Effect of red blood cell aggregation on arteriolar cell free layer formation and its physiological functions

EFFECT OF RED BLOOD CELL AGGREGATION ON
ARTERIOLAR CELL-FREE LAYER FORMATION AND
ITS PHYSIOLOGICAL FUNCTIONS







ONG PENG KAI








NATIONAL UNIVERSITY OF SINGAPORE
2011




EFFECT OF RED BLOOD CELL AGGREGATION ON
ARTERIOLAR CELL-FREE LAYER FORMATION AND
ITS PHYSIOLOGICAL FUNCTIONS

ONG PENG KAI
(B.Eng.(Hons.),NUS)




A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DIVISION OF BIOENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2011
i







To my wife, Jia Wen,
for her unwavering love, sacrifice and everything that made all this possible,

and to my parents
for their much needed support and encouragement

ii



ACKNOWLEDGEMENTS
I wish to thank the expert reviewers for their insightful comments on my research
work. I am extremely grateful to my dissertation supervisor, Dr. Kim Sangho, for his
selfless guidance and unfailing support in my personal and scientific development,
bestowing me with countless opportunities to enrich my well-being and knowledge during
the course of my doctoral studies.
It would have been impossible to have completed this project without the support and
hard work from many co-workers. I would like to express my utmost gratitude to my
Final Year Project student, Ms. Swati Jain, for her tireless contribution to the experiments,
data processing and valuable discussions regarding the research. There are several other
people in my laboratory that require special mention: (1) Mr. Yang Shihong for his
relentless assistance in setting up the experiment and maintaining the laboratory in an
always conducive manner, (2) Ms. Woo Yeon I for transporting the rat, be it rain or shine,
from the animal holding unit to the laboratory and for her expertise in preparing the
cremaster muscle, rendering the entire experimental process more smooth sailing and (3)
Mr. Namgung Bumseok for sharing with me his enlightening advice on the theoretical and
experimental aspects of our research.
I am grateful to our collaborators from the University of California San Diego, Drs.
Paul C. Johnson and Ozlem Yalcin, for the kind opportunity to learn about animal surgery
as well as their guidance in my work. Many thanks to Ms. Christine Choi and Ms.
Cynthia Walser, who have shown so much patience in imparting their knowledge and
clarifying my doubts about the cremaster muscle preparation.
iii

Last but not least, I would like to extend my deepest appreciation to the staff from the
Division of Bioengineering, namely Dr. Lim Chwee Teck, Dr. Toh Siew Lok, Dr. Partha
Roy, Dr. Leo Hwa Liang, Dr. Lee Taeyong, Mr. Matthew Tham, Ms. Millie Chong, Ms.
Lee Yee Wei, Ms. Jacqueline Teo, Ms. Teh Yan Ping and Mr. Tang Kang Wei for their
support in any aspect during my stay in the National University of Singapore.
This research project was generously funded by the Office of Research at the National
University of Singapore under NUS FRC Grant R-397-000-076-112 and NUS URC Grant
R-397-000-091-112.
Chapters 1, 2, 3, 4.1, 6.1 and 6.2 contain reprints of the material as appears in the
Physiological Measurement, The American Journal of Physiology: Heart and Circulatory
Physiology, Annals of Biomedical Engineering and Microvascular Research. I was the
primary researcher and author of these studies and permission for the use of these
published data in the dissertation has been kindly approved by my co-authors and the
magnanimous publishers of these journals.










iv

TABLE OF CONTENTS
DEDICATION i


ACKNOWLEDGEMENTS ii


TABLE OF CONTENTS iv


SUMMARY xi


LIST OF TABLES xiii


LIST OF FIGURES xiv


LIST OF SYMBOLS AND ABBREVIATIONS xviii


1. BACKGROUND 1

1.1. Functional roles of arterioles 1
1.2. NO transport and vascular responses in arterioles 2
1.3. Cell-free layer formation in microvessels 4
1.4. Cell-free layer measurement in arterioles 8
1.5. Rheological effects on cell-free layer formation 12
1.6. Rheological disorders in diseases 16

1.7. Physiological implications of cell-free layer 19
1.8. Cell-free layer formation at arteriolar bifurcations 23


2. HYPOTHESES & OBJECTIVES 28

v



2.1. Key Hypothesis 28
2.2. Objectives 28


3. STAGE I: AN AUTOMATED METHOD FOR CELL-FREE LAYER
WIDTH MEASUREMENT IN SMALL ARTERIOLES 34

3.1. Objective 34
3.2. Materials and Methods 34
(a) Animal preparation 34
(b) Acquisition of arteriolar flow data 37
(c) Image analysis and Grayscale method 38
(d) Histogram-based thresholding methods 42
(e) Manual measurement 43
(f) Statistical analysis 43
3.3. Results and Discussion 43


4. STAGE II(a): EFFECT OF ERYTHROCYTE AGGREGATION ON
CELL-FREE LAYER FORMATION IN ARTERIOLES 52

4.1. Arteriolar Cell-Free Layer Formation at Physiological Levels of Erythrocyte
Aggregation 52

4.1.1. Objective 52
4.1.2. Materials and Methods 53
(a) Animal preparation 53
(b) Hematocrit, aggregation and pressure measurements 53
(c) Adjustment of red blood cell aggregation level and flow rate 54
(d) Experimental protocol 54
(e) Cell-free layer width measurement 55
(f) Temporal variations of the cell-free layer width 56
(g) Mean cellular velocity and pseudoshear rate 57
(h) Statistical analysis and data presentation 57
vi



4.1.3. Results 58
(a) Systemic parameters 58
(b) Relation between mean and SD of cell-free layer widths 59
(c) Effect of aggregation and flow reduction on mean and SD of cell-free layer
widths 60
(d) Effect of aggregation and flow reduction on dynamics of cell-free layer
formation 62
(e) Frequency distribution of cell-free layer variations 63
4.1.4. Discussion 66
(a) Relation between mean and SD of cell-free layer widths 67
(b) Effect of aggregation and flow rate on mean and SD of cell-free layer
widths 68

(c) Cell-free layer variations in terms of frequency distribution and magnitude
of deviation from its mean width 71
(d) Potential influences on oxygen and NO diffusion 72
(e) Consideration of glycocalyx layer 72

4.2. Arteriolar Cell-Free Layer Formation at Pathological Levels of Erythrocyte
Aggregation 74

4.2.1. Objective 74
4.2.2. Materials and Methods 75
(a) Animal preparation, experimental setup, rheological and physiological
measurements and arterial pressure reduction 75
(b) Adjustment of aggregation 75
(c) Experimental protocol 76
(d) Cell-free layer width measurement 76
(e) Cellular velocity and pseudoshear rate 77
(f) Statistical analysis and data interpretation 77
4.2.3. Results 78
(a) Systemic parameters 78
(b) Effect of aggregation and flow rate on normalized mean and SD of the layer
width 79
vii



(c) Effect of vessel radius on normalized mean and SD of the layer width 80
(d) Effect of pseudoshear rate on normalized mean and SD of the layer width 82
(e) Histogram and cumulative frequency distribution (CFD) of the layer
widths 85
4.2.4. Discussion 86

(a) Effect of aggregation and flow rate on the layer characteristics 87
(b) Effect of vessel radius on the layer characteristics 88
(c) Effect of pseudoshear rate on the layer formation 90
(d) Physiological significance 90
(e) Potential limitations 94


5. STAGE II(b): CELL-FREE LAYER FORMATION NEAR AN
ARTERIOLAR BIFURCATION: EFFECTS OF ERYTHROCYTE
AGGREGATION 96

5.1. Spatial-temporal Variations in Cell-Free Layer Formation near an Arteriolar
Bifurcation 96

5.1.1. Objective 96
5.1.2. Materials and Methods 97
(a) Animal preparation, experimental setup, rheological and physiological
measurements and red blood cell aggregation level adjustment 97
(b) Experimental protocol 97
(c) Cell-free layer width measurement around an arteriolar branch point 98
(d) Mean flow velocity, pseudoshear rate and volume flow rate 99
(e) Statistical analysis and data presentation 100
5.1.3. Results 100
(a) Physiological and rheological parameters 100
(b) Spatial and temporal variations in cell-free layer formation 100
(c) Feeding of the layer in the parent vessel into the downstream vessels 103
(d) Asymmetry of the layer widths on opposite sides of the arteriole 104
(e) Relationship between fractions of volume flow and the layer formation in
side branch 105
viii

5.1.4. Discussion 106
(a) Spatial variations of the layer formation around the bifurcation 107
(b) Asymmetry of the layer formation on opposite sides of downstream vessel 110
(c) Relationship between fractions of volume flow and the layer formation in
side branch 111
(d) Conclusion 112

5.2. Effect of Erythrocyte Aggregation on Cell-Free Layer Formation near an
Arteriolar Bifurcation 113

5.2.1. Objective 113
5.2.2. Materials and Methods 113
(a) Animal preparation, experimental setup, rheological and physiological
measurements and aggregation level adjustments 113
(b) Experimental protocol 114
(c) Cell-free layer width determination around an arteriolar branch point 115
(d) Cellular velocity, pseudoshear rate and volume flow rate 115
(e) Rate of the layer formation in downstream vessel 116
(f) Statistical analysis and data presentation 116
5.2.3. Results 117
(a) Physiological and rheological parameters 117
(b) Spatial and temporal variations in the cell-free layer formation around the
bifurcation 117
(c) Asymmetry of the layer formation on opposite sides of the arteriole 121
(d) Relation between the layer formation in upstream and downstream
vessels 123
(e) Relationship between fractions of volume flow and the layer formation in

side branch 124
(f) Rate of the layer formation in downstream vessel 126
5.2.4. Discussion 128
(a) Principal findings 128
(b) Spatial and temporal variations in the layer formation around the
bifurcation 128
ix



(c) Asymmetry of the layer formation on opposite sides of the arteriole 129
(d) Plasma skimming effect on heterogeneity in the layer formation between
downstream vessels 131
(e) Rate of the layer formation in downstream vessel 133


6. STAGE III: MODULATION OF NO BIOAVAILABILITY BY TEMPORAL
VARIATIONS OF THE CELL-FREE LAYER WIDTH IN ARTERIOLES:
EFFECTS OF ERYTHROCYTE AGGREGATION 135

6.1. Modulation of NO Bioavailability by Temporal Variation of the Cell-Free
Layer Width in Small Arterioles 135

6.1.1. Objective 135
6.1.2. Materials and Methods 136
(a) Experimental data and statistical analysis 136
(b) Mathematical model 136
6.1.3. Results 147
(a) Physiological and rheological parameters 147
(b) Simulation results 147

(c) Effects of layer width variability on NO bioavailability 148
(d) Effects of layer width variability on sGC activation 150
6.1.4. Discussion 151
(a) Principal findings 151
(b) Temporal variability of cell-free layer width 152
(c) Effect of varying core hematocrit on NO bioavailability 152
(d) Effect of varying WSS on NO bioavailability 154
(e) Effect of cell-free layer variability on sGC activation 155
(f) Limitations of the model 155
(g) Conclusion 157

6.2. Temporal Variations of the Cell-Free Layer Width May Enhance NO
Bioavailability in Small Arterioles: Effects of Erythrocyte Aggregation 158

x



6.2.1. Objective 158
6.2.2. Materials and Methods 158
(a) Mathematical model 158
(b) Statistical analysis and data presentation 159
6.2.3. Results 160
(a) Physiological and rheological parameters 160
(b) Effect of dextran infusion on the layer width variations 161
(c) Influence of the layer width variations on NO bioavailability 162
(d) Influence of the layer width variations on sGC activity 165
6.2.4. Discussion 167
(a) Principal findings 167
(b) Effect of aggregation on temporal variations of cell-free layer 167

(c) Influence of the layer variations on NO bioavailability 168
(d) Comparison of NO values with previous models and experimental studies 169
(e) Plasma viscosity effect on NO bioavailability 171
(f) Influence of temporal variations of the layer on vascular tone 172
(g) Other potential physiological implications 173
(h) Limitations of current study 174


7. CONCLUSION 176


8. RECOMMENDATIONS 179


9. BIBLIOGRAPHY 181


10. APPENDICES 194


11. VITA, PUBLICATIONS AND CONFERENCES 212


xi



SUMMARY
Blood flow in small arterioles is characterized by the formation of a red blood cell-
depleted zone (cell-free layer) near the vessel wall that could have important implications

on microvascular functions. However, the progress made in understanding its
physiological impact in the arterioles has been hampered by the lack of quantitative
information that depicts its spatial and temporal variability under physiological (normal)
and pathological (hyper) levels of red blood cell aggregation seen in humans. This
highlights a strong need to quantify the effect of red blood cell aggregation, with
hemorheological relevance to humans, on the layer and its variability in the arterioles.
The new information can be used to provide a deeper insight into how the layer formation
in arterioles could modulate nitric oxide (NO) bioavailability and vascular tone. To
achieve these objectives, the project is divided into four stages: (I) development of a new
computer-based method for the layer width measurement, (II) investigation of the effect of
aggregation on the layer and its variability in the arteriolar network and (III)
implementation of a computational model to predict the effect of temporal variations in
the layer width on NO transport in the arteriole by considering the influence of
aggregation.
The newly developed Grayscale method offers a good alternative to conventional
histogram-based methods for layer width measurements. In addition, it could overcome a
possible problem of layer width overestimation associated with conventional methods.
The mean and temporal variations of the layer width in unbranched regions of the
arterioles were found to be enhanced by aggregation at reduced flow conditions and this
effect was more prominent with hyper-aggregation than normal-aggregation. The
xii



temporal variations in width were asymmetric with a greater excursion into the red blood
cell core than toward the vessel wall.
Spatial variations in the layer width were apparent in the vicinity of an arteriolar
bifurcation which can be modulated by aggregation. A positive correlation was generally
found between the extents of the cell-free layer formation in the upstream and downstream
vessels. A greater fraction of flow into the side branch generally led to a decrease in the

fraction of downstream layer formation constituted by the side branch. At reduced flow
conditions, large asymmetries of the layer widths that developed on opposite sides of the
downstream vessel were attenuated by hyper-aggregation while the tendency of the layer
formation in the side branch was enhanced by hyper-aggregation.
Predictions based on a time-dependent NO transport computational model of the
arteriole revealed that NO preservation in the arteriole could be improved by considering
transient responses in wall shear stress (WSS) and NO production. This effect became
significantly enhanced by aggregation induction at reduced flow rates. Corresponding
analyses on sGC activity levels in the smooth muscle layer showed that such enhanced
NO bioavailability by aggregation could promote vasodilation.
Overall, the findings from this study provide quantitative information on the effect of
red blood cell aggregation on the layer width and its variability in the arterioles which
reveals new insights into functional roles played by the layer.




xiii



LIST OF TABLES
Table 3-1: Comparison between manual and automated methods for cell-free
layer width measurements. 46
Table 4.1-1: Distribution parameters for boxplots shown in Fig. 4.1.6 (All units
in µm) 63
Table 4.1-2: Frequency of cell-free layer deviations > 1.5 µm at reduced flow 73
Table 4.2-1: Systemic parameters 79
Table 4.2-2: Distribution parameters for normalized layer widths in Fig. 4.2.4 84
Table 6.1-1: Different cases of the time-dependent model 136

Table 6.1-2: Model parameters 144
Table C-1: Cell-free layer width measurements based on Grayscale Method 198
Table C-2: Cell-free layer width measurements based on Minimum Method 199
Table C-3: Cell-free layer width measurements based on Otsu’s Method 200
Table E.1-1: Normalized mean of the cell-free layer width at normal arterial
pressures 202
Table E.2-1: Normalized mean of the cell-free layer width at reduced arterial
pressures 203
Table E.2-2: Normalized SD of the cell-free layer width at reduced arterial
pressures 204







xiv



LIST OF FIGURES
Figure 1.1: Tank-treading mechanism of a red blood cell 5
Figure 1.2: Cell-free layer formation in small vessels in vivo and in vitro 6
Figure 1.3: Temporal variability of cell-free layer width on opposite sides of a
40 µm ID arteriole determined by a computer-based method 10
Figure 1.4: Image analyses for cell-free layer width measurement based on the
Minimum thresholding algorithm. Probability distribution of
reconstructed grayscale image 11
Figure 1.5: Relationship between the extents of red blood cell aggregation for

human red blood cells suspended in 70 kDa dextran and in
autologous plasma 15
Figure 1.6: Aggregates formation in blood of healthy human and cardiac patient 16
Figure 1.7: Hemorheological vicious cycle in the microcirculation 17
Figure 1.8: Diagram illustrating the effect of temporal variations in the cell-free
layer width on WSS 20
Figure 1.9: Effects of the cell-free layer on NO transport in an arteriole 21
Figure 1.10: Cell screening and plasma skimming effects 23
Figure 1.11: Plasma skimming at an arteriolar bifurcation 26
Figure 2.1: Flowchart summarizing the three key stages of the research project 33
Figure 3.1: Animal stage design 35
Figure 3.2: Rat subject to surgery 36
Figure 3.3: Rat cremaster muscle preparation 36
Figure 3.4: Schematic diagram of experimental setup 37
Figure 3.5: Computer-based methods for cell-free layer width measurement 39
Figure 3.6: Digital image analyses for cell-free layer width measurement 41
xv



Figure 3.7: Statistical analyses to compare between the automated and manual
measurements of the cell-free layer width 45
Figure 3.8: Cell-free layer width measurement on reconstructed image with faint
areas of grey at the edge of the erythrocyte column 47
Figure 3.9: Statistical comparison of automated and manual measurements of
cell-free layer width with faint grey areas at the edge of the
erythrocyte column 48
Figure 3.10: Images of blood flow in an arteriole showing movement of the faint
grey region 49
Figure 4.1.1: Apparatus used for rheological and physiological measurements 53

Figure 4.1.2: Example of temporal variation of cell-free layer width in a 47.1 µm
ID arteriole 56
Figure 4.1.3: Relation between SD and mean value of the cell-free layer width 59
Figure 4.1.4: Normalized mean value and SD of cell-free layer width variations at
different flow conditions before and after aggregation induction 60
Figure 4.1.5: Frequency of cell-free layer width deviations towards vessel wall 62
Figure 4.1.6: Frequency distribution of cell-free layer variations from the vessel
wall 64
Figure 4.2.1: Effect of hyper-aggregation on cell-free layer width characteristics 80
Figure 4.2.2: Relationship between normalized mean or normalized SD of
cell-free layer width and vessel radius 82
Figure 4.2.3: Relationship between normalized mean or normalized SD of cell-free
layer width and pseudoshear rate 83
Figure 4.2.4: Histograms and cumulative frequency distribution (CFD) of the
cell-free layer widths 86
Figure 4.2.5: Ratio between WSS values with and without consideration of the
cell-free layer width variations as a function of C
v
92
Figure 5.1.1: Schematic diagram of a typical arteriolar bifurcation 99
xvi



Figure 5.1.2: Spatial variations of the normalized mean layer width in parent
vessel and larger daughter vessel at normal arterial pressures 102
Figure 5.1.3: Temporal variations (Normalized SD) of the layer width in parent
vessel and larger daughter vessel at normal arterial pressures. 102
Figure 5.1.4: Relationship between normalized mean layer widths in the parent
vessel and downstream vessels at normal arterial pressures 103

Figure 5.1.5: Asymmetry of normalized mean layer widths on opposite sides of
the upstream and downstream arterioles at normal arterial pressures 105
Figure 5.1.6: Relationship between fractions of normalized mean layer width and
volume flow in the side branch at normal arterial pressures 106
Figure 5.1.7: Trajectories of cells along the streamlines of homogeneous plasma
flow at an arteriolar bifurcation 109
Figure 5.1.8: Plot of interbifurcation distance vs. arteriole diameter 111
Figure 5.2.1: Schematic diagram of an arteriolar bifurcation defining the rate of
the layer formation in the larger daughter vessel 114
Figure 5.2.2: Spatial variations of the normalized mean layer width in parent
vessel and larger daughter vessel at reduced arterial pressures 118
Figure 5.2.3: Temporal variations (Normalized SD) of the layer width in the
parent vessel and larger daughter vessel at reduced arterial
pressures 120
Figure 5.2.4: Asymmetry of normalized mean layer widths on opposite sides of
the upstream and downstream arterioles at reduced arterial
pressures 122
Figure 5.2.5: Relation between normalized mean layer widths at the opposite
walls of the parent vessel and larger daughter vessel at reduced
arterial pressures. Relation between fractions of normalized mean
layer width at the adjacent wall of the parent vessel and in the side
branch at reduced arterial pressures 124
Figure 5.2.6: Relationship between fractions of normalized mean layer width and
volume flow in the side branch at reduced arterial pressures 125
xvii



Figure 5.2.7: Relation between the rate of the layer formation and edge velocity
on opposite sides of the larger daughter vessel 127

Figure 6.1.1: Schematic diagram of the arteriole model in Cartesian coordinates 137
Figure 6.1.2: Dependence of grid spacing and infinite domain distances on
numerical solutions 146
Figure 6.1.3: Simulated peak NO concentration profile in an arteriole in response
to temporal changes in the layer width 148
Figure 6.1.4: Relationship between ∆Mean Peak NO and Cv for CASE I and
CASE II 149
Figure 6.1.5: Effect of C
v
on ∆Mean Peak NO for CASE III 150
Figure 6.1.6: Relationship between ∆sGC activation and C
v
for CASE III 151
Figure 6.2.1: Computational model of an arteriole in a Cartesian coordinate
system with temporal variations in the blood lumen-CFL border.
Hematocrit and velocity profiles used for simulation 160
Figure 6.2.2: Effect of aggregation on temporal variations in the cell-free layer
width in an arteriole 161
Figure 6.2.3: Simulated peak NO concentration profile in an arteriole in response
to temporal changes in the cell-free layer width before and after
dextran treatment 163
Figure 6.2.4: Relation between ∆Mean Peak NO and Cv before and after dextran
infusion in CASE I 164
Figure 6.2.5: Relation between ∆Mean Peak NO and Cv before and after dextran
infusion in CASE II. Effect of transient changes in the layer width
on mean peak NO concentration before and after dextran infusion 165
Figure 6.2.6: Relation between ∆sGC Activation and Cv before and after dextran
infusion. Effect of transient changes in the layer width on sGC
activation before and after dextran infusion 166
Figure D.1: Time course of the change in femoral arterial pressure during the

experiment 201

xviii



LIST OF SYMBOLS AND ABBREVIATIONS
ANOVA analysis of variance statistical test
BCs boundary conditions
BMP bitmap
CFD cumulative frequency distribution
CFL cell-free layer


mean of CFL width variations


SD of CFL width variations
C
C,NO
NO concentration in compartment (c) where c can be either LU, CFL, EC
or T
C
SM,NO
averaged NO concentration in the smooth muscle layer
C
v
coefficient of variation
cGMP cyclic guanosine monophosphate
cP centipoises

D, ID internal vessel diameter
D
C
diffusivity of NO in water in compartment (c) where c can be either LU,
CFL, EC or T
D
m
mean D along the vessel
dl decilitre
EC endothelial cell layer
ESL endothelial surface layer
EC
50
NO

concentration eliciting half-maximal activation of sGC
eNOS endothelial NO synthase
GTP guanosine triphosphate
H
c
core hematocrit
H
SYS,ref
reference systemic hematocrit
IU international unit
xix



I

i,j
light intensity of image pixel at location i,j
ip intraperitoneal
K-S Kolmogorov-Smirnov statistical test
K
m
apparent Michealis constant
kDa kiloDalton
k
C,NO
NO reaction rate constant in compartment (c) where c can be either LU, EC
or T
k
SYS,NO
NO scavenging rate at H
SYS,ref
45%
LU blood lumen
ldv larger daughter vessel
M aggregation index from Myrenne aggregometer
MW molecular weight
mmHg millimeters of mercury
NO

nitric oxide
NO
peak
peak NO concentration
N total number of video frames
nM concentration in nanomolar

n Hill coefficient
P
A
femoral arterial pressure
 volume flow rate


volume flow rate in larger daughter vessel


 volume flow rate in side branch



volume flow rate in side branch as a fraction of total volume flow rates in
downstream vessels


 NO production rate at the luminal boundary of EC


NO production rate at the abluminal boundary of EC
q
NO,control
basal rate of NO production
 vessel radius
xx

RBC red blood cell
RMS root mean square
R total number of column pixels in reconstructed image
Re
p
particle Reynolds number
SD standard deviation
SEM standard error of mean
sGC soluble guanylyl cyclase
sb side branch
T tissue layer
V mean cellular velocity

V
c
centerline velocity


V
edge
edge cellular velocity of blood core
WSS, τ
w
wall shear stress
WSR, 

wall shear rate
W watt
W layer width at a particular time point



mean layer width normalized by R



normalized mean layer width in larger daughter vessel



normalized mean layer width in side branch



normalized mean layer width at the adjacent wall of vessel (c) where c can
be either parent vessel (p) or larger daughter vessel (ldv)



normalized mean layer width at the opposite wall of vessel (c) where c can
be either parent vessel (p) or larger daughter vessel (ldv)



fraction of normalized mean layer width in downstream vessels constituted
by side branch



fraction of normalized mean layer width in parent vessel at its adjacent wall
y

0
location of vessel centerline
y
1
distance of interface between blood lumen and cell-free layer from y
0

xxi



y
2
distance of luminal surface of EC from y
0
y
3
distance of abluminal surface of EC from y
0

µ
rel
relative apparent blood viscosity
µ
c
blood core viscosity
µ
p
blood plasma viscosity
 pseudoshear rate based on V

c


pseudoshear rate based on 


τ
w,ref
reference WSS
∆
+

increase in mean peak NO concentration
Ω ohm


1



1. BACKGROUND

1.1. Functional roles of arterioles
The microcirculation is often found embedded in major tissues and organs and is
physiologically significant by providing a principal form of transport mechanism for
material (oxygen, nutrients and metabolic waste) exchange between the blood stream and
surrounding tissues in order to maintain homeostasis and bodily functions. The final
arterial ramification in the microcirculation, termed as the terminal arterioles (10 – 60 µm
in diameter), are especially important for this purpose as they play a concerted role with
postcapillary components (venules) to maintain a constant hydrostatic pressure in the

capillaries to ensure efficient red blood cells perfusion and oxygen delivery to the tissues.
Since these small arterioles can account for a large part of the intravascular pressure drop
in the microvascular bed, they are often regarded as the resistance vessels (49, 125).
Accordingly, the arterioles are normally responsible for at least 50% of total vascular
resistance, primarily by changing vessel diameter. However, any factor that changes
resistance in the arterioles could have a significant effect on blood flow to the tissues.
Arteriolar resistance would also be determined by a number of rheological parameters that
include red blood cell aggregability, tube hematocrit and red cell flexibility. These factors
may vary in individual vessel segments of the network.
The blood flow regulation by the arterioles provides an upstream mechanism that leads
to the downstream recruitment of capillaries during hyperemia and exercise, which is
essential for augmenting the blood delivery to actively meet the metabolic demands of the
working tissue or muscle. To perform this function, the arteriolar blood vessels are
2



anatomically endowed with a continuous single layer of smooth muscle cells, which
enables their dynamic adaptations in diameters to changes in both local blood flow
properties and signals from the nervous system (50). The inability to dynamically respond
to these hemodynamic and neurogenic signals has important clinical implications, often
associated with endothelial dysfunction and pathogenesis of vascular diseases (65).

1.2. NO transport and vascular responses in arterioles
The functional role of NO in the regulation of vascular tone is especially important in
the arteriolar network of the microcirculation (47) and is mainly attributed to the
specialized structure of the arterioles that enables active diameter changes in response to
blood flow induced signals. These small blood vessels are distinctively characterized by
the presence of a NO-responsive smooth muscle layer that surrounds the endothelial cells
which forms part of the vascular wall. The endothelial cells serve as essential sites for NO

production in the arterioles (43, 120) by responding to hemodynamic signals acting on the
luminal surface of these cells exposed to blood flow. NO is a highly reactive free radical
that is formed from a two-step oxidation of L-arginine (1). Due to its high diffusivity in
interstitial fluids, the newly synthesized NO can readily diffuse from the endothelium in
opposite radial directions into either the blood lumen or the smooth muscle layer.
The bioavailability of NO in the smooth muscle layer is a critical determinant of
vascular tone since NO can activate soluble guanylate cyclase (sGC), an enzyme that
stimulates the release of cyclic GMP (cGMP). This signaling molecule is responsible for
relaxing the smooth muscle cells, causing vasodilation (4, 121). Thus, physiological
concentrations of NO required for eliciting smooth muscle relaxation often refer to the NO
level required for eliciting half-maximum activity of sGC (EC
50
) which ranges from 23