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Mechanical characterization of the posthilar pulmonary arteries in pulmonary hypertension

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Mechanical characterization of the posthilar pulmonary arteries in pulmonary hypertension
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Reusser, Mark
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Denver, CO
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University of Colorado Denver
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Pulmonary artery -- Diseases ( lcsh )
Pulmonary hypertension ( lcsh )
Pulmonary artery -- Diseases ( fast )
Pulmonary hypertension ( fast )
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non-fiction ( marcgt )

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ABSTRACT The pulmonary circulation is highly dynamic and both physiologically and mechanically complex. The proper function of this system is dependent on many factors. Here we focus on the mechanical characteristics of the arterial walls and develop a new pressure-diameter method of mechanical measurement for ex-vivo arteries. This pressure-diameter method, based on Lame's Law, demonstrates similar accuracy and effectiveness to uni-axial methods in determining stress-strain curves of arterial walls. The new technique more closely mimics the in-vivo state of the pulmonary arteries and allows stress-strain testing for many arterial generations in less time. Using this method and others, the mechanics of the pulmonary arterial walls of healthy and pulmonary hypertensive neonatal calves were studies. This data indicated significant stiffening in the pulmonary hypertensive model due to arterial wall thickening, further resulting in significantly decreased compliance over the in-vivo pressure ranges. This decreased compliance is not limited to the proximal arteries, and will be a significant detriment to those suffering from pulmonary hypertension. It was further demonstrated in the posthilar arteries that the major cause of passive stiffening is associated with increased arterial wall thickness and the stiffening is less dependent on changes in material modulus. These previously unexplored arteries demonstrate mechanical adaptation to pulmonary hypertension that varies from what has been shown in the most proximal conduit arteries. Finally, this study sheds light on the predictability of the mechanical nature of the distal conduit arteries, based on the mechanics and loading of the more proximal arteries. This piece shows that the stiffness and the thickness of the arterial walls are linearly related to both the diameter of the vessel and the mean pulmonary arterial pressure in-vivo. This will allow the mechanics of the distal arteries to potentially be predicted without direct measurement. Overall, this study improves the breadth of understanding of mechanical changes to the pulmonary arteries in the presence of pulmonary hypertension by exploring the mechanics of the generally neglected posthilar pulmonary arteries. The form and content of this abstract are approved. I recommend its publication. Approved: Kendall Hunter
Thesis:
Thesis: (M.S.)--University of Colorado Denver. Bioengineering
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Includes bibliographic references.
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Department of Bioengineering
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by Mark Reusser.

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Full Text
MECHANICAL CHARACTERIZATION OF THE POSTHILAR PULMONARY
ARTERIES IN PULMONARY HYPERTENSION
by
Mark Reusser
B.S., University of Colorado, 2009
M.S., University of Colorado, 2009
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
BioEngineering
2012


This thesis for the Master of Science degree by
Mark Reusser
has been approved for the
Bioengineering
by
Dr. Robin Shandas, Chair
Dr. Kendall Hunter, Advisor
Dr. Kurt Stenmark
November 29, 2012


Reusser, Mark (M.S., Bioengineering)
Mechanical Characterization Of The Posthilar Pulmonary Arteries In Pulmonary
Hypertension
Thesis directed by Dr. Kendall Hunter
ABSTRACT
The pulmonary circulation is highly dynamic and both physiologically and
mechanically complex. The proper function of this system is dependent on many factors.
Here we focus on the mechanical characteristics of the arterial walls and develop a new
pressure-diameter method of mechanical measurement for ex-vivo arteries. This
pressure-diameter method, based on Lames Law, demonstrates similar accuracy and
effectiveness to uni-axial methods in determining stress-strain curves of arterial walls.
The new technique more closely mimics the in-vivo state of the pulmonary arteries and
allows stress-strain testing for many arterial generations in less time.
Using this method and others, the mechanics of the pulmonary arterial walls of
healthy and pulmonary hypertensive neonatal calves were studies. This data indicated
significant stiffening in the pulmonary hypertensive model due to arterial wall thickening,
further resulting in significantly decreased compliance over the in-vivo pressure ranges.
This decreased compliance is not limited to the proximal arteries, and will be a
significant detriment to those suffering from pulmonary hypertension. It was further
demonstrated in the posthilar arteries that the major cause of passive stiffening is
associated with increased arterial wall thickness and the stiffening is less dependent on
changes in material modulus. These previously unexplored arteries demonstrate
mechanical adaptation to pulmonary hypertension that varies from what has been shown
in the most proximal conduit arteries.
in


Finally, this study sheds light on the predictability of the mechanical nature of
the distal conduit arteries, based on the mechanics and loading of the more proximal
arteries. This piece shows that the stiffness and the thickness of the arterial walls are
linearly related to both the diameter of the vessel and the mean pulmonary arterial
pressure in-vivo. This will allow the mechanics of the distal arteries to potentially be
predicted without direct measurement.
Overall, this study improves the breadth of understanding of mechanical changes
to the pulmonary arteries in the presence of pulmonary hypertension by exploring the
mechanics of the generally neglected posthilar pulmonary arteries.
The form and content of this abstract are approved. I recommend its publication.
Approved: Kendall Hunter
IV


TABLE OF CONTENTS
Chapter
1. Introduction And Literature Review........................................1
1.1. Introduction..............................................................1
1.2. Pulmonary Artery Mechanics................................................1
1.2.1. Pulmonary Artery Mechanics And Physiology.................................1
1.2.2. Pulmonary Hypertension and Arterial Compliance............................6
1.3. Methods of Mechanical Characterization and Modeling of the Pulmonary
Arteries and the Pulmonary Circulation............................................7
1.3.1. Methods of Mechanical Testing.............................................8
1.3.2. System Models............................................................18
1.4. Conclusion...............................................................23
2. Validation Of A Pressure Diameter Method For Determining Modulus And
Strain Of Collagen Engagement For Long Branches Of Bovine Pulmonary Arteries.....24
2.1. Motivation...............................................................24
2.2. Methods..................................................................25
2.2.1. Dissection...............................................................25
2.2.2. PD Method Inflation......................................................25
2.2.3. MTS Method...............................................................31
2.2.4. Ad-Hoc Variance Testing..................................................31
2.2.5. Ad-Hoc Longitudinal-Strain Variance Testing..............................32
2.2.6. Calculations.............................................................32
2.3. Results..................................................................36


36
38
39
40
41
41
45
45
46
46
46
47
47
48
50
54
55
57
57
57
58
60
61
vi
Modulus:
Engagement Strain................................................
Theoretical Error................................................
Ad-Hoc Variance Testing..........................................
Ad-Hoc Longitudinal Variance Testing.............................
Discussion.......................................................
Mechanics Of Posthilar, Pulmonary, Conduit Arteries In Hypertension
Motivation.......................................................
Methods..........................................................
Animal Models....................................................
Dissection.......................................................
Mechanics Testing................................................
Wall Thickness and Unstretched Circumference.....................
Histology........................................................
Calculations.....................................................
In-vivo Change in Cross-Sectional Area...........................
Statistics.......................................................
Results..........................................................
Mean Pulmonary Pressure..........................................
Modulus of Elasticity............................................
Thickness........................................................
Collagen Engagement..............................................
Stiffness:


3.3.6. Area Compliance...........................................................63
3.3.7. Histology.................................................................65
3.4. Discussion................................................................72
3.4.1. Modulus of Elasticity.....................................................74
3.4.2. Thickness.................................................................75
3.4.3. Engagement................................................................76
3.4.4. Stiffness.................................................................76
3.4.5. Rel ative Area Change.....................................................77
3.4.6. Histology.................................................................77
3.4.7. Limitations:..............................................................78
4. Final Notes...............................................................79
References.......................................................................82


LIST OF TABLES
Table
3.1. Summary of findings...........................................................73
Vlll


LIST OF FIGURES
Figure
1.1. - Idealized stress-strain curve for pulmonary arterial tissue under axial tension.4
1.2 the two-element Windkessel model in both hydraulic and electrical form. Adapted
from (Westerhof & Lankhaar, 2009)..................................................5
1.3. - Typical uni-axial loading diagram...............................................9
1.4. Uni-axial mounting image..........................................................12
1.5. Three element Windkessel in both hydraulic and electrical form...............19
1.6. Four Element Windkessel in both hydraulic and electrical form................20
2.1. Image of excised pulmonary artery branch showing placement of Loctite dots........27
2.2. Basic schematic of PD test setup.............................................28
2.3. Typical pressure diameter curve for PD test..................................28
2.4. Flow diagram of tissue sectioning for PD testing.............................30
2.5. Smoothing function applied to typical stress-strain curve using PD method....35
2.6. Bland-Altman plot for modulus of elasticity, PD vs Uniaxial..................37
2.7. Bland-Altman plot for collagen engagement strain, PD vs Uniaxial.............39
2.8. Typical PD and MTS stress-strain curves with PD error bars...................40
3.1. Pentachrome staining features for analysis...................................50
3.2. Mean modulus of each circumference group bar plot............................58
3.3. Mean thickness for each circumference group bar plot.........................59
3.4. Thickness vs. circumference scatter plot with regressions plotted............60
3.5. Mean engagement strain for each stiffness group bar plot.....................61
3.6. Mean stiffness or each stiffness group bar plot..............................62
3.7. Stiffness vs. circumference scatter plot with regressions....................63
IX


3.8. Change in relative cross-sectional area per pressure vs. circumference group.....64
3.9. Total elastin content (VVG)......................................................66
3.10. Sample VVG stained tissue images...............................................67
3.11. Relative cell count (cell count per area) (H&E)................................68
3.12. Total cell count................................................................69
3.13. Sample H&E stained tissue images...............................................70
3.14. Sample pentachrome stained tissue images.......................................71
x


LIST OF EQUATIONS
Equation
1.1. Uni-axial strain..................................................................9
1.2. Uni-axial stress..................................................................9
1.3 Uni-axial cross-sectional area.....................................................9
1.4. Uni-axial cross-sectional area (strained)......................................10
1.5. Resistance of elastic tube.....................................................21
1.6. Inductance of elastic tube.......................................................21
1.7. Capacitance of elastic tub.......................................................21
2.1 Pressure diameter strain.........................................................33
2.2. Pressure diameter stress.........................................................33
2.3. Pressure diameter strained wall thickness........................................33
2.4. Curvature of a function..........................................................34
2.5. Error due to rotation of artery in PD testing....................................36
3.1. Uniaxial strained length.........................................................51
3.2. Unstrained plain of stress area..................................................51
3.3. Strained plain of stress area....................................................51
3.4. Uniaxail stress..................................................................51
3.5. Unstrained radius for cross-sectional area calculation...........................54
3.6. Strained radius for cross-sectional area calculation.............................54
3.7. Internal pressure for cross sectional area calculation...........................54
3.8. Strained radius for cross sectional area calculation.............................55
3.9. Change in cross sectional area over in-vivo pressure range.......................55
XI


LIST OF ABBREVIATIONS
AC percent change in area per pressure unit
ANCOVA Analysis of covariance
ANOVA Analysis of variance
H&E Hematoxylin and Eosin staining protocol
MPAP mean pulmonary arterial pressure
MTS Material testing system, Insight 2 (MTS Systems, Eden Prairie, MN)
PD Pressure diameter
PENTACHROME Modified Movat's pentachrome staining protocol
PH Pulmonary hyptertension
RA relative area
VVG Verhoeff-Van staining protocol


1 Introduction And Literature Review
1.1 Introduction
In this effort, mechanical quantification of the posthilar conduit arteries of the
pulmonary circulation is sought in both the presence and absence of pulmonary
hypertension (PH). In this way, engineering models of the pulmonary circulation can be
improved to include these findings, improving the analytical, diagnostic and prognostic
capabilities of these models.
1.2 Pulmonary Artery Mechanics
The following section will give an overview of the anatomy of the arterial walls in
the pulmonary circulation. This overview will focus specifically on their mechanical
attributes and the function of these attributes within the pulmonary circulation. This will
be followed by a description of PH and a review of literature studying the effects of PH
on arterial mechanics. Finally, some of the inadequacies in the present understanding of
arterial mechanics in PH will be discussed.
1.2.1 Pulmonary Artery Mechanics And Physiology
The mechanical nature of arterial tissue is significantly more complicated than a
Hookean solid, or even a viscoelastic solid. The elastic properties of the arterial wall
vary largely, among other factors, with changes in the magnitude, direction and rate of
deformation, and the magnitude, direction and rate of application of the forces applied to
the material. Furthermore, these properties are not static, but are adaptive to changes
within the physiological environment of the artery wall. Changes in these mechanics can
have significant consequences to the circulatory system and the heart.
1


1.2.1.1 Mechanical Characteristics Of Pulmonary Arterial Tissues
The mechanics of pulmonary arterial walls are dictated by both the active and
passive features of the structure (Bia, et al., 2004), both of which play an important roll in
the progression of PH. The active mechanical characteristics of arterial walls result from
the presence of smooth muscle cells. The activation states of the smooth muscle cells are
dependent on the presence of cellular signal factors that are released by both local and
non-local cells. Changes in the size, number and activation state of the smooth muscle
cells can cause significant changes in the mechanical response of the pulmonary
arteries(Grover, Wagner, McMurty, & Reeves, 1980). In many ways, these effects have
been well studied and characterized in previous research. The research presented here
will, therefore, focus on the passive mechanics of the pulmonary arteries.
Numerous tensile studies of arterial tissues have shown that arterial walls have a
unique, non-linear stress-strain response (Bergel, 1961), (Gow, 1980). An idealized
representation of the stress-strain response is included in Figure 1.1. As can be seen in
this idealized curve, lower strains result in significantly lower moduli, while higher
strains result in much higher moduli. Two linearly elastic regions separated by a non-
linear transition region can generally represent the curve. Shadwick showed that this
overall non-linear stress-strain response is a result of the non-homogeneous structure of
the vessel walls. The main mechanical components of the walls of the arteries are
comprised of both rubbery and stiff fibrous materials (Shadwick, 1999). A study
conducted by Roach and Burton tested the stiffness of arterial walls with either elastin or
collagen selectively digested, showing that the low modulus of the artery at low stresses
is due to the load being primarily supported by elastin and the higher modulus is due to
2


the primary load support of collagen fibers (Roach & Burton, 1957). Based on
morphometric data, the lack of load support in the collagen fibers at low strain is believed
to be the result of the orientation and alignment of collagen fibers within the arterial wall
(Roach & Burton, 1957)(Sokolis, Kefaloyannis, Kouloukoussa, Boudoulas, Marinos, &
Karayannacos, 2006). The significantly increased slope of the stress-strain curve, at
larger deformations is due to the primary load support of collagen and a significantly
higher elastic modulus of collagen compared to elastin (Lammers, et al., 2008).
Although the research presented here does not study, in particular, the phenomenon, it
should be noted that the arterial wall exhibits visco-elastic characteristics throughout the
stress-strain curve. This feature adds a time and rate dependency to any stress or strain
response of the arterial wall.
The ideal elastic curve generally maintains this same shape, represented in Figure
1.1, but has varying slopes and numerical values based on the animal, the location of the
tissue in the pulmonary tree and many other physiological factors. Furthermore, the
stress-strain curve, does not necessarily remain static as physiological changes occur.
Like other extra cellular matrices, the components of the arterial wall interact and change
with the cells around them. As physiological changes occur, due to development or
disease, the interaction between the cellular population of the arterial wall and elastin,
collagen and other connective tissues change. These changes can often result in dramatic
changes to the mechanical characteristics of these proteins and the arterial wall itself
(Reuben, 1971) (Stenmark, Fagan, & Frid, 2006). The elastic nature of the pulmonary
arteries serves important roles in both the function of the pulmonary circulation and in the
progression of disease. These roles will be summarized in the following sections.
3


Figure 1.1 Idealized stress-strain curve for pulmonary arterial tissue under axial
tension
1.2.1.2 Elasticity And Compliance In The Pulmonary Circulation
The elastic nature of the pulmonary arterial wall serves an essential function by
temporarily storing mechanical energy in the pulmonary circulation. This feature is
especially prominent and essential in the more proximal portions of the circulation
(Grover, Wagner, McMurty, & Reeves, 1980). The elastic nature of the proximal arteries
serves as energy storage to the circulation, which is essential because it reduces the peak
pressure seen by the distal vasculature and maintains flow to the distal vasculature during
diastole (Dobrin, 1983).
This relationship between the arterial wall elasticity and the pulmonary circulation
can be most easily understood through study of an electrical analogue. The simplest of
such models, known as the Windkessel model, was designed by Frank as a two element
4


electrical circuit (Frank, 1899). In this model, represented in Figure 1.2, the energy
storage in the arteries, resulting from the elasticity of the arterial wall, is represented by a
capacitor and the flow resistance of the arterioles and capillaries is represented by a
resistive element. In both the hemodynamic and electrical models, the function of the
arteries as an energy store is apparent. Considering an oscillatory input to the electrical
analogue, energy is stored in the capacitor (conduit arteries) when the input current is
increased. When the input is decreased, the stored energy is released as a current flow
through the resistive elements (arterioles and capillaries). This feature is similarly true
for hemodynamic representation, only with a hemodynamic flow rather than a current
flow. Although this representation is highly limited by its simplicity, it remains
effective as a basic description of the function of arterial compliance, or capacitance in
the pulmonary circulation. This feature is essential to the health of the distal vasculature
because it reduces the peak flow during systole, maintains flow during diastole and
provides a smoothing function to the dynamic pressures from the heart.
Figure 1.2 The two-element Windkessel model in both hydraulic and electrical form.
Adapted from (Westerhof & Lankhaar, 2009).
A significant body of research has also shown that reductions in the compliant
nature, or capacitance, of the pulmonary circulation are highly detrimental to the system.
Resulting from decreased compliance in the conduit arteries, increased pulsatility and
decreased diastolic flow have been characterized as causing increased, detrimental
5


signaling of the distal endothelial cells (Chiu & Chien, 2011). The importance of changes
in arterial compliance as a result of disease was further demonstrated by Reuben, who
showed that in humans with both healthy and diseased pulmonary circulation, a decrease
in the lumped compliance of the pulmonary system results in a higher mean pulmonary
arterial pressure (Reuben, 1971). The study also correlated decreases in pulmonary
arterial compliance with increased pulmonary arterial resistance, which, along with
systolic pulmonary arterial pressure is the classical diagnostic for PH. It has been further
asserted that the stiffening of the arterial wall is a natural consequence of chronic PH
(Stenmark, Fagan, & Frid, 2006), (Chiu & Chien, 2011).
1.2.2 Pulmonary Hypertension and Arterial Compliance
PH, defined as a mean pulmonary arterial pressure above 25[mmHg], leads to
increased loading on the right ventricle of the heart, high rates of morbidity and death
(Hunter, et al., 2008).
Recent studies have shown that the progression of the disease is related to
decreased compliance of the arterial wall. Increased arterial wall stiffness and elastic
modulus, caused by tissue remodeling, cause increased impedance and decreased
compliance of the pulmonary arterial tree. This leads to increased loading on the right
ventricle (Stenmark, Fagan, & Frid, 2006) and other detrimental effects. Even so, the
majority of clinical diagnostics, presently used, consider only increases in overall
resistance of the pulmonary circulation (Barst, et al., 2004). Such diagnostics neglect any
consideration or measurement of the compliance of the pulmonary vasculature, which has
been shown to greatly affect the energy expenditure of the right ventricle (Engelberg &
Dubois, 1959). Increases in the stiffness of the proximal PAs have been noted, clinically,
6


in the presence of PH and studies of the artery wall stiffness have been shown to improve
predictions of the outcomes of patients in a clinical setting (Hunter, et al., 2008).
Such studies have demonstrated a significantly decreased compliance in the
pulmonary circulation as a result of PH (Hunter, et al., 2008). This leads to increases in
right heart afterload, and may additionally be related to detrimental effects in the distal
vasculature, such as endothelial dysfunction (Chiu & Chien, 2011). The decreases in the
capacitive nature of the PAs have been attributed to increased smooth muscle cell activity
(Stenmark, Fagan, & Frid, 2006) and changes in the passive mechanics of the conduit
arteries. Passive mechanics in the conduit arteries have been shown to change as a result
of vascular remodeling and changes in the dominant load carrying components of the
vascular wall, due to the increased internal pressure associated with the disease. The
effects of these changes on the volumetric compliance of the proximal (i.e., pre-hilar)
arteries have been well characterized in both in-vitro studies (Lammers, et al., 2008) and,
to some extent, in-vivo studies (Gan, et al., 2007).
Due to the highly detrimental effects of mechanical changes in the pulmonary
circulation, we believe it necessary to continually improve the understanding of arterial
mechanics in the pulmonary circulation and the mechanical changes that occur due to PH.
1.3 Methods of Mechanical Characterization and Modeling of the Pulmonary
Arteries and the Pulmonary Circulation
In this section, a review of some of the most common methods of testing the
mechanics of arterial tissues is presented. The benefits and the limitations of these
methods will also be discussed. Some of the different mathematical models of the entire
pulmonary circulation are also discussed.
7


1.3.1
Methods of Mechanical Testing
1.3.1.1 Uniaxial Testing
1.3.1.1.1 Description
Uniaxial testing is one of the simpler methods of testing arterial tissue, but it in is
often considered one of the gold standards. A section of artery is tested in an ex-vivo
setting and is generally submersed in a liquid that mimics the physiological environment
of blood. This is often as simple as a liquid matching the temperature and pH balance.
The tissue section is generally a long, thin strip of arterial tissue that has its longest
dimension in either the longitudinal or circumferential axis of the artery. For the most
accurate results, the longest dimension of the tissue should be at least 10 times the length
of the second longest dimension of the section.
Once the arterial tissue is sectioned, as described above, it is mounted in an
apparatus that applies a varying stretch along the longest axis of the sectioned tissue. A
diagram of typical tissue mounting can be seen in Figure 1.3. During the stretching of the
tissue, the testing apparatus generally records the force, and displacement of the ends of
the tissue. In most arterial tissue testing applications, the specimen is stretched at
predefined rate of strain, although predefined rates of stress are occasionally applied
instead. The tissue is also stretched until a predefined strain or force is achieved.
8


Buffer
Figure 1.3. Typical uni-axial loading diagram
From this procedure, one gains a force displacement curve. In order to extrapolate a
stress-strain curve or the modulus of elasticity from this data, one must apply
assumptions of material incompressibility, continuity and small deformation. Using these
assumptions, the calculation for strain and stress cab be simply calculated as follows:
i.
Equation. 1.1 Uni-axial strain
F
<5
A
Equation 1.2 Uni-axial stress
Equation 1.3 Uni-axial cross-sectional area
9


e = AWt
c nQrr Qi0
Equation 1.4 Uni-axial cross-sectional area (strained)
where s was strain, o was stress, L0 and L were the unstrained and strained length of the
tissue, respectively, F was the applied force, A0 and A were the unstrained and strained
cross sectional area, respectively, Wo was the unstrained tissue width, and to was the
unstrained tissue thickness. The modulus of elasticity is then the derivative of the strain
with respect to stress.
1.3.1.1.2 Discussion
This particular method of mechanical study has been used in to great success in
the study of arterial mechanics in pulmonary hypertension, especially in animal models,
of the disease (Sokolis, Boudoulas, & Karayannacos, Assessment of the Aortic Stress-
Strain Relation in Uniaxial Tension, 2002), (Lammers, et al., 2008), (Kao, et al., 2011).
The method is also well established in tests of other engineering materials. This method
allows relatively rapid and highly accurate testing within the constraints of its limitations
(discussed below). There are also numerous, commercially available testing apparatuses
for such tests.
On the other hand, this testing method also suffers its drawbacks when compared
to other testing methods. The method does not allow any form of testing in-situ or in-
vivo; rather, the artery must be fully removed and then sectioned, so it is limited to very
localized testing. The method requires the assumption of material incompressibility to
extract stress and strain data, which is not entirely accurate (Kao, Biaxial mechanical
10


characterization and microstructure-driven modeling of elastic pulmonary artery walls of
large mammals under hypertensive conditions, 2010). The method does not allow any
measurement of stresses or strains in more than one axis simultaneously. This is
detrimental to the overall accuracy of the test, because longitudinal and circumferential
stresses vary constantly in-vivo (Dobrin, 1983). Finally, the method induces stress
concentrations near the mounting points because the mounts constrain any strain in the
axes parallel to the long axis, as can be seen in Figure 1.3.
1.3.1.2 Bi-Axial Testing Method
1.3.1.2.1 Description
The bi-axial testing method, in many ways, is similar to the uni-axial testing
method described in the previous section. This method was, on the other hand, designed
to remove some of the limitations present in the uni-axial method. In this case, the
section of tissue removed from the artery is as close to a square as possible in the plane
perpendicular to the radius of the artery. Figure 1.4 is an image of a somewhat typical
tissue mount for a bi-axial tissue testing system. The strings attached to the sides of the
tissue are attached to four separately controlled linear actuators (not included in the
image), one on each side of the square tissue section.
11


Figure 1.4 Uni-axial mounting image. Adapted from (Kao, Biaxial mechanical
characterization and microstructure-driven modeling of elastic pulmonary artery
walls of large mammals under hypertensive conditions, 2010)
After proper mounting, the tissue is then strained in tension along both the
circumferential and the radial axes. In a similar fashion to the uni-axial method, the force
applied in both axes is measured as the tissue is strained. In this method, the rate of strain
in both axes is pre-defined and the tissue is strained to a pre-defined value. In this
particular bi-axial testing method, the locations of the four dots on the tissue sample were
tracked with a digital camera while the tests were conducted. In this way the strain was
directly measured. Other methods of bi-axial testing determine the strain of the tissue
based on the displacement of the linear actuators and the dimensions of the tissue. In
either case, the data from these tests, along with the dimensions of the tissue section, are
able to provide data with regards to the stress and strain curves, strain energy fields, the
modulus of elasticity, and the Poissons Ratio of the tissue. Because this piece does not
focus on this particular method, the calculations are not included here.
12


1.3.1.2.2 Discussion
The main benefit of the bi-axial testing method is the ability to apply
predetermined strain in both the radial and the longitudinal axes of the tissue,
simultaneously. This is a significant improvement in comparison to the uni-axial testing
method. Because of this feature, it is no longer necessary to assume a Poisons ratio for
the material, and more robust strain-energy functions can be determined for the material.
Furthermore, this testing method can more closely mimic the in-vivo conditions of the
artery. The pressure in the artery and the constraints applied by surrounding tissues apply
forces in both the longitudinal and radial directions, which are not accounted for in uni-
axial testing, but can be applied in bi-axial tests.
On the other hand, the bi-axial testing method still suffers many of the drawbacks
of the uni-axial method. Both methods are significantly limited in that they can test only
highly local mechanical features of the artery. The bi-axial test cannot perform tests in-
situ or in-vivo. A final drawback to the method is that the testing time and preparation
time, specifically tissue mounting, is significantly longer than that of uni-axial testing
methods, making the test impractical for use in large sample populations. Despite these
limitations, Kao was able to significantly improve the understanding of pulmonary
arterial mechanics in Pulmonary Hypertension using this method (Kao, Biaxial
mechanical characterization and microstructure-driven modeling of elastic pulmonary
artery walls of large mammals under hypertensive conditions, 2010).
13


1.3.1.3 X-ray CT Imaging
1.3.1.3.1 Description
Computed tomography X-Ray imaging has recently been used as a method of
studying arterial mechanics in some more recent studies. This method is one of the more
technologically advanced methods of studying the tissue mechanics of pulmonary
arteries. In this method, the entire lung of the animal is excised, but the circulation is left
intact within the lungs. The circulation is then inflated to predefined pressures, generally
using a pressure head. The fluid used to induce this pressure is generally chosen to be
highly opaque to x-rays in order to give the arteries high contrast in the x-ray imaging.
Fluids can also be chosen to have a high enough surface tension to prevent their entry to
the capillary bed, preventing inflation and imaging of the venous system (Karau, et al.,
2001). At this point, x-rays are acquired of the lung from multiple angles, to create a
complete circle around the lungs. All images are taken with imaging planes
perpendicular to the radii of the main pulmonary artery.
After acquiring the images digital, geometric processing is preformed on the two
dimensional x-ray images to generate a digital volume representing the inflated arterial
tree. Many different algorithms have been developed to calculate the object volumes
based on two-dimensional images. Each requires varying levels of pre-processing of the
initial images, processing power and time and each method results in varying levels of
accuracy in the final volume (Herman, 2009). After generating the digital volume, the
internal area of the artery can be determined on essentially any plane chosen by the
investigator, using computer algorithms.
14


By repeating this process with varied internal pressures, a pressure verse cross
sectional area or pressure verse diameter curve can be developed for the pulmonary
arteries at any point in the pulmonary arterial tree. From this data, a stiffness verse force
per longitudinal length curve can be determined, where stiffness is the modulus
multiplied by the instantaneous wall thickness. Because the x-ray opacity of the arterial
wall is too similar to the surround tissue, the thickness of the arterial wall cannot be
determined using this method. Without assuming a tissue thickness, a stress-strain curve
cannot be determined.
1.3.1.3.2 Discussion
The use of X-ray computed tomography in the determination of pulmonary
arterial mechanics has many significant advantages over other methods. One obvious
advantage is the ability to gain mechanical data for many different locations in the
pulmonary tree, in a single test. The method also allows for testing in-situ and in-vivo for
animal models (Karau, et al., 2001)(Herman, 2009), allowing mechanical characterization
within a more physiologically accurate environment. In fact, the lungs can even be
inflated during the test to mimic different stages of respiration when in an ex-vivo setting.
Finally, the measurement resolution of this method is very high, allowing measurement
of very small arteries. This allows the use of smaller animal models and the testing or
more distal arteries.
On the other hand, the method also suffers its drawbacks. The most obvious of
which is the availability of the test equipment. Not only does the equipment require a
high-resolution, digital x-ray system, but also requires a computer with the proper
software and the computational power to perform the image analysis. A second
15


drawback is the lack of data regarding the artery wall thickness. This makes
determination of wall strain, and therefore modulus, impossible, without making
assumptions of these dimensions or further dissection and measurement. Lacking this
data, changes in stiffness due to wall thickening and changes due to change in modulus
are indistinguishable. Finally, the need to take many x-ray images for each pressure point
makes the process slow and makes the acquisition of high-resolution data curves
impractical.
1.3.1.4 In-Vivo Testing Methods
1.3.1.4.1 Description
Many different in-vivo arterial mechanic testing methods exist and have been
used to varying degrees of success. A detailed description of each method is beyond the
scope of this paper. Instead, a brief description of some of the available methods is
provided.
Earlier studies of the pulmonary circulation were generally highly invasive and
limited in their scope. A study by (Patel, Schilder, & Mallos, 1960) examined the local
mechanical characteristics of the main pulmonary arteries of dogs. In this method, the
dogs were studied under anesthesia. The pressure of the pulmonary artery was measured
using a catheter, while the diameter of the artery was determined using a custom designed
electrical diameter caliper. This method, although highly invasive, provided a significant
bank of data describing the mechanics of the pulmonary tissue.
More contemporary methods have been able to extract similar data, with less
invasive methods. These tests have allowed for study in human subjects and have
improved the clinical relevance of such methods. Some of these methods utilize cardiac
16


gated x-ray computerized tomography to image the dimensions of the large pulmonary
arteries and catheterization of the pulmonary arteries to determine the instantaneous
pressure of the arteries (Moore, Scott, Flower, & Higenbottam, 1988). As discussed in
the previous X-Ray CT Imaging section, the data resolution of such methods is limited.
Furthermore, in human subjects, the image resolution is limited to lowering subject
radiation exposure and the availability non-toxic blood borne x-ray contrast enhancing
agents. Similar methods have utilized ultra-sonic imaging to determine the wall
thickness and diameter of the main-pulmonary artery (Hunter, et al., 2010).
Other in-vivo methods have been developed that do not directly measure the
diameters of the arteries. Instead these methods utilize pressure velocity catheterization,
or non-invasive pulse wave ultra-sonic Doppler imaging (Kosturakis, Goldberg, Allen, &
Loeber, 1984). Such methods are then able to extract a time-varying pressure vs. flow
relationship of the blood flow. By analyzing this data in the frequency domain, complex
impedance, analogous to electrical or acoustic impedance, can be developed. Based on
this impedance, and different mathematical models of the arterial flow (discussed in
further detail below), a global compliance of the circulation can be developed (O'Rourke,
1982).
1.3.1.4.2 Discussion
In-vivo testing methods of arterial mechanics have been readily sought over the
past decades in the study of pulmonary hypertension. Such methods have many intrinsic
advantages over other methods of mechanical studies. These methods allow the study of
the mechanics of the pulmonary circulation in a setting that matches exactly, or close to
17


the true physiological environment of the tissue. Furthermore, the development of such
methods is necessary for the clinical application of any arterial mechanics study.
Many of such studies are, on the other hand, limited by their invasiveness. For
many of these studies, the process is highly invasive, requiring sedation and anesthesia of
the subject. The implementation of which, can have adverse consequences on the test,
due to reduced blood pressure and heart rate. Furthermore, the stress and strain ranges
tested using in-vivo methods are dictated by the blood pressure of the subject during the
time of the test.
1.3.2 System Models
1.3.2.1 Motivation
Mathematical, computational and physical models have been readily used in
engineering and scientific applications throughout history. Models such as these are
often sought to study physiological systems, such as the pulmonary circulation for many
reasons. In many cases, these models provide access to information that cannot be
readily measured, due to the availability of testing methodologies or the invasiveness of
such tests. Such models can be used to predict the vascular mechanics and characteristics
throughout the arterial tree. Some models can determine the effect of arterial wall
distensibilty, or predict the energy expenditure of the heart during the cardiac cycle.
Models, such as these, can be useful in predicting the effect of changes in the pulmonary
circulation and are therefore useful in diagnostic and prognostic applications.
1.3.2.2 The Windkessel Model
The simplest version of the Windkessel model was briefly introduced in the
Elasticity And Compliance In The Pulmonary Circulation section. The Windkessel
18


model makes an analogue between the pulmonary circulation (or systemic) and an
electrical circuit. Input pressure is modeled by a source voltage and blood flow by
electrical current. The simplest model lumps together the global capacitance of the
pulmonary circulation and the total resistance of the system. From these two factors, a
two element electrical model of the entire circulation can be created as depicted in Figure
1.2. More complex Windkessel models have also been proposed that include inductors
and/or second resistors to further model the inertia of a moving mass of blood and the
resistance of the conduit arteries, respectively (Figure 1.5 Figure 1.6). Such models are
especially useful for determining the variances in the energy expenditure of the heart
(voltage source) with changes in the global resistance or compliance of the circulation.
Such models have also proven useful for predicting the global compliance of the
circulation, based on the decay rate of pressure within the main arteries immediately after
systole. Similarly, measured arterial flow can be used to predict the pressure using the
model. Using the sum of least squares on the elements of three or four element
Windkessel models, the elements of the model can be adapted to give the most accurate
representation of the measured pressures, yielding estimates of the global capacitance,
resistance and inductance of the circulation (Westerhof & Lankhaar, 2009), (Wang,
O'Brien, Shrive, Parker, & Tyberg, 2002).
Figure 1.5 Three element Windkessel in both hydraulic and electrical form.
Adapted from (Westerhof & Lankhaar, 2009).
19


Figure 1.6 Four element Windkessel in both hydraulic and electrical form. Adapted
from (Westerhof & Lankhaar, 2009).
1.3.2.3 The Transmission Line Model
The transmission line model can be simply viewed as an expansion of the Windkessel
model. The transmission line model, as is implied by the name, based on analogue
between the circulation and electrical transmission lines. Instead of single components,
like the Windkessel model, the transmission line model breaks the circulation into many
different segments. Each segment of the circulation is then modeled like an individual
Windkessel model. The segments are then connected in series. The capacitance,
resistive and inductive features of each segment can be estimated based on the wall
thickness, modulus of elasticity, youngs modulus, fluid characteristics of blood and the
geometric dimensions of the artery section. Equation 1.5 Equation 1.7 describe, in the
simplest form, as presented by (Rideout & Dick, 1967), the resistance, inductance and
capacitance of fluid motion in an elastic tube. Here E is the modulus of elasticity, h is the
wall thickness, Az is the longitudinal length of the segment, r is the average radius of the
segment, p is the density of the fluid (blood) and p is the viscosity. The application of
this model results in large system of differential equations. For more complex models,
this system of equations does not have an analytical solution but requires numerical
methods to solve the system (Avolio, 2009). An alternative method is to build the
20


physical circuit and apply the desired input function and measure the desired outputs
(Snyder, Rideout, & Hillestad, 1968).
/? = 81Ju Az
8 Jl r4
Equation 1.5 Resistance of elastic tube
9 P

4 n r2
Equation 1.6
3nr3Az
2 Eh
Inductance of elastic tube
Equation 1.7 Capacitance of elastic tub
Transmission line models offer increased utility, in many ways, compared to the
less complicated Windkessel model. Such models are able to predict the effect of
localized changes on the entire circulation. These models are also able to account for
pressure wave reflections due to varying impedances at branch points. These models
generally provide a more accurate representation of the pressure flow response of the
circulation for varied input pressures compared to the simple Windkessel method. On the
other hand, transmission line models of the circulation generally require a large set of
data to describe the local arterial dimensions and mechanical characteristics. Because
such data often doesnt exist in specific diseases, such as pulmonary hypertension, the
models may result in significant inaccuracy due to the number of assumptions that must
be made.
21


1.3.2.4 Computational Fluid Dynamics
The use of computational fluid dynamics has only become relevant in practice
since the 1990s (Steinman & Taylor, 2005). This is mainly due to the advance of
computer technology. In this practice, digital, three-dimensional representations of the
blood volume within an area of interest are developed. These models are generally based
off computed tomographic x-ray images or magnetic resonance images of the circulation.
The volume is then discretized into much smaller three-dimensional sections. Within
each section, the flow is generally described by Navier-Stokes equations for fluid flow.
The neighboring sections of each section determine the boundary conditions of that
particular section, or the boundary conditions applied to the edges of the volume. The
result of this is a very large system of equations that can be computationally solved for
highly complex flows. Similarly, a volume can be created for the vessel walls of the
circulation. This volume can similarly be discretized and mechanical constraints can be
applied. The interaction between the vessel walls, the mechanics of these walls and their
effects on the hemodynamics of the pulmonary circulation can then be accurately
modeled.
Such models can produce accuracy and detail beyond the capabilities of most
other models. These models can produce data beyond what is clinically measureable and
have the potential to deliver significant information in the analysis of disease progression
in PH and other circulatory diseases. The accuracy of computational fluid dynamic
models is highly dependent on detailed knowledge of the mechanical nature of the vessel
wall throughout the tree. It is further dependent on the number and size of discrete
22


sections. Decreased section size can greatly increase the accuracy of such models, but
also drastically increase computational time and demand. For this reason, most studies
focus on specific segments of the circulation and cannot compute flow in the entire tree
due to the computational demands (Steinman & Taylor, 2005).
1.4 Conclusion
The pulmonary circulation is a highly complex system. The proper function of
this system is highly dependent upon the mechanical characteristics of the arterial walls,
which are in themselves, very complicated and highly dynamic. These characteristics
vary significantly with changes in physiology, disease and development. Due to the level
of complexity in the system, many different methods of modeling the pulmonary
circulation have been developed. The most accurate and detailed of these models are
reliant on the mechanical characterization of the arterial walls at varied locations along
the pulmonary tree. Even the most robust techniques for testing such mechanics are in
some ways limited. In order to develop better models of the pulmonary circulation in
healthy and pulmonary hypertensive subjects, one must first characterize the mechanics
of the pulmonary arteries at different locations throughout the pulmonary tree. This may
require the development of a customized testing methodology for this purpose.
23


2 Validation Of A Pressure Diameter Method For Determining Modulus And
Strain Of Collagen Engagement For Long Branches Of Bovine Pulmonary
Arteries
It should be noted that the contents of this chapter is adapted from our previously
published work in the Journal of Biomechanical Engineering (Reusser, Hunter, Lammers,
& Stenmark, 2012). The only changes made are to improve the readability and to match
the formatting of the rest of this document.
2.1 Motivation
Tissue mechanics of the pre-hilar pulmonary arteries have been well documented
(Lammers, et al., 2008), (Tian, et al., 2011), providing significant insight into the role of
the passive tissue mechanics of these arteries in PH. As conduit arteries can be classified
as arteries of diameters greater than l[mm] (Grover, Wagner, McMurty, & Reeves,
1980), these studies have not quantified the mechanics of 37% of the conduit volume
(Singhal, Henderson, Horsfield, Harding, & Cumming, 1973). Because compliance is a
function of the entire bed of conduit arteries, the tissue mechanics of the post-hilar
arteries should also be studied to truly understand the pathophysiology of arterial
stiffening in PH, which would require hundreds of tests using traditional testing methods.
The goal of this chapter is to provide validation of a pressure-diameter (PD)
measurement of long, post-hilar pulmonary artery branches, as a method of comparing
the strain of collagen engagement and the elastic modulus for multiple generations of the
pulmonary artery, between different animal groups. It is believed that the PD method
will provide an improvement over uniaxial stress-strain measurements of individual
segments by improving the rapidity of testing and limiting the effect of end constraints,
while maintaining a similar level of accuracy.
24


2.2 Methods
2.2.1 Dissection
The main branches of left and right post-hilar pulmonary arteries were isolated
from five adult cows and three neonatal calves from both of the largest two lung lobes.
Dissection was performed from the hilum and moved distally until the outer artery
diameter reached approximately 3[mm]. At each branch point, the largest diameter
branch was followed for dissection and separated from the smaller branches, which were
not isolated. Any loose connective tissue was removed. In this way, a continuous section
of artery was removed from each lung lobe with a range of diameters from the largest
diameter artery in the lobe to a smallest outer diameter of approximately 3 [mm]. All
arteries were tested within 72 hours of animal sacrifice and tissues were stored in calcium
and magnesium-free NaCl-PBS buffer (0.01[mol/l], ionic strength 0.15, pH 7.4).
2.2.2 PD Method Inflation
After isolation, longitudinal sections were chosen between each major branch and
marked with two small dots (diameter = 1-3 [mm]) of Loctite 280 (Henkel Corpoation,
Westlake, OH) black glue. The two dots per section were placed in approximately the
same location circumferentially and separated longitudinally by approximately 10[mm].
Sections were chosen to be longitudinally distant from major branch points, while
avoiding proximity to holes, branches or tears. Figure 2.1 is an image of the arterial
marking. A thin latex liner (0.0685[mm]-wall thickness, 10.2[cm]-circumference) was
inserted along the lumen of the arterial section to prevent pressure leaks through the
branches. A liner diameter larger than the tissue diameter was chosen to avoid stretch or
load support in the liner. The proximal end of the artery was cannulated and secured
25


with umbilical tape. A thin nylon line was fed through the artery to maintain the arteries
longitudinal alignment in the tissue bath during testing. This string was attached to the
cannulation point and the same point on the opposing wall of the tissue bath. The tissues
were submerged in calcium and magnesium-free NaCl-PBS buffer (0.01[mol/l], ionic
strength 0.15, pH 7.4). The distal end of the artery was closed with a suture, preventing
pressure leaks while allowing longitudinal movement. Each arterial section was then
inflated with water to an internal pressure of approximately 110mm Hg (gauge). A
Millar Mikro-Tip SPC-350 (Millar Instruments INC., Huston, TX) catheter, just upstream
of the cannulation point, measured pressure. Figure 2.2 provides a basic schematic of the
testing setup. Prior to any pressure diameter measurement, each tissue was subjected to 9
cycles in which the internal pressure was increased from atmospheric pressure to
110[mmHg] (gauge) and then released. In this way, the artery was pre-strained and any
hysteresis was reduced (Bergel, 1961).
Immediately following artery pre-strain, PD measurements were made.
Increasing the head height applied through the artery cannula gradually increased internal
pressure. This was done using a constant flow DC pump, with a flow control valve used
to limit the rate of change in the height of the pressure head. As the internal artery
pressure was increased, digital photographs of the entire tissue lengths were taken with a
Cannon RebelXTi (Canon U.S.A., Lake Success, NY) with an EFS 55-150mm (Canon
U.S.A., Lake Success, NY) zoom lens, at a rate of 1.7[Hz], A ruler with inch markings
was also placed in the imaging plane of the artery, which enabled determination of pixel
length. The camera shutter was triggered by a transistor driven switch, signaled by a
1.7[Hz], 5[V] peak-to-peak square wave signal. In this way, the shutter was released at
26


every moment the voltage wave reversed polarity from negative to positive. By
simultaneously recoding the voltage wave and the pressure signal from the catheter on a
12-bit data acquisition system, the internal pressure at the time of each image was
determined. The images were used to measure the outer diameter of the artery and the
longitudinal distance between the two dots in each section. Thus, the result was a
pressure-diameter data point and longitudinal strain for each image. Figure 2.3 is a
typical pressure diameter plot.
Figure 2.1 Image of excised pulmonary artery branch showing placement of Loctite
dots
27


Figure 2.2 Basic schematic of PD test setup
Typical Pressure Diameter Curve
Figure 2.3 Typical pressure diameter curve for PD test
28


After completion of the PD test, the internal pressure was relieved and the tissue
was removed from the bath. The tissue was then cut twice along the plane normal to the
longitudinal axis of the artery in each section. This formed rings with a width of l[mm]-
3 [mm] for each section. Using the same camera and lens, a digital photo was taken of
each ring with the imaging plane normal to the longitudinal axis of the ring. Again, a
ruler was placed in the imaging plane. Using these images, the wall thickness was
measured for each section. This was accomplished by tracing regions of interest around
the inner and outer edges of the ring. The difference between the two areas was then
divided by the circumference, resulting in the average, un-stretched thickness. After
taking images of the rings, each ring was opened, creating a circumferential strip. The
circumferential strip length was measured using digital calipers, giving the circumference
of the artery for each section. A flow diagram of tissue sectioning is given in Figure 2.4.
29


Figure 2.4 Flow diagram of tissue sectioning for PD testing
Image processing and measurement was conducted using custom-written software
in Matlab R2011a (The Math Works, Natick, MA). Tissue diameter was determined for
each section by counting the number of pixels in the radial direction from edge to edge of
the tissue at the most proximal Loctite marking of each section. Large data sets used in
the PD method made manual edge selection impractical, so it was automated using the
Canny method, included in Matlabs image processing toolkit.
Changes in the orientation of the radial axis due to changes in pressure were taken
into account by manually orienting every tenth image so the longitudinal axis of the
measured section was horizontal. A cubic spline was then created relating the rotation of
the longitudinal axis to the internal pressure. Diameter measurements were made
perpendicular to the orientation of the longitudinal axis described by the cubic spline. It
30


was believed that significant changes in the longitudinal axis occurred only in the vertical
direction and were due to buoyancy forces caused by air pockets in the system. As there
were no significant forces in the horizontal direction (perpendicular to the imaging plane)
and such motion was constrained by the nylon line, it was assumed that the longitudinal
axis remained in the imaging plane.
The longitudinal distance between the two Loctite dots in each section was
measured as a determinant of the longitudinal strain. This was done by manually
selecting the center of each of the two dots in every tenth image and measuring the
distance in pixels along the already defined longitudinal axis. A cubic spline was then
created describing the longitudinal distance between the two markings in each section as
a function of pressure.
2.2.3 MTS Method
Stress-strain data was acquired with an MTS, Insight 2 (MTS Systems, Eden
Prairie, MN) material testing system with a 5[N] load cell. Tissue strip widths were
measured with digital calipers. The circumferential strips were tested in an auxiliary
environmental chamber with the same buffer solution as storage and pressure diameter
testing. Tissues were pre-strained by applying 9 extension-relaxation cycles and data was
collected on the 10th cycle. Tissues were strained at a rate of 10% strain per second in
the circumferential direction until collagen-engagement was fully formed. The MTS
testing method was based on the previous work of Lammers et al (Lammers, et al., 2008).
2.2.4 Ad-Hoc Variance Testing
During analysis of the data, a large variance in the difference between modulus
calculated by PD and MTS testing was noticed. For this reason, further testing was done
31


to determine the variance of each section for both testing methods. This was done by
conducting the MTS and PD tests at five different locations within the same section of an
artery. This was completed for four different arterial sections.
2.2.5 Ad-Hoc Longitudinal-Strain Variance Testing
There was concern that the measured longitudinal stretch may not be representative of
the average longitudinal stretch for the section of artery being tested. Although sections
were carefully chosen to avoid branch points and tears in the artery, it was possible that
the locations marked for longitudinal measurements contained non-uniformities at
varying radial locations that would prevent accurate results. For this reason ad-hoc tests
were preformed to determine the variance of the longitudinal strain at different radial
locations but the same longitudinal location. This was done by performing PD tests on
six sections in two different arteries. In each section, the longitudinal strain was
measured normally, except that it was measured at five different radial locations. The
standard deviation of the measured strain was then found for each section at five evenly
distributed pressures ranging from atmospheric to ~110 mmHg.
2.2.6 Calculations
2.2.6.1 Strain and Stress
Cauchy stress and strain were calculated for the MTS data sets using assumptions of
material incompressibility, continuity and small deformation. Using these assumptions,
the calculation for strain and stress were as described in Equation 1.1- Equation 1.4.
Stress-strain curves were developed for the pressure diameter method using Lames
Law. For these calculations, material incompressibility, continuity and small deformation
were assumed. Lames Law further requires the assumption of an infinitely long tube of
32


constant diameter. Using these assumptions, the stress and strain were calculated as
follows:
Equation 2.1 Pressure diameter strain
__{D-2t)P-DP0
21
Equation 2.2 Pressure diameter stress
_ tQPQdQ
Dd
Equation 2.3 Pressure diameter strained wall thickness
where D0 and D were the unstrained and strained outer diameter, respectively, P, and P0
were the inner and outer pressure, respectively, to and t were the unstrained and strained
wall thicknesses, respectively, and do and d are the unstrained and strained longitudinal
distance between the Loctite marks in each section, respectively.
2.2.6.2 Engagement Strain
For the purposes of comparison, collagen engagement points were defined for
both the MTS method and the PD method. For both methods, a Ninth order polynomial
was fit to the stress-strain trace. After application of the polynomial fit, the collagen
33


engagement point was defined as the point of maximum curvature of the polynomial
within the range of the tested data points. The curvature was calculated as:
a"
K~(l + a'2f2
Equation 2.4 Curvature of a function
where the stress derivatives are taken with respect to strain.
Prior to polynomial fitting, data smoothing of the stress-strain trace was necessary
for the PD method due to noise introduced by the edge (diameter) detection process.
Although the use of automated edge detection for diameter measurement was typically
very accurate as shown below, it occasionally introduced noise to the stress-strain curve
by improperly selecting the edge of the artery due to tissue discoloration or the presence
of connective tissue. This error appears as noise, rather than a consistent offset for each
sample, due to inconsistent radial orientation of the artery with changes in pressure and
artery motion due to fluid flows within the tissue bath (caused by pressure leaks in the
artery or artery liner). The data was smoothed using a moving average filter. Smoothing
was conducted with the minimum span size, to produce a smooth polynomial fit. The
maximum smoothing span for all data sets used was a span of 7 [data points] and an
average span of 5.3[data points]. Figure 2.5 shows the original, unsmoothed stress-strain
curve with a solid line and the smoothed data curve with a dashed line. This figure
illustrates the effectiveness of the smoothing function for noise reduction while
maintaining the shape of the curve.
34


Figure 2.5 Smoothing function applied to typical stress-strain curve using PD
method
2.2.6.3 Modulus
The modulus of elasticity was defined for both measurement methods as the slope
of the stress-strain curve. The modulus was calculated at 30% strain for all tissue
sections. This strain level was chosen to maintain consistency as data for this strain was
present in all tissue data sets and was lower than engagement strain for all tissues. The
modulus was determined by applying a linear fit to the stress-strain curve between 27.5%
strain and 32.5% strain, using the least squares method. The modulus was then defined
as the slope of the linear fit.
2.2.6.4 Error
Theoretical error was calculated for the stress and strain determined by the PD
method. Precision error was defined as half of the resolution of the measuring device for
each measurement. Random error was defined using a tissue that demonstrated typical
deviation from the MTS method in the PD data set. For the majority of measurements,
random error was defined as the standard error in a population of 5 sample
35


measurements. For the diameter measurements, random error was defined as the
standard error in a population of 10 sample measurements, as 10 measurement samples
were taken in an effort to reduce noise in the diameter measurement during all tests.
Unlike the other measurements, error in the diameter was the result of four different
sources: random error, precision error, random error in the orientation of the longitudinal
axis, and precision error in the orientation of the longitudinal axis. Total rotational error
was defined as:
Ed = p1 ([1- COS(£)]! + [1 cos(£,)]! + E\ + E
Equation 2.5 Error due to rotation of artery in PD testing
where ED was the total error of the diameter due to longitudinal alignment error, Epa was
the precision error in longitudinal alignment (degrees), Era was the random error in
longitudinal alignment, Ep was the precision error in diameter measurement, E, is was the
random error in diameter measurement and D was the measured outer diameter of the
tissue.
2.3 Results
2.3.1 Modulus
The modulus of elasticity was determined for 35 tissue samples with one outlier
removed, resulting in 34 samples for both the PD method and the MTS method. The
average slope found was 118[kPa], which represent typical values as reported by
Lammers et al (Lammers, et al., 2008). The mean of the difference (MTS method PD
method) between the modulus found using both methods was determined as 8.7[kPa],
36


The standard deviation for the differences between the two methods was determined as
32.7 [kPa]. A paired t-test did not show a significant difference between the results of the
two tests at a 95% confidence interval. Figure 2.6 is a Bland-Altman plot comparing the
modulus for the two methods. These plots are presented through the remainder of the
chapter, so we provide a brief explanation. The x-axis shows the mean value of both
measurement methods for each data point. The y-axis is the difference between the
measured values. The dashed line is the mean of differences between the two testing
methods for each data point and the dot-dashed lines represent +/- two standard
deviations of the differences. When two testing methods are similar, the mean line
should be close to zero and the magnitude of the vertical distance between the mean line
and each data point should be small in comparison to their value on the x-axis. Finally,
there should be no obvious trends in the data points.
Figure 2.6 Bland-Altman plot for modulus of elasticity, PD vs Uniaxial
37


2.3.2
Engagement Strain
The Engagement Strain was determined for 31 tissues samples with one outlier
removed, resulting in 30 samples for both the PD method and the MTS method. Four
tissues were not included because they were not strained to the point of collagen
engagement during PD testing, as determined by the MTS method. The average
calculated engagement strain for the tests of calves using both methods was 51.3%. This
value compares well with a study preformed by Lammers et al (Lammers, et al., 2008),
where engagement strains were reported as 49% and 51% for control and hypoxic calves
for the main pulmonary artery. The mean of the differences of collagen engagement
strain (PD method MTS method), as determined by the two methods, was -0.0212%
strain. The standard deviation of the differences of collagen engagement strain was
0.0417% strain. On the other hand, a paired t-test did show a significant difference
between the results of the two testing methods (p=0.007. Figure 2.7 is a Bland-Altman
plot comparing the collagen engagement strain for the two methods.
38


e

a
Bland-Attman Plot for Collagen Engagement Strain
Average of MTS and PD Engagement Strain
[(MTS-PD) / 2) (mm/mm)
Figure 2.7 Bland-Altman plot for collagen engagement strain, PD vs Uniaxial
2.3.3 Theoretical Error
Calculation of the theoretical error was described in the methods section. The
maximum relative error found for the selected tissue sample was found as 20.3%. Each
error element was set to zero individually, and error was recalculated to determine which
measurement contributed the most to the error. It was determined that the majority of the
error is due to the high error in precision of the longitudinal length measurement. With
the precision error of the longitudinal length set to zero, the remaining error is only 7.8%.
It should be noted that the estimate of precision error in longitudinal strain is likely a
significant overestimate of the true error because of the care used in selecting the center
of the dots used to measure the longitudinal stretch. This assumption is supported by the
random error in longitudinal strain, which was approximately 13% of the calculated error
in precision. Figure 2.8 is a typical stress-strain curve calculated with the PD method
with error bars plotted.
39


Typical Curve with Error Bars
Strain (mm/mm)
Figure 2.8 Typical PD and MTS stress-strain curves with PD error bars
2.3.4 Ad-Hoc Variance Testing
The four tissue sections used for variance testing showed an average standard
deviation in measured modulus 11.6% of the mean modulus for the PD method and
17.6% of the mean modulus for the MTS method. Using a t-test and a 95% confidence
interval, it was shown that these two means couldnt be assumed different. On the other
hand, equivalence of the two methods was not established unless an equivalence interval
equal to or greater than 38% of the average value of the standard deviation of both groups
was assumed at a 95% confidence interval. Equivalence was established as described by
Hatch (Hatch, 1996).
40


2.3.5
Ad-Hoc Longitudinal Variance Testing
Analysis was preformed by defining the error in each longitudinal strain
measurement as the difference between the measured longitudinal strain and the average
longitudinal strain measured at the corresponding pressure and longitudinal location. The
mean error found was 2.6% strain and the standard deviation of the error was 3.1% strain.
The maximum error found over 120 data points was 15% strain. When the error is
applied to the calculation of thickness (Equation 2.3) the error in thickness is also 2.6%
and 8.7% of the measured thickness for the mean error and the mean error plus two
standard deviations of the error. These values also approximate the error in the
calculated stress (Equation 2.2) if it is assumed that the diameter of the artery is
significantly larger than the thickness.
2.4 Discussion
The results of the tests indicated that the PD method is comparably effective
to the uniaxial test method for making comparisons of the strain of collagen engagement.
The mean of the differences between the engagement strains represented only 3.3% of the
average engagement strain of both methods. This small value indicated little or no
difference between the methods and this difference was easily accounted for by the
overall theoretical error calculated for the PD method. Furthermore, there was no
apparent trend in the error data that would have indicated systematic error. The standard
deviation of the differences between the engagement strains represented only 6.5% of the
average engagement strain of both methods. This small standard deviation showed that
not only was the mean of the differences small, but it was consistently small over the
entire population of tissues tested. Even so, it was also shown that there was a significant
41


difference between the two test methods for engagement strain using a paired t-test. We
believe that this is not a significant detriment to the PD testing method, as the mean
difference between the two methods is very small in comparison to the actual strain of
engagement and remains consistent as can be seen by the low standard deviation in the
difference between the two methods. Furthermore, we present this testing method as a
means of rapidly comparing the engagement strains between different animal groups, and
not a method for determining the precise in-vivo engagement strain.
Similarly, the results of the tests indicated the PD method was well correlated to
the uniaxial test method for determining the modulus of the elastin. The mean of the
differences between the two methods was equivalent to 7.4% of the average modulus.
This difference was not shown to be significant using a paired t-test.
Error calculations were also preformed to demonstrate the effectiveness of the PD
method. The maximum, relative, theoretical error in the stress measurement, in the range
of stress normal for the PD method, was found to be 20.3%. Although this error was
relatively high, a large portion of this error was due to the assumed precision of the
longitudinal stress. Therefore, the use of an automated dot-tracing algorithm would
greatly reduce the error when used in place of the manual dot selection. This method was
not used because the proximity of the two dots in each section caused automated dot
tracing algorithms to often select the wrong dot. It is believed that an improved
algorithm could solve this issue.
The tests preformed showed the utility of the PD method for determining
differences in the strain state of collagen engagement for long pulmonary arterial
branches, excised from healthy and hypertensive calves and cows. Further, the small
42


average difference between the two methods indicates that the PD method was an
effective predictor for changes in the elastic modulus of the elastin dominant region of
the stress-strain curve, between animal groups.
The ad-hoc longitudinal variance testing preformed in this study indicated only
small error based on the radial location of the placement of longitudinal strain markers.
Although we do believe that the addition of multiple longitudinal strain measurements
would increase the overall accuracy of the testing method, we believe that the spread in
error found in the ad-hoc testing indicates that the use of only a single measurement is
acceptable based on the accuracy of the other measurements made in the study and the
number of tissues tested in this study.
Overall, we believe that the validation of the PD method was a success. This
method allowed a significant decrease in testing time and effort, in comparison to the
MTS method, because sections of multiple different diameters were tested
simultaneously and the data correlated well with data collected using MTS methods.
Finally, the data collected in these tests showed the validity of lining the artery lumen
with a latex liner to prevent pressure leaks during a PD test.
This new testing method also suffered its limitations. Although the mean difference
in modulus between the two methods was small, the standard deviation of the differences
was found as 27.8% of the average modulus. We believe that although this indicated a
high degree of variation over the sample population, this could be the result of
inconsistencies in the tissues and not error in the method. This was supported by the
mutually high standard deviation shown in the ad-hoc variation testing. Furthermore,
there was no apparent trend in the error that would have indicated systematic error.
43


The PD method was also less effective than the MTS for testing localized changes in
stiffness. The PD method applied consistent pressures over the entire section and should
therefore have given a stress-strain curve that was representative of the average material
mechanics for the entire section. The MTS was able to test very specific circumferential
strips. This was not believed to be useful for the majority of compliance studies in PH.
Finally, both the PD and MTS testing methods presented here did not match the in-
vivo, longitudinal stretch of the arteries. Because of inhomogeneity in the arterial wall
material, the exact stress-strain characteristics of the tissue, in-vivo, cannot be predicted
exactly, by tests with stress or strains prescribed only in the circumferential direction. It
is for this reason, that we present this methodology as a tool for comparing the material
characteristics of multiple animals, and not a method for predicting the true stresses and
strains present in-vivo.
44


3 Mechanics Of Posthilar, Pulmonary, Conduit Arteries In Hypertension
3.1 Motivation
As mentioned previously, increases in the stiffness of the proximal pulmonary
arteries have been noted, clinically, in the presence of PH. Studies of the artery
mechanics have been shown to improve predictions of the outcomes of patients in a
clinical setting (Gan, et al., 2007). These studies have demonstrated that large decreases
in artery wall compliance are well correlated with increased likelihood of morbidity and
mortality. Such studies have demonstrated a significantly decreased compliance in the
pulmonary circulation as a result of PH (Barst, et al., 2004). This leads to increases in
right heart afterload, and may additionally be related to detrimental effects in the distal
vasculature, such as endothelial dysfunction (Chiu & Chien, 2011). The decreases in the
capacitive nature of the pulmonary arteries have been attributed to increased smooth
muscle cell activity (Stenmark, Fagan, & Frid, 2006) and changes in the passive
mechanics of the conduit arteries. Passive mechanics in the conduit arteries have been
shown to change as a result of vascular remodeling and changes in the dominant load
carrying components of the vascular wall, due to the increased internal pressure
associated with the disease. The effects of these changes on the volumetric compliance
of the proximal (i.e., prehilar) arteries have been well characterized in both in-vitro
studies (Lammers, et al., 2008) and, to some extent, in-vivo studies (Hunter, et al., 2008).
To our knowledge, little has been done to quantify the changes in passive mechanics
distal to the hilum of the lung in pulmonary hypertension, other than studies of the
lumped capacitance of the entire lung. This is believed to be a significant oversight,
45


because the compliant nature of the pulmonary arteries continues well beyond this point,
and is exposed to different hemodynamic loading.
As discussed earlier, the use of mathematical models of the pulmonary circulation
in PH can add to the understanding of the disease. Because the more advanced of these
models are reliant on an understanding of the artery mechanics throughout the pulmonary
tree, it is essential to characterize the mechanics of the more distal pulmonary arteries in
both health and PH. This chapter will attempt to do so.
3.2 Methods
3.2.1 Animal Models
Three groups in total were used: control, hypoxic, and brisket. The control and
hypoxic animal groups consisted of neonatal male Holstein calves (70 -110 lbs.).
Hypertension was induced in the hypoxic group through a two-week stay in a hypobaric
chamber at 430 mmHg (4,600-m equivalent air pressure). Hypoxic animals were
sacrificed at 430-mmHg pressure after 14 days at hypoxic conditions. All animals in
these groups were studied and sacrificed at 15 +/- 2 days of age. A third group was
brisket calves, which were born and raised for commercial slaughter at altitudes of
greater than 2500 meters. A subset of these animals naturally develops PH over their first
summer of life similar to that seen in the neonatal model. These animals were tested for
PH at 6 weeks and were sacrificed for study only if found to be hypertensive.
3.2.2 Dissection
The dissection methods used for this study followed the methods discussed in the
Validation of a Pressure Diameter Method for Determining Modulus and Strain of
Collagen Engagement for Long Branches of Bovine Pulmonary Arteries section of the
46


previous chapter. In order to use tissues to their fullest extent and avoid waste, applicable
tissues used in the validation study were also used in this study when applicable.
3.2.3 Mechanics Testing
Tissues were tested at locations similar to those described in the previous chapter
PD Method Inflation section. Due to the success of the methods development
discussed in the precious chapter, tissues were tested using the PD method. However, to
maintain consistency with previously published data, these animal tissues were also
tested with the uni-axial pull tester. Both methods continued to deliver results similar to
each other.
After the PD testing, the artery was sectioned into two circumferential rings at
each test location. One ring was then set aside for histology. The other ring was then
measured for wall thickness (see wall thickness and unstretched circumference section).
The ring was then opened into a circumferential strip. The width of the strip was
measured with electric calipers and a uni-axial pull test was preformed on the sample.
The pull test was preformed with an MTS, Insight 2 (MTS Systems, Eden Prairie, MN)
material testing system, in an isolated tissue bath, in the circumferential direction.
During this test, the strain and the applied force were recorded. This test is also described
in more detail in the previous chapter and by Lammers et. al. (Lammers, et al., 2008).
3.2.4 Wall Thickness and Unstretched Circumference
The wall thicknesses and unstretched circumferences of the arteries were
determined at each test location photographically in the same method as described in the
previous chapter PD Method Inflation section.
47


3.2.5 Histology
Images of histological samples of the arteries were taken based on availability
from four hypoxic calves and three normoxic calves. Samples were taken to image the
plane perpendicular to the longitudinal axis, providing a ring section of the artery. These
samples were taken after testing from the most proximal, the middle and the most distal
tissue section of each artery tree. This resulted in samples for the third, fifth and seventh
post-hilar generations. Samples from all seven animals were stained with Verhoeff-Van
Gieson (VVG) staining protocol. Three hypoxic and two control animals were stained
with the Hematoxylin and Eosin (H&E) protocol and Modified Movat's Pentachrome
Stain (pentachrome). Images of each sample were taken on a Zeiss microscope with a
digital imaging system and a lOx zoom lens. Images were taken and analyzed at three
different locations in each arterial ring. For numerical analysis, the data from each set of
three images was then averaged. All images were taken with the same image settings and
lighting in order to maintain consistency in all of the images.
3.2.5.1 VVG
Image analysis was preformed on the VVG samples to determine the relative
volume of elastin in comparison to the overall volume of the arterial wall. Image analysis
was completed using custom written software in Matlab. Using image thresholding, the
background of the image was removed and the area of the tissue was determined. Within
the tissue area, a color mask was used to remove non-blue portions of the image. Further
thresholding was performed to remove any light-blue areas in the tissue surrounding the
elastin, leaving only the area of the tissue that was elastin. Consistent image threshold
and mask values were used for all of the VVG samples, so that comparisons between
48


samples of relative elastin volume were accurate, even if the exact values were not
correct due to improper thresholding. Assuming the cross-section was representative of
the entire volume of the artery section, a relative volume of elastin was assumed to be the
same as the relative area for the cross-section. Further analysis was conducted by
multiplying the relative elastin volume by the artery wall thickness resulting in the total
volume of elastin per circumference length, per longitudinal length (referred to as total
elastin content in the following sections).
3.2.5.2 H&E
H&E staining dyes the tissues blue in cellular nuclei, but a light red color in the
remaining tissue. Image analysis was preformed on the H&E samples to determine the
relative number of nuclei in the artery wall. This was done manually in Osirix. Three,
10,000 pm2 circular areas, were placed in each image one with a border on the intima,
one with a border on the adventitia and one centered in the media. The nuclei in each
region were counted and then averaged for the image. These values were also multiplied
by the thickness to determine a value not normalized for thickness (referred to as total
cell count in the following sections)
3.2.5.3 Pentachrome
Unlike the other stain types, all of the analysis preformed on the pentachrome
stained samples were qualitative in nature. The samples were examined for degradation
of the elastin, which generally presented itself as elastic clipping or discontinuities in
the elastin fibers. The samples were also examined for neo-intimal formation. The
spacing between the elastin fibers was examined. Finally, the samples were examined for
49


the presence of elastin formation sites. All of these features are indicated in a sample
image provided below (Figure 3.1).
Figure 3.1 Pentachrome staining features for analysis
3.2.6 Calculations
From the tests described above, calculations were preformed to develop a stress
strain curve for the arterial wall at each test location. From this curve and in-vivo PA
pressure data, the material modulus and stiffness of the arterial wall was calculated over
the in-vivo pressure range. Furthermore, the stress-strain curve was used to calculate the
strain at collagen engagement for each animal. Finally, the change in the cross-sectional
area of the plane normal to the longitudinal axis of the artery was determined at each test
location.
50


3.2.6.1
PD Data Smoothing
As described in the previous chapter in the Engagement Strain section,
smoothing was once again applied to the PD data.
3.2.6.2 Stress-Strain
As described in the previous chapter, ten consecutive iterations of strain-
relaxation cycles were applied to each circumferential strip of arterial tissue using the
uni-axial MTS. From the tenth cycle, a force-strain trace was recorded. By assuming a
constant material volume (Lawton, 1954), material isotropy and material continuity and
using small strain assumptions, a stress was calculated for each force-strain point based
on the equations presented in the previous chapter (printed below in a different form).
L = (e + 1)L0
Equation 3.1 Uniaxial strained length
\=W0T0
Equation 3.2 Unstrained plain of stress area
_ ^0^0
L
Equation 3.3 Strained plain of stress area
F
A
Equation 3.4 Uniaxail stress
51


In the above equations, L is the length of the circumferential strip at a given data
point, A is the cross sectional area at a given strain, A0 is the cross sectional area in the
unstretched state and o is the stress. Equation 3.3 is a consequence of the assumption of
constant material volume and describes the cross sectional area as a function of the state
of strain. This allows for an approximation of true-strain, rather than engineering strain,
shown in Equation 3.1.
When available, stress-strain traces were also extracted from the PD data using
Lames Law for thick walled tubes as described in detail in the previous chapter. In order
to use this model, it was assumed that a section of artery at each test location could be
considered a tube of infinite length. Once again, material continuity, isotropy, constant
volume and small strain assumptions were made. Our work, presented in the previous
chapter, demonstrated strong agreement between stress-strain traces determined using the
PD method and those determined using the uni-axial testing method. Calculations for
Lames Law are presented in Equation 2.1- Equation 2.3.
For both PD and uni-axial stress-strain data sets, a ninth order polynomial was fit
to the data. For all data sets, the revalue was no less than 0.98. When both PD and uni-
axial data sets were available, values of the ninth-order polynomial were discretized in
the in-vivo pressure range and averaged between the two data sets.
Both PD and uni-axial pull testing were used to alleviate concerns of method
accuracy. Although our work presented in the previous chapter indicated an
interchangeability of the two testing methods, advantages to both methods were noted.
Implementing both methods in the study enabled us to have a check system for each data
point with little increase in testing time. Had the results of the two methods varied
52


significantly for specific tissues, these data points could have been removed from the data
pool. This was never the case in our data set. Data points acquired with only the uni-
axial testing method were not found to be outliers, or to vary significantly from their
perspective data pools or to display any unique trends.
3.2.6.3 Material Modulus and Stiffness
To determine modulus changes resulting from PH, it was necessary to compare
the modulus at similar strains for all of the tissues. The modulus was therefore defined as
the mean slope of the stress-strain curve between 22.5% and 27.5% strain. This point
was chosen because there was data available for all animals at this strain state and it was
well below the strain of collagen-engagement for all of the animals. The average slope
was determined by applying a linear fit to the discretized data points. Material stiffness
was again determined at strains ranging between 22.5% and 27.5% for similar reasoning.
Stiffness was defined as the modulus at a given strain multiplied by the calculated
thickness at that given strain.
3.2.6.4 Strain of Collagen-Engagement
The collagen-engagement strain is the amount of strain where it is assumed that
collagen fibers begin to carry a significant portion of the stress. At strains beyond this
point, collagen carries an increasingly larger portion of the stress, until the collagen is
fully engaged. For the sake of comparison, the strain of collagen-engagement is defined
as the point of maximum curvature in the stress-strain curve, in similar fashion to the
methodology of the previous chapter (Lammers, et al., 2008). Using the already defined
stress-strain functions, the curvature is defined by Equation 2.4.
53


3.2.7
In-vivo Change in Cross-Sectional Area
Calculation of pressure-strain traces was a straightforward process when PD
diameter data was available for the in-vivo pressure range. This is because the strain can
easily be calculated as described in Equation 2.1, and the pressure was directly measured.
Calculation of a similar trace required more manipulation for uni-axial data sets.
Even so, the calculations were relatively straightforward using the same assumptions
described to develop a stress-strain trace from the PD data set (see Calculations: Stress-
Strain section). Again, Lames Law was used. In this case, the pressure-strain trace was
derived from the previously calculated stress-strain trace. For each discrete stress-strain
point, pressure was calculated as below,
r=^
0 2n
Equation 3.5 Unstrained radius for cross-sectional area calculation
r = r0(l + e)
Equation 3.6 Strained radius for cross-sectional area calculation
D \(r + T)2 r2\a
1 \(r + T)2 + r2]
, where T
(1+e)
Equation 3.7 Internal pressure for cross sectional area calculation
where r0 and r are the initial and strained internal radius, respectively, T and T0 are the
unstrained and strained thickness, respectively and C, is the measured internal
circumference. Equation 3.6 is a consequence of an assumption of material isotropy and
54


incompressibility and Equation 3.7 is the result of Lames Law and an assumption of
constant volume.
After calculation of the pressure-strain trace, a ninth-order polynomial was fit to
both the PD and uni-axial data sets. Using this function, discretized values were
calculated for the in-vivo pressure range. If both data sets were available, the two were
averaged. By assuming a circular cross section of the artery, the in-vivo change in
diameter was calculated as described in Equation 3.8- Equation 3.9,
r =r0(l + £,),/ = {1.2}
Equation 3.8 Strained radius for cross sectional area calculation
AA = (r:: r~)n
Equation 3.9Change in cross sectional area over in-vivo pressure range
where 8i and 8 2 are the strains corresponding to the minimum diastolic and peak systolic
measured pressure, respectively and AA is the change in cross-sectional area.
3.2.8 Statistics
Statistical analysis was performed for each of the calculations described above.
This analysis was completed in two broad categories, ANOVA analysis and regression
analysis. For the remainder of this chapter, statistical significance will be defined as
slightly significant for a<0.10 and significant for a<0.05. All other values of a are
considered insignificant.
For each test, material modulus of elasticity, stiffness, thickness, engagement
strain, or change in relative area (AC), a multi-factor ANOVA was completed with
independent variables of circumference group and treatment group (control or
55


hypoxic/brisket). Four circumference groups were chosen to most evenly distribute the
tissues. Groups were 7-15[mm], 15-20[mm], 20-25[mm] and 25-32[mm]. Artery section
circumferences were used to group the tissue sections for analysis, rather than artery
branch generation. This grouping was chosen because our theoretical understanding of
pressure vessels dictates that the circumference of the artery and the internal pressure, not
the branch location, determines the mechanical forces experienced by the artery wall in-
vivo. It therefore follows that the artery circumference will best categorize adaptations to
the arterial wall resulting from changes in internal pressure. ANOVA tests did not
consider the two brisket calves because of their low population number and they could
not be considered control or hypoxic. Bar plots of the means of size group for each test
are provided below, with the standard deviation in the test value for each size group
represented with error bars.
Linear regressions were also completed for each test; for these analyses, the
brisket calves were pooled with the hypoxic group. Brisket animals were included in the
linear regressions to provide a more complete range of MPAP because the hypoxic and
control groups had a large gap between their MPAPs. Multivariate regressions were
calculated to determine the dependence of each test on MPAP and Circumference.
ANCOVA calculations were also completed to determine if the slope constants for the
regressions were differed significantly between circumference groups. This was
completed by performing the same multi-varriate regression with an addition independent
predictor two more times. The additional independent predictor was equal to either the
MPAP or the circumference (depending on which slope is being tested for treatment
dependence) for control animals. The value of the independent predictor was always zero
56


for hypoxic/brisket animals. If there were a significant difference between treatment
groups, then the additional independent variable would be significant. In essence, this
value was the difference in the slopes of the two groups. In these cases, regressions were
run for each treatment group separately. For some test results, uni-variate regressions
were conducted between either MPAP or circumference and the test results. In these
cases differences in treatment slopes were computed in a similar fashion as multivariate
regressions.
3.3 Results
3.3.1 Mean Pulmonary Pressure
Analysis was conducted on the MPAP for both the hypoxic and control groups.
Due to catheterization issues, pressure data was unavailable for one control animal. The
mean MPAP for the control groups was 25.5[mmHg], 39.2 [mmHg] for the brisket calves
and 102.0[mmHg] for the hypoxic group. A single factor ANOVA indicated a significant
difference in MPAP between groups (a<0.0005).
Note: For the remainder of the Results section, any analysis involving MPAP will be
based upon study of five control, six hypoxic and two brisket animals. Analysis
independent of MPAP will be based upon study of seven control and seven pooled
hypoxic/brisket animals.
3.3.2 Modulus of Elasticity
Results of the multifactor ANOVA for the modulus showed no significant
difference in modulus between circumference groups (a=0.671) or between control and
hypoxic treatment (a=0.613). Figure 3.2 is a bar chart of the elastic modulus means for
57


each size group. The multivariate regression showed no linear dependence for the
modulus based on either circumference or MPAP (a=0.992, a=.347, respectively). When
the treatment groups are analyzed separately, there is a significant linear relationship
between MPAP and modulus for the control group and the sick (hypoxic/brisket) group
(a=0.030 and a<0.0005, respectively). The slopes were also significantly different
(a=0.022). Interestingly, the slope of the sick animals is negative and the slope of the
control animals is positive.
Modulus Vs Circumference Group
Circumference Group
Figure 3.2 Mean modulus of each circumference group bar plot
3.3.3 Thickness
The ANOVA results indicate a significant difference for unstretched wall
thickness between circumference groups (a<0.0005) and between treatment groups
(a<0.0005). Figure 3.3 is a bar plot showing the mean thicknesses for each


circumference group. The mutivariate regression agreed with these findings, showing a
strong linear dependence of unstretched wall thickness on both unstretched circumference
(a<0.0005) and MPAP (a<0.0005). Notably, error residuals were calculated for the
linear approximation and were evenly distributed over the range of unstretched
circumferences, supporting the validity of a linear model. The significance of the overall
model was found as a<0.0005.
Thickness Vs Circumference Group
Circumference Group
Figure 3.3 Mean thickness for each circumference group bar plot
Univariate, linear regressions relating unstretched circumference and unstretched
wall thickness for the control and hypoxic groups, independently, indicated a significant
difference in slope between the groups (a=0.002). Figure 3.4 is a plot of the unstretched
wall thickness verse unstretched circumference, with the two regressions plotted.
59


Thickness Vs Circumference
Figure 3.4 Thickness vs. circumference scatter plot with regressions plotted
3.3.4 Collagen Engagement
The ANOVA indicated a significant difference in engagement strain between the
circumference groups (a=0.021), but showed no evidence for a difference between the
hypoxic and control treatment groups (a=0.740). Figure 3.5 is a bar plot of the mean
engagement strain for each circumference group. Similarly, a multivariate regression
indicated a significant linear relationship between the circumference and engagement
strain (a<0.0005), but there was no significant linear relationship between the MPAP and
engagement strain (a=0.219). Furthermore, univariate analysis of the dependence of
engagement on circumference did not indicate a statistical difference between the slopes
of the control animals and the sick animals (a=0.915).
60


Engagement Strain Vs Circumference Group
Figure 3.5 Mean engagement strain for each stiffness group bar plot
3.3.5 Stiffness
Analysis of the stiffness multivariate ANOVA indicated a significant difference
between treatment groups (a=0.015) and circumference groups (a<0.0005). Figure 3.6 is
a bar plot of the mean stiffness for each circumference group. A multivariate regression
was able to show a significant linear relationship between stiffness and circumference
(a<0.0005) and a trend toward a slightly significant linear relationship between MPAP
and stiffness (a=0.061). The slope of the regression indicated a positive relationship
between circumference and stiffness and a positive relationship between MPAP and
stiffness. Furthermore, it was found that the dependence of stiffness on circumference
was also dependent on the treatment group, in that the slope of stiffness vs. MPAP for the
sick treatment group was significantly higher than the slope for the control group. Figure
61


3.7 is a plot of the stiffness vs. unstretched circumference, with the two regressions
plotted.
Stiffness Vs Circumference Group
Circumference Group
Figure 3.6. Mean stiffness for each stiffness group bar plot
62


Stiffness Vs Circumference
Figure 3.7 Stiffness vs. circumference scatter plot with regressions
3.3.6 Area Compliance
Change in the relative area of the artery sections over their respective, in-vivo
pressure ranges (min diastolic to maximum systolic) were studied relative to their
unstretched cross-sectional area, yielding area compliance. These values were then
normalized by dividing the result by the span of their respective pressure ranges, resulting
in percent change in area per pressure unit [(mmA2/mmA2)/mmHg], or the AC. A
multifactor ANOVA showed a significant increase in AC between control and hypoxic
groups (a<0.0005), but no significant difference between the circumference groups.
Figure 3.8 is a bar chart showing the mean change in AC for each circumference group.
A multivariate regression showed a significant linear dependence of the AC on the
63


MPAP (a<0.0005), but no significant linear relationship between the AC and the
unstretched circumference. When a multivariate regression is considered with the same
factors and treatment groups considered independently, both the sick animals and control
animals showed a significant linear dependence on MPAP (a<0005 and a=.011,
respectively). The difference of the dependence of AC on MPAP between treatment
groups was also found to be significant (a=.015). Only the hypoxic group showed any
linear dependence of AC on the unstretched circumference (a<0.0005).
Change in Relative Cross-Sectional Area per Pressure Vs Circumference Group
Circumference Group
Figure 3.8 Change in relative cross-sectional area per pressure vs. circumference
group
64


3.3.7 Histology
3.3.7.1 VVG
A multifactor ANOVA was preformed for the relative elastin volume based on
circumference group and animal treatment. No significant difference in the elastin
fraction was found based on either the circumference group or the animal treatment.
Similarly, a multivariate linear regression was unable to correlate the elastin fraction to
circumference or MPAP. A multifactor ANOVA, preformed on the total elastin content
based on circumference group and animal treatment showed a significant dependence on
circumference group (a<0.0005), but none based on animal treatment. Figure 3.8 shows
a bar plot that would seem to indicate an increase in the total elastin content for the
hypoxic animals, but the differences were not significant. Similarly, a multivariate linear
regression indicated a linear dependence of total elastin content on circumference
(a<0.0005), but none on mean pulmonary pressure. Sample images from WG stained
slides are provided below in Figure 3.10.
65


Total Elastin Content
Circumference (mm)
Figure 3.9 Total elastin content (WG)
66


Figure 3.10 Sample VVG stained tissue images
3.3.7.2 H&E
A multifactor ANOVA was performed for the cell count based on circumference
group and animal treatment. No significant difference in the cell count per area was
found based on either the circumference group or the animal treatment. Similarly, no
linear dependence was found between the cell count and the circumference group or
animal treatment. A multifactor ANOVA did find a significant dependence of total cell
count on circumference (a=0.0461), but no dependence on animal treatment. A
67


multivariate regression showed linear dependence of total cell count on circumference,
but no dependence on the mean pulmonary pressure. Plots of the data mentioned above
are provided below Figure 3.11- Figure 3.12. Sample H&E images are provided below
in Figure 3.13.
Relative Cell Count
Circumference (mm)
Figure 3.11 Relative cell count (cell count per area) (H&E)
68


Total Cell Count
Circumference (mm)
Figure 3.12 Total cell count
69


Figure 3.13 Sample H&E stained tissue images
3.3.7.3 Pentachrome
Although the data gathered from the pentachrome stained slides was qualitative in
nature, distinct differences were noticed as a result of both animal treatment and artery
size. Neointimal lining was generally present in the hypertensive animals, but not in the
control animals. This feature appeared to be most pronounced in the largest arteries, yet
still present in the smallest artery sections. Punctate elastin appears to be present in the
hypoxic animals at much higher levels than in the control animals, especially in the
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smaller arteries. Similarly, elastic clipping appears to be much more prevalent in the
hypoxic animals compared to the control animals. Finally, there appears to be increased
radial spacing between the elastin fibers. Sample pentachrome stained images are
provided below in Figure 3.14.
Figure 3.14 Sample PENTACHROME stained tissue images
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3.4 Discussion
Overall, our study indicated a strong correlation between stiffening of the arterial
wall and the presence of hypoxia-induced PH. This stiffening appears to be associated
with an increased wall thickness in the hypoxic animals, and not associated with changes
in the material modulus of the tissue. The significant linear relationship present between
the MPAP and thickness suggests that this remodeling is a reaction to increases in
pulmonary pressure. We have also shown that the engagement strain of the distal,
conduit, pulmonary arteries remains fairly constant regardless of the treatment or the
MPAP in this animal model. The consequence of both the arterial stiffening and the
constant engagement strain, in conjunction with increased arterial pressures, is
dramatically decreased AC in the hypertensive animals. These points and their
implications are discussed in further detail in the following subsections. Table 3.1
(below) provides a brief synopsis of the relationships shown in the results section, above.
The column on the left describes the relationship studied; the center column describes the
type of correlation and the right column notes whether or not a significant relationship
was found.
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Table 3.1 Summary of findings
Comparison Relationship Significance
Modulus of elasticity vs.
-MPAP None No
-Treatment None No
-Circumference None No
Thickness vs.
-MPAP Positive Linear Yes
-Treatment Increased in Hypoxic Yes
-Circumference Positive Linear Yes
Engagement vs.
-MPAP None No
-Treatment None No
-Circumference Positive Linear Yes
Stiffness vs.
-MPAP Positive Linear Trend Only
-Treatment Increased Stiffness in Hypoxi Yes
-Circumference Positive Linear Yes
AC vs.
-MPAP Negative Linear Yes
-Treatment Decreased AC in Hypoxic Yes
-Circumference None No
Relative Elastin Content vs.
-MPAP None No
-Treatment None No
-Circumference None No
Total Elastin Content vs.
-MPAP Positive Trend Only
-Circumference Positive Yes
Relative Cell Count vs.
-Treatment Increased Cell Count in Trend Only
-Circumference Hypoxic None No
Total Cell Count vs.
-Treatment Increased Cell Count in Trend Only
-Circumference Hypoxic Positive Yes
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3.4.1
Modulus of Elasticity
There was no significant difference in the group means for modulus of elasticity
between the control and the hypoxic groups. This may indicate a lack of change in the
intrinsic mechanical properties of the arterial wall resulting from the hypoxic treatment.
Thus, any stiffening in the artery wall resulting from treatment is mainly the result of
geometrical changes. These findings do not agree with the previous findings of Lammers
et al. (Lammers, et al., 2008), although this study characterized the mechanics of the
main and first branches of the pulmonary arteries, not the post-hilar arteries. We cannot
conclude as to whether or not this discrepancy between the two studies is due to the size,
generation or location of the arteries.
In agreement with the above conclusions, no significant linear dependence
between the MPAP and the modulus in the elastin region was found in the pooled data.
This, again, suggests little intrinsic mechanical remodeling of the cellular wall resulting
from increased MPAP. This is, however, contrary to the significant linear dependence of
modulus on MPAP discovered within both the sick and control treatment groups.
We also purpose a theory in regards to the opposing slopes of the two animal
groups. We suggest the theory that within a healthy population, the vasculature reacts to
increased pressure and distension through remodeling to increase the modulus and
stiffness, protecting the animal from the adverse effects of collagen engagement,
resulting in a positive relationship between MPAP and modulus. Within the sick
animals, we propose a different causal relationship. Increased MPAP beyond the norm
for the group occurs due to an animals lack of remodeling, while MPAPs below the
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norm occur in the animals that display more protective remodeling, causing a negative
dependence of modulus on MPAP in the sick animals. In other words, some of the
animals in the sick group may have a greater ability to protect themselves from the
detrimental effects of collagen engagement through increased levels of remodeling,
resulting in lower MPAP in the animals that present higher modulus.
3.4.2 Thickness
The significant increase in thickness as a result of hypoxic treatment supports
previous studies of the pre-hilar arteries, which displayed geometric remodeling resulting
from hypertension. This is in agreement with the significant, positive linear relationship
between the MPAP and the wall thickness. The increased thickness is likely the result of
both increases in cellular reproduction and migration to the arterial walls and an increase
in the production of extra cellular matrix. It is hypothesized that this is a protective
response against the increased pulsatility resulting from collagen engagement.
Furthermore, the significant thickening found in absence of significant changes in the
modulus confirms that increases in stiffness and decreases in capacitance are the result of
geometric remodeling and not necessarily changes in the intrinsic properties of the artery
wall.
We further note the significant linear dependence of the wall thickness on both
the MPAP and the artery circumference. This relationship implies that the wall thickness
of the distal conduit arteries may be predictable based on studies of only MPAP and the
proximal arteries. This feature could be very useful in the creation of numerical models
of the pulmonary arteries in disease. Further, this data supports the utility of in-vivo
mechanics testing focused on the proximal regions of the pulmonary arteries, i.e.
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localized testing of arterial wall mechanics using ultrasonic and catheterization
techniques (Hunter, et al., 2010), as these studies will be helpful in the prediction of the
distal mechanics based solely on the mechanics of the proximal arteries and the MPAP.
3.4.3 Engagement
The strain of collagen engagement cannot be shown to change by the presence of
PH in the post-hilar pulmonary arteries, in this animal model. This suggests that the
length of the collagen fibers, with respect to the length of the unstretched artery
circumference, must remain consistent regardless of the presence of PH in the post-hilar
pulmonary arteries. Interestingly, the strain of collagen engagement is dependent on the
size of the artery, as indicated by the linear relationship between unstretched
circumference and engagement strain. This relationship may also be useful in future
modeling investigations of the pulmonary arteries.
3.4.4 Stiffness
Stiffening is clearly occurring as a result of PH in arteries distal to the hilum of
the lung. This stiffening will contribute significantly to decreases in the capacitive nature
of the pulmonary arterial tree. We further note the dependence of wall stiffness on the
artery size within each treatment group. Because this dependence changes based on the
animal treatment (the sick animals had a significantly different slope from the control
animals), we believe that the amount of remodeling to the arterial wall is dependent on
the size or generation of the artery. This study also demonstrates that relationship
between the stiffness and the artery size is a consequence of the relationship between the
wall thickness and the artery size and not the result of changes in modulus, in this animal
model.
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3.4.5
Relative Area Change
AC is representative of the in-vivo capacitance of each section of artery relative to
the artery size, as described by Gan et al. (Gan, et al., 2007). The data presented here
shows highly significant changes in the capacitance resulting from animal treatment and
animal MPAP. The relative capacitance of the arteries, on the other hand, seems to
remain fairly constant based on the size of the artery. The very large changes in
capacitance between the control and sick animals are due both to wall stiffening, resulting
from increased wall thickness, and collagen engagement. This demonstrated loss of
capacitance will result in increased loading to the heart and increased pulsatility in the
distal vasculature, potentially leading to endothelial dysfunction or other detrimental
effects to the circulation. This data indicates the importance of the passive mechanical
changes present in the posthilar conduit arteries.
3.4.6 Histology
We would like to call the readers attention to the trend of increased cell counts
and increased total elastin. We believe this to be indicative of increased cellular
proliferation and migration to the cellular wall and increased production of extra-cellular
matrix.
Our observational analysis of the pentachrome stained samples seems to indicate
similar features. Here we notice the presence of newly developing intima and new elastin
fibers in the hypertensive animals. We are also seeing degradation of the existing elastin
fibers in the hypertensive animals, which may be responsible for the negative linear
relationship between MPAP and modulus in the hypertensive animals. We believe these
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changes to be indicative of increases in cellular activity and changes in the structure of
the extra-cellular matrix. Based on these observations, we recommend that further study,
with increased sample numbers be conducted, histologically, on these sections of the
artery to truly gain an understanding of the changes taking place in the arterial walls.
3.4.7 Limitations
We first of all note that these studies were conducted ex-vivo and did not apply
longitudinal strains that match in-vivo conditions. The mechanical values presented will
therefore be skewed from the true in-vivo values. We justify this limitation by noting
that this chapter is intended to be a comparison between treatment groups and an
exploration of the predictability of distal mechanics based on measured hemodynamics
and the mechanical behavior of more proximal arteries.
We note the lower population size for our histological study. We justify this by
stating that this study was meant to analyze the mechanics of arterial changes in PH and
not produce significant histological results. We therefore kept our efforts focused in the
mechanics study and included a very brief study of the histology of these portions of the
arteries as a side-note. On the other hand, we do believe that this portion of the study is
very informative and deserves attention.
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4 Final Notes
In order to avoid some of the drawbacks of previously used arterial tissue
mechanic testing methods, a new methodology was developed, the pressure-diameter or
PD method. This method, of course, had its own limitations, but it proved to be an
effective testing method overall. It was also shown to have similar accuracy to the gold
standard method (namely, uniaxial testing) for determining the stress-strain relationship
of arterial wall tissue. This PD method allowed for increased rapidity in testing the tissue
mechanics of the multiple generations of arterial walls. Furthermore, this testing method
allowed the determination of longitudinal strain, reducing the number of assumptions
made in comparison to the uni-axial method. Finally, the PD method allowed the direct
measurement of relative area change, which is directly related to capacitance.
Determination of this value using the uni-axial method relies heavily on assumptions of
material characteristics. For these reasons, it is believed that the PD method developed
here was not only effective for theses studies, but will prove effective in future research.
Using the PD method as well as a uni-axial testing method, a significant body of
data was developed, studying the mechanics distal to the hilum of the lung in the
presence of and absence of hypoxically induced hypertension. The previously unstudied
data strongly indicates the importance of the role of passive mechanical changes in the
post-hilar pulmonary arteries in the progression of PH. The clearly demonstrated
stiffening of these arteries will, in conjunction with collagen engagement, lead to large
decreases in the capacitive nature of pulmonary arterial tree, which was dramatically
shown in our study of the in-vivo relative area change of the pulmonary arteries. We
believe that these changes in capacitance hugely impact the outcome of patients suffering
79


from PH (Hunter, et al., 2008), due to significant increases in pulsatility, wave reflection
and loading on the right heart.
The data presented here has significantly added to the understanding of the overall
mechanical changes that occur in the pulmonary circulation as a result of pulmonary
hypertension. By studying the arterial wall mechanics we have discovered many key
similarities and differences between the previously studied mechanical changes of the
proximal arteries and the changes that occur distal to the hilum in pulmonary
hypertension. It is clear that both areas suffer dramatic increases in stiffness. This
increased stiffness is associated with both thickening and increased modulus in the
proximal arteries but is not well correlated with increased modulus in the posthilar
arteries. Furthermore, we have shown that the result of the increased stiffness, along with
collagen engagement, results in severely decreased capacitance in the posthilar
pulmonary arteries. Due to the large contribution of these arteries to the overall
capacitance of the pulmonary circulation, this understanding of the dependency of the
arterial mechanics on artery location and size in both healthy and diseased models will
prove to be essential in the future understanding of pulmonary hypertension.
In the posthilar arteries, we have demonstrated a clear dependence of the arterial
mechanical nature on not only artery size, but also changes in MPAP and the presence of
PH. We believe that this data will lead to an improved understanding of the dynamics of
the pulmonary circulation in the presence of PH, allowing a deeper understanding of the
disease, by improving the overall understanding of the system mechanics. We further
believe that this data can help in the production of detailed mechanical models that will
further increase understanding of the disease. Finally, this data also helps demonstrate
80


the validity of localized, proximal, in-vivo studies of arterial mechanics, due to the
predictability of the thickness and stiffness of the distal arteries.
81


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Full Text

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! MECHANICAL CHARACTERIZATION OF THE POST HILAR PULMONARY ARTERIES IN PULMONARY HYPERTENSION by Mark Reusser B.S., University of Colorado, 2009 M.S., University of Colorado, 2009 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science BioEngineering 2012

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! This thesis for the Master of Science degree by Mark Reusser has been approved for the Bioengineering by Dr. Robin Shandas, Chair Dr. Kendall Hunter, Advisor Dr. Kurt Stenmark November 29 2012

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""" ! Reusser, Mark (M.S., Bioengineering) Mechanical Characterization Of The Post hilar Pulmonary Arteries In Pulmonary Hypertension Thesis directed by Dr. Kendall Hunter ABSTRACT The pulmonary circulation is highly dynamic and both physiologically and mechanically complex The proper function of this system is dependent on many factors. Here we focus on the mechanical charac teristics of the arterial walls and develop a new pressure diameter method of mechanical me asurement for ex vivo arteries. Th is pressure diameter method based on Lame's Law, demonstrates similar accuracy and effectiveness to uni axial methods in deter mining stress strain curves of arterial walls The new technique more closely mimics the in vivo state of the pulmonary arteries and allows stress strain testing for many a rterial generations in less time. Using this method and others, the mechanics of the pulmonary arterial walls of healthy and pulmonary hypertensive neonatal calves were studies. This data indicated significant stiffening in the pulmonary hypertensive mo del due to arterial wall thickening further resulting in significantly decreased compliance over the in vivo pressure ranges This decreased compliance is not limited to the proximal arteries, and will be a significant detriment to those suffering from pulmonary hypertension. It was further demonstrated in the posthilar arteries that the major cause of passive stiffening is associated with increased arterial wall thickness and the stiffening is less dependent on changes in material modulus. These previ ously unexplored arteries demonstrate mechanical adaptation to pu lmonary hypertension that varies f rom what has been shown in the most proximal conduit arteries.

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"# ! Finally, this study sheds light on the predictability of the mechanical nature of the distal conduit arteries, based on the mechanics and loading of the more proximal arteries. This piece shows that the stiffness and the thickness of the arterial walls are linearly related to both the diameter of the vessel and the mean pulmonary arterial pressu re in vivo. This will allow the mechanics of the distal arteries to potentially be predicted without direct measurement. Overall, this study improves the breadth of understanding of mechanical changes to the pulmonary arteries in the presence of pulmonary hypertension by exploring the mechanics of the generally neglected posthilar pulmonary arteries. The form and content of this abstract are approved. I recommend its publication. Approved: Kendall Hunter

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# ! TABLE OF CONTENTS Chapter 1. Introduction And Literature Review ................................ ................................ ..... 1 1.1. Introduction ................................ ................................ ................................ ........... 1 1.2. Pulmonary Artery Mechanics ................................ ................................ ................ 1 1.2.1. Pulmonary Artery Mechanics And Physiology ................................ ..................... 1 1.2.2. Pulmonary Hypertension and Arterial Compliance ................................ .............. 6 1.3. Methods of Mechanical Characterizati on and Modeling of the Pulmonary Arteries and the Pulmonary Circulation ................................ ................................ ............. 7 1.3.1. Methods of Mechanical Testing ................................ ................................ ............ 8 1.3.2. System Models ................................ ................................ ................................ .... 18 1.4. Conclusion ................................ ................................ ................................ ........... 23 2. Validation Of A Pressure Diameter Method For Determining Modulus And Strain Of Collagen Engagement For Long Branches Of Bovine Pulmonary Arteries ..... 2 4 2.1. Motivation ................................ ................................ ................................ ........... 24 2.2. Methods ................................ ................................ ................................ ............... 25 2.2.1. Dissection ................................ ................................ ................................ ............ 25 2.2.2. PD Method Inflation ................................ ................................ ............................ 25 2.2.3. MTS Method ................................ ................................ ................................ ....... 31 2.2.4. Ad Hoc Variance Testing ................................ ................................ .................... 31 2.2.5. Ad Hoc Longitudinal Strain Variance Testing ................................ ................... 32 2.2.6. Calculations ................................ ................................ ................................ ......... 32 2.3. Results ................................ ................................ ................................ ................. 36

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#" ! 2.3.1. Modulus: ................................ ................................ ................................ .............. 36 2.3.2. Engagement Strain ................................ ................................ .............................. 38 2.3.3. Theoretical Error ................................ ................................ ................................ 39 2.3.4. Ad Hoc Variance Testing ................................ ................................ .................... 40 2.3.5. Ad Hoc Longitudinal Variance Testing ................................ .............................. 41 2.4. Discussion ................................ ................................ ................................ ........... 41 3. Mechanics Of Posthilar, Pulmonary, Conduit Arteries In Hypertension ............ 45 3.1. Motivation ................................ ................................ ................................ ........... 45 3.2. Methods ................................ ................................ ................................ ............... 46 3.2.1. Animal Models ................................ ................................ ................................ .... 46 3.2.2. Dissection ................................ ................................ ................................ ............ 46 3.2.3. Mechanics Testing ................................ ................................ ............................... 47 3.2.4. Wall Thickness and U nstretched Circumference ................................ ................ 47 3.2.5. Histology ................................ ................................ ................................ ............. 48 3.2.6. Calculations ................................ ................................ ................................ ......... 50 3.2.7. In vivo Change in Cross Sectional Area ................................ ............................. 54 3.2.8. Statistics ................................ ................................ ................................ ............... 55 3.3. Results ................................ ................................ ................................ ................. 57 3.3.1. Mean Pulmonary Pressure ................................ ................................ ................... 57 3.3.2. Modulus of Elasticity ................................ ................................ .......................... 57 3.3.3. Thickness ................................ ................................ ................................ ............. 58 3.3.4. Collagen Engagement ................................ ................................ .......................... 60 3.3.5. Stiffness: ................................ ................................ ................................ .............. 61

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#"" ! 3.3.6. Area Compliance ................................ ................................ ................................ 63 3.3.7. Histology ................................ ................................ ................................ ............. 65 3.4. Discussion ................................ ................................ ................................ ........... 72 3.4.1. Modulus of Elasticity ................................ ................................ .......................... 74 3.4.2. Thickness ................................ ................................ ................................ ............. 75 3.4.3. Engagement ................................ ................................ ................................ ......... 76 3.4.4. Stiffness ................................ ................................ ................................ ............... 76 3.4.5. Relative Area Change ................................ ................................ .......................... 77 3.4.6. Histology ................................ ................................ ................................ ............. 77 3.4.7. Limitations: ................................ ................................ ................................ ......... 78 4. Final Notes ................................ ................................ ................................ .......... 79 References ................................ ................................ ................................ ......................... 8 2

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#""" ! LIST OF TABLES Table 3.1. Summary of findings ................................ ................................ ................................ .. 73

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"$ ! LIST OF FIGURES Figure 1.1. Idealized stress strain curve for pulmonary arterial tissue under axial tension ......... 4 1.2 the two element Windkessel model in both hydraulic and electrical form. Adapted from (Westerhof & Lankhaar, 2009). ................................ ................................ ................. 5 1.3. Typical uni axial loading diagram ................................ ................................ ............. 9 1.4. Uni axial mounting image ................................ ................................ ......................... 12 1.5. Three element Windkessel in both hydraulic and electrical form ............................. 19 1.6 Four Element Windkessel in both hydraulic and electrical form .............................. 20 2.1. Image of excised pulmonary artery branch showing placement of Loctite dots ....... 27 2.2. Basic schematic of PD test setup ................................ ................................ ............... 28 2.3. Typical pressure diameter curve for PD test ................................ .............................. 28 2.4. Flow diagram of tissue sectioning for PD testing ................................ ...................... 30 2.5. Smoothing function applied to typical stress strain curve using PD method ............ 35 2.6. Bland Altman plot for modulus of elasticity, PD vs Uniaxial ................................ ... 37 2.7. Bland Altman plot for collagen engagement strain, PD vs Uniaxial ......................... 39 2.8. Typical PD and MTS s tress strain curves with PD error bars ................................ ... 40 3.1. Pentachrome staining features for analysis ................................ ................................ 50 3.2. Mean modulus of each circumference group bar plot ................................ ............... 58 3.3. Mean thickness for each circumfere nce group bar plot ................................ ............. 59 3.4. Thickness vs. circumference scatter plot with regressions plotted ............................ 60 3 .5. Mean engagement strain f or each stiffness group bar plot ................................ ........ 61 3.6. Mean stiffness or each stiffness group bar plot ................................ ......................... 62 3.7. Stiffness vs. circumference scatter plot with regressions ................................ .......... 63

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$ ! 3.8. Change in relative cross sectional area per pressure vs. circumference group .......... 64 3.9. Total elastin content (VVG) ................................ ................................ ....................... 66 3.10. Sample VVG stained tissue images ................................ ................................ ......... 67 3.11. Relative cell count (cell count per area) (H&E) ................................ ...................... 68 3.12. Total cell count ................................ ................................ ................................ ........ 69 3.13. Sample H&E stained tissue images ................................ ................................ ......... 70 3.14. Sample pentachrome stained tissue images ................................ ............................. 71

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$" ! LIST OF EQUATION S Equation 1 .1. Uni axial strain ................................ ................................ ................................ ............. 9 1 .2. Uni axial stress ................................ ................................ ................................ ............. 9 1 .3 Uni axial cross sectional area ................................ ................................ ....................... 9 1 .4. Uni axial cross sectional area (strained) ................................ ................................ .... 10 1 .5. Resistance of elastic tube ................................ ................................ ........................... 21 1 .6. Inductance of elastic tube ................................ ................................ ........................... 21 1 .7. Capacitance of elastic tub ................................ ................................ .......................... 21 2. 1 Pressure diameter strain ................................ ................................ .............................. 33 2. 2. Pressure diameter stress ................................ ................................ ............................. 33 2. 3. Pressure diameter strained wall thickness ................................ ................................ .. 33 2. 4. Curvature of a function ................................ ................................ .............................. 34 2. 5. Error due to rotation of artery in PD testing ................................ .............................. 36 3. 1. Uniaxial strained length ................................ ................................ ............................. 51 3. 2. Unstrained plain of stress area ................................ ................................ ................... 51 3. 3. Strained plain of stress area ................................ ................................ ....................... 51 3. 4. Uniaxail stress ................................ ................................ ................................ ............ 51 3. 5. Unstrained radius for cross sectional area calculation ................................ ............... 54 3. 6. Strained radius for cross sectional area calculation ................................ ................... 54 3. 7. Internal pressure for cross sectional area calculation ................................ ................ 54 3. 8. Strained radius for cross sect ional area calculation ................................ ................... 55 3. 9 Change in cross sectional area over in vivo pressure range ................................ ...... 55

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$"" ! LIST OF ABBREVIATIONS AC percent change in area per pressure unit ANCOVA Analysis of covariance ANOVA Analysis of variance H&E Hematoxylin and Eosin staining protocol MPAP mean pulmonary arterial pressure MTS Material testing system, Insight 2 (MTS Systems, Eden Prairie, MN) PD Pressure diameter PENTACHROME Modified Movat's pentachrome staining protocol PH Pulmonary hyptertension RA relative area VVG Verhoeff Van staining protocol

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% ! 1 Introduction And Literature Review 1.1 Introduction In this effort, mechanical quantification of the posthilar conduit arteries of the pulmonary circulation is sought in both the presence and absence of pulmonary hypertension (PH). In this way engineering models of the pulmonary circulation can be improved to include these findings, improving the analytical, diagnostic and prognostic capabilities of these models. 1.2 Pulmonary Artery Mechanics The following section will give an overview of the anatomy of the arterial walls in the pulmonary circulation. This overview will focus specifically on their mechanical attributes and the function of these attributes within the pulmonary circulation. Thi s will be followed by a description of PH and a review of literature studying the effects of PH on arterial mechanics. Finally, some of the inadequacies in the present understanding of arterial mechanics in PH will be discussed. 1.2.1 Pulmonary Artery Mechanics And Physiology The mechanical nature of arterial tissue is significantly more complicated than a Hookean solid, or even a viscoelastic solid. The elastic properties of the arterial wall vary largely, among other factors, with changes in the magnitude, d irection and rate of deformation, and the magnitude, direction and rate of application of the forces applied to the material. Furthermore, these properties are not static, but are adaptive to changes within the physiological environment of the artery wall Changes in these mechanics can have significant consequences to the circulatory system and the heart.

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& ! 1.2.1.1 Mechanical Characteristics Of Pulmonary Arterial Tissues The mechanics of pulmonary arterial walls are dictated by both the active and passive features of the structure (Bia, et al., 2004) both of which play an important roll in the progression of PH. The active mechanical characteristics of arterial walls result from the presence of smooth muscle cells. The activation states of the smooth muscle cell s are dependent on the presence of cellular signal factors that are released by both local and non local cells. Changes in the size, number and activation state of the smooth muscle cells can cause significant changes in the mechanical response of the pul monary arteries (Grover, Wagner, McMurty, & Reeves, 1980) In many ways, these effects have been well studied and characterized in previous research. The research presented here will, therefore, focus on the passive mechanics of the pulmonary arteries. Numerous tensile studies of arterial tissues have shown that arterial walls have a unique, non linear stress strain response (Bergel, 1961) (Gow, 1980) An idealized representation of the stress strain response is included in Figure 1.1 As can be seen in this idealized curve, lower strains result in significantly lower moduli, while higher strains result in much higher moduli. Two linearly elastic regions separated by a non linear transition region can generally represent the curve. Shadwick showed th at this overall non linear stress strain response is a result of the non homogeneous structure of the vessel walls. The main mechanical components of the walls of the arteries are comprised of both rubbery and stiff fibrous materials (Shadwick, 1999) A study conducted by Roach and Burton tested the stiffness of arterial walls with either elastin or collagen selectively digested, showing that the low modulus of the artery at low stresses is due to the load being primarily supported by elastin and the high er modulus is due to

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' ! the primary load support of collagen fibers (Roach & Burton, 1957) Based on morphometric data, the lack of load support in the collagen fibers at low strain is believed to be the result of the orientation and alignment of collagen fi bers within the arterial wall (Roach & Burton, 1957)(Sokolis, Kefaloyannis, Kouloukoussa, Boudoulas, Marinos, & Karayannacos, 2006) The significantly increased slope of the stress strain curve, at larger deformations is due to the primary load support of collagen and a significantly higher elastic modulus of collagen compared to elastin (Lammers, et al., 2008) Although the research presented here does not study, in particular, the phenomenon, it should be noted that the arterial wall exhibits visco elas tic characteristics throughout the stress strain curve. This feature adds a time and rate dependency to any stress or strain response of the arterial wall. The ideal elastic curve generally maintains this same shape, represented in Figure 1.1, but has var ying slopes and numerical values based on the animal, the location of the tissue in the pulmonary tree and many other physiological factors. Furthermore, the stress strain curve, does not necessarily remain static as physiological changes occur. Like oth er extra cellular matrices, the components of the arterial wall interact and change with the cells around them. As physiological changes occur, due to development or disease, the interaction between the cellular population of the arterial wall and elastin collagen and other connective tissues change. These changes can often result in dramatic changes to the mechanical characteristics of these proteins and the arterial wall itself (Reuben, 1971) (Stenmark, Fagan, & Frid, 2006) The elastic nature of the pulmonary arteries serves important roles in both the function of the pulmonary circulation and in the progression of disease. These roles will be summarized in the following sections.

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( ! Figure 1. 1 Idealized stress strain curve for pulmonary arterial tissue under axial tension 1.2.1.2 Elasticity And Compliance In The Pulmonary Circulation The elastic nature of the pulmonary arterial wall serves an essential function by temporarily storing mechanical energy in the pulmonary circulation. This feature is especially prominent and essential in the more proximal portions of the circulation (Grover, Wagner, McMurty, & Reeves, 1980) The elastic nature of the proximal arteries serves as energy storage to the circulation, which is essential beca use it reduces the peak pressure seen by the distal vasculature and maintains flow to the distal vasculature during diastole (Dobrin, 1983) This relationship between the arterial wall elasticity and the pulmonary circulation can be most easily understoo d through study of an electrical analogue. The simplest of such models, known as the "Windkessel" model, was designed by Frank as a two element

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) ! electrical circuit (Frank, 1899) In this model, represented in Figure 1.2 the energy storage in the arteries resulting from the elasticity of the arterial wall, is represented by a capacitor and the flow resistance of the arterioles and capillaries is represented by a resistive element. In both the hemodynamic and electrical models, the function of the arterie s as an energy store is apparent. Considering an oscillatory input to the electrical analogue, energy is stored in the capacitor (conduit arteries ) when the input current is increased. When the input is decreased, the stored energy is released as a curre nt flow through the resistive elements (arterioles and capillaries) This feature is similarly true for hemodynamic representation, only with a hemodynamic flow rather than a current flow. Although this representation is highly limited by it's simplicity it remains effective as a basic description of the function of arterial compliance, or capacitance in the pulmonary circulation. This feature is essential to the health of the distal vasculature because it reduces the peak flow during systole, maintains flow during diastole and provides a smoothing function to the dynamic pressures from the heart. Figure 1 2 T he two element Windkessel model in both hydraulic and electrical form. Adapted from (Westerhof & Lankhaar, 2009) A significant body of research has also shown that reductions in the compliant nature, or capacitance, of the pulmonary circulation are highly detrimental to the system. Resulting from decreased compliance in the conduit arteries, increased pulsatility an d decreased diastolic flow have been characterized as causing increased, detrimental

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* ! signaling of the distal endothelial cells (Chiu & Chien, 2011) The importance of changes in arterial compliance as a result of disease was further demonstrated by Reuben, who showed that in humans with both healthy and diseased pulmonary circulation, a decrease in the lumped compliance of the pulmonary system results in a higher mean pulmonary arterial pressure (Reuben, 1971) The study also correlated decreases in pulmona ry arterial compliance with increased pulmonary arterial resistance, which, along with systolic pulmonary arterial pressure is the classical diagnostic for PH. It has been further asserted that the stiffening of the arterial wall is a "natural consequence of chronic PH (Stenmark, Fagan, & Frid, 2006), (Chiu & Chien, 2011) 1.2.2 Pulmonary Hypertension and Arterial Compliance PH, defined as a mean pulmonary arterial pressure above 25[mmHg], leads to increased loading on the right ventricle of the heart, high rat es of morbidity and death (Hunter, et al., 2008) Recent studies have shown that the progression of the disease is related to decreased compliance of the arterial wall. Increased arterial wall stiffness and elastic modulus, caused by tissue remodeling, cause increased impedance and decreased compliance of the pulmonary arterial tree. This leads to increased loading on the right ventricle (Stenmark, Fagan, & Frid, 2006) and other detrimental effects. Even so, the majority of clinical diagnostics, presen tly used, consider only increases in overall resistance of the pulmonary circulation (Barst, et al., 2004) Such diagnostics neglect any consideration or measurement of the compliance of the pulmonary vasculature, which has been shown to greatly affect th e energy expenditure of the right ventricle (Engelberg & Dubois, 1959) Increases in the stiffness of the proximal PAs have been noted, clinically,

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+ ! in the presence of PH and studies of the artery wall stiffness have been shown to improve predictions of th e outcomes of patients in a clinical setting (Hunter, et al., 2008) Such studies have demonstrated a significantly decreased compliance in the pulmonary circulation as a result of PH (Hunter, et al., 2008) This leads to increases in right heart afterloa d, and may additionally be related to detrimental effects in the distal vasculature, such as endothelial dysfunction (Chiu & Chien, 2011) The decreases in the capacitive nature of the PAs have been attributed to increased smooth muscle cell activity (Ste nmark, Fagan, & Frid, 2006) and changes in the passive mechanics of the conduit arteries. Passive mechanics in the conduit arteries have been shown to change as a result of vascular remodeling and changes in the dominant load carrying components of the va scular wall, due to the increased internal pressure associated with the disease. The effects of these changes on the volumetric compliance of the proximal (i.e., pre hilar ) arteries have been well characterized in both in vitro studies (Lammers, et al., 2 008) and, to some extent, in vivo studies (Gan, et al., 2007) Due to the highly detrimental effects of mechanical changes in the pulmonary circulation, we believe it necessary to continually improve the understanding of arterial mechanics in the pulmonary circulation and the mechanical changes that occur due to PH. 1.3 Methods of Mechanical Characterization and Modeling of the Pulmonary Arteries and the Pulmonary Circulation In this section, a review of some of the most common methods of testing th e mechanics of arterial tissues is presented. The benefits and the limitations of these methods will also be discussed. Some of the different mathematical models of the entire pulmonary circulation are also discussed.

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, ! 1.3.1 Methods of Mechanical Testing 1.3.1.1 Uniaxi al Testing 1.3.1.1.1 Description Uniaxial testing is one of the simpler methods of testing arterial tissue, but it in is often considered one of the "gold standards". A section of artery is tested in an ex vivo setting and is generally submersed in a liquid that m imics the physiological environment of blood. This is often as simple as a liquid matching the temperature and pH balance. The tissue section is generally a long, thin strip of arterial tissue that has its longest dimension in either the longitudinal or circumferential axis of the artery. For the most accurate results, the longest dimension of the tissue should be at least 10 times the length of the second longest dimension of the section. Once the arterial tissue is sectioned, as described above, it i s mounted in an apparatus that applies a varying stretch along the longest axis of the sectioned tissue. A diagram of typical tissue mounting can be seen in Figure 1.3 During the stretching of the tissue, the testing apparatus generally records the force, and dis placement of the ends of the tissue. In most arterial tissue testing applications, the specimen is stretched at predefined rate of strain, although predefined rates of stress are occasionally applied instead. The tissue is also stretched until a predefin ed strain or force is achieved.

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! Figure 1 3 Typical uni axial loading diagram From this procedure, one gains a force displacement curve. In order to extrapolate a stress strain curve or the modulus of elasticity from this data, one must apply assumptions of material incompressibility, continuity and small deformation. Using these assumptions, the calculation for strain and stress cab be simply calculated as follows: = L L 0 L 0 Equation 1 1 Uni axial strain = F A Equation 1 2 Uni axial stress = A 0 L 0 L 0 Equation 1 3 Uni axial cross sectional area width,andlength,respectively; A elast istheareafractionofelastin; and isPoisson'sratio(0.5forincompressibletissue).Duetothe layeredstructureofthefenestratedelasticsheets,stressesforthe digestedelastinsamples( elast )werecalculatedwiththeconditionof incompressibilityappliedtothewidthdirectiononly.Tofacilitate modulus( E )calculations,stress-straindataforfreshandelastin samplesweretwithninth-andfourth-orderpolynomials,respectively.Theninth-andfourth-orderpolynomialsweredeterminedtobe thelowestorderpolynomialsnecessarytoachieveanaveragesquared correlationcoefcient R avg 2 0.995forallfreshandelastindatasets, respectively. E d d ( 4 ) Stiffness( # )isthederivativeofthewidth-normalizedforce(F n : forcedividedbycurrentwidth)bystrain,and,assuch,stiffnessis dependentonthicknessgeometryandrepresentstheextensiveequivalentofelasticmodulus. # d d ! F W $ % " d d & F n $ %' ( 5 ) Theconditionofincompressibilitywasappliedtothestiffness calculationtoaccountforanyvariationinwidthasafunctionof imposedstrain.F n datawerettopolynomialsinthesamemanneras wasusedforthestress.Unlessotherwisenoted,allresultsforthe materialparameters( E # )werecalculatedatastrainof35%,sothat tissuescouldbecompared.Strainshigherthan35%resultedinoneor moreofthestress-straincurvesextendingintothecollagen-dominant, strain-stiffeningregion.Atstrains ( 35%,anycomparisonbetween freshandelastinstress-straindatawouldbecomplicatedbytheactive loadingofcollagen.Sincethiscollagencomponentcannotberemovedfromthefresharterydataset,anycomparisonofthemechanicalpropertiesmadeatstrains ( 35%wouldincludecollagenand, therefore,notallowforthedirectcomparisonofelastinmechanical propertychangesfromthefreshtodigestedstate. Lame'sequationforstressinthick-walledtubes( L )(6)wasused todeterminethestrainsthatcorrespondtothemeasuredphysiologic pressures. L P i & r 2 # $ r # T % 2 $ r # T % 2 $ r 2 r r 0 $ 1 # % ( 6 ) Lame'sequationwasequatedtothepolynomialstress-strainfunctionandsolvediterativelyforthestrainsthatcorrespondtotheinvivo measuredsystolic,diastolic,andmeanpressures(P i ); r and r 0 arethe internalradiiofthearteryintheloadedandinitialstate,respectively. Theestimatedphysiologicalstrainswerethenusedtocalculatethe systolicanddiastolicmoduliusing Eq.4 Curvature( ) )ofthestress-straincurvewasusedtodeterminethe onsetofcollagenengagement(Fig.4). ) "* $ 1 # "+ 2 % 3 2 ( 7 ) Thesecond-orderderivativeinthenumeratorofthecurvature equationledtolargevarianceswhencalculatedfromthepolynomial ttotheoriginalstress-straindata.We,therefore,appliedazerophase,low-pass,ellipticdigitalltertosmooththedata.Anew ninth-orderpolynomialwasthenttotheltereddata,resultingin reducedcurvaturevariance. Averageprestrain-stiffeningcurvature( ) PSS )wascalculatedforthe strainrangebetween L and H ,where L equals20%strainand H equalsthestrainassociatedwithmaximumcurvatureminus20% strain(Fig.4).The L and H weredenedinthiswaysothatany curvatureassociatedwiththelow-strainloadingregionorhigh-strain strain-stiffeningregionwouldnotinuencethe ) PSS value.Transition strain( trans )wasthendeterminedbytherelationship: ) trans H 100 H ) max $ ) PSS ( 8 ) suchthat trans isassociatedwiththeonsetofcurvatureelevation; ) trans isthecurvatureofthestress-straincurveatthetransitionstrain; and ) max isthemaximumcurvaturecalculatedforagiventissue sample.The trans resultscomparefavorablywiththosepreviously Fig.2.Detailofmaterialtestingsystem(MTS)usedtogeneratestress ( )-strain( )dataforarterialtissuesamples. Fig.3.Typicalloading/unloadingcurvesforfreshandelastintissuetests.F n width-normalizedforce. H1453 ELASTINMECHANICSINPULMONARYHYPERTENSION AJP-HeartCircPhysiol VOL295 OCTOBER2008 www.ajpheart.org on December 29, 2011 ajpheart.physiology.org Downloaded from !"#$"%&'#"()*& +)",-./$"$*0(1& 2#")3&

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%. ! = A 0 W 0 t 0 Equation 1 4 Uni axial cross sectional area (strained) where was strain, was stress, L 0 and L were the unstrained and strained length of the tissue, respectively, F was the applied force, A 0 and A were the unstrained and strained cross sectional area, respectively, W 0 was t he unstrained tissue width, and t 0 was the unstrained tissue thickness. The modulus of elasticity is then the derivative of the strain with respect to stress. 1.3.1.1.2 Discussion This particular method of mechanical study has been used in to great success in the study of arterial mechanics in pulmonary hypertension, especially in animal models, of the disease (Sokolis, Boudoulas, & Karayannacos, Assessment of the Aortic Stress Strain Relation in Uniaxial Tension, 2002), (Lammers, et al., 2008), (Kao, et al., 2011) The method is also well established in tests of other engineering materials. This method allows relatively rapid and highly accurate testing within the constraints of its limitations (discussed below). There are also numerous, commercially available t esting apparatuses for such tests. On the other hand, this testing method also suffers its drawbacks when compared to other testing methods. The method does not allow any form of testing in situ or in vivo; rather, the artery must be fully removed and t hen sectioned, so it is limited to very localized testing. The method requires the assumption of material incompressibility to extract stress and strain data, which is not entirely accurate (Kao, Biaxial mechanical

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%% ! characterization and microstructure driv en modeling of elastic pulmonary artery walls of large mammals under hypertensive conditions, 2010) The method does not allow any measurement of stresses or strains in more than one axis simultaneously. This is detrimental to the overall accuracy of the test because longitudinal and circumferential stresses vary constantly in vivo (Dobrin, 1983) Finally, the method induces stress concentrations near the mounting points because the mounts constrain any strain in the axes parallel to the long axis, as c an be seen in Figure 1.3 1.3.1.2 Bi Axial Testing Method 1.3.1.2.1 Description The bi axial testing method, in many ways, is similar to the uni axial testing method described in the previous section. This method was, on the other hand, designed to remove some of the limitations present in the uni axial method. In this case, the section of tissue removed from the artery is as close to a square a s possible in the plane perpendicular to the radius of the artery. Figure 1.4 is an image of a somewhat typical tissue mount for a bi axial tissue testing system. The strings attached to the sides of the tissue are attached to four separately controlled l inear actuators (not included in the image), one on each side of the square tissue section.

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%& ! Figure 1 4 Uni axial mounting image. Adapted from (Kao, Biaxial mechanical characterization and microstructure driven modeling of elast ic pulmonary artery walls of large mammals under hypertensive conditions, 2010) After proper mounting, the tissue is then strained in tension along both the circumferential and the radial axes. In a similar fashion to the uni axial method, the force appli ed in both axes is measured as the tissue is strained. In this method, the rate of strain in both axes is pre defined and the tissue is strained to a pre defined value. In this particular bi axial testing method, the locations of the four dots on the tiss ue sample were tracked with a digital camera while the tests were conducted. In this way the strain was directly measured. Other methods of bi axial testing determine the strain of the tissue based on the displacement of the linear actuators and the dime nsions of the tissue. In either case, the data from these tests, along with the dimensions of the tissue section, are able to provide data with regards to the stress and strain curves, strain energy fields, the modulus of elasticity, and the Poisson's Rat io of the tissue. Because this piece does not focus on this particular method, the calculations are not included here.

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%' ! 1.3.1.2.2 Discussion The main benefit of the bi axial testing method is the ability to apply predetermined strain in both the radial and the long itudinal axes of the tissue, simultaneously. This is a significant improvement in comparison to the uni axial testing method Because of this feature, it is no longer neces sary to assume a Poison's ratio for the material, and more robust strain energy fu nctions can be determined for the material. Furthermore, this testing method can more closely mimic the in vivo conditions of the artery. The pressure in the artery and the constraints applied by surrounding tissues apply forces in both the longitudinal and radial directions, which are not accounted for in uni axial testing, but can be applied in bi axial tests. On the other hand, the bi axial testing method still suffers many of the drawbacks of the uni axial method. Both methods are significantly lim ited in that they can test only highly local mechanical features of the artery. The bi axial test cannot perform tests in situ or in vivo. A final drawback to the method is that the testing time and preparation time, specifically tissue mounting, is sign ificantly longer than that of uni axial testing methods, making the test impractical for use in large sample populations. Despite these limitations, Kao was able to significantly improve the understanding of pulmonary arterial mechanics in Pulmonary Hyper tension using this method (Kao, Biaxial mechanical characterization and microstructure driven modeling of elastic pulmonary artery walls of large mammals under hypertensive conditions, 2010)

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%( ! 1.3.1.3 X ray CT Imaging 1.3.1.3.1 Description Computed tomography X Ray imagi ng has recently been used as a method of studying arterial mechanics in some more recent studies. This method is one of the more technologically advanced methods of studying the tissue mechanics of pulmonary arteries. In this method, the entire lung of t he animal is excised but the circulation is left intact within the lungs The circulation is then inflated to predefined pressures, generally using a pressure head. The fluid used to induce this pressure is generally chosen to be highly opaque to x rays in order to give the arteries high contrast in the x ray imaging. Fluids can also be chosen to have a high enough surface tension to prevent their entry to the capillary bed, preventing inflation and imaging of the venous system (Karau, et al., 2001) A t this point, x rays are acquired of the lung from multiple angles, to create a complete circle around the lungs. All images are taken with imaging planes perpendicular to the radii of the main pulmonary artery. After acquiring the images digital, geome tric processing is preformed on the two dimensional x ray images to generate a digital volume representing the inflated arterial tree. Many different algorithms have been developed to calculate the object volumes based on two dimensional images. Each req uires varying levels of pre processing of the initial images, processing power and time and each method results in varying levels of accuracy in the final volume (Herman, 2009) After generating the digital volume, the internal area of the artery can be d etermined on essentially any plane chosen by the investigator, using computer algorithms.

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%) ! By repeating this process with varied internal pressures, a pressure verse cross sectional area or pressure verse diameter curve can be developed for the pulmonary arteries at any point in the pulmonary arterial tree. From this data, a stiffness verse force per longitudinal length curve can be determined, where stiffness is the modulus multiplied by the instantaneous wall thickness. Because the x ray opacity of the arterial wall is too similar to the surround tissue, the thickness of the arterial wall cannot be determined using this method. Without assuming a tissue thickness, a stress strain curve cannot be determined. 1.3.1.3.2 Discussion The use of X ray computed tomography in the determination of pulmonary arterial mechanics has many significant advantages over other methods. One obvious advantage is the ability to gain mechanical data for many different locations in the pulmonary tree, in a single test. The method also allows for testing in situ and in vivo for animal models (Karau, et al., 2001)(Herman, 2009) allowing mechanical characterization with in a more physiologically accurate environment. In fact, the lungs can even be inflated during the test to mimic different stages of respiration when in an ex vivo setting. Finally, the measurement resolution of this method is very high, allowing measurement of very small arteries. This a llows the use of smaller animal models and the testin g or more distal arteries. On the other hand, the method also suffers its drawbacks. The most obvious of which is the availability of the test equipment. Not only does the equipment require a high resolution, digital x ray system, but also requires a com puter with the proper software and the computational power to perform the image analysis. A second

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%* ! drawback is the lack of data regarding the artery wall thickness. This makes determination of wall strain, and therefore modulus, impossible without makin g assumptions of these dimensions or further dissection and measurement Lacking this data, changes in stiffness due to wall thickening and changes due to change in modulus are indistinguishable. Finally, the need to take many x ray images for each press ure point makes the process slow and makes the acquisition of high resolution data curves impractical. 1.3.1.4 In Vivo Testing Methods 1.3.1.4.1 Description Many different in vivo arterial mechanic testing methods exist and have been used to varying degrees of success. A detailed description of each method is beyond the scope of this paper. Instead, a brief description of some of the available methods is provided. Earlier studies of the pulmonary circulation were generally highly invasive and limited in their scope. A study by (Patel, Schilder, & Mallos, 1960) examined the local mechanical characteristics of the main pulmonary arteries of dogs. In this method, the dogs were studied under anesthesia. The pressure of the pulmonary artery was measured using a catheter, while the diameter of the artery was determined using a custom designed electrical diameter caliper. This method, although highly invasive, provided a significant bank of dat a describing the mechanics of the pulmonary tissue. More contemporary methods have been able to extract similar data, with less invasive methods. These tests have allowed for study in human subjects and have improved the clinical relevance of such metho ds. Some of these methods utilize cardiac

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%+ ! gated x ray computerized tomography to image the dimensions of the large pulmonary arteries and catheterization of the pulmonary arteries to determine the instantaneous pressure of the arteries (Moore, Scott, Flow er, & Higenbottam, 1988) As discussed in the previous X Ray CT Imaging section, the data resolution of such methods is limited. Furthermore, in human subjects, th e image resolution is limited to lowering subject radiation exposure and the availability n on toxic blood borne x ray contrast enhancing agents. Similar methods have utilized ultra sonic imaging to determine the wall thickness and diameter of the main pulmonary artery (Hunter, et al., 2010) Other in vivo methods have been developed that do not directly measure the diameters of the arteries. Instead these methods utilize pressure velocity catheterization, or non invasive pulse wave ultra sonic Doppler imaging (Kosturakis, Goldberg, Allen, & Loeber, 1984) Such methods are then able to extr act a time varying pressure vs. flow relationship of the blood flow. By analyzing this data in the frequency domain, complex impedance, analogous to electrical or acoustic impedance, can be developed. Based on this impedance, and different mathematical m odels of the arterial flow (discussed in further detail below), a global compliance of the circulation can be developed (O'Rourke, 1982) 1.3.1.4.2 Discussion In vivo testing methods of arterial mechanics have been readily sought over the past decades in the study of pulmonary hypertension. Such methods have many intrinsic advantages over other methods of mechanical studies. These methods allow the study of the mechanics of the pulmonary circulation in a setting that matches exactly, or close to

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%, ! the true physiolog ical environment of the tissue. Furthermore, the development of such methods is necessary for the clinical application of any arterial mechanics study. Many of such studies are, on the other hand, limited by their invasiveness. For many of these studie s, the process is highly invasive, requiring sedation and anesthesia of the subject. The implementation of which, can have adverse consequences on the test due to reduced blood pressure and heart rate. Furthermore, the stress and strain ranges tested us ing in vivo methods are dictated by the blood pressure of the subject during the time of the test. 1.3.2 System Models 1.3.2.1 Motivation Mathematical, computational and physical models have been readily used in engineering and scientific applications throughout history. Models such as these are often sought to study physiological systems, such as the pulmonary circulation for many reasons. In many cases, these models provide access to information that cannot be readily measured, due to the availability of testing methodologies or the invasiveness of such tests. Such models can be used to predict the vascular mechanics and characteristics throughout the arterial tree. Some models can determine the effect of arterial wall distensibilty, or predict the energy expenditure of the heart during the cardiac cycle. Models, such as these, can be useful in predicting the effect of changes in the pu lmonary circulation and are therefore useful in diagnostic and prognostic applications. 1.3.2.2 The Windkessel Model The simplest version of the Windkessel model was briefly introduced in the Elasticity And Compliance In The Pulmonary Circulation section. The Windkessel

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%! model makes an analogue between the pulmonary circulation (or systemic) and an electrical circuit. Input pressure is modeled by a source voltage and blood fl ow by electrical current. The simplest model lumps together the global capacitance of the pulmonary circulation and the total resistance of the system. From these two factors, a two element electrical model of the entire circulation can be created as de picted in Figure 1.2 More complex Windkessel models have also been proposed that include inductors and/or second resistors to further model the inertia of a moving mass of blood and the resistance of the conduit arteries, respectively ( Figure 1.5 Figur e 1.6 ). Such models are especially useful for determining the variances in the energy expenditure of the heart (voltage source) with changes in the global resistance or compliance of the circulation. Such models have also proven useful for predicting the global compliance of the circulation based on the decay rate of pressure within the main arteries immediately after systole. Similarly, measured arterial flow can be used to predict the pressure using the model. Using the sum of least squares on the el ements of three or four element Windkessel models, the elements of the model can be adapted to give the most accurate representation of the measured pressures, yielding estimates of the global capacitance, resistance and inductance of the circulation (West erhof & Lankhaar, 2009), (Wang, O'Brien, Shrive, Parker, & Tyberg, 2002) Figure 1 5 Three e lement Windkessel in both hydraulic and electrical form. Adapted from (Westerhof & Lankhaar, 2009)

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&. ! Figure 1 .6 Four e lement Windkessel in both hydraulic and electrical form. Adapted from (Westerhof & Lankhaar, 2009) 1.3.2.3 The Transmission Line Model The transmission line model can be simply viewed as an expansion of the Windkessel model. The transmission line model, as is implied by the nam e, based on analogue between the circulation and electrical transmission lines. Instead of single components, like the Windkessel model, the transmission line model breaks the circulation into many different segments. Each segment of the circulation i s then modeled like an individual Windkessel model. The segments are then connected in series. The capacitance, resistive and inductive features of each segment can be estimated based on the wall thickness, modulus of elasticity, young's modulus, fluid c haracteristics of blood and the geometric dimensions of the artery section. Equation 1.5 Equation 1.7 describe, in the simplest form as presented by (Rideout & Dick, 1967) the resistance, inductance and capacitance of fluid motion in an elastic tube. Here E is the modulus of elasticity, h is the wall thickness, #z is the longitudinal length of the segment, r is the average radius of the segment, $ is the density of the fluid (blood) and is the viscosity. The application of this model results in lar ge system of differential equation s. For more complex models, this system of equation s does not have an analytical solution but requires numerical methods to solve the system (Avolio, 2009) An alternative method is to build the

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&% ! physical circuit and appl y the desired input function and measure the desired outputs (Snyder, Rideout, & Hillestad, 1968) R = 81 8 z r 4 Equation 1 5 Resistance of elastic tube R = 9 4 # z r 2 Equation 1 6 Inductance of elastic tube C = 3 r 3 z 2 Eh Equation 1 7 Capacitance of elastic tub Transmission line models offer increased utility, in many ways, compared to the less complicated Windkessel model. Such models are able to predict the effect of localized changes on the entire circulation. These models are also able to account for pressure wave reflections due to varying impedances at branch points These models generally provide a more accu rate representation of the pressure flow response of the circulation for varied input pressures compared to the simple Windkessel method. On the other hand, transmission line models of the circulation generally require a large set of data to describe the local arterial dimensions and mechanical characteristics. Because such data often doesn't exist in specific diseases, such as pulmonary hypertension, the models may result in significant inaccuracy due to the number of assumptions that must be made.

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&& ! 1.3.2.4 Compu tational Fluid Dynamics The use of computational fluid dynamics has only become relevant in practice since the 1990's (Steinman & Taylor, 2005) This is mainly due to the advance of computer technology. In this practice, digital, three dimensional repres entations of the blood volume within an area of interest are developed. These models are generally based off computed tomographic x ray images or magnetic resonance images of the circulation. The volume is then discretized into much smaller three dimensi onal sections. Within each section, the flow is generally described by Navier Stokes equation s for fluid flow. The neighboring sections of each section determine the boundary conditions of that particular section, or the boundary conditions applied to th e edges of the volume. The result of this is a very large system of equation s that can be computationally solved for highly complex flows. Similarly, a volume can be created for the vessel walls of the circulation. This volume can similarly be discretiz ed and mechanical constraints can be applied. The interaction between the vessel walls, the mechanics of these walls and their effects on the hemodynamics of the pulmonary circulation can then be accurately modeled. Such models can produce accuracy and de tail beyond the capabilities of most other models. These models can produce data beyond what is clinically measureable and have the potential to deliver significant information in the analysis of disease progression in PH and other circulatory diseases. The accuracy of computational fluid dynamic models is highly dependent on detailed knowledge of the mechanical nature of the vessel wall throughout the tree. It is further dependent on the number and size of discrete

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&' ! sections. Decreased section size can greatly increase the accuracy of such models, but also drastically increase computational time and demand. For this reason, most studies focus on specific segments of the circulation and cannot compute flow in the entire tree due to the computational dema nds (Steinman & Taylor, 2005) 1.4 Conclusion The pulmonary circulation is a highly complex system. The proper function of this system is highly dependent upon the mechanical characteristics of the arterial walls, which are in themselves, very complicated and highly dynamic. These characteristics vary significantly with changes in physiology, disease and development. Due to the level of complexity in the system, many different methods of modeling the pulmonary circulation have been developed. The most ac curate and detailed of these models are reliant on the mechanical characterization of the arterial walls at varied locations along the pulmonary tree. Even the most robust techniques for testing such mechanics are in some ways limited. In order to develo p better models of the pulmonary circulation in healthy and pulmonary hypertensive subjects, one must first characterize the mechanics of the pulmonary arteries at different locations throughout the pulmonary tree. This may require the development of a cu stomized testing methodology for this purpose.

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&( ! 2 Validation Of A Pressure Diameter Method For Determining Modulus And Strain Of Collagen Engagement For Long Branches Of Bovine Pulmonary Arteries It should be noted that the contents of this chapter is adapted from our previously published work in the Journal of Biomechanical Engineering (Reusser, Hunter, Lammers, & Stenmark, 2012) The only changes made a re to improve the readability and to match the formatting of the rest of this document. 2.1 Motivation Tissue mechanics of the pre hilar pulmonary arteries have been well documented (Lammers, et al., 2008) (Tian, et al., 2011) providing significant insight into the role of the passive tissue mecha nics of these arteries in PH. As conduit arteries can be classified as arteries of diameters greater than 1[mm] (Grover, Wagner, McMurty, & Reeves, 1980) these studies have not quantified the mechanics of 37% of the conduit volume (Singhal, Henderson, Ho rsfield, Harding, & Cumming, 1973) Because compliance is a function of the entire bed of conduit arteries, the tissue mechanics of the post hilar arteries should also be studied to truly understand the pathophysiology of arterial stiffening in PH, which would require hundreds of tests using traditional testing methods. The goal of this chapter is to provide validation of a pressure diameter (PD) measurement of long, post hilar pulmonary artery branches, as a method of comparing the strain of collagen enga gement and the elastic modulus for multiple generations of the pulmonary artery, between different animal groups. It is believed that the PD method will provide an improvement over uniaxial stress strain measurements of individual segments by improving th e rapidity of testing and limiting the effect of end constraints, while maintaining a similar level of accuracy.

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&) ! 2.2 Methods 2.2.1 Dissection The main branches of left and right post hilar pulmonary arteries were isolated from five adult cows and three neonatal c alves from both of the largest two lung lobes. Dissection was performed from the hilum and moved distally until the outer artery diameter reached approximately 3[mm]. At each branch point, the largest diameter branch was followed for dissection and separ ated from the smaller branches, which were not isolated. Any loose connective tissue was removed. In this way, a continuous section of artery was removed from each lung lobe with a range of diameters from the largest diameter artery in the lobe to a smal lest outer diameter of approximately 3[mm]. All arteries were tested within 72 hours of animal sacrifice and tissues were stored in calcium and magnesium free NaCl PBS buffer (0.01[mol/l], ionic strength 0.15, pH 7.4). 2.2.2 PD Method Inflation After isolation, longitudinal sections were chosen between each major branch and marked with two small dots (diameter = 1 3[mm]) of Loctite 280 (Henkel Corpoation, Westlake, OH) black glue. The two dots per section were placed in approximately the same location circumfer entially and separated longitudinally by approximately 10[mm]. Sections were chosen to be longitudinally distant from major branch points, while avoiding proximity to holes, branches or tears. Figure 2.1 is an image of the arterial marking. A thin latex liner (0.0685[mm] wall thickness, 10.2[cm] circumference) was inserted along the lumen of the arterial section to prevent pressure leaks through the branches. A liner diameter larger than the tissue diameter was chosen to avoid stretch or load support in the liner. The proximal end of the artery was cannulated and secured

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&* ! with umbilical tape. A thin nylon line was fed through the artery to maintain the arteries longitudinal alignment in the tissue bath during testing. This string was attached to the c annulation point and the same point on the opposing wall of the tissue bath. The tissues were submerged in calcium and magnesium free NaCl PBS buffer (0.01[mol/l], ionic strength 0.15, pH 7.4). The distal end of the artery was closed with a suture, preve nting pressure leaks while allowing longitudinal movement. Each arterial section was then inflated with water to an internal pressure of approximately 110mm Hg (gauge). A Millar Mikro Tip SPC 350 (Millar Instruments INC., Huston, TX) catheter, just upstre am of the cannulation point, measured pressure. Figure 2.2 provides a basic schematic of the testing setup. Prior to any pressure diameter measurement, each tissue was subjected to 9 cycles in which the internal pressure was increased from atmospheric pre ssure to 110[mmHg] (gauge) and then released. In this way, the artery was pre strained and any hysteresis was reduced (Bergel, 1961) Immediately following artery pre strain, PD measurements were made. Increasing the head height applied through the art ery cannula gradually increased internal pressure. This was done using a constant flow DC pump, with a flow control valve used to limit the rate of change in the height of the pressure head. As the internal artery pressure was increased, digital photogra phs of the entire tissue lengths were taken with a Cannon Rebel XTi (Canon U.S.A., Lake Success, NY) with an EFS 55 150mm (Canon U.S.A., Lake Success, NY) zoom lens, at a rate of 1.7[Hz]. A ruler with inch markings was also placed in the imaging plane of the artery, which enabled determination of pixel length. The camera shutter was triggered by a transistor driven switch, signaled by a 1.7[Hz], 5[V] peak to peak square wave signal. In this way, the shutter was released at

PAGE 39

&+ ! every moment the voltage wave r eversed polarity from negative to positive. By simultaneously recoding the voltage wave and the pressure signal from the catheter on a 12 bit data acquisition system the internal pressure at the time of each image was determined. The images were used to measure the outer diameter of the artery and the longitudinal distance between the two dots in each section. Thus, the result was a pressure diameter data point and longitudinal strain for each image. Figure 2 3 is a typical pressure diameter plot. Figure 2 1 Image of excised pulmonary artery branch showing placement of Loctite dots

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&, ! Figure 2 2 Basic schematic of PD test setup Figure 2 3 Typical pressure diameter curve for PD test

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&! After completion of the PD test, the internal pressure was relieved and the tissue was removed from the bath. The tissue was then cut twice along the plane normal to the longitudinal axis of the artery in each section. This formed rings with a width of 1[mm] 3[mm] for each sectio n. Using the same camera and lens, a digital photo was taken of each ring with the imaging plane normal to the longitudinal axis of the ring. Again, a ruler was placed in the imaging plane. Using these images, the wall thickness was measured for each se ction. This was accomplished by tracing regions of interest around the inner and outer edges of the ring. The difference between the two areas was then divided by the circumference, resulting in the average, un stretched thickness. After taking images o f the rings, each ring was opened, creating a circumferential strip. The circumferential strip length was measured using digital calipers, giving the circumference of the artery for each section. A flow diagram of tissue sectioning is given in Figure 2 4

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'. ! Figure 2 4 Flow diagram of tissue sectioning for PD testing Image processing and measurement was conducted using custom written sof tware in Matlab R2011a (The Math Works, Natick, MA). Tissue diameter was determined for each section by counting the number of pixels in the radial direction from edge to edge of the tissue at the most proximal Loctite marking of each section. Large data sets used in the PD method made manual edge selection impractical, so it was automated using the Canny method, included in Matlab's image processing toolkit. Changes in the orientation of the radial axis due to changes in pressure were taken into account by manually orienting every tenth image so the longitudinal axis of the measured section was horizontal. A cubic spline was then created relating the rotation of the longitudinal axis to the internal pressure. Diameter measurements were made perpendicul ar to the orientation of the longitudinal axis described by the cubic spline. It

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'% ! was believed that significant changes in the longitudinal axis occurred only in the vertical direction and were due to buoyancy forces caused by air pockets in the system. A s there were no significant forces in the horizontal direction (perpendicular to the imaging plane) and such motion was constrained by the nylon line, it was assumed that the longitudinal axis remained in the imaging plane. The longitudinal distance betwee n the two Loctite dots in each section was measured as a determinant of the longitudinal strain. This was done by manually selecting the center of each of the two dots in every tenth image and measuring the distance in pixels along the already defined lon gitudinal axis. A cubic spline was then created describing the longitudinal distance between the two markings in each section as a function of pressure. 2.2.3 MTS Method Stress strain data was acquired with an MTS, Insight 2 (MTS Systems, Eden Prairie, MN) ma terial testing system with a 5[N] load cell. Tissue strip widths were measured with digital calipers. The circumferential strips were tested in an auxiliary environmental chamber with the same buffer solution as storage and pressure diameter testing. Ti ssues were pre strained by applying 9 extension relaxation cycles and data was collected on the 10th cycle. Tissues were strained at a rate of 10% strain per second in the circumferential direction until collagen engagement was fully formed. The MTS test ing method was based on the previous work of Lammers et al (Lammers, et al., 2008) 2.2.4 Ad Hoc Variance Testing During analysis of the data, a large variance in the difference between modulus calculated by PD and MTS testing was noticed. For this reason, fur ther testing was done

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'& ! to determine the variance of each section for both testing methods. This was done by conducting the MTS and PD tests at five different locations within the same section of an artery. This was completed for four different arterial se ctions. 2.2.5 Ad Hoc Longitudinal Strain Variance Testing There was concern that the measured longitudinal stretch may not be representative of the average longitudinal stretch for the section of artery being tested. Although sections were carefully chosen to avoid branch points and tears in the artery, it was possible that the locations marked for longitudinal measurements contained non uniformities at varying radial locations that would prevent accurate results. For this reason ad hoc tests were preformed to determine the variance of the longitudinal strain at different radial locations but the same longitudinal location. This was done by performing PD tests on six sections in two different arteries. In each section, the longitudinal strain was measured nor mally, except that it was measured at five different radial locations. The standard deviation of the measured strain was then found for each section at five evenly distributed pressures ranging from atmospheric to ~110 mmHg. 2.2.6 Calculations 2.2.6.1 Strain and Stres s Cauchy stress and strain were calculated for the MTS data sets using assumptions of material incompressibility, continuity and small deformation. Using these assumptions, the calculation for strain and stress were as described in Equation 1.1 Equation 1.4. Stress strain curves were developed for the pressure diameter method using Lame's Law. For these calculations, material incompressibility, continuity and small deformation were assumed. Lame's Law further requires the assumption of an infinitely lon g tube of

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'' ! constant diameter. Using these assumptions, the stress and strain were calculated as follows: = D D 0 D 0 Equation 2 1 Pressure diameter strain = ( D 2 t ) P i DP 0 2 t Equation 2 2 Pressure diameter stress t = t 0 D 0 d 0 Dd Equation 2 3 Pressure diameter strained wall thickness where D 0 and D were the unstrained and strained outer diameter, respectively, P i and P o were the inner and outer pressure, respectively, t 0 and t were the unstrained and strained wall thicknesses, respectively, and d 0 and d are the unstrained and strained longitudinal distance between the Loctite marks in each section, respectively. 2.2.6.2 Engagem ent Strain For the purposes of comparison, collagen engagement points were defined for both the MTS method and the PD method. For both methods, a Ninth order polynomial was fit to the stress strain trace. After application of the polynomial fit, the coll agen

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'( ! engagement point was defined as the point of maximum curvature of the polynomial within the range of the tested data points. The curvature was calculated as: = ' ( 1 + 2 ) 3 / 2 Equation 2 4 Curvature of a function where the stress derivatives are taken with respect to strain. Prior to polynomial fitting, data smoothing of the stress strain trace was necessary for the PD method due to noise introduced by the edge (diameter) detection process. Although the use of automated ed ge detection for diameter measurement was typically very accurate as shown below, it occasionally introduced noise to the stress strain curve by improperly selecting the edge of the artery due to tissue discoloration or the presence of connective tissue. This error appears as noise, rather than a consistent offset for each sample, due to inconsistent radial orientation of the artery with changes in pressure and artery motion due to fluid flows within the tissue bath (caused by pressure leaks in the artery or artery liner). The data was smoothed using a moving average filter. Smoothing was conducted with the minimum span size, to produce a smooth polynomial fit. The maximum smoothing span for all data sets used was a span of 7[data points] and an average span of 5.3[data points]. Figure 2 5 shows the original, unsmoothed stress strain curve with a solid line and the smoothed data curve with a dashed line. This figure illustrates the effectiveness of the smoothing function for noise reduction while maintaining the shape of the curve.

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') ! Figure 2 5 Smoothing function applied to typical stress strain curve using PD method 2.2.6.3 Modulus The modulu s of elasticity was defined for both measurement methods as the slope of the stress strain curve. The modulus was calculated at 30% strain for all tissue sections. This strain level was chosen to maintain consistency as data for this strain was present i n all tissue data sets and was lower than engagement strain for all tissues. The modulus was determined by applying a linear fit to the stress strain curve between 27.5% strain and 32.5% strain, using the least squares method. The modulus was then define d as the slope of the linear fit. 2.2.6.4 Error Theoretical error was calculated for the stress and strain determined by the PD method. Precision error was defined as half of the resolution of the measuring device for each measurement. Random error was defined using a tissue that demonstrated typical d eviation from the MTS method in the PD data set. For the majority of measurements, random error was defined as the standard error in a population of 5 sample

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'* ! measurements. For the diameter measurements, random error was defined as the standard error in a population of 10 sample measurements, as 10 measurement samples were taken in an effort to reduce noise in the diameter measurement during all tests. Unlike the other measurements, error in the diameter was the result of four different sources: random er ror, precision error, random error in the orientation of the longitudinal axis, and precision error in the orientation of the longitudinal axis. Total rotational error was defined as: E D = D 2 ( [ 1 c o s ( E p a ) ] 2 + [ 1 c o s ( E r a ) ] 2 + E p 2 + E r 2 Equation 2 5 Error due to rotation of artery in PD testing where E D was the total error of the diameter due to longitudinal alignment error, E pa was the precision error in longitudinal alignment (degrees), E ra was the random error in longitudinal alignment, E p was the precision e rror in diameter measurement, E r is was the random error in diameter measurement and D was the measured outer diameter of the tissue. 2.3 Results 2.3.1 Modulus The modulus of elasticity was determined for 35 tissue samples with on e outlier removed, resulting in 34 samples for both the PD method and the MTS method. The average slope found was 118[kPa], which represent typical values as reported by Lammers et al (Lammers, et al., 2008) The mean of the difference (MTS method PD me thod) between the modulus found using both methods was determined as 8.7[kPa].

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'+ ! The standard deviation for the differences between the two methods was determined as 32.7 [kPa]. A paired t test did not show a significant difference between the results of t he two tests at a 95% confidence interval. F i gure 2.6 is a Bland Altman plot comparing the modulus for the two methods. These plots are presented through the remainder of the chapt er, so we provide a brief explanation. The x axis shows the mean value of both measurement methods for each data point. The y axis is the difference between the measured values. The dashed line is the mean of differences between the two test ing methods for each data point and the dot dashed lines represent +/ two standard deviations of the differences. When two testing methods are similar, the mean line should be close to zero and the magnitude of the vertical distance between the mean line and each data point should be small in comparison to their value on the x axis. Finally, there should be no obvious trends in the data points. Figure 2 .6 Bland Altman plot for modulus of elasticity, PD vs Uniaxial

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', ! 2.3.2 Engagement Strain The Engagement Strain was determined for 31 tissues samples with one outlier removed, resulting in 30 samples for both the PD method and the MTS method. Four tissues were not included because they were not strained to the point of collagen engagement duri ng PD testing, as determined by the MTS method. The average calculated engagement strain for the tests of calves using both methods was 51.3%. This value compares well with a study preformed by Lammers et al (Lammers, et al., 2008) where engagement str ains were reported as 49% and 51% for control and hypoxic calves for the main pulmonary artery. The mean of the differences of collagen engagement strain (PD method MTS method), as determined by the two methods, was 0.0212% strain. The standard devia tion of the differences of collagen engagement strain was 0.0417% strain. On the other hand, a paired t test did show a significant difference between the results of the two testing methods (p=0.007 Figure 2.7 is a Bland Altman plot comparing the collagen engagement strain for the two methods.

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'! Figure 2 .7 Bland Altman plot for collagen engagement strain, PD vs Uniaxial 2.3.3 Theoretical Error Calculation of the theoreti cal error was described in the methods section. The maximum relative error found for the selected tissue sample was found as 20.3%. Each error element was set to zero individually, and error was recalculated to determine which measurement contributed the most to the error. It was determined that the majority of the error is due to the high error in precision of the longitudinal length measurement. With the precision error of the longitudinal length set to zero, the remaining error is only 7.8%. It shoul d be noted that the estimate of precision error in longitudinal strain is likely a significant overestimate of the true error because of the care used in selecting the center of the dots used to measure the longitudinal stretch. This assumption is support ed by the random error in longitudinal strain, which was approximately 13% of the calculated error in precision. Figure 2.8 is a typical stress strain curve calculat ed with the PD method with error bars plotted.

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(. ! Figure 2 .8 Typical PD and MTS stress strain curves with PD error bars 2.3.4 Ad Hoc Variance Testing The four tissue sections used for variance testing showed an average standard deviation in measured modulus 1 1.6% of the mean modulus for the PD method and 17.6% of the mean modulus for the MTS method. Using a t test and a 95% confidence interval, it was shown that these two means couldn't be assumed different. On the other hand, equivalence of the two methods was not established unless an equivalence interval equal to or greater than 38% of the average value of the standard deviation of both groups was assumed at a 95% confidence interval. Equivalence was established as described by Hatch (Hatch, 1996)

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(% ! 2.3.5 Ad H oc Longitudinal Variance Testing Analysis was preformed by defining the error in each longitudinal strain measurement as the difference between the measured longitudinal strain and the average longitudinal strain measured at the corresponding pressure an d longitudinal location. The mean error found was 2.6% strain and the standard deviation of the error was 3.1% strain. The maximum error found over 120 data points was 15% strain. When the error is applied to the calculation of thickness ( Equation 2.3) the error in thickness is also 2.6% and 8.7% of the measured thickness for the mean error and the mean error plus two standard deviations of the error. These values also approximate the er ror in the calculated stress ( Equation 2.2) if it is assumed that t he diameter of the artery is significantly larger than the thickness. 2.4 Discussion The results of the tests indicated that the PD method is comparably effective to the uniaxial test method for making comparisons of the strain of collagen engagement. The mean of the differences between the engagement strains represented only 3.3% of the average engagement strain of both methods. This small value indicated little or no difference between the methods and this difference was easily accounted for by the o verall theoretical error calculated for the PD method. Furthermore, there was no apparent trend in the error data that would have indicated systematic error. The standard deviation of the differences between the engagement strains represented only 6.5% o f the average engagement strain of both methods. This small standard deviation showed that not only was the mean of the differences small, but it was consistently small over the entire population of tissues tested. Even so, it was also shown that there w as a significant

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(& ! difference between the two test methods for engagement strain using a paired t test. We believe that this is not a significant detriment to the PD testing method, as the mean difference between the two methods is very small in comparison to the actual strain of engagement and remains consistent as can be seen by the low standard deviation in the difference between the two methods. Furthermore, we present this testing method as a means of rapidly comparing the engagement strains between di fferent animal groups, and not a method for determining the precise in vivo engagement strain. Similarly, the results of the tests indicated the PD method was well correlated to the uniaxial test method for determining the modulus of the elastin. The mean of the differences between the two methods was equivalent to 7.4% of the average modulus. This difference was not shown to be significant using a paired t test. Error calculations were also preformed to demonstrate the effectiveness of the PD method. Th e maximum, relative, theoretical error in the stress measurement, in the range of stress normal for the PD method, was found to be 20.3%. Although this error was relatively high, a large portion of this error was due to the assumed precision of the longit udinal stress. Therefore, the use of an automated dot tracing algorithm would greatly reduce the error when used in place of the manual dot selection. This method was not used because the proximity of the two dots in each section caused automated dot tra cing algorithms to often select the wrong dot. It is believed that an improved algorithm could solve this issue The tests preformed showed the utility of the PD method for determining differences in the strain state of collagen engagement for long pulmonary arterial branches, excised from healthy and hypertensive calves and cows. Further, the small

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(' ! average differen ce between the two methods indicates that the PD method was an effective predictor for changes in the elastic modulus of the elastin dominant region of the stress strain curve, between animal groups. The ad hoc longitudinal variance testing preformed in th is study indicated only small error based on the radial location of the placement of longitudinal strain markers. Although we do believe that the addition of multiple longitudinal strain measurements would increase the overall accuracy of the testing meth od, we believe that the spread in error found in the ad hoc testing indicates that the use of only a single measurement is acceptable based on the accuracy of the other measurements made in the study and the number of tissues tested in this study. Overall we believe that the validation of the PD method was a success. This method allowed a significant decrease in testing time and effort, in comparison to the MTS method, because sections of multiple different diameters were tested simultaneously and the da ta correlated well with data collected using MTS methods. Finally, the data collected in these tests showed the validity of lining the artery lumen with a latex liner to prevent pressure leaks during a PD test. This new testing method also suffered its limitations. Although the mean difference in modulus between the two methods was small, the standard deviation of the differences was found as 27.8% of the average modulus. We believe that although this indicated a high degree of variation over the sampl e population, this could be the result of inconsistencies in the tissues and not error in the method. This was supported by the mutually high standard deviation shown in the ad hoc variation testing. Furthermore, there was no apparent trend in the error t hat would have indicated systematic error.

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(( ! The PD method was also less effective than the MTS for testing localized changes in stiffness. The PD method applied consistent pressures over the entire section and should therefore have given a stress strain curve that was representative of the average material mechanics for the entire section. The MTS was able to test very specific circumferential strips. This was not believed to be useful for the majority of compliance studies in PH. Finally, both the PD and MTS testing methods presented here did not match the in vivo, longitudinal stretch of the arteries. Because of inhomogeneity in the arterial wall material, the exact stress strain characteristics of the tissue, in vivo, cannot be predicted exactly, by tests with stress or strains prescribed only in the circumferential direction. It is for this reason, that we present this methodology as a tool for comparing the material characteristics of multiple animals, and not a method for predicting the true stre sses and strains present in vivo.

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() ! 3 Mechanics Of Posthilar, Pulmonary, Conduit Arteries In Hypertension 3.1 Motivation As mentioned previously, i ncreases in the stiffness of the proximal pulmonary arterie s have been noted, clinically, in the presence of PH. Studies of the artery mechanics have been shown to improve predictions of the outcomes of patients in a clinical setting (Gan, et al., 2007) These studies have demonstrated that large decreases in arte ry wall compliance are well correlated with increased likelihood of morbidity and mortality. Such studies have demonstrated a significantly decreased compliance in the pulmonary circulation as a result of PH (Barst, et al., 2004) This leads to increases in right heart afterload, and may additionally be related to detrimental effects in the distal vasculature, such as endothelial dysfunction (Chiu & Chien, 2011) The decreases in the capacitive nature of the pulmonary arteries have been attributed to inc reased smooth muscle cell activity (Stenmark, Fagan, & Frid, 2006) and changes in the passive mechanics of the conduit arteries. Passive mechanics in the conduit arteries have been shown to change as a result of vascular remodeling and changes in the domi nant load carrying components of the vascular wall, due to the increased internal pressure associated with the disease. The effects of these changes on the volumetric compli ance of the proximal (i. e., pre hilar ) arteries have been well characterized in bo th in vitro studies (Lammers, et al., 2008) and, to some extent, in vivo studies (Hunter, et al., 2008) To our knowledge, little has been done to quantify the changes in passive mechanics distal to the hilum of the lung in pulmonary hypertension, other t han studies of the lumped capacitance of the entire lung. This is believed to be a significant oversight,

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(* ! because the compliant nature of the pulmonary arteries continues well beyond this point, and is exposed to different hemodynamic loading. As discuss ed earlier, the use of mathematical models of the pulmonary circulation in PH can add to the understanding of the disease Because the more advanced of these models are reliant on an understanding of the artery mechanics throughout the pulmonary tree, it is essential to characterize the mechanics of the more distal pulmonary arteries in both health and PH This chapter will attempt to do so. 3.2 Methods 3.2.1 Animal Models Three groups in total were used: control, hypoxic, and brisket. The control and hypoxic animal groups consisted of neonatal male Holstein calves (70 110 lbs.). Hypertension was induced in the hypoxic group through a two week stay in a hypobaric chamber at 430 mmHg (4,600 m equivalent ai r pressure). Hypoxic animals were sacrificed at 430 mmHg pressure after 14 days at hypoxic conditions. All animals in these groups were studied and sacrificed at 15 +/ 2 days of age. A third group was brisket calves, which were born and raised for commer cial slaughter at altitudes of greater than 2500 meters. A subset of these animals naturally develops PH over their first summer of life similar to that seen in the neonatal model. These animals were tested for PH at 6 weeks and were sacrificed for study only if found to be hypertensive. 3.2.2 Dissection The dissection methods used for this study followed the methods discussed in the "Validation of a Pressure Diameter Method for Determining Modulus and Strain of Collagen Engagement for Long Branches of Bovine P ulmonary Arteries" section of the

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(+ ! previous chapter In order to use tissues to their fullest extent and avoid waste, applicable tissues used in the validation study were also used in this study when applicable. 3.2.3 Mechanics Testing Tissues were tested at l ocations similar to those described in the previous chapter PD Method Inflation section. Due to the success of the methods development discussed in the precious ch apter, tissues were tested using the PD method. However, to maintain consistency with previously published data, these animal tissues were also tested with the uni axial pull tester Both methods continued to deliver results similar to each other. After the PD testing, the artery was sectioned into two circumferential rings at each test location. One ring was then set aside for histology. The other ring was then measured for wall thickness (see wall thickness and unstretched circumference section). Th e ring was then open ed into a circumferential strip. T he width of the strip was measured with electric calipers and a uni axial pull test was preformed on the sample. The pull test was preformed with an MTS, Insight 2 (MTS Systems, Eden Prairie, MN) mater ial testing system, in an isolated tissue bath, in the circumferential direction. During this test, the strain and the applied force were recorded. This test is also described in more detail in the previous chapter and by Lammers et. al. (Lammers, et al. 2008) 3.2.4 Wall T hickness and U nstretched Circumference The wall thicknesses and unstretched circumferences of the arteries were determined at each test location photographically in the same method as described in the previous chapter PD Method Inflation section.

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(, ! 3.2.5 Histology Images of histological samples of the arteries were taken based on availability from four hypoxic calves and three normoxic c alves. Samples were taken to image the plane perpendicular to the longitudinal axis, providing a ring section of the artery. These samples were taken after testing from the most proximal, the middle and the most distal tissue section of each artery tree. This resulted in samples for the third, fifth and seventh post hilar generations. Samples from all seven animals were stained with Verhoeff Van Gieson (VVG) staining protocol. Three hypoxic and two control animals were stained with the Hematoxylin and E osin (H&E) protocol and Modified Movat's Pentachrome Stain (pentachrome). Images of each sample were taken on a Zeiss microscope with a digital imaging system and a 10x zoom lens. Images were taken and analyzed at three different locations in each arter ial ring. For numerical analysis, the data from each set of three images was then averaged. All images were taken with the same image settings and lighting in order to maintain consistency in all of the images. 3.2.5.1 VVG Image analysis was preformed on the V VG samples to determine the relative volume of elastin in comparison to the overall volume of the arterial wall. Image analysis was completed using custom written software in Matlab. Using image thresholding, the background of the image was removed and t he area of the tissue was determined. Within the tissue area, a color mask was used to remove non blue portions of the image. Further thresholding was performed to remove any light blue areas in the tissue surrounding the elastin, leaving only the area o f the tissue that was elastin. Consistent image threshold and mask values were used for all of the VVG samples, so that comparisons between

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(! samples of relative elastin volume were accurate, even if the exact values were not correct due to improper thresho lding. Assuming the cross section was representative of the entire volume of the artery section, a relative volume of elastin was assumed to be the same as the relative area for the cross section. Further analysis was conducted by multiplying the relative elastin volume by the artery wall thickness resulting in the total volume of elastin per circumference length, per longitudinal length (referred to as total elastin content in the following sections). 3.2.5.2 H&E H&E staining dyes the tissues blue in cellular nu clei, but a light red color in the remaining tissue. Image analysis was preformed on the H&E samples to determine the relative number of nuclei in the artery wall. This was done manually in Osirix. Three, 10,000 m 2 circular areas, were placed in each i mage one with a border on the intima, one with a border on the adventitia and one centered in the media. The nuclei in each region were counted and then averaged for the image. These values were also multiplied by the thickness to determine a value not n ormalized for thickness (referred to as total cell count in the following sections) 3.2.5.3 Pentachrome Unlike the other stain types, all of the analysis preformed on the pentachrome stained samples were qualitative in nature. The samples were examined for degrad ation of the elastin, which generally presented itself as "elastic clipping" or discontinuities in the elastin fibers. The samples were also examined for neo intimal formation. The spacing between the elastin fibers was examined. Finally, the samples we re examined for

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). ! the presence of elastin formation sites. All of these features are indicated in a sample image provided below ( Figure 3 .1 ). Figure 3 .1 Pentachrome staining features for analysis 3.2.6 Calculations From the tests described above, calculations were preformed to develop a stress strain curve for the arterial wall at each test location. From this curve and in vivo PA pressure data, the material modulus and s tiffness of the arterial wall was calculated over the in vivo pressure range. Furthermore, the stress strain curve was used to calculate the strain at collagen engagement for each animal. Finally, the change in the cross sectional area of the plane norma l to the longitudinal axis of the artery was determined at each test location.

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)% ! 3.2.6.1 PD Data Smoothing As described in the previous chapter in the Engagem ent Strain sect ion, smoothing was once again applied to the PD data. 3.2.6.2 Stress Strain As described in the previous chapter ten consecutive iterations of strain relaxation cycles were applied to each circumferential strip of arterial tissue using the uni axial MTS. From the tenth cycle, a force strain trace was recorded. By assuming a constant material volume (Lawton, 1954) material isotropy and material continuity and using small strain assumptions, a stress was calculated for each force strain point based on the equation s presented in the previous chapter (printed below in a different form). L = ( + 1 ) L 0 Equation 3 1 Uniaxial strained length A 0 = W 0 T 0 Equation 3 2 Unstrained plain of stress area A = A 0 L 0 L Equation 3 3 Strained plain of stress area = F A Equation 3 4 Uniaxail stress

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)& ! In the above equation s, L is the length of the circumferen tial strip at a given data point, A is the cross sectional area at a given strain, A 0 is the cross sectional area in the unstretched state and is the stress. Equation 3 .3 is a consequence of the assumption of constant material volume and describes the c ross sectional area as a function of the state of strain. This allows for an approximation of true strain, rather than engineering strain, shown in Equation 3.1. When available, stress strain traces were also extracted from the PD data using LamÂŽ's Law fo r thick walled tubes as described in detail in the previous chapter. In order to use this model, it was assumed that a section of artery at each test location could be considered a tube of infinite length. Once again, material continuity, isotropy, const ant volume and small strain assumptions were made. Our work presented in the previous chapter demonstrated strong agreement between stress strain traces determined using the PD method and those determined using the uni axial testing method. Calculation s for LamÂŽ's Law are presented in Equation 2.1 Equation 2.3. For both PD and uni axial stress strain data sets, a ninth order polynomial was fit to the data. For all data sets, the r 2 value was no less than 0.98. When both PD and uni axial data sets wer e available, values of the ninth order polynomial were discretized in the in vivo pressure range and averaged between the two data sets. Both PD and uni axial pull testing were used to alleviate concerns of method accuracy. Although our work presented in the previous chapter indicated an interchangeability of the two testing methods, advantages to both methods were noted. Implementing both methods in the study enabled us to have a check system for each data point with little increase in testing time. Ha d the results of the two methods varied

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)' ! significantly for specific tissues these data points could have been removed from the data pool. This was never the case in our data set. Data points acquired with only the uni axial testing method were not found t o be outliers, or to vary significantly from their perspective data pools or to display any unique trends. 3.2.6.3 Material Modulus and Stiffness To determine modulus changes resulting from PH, it was necessary to compare the modulus at similar strains for all of the tissues. The modulus was therefore defined as the mean slope of the stress strain curve between 22.5% and 27.5% strain. This point was chosen because there was data available for all animals at this strain state and it was well below the strain of co llagen engagement for all of the animals. The average slope was determined by applying a linear fit to the discretized data points Material stiffness was again determined at strains ranging between 22.5% and 27.5% for similar reasoning. Stiffness was d efined as the modulus at a given strain multiplied by the calculated thickness at that given strain. 3.2.6.4 Strain of Collagen Engagement The collagen engagement strain is the amount of strain where it is assumed that collagen fibers begin to carry a significant portion of the stress. At strains beyond this point, collagen carries an increasingly larger portion of the stress, until the collagen is fully engaged. For the sake of comparison, the strain of collagen engagement is defined as the point of maximum curv ature in the stress strain curve, in similar fashion to the methodology of the previous chapter (Lammers, et al., 2008) Using the already defined stress strain functions, the curvature is defined by Equation 2.4.

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)( ! 3.2.7 In vivo Change in Cross Sectional Area Calculation of pressure strain traces was a straightforward process when PD diameter data was available for the in vivo pressure range. This is because the strain can easily b e calculated as described in Equation 2.1, and the pressure was directly measure d. Calculation of a similar trace required more manipulation for uni axial data sets. Even so, the calculations were relatively straightforward using the same assumptions described to develop a stress strain trace from the PD data set (see Calculations: Stress Strain section). Again, Lame's Law was used. In this case, the pressure strain trace was derived from the previously calculated stress strain trace. For each discrete stress strain point, pressure was calculated as below, r 0 = C i 2 E quation 3 5 Unstrained radius for cross sectional area calculation r = r 0 ( 1 + ) Equation 3 6 Strained radius for cross sectional area calculation P i = [( r + T ) 2 r 2 ] [( r + T ) 2 + r 2 ] where T = T 0 ( 1 + ) Equation 3 7 Internal pressure for cross sectional area calculation where r 0 and r are the initial and strained internal radius respectively, T and T 0 are the unstrained and strained thickness respectively and C i is the measured i nternal circumference. Equation 3.6 is a consequence of an assumption of material isotropy and

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)) ! incompressibility and Equation 3.7 is the result of LamÂŽ's Law and an assumption of constant volume After calculation of the pressure strain trace, a ninth or der polynomial was fit to both the PD and uni axial data sets. Using this function, discretized values were calculated for the in vivo pressure range. If both data sets were available, the two were averaged. By assuming a circular cross section of the a rtery, the in vivo change in diameter was calculated as described in Equation 3.8 Equation 3 .9 Equation 3 8 Strained radius for cross sectional area calculation Equation 3 9 Change in cross sectional area over in vivo pressure range where 1 and 2 are the strains corresponding to the minimum diastolic and peak systolic measured pressure, respectively and #A is the change in cross sectional area. 3.2.8 Statis tics Statistical analysis was performed for each of the calculations described above. This analysis was completed in two broad categories, ANOVA analysis and regression analysis. For the remainder of this chapter statistical significance will be defined as slightly significant for %<0.10 and significant for %<0.05. All other values of % are considered insignificant. For each test, material modulus of elasticity, stiffness, thickness, engagement str ain, or change in relative area ( AC ), a multi factor AN OVA was completed with independent variables of circumference group and treatment group (control or

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)* ! hypoxic/brisket). Four circumference groups were chosen to most evenly distribute the tissues. Groups were 7 15[mm], 15 20[mm], 20 25[mm] and 25 32[mm]. A rtery section circumferences were used to group the tissue sections for analysis, rather than artery branch generation. This grouping was chosen because our theoretical understanding of pressure vessels dictates that the circumference of the artery and th e internal pressure, not the branch location, determines the mechanical forces experienced by the artery wall in vivo. It therefore follows that the artery circumference will best categorize adaptations to the arterial wall resulting from changes in inter nal pressure. ANOVA tests did not consider the two brisket calves because of their low population number and they could not be considered control or hypoxic. Bar plots of the means of size group for each test are provided below, with the standard deviati on in the test value for each size group represented with error bars. Linear regressions were also completed for each test; for these analyses, the brisket calves were pooled with the hypoxic group. Brisket animals were included in the linear regressions to provide a more complete range of MPAP because the hypoxic and control groups had a large gap between their MPAPs. Multivariate regressions were calculated to determine the dependence of each test on MPAP and Circumference. ANCOVA calculations were als o completed to determine if the slope constants for the regressions were differed significantly between circumference groups. This was completed by performing the same multi varriate regression with an addition independent predictor two more times. The a dditional independent predictor was equal to either the MPAP or the circumference (depending on which slope is being tested for treatment dependence) for control animals. The value of the independent predictor was always zero

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)+ ! for hypoxic/brisket animals. If there were a significant difference between treatment groups, then the additional independent variable would be significant. In essence, this value was the difference in the slopes of the two groups. In these cases, regressions were run for each treat ment group separately. For some test results, uni variate regressions were conducted between either MPAP or circumference and the test results. In these cases differences in treatment slopes were computed in a similar fashion as multivariate regressions. 3.3 Results 3.3.1 Mean Pulmonary Pressure Analysis was conducted on the MPAP for both the hypoxic and control groups. Due to catheterization issues, pressure data was unavailable for one control animal. The mean MPAP for the control groups was 25.5[mmHg], 39.2 [mmHg] for the brisket calves and 102.0[mmHg] for the hypoxic group. A single factor ANOVA indicated a significant difference in MPAP between groups (%<0.0005). Note: For the remainder of the Results section, any analysis involving MPAP will be based upo n study of five control, six hypoxic and two brisket animals. Analysis independent of MPAP will be based upon study of seven control and seven pooled hypoxic/brisket animals. 3.3.2 Modulus of Elasticity Results of the multifactor ANOVA for the modulus showed n o significant difference in modulus between circumference groups (%=0.671) or between control and hypoxic treatment (%=0.613). Figure 3 .2 is a bar chart of the elast ic modulus means for

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), ! each size group. The multivariate regression showed no linear dependence for the modulus based on either circumference or MPAP ( %=0.992, %=.347, respectively). When the treatment groups are analyzed separately, there is a significant linear relationship between MPAP and modulus for the control group and the sick (hypoxic/brisket) group ( %=0.030 and %<0.0005, respectively). The slopes were also significantly different ( %=0.022). Interestingly, the slope of the sick animals is negative and the slope of the control animals is positive. Figure 3 .2 Mean modulus of each circumference group bar plot 3.3.3 Thickness The ANOVA results indicate a significant difference for unstretched wall thickness between circumference groups ( %<0.0005) and between treatment groups ( %<0.0005). Figure 3 3 is a bar plot showing the mean thicknesses for each !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ '/'$ '/# '/#$ '/& '/&$ 01,23%4+,+52+"6,738 97:3;3<"=9>-? 97:3;3<"@<"01,23%4+,+52+"6,738 " 075A,7; BC87D12

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)! circumference group. The mutivariate regression agreed with these findings, showing a strong linear dependence of unstretched wall thickness on both unstretched circumference ( %<0.0005) and MPAP ( %<0.0005) Notably, error residuals were calculated for the linear approximation and were evenly distributed over the r ange of unstretched circumferences, supporting the validity of a linear model. The significance of the overall model was found as %<0.0005. Figure 3 3 Mean thickness for each circumference group bar plot Univariate, linear regressions relating unstret ched circumference and unstretched wall thickness for the control and hypoxic groups, independently, indicated a significant difference in slope between the groups (%=0.002). Figure 3 .4 is a plot of the unstretched wall thickness verse unstretched circumference, with the two regressions plotted. !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ '/& '/0 '/1 '/! # #/& #/0 23,45%6+,+74+"8,95: ;<34=7+>>"?%%@ ;<34=7+>>"A>"23,45%6+,+74+"8,95: " 297B,9C DE:9F34

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*. ! Figure 3 .4 Thickness vs. circumference scatter plot with regressions plotted 3.3.4 Collagen Engagement The ANOVA indicated a significant difference in engagement strain between the circumference groups ( %=0.021) but showed no evidence for a difference between the hypoxic and control treatment groups ( %=0.740) Figure 3.5 is a bar plot of the mean engagement strain for each circumference group. Similarly, a multivariate regression ind icated a significant linear relationship between the circumference and engagement strain ( %<0.0005), but there was no significant linear relationship between the MPAP and engagement strain (%=0.219). Furthermore, univariate analysis of the dependence of e ngagement on circumference did not indicate a statistical difference between the slopes of the control animals and the sick animals (%=0.915). 5 10 15 20 25 30 35 40 45 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Circumference (mm) Thickness (mm) Thickness Vs Circumference Control Control linear fit Hypoxic Hypoxic linear fit /0.1.&&!$!2"324.1&'-! 5667 /0.1.''!$!2"324.1%*%! 5667

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*% ! Figure 3 .5 Mean engagement strain f or each stiffness group bar plot 3.3.5 Stiffness Analysis of the stiffness multivariate ANOVA indicated a significant difference between treatment groups (%=0.015) and circumference groups (%<0.0005). Figure 3 6 is a bar plot of the mean stiffness for each circumference group. A multivariate regression was able to show a significant linear relationship between stiffness and circumference ( %<0.0005) and a trend toward a slightly significant linear relationship bet ween MPAP and stiffness (%=0.061). The slope of the regression indicated a positive relationship between circumference and stiffness and a positive relationship between MPAP and stiffness. Furthermore, it was found that the dependence of stiffness on ci rcumference was also dependent on the treatment group, in that the slope of stiffness vs. MPAP for the sick treatment group was significantly higher than the slope for the control group. F i gure !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ '/# '/& '/( '/0 '/$ '/1 '/2 34,56%7+,+85+"9,:6; <8.-.+%+8=">=,-48"?%%@%%A <8.-.+%+8=">=,-48"BC"34,56%7+,+85+"9,:6; " 3:8=,:D EF;:G45

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*& ! 3.7 is a plot of the stiffness vs. unstretched circumference, with the two regressions plotted. Figure 3 6 Mean stiffness f or each stiffness group bar plot !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ '/'# '/'& '/'( '/'0 '/'$ '/'1 23,45%6+,+74+"8,95: ;<3667+==">%%?@A-B ;<3667+=="C="23,45%6+,+74+"8,95: " 297<,9D EF:9G34

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*' ! Figure 3 7 Stiffness vs. circumference scatter plot with regressions 3.3.6 Area Compliance Change in the relative area of the artery sections over their respective, in vivo pressure ranges (min diastolic to maximum systolic) were studied relative to their unstretched cross sectional area, yielding area compliance These values were then normalized by dividing the result by the span of their respective pressure ranges, resulting in percent change in area per pressure unit [(mm^2/mm^2)/mmHg], or the AC. A multifactor ANOVA showed a significant increase in AC between control and hypoxic groups (%<0.0005), but no significant difference between the circumference groups Figure 3.8 is a bar chart showing the mean change in AC for each circumference group. A multivariate regression showed a significant linear dependence of the AC on the 5 10 15 20 25 30 35 40 45 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Circumference (mm) Stiffness (MPa*mm) Stiffness Vs Circumference Control Control linear fit Sick Sick linear fit /0.1..%!$!2"324.1.%&!589:!$! 667 /0.1..&!$!2"324.1.%&!589:!$! 667

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*( ! MPAP (%< 0.0005), but no significant linear relationship between the AC and the unstretched circumference. When a multivariate regression is considered with the same factors and treatment groups considered independently, both the sick animals and control animals s howed a significant linear dependence on MPAP (%<.0005 and %=.011, respectively). The difference of the dependence of AC on MPAP between treatment groups was also found to be significant (%=.015). Only the hypoxic group showed any linear dependence of AC o n the unstretched circumference (%<0.0005). Figure 3 8 Change in relative cross sectional area per pressure vs. circumference group !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ '/''$ '/'# '/'#$ '/'& '/'&$ '/'( 01,23%4+,+52+"6,738 09-5.+"15":+;-<1*+"0,7==">+2<175-;"),+-"8+,"?,+==3,+"@A%% & B%% & CB%%D.E 09-5.+"15":+;-<1*+"0,7== >+2<175-;"),+-"8+,"?,+==3,+"F="01,23%4+,+52+"6,738 " 075<,7; DG87H12

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*) ! 3.3.7 Histology 3.3.7.1 VVG A multifactor ANOVA was preformed for the relative elastin volume based on circumference group and anim al treatment. No significant difference in the elastin fraction was found based on either the circumference group or the animal treatment. Similarly, a multivariate linear regression was unable to correlate the elastin fraction to circumference or MPAP. A multifactor ANOVA, preformed on the total elastin content based on circumference group and animal treatment showed a significant dependence on circumference group (%<0.0005), but none based on animal treatment. Figure 3 8 shows a bar plot that would seem to indicate an increase in the total elastin content for the hypoxic animals, but the differences were not significant. Similarly, a multivariate linear regressio n indicated a linear dependence of total elastin content on circumference ( %<0.0005), but none on mean pulmonary pressure. Sample images from VVG stained slides are provided below in Figure 3 10

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** ! Figure 3 9 Total elastin content (VVG) !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ '/'$ '/# '/#$ '/& '/&$ '/( '/($ '/0 12,34%5+,+63+"7%%8 9:-;<26"=,-3<2>6?@A23B6+;;"7%%8 @><-:"9:-;<26"1>6<+6< " 1>6<,>: CDE>F23

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*+ ! Figure 3.10 Sample VVG stained tissue images 3.3.7.2 H&E A multifactor ANOVA was performed for the cell count based on circumference group and animal treatment. No significant difference in the cell count per area was found based on either the circumference group or the animal treatment. Similarly, no linear dependence was found between the cell count and the circumference group or animal treatment. A multifactor ANOVA did find a significant dependence of total cell count on circumference (%=0.0461), but no dependence on animal treatment. A 200 m !"#$"%%& '"#!"%%&& "#'"%%& ()*+,-.& /+012+3&

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*, ! multivariate regr ession showed linear dependence of total cell count on circumference, but no dependence on the mean pulmonary pressure. Plots of the data mentioned above are provided below Figure 3 .1 1 Figure 3 .1 2 Sample H&E images are provided below in Figure 3.13 Figure 3 .1 1 Relative cell co unt (cell count per area) (H&E) !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ $ #' #$ &' &$ (' ($ /0,12%3+,+41+"5%%6 /+77"/8249":+,"#''''"%01,84; & <+7-90*+"/+77"/8249 " /849,87 =>:8?01

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*! Figure 3 .1 2 Total cell count !" "#$%% #$" "&'%% &'" "&$%% &$" "(&%% )*+,-.+ $ #' #$ &' &$ (' /0,12%3+,+41+"5%%6 /+77"/8249":+,"#''''"%01,84; & "<"=>01?4+;;"51+77;<%%6 =89-7"/+77"/8249 " /849,87 @A:8B01

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+. ! Figure 3.13 Sample H&E stained tissue images 3.3.7.3 Pentachrome Although the data gathered from the pentachrome stained slides was qualitative in nature, distinct differences were noticed as a r esult of both animal treatment and artery size. Neointimal lining was generally present in the hypertensive animals, but not in the control animals. This feature appeared to be most pronounced in the largest arteries, yet still present in the smallest ar tery sections. Punctate elastin appears to be present in the hypoxic animals at much higher levels than in the control animals, especially in the 200 m !"#$"%%& '"#!"%%& "#'"%%& ()*+,-.& /+012+3&

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+% ! smaller arteries. Similarly, elastic clipping appears to be much more prevalent in the hypoxic animals compa red to the control animals. Finally, there appears to be increased radial spacing between the elastin fibers. Sample pentachrome stained images are provided below in Figure 3.14 Figure 3.14 Sample PENTACHROME stained tissue images 200 m !"#$"%%& '"#!"%%& "#'"%%& ()*+,-.& /+012+3&

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+& ! 3.4 Discussion Overall, our study indicated a strong correlation between stiffening of the arterial wall and the presence of hypoxia induced PH. This stiffening appears to be associated with an increased wall thickness in the hypoxic animals, and not associated with cha nges in the material modulus of the tissue. The significant linear relationship present between the MPAP and thickness suggests that this remodeling is a reaction to increases in pulmonary pressure. We have also shown that the engagement strain of the di stal, conduit, pulmonary arteries remains fairly constant regardless of the treatment or the MPAP in this animal model. The consequence of both the arterial stiffening and the constant engagement strain, in conjunction with increased arterial pressures, i s dramatically decreased AC in the hypertensive animals. These points and their implications are discussed in further detail in the following subsections. Table 3.1 (below) provides a brief synopsis of the relationships shown in the results section, above. The column on the left describes the relationship studied; the center column describes the type of correlation and the right column notes whether or not a significant relationship was found.

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+' ! Table 3 1 Summary of find ings Comparison Relationship Significance Modulus of elasticity vs. MPAP Treatment Circumference None None None No No No Thickness vs. MPAP Treatment Circumference Positive Linear Increased in Hypoxic Positive Linear Yes Yes Yes Engagement vs. MPAP Treatment Circumference None None Positive Linear No No Yes Stiffness vs. MPAP Treatment Circumference Positive Linear Increased Stiffness in Hypoxic Positive Linear Trend Only Yes Yes AC vs. MPAP Treatment Circumference Negative Linear Decreased AC in Hypoxic None Yes Yes No Relative Elastin Content vs. MPAP Treatment Circumference None None None No No No Total Elastin Content vs. MPAP Circumference Positive Positive Trend Only Yes Relative Cell Count vs. Treatment Circumference Increased Cell Count in Hypoxic None Trend Only No Total Cell Count vs. Treatment Circumference Increased Cell Count in Hypoxic Positive Trend Only Yes

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+( ! 3.4.1 Modulus of Elasticity There was no significant difference in the group means for modulus of elasticity between the control and the hypoxic groups. This may indicate a lack of change in the intrinsic mechanical properties of the arterial wall resulting from the hypoxic treatmen t. Thus, any stiffening in the artery wall resulting from treatment is mainly the result of geometrical changes. These findings do not agree with the previous findings of Lammers et al. (Lammers, et al., 2008) although this study characterized the mecha nics of the main and first branches of the pulmonary arteries, not the post hilar arteries. We cannot conclude as to whether or not this discrepancy between the two studies is due to the size, generation or location of the arteries. In agreement with the above conclusions, no significant linear dependence between the MPAP and the modulus in the elastin region was found in the pooled data. This, again, suggests little intrinsic mechanical remodeling of the cellular wall resulting from increased MPAP. This is, however, contrary to the significant linear dependence of modulus on MPAP discovered within both the sick and control treatment groups. We also purpose a theory in regards to the opposing slopes of the two animal groups. We suggest the theory tha t within a healthy population, the vasculature reacts to increased pressure and distension through remodeling to increase the modulus and stiffness, protecting the animal from the adverse effects of collagen engagement, resulting in a positive relationship between MPAP and modulus. Within the sick animals, we propose a different causal relationship. Increased MPAP beyond the norm for the group occurs due to an animal's lack of remodeling, while MPAP s below the

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+) ! norm occur in the animals that display more p rotective remodeling, causing a negative dependence of modulus on MPAP in the sick animals. In other words, some of the animals in the sick group may have a greater ability to protect themselves from the detrimental effects of collagen engagement through increased levels of remodeling, resulting in lower MPAP in the animals that present higher modulus. 3.4.2 Thickness The significant increase in thickness as a result of hypoxic treatment supports previous studies of the pre hilar arteries, which displayed geomet ric remodeling resulting from hypertension. This is in agreement with the significant, positive linear relationship between the MPAP and the wall thickness. The increased thickness is likely the result of both increases in cellular reproduction and migra tion to the arterial walls and an increase in the production of extra cellular matrix. It is hypothesized that this is a protective response against the increased pulsatility resulting from collagen engagement. Furthermore, the significant thickening fou nd in absence of significant changes in the modulus confirms that increases in stiffness and decreases in capacitance are the result of geometric remodeling and not necessarily changes in the intrinsic properties of the artery wall. We further note the s ignificant linear dependence of the wall thickness on both the MPAP and the artery circumference. This relationship implies that the wall thickness of the distal conduit arteries may be predictable based on studies of only MPAP and the proximal arteries. This feature could be very useful in the creation of numerical models of the pulmonary arteries in disease. Further, this data supports the utility of in vivo mechanics testing focused on the proximal regions of the pulmonary arteries, i.e.

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+* ! localized tes ting of arterial wall mechanics using ultrasonic and catheterization techniques (Hunter, et al., 2010) as these studies will be helpful in the prediction of the distal mechanics based solely on the mechanics of the proximal arteries and the MPAP. 3.4.3 Engageme nt The strain of collagen engagement cannot be shown to change by the presence of PH in the post hilar pulmonary arteries, in this animal model. This suggests that the length of the collagen fibers, with respect to the length of the unstretched artery c ircumference, must remain consistent regardless of the presence of PH in the post hilar pulmonary arteries. Interestingly, the strain of collagen engagement is dependent on the size of the artery, as indicated by the linear relationship between unstretche d circumference and engagement strain. This relationship may also be useful in future modeling investigations of the pulmonary arteries. 3.4.4 Stiffness Stiffening is clearly occurring as a result of PH in arteries distal to the hilum of the lung. This stiff ening will contribute significantly to decreases in the capacitive nature of the pulmonary arterial tree. We further note the dependence of wall stiffness on the artery size within each treatment group. Because this dependence changes based on the animal treatment (the sick animals had a significantly different slope from the control animals), we believe that the amount of remodeling to the arterial wall is dependent on the size or generation of the artery. This study also demonstrates that relationship between the stiffness and the artery size is a consequence of the relationship between the wall thickness and the artery size and not the result of changes in modulus, in this animal model.

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++ ! 3.4.5 Relative Area Change AC is representative of the in vivo capacitance of each section of artery relative to the artery size, as described by Gan et al. (Gan, et al., 2007) The data presented here shows highly significant changes in the capacitance resulting from animal treatm ent and animal MPAP. The relative capacitance of the arteries, on the other hand, seems to remain fairly constant based on the size of the artery. The very large changes in capacitance between the control and sick animals are due both to wall stiffening, resulting from increased wall thickness, and collagen engagement. This demonstrated loss of capacitance will result in increased loading to the heart and increased pulsatility in the distal vasculature, potentially leading to endothelial dysfunction or o ther detrimental effects to the circulation. This data indicates the importance of the passive mechanical changes present in the posthilar conduit arteries. 3.4.6 Histology We would like to call the readers attention to the trend of increased cell counts and increased total elastin. We believe this to be indicative of increased cellular proliferation and migration to the cellular wall and increased production of extra cellular matrix. Our observational analysis of the pentachrome stained samples seems to indi cate similar features. Here we notice the presence of newly developing intima and new elastin fibers in the hypertensive animals. We are also seeing degradation of the existing elastin fibers in the hypertensive animals which may be responsible for the negative linear relationship between MPAP and modulus in the hypertensive animals We believe these

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+, ! changes to be i ndicative of increases in cellular activity and changes in the structure of the extra cellular matrix. Based on these observations, we recommend that further study, with increased sample numbers be conducted histologically on these sections of the arter y to truly gain an understanding of the changes taking place in the arterial walls. 3.4.7 Limitations We first of all note that these studies were conducted ex vivo and did not apply longitudinal strains that match in vivo conditions. The mechanical values pres ented will therefore be skewed from the true in vivo values. We justify this limitation by noting that this chapter is intended to be a comparison between treatment groups and an exploration of the predictability of distal mechanics based on measured hemo dynamics and the mechanical behavior of more proximal arteries. We note the lower population size for our histological study. We justify this by stating that this study was meant to analyze the mechanics of arterial changes in PH and not produce significa nt histological results. We therefore kept our efforts focused in the mechanics study and included a very brief study of the histology of these portions of the arteries as a side note. On the other hand, we do believe that this portion of the study is ve ry informative and deserves attention.

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+! 4 Final Notes In order to avoid some of the drawbacks of previously used arterial tissue mechanic testing methods, a new methodology was developed the pressure diameter or "PD" method This method, of course, had its own limitations, but it proved to be an effective testing method overall. It was also shown to have similar accuracy to the gold standard method (namely, uniaxial testing) for determining the stress strain relationship of arterial wall tissue. This P D method allowed for increased rapidity in testing the tissue mechanics of the multiple generations of arterial walls Furthermore, this testing method allowed the determination of longitudinal strain, reducing the number of assumptions made in comparison to the uni axial method. Finally, the PD method allowed the direct measurement of relative area change, which is directly related to capacitance. Determination of this value using the uni axial method relies heavily on assumptions of material characteri stics. For these reasons, i t is believed that th e PD method developed here was not only effective for the ses studies, but will prove effective in future research. Using the PD method as well as a uni axial testing method, a significant body of data was developed, studying the mechanics distal to the hilum of the lung in the presence of and absence of hypoxically induced hypertension. The previously unstudied data strongly indicates the importance of the role of passive mechanical changes in the post hil ar pulmonary arteries in the progression of PH The clearly demonstrated stiffening of these arteries will, in conjunction with collagen engagement, lead to large decreases in the capacitive nature of pulmonary arterial tree which was dramatically shown in our study of the in vivo relative area change of the pulmonary arteries We believe that these changes in capacitance hugely impact the outcome of patients suffering

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,. ! from PH (Hunter, et al., 2008) due to significant increases in pulsatility, wave refl ection and loading on the right heart. The data presented here has significantly added to the understanding of the overall mechanical changes that occur in the pulmonary circulation as a result of pulmonary hypertension. By studying the arterial wall mec hanics we have discovered many key similarities and differences between the previously studied mechanical changes of the proximal arteries and the changes that occur distal to the hilum in pulmonary hypertension. It is clear that both areas suffer dramati c in creases in stiffness. This increased stiffness is associated with both thickening and increased modulus in th e proximal arteries but is not well correlated with increased modulus in the posthilar arteries. Furthermore, we have shown that the result o f the increased stiffness, along with collagen engagement, results in severely decreased capacitance in the posthilar pulmonary arteries. Due t o the large contribution of these arteries to the overall capacitance of the pulmonary circulation, this underst anding of the dependency of the arterial mechanics on artery location and size in both healthy and diseased models will prove to be essential in the future understanding of pulmonary hypertension. In the posthilar arteries, we have demonstrated a clear d ependence of the arterial mechanical nature on not only artery size, but also changes in MPAP and the presence of PH. We believe that this data will lead to an improved understanding of the dynamics of the pulmonary circulation in the presence of PH, allow ing a deeper understanding of the disease by improving the overall understanding of the system mechanics We further believe that this data can help in the production of detailed mechanical models that will further increase understanding of the disease Finally, this data also helps demonstrate

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,% ! the validity of localized, proximal, in vivo studies of arterial mechanics, due to the predictability of the thickness and stiffness of the distal arteries.

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