Detection of Placental Pathology Based on Umbilical Artery ... › bitstream › 1807 › ... ·...

Detection of Placental Pathology Based on Umbilical ArteryWave Mechanics

by

Anum Rahman

A thesis submitted in conformity with the requirementsfor the degree of Master of Science

Graduate Department of Medical BiophysicsUniversity of Toronto

c© Copyright 2016 by Anum Rahman

Abstract

Detection of Placental Pathology Based on Umbilical Artery Wave Mechanics

Anum Rahman

Master of Science

Graduate Department of Medical Biophysics

University of Toronto

2016

Abnormally pulsatile umbilical artery (UA) Doppler waveforms (characterized through the

UA pulsatility index) are widely used as a screening tool to detect intrauterine growth

restriction (IUGR) due to placental disease. However, the sensitivity of UA Doppler in

detecting IUGR is quite poor. One explanation for this is that the pulsatility in the UA

consists of intermixed cardiac and placental signals. Here, we overcome this limitation with

a new ultrasound approach in which the observed UA Doppler waveforms are decomposed

into forward propagating waves (developed by the fetal heart) and reverse propagating waves

reflected back from the placental circulation. A proof-of -principle experiment was conducted

in mice. Results show that the patterns of reflected waves in the UA parallel the variations

in the downstream fetoplacental morphology and are more sensitive to these variations than

the UA pulsatility index. Thus, this methodology has the potential to improve the detection

of placental-mediated IUGR.

ii

Dedication

This work is dedicated to my parents, who have always encouraged me to pursue my dreams.

iii

Acknowledgements

I would like to acknowledge my supervisor, Dr. John Sled, for his guidance and encourage-

ment. Two years ago, I did not think I would be learning about wave mechanics and image

processing, topics that were outside my field of study. In this regard, I am extremely grateful

for John’s patience in answering my questions as well as for our scientific discussions, which

always prompted me to think about my project in new ways. I would also like to thank him

for giving me the opportunity to work as a summer student in my first year of undergraduate

studies. It was here that I first developed a passion for analyzing placental networks in all

their fractal-like glory.

In addition, I am immensely grateful to my committee members, Dr. Christopher Mac-

gowan, Dr. Peter Burns and Dr. John Kingdom, for their suggestions and support. This

project has greatly evolved from what was initially proposed due to their valuable input.

In particular, I would like to thank Dr. Kingdom for taking the time to mentor me at the

placenta clinic. I always felt inspired and enthusiastic after our conversations.

Furthermore, this project would not have been successful without the support of my

colleagues at the Mouse Imaging Centre (MICe). I would like to thank Yu-Qing Zhou, for all

his hard work in obtaining the ultrasound recordings. Jun Dazai, for his creative approach

in developing a protocol that could account for motion confound. Darren Fernandes, for our

discussions on fluid mechanics and many other conversations that shall not be disclosed here,

but they made my experience at MICe truly enjoyable. Lindsay Cahill, Sharon Portnoy and

Monique Rennie (the pregnancy journal club folks), for their critique and advice in terms of

oral talks/posters/abstracts that were tremendously helpful.

Lastly, I would like to express my gratitude to Yohan Yee, whose friendship and advice

were invaluable. This project would not have been possible without his insight. I appreci-

ated our discussions on wave mechanics and scientific research in general. In particular, I

want to thank him for going above and beyond what was required in many aspects of code

development, as well as his endless patience and support over these last two years.

iv

Contents

1 Introduction 1

1.1 Human placental development . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Fetoplacental vasculature and Intrauterine Growth Restriction . . . . . . . . 5

1.3 Doppler ultrasound and IUGR diagnosis . . . . . . . . . . . . . . . . . . . . 6

2 Umbilical artery wave mechanics 8

2.1 Steady pressure-flow relationship . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Pulsatile pressure-flow relationship . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Input impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 Pulse wave propagation and wave speed . . . . . . . . . . . . . . . . . . . . 15

2.5 Closed-type versus open-type reflection . . . . . . . . . . . . . . . . . . . . . 17

2.6 Early studies of wave reflection . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.7 Decomposition of measured waveforms using the velocity-area method . . . . 20

2.8 Characterizing umbilical artery wave reflection through ultrasound imaging . 21

3 Mouse as a model organism 26

3.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Methods 28

4.1 Animal Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 Ultrasound imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 Semi-automated Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3.1 M-mode recording: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3.2 Doppler recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 Wave Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5 Wave Reflection Characterization . . . . . . . . . . . . . . . . . . . . . . . . 37

4.6 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

v

5 Results 39

5.1 Shapiro-Wilk Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Strain and gestational age interaction . . . . . . . . . . . . . . . . . . . . . . 40

5.3 Intrastrain effects from E15.5 to E17.5 . . . . . . . . . . . . . . . . . . . . . 41

5.4 Reflection coefficient and UA pulsatility index sensitivity . . . . . . . . . . . 45

6 Discussion 46

6.1 Fetoplacental intrastrain effects on UA reflection coefficient . . . . . . . . . . 46

6.2 Fetoplacental interstrain effects on UA reflection coefficient . . . . . . . . . . 49

6.3 Fetoplacental intrastrain and interstrain effects on UA pulsatility index . . . 49

6.4 Reflection coefficient and UA pulsatility index sensitivity . . . . . . . . . . . 50

6.5 Application to human pregnancies . . . . . . . . . . . . . . . . . . . . . . . . 51

6.5.1 Detection of IUGR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.6 Study limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7 Conclusion 55

7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Appendices 58

Bibliography 74

vi

List of Tables

5.1 Animals used in the wave decomposition analysis . . . . . . . . . . . . . . . 39

5.2 Two-way ANOVA of the mean reflection coefficient . . . . . . . . . . . . . . 41

5.3 Two-way ANOVA of the mean pulsatility index . . . . . . . . . . . . . . . . 41

5.4 Average wave reflection parameters and UA pulsatility index . . . . . . . . . 42

C.1 Animals used in invasive experiments . . . . . . . . . . . . . . . . . . . . . . 68

C.2 Average wave reflection parameters and UA pulsatility index (invasive exper-

iment) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

C.3 Comparison of invasive and non-invasive protocols . . . . . . . . . . . . . . . 70

vii

List of Figures

1.1 Human placental anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1 Steady vs. pulsatile flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Pressure wave propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Pulse wave reflection from distal vasculature . . . . . . . . . . . . . . . . . . . . 14

2.4 Closed vs. open type reflection . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Wave decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.6 Reflected wave quantification . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 M-mode recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Umbilical artery wall detection and filtering . . . . . . . . . . . . . . . . . . 30

4.3 M-mode image systole detection . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4 Area wave average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.5 M-mode pre-processing criteria . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.6 M-mode post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 Doppler velocity waveform average . . . . . . . . . . . . . . . . . . . . . . . 36

5.1 CD1 and C57BL/6 umbilical artery flow wave decomposition . . . . . . . . . 43

5.2 Strain and gestational age difference in wave reflection parameters . . . . . . 44

5.3 Reflection coefficient and UA pulsatility index ROC curves . . . . . . . . . . 45

6.1 Reflection coefficient as a function of area ratio . . . . . . . . . . . . . . . . 48

A.1 Arterial bifurcation schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A.2 Reflection coefficient in relation to area ratio . . . . . . . . . . . . . . . . . . . 64

B.1 Distribution of measured parameters . . . . . . . . . . . . . . . . . . . . . . . . 66

C.1 Comparison of wave reflection parameters under invasive protocol . . . . . . . . . 71

C.2 Comparison of wave reflection parameters under invasive and non-invasive protocol 72

viii

List of Appendices

Appendix A Area ratio at arterial bifurcations . . . . . . . . . . . . . . . . . . . . . 59

Appendix B Distribution of measured parameters . . . . . . . . . . . . . . . . . . . 66

Appendix C Invasive wave reflection measurements . . . . . . . . . . . . . . . . . . . 67

ix

Chapter 1

Introduction

During pregnancy, the proper development of placental vessels is crucial in facilitating the

exchange of nutrients and gases between the mother and the growing fetus [1]. Indeed,

impairments in the placental blood vessels are thought to be most common factor underly-

ing intrauterine uterine growth restriction (IUGR), a severe pregnancy complication [2, 3].

In IUGR, the growth of the fetus is less than its genetic potential due to a pathological

cause [4, 5]. For instance, studies show that IUGR placentas have malformed capillaries

and abnormalities in the fetoplacental arterial vessels that branch off of the umbilical artery

(UA) [6, 7].

Currently, Doppler ultrasound is the gold standard for evaluating placental health in

pregnancies suspected of IUGR [8, 9]. Through Doppler ultrasound, clinicians can observe

the pulsatile UA flow velocity that accompanies the fetal cardiac cycle (i.e. the flow velocity

wave pattern). The pulsatile nature of these waveforms is thought to represent the properties

of the downstream placental vasculature [10]. For instance, defects in the fetoplacental vessels

of IUGR fetuses are associated with abnormal UA Doppler waveforms [6,11]. Consequently,

numerous metrics have been developed to characterize the UA velocity waveform, with the

UA pulsatility index being a common metric used in clinical practice [12,13,14].

The UA pulsatility index, defined as the ratio of peak-peak velocity to the mean velocity

over a cardiac cycle, is often used as a surrogate for downstream placental function [10]. This

is because it correlates with defects in the fetoplacental vessels [10, 14, 15], and elevations

in this index with deteriorating placental health are thought to reflect increased placental

vascular resistance (opposition to blood flow) [16].

However, despite their usage, Doppler indices based on the observed UA velocity wave

(such as the UA pulsatility index), have low antenatal utility in screening for IUGR [13,17]

and often perform poorly in detecting placental abnormalities [18]. This is likely because

the observed UA velocity waveform is not only a function of the downstream placental

characteristics, but also the fetal heart.

In this thesis, I have overcome the current diagnostic limitation in detecting placental

1

Chapter 1. Introduction 2

disease by using wave mechanics theory to isolate the placental associated signal from the

observed UA Doppler waveforms. Under this framework, the observed UA flow wave is the

summation of two counter-running waves: a forward travelling wave (generated by the fetal

heart) which propagates along the UA, and a backward travelling placental wave. This

reflected waveform is the combination of many reflected waves that arise at various sites

in the downstream fetoplacental vasculature, whenever the physical characteristics of the

vessels change (i.e. if a vessel bifurcates, becomes stiffer, etc) [19]. As such, the composite

UA reflected flow wave is dependent on the properties of the downstream placental network

and can be used to detect changes in the placental vascular patterning.

The novel, non-invasive (ultrasound-based), UA wave reflection methodology described

here has been developed in mice. Mice have been widely used as a model for human placental

development due to the similarities in their placental structure and genetics [20]. More

importantly, however, the morphology of the mouse fetoplacental vessels has been previously

described in great detail [21, 22], and thus offers a huge advantage in linking variations in

the downstream placental vascular characteristics to the measured UA reflected flow wave.

Therefore, to determine if the reflected wave is sensitive to variations in placental mor-

phology, I have compared the pattern of UA reflected wave in two strains of mice with

known differences in their fetoplacental vasculature [21]. In addition, I have compared the

sensitivity of the reflected wave and the UA pulsatility index (a current clinical standard)

in detecting differences in mouse fetoplacental morphology. Lastly, by isolating the signal

reflected back from the placental vasculature, the UA wave decomposition methodology may

improve the sensitivity for detecting IUGR due to placental disease in humans.

The following sections of the introduction provide a general background on normal human

placental development (1.1), placental defects that lead to IUGR (1.2) and the current

limitations in diagnosing IUGR due to placental disease (1.3). Section 2 introduces UA

wave mechanics theory, which is the framework used to decompose the observed Doppler

waveforms into their forward (cardiac) and reflected (placental) components. Section 3

describes the rationale for using mice to develop the UA wave reflection methodology and

the aims of this thesis (3.1).

1.1 Human placental development

The placenta develops during pregnancy in order to meet the metabolic demands of the

growing fetus. It fulfils this role by facilitating the transport of nutrients and oxygen from the

maternal circulation to the fetus, along with fetal waste disposal. Furthermore, the placenta

protects the fetus from the maternal immune system and also secretes hormones and growth

factors that are important for modifying maternal physiology during pregnancy [1,23]. Thus,

proper placental functioning is intrinsically linked to fetal health outcomes.


Anatomically, the human placenta can be divided into three distinct components: the

uteroplacental (maternal) side, the fetoplacental side, and the basal plate [24] (Figure 1.1).

Oxygen-rich maternal blood enters the uteroplacental vasculature through the uterine arter-

ies, which give rise to coiled, amuscular spiral arteries that grow in diameter and increase

blood flow to the intervillous space with increasing gestation [25,26]. The intervillous space is

a vast interconnected region consisting of pools of maternal blood and is separated from the

fetoplacental vasculature by the basal plate (which consists of maternal blood channels) [27].

These maternal vessels in the basal plate region are lined by trophoblast cells, which are

unique to the placenta and are involved in vascular remodelling and hormone secretion [24].

While both the fetoplacental and uteroplacental vasculatures develop into low resistance

beds during pregnancy [27,28], the structure of the fetoplacental unit is vastly different from

that of the maternal side.

The fetoplacental circulation begins as follows: first, oxygen-depleted blood pumped by

the fetal heart travels down the descending aorta and enters each branch of the internal iliac

artery, each of which give rise to a single umbilical artery [29]. The two umbilical arteries

coil around the umbilical vein (collectively, these three vessels are referred to as the umbilical

cord) and branch off into repeating functional units called the cotyledon [24].

Within each cotyledon, the umbilical arteries continue to branch into a dichotomous

(fractal-like) network of progressively smaller diameter arteries, the smallest of which give

rise to the capillaries [24]. The branching fetoplacental vessels are encased within finger-like

structures called the placental villi, which are lined by a single layer of trophoblast cells and

project into the intervillous space [24]. This trophoblast layer prevents the mixing of fetal

and maternal blood and also contains microvilli, which increase the surface area required to

extract nutrients from maternal blood [27,30].

Furthermore, the capillaries within the villi and the intervillous space form the maternal-

fetal exchange region: while the waste from the fetus diffuses back into maternal blood

being taken up by the uterine vein, the oxygen and nutrients are transported across the

trophoblast layer (lining the villi), and into the venous vessels of the placental villi [27].

These vessels terminate into the umbilical vein which delivers nutrient-rich blood to the

fetal organs. Ultimately, the umbilical cord and the cotyledons (15-28 per placenta) form

the discoid-shaped fetoplacental vasculature [24].


Figure 1.1: Schematic of the placental circulation. The maternal and fetal sides of the placenta

are separated by the basal plate region. The paired umbilical arteries (UA) and umbilical vein

(UV) branch off into repeating units called the cotyledon. Within each cotyledon, the branching

fetal vessels are encased within structures called the villi. The fetal villous vessels uptake nutrients

and oxygen from the maternal blood contained within the intervillous space. This fresh blood is

delivered to the placenta by maternal spiral arteries. The maternal veins carry back the fetal waste

that diffuses across the villi and into maternal blood.


1.2 Fetoplacental vasculature and Intrauterine Growth

Restriction

Since the branching fetoplacental arterial network dictates how much blood passes through

the placenta, any malformations within this vasculature can be quite detrimental for fetal

growth [31]. Indeed, structural defects in the fetoplacental unit (leading to inadequate

placental exchange) has been linked to intrauterine growth restriction (IUGR), a severe

pregnancy disorder [32].

IUGR is defined as the failure of the fetus to reach its genetic growth potential due

to a pathological cause and it affects up to 10% of all pregnancies [33]. Clinically, it is

characterized as the estimated fetal weight less than 10th percentile for gestational age

and apart from a higher risk of prematurity and perinatal mortality (IUGR is the cause of

50% of perinatal deaths occurring in early gestation and 20% at term) [10], IUGR babies

are more prone to developing neurological (cerebral palsy), metabolic (Type 2 diabetes,

central obesity) and cardiac disorders (hypertension, coronary artery disease) later on in

life [3, 33,34,35,36,37].

While causes of IUGR can be of maternal (smoking, living at high altitudes, undernour-

ishment) or fetal (chromosomal abnormalities) origins [38], placental insufficiency is consid-

ered to be the most common cause [3]. In general, the placenta of IUGR babies exhibit a

higher frequency of pathology as compared to healthy pregnancies [32, 39]. Several studies

have shown association of IUGR placentas with abnormalities in the fetal vessels, such as:

villous infarcts, decreased villous diameter, branching and surface area, villous fibrosis and

hypertrophy, as well as a decrease in arterial number [7, 32, 40, 41, 42]. These structural de-

fects can adversely affect fetoplacental function and deprive the fetus of the nutrients needed

for growth.

IUGR pregnancies have also been shown to exhibit hypovascular terminal villi (reduced

capillary volume), with capillaries that are slender, elongated and poorly branched as com-

pared to the distinct loops and increased capillarization observed in placentas of healthy

women [6]. This lack of capillary loops in IUGR pregnancies is thought to result in a lower

surface area for the exchange of oxygen and thus, can lead to fetal hypoxia and an emaciated

fetus, as seen in IUGR.

As defects in the villous structure are more commonly present in IUGR pregnancies

as compared to normal pregnancies, evaluating fetoplacental function throughout gestation

is a critical component in the diagnosis of IUGR. Currently, the standard for quantifying

fetoplacental health clinically is Doppler ultrasound of the UA [8].


1.3 Doppler ultrasound and IUGR diagnosis

Doppler ultrasound is widely used as a non-invasive tool to observe UA blood velocity pat-

terns [43], which is thought to reflect properties of the downstream placental network [44].

In healthy pregnancies, there is a considerable increase in the UA end-diastolic flow with

increasing gestation (positive end-diastolic flow), and this is associated with decreases in

fetoplacental vascular resistance [45]. In pregnancies complicated with IUGR, however, the

UA end-diastolic velocity is either absent or reversed (negative) [46,47]

Placental studies show that abnormal end-diastolic flow is associated with the placental

villous structure being compromised/obliterated: when 50%-70% of the placental tree is

compromised, the UA end-diastolic flow shows reversal in the Doppler velocity spectrum [48].

For instance, in one study, absent end-diastolic flow in the UA was associated with a ∼30%

decrease in the number of branches per fetoplacental capillary loop, while close to 80% of

these capillary loops lacked coiling [24]. Furthermore, as umbilical cord blood gas analysis

with absent end-diastolic flow shows that ∼ 80% of these fetuses are hypoxic and ∼46%

have acidosis, this indicates that abnormal UA Doppler velocity patterns give information

regarding placental and fetal health [49].

Along with evaluating fetal-placental health, Doppler ultrasound is also used to guide the

timing of delivery [10]. The timing of delivery is critical in IUGR as deteriorating placental

function can lead to stillbirth [10]. The only effective treatment for IUGR due to placental

disease is early delivery [11]. This is based in large portion on monitoring changes in the

UA pulsatility index (calculated as the ratio between velocity amplitude (difference in peak

systolic and end-diastolic velocity) and mean blood velocity over a cardiac cycle) [11,14]. If

the pulsatility index increases over the course of gestation, this indicates elevated downstream

hemodynamic placental resistance (which is thought to reflect poor placental function) [14]

and can aid a clinician in determining when to deliver.

However, a difficulty with using the UA pulsatility index as a measure of placental func-

tion is that the pulsatility differs between the placental and fetal end of the umbilical cord

(fetal end has a higher peak systolic and lower end-diastolic velocity) [50,51,52], and selecting

different sites along the cord to measure the pulsatility index can result in a lower sensitivity

for detecting IUGR due to placental disease. Indeed, studies indicate that in pregnancies

with a high-risk for IUGR, current methods to evaluate placental function (based on UA

velocity pattern assessment) have a poor sensitivity for detecting IUGR and fetal distress

(55% sensitivity), and these methods do not completely represent the hemodynamics of the

fetoplacental circulation [11,53].

As the most common factor underlying growth restriction is placental insufficiency [11],

the poor sensitivity for detecting IUGR is likely due to the inability of UA Doppler assess-

ments to detect placental pathology. For instance, in one retrospective cohort study, with


pregnancies where the estimated fetal weight was less than 10th percentile for gestational

age and placental abnormalities were evident in 79% of the cases, it was found that the

sensitivity for Doppler indices (the UA pulsatility index and systolic to diastolic ratio) in

detecting placental defects was 42% [18].

Apart from variations in the pulsatility index along the UA, another factor which has

a huge impact on the detection of IUGR is the gestational age at which growth restriction

begins [39]. In early-onset IUGR (before 32-34 weeks of gestation), while UA Doppler ultra-

sound measurements often demonstrate absent or reversed end-diastolic velocities, late-onset

IUGR often exhibits normal UA Doppler blood velocity patterns [11, 39]. For instance, in

a cohort of singleton fetuses with suspected late-onset IUGR at ∼34 weeks of gestation

(confirmed with birthweight less than 10th centile) and normal UA pulsatility index, it was

found that the proportion of cases progressing to abnormal UA pulsatility index was really

low (∼3%) [54].

As UA Doppler largely remains normal in late-onset IUGR fetuses, detection of growth

restriction in late gestation remains to be a challenge. The poor antenatal detection of

late-onset IUGR may be due to association with milder forms of placental pathology [39,

55]. Indeed, it has been suggested that the UA pulsatility index may not be sensitive to

mild placental defects as abnormalities in the velocity waveform, and Doppler resistance

indices, only begin to appear when placental insufficiency is severe [39,56]. This is especially

concerning as late-onset growth failure is more common than early-onset disease. [11,55].

It has been estimated that the placenta is the cause of death in 60% of stillbirths, whereas

IUGR is an underlying disorder in 40% of stillbirths [57, 58]. For instance, in one study, it

was found that from the total number of stillbirths classified as IUGR (under Morrison’s

perinatal mortality classification system), 90% had some type of a placental pathology [57].

In the same study, under Morrison’s classification scheme, 22% of all perinatal mortalities

were attributed to IUGR with an underlying placental pathology [57].

In summary, current UA Doppler methods perform poorly in detecting IUGR and placen-

tal abnormalities. Furthermore, given the association between IUGR, placental pathologies

and perinatal mortality, there is a pressing need to develop a better method to evaluate

placental function and detect placental pathologies in order to improve pregnancy outcomes.

Chapter 2

Umbilical artery wave mechanics

A potential explanation for why UA Doppler ultrasound has poor sensitivity to placental

defects is that the observed velocity waveforms in the UA consist of intermixed cardiac and

placental contributions. When the fetal heart contracts, it generates a forward propagating

flow wave which travels along the UA. When this forward wave interacts with the down-

stream fetoplacental vasculature, a proportion of this forward wave is reflected back due

to a mismatch in the impedance of fetoplacental vessels. Thus, the observed UA Doppler

velocity waveform is the superposition of a forward travelling (cardiac) and a backward

travelling reflected (placental) wave. By employing wave mechanics theory, it is possible to

isolate the portion of the Doppler signal specific to the placenta (the backwards travelling

reflected wave) in order to improve the sensitivity for detecting abnormal placental vascular

morphology.

The following chapter will discuss the theory behind pressure and flow wave decomposi-

tion into forward (cardiac) and reflected (placental) components. It starts with a background

on the pressure-flow relationship in the arterial system under conditions of steady flow (2.1),

and extends to pulsatile pressure and flow, as well as its relation to vascular impedance in the

next section (2.2). Section 2.3 introduces input impedance and its relation to the composite

reflected wave observed in the UA. Section 2.4 describes pulse wave propagation and wave

speed.

The next two sections explore the boundary conditions which are responsible for the dif-

ference in the phase of reflected pressure and flow waves (2.5), and how this phase difference,

in earlier studies, was used to explain the shape of the observed pressure and flow waveforms

on the basis of wave reflection (2.6).

Lastly, section 2.7 combines earlier concepts on the pulsatile pressure-flow relationship,

input and characteristic impedance as well as wave speed as the basis for separating the

observed UA flow waveform into its forward and backward components. The chapter closes

with the use of ultrasound imaging to measure and characterize UA wave reflection (2.8).

8

Chapter 2. Umbilical artery wave mechanics 9

2.1 Steady pressure-flow relationship

The cardiovascular system is responsible for delivering nutrients and oxygen to and taking up

waste from each cell in the body. It achieves this task by circulating blood through a system

of vessels. The driving force behind the circulating blood is the heart, which pumps blood in

a rhythmic pattern (in the form of an oscillating pressure gradient) to ensure that the cells are

adequately nourished at all times and their metabolic demands are met. Historically, when

considering the pressure-flow relationship in the arterial portion of the circulatory system,

there has been a large focus on understanding this concept based on Poiseuille law [19]. J. L.

M. Poiseuille recognized that volume flow (Q) and pressure gradient (P1 − P2) along a tube

(with length (L), radius (r) and carrying a fluid with viscosity η), were related as follows:

Q =πr4(P1 − P2)

8ηL(2.1)

We can better understand the above equation by rearranging it as the ratio of pressure to

flow. In other words, Poiseuille’s law states that the magnitude of pressure gradient needed

to drive flow through a vessel depends on the physical properties of the vessel and the fluid

it carries. Thus, the pressure-flow ratio is related to how much a vessel resists flow; this is

defined as vascular resistance [19],

R =(P1 − P2)

Q(2.2)

where R is related to the vessel properties:

R =8ηL

πr4(2.3)

As can be seen from the equation above, physiologically, the vessel diameter has the most

profound effect on resistance. Furthermore, this expression of resistance is analogous to one

defined by Ohm’s law, where electrical resistance, Relec (similar to vascular resistance), is

determined as the ratio of voltage drop, V (similar to drop in pressure), to current, I (similar

to flow):

Relec =V

I(2.4)

As this electrical resistance represents dissipation of energy, so does the vascular resis-

tance, where viscous friction between fluid and vessel wall opposes flow and is the source of

energy loss from the system [59].

Although calculations of hemodynamic resistance have aided clinicians in understanding

pathological disease states immensely (where often, arterial vascular beds have an elevated

resistance due to constriction) [59], the expression of resistance resulting from Poiseuille


law can only be understood under the conditions of steady, full developed laminar flow

and rigid tube walls [19]. These conditions (a requirement for Poiseuille law), however, are

not met in the arterial system where flow is largely pulsatile and vessel walls are elastic.

This introduces phenomena such as wave propagation and wave reflection within the arterial

system [60]. Thus, to obtain a better understanding of how arterial networks function,

vascular impedance (which takes these two phenomena into account) must be considered

instead [59].


2.2 Pulsatile pressure-flow relationship

Under Poiseuille law, the flow velocities at fixed positions along a tube are constant in time

(steady flow). In contrast, the arterial system exhibits unsteady or pulsatile flow, meaning

that at fixed positions, the flow velocities change with time (Figure 2.1). This pulsatile

blood flow is a result of a driving pressure which is not constant but rather, oscillates due

to rhythmic contractions of the heart (the systole-diastole cycle).

Figure 2.1: Panel A: Under Poiseuille flow, the flow profile at a fixed position along the vessel is

constant at different timepoints (t1, t2, t3). Panel B: In pulsatile flow, the flow profile at a fixed

position along the vessel changes with time due to acceleration and decceleration of the blood.

When the oscillatory pressure gradient increases, there is a time delay before the flow

can increase in response (i.e. the peak of the blood flow lags behind the pressure peak) [60].

This is due to the fluid’s inertia. The flow lag, a result of fluid’s inertia resisting the pressure

change driving the flow, is a form of resistance known as inertance, or inductance in terms

of its electrical analog [60].

Furthermore, the elasticity of arterial vessels (equivalent to capacitance in an electric

circuit) introduces the possibility of wave propagation and wave reflection, two features not

considered under calculations of vascular resistance due to the rigid tube assumption. In

a rigid tube (with incompressible fluid), the pressure is transmitted instantaneously to all

parts of the tube (i.e. infinite speed) and as a result, the fluid travels as a bolus. In an

elastic vessel, a local increase in pressure resulting from ventricular ejection during systole,


expands the vessel wall outwards. In turn, the elasticity of the wall also resists the change

in driving pressure [60]. During diastole, when the pressure decreases, this outward bulge

recoils and the fluid is pushed forward along the tube [60]. Due to this vessel expansion and

recoil with each cardiac cycle, pressure (and the resulting flow) propagate like a wave in the

arterial system (i.e. with finite speed) (Figure 2.2).

Figure 2.2: A local increase in pressure at one end of an elastic vessel (during systole) causes

the vessel wall to expand outwards (panel A). During diastole, when the pressure decreases, the

local bulge recoils and advances towards the other end of the vessel with some finite speed (panel

B). This motion of the local bulge (or disturbance) is pulse wave propagation. With consecutive

systole-diastole cycles (oscillatory pressure), a train of pulse waves propagate along the vessel.

In addition, when this wave propagates along a vessel, a portion of it can get reflected

back (counter to direction of net flow) when the medium it is travelling through encounters a

change in vessel diameter, elasticity, a vessel bifurcation, fluid viscosity, etc. These physical

changes in the vessel determine a system’s resistance and reactance [60], where the former

represents the opposition to flow due to viscous friction along the vessel wall. Reactance, on

the other hand, represents opposition to wave propagation along a vessel and is caused by

dual effects of fluid inertia and vessel elasticity, as described previously [60].

When combined together, resistance and reactance are referred to as impedance [60].

Thus, it can be said that wave reflections arise at points where the impedance (i.e. the

physical properties of the blood vessel and the blood) changes. Furthermore, since impedance


takes into account wave propagation, wave reflection and resistance due to viscous friction,

it can be thought of as a frequency-dependent generalization of vascular resistance [61,62].

2.3 Input impedance

In hemodynamics, the ratio of pulsatile pressure to flow when reflected waves are present is

called the input impedance (Zi):

Zi(f) =Pm(f)

Qm(f)(2.5)

where f is the frequency in Hz and Pm and Qm are the measured pressure and flow, respec-

tively [59].

In comparison to the characteristic impedance, which depends only on the local physical

properties of the vessel (such as the vessel radius or elasticity), the input impedance is

determined by not only the local conditions of the vessel at a particular cross-section, but

the physical properties of the vessels distal to that point as well [59]. For instance, when the

local physical properties of the consecutive vessel segments change from one vessel to the

next in a branching network, this mismatch in the characteristic impedance of the vessels

along the flow pathway generates reflected waves which travel backwards towards the input

vessel. If the vessel impedances were matched, there would be no reflections [59].

Thus, as the forward cardiac pressure wave generated by the fetal heart travels along

the umbilical artery and then encounters a fractal network of smaller diameter fetoplacental

arteries, the consecutive mismatch in the vessel impedances along this path generates multi-

ple reflected waves (Figure 2.3). These reflected waves combine together into a composite

wave travelling opposite to the direction of net forward flow. Thus, the single reflected wave

at the umbilical artery (input to the fetoplacental system) gives information regarding the

downstream fetoplacental arterial vasculature from which the reflections arise.


Figure 2.3: Schematic of the fetoplacental vasculature. The composite reflected wave in the

umbilical artery (in black) represents the summation of multiple reflected pulse waves (in

grey) that arise at points of impedance mismatch in the fetoplacental vasculature. Arrows

indicate the direction of pressure wave propagation.


2.4 Pulse wave propagation and wave speed

The speed at which the pulse wave (pressure or flow) propagates along the vessel, the pulse

wave velocity or PWV, depends primarily on the elasticity of the vessel. This relationship

is formalized in the Moens-Korteweg equation [19] where wave speed, PWV , is defined as:

PWV =

√Eh

2ρr(2.6)

where E is the Young’s modulus of elasticity (ratio of stress to strain), ρ is the density of

the fluid, h is the wall thickness and r is the radius of the vessel. From this equation, it can

be seen that for a stiffer vessel (i.e. high Young’s modulus), the pulse will propagate at a

higher speed along the tube. Indeed, studies show that with increasing age in humans, as the

aorta becomes less elastic, the PWV along this vessel increases [19]. In general, the PWV in

human arterial system is thought to range from 6m/s-8m/s in the aorta to as low as 2m/s

in the pulmonary artery [19]. In the fetal sheep, the umbilical artery PWV is approximately

6m/s, similar to the values in the human aorta [63].

Rather than measure elasticity directly, another way to estimate the PWV is through

the vessel’s characteristic impedance and compliance [64]. The characteristic impedance (Zc)

depends on the local physical properties of the vessel and is defined as the ratio of pressure

to flow in the absence of wave reflections:

Zc =∆P

∆Q(2.7)

Furthermore, the vessel compliance (C) (i.e. the change in vessel cross-sectional area,

∆A, in response to a change in pressure, ∆P ) is related to Zc as follows [64]:

C =∆A

∆P(2.8)

Zc =

√ρ

A· 1

C(2.9)

where ρ is blood density and A is the vessel cross-sectional area. Since measuring Zc directly

is not possible (due to the presence of reflected waves), and measuring pressure change

requires invasive catheters [19], rearranging equations (2.7) and (2.8) in terms of pressure

and substituting for Zc into equation (2.9) results in the following expression for compliance:


Zc∆Q = ∆P (2.10)

Zc∆Q =∆A

C(2.11)

Zc =∆A

C∆Q(2.12)√

ρ

A· 1

C=

∆A

C∆Q(2.13)

C =

(∆A

∆Q

)2

· Aρ

(2.14)

Furthermore, as compliance is related to PWV as follows [64]:

PWV =

√A

ρ· 1

C(2.15)

Substituting for compliance from equation (2.14) into equation (2.15) yields the PWV in

terms of flow change (∆Q) and area change (∆A):

PWV =∆Q

∆A(2.16)

Thus, the PWV can be estimated by measuring the slope of the flow-area curve during the

reflection free period (i.e. the linear portion of the curve). It is generally assumed that early

systole is free of reflections [64].


2.5 Closed-type versus open-type reflection

Modelling the UA as a linear system with respect to pressure and flow, the superposition

principle dictates that the total pressure/flow waveform is a summation of the forward wave

and reflected wave [19]. Interestingly, the reflected pressure and flow waveforms always

have opposing effects on the incident (forward travelling) waveform due to the boundary

conditions at the distal end of a vessel. If the vessel ends in a closed-type termination (i.e.

the vessel diameter narrows or if the vessel branches into two smaller diameter arteries), the

reflected pressure wave will be upright (positive) and the reflected flow wave will be inverted

(negative) [19].

This is because at a closed end boundary, while pressure is allowed to vary (positive),

the flow must be zero (as flow cannot pass a closed end termination). A negative reflected

flow wave, when added to the positive forward flow waveform at the boundary, will result in

zero flow while the converse is true for the pressure waveform (i.e. to obtain total positive

pressure at the boundary, a positive reflected pressure wave must be added to the forward

pressure wave).

On the other hand, at open-type terminations (i.e. the input vessel branches off into a

vascular bed with larger diameter arteries or a fluid reservoir), the reflected pressure wave

at the boundary will be inverted (at an open-end, pressure is released so that pressure is

approximately equal to zero there) while the reflected flow wave will be upright (as fluid is

allowed to flow without impediment at an open-end termination) (Figure 2.4).

In general, the arterial system largely consists of closed-type while the venous system

consists of open-type terminations [19]. In particular, for the fetoplacental arterial network,

the narrowing of vessel branches with each successive branching generation indicates a closed-

type junction at the bifurcation points. Thus, it is expected that in the umbilical artery, the

reflected flow wave will be negative while the reflected pressure wave will be positive. More

importantly, the opposing effects of the reflected pressure and flow waves on the forward

wave allows the decomposition of the observed UA pressure or flow waveforms into their

forward and reflected components (section 2.8).


Figure 2.4: The measured wave is the summation of the forward and reflected waves. In closed type

reflections (panel A), the reflected area wave is upright while the reflected flow wave is inverted. In

open-type reflections (panel B), the reflected area wave is negative while the reflected flow wave is

positive. AM = measured area wave; A+ = forward area wave; A− = reflected area wave; QM =

measured flow wave, Q+ = forward flow wave; Q− = reflected flow wave. Area and flow given in

arbitrary units (AU).


2.6 Early studies of wave reflection

The first formal study of the arterial pulse waveform dates back to 1800s, when the develop-

ment of sphygmographs made possible the recording of pressure pulse waveforms [65]. While

the difference between the shape of the recorded pressure waves in the central and peripheral

arteries was recognized back then [65], it was Donald A. McDonald and John Womersley

who later explained why such a difference existed on the basis of wave reflection [59]. In the

1970s, McDonald’s measurements of pressure and flow waveforms in the canine descending

aorta showed that while the contour of the pressure pulse exhibited a sustained positive

pressure during diastole, the flow pulse contour (scaled to the pressure waveform) diverged

from this pattern and showed a steep decline during diastole [59]. If there were no wave

reflections present (i.e. under conditions of pure vascular resistance and no opposition to

wave propagation), the pressure wave would follow the contour of the flow wave.

Furthermore, another piece of evidence which supported the presence of reflected waves

was the amplification of pressure wave as it traveled down from the ascending aorta towards

the terminal aorta [59]. Due to viscoelastic properties of the aortic vessel wall, it would

be expected that the amplitude of the pressure wave as it travelled downwards would de-

crease, due to energy dissipation. However, studies showed the opposite: the pressure pulse

amplitude increased as it travelled downwards from the ascending aorta [59].

These two phenomenon, differences in pressure and flow waveform contours and pressure

wave amplification in the aorta, can be explained by the presence of reflected pressure and

flow waves having opposing effects on the incident wave as mentioned before. Due to closed-

end type boundary condition, the observed pressure wave in the canine aorta showed a

sustained positive pressure in diastole (due to the addition of a positive reflected pressure

wave to the incident wave) while the observed flow waveform exhibited a ’dip’ in its contour

(due to the addition of a negative reflected flow wave to the incident flow wave).

In addition, pressure wave amplification (travelling downwards along the aorta) can also

be explained by the presence of upright reflected pressure waves: at distal aortic locations,

the upright reflected pressure wave has a higher amplitude than at more proximal sites.

This is due to attenuation of the reflected wave as it travels back towards the heart. Thus,

when these reflected waves are added to the forward travelling incident wave, it results in an

observed pressure wave with a greater amplitude at the distal end than at the proximal end.


2.7 Decomposition of measured waveforms using the

velocity-area method

As the measured pressure and flow waveforms in the umbilical artery are the summation

of a forward wave (generated by the fetal heart) and a reflected wave (generated by the

downstream fetoplacental vasculature), isolating the reflected waveform from the combined

signal can improve the sensitivity for detecting fetoplacental arterial defects.

Westerhof et al provided a method to calculate the forward and reflected components of

the observed pressure and flow waveforms through Fourier analysis [66] while more recently,

Parker and Jones have used time-domain analysis to decompose arterial waveforms using the

method of characteristics [67]. Rather than utilize a frequency-domain analysis, it has been

recognized that the forward and backward components can be determined more simply from

the measured waveforms (in the time-domain) by estimating the characteristic impedance of

the vessel and using the following linear wave separation analysis described by Westerhof et

al [66]:

1. The total pressure change and flow change at a given location in the UA is given by:

∆Qm(t) = ∆Q+(t) + ∆Q−(t) (2.17)

∆Pm(t) = ∆P+(t) + ∆P−(t) (2.18)

where ∆Pm(t) and ∆Qm(t) are the measured change in pressure and flow waves over

time, respectively, while ∆P+(t) and ∆Q+(t) are their forward and ∆P−(t) and ∆Q−(t)

are their backward components. ∆P−(t) and ∆Q−(t) are composite waves, the combi-

nation of many reflected waves from the distal vasculature.

2. Recognizing that pressure change can be substituted for cross-sectional area change

(by assuming a linear relationship between the two quantities and neglecting the vis-

coelastic properties of the arterial wall), equation (2.18) can be written as:

∆Am(t) = ∆A+(t) + ∆A−(t) (2.19)

where ∆Am(t), ∆A+(t) and ∆A−(t) are the measured, forward and reflected area

waveforms, respectively.

3. Substituting for ∆A+(t) and ∆A−(t) in equation (2.19) using ∆Q+(t)/PWV and


−∆Q−(t)/PWV from equation (2.16)1:

∆Am(t) =∆Q+(t)

PWV− ∆Q−(t)

PWV(2.20)

∆Am(t) =1

PWV(∆Q+(t)−∆Q−(t)) (2.21)

4. Rearranging equation (2.17) for ∆Q+(t) and ∆Q−(t) and substituting in equation

(2.21) gives:

∆Am(t) =1

PWV(∆Q+(t)− (∆Qm(t)−∆Q+(t))) (2.22)

Q+(t) =1

2(Qm(t) +Qm(0) + PWV (Am(t)− Am(0)) = Qm(t)−Q−(t) (2.23)

and

∆Am(t) =1

PWV(∆Qm(t)−∆Q−(t)−∆Q−(t)) (2.24)

Q−(t) =1

2(Qm(t)−Qm(0)− PWV (Am(t)− Am(0)) (2.25)

This method to decompose measured flow waves into their forward and reflected compo-

nents is referred to as the velocity-area method (Figure 2.5).

2.8 Characterizing umbilical artery wave reflection through

ultrasound imaging

Historically, wave reflection measurements have required the use of invasive catheters to

measure pressure change in vessels [19]. However, invasive methods have limited utility in

measuring the wave reflection phenomenon in the umbilical arteries of pregnant women.

Ultrasound imaging of the UA overcomes this limitation by providing a clinically relevant,

non-invasive tool to measure: (1) luminal area change (as a surrogate for pressure change)

and (2) flow change in a vessel. These two measurements, apart from the PWV, are necessary

for flow wave decomposition [equations (2.23),(2.25)]:

1. In M-mode ultrasound, ultrasound pulses are emitted (perpendicular to the UA) in

quick succession over time at a single location of the vessel. For each emitted pulse,

a 2D B-mode image of the UA is acquired and multiple 2D images are then ’stacked’

together to represent the final image. Thus, the umbilical artery vessel wall motion

1The forward and backward waves travel with the same PWV. The negative sign in the relationship

PWV = −∆Q−(t)∆A−(t) is due to the fact that the reflected area and flow waves are out of phase/inverted with

respect to each other, as mentioned in section 2.5


at a single location, as it moves towards and away from the scan line (across a series

of emitted pulses), represents how the lumen diameter is changing as a time series.

From the lumen diameter, one can determine the area of the UA over time through

the following relationship:

area = π

(d

2

)2

(2.26)

2. The UA flow can be determined through Doppler ultrasound. For a chosen UA sample

volume, the shift in the frequency between the transmitted ultrasound beam and the

reflected echo from red blood cells (RBCs) is proportional to the velocity of the RBCs.

This information is used to generate the UA velocity pattern image over time. The

flow waveform is determined by the following relationship:

Qm(t) = Vm(t)× Am(t) (2.27)

where Qm(t) is the measured flow waveform (mm3/s), Vm(t) is the measured velocity

waveform (mm/s), and Am(t) is the measured area waveform over time.

Combining the measured area wave, flow wave, and the PWV according to equations

(2.23) and (2.25) results in the decomposition of the observed UA flow wave into its forward

and reflected components (Figure 2.5). Since the reflected waveform depends on the pattern

of reflections occurring from the distal vasculature, several properties of this composite wave

are important for probing the downstream fetoplacental vasculature. In this thesis, I have

characterized the reflected wave in terms of its (1) amplitude (reflection coefficient), (2) time

delay and (3) dispersion (Figure 2.6):

1. The umbilical artery reflection coefficient (ratio of backward to forward wave ampli-

tude) is a measure of how much of the forward wave is being reflected back by the

fetoplacental network. Thus, a higher reflection coefficient would indicate a bigger

mismatch in fetoplacental vascular impedance. In general, the local reflection coeffi-

cient at arterial bifurcations (in humans) is found to be less than 0.2 [68].

2. The time delay (time difference between the peak of the backward wave and peak of

forward wave over a single cardiac cycle), depends on the speed of the pulse wave

propagation (PWV). An increase in the PWV (i.e. if the UA was stiffer) would result

in a shorter time delay and would indicate that the reflected wave is occurring earlier

in the cardiac cycle.

3. Dispersion quantifies the number of underlying reflected waves (produced at various

sites in the fetoplacental vasculature) that contribute to the single, composite UA

reflected wave. It can be calculated by taking the difference in the widths of the


backward and forward wave (where width is determined as the full-width half maximum

value). A higher dispersion value (i.e. reflected wave has a greater width) would

indicate a greater range of transit times to and from reflection sites.


Figure 2.5: Decomposition of the observed UA flow wave (Qm(t)) into its forward (Q+(t)) (in

red) and reflected components (Q−(t)) (in blue). PWV is determined from the slope of the linear

portion of the flow-area curve (in green).


Figure 2.6: The reflected wave (in blue), characterized in terms of its reflection coefficient (reflected

to forward wave amplitude), time delay (peak reflected time - peak forward time) and dispersion

(reflected width - forward width).

Chapter 3

Mouse as a model organism

In this thesis, the method for measuring umbilical artery wave reflection has been developed

in mice. Although the reproductive strategy between humans and mice is quite different

(i.e. in humans, the 40 week long gestation period usually results in a single, well-developed

fetus while the 18-20 day long mouse gestation produces up to 15 underdeveloped pups),

both show similarities in their placental gene expression and hemodynamics [20, 69, 70]. As

well, the fetoplacental vascularity between the two is remarkably similar. For instance, the

villous portion of the mouse placenta (called the labyrinth zone) forms an elaborate, branched

network of fetoplacental vessels that are similar in structure and function to the villous tree

of a single, human placental cotyledon [71]. One difference, however, is that humans have

two umbilical arteries but the mouse has only one.

In addition, both mice and humans have hemochorial placentas, meaning that the tro-

phoblast layer lining the villi comes into direct contact with the maternal blood [71]. Further-

more, from midgestation to term, both species show comparable growth in their placental

vascular trees and capillaries. This growth is paralleled by increases in the umbilical artery

peak and end-diastolic velocities (however, the end-diastolic velocity is larger in humans as

compared to mice at term) [69,72,73].

More importantly, over the past few years, the physical properties of the mouse fetopla-

cental vasculature has been studied in depth through X-ray micro-computed tomography

(CT) imaging [21, 22]. Using 3D micro-CT datasets and automated vessel segmentation

techniques, these studies have characterized the morphology of the vast number of placental

vessels in terms of their diameters, lengths and branching pattern [22]. Furthermore, in mice,

these techniques to study vascular patterning have been used to characterize the growth of

the fetoplacental tree across gestation, as well as to detect abnormal vascular patterning in

numerous mouse models of impaired fetal growth [74,75,76].

Thus, as compared to human placental studies, the well-established details on the mouse

fetoplacental vasculature under normal and pathological conditions offers a huge advantage

in linking the composite UA reflected waveform to microvascular fetoplacental properties.

26

Chapter 3. Mouse as a model organism 27

3.1 Aims

As current UA Doppler based assessments perform poorly in detecting placental pathologies,

which in turn has huge implications for the in-utero detection of IUGR due to placental

disease [13, 17, 18, 57, 58], the goal of this thesis was to develop a non-invasive, clinically

translatable tool sensitive to fetoplacental morphological changes.

The aims of this thesis were as follows:

1. To develop the methodology for measuring umbilical artery wave reflection in mice.

2. To determine if UA wave reflection patterns are sensitive to variations in mouse feto-

placental morphology.

3. To evaluate the sensitivity of UA reflected wave and UA pulsatility index (current

clinical standard) in detecting fetoplacental vascular changes.

To obtain reflected wave measurements using the velocity-area method and ultrasound

imaging (Figure 2.5), I developed a semi-automated image processing pipeline to extract

the velocity and area waveforms from Doppler and M-mode images. Furthermore, I im-

plemented data quality control and signal processing criteria for consistent and non-biased

decomposition of the measured UA flow wave.

To determine if UA reflected wave patterns are sensitive to variations in fetoplacental

morphology, I conducted a proof-of-principle experiment in two common strains of mice,

CD1 and C57BL/6. Detailed micro-CT work has shown that in late gestation, the fetopla-

cental vascular growth between these two strains diverges [21]. Thus, to determine if the

UA reflected wave pattern in late gestation would parallel this divergence in fetoplacental

morphology, I measured and characterized the reflected wave between these two strains at

two different time points: embryonic (E) day E15.5 and E17.5. From previous studies, it

has been shown that the fetoplacental vascular patterning between the two strains is similar

at the earlier gestational age (E15.5) while at E17.5, the C57BL/6 strain has less capillaries

and larger diameter fetoplacental arteries as compared to CD1 mice [21]. Thus, I predicted

that the wave reflection patterns would differ between the two strains only in late gestation.

Lastly, I compared the sensitivity of the UA pulsatility index and the reflected wave to

mouse fetoplacental vascular changes.

Chapter 4

Methods

Pregnant CD1 and C57BL/6 mice from the Toronto Centre for Phenogenomics (TCP) in-

house colony were studied cross-sectionally at E15.5 and E17.5. All animal experiments were

approved by the Animal Care Committee at the TCP.

4.1 Animal Preparation

To limit the effects of maternal respiration on UA motion, the maternal respiration rate

was reduced so that a longer recording of the UA wall signal could be analyzed in-between

the respiration cycle (i.e. during the relatively movement-free time period) (Figure 4.1).

The time interval between successive maternal inhalations was lengthened by keeping the

pregnant mouse under an elevated concentration of 2.5% isoflurane, as compared to the

1.5% isoflurane concentration often employed for non-invasive mouse ultrasound imaging.

At this anaesthesia concentration, the respiration rate of the pregnant mouse decreased to

40-60 breaths/minute, rather than the 160-170 breaths/minute range observed under 1.5%

isoflurane concentration.

To obtain the ultrasound recordings of CD1 and C57BL/6 strains at E15.5 and E17.5

timepoints, the pregnant dam was placed in a supine position and hair from the abdominal

region was removed using Nair (Church & Dwight Co., Inc., Erwing, NJ, USA). Warmed

ultrasound gel was then placed on the abdomen and the body temperature of the pregnant

mouse was maintained at 37◦C by using a temperature-regulated platform. The heart rate

and respiration of the pregnant mouse was monitored throughout the entire recording session.

28

Chapter 4. Methods 29

Figure 4.1: Umbilical artery M-mode acquired using non-invasive protocol. Maternal respi-

ration cycle was lengthened by decreasing the breathing rate with 2.5% isoflurane concentra-

tion. The UA wall signal was analyzed during the relatively motion free period in-between

successive maternal inhalations. The red box highlights umbilical artery displacement result-

ing from maternal inhalation. The yellow and green traces represent the maternal respiration

and ECG signal, respectively.

4.2 Ultrasound imaging

Recordings were obtained from the fetal end of the UA by using a high frequency (40 MHz)

linear array transducer (VisualSonics Vevo 2100). The UA Doppler and M-mode signals were

recorded at approximately the same location during a five second window. The UA luminal

diameter change was measured using M-mode ultrasound (frame rate = 3000 frames/second),

with the ultrasound beam perpendicular to the vessel. The velocity spectrum was mea-

sured using pulsed-wave (PW) Doppler (pulse repetition frequency = 3 kHz to 10 kHz) and

choosing a sample volume large enough to cover the entire UA luminal region (the angle

of insonation between the ultrasound beam and direction of flow was less than 60o). The

Doppler wall filter was set between 150 Hz to 200 Hz, to account for low-frequency Doppler

signals due to vessel wall motion.

4.3 Semi-automated Image Analysis

4.3.1 M-mode recording:

All image analysis was performed in Python, version 2.7.3 (https://www.python.org/). For

each five second M-mode acquisition, the two walls of the UA were outlined using an edge

detection technique. First, the upper and lower bounds containing the top and bottom walls


were specified manually. Next, for each column of pixels within the bounded region, the wall

location at which the maximum pixel intensity occurred was determined. Finally, the inner

location where the pixel intensity crossed 95% of this maximum (in each pixel column) was

recorded to trace the edge of the top and bottom wall (Figure 4.2, panel A).

Figure 4.2: Panel A shows the tracking of the top and bottom umbilical artery vessel walls

(in red). Panel B depicts the raw umbilical artery bottom wall signal (in green) and its

corresponding smoothed signal (in red), in terms of pixel position. The wall signal was

smoothed using a lowpass Butterworth filter.

The tracked luminal outline was smoothed by using a lowpass, second order Butterworth

filter (from scipy.signal library in the SciPy package). The cutoff frequency of the filter was

set to 5 times the fundamental frequency of the fetal heart. This cutoff (through visual

inspection) preserved the shape of the diameter signal while removing the jitter in the signal

due to noise (Figure 4.2, panel B). The resulting smoothed waveform was partitioned into

individual fetal cardiac cycles based on the onset of systole.

A specific challenge for applying this method in the fetus is that the electrocardiogram

(ECG) is not available to determine the start of systole. To overcome this, the sharp change

in the UA speckle pattern between diastole and systole was used to infer the beginning of


consecutive cardiac cycles on M-mode images (i.e. a change from the globular fetal red blood

cell (RBC) speckle pattern in diastole to a striated pattern in systole due to acceleration of

RBCs).

To detect the onset of systole, the following automated pipeline was implemented (using

the ndimage.filters and ndimage.morphology libraries from the SciPy package): first, the

region of UA containing the speckle pattern was selected and a Sobel filter was applied to

detect vertical edges in the speckle pattern (Figure 4.3, panel A). As such, mainly the

vertical striated patterns in systole were detected. This vertical edge image was binarized

and morphological closing (edge dilation and erosion) was applied to close holes between

the vertical edges and to remove noise (i.e. vertical edges detected in the diastolic region)

(Figure 4.3, panels B and C).

The intensities of this binarized image were then projected onto the x-axis, and the start

of systole was determined at the pixel location where the intensities changed from 0 to 1

(Figure 4.3, panels D and E). Next, the pixel coordinate was converted to physical

distance and the perpendicular distance between the partitioned, smoothed vessel walls

was used to compute the cross-sectional area as a function of time [using equation (2.26)]

(Figure 4.3, panel A). The individual UA area waveforms from each fetal cardiac cycle

were temporally aligned to have a uniform length (Figure 4.4, panel B). These aligned

waveforms were then averaged into a single area waveform (Figure 4.4, panel C).


Figure 4.3: In panel A, the yellow circle highlights the smeared RBC speckle pattern during

diastole while the red box highlights the striated RBC speckle pattern during systole. The

region encompassing the speckle pattern was binarized (panel B) and the holes between the

binarized vertical edges were closed using edge dilation and erosion (panel C). The pixel

intensities from panel C were projected onto the x-axis (panel D) and the change in pixel

intensity from 0 to 1 was used to detect the start of systole, as indicated by the red crosshairs

in panel E.


Figure 4.4: From the perpendicular distance between the umbilical artery top and bottom

walls, the cross-sectional area across time was calculated for each fetal cardiac cycle (panel

A). The black arrows in panel A indicate non-physiological area waveforms (due to maternal

respiration/fetal motion) that were excluded from analysis. The area waveforms were aligned

to have a uniform length (panel B) and were subsequently averaged to obtain a single area

waveform (panel C).


Pre-processing and post-processing steps

To preserve data quality and physiological consistency in the area waveforms, pre- and post-

processing criteria were applied to the M-mode raw signal and extracted area waveforms,

respectively. The pre-processing criteria was as follows:

1. Datasets were excluded if during ultrasound imaging, it was observed that there were

high levels of maternal gasping/fetal movements.

2. Datasets were excluded if after plotting the raw M-mode UA wall signal, it was observed

that the recorded signal was clearly non-physiological (i.e. the signal pattern was

completely non-cyclical) and had excessive high frequency components (Figure 4.5)

Figure 4.5: Raw umbilical artery wall signal. This dataset was excluded after visual inspec-

tion as the wall signal (over several fetal cardiac cycles) appeared non-physiological and had

pronounced high frequency components (compare with Figure 4.2, panel B).

If the M-mode wall signal met the pre-processing criteria, the following post-processing

criteria were applied after extracting the filtered area waveforms from the wall signal:

1. Individual area waveforms that appeared to be contaminated with maternal gasps or

appeared non-physiological were removed before the alignment and averaging process

(Figure 4.4, panel A).

2. Datasets were excluded if more than 35% of the total aligned waveforms were outside

bands representing ± 20% of the average area change. Visually, at this threshold, the


area waveforms separated into two distinct clusters, representing datasets with low and

high variation between the individual area waveforms (Figure 4.6)

3. Datasets were excluded if there were not enough individual area traces to average (less

than 4)

Other studies measuring arterial wave reflection have accounted for noise in the pressure

waveform signal through similar post-processing steps [77].

Figure 4.6: The grey lines show the individual, aligned area waveforms. The red line rep-

resents the average area waveform while the upper and lower blue lines represent ± 20%

of the average area change, respectively. In panel A, the dataset was discarded after post-

processing as more than 35% of the total aligned area waveforms were outside the upper and

lower bounds represented by the blue line while the dataset in panel B was included in the

analysis, as less than 35% of the total aligned waveforms were outside the bounds.


4.3.2 Doppler recording

For each column of pixels in the image, the centroid between the upper envelope and lower

bound of the velocity spectrum was computed based on pixel intensities (Figure 4.7, panel

A). After applying a lowpass Butterworth filter with the same properties as the filter used

for M-mode recordings, the extracted velocity waveform was divided into individual fetal

cardiac cycles, temporally aligned and averaged (Figure 4.7, panels B and C). The start

of systole was manually marked as the point where the blood velocity first began to rise at

the end of diastole (Figure 4.7, panel A).

Figure 4.7: Panel A shows the umbilical artery Doppler velocity spectrum and its extracted

centroid (red line). The red arrows indicate the start of systole. The extracted velocity

spectrum was aligned (panel B) and an average velocity waveform was obtained from the

total aligned velocity waveforms (panel C).


4.4 Wave Decomposition

From the average velocity and area waveforms, the average flow waveform was calculated

from equation (2.27). Next, the average flow and area waveforms were plotted (QA loop)

and a line was fitted (using total least squares) to 20%-80% of systolic region in the curve.

This initial systolic portion is assumed to be free of reflections [64, 78]. The slope of this

line was calculated to obtain the PWV (equation (2.16)). Together, the measured area and

flow waves, along with their PWV, were used to decompose the observed flow waveform into

its forward and reflected components by using the velocity-area method, as described earlier

(see section 2.7: equations (2.23) and (2.25); Figure 2.5).

4.5 Wave Reflection Characterization

The reflected placental wave was summarized in terms of the reflection coefficient (ratio

of the absolute peak-to-peak variation between backward and forward wave), time delay

(the time difference between the peak of backward and forward wave) and dispersion (the

difference between the full width at half maximum of the backward and forward wave) (see

Figure 2.6).

Furthermore, the UA pulsatility index (a common clinically used metric for inferring

placental resistance) was calculated from the extracted Doppler velocity spectrum as follows:

UA pulsatility index =S −DM

(4.1)

where S is the systolic velocity maximum, D is the diastolic velocity minimum and M is the

mean velocity (velocity time-integral divided by the length of the cardiac cycle).

The receiver operating characteristic (ROC) curve was computed to evaluate the sen-

sitivity of the UA pulsatility index and wave reflection metrics to intrastrain fetoplacental

vascular differences at E17.5. Lastly, to determine if the variation in the wave reflection

parameters could be explained by non-placental factors, a Pearson’s correlation test between

the reflection metrics and the fetal heart rate was performed.

4.6 Statistical Analysis

The following statistical tests were performed using R statistical software, version 3.1.1

(http://www.r-project.org/):

1. A two-way ANOVA to evaluate the interaction of strain and gestational age on the

wave reflection metrics and UA pulsatility index.


2. A two-tailed independent samples t-test (with Welch’s correction for non-homogeneity

of variance) to determine if the wave reflection metrics differed between E15.5 and

E17.5 timepoints within each strain.

Results are reported as mean ± standard error of mean (SEM). Statistical significance was

defined as p < 0.05. Lastly, the normality of the distribution of the data were examined

with the Shapiro-Wilk test (see Appendix B for plots of the data distribution).

Chapter 5

Results

The number of animals used is summarized in Table 5. After applying the pre- and post-

processing steps to the M-mode recordings, 43% of the UA scans met the quality control

criteria and were included in the wave decomposition analysis. The following sections sum-

marize the main findings.

Strain Gestational

Age

m n-total n-removed n

C57BL/6 E15.5 4 22 12 10

CD1 E15.5 4 22 14 8

C57BL/6 E17.5 6 22 13 9

CD1 E17.5 7 29 15 14

Table 5.1: Animals used in the wave decomposition analysis. m = number of pregnant mice,

n-total = total number of fetuses scanned, n-removed = number of UA fetal scans removed

based on pre- and post-processing criteria, and n = number of UA fetal scans included in

the analysis.

5.1 Shapiro-Wilk Test

In general, the Shapiro-Wilk test for determining the normality of distribution was non-

significant for all wave reflection parameters and the pulsatility index, barring two exceptions:

1. For CD1 strain at E17.5, the reflection coefficient distribution was significantly different

from the normal distribution (p < 0.05) due to the presence of two data points ∼ 2

standard deviations away from the mean (see Figure B.1, panel D in Appendix

39

Chapter 5. Results 40

B). Removing the two datasets did not change the statistical significance for the various

inter- and intrastrain comparisons made and were therefore included in the analysis.

2. The UA pulsatility index distribution was significantly different from the normal dis-

tribution for the C57BL/6 strain at E17.5 (p < 0.05). This was due to the presence of

one data point, which was ∼ 3 standard deviations away from the mean (see Figure

B.1, panel B in Appendix B). In particular, the UA pulsatility index value of this

fetus was much higher (approximately 7) than that observed in the rest of the 41 UA

fetal scans (between approximately 2 to 4). Given these observations, this C57BL/6

fetal dataset was removed from the analysis.

Removing this dataset changed the statistical significance for detecting a difference in

the average UA pulsatility index of the C57BL/6 mouse at E15.5 vs. E17.5 (t-test).

With the inclusion of the dataset, the decrease in the pulsatility index metric from

early to late gestation was non-significant (t-test: p = 0.82) while with its exclusion,

the late gestation decrease was significant (t-test: p = 0.02). Furthermore, the UA

pulsatility index strain and gestational age interaction changed from p = 0.0404 to p

= 0.0506 (two-way ANOVA), after exclusion of this dataset.

5.2 Strain and gestational age interaction

The UA wave decomposition results for each strain and gestational age are shown in Figure

5.1. The effect of strain (CD1 vs. C57BL/6) on the reflection coefficient differed at E15.5 and

E17.5 (two-way ANOVA; strain × gestational age interaction: F-value = 4.44, p = 0.0420).

More specifically, at E15.5, the average reflection coefficient was not different between the

two strains while at E17.5, the reflection coefficient was 33% higher in C57BL/6 mice as

compared to CD1 (p < 0.05).

Similarly, the UA pulsatility index showed a trend towards a strain and gestational age

interaction. The pulsatility index was ∼ 14% higher in C57BL/6 mice at E17.5 while not

significantly different between the two strains at E15.5 (two-way ANOVA; strain x gestational

age interaction: F-value = 4.08, p = 0.0506). Tables 5.2 and 5.3 present the two-way

ANOVA results for the reflection coefficient and UA pulsatility index response variables,

respectively. The time delay, dispersion and PWV parameters showed no significant strain

and gestational age interaction (Figure 5.2).

Lastly, the reflection coefficient showed no evidence of correlation to the fetal heart rate

for all strains and gestational ages (Pearson’s correlation between -0.14 to 0.32; p-values

ranged from 0.40 to 0.62). The average of the measured parameters are presented in Table

5.4.


Source of variation dF Mean Square (×10−2) F value pStrain 1 3.59 5.53 0.02

Gestational Age 1 1.24 1.91 0.18Strain × Gestational Age 1 2.88 4.44 0.04

Residuals 37 0.65

Table 5.2: Analysis of variance (two-way ANOVA with interaction) of the mean reflectioncoefficient by strain and gestational age. dF = degrees of freedom and p = probability ofsignificance.

Source of variation dF Mean Square F value pStrain 1 0.35 1.32 0.26

Gestational Age 1 6.88 26.28 < 0.01Strain × Gestational Age 1 1.07 4.08 0.0506

Residuals 37 0.26

Table 5.3: Analysis of variance (two-way ANOVA with interaction) of the mean pulsatil-ity index by strain and gestational age. dF = degrees of freedom and p = probability ofsignificance.

5.3 Intrastrain effects from E15.5 to E17.5

For CD1 mice, there were no differences in the wave reflection parameters across gestation.

However, the average UA pulsatility index was 32% lower at E17.5 as compared to E15.5 (p

< 0.01, t-test).

For C57BL/6 mice, the average UA reflection coefficient and the pulsatility index differed

across gestation. More specifically, the reflection coefficient was 26% higher at the later

gestational age (p < 0.05, t-test) while the UA pulsatility index was ∼ 15% lower at the

later gestational age (p < 0.05, t-test) (Figure 5.2).


Str

ain

Ges

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)

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Figure 5.1: Umbilical artery flow wave decomposition showing the average forward and backward

flows for each cohort of mice. For each fetus, the decomposed forward and backward flow waves

were normalized to the time averaged forward flow mean. Next, within each strain and gestational

age cohort, these normalized waveforms were aligned in time and averaged together. Dotted lines

represent ± sem.


Figure 5.2: Wave reflection parameters and UA pulsatility index. Data shown as mean ± sem.

Within each strain, means not sharing a common letter (a,b) are significantly different (t-test; p

< 0.05). * p < 0.05 denotes a significant strain and gestational age interaction, as determined by

two-way ANOVA.


5.4 Reflection coefficient and UA pulsatility index sen-

sitivity

The reflection coefficient was more sensitive than UA pulsatility index to differences in the

fetoplacental networks of CD1 and C57BL/6 mice at E17.5. The AUC for the ROC curve

was 0.94 for the reflection coefficient metric and 0.81 for the UA pulsatility index metric

(Figure 5.3).

Figure 5.3: Reflection coefficient and UA pulsatility index ROC curves for detecting inter-

stain fetoplacental vascular differences at E17.5.

Chapter 6

Discussion

In this thesis, a novel, non-invasive method to measure and characterize UA wave reflections

has been developed. Results indicate that the wave reflection methodology can detect dif-

ferences in the mouse fetoplacental vasculature. More specifically, the reflection coefficient

parameter was sensitive to variations in fetoplacental arterial morphology with strain and

gestational age effects, while the time delay and dispersion metrics were not. As seen in other

vascular beds, the reflection coefficient metric has utility for detecting arterial diseases and

inferring vascular properties, such as increased vessel stiffness. For instance, in pulmonary

arterial hypertension patients, where pathological changes are often observed in the elastic

and resistive compartments of the pulmonary vasculature, the reflection coefficient is more

than twice that of healthy subjects [79]. In C57BL/6 mouse lungs exposed to chronic hy-

poxia, structural remodeling of the vasculature (i.e. increases in proximal pulmonary arterial

stiffness) is correlated with greater magnitude of pulse wave reflections [80].

As such, the reflection coefficient metric has relevance for the in-utero detection of fe-

toplacental vascular defects, such as those associated with IUGR. The following sections

examine how the reflection coefficient parameter varies with interstrain differences in the

mouse fetoplacental morphology.

6.1 Fetoplacental intrastrain effects on UA reflection

coefficient

CD1 mice

From E15.5 to E17.5, previous morphological data shows that while there is no growth in

the fetoplacental arterial network of CD1 mice (i.e arterial diameters, lengths and branching

pattern are relatively constant), the capillary volume increases substantially over this time-

point [21]. Interestingly, the reflection coefficient in the present study did not change with

increases in capillary volume, which suggests that this parameter is insensitive to growth in

46

Chapter 6. Discussion 47

the capillaries.

As arterial pulsations are highly attenuated by the time they reach the capillary bed [14],

it is likely that the magnitude of reflected waves emanating from the many arteriole-capillary

junctions are quite small or negligible. Thus, their contribution to the UA composite reflected

wave would be minimal, despite increases in capillary volume. For instance, previous work on

the microvasculature of the rat spinotrapezius muscle shows that variations in the dimensions

and network topology of the capillary bed (i.e. by modifying capillary diameters, lengths

or connectivity) has little effect on the input impedance spectrum [81]. Since the spectral

oscillations in the input impedance spectrum are determined by the extent to which forward

pressure and flow waves are reflected from distal sites, this is consistent with the capillary

network having little effect on the reflected waveform at the input.

Indeed, it has been suggested that the frequency dependence of the input impedance

is independent of physical properties of vessels distal to the arterioles due to cardiac pulse

attenuation [14]. Thus, the observation that the reflection coefficient did not change with

increases in fetoplacental capillary volume is plausible in the context of previous findings.

C57BL/6 mice

In contrast to CD1 mice, C57BL/6 mice have growth in both the fetoplacental arterial and

capillary compartments from E15.5 to E17.5 timepoints [21]. Parallel to this growth in the

fetoplacental vasculature, we found that the average UA reflection coefficient increased with

gestation in this strain by 26%. Accepting that this metric is insensitive to increases in

capillary volume, as mentioned previously, then the observation of an elevated UA reflection

coefficient is likely due to changes in the fetoplacental arterial morphology.

Indeed, micro-CT geometric data show that from E15.5 to E17.5 in C57BL/6 mice, there

is growth in the 75µm - 150µm diameter intraplacental arteries (i.e. these vessels have a

larger diameter at E17.5 as compared to E15.5) [21]. Consequently, the daughter to parent

vessel area ratio at arterial bifurcations increases from 1.26 at E15.5 to 1.35 at E17.5 [21].

An area ratio of 1.26, as observed in the C57BL/6 mouse at E15.5, is consistent with min-

imization of energy dissipation due to viscous friction in a biological system and is predicted

by Murray’s law for scaling radii in a hierarchical branching network [82,83] (see Appendix

A, section A.1, for derivation of area ratio under Murray’s law).

In contrast, minimizing pulse wave reflections by matching vascular impedances leads

to an area ratio of 1.0, under the assumption that only the radius is allowed to vary at

a bifurcation. This area ratio is predicted by the square-law for scaling vessels and in

comparison to Murray’s law, it is found to preserve the cross-sectional area across an arterial

junction (see Appendix A, section A.2, for derivation of area ratio under the square law) [82].

In other words, when the ratio of the daughter to parent vessel cross-sectional areas is 1.0,

the impedances are matched and reflections at this bifurcation will be zero.


Interestingly, the local reflection coefficient as a function of the area ratio behaves as

a parabola with the global minimum (reflection coefficient = 0) occuring at an area ratio

of 1.0. Under this construct, deviations away from an area ratio of 1.0 leads to greater

reflections [82]. This suggests that in the C57BL/6 mouse at E17.5, where the area ratio is

found to be 1.35, the reflection coefficient at a single bifurcation will be greater than at E15.5,

where the area ratio is 1.26 (Figure 6.1). Thus, the finding that the global UA reflection

coefficient (representing reflections from multiple downstream bifurcation sites) is higher at

E17.5 as compared to E15.5 is plausible (see Appendix A, section A.3, for derivation of

reflection coefficient as a function of the area ratio).

Lastly, it appears that a late gestation increase in the area ratio of C57BL/6 mice occurs in

response to reduced fetoplacental capillarization, such that the more upstream intraplacental

arteries are enlarged to lower the total fetoplacental arterial resistance and maintain flow [21].

However, minimizing losses due to viscous friction by increasing upstream arterial diameters

appears to be at the cost of increased pulse wave reflections.

Figure 6.1: Reflection coefficient (independent of wave velocity and blood density) as a

function of the area ratio at a single arterial bifurcation.


6.2 Fetoplacental interstrain effects on UA reflection

coefficient

Geometric data indicate that at E15.5, the fetoplacental vasculatures of CD1 and C57BL/6

mice are similar while at E17.5, the two vascular networks differ [21]. The UA reflection

coefficient values parallel this fetoplacental morphological data. More specifically, earlier

work characterizing the fetoplacental vasculature shows that at E15.5, the capillary volume

and fetoplacental arterial characteristics (in terms of vessel diameters, lengths and Murray’s

scaling law) are similar between CD1 and C57BL/6 mice [21].

In late gestation, however, C57BL/6 mice exhibit blunted fetoplacental capillarization

as compared to CD1 [21]. Furthermore, while the CD1 fetoplacental vasculature follows

Murray’s law for minimizing viscous dissipation (i.e. the daughter to parent vessel area-ratio

is 1.26), the C57BL/6 fetoplacental network at E17.5 deviates from Murray’s law and has an

elevated area ratio of 1.35 [21]. As discussed previously, since an area ratio of 1.35 is farther

away from the condition for minimal reflections as compared to an area ratio of 1.26, this

indicates that the fetoplacental vascular impedances in C57BL/6 mice are more mismatched

than CD1 vessels. Consequently, C57BL/6 mice at E17.5 would be predicted to have a

higher UA reflection coefficient (Figure 6.1).

Indeed, these fetoplacental intrastrain differences are captured in our finding of a 33%

larger UA reflection coefficient in late gestation C57BL/6 mice while at E15.5, the aver-

age reflection coefficient is similar between the two strains (two-way ANOVA: strain and

gestational age interaction, p < 0.05).

Lastly, as our results show that UA reflection coefficient is independent of variations in

the fetal heart rate and can detect differences in fetoplacental arterial growth patterns, it

appears to be a robust parameter for probing the downstream fetoplacental vasculature.

6.3 Fetoplacental intrastrain and interstrain effects on

UA pulsatility index

In comparison to the UA reflection coefficient measure, the UA pulsatility index decreased

across gestation in CD1 and C57BL/6 mice. Electrical models of the Doppler waveform

pulsatility suggest that if the arterial pressure pulsatility (which drives flow through the

placental vasculature) is constant, then the UA pulsatility index is dependent on the ratio

of the placental to umbilical artery resistances [84]. Assuming that the aortic pressure

pulsatility and umbilical artery properties do not vary across gestation in C57BL/6 and

CD1 mice, then the decline in the UA pulsatility index is likely due to decreases in the

placental resistance across gestation.


Indeed, in both strains, it is observed that the capillary volume increases from E15.5 to

E17.5 timepoints while in C57BL/6 mice, there is also growth in the intraplacental arteries

[21]. These vascular changes may be responsible for decreases in the placental resistance and

consequently, the decline in the UA pulsatility index across gestation. Previous studies have

shown a similar decrease in the UA pulsatility index and other Doppler indices over these

timepoints [69,85].

In terms of strain and gestational age interaction, it was observed that the UA pulsatil-

ity index showed a trend towards significance. At E15.5, the pulsatility index was similar

between the two strains. Likewise, geometric data indicate that the capillary volumes and

arterial properties between the two strains are similar at this gestational age [21]. In late

gestation, however, the average UA pulsatility index was 14% higher in C57BL/6 mice.

This is likely due to interstrain differences in the capillary volume at E17.5, where the CD1

mice capillary volume is approximately twice that in C57BL/6 mice [21]. Indeed, in human

pregnancies, a decline in the UA pulsatility index from midgestation to term is attributed

to substantial proliferation of the capillary network, such that the capillary bed resistance

becomes lower than that of the arterial network [86]. Therefore, it is plausible that blunted

fetoplacental capillarization in C57BL/6 mice results in a higher UA pulsatility index as

compared to CD1 mice.

6.4 Reflection coefficient and UA pulsatility index sen-

sitivity

Since the fetoplacental vasculatures of CD1 and C57BL/6 differ at E17.5, the sensitivity

of the reflection coefficient and UA pulsatility index metrics to late gestation interstrain

differences was determined. Our results showed that the reflection coefficient metric was

more sensitive to differences in fetoplacental morphology as compared to the UA pulsatility

index.

Previous studies have shown that the UA pulsatility index is directly related to the

total umbilico-placental vascular resistance if the pressure pulsatility (dependent on cardiac

function) and the properties of the umbilical artery are invariant [14]. Although these latter

two factors were not evaluated in this study, it is possible that interstrain variation in these

parameters may have resulted in a lower UA pulsatility index sensitivity to fetoplacental

morphological changes.


6.5 Application to human pregnancies

Currently, the UA pulsatility index is commonly used to characterize Doppler waveforms

and infer placental function, such that elevated values of the pulsatility index are thought

to signify increased fetoplacental vascular resistance [10]. However, studies show that the

correlation between UA flow pulsatility index and placental resistance does not hold un-

der all hemodynamic conditions [14]. Indeed, earlier studies showed that when vasoactive

agents were used to change the total umbilico-placental vascular resistance from baseline

conditions in fetal sheep, the correlation between the UA flow pulsatility index and the

umbilico-placental vascular resistance was quite poor [14].

This is because the pulsatile UA Doppler flow waveform is determined by not just the

umbilico-placental vascular resistance, but also the vascular impedance at the UA, which

depends on the attributes of the umbilical artery and downstream reflections [14]. For

instance, when microsphere embolization of the small placental vessels was used to increase

the cotyledon resistance in fetal sheep, a positive, linear relationship was observed between

placental resistance and UA pulsatility index [87]. However, when angiotensin II was used to

selectively increase the resistance of the umbilical artery in fetal sheep, it was observed that

even though the umbilico-placental resistance increased by a factor of 6 and the fetoplacental

perfusion decreased considerably, the UA Doppler flow pulsatility did not change [87]. This

was due to coincident decreases in pulse flow and mean flow, the two determinants of the UA

pulsatility index. Based on these observations, it has been suggested that the pulsatility index

does not detect increases in umbilico-placental resistance due to changes in the umbilical

artery resistance [14].

Furthermore, pressure pulsatility, which is determined by upstream cardiac factors such

as the cardiac output (heart rate × stroke volume) and aortic compliance, can also impact

the flow pulsatility index in the UA [14]. For instance, one study found a statistically

significant negative correlation between the pulsatility index and the fetal heart rate in

human pregnancies [88]. In particular, 17% of the total UA pulsatility index variance was

attributed to the fetal heart rate. Thus, the dependency of the pulsatility index on placental,

umbilical and cardiac factors may explain why the sensitivity of this measure in detecting

IUGR due to placental pathology is quite poor. In particular, if these factors have offsetting

effects on the pulsatile and mean flow components of the pulsatility index ratio, or if the

pulse pressure varies considerably, it may lead to erroneous conclusions about the umbilico-

placental vascular resistance.

Given that the UA wave reflection methodology allows for the removal of cardiac signal

from the observed UA waveform, and that the reflected flow waveform is determined by

the physical properties of the umbilical artery and the associated downstream vasculature,

the wave decomposition methodology has the potential to reliably detect changes in the


fetoplacental microcirculation due to umbilical or fetoplacental arterial defects.

6.5.1 Detection of IUGR

Defects in the fetoplacental arterial and capillary compartments have both been associated

with IUGR. For instance, vessel wall thickening and degeneration of the small to medium

sized arterial vessels (50µm− 149µm in diameter) has been previously found in IUGR pla-

centas [89]. However, the sensitivity of UA Doppler (the current clinical gold standard)

to placental defects is quite low [18]. Indeed, in one study, the abnormal stereological pa-

rameters of the intermediate and terminal villi in the IUGR group showed no correlation

with various UA Doppler indices (such as the pulsatility index, resistivity index, etc) [90].

Furthermore, as a change in UA Doppler indices represents a late pathological process, it

has been shown that resistance measures of intraplacental artery perform better in detecting

early placental disease as compared to UA pulsatility index of the UA [91].

Since our results suggest that the reflected waveform can detect subtle differences in feto-

placental arterial morphology, and it is more sensitive to detecting interstrain fetoplacental

vascular differences as compared to the UA pulsatility index, this technique may offer an

advantage in detecting early, and milder forms of placental pathologies underlying IUGR .

Furthermore, defects in the morphology of the non-muscularized capillaries have also been

observed in IUGR [6]. Although results indicate that the reflection coefficient parameter is

insensitive to increases in capillary volume, models of the capillary bed by Wiedeman et al

indicates that it is the relative difference in the characteristic impedances of capillaries and

their parent vessel, the arterioles, which is the determining factor [92]. For instance, if the

capillary impedance is not very different from its parent arteriole, then the input impedance

(normalized to that of the parent vessel) is constant, regardless of increases in capillary vessel

branching. As oscillations in the input impedance spectrum are determined by reflections

from the downstream vasculature, this suggests that reflections from capillary branching,

under these conditions, do not have a large effect on the input waveform. This may be

the case in CD1 and C57BL/6 mouse fetoplacental vasculature where despite increases in

capillary volume, the characteristic impedances of the capillaries may not change greatly

across gestation.

In comparison, if the capillary impedance is more than 100 times that of the arterioles,

then the input impedance magnitude varies greatly with increases in the number of capillary

branches [92]. The latter may be the case in IUGR pregnancies where the morphology

of the capillaries becomes abnormal, such that they have a lower number of loops, and

become slender and elongated [6]. Thus, if the characteristic impedance of the capillaries

was substantially different from that of the arterioles, the wave reflection methodology may

detect defects in the capillary vasculature. However, the effect of capillary morphology on


the reflected waveform requires further investigation.

6.6 Study limitations

Despite the success of non-invasive experiments, a large proportion of datasets (∼ 60%)

were discarded after applying pre- and post-processing quality control criteria to the UA

M-mode recordings. Applying such stringent criteria was necessary as even small sources

of maternal respiration and fetal/umbilical cord movements had a large effect on the lumen

diameter signal. For instance, contamination of the M-mode signal with maternal gasping

often resulted in non-physiological area waveforms and these signals had to be accounted for

in the post-processing steps. Furthermore, as the measured UA area change was quite small

(on the order of 3%-6%), any source of noise, such as out-of-plane UA motion during M-mode

scanning or fetal motion, could have resulted in poor data quality. It is also possible that

the measured UA pulsation for some excluded datasets was below the limits of resolution for

the ultrasound system.

While the finding that the UA wave reflection signature differs between the two strains is

promising, another limitation of this study is that we cannot determine with certainty which

morphological changes in the fetoplacental network of C57BL/6 mice result in a higher re-

flection coefficient as compared to CD1. For instance, it is possible that across an arterial

bifurcation, the local wave velocity changes as it propagates from parent to daughter ves-

sels. Under these conditions, our interpretation of the data based solely on geometric area

ratios will not hold. However, biomechanical models, where individual vessels are treated

as 1D transmission lines and their physical properties are known, can allow for associating

morphological parameters with wave reflection metrics [93]. Such models have been devel-

oped in the past for assessing the pulmonary fractal network, albeit with approximations

on the branching pattern and vessel diameters [93]. Transmission line models of pulse wave

reflections suggest that the local reflection coefficient at a bifurcation is related to frequency

dependent (such as fluid viscosity, vessel elasticity) and frequency independent sources of

reflection (such as daughter to parent vessel area ratio) [93]. By taking both these factors

into account in a model of the fetoplacental network, it may be possible to determine which

changes in the physical properties of the C57BL/6 fetoplacental vasculature result in the

observed increase in UA wave reflection.

A third limitation of this study is that the viscoelastic property of the umbilical artery

is not considered. As the viscoelastic vessel wall attenuates the pulse wave as it propagates

along the UA, it is possible that the measured reflected wave at the fetal end of UA may

differ between different datasets simply due to attenuation, if the reflected wave was not

measured at the exact same location for all fetuses.

Furthermore, while the PWV values obtained were consistent with those reported in


mouse aortic PWV measurements [94], the UA wave decomposition process used in this

thesis assumed a constant PWV between the site of measurement and downstream reflection.

However, it is possible that the PWV may vary along the UA if the ratio of wall thickness to

lumen diameter is not constant, or if the composition of elastin and collagen varies. This may

result in acceleration or deceleration of the pulse wave along the vessel and it may explain

why the calculated distance to the reflection site (in the range of 7cm-9cm), by assuming

a constant PWV, appears to be beyond the length of fetoplacental vasculature (distance to

reflection site = 12× PWV × time delay) [78].

Lastly, although the time delay and dispersion metrics did not change with variations in

fetoplacental morphology, it is possible that with an increase in sample size, these parameters

might show a significant effect. Indeed, as the UA pulsatility index strain and gestational

interaction showed a trend toward significance, increasing the sample size may result in a

significant effect of this parameter.

Chapter 7

Conclusion

In summary, I have developed a non-invasive method to measure and characterize UA wave

reflections in mice. By using high frequency ultrasound and semi-automated image analysis,

I have isolated the forward cardiac and reflected placental components from the observed UA

flow waveforms. In addition, I have shown that the patterns of reflected waves differ with

variations in fetoplacental morphology. More specifically, results indicate that the reflection

coefficient measure is able to detect differences in the fetoplacental arterial growth patterns

of CD1 and C57BL/6 mice, and that it is a more sensitive measure than the UA pulsatility

index.

Furthermore, as the reflection coefficient did not change with increases in fetoplacental

capillary volume, I conclude that this metric is insensitive to growth in the capillaries. In

contrast, with abnormal elevation of Murray’s law exponent in fetoplacental arterial vessels

of E17.5 C57BL/6 mice, it was observed that the reflection coefficient became elevated as

compared to fetoplacental vasculatures which followed Murray’s law for optimal arrangement

of vessels. From this observation, I conclude that the UA reflection coefficient measure can

be used to probe the properties of the downstream vasculature.

Lastly, as the wave reflection methodology developed in this thesis is based on ultrasound

and can detect differences in the vascular morphology of the placenta, it can be used for

the detection of placental defects in human pregnancies at-risk of IUGR. As previous work

suggests that more than 60% of the placental vasculature has to be compromised before

abnormalities in the UA Doppler spectrum are observed [48], the current methodology offers

the potential to overcome this limitation as it can detect subtle variations in the fetoplacental

arterial vasculature and consequently, may allow for the detection of pathologies at an earlier

stage.

55

Chapter 7. Conclusion 56

7.1 Future Work

While the wave reflection measure in the mouse UA is novel and also has clinical relevance in

human pregnancies, I suggest the following work in the future to improve this methodology

and its biological implications:

1. Improvement of data quality: One of the limitations of this study was that the

area waveform measurement was highly susceptible to noise, especially since the mea-

sured pulsation in the UA was quite small. The use of higher frequency ultrasound

transducers (i.e. 70 MHz systems as compared to 40 MHz transducer used in this

thesis) may provide better spatial resolution for the measurement of the area wave.

2. Biomechanical model of the fetoplacental network: Previous work has shown

that a model of the fetoplacental network can be obtained through high-resolution 3D

micro-CT imaging, followed by automated vascular segmentation techniques to obtain

the geometry of the arterial vessels (i.e. their diameters, lengths, and connectivity) [21].

Furthermore, the local mechanical properties of the placental vessels can be determined

through wire myography, which allows for the calculation of the elastic modulus for

very small diameter vessels [95]. Briefly, excised arteries are mounted onto two wires

in an organ bath where one wire is in a fixed position, and the other wire is connected

to a force transducer for recording tension [96]. Next, the mounted vessel is stretched

and with each successive stretch (i.e. change in lumen circumference), the resulting

tension is recorded [96]. From the stress-strain curve (i.e. tension-stretch), the Young’s

modulus for elasticity is determined as the ratio of tensile stress to tensile strain.

Combined with the elasticity data, the geometric model of the fetoplacental vessels

may allow for determining which morphological changes in the downstream network

have an effect on the UA wave reflection parameters (i.e. the reflection coefficient,

time delay, and dispersion). Thus, a biomechanical model can be a strong tool for

linking microvascular characteristics with reflection patterns, and can also be used to

simulate wave propagation and reflection to validate ultrasound-based wave reflection

measurements.

3. The effect of cardiac function on wave reflection: While the reflection coefficient

did not covary with fetal heart rate, a more stringent test to determine how the cardiac

function affects patterns of wave reflection is required. For instance, in the fetal sheep,

atrial pacing (to increase the heart rate) and vagus nerve stimulation (to decrease the

heart rate) have been shown to alter umbilicoplacental hemodynamics [97]. Similar

experiments have been carried out in the mouse and can be applied to the current

methodology to determine if wave reflection parameters are influenced by upstream

cardiac factors [98]. This is important as factors affecting cardiac output can alter the

Chapter 7. Conclusion 57

UA Doppler waveform and consequently, confound assessments of placental function

based on metrics such as the pulsatility index [88,97].

4. Wave reflection in mouse models of IUGR: While the finding that the UA reflec-

tion coefficient measure is sensitive to fetoplacental morphology is promising, these ex-

periments were conducted on two commonly used mouse strains for biological research.

Future work applying the wave reflection methodology in mouse models of fetal growth

restriction may allow for linking the underlying genetic and physiological variation in

growth restriction mouse models to specific patterns of wave reflection. For instance,

in an experimental model induced by pre-pregnancy maternal exposure to cigarette

toxicants, it was found that there were reductions in fetal weight and the number

of arteriole-sized vessels, as well as an increase in fetoplacental resistance [75, 99]. In

comparison, mice lacking endothelial nitric oxide synthase (eNOS) also exhibit reduced

fetal growth but as opposed to having fewer arterioles, these placentas have smaller

diameter arterioles [76]. Thus, correlating these varying placental phenotypes with

UA wave reflection patterns may allow for associating fetoplacental vascular defects to

specific wave reflection signatures.

Appendices

58

Appendix A

Area ratio at arterial bifurcations

Figure A.1: Schematic of an arterial bifurcation where the parent vessel with radius r0 and area

A0, branches off into two daughter vessels with radii r1 and r2, and areas A1 and A2. In this

schematic, the two daughter vessels have the same geometry.

A.1 Minimizing viscous dissipation: cube-law

According to the cube-law for scaling vessels (to minimize viscous dissipation) [83], the radius

of the parent vessel (r0) is related to the radii of the daughter vessels (r1 and r2) as follows

(see Figure A.1):

r30 = r31 + r32 (A.1)

If r1 = r2, then

59

60

r30 = 2r31 (A.2)

and:

A0 = πr20 and A1 + A2 = 2πr21 (A.3)

where A0 is the area of the parent vessel, and A1 and A2 are the areas of the daughter vessels.

Rearranging (A.2) in terms of daughter to parent vessel ratio and substituting for r20 and

r21 in terms of area from (A.3) gives:

r31r30

=1

2(A.4)(

r21r20

) 32

=1

2(A.5)(

(A1 + A2)/2π

A0/π

) 32

=1

2(A.6)(

A1 + A2

2A0

) 32

=1

2(A.7)

A1 + A2

A0

= 2 · 2− 23 (A.8)

A1 + A2

A0

= 1.26 (A.9)

Therefore, the daughter to parent vessel area ratio under the cube-law is 1.26.

A.2 Minimizing wave reflection: square-law

The square-law for scaling vessels results from minimization of wave reflection at an arterial

bifurcation. From Figure A.1, the parent vessel branching off into two daughter vessels can

be conceptualized as a parallel circuit, where the total impedance (ZT ) of 2 parallel, daughter

vessels (assumed to be infinitely long) is:

1

Z1

+1

Z2

=1

ZT

(A.10)

Reflection at an arterial bifurcation is zero when the total impedance of the daughter

vessels (ZT ) is equal to the impedance of the parent vessel (ZP ) (i.e. the impedances are

matched):

1

Z1

+1

Z2

=1

ZP

(A.11)

The impedance of a vessel is defined as [82]:

61

Z =ρc20πr2c

(A.12)

where r is the radius, c is the wave velocity, c0 is the Moens-Korteweg wave velocity [82],

and ρ is density of the blood in a vessel. Assuming the wave velocities and densities are the

same across a bifurcation, and if the daughter vessels are of equal calibre (r1 = r2), then the

impedances across a bifurcation from equation (A.11) become frequency-independent and

are related to the geometry of the vessel as follows:

πr21c

ρc20+πr21c

ρc20=πr20c

ρc20(A.13)

πr21 + πr22 = πr20 (A.14)

Substituting for radii in terms of area from equation (A.3):

A1 + A2

A0

= 1 (A.15)

Therefore, the daughter to parent vessel area ratio, when the total impedance of the daughter

vessels matches the impedance of the parent vessel, is 1.0.

A.3 Reflection coefficient in relation to area ratio

The relationship between reflection coefficient and the area ratio, as discussed here, is

adapted from [82]. Under pulsatile flow, the forward (f ), transmitted (t) and reflected

(r) pressures (p) and flows (q) are related to the impedance of the parent (ZP ) and daughter

vessels (ZT ) as follows:

ZP = Pf/Qf (A.16)

ZP = −Pr/Qr (A.17)

ZT = Pt/Qt (A.18)

From continuity, it follows that:

Pf + Pr = Pt (A.19)

Qf +Qr = nQt (A.20)

where n is the number of branching daughter vessels. Substituting for flow from equations

(A.16), (A.17) and (A.18) into equation (A.20) yields:

62

Pf

ZP

− Pr

ZP

= n · Pt

ZT

(A.21)

Pf − Pr = nZp ·Pt

ZT

(A.22)

Substituting for Pf from equation (A.19) into equation (A.22) results in:

Pt − Pr − Pr = nZP ·Pt

ZT

(A.23)

2Pr = Pt − nZP ·Pt

ZT

(A.24)

2Pr = Pt ·(

1− nZP

ZT

)(A.25)

while substituting for Pr results in:

Pf − (Pt − Pf ) = nZP ·Pt

ZT

(A.26)

2Pf = Pt ·(

1 + nZP

ZT

)(A.27)

Since the reflection coefficient, Γ, is defined as the ratio of Pr to Pf , taking the ratio of

equations (A.25) and (A.27) we get the following:

Γ =1− nZP/ZT

1 + nZP/ZT

(A.28)

Now, from (A.10), it can be seen that if Z1 = Z2 (i.e. the daughter vessels are the same),

then ZT can be written as:

ZT =Z1

n(A.29)

where n is the number of daughter vessels in parallel. Rewriting (A.29) and ZP in terms of

areas:

ZT =ρc20nπr21c

(A.30)

ZT =ρc20nA1c

(A.31)

63

and for the parent vessel,

ZP =ρc20πr21c

(A.32)

ZP =ρc20A0c

(A.33)

Thus, the nZP/ZT factor in (A.28) can be replaced with:

n · ZP

ZT

=ρc20/A0c

ρc20/nA1c(A.34)

n · ZP

ZT

=nA1

A0

(A.35)

after substituting for ZP and ZT from (A.33) and (A.31), respectively. Noting that nA1 is

the total area for n daughter vessels, then for a bifurcation with 2 daughter vessels as in

Figure A.1, nA1 = A1 + A2 and (A.35) can be written as:

n · ZP

ZT

=A1 + A2

A0

(A.36)

Finally, substituting (A.36) into (A.28) gives:

Γ =1−

(A1+A2

A0

)1 +

(A1+A2

A0

) (A.37)

Plotting | Γ | in terms of the area ratio(

A1+A2

A0

)gives the following relationship:

64

Figure A.2: Plot of reflection coefficient (independent of wave velocity and blood density)

as a function of the area ratio (sum of the areas of two equal radii daughter vessels to area

of the single parent vessel). As expected, when the area ratio is 1.0, the reflection coefficient

is zero.

66

Appendix B

Distribution of measured parameters

Figure B.1: The distribution of measured parameters. Panel A: C57BL/6 at E15.5; Panel

B: C57BL/6 at E17.5; Panel C: CD1 at E15.5; Panel D: CD1 at E17.5. p < 0.05 indicates

a significant Shapiro-Wilk result and suggests that the distribution is non-normal.

Appendix C

Invasive wave reflection measurements

As motion due to maternal respiration/fetal movement may confound accurate M-mode

measurements, a pilot study was conducted to measure UA wave reflection through an

invasive protocol.

C.1 Methods

Pregnant CD1 and C57BL/6 mice at E17.5 were anaesthetized with 2.5% isoflurane and

placed on a temperature-regulated platform at 37◦C. The mouse abdominal cavity was then

exposed and the uterine horn, while still connected to the maternal circulation, was removed

from the abdomen and submerged in a petri dish containing warm PBS (37◦C-40◦C). The

existing solution in the petri dish was replaced with fresh, warm PBS at approximately 3-

5 minute intervals to keep the fetuses warm. Using forceps, the fetus (while still encased

in its uterine sac and amniotic fluid) was repositioned in order to obtain the best possible

orientation for the UA M-mode recording. Similar invasive experiments have been performed

in the past for ultrasound assessment of the mouse embryonic aortic curvature [100]. Lastly,

ultrasound gel was placed on each fetus for subsequent recordings.

Image analysis and quality control criteria were the same as those applied in the non-

invasive protocol. To compare interstrain effects and invasive and non-invasive methods, a

two-tailed independent samples Welch’s t-test was performed.

67

68

C.2 Results

The number of animals used for invasive experiments is summarized in Table C.1. After

applying quality control criteria to M-mode recordings, 27% of UA scans were included in

the study.

Strain Gestational

Age

m n-total n-removed n

C57BL/6 E17.5 13 33 22 11 (from 8 litters)

CD1 E17.5 16 26 21 5 (from 4 litters)

Table C.1: Animals used in the wave decomposition analysis. m = number of pregnant mice,

n-total = total number of fetuses scanned, n-removed = number of UA fetal scans removed

due to quality control criteria/fetal demise, n = number of UA fetal scans included in the

analysis.

C.2.1 Shapiro-Wilk test

The Shapiro-Wilk test was non-significant for all wave reflection parameters and the pul-

satility index.

C.2.2 Interstrain effects at E17.5

In terms of the measured parameters, the wave reflection and UA pulsatility index metrics did

not differ between the two strains (Figure C.1). Average values of the measured parameters

from invasive experiments are presented in Table C.2.

C.2.3 Invasive vs. non-invasive experiment

In general, the wave reflection and UA pulsatility index metrics between invasive and non-

invasive experiments were different (Figure C.2). Under invasive conditions, for the CD1

strain at E17.5, the time delay was 62% higher while the PWV was 72% lower as compared

to non-invasive experiments (p < 0.05, t-test). In comparison, for the C57BL/6 strain under

invasive conditions, the average UA reflection coefficient was 26% lower while the pulsatility

index was 57% higher as compared to non-invasive conditions (Table C.3).

69

Str

ain

Ges

tati

onal

Age

nR

eflec

tion

Coeffi

cien

tU

Apuls

atilit

yin

dex

Tim

eD

elay

(×10

−1

s)D

isp

ersi

on(×

10−1

s)P

WV

(m/s

)

C57

BL

/6E

17.5

110.

35±

0.03

4.36±

0.34

1.12±

0.20

0.80±

0.19

1.49±

0.22

CD

1E

17.5

50.

29±

0.04

3.34±

0.66

0.96±

0.11

0.65

0.35

0.86±

0.25

Tab

leC

.2:

Dat

ash

own

asm

ean±

sem

.n

=num

ber

offe

tuse

s.

70

Str

ain

Met

hod

nR

eflec

tion

Coeffi

cien

tU

Apuls

atilit

yin

dex

Tim

eD

elay

(×10

−1

s)D

isp

ersi

on(×

10−1

s)P

WV

(m/s

)

C57

BL

/6N

on-i

nva

sive

90.

44±

0.03

∗2.

78±

0.12

∗0.

82±

0.08

0.36±

0.21

2.63±

0.48

C57

BL

/6In

vasi

ve11

0.35±

0.03

4.36±

0.34

1.12±

0.20

0.80±

0.19

1.49±

0.22

CD

1N

on-i

nva

sive

140.

33±

0.02

2.44±

0.12

0.59±

0.03

∗0.

21±

0.07

3.07±

0.30

∗

CD

1In

vasi

ve5

0.29±

0.04

3.34±

0.66

0.96±

0.11

0.65

0.35

0.86±

0.25

Tab

leC

.3:

Dat

ash

own

asm

ean±

sem

.n

=num

ber

offe

tuse

s.W

ithin

each

stra

in,

*p<

0.05

indic

ates

asi

gnifi

cant

diff

eren

ceb

etw

een

inva

sive

and

non

-inva

sive

met

hods,

asdet

erm

ined

by

t-te

st.

71

Figure C.1: Difference in wave reflection parameters, heart rate, PWV and UA pulsatility

index between C57BL/6 and CD1 mice at E17.5. To acquire these metrics, invasive UA

fetal scans were performed in order to reduce maternal respiration related motion artifacts.

The wave reflection and UA pulsatility index parameters were not different between the two

strains. Data shown as mean ± sem.

72

Figure C.2: Difference in wave reflection parameters, heart rate, PWV and UA pulsatility

index between invasive and non-invasive protocols. Data shown as mean ± sem. Within

strain, means not sharing a common letter (a, b) are significantly different (t-test,

p < 0.05).

73

C.3 Discussion

Invasive experiments were difficult to perform and often resulted in poor fetal survival.

This was largely due to adverse effects associated with exposing the uterine horn to non-

physiological conditions. Most fetuses did not survive long enough to obtain the full 5 second

Doppler and M-mode recordings. Furthermore, the temperature of the PBS solution dropped

very quickly and it was difficult to keep the fetuses warm at a constant temperature. Com-

bined with the observation that on average, the fetal heart rates under invasive conditions

were substantially lower as compared to non-invasive experiments (∼ 30%-50% lower, p <

0.05), it appears that the invasive protocol had a significant impact on the optimal phys-

iological status of the fetus. This may explain why the number of fetuses included in the

invasive study was quite low.

In terms of interstrain effects at E17.5, there were no differences between the wave re-

flection parameters and UA pulsatility index. While the average UA reflection coefficient

appeared to be lower in the CD1 strain as compared to C57BL/6, this difference was not

statistically significant (as compared to non-invasive experiments). Since the number of suc-

cessful UA fetal scans was quite low in the CD1 group (n=5), increasing the sample size may

result in the detection of a significant difference in this parameter between the two strains.

Lastly, as the wave reflection and UA pulsatility index measurements differed between

invasive and non-invasive methods, this indicates that the invasive protocol may be changing

the in-utero physiological conditions. Indeed, earlier studies on fetal sheep exteriorization

(with placental circulation continuing) have shown that invasive procedures can impact the

fetal circulation [101]. For instance, it has been found that upon fetal sheep exterioriza-

tion, the placental resistance increases while the umbilical artery blood flow decreases [101].

Therefore, physiological changes in the fetal circulation may be responsible for the observed

differences between the two experimental protocols.

C.4 Conclusion

Results from the pilot invasive study show that fetal survival is poor under invasive experi-

ments. Combined with the observation that wave reflection parameters and pulsatility index

differ between invasive and non-invasive experiments, the non-invasive measurement may be

more practical moving forward.

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