Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 6.7.2 - Hemodynamic Analysis of Atherosclerotic Plaques
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 Material Information
Title: 6.7.2 - Hemodynamic Analysis of Atherosclerotic Plaques Bio-Fluid Dynamics
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Adhikari, S.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: exercise
atherosclerosis
finite element analysis
carotid bifurcation
blood flow
wall shear stress
CFD
 Notes
Abstract: Exercise, Atherosclerosis, Finite element analysis, Carotid bifurcation, Blood flow, Wall shear stress, Computational Fluid Dynamics (CDF)
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Resource Identifier: 672-Adhikari-ICMF2010.pdf

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Hemodynamic Analysis of Atherosclerotic Plaques


1Sam Adhikari



1Sysoft Center for Systems Biology and Bioengineering
Integratise Inc. P.O. Box 219, Whitehouse Station, NJ 08889, USA
E-mail: sadhikari@ sysoft.com


Keywords: Exercise, Atherosclerosis, Finite element analysis, Carotid bifurcation, Blood flow, Wall shear stress,
Computational Fluid Dynamics (CDF).




Abstract

Atherosclerosis is a condition in which fatty material collects along the walls of arteries. This fatty material thickens, hardens,
and may eventually block the arteries. Atherosclerosis is preferentially initiated at bifurcation sidewalls with reversing or
vortexing flows, or regions of low mean wall shear stress. Exercise training contributes to the arrest and even reversal of
atherosclerosis by inducing an atheroprotective phenotype in endothelial and T cells. Elevated wall shear stress activates the
glucocorticoid receptor (GR) and its transcriptional signaling pathway to induce antiatherosclerosis actions inthe vasculature.
Our computational and quantitative research focuses on understanding the effect of wall shear stress from exercise. We study
the differences in hemodynamics produced by varying heart rate in a fully coupled fluid-structure three-dimensional finite
element model of a carotid bifurcation. Two cases with a gradual controlled 100% increase in heart rate are considered: one in
which peripheral resistance is uniformly reduced to maintain constant mean arterial pressure, resulting in an increase in mean
flow, and a second in which cerebral vascular resistance is held constant so that mean carotid artery flow is nearly unchanged.
In the former case, the wall shear stress values are generally higher, nearly 42% higher on an average in various locations, but
only in proportion to the increase in flow rate. This observation provides some support to the hypothesis that exercise
promotes an atheroprotective phenotype through elevated wall shear stress. When the flow rate is held constant, the analysis
provides a little different result. Shear stress magnitudes is still higher, nearly 12% higher in some locations. This observation
provides support to the hypothesis that exercise promotes an atheroprotective phenotype in endothelial and T cells through
elevated wall shear stress. It slows down the formation of plaques, slabilizes the same, and to some extent reverses it through
diverse signaling pathways involving, among others, NO, heat shock proteins, and protein kinases such as PI 3-kinase and
MAPK.However, it is necessary to extend the analysis to include investigation of regions of high and low shear stress in the
vasculature.


Introduction

The heart at rest pumps out a volume per minute
approximately equal to the total amount of blood in the
body, but in situations with increased demands of oxygen,
the cardiac output rises about six-fold and, at the same time,
oxygen extraction in the tissues augments three-fold. The
heart rate and the stroke volume determine cardiac output.
The regulation of cardiac output is extremely complex.
Many investigators, for many years, have reported that the
heart rate is the main factor in this increase of the cardiac
output [1-3].
The linear relationship between the heart rate and oxygen
uptake is well established for many years, from many
investigations. At very heavy exercise close to the maximal
oxygen uptake, the relationship between heart rate and
oxygen uptake takes an asymptotic form, due to a relatively
smaller increase in heart rate [4-5].
Cardiac output can increase at exercise about three to four
times in persons with a lack of physical exercise. It
increases six to eight times in well-trained individuals with
athletic body. Some investigations show that even at nearly


maximal heart rate, there is no fall in the cardiac output in
healthy individuals. However, in case of patients with heart
diseases, cardiac output and stroke volume may fall during
exercise of certain intensity.
During exercise, there is generally an augmentation in the
systolic blood pressure in the systemic circulation. The
diastolic and mean pressures rise far less, resulting in
extensive pulse amplitude. Holmgren made a
comprehensive investigation on the arterial blood pressure
during bicycle ergometry in physically fit young men and
found a correlation between the arterial blood pressure and
the relative workload, expressed in terms of heart rate. In
Holmgren's research, an increase of 300 kpm/min (rise in
oxygen consumption of 0.5 to 0.6 lit/min) in workload
corresponded to an average augmentation in the systolic
pressure of 8 mm Hg. In persons with a lack of physical
exercise in life style, the same increase in work load raises
the systolic blood pressure as much as 19 mm Hg. This
divergence in results can be explained by differences in
physical fitness [6]. Consequently, when comparing the
levels of the blood pressure during exercise, physical fitness
is a major factor. However, it is also true that age must also









be considered, as the blood pressure increases more in older
than in younger men [7]. The total peripheral resistance in
the vasculature can be determined from the cardiac output
and the arterial mean pressure.
The arterial blood pressure decreases over time, during
exercise at a certain augmented workload as a result of a
peripheral vaso-dilatation taking place in the skin vessels.
The cardiac output remains constant. An increased skin
blood flow is reflected in a lower flow to some other
regions. The blood flow through working muscles during
prolonged exercise in individuals is steady, after an initial
period of time, as it is regulated by the metabolic activity
[6].
Levy, Tabakin and Hansson and Grimby et al. investigated
the variability of cardiac output during twenty to thirty
minutes of exercise on a continuous workload. They
reported substantial variations in the cardiac output in the
majority of the examined normal individual during a
continuous moderate workload on a treadmill [8].


Average cardiac output

20
15-
10
5 5
0 -
0 1 2 3
oxygen uptake {litimin)


Average Stroke Volume

110
E 100-
90 --i
0 1 2 3
Oxygen uptake(litJmin)

Figure 1: Variation in cardiac output and stroke
volume with respect to oxygen uptake in healthy
young men


Hemodynamic variations from exercise due to increased
heart rate, cardiac output, and stroke volume during
exercise create the fluctuations in mean wall shear stress in
the arteries, which in turn affects the formation of, or
reversal in atherosclerotic plaque.
Atherosclerotic plaque formation of specific arterial regions
with curvature, such as the carotid bifurcation is well
recognized. Hemodynamics and arterial geometry both
offer useful information for artery stenosis evaluation.
Carotid artery stenosis can be effectively used to understand
the effects of exercise on the phenomenon of plaque
formation, stability, and reversal. Atherosclerotic disease of
the carotid artery is a leading cause of stroke.
Atherosclerotic plaque in the carotid artery obstructs blood
flow to brain and stimulates the formation of thromoembli
that occlude downstream vessels. Unusual shear stress
patterns and disturbed flows are related to plaque rupture,
plaque erosion, and the formation of thromboembli. The


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

risk of stroke from carotid artery stenosis progressively
increases with increasing degree of stenosis. Effects of
exercise the increased heart rate, cardiac output, and
stroke volume can induce increased wall shear stress in the
artery. What is its effect on atherosclerotic plaque
formation, stability and reversal in the carotid artery?


Stroke Volume

120
100 -
80 -
E 60 -
40 -
20
0
0 10 min 20 30



Heart Rate

140
120 -
.E 100 -
E 80- 1
S60-
40 -
20
0i
0 10 20 30
min


Cardiac Output

1 5 ----------------

c 10 -

5-

0
0 10 20 30
REST EXERCISE


Figure 2: Shows the average heart rate,
cardiac output, and stroke volume at rest and
during exercise on a bicycle ergometer.

To date there are no reliable methods to determine wall
shear stress in the recirculation zones downstream of the
stenosis in clinical evaluation. Thus, hemodynamics
generated from computational fluid dynamics (CFD)
simulations complement the evaluation of carotid and other
artery stenosis. It can be used to find the effect of exercise
on the atherosclerotic plaque formation, stability and
reversal in the carotid artery.
A strong correlation exists between sites of atherosclerosis
and variations in local hemodynamics. Hence, arterial
blood flow in bifurcations, junctions, and grafts have been
investigated by considerable researchers. These studies
include numerical simulations that allow detailed and direct









examination of the hemodynamic flow and shear stress
patterns in regions of interest. These simulations are often
theoretical computational exercises. However, using
non-Newtonian blood properties, arterial wall compliance,
and treating the blood as a two-phase medium create
increased realism of these simulations. This helps in
realistic prediction of wall shear stress and other related
parameters to understand the effects of exercise in
atherosclerotic plaque formation, stability and reversal.
Gijsen et al. [9] found the influence of non-Newtonian
properties of blood on the hemodynamic analysis in the
carotid bifurcation. Noteworthy is the higher velocity
gradients at the outside wall and lower gradients at the flow
divider due to flattened axial velocity field of the
non-Newtonian fluid [10]. According to Steinman and
Ethier [11] the arterial wall compliance has major influence
on the arterial blood flow characteristics. Perktold and
colleagues [12] also confirms the observation. In addition,
the pattern of pressure and velocity variations changes
significantly due to the effect of pulse wave reflections on
shaping the local pressure waveform. These variations are
less significant in mild exertion such as brisk walk.
However, it is extremely prominent in case of intense
exercise.
Elevated wall shear stress in arteries activates the
glucocorticoid receptor (GR) and its transcriptional
signaling pathway to induce antiatherosclerosis actions in
the vasculature through an atheroprotective phenotype in
endothelial and T cells [13].


Methods

Hemodynamic flow can be mathematically modeled using
the time-dependent Navier-Stokes equations for an
incompressible fluid. Assuming the flow is laminar, the
governing equations are written as:

V =Ou 0 ()


P + u Vu = -V + /V2u
at? I=


where u is the fluid velocity, p the density, u the viscosity
and p the pressure. Solution of these partial differential
equations requires the geometric boundaries and Diriclet
and/or Neumann conditions to be specified, and the choice
of boundary conditions is very important since the
predicted velocity field and shear stress can be quite
sensitive to the flow conditions imposed at the boundaries.
However, to achieve increased realism, it is essential to use
non-Newtonian blood properties, arterial wall compliance
adjustments, and treating the blood as a two-phase medium.
The Fahraeus-Lindquist effects in Cell-Free marginal layer
model is characterized by the laminar Poiseuille flow in an
RBC-rich core and a plasma region. Four sets of
boundary conditions define the flow. At the center of the
artery, the velocity is the maximum. No slip boundary
condition exists. Continuity of velocity is maintained at
the interface between the two phase flow of RBC-rich core
and a plasma region. Continuity of shear stress is
maintained at the interface between the two-phase flow.
Fully developed velocity profiles are affected by these four


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

boundary conditions. When the plasma layer thickness is
negligible compared to the overall radius of the artery, the
effective viscosity is the viscosity of the core.
Assumption of fully developed flows at the inlet and the
outlet is not practical in case of arterial flows because of
their non-planar curvature and short length. The
turbulence is marked by random fluctuations. With
fluctuating turbulence the velocity field can no longer be
predicted with absolute precision, but its statistical features
(mean velocity, root mean square velocity, mean pressure
gradient, etc) are perfectly well defined. Turbulence in
blood flow implies fluctuating pressure acting on the
arterial wall and an increased shear stress. These stresses
are implicated in murmurs, poststenotic dilatation, and
atherogenesis [14-15].
For pulsatile flow in a tube, when the Wombersley number
is large, the effect on the viscosity of the fluid does not
propagate far from the wall. In the central portion of the
tube the transient flow is determined by the balance of the
inertial forces and the pressure forces as if the fluid were
non-viscous. Real blood vessels are curved and of
variable cross section. The non-uniform cross-sectional
area is associated with branching and elastic deformation
of the vessel wall in response to a non-uniform pressure
with a finite gradient. On top that the realistic model has
to consider the effects of non-linearities. The viscous
force is nonlinear if the constitutive equation of the fluid is
non-newtonian. Blood is non-Newtonian, and the effect
of nonlinear blood viscosity is especially important with
regard to flow separation at points of bifurcation in
pulsatile flow. In the equation governing the blood vessel
wall, the most significant nonlinearity comes from the
finite strain and nonlinear viscoelasticity. In a pulsatile
flow, the point of separation and the size of the separated
region may vary with time. In the separated region, the
flow is unsteady and the shear stress is lower than in the
unseparated regions. These unseperated regions become
matter of utmost importance for hemodynamic analysis
since atherosclerotic plaques correlate with the sites of
flow separation. In addition there are many other
non-uniformities in arteries. Existing stenosis, or local
narrowing of the vessel is important. Dilation, or existing
local enlargement of vessel is equally important. The
detailed flow condition at each branching point is
important, because at such a site there is a stagnation point
where the velocity and velocity gradient are zero, and too
far away is a region with a high velocity gradient. The
shear stress acting on the wall is non-uniform.


Flow velocity during the cardiac
cycle
0

a



o& 0 0.5 1 1.5
E Axial Velocity (Mean)

Fiure 3: The flow velocity during the cardiac cycle.
Figure 3: The flow velocity during the cardiac cycle.








Because of the above complexities, the solution of the
resulting governing equations is impossible to achieve by
the traditional analytical techniques. Numerical
techniques are required; hence CFD is used [16].


Arteria Vertebralis
Dextra


Arterla Vertebralis
Sinlstra


Arteada Basllarls


I Figure 4: Natural carotid bifurcation


The CFD code implemented in a dynamic J2E/ASP/Flash
environment shows hemodynamic flow variations in a
natural junction, arteria vertebralis dextra and sinistra with
ateria basilaris.
Pulsatile blood flow with non-Newtonian blood properties,
arterial wall compliance adjustments, and treating the
blood as a two-phase medium in a software simulated
carotid bifurcation model is simulated using fully coupled
fluid-structure interaction finite element methods at
different heart rates: from 65 bpm representing a person at
rest to 130 bpm representing a person in physical exercise
mode. Two cases are considered for each case of heart rate.
In first case, the peripheral resistance is uniformly reduced
resulting in an increase in mean flow. In the second case,
the cerebral vascular resistance is held constant so that
mean carotid artery flow is nearly unchanged. For each
case, wall shear stress values, relevant adjusted nonlinear
wall shear stress over the cycle as well as dynamic
temporal gradients of wall shear stress are compared to
identify significant differences among them.
The dynamic simulations employ standard dynamic
nonlinear, isotropic, hyperelastic finite element analysis for
the arterial walls. Blood is treated as a non-Newtonian fluid
and the flow is adjusted to simulate pulsatile nonlinearity
and other factors discussed above. Convex optimization
and sequential stochastic optimization techniques are
employed to simulate the dynamic environment within the
finite elements analysis code. Maximum dynamic temporal
gradient is the maximum value of the gradient in wall shear
stress. The dynamic oscillatory shear index (OSI) is a
nondimensional measure obtained through convex
optimization of an algorithm that quantifies the fractional
time a particular wall region in the cycle experiences
reverse flow.

Results

First, a gradual controlled 100% increase in heart rate is
considered in which peripheral resistance is uniformly
reduced to maintain constant mean arterial pressure,
resulting in an increase in mean flow. The heart rate is


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

gradually increased from 65 bpm to 130 bpm. The wall
shear stress averaged over different locations (Tw)ave
increases by 42% in a nonlinear manner with a flow rate
rise of 45%.

Rise in Wall Shear Stress (WSS) with Heart Beat


Figure 5: Rise is Wall Shear Stress with increase in
Heart Beat when peripheral resistance is uniformly
reduced to maintain constant mean arterial pressure,
resulting in an increase in mean flow

In the second case, the cerebral vascular resistance is held
constant so that mean carotid artery flow is nearly
unchanged. In this case the heart rate is also gradually
increased from 65 bpm to 130 bpm. The wall shear stress
averaged over different locations (Tw)ave increases by 12%
in a nonlinear chaotic manner with a flow rate rise of 1%.


Rise in Wall Shear Stress (WSS) with increasing Heart Beat under
constant flow


Heart Beat (bpm)


Figure 6: Rise is Wall Shear Stress with increase in
Heart Beat when cerebral vascular resistance is held
constant so that mean carotid artery flow is nearly
unchanged

The area of low average wall shear stress (Tw)ave (<1.0 Pa)
reduces considerably (22%) as the heart beat is raised from
65 bpm to 130 bpm as peripheral resistance is uniformly
reduced to maintain constant mean arterial pressure,
resulting in an increase in mean flow. The area of low
average wall shear stress (T)ave (<1.0 Pa) reduces less
considerably (7%) as the cerebral vascular resistance is held
constant so that mean carotid artery flow is nearly
unchanged.


-
C1 -


Heart Beat (bpm)


! I .

'S An


8
s









Ratio of Area of of low WSS with increasing Heart Beat (increasing flow)




0.4
03
02
0 1

65 70 75 80 85 90 95 100 105 110 115 120 125 130
Heart Beat (bpm)



Figure 7: Fall in the ratio of low Wall Shear Stress
(<1.0 Pa) with increase in Heart Beat when
peripheral resistance is uniformly reduced to
maintain constant mean arterial pressure, resulting in
an increase in mean flow


Discussion

The low mean wall shear stress zones are more prone to
atherosclerosis. Average wall shear stress levels greater
than 1.5 Pa induce endothelial quiescence and an
atheroprotective gene expression profile, whereas low
shear stress levels (less than 1.0 Pa) stimulate an
atherogenic phenotype and are generally observed at
atherosclerosis-prone sites [17].
It is evident that when the heart rate is increased from 65
bpm to 130 bpm, in which peripheral resistance is
uniformly reduced to maintain constant mean arterial
pressure, resulting in an increase in mean flow, the mean
wall shear stress rises significantly. More importantly, the
zones with average wall shear stress below 1.0 Pa drops
rapidly as the heart beat rate is increased from 65 bpm to
130 bpm. A 42% increase in average overall wall shear
stress with 22% reduction in low (below 1.0 Pa) wall shear
stress zone provide significant atheroprotective gene
expression profile resulting in reduction of proneness to
atherosclerosis. When the flow is kept constant, the
average overall wall shear stress rises by 12% while zones
with low wall shear stress drops by 7%. Although it is
less significant than the previous case, nevertheless, it
confirms that rise in the rate of heart beat provides higher
wall shear stress in the arteries and in general lowers the
zones of low shear stress in the vasculature. Figure 2,
shows that the average heart rate, cardiac output, and
stroke volume rise rapidly during exercise. It is
significant that the cardiac output and stroke volume rise
very rapidly during brisk exercise. Figure 1, shows rapid
rise in cardiac output and stroke volume with respect to
increased oxygen uptake which is very common during
exercise. This observation provides support to the
hypothesis that physical exercise promotes an
atheroprotective phenotype [18,19].
It is important to note that in this model, we have applied
significant modification to the fundamental mathematical
model of the Hemodynamic flow of the time-dependent
Navier-Stokes equations for an incompressible fluid to
simulate realistic conditions of the vasculature. To
achieve this increased realism, we have used


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

non-Newtonian blood properties, arterial wall compliance
adjustments, and treated the blood as a two-phase medium.
In addition, effect of nonlinear blood viscosity has also
been included in the model. Use of convex optimization
and sequential stochastic optimization techniques
employed to simulate the dynamic environment within the
finite elements analysis code made the simulation even
more realistic.
However, it is also true that exercise affects the
cardiovascular system via a complex mechanism, giving
rise to a wide range of changes in the dynamics of the
physiological system, far beyond just hemodynamic
modeling. Here, we only focused on a specific bifurcation,
a specific part of the vaculature, and simulated how a
relatively narrow range of physiologically conceivable
changes in regional arterial blood flow would impact the
atherogenically relevant hemodynamic mathematical
pattern. A detailed analysis of the effect of exercise
requires a comprehensive model of the whole
cardiovascular network, incorporating various dynamical
and neural pathways that play a role in this complex
mechanism.
The vascular endothelium plays a central role in vessel
tone regulation while endothelial dysfunction is implicated
in various wall-thickening pathologies. Atherosclerosis is
preferentially initiated at bifurcation sidewalls with
reversing or vortexing flows, or regions of low mean wall
shear stress [20]. In cultured endothelium, the onset of
flow causes the transient induction of proatherogenic genes
such as platelet-derived growth factor A and B chain,
macrophage chemoattractant protein 1 (MCP-1), and
endothelin-1 (ET-1), whereas arterial shear stress over
many hours downregulates these genes [21,22,23,24] .
Sustained shear is also associated with long-term elevated
expression of tissue plasminogen activator (tPA),
endothelial nitric oxide synthase (eNOS), and C-type
natriuretic peptide, genes typically associated with an
atheroprotective phenotype. The atheroprotective
phenotype not only stabilizes the plaque formation, it also
reverses the process to some extent [25,26].
A variety of kinases and signaling proteins are involved in
shear-modulated responses. Shear stress activates
phosphatidylinositol 3-kinase (PI3-kinase), leading to
phosphorylation of Akt (protein kinase B). Related studies
also show, however, that shear stress phosphorylates eNOS
through an Akt-independent mechanism that involves
protein kinase A [27]. The subsequent eNOS activation
results in elevated production of NO, another potent
endothelial signaling molecule. Garcia-Cardena also
demonstrated the association of heat shock protein 90
(hsp90) with eNOS in human umbilical vein endothelial
cells (HUVECs) after 15 to 30 minutes of shear, whereas
NO production occurs within seconds after flow onset [28].
Mitogen-activated protein kinase (MAPK) activation in
shear-stressed endothelium is also well documented;
extracellular signal-regulated kinases (ERK1/2), c-Jun
N-terminal kinase (JNK), big MAPK (BMK1), and to a
lesser extent, p38 are all activated by shear stress [29,30].
Proximal to gene expression changes in steady flow,
kinases activated during mechanotransduction can alter the
activity of transcription factors such as nuclear factor
(NF)-B, AP-1, and erg-1[31,32,33]. Hence in the
endothelium, cellular responses to shear stress occur









through diverse signaling pathways involving, among
others, NO, heat shock proteins, and protein kinases such
as PI 3-kinase and MAPK.
The anti-inflammatory effects of glucocorticoids on the
endothelium suggest a possible role for the glucocorticoid
receptor (GR) in mediating atheroprotective actions of
shear stress in the vasculature.


Acknowledgements


The author wishes to acknowledge the hard work of
Sysoft's software engineers for providing the
computational support for the project. In addition, the
author also acknowledges the cooperating Sysoft clients.
The work is funded by the product innovation initiative of
the Sysoft Center for Computational Biology and
Bioengineering.


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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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7th International Conference on Multiphase Flow
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