................. 114
6.6. Flow pre-conditioning studies suggest cell phenotype affects nanoparticle accumulation
115
6.7. Possible blood components affecting nanoparticle localization in blood vessels ........ 116
6.8. Implications of flow effects on nanoparticle accumulation ......................................... 120
v
Chapter 7: Future work ........................................................................................................... 121
Chapter 8: Conclusion .............................................................................................................. 125
References ................................................................................................................................... 127
Appendices .................................................................................................................................. 151
vi
List of Tables
Table 1. Methods used to determine the appropriate number of bins that should be included in a
histogram to adequately represent the distribution of the data. .................................................... 49
Table 2. Blood flow velocity calculations for three different zebrafish embryos (52 hpf) obtained
from quantification of flow in the caudal artery and vein showing the average velocity during the
whole recording, the average highest velocity per cycle, and the average lowest velocity per
cycle. Measurements of the same vessel in the same fish were taken from different segments of
the same vessel. ............................................................................................................................. 70
Table 3. Mass balances of the fluid in the vessel to confirm convergence of the steady state
simulation. ..................................................................................................................................... 76
Table 4. Statistical evaluation of the correlation between nanoparticle accumulations measured
in voxel count and total fluorescence intensity and local wall shear stress in the zebrafish embryo
caudal vein. ................................................................................................................................... 93
vii
List of Figures
Figure 1. Blood vessel structure ..................................................................................................... 4
Figure 2. Endothelial cell surface in physiological and pathological conditions ......................... 13
Figure 3. Differences between physiological and abnormal tumor vasculature .......................... 15
Figure 4. Schematic of the relation between flow-induced gene expressions which affects
endothelial cell phenotype and/or vessel architecture. ................................................................. 17
Figure 5. Two-dimensional geometry of the sudden expansion flow chamber used to exposed
cultured human umbilical vein endothelial cells to flow and nanoparticle .................................. 57
Figure 6. Nanoparticle distribution in the zebrafish embryo vasculature .................................... 61
Figure 7. Higher levels of nanoparticles accumulate in the caudal vein as compared to the artery.
Single slices from confocal microscopy image of transgenic zebrafish ....................................... 62
Figure 8. Quantification of the number of nanoparticle voxels present in different regions of the
zebrafish embryo vasculature ....................................................................................................... 63
Figure 9. Line-scan particle image velocimetry to track movement of red blood cells ............... 65
Figure 10. Quantitative analysis of blood flow in the developing zebrafish vasculature ............ 66
Figure 11. Blood flow waveform in the caudal artery ................................................................. 67
Figure 12. Comparison of caudal vessels and fish-to-fish variability for anatomical and flow
characteristics found in the developing zebrafish at 52 hpf .......................................................... 71
Figure 13. 3D geometry of the zebrafish caudal vein. ................................................................. 74
Figure 14. Mesh sensitivity analysis for 14 tetrahedral meshes with a different number of mesh
elements ........................................................................................................................................ 75
Figure 15. Geometry and selected mesh for the caudal vein segment used to perform the
simulations. ................................................................................................................................... 77
viii
Figure 16. Total number of wall elements at each wall shear stress level obtained by the
simulation of the caudal vein segment .......................................................................................... 79
Figure 17. Wall shear stress contours obtained by computational fluid dynamics simulation of
the caudal vein segment in the developing zebrafish embryo modeled using a steady state
condition with laminar inlet velocity of 239 µm/s ........................................................................ 80
Figure 18. Time-average wall shear stress contours obtained by computational fluid dynamics
simulation of the caudal vein segment in the developing zebrafish embryo modeled using a
transient study with velocity waveform as an inlet simulated for one period .............................. 81
Figure 19. Velocity streamlines obtained by computational fluid dynamics simulation of the
caudal vein segment in the developing zebrafish embryo modeled using a steady state condition
with laminar inlet velocity of 239 µm/s ........................................................................................ 83
Figure 20. Quantification of the number elements in the fluid region of the caudal vein segment
in each dispersion factor interval. ................................................................................................. 84
Figure 21. Overlay of a confocal image showing blue fluorescent 200 nm carboxylate coated
polystyrene nanoparticles accumulating in the caudal vein segment of the zebrafish embryo one
hour post injection and the wall shear stress level contours ......................................................... 86
Figure 22. Comparison of the effect of number of bins in a histogram using different empirical
models for non-normal distributions. ............................................................................................ 87
Figure 23. Quantification of number of nanoparticle voxels per wall shear stress region for
steady state instantaneous wall shear stress .................................................................................. 88
Figure 24. Wall shear stress spatial gradient effect on nanoparticle distribution. ....................... 90
Figure 25. Fluorescence intensity per nanoparticle voxel.. .......................................................... 91
ix
Figure 26. Quantification of the total fluorescence intensity of the nanoparticles in each wall
shear stress region of the caudal vein segment of the embryo. ..................................................... 91
Figure 27. Nanoparticle accumulation quantified as number of nanoparticle voxels .................. 95
Figure 28.Average fluorescence intensity per voxel found in each region of flow characterized
by the dispersion factor ................................................................................................................. 96
Figure 29. Quantification of nanoparticle accumulation to regions of flow with different
dispersion factors and the corresponding wall shear stress values for each flow region. ............. 97
Figure 30. Flow circuit used to expose human umbilical vein endothelial cells to flow ............. 99
Figure 31. Velocity streamlines obtained from the computational fluid dynamics simulation of
the flow chamber in 2D............................................................................................................... 100
Figure 32. Nanoparticle association with human umbilical vein endothelial cells (HUVECs)
exposed to different levels of wall shear stress and flow patterns .............................................. 102
Figure 33. Effect of flow pre-conditioning on nanoparticle accumulation ................................ 104
Figure 34. Sensitivity analysis for the number of harmonics included in the Fourier series to
reduce the difference between the measured velocity in the vessel segment and the Fourier
approximation ............................................................................................................................. 152
Figure 35. Number of paired nanoparticle voxels to a wall shear stress value at different
combinations of tolerances in the y and z positions.. ................................................................. 153
Figure 36. General view of distance accepted by tolerances in x, y, and z. .............................. 154
x
List of Appendices
Appendix 1. Summary of the z-stack parameters defined during the confocal microscopy image
acquisition for each zebrafish embryo. ....................................................................................... 151
Appendix 2. Levels of threshold selected to generate each mask for the different zebrafish
embryos evaluated. ..................................................................................................................... 151
Appendix 3 . Sensitivity analysis for the number of harmonics included in the Fourier series 152
Appendix 4. Numerical values of Fourier coefficients for the first fifteen harmonics of the
zebrafish embryo blood velocity waveform. .............................................................................. 152
Appendix 5. Effect of the tolerance value for absolute difference in position x,y, and z on the
number of nanoparticle voxels matched with wall shear stress values. ...................................... 153
Appendix 6. Effect of change in tolerances in relative number of NP voxels. .......................... 153
Appendix 7. Estimation of the difference between positions of the nanoparticle (NP) voxels and
the wall shear stress (WSS) coordinates they were assigned to depending on the organization of
the matrices. ................................................................................................................................ 154
Appendix 8 Tolerances accepted by the established parameters ............................................... 154
Appendix 9. Matlab script for the quantification of nanoparticles by voxel count and
fluorescence intensity per wall shear stress region ..................................................................... 155
Appendix 10. Matlab script for the error estimation calculated as the mismatch between
nanoparticle voxel position and wall shear stress position. ........................................................ 156
Appendix 11. Matlab script to normalize the data by the number of wall shear stress elements in
each region .................................................................................................................................. 157
Appendix 12. Matlab script to calculate the dispersion factor for each fluid element in the
computational domain. ................................................................................................................ 159
xi
Abbreviations
ACE Angiotensin converting enzyme
APN Aminopeptidase N
APP Aminopeptidase P
CFD Computational fluid dynamics
CFL Cell-free layer
D Diameter
DF Dispersion factor
dpf Days post-fertilization
ECs Endothelial cells
ECM Extracellular matrix
eNOS Endothelial nitric oxide synthase
EPR Enhanced permeability and retention
GFP Green fluorescent protein
hpf Hours post fertilization
HUVECs Human umbilical vein endothelial cells
ICAM Intercellular cell adhesion molecule
KLF2 Kruppel-like factor 2
NO Nitric oxide
NPs Nanoparticles
PECAM Platelet endothelial cell adhesion molecule
PV1 Plasmalemma vesicle protein 1
RBC Red blood cell
SMCs Smooth muscle cells
TAWSS Time-average wall shear stress
TEM-1 Tumor endothelial marker 1
v Velocity
VCAM Vascular cell adhesion molecule
VEGF Vascular endothelial growth factor
VVOs Vesiculo-vacuolar organelles
WSS Wall shear stress
WSSG Wall shear stress gradient
ρ Density
τ Shear stress
µ Dynamic viscosity
xii
Contributions
Maria Juliana Gomez helped design the in vivo experiment, performed the live imaging
experiment, generated the 3D models of the zebrafish vasculature, quantified nanoparticle
accumulation in vivo, generated the computational fluid dynamics simulation for the in vivo and
in vitro models, developed the algorithms to correlate particle accumulation with flow profiles and
shear stress, and analyzed the data.
Dr. Kristina Rinker, Dr. Sarah Childs, Dr. David Cramb, designed the in vivo and in vitro
experiments.
Dr. Sarah Childs developed the transgenic zebrafish model and performed the nanoparticle
injection.
Dr. Bahareh Vafadar developed the Matlab script with the algorithm for the cross-correlation
methodology used to calculate the zebrafish blood velocities. Dr. Vafadar also participated in some
of the live imaging sessions and collaborated with the line scans acquisition.
Dr. Hagar Labouta did the physicochemical characterization of the nanoparticles used in this study.
Dr. Amber Doiron and Robyn Steele performed the in vitro studies with human umbilical vein
endothelial cells exposed to nanoparticles under static and flow conditions using a parallel plate
flow chamber. Dr. Amber Doiron did the image and statistical analysis for the in vitro experiment.
1
1. Chapter 1: Introduction
Nanoparticles developed in the biomedical field as drug delivery or imaging systems have a great
potential to treat and diagnose diseases more efficiently. However, the translation of these systems
into the clinic has been limited due to the complex environment found in vivo and the low
predictability of in vitro models commonly used to test nanoparticles. Most medical nanoparticle
applications require a vascular administration. When particles enter the bloodstream they are in
continuous movement; physical forces such as shear stress caused by blood flow affect the
distribution of particles and have the capacity to change the phenotype of endothelial cells which
can affect cell-nanoparticle interactions. Additionally, the ability of particles to reach the vascular
wall in flowing blood and target the endothelium are each flow-dependent processes. Therefore,
understanding nanoparticle localization in a physiologically relevant flow environment is
important for determining delivery efficacy, toxicity risk profiles, and predicting their distribution
once they enter the blood stream.
Vessel dimensions and vascular branching architecture affect blood flow patterns and shear stress
magnitudes. Regions of disturbed flow are usually present in angiogenic tissues, such as tumors
or atherosclerotic plaques, where physical barriers arise from an increase in vessel curvature,
intersections and branching points, which also affect wall shear stress. Recent in vitro studies have
shown that nanoparticle accumulation is affected by shear stress and in general, lower shear stress
results in higher accumulation. However, no studies have evaluated the effect of different flow
patterns found in vivo on nanoparticle distribution or determined if a correlation between
nanoparticle localization and vessel wall shear stress exists.
2
Despite the lack of in vivo evaluation of flow effects on nanoparticle localization, models that
predict nanoparticle biodistribution take into account fluid forces as key factors of margination
and accumulation.1–5 Hence, investigating flow effects on nanoparticle accumulation in vivo is
imperative to validate and improve in vitro and in silico predictive models.
In this study, an in vivo zebrafish embryo model with angiogenic tissues was used to evaluate the
localization of nanoparticles to regions of laminar and disturbed flow generated by different vessel
architectures. Polystyrene carboxylate coated spherical nanoparticles of 200 nm diameter were
used as model particles of vascular carriers. To our knowledge, this is the first study to correlate
vessel wall shear stress and flow pattern found in vivo with nanoparticle accumulation. We
developed a methodology that exploits the optical transparency of zebrafish embryos and the
capacity to fluorescently label their vascular cells in order to acquire blood flow velocities by
tracking red blood cells and vessel geometries by 3D reconstruction of confocal z-stacks from
endothelial cells. We used flow velocities to computationally simulate fluid flow on the vessel
geometry and obtain numerical approximations of the shear stress and flow patterns potentially
affecting particle accumulation. Flow patterns in zebrafish embryos resemble those in tumor tissue
vasculature due to high branching vessel segments with uneven diameters resulting from
angiogenesis, therefore the zebrafish model provides a relevant platform to study nanoparticle
distribution. Additional in vitro experiments were performed with human umbilical vein
endothelial cells (HUVECs) using a sudden expansion parallel-plate flow chamber to determine
the effect of different flow patterns and different shear stress magnitudes on nanoparticle adhesion
and internalization.
3
2. Chapter 2: Literature Review
The following sections summarize some key aspects that need to be taken into account to
understand nanoparticle distribution throughout the vasculature. First, there is a section on the
vasculature focused on endothelial cells, which are the major barrier for therapeutic agents that
travel from the bloodstream to the target tissues. Second, the hemodynamics section introduces
the forces generated by blood flow in the vasculature. Then, previous studies evaluating the effect
of fluid forces on nanoparticle uptake and/or accumulation are discussed. The final section
introduces the zebrafish embryo animal model used in this study.
2.1.Endothelial cells
Blood vessels, except capillaries and venules, consist of three layers or tunicae as shown in Figure
1. In the tunica intima, endothelial cells (ECs) are anchored to a connective tissue called the basal
lamina, made of elastic fibers and type I collagen fibrils which serve as a scaffold to all blood
vessels. ECs synthesize the proteins that constitute the basal lamina, they produce matrix
metalloproteinases, which degrade the extracellular matrix (ECM) and allows for vessel
remodeling and angiogenesis. The outside of the basal lamina is covered by smooth muscle cells
(SMCs) or pericytes, depending on the type of vessel and the region of the body where they are
located. The tunica media is formed by the SMC layer and an external lamina, a second layer of
elastic fibers which separates the media from the tunica adventitia. The media is absent in
capillaries and thinner in veins compared to arteries. The tunica adventitia consists of connective
tissue, nerves, vessel capillaries, and cells such as fibroblasts, macrophages, and mast cells.
4
Figure 1. Blood vessel structure consists of three main layers called tunicae. The tunica intima is
made by endothelial cells and basal lamina. The tunica media has smooth muscle cells (in the case
of conduit vessels) and an external lamina. The tunica adventitia is made up of connective tissue
and cells such as fibroblasts.
Particles travelling through blood vessels, in most cases, will interact with the endothelium before
they reach target tissues. The endothelium is formed by a single cell layer of ECs that lines the
walls of the entire vascular system. Healthy endothelium responds to physical and chemical signals
by producing a variety of factors that regulate vascular tone, cellular adhesion, thrombo-resistance,
smooth muscle cell proliferation, and vessel wall inflammation.6 Additionally, the endothelium
controls blood fluidity, hemostasis,7 and vascular permeability8 including the passage of molecules
and transit of white blood cells into and out of the arteries, veins, and capillaries.
These functions are differentially enhanced depending on the vascular bed. For example, artery
and vein ECs regulate tone by releasing nitric oxide (NO). NO activates a signaling pathway that
results in the constriction or relaxation of smooth muscle cells, causing the blood vessel to change
5
its diameter and regulate blood flow. ECs lining smaller vessels, such as post-capillary venules
focus on mediating leukocyte trafficking.7
2.1.1. Endothelial cell heterogeneity
Since ECs are present in different regions of the vascular tree and cardiovascular tissues, they are
exposed to various microenvironments that affect their physiology and phenotype. Therefore, ECs
in different regions of the body and vascular beds (arteries, arterioles, veins, venules, and
capillaries) are expected to differ structurally and functionally.9,10 ECs also vary depending on the
species, so it is important to specify the species when discussing EC characteristics.
Generally, in human arteries, ECs are 0.1-10 µm thick, thin (10-30 µm wide), and elongated (50-
70 µm long) along the direction of flow, an adaptation that allows them to minimize the shear
stress forces generated by blood flow.11 Experiments done in various species show that flow
dependent EC-alignment occurs in straight vessel segments but not in branch points with disturbed
flow.9 ECs have a negatively charged surface due to a glycosaminoglycan layer approximately 10
nm thick.12
EC shape is influenced by the fluid forces present in the vessel, therefore, cell morphology can
provide information about the fluid environment in different vessel segments. Studies done in rats
and mice blood vessels found elongated and narrow ECs in the aorta,13 cremaster muscle14 and
tracheal arterioles,15 and rectangular ECs in the pulmonary artery.13 In veins, ECs tend to be shorter
and have a lower surface area than those found in the arterioles.14 Round shaped ECs were found
in rat pulmonary veins and tracheal venules,15 while narrow rectangular ECs were found in the
inferior vena cava.13 Rat capillaries were reported to have irregularly shaped ECs.15 ECs in high
endothelial venules have been described as cuboidal in shape and have a plump morphology.
6
Veins and capillaries usually have ECs that are less than 0.1 µm in thickness,10 and are more
permeable to blood-borne factors than arteries.16 Most blood vessels have a continuous
endothelium due to tight junctions between the ECs and a continuous basal lamina. Continuous
endothelium can be fenestrated or non-fenestrated. Non-fenestrated endothelium is present in
brain, skin, heart and lung vessels. Fenestrations, which are small pores in ECs, range between 50
and 60 nm in vessels where tissues require an increased exchange of molecules or have a filtration
role such as kidneys, endocrine and exocrine glands, and the gastrointestinal tract.11 On the other
hand, there are vascular beds (sinusoidal vessels) that have a discontinuous endothelium due to an
unstructured basal lamina that generates fenestrations of 100 to 200 nm.11 Discontinuous
endothelium allows cellular trafficking between intercellular gaps. The liver, spleen, and bone
marrow are examples of locations where this occurs.11
Capillary thickness also varies depending on the region, thick capillaries (EC > 2 µm) are found
in skeletal, cardiac, testes, and ovary tissues. On the contrary, thin capillaries (EC < 1 µm) are
found on the central nervous system and dermis. EC heterogeneity occurs even in one same organ,
for example, the kidney has fenestrated EC in the peritubular capillaries, discontinuous
endothelium in the glomerular capillaries and continuous endothelium in the remaining vessels.12
It is important to highlight, that the size and density of fenestrations also vary depending on the
species.17
The expression of proteins in ECs is also different depending on the vascular bed. For example,
the von Willembrand factor, a glycoprotein that helps mediate platelet-recruitment and thrombus
formation, has a higher expression in larger vessels in humans and canine ECs in cell culture18
compared to smaller resistance vessels.19 ECs in high endothelial venules mediate leukocyte
trafficking, they express unique cell adhesion molecules such as glycosylation-dependent cell
7
adhesion molecule, CD34, podocalyxin, endoglycan, and endomucin.20 Additionally, they express
high levels of lymphoid chemokines which are important in lymphocyte trafficking. Another
example of vascular bed-dependent protein expression is the density of caveolae. Caveolae are
membrane-bound 70 nm vesicles which mediate transcytosis, the process by which molecules are
transported across the interior of the cell, their presence is increased in capillary endothelium
compared to other vessels.9 It is also overexpressed in regions with continuous endothelium such
as heart, lung, and skeletal muscle.21 Other mediators of transcytosis are vesiculo-vacuolar
organelles (VVOs), which are most commonly present in venules, specifically, post capillary
venules. Their size is directly proportional to the thickness of the ECs, and their density is
proportional to permeability.22
Permeability is inversely proportional to the number and complexity of tight junctions. Tight
junctions in large arteries exposed to higher shear rates and pulsatile flow are usually stronger than
those in the microvasculature. In arterioles, junctions are tighter than capillaries and venules.9
Similarly, there are other receptors that depend on the organ where the vessel is located. In mice,
for example, ECs in the lung post-capillary venules express the adhesion molecule Lu-ECAM-1,23
while venules in the small intestine express adhesion molecule Mad-CAM-1.24 Receptor
expression also depends on the condition, physiological or pathological, as discussed in the section
physiological vs. pathological vasculature. In order to enhance nanoparticle adhesion to the
endothelium, nanoparticles targeting specific tissues can be functionalized depending on the
surface receptors expressed by the cells in those regions.
The expression of different markers and morphological characteristics are physiological responses
to the microenvironment. Therefore, ECs are required to sense their environment in order to adapt
and maintain homeostasis. This is achieved through mechanotransduction.
8
2.1.2. Endothelial cell mechanotransduction
ECs sense their physical surroundings through mechanoreceptors which allow them to sense
mechanical forces and translate them into biochemical signals through a process called
mechanotransduction. Mechanoreceptors are proteins which react to mechanical stimuli by
opening membrane channels or altering affinities to bind molecules that will activate signaling
pathways.25 Mechanoreceptors are located on all ECs surfaces, luminal, junctional, and basal.26
Some mechanoreceptors identified for ECs include: integrins, platelet endothelial cell adhesion
molecule (PECAM-1), glycocalyx, caveolae, ion channels, G-protein kinases, and primary cilia.27–
29 Additionally, cell cytoskeleton is crucial for cell signaling since it bonds all surfaces together
and provides a scaffold that enables signal molecules to translocate. Evidence has shown there is
complex network of intercellular pathways that are activated by mechanical forces and can cross-
talk between each other. However, the mechanisms by which ECs sense flow and the pathways
they activate have not been completely elucidated.
Mechanotransduction is essential to maintain normal homeostasis since it modulates protein
synthesis, secretion, adhesion, migration, proliferation, morphology, viability, and apoptosis.
Blood flow is the main mechanical stimuli for ECs. The forces exerted by blood on the vessel wall
can be divided into two categories: Shear stress which is the tangential force caused by the blood
flow on the surface of the cell, and pressure which is a normal force caused by the intravascular
hydrostatic blood pressure. In regions of pulsatile flow, a circumferential stress arises from the
pulse pressure variation in the vessel.30 Since these are the main triggers for mechanotransduction,
it has been established that the physiology and morphology of the cardiovascular system, heart,
and vessels, is influenced by shear stress and pressure caused by blood flow.31–33
9
ECs transduce the vessel wall shear stress (WSS) into biochemical signals that regulate gene
expression and can modify cell function. Additionally, shear stress promotes the cytoskeletal
reorganization of ECs by inducing the formation of dense F-actin stress fibers, previously reported
in human umbilical vein endothelial cells (HUVECs).34 The signaling pathways activated during
mechanotransduction, coordinate the development and function of the vascular system in order to
optimize blood flow in tissues during embryogenesis, postnatal, and adult life.35
The expression of approximately 3000 genes is altered by shear stress in ECs.36 Generally, the
expression of these genes affects growth factors, adhesion molecules, vasoactive substances,
endogenous antioxidants, and coagulation factors.37 DNA microarray experiments done in human
aortic ECs exposed during 24 hours to shear stress of 1.2 Pa showed a significant downregulation
of genes related to inflammation and EC proliferation compared to cells grown statically.38
Upregulated genes included Tie2 and Flk-1, which have been involved in viability and
angiogenesis. Other experiments with aortic ECs have reported the upregulation of endothelial
nitric oxide synthase (eNOS) which stimulates NO production, in regions of physiological shear
stress.39 Low WSS has been shown to reduce vasodilation by downregulation of eNOS and
prostacyclin while increasing vasoconstriction by upregulation of endothelin-1 and mitogenic
molecule.40 Low WSS also induces the activation and translocation to the nucleus of the
transcription factor nuclear factor-kappa β (NF-kβ),41,42 which upregulates genes that encode
adhesion molecules such as vascular cell adhesion molecule (VCAM-1), intercellular adhesion
molecule (ICAM-1), and E-selectin.43 NF-kβ also activates the expression of chemoattractant
chemokines such as monocyte chemoattractant protein (MCP)-1, and pro-inflammatory cytokines
such as tumor necrosis factor (TNF)-α and interleukin (IL)-1.44 The expression of adhesion
molecules on the surface of ECs has been considered a marker for pathological vasculature since
10
it mediates the rolling and adhesion of leukocytes to the endothelium. Therefore, they have been
explored as potential targets for nanoparticles to increase drug delivery or imaging efficacy.
2.2. Physiological vs. pathological vasculature
Pathological vasculature is implicated in ischemia, thrombosis, inflammation hypertension, stroke,
atherosclerosis, and tumor growth and metastases, among others.45 Pathological endothelium
commonly occurs when there is endothelial cell dysfunction and is characterized by the expression
of procoagulant, pro-adhesive and vasoconstriction properties. In contrast, physiological
endothelium has anticoagulant, antiadhesive and vasodilatory properties.7 Properties of
physiological endothelium in adult vessels usually require laminar unidirectional flow to suppress
proliferation and induce the expression of transcription factors such as the Kruppel-like factor 2
(KLF2) which promotes the expression of anti-inflammatory, anti-thrombic, and anti-oxidative
mediators.46 KLF2 is suppressed in regions of oscillatory shear stress.46
From a cellular perspective, pathological conditions arise when there are: 1) changes in the cellular
microenvironment that enable a disease state despite mechanotransduction processes functioning
properly or 2) defects in the mechanotransduction process despite cells being exposed to a healthy
microenvironment. An example of the first scenario are atherosclerotic lesions forming in regions
of disturbed flow in the mature cardiovascular system. Disturbed or turbulent flow arise from
blood flow on bifurcations in the arterial tree and generate an oscillatory vessel wall shear stress
that affects ECs phenotype.44 The second scenario, requires gene mutations that usually affect
molecules involved in signalling pathways.25 In both scenarios, disease is explained by an
alteration in mechanotransduction signalling that affects phenotype and function of the cells and
the ECM they produce.
11
It is important to highlight that branching vessels are present in both physiological and pathological
conditions. Pathological branching architecture arises when the vascular pattern is chaotic and
nonhirerchical as shown in Figure 3b versus 3a which shows a physiological branching
architecture.
In terms of the ECM, endothelial basal lamina differs in physiological and pathological
vasculature. This membrane is usually composed by collagen, elastin, proteoglycans, and
glycoproteins.44 During angiogenesis and flow-dependent remodeling the ECM is broken down
and partially replaced by a matrix of fibronectin.47,48 This process has been also found to occur in
vivo and in vitro in atheroprone regions where low WSS occurs. In mice, it has been shown that
ECM degradation occurs along with the upregulation of inflammatory adhesion molecules ICAM-
1 and VCAM-1 on the vascular wall.49 Upregulation of matrix metalloproteinase (MMPs) genes
which control matrix degradation, have been shown to occur in regions with atherosclerotic
plaques where flow is disturbed and WSS is low.50 Disturbed flow also decreases ECM synthesis44
and induces endothelial dysfunction by suppressing NO production.51
The presence of disease modifies the phenotype of cells, therefore, ECs present in pathological
conditions have a different surface marker expression and morphology than ECs in physiological
or healthy vasculature. Figure 2 shows a schematic comparing physiological (a) to pathological
(b) endothelium. In pathological sites, APP, ACE, and PV1 are not expressed by the endothelial
cells, they only appear in physiological endothelium.52,53 However, some adhesion molecules such
as VCAM-1, ICAM-1, APN, TEM-1, and selectins (E-selectin and P-selectin) are induced or
overexpressed in pathological endothelium.54–58 E-selectin is only expressed when pathological
conditions are present and the endothelium is activated, except for bronchial vessels.59 P-selectin
is stored in Weibel-Palade bodies located on the intracellular space. The expression of adhesion
12
molecules also depends on the type of pathology, organ, and vessel. In most cases selectins are
expressed in post-capillary venules where most leukocyte adhesion takes place, while ICAM-1
and VCAM-1 are expressed in many vascular and nonvascular cell types. VCAM-1 and selectins
are essentially regulated at sites of inflammation,60 while APN and TEM-1 are usually expressed
in tumor angiogenesis and inflammation.61,62 In physiological endothelium, glycocalyx consists of
a layer of carbohydrate-rich proteins that covers the surface of ECs, mediates mechanotransduction
signaling stimulated by shear stress,25 and masks surface markers. In diseased conditions, shedding
of glycocalyx occurs and surface molecules are exposed, this causes endothelial contraction which
increases permeability by generating larger gaps between the cell junctions.45,63 PECAM-1 and
vascular endothelial (VE)-cadherin, proteins localized at the cell-cell junctions, are key regulators
of permeability, migration, and assembly and stabilization of blood vessels.12 In pathological
vasculature, their expression is reduced and the increase in gap size between ECs makes their
connection to neighbor cells weaker, this is common in tumor vasculature.
13
Figure 2. Endothelial cell surface in (a) physiological and (b) pathological conditions. Healthy
endothelium (a) expresses molecules such as APP and PV1 which are present inside caveoli, cell
surface molecules such as VCAM-1 and ICAM-1, glycocalyx which coats the surface of the cells
and masks adhesion molecules, and some molecules such as PECAM-1 and VE-cadherin are
localized at cellular junctions and help regulate permeability. Pathological endothelium (b) some
molecules such as P-Selectin are induced and exteriorize from intracellular space. Others such as
ICAM-1, E-Selectin and VCAM-1 are overexpressed. Clustering or rearrangement of molecules
on the cell surface can occur as well as glycocalyx shedding and endothelial contraction. Usually,
permeability increases due to weak VE-cadherin and PECAM-1 adhesions.
A significant body of research has been focused on the design of injectable carrier systems that
target tumor or atherosclerotic diseased tissues via the endothelium. The immaturity of the tumor
14
or plaque neo-vasculature provides a good platform for efficient drug delivery. The next
paragraphs will focus on the characteristics of the pathological vasculature in these diseases.
Tumor vasculature differs morphologically and functionally from physiological vasculature. As
shown in Figure 3, tumor vasculature is disorganized and tortuous, vessels are leakier than
physiological vessels, which contributes to the generation of interstitial hypertension.64 There is a
lack of blood vessel hierarchy that makes arterioles, capillaries, and venules difficult to identify.65
Disorganized blood vessel networks are a result of pro-angiogenic factor overexpression caused
by the aggressive growth of neoplastic cell population.66,67
Endothelial cells in tumor vessels are poorly aligned, exhibit wide gaps between them that can
range from 300 nm to 1.2 µm, as well as no smooth muscle layer or pericytes surrounding the
endothelium.68 Tumor vessels have a wider lumen, impaired function for vasoregulation, and
enhanced production of vascular mediators such as VEGF, bradykinin, nitric oxide peroxynitrite,
and matrix metalloproteinases.69–71 Vessels exhibit a greater variability in diameter which
enhances tumor environment heterogeneity by generating variable blood flow rates and stagnation
points.72 All of these factors contribute to an increase in tumor tissue permeability. The
combination of leaky vessels and poor lymphatic drainage results in the enhanced permeability
and retention (EPR) effect, which modifies the biodistribution of nano- and micro-size carriers by
allowing a greater accumulation in tumor tissues due to an increase in vascular permeability.68,70
There is also an increase plasma half-life of the carriers due to impaired clearance of particles in
the interstitial space of tumors.70,73 The characteristics of tumor vasculature have made
nanoparticles a good alternative for solid tumor treatment because of their size range and targeting
capabilities, and their capacity to remain entrapped in the tumor.
15
Figure 3. Differences between physiological vasculature (a) composed of mature vessels
maintained by a balance of pro- and anti-angiogenic molecules and abnormal tumor vasculature
(b) composed mostly of immature vessels with increased permeability, vessel diameter, vessel
length, vessel density, tortuosity and interstitial fluid pressure.
Atherosclerosis is another site of pathological angiogenesis. The formation of blood vessels is a
key factor in the progression and vulnerability of atherosclerotic plaques. As the plaque thickens,
the diffusion of oxygen is restricted causing a hypoxic environment, this increases angiogenic
factors to promote vessel formation that can sustain plaque growth by supplying lipoproteins,
inflammatory cells, matrix proteases, and reactive oxygen species. Microvascular endothelial cells
found in atherosclerotic plaque, have pathological characteristics such as membrane outgrowths,
intra-cytoplasmic vacuoles, weak intercellular junctions, and basement membrane detachment.74
Low WSS and disturbed flow promote angiogenesis in this region by helping up-regulate the
expression of pro-angiogenic factors such as vascular endothelial growth factor (VEGF) and
16
angiopoietin-2.75 Gene expression studies done in atherosclerotic arterial wall have identified
several genes expressed in both atherosclerosis and cancer tumors. Examples include EDG1,
which is highly upregulated during tumor angiogenesis; VE-cadherin, which promotes tumor
progression by enhancing angiogenesis; CLEC14A, strongly induced in solid tumors and highly
angiogenic, it promotes EC migration, tube formation, and appears to be regulated by shear stress;
Robo4, tumor EC marker regulated by shear stress; and Tie1, EC tyrosine kinase receptor
upregulated in tumor angiogenesis and atherosclerosis depending on shear stress.72
Evidence from different studies suggests that hemodynamics (flow pattern and shear stress in
particular), play a very important role in vascular pathology by triggering the expression of genes
that modify ECs phenotype and promote angiogenesis which result in different vessel
architectures, which can continue to affect the blood flow patterns and shear stress levels as
summarized in Figure 4. For example, disorganized hypervascularization promoted by pro-
angiogenic factors in tumor tissue leads to physical barriers caused by vessels with uneven
diameter and shape, and abnormal branching architecture with bulges and blind ends.76 Flow in
these tumor vessels is highly heterogeneous due to the uneven vasculature, which generates
different flow patterns and shear stresses that are likely to continue inducing the expression of
genes that promote a pathological phenotype.
17
Figure 4. Schematic of the relation between flow-induced gene expressions which affects
endothelial cell phenotype and/or vessel architecture.
As mentioned before, non-physiological stimuli present on the cellular microenvironment makes
cells prone to pathologies. Cells, specially ECs, are affected by flow to a large extent. ECs exposed
to laminar physiological shear usually exhibit elongation and orientation in the direction of flow
that is mediated by the activation of Rho family GTPases resulting in the formation of stress fibers,
focal adhesions, and cytoskeletal reorganization.77 Low or oscillatory shear stress, as well as
disturbed flow, fail to induce ECs morphological adaptations and usually activate inflammatory
markers.78 It has been suggested that transverse flow, perpendicular to the vessel and cell axis,
exhibited the highest correlation to plaque formation in aortas from rabbits.79 Flow pattern also
has an effect on ECs phenotype. Regions of disturbed flow usually fail to express endothelial-
protective KLF280 and have very low expression, if at all, of VE-cadherin.81 In vivo models of
disturbed flow such as the carotid artery partial ligation murine model have shown the upregulation
of adhesion molecules ICAM-1 and VCAM-1, and impairment of vaso-relaxation due to a
18
downregulation of eNOS.82 These results suggest that flow patterns also play a significant role in
vascular homeostasis.
In terms of nanoparticle drug delivery and imaging , vessel dimensions and branching architecture
affect blood flow patterns which have the capacity to modify nanoparticle distribution.83
Therefore, it is important to investigate the effects that shear stress and flow patterns have on
nanoparticle accumulation.
2.3. Hemodynamics
Endothelial cells are constantly exposed to hemodynamic forces generated by blood flow and by
the pulse wave of the cardiac cycle. Shear stress is the force parallel to the vessel wall that the
blood flow exerts on the endothelium. If the shear stress occurs near the vessel wall, it is referred
to as wall shear stress (WSS). WSS is mathematically equal to the product of blood viscosity and
shear rate, which is the spatial gradient of blood velocity on the vessel wall and is measured in
units of force per units of area. The calculation of shear rate is based on the assumption that the
velocity of fluid on the wall of the vessel is zero. This is known as the no-slip condition and arises
from the observation of stationary flow on the surface suggesting that adhesion forces between the
fluid molecules and the solid wall are stronger than the cohesion forces between neighboring
molecules. The velocity gradient arises from fluid particles moving parallel to the wall and having
velocity that increases as they move towards the center of vessel.
Blood is a suspension of elements that include red blood cells (RBCs), white blood cells (WBCs),
and platelets. The fluid portion is made up of plasma which is an aqueous solution of ions and
macromolecules. RBCs usually have a diameter of 6 to 8 µm, are shaped as biconcave disks, and
have a thickness of 2 µm. Mammals have non-nucleated RBCs which consist of concentrated
hemoglobin constrainted by a flexible membrane. WBCs or leukocytes can be divided into
19
different classes: granulocytes (include neutrophils), monocytes, lymphocytes, macrophages, and
phagocytes, among others. Under physiological conditions, blood has a volume concentration of
RBCs or hematocrit between 40-45%.84
The viscosity of a fluid depends on its rheological characteristics, Newtonian or non-Newtonian,
and temperature. A fluid with a Newtonian behavior is characterized by having a linear relation
between shear stress and shear rate where the slope is equal to the dynamic viscosity, while non-
Newtonian fluids do not exhibit a linear relation. Blood is a non-Newtonian fluid, where viscosity:
decreases with increasing flow rate (shear thinning); increases with increasing hematocrit; and
decreases with increasing temperature. For vessels with high shear rates (above 100 s-1), blood has
been shown to behave as a Newtonian fluid, therefore, the assumption of a viscosity of 3.0cP (45%
hematocrit) is commonly made to simplify the calculations.84 This assumption is not accurate for
smaller vessels in the microcirculation since changes in hematocrit vary greatly depending on
vessel diameter; this is known as the Fahraeus-Lindquist phenomenon. This phenomenon occurs
because red blood cells tend to travel closer to the center of the vessel, when there is a decrease in
vessel diameter, the number of red blood cells that can travel through the lumen decreases, causing
a decrease in viscosity. This effect occurs in vessels with diameters below 200 µm.84
The vessel WSS in humans varies depending on the vascular bed. However, physiological shear
stress magnitudes range between 1 and 7 Pascals (Pa) in arteries, 0.1-0.6 Pa in veins,85 and 0.3 to
1 Pa in the microvasculature.86 The WSS on human umbilical vein endothelial cells, used in this
study, is on average 0.5 Pa.87 Shear stress and flow pattern are affected by blood flow velocity and
vascular architecture. Geometric features including branching, bifurcation, and curvature, affect
the flow field and consequently the shear stress distribution on the endothelial surface.88 Vessels
with branches and geometric irregularities usually have lower wall shear stresses than straight
20
vessels with similar blood flow velocities. Flow regime can be laminar or turbulent depending on
the ratio between viscous and inertial forces; this relation is described by the Reynolds number.
𝑅𝑒 =𝜌𝑣𝐷
𝜇
(1)
Where ρ is the density of the fluid, v is the velocity of the fluid, D the diameter of the pipe, and µ
the dynamic viscosity.
The laminar regime is characterized by Reynolds numbers below 1800 and consists of a
streamlined flow that can have an undisturbed flow pattern, characterized by smooth parallel
streamlines, or a disturbed flow pattern, characterized by flow separation and reattachment,
recirculation, or velocities which result in high dispersion factors. The turbulent regime has
Reynolds numbers above 4000, hence inertial forces are more significant than viscous forces. Flow
velocity at any given point varies continuously over time in the turbulent regime, even though the
flow is overall steady. Turbulent flow is rarely present in human vasculature, however, it has been
reported in aneurysms, in the aorta at peak systole, in central arteries during intense exercise, and
distal to stenosis severely occluded. 44
Flow is highly pulsatile in arteries and minimally pulsatile in veins. Straight segments in arteries
where flow is pulsatile typically have a unidirectional WSS, whereas branching segments or
vasculature with geometrical irregularities, typically have a disturbed laminar flow with low
oscillatory WSS. Unidirectional low WSS usually occurs at curvatures or upstream stenosis.
Oscillatory WSS has changes in both magnitude and direction between systole and diastole, it
usually occurs downstream of stenosis, at the lateral walls of bifurcations, and proximal to branch
points. The interaction between pulsatile blood flow and vessel geometries results in complex
biomechanical forces on the vessel wall with spatial and temporal variations.89 The temporal
gradient of WSS arises from the change in blood flow during systole and diastole, while the spatial
21
gradient that depends on the geometry of the vessel. ECs are able to sense different flow
magnitudes, direction, amplitude, and frequency of waveform, and adapt physiologically
according to these conditions.90–94 However, more systematic studies on the effects of pulsatile
flow on ECs are required in order to determine its effect on endothelium phenotype and function.
Since the vascular geometries are usually tortuous and pulsating, we cannot obtain an analytical
solution for the laminar flows. Nonetheless, we can obtain analytical solutions for idealized
geometries that help validate results from computational fluid dynamics simulations. The Hagan-
Poiseuille equation can be used for straight pipes.
The Hagan-Poiseuille equation has the following assumptions:
Blood behaves as a Newtonian fluid.
The vessel is a cylindrical tube of constant cross-section.
Vessel walls are rigid.
Blood flow is steady and laminar.
The equation to calculate shear stress in a vessel using Hagan-Poiseuille is:
𝜏 = 4 ∙ 𝜇 ∙𝑄
𝜋 ∙ 𝑟3 (2)
Where τ is the shear stress, Q is the flow rate, and r is the radius of the vessel.
For pulsatile flow, the Womersley number (Wo) can be thought of as the unsteady corollary to the
Reynolds number, since it provides the ratio of transient inertial forces to viscous forces in a flow.
It can be calculated:
𝑊𝑜 = 𝑟√𝜔𝜌
𝜇
(3)
22
Where r is the radius of the pipe in m, ω is the angular frequency of oscillations in rad/s, ρ is the
density of the fluid in kg/m3, and µ is the fluid viscosity in N-s/m2.
For Wo values less than one, the frequency of pulsations is sufficiently low for a parabolic velocity
profile to develop during each cycle assuming that the channel is circular. In this case, Poiseuille
law can be used as a good approximation. For large Wo (ten or higher), the frequency of pulsations
are large enough to generate a plug-like flow since the velocity profile is relatively flat.
2.4. Nanoparticles for biomedical applications
Targeted delivery of therapeutic and diagnostic agents is a critical medical goal. The objective of
a targeted delivery system is to improve the efficacy of delivery to the pathological site while
reducing side effects on healthy organs and tissues.95 The development of nanomedicines, drug
delivery systems in the nanometer size range, has provided great advances towards achieving this
objective. Other advantages of nanomedicines or nanocarrier systems include reduced volume of
drugs and imaging agents required, improved pharmacokinetics, and increased biodistribution of
agents to target organs or tissues.96 Target delivery results in a lower concentration of the
therapeutic agent in healthy tissues which consequently reduces drug toxicity.97
Nanoparticles used as drug delivery systems are made of a variety of materials including polymers
(polymeric nanoparticles, micelles, or dendrimers), lipids (liposomes), viruses (viral
nanoparticles), and organometallic compounds (nanotubes).98 This variety of materials result in
nanocarriers with different sizes, geometries, morphologies, and physical properties.45 Most of
these nanoparticles are engineered to either passively or actively target certain pathophysiological
characteristics such as the permeable vasculature present in tumors or inflammatory markers
expressed by cells.
23
Treatment of solid tumors has been one of the main areas of research in nanomedicine. As
mentioned before, the formation of tumor vasculature arises from the imbalance of factors such as
vascular endothelial growth factor (VEGF), which results in angiogenesis. This pathological
process increases the vascular permeability and chaotic vessel architecture. Due to their
biodegradable and biocompatible properties, the most common types of nanocarriers used for drug
delivery are liposomes and polymeric nanoparticles. Liposomal formulations of anticancer drugs
approved for human use include Doxil® (ovarian cancer), Marquibo® (lymphatic leukemia), and
Myocet® (breast cancer).99 Polymer-based nanoparticles include Genexol® (breast and pancreatic
cancer), Opaxio® (glioblastoma), and Abraxtane® (breast, lung, and pancreatic cancer).99 Most
of these formulations take advantage of the leaky tumor vasculature to passively target tumor
tissues and reduce the concentration of anticancer drugs in healthy tissue sites.100 However, recent
research has focused on active targeting to further enhance the delivery of nanoparticles to the site
of interest. Active targeting requires the attachment of a ligand to the nanocarrier surface. This is
a common strategy to target molecules uniquely present in certain type of cells, tissues, or
pathological sites. Antibodies, hormones, receptor ligands, peptides, aptamers, and nucleic acids
are some of the ligands examined as targeting ligands.57,101–103 On the other hand, ‘passive
targeting’ usually occurs when the cells of the vascular wall have enlarged gap junctions that allow
particles to migrate to the abluminal region. This phenomenon is present in tumor vasculature and
is referred to as the enhanced permeability and retention (EPR) effect, discussed in more detail in
section 2.2 Physiological vs. pathological vasculature. Targeting requires the delivery of the
nanoparticle to the target site, physical contact with the surface or molecule of interest, anchoring,
residence on the surface and/or internalization, and excretion or storage.45,104
24
Nanoparticles can enter the body via oral ingestion, inhalation, dermal penetration, and
intravascular injection. Oral and intravenous administrations are the most commonly used for
nanocarriers developed for drug delivery and imaging purposes. Despite the route of exposure,
nanoparticles are distributed throughout the body via the vasculature and are able to reach different
organs including the brain.105 Since most nanoparticles reach the vasculature, it is important to
understand how blood flow, vessel architecture, and endothelial surface affect their distribution.
2.5.Flow effects on nanoparticle localization
Particle-cell interactions have been traditionally characterized using static in vitro assays
consisting of cultured cells or tissues exposed to particles during a period of incubation. These
static assays fail to mimic the complex in vivo microcirculation environment, in which fluid flow
and vessel architecture determine the hemodynamic conditions cells and particles are exposed to
and affect their interaction by enhancing or restricting adhesion of particles to cells. Recently, flow
chambers and microfluidic devices with simple geometries have been used to study the interactions
between particles and cells in an attempt to resolve the shortcomings of static assays. These devices
have been engineered to reproduce in vivo conditions including shear stress and flow profiles
generated by bifurcations or stenosis.
The interaction between nanoparticles and endothelial cells is very important for intravenous
delivery of nanomedicines because the endothelium is the main barrier between the blood flow
and tissues. Particle-cell interaction can be affected by flow dynamics, elements present in the
blood such as macrophages, and vascular architecture. The following sub-sections will summarize
the studies found regarding flow effects on nano- and micro-particle localization in vitro, in vivo
and in silico. The literature search was focused on the effect of flow magnitude (shear stress, shear
rate and flow velocity) and flow pattern (disturbed or undisturbed laminar flow) on nanoparticle
25
accumulation and uptake. Since flow magnitude and pattern are external factors which affect
particle-cell interactions, each section will also discuss factors related to physical characteristics
of particles (size, shape, density, flexibility, surface functionalization, and charge) that affect their
accumulation under flow conditions.
2.5.1. Effect of flow magnitude: shear stress, shear rate, and velocity
Carriers targeting the vasculature must be able to find and bind to the vessel wall, and remain
bound to the surface until they release their cargo or are internalized by the cell.106 Torque and
drag forces that act on the particle and the cell surface will help to either internalize the particle or
to release it. Therefore, in order to closely mimic and understand the factors involved in the
accumulation and distribution of nanoparticles flow and shear stress must be included as
experimental design factors.
Particles injected intravenously, will be in contact with blood flow. In blood flow, red blood cells
gather in the center of flow forming a ‘cell-free layer’ (CFL) adjacent to the endothelium.107 This
effect plays an important role in the margination of leukocytes and platelets since it forces them to
concentrate in the CFL and interact with the vessel wall.108 In vitro studies have shown that this
effect is also present neutrally-buoyant microspheres,109 however, this effect seems to be size
dependent since it affects microparticles ( >1µm) and not nanoparticles, as reported by in silico
modeling of 10-1000 nm particles.4 The margination of nanoparticles is therefore restricted since
they have a reduced capacity to localize to the CFL.110 However, the width of the CFL changes
depending on the organism due to differences in RBC size, shear rate, vessel dimensions and
hematocrit. A study evaluating the role of RBC geometry (from human, rabbit, pig and mouse) in
binding efficiency of polystyrene spherical (200, 500, 2000 and 5000 nm) particles in different
flow patterns was done by Eniola-Adefeso and collaborators.111 A quadratic relation was found
26
between particle binding and the ratio of particle diameter to RBC diameter, for both buffer-RBCs
and whole blood laminar flow at 500/s. They found a decrease in particle adhesion with ECs
exposed to whole blood compared to buffer flow with RBCs. Overall, microparticles had a higher
binding density than nanoparticles suggesting that a smaller size is not always more effective in
terms of interaction with the endothelium.
In terms of wall shear stress level, several results from in vitro studies have shown an inverse
relation between WSS and nanoparticle accumulation. Samuel et al. studied the uptake of
negatively charged CdTe-quantum (2 and 5 nm) dots and fluorescent silica (50 nm) nanoparticles
on human umbilical vein endothelial cells (HUVECs) under controlled shear stress rates (0.05,
0.10, and 0.50Pa) using a microfluidic platform.112 Highest uptake for both quantum dots and silica
nanoparticles occurred at the lowest shear stress 0.05 Pa, and higher values of shear stress reduced
particle uptake. Similar results were found in an in vitro study done using ferromagnetic particles
of 30 nn, where higher shear stress of 0.322 Pa resulted in fewer intracellular agglomerates of
particles in human aortic endothelial cells compared to 0.057 Pa and static.113 However,
agglomerates formed due to the high magnetic dipole-dipole interaction between particles
generated large particle aggregates (>300 nm) that interfere with the evaluation of how disperse
particles are affected by shear stress. On the other hand, Charoenphol et al. found a threshold for
particle adhesion and wall shear rate, highest adhesion of polymeric spheres was found at an
intermediate shear rate value of 1000 s-1, compared to 200, 500 and 1500 s-1 shear rates.106
Additionally, they found that increasing particle size (100 nm up to 10 µm), and decreasing channel
height, which increases shear rate, increased the binding efficiency of spheres under flow.
Contrary to the effect of particle size on adhesion that Charoenphol et al. found, Lin et al. found
that under physiological flow conditions, human aortic endothelial cells exhibit a decrease in
27
carboxylate-coated polystyrene nanoparticle uptake with an increase in size (100 nm up to 1
µm).114 Additionally, the same study found a decrease of nanoparticle uptake with an increase in
shear stress. The decrease was not as pronounced when the experiment was performed with
particles coated with P-selectin targeting molecules. In a different study using targeted particles,
Kusunose et al. evaluated the uptake of liposomes coated with APN and VCAM-1-targeting by
HUVECs at different shear environments in a microfluidic chamber.5 They found that the affinity
of the ligand with the cell determined the effect that shear had on the uptake. Uptake of liposomes
with low affinity decreased with shear. Liposomes with higher affinity had the highest uptake in a
low shear environment of 0.24 Pa.
Most experiments evaluating the efficiency of targeting ligands or the accumulation of particles to
pathological endothelium activate the cells with a cytokine to induce an inflammatory phenotype.
Endothelial cells previously activated with TNF-alpha, have been shown to have a higher
accumulation of nanoparticles in comparison to control cells, suggesting that an inflammation
phenotype also increases the uptake of untargeted particles.113 Similar results were found for
activated HUVECs exposed to 80 nm gold NPs with an anti-ICAM-1 targeting moiety.115 These
results suggest that preferential accumulation of nanoparticles to sites of inflammation can be
achieved by targeting inflammatory ECs surface markers or by passively targeting the
inflammation-induced permeability of the cells. Lower nanoparticle accumulation at higher levels
of shear stress might also occur because endothelial cells conditioned to flow induces cytoskeletal
reorganization and the formation of actin fibers which has been shown to inhibit endocytosis of
antibody functionalized particles, in contrast to ECs not adapted to flow.116
Cell culture studies have reported that endothelial cell morphological changes including
orientation and cell elongation usually require 24 to 48 hours to be identifiable.117,118 Pre-
28
conditioning of endothelial cells to flow has been shown to influence cellular interaction with
nanoparticles. Freese et al studied the effects of cyclic stretch on amorphous silica nanoparticle
uptake by HUVECs.119 Cells grown during 48 hours under cyclic stretch conditions (1Hz, 5%
cyclic elongation) before being exposed to nanoparticles had lower nanoparticle uptake than those
grown statically due to decreased endocytosis. Reduced internalization of nanoparticles was also
found by Klingberg et al. after pre-conditioning HUVECS during 24 hours to 1 Pa flow before
exposing them to 80 nm spherical gold nanoparticles.120
Few studies have evaluated the flow effects on nanoparticle accumulation in vivo using animal
models. Mice have been used to evaluate the effects of acute and chronic flow on endocytosis of
nanocarriers targeted to PECAM.116 Nanocarriers showed a higher uptake in the capillaries than
in the arterial vessels, leading to the hypothesis that hydrodynamic differences are responsible for
the differential uptake. The hypothesis was tested using cultured HUVECs pre-exposed to flow
during 16 hours at 5 Pa. After pre-exposure, endothelial cells aligned to flow and actin rearranged
causing a decrease in nanoparticles uptake, suggesting that the cytoskeleton rearrangement
inhibited uptake by inhibiting endocytosis. Similar results were obtained in vivo and in vitro for
nanoparticles targeting ICAM.121
A different study with the same ICAM-targeting nanoparticles evaluated the effect of shear stress
and surface density of anti-ICAM antibody. A significant increase in the number of nanoparticles
bound to the cell at low shear stress (0.1 Pa) compared to high shear stress (0.5 Pa) was found.
These differences were enhanced as the density of anti-ICAM in the nanoparticle surface
increased. However, the increase in the amount of antibody allowed the nanoparticles to withstand
a shear stress over 3 Pa without detaching from the cells.122 Charoenphol et al. found similar results
29
in vitro by varying the ligand density of vascular-targeted polymeric nanospheres and exposing
them to flow using a parallel plate flow chamber.123
2.5.2. Effect of flow pattern: disturbed and undisturbed laminar flow
The adhesion of functionalized particles in vitro using synthetic microvascular networks and fluid
flow chambers has been shown to be affected by geometric features of vessels.124 This has also
been observed for leukocytes in vitro and in vivo. 125
Pulsatile flow has been shown to affect the adhesion of larger particles to the endothelium; 5 µm
polystyrene particles had a significant decrease in adhesion to the endothelial cells exposed to
pulsatile flow (10-500/s) compared to laminar flow (500/s). For smaller particles, the overall trends
seem to be the same as in laminar flow.111,126,127 Flow recirculation was also evaluated by the same
group, interestingly, they found that particle adhesion increased using whole blood compared to
buffer with RBCs in the recirculation region, contrary to what they found using laminar flow.
Particle density affects the adhesion of particles to ECs exposed to recirculating and unidirectional
flow. Non-neutrally buoyant spherical particles had increased adhesion in recirculation flow
compared to laminar flow.126 Polystyrene particles (500 nm) exhibited the lowest accumulation in
the recirculating region compared to silica and titanium dioxide particles of the same size and
shape. Other studies from the same group have shown that neutrally-buoyant spheres and rods had
no significant change in adhesion.128
In vivo, Kheirolomoom et al. showed an upregulation of VCAM-1 expression on endothelial cells
exposed to disturbed flow in a partial carotid ligation mice model. To exploit this characteristic of
atheroprone regions, they designed stealth liposomes (160nm) targeted to VCAM-1 and showed
that these particles accumulated preferentially in regions of disturbed flow and not in laminar flow
regions with lower VCAM-1 expression.127
30
No studies have quantified the effect of flow patterns and wall shear stress on the accumulation of
nanoparticles in the vasculature using in vivo models. Most in vivo studies report accumulation of
particles in different organs, but they do not evaluate the effect of different vessel wall shear
stresses on particle localization. Since flow pattern varies depending on the geometry of the vessel
and physical barriers present in the vasculature, it is important to understand the effects that both
shear stress and flow pattern have on the distribution of nanoparticles. For this, an in vivo model
is required to obtain the geometry and flow parameters that are hypothesized to affect nanoparticle
distribution.
2.6. Zebrafish embryo model for nanoparticle research.
The zebrafish model has gained significant attention over the last decades as a model for human
diseases. Zebrafish genome sequencing revealed that 70% of human genes have at least one ZF
orthologue, this suggests that the initiation and development of many diseases in zebrafish involves
the same molecular and cellular components than humans.129 Zebrafish embryos, in particular,
have been used to study development, disease progression and diagnosis, and for drug screening
purposes.130
In the nanotechnology field, embryonic zebrafish have been mostly used to evaluate toxicity of
nanoparticles by assessing their effect on normal development.131–134 Other studies have evaluated
the efficacy of nanoparticles designed to treat a disease.129,135 The evaluation of the treatment of
diseases such as cancer can be done using zebrafish embryos because they support the growth of
human cancer cell lines and develop tumors similar to mammalian animal models such as
mice.136,137 Transplantation of exogenous cells can be done without suppression of the immune
system to avoid rejection since embryos lack a functional adaptive immune system during the first
month of development.138
31
Zebrafish embryos are optically transparent; this characteristic has made them especially useful to
evaluate distribution and interaction of fluorescently tagged nanoparticles using fluorescence
microscopy. There have been very few studies evaluating the interactions of nanoparticles with
the endothelium in vivo.129 Transgenic embryos, as well as wild type embryos, have been used to
test nanoparticle clearance by macrophages,129 as well as platelet aggregation induced by
nanoparticles injected to the vasculature.139 However, a weakness of these studies is that they have
not quantified nanoparticle accumulation in vivo therefore, the conclusions from in vivo
experiments arise from qualitative descriptions.
32
3. Chapter 3: Hypothesis and objectives
Hypothesis: Since previous studies done in vitro have found an inverse correlation between shear
stress and nanoparticle accumulation, we hypothesized that:
Regions of the vessel with low shear stress will have a higher nanoparticle accumulation
than regions with high shear stress.
Higher nanoparticle accumulation will occur in regions of the vessel with disturbed flow
compared to regions of undisturbed laminar flow. Therefore, we expect higher
nanoparticle accumulation in high branching regions of the vasculature compared to
vessels with straight segments.
To test this hypothesis, we will investigate the following aims:
Aim 1: Evaluate nanoparticle distribution in vivo using zebrafish embryos and compare it
with in vitro results of cultured human endothelial cells exposed to nanoparticles. Zebrafish
embryos exhibiting angiogenesis will be injected with polymeric nanoparticles. Different
segments of the vasculature (arteries, veins, and capillaries) will be imaged in order to identify the
regions where most particles accumulate. These in vivo results will be compared to in vitro results
previously obtained by our lab using the same nanoparticles and a parallel plate flow chamber to
expose human endothelial cells to different flow patterns (laminar and disturbed), and different
shear stresses.
Aim 2: Determine the flow patterns and quantify wall shear stress in the zebrafish vessels
and establish the relationship between flow and nanoparticle localization in vivo. Confocal
images of zebrafish vasculature will be collected to develop the 3D model of the vessels using
Simpleware®. Line scans will be obtained for each vessel to determine the blood flow velocity
by tracking red blood cells displacements. Flow inside the vessels will be simulated using
33
computational fluid dynamics software ANSYS Fluent®. The profiles for shear stress and
velocity, as well as the streamlines, will be obtained. Nanoparticle localization will be quantified
by 3D analysis of the confocal z-stacks and correlated with flow parameters found in the vessel
segment.
34
4. Chapter 4: Methods and Materials
4.1. In vivo zebrafish model
Transgenic zebrafish (Danio rerio) Tg(kdrl:GFP)1a116, Tg(gata1:mCherryRed)sd2 embryos were
obtained and manipulated by Dr. Sarah Childs. In order to enable the visualization of the
vasculature and the red blood cell movement, the embryos were genetically modified to express
green fluorescent protein (GFP) in endothelial cells under the kdrl promoter and red fluorescent
protein in red blood cells. The transgenic embryos were collected in petri dishes without removing
the chorion.140,141 Embryos were bathed in E3 standard fish media (5 mM NaCl, 170 µM KCl, 330
µM CaCl2, and 330 µM MgSO4). The transparency of the embryos was maintained by treating
them with 0.003% phenylthiourea (PTU; Sigma) at 8 hours post-fertilization (hpf) in order to
prevent pigment formation.
At 52 hpf, the embryos were immobilized in 5% tricaine methanesulfonate (Sigma-Aldrich), an
anesthetic for aquatic species. A side effect from tricain is a reduced heart rate which increases the
risk of death, therefore this step of the procedure was done in a very short period followed by a
dilution of the anesthetic once the embryos are immobilized and can be injected. Fluorescently
tagged carboxylate coated polystyrene spherical nanoparticles of 200 nm (Life Technologies Inc.)
were sonicated for 30 minutes to evenly disperse them in the liquid before injection. The blue
fluorophore on the nanoparticles had an excitation/emission maxima of 365/415 nm.
Approximately 2-4 nL of 2% nanoparticle dispersion were injected via microinjection needle to
the sinus venous, a chamber immediately anterior to the heart of the embryo.
To prepare the embryos for imaging, embryos were mounted on 1.0% low-melting point agarose
(Invitrogen) on a glass cover slip imaging dish (MatTek). It is important to note that no anesthetic
was present in the agarose or the imaging chamber, so the heart rate of the embryos was no longer
35
affected by the tricaine. Images were captured 1 hour after nanoparticle solution was injected using
a Zeiss LSM700 inverted confocal microscope with a 20x objective lens and 0.8 numerical
aperture at 512 pixels by 512 pixels. Lasers with 405, 488, and 555 nm were used to image blue
nanoparticles, red erythrocytes, and green endothelial cells. Frames were taken at 1.94 s. Details
of the imaging parameters are shown on Appendix 1. During the imaging process, line scans were
collected in order to calculate the blood flow velocity in each vessel as described on the following
sub-section.
4.2.Calculation of blood flow in the zebrafish embryo vasculature
To calculate the velocity of blood flow in different vessel segments, a cross-correlation particle
image velocimetry technique was employed to determine the red blood cells displacements. For
this, line scans were collected along the centerline of the vessels segments within a region of
interest along a straight segment over a length of 128 x 1 pixels, which spanned for a 22.76 length
x 0.18 µm width. The frequency at which the frames were acquired had to be higher than the heart
beat frequency for the zebrafish embryos in order to capture the changes in velocity throughout
the cardiac cycle. The reported cardiac frequency for the same transgenic zebrafish embryos used
in this study is approximately 2.6 Hz and 3.5 Hz, for embryos 48 hpf and 72 hpf, respectively.142
Therefore, data points were acquired at a much higher frequency of 520 Hz, which corresponds to
3000 frames obtained in 5.8s to determine the blood flow velocity throughout the whole cycle. The
calculation of the velocity from the line scans was done using a Matlab script developed by Dr.
Bahareh Vafadar at Zymetrix. A graphic description of how the line-scans work is shown in Figure
9.
Red blood cells were used as particle markers present in the fluid flow to measure instantaneous
velocity field using particle image velocimetry. The displacement of the cells was calculated as a
36
spatial shift between image frames, the shift in pixels was then converted into microns and the
velocity was calculated by dividing the change in position by the change in time between line-
scans. Blood flow velocities were calculated for the arteries, veins and capillaries of 5 zebrafish
embryos. In total, 12 arteries, 24 veins, and 7 capillaries were analyzed.
4.3.Computational fluid dynamics of zebrafish vein
Computational fluid dynamics (CFD) usually consists in three main steps, pre-processing which
includes defining and generating the geometry and mesh, simulation, and post-processing which
consists in plotting the results obtained by the simulation. For the pre-processing step, the
geometry for the zebrafish vasculature was generated. This section will be further divided into sub
sections describing the methodology used for each step in the CFD process.
4.3.1. Pre-processing: Surface model construction and computational mesh generation
Since the geometry can greatly affect the results of the CFD simulation, the confocal images from
the vasculature were taken at very small intervals in order to obtain as much spatial detail as
possible. The data set used to construct the geometry corresponds to Fish 1 described on Appendix
1. This z-stack consists of a total of 363 confocal slices acquired at 0.3µm intervals. Before
exporting the stack into an image processing software, the z-stack was separated into the three
different channels, red for RBCs, green for ECs, and blue for NPs. The images were separated
using Zen black and exported in 8 bit TIFF format into folders for each channel. The stack of
images for each channel was imported separately into ScanIP Simpleware to generate the 3D
geometry of the vasculature. Once the stacks were imported, an image segmentation process was
performed on each set of images. Image segmentation is done to determine which pixels represent
actual parts of the image and those which are likely to represent background noise. The
37
segmentation in ScanIP is based on pixel thresholding using a 0 to 255 grayscale where 0
represents black, 255 is white, and the values in between represent the different shades of gray.
The threshold values used are shown in Appendix 2 and correspond to ‘Fish 1’. After the
segmentation of each set of images was performed, a mask of voxels was generated for each
element: RBCs, ECs and NPs. The voxel size depends on the spatial resolution, each voxel had a
volume of 0.119 µm3. A region of interest was selected on the caudal vein as shown in Figure
13a.The geometry of the vasculature was cropped to include only the region of interest and exclude
vessels that were not fully lumenized (Figure 13b). To create the geometry of the vessel segment
the three mask were combined into one mask, this allowed the gaps on the surface to be filled and
form a continuous surface. Further processing was done to smooth the surface using recursive
Gaussian smoothing filter, with a Gaussian sigma of 2. Smoothing filters get rid of noise and
attenuate contours, sigma is a spatial parameter that refers to the width of the 3D Gaussian that is
used to weigh how each neighbor pixel will affect the pixel being evaluated. It must be given in
units of pixels that contribute to the smoothing operation. The larger the value of sigma, the
smoother the surface. However, since the Gaussian filter reduces the detail levels of the geometry,
and due to the nature of the present study it is important to maintain surface detail, a conservative
value was selected according to the recommendations of the Simpleware reference guide and a
trial and error approach to determine which value seem to generate the most accurate model
(Figure 13c).
The initial geometry was closed, so an inlet and two outlet surfaces were defined by selecting the
contours on the terminal regions (Figure 13d). After performing a simulation with this geometry,
it was evident that there was a need of a flow extension so that the boundary flow effects have a
minimum influence on the flow present on computational domain. Therefore, the vessel inlet was
38
extruded by a total length of two diameters (total extrusion length= 52.8 µm) (Figure 13d). The
extruded region was excluded when performing the quantification of the NP voxels and
fluorescence intensity.
The vessel segment geometry was then discretized into finite volume elements. Finite volume
refers to the volume surrounding the node of each element on a mesh, and is referred to as mesh
element or cell. For a computational simulation, the solution of the problem is obtained by solving
a set of equations, described in the following subsection, for each element.
The meshing module from ScanIP was used to create meshes with different sizes in order to
perform a sensitivity analysis to determine which mesh provided the most accurate results without
representing a great computational cost in terms of time and memory used to simulate. In general
terms, a finer mesh which consists in a greater number of elements, should theoretically provide
more accurate results but at the same time represents an increase in the time and memory required
to perform the simulation. Therefore, a sensitivity analysis was done for 14 meshes which
consisted of different numbers and distributions of tetrahedral elements. For every mesh a
simulation was done using ANSYS Fluent 15.2, a commercial software for fluid dynamics
simulations. For this, each mesh was imported as in msh format. The simulations were done for
steady state with the parameters described in the following sub section. To analyze the results,
average wall shear stress, peak wall shear stress, Euclidean norm of wall shear stress, average axial
velocity measured at the main outlet, peak axial velocity, and Euclidean norm of the axial velocity
vector. The mesh that seemed to provide the most accurate results with the lowest number of
elements was selected for the simulations used in data analysis.
39
4.3.2. Flow simulation in the vein segment
The geometry of the caudal vein segment was imported into CFD commercial code ANSYS Fluent
15.2. Simulation of steady-state flow was performed assuming blood plasma and red blood cell
hemoglobin behave as Newtonian fluids since embryonic great vessel microcirculation is governed
by rigid blood cells.143 The material properties were obtained from values previously reported in
other investigations for zebrafish embryo blood, the density was defined as 1025kg/m3 and the
dynamic viscosity was 3cP.144–146 Blood was considered incompressible and the wall was assumed
to be rigid. The domain was discretized into 2,016,214 (including extrusion: 3,303,489) tetrahedral
finite volume elements, 247,103 elements were at the wall. The fluid flow velocity at the inlet for
the steady state simulation was defined as 239 µm/s, the mean velocity measured for the blood
flow in the vein segment in vivo. The inlet for the transient study was defined as the cardiac
waveform obtained from the velocity measurements, details are found below. For outlet
boundaries, the pressure was specified as 0 Pa. The simulation of the flow in the zebrafish vein
segment solved Navier-Stokes and mass continuity equations using the finite volume method.
Navier-Stokes equations assume fluid is a continuum and is not made up of discrete particles, the
fields of interest for example velocity and pressure are differentiable, this means that they have a
derivative at each point in the domain.
Navier-Stokes equation for a Newtonian fluid can be expressed as:
𝜌 (𝜕𝑢
𝜕𝑡+ 𝑢 ∙ ∇𝑢) = −∇𝑝 + ∇ ∙ (𝜇(∇𝑢 + (∇𝑢)𝑇) −
2
3𝜇(∇ ∙ 𝑢)𝐼) + 𝐹 (4)
Where u is the fluid velocity, p is the pressure, ρ is the density, µ is the dynamic viscosity, I is the
identity matrix, ∇ is nabla or del operator, and F represents the external forces applied to the fluid.
The equation can be simplified since the Reynolds number in microvascular vessels with low flow
is very small (Re<1), meaning the inertial forces are very small compared to viscous forces and
40
can be neglected. Additionally, gravity is neglected and the divergence of the velocity is equal to
zero since the fluid is incompressible. The simplified Navier-Stokes equation is:
0 = −∇𝑝 + ∇ ∙ (𝜇(∇𝑢 + (∇𝑢)𝑇)) (4.2)
Mass continuity equation:
𝜕𝜌
𝜕𝑡+ ∇ ∙ (𝜌𝑢) = 0 (5)
For incompressible flows the continuity equation yields since the derivative of density over time
is zero:
∇ ∙ 𝑢 = 0 (5.2)
These equations along with the conservation of energy equation, for a coupled set of equations
which cannot be solved analytically for most engineering problems, but can be approximated by
numerical methods. CFD simulations find a solution to a flow problem by dividing the continuous
problem into discrete domains using mesh elements to find a solution. Fluent in particular uses a
discrete volume element approach which consists on dividing the entire space of the geometry into
volume elements and solving the set of equations for each grid point. To obtain a continuous
solution for the whole volume, values between grid points are interpolated. The solution of the
equations for the volume elements is done by integrating the equations previously described, to
yield discretized equations.
A pressure-based solver was used since it is recommended for a wide range of flow regimes from
low speed incompressible flow, such as the one simulated, to high speed compressible flow. This
solver requires less memory than the density based solvers which are usually recommended for
problems where there is an interdependence between density, energy, momentum, and/or species
(e.g. compressible, hypersonic flows). Discretization was done by second-order-upwind method
recommended for tetrahedral meshes or for situations where the flow is not expected to be aligned
41
with the grid. The interpolation was done by a Green-Gauss node-based method which was also
selected because of the tetrahedral mesh according to the suggestions present in the Fluent manual.
The calculation of cell-face pressures was done using a standard interpolation scheme, which is
the default option in Fluent. Following the recommendations in the software’s manual,
initialization for a single phase, steady state flow was done using a 15 iteration hybrid initialization,
while standard initialization was used for unsteady flows. The default values were used for the
under-relaxation factors for pressure and momentum which control how much a variable can
change between iterations.
Convergence was monitored using the residual history, qualitative convergence occurs when the
residuals (x-, y-, and z-velocity) decrease by three order of magnitude. However, the scaled energy
and species residuals were also evaluated to monitor convergence. The scaled energy for a pressure
based solver must decrease to 10e-4, while the species residual must decrease to 10e-5 to achieve
species balance. Additionally, the overall mass balanced was checked to ensure that the net
imbalance was below 1% of the smallest flux through the domain boundary.
To obtain the wave form of flow in the zebrafish vein segment generated by the cardiac cycle, a
Fourier analysis was done to express the blood flow velocity, a periodic function, as a sum of sine
and cosine functions such that:
f(t) = ∑ An cos (2nπt
T) + ∑ Bn sin (
2nπt
T)
∞
n=1
∞
n=0
= A0 + A1 cos (2πt
T) + A2 cos (
4πt
T) + ⋯ + B1 sin (
2πt
T) + B2 sin (
4πt
T) + ⋯
(6)
Where T is the period of the function, t is time, and A and B are the Fourier coefficients given by:
A0 =1
T ∫ f(t)dt
T
0
(7)
42
An =2
T∫ f(t) cos (
2nπt
T) dt
T
0
(8)
Bn =2
T∫ f(t) sin (
2nπt
T) dt
T
0
(9)
From the mathematical definition of A0 we note that it represents the average value of the periodic
function f(t) over one period. The velocity measurements used to obtain the waveform were
obtained from the line-scan cross correlation PIV methodology previously described. The
velocities used correspond to the profile measured in the vessel segment that was simulated. The
entire measurements for velocity were divided into cycles, in total five cycles were used to obtain
the average waveform of the blood present in the vein segment as shown in Figure 11c-d. The
calculation of the waveform and the Fourier approximation was also done for the caudal artery;
the same methodology was used, except the number of cycles was nine as shown in Figure 11a-b.
To determine the Fourier coefficients, a trapezoid approximation was used to approximate the
definite integral of each term Ao, An, and Bn. The trapezoidal method is based on the approximation
of the integral between two points by calculating the region under the curve as the area of a
trapezoid. To increase accuracy, the trapezoid can be divided into multiple trapezoids and the total
area can be calculated as a sum of the individual areas. Two sensitivity analyses were done to
determine: 1) the most appropriate number of trapezoids to describe the integrals of the Fourier
coefficients and 2) the minimum number of harmonics required to accurately describe the
waveform of blood in the zebrafish vein segment. The sensitivity analysis showed that 30
trapezoids led to the smallest difference between Fourier approximation and the average velocity
profile. As shown in
43
Appendix 3 the minimum number of harmonics that decreases the difference between the Fourier
approximation and the average measured value is 15 harmonics.
For the time-dependent study, the boundary condition for the inlet was defined using a ‘User-
defined-function’ or UDF in Fluent that allows the user to define the boundary condition as a
profile described by the Fourier series using the coefficients in Appendix 4.
Courant number was used to determine the maximum time step size to ensure that the time step
duration is less than the time for the velocity wave form to travel to adjacent grid points.
The Courant number can be expressed as
𝐶 =𝑢 ∆𝑡
∆𝑥≤ 𝐶𝑚𝑎𝑥
(10)
Where u is the magnitude of the velocity, Δt is the time step, and Δx is the length between grid
points. Cmax is equal to 1 when a time-marching solver is used. In this case, the peak velocity of
the waveform (315 µm/s) was used as the velocity magnitude, and Δx was the minimum length of
a tetrahedral element in the mesh (0.146 µm). Using this expression, the time step was set to
0.000463s and the simulation was performed for 820 steps since the total cycle was of 0.38s.
Convergence for each time step of the transient study was set by x,y,z residuals below 1e-4 and
continuity convergence of 1e-3.
4.3.3. Post-processing simulation results
After the simulation had converged, the results were exported into CFD-post. As mentioned in the
introduction, one of the most important flow parameters that has been shown to affect NP
localization is shear stress. Therefore, wall shear stress was plotted as a contour on the vessel wall.
The range of the scale was later modified to fit the range of WSS at which the NPs seem to localize
in order to generate an overlay of the particle accumulation and the shear stress levels.
44
To determine if flow disturbances such as recirculation or flow splitting were present, streamlines
were plotted from the inlet of the vessel. As mentioned before, all the results excluded the area of
extrusion since this segment was not part of the actual geometry of the vein.
For the time dependent study, the time averaged wall shear stress (TAWSS) was calculated as:
𝑇𝐴𝑊𝑆𝑆 =1
𝑇∫ |𝑊𝑆𝑆|𝑑𝑡
𝑇
0
(11)
Where T is the time interval during which the values of WSS are measured, in this case, it
corresponds to the zebrafish embryo cardiac cycle which is 0.38 s-1.
4.4.Quantification of nanoparticles in zebrafish vasculature
The quantification of particles present on caudal aorta, venous plexus, and caudal vein was done
by generating a three dimensional model of the vasculature using Simpleware ScanIP. In order for
Simpleware to read the images from the confocal stack, the z-stacks of the zebrafish vasculature
had to be exported into separate channels (blue: NPs, green:ECs, red:RBCs) and tagged image file
format (or TIF). Each channel was imported separately into Scan IP, the first parameter the
software requests in order to generate a proper 3D-model are the scaling dimensions, this
dimensions depend on the parameters selected during image acquisition in the confocal
microscope. The scaling dimensions for each sample can be found in Zen black under the ‘info’
tab, this shows the x, y, and z scaling. Once the first channel was imported, the other two channels
were imported using the ‘add to background’ option in the Scan IP interface. Masks for each
component, NPs, ECs, and RBCs, were generated after thresholding in each channel. Appendix 2
summarizes the threshold levels used for each channel to generate the masks. Segmentation, was
done by thresholding each set of images. The first set of results comparing NP accumulation in
different regions of the vasculature was done without any further processing. A region of interest
45
was defined for the section of the vein, artery, and the plexus between those two. Images of the
region of interest are shown in Figure 8. The total number of voxels for each of the masks was
obtained by using the ‘mask statistics’ option in ScanIP.
The normalized number of nanoparticle voxels present in each region was obtained by dividing
the number of nanoparticle voxels by the total number of endothelial cell voxels present in the
region of interest. Quantification was done for three different zebrafish embryos. Data are
expressed as mean ± SD. Changes in variables were analyzed by one-way ANOVA and Tukey
posthoc tests.
4.4.1. Quantification of nanoparticles in each wall shear stress region
To quantify the nanoparticles in each wall shear stress region, a matrix with the fluorescence
intensity and the coordinates (x,y,z) of each nanoparticle voxel found in the vein segment used for
the simulation was obtained using ScanIP Simpleware. The script that allowed for this matrix was
obtained from the Simpleware support team upon request. After running the script, a csv file is
generated with the information for each voxel, this included x,y,z coordinates, and fluorescence
intensity. The file was opened using Matlab R2015a and a matrix of four columns and 136311
rows was created and named ‘NPF’ (Nanoparticle fluorescence). Results for wall shear stress from
the CFD simulation were imported as a matrix into Matlab and named ‘WSZ’. This matrix had
wall shear stress values with their corresponding spatial coordinates (x,y,z), WSZ had four
columns and 247102 rows, which made reference to the number of elements found on the vessel
wall geometry used for the simulation. It is important to note, that WSZ only includes the values
of the vein geometry and not the values from the extrusion that was added to the geometry before
the simulation. A Matlab script was developed to find a match between x,y,z positions of the two
matrices. In order to increase match accuracy, matrices were organized in descending order of x-
46
position, this was defined by comparing the different organizations of the matrices and identifying
the one that minimized the absolute difference between the x,y,z coordinates of each point,
Appendix 5 shows the results obtained for each combination. A wall shear stress value was
assigned to a voxel when the absolute difference between positions met the following: Δx<1.0e-7,
Δy<1.4e-6, and Δz<2.0e-6. These values for the absolute difference between positions were
selected since they provide the highest number of paired voxels with WSS values, and the lowest
tolerance. As shown in Appendix 6 as the value of the tolerance decreases, the number of paired
NP voxels with WSS values also decreases.
The limits accepted by the tolerances for a given position on the vessel wall are shown in Figure
36 in Appendix 8. If the conditions for the absolute difference were not met, the voxel was assumed
to be distant from the vessel wall and excluded from the quantification. The script for the
quantification is shown in Appendix 9 ‘Quantification_Fluorscence’. Additionally, the actual
absolute difference between the position of the voxels and the position of the WSS they were
assigned, from now on referred to as the pairing error, was quantified. The average pairing error
for the x position was 0.07± 0.02 µm, for y position 0.80 ± 0.42 µm, and for z position 1.16 ±0.50
µm. The calculations for pairing error were done using a Matlab script found in Appendix 10
‘Error_position’. This difference was reduced by organizing the matrices in ascending x value, as
shown on Appendix 7. In order to show the pairing error graphically, the reference point shown in
Figure 36b,c was used to plot the mean error of each position, since the error represents an absolute
value, it was added and subtracted from the reference point and plotted as six points, two for each
dimension (e.g. xreference -xaverage_error, xreference +xmean_error) in Figure 36c.
The number of nanoparticle voxels in each WSS region was presented as a histogram since it
represents the count of how many voxels fall into each interval. The number of intervals into which
47
the data is divided for a histogram, is referred to as bins. The number of bins affects the
representation of the data and can influence the way the data is interpreted, fewer bins with larger
intervals decrease the noise of the data and can mask outliers, while more bins with smaller
intervals present more noise but are more adequate to identify trends and density distributions.
Several equations have been proposed as guidelines and can be used as rules of thumb to calculate
an appropriate number of bins in order to represent the data. Most of the equations assume a normal
distribution, therefore, the first step was to evaluate if the data was normally distributed. For this,
IBM SPSS statistics 22 was used to test the normality of the 124,711 data points for the NP voxels
matched to a WSS value.
The test for normality produces a histogram, stem-and-leaf plot, and box plot for the data. As
shown by the histogram (Figure 22), the data were skewed and did not have a normal distribution.
The Kolmogorov-Smirnov test of normality gave a p value below 0.0001, which rejects the null
hypothesis that the data follow a normal distribution. To determine the appropriate number of bins
to represent the data, equations that accounted for skewness and non-normality were used and
results are shown in Table 1. The square root approach is the most general method that can be used
but produces the largest errors. Sturge’s formula was originally developed for normally distributed
data, however it was modified to include a kurtosis measure to take into account that the
distribution can include steep peaks or be flat regions. Doane’s formula was formulated based on
Sturge’s formula to account for the skewness of the data. Scott’s rule was also modified to account
for skewness by multiplying the original expression, used for normal data, by a skewness factor.
Histograms obtained using each method are shown in Figure 22. Since the Scott’s reference rule
provides a balance between noise and shape of the trend, it was chosen to continue with the analysis
of the data. The histogram was divided into 78 bins with 0.0045 Pa intervals between bins.
48
49
Table 1. Methods used to determine the appropriate number of bins that should be included in a
histogram to adequately represent the distribution of the data.
Method Equation Number of bins (k)
Square root 𝑘 = √𝑛 353
Sturges’ formula 𝑘 = (log2 𝑛) + 1 + log2(1 + 𝐾 ∗ √
𝑛
6)
𝐾 =∑ (𝑋𝑖 − �̅�)4𝑛
𝑖=1
(𝑛 − 1)𝜎4
18
Doane’s formula 𝑘 = 1 + log2(𝑛) + log2(1 +
√𝑏
𝜎√𝑏)
√𝑏 =∑ (𝑋𝑖 − �̅�)3𝑛
𝑖=1
[∑ (𝑋𝑖 − �̅�)2𝑛𝑖=1 ]3/2
𝜎√𝑏 = √6(𝑛 − 2)
(𝑛 + 1)(𝑛 + 3)
25
Scott’s reference
rule 𝑘 =
max 𝑥 − min 𝑥
ℎ
ℎ =3.5𝜎
𝑛1/3∗
21/3𝜎
𝑒5𝜎2
4 (𝜎2 + 2)13(𝑒𝜎2
− 1)1/2
78
The number of nanoparticle voxels was normalized by surface area in each wall shear stress region.
For this, the number of mesh elements at the wall in each wall shear stress interval were calculated
and multiplied by the average surface area of a tetrahedron face. This calculation assumed that the
tetrahedral mesh elements had the same size and the surface area of each tetrahedron element can
be calculated by the expression:
𝐴𝐹 =√3
4𝑙2
(12)
Where AF is the area of the tetrahedron face and l is the length of a tetrahedron edge. The length
used was the average edge length for all the elements in the selected mesh, for the selected mesh,
the AF was equal to 0.0564 µm2. The approximate volume of each computational element was
0.00554 µm3. The normalization was done by developing a Matlab script
50
‘Normalization_change_divisions’ (see Appendix 11) which calculated the number of mesh
elements on the wall that were present in each region of wall shear stress defined by the number
of intervals and the number of NP voxels in each region. This script can be modified to plot
different number of intervals by changing the ‘divisions’ variable. It can also be used to analyze
other sets of results from other vessels by adjusting the minimum and maximums WSS, ‘ssmin’
and ‘ssmax’, respectively. These values of WSS represent the minimum and maximum WSS found
for the NP voxels, not for the vessel.
The quantification of nanoparticles was also done by evaluating the fluorescence intensity of the
NP voxels. As mentioned at the beginning of the sub-section, the script provided by the
Simpleware support team that allowed us to export the information of the voxels in the model,
included fluorescence intensity values for each voxel. The histogram for values of fluorescence
intensity per voxel was obtained in order to evaluate the distribution of the variable and determine
if the quantification of particles could be done by voxel count or a fluorescence intensity evaluation
was necessary.
To compare both methods of quantification, the fluorescence intensity was evaluated for each WSS
region. The total fluorescence intensity for each WSS interval was obtained by adding the
fluorescence of all the voxels in one region and dividing it by the surface area as previously
described. To determine if the methodology of voxel counting was an appropriate measure of the
number of particles per region, the average fluorescence intensity per voxel was plotted for each
WSS interval along with the standard deviation shown as error bars. The relation between the
variables was evaluated by a correlation test. The first attempted test was a Perason product-
moment correlation to determine the strength and direction of a linear relation between the two
continuous variables WSS and voxel fluorescence intensity. One of the assumptions of the
51
Pearson’s correlation is that the two variables have a linear relationship, however by inspecting
the scatter plot of WSS versus nanoparticle voxel fluorescence intensity (Figure 26) there is no
clear evidence of a linear trend. A Spearman’s rank-order correlation, which does not rely on the
assumption of linearity, was then used to determine whether there is an association between the
two variables. Spearman’s correlation test has three assumptions that need to be met in order to
obtain a reliable result and analyze the data appropriately. The assumptions are: the two variables
are continuous, the two variables represent paired observations, and the relationship between the
variables is monotonic. The null hypothesis of the test is that there is no association between the
variables. Spearman’s test was used to determine the correlation between WSS and NP
accumulation on the region from lowest WSS to peak accumulation (WSS<0.056 Pa), since the
data points on this region had a monotonic behavior.
To evaluate if the correlation of WSS and accumulation on the whole dataset, the monotonic
assumption was evaluated by inspection of the scatter plot shown in Figure 26. The plot does not
show a clear monotonic trend. For the first values of WSS, the intensity seems to increase before
it reaches a peak and then decreases with an increase in WSS, this suggest there is a bivariate
behavior which cannot be analyzed by any test that requires a monotonic trend. The Hoeffding’s
D test is a nonparametric measure of association test used for non-monotonic variables, the statistic
ranges from -0.5 to 1, with positive values indicating dependence, it is important to highlight that
the signs of the statistic do not have any interpretation because the measure takes into account non-
monotonic relationships. This test was done using Wolfram Mathematica 9.0 and the null
hypothesis (H0: variables are independent) was rejected for p<0.05.
To determine the effect on spatial wall shear stress gradient on nanoparticle accumulation, the
spatial gradient was calculated using a modified Matlab script originally developed G. Ricardello
52
and collaborators which calculates the change of wall shear stress in a specific region by comparing
the wall shear stress value of the closest neighbors to the query. 147 To perform the calculation, a
point cloud with the WSS values was generated using CFD-post for a total of 100,000 points along
the vessel wall geometry.148 The least square approximation method suggested by Anderson et al.
for the surface gradient was used to calculate the change in wall shear stress magnitude in each
component (x,y, and z). The overall WSS gradient is then calculated by taking the derivatives of
the WSS magnitude parallel and normal to the flow direction as described by Mut et al.149:
𝑊𝑆𝑆𝐺 = √(𝜕𝜏
𝜕𝛼)2 + (
𝜕𝜏
𝜕𝛽)2 (13)
𝜕𝜏
𝜕𝛼= ∇𝜏 ∙ 𝛼,
𝜕𝜏
𝜕𝛽= ∇𝜏 ∙ 𝛽, 𝛼 =
𝜏
|𝜏|, 𝛽 = 𝑛 × 𝛼 (13.2)
Where 𝜏 is shear stress magnitude, 𝛼 is parallel to flow direction, 𝛽 is normal to flow direction, ∇
gradient operator denotes partial derivatives in the coordinate directions, and n is the normal to the
surface.
Number of nanoparticle voxels were quantified for each WSS gradient region, values were
normalized by the total number of elements in the vessel wall with the same value of WSS spatial
gradient. Spatial gradient is reported as the change in force [Pa] over a change in position measured
in microns.
4.4.2. Quantification of nanoparticles in each flow region
To quantify the nanoparticles in each flow region, results from the CFD simulation were imported
into ANSYS CFD-Post. The dispersion factor was calculated for each nanoparticle voxel in order
to have a quantitative measure of the flow disturbance in the region where the voxel was found.
The dispersion factor represents the ratio between radial velocity (towards the vessel wall) and the
longitudinal velocity (towards the outlet). The radial velocity (Vr) can be calculated as:
53
𝑉𝑟 = √𝑉𝑦2 + 𝑉𝑧
2 (14)
Where Vy is the velocity in the y-direction, and Vz is the velocity in the z direction. The dispersion
factor (Df) can be calculated as:
𝐷𝑓 =𝑉𝑟
𝑉𝑥
(15)
Where Vx is the velocity in the x-direction.
A flow completely undisturbed laminar flow with streamlines parallel to the vessel wall has a
dispersion factor of 0, this means that there is no lateral dispersion. A positive dispersion factor
indicates there is a trajectory non-parallel to the wall, therefore, the greater the dispersion factor,
the more disturbed or non-parallel the flow is. A negative dispersion factor indicates regions of
flow recirculation where flow is moving on the opposite direction. The calculation for the
dispersion factor of each nanoparticle voxel was done using a Matlab script
‘Dispersion_factor_per_NPvoxel’ that can be found on Appendix 12. The calculation for the
dispersion factor took into account the branching point of the vessel. Since the branching vessel
has a vertical orientation, the calculation for the dispersion factor was obtained by:
𝑉𝑟 = √𝑉𝑥2 + 𝑉𝑧
2 (14.2)
𝐷𝑓 =𝑉𝑟
𝑉𝑦 (15.2)
The histogram for the nanoparticle voxel count showing the distribution of the particles according
to their dispersion factor is shown in Figure 27. Since the data shows a normal distribution,
Sturge’s formula was used as an approximation of the number of bins in which the data could be
divided to still provide an appropriate representation of the trend. The data was divided into 19
bins so that each interval would correspond to 0.01 range in dispersion factor values.
54
The count of nanoparticle voxels and total fluorescence per dispersion factor was normalized by
the total volume of the flow exposed to the same dispersion factor. This volume was calculated as
the number of tetrahedral elements times the average volume per element. The volume of each
element is assumed to be described by the expression for a regular volume tetrahedron (VT):
𝑉𝑇 =𝑙3
6√2
(16)
The dispersion factor was calculated for each of the elements present on the fluid region of the
modeled vessel. A histogram with the distribution of the data based on number of elements with a
certain value of dispersion factor is shown in Figure 20.
The calculation of the fluorescence intensity per for each value of dispersion factor where the
particles localized, and the total fluorescence in each region of dispersion were obtained by
dividing the matrix with the nanoparticle data into 19 different matrices according to the value of
dispersion factor.
4.5. In vitro cell culture
Previous research in Dr. Rinker’s lab evaluated the effect of shear stress and flow pattern on
nanoparticle accumulation using human umbilical vein endothelial cells (HUVECs) and a parallel-
plate flow chamber to expose the HUVECs to different flow conditions. Results obtained for the
in vitro experiment will be compared with the in vivo results using the zebrafish embryos in order
to identify the effects of different shear stress levels and flow regimes. The following sub sections
are a summary of the methodology used to obtain the in vitro results.
4.5.1. Nanoparticle size and zeta potential measurements
To test the mean diameter and the dispersity of the nanoparticles used for both the in vivo and the
in vitro analysis, polystyrene carboxylate-coated FluoSpheres (2% w/v, blue fluorophore-loaded,
55
200 nm diameter, Life Technologies) were diluted to nanomolar concentrations in ultrapure water
and tested for mean size diameter, polydispersity index (PdI) and zeta-potential using Zetasizer
Nano ZS (DTS 1060, Malvern Instruments Ltd., Worcestershire, UK) at 25C. Dynamic light
scattering was used to determine the hydrodynamic diameter of the particles. Zeta potential was
calculated by laser Doppler velocimetry to determine colloidal stability. Measurements were
conducted in triplicates and values were reported as mean standard deviation. This measurements
were performed by Dr. Hagar Labouta in the Rinker and Cramb’s labs.
4.5.2. Cell culture and parallel plate flow chamber
Pooled HUVECs (Lonza) were seeded at a density of 5,000 cells/cm2 on glass microscope slides
pre-treated with 8 µg/cm2 collagen I (Gibco, Invitrogen) in PBS for 3 hours and grown in an
incubator at 37C and 5% CO2 in endothelial growth medium-2 (EGM-2, Lonza), until confluent.
A parallel-plate flow chamber was modified to incorporate a step gasket to enable a sudden
expansion recirculation region.78,150,151 Two rectangular silicon gaskets with cut-outs to form a
flow channel with a backwards facing step were sandwiched between a ported polycarbonate top
plate and a cell-seeded glass slide. The top gasket was 254 µm thick, h1, and had a cut-out region
of 1.25 cm width, w, by 4.59 cm length, while the bottom gasket formed the backward facing step
and was 381 µm thick, h2, with a cut-out region of 1.25 cm width and 3.4 cm length. Figure 30
shows the flow loop used for the experiments and the assembly of the sudden expansion flow
chamber. Additionally a glass field finder slide (Gurley Precision Instruments) for distance
measurements was placed underneath the cell-seeded slide. The entire assembly was held together
with hand-tightened clamps. The upstream flow path was 1.19 cm long and accommodated the
entrance length for flow development prior to encountering the step. The entrance length (L) for a
rectangular channel was defined as:
56
𝐿 = 0.08𝐻𝑅𝑒 (17)
Where H was the height of the chamber (h1 + h2) and Re was the Reynolds number (21.0 for 0.1
Pa, 42.1 for 0.2 Pa, and 168 for 0.8 Pa). The Reynolds number was calculated for each flow rate
as previously described for a similar flow chamber by150:
𝑅𝑒 =2𝑄
𝑣(𝑤 + 𝐻) (18)
Where v is the kinematic viscosity (0.007964 cm2/s) of the flow media, Q is the volumetric flow
rate (6.6 mL/min at 0.1 Pa, 13.2 mL/min at 0.2 Pa, and 52.8 mL/min at 0.8 Pa), and w is the width
of the chamber. Therefore, the flow entering the sudden expansion was considered fully developed
at all values of shear stress used here. The expansion ratio (H/h1) was 2.5.
Downstream of the expansion, fully-developed laminar flow was established and the wall shear
stress, τ, for the channel described by
𝜏 =6𝑄𝜇
𝑤𝐻2 (19)
Where μ is the fluid viscosity of the flow media at 37°C. These experiments were performed by
Dr. Amber Doiron at the Rinker lab.
4.5.3. Computational fluid dynamics sudden expansion flow chamber
To obtain the numerical solution for the recirculation region formed by the sudden expansion in
the flow chamber, a CFD model was constructed using COMSOL 5.0. In this CFD software, the
Navier-Stokes equations are solved by using the finite element method. Since the geometry of the
parallel plate flow chamber is symmetrical, a 2D approximation was done to simplify the
simulation. The domain with gap dimensions and boundary conditions (BC) is shown in Figure 5.
57
Figure 5. Two-dimensional geometry of the sudden expansion flow chamber used to exposed
cultured human umbilical vein endothelial cells to flow and nanoparticles. Arrows show the
direction of flow. Inlet was adjusted to flow rates that would generate shear stresses of 0.1, 0.2,
and 0.8 Pa.
The material properties were obtained from the characterization of EGM2 cell culture media, the
density was defined as 1kg/m3 and the dynamic viscosity at 37˚C was 0. 79464 cP. The domain
was discretized into 569,744 triangular (mostly within the central parts of the domain) and
quadrilateral (mostly near the boundaries) finite elements; the minimum and maximum sizes of
the finite elements were equal to about 1.02 and 28.5µm, respectively. At the inlet boundary, the
liquid flow rate was imposed whereas at the outlet boundary, the pressure was specified with zero
viscous stress. This simulation was performed for each of the three inlet conditions stated in the
previous section (6.6 mL/min at 0.1 Pa, 13.2 mL/min at 0.2 Pa, and 52.8 mL/min at 0.8 Pa). At the
walls, the no-slip condition was applied. The simulation for the laminar incompressible flow
present in the flow chamber was performed using the PARDISO direct solver. Recirculation areas
were identified by plotting 250 velocity streamlines for each inflow condition. Additionally, a
graph with shear stress as a function of distance from the step was plotted in order to define the
region of flow disturbance, the reattachment point (where shear stress = zero) and the laminar
region.
58
4.6.Nanoparticle flow exposure assay
For the flow and nanoparticle exposure assays, HUVECs grown statically in a microscope slide
were transferred into a sudden expansion parallel plate flow chamber, as described previously, and
exposed to media containing 10 L of 2% w/v nanoparticle solution of 200 nm polystyrene
carboxylate coated particle (red fluorophore-loaded, Invitrogen FluoSpheres®) per mL DMEM
(Sigma) with 2% serum for 30 minutes in the presence of flow that generated shear stresses of 0.1,
0.2, or 0.8 Pa on the surface of the cells. The parallel plate flow chamber was connected to a flow
loop in which media was pumped using a peristaltic pump (MasterFlex L/S, Cole Parmer) to a
pulse dampener (Cole Parmer) to minimize flow pulsations caused by the cyclic nature of the
peristaltic pump. The flow chamber was connected to the pulse dampener through the inlet (side
of the step gasket), and connected through the outlet back into the media bottle. The media bottle,
pulse dampener, and flow chamber were maintained in an incubator at 37°C and 5% CO2 to ensure
that the cells were always exposed to conditions that resembled the physiological environment.
After 30 minutes of nanoparticle exposure, slides were washed three times with warm HEPES
buffered saline solution to remove the particles that were not adhered or loosely adhered to the
surface of the cells, fixed with 4% paraformaldehyde for 10 minutes, stained with 1 µL/mL
Hoechst 33258 (Invitrogen) and 1 µL/mL CellMask Deep Red (Invitrogen) in HBSS for 10
minutes, and washed prior to being mounted with VectaShield (Vector Labs) and covering with a
coverslip. The results of the flow exposure were compared to a static control. For the static control,
the slides were grown until confluence, exposed to nanoparticles at 10 µL/mL in DMEM or EGM-
2 in a culture dish at 37˚C for 30 minutes prior to washing, fixing, staining, and mounting as
described in the procedure for flow exposed cells.
59
4.6.1. Flow pre-conditioning of endothelial cells
As mentioned in the introduction, ECs are sensible to flow and are able to adapt and sense different
flow conditions. Therefore, an experiment was done to compare nanoparticle accumulation to cells
pre-exposed to flow. For this, HUVECs were grown under static conditions until confluent. They
were then transferred to a sudden expansion flow chamber where they were exposed during 24
hours to flow at shear stress level of 0.1 Pa. After 24 hours, nanoparticles were injected into the
flow loop so that a concentration of particles of 10 L/mL in circulating EGM-2 (Lonza) media
was obtained. Similar to the previous flow experiments, nanoparticles in the flow were allowed to
circulate for 30 minutes before flow was stopped and slides were treated as described above in
preparation for image analysis.
4.7. In vitro image acquisition and analysis
The images of the slides from the nanoparticle cellular association assays were obtained using an
Olympus IX71 (Nagano, Japan) fluorescence microscope and a 40x objective. Confluent regions
were imaged at different areas of interest down the flow path, starting at the step gasket edge
location where the flow was found to be disturbed and the laminar region of flow closer to the
outlet of the flow. For a given region of interest, images were acquired on separate channels using
different filters for nanoparticles (red), plasma membrane (deep red), and nuclei (blue). Overlays
of representative images were created using Image J, and the intensity of signal from nanoparticles
was quantified in Matlab and reported as mean ± standard error. ANOVA and t-tests were
performed to determine statistical significance. These analysis was performed by Dr. Amber
Doiron at the Rinker lab.
60
5. Chapter 5: Results
5.1.Nanoparticle localization in zebrafish embryo vasculature
To evaluate the localization of nanoparticles in vivo, 200 nm polystyrene carboxylate coated
nanoparticles were injected directly into the zebrafish circulation and imaged in live embryos (51-
53 hpf) using confocal microscopy. The presented images were representative, and results were
reproducible over a sample size of five. The caudal region of the zebrafish vasculature (Figure 6a)
was the region of interest since it is where most of the angiogenesis is occurring, therefore highly
tortuous and heterogeneous vessels are present. The accumulation of nanoparticles in different
regions of the vasculature could be determined by the use of transgenic embryos with mCherry
labelled red blood cells and GFP labelled endothelial cells, injected with blue fluorescently tagged
200 nm carboxylate coated polystyrene particles as shown in the schematic in Figure 6b. Embryos
exposed to nanoparticles (Figure 6c, d) were imaged 1 hour after nanoparticle injection, with
nanoparticles shown in blue. Higher nanoparticle accumulation was found near branching areas
and irregular surfaces as shown by yellow arrowheads compared to straight regions of the
vasculature. Straight vessels like the caudal aorta (CA, dashed white lines) exhibited lower
nanoparticle accumulation (Figure 7a,c,e) than that of highly branched vessels in the venous plexus
and the caudal vein (Figure 7b,d,f).
Along the caudal vein, nanoparticles localized to areas where blood flow is likely to be disturbed
immediately downstream of branches and curves in the vessel (yellow arrowheads). Blood flow
(white arrows) moves from anterior to posterior (left to right) in the CA and posterior to anterior
(right to left) in the caudal vein of the venous plexus. Large nanoparticle accumulation regions
were visible as concentrated areas of blue fluorescence while smaller accumulations of particles
resulted in a punctuate pattern of blue fluorescence. Nanoparticle signal was observed in the caudal
61
venous plexus 5 minutes after injection (data not shown). The tortuous vessels of the caudal plexus
showed the highest degree of nanoparticle localization in the zebrafish vascular system.
Figure 6. Nanoparticle distribution in the zebrafish embryo vasculature. (a) Schematic of the
caudal region of the embryo vasculature at 52 hpf where the localization of nanoparticles was
evaluated using transgenic zebrafish embryos (b) with mCherry labelled red blood cells shown in
red, GFP labelled endothelial cells in green, and blue fluorescently tagged 200 nm carboxylate
coated polystyrene particles. (c,d) Confocal microscopy image of transgenic zebrafish after one
hour of nanoparticle injection. The caudal artery (CA; region between the dashed white lines) had
a lower nanoparticle accumulation than the caudal tail plexus (CTP) and the caudal vein (CV) as
shown by the blue signal intensity. White arrows show the direction of flow and yellow arrowheads
denote particle accumulation in the CV. Representative image from n=5 zebrafish embryos.
62
Figure 7. Higher levels of nanoparticles accumulate in the caudal vein as compared to the artery.
Single slices from confocal microscopy image of transgenic zebrafish with GFP-labelled
endothelial cells (EC; green), mCherry labelled red blood cells (RBC; red) after one hour of
exposure to 200 nm carboxylate coated blue polystyrene particles (NP; blue). The caudal aorta
(CA; dashed white lines) shows rapid erythrocyte movement (a), but little nanoparticle
accumulation (c) within the vessel wall (e). White arrows show the direction of flow. In the caudal
vein, erythrocytes move more slowly (b), and higher nanoparticle accumulation occurs (d),
especially in branching areas or curved regions (yellow arrowheads; f). Representative images
from n=5 zebrafish.
63
Figure 8. Quantification of the number of nanoparticle voxels present in different regions of the
zebrafish embryo vasculature. (a) Number of nanoparticle voxels for three different zebrafish
embryos present in the caudal artery, vein, and plexus normalized by the total number of voxels in
each region of interest. Particles accumulating in the artery where significantly lower (*p<0.05)
than those in vein and plexus. No statistical difference was found between vein and plexus.(b) 3D
model of the caudal vasculature showing masks for endothelial cells (green), red blood cells (red),
and nanoparticles (blue). Regions of interest for caudal aorta and vein are shown in the boxed areas
where vessels appear grey.
The quantification of nanoparticle accumulation in the caudal region of the zebrafish embryo
shows that most of the nanoparticles accumulate in the caudal vein (Figure 8a). The accumulation
of nanoparticles is significantly lower in the artery compared to the vein and the plexus. There
was no statistical significance in the difference of means between the accumulation in the caudal
vein and the caudal plexus. The quantification was done in terms of the number of nanoparticle
voxels found in each vessel. The number of voxels was obtained by building the 3D model of the
vasculature as shown in Figure 8b and defining different vessels or segments of the vasculature as
64
regions of interest and obtaining the number of voxels per mask. The 3D models of the vasculature
were analyzed without further pre-processing such that the voxels were only generated by the
threshold levels of the original confocal images and not the processing filters.
5.2.Blood flow velocity and waveform in the zebrafish embryo
Blood flow velocities in different vessel segments of zebrafish vasculature were determined using
line-scanning particle image velocimetry. Line scans contain a single row of pixels and can acquire
more frames per second than two-dimensional imaging. The acquisition of the line scans was done
on the center axis of the vessel and tracked the movement of fluorescent mCherry red blood cells.
The reconstruction of the frames obtained by the line scans resulted in a planar image with red
streaks as shown in Figure 9b where the x axis corresponds to the spatial component and the y axis
to the temporal component. The red streaks correspond to the red blood cells movement in time
(Δx/Δt), which is proportional to the velocity. The temporal resolution to characterize the
movement of red blood cells was approximately 2 ms per frame, for a total of 3000 frames. The
time between streaks at a fixed position (Δt) is inversely proportional to the flux of red blood cells
in the vessel. The distance between streaks at a fixed time (Δx) is inversely proportional to the
density of red blood cells. Velocities of blood flow were assumed to be equal to the velocity of red
blood cells, and calculations were performed by an automated Matlab script developed by Dr.
Bahareh Vafadar at Zymetrix, University of Calgary.
65
Figure 9. Line-scan particle image velocimetry to track movement of red blood cells (a) Schematic
of red blood cell tracking using line-scans. (b) Change in position (x) of red blood cells in time (t)
for caudal artery and vein.
Blood flow velocities in the arteries were higher than velocities in veins and capillaries (Figure
10a). There was a considerable variation between blood flow velocities in different arteries and
different veins within and among animals. It is important to highlight that this quantification was
done in different regions of the vasculature, not only in the caudal region. Therefore, results show
a large variation even in the same type of vessels. In general, lower velocities were found in the
caudal region compared to the blood flow velocity of vessels in the trunk of the zebrafish embryo
such as the dorsal artery and the posterior cardinal vein. Different velocities likely reflect the size
and the structure of the developing plexus where newer, smaller vessels have less flow. Mean
blood flow in arteries was 830±290 µm/s (n=12), 530±180 µm/s (n=24) in veins, and 180±140
µm/s (n=7) in capillaries. Since the caudal region of the vasculature had the highest nanoparticle
localization, flow was characterized in this region for three different zebrafish to evaluate
velocities, waveform, and pulsatility in the caudal artery and vein. Velocities of blood flow for the
caudal artery and vein from the zebrafish embryo in Figure 7 are shown in Figure 10c and e,
66
respectively. Average blood flow was 341 µm/s in the caudal artery and 239 µm/s in the caudal
vein, similar blood flow velocities for zebrafish in early developmental stages have been
previously reported.152–154
The waveform per cycle was calculated for the caudal artery and vein using nine and five cycles,
respectively, to calculate the average cycle as shown in Figure 11a and c. The blood flow waveform
in the vein was not as clearly defined as in the caudal artery as can be seen by comparing the
velocity measurements shown in Figure 10c and e. The average waveform per cycle for each vessel
shown as a green thick solid line in Figure 11a and c was used to further calculate the equation of
the waveform in the caudal artery and vein (Figure 11b,d) as an approximation of Fourier
coefficients. The duration of each cycle was roughly the same for the caudal artery and vein, 0.35
and 0.38 s, respectively.
Figure 10. Quantitative analysis of blood flow in the developing zebrafish vasculature (a) Mean
blood flow velocity for five different zebrafish embryos. Mean blood flow in arteries was
830±290µm/s (n=12), 530±180µm/s (n=24) in veins, and 180±140µm/s (n=7) in capillaries.
Confocal microscopy image of 52hpf transgenic zebrafish caudal artery (b) and vein (d) after 60
67
minutes of exposure to 200 nm carboxylate coated polystyrene nanoparticles fluorescently labelled
(blue). White arrow shows the point where the line scan was recorded and the direction of flow,
graphs show the velocity profile for the blood flow in the caudal artery (c) and vein (e) segment
obtained using particle image velocimetry and a cross correlation method.
Figure 11. Blood flow waveform in the caudal artery (a,b) and vein (c,d) of the developing
zebrafish at 52 hpf. The waveform for the caudal artery (a) obtained by tracking the red blood cells
movement during 9 cycles shows an approximate duration of 0.35s per pulse. Approximation of
68
the caudal artery (b) and the caudal vein (d) waveform using Fourier series with 15 harmonics.
The waveform for the caudal vein (c) obtained by tracking the red blood cells movement during 5
cycles shows an approximate duration of 0.38s per pulse.
To determine the fish-to fish variation, three different zebrafish embryos at 52 hpf were analyzed.
Results for the mean velocity found in the vessel are reported as well as the average peak and low
velocity. These results are shown in Table 2 and are separated by fish and vessel type. All
measurements were acquired from the caudal region of the zebrafish embryos. The calculation of
the vessel diameter, waveform duration or pulse frequency, dimensionless number to characterize
flow, and forces present in the vessel wall were also quantified and shown in Figure 12. In general,
there was little variability for the same vessel in the same fish. The variability of different vessels
(artery vs. vein) in the same fish was also small, even though as shown before, there is a large
difference between blood flow velocities. There was pronounced variability between embryos. On
average the approximate diameter of the caudal artery measured using 2D confocal images was 20
µm, slightly higher than the diameter of the caudal vein which was approximately 19 µm as shown
in Figure 12a. The duration of each waveform, calculated as described previously for the data on
Figure 11 using the number of cycles in Table 2, was very similar for the caudal artery and vein,
0.39 and 0.42 s, respectively (Figure 12b). Dimensionless numbers were calculated in order to
determine the approximate ratio of fluid inertial forces to viscous forces for the Reynolds number
(equation 1), and the ratio of pulsatile flow frequency to viscous effects for the Womersley number
(equation 3). For both cases, the geometry was assumed to be cylindrical in shape; therefore the
results must be taken as approximations of the real values. For both the caudal artery and vein,
Reynolds number was below 1 (Re<1) as shown in Figure 12c, this suggest that the flow in these
vessels is a creeping or Stokes flow, where the inertial forces are very small compared to the
69
viscous forces. This occurs when the fluid velocities are very slow, and is likely to occur in
microfluidic ranges, such as the vessels of zebrafish embryos. The Reynolds number depends on
the velocity of the blood flow in the vessel, therefore it is expected to increase during peak velocity
and decrease during the lowest velocity. However, since the range of the average values is in the
order of 10e-3, Reynolds number is expected to be below 1 when evaluated at any point in the
velocity range of the waveform.
Since flow in the caudal artery and vein have a pulsatile nature, a more appropriate dimensionless
number is the Womersley number (equation 3) to determine the relation of the pulsation frequency
and the viscous forces. Even though there is a slight change in the pulsation frequency of the caudal
artery and vein, as shown in Figure 12b, the Womersley number defines a system by an order of
magnitude; therefore slight changes in pulsation frequency do not affect the overall characteristics
defined by the Womersley number. In both cases, the Womersley number was below 1 (Figure
12d), this means that the frequency of pulsations in the caudal artery and vein is low enough to
enable the formation of a parabolic velocity profile during each cycle, and the flow is predicted to
faithfully track the oscillating pressure gradient since inertia forces become negligible and flow is
determined by viscous forces and the pressure gradient. Flow with Womersley numbers below 1
have a quasi-steady behavior and can be evaluated at each point in the velocity profile using
Poiseuille’s law to obtain the instantaneous values or the average values of shear rate (Figure 12e)
and shear stress (Figure 12f).
Shear rate and shear stress were calculated using Poiseuille’s law for cylindrical pipes (equation
2). The caudal artery had on average, a higher shear rate of 190 s-1 compared to the caudal vein
which had a shear rate of 160 s-1. The calculation of shear stress was done by assuming a blood
viscosity of 3 cP which corresponds to a hematocrit of 45%. However, since no published studies
70
have evaluated the viscosity of 52 hpf zebrafish embryos, an assumption based on previous studies
evaluating flow parameters in zebrafish embryos was made.144–146 Shear rate and shear stress
values represent an ideal approximation of the actual values present in the vessels since they are
based on an ideal geometry and an average velocity for each case.
Table 2. Blood flow velocity calculations for three different zebrafish embryos (52 hpf) obtained from
quantification of flow in the caudal artery and vein showing the average velocity during the whole
recording, the average highest velocity per cycle, and the average lowest velocity per cycle. Measurements
of the same vessel in the same fish were taken from different segments of the same vessel.
Fish Vessel
Mean
velocity
(µm/s)
Standard
deviation
Peak
systole
velocity
(µm/s)
Standard
deviation
Low
diastole
velocity
(µm/s)
Standard
deviation
Number
of cycles
analyzed
1
Vein 436 126 629 31 261 52 7
Vein 492 118 653 76 332 47 9
Artery 615 185 901 70 384 69 9
2
Vein 496 271 946 48 162 32 8
Vein 489 319 1130 182 120 58 7
Vein 467 306 1153 85 147 53 3
Artery 580 291 1082 58 217 43 8
3
Vein 228 65 325 42 143 192 10
Vein 239 74 323 19 121 39 5
Vein 275 66 375 40 172 47 11
Vein 187 72 291 52 73 43 7
Artery 322 300 868 79 30 11 9
Artery 337 291 853 70 45 22 9
71
Figure 12. Comparison of caudal vessels and fish-to-fish variability for anatomical and flow
characteristics found in the developing zebrafish at 52 hpf. (a) Vessel diameter of the caudal artery
72
and the caudal vein. (b) Average waveform duration analyzed using at least 3 cycles of velocity
per recording. (c) Relation of inertial to viscous forces by Reynolds number assuming straight pipe
geometry shows creeping flow in both vessels (Re<1). (d) Relation of pulsatile forces to viscous
forces by Womersley number shows fully developed profile in each pulse (Wo<1) for each vessel.
(e) Shear rate and shear stress (f) calculations using Poiseuille estimation for straight pipes to
obtain the ‘ideal’ shear present in each vessel. Results show high variability between fish and lower
variability between different vessels of the same fish. Different measurements of the same fish in
the same vessel correspond to measurements in different segments of the vessel evaluated.
5.3.Zebrafish embryo vein segment surface model construction and computational mesh
generation
Since nanoparticles localized strongly in the caudal vein, a vessel segment from this region was
selected for computational fluid dynamics simulation to determine blood flow profiles and wall
shear stresses in the vessel. The caudal vein evaluated in the computational fluid dynamics
simulation is shown in Figure 13a. At 52 hpf, embryos are undergoing angiogenesis, therefore,
some of the vessels are not fully developed and did not have a formed lumen which prevented the
flow of blood to these regions. The 3D model of the caudal vein was generated from the confocal
z-stack using the image processing software ScanIP, Simpleware. The 3D model obtained after
selecting the threshold values for the endothelial cell, red blood cell, and nanoparticle channel is
shown in Figure 13b. A region of interest, shown inside the black box in Figure 13b, was selected
based on the section where the line-scans were taken to obtain the blood flow velocity as shown
in Figure 10d. Further processing was done in order to eliminate noise voxels and smooth the
surface of the vessel segment as described in the Methodology section. The geometry for the vein
segment is shown in Figure 13c, vessels that did not have a lumen were modeled as bumps as
shown by the black arrows. An extension for the inlet was added in order to enable a path where
73
the flow could develop before entering the region of interest (Figure 13d), this extension was
equivalent to two diameters approximately 52.8 µm. The side vessel was defined as an outlet since
it did not have a fully developed lumen distal to the branching point. There was not a clear
movement of red blood cells through this vessel, however, the presence of blue fluorescent signal
suggest that there is flow going through the side vessel.
Once the geometry was created, a mesh was generated using the meshing option in ScanIP before
importing the model into ANSYS Fluent. A mesh sensitivity analysis was done in order to
determine the optimal size and distribution of the tetrahedral elements used to divide the geometry.
For this, a steady state simulation was done in 14 different meshes, for each case the average and
maximum values for the wall shear stress and the axial velocity of the main outlet was compared.
The aim of the sensitivity analysis was to determine the mesh with the lowest number of elements,
but the highest accuracy. This evaluation works under the premise that higher number of mesh
elements generates more accurate results but also requires higher computational memory and time.
Therefore, the point with a mesh size greater than 6 million elements, shown in Figure 14,
theoretically represents the most accurate result. The green square represents the mesh that was
selected to perform the simulation since it seems to provide the most accurate results with the
lowest number of mesh elements, for most cases shown in Figure 14.
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Figure 13. 3D geometry of the zebrafish caudal vein. (a) Confocal image of the transgenic caudal
vein with mCherry labelled red blood cells shown in red, GFP labelled endothelial cells in green,
and blue fluorescently tagged 200 nm carboxylate coated polystyrene particles. Embryos
undergoing angiogenesis exhibit vessels not fully lumenized. (b) 3D model of the caudal vein
region built using ScanIP from the z-stack confocal images, the segment in the black box
corresponds to the region of interest evaluated in the study. (c) Smoothed model of the vein
segment outlined in the region of interest, black arrows show the vessels that were cropped and
modelled as bumps since they were not fully formed and did not have flow in the luminal region.
75
(d) Model with the extruded inlet (2 diameters in length) to provide a path for the flow to develop
before entering the region of interest. Inlet condition for the steady state simulation was defined as
the average velocity recorded by the line scans in that same vessel (239 µm/s), and two outlets
with zero pressure.
Figure 14. Mesh sensitivity analysis for 14 tetrahedral meshes with a different number of mesh
elements. (a,b,c) Wall shear stress and (d,e,f) axial velocity at the main outlet were used to compare
the different meshes. Green square represents the mesh that was selected to perform the
simulations in this study. The selected mesh has 2,016,214 tetrahedral elements in the region of
interest (excluding the extrusion) and represents the lowest number of mesh elements required
improve the theoretical accuracy of the results.
76
Table 3. Mass balances of the fluid in the vessel to confirm convergence of the steady state
simulation.
Number of
mesh
elements
Inlet
(kg/s)
Main
Outlet
(kg/s)
Side outlet
(kg/s) Difference % difference
252,813 1.37E-10 9.62E-11 4.07E-11 8.75E-16 2.15E-03
465,184 1.37E-10 9.59E-11 4.10E-11 4.82E-16 1.17E-03
557,673 1.37E-10 9.52E-11 4.17E-11 -1.95E-15 -4.68E-03
922,072 1.37E-10 9.07E-11 4.62E-11 -7.94E-16 -1.72E-03
1,232,588 1.37E-10 8.95E-11 4.75E-11 1.90E-16 4.00E-04
1,944,993 1.37E-10 8.75E-11 4.94E-11 -4.07E-15 -8.24E-03
2,626,244 1.37E-10 8.81E-11 4.89E-11 -6.84E-16 -1.40E-03
957,698 1.37E-10 9.08E-11 4.62E-11 3.84E-15 8.31E-03
2,016,214 1.37E-10 8.77E-11 4.92E-11 -5.69E-16 -1.16E-03
2,680,999 1.37E-10 8.69E-11 5.00E-11 -5.50E-16 -1.10E-03
2,927,455 1.37E-10 8.64E-11 5.05E-11 -9.09E-16 -1.80E-03
To determine if each simulation had fully converged and no mass was accumulating in the system,
mass balances for each mesh were done after the simulation was performed. These results are
shown in Table 3, where the difference represents the difference between the mass entering the
system, and the mass that left the system. In theory, since the simulation is done in a steady state,
the difference should be equal to zero since there should be no accumulation of matter in the
system. However, some discrepancies occur during the convergence of the simulation since it is
based on the definition of tolerances and not absolute values. Nevertheless, a percentage of
difference below 1% is considered to be appropriate for steady state simulations. As shown in
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Table 3, the absolute percentage difference was always below 0.01%, therefore it is assumed that
convergence has been reached since the residuals for x-, y-, and z-velocity decrease by three orders
of magnitude and the overall mass net imbalance was below 1% of the smallest flux through the
domain boundary.
The final mesh selected for the simulation is shown in Figure 15b and c. The zoomed image shows
a fine mesh on the vessel wall. The mesh had to be fine on the vessel wall in order to provide
accurate results of the wall shear stress. The geometry of the vein segment with the extrusion was
divided into tetrahedral mesh elements the total number of elements in the region of interest was
2,016,214.
Figure 15. Geometry and selected mesh for the caudal vein segment used to perform the
simulations. (a) Geometry with the extrusion was divided into (b) tetrahedral mesh elements with
78
the mesh size selected after the sensitivity analysis (2,016,214). (c) The mesh at the wall was very
fine in order to quantify accurately the forces of flow acting on it.
5.4.Zebrafish embryo vein segment computational fluid dynamics results for steady state
simulation
The simulation of the caudal vein segment of the zebrafish embryo was done using as an inlet
condition the average velocity (239 µm/s) calculated for the profile shown in Figure 10e, for the
steady state. Since the Womersley numbers for the caudal vessels in different zebrafish embryos,
including the one under evaluation, were below one, a steady flow was selected to determine the
instantaneous values generated by the average velocity blood flow. The velocities residuals were:
7.16e-5, 2.42e-5, and 1.08e-5, for x, y, and z, respectively. The continuity residual reached a value
of 3.39e-4. Mass balance done after convergence produced an approximate discrepancy of 0.001%.
Additionally a time-dependent simulation was done in order to contrast the effect of pulsatile blood
flow. For this, the inlet velocity was defined as the waveform for the zebrafish embryo caudal vein
segment shown in Figure 11d. Results for one period (0.38s) were used to calculate the time
average wall shear stress (TAWSS).
The steady state simulation provided information of the instantaneous WSS for an average velocity
inlet condition. For steady state, most of the elements found in the wall had WSS values ranging
between ≈0 and 0.5 Pa as shown in the histogram skewed right in Figure 16 and the contour plots
from the CFD simulation in Figure 17. The minimum value of WSS was close to 0.001 Pa and the
maximum value was 2.92 Pa. The mean WSS was 0.20 ± 0.13 Pa.
Similar to the instantaneous WSS, most of the elements of the wall had a TAWSS from 0 to 0.5
Pa. However, the maximum value was found at 1.54 Pa and the mean TAWSS was 0.16 ± 0.10
Pa. As seen by the plots in Figure 16, TAWSS is overall lower than the instantaneous WSS
obtained by the steady state simulation. The TAWSS of the vein segment from different views in
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Figure 18 shows slight differences from the instantaneous WSS in Figure 17, specially in regions
where WSS is 0.36 Pa or higher. Still, the general distribution of the shear stresses is the same
despite the difference in the calculation process, and the simplification of the steady state model
compared to the time-dependents study.
Figure 16. Total number of wall elements at each wall shear stress level obtained by the simulation
of the caudal vein segment using (a) steady state with inlet velocity of 239µm/s. Even though shear
stress ranged from almost 0 Pa to 2.92 Pa, most of the vessel wall had shear stresses from 0 to 0.5
Pa. (b) Time-average wall shear stress calculation for one cardiac cycle. Overall, most of the vessel
wall seems to be exposed to the same magnitudes of shear stress, as those found in the steady state.
However, the maximum value of shear stress is 1.54 Pa, which almost half the value found for the
instantaneous WSS.
80
Figure 17. Wall shear stress contours obtained by computational fluid dynamics simulation of the
caudal vein segment in the developing zebrafish embryo modeled using a steady state condition
with laminar inlet velocity of 239 µm/s. Different views show lower wall shear stress in the regions
with bumps and surface irregularities as shown by the darker blue colors in front view (a), back
view (b), and top view (c).The bottom view (d), shows slightly higher wall shear stress levels at
the base of the vessel where no vessels were sprouting.
81
Figure 18. Time-average wall shear stress contours obtained by computational fluid dynamics
simulation of the caudal vein segment in the developing zebrafish embryo modeled using a
transient study with velocity waveform as an inlet simulated for one period. Different views show
lower wall shear stress in the regions with bumps and surface irregularities as shown by the darker
82
blue colors in front view (a), back view (b), and top view (c).The bottom view (d), shows slightly
higher wall shear stress levels at the base of the vessel where no vessels were sprouting.
The contour plots show that regions with branches and downstream of bumps had the lowest values
of wall shear stress (Figure 17 and Figure 18 a,b,c). Straight regions had the highest values of wall
shear stress as shown by the red contours in Figure 17 and Figure 18. TAWSS shows less regions
with high WSS than the instantaneous WSS calculation obtained using a steady state simulation.
Straight regions had laminar blood flow profile shown by the straight streamlines in Figure 19.
Branches and curvatures generated flow disturbances in the vessel. The branching vessel caused
the flow to split between the two outlets. In steady state, the streamlines do not seem to show any
flow recirculation regions. In general, lower wall shear stress seemed to correlate with flow
disturbances as can be seen in the regions where the streamlines deviate from a parallel orientation
in reference to the vessel wall.
The calculation of the dispersion factor in all the fluid elements is summarized by the histogram
in Figure 20. The majority of the elements had a dispersion factor ranging from 0.07 to 0.5. The
higher the dispersion factor, the more the flow deviates from a parallel orientation in reference to
the vessel wall. Flow that is completely parallel to the wall has a dispersion factor of 0.
83
Figure 19. Velocity streamlines obtained by computational fluid dynamics simulation of the
caudal vein segment in the developing zebrafish embryo modeled using a steady state condition
84
with laminar inlet velocity of 239 µm/s. The curvature of the streamlines increased in regions were
the geometry had branching points and surface irregularities. Highest velocity was found at the
center of the vessel, lowest velocity was found near the vessel wall, particularly in branching
regions as can be seen in the front (a) and back (b) views.
Figure 20. Quantification of the number elements in the fluid region of the caudal vein segment
in each dispersion factor interval. Most of the flow in the vein segment had low dispersion factors
(≤0.5), indicating that most of the flow was parallel to the vessel wall suggesting an undisturbed
laminar flow. Calculations of the dispersion factor were done using the velocities in x, y, and z
obtained from the steady state simulation.
5.5.Nanoparticle quantification in regions with different wall shear stresses
Nanoparticle voxels present in the 3D model generated using the confocal images from the z-stack
were quantified as an indirect measure of the localization of the particles in the caudal vein
segment. The confocal images acquired for the nanoparticle channel were overlaid with the wall
85
shear stress contours obtained from the steady state simulation Figure 21a and the TAWSS
contours in Figure 21b. Regions with lower wall shear stress (<0.1Pa) have an increase blue signal
which corresponds to the accumulation of 200 nm carboxylate coated polystyrene fluorescently
tagged nanoparticles. While higher levels of wall shear stress (>0.2Pa) shown by orange and red
solid lines, had lower nanoparticle accumulation.
To quantify the accumulation of particles in different WSS and TAWSS regions, the x,y,z position
of the wall shear stress element was paired to the x,y,z position of each NP voxel, as described in
the Methods and Materials section. Using the values for instantaneous WSS, nanoparticle voxels
where found in regions with WSS lower than 0.35 Pa and higher than 0.03Pa as shown by the
histograms in Figure 22. The histograms in this figure all represent the same data but use different
empirical approaches to determine the number of bins, or in this case the number of intervals used
to divide the wall shear stress span.
The number of NP voxels present in each WSS interval was normalized by the number of wall
shear stress elements present in each interval (Figure 23). Particles seem to accumulate more in
regions of the vessel where WSS ranges between 0.04 Pa and 0.07 Pa, these are regions below the
average instantaneous WSS, in fact, and these regions correspond to 17% of the total number of
elements on the wall. However, as shear stress increases (above 0.07Pa) there is not a clear trend.
Nanoparticle accumulation with TAWSS seemed to have a more defined trend, with a slight
increase in accumulation with increasing TAWSS, but beyond peak accumulation, a constant
decrease in accumulation occurred with increasing shear stress.
86
Figure 21. Overlay of a confocal image showing blue fluorescent 200 nm carboxylate coated
polystyrene nanoparticles accumulating in the caudal vein segment of the zebrafish embryo one
hour post injection and the wall shear stress level contours. (a) Contours obtained from a steady
state simulation using inlet velocity of 239 µm/s and from (b) transient simulation using the
average cardiac waveform as the inlet parameter. The overlay shows high nanoparticle localization
of darker blue contours which correspond to lower wall shear stresses (≤0.0573 Pa), nanoparticle
signal decreases in regions with higher wall shear stresses (≥0.225 Pa) depicted by yellow, orange
and red contours.
87
Figure 22. Comparison of the effect of number of bins in a histogram using different empirical
models for non-normal distributions. (a) Standard square root approach shows the distribution of
nanoparticle voxel count per wall shear stress level, dividing the wall shear stress range into 353
bins. (b) Sturge’s rule for skewed data divided the WSS range into 18 bins. (c) Doane’s rule divided
the range in 25 bins and (d) Scott’s rule in 78 bins. Despite the number of bins used to divide the
range of wall shear stresses, the general trend remains the same, there is an increase in nanoparticle
accumulation with wall shear stress until a peak is reached, after which the number of nanoparticle
voxels present decreases.
88
Figure 23. Quantification of number of nanoparticle voxels per wall shear stress region for steady
state instantaneous wall shear stress (a) obtained by the simulation of the vein segment using an
inlet of 239 µm/s. Scale shows an increase in accumulation until a peak wall shear stress occurs at
0.055 Pa after peak accumulation occurs, there is a decrease in nanoparticle accumulation in the
region of higher shear stresses. Nanoparticles accumulated in regions between 0.037 and 0.346 Pa.
89
(b) Time-average wall shear stress values obtained for the average of one cycle using the waveform
inlet for the caudal vein segment. Particles accumulate in regions of lower wall shear stress,
showing a decrease accumulation with increasing shear stress. Peak accumulation occurred at
0.033 Pa, while accumulation occurred between 0.028 and 0.256 Pa. Histogram on the top right
corners shows the number of computational elements at the wall for each wall shear stress level,
and the regions of wall shear stress where the particles were found (in red).
Additionally, the effect of spatial wall shear stress gradient on nanoparticle accumulation was
evaluated and results are shown in Figure 24. Higher wall shear stress gradients seem to have
higher nanoparticle localization, especially quantified using the instantaneous WSS. However,
there is not a clear trend in the data for both the instantaneous WSS and the TAWSS. The overall
distribution of the spatial gradient was very similar for the instantaneous WSS and the TAWSS.
Voxel count can provide appropriate information about the localization of particles; however, this
measure can be used when most of the voxels have similar fluorescence intensity. When there is a
high heterogeneity of fluorescence intensity per voxel, voxel count is no longer an appropriate
measure of NP accumulation. Therefore, the analysis of fluorescence intensity has to be taken into
account as well. The histogram in Figure 25a shows the total number of NP voxels per fluorescence
intensity value. The values of fluorescence intensity varied from 2 to 7, however, most of the
voxels had an associated intensity of two. The value of fluorescence intensity represents the
number of photons detected by the camera for the specific region where the voxel is located. Even
though there was not a big difference between the fluorescence intensity values of each voxel
(mean 2 ± 1), the total fluorescence intensity (Figure 26) and the average fluorescence intensity
per voxel in each WSS region was calculated (Figure 25b).
90
Figure 24. Wall shear stress spatial gradient effect on nanoparticle distribution. (a) Quantification
of the number of nanoparticle voxels per spatial wall shear stress gradient, using the results from
the steady state simulation (instantaneous WSS). Number of nanoparticle voxels was normalized
by the (b) total number of elements in the wall for each spatial wall shear stress gradient interval.
(c) Spatial TAWSS gradient calculated by the gradient of shear stress in the parallel and normal
directions for each node in the vessel wall and normalized by the (d) total number of elements in
each TAWSS region.
91
Figure 25. Fluorescence intensity per nanoparticle voxel. (a) Number of nanoparticle voxels with
different fluorescence intensity values shows that most of the nanoparticle voxels have lower
values of fluorescence. (b) Average fluorescence intensity of each nanoparticle voxel vs. the wall
shear stress region shows most voxels with higher fluorescence intensity levels are found in
regions of low wall shear stress.
Figure 26. Quantification of the total fluorescence intensity of the nanoparticles in each wall shear
stress region of the caudal vein segment of the embryo. Values for the wall shear stress intervals
were obtained from the steady state simulation of the vein using an inlet of 239 µm/s.
92
The correlation of WSS with different NP localization measures present in this study are
summarized in Table 4. Hoeffding’s D test for non-parametric and non-monotonic data was used
to determine if there was a relation between wall shear stress and voxel count, fluorescence
intensity per voxel, and total fluorescence intensity for the steady and transient study. This test
calculates the distance between the products of the marginal distributions to evaluate the
independence of the data sets. The null hypothesis of this test is that the variables are independent.
The Hoeffding D statistic for the dataset was in all cases approximately zero, for the steady state
results, suggesting that there is independence between WSS and nanoparticle localization
measured as voxel count or voxel intensity. From the trends present in the histogram and scatter
plots used to represent the different measures of localization, there seems to be a relation between
NP localization and WSS for the first intervals of shear stress. In order to determine if the lowest
WSS levels have a correlation with WSS, the values below or equal to the WSS where the peak
voxel count occurred was found (WSS≤0.056 Pa) were evaluated. There was a strong positive
correlation between WSS and NP voxel count(r= 0.889, p<0.0005) and between total fluorescence
intensity (r=0.840, p<0.001).
Additionally, the independence test for the TAWSS results showed a weak dependence between
accumulation and TAWSS when evaluating the entire trend. This results suggest the test lacks
statistical power and more observations are required in order to reduce type II errors.
93
Table 4. Statistical evaluation of the correlation between nanoparticle accumulations measured in
voxel count and total fluorescence intensity and local wall shear stress in the zebrafish embryo
caudal vein.
Study Variables
correlation
Region Statistic
value
(r)
Significance Interpretation
Steady WSS vs. NP
voxel count
All 0.0005 N.S. Independent
variables
WSS vs. NP
voxel Intensity
0.0047 N.S Independent
variables
WSS vs. Total
fluorescence
intensity
-0.0009 N.S. Independent
variables
WSS vs. NP
voxel count
From lowest
WSS to peak
accumulation
0.889 p<0.0005 Strong correlation
WSS vs. NP
voxel Intensity
0.310 N.S. No correlation
WSS vs. Total
fluorescence
intensity
0.840 p<0.001 Strong correlation
Transient TAWSS vs.
NP voxel count
All 0.117 p<0.05 Weak dependent
variables
TAWSS vs.
NP voxel
Intensity
0.0052 N.S. Independent
variables
TAWSS vs.
Total
fluorescence
intensity
0.110 p<0.5 Weak dependent
variables
5.6.Nanoparticle quantification in regions with different dispersion factors as a measure of
flow disturbances
The calculation of the dispersion factor in all the fluid elements has been previously shown in the
histogram in Figure 20. The majority of the elements had a dispersion factor ranging from 0.07 to
0.37. Interestingly, none of the nanoparticle voxels were present in this regions, most of the
particles were found to accumulate in regions with a higher dispersion factor (from 0.81 to 1.00),
94
as shown in Figure 27. Nanoparticle accumulation was normalized by the total volume of fluid
elements at a given dispersion factor interval. The highest accumulation occurred where fluid
elements had a dispersion factor of 0.91.
Values closer to 0 represent a region where the flow is parallel to the vessel wall, therefore, the
higher the dispersion factor, the more the flow deviates from a parallel orientation. Since the
dispersion factor is calculated as the ratio between longitudinal velocity and radial velocities, a
dispersion factor that tends to infinity means that the velocity in the longitudinal direction tends to
0, and the flow is perpendicular to the vessel wall.
The trend of nanoparticle accumulation vs dispersion factor is the same for nanoparticles
quantified as voxel count (Figure 27a) or as total nanoparticle fluorescence intensity (Figure 27b)
per volume. This suggests that the fluorescence intensity per voxel is roughly the same. To
determine whether this was the case, the average fluorescence intensity per voxel found was
determined in each region of flow characterized by a particular dispersion factor. As shown in
Figure 28 a higher variation of fluorescence intensity per NP voxel was found at higher levels of
dispersion factor. However, since the only point with a statistically significant higher average value
of fluorescence intensity per voxel was at dispersion factor 0.91, this only resulted in the
accentuation of a higher accumulation at this level.
95
Figure 27. Nanoparticle accumulation quantified as number of nanoparticle voxels (a) and
nanoparticle fluorescence intensity per volume (b) found in different flow regions characterized
by the dispersion factor. Higher nanoparticle accumulation measured in voxel count or
fluorescence intensity was found in regions with higher dispersion factor where flow is likely to
be disturbed since it diverges from the parallel direction.
96
Figure 28.Average fluorescence intensity per voxel found in each region of flow characterized by
the dispersion factor. Higher variation of fluorescence was found at higher levels of dispersion
factor.
Average wall shear stress levels were calculated for each region in a certain range of dispersion
factor. Since shear stresses are measured at the vessel wall and dispersion factor was calculated
for all the elements in the fluid region inside the vessel, the average value is an approximation of
the shear stress in each flow region. Higher shear stresses were found in regions were the
dispersion factor had a high value (>0.98). The region of dispersion factor with the highest
nanoparticle accumulation measured as fluorescence intensity per volume had a wall shear stress
value statistically equal to those found in regions where the dispersion factor ranged from 0.82 to
0.97. This suggests, that the difference in accumulation was likely to be caused by flow
disturbances and not to wall shear stresses.
97
Figure 29. Quantification of nanoparticle accumulation to regions of flow with different dispersion
factors and the corresponding time average wall shear stress values for each flow region.
5.7.Nanoparticle characterization for in vitro experiments
The hydrodynamic diameter of the carboxylate coated polystyrene particles measured using
dynamic light scattering was 180.8 ± 1.2 nm based on number size measurements, similar to the
size stated on the label from the manufacturers (200 nm). Measurements of colloidal stability were
done by measuring the zeta-potential. Nanoparticles were negatively charged with high surface
charge (zeta potential= -41.7 ± 1.0 mV) indicating particles were colloidally stable in the buffer
solutions used in this study. These measurements were done by Dr. Hagar Labouta in the Rinker
and Cramb laboratories.
0
0.05
0.1
0.15
0.2
0.25
0.3
0
1000
2000
3000
4000
5000
6000
7000
0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00
Wall
sh
ea
r str
ee
s (
Pa
)
NP
flu
ore
sce
nce
inte
nsity p
er
vo
lum
e (
µm
-3)
Dispersion factor
Fluorescenceintensity
TAWSS
98
5.8.Flow profiles in the sudden expansion parallel plate flow chamber
A sudden expansion parallel plate flow chamber was used to investigate if fluid flow effects similar
to those found on the zebrafish model occurred in human cells when exposed to shear stress values
and flow patterns commonly found in human veins (0.1, 0.2, and 0.8 Pa). Additionally, in vitro
experimentation was done to further examine the effect of endothelial physiology on nanoparticle
association. Sudden expansion flow chamber (Figure 30a,b) had a step gasket which at the
velocities used in this study, generated a region of recirculating flow as shown by the velocity
streamlines and wall shear stress values shown in Figure 31a and b. The recirculation region
increased in size as the flow rate increased, downstream the flow chamber had an undisturbed
laminar region with streamlines parallel to the surface (Figure 31a). Wall shear stresses were
determined at the bottom surface of the chamber where the endothelial cells were seeded and
attached to the collagen matrix used to coat the glass slides. Wall shear stresses vary in the regions
of flow recirculation, with a value of zero at the reattachment point where the recirculation region
contacts the bottom surface (Figure 31b). The negative wall shear stress indicates flow is moving
in the opposite direction, this occurs in the recirculating flow region.
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Figure 30. Flow circuit used to expose human umbilical vein endothelial cells to flow. (a) Cell
media was pumped using a peristaltic pump to a pulse damper to reduce pulsations of the flow
before it enters the sudden expansion flow chamber which had a step gasket (b) to allow for flow
disturbances in the vicinity of the step and laminar flow downstream. Media was collected back
into the cell media reservoir and was pumped into the circuit again.
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Figure 31. (a) Velocity streamlines obtained from the computational fluid dynamics simulation of
the flow chamber in 2D, each panel represents a different inlet volumetric flow rate for each shear
stress level 0.1, 0.2 and 0.8 Pa. For all the velocities used in the in vitro study, there was a region
of recirculation causing disturbed laminar flow (b) Values for the wall shear stress for each of the
inlet conditions evaluated as a function of distance from the step, negative wall shear stress
indicates recirculating flow region. The reattachment point occurs at a wall shear stress of 0 Pa.
5.9.Nanoparticle accumulation in endothelial cells in vitro
To examine the influence of shear stress and flow pattern on cell-association of nanoparticles,
HUVEC grown in the absence of flow were exposed to 200 nm diameter nanoparticles for 30
minutes under static (no flow) conditions or at 0.1, 0.2, or 0.8 Pa fluid shear stress. The following
results and statistical analysis were done by Dr. Amber Doiron and Robyn Steele at the Rinker
laboratory and are presented in this thesis for the purpose of comparison between the in vivo and
in vitro effects of flow on nanoparticle accumulation.
Overall, there was an increase in nanoparticle accumulation with a slight increase in the wall shear
stress level despite the flow pattern. At the highest level of wall shear stress, the accumulation
significantly decreased by approximately 90% comparted to the lowest level of shear stress, and
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98% compared to the accumulation of nanoparticles by cells exposed to 0.2 Pa. Interestingly, the
accumulation of nanoparticles at 0.1 and 0.2 Pa was significantly higher than the accumulation
found in static conditions. In vitro results seem to have a similar threshold effect than the in vivo
results for nanoparticle-cell association at different wall shear stress levels.
The mean nanoparticle association with endothelial cells was statistically different for all flow
conditions compared to static conditions (Figure 32). Nanoparticle accumulation for the
undisturbed laminar region was evaluated closer to the outlet of the flow chamber, while
accumulation in the disturbed region was evaluated closer to the step gasket. Accumulation in the
disturbed region was higher compared to the laminar region, at 0.2 and 0.8 Pa. A greater difference
between the accumulations in different flow regions was found at 0.8 Pa where the accumulation
in the disturbed region was 40% higher than the undisturbed laminar flow region. While the
accumulation in the disturbed region at 0.2 Pa was 7% higher than the laminar region. There was
no statistical difference between the mean accumulations of particles in the laminar region versus
the disturbed region at shear stress levels of 0.1 Pa. The parallel-plate flow system enabled analysis
of flow magnitude and pattern separately.
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Figure 32. Nanoparticle association with human umbilical vein endothelial cells (HUVECs)
exposed to different levels of wall shear stress and flow patterns. (a) Fluorescence microscopy
images of HUVECs exposed to 200 nm carboxylate coated polystyrene nanoparticles for 30
minutes under static or disturbed and undisturbed laminar flow of specified shear stress.
White/grey fluorescent signal corresponds to cell membrane stained with Cell Mask, blue signal
is the cell nuclei stained with Hoechst, and red corresponds to fluorescently tagged nanoparticles.
Scale bar in the top left image applies to all images and denotes 50 µm. (b) Relative nanoparticle
fluorescence intensity quantified under static conditions or during flow at 0.1, 0.2, or 0.8 Pa in
laminar (L) and disturbed (D) regions of flow. Sample numbers (number of images analyzed from
four static, three 0.1 Pa, two 0.2 Pa, and three 0.8 Pa experimental replicates) were as follows:
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static: 36; 0.1Pa: 115 laminar, 63 disturbed; 0.2Pa: 60 laminar, 48 disturbed; 0.8Pa: 42 laminar, 36
disturbed. Statistical significance is as follows: all comparisons to static are significant to
p<0.0001, * significance to p<0.05 between laminar and disturbed regions, and † denotes statistical
significance of both laminar and disturbed regions to p<0.0001 when compared to other shear
stress levels.
5.10. Flow preconditioned nanoparticle accumulation in endothelial cells
Endothelial cells respond to mechanical stimulation. When exposed to flow, endothelial cells align
to flow relative to their morphological and cytoskeletal axis.92 Shear stress exerted by flow
mediates endothelial morphological adaptation and permeability, among others.155 Therefore,
nanoparticle association with endothelial cells pre-exposed to fluid flow might differ from cells
statically grown or exposed to flow for a short period.
HUVECs were exposed to 0.1 Pa flow for 24 hours then exposed to nanoparticles in the presence
of flow for 30 minutes in a sudden expansion chamber. Pre conditioning of the cells to flow for 24
hours had an effect on the accumulation of nanoparticles in different regions of flow, the laminar
undisturbed region had a significantly lower nanoparticle accumulation than the disturbed region
(21%, p<0.005) as shown in Figure 33. Accumulation in the laminar region in the pre-conditioned
cells was reduced by 16% (p< 0.0001) compared to the non-preconditioned cells. As shown in the
results on Figure 32 for 0.1 Pa, cells that have not been conditioned to flow show no difference
between the nanoparticle accumulations in different flow regions.
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Figure 33. Effect of flow pre-conditioning on nanoparticle accumulation (a) Fluorescence
microscopy images of non-preconditioned and pre-conditioned HUVEC to 0.1 Pa shear stress for
24 hours followed by exposure to 200 nm nanoparticles for 30 minutes at 0.1Pa. Fluorescence
signal shown in white/grey is the cell membrane stained with Cell Mask, blue is the cell nuclei
stained with Hoechst, and red corresponds to fluorescently tagged nanoparticles. Scale bar in the
top left image applies to all images and denotes 50 µm. (b) The relative nanoparticle fluorescence
intensity quantified from images of cells exposed to laminar (L) and disturbed (D) regions of flow
in preconditioned and non-preconditioned HUVEC. Statistical significance is as follows: * denotes
significance to p<0.0001 and † denote significance to p<0.005.
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6. Chapter 6: Discussion
The evaluation of flow effects on nanoparticle distribution was done in vivo using zebrafish
embryos and in vitro using cultured human endothelial cells. For the in vivo evaluation, a new
method is proposed to quantify the accumulation of fluorescently tagged nanoparticles using 3D
modelling based on confocal microscopy images. The xyz coordinates for each nanoparticle voxel
were paired to the nearest vessel wall element to obtain the shear stress level and flow profile
where the nanoparticles accumulated. A sudden expansion flow chamber was then used to
investigate if physiologically-relevant changes in shear stress and flow profile had an effect on the
accumulation of untargeted polystyrene nanoparticles in human umbilical vein endothelial cells.
6.1.Polystyrene nanoparticle as model particles for biomedical applications
Untargeted particles were used to separate the effects of fluid forces from the binding forces of
nanoparticle surface moieties and endothelial cell surface molecules. Carboxylate coated-
polystyrene nanoparticles were used to model vascular nanocarriers, these particles have been used
by several research groups to model drug carriers for biomedical applications.110,124,156 Polystyrene
particles have a density comparable to typically proposed polymeric systems such as
polycaprolactone or PMMA and neutrally buoyant liposomes.126 Particles of approximately 200
nm diameter, such as the ones used in this study, have been evaluated in vivo in zebrafish
embryos129 and mice with no significant adverse effects reported.157–159 Additionally, carriers with
similar sizes (250 nm;158 190 nm;160 and 330 nm161) have been proposed as vascular targeting
carriers.
Nanoparticles with a zeta potential above ± 30 mV are considered colloidally stable in the buffer
solution they were tested since their surface charge prevents their aggregation. The particles used
in this study had a good colloidal stability in endothelial cell media and water (zeta potential <-40
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mV). Since zeta potential is dependent on the solvent composition, in particular to the ionic
strength of a fluid, water is assumed to have a similar pH to that of blood at physiological
conditions (≈ 7.3). The negative value of the zeta potential indicates that the particles carry a
negative electrostatic surface charge in the buffer solutions evaluated. Negatively charged particles
were selected to study flow effects on nanoparticle localization since they are not attracted to the
endothelium due to electrostatic forces, contrary to cationic particles, which are attracted by the
glycocalyx present on the endothelial cell surface which has a net negative charge.
The approximate number of nanoparticles injected into the zebrafish circulation was 1.4e-7
nanoparticles according to the equation provided by the fabrication manual. The blood volume of
the zebrafish embryos at 2 dpf has been reported to be in the range of 60 to 90 nL,162,163 therefore
the concentration of particles in the bloodstream was approximately 400 µg/mL, which is almost
ten times higher than the concentrations used to evaluate nanoparticles in other animal models 45-
60 µg/mL including rodents and humans.164,165 However, the molar concentration was
approximately 2 nM, which implies the number of particles present in the bloodstream was low.
Therefore, effects of high particle concentrations which induce toxicity in zebrafish embryos were
unlikely. No changes in the circulation or death of the animals was seen during the evaluation
period, probably due to the low particle number and short period during which the embryos were
analyzed. Others have reported toxicity induced by long exposure (>10 hours) of polystyrene
micro and nanoparticles in zebrafish embryos leading to their death.166,167 For in vitro studies, the
concentration of particles per volume of cell media was around 20 µg/mL which is low compared
to the proposed concentration for medical applications, however, since the aim of this study was
to evaluate flow effects on the accumulation of particles, a lower but still relevant concentration is
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appropriate since there are enough particles being exposed to the cells and side effects such as
cytotoxicity induced by high polystyrene nanoparticle concentrations becomes unlikely.
6.2.Quantification of nanoparticle accumulation using 3D modelling
The quantification of nanoparticles in the zebrafish vessels using 3D modelling depends to a large
extent on the spatial resolution set for image acquisition. To obtain a direct quantification of the
number of particles using voxel count, the voxels should have a size in the order of 200 nm.
However, due to the diffraction limit of the objective lens the smallest size is expected to be greater
than the particle size. The ratio of the particle size and the voxel size is a limitation in our study
since the voxel size (0.119 µm3) is approximately 30 times greater than the nanoparticle volume
(0.00419 µm3). We tried to circumvent this issue by comparing the quantifications done using
voxel count with those reporting total fluorescence intensity. Additionally, the comparison of the
average fluorescence intensity per voxel in each region of flow showed no significant differences
suggesting that our assumption of homogeneous dispersion of particles along the vessels was
appropriate. There are very few studies which use 3D-reconstruction of models to quantify
nanoparticle localization. Super resolution microscopy, transmission electron microscopy, and x-
ray nanotomography have been used to determine the localization of nanoparticles inside the
cells.168–170 However, this seems to be the first study to use 3D reconstruction to quantify
accumulation of nanoparticles in vivo.
The spatial resolution used to acquire the images did not allow for the quantification of uptake
versus adhesion. Confocal images and the separation between the vessel wall voxels and the
nanoparticle voxels in the 3D model indicate that most of the particles are bound to the cell surface.
However, more detailed imaging techniques such as those used in the studies previously discussed,
are required to make a clear differentiation between uptake and adhesion. It is also unclear if most
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particles are interacting with the vessel wall surface, or accumulating with other particles forming
small aggregates. Accumulation of particles did not seem to vary with time during the first hour
post-injection, suggesting that particles remained on the same region they initially adhered to.
Adhesion of nanoparticles to the endothelium of zebrafish embryos in vivo was recently evaluated
using optical tweezers to achieve optical micromanipulation of particles bound to the endothelium,
showing that untargeted polystyrene nanoparticles (100 to 1000 µm diameter) exhibit a strong
interaction with the endothelial cells lining the blood vessels. For instance, after being forced to
separate from the endothelium, particles returned to the same region they originally adhered to
once released back into flow.171
6.3.Blood flow velocity quantification and effect on nanoparticle accumulation on the
zebrafish embryo vasculature
Highest nanoparticle localization occurred in the region of the caudal plexus where angiogenesis
is occurring to form the plexus. In accordance to our findings, a recent study reported polystyrene
nanoparticle and liposome accumulation in all regions of the zebrafish embryo vasculature with
increased concentration of particles on the caudal vein. Nevertheless, the study did not quantify
these accumulations.129 Taken together with the velocity calculations, nanoparticles seem to
accumulate more in the caudal region due to low flow velocities. Additionally, higher
accumulation of particles is found in the vein and capillaries, where blood flow velocity was the
lowest. The number of nanoparticle voxels accumulating on the capillaries was slightly lower and
not statistically significant from the accumulation in the vein (≈530 µm/s) despite having a lower
average velocity (≈ 180 µm/s). However, since the quantification was done for the caudal region,
velocities for the vein are lower than the reported for veins in the whole vasculature. Velocities
quantified only in the caudal region showed an average a velocity of ≈ 360 ± 120 µm/s (n=3 fish)
for the caudal vein as shown in Table 2 which is still double the velocity found in the capillaries.
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Taking into consideration that the nanoparticle voxel count was normalized by the number of
endothelial cell voxels as an indirect measure of the number of cells and/or cell area, it is possible
that capillaries had regions where the vessel lumen was not completely formed therefore restricting
the presence of nanoparticles, but still having endothelial cells present. Another possible
explanation is that blood velocity affects nanoparticle accumulation in vessels by shear stress or
shear rate, as shown by our in vivo and in vitro findings, as well as other groups which have
reported in vitro dependency of accumulation of particles to shear stress magnitude.5,110,128,172–174
The lower diameter of vessels in capillaries increases wall shear stress on the vessel wall despite
having a lower blood flow velocity, these wall stress levels might be similar to those found in the
vein, causing a similar accumulation of particles. However, the wall shear stress quantification of
these regions needs to be determined computationally in order to have an approximation of the
forces acting on the vessel wall of capillaries.
Blood flow velocity calculated using particle image velocimetry with erythrocytes as tracer
particles has the advantage of exploiting transgenic and optical clarity characteristics of the
zebrafish embryo. Erythrocyte mapping has been used in other studies to detect vessel occlusion
and distribution of blood flow in zebrafish.175,176 Erythrocyte movement can be used to compare
differences in bulk flow; nonetheless, the large size of these cells relative to the diameter of the
embryo blood vessels represents a limitation for accurate measurement of velocity. Inaccuracies
might occur due to the possible interactions of these cells with the vessel wall, which are likely to
modify their velocity in the bloodstream. Measurements of blood flow in microcirculation require
tracer particles that are: neutrally buoyant, highly contrasting, small size (≈1 µm diameter), and
must not harm the animal or disrupt normal physiologic functions or alter blood flow.163
Nevertheless, introducing a new tracer is likely to affect the distribution of the nanoparticles of
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interest. Therefore, an endogenous tracer was selected to quantify blood flow velocity despite some
inaccuracy especially in the regions of the capillaries and some vein segments where the
erythrocytes deform to pass through the lumen.
Blood flow velocities in the zebrafish embryo exhibit a great variability among different regions
(caudal or ventral), vessels, and fish. The maximum and minimum values for velocities recorded
for the arteries and veins shown in Figure 10, display a great variability in velocity magnitude
which is mainly due to the different regions selected to measure the velocities. For the ventral
region, the dorsal aorta had average velocities of approximately 1000 µm/s and the posterior
cardinal vein had average velocities of 600 µm/s. While the velocities in the caudal region were
much lower as shown by the values on Table 2. Additionally the variability from fish to fish was
considerable, and this was the main reason why a local velocity was chosen to perform the
simulation studies instead of an average velocity from different fish. This variability might be due
to the developing nature of the vasculature of zebrafish embryos, where angiogenesis causes the
sprouting of new blood vessels and flow is eventually divided to perfuse different tissues. Similar
to our findings, blood flow velocities in zebrafish embryos (5 dpf) evaluated in the caudal region
obtained average velocities of 200 µm/s for the caudal vein and 700 µm/s for the caudal artery.152
Also, a different study using our methodology for calculating blood velocity on embryos 3 dpf
found average arterial blood flow of 750 µm/s with a similar pulse frequency than ours (≈ 0.5 s),153
and an oscillatory pattern comparable to the one in Figure 10. The irregular pattern of the blood
flow in the caudal vein was also found by Fieramonti et al. using 3D imaging to reconstruct the
blood cells velocity vector.152 This might be due to the deformation of erythrocytes which hinders
the accurate measurement of the profile, however, this remains to be further explored using
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external tracking particles which allow for the measurement of blood velocity and other
hemodynamic parameters without obstructing blood flow.
Calculations of the ideal Reynolds number and Womersley number suggest that the flow in both
the caudal vein and artery behave as creeping or stokes flow, where the inertial forces are
negligible compared to the viscous forces. This effect is very common in microfluidics since the
size of the channels and the velocities of flow are very small. Additionally, it represents a
simplification of the Navier-Stokes equations by eliminating the inertial terms of the momentum
balance which in turn, reduces the computational time required to solve the system.
6.4.Nanoparticle accumulation to regions of lower wall shear stress
Nanoparticle accumulation occurred in regions of lower wall shear stress in vivo and in vitro.
Interestingly in both cases, there seemed to be a threshold value in which peak accumulation
occurred at a low wall shear stress which was not the lowest wall shear stress, contrary to what
was expected. In vivo, nanoparticle accumulation to regions of different shear stresses was
quantified using the instantaneous WSS, obtained from the steady state simulation, and the
TAWSS obtained by averaging the shear stress obtained during one cardiac cycle. Overall, the
trends were the same, low regions of wall shear stress had the highest accumulation and increasing
shear stress decreased particle accumulation. However, the quantification done using
instantaneous WSS showed a more pronounced bi-variant trend for nanoparticle accumulation vs.
WSS, while the TAWSS showed a clearer decrease of accumulation with increase in shear stress.
These slight differences are possibly due to the overall lower values of shear stress that are obtained
by averaging the tangential forces acting on the wall throughout an entire cycle. Still, since
TAWSS takes into account all of the forces present on the wall, it represents a better approximation
of the shear stresses on each region. Spatial wall shear stress gradient did not have a clear effect
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on accumulation, except higher particle accumulation was found in regions with high gradients,
however, there was not a clear trend.
Lower accumulation of particles in regions of high wall shear stress can be explained by greater
fluid forces acting on the particles and preventing them to interact with the endothelium forcing
them to continue flowing. Additionally, high shear stress regions are caused by increased velocity
which has been shown to decrease particle margination in vitro.177 Regions of lower wall shear
stress have decreased tangential forces acting on the endothelial surface. This suggests, that the
adhesion force between the particles and the cells is stronger than the fluid forces. Several studies
have reported an inverse correlation between shear stress and nanoparticle uptake and/or adhesion
to different cultured endothelial cells including human microvascular,178,179 umbilical vein,124,180–
183 and aortic,113 as well as in tumor tissue.184–187 It is still unclear why there might be a critical
shear rate for the particles used in this study.
A critical shear rate above which particle adhesion decreases with increasing shear rate has been
previously reported.126 Above the critical shear rate, shear forces are greater than adhesion forces
and there is decrease in particle adhesion. However, this has mostly been reported for particles
with targeting moieties which exhibit higher adhesion forces counteracting fluid forces. The
critical shear rate point depends on the particle diameter since an increase in size leads to an
increase shear felt by the particle exposed to flow, therefore larger particles are expected to be
more affected by shear forces. A recent study by Rinkenauer et al. also found a bi-variant trend in
untargeted nanoparticle accumulation on HUVECs exposed to laminar flow with an increase in
wall shear stress (0.07, 0.3, 0.6, and 1 Pa) in vitro.186 This experiment was also done with
approximately 200 nm polymeric nanoparticles, which where functionalized to have different
charges but had no targeting moiety. The increase of shear stress at the lower levels resulted in an
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increase in particle uptake despite the charge. For negatively charged particles, such as the ones
used in our experiments, there was a plateau level followed by a decrease in particle uptake with
increasing shear stress. The same trend was found for nanoparticle uptake by monocytes in a co-
culture with HUVECs. The peak accumulation found in this study occurred at 0.3 Pa, similar to
the peak found in our in vitro experiments which was 0.2 Pa. A study recently published
characterized the in vivo wall shear stress of human umbilical vein endothelial cells and reported
and average WSS of 0.52 Pa.87 Therefore, highest accumulation of particles occurs in the low
regions of physiologically relevant wall shear stresses for HUVECs.
A slight increase in particle accumulation with increase in WSS might be due to an increase in
effective particle concentration on the surface of the cells occurring at slightly higher flow rates.
The flow rate for peak accumulation should be high enough to increase the number of particles
that are exposed to the endothelial surface per minute, but low enough to allow for particle
margination at a given shear stress region. Another possible hypothesis that needs to be further
investigated, are the early changes in glycocalyx organization during the initial 30 minutes of flow
described by the Tarbell research group.188 Fluid shear stress induced clustering of the heparan
sulfate, a glycosaminoglycan adhered to the proteoglycan forming the glycocalyx, to the junctional
region reducing the coverage of the endothelial cell apical surface. Reduced shielding by
glycocalyx has been shown to increase nanoparticle uptake compared to healthy glycocalyx
coating which hinders nanoparticle uptake and accumulation of anionic particles.189 Glycocalyx
is present in zebrafish embryos endothelial cells at the same time as blood flow starts, therefore it
might have an effect on the accumulation of particles. Still, further experimentation needs to be
done since the changes in WSS used in our in vitro studies and found in vivo might be too small
to cause glycocalyx reorganization.
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Wall shear stress magnitudes found in vivo might be slightly inaccurate due to the assumption of
a Newtonian fluid and a viscosity of 3 cP based on a 45% blood hematocrit. However due to the
small amount of blood (≈ 60 nL) found in zebrafish embryos at 52 hpf, a rheological test to
characterize the blood behavior is not possible. During the writing stage of this thesis, unpublished
results from the Hsiai research group presented at a conference estimated the hematocrit and
viscosity of zebrafish blood for 2 dpf at 45% and 4.85 cP, and for 3 dpf at 60% and 7.23 cP,
respectively.190 This suggests that the values for the WSS might be underestimated by our
simulations. Despite the difference in viscosity, the overall distributions of WSS are expected to
be the same as well as the trends for nanoparticle accumulation with WSS. Additionally, due to
the Fahraeus-Lindqvist effect present in vessels with small diameters (<100 µm) such as the caudal
vein (≈20 µm), the viscosity is expected to decrease since erythrocytes move to the center of the
vessel creating a cell free layer near the vessel wall.
6.5.Nanoparticle accumulation to regions of disturbed flow
Highest nanoparticle accumulation was found in regions of flow disturbances in vivo and in vitro.
In vivo, all of the particles accumulated in the most disturbed regions where the dispersion factor
was above 0.8. Laminar undisturbed flow characterized by streamlines parallel to the wall did not
have any particle accumulation even though most of the computational elements of the vein
segment model were found to have dispersion factor values below 0.6. Although the disturbed
regions generated with the sudden expansion flow region were different than those found in vivo
due to the recirculation of flow, similar results were found for all shear stress levels evaluated.
Since flow disturbances are different in each model (in vivo vs. in vitro), nanoparticle localization
to these regions might be caused by different reasons. In vivo, flow disturbances might enhance
particle margination by generating a force towards the vessel wall caused by the high radial flow
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velocities in the vessel. In vitro, higher accumulation in the recirculating region might occur due
to an increase in the residence time of particles close to the endothelial cell surface. Higher
accumulations of particles in cells exposed to regions of disturbed flow have been found by others
using sudden expansion flow chambers and microfluidic bifurcating channels.124,159 Similar
findings have been reported in vivo using the partial carotid ligation mice model which generates
regions of disturbed and undisturbed laminar flow exposed to different targeted particles. Results
using this animal model have shown a preferential localization of nanoparticles in disturbed flow
regions. In one study, endothelial cells in the disturbed region were found to have high VCAM-1
expression, which enabled particles targeted to VCAM-1 to accumulate almost exclusively in
regions of disturbed flow and not in laminar flow regions.127 On the same line, another study found
targeted particles accumulated more in regions of disturbed shear and further modified the particles
to carry BH4 a drug candidate to treat atherosclerosis and found a reduction in superoxide
production in the ligated artery and reduced plaque formation.187
6.6.Flow pre-conditioning studies suggest cell phenotype affects nanoparticle accumulation
In both the in vivo and in vitro studies, there might also be differences in cell phenotype that
enhance the accumulation of particles in disturbed regions and hinder accumulation in laminar
undisturbed region. Results found in vitro for endothelial cells pre-conditioned to flow suggest
that there is a phenotypic adaptation to flow that might explain higher accumulation of particles
on disturbed regions compared to laminar regions even without using targeting particles to exploit
adhesion molecules on the cell surface.
Changes in accumulation of particles might be explained by actin filament reorganization that
occurs when endothelial cells are exposed to shear. In static conditions, actin fibers are located on
the cell borders, while under flow conditions actin fibers reorganize as a part of the cytoskeletal
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reorganization of the cell to reduce the shear forces sensed on the cell surface resulting in elongated
cells. This change in morphology can impact membrane traffic by modifying the endocytotic and
exocytotic properties of the cells.191,192 Studies evaluating effects of mechanical forces on
nanoparticle accumulation have shown morphological changes in endothelial cells when exposed
to fluid or cyclic stretch forces. These morphological changes which include the arrangement of
actin fibers resulted in a decrease in nanoparticles uptake of spherical polystyrene particles coated
with PECAM antibodies and amorphous silica nanoparticles.119,185
Nevertheless, future studies evaluating pre-conditioning flow effects in vitro and in vivo should
be modified to include markers for cell surface adhesion molecules and to track cytoskeleton re-
organization. Due to the length of our flow pre-conditioning study, it is likely that some actin
reorganization occurred, however, this must be checked in order to determine if a threshold shear
value is required to initiate those changes. Especially, since the in vitro images do not show a clear
morphological change which is expected in the region exposed to undisturbed laminar flow.
6.7.Possible blood components affecting nanoparticle localization in blood vessels
Blood is composed of cellular and molecular elements such as red blood cells, white blood cells,
platelets and plasma containing proteins, sugars, and electrolytes. These elements can interact with
nanoparticles and affect their distribution in the vasculature. Despite their small diameter, blood
flow in zebrafish vessels had a RBC-rich core in the center of the vessel which generated a cell-
free layer (CFL) near the endothelium. Leukocytes and platelets have been shown to accumulate
in the CFL in order to decrease hydrodynamic resistance and have a more efficient margination to
the vessel wall.193,194 The localization of nanoparticles to the CFL depends mainly on particle
characteristics such as geometry, shape, and flexibility, and vessel geometry.195 In vitro and in
silico studies of the localization of micro- and nanoparticles to the CFL studied under flow
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conditions with red blood cells have shown that NPs in the range of 100 to 500 nm have a reduced
adhesion relative to microparticles (2-5 µm diameter) due to their co-localization with the RBC
rich core, contrary to microparticles preferentially localizing in the CFL.4,106,157,196 However,
studies done in capillaries and vessels with small diameters, in the range of those of the present
study (10-50 µm in diameter), have shown a higher margination and targeting efficiency of smaller
particles compared to larger microparticles.110,177,197 The region where the 200 nm polystyrene
particles localized in flowing blood of zebrafish embryos could not be clearly evaluated since the
majority of particles adhered to the vessel wall a few minutes after injection (<5 minutes).
Tracking of nanoparticles at the center of the vessel using line-scans was attempted approximately
15 minutes post-injection but no signal was obtained. This suggests that particles were either
mostly adhered to the vessel wall and not circulating or preferentially localized at the CFL. Caudal
vessel walls had a high NP fluorescent signal shortly after particle injection (3 minutes
approximately), this suggests that particle margination occurred very fast compared to the
circulation times of particles in larger animal models and humans, which can be several minutes.
However, distribution of nanoparticles in animals with high heart rates and small blood volume,
such as zebrafish embryos, is usually less than one minute.45 In a similar experiment, zebrafish
embryos at 2 days post fertilization (dpf) were injected with polystyrene (200 nm) nanoparticles
and liposomes (200 nm).129 Similar to our findings, they observed a high affinity between the non-
functionalized polystyrene particles and the endothelium. After a couple of minutes, all particles
seemed to localize to the endothelium and no longer in circulation. Approximately 2 minutes after
injection, most polystyrene nanoparticles had adhered to the endothelium, and after 20 minutes,
they had all adhered to the endothelium. On the contrary, liposomes had circulation times of hours
until cleared by macrophages 20 hours post-injection.
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Adult zebrafish have at least two granulocyte lineages; neutrophil granulocytes which correspond
to 95% of the circulating granulocytes and eosinophil granulocytes. Neutrophils have been found
in tissues and axial vessels of embryos as early as 48 hpf, while eosinophils have been detected as
early as 5 dpf. Experiments done to evaluate the functionality of leukocytes in 2-dpf embryos
showed neutrophil migration to the region of induced trauma and clearance of circulating carbon
micro-particles by macrophages one hour post-injection.198 Leukocytes recognize foreign particles
by globulin antibodies and clear them from the blood stream. Negatively charged particles without
surface modification, such as those in the present study, have been shown to be cleared by
macrophages.199 Mouse macrophage cell cultures exposed to the same carboxylate coated
polystyrene 200 nm nanoparticles used in the present study, have shown high uptake of these
particles in in vitro static assays.200 In vivo results, on the other hand, have shown contradictory
results. Particles injected to mice tumor models preferentially accumulated in the liver but were
not cleared by Kupffer cells even 24 hours post-injection. Particles injected to adult zebrafish by
retro-orbital injection, localized near injection region without reaching the cardiovascular system
and did not seem to be cleared after 1 hour post-injection.200 However, zebrafish embryos injected
with different nanoparticles including those used in this study, have shown localization to the
vasculature followed by macrophage clearance hours (>8 hours) after injection.129 Since imaging
of the zebrafish embryos in our experiments occurred during the first hour post-injection, no
clearance by macrophages is expected, especially since the number of macrophages present at this
developmental stage are low and require a longer period to migrate and clear the particles in the
bloodstream.
Nevertheless, since neutrophils co-localize to the CFL of the bloodstream, they are likely to collide
with particles adhered to the vessel wall and physically detach them.195 Competition of adhesion
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and detachment of particles by leukocytes has been shown in vitro in both human pulsatile and
recirculating blood flow.123 The number of neutrophils and macrophages present in the zebrafish
embryo (2-6 dpf) have been reported to range from 50-300 and 50-400 per embryo,
respectively.201,202 In physiological conditions, most of the leukocytes localize closer to the heart
or the ventral region compared to the caudal region. Even though the presence of leukocytes in the
blood flow on the caudal region might be reduced, the effect of the neutrophil competition and
possible detachment of adhered particles must be further investigated to determine if they have an
effect on the distribution of particles in vivo and in vitro.
Additionally, nanoparticles can cause platelet aggregation in zebrafish embryos modifying their
distribution. Cationic dendrimers injected into 3-6 dpf zebrafish embryos produced immediate
coagulation which resulted in occlusion of caudal vessels.139 Neutrally charged dendrimers
produced no occlusion in the zebrafish vasculature, similar to results found in rodents injected with
either neutral or anionic dendrimers.203 Nevertheless, the effect that nanoparticles have on
coagulation is still poorly understood. Effects seem to depend on the particle composition, size,
and the animal model. In vivo, carboxylate polystyrene nanoparticles (60 nm) did not induce
thrombosis in mice and hamsters. However, studies done in vitro with the same kind of particles
with different sizes show platelet activation induced by particles in the range of 20 to 220 nm.204–
207 Non-mobile thrombocytes have been found in zebrafish embryos at 36 hpf, their circulation
appeared 48 hpf close to the dorsal artery and caudal vein. Therefore, 50-52 hpf embryos used in
this study, are expected to have circulating thrombocytes that may interact with nanoparticles. To
our knowledge, no study has evaluated platelet activation induced by carboxylate polystyrene
nanoparticles in zebrafish embryos. This is a shortcoming of our study and should be taken into
120
account in future studies since it can have a large impact on nanoparticle accessibility to different
vessels, as well as vascular flow profiles and forces.
6.8.Implications of flow effects on nanoparticle accumulation
Regions of flow disturbances and low wall shear stresses are usually implicated in pathological
conditions. In the case of solid tumor vasculature, average blood flow and wall shear stress are
frequently lower compared to physiological tissues. Shear stress in murine tumors range from 0.03
to 0.6 Pa, depending on the type of tumor.184,208Additionally, lower values have been reported for
approximations obtained from human tumor vasculature 0.17±0.01 Pa.208 The decreased shear
stress in the abnormal tumor vasculature compared to physiological microvasculature vessels
might favor nanoparticle accumulation on the tumor endothelium. Additionally, the angiogenic
vasculature of the tumor is likely to generate flow disturbances similar to those found in the
zebrafish embryo model, which according to our results, favor particle accumulation. Others have
shown the advantage that disturbed flow generates when targeting atherosclerotic lesions in
mice.127,209
Overall, our findings suggest that flow effects are likely to enhance the accumulation of
nanoparticles in pathological regions with disturbed flow and low wall shear stress. This would
imply, that even untargeted particles can have a preferential localization to pathological regions
where vessel architecture allows for favorable flow conditions. However, it is important to
highlight that the zebrafish vasculature is still different than the pathological vasculature found in
solid tumors and atherosclerotic plaques which are likely to be more permeable than the embryo
vessels due to the large fenestrations between cells. Nonetheless, the zebrafish embryo represents
a good model to study nanoparticle distribution in vivo since the optical transparency properties
are a great advantage when it comes to live imaging. Similar to in vitro models of flow chambers,
121
which according to our findings; follow the same trends found in vivo for flow effects on
nanoparticle accumulation.
7. Chapter 7: Future work
Future studies need to be conducted to increase the accuracy and statistical power of the study,
further understand the effects of flow on cell phenotype, and evaluate the possible interactions of
blood elements and cells (e.g. platelets and leukocytes) on nanoparticle accumulation.
More samples of zebrafish embryos need to be fully evaluated using the nanoparticle
quantification methodology developed in this thesis. The quantification of flow effects in more
zebrafish embryos would increase the statistical power which reduces the probability of making a
type II error. Since this type of error leads to concluding there is no effect when in fact there is
one, it is likely that an increase in observations would help to better define the relation between
WSS and accumulation, as well as flow pattern and accumulation.
In terms of increasing the accuracy of our results some of the main modifications need to be done
are the following: the calculation of flow velocities in vivo need to be validated using smaller,
neutrally buoyant particles, seeded at appropriate densities as described by Craig et al. for
measurements of blood flow in zebrafish embryos using polymeric microspheres.163 This is
important especially in the caudal vein and capillaries since the diameter of the vessel and red
blood cells is very similar which in certain regions causes the cells to deform leading to inaccurate
recordings. Imaging of zebrafish embryos should be done using a higher magnification, for
example 40x and a numerical aperture of 1.4, to reduce the size of the voxels in the image and
improve the accuracy of the 3D model. A higher numerical aperture will provide higher resolution
and the capacity to image particles of 200 nm. Also, a higher magnification with an appropriate
122
spatial resolution can also be used to separate nanoparticle uptake from adhesion, which is
important when predicting drug efficacy or toxicity. Newtonian fluid approximation should be
validated or modified by performing a rheological test on adult zebrafish blood, to determine if
there is a linear relation between viscosity and shear rate. If a linear relation does not exist, a non-
Newtonian model such as a power law or Carreau-Yasuda model should be adopted for the
simulation to obtain more accurate results. Adult zebrafish blood can be used to have enough
volume to perform a rheological analysis, and also because it has a similar hematocrit (30-40 %)
to the 2 dpf embryos.210,211 Finally, to better characterize the pulsatile effect on flow a particle
tracing model should be coupled with the transient simulation to determine the paths that particles
are likely to take in those flow conditions. Defining particles with similar characteristics to those
used in the present study might help validate the simulation or determine if other factors such as
charge or steric interaction play a role in particle accumulation.
The use of transgenic embryos represents a great advantage when evaluating nanoparticle
accumulation since different cellular components can be tagged. Future studies should also include
the use of transgenic embryos with fluorescently labeled macrophages, neutrophils, and
platelets.139,212 Experiments should evaluate if particles are phagocytosed by macrophages or
neutrophils during the time period analyzed. Also, if the circulation of neutrophils or platelets in
the bloodstream interferes with the accumulation of particles on the endothelium. Coagulation due
to nanoparticle injection should be evaluated by observing platelet aggregation, this can be used
to further explore blood vessel occlusions that affect flow patterns in the vasculature. It is important
to highlight, that the concentration of nanoparticles injected into the zebrafish bloodstream should
be reduced to be more relevant to actual formulations and reduce any possible toxic effects, the
target concentration should be approximately 50 µg/mL.164,165
123
In vivo and in vitro experiments should also be done using medically relevant nanoparticles which
target the endothelium or are pegylated to determine if flow effects are also present for these types
of particles. Since the approved nanoparticles used for drug delivery are liposomal formulations,
pegylated and un-pegylated liposomes mimicking Doxil and Myocet, respectively, should be
evaluated. Additionally, particles which include targeting moieties for cell adhesion molecules
such as antibodies for ICAM-1,120 VCAM-1,182,213 or PECAM-1,185,187 E-selectin,214 among others,
should also be evaluated to determine if the adhesion forces between the particles and cells are
strong enough to withstand fluid forces. Additionally, determining the effects of flow on targeted
nanoparticles can help to determine parameters such as optimal surface coating density to improve
their targeting capacity and binding efficiency to the endothelium.
Additionally, the targeting efficiency of particles under flow might require the activation of the
endothelial cells with TNF-alpha to induce the expression of adhesion molecules. To determine if
molecules are expressed antibodies can be used to stain adhesion molecules such as E-selectin to
analyze their expression using fluorescence microscopy. The presence of cell adhesion molecules
can be evaluated by immunofluorescence using fluorescently tagged monoclonal antibodies for
human adhesion molecules. This expression needs to be quantified in order to claim an inflamed
or pathological endothelium phenotype. In vitro evaluation of glycocalyx reorganization induced
by shear can also be done using immunofluorescence to determine if the flow patterns and WSS
magnitudes used in this study modify the spatial distribution of glycocalyx. Effects of the
glycocalyx on particle accumulation can also be explored by inducing glycocalyx collapse by
reducing the proteins in the cell media and degrading glycocalyx by cleaving heparin sulphate
using heparinase enzyme. The effect of glycocalyx restoration can also be evaluated by adding
exogenous heparin sulphate into the media and neutralizing the enzyme.189
124
Further in vitro experiments should also look into co-culture to take into consideration cell-cell
interactions which can influence cellular physiology and affect nanoparticle distribution, such as
leukocytes or red blood cells. In terms of leukocytes, they can be introduced into dynamic cell
culture experiments using the parallel plate flow chamber to evaluate nanoparticle clearance from
the circulation. Studies have shown that monocytes also exhibit a shear stress dependent uptake of
nanoparticles, and in general, have a higher uptake rate than HUVECs exposed to the same
conditions. This suggests, that the localization of particles might be even more influenced by the
presence of monocytes and the effect that shear stress has on them than endothelial cells.186
In order to make sure that the cultured cells are able to tolerate the shear stress they are exposed
to, a control experiment exposing cells to flow and evaluating the actin filaments is required in
order to indicate if the shear stress applied to the cells causes any damage to the filaments.
Labelling the actin filaments should also be done in order to determine if a cytoskeleton
reorganization occurs at the levels of shear stress used in vitro (0.1, 0.2 and 0.8 Pa). The
visualization of the actin cytoskeleton can be done by staining the cells after shear exposure with
Alexa Fluor 488 phallotoxin, which has high affinity with actin fibers.
125
8. Chapter 8: Conclusion
Shear stress magnitude and fluid flow profile were found to influence nanoparticle accumulation
through a mechanism involving fluid flow control of nanoparticle deposition in the endothelium
as well as fluid flow modification of endothelial cell properties. A methodology that combined in
vivo imaging of fluorescently tagged-nanoparticles injected to transgenic zebrafish embryos, 3D
modeling, and computational fluid dynamics was used to assess the in vivo flow effects on
nanoparticle accumulation. In vitro studies using a sudden-expansion flow, chamber provided
insight about the possible flow induced phenotypic changes that might influence nanoparticle
accumulation. The new methodology proposed in this study allowed for the first time, an in vivo
evaluation of the effects of vessel wall shear stress and flow profile on nanoparticle accumulation.
In general, nanoparticles localized in regions of low wall shear stress and disturbed or non-parallel
stream flow. These flow characteristics were present at vascular branch points and downstream of
curved regions. Lower accumulation was found in areas of straight vasculature with uniform flow
and high wall shear stress and blood flow velocities. In vitro results suggest that physiological
adaptations of endothelial cells exposed to disturbed flow enable a higher nanoparticle
accumulation. The similarity of results obtained with preconditioned human endothelial cells in
the flow chamber and results from the zebrafish studies support the use of the flow chamber model
for detailed mechanistic studies into nanoparticle-endothelial interactions.
Nanoparticles targeting angiogenic tissues with irregular vessel architectures such as those present
in solid tumors should be designed to exploit the benefits of disturbed flow regions and low shear
stress regions. For these regions, a lower concentration of targeting moieties on the particle surface
might be as effective as highly concentrated surfaces. Changes in nanoparticle localization with
126
flow result in differing concentrations of nanoparticles, which will influence toxicity, therapeutic
efficacy and have an effect on nanocarriers design for targeted drug delivery.
127
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10. Appendices
Appendix 1. Summary of the z-stack parameters defined during the confocal microscopy image
acquisition for each zebrafish embryo.
Zebrafish
embryo
Scaling X
(µm/pixel)
Scaling Y
(µm/pixel)
Scaling Z
(µm/pixel)
Dimension
X (pixels)
Dimension
Y (pixels)
Dimension
Z (pixels)
1 0.625 0.625 0.300 512 512 363
2 0.625 0.625 0.300 512 300 201
3 0.521 0.521 0.300 512 512 196
Appendix 2. Levels of threshold selected to generate each mask for the different zebrafish
embryos evaluated.
Fish
Threshold value on grayscale
Red blood cells Endothelial cells Nanoparticles
Minimum Maximum Minimum Maximum Minimum Maximum
1 3 255 6 255 2 255
2 4 255 8 255 3 255
3 3 255 7 255 3 255
152
Appendix 3 . Sensitivity analysis for the number of harmonics included in the Fourier series
Figure 34. Sensitivity analysis for the number of harmonics included in the Fourier series to reduce
the difference between the measured velocity in the vessel segment and the Fourier approximation.
This graph shows that 15 harmonics is the minimum number of terms required to reduce the error
between Fourier approximation and average of the measured velocities.
Appendix 4. Numerical values of Fourier coefficients for the first fifteen harmonics of the
zebrafish embryo blood velocity waveform.
n An Bn
0 219.6282 0
1 -7.25164 85.03141
2 -23.2605 6.214744
3 -1.13592 22.56835
4 -0.1513 3.764641
5 -1.45675 6.852409
6 -4.72299 5.597637
7 2.191213 4.958821
8 0.275048 5.749286
9 -0.67398 3.682234
10 -2.28223 2.958935
11 -1.71083 3.205272
12 -0.63147 2.737515
13 -0.52313 2.375197
14 -0.52521 2.36041
15 -0.61791 2.217675
5 10 15 20 25 30 35-5
0
5
10
15
20
25
30
Number of harmonics in the Fourier series
Diffe
rence b
etw
een m
easure
d v
elo
city a
nd F
ourier
appro
xim
ation
153
Appendix 5. Effect of the tolerance value for absolute difference in position x,y, and z on the
number of nanoparticle voxels matched with wall shear stress values.
Tolerance for absolute difference in the
position
Number of
NP voxels
matched to
WSS values
Percentage
NPs
quantified X (m) Y (m) Z (m)
1.0e-08 2.0e-06 1.0e-05 81,189 59.56%
1.0e-07 2.0e-06 1.0e-05 136,273 99.97%
1.0e-07 5.0e-07 1.0e-06 65,045 47.72%
1.0e-07 1.0e-06 1.0e-06 81,310 59.65%
1.0e-07 2.0e-06 1.0e-06 103,023 75.58%
1.0e-07 2.0e-06 2.0e-06 131,524 96.49%
1.0e-07 1.8e-06 2.0e-06 130,159 95.49%
1.0e-07 1.8e-06 1.8e-6 123,365 90.50%
1.0e-07 1.6e-06 1.8e-6 119,291 87.51%
1.0e-07 1.6e-06 1.6e-6 115,218 84.52%
1.0e-07 1.4e-6 1.6e-6 115,209 84.52%
1.0e-07 1.4e-6 1.4e-6 104,363 76.56%
1.0e-07 1.4e-6 1.8e-6 117,928 86.51%
1.0e-07 1.4e-6 2.0e-6 124,711 91.49%
1.0e-07 1.2e-6 2.0e-6 121,997 89.50%
Appendix 6. Effect of change in tolerances in relative number of NP voxels.
Figure 35. Number of paired nanoparticle voxels to a wall shear stress value at different
combinations of tolerances in the y and z positions. Highest number of paired nanoparticle voxels
with lowest tolerances resulted in the pairing of 91.5% of the total number of voxels found in the
caudal vein segment evaluated.
154
Appendix 7. Estimation of the difference between positions of the nanoparticle (NP) voxels and
the wall shear stress (WSS) coordinates they were assigned to depending on the organization of
the matrices.
Organization
WSS matrix
Organization
NP matrix
Sum of absolute difference in position: Total
absolute
difference
(m)
X (m) Y (m) Z (m)
Ascending X Ascending X 0.0082 0.0997 0.1443 0.2523
Ascending Y Ascending Y 0.0081 0.1517 0.0978 0.2577
Ascending Z Ascending Z 0.0081 0.1517 0.0978 0.2577
Appendix 8 Tolerances accepted by the established parameters
.
Figure 36. a) General view of distance accepted by tolerances in x (red cube), y (green cube), and
z (blue cube). (b) Zoom of the region encompassed by the relative tolerances, when nanoparticle
voxels are found inside the boundaries set by the tolerances they are paired with the reference
point. (c) Average pairing error shown as the mismatch in distance between the reference point
(black sphere) and the nanoparticle voxel in each direction shown as black crosses.
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Appendix 9. Matlab script for the quantification of nanoparticles by voxel count and
fluorescence intensity per wall shear stress region
clear all clc %Quantification of nanoparticles by voxel count and fluorescence intensity %in an x,y,z position load NPF; %Length for the Nanoparticle array lNP=length(NPF); load WSZ; %Length for the WSZS array %File WSZ is organized from Zmax to %Zmin lWSS=length(WSZ);
%Matrix to save the data column1:X from NPF, column 2:X from WSZ, column
3:Y %from NPF, column 4:Y from WSZ, column 5:Z from NPF, column 6:Z from WSZ, %column7: WSS, %Column8: Fluorescence intensity from NPF
%Preallocate matrix wsvox=zeros(lNP,7);
for i=1:lNP xnp=NPF(i,1); ynp=NPF(i,2); znp=NPF(i,3); j=1; for j=1:lWSS xwss=WSZ(j,1); ywss=WSZ(j,2); zwss=WSZ(j,3); difx=abs(xnp-xwss); dify=abs(ynp-ywss); difz=abs(znp-zwss); if difx<0.0000001 && dify<0.0000014 && difz<0.000002 wsvox(i,1)=xnp; wsvox(i,2)=xwss; wsvox(i,3)=ynp; wsvox(i,4)=ywss; wsvox(i,5)=znp; wsvox(i,6)=zwss; wsvox(i,7)=WSZ(j,4); wsvox(i,8)=NPF(i,4); end end end
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Appendix 10. Matlab script for the error estimation calculated as the mismatch between
nanoparticle voxel position and wall shear stress position.
clear all clc %Estimation of the error in the match between NP voxel position and WSS %position. Depending on the organization of NPF and WSZ (x ascending, y %ascending, z ascending)
load results %Length for the Nanoparticle array lmat=length(wsvox);
for i=1:lmat xnp=wsvox(i,1); ynp=wsvox(i,3); znp=wsvox(i,5); xwss=wsvox(i,2); ywss=wsvox(i,4); zwss=wsvox(i,6); wsvox(i,9)=abs(xnp-xwss); wsvox(i,10)=abs(ynp-ywss); wsvox(i,11)=abs(znp-zwss); end
Sumx= sum(wsvox(:,9)); Sumy= sum(wsvox(:,10)); Sumz= sum(wsvox(:,11)); Totalsum= Sumx+ Sumy+ Sumz;
Errorx=mean(wsvox(:,9)); stdx=std(wsvox(:,9)); Errory=mean(wsvox(:,10)); stdy=std(wsvox(:,10)); Errorz=mean(wsvox(:,11)); stdz=std(wsvox(:,11));
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Appendix 11. Matlab script to normalize the data by the number of wall shear stress elements in
each region
clc clear all %Script to count the number of cells in every region of wall shear stress %and the number of voxels in each region load WSZ lW=length(WSZ); load results lmat=length(wsvox);
ssmax=0.35; ssmin=0.0016; divisions=78; cortes=zeros([divisions 1]); step=(ssmax-ssmin)/divisions; areaface=0.05643; %value in um2
for j=1:divisions matstep(j,1)=ssmin+(j*step); end
for i=1:lW w=WSZ(i,4); for k=1:divisions if k==1 && w<=matstep(k,1) cortes(k,1)=cortes(k,1)+1; else if k>1 && k<=(divisions-1)&& w>matstep(k-1,1) &&
w<=matstep(k,1) cortes(k,1)=cortes(k,1)+1; else if k==divisions && w>matstep(k-1,1) cortes(k,1)=cortes(k,1)+1; end end end end end
sumcortes=sum(cortes(:,1));
count=zeros([divisions 1]);
for p=1:lmat v=wsvox(p,7); for q=1:divisions if q==1 && v<=matstep(q,1) count(q,1)=count(q,1)+1; else if q>1 && q<=(divisions-1)&& v>matstep(q-1,1) &&
v<=matstep(q,1) count(q,1)=count(q,1)+1; else if q==divisions && v>matstep(q-1,1) count(q,1)=count(q,1)+1; end
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end end end end
sumcount=sum(count(:,1));
%Normalization of the data for t=1:divisions normal(t,1)=count(t,1)/((cortes(t,1))*areaface); end
%Relative data maxn=max(normal(:,1)); for u=1:divisions relative(u,1)=normal(u,1)/maxn; end
figure() histogram(wsvox(:,7),divisions); figure() bar(matstep(:,1),normal(:,1)); figure() bar(matstep(:,1),relative(:,1));
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Appendix 12. Matlab script to calculate the dispersion factor for each fluid element in the
computational domain.
clc clear all
%Script calculates the dispersion factor for each value in the flow
load Vall lVel=length(Vall);
ymax=0.00029808; xmax=0.000261495; xmin=0.000238586;
for i=1:lVel xmat1=Vall(i,2); ymat1=Vall(i,3); zmat1=Vall(i,4); Vx=Vall(i,6); Vy=Vall(i,7); Vz=Vall(i,8); if ymax>ymat1&& xmax>xmat1 && xmat1>xmin Vr=sqrt((Vz^2)+(Vx^2)); Df=Vr/Vy; Vall(i,11)=Vr; Vall(i,12)=Df; Vall(i,13)=abs(Df); i=i+1; else %Calculate Radial Velocity Vr=sqrt((Vz^2)+(Vy^2)); %Calculate the Dispersion factor Df=Vr/Vx; Vall(i,11)=Vr; Vall(i,12)=Df; Vall(i,13)=abs(Df); i=i+1; end end