This document describes a study analyzing the effects of patent ductus arteriosus (PDA) on blood flow, pressure, and oxygen concentration within the pulmonary artery and aorta. Four 3D heart models were created in COMSOL: one control model without defects and three models with PDA defects of varying sizes. Results showed that PDA caused blood flow from the aorta into the pulmonary artery, mixing oxygenated and deoxygenated blood. Larger PDA sizes increased this flow, as well as pressure within the pulmonary artery and oxygen concentration. PDA size also increased flux through the defect. The study confirms established consequences of PDA such as increased lung pressure and decreased oxygen delivery to the body.

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Analysis of Patent Ductus Arteriosus on Blood
Flow, Pressure and Concentration Within the
Pulmonary Artery and Aorta
Group M:
Khalid Akari
Larry Chang
Kaylene Cobarrubia
Table of Contents

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I. Abstract …………………………………………………………….....3
II. Introduction…………………………………………………………..3
III. Theory …………………………………………………………….......5
IV. Experiment …………………………………………………………...6
V. Results and Discussion ……………………………………………11
VI. Conclusionsand Recommendations…………………….20
VII. Bibliography…………………………………………………………22
VIII. Appendix …………………………………………………………...23
I. Abstract
Patent ductus arteriosus (PDA) is a disorder within the heart that causes fluid to flow
from the aorta into the pulmonary artery via the ductus arteriosus consequently causing a

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mixture of oxygenated and deoxygenated blood within the pulmonary artery and an increase in
pressure towards the lungs. Within this study four three-dimensional models were constructed
in order to perform an analysis of how PDA affects the heart, specifically looking at the
pulmonary artery. One model shall act as a control containing no defects whereas the
remaining models will consist of defects varying in size. Results from this indicate that there
indeed is fluid flow into the pulmonary artery from the aorta causing a mixture of blood and
increased pressure. Furthermore increasing PDA size causes an increase in fluid flow, pressure
and concentration of oxygenated blood within the pulmonary artery. Additionally increase in
size of the PDA causes an increase of flux within the PDA. These results confirm established
consequences of the PDA defect.
II. Introduction
Patent ductus arteriosus is a congenital disorder that occurs in the hearts of newborn
infants when the ductus arteriosus fails to close after birth. Figure 1 provides an image of a
healthy heart in comparison with a heart with the defect present. Early symptoms are
uncommon however, within the first year symptoms seen include increased strain on breathing
and poor weight gain due to the fact that more calories are required to make up for the
additional work on the lungs and heart. PDA may also lead to congestive heart failure if left
uncorrected. As a fetus the infant is unable to supply oxygen to the lungs on its own therefore it
must receive oxygen from the mother. The ductus arteriosus functions to aid in this process
where it serves as a normal fetal blood vessel that allows blood to bypass circulation through
the lungs and delivers oxygenated blood straight to the heart from the pulmonary artery to the
aorta, supplying the fetus with oxygen. In normal infants, the ductus arteriosus typically closes

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within the range of minutes to a few days after birth. After the umbilical cord is cut, the
newborn infant must be dependent on its own supply of oxygen therefore the duct must close
to allow blood to circulate through the lungs which provides a new permanent oxygen supply.
However, in some cases this does not occur and the ductus arteriosus remains open. As a
consequence oxygen rich blood from the aorta mixes with the oxygen poor blood from the
pulmonary artery causing a higher concentration of oxygenated blood to flow through the
lungs. This mixing, also known as shunting, will decrease the supply of oxygenated blood to the
rest of the body thus causing strain on the heart as it must work harder to make up for this
detriment. Pressure to the lungs also increases as there is additional blow flow coming into the
lungs causing stress on the lungs.
Patent ductus arteriosus is usually diagnosed through Echocardiography, in which sound
waves are used to capture the motion of the heart to determine if the defect is present. An
alternative method to diagnose PDA includes X-ray. This method will reveal an image of the
duct to determine size and position.
The physiological impact of PDA depends largely on its size and the cardiovascular status
of the patient. The PDA can be small or large, but regardless of these factors, complications
may arise, therefore it is important to understand the effect of different sizes. Treatment can
be done simply by the surgical closure of the ductus arteriosus. The closing of the ductus will
allow prevention of shunting of deoxygenated blood and oxygenated blood thus eliminating
detriments.

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Figure 1 (http://www.merckmanuals.com)10
III. Theory
After birth the pressure in the pulmonary artery decreases, while the aortic pressure
increases. If the ductus arteriosus closes, the heart functions normally. The left ventricle
receives deoxygenated blood from the body where it is then pumped through the pulmonary
artery to become oxygenated in the lungs. The newly oxygenated blood moves into the left
ventricle, where it is then pumped through the aorta to provide oxygen to the rest of the body.
If the ductus remains open, the shift in pressure after birth creates left-to-right shunting
through the PDA. This causes the highly oxygenated blood from the aorta to mix with the less
oxygenated blood in the pulmonary circulation. Many problems arise from this shunt. In the
systemic circulation, since blood leaves the aorta through the PDA, the rest of the body does
not get enough oxygen. In the pulmonary circulation, an overload of blood enters the
pulmonary artery, causing increased pressure in the lungs, less lung compliance, and an
increase of fluid volume into the left ventricle.

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The goal of this study is to examine the effect that change in the PDA diameter will have
on pressure, concentration, and flux in the pulmonary artery, aorta, and PDA. The oxygen
concentration in blood will be taken into account to observe the mixture of oxygen from the
aorta to the pulmonary artery. The flux through the different sized PDAs will be observed to
determine the amount of oxygen that enters the pulmonary artery from the aorta.
IV. Experiment
A. Apparatus
Utilizing COMSOL Multi-physics analysis software multiple three-dimensional models
will be modeled after the heart. The models will fall under two categories, the first
category will act as a control group consisting of no defects whereas the latter will
consist of the PDA defect. For simplification purposes the models constructed will be
similar to the highlighted areas in Figure 2.
Figure 2 (http://www.daquandisease.com)9
The model in the first category will simply consist of a three dimensional model of a
healthy heart with no defects. Models in the second category will consist of three three-
dimensional models. The differences between the models consisting defects will be the
size of the PDA ranging from 0.14 cm to 0.40 prescribed in previous literature5. The

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sizes of the vessels are modeled after the vessels of infant hearts described by Kim et
al.6. These values can be seen in Table 1.
Vessel Diameter
Pulmonary Trunk 0.90 cm
Pulmonary Branches 0.45 cm
Aorta 0.83 cm
PDA Model 1 0.14 cm
PDA Model 2 0.28 cm
PDA Model 3 0.40 cm
Table 1: Vessel Diameters
The heights of the vessels in our model are considered arbitrary values due to
simplification purposes . Figure 3 provides some examples of the geometries used in the
study.
Figure 3: Three-Dimensional Geometries. The model on the left contains a PDA defect with
radius size of 0.28 cm whereas the latter has no defect.
As this study is analyzing flow within vessels, the cylindrical coordinate system would be
the most fitting. This experiment is modeling blood flow therefore, assumptions will be
based off properties of blood. Assuming that blood behaves as an incompressible

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Newtonian fluid is essential for this study therefore, the Navier-Stokes equation (3) will
be the governing equation utilized. This equation requires consideration of the
continuity equation (4) as we need to consider the conservation of mass. Fully
developed flow will be assumed and shall be characterized by laminar flow.
Concentration and Flux will be observed and characterized by Transport of Diluted
species . The assumption that blood is a dilute solution shall be taken in account
therefore, the Conservation of Mass for Dilute Solutions equation (1) and Fick’s Law (2)
shall be utilized to obtain concentration and flux values. We will model our
concentration based off the concentrations of oxygen within the blood of the aorta and
pulmonary artery. No-slip conditions (5) and no flux at the vessel walls shall also be
considered to model the boundary conditions of blood vessels. The properties of the
fluid will be that of blood; these values can be seen in Table 2.
Parameter Value
Density 1060 kg/m3
Viscosity 0.003 Pa*s
Pulmonary Artery Oxygen Concentration
[1]
8.71 mol/m3
Aortic Oxygen Concentration [1] 6.48 mol/m3
Table 2: Fluid Properties
Values for inlet velocities and pressure shall be based off established average values of
the aorta and pulmonary artery. These values can be seen in Table 3.
Parameter Value

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Aortic Inlet Velocity 0.11 m/s
Pulmonary Artery Inlet Velocity 0.10 m/s
Diffusion Coefficient 1.74x10-5 m2/s
Aortic Blood Pressure 8000 Pa
Pulmonary Artery Blood Pressure 7900 Pa
Table 3: Velocity, Pressure and Concentration Values
B. Equations
C. Procedure
This study is meant to analyze the effects of PDA. Literature indicates that the PDA
defect causes irregular blood flow into the pulmonary artery from the aorta. This
irregularity causes two main consequences: increased pressure to the lungs via the

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pulmonary artery and the mixing of non-oxygenated and oxygenated blood within the
pulmonary artery. Examinations of these consequences will be done though the
constructed models by creating four categories of profiles including: Velocity, Pressure
,Concentration and Flux These profiles will be compared between each model to analyze
the varying effects of PDA.
1. Velocity Profile
The purpose of the velocity profile is to merely examine the direction of blood
flow. Particle tracing and arrow plots will be tools within COMSOL used to
analyze the direction of blood flow. With these tools it will be possible to
observe the direction of blood flow without the need of calculations.
2. Pressure Profile
The purpose of the pressure profiles is to examine the pressure differences
between each model within the pulmonary artery. COMSOL provides pressure
values within the domains. These values will be quantified and analyzed by
calculating pressure differences between each model. This will allow comparable
results to provide an analytical
approach to determine pressure differences.
3. Concentration Profile
The purpose of the concentration profile is to examine the mixing of non-
oxygenated blood and oxygenated blood within the the pulmonary artery.
COMSOL provides concentration values within the domains. These values then

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shall be used to analyze how PDA effects the concentration values of oxygen
within the pulmonary artery.
4. Flux Profile
Flux will be determined calculations determined by COMSOL models. The
purpose of the flux profile will be to analyze the amount of moles of oxygen that
enter the PDA from the aorta. The area to be examined will be a cross-section of
the PDA in proximation to the pulmonary artery. Comparisons between PDA
model 1 and PDA model 2 shall be made with the purpose of analyzing how
doubling the size of PDA may affect flux.
V. Results and Discussion
A. Velocity Profiles
Figure 4: Direction of flow within Aorta and Pulmonary Artery with no defect. Maximum velocity
within pulmonary artery: 0.3149 m/s.

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Figure 5: Direction of flow within Aorta and Pulmonary Artery with PDA defect of radius 0.14 cm.
Indication of fluid flow from the aorta into the pulmonary artery is present. Maximum velocity within
pulmonary artery: 0.3249 m/s.
Figure 6: Direction of flow within Aorta and Pulmonary Artery with with PDA defect of radius 0.28
cm. Indication of fluid flow from the aorta into the pulmonary artery is present. Maximum velocity
within pulmonary artery: 0.3440 m/s.

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Figure 7: Direction of flow within Aorta and Pulmonary Artery with with PDA defect of radius 0.40
cm. Indication of fluid flow from the aorta into the pulmonary artery is present. Maximum velocity
within pulmonary artery: 0.3717 m/s.
Discussion:
From these results, flow entering the pulmonary artery via the ductus arteriosus is confirmed.
The velocity profiles indicate that there is indeed blood flowing from the aorta into the
pulmonary artery due to the Patent Ductus Arteriosus defect. Furthermore, results indicate that
there is higher velocity flow within the pulmonary artery when the PDA defect is present.
Additionally as the size of the PDA increases, velocity within the pulmonary artery also
increases. The max value within the pulmonary artery with no defect reaches 0.3194 m/s. In
ascending order of PDA sizes maximum velocity values within the pulmonary artery are as
follows: 0.3249 m/s, 0.3440 m/s, 0.3717 m/s. This is due to the fact that since there is a larger
area for fluid to flow into the pulmonary artery through the PDA, it will cause an increase in
fluid flow from the aorta into the pulmonary artery causing an increase fluid attempting to
travel through the pulmonary artery.

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B. Pressure Profiles
Figure 8: Pressure within Aorta and Pulmonary Artery with no defect. Range of pressure within
pulmonary artery: 7890 - 7957 Pa.
Figure 9: Pressure within Aorta and Pulmonary Artery with with PDA defect of radius 0.14 cm. Range
of pressure within pulmonary artery: 7900 - 7960 Pa.

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Figure 10: Pressure within Aorta and Pulmonary Artery with no defect with PDA defect of radius 0.28
cm. Range of pressure within pulmonary artery: 7900 - 7970 Pa.
Figure 10: Pressure within Aorta and Pulmonary Artery with no defect with PDA defect of radius 0.40
cm. Range of pressure within pulmonary artery: 7900 - 7980 Pa.
Discussion:

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From these results pressure increase within the pulmonary artery due to PDA is confirmed. The
pressure profiles indicate pressure increases within the pulmonary artery with the presence of
PDA. Furthermore, as the size of the PDA increases, pressure within the pulmonary artery also
increases. The max value within the pulmonary artery with no defect reaches approximately
7957 Pa. In ascending order of PDA sizes approximate maximum pressure values within the
pulmonary artery are as follows: 7960 Pa, 7970 Pa (0.16% increase), 7980 Pa (0.29% increase).
Approximately there is a total 0.716% increase in pressure compared between no PDA defect
and the largest PDA defect. This is due to a larger area for fluid to flow into the pulmonary
artery through the PDA, it will cause an increase in fluid flow from the aorta into the pulmonary
artery hence, there is a increase in pressure as more fluid attempts to travel through the
pulmonary artery.
C. Concentration Profiles
Figure 12: Concentration within Aorta and Pulmonary Artery with no defect

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Figure 13: Concentration within Aorta and Pulmonary Artery with with PDA defect of radius 0.14 cm.
Take note mixing of deoxygenated blood and oxygenated blood.
Figure 14: Concentration within Aorta and Pulmonary Artery with PDA defect of radius 0.28 cm. Take
note mixing of deoxygenated blood and oxygenated blood.

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Figure 12: Concentration within Aorta and Pulmonary Artery with with PDA defect of radius 0.4 cm.
Take note mixing of deoxygenated blood and oxygenated blood.
Discussion:
From these results there is a clear indication that there indeed is a mixture of oxygenated and
deoxygenated blood within the pulmonary artery due to PDA. Furthermore comparisons
between varying sizes of PDA indicate that larger PDA size causes an increase of mixture of
oxygenated and deoxygenated blood within the pulmonary artery. This is due to the fact that
since there is a larger area for fluid to flow into the pulmonary artery through the PDA, it will
cause an increase in fluid flow from the aorta into the pulmonary artery causing an increase in
the mixing of blood from the aorta into the pulmonary artery.
D. Flux Profiles

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Figure 13: Horizontal Cross section of PDA defect of radius 0.14 cm indicating flux through PDA.
Maximum Flux value within PDA: 2.1494 mol/m2
s
Figure 14: Horizontal Cross section of PDA defect of radius 0.28 cm indicating flux through PDA.
Maximum Flux value within PDA: 2.3137 mol/m2
s
Discussion:
From these results one can see that the increase in diameter causes an increase in flux, that is,

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an increase in the number of moles of oxygen that cross this cross-sectional area. In the 0.14
cm model, the max flux was 2.1494 mol/m2s and the 0.28 cm model had a max flux of 2.3137
mol/m2s. This shows that by doubling the diameter of the ductus, there is a 7% increase in the
amount of oxygen that enters the pulmonary artery. This is due to the increase in area for the
blood to flow through.
VI. Conclusion
In conclusion from the result collected there can be an inference that an increase in
diameter of the patent ductus arteriosus will cause an overall increase of fluid flow into the
pulmonary artery. This consequently causes a higher pressure and oxygen concentration within
the pulmonary artery. The flux profiles provide evidence that the amount of oxygen flowing
through the ductus also increases as the diameter becomes larger. These inferences confer with
previous literature indicating that the models formed are closely accurate to that of the aorta
and pulmonary artery.
Within the study there are limitations as the models consist of geometric imperfections.
The current models do not replicate real human vessels due to its lack of curvatures in the
vessels. Furthermore non-pulsatile flow has not been taken into account and our
concentrations were based solely off the concentration of oxygen versus the actual dynamic
that blood is consistent of other species such as hemoglobin and carbon dioxide.
Future work may include addressing these limitations to allow formation of a more
precise model to allow for more accurate results. Looking into how changes within the
pulmonary artery affect the lungs may also be an appealing aspect as the lungs are greatly
affected by this condition such as analyzing how much stress the lungs encounter due to this

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condition or how the alveoli within the lungs may be affected. Also as this condition causes
strain on the heart it may also be
advantageous to further investigate how this may influence the remainder of patient’s
circulatory systemand how the heart may adapt. Overall this study is minimal in its analysis on
the effects of PDA and future work would consist of furthering these studies to be better
analyze this condition and its consequences.
VII. Bibliography
1Adapted from R.C. Seagrave. Biomedical Applications of Heat and Mass Transfer. Iowa State
Univ. Press, Ames. 1971, p. 66.
2Arcilla R.A., Oh W., Lind J., and Gessner I.H. (1966). Pulmonary Arterial Pressures of Newborn
Infants Born with Early and Late Clamping of the Cord. Acta Paediatrica Scandinavica 55: 305-
315.
3Arlettaz, R., Archer, N., and Wilkinson, A.R. (1998). Natural history of innocent heart murmurs
in newborn babies: controlled echocardiographic study. Natural history of innocent heart
murmurs in newborn babies 78: F166-F170.

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4Crossley K.J., Alllison B.J., Polglase G.R., Morley C.J., Davis P.G., and Hooper S.B. (2009).
Dynamic changes in the direction of blood flow through the ductus arteriosus at birth. J Physiol
587.19: 4695-4703.
5Hijazi, Z.M., Lloyd, T.R., Beekman III, R.H, and Geggel, R.L. (1996). Transcatheter closure with
single or multiple Gianturco coils of patent ductus arteriosus in infants weighing -<8 kg:
Retrograde versus antegrade approach. American Heart Journal 132.4: 827-835.
6Kim H.S., Hong Y.M., Sohn S., and Choi J.Y. (2009). Perinatal Changes in Size of the Fetal Great
Arteries. Korean circ J. 39(10): 414-417.
7Knight, D.B. (2001). The treatment of patent ductus arteriosus in preterm infants. A review and
overview of randomized trials. Semin Neonatal 6: 63-73.
8Moore, J.W. and Schneider, D.J. (2006). Patent Ductus Arteriosus. American Heart
Association.114:1873-1882.
9"Patent Ductus Arteriosus." Disease-related Knowledge. University of Kansas. Web. 21 Mar.
2012. <http://daquandisease.com/patent-ductus-arteriosus/>.
10"Heart Defects: Birth Defects: Merck Manual Home Edition." THE MERCK MANUALS. The
Merck Manual. Web. 23 Mar. 2012.
<http://www.merckmanuals.com/home/childrens_health_issues/birth_defects/heart_defects.html
>.
VIII. Appendix