This document summarizes a computational fluid dynamics (CFD) study that examined the relationship between arterial stenosis severity and hemolysis for an artificial tricuspid heart valve. The CFD study modeled four stenosis severities: healthy, 5%, 10%, and 25% reductions in arterial diameter. Results showed increased velocity, shear stress magnitudes, and risk of hemolysis with increasing stenosis severity. The 25% reduction in diameter produced shear stresses exceeding 150 Pa, indicating a high risk of hemolysis.

1. Relationship between Arterial Stenosis and Hemolysis: A CFD
Study
Bryson Hayes a
, Alex Germano a
, Frederick Fahima
a
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, K1N 6N5
bhaye024@uottawa.ca, 6354919
agerm039@uottawa,5610234
ffahim090@uottawa.ca,4874185
Article Info
Article History:
Received 19 March 2015
Keywords:
Artificial Heart Valve
Hemolysis
Stenosis
Word Count : 4488
University of Ottawa
2015
Abstract
In recent years, the design ofartificial heart valves has begunto be increasinglyimportant, as there has
been a steadyincrease inthe number of heart diseases andpotential failures. In order to aidthisfield of
research, medical teams have attempted to recreate the anatomicalheart valve with useof scaffolds, stem
cells, andother artificial heart valves. The increase inprevalence with regards to this type of graft is due to
their more natural behavior, and the increasedriskof hemolysis whenusing a mechanical heart valve. This
studyattemptedto demonstrate a relationship between stenosis andincreased velocityandshear stress
magnitudeswhenusing anartificial triscupid heart valve. A CFD studywas conducted at four different
stenosisseverities, healthy, 5%, 10% and 25% reductionina rterial diameter. Results clearlydemonstrate a
relationshipbetweenseverityof stenosis andincreasedrisk ofhemolysis, withthe 25% reduction in
diameter demonstratingshear stressesexceeding150 Pa. (158 words)
Artificial Heart Valves
In recent years, advancements made in the field of
tissue engineering have led to vast improvements in
the design of biological, synthetic heart valves. In
general, the biological heart valve demonstrates
improvements over its mechanical counterpart, as it
removes the necessity to take anti-coagulation
medication. The concept of tissue engineered heart
valves lies in 3D scaffold. This neotissue, which can
be formed of many different materials, replaces the
biological heart valve, and as such, must be similar in
size while demonstrating similar mechanical
properties. Furthermore, it must include the various
layers of the native heart valve. As such, the scaffold
matrix represents the extracellular matrix of the
biological heart valve, as well as the spongy layer.
Continuing, the matrix should provide a porous,
interconnecting network which allows the blood to
flow through, Finally, the material chosen must be
biocompatible, and it some cases biodegradable
when sufficient integration into the biological system
is completed. Although the concepts presented make
3D scaffolds seem like an attractive option, it may be
prone to calcification, breakdown, mechanical failure
or various other complications.
As previously mentioned, various different
cell sources are available when creating a bioscaffold.
Currently, the most practiced technique is the use of
xenogafts. Although these types of decellularized cells
are easily obtainable, there is an increased risk of
immune response. As such, the most logical choice for
cell cultivation is the valve interstitial cells (VIC).
Both semilunar valves are comprised of two general
types, the endothelium cells and the interstitial cells.
Although the VICs provide the most natural tissue
behavior, it requires the sacrifice of an intact vascular
structure of a patient with no previous heart
diseases. Continuing, recent works have concentrated
on different cell sources, such as stem cells. These
cells, which are readily available from peripheral and
human umbilical cord blood, as well as bone marrow,
provide smooth muscle action much like the VICs,
while also providing the benefit of producing both
type I and type II collagens. Furthermore, the stem
cells can further differentiate into various cell types,
which effectively allow an even distribution of cells
throughout the entire scaffold. [13]

2. Aortic Valve
The aortic valve is located between the left
ventricular outflow tract and the ascending aorta. It
forms the centerpiece of the heart and closely
approximates many other important cardiac
structures, specifically, the pulmonic valve, mitral
valve, and tricuspid valves. The aortic valve functions
to prevent the regurgitation of blood from the aorta
into the left ventricle during ventricular diastole and
to allow the appropriate flow of blood from the left
ventricle into the aorta during ventricular systole.
The aortic valve cusps have 3 identifiable
layers: the lamina fibrosa, lamina spongiosa, and
lamina radialis. The lamina fibrosa is the widest layer
and faces the aortic or arterial side of the valve cusp.
The lamina radialis is the thinnest of the 3 layers and
faces the ventricular side of the valve. The lamina
spongiosa lies between the lamina fibrosa and lamina
radialis. A thin layer of endothelial cells covers the
entire cusp, which is smooth on the ventricular side
and ridged on the arterial side.
The extracellular components of these layers
are primarily composed of collagen fibers arranged in
a honeycomb-like structure that serves to preserve
the geometry of the collagen fibers under the
hemodynamic stresses that the valve apparatus
encounters. Within the extracellular matrix of the
leaflets lie interstitial cells that are similar to smooth
muscle cells and fibroblasts and that have been
termed myofibroblasts. These cells are supplied with
oxygen via diffusion and a microvascular network.
Bicuspid aortic valve is the most common
congenital cardiac abnormality, occurring in 1-2% of
the population, with a 2:1 male predominance. It may
be clinically silent, but can lead to early development
of aortic stenosis or aortic insufficiency. [15]
Pulmonic Valve
The pulmonic valve divides the right ventricular tract
from the pulmonary artery. In normal conditions, the
pulmonic valve prevents regurgitation of the
deoxygenated blood from the pulmonary artery back
to the right ventricle. Like the aortic valve, the
pulmonic valve is formed by 3 cusps, each with a
fibrous node at the midpoint of the free edges, as well
as lunulae, which are the thin, crescent-shaped
portions of the cusps that serve as the coaptive
surfaces of the valve.In contrast with the aortic valve,
the cusps of the pulmonic valve are supported by
freestanding musculature with no direct relationship
with the muscular septum; its cusps are much thinner
and lack a fibrous continuity with the anterior leaflet
of the right atrioventricular (AV) valve.
Pulmonic Valvular Stenosis (PVS) is the most
prevalent pulmonary valve pathology, and it accounts
for up to 80% of the cases of right ventricular outflow
tract obstruction. This condition can be detected
throughout different stages of life, depending on its
severity. The more severe the obstruction, the earlier
in life, PVS manifests itself. Neonates usually present
with critical stenosis, manifested as cyanosis at birth,
although infants are usually diagnosed when a
murmur auscultated in the pulmonic area. Pulmonic
stenosis symptoms tend to worsen and progress with
time. [14]
Hemodynamic Complications: Stenosis
Both arterial and aortic stenoses are major causes of
concern when modeling and understanding blood
flow patterns. Plaque deposits and platelet
aggregation leading to narrowing of arteries are
known to result in increased flow velocities and
create downstream turbulence [5]. Narrowing of the
aortic valve impedes the delivery of blood to the rest
of the body, making the heart work harder. For these
reasons, it is imperative that the direct causes of
stenosis are clearly understood when considering
valve design.
Shear stress/Hemolysis
When blood is in motion through an artery, a series
of complex events associated with the movements of
the individual cells and surrounding plasma takes
place. Considering the enormous number of cells
involved in the flow, hydrodynamic factors play a
significant role for atherosclerosis and deposition of
blood platelets and lipids. The shear stresses
developed towards the wall surface are believed to
be responsible for adhesion and deposition of
platelets and lipids [2]. It has been found that initially
blood cells are damaged or their surface changes in a

3. high shear field and then the particles stick to the
wall and form deposits at low shear stress fields [2].
Over a period of years, localized accumulation of
material within or beneath the intimal causes the
deposits to turn into atherosclerotic plaques that
greatly reduce the arterial diameter. Thus, the flow to
the vascular bed is disturbed significantly.
It has been established that shear stresses in
the order of 1500-4000 can cause lethal
damage to red blood cells. However, in the presence
of foreign surfaces, red blood cells can be destroyed
by shear stresses in the order of 10-100
[5]. As the intensity of shear stress increases,
platelet aggregation also increases, leading to shear-
induced platelet damage. Although the exact
mechanism of turbulent stress damage to the cell is
not precisely known, there is no disagreement that
cell damage can be created by high turbulent
stresses; minimizing these is conducive to better
valve performance from the standpoints of thrombus
formation, thromboembolic complications, and
hemolysis and from energy loss considerations [12].
Thrombosis/Embolism
The formation of blood clots is a natural biological
process used most often in immune response and
wound repair. The aggregation of platelets and
clotting enzymes creates thrombi at the site of the
wound, whether that site is arterial, venous, or
otherwise. This becomes very important when
looking at valve design, as the growing geometry of
thrombi have been shown to lead to an increasing
risk of interrupted flow patterns and creation of
turbulent vortices in the bloodstream [6].
Furthermore, the regions of flow stagnation and/or
flow separation that occur adjacent to mechanical
and tissue valves can promote further deposition of
damaged blood elements, leading to further
deposition of thrombi [12]. Under certain flow
conditions, thrombi can break free and travel through
the bloodstream. At this point, the clot is referred to
as an embolus; a free-flowing thrombus. Arterial
embolism can cause occlusion in any part of the body,
no matter its origin, but when an embolus is large
enough to impede blood flow in the brain, it results in
a stroke, whereas if it occurs in the heart it can cause
a heart attack.
Regurgitation
Regurgitation results from the reverse flow of blood
created during valve closure and from backward
leakage once closure occurs. In general, regurgitation
reduces the net flow through the valve. Closing
regurgitation is closely related to the valve geometry
and closing dynamics, and the percentage of stroke
volume that succumbs to this effect ranges from 2.0–
7.5% for mechanical valves [1]. For tissue valves it is
typically less, at around 0.1–1.5%. Leakage depends
upon the effective orifice area (EOA) and how well
the orifices are sealed upon closure, and it has a
reported incidence of 0–10% in mechanical valves
and 0.2–3% in bioprosthetic valves. The EOA is a
measure of how well the prosthesis utilizes its
primary orifice area. In other words, it is related to
the degree at which the prosthesis itself obstructs
blood flow. A larger EOA corresponds to a smaller
pressure drop and therefore a smaller energy loss. It
is desirable to have as large an EOA as possible [12].
The equation for EOA is shown below:
√
In this case, is the root mean square of
the systolic/diastolic flow rate, and is the mean
systolic/diastolic pressure. The overall tendency is
for regurgitation to be less for the trileaflet
bioprosthetic heart valves than for mechanical valve
designs. Regurgitation has implications other than
simply for flow delivery. On the negative side, back
flow through a narrow slit, such as can occur in
leakage regurgitation through a bileaflet valve, can
create relatively high laminar shear stresses, thus
increasing the tendency toward blood cell damage
[1,4]. However, regurgitation can have a beneficial
effect in that the backflow over surfaces may serve to
wash out zones that would otherwise produce
regions of flow stagnation throughout the cycle. This
is particularly true for the “hinge” region in some
tilting disc and bileaflet designs.
Structural Complications: Durability
Stuctural mechanics play an important role in the
overall performance of prosthetic heart valves. The
design configuration has an effect on load
distribution and the dynamics of valve components,

4. both of which, when paired with material properties,
determine durability [8,12]. The choice of valve
materials is closely related to structural factors, since
the fatigue and wear performance of a valve depends
not only on its configuration and loading, but on the
material properties as well. In addition, the issue of
biocompatibility is crucial to prosthetic valve
design—and biocompatibility depends not only upon
the material itself but also on its in vivo environment
[11]. In the design of heart valves there are
engineering design trade-offs: Materials that exhibit
good biocompatibility may have mediocre durability
and vice versa.
Wear
Abrasive wear and degradation of valve components
has been and continues to be a serious issue in the
design of mechanical prosthetic valves. Various parts
of these valves come in contact repeatedly for
hundreds of millions of cycles over the lifetime of the
device. A breakthrough occurred with the
introduction of pyrolitic carbon (PYC) as a valve
material: It has relatively good blood compatibility
characteristics and wear performance. However,
although PYC wear upon PYC and upon metals is
relatively low, PYC wear by metals is considerably
greater [11]. The first valve to employ a PYC-PYC
couple was the St. Jude Medical valve, which has fixed
pivots for the leaflets. Tests indicate that it would
take 200 years to wear halfway through the PYC
coating on a leaflet pivot. By creating designs that
allow wear surfaces to be distributed rather than
focal, it is possible to reduce wear even further [11].
Thus, materials technology continues to progress and
in fact has reached the point where wear need not
negatively impact the performance of prosthetic
mechanical valves.
Fatigue
Metals are prone to fatigue failure. Their
polycrystalline nature contains structural
characteristics that may produce progressive
dislocations under mechanical loading. These
dislocations can migrate when subjected to repeated
loading cycles and can accumulate at intercrystalline
boundaries, and the end result is microcracks. These
tiny cracks are sites of stress concentration, and the
fissures can worsen until fracture occurs. Previous
investigations suggested that fatigue was not a
problem for PYC; however, recent data contradict
this, suggesting that cyclic fatigue- crack growth
occurs in graphite/pyrolitic carbon composite
material [10]. This work suggests a fatigue threshold
as low as 50% of the fracture toughness, and those
authors view cyclic fatigue as an essential
consideration in the design and life prediction of
heart valves constructed from PYC [10]. As of
December 1993, the FDA requires detailed
characterization of PYC materials used in different
valve designs [12].
Mineralization
The mechanisms of calcification, and the methods of
preventing calcification are active areas of current
research. The most common methods of studying
calcification involve valve tissue implanted either
subcutaneously in 3-week old weanling rats or valves
implanted as mitral replacements in young sheep or
calves [8,12]. Results of both types of studies show
that bioprosthetic tissue calcifies in a fashion similar
to clinical implants, but at an accelerated rate. The
subcutaneous implantation mode is a well accepted,
technically convenient, economical, and quantifiable
model for investigating mineralization issues. It is
also very useful for determining the potential of new
anti-mineralization treatments. Host, implant, and
biomechanical factors impact the calcification of
tissue valves as well. Pretreatment of valve tissue
with an aldehyde agent has been found to cause
calcification in rat subcutaneous implants; non-
preserved cusps do not mineralize [7]. In general,
collected data suggests that the basic mechanisms of
tissue valve mineralization result from aldehyde
pretreatment, which changes the tissue
microstructure.
Follow-up After Surgery
The first post-operative appointment should be
scheduled within 6 weeks of discharge, or within 12
if a rehabilitation program has been set [3]. At the
first post-op meeting, it is important to approach the
completeness of wound healing in terms of:
 Symptomatic status and physical signs
 Heart rhythm and ECG readings

5.  Chest X-ray for resolution of any post-
operative abnormalities
 Echocardiography pertaining to pericardial
effusion, ventricular function, prosthetic
competence and function, and disease at
other valve sites
 Routine hematology and biochemistry and
tests for hemolysis
The frequency of future follow-up should be
determined by the patient's progress and by local
facilities, but ideally all patients who have undergone
valve surgery should continue to be followed-up at a
cardiac centre in order to detect, at an early stage,
deterioration in prosthetic function, recurrence of
regurgitation following valve repair, or progression
of disease at another valve site, any of which can
occur with relatively little or no change in symptoms
[3]. The frequency of echocardiography during
follow-up should be determined by the results of
previous echocardiography, symptomatic status, the
type of surgery and the existence of other pathology
[3].
Quality of Life After Replacement Surgery
Over the last three decades, heart valve replacement
has become a safe and routine surgical procedure,
but replacement devices are still far from ideal.
Despite improvements in materials and design, life-
long anticoagulation remains mandatory for
mechanical valves. The major shortcoming of the less
thrombogenic bioprosthetic valves is early tissue
failure[ 9]. The potential quality of life for survivors
has been becoming increasingly important in
evaluating the late results and in selecting the
appropriate device for the given patient. All factors
that determine the quality of life are strongly affected
by the operation due to the usually dramatic
improvement in both subjective status and objective
parameters postoperatively. The patient, thus, can
return to normal activities, maintain self-esteem and
keep normal relationships at work, in the community
and at home.
Methods
When performing a CFD analysis, it is vital to have
previous hypotheses surrounding the field of study,
as well as main objective in terms of desired result.
As an initial model, the proposed objective of the
model is to demonstrate the effect of arterial stenosis
on the systolic flow rates through the pulmonary
heart valve, as well as the wall shear stresses acting
on it. In order to do so, a 3D CAD model of a triscupid
heart valve was obtained, and imported into CAD
software Solidworks. Upon inspection of the model, a
few changes were necessary, which included proper
dimensioning through scaling, as well as defining
relations such as the degree at which the valves were
open. The proposed model is comprised of a valve
ring of 19.55mm in diameter and 5mm in length.
Each of the three triscupid valves measure 9mm in
length, and at its most thick section 3.5mm. The valve
in its entirety is 14mm in length. Following, it was
also necessary to extrude an artery, and insert the
heart valve into it. The diameter used for the
pulmonary artery was 21.5mm. Then, in order to
model stenosis, three tests were conducted at 5%,
10% and 25% reduction in diameter, corresponding
to an arterial diameter s of 20.5, 19.4 and 16.2mm
respectively. In all but the most severe case, the
positions of the leaflets were left unchanged. For the
most severe case of stenosis, it is necessary to close
the valve by 10° in order to maintain the validity of
the model. As the diameter of the artery decreased,
the leaflets of the valve began to pass through the
walls of the artery model. As such, the leaflets were
set to a more closed position, as would be the case in
an anatomical model of a patient suffering of arterial
stenosis. The inlet section was 2mm upstream of the
valve entrance, and the outlet section 35mm
downstream. Presented in Figure 1 are each of the
stenosis models, where a distinct change in diameter
can easily be seen.

6. Figure 1: Arterial stenosis at various severities
Once the CAD model was completed, it was then
imported in Computational Fluid Dynamics software
Star-CCM+. First and foremost, it was necessary to
determine the required flow model. For the fluid
properties of the blood, the commonly accepted
values for density, 1060 kg/m3, and dynamic
viscosity, 0.0035 kg/m·s, were used. Following, a
cardiac output of 8L/min, corresponding to a systolic
flow rate of 24L/min, were used in order to simulate
strenuous exercise. Under these conditions, the
Reynolds numbers for each of the severities
remained in the turbulent range. Numerous
assumptions were made in order to complete the
analysis. Most importantly, the flow was assumed to
be steady in order to simulate flow during the peak
systolic phase. Furthermore, the fluid was assumed to
Newtonian, which allowed us to model it as a fluid
with constant density, and also obtain the shear
stress in the boundary layer near the walls. Finally, as
previously mentioned, the flow was assumed to be
turbulent, and was solved using the κ-ε model. No
initial conditions were changed in this turbulent
solver for the case of this study. With regards to
boundary conditions, the inlet was considered as a
stagnant pressure, and the outlet as a zero static
pressure. The inlet pressure was changed for each of
the cases in order to maintain a constant output flow
rate. Since volumetric flow rate is proportional to the
cross sectional area, it is necessary to increase the
inlet pressure as the diameter of the artery decreases.
No-slip conditions were used at all of the other walls.
Presented in Figure 2 are the velocity
contours for each of the modeled severities.
Beginning the top left is the healthy case, and
continuing in a clockwise fashion are the 5%, 10%
and 25% cases. As clearly demonstrated, the flow
contours are very similar throughout each of the four
cases, but a clear increase in magnitude is
demonstrated from case to case. As one would expect,
the peak velocity is found in the case of 25% stenosis,
and is found to be approximately 2.5 m/s. In each of
the cases, the fluid experiences its greatest velocities
as it passes through the valve, and is at its peak near
each of the leaflets. Furthermore, in each of the cases,
instances of vorticity are found at the trailing edges
of each of the leaflets, and these vortices increase as
the severity of stenosis also increases. Presented in
Figure 3 are the velocity contours 1mm downstream
of the valves. As one would expect, the velocity of the
fluid exiting the valve increases as the severity of
stenosis also increases.

7. Figure 2: Velocity Magnitude (m/s) for each case
Figure 3: Velocity profile for each case
Finally, presented in Figure 4 are the
magnitudes of shear stress located at the wall of the
leaflets. As previously mentioned, localized shear
stresses exceeding 150 Pa are shown to increase the
risk of platelet damage in the red blood cells. This
magnitude of shear stress is only found in the 25%
stenosis case, where the maximum wall shear stress
is approximately 194 Pa. In each of the other cases,
the wall shear stress on the face of the leaflets does
not exceed 100 Pa. As such, based on the results of
the proposed model, a patient suffering from 25%
arterial stenosis is at high risk of hemolysis.
Furthermore, a direct correlation between the

8. severity of stenosis and velocity and shear stress magnitudes has been demonstrated.
Figure 4: Shear stresses (Pa) encountered at the heart valves
Future Considerations
The most recent tissue valve design is the stentless
bioprosthesis, used for aortic valve replacement. The
aortic root bioprostheses are similar in concept to
homografts. Absence of the stent is thought to
improve hemodynamics, as there is less obstruction
in the orifice [12]. The absence of the stent is also
thought to improve durability of the tissue, as there is
less mechanical wear. Currently, three designs of
stentless aortic valves (Medtronic’s Freestyle,
Baxter’s Prima, and St. Jude’s Toronto Non- Stented)
are undergoing clinical evaluation in the United
States and Europe. New anti-mineralization
treatments are also being developed with the goal of
increasing the durability of the tissue [11].
There are three promising directions for further
improvement in cardiac valve design:
 Improved thromboresistance with the use of
new and better biomaterials
 Improved durability of new tissue valves
through the use of non-stented tissue valves,
new anti-calcification treatments, and better
fixation treatments
 Improved hemodynamics characteristics,
especially reduction or elimination of low shear
stress regions near valve and vessel surfaces
If the above-mentioned design challenges are met, so
that bioprostheses can be produced that are durable
and thromboresistant, and anticoagulant therapy is
not required, there most likely will be another swing
toward increased bioprosthesis use.

9. Although the proposed model demonstrated an
increased risk of hemolysis due to arterial stenosis,
there exist many limitations whichmust be
discussed. First and foremost, attempting to a model
a biological tissue will always present difficulties,and
the artificial heart valveis no exception. The readily
available heart valveused for the project was made
out of pure interest by its designer. As such, although
its geometry closely resembles its anatomical
counterpart, its validity cannot be confirmed by a
medical institution. Furthermore, as previously
mentioned, the dimensions of the heart valvewhen
initially downloaded were not to scale, and in order
to properly use the model forthis study, the entire
model was scaled down in order to more closely
represent the anatomical dimensions. Continuing,
since the goal of the project was to represent the
systolic phase of the heart cycle,assumptions with
regards to the degree at which the leaflets were open
were made in order to best represent this phase of
the cycle.
With regards to the validity of the results,
many different limitations must be taken into
account. First and foremost, due to a lack of
processing power, it was difficult to use Star-CCM+ to
its full capabilities. When performing computational
fluid dynamics, it is essential to perform many
iterations of the mesh refinement in order to
demonstrate convergence of the results. However,
since the availability of the program was limited, the
mesh refinement process was not as extensive as
desired. Furthermore, the number of iterations when
solving the model was limited to 250 steps. This
again is due to the limited processing power of the
computers used.
Conclusion
In conclusion, although there are many limitations to
the model due to various assumptions, the trend
shown based on the results is not insignificant.
Further research in this field can be continued, and
would include modelling blood as a Non-Newtonian
fluid, as well as at various systolic flow rates.
Furthermore, the entire cardiac cycle can be
modelled in order to demonstrate the occurrence of
regurgitation that is often associated with artificial
heart valves. In order to do so, further research must
also be conducted in the field of material science in
order to properly model the properties of a stent
graft valve. Proposed research topics would include
stress and bending tests of 3D printed stent graft in
order to model its elastic properties.
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