Metric Optimized Gating for Fetal Cardiac MRI

by

Michael Jansz

A thesis submitted in conformity with the requirements for the degree of Master of Science Department of Medical Biophysics

University of Toronto

© Copyright by Michael Shelton Jansz 2010

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Metric Optimized Gating for Fetal Cardiac MRI

Michael Jansz

Master of Science

Department of Medical Biophysics University of Toronto

2010

Abstract

Phase-contrast magnetic resonance imaging (PC-MRI) can provide a complement to

echocardiography for the evaluation of the fetal heart. Cardiac imaging typically requires gating

with peripheral hardware; however, a gating signal is not readily available in utero. In this

thesis, I present a technique for reconstructing time-resolved fetal phase-contrast MRI in spite of

this limitation. Metric Optimized Gating (MOG) involves acquiring data without gating and

retrospectively determining the proper reconstruction by optimizing an image metric, and the

research in this thesis describes the theory, implementation, and evaluation of this technique. In

particular, results from an experiment with a pulsatile flow phantom, an adult volunteer study, in

vivo application in the fetal population, and numerical simulations are presented for validation.

MOG enables imaging with conventional PC-MRI sequences in the absence of a gating signal,

permitting flow measurements in the great vessels in utero.

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Acknowledgments

This work was supported by a Canadian Graduate Scholarship from the Natural Sciences and

Engineering Research Council of Canada.

I would like to begin by thanking my committee members, Mark Henkelman and Graham

Wright, for their flexibility, guidance, and confidence.

Thank you to Lars Grosse-Wortmann, Mike Seed, Derek Wong, and Shi-Joon Yoo for their

enthusiastic support of my work and their help acquiring clinical data. Mike, in particular, has

been the driving force behind this project and I am deeply indebted to him for his contributions

to this thesis, and his invaluable feedback that has influenced not only this project but also my

future career path.

Sina Fazelpour, Peter Leimbigler, and Chris Wernik for a great work environment, and Joshua

van Amerom, who is the cornerstone of our lab. While he truly has a hand in everything that

happens in our lab, he was particularly instrumental in this project.

My supervisor, Chris Macgowan, for his unwavering support and for teaching me more than he

will ever realize. I will always count myself lucky to have spent the last two years in his lab.

Finally, my family for supporting me in everything I do, and my fiancée, Nicole, for her love,

encouragement, patience—as well as all the little things.

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Table of Contents

Acknowledgments.......................................................................................................................... iii  

Table of Contents........................................................................................................................... iv  

List of Tables ................................................................................................................................ vii  

List of Figures .............................................................................................................................. viii  

Prologue ...........................................................................................................................................1  

Chapter 1 Background .....................................................................................................................2  

1.1   Motivation............................................................................................................................2  

1.2   Relevant Biology .................................................................................................................3  

1.2.1   Fetal Circulation.......................................................................................................3  

1.2.2   Congenital Heart Disease.........................................................................................5  

1.3   Fetal Cardiac Imaging..........................................................................................................7  

1.3.1   Cardiac Evaluation...................................................................................................7  

1.3.2   Imaging Modalities ..................................................................................................8  

1.4   Cardiac Gating ...................................................................................................................10  

1.4.1   The Role of Gating.................................................................................................10  

1.4.2   Alternative Solutions .............................................................................................12  

1.5   Fetal Heart Rate Variation .................................................................................................14  

1.5.1   General Structure ...................................................................................................14  

1.5.2   Indices ....................................................................................................................15  

1.5.3   Modelling...............................................................................................................15  

1.6   Image Metrics and Autocorrection ....................................................................................16  

1.7   Thesis Statement ................................................................................................................17  

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Chapter 2 Metric Optimized Gating ..............................................................................................18  

2.1   Introduction........................................................................................................................18  

2.2   Theory ................................................................................................................................18  

2.3   Oversampling.....................................................................................................................18  

2.3.1   Metric Optimized Gating .......................................................................................19  

2.3.2   HR Modeling .........................................................................................................20  

2.3.3   Misgating Artifacts ................................................................................................20  

2.3.4   Image Metrics ........................................................................................................22  

2.4   Methods..............................................................................................................................24  

2.4.1   Heart Rate Models .................................................................................................24  

2.4.2   MR Data.................................................................................................................24  

2.4.3   Simulation ..............................................................................................................25  

2.4.4   Phantom .................................................................................................................26  

2.4.5   Volunteer Experiment............................................................................................26  

2.5   Results................................................................................................................................27  

2.5.1   Heart Rate Models .................................................................................................27  

2.5.2   Phantom Experiment..............................................................................................28  

2.5.3   Volunteer Measurements .......................................................................................29  

2.5.4   Fetal Measurements ...............................................................................................31  

2.5.5   Simulation ..............................................................................................................33  

2.6   Discussion ..........................................................................................................................35  

2.6.1   Validation...............................................................................................................35  

2.6.2   Fetal Application....................................................................................................35  

2.6.3   Limitations .............................................................................................................35  

2.7   Conclusion .........................................................................................................................36  

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Chapter 3 Future Work ..................................................................................................................37  

3.1   Introduction........................................................................................................................37  

3.2   Improvements ....................................................................................................................37  

3.3   Further Investigation..........................................................................................................38  

3.4   Extensions ..........................................................................................................................40  

3.5   Final Remarks ....................................................................................................................40  

References......................................................................................................................................41  

Copyright Acknowledgements.......................................................................................................47  

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List of Tables

Table 1: Results of 1000 simulated reconstructions testing the ability of the three heart-rate

models to account for variability in the simulated heart rate traces. The simulated traces were

generated using Eq. 2, with σ = 7, Δ = 0.1, and a baseline heart rate of 150 bpm. The same 1000

simulated measurements were reconstructed using each heart rate model. The residual is the

mean reduced χ2 residual between the measured and known flow patterns. ................................ 28  

Table 2: Measured mean flow values and fractional distributions corresponding to the 37 week

fetal case shown in Figure 5, as well as reference values derived from the literature (5,7,9,25-28).

Literature values are based on measurements with Doppler ultrasound and experiments involving

the injection of radionuclide-labelled microspheres. .................................................................... 33  

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List of Figures

Figure 1: Diagram of the fetal circulation reproduced from the third edition of “Congenital

Diseases of the Heart: Clinical-Physiological Considerations” written by Abraham M. Rudolph

and published by Wiley-Blackwell (5).1 DV denotes the ductus venosus; DA denotes the ductus

arteriosus; and forked arrow in the right atrium shows the foramen ovale, which is not explicitly

labeled. ............................................................................................................................................ 5  

Figure 2: Illustration of the temporal averaging that reduces the pulsatility of the flow. The

diagram on the left shows properly gated flow and the diagram on the right shows flow with

linearly accumulating CPE. On the top axes the line shows the true flow and the dots the

measured values. The power in k-space is shown on the far right and determines the relative

weighting in the averaging kernel. Each dashed line shows a frame in the series of images and

the solid line shows the frame of interest. The slope of the dashed lines is inversely related to the

difference between the true and reconstructed heart rates. ........................................................... 21  

Figure 3: Results from an experiment with a pulsatile flow phantom. (a) Images of the tube

reconstructed at a range of hypothetical pump frequencies using the one-parameter heart rate

model. The frequency at which the images were reconstructed is given on the axis below, where

the axis values denote the difference between the supposed pump frequency used in the

reconstruction and the true frequency. (b) The time-entropy values corresponding to the images

in (a). (c) Flow patterns extracted from the image series indicated with the corresponding letters,

as well as the flow pattern extracted from the ECG gated images. .............................................. 29  

Figure 4: Results from an experiment using the carotid arteries in adult volunteers. (a)

Comparison of the optimized heart rate model and the true heart rate trace, as measured by ECG.

The two-parameter model was used, and the two model parameters converged to nearly identical

values. (b) and (c) show a single frame from the ECG gated and MOG image series, respectively.

The magnitude images are shown on the left and the masked phase images are shown on the

right. (d) Right carotid artery flow patterns extracted from the images shown in (b) and (c). The

left carotid artery flow patterns were indistinguishable and were not included for clarity. (e)

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Metric values corresponding to four one-parameter heart rate searches in the left carotid artery

(LC), right carotid artery (RC), left jugular vein (LJ), and right jugular vein (RJ). ..................... 30  

Figure 5: Results from a 37 week fetal case with normal cardiac anatomy and function. (a) The

metric value as a function of the model parameters for one representative measurement. (b) The

magnitude and phase images corresponding to the optimum in (a), with the fetal pulmonary

artery indicated by the arrow. (c) Three repeated measurements of the flow in the pulmonary

artery. The inset shows the expected shape of the flow pattern in the pulmonary artery in a late-

gestation fetus as measured by Doppler ultrasound...................................................................... 32  

Figure 6: Results of a simulation with σ = 7, Δ = 0.1, and a baseline heart rate of 150 bpm. (a)

The simulated heart rate trace generated by Eq. 2 using the aforementioned parameters, as well

as the optimized piecewise-constant heart rate model. (b) Comparison of the reference and

calculated flow patterns. ............................................................................................................... 34  

Figure 7: Results of a Monte Carlo simulation testing the effects of HRV on the quality of MOG

reconstruction. Each data point represents the mean and standard deviation of 1000 simulations

with random HRV, determined by Δ = 0.1 and σ as shown. The mean and pulsatility are

normalized against the correct values. The two-sided arrow denotes the typical range of fetal

HRV based on reports in the literature (55,76)............................................................................. 34  

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Prologue

Quantitative fetal blood flow measurements provide an important tool for the assessment of the

healthy and diseased circulation. Specifically, flow measurements in utero can improve our

understanding of fetal physiology and pathophysiology, and aid in the assessment of congenital

heart disease and pregnancy management. This thesis is concerned with the measurement of

volumetric blood flow rates (volume of blood flow through a vessel per unit time) in fetal vessels

with phase-contrast MRI (PC-MRI). It describes a new technique that allows quantitative, time-

resolved flow measurements by addressing the issue of cardiac gating, which has prevented the

application of MR to fetal cardiac assessment until now.

Chapter 1 describes the motivation, applications, and relevant background; chapter 2 addresses

the theory, implementation, and validation of the technique; and chapter 3 discusses of the

potential for further validation and improvements.

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Chapter 1 Background

This chapter provides an overview of the background information on which the second chapter is

built. It begins by outlining the motivation for fetal flow measurements, including a discussion

of fetal circulation and its associated pathology, as well as an overview of the role of imaging in

the assessment of the fetal heart. The subsequent sections summarize a number of relevant

technical fields including the use of gating in MRI, the principles and limitations of phase-

contrast MRI, the quantitative assessment of fetal heart rate variability (HRV), and metric-based

correction of MR images. Finally, this chapter concludes by introducing metric optimized

gating, which will be discussed in detail in the second chapter.

1.1 Motivation

Congenital heart disease (CHD) is the most common congenital abnormality in North America

with an incidence of nine per thousand live births (1). It is responsible for more deaths than any

other congenital defect, and 2.3 per thousand live births will require invasive treatment or result

in death in the first year of life (1). Even cases that are successfully treated are often associated

with significant morbidity and a lifetime of medical care.

Fetal cardiac imaging is a useful tool for the assessment of CHD. In cases such as transposition

of the great arteries, pulmonary atresia, and coarctation of the aorta, it is crucial that CHD be

treated immediately after birth. Imaging enables prenatal diagnosis of CHD, allowing for

informed pregnancy counseling and improved management. Furthermore, advances in

quantitative imaging could facilitate further study of the healthy and diseased circulation during

development. This would improve our understanding of normal fetal physiology and

development, and lead to better characterization of the natural history of CHD. A reliable

measure of disease progression may also aid prognosis.

Ultrasound is the standard modality for fetal cardiac imaging. Its high spatial and temporal

resolutions, lack of ionizing radiation, and relative availability make it well suited to this

application. It is not without limitations, however, and several investigators have suggested that

MRI may provide a useful adjunct (2,3). Of particular interest is the ability to make quantitative

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measurements of blood flow with phase-contrast MRI (PC-MRI). Unfortunately, fetal cardiac

MRI is currently limited by the inability to synchronize acquisitions to the beating of the fetal

heart (4). Without accurate synchronization, the motion of the heart and the pulsatility of the

blood in the great vessels introduce artifacts, preventing time-resolved measurements and

corrupting mean flow measurements.

The inability to properly gate acquisitions is the primary limitation of PC-MRI flow

measurements in utero, and it is this problem that is addressed in my research. My ultimate goal

is to enable time-resolved flow measurements in utero, to investigate fetal cardiac physiology

and eventually improve patient management. Here I present the theory and experimental

validation for a new technique to reconstruct PC-MRI data in the absence of a gating signal.

1.2 Relevant Biology

As the principal application of the research in this thesis is assessment of the fetal circulation and

its pathology, it is necessary to begin with a discussion of the relevant biology in order to

appreciate the motivation and potential applications of this research. It this section I will present

an overview of the fetal circulation and its pathology.

1.2.1 Fetal Circulation

As shown in Figure 1, the fetal circulation differs significantly from that of an adult. The primary

difference is that the placenta—as opposed to the lungs—is the site of gas exchange and the

source of oxygen. There are a number of adaptations that compensate for this difference. First,

umbilical circulation exists to exchange blood between the fetus and the placenta. The umbilical

arteries draw blood from the internal iliac arteries and direct it to the placenta, and the umbilical

vein and the ductus venosus stream highly oxygenated blood directly from the placenta to the

right atrium. Second, the foramen ovale connects the two atria and directs blood from the right

heart to the left, reducing the flow to the pulmonary circulation and directing the most highly

oxygenated to the brain via the left heart. Third, the ductus arteriosus connects the main

pulmonary artery to the aortic arch, bypassing the lungs. This decreases the afterload on the

right ventricle and allows distribution of blood to the body. Together, these three shunts act to

reduce the blood flow to the lungs and preferentially direct oxygenated blood to the brain. These

modifications results in a greater relative flow through the right heart, reduced flow to the lungs,

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and considerably more mixing between the pulmonary and systemic systems, as compared to the

adult circulation.

At birth, the process of gas exchange is transferred to the lungs and several changes occur in the

circulation. First, the umbilical cord is tied off and severed leading to the closure of the ductus

venosus, umbilical arteries and umbilical vein. Second, the ventilation and oxygenation of the

lungs decreases the pulmonary vascular resistance, which increases the blood flow to the

pulmonary circulation. This increases the pressure in the left side of the heart, leading to the

closure of the foramen ovale. Finally, a decrease in prostaglandin levels leads to the closure of

the ductus arteriosus.

Although the general course of the human fetal circulation is known, many elements have not

been well characterized. Much of the current knowledge of the fetal circulation is based on

experiments in fetal sheep and postnatal measurements due to the difficulties involved in

studying the human fetus (5). The experiments in sheep determined the volumetric flow rates,

fractional distributions, and oxygen saturations using injections of radionuclide-labeled

microspheres and invasive pressure and oxygen saturation measurements (6). Subsequent

experiments with radionuclide-labeled microspheres in pre-viable human fetuses indicate that the

human fetal circulation is similar to that in the lamb, in general, but with significant differences

in flow rates, fractional distributions, and oxygen saturations (7). The difficulties associated with

non-invasive measurements of flow in the human fetus have prevented proper characterization of

these differences in the healthy human fetus (5).

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Figure 1: Diagram of the fetal circulation reproduced from the third edition of “Congenital Diseases of the Heart: Clinical-Physiological Considerations” written by Abraham M. Rudolph and published by Wiley-Blackwell (5).1 DV denotes the ductus venosus; DA denotes the ductus arteriosus; and forked arrow in the right atrium shows the foramen ovale, which is not explicitly labeled.

1.2.2 Congenital Heart Disease

Overview

CHD refers to any cardiac defect acquired during development and can be present in utero or

acquired during the transition from prenatal to postnatal life. These abnormalities include

aberrant connections, patent shunts, hypoplasia, valvular defects, septal defects, and stenoses—or

any combination of these. Although there is a wide range of potential conditions, all types of

CHD are associated with anomalous blood flow patterns.

Some instances of CHD are simple lesions, such as minor septal defects, that cause mild

symptoms and occasionally resolve spontaneously. Some, however, are very complex and

severe, requiring major surgery and a lifetime of follow-up care. Complex lesions are usually

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fatal without treatment (8), and it is often the closing of shunts at birth that triggers the

development of severe symptoms. Although they are not strictly malformations of the heart,

intra-uterine growth restriction and twin-twin transfusion syndrome are also developmental

abnormalities associated with altered blood flow. Intra-uterine growth restriction refers to

underdevelopment and reduced fetal size, and is often associated with insufficient placental

blood flow (9), and twin-twin transfusion syndrome is defined as the transfusion of blood

between twins sharing a single placenta.

Altered blood flow in cases of CHD may cause changes in both hemodynamics and oxygen

delivery. Before birth, these changes can affect development and may lead to fetal hydrops in

some cases. Hemodynamic perturbations are known to induce morphologic changes, and

restrictive inflow and outflow tracts can lead to hypo- and hyperplasia of the cardiac chambers,

respectively (10). Similarly, increased flow distribution to the lungs can lead to increased

pulmonary vascular resistance, and decreased pulmonary blood flow can lead to hypoplasia of

the pulmonary vasculature (11,12). Furthermore, development may also be affected by changes

in oxygen delivery. While the inter-connected nature of the fetal circulation may provide some

protection against damage to end organs resulting from obstructive lesions, these malformations

can disrupt the streaming of oxygenated blood to the brain resulting in biochemical and

morphological changes and delay in brain maturation (13). In addition to developmental

changes, CHD can cause fetal hydrops due to raised systemic venous pressures associated with

obstructive lesions and cardiac dysfunction (5). Hydrops is the collection of fluid in fetal

compartments—including the peritoneum, pleural cavity, pericardium, and skin—and is

commonly associated with fetal demise. After birth, the primary consequence of CHD is

hypoxemia, or insufficient oxygen delivery to tissues. The degree of hypoxemia varies with the

lesion type and severity, with clinical presentations ranging from circulatory collapse with or

without cyanosis in the neonatal period through to incidental detection later in childhood or

adulthood.

Treatment

The treatments of CHD vary considerably, depending on the type and severity. Mild simple

lesions are often untreated and may resolve spontaneously. Complex and severe lesions, on the

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other hand, require prompt treatment to avoid poor outcomes. Antenatal diagnosis allows proper

planning of perinatal management, improves outcomes, and reduces the cost of neonatal care.

Complex lesions are usually palliated with open-heart surgery and less severe lesions can be

corrected with cardiac surgery or percutaneous interventions. Prior to surgery, ductal patency

may be maintained with prostaglandins to provide adequate systemic or pulmonary blood flow to

prevent hypoxia. Conversely, non-steroidal prostaglandin inhibitors may be successful in closing

a patent ductus arteriosus associated with premature delivery. Other medications such as

inotropic agents, ACE inhibitors, beta blockers, and diuretics can be used on occasion to improve

symptoms associated with cardiac failure, and anti-arrhythmic drugs may also be required in

patients with CHD. In addition to conventional therapies, in utero interventions are now under

investigation at a number of institutions. These procedures include laser ablation for the

treatment of twin-twin transfusion syndrome (14,15) as well as atrial septoplasties and aortic

valvuloplasties in cases of hypoplastic left heart syndrome with a highly restrictive atrial septum

(16,17).

1.3 Fetal Cardiac Imaging

Having discussed the fetal circulation and CHD, we now move on to investigate the role of

imaging in the assessment of the healthy and diseased fetal circulation. This section outlines the

typical methodology of assessing the fetal heart, as well as contributions of imaging to this field.

It ends with a discussion of the role PC-MRI may play in this assessment, touching on the

principles, strengths, and limitations of this technology.

1.3.1 Cardiac Evaluation

Standard pregnancy monitoring involves two ultrasound scans at around 7 and 18 weeks. The

early scan is used to confirm cardiac pulsation and measure fetal size to determine gestational

age. The later scan screens for malformations and includes a brief examination of the fetal heart.

In addition to these two scans, a thorough echocardiographic workup may be completed in high-

risk pregnancies or those suspected of having CHD.

Fetal echocardiography involves the use of several ultrasound modes to assess both the structure

and function of the heart. 2D greyscale (B-mode) imaging is used to establish the sequential

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segmental anatomy of the heart and assess cardiac function. Rapid 1D (M-mode) imaging is

used to evaluate the motion of the chamber walls as well as the rhythm of the heart. Doppler

ultrasound can measure blood velocities through the cardiac chambers, valves, great vessels and

ductus arteriosus, providing information about the spatial and temporal patterns of the flow.

Disease is indicated by structural abnormalities, reduced or altered wall movement, or changes in

the blood flow patterns in the heart and great vessels. Changes in velocity waveforms may

indicate reduced ventricular function; the presence or absence of shunts; or abnormalities in

vascular resistance, blood pressure, vessel diameter, or valve function.

Time-resolved blood flow measurements provide a valuable tool for assessing congenital heart

disease after birth (18,19); however, flow volumes are not typically evaluated in utero due to

technical limitations. If these technical limitations can be overcome, reliable measurement of

volume blood flow may assist in the assessment of CHD by providing information regarding

ventricular function, flow redistribution, and perfusion of blood to vital tissue beds (20).

Additionally, it could provide a measure of the severity and progression of disease, aiding in

prognosis and indicating which cases may benefit from in utero intervention.

In addition to clinical management, imaging also plays an important role in the basic scientific

understanding of the fetal circulation and the pathogenesis of CHD. Flow measurements, in

particular, may be used to validate baseline flow parameters in the healthy human fetus,

characterize altered blood flow in fetuses with lesions such as hypoplastic left heart syndrome,

and evaluate the hemodynamic changes in twin-twin transfusion syndrome and intrauterine

growth restriction.

1.3.2 Imaging Modalities

Ultrasound

Ultrasound is the primary modality for fetal imaging. It is relatively cheap and accessible,

capable of providing high spatial resolution in real-time, and does not involve ionizing radiation.

Furthermore, it is also capable of hemodynamic assessment with the use of power and colour

Doppler. Ultrasound does, however, have two main limitations.

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First, the nature of the measurements requires an acoustic window between the transducer and

the structure to be imaged, resulting in acoustic shadowing where acoustically opaque structures,

such as bone, obscure the tissue beneath them. This can prevent proper assessment in cases with

low amniotic fluid levels, adverse fetal position, or maternal obesity (21).

Second, the assessment of volume flow rates requires the measurement of both blood velocity

and the cross-sectional area of the vessel. While Doppler ultrasound can effectively assess blood

velocities, the velocity measurements are confined to the component parallel to the ultrasound

beam, making simultaneous measurement of vessel area and blood velocity impractical.

Ultrasound flow measurements typically rely on assumptions regarding the shape of the vessel,

the insonation angle, and the velocity profile (22). These assumptions, along with the

challenging nature of vessel diameter measurement, introduce large uncertainties in the final

flow rates (23,24). While there have been many reports of flow volume measurements in fetal

vessels with Doppler ultrasound in the literature (9,25-28), there is significant disagreement

between studies. Furthermore, validation experiments have also demonstrated large inter- and

intra-observer variability and poor repeatability (23,29). As a result, ultrasound has been used

primarily to assess blood velocities.

MRI

MR may serve two roles in fetal cardiac imaging. First, it can offer an alternative in cases where

ultrasound is not feasible due to acoustic shadowing. Second, PC-MRI provides a well-

established technique for measuring blood flow (30), which may provide additional

hemodynamic information beyond that which is provided by Doppler assessment of blood

velocity. The research in my thesis focuses on the technical challenges associated with the

application of PC-MRI for time-resolved flow measurement in the fetus.

Phase-contrast MRI

MR data has both a magnitude and a phase; however, conventional MR imaging considers only

the signal magnitude. Phase-contrast imaging, on the other hand, uses the signal phase in each

voxel to encode the component of the local tissue velocity in an arbitrary, user-specified

direction. In practice, eddy currents, field inhomogeneities, and gradient imperfections also

produce phase shifts; however, these can be removed by taking the difference between two

10

interleaved acquisitions with positive and negative velocity encodings. If the imaging plane is

prescribed orthogonal to the vessel and through-plane velocity encoding is used, a reliable

measure of the volume flow rate can be determined by integrating the velocity over the vessel

lumen (30). If a series of images are acquired at different points in the cardiac cycle, the time-

evolution of the flow rate can also be quantified.

There are several limitations of PC-MRI, especially when applied in the fetal population. First,

low spatial resolution can lead to partial volume effects where the phases in voxels at the vessel

boundary do not reflect the true mean velocity of the protons in those voxels. This problem will

always be present to some degree, but it can be adequately reduced with sufficiently high spatial

resolution (31,32). Second, the need for interleaved positive and negative flow encodes and

short echo times makes accelerating phase-contrast scans difficult, resulting in long scan times.

This can be overcome by acquiring the data in segments, where several lines of k-space are

acquired in each R-R interval in an interleaved fashion. This decrease the scan time by an

integer factor given by the number of lines-per-segment, although it also reduces the temporal

resolution by the same factor. Third, there is an unavoidable trade-off between spatial resolution

and scan time. In the case of fetal imaging high spatial resolution is important to reduce partial

volume effects; however, long scan times increase the likelihood of fetal movement during the

scan. Fourth, accurate flow measurements require orthogonal slice prescriptions which are more

difficult in fetal subjects due to the possibility of bulk motion between the acquisition of

localizers and the prescription of the phase-contrast imaging plane. Finally, there is the issue of

cardiac gating, which will be discussed below.

1.4 Cardiac Gating

The absence of cardiac gating is the primary limitation of the assessment of the fetal heart with

PC-MRI. This section describes the role of cardiac gating in cine PC-MRI, and further explains

the consequences of not having a gating signal. It concludes with an overview of the literature,

discussing potential solutions to this problem that have already been proposed.

1.4.1 The Role of Gating

In PC-MRI, the time required to acquire a single image is comparable to the length of a cardiac

cycle. This poses a problem, as both the position of the heart and the velocity of the blood in the

11

great vessels will vary considerably during the time each image is acquired, and k-space will not

reflect a single point in the cardiac cycle. This results in image artifacts such as blurring and

ghosting of moving structures and temporal smoothing of the flow waveform.

To overcome this problem, the data acquisition must be divided over several heartbeats with each

segment acquired in a different cardiac cycle. The acquisition is then gated such that every echo

is acquired within an appropriately small window centred on the desired cardiac phase. In this

case, data can also be acquired at other cardiac phases at no cost to scan time, to enable

reconstruction of a time-series of images reflecting a number of different points in the cardiac

cycle. This is referred to as cine imaging.

There are two strategies for cardiac gating. The first is prospective gating where the scanner

waits for the beginning of each cardiac cycle and then acquires a predetermined number of

measurements with specific delays before stopping to wait for the beginning of the next cycle.

These measurements are then inserted into an equivalent number of k-space matrices that are

reconstructed to produce a series of images corresponding to precise points in the cardiac cycle,

with the disadvantage that imaging at late diastole is difficult. The second is retrospective gating

where the data are acquired continuously and the segment number is incremented with each

cardiac cycle. The ECG signal is recorded simultaneously and the cardiac phase of each

measurement is determined retrospectively, relative to the start and end of the cardiac cycle in

which it was acquired. The data are then interpolated to a set of desired cardiac phases. This

produces a series of images with slightly reduced temporal resolution due to the interpolation,

but with full coverage of the cardiac cycle. A modified retrospective gating approach is used in

this work.

Needless to say, cardiac gating requires the measurement of a signal that indicates the beginning

of each cardiac cycle. In adults, this is accomplished with either ECG electrodes attached to the

patient’s chest or a peripheral pulse monitor attached to an extremity; however, these signals are

not readily available in utero—precluding the use of gating for fetal cardiac PC-MRI. This

results in an appreciable loss of image quality, loss of the dynamic information in flow

measurements, and corruption of mean flow values. The next section discusses potential

solutions to this problem.

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1.4.2 Alternative Solutions

In the absence of a traditional ECG or peripheral pulse monitor signal, there is a range of

potential solutions for cardiac gating for MRI. These include the detection of an alternative

gating signal with additional hardware, and the use of real-time imaging, self-gating, or

nontriggered acquisitions.

Hardware

There are a number of hardware solutions capable of measuring the fetal heart rate, although

their applicability to human fetal cardiac MR gating has yet to be determined. These include

fetal electrocardiography (fECG), magnetocardiography (MCG), and both imaging and non-

imaging ultrasound.

fECG involves the acquisition of a composite fetal-maternal ECG signal with electrodes attached

to the mother’s abdomen, and the extraction and amplification of the fetal component with

advanced signal processing. Unfortunately, the fetal signal is typically an order of magnitude

weaker than the maternal signal, and the extraction is only possible with a sufficient SNR (33).

In an MR magnet, the excess noise due to gradient switching and magnetohemodynamic effects

is likely to make fECG extraction unfeasible.

MCG involves the use of a superconducting quantum interference device (SQUID) in a

magnetically shielded environment to measure minute magnetic fields associated with the

beating of the fetal heart. Needless to say, this technology is also not applicable for MR gating.

The last, and most promising, hardware for measuring the fetal heart rate is ultrasound.

Ultrasound is an established technique for measuring the fetal heart rate, and MR-compatible

ultrasound devices have been reported in the literature (34). The most common technology for

measuring the fetal heart rate is cardiotocography (CTG), which operates by identifying the

dominant frequency in a signal acquired with a non-imaging ultrasound transducer directed at the

fetal heart. Typically, CTG returns a time-averaged measure of the fetal heart rate at regular

intervals, which is insufficient for MR gating; however, it may be possible to extract a more

useful gating signal with improved signal processing. Alternatively, feature tracking with

conventional B-mode ultrasound has been applied to respiratory gating in adults and it may be

13

possible to extend this approach to fetal cardiac gating. These techniques both show potential for

fetal cardiac gating; however, the extension is non-trivial, and there have not been any reports of

fetal cardiac gating with ultrasound to date.

Real-time MRI

Real-time imaging does not require a gating signal because the acquisition of each image is

sufficiently fast to eliminate motion artifact. Significant advances have been made in real-time

PC-MRI; however, these sequences necessarily compromise spatial and temporal resolution as

compared to a regular ECG-gated acquisition. In fetal cardiac imaging the spatial and temporal

resolution are both at a premium, as the vessels of interest are on the order of 5 mm or less, the

cardiac cycle length (R-R interval) is shorter than 500 ms, and the field of view is necessarily

large to encompass the mother’s abdomen and avoid the image artifacts known as “wrap”.

Current state-of-the-art “real-time” methods provide phase-contrast data with 20x20 cm2

coverage, 1.5 mm in-plane resolution, and 150 ms temporal resolution, which are still

insufficient for this application (35).

Self-gating

Self-gating or “wireless” strategies were first proposed by Spraggins (36) and Hinks (37). These

techniques sample k-space such that a periodic gating signal can be extracted from the MR data

themselves, which can then be used to sort the data retrospectively. Modern implementations

exist for both radial and Cartesian trajectories and use a variety of signal detection algorithms

including signal intensity modulation, centre-of-mass tracking, image correlation, and low-

resolution flow measurement (38-40). Previous publications have suggested fetal imaging as a

potential application for their techniques and Nieman (41) and Holmes (42) have even

implemented cardiac self-gating for the mouse and chick fetus, respectively. These techniques

may be applied to human fetal cardiac PC-MRI, but no such application has been reported in the

literature to date. Additionally, these techniques often require specialized pulse sequences in

order to extract a suitable self-gating signal.

Nontriggered imaging

A nontriggered acquisition provides a simple alternative to complex gating schemes by

circumventing the need for gating altogether. In this case, an image is acquired with complete

14

disregard for the cardiac phase, generally with several averages. In theory, the acquisition will

sample evenly across a number of cardiac cycles producing a flow value in each pixel that

reflects the mean flow during the scan. This process is complicated by factors such as oscillation

of the vessel size and position, and varying magnitude in the vessel due to inflow effects. It has

been shown that the pulsatility of the flow as well as the choice of scan parameters can greatly

affect the degree of inflow enhancement and consequently the measured mean flow (43,44).

Sequences that minimize inflow effects may reduce this problem; however, problems with vessel

motion and dilation will remain. Additionally, these methods disregard the dynamic information,

producing only a mean flow measurement.

1.5 Fetal Heart Rate Variation

In cine PC-MRI imaging, the objective is to produce a series of images where the dynamic

information in the cardiac cycle is resolved in a series of time-frames. It is therefore important

that each image corresponds to data from a single phase of the cardiac cycle, which is typically

accomplished with gating.

In the absence of any heart rate variability, gating would be unnecessary as the period of the

acquisition could simply be matched to the R-R interval length. Unfortunately, this is not usually

the case and a more sophisticated acquisition and reconstruction is required. While the case with

no gating or heart rate variability is clearly extreme, it highlights the fact that the level of heart

rate variability, the complexity of the reconstruction method, and the quality of the

reconstruction are all intimately related. In light of this, it is important to understand the nature

of fetal rate heart variability as it will constrain and motivate possible solutions, and ultimately

determine the quality of the reconstruction.

1.5.1 General Structure

Fetal HRV is used as a clinical measure of fetal well-being both ante- and intrapartum (45),

which has motivated an appreciable amount of research in the area. Heart rate traces are visually

inspected by the obstetrician, and guidelines for this evaluation are well-established (45). A

healthy human fetus usually displays moderate variation, asymmetrically distributed about a

baseline value which is between 110-160 bpm (45). Healthy variation includes plateau-like

accelerations, random variation, and some oscillatory components related to fetal proto-breathing

15

(46-48). In this work, random motion refers to the heart rate variation that is not obviously

structured, although it is typically fractal in nature (49). Heart rate variation also depends on

fetal behavioural state with more pronounced variation in the active awake and active sleep states

(50).

HRV can be subdivided into short- and long-term variation, where short-term variation refers to

beat-to-beat changes and high frequency changes, and long-term variation refers to the power in

the low frequency components and the breadth of the distribution of achieved heart rates.

Compared with adults, fetal HRV shows a smaller dynamic range and less beat-to-beat variation

(45,51).

1.5.2 Indices

Due to the subjective nature of fetal HRV interpretation, many researchers have attempted to

quantify and automate the process through the use of computer-calculated indices. More than 20

different indices have been proposed over the last 40 years, with varying degrees of utility (52).

Very few of these have entered standard clinical practice; however, these indices allow the

quantification and characterization of fetal HRV, permitting validation of simulations against the

literature. An exhaustive description of the definitions and normal values of these indices is

beyond the scope of this thesis.

1.5.3 Modelling

There have been a number of attempts to simulate fetal heart rate traces and their corresponding

signals as measured by different devices. These simulations were created using a wide range of

methodologies and varying degrees of realism.

Trace Generation

Several authors have attempted to generate simulated fetal heart rate traces based on existing

knowledge of the characteristics and structure of fetal HRV, generally with poor results.

Cesarelli et al. (53) generated synthetic traces for signal processing validation by combining an

existing model for simulating adult ECG signals with knowledge about the spectral properties of

fetal HRV from the literature (46). van Meurs et al. (54) produced a simulation that mimics fetal

distress by generating realistic decelerations, which were used for educational purposes.

16

Magalhães et al. (55) adapted this technique and added white noise, which they then applied to

signal-processing validation. In all of these cases the resulting traces were qualitatively and

quantitatively unrepresentative of real fetal HRV. While these simulations may be appropriate

for validation of signal-processing algorithms, their unrealistic nature makes them inappropriate

for validation in this work.

Parameter Extraction

In addition to the generation of simulated fetal heart rate traces based on existing parameters,

several groups have attempted to analyze real heart rate traces within the confines of different

models.

Jarisch and Detwiler (56) attempted to overcome the inherently random nature of fetal HRV

through the use of a Kalman filter to fit a parameterized stochastic model to real datasets. Their

model included white noise for beat-to-beat variation, asymmetric variation around a slowly

varying baseline, and a “jitter” component that had no physiologic motivation but was

determined empirically to be necessary. They reported good fit quality in general, but

unfortunately, their work did not include parameter value ranges derived from their training data,

precluding the use of this model for the generation of simulated traces in this work.

Gough (57) modeled the fetal heart rate as Brownian motion and determined the fractal

dimension through repeated measurements of the curve length with varying ruler sizes. This

model assumes nothing about the underlying structure of the fetal HRV, other than the existence

of fractal properties, which had already been demonstrated (49). This model has since been

adapted by a number of researchers (58-60), and motivated the simulation used in this work.

1.6 Image Metrics and Autocorrection

The final section of this chapter discusses an existing image correction technique of particular

relevance to the work. As will become apparent, my research draws upon the existing theory and

methodology of metric-based autocorrection. Metric-based autocorrection has been applied in a

number of fields, including astronomy, photography, and most recently medical imaging.

Although the undesired artifact, cost function, and correction strategy vary between applications,

17

at the most basic level all implementations use an image metric to quantify image quality, and

then iteratively adjust the image to optimize the metric value.

Metric-based autocorrection was first applied to MR imaging by Noll et al. in 1992 (61), where a

maximum-intensity focus criterion was used to reduce blurring caused by field inhomogeneities.

It was subsequently applied to ghost artifact suppression by Xiang and Henkleman (62) with an

image gradient power criterion. The most relevant implementation of metric-based

autocorrection was first introduced by Atkinson et al. in 1997 (63) and further developed by the

Ehman group (64). This implementation determines a “motion record” that describes the

position and orientation of the patient during the scan, and applies phase shifts and rotations in k-

space to reduce artifacts resulting from in-plane motion during the scan.

These authors used a number of different focus criteria including image entropy (65) and the

entropy of the gradient image (66,67), among others (68). The technique has been applied to a

number of different image types including brain (65) and shoulder imaging (65,66) as well as

angiography (67). In all cases the metric was evaluated on the anatomical magnitude images.

1.7 Thesis Statement

The objective of this work is to develop a retrospective data-processing technique that permits

time-resolved flow measurements in utero without the need for gating. I propose a new gating

strategy called metric optimized gating (MOG), that is based on previous work in metric-based

autocorrection that is motivated by knowledge of fetal heart rate variation. In the next chapter I

discuss the theoretical basis and practical implementation of this technique, and provide

experimental validation. This technique enables time-resolved PC-MRI in utero, providing a

useful tool for the assessment of the fetal heart. The hope is that this will lead to improved

clinical management for cases of complex CHD and a better understanding of the fetal

circulation.

18

Chapter 2 Metric Optimized Gating*

2.1 Introduction

The previous chapter outlined the potential utility of cine PC-MRI for evaluating the fetal heart,

as well as the issue of gating that has precluded these types of measurements. Without the ability

to gate acquisitions, cardiac motion produces appreciable artifacts that corrupt both time-

resolved and time-average flow measurements.

This chapter draws on several concepts presented in the last chapter including retrospective

cardiac gating, fetal heart rate variability, and metric-based image correction. These concepts

motivate an alternative strategy for reconstructing fetal PC-MRI data acquired without explicit

gating, where the gating is retrospectively determined by adjusting a heart rate model to optimize

an image metric. In this chapter I present the theory and implementation of this technique, as

well as the results from a number of validation experiments. These include the construction of a

numerical simulation, an experiment with a pulsatile flow phantom, a study in adult volunteers,

and finally preliminary application in the target fetal population.

2.2 Theory

The technique proposed in this study involves the use of image metrics to detect misgating

artifact. Specifically, the image metrics are evaluated on the time-series of PC-MRI images of

vessels with pulsatile flow. For this reason, it is important to understand how the data are sorted

according to cardiac phase, what artifacts result from incorrect sorting, and how these artifacts

can be detected.

2.3 Oversampling

As described in the previous chapter, retrospective cardiac gating involves the continuous

acquisition of data with each block of consecutive k-space lines (referred to as a segment) being

* This chapter is based on a manuscript that has been accepted for publication in the journal Magnetic Resonance in

Medicine (69).2

19

acquired for an entire R-R interval. In addition to recording the times of the R-waves during the

scan for later use, the heart rate monitor triggers the transition from the acquisition of one

segment to the next. In this sense, the technique is not strictly retrospective; however, the term

“retrospective” is used to reflect the fact that the data are subsequently interpolated to a

predetermined set of cardiac phases. Larson et al. (39) implemented a more literal interpretation

of retrospective gating where each segment of k-space was acquired repeatedly for a

predetermined period that was longer than the longest anticipated R-R interval. These data were

then temporally interpolated in the traditional way. This technique involves a slight loss in scan

efficiency but improves the flexibility in accommodating heart rate variability (HRV) and

eliminates the requirement for any real-time feedback from a heart rate monitor.

To allow retrospective reconstruction, each segment must be sampled at every cardiac phase.

For fetal imaging, this requirement is complicated by the fact that the heart rate is unknown and a

heart monitor is unavailable to trigger the transition from one segment to the next. The technique

implemented by Larson et al. can be used to circumvent this problem if the period of acquisition

is chosen to be sufficiently long to accommodate the full range of heart rates found in the fetal

population. This can reduce the scan efficiency by up to 30 % in some cases, but it also

guarantees that a complete reconstruction is possible. Additionally, the excess data can be used

to improve the SNR in the final images. As the fetal heart rate usually ranges between 110-

180 bpm throughout pregnancy, oversampling of the cardiac cycle can be accomplished for the

entire fetal population with a sampling period greater than or equal to 545 ms (the reciprocal of

110 bpm) (45).

2.3.1 Metric Optimized Gating

The oversampling process described above ensures that every segment of k-space is acquired at

every cardiac phase. This guarantees the existence of perfect reconstruction, provided the data

can be properly sorted according to cardiac phase retrospectively. The sorting by cardiac phase

is accomplished by distributing hypothetical triggers throughout the scan according to a

parameterized model of the fetal heart rate. The data are grouped according to cardiac phase and

temporally interpolated to produce a series of images and an image metric is evaluated on the

reconstructed images to determine the level of misgating artifact. This process is repeated and

the heart rate model parameters are iteratively adjusted to optimize the image metric.

20

2.3.2 HR Modeling

The first chapter discussed the fact that fetal HRV is fractal and random in nature over short

periods of time (51,57), and displays a much smaller dynamic range (45) and less short-term

variation (51) as compared to adult HRV. These characteristics suggest that it may be possible to

approximate the fetal heart rate well with a fairly simple model, as the variation is relatively

small and unstructured. In addition, the fact that the velocity-induced phase shifts in PC-MRI are

primarily encoded in the central portion of k-space (70) suggests that the heart rate model need

only be accurate over the short period of time during which the centre of k-space is acquired.

For linear phase-encode orderings, as considered in this study, this is the middle of the scan.

An ideal heart rate model provides sufficient flexibility to account for fetal HRV, reasonable

search times, and adequate SNR in the image metric to eliminate over-fitting. On one extreme, a

one-parameter model assumes the heart rate is constant and provides the least flexibility with the

fastest search times. On the other extreme, a many-parameter model, where each trigger time is

specified by an independent parameter, can completely account for the HRV, at the cost of a long

search time. Between these extremes, there exists a wide range of potentially applicable models.

2.3.3 Misgating Artifacts

Misgating refers to the incorrect detection of one or more triggers that mark the beginning of

each cardiac cycle during the scan. This results in a cardiac phase error (CPE) between the true

cardiac phase at which an echo was acquired and the presumed cardiac phase based on the

incorrect gating. In metric optimized gating (MOG), the timing of each trigger is determined by

“dead reckoning” according to the parameterized model of the fetal heart rate during the scan.

This makes CPE cumulative from one R-R interval to the next, as it is given by the integral of

the difference between the true and modelled heart rates. In general, misgating can be either

systematic or random. Systematic misgating refers to a structural discrepancy between the

modelled and true heart rates, causing the modelled and true trigger times to drift apart and the

CPE to grow from one interval to the next. Random misgating refers to short-term variability in

the heart rate that is not properly accounted for in the model, causing the CPE to wander

randomly about zero throughout the scan.

21

Systematic misgating produces two principal effects in vascular PC-MRI images: ghosting in the

phase-encoding direction and a loss of pulsatility in the vessels, where pulsatility is defined as

, and Q is the volume flow rate. The ghosting in the phase-encoding

direction is caused by the distribution of the non-zero temporal frequency components in the

vessel. This is a well-known artifact that was clearly explained by Xiang (71) using a k-t-space

formalism. The locations, powers, and phases of these ghosts can be determined analytically in

very simple cases and numerically in more realistic cases. The loss of pulsatility in the extracted

flow patterns is due to mixing of data from different parts of the cardiac cycle into each image.

As shown in Figure 2, reconstruction of data at an incorrect heart rate produces an oblique

trajectory in k-t-space due to an accumulation of CPE with time, or equivalently ky. In this case,

each cardiac phase represents a weighted average of the entire cardiac cycle, where the weighting

is determined by the power distribution in k-space.

The artifacts resulting from random misgating are more difficult to characterize. This type of

CPE produces dispersion in the phase-encoding direction that is smeared rather than discrete,

with pulsatility less affected.

Figure 2: Illustration of the temporal averaging that reduces the pulsatility of the flow. The diagram on the left shows properly gated flow and the diagram on the right shows flow with linearly accumulating CPE. On the top axes the line shows the true flow and the dots the measured values. The power in k-space is shown on the far right and determines the relative weighting in the averaging kernel. Each dashed line shows a frame in the series of images and the solid line shows the frame of interest. The slope of the dashed lines is inversely related to the difference between the true and reconstructed heart rates.

22

2.3.4 Image Metrics

In MOG, the “correctly gated” series of images is defined as the one that optimizes the image

metric value, making the selection of an appropriate metric essential. There are several criteria

that define an effective image metric: the metric should be able to discriminate between good and

bad reconstructions (sensitivity); the definition of a “good” reconstruction should agree with

reality (accuracy); the difference in the metric value between correct and incorrect

reconstructions should be large compared to random error in the metric value (high contrast-to-

noise); the metric should operate well on images with low SNR and be insensitive to user-

controlled parameters such as ROI placement (robustness); and it should have a single, well-

defined optimum (well-behaved). Additionally, the metric should be straightforward to compute

in a short period of time.

The characteristic effects of misgating provide several means by which misgated reconstructions

might be identified. Spatially, the smearing of the vessels in the phase-encoding direction makes

the power distribution more diffuse and the vessel boundaries less abrupt. Temporally, the loss

of pulsatility results in a more even distribution of flow across the cardiac cycle and a reduction

in the power of the derivative of the flow waveform. Previous work in metric-based auto-

correction (63,68,71) provided several potential metrics that have been shown to be sensitive to

similar effects in other applications. The metrics investigated in this study included the image

gradient power (with a variety of derivative kernels), the image entropy, the entropy of the

gradient, and the normalized gradient squared. These metrics were implemented spatially,

temporally, and spatio-temporally. In addition to these metrics, the pulsatility index and mean

value of the flow waveform extracted from the vessel lumen were tested for their ability to detect

misgating.

Of the proposed metrics, time-entropy was best able to satisfy the above criteria and hence was

selected for use in this work. Time-entropy refers to the entropy evaluated in time on a voxel-by-

voxel basis and summed spatially, which provides a surrogate measure of pulsatility. This is

because pulsatility is equivalent to non-uniform flow distribution in time, which has a lower

likelihood of random occurrence. It relies on the assumption that the most correct reconstruction

produces the most pulsatile waveform. Apart from small effects where noise can add

constructively to slightly increase the pulsatility near the correct reconstruction, it is true that the

23

pulsatility only decreases with misgating. This provides a type of template-matching, where the

reconstruction is guided by an assumption regarding the measured flow; however, it requires less

a priori knowledge about the anatomy and physiology of the vessel than a true template-

matching approach. Additionally, the fact that time-entropy considers the data as a set instead of

a sequence makes it less susceptible to noise and less biased by the specific shape of the flow

curve than derivative-based metrics. Finally, time-entropy is insensitive to ROI placement and it

does not require vessel boundary delineation prior to the optimization, which is important

because severe misgating can obscure and distort images to the point where even locating vessels

can be challenging.

The time-entropy was evaluated on the phase images of the PC-MRI series, as they contain most

of the dynamic information. It was necessary to mask out regions with large phase error (i.e. low

signal) as they impair the performance of the metric. This was accomplished by multiplying the

phase images by the corresponding magnitude images. Although the magnitude images contain

strictly non-negative values, the phase images can contain any value between , making it

necessary to rectify the masked images before evaluating the metric. Evaluation of the metric on

the entire field of view introduces background signal and noise, which decreases the sensitivity

and contrast of the metric. This was solved by evaluating the metric on a small neighborhood

surrounding the vessel of interest. An 11×11 voxel region was chosen as a compromise between

robustness and sensitivity. With the resolution used in this study and the typical size of fetal

vessels, 11 voxels corresponded to approximately 2-3 vessel diameters, which was sufficiently

large to allow reliable placement around a vessel and its accompanying artifact. To compensate

for the fact that this neighborhood contains a large proportion of extra-vascular voxels, the

spatial sum of the entropy values was weighted by the total signal in each voxel. This increases

the sensitivity of the metric to changes in pulsatility in the vessel by enhancing the contribution

from the voxels in the vessel to the spatial sum.

The time-entropy was given by the expression:

€

E =Bi

Bii∑i

∑ Si,tBit

∑ logSi,tBi

⎛

⎝ ⎜

⎞

⎠ ⎟ (1)

24

where i indexes over space, t over time, S is the product of the phase and magnitude images,

and

€

Bi = Si,t2

t∑[ ]

1/ 2. The normalization factor used in this work was adapted from the work of

Atkinson et al. (63) and was found to provide less contrast but more accuracy than the usual

entropy normalization of

€

Bi = Si,t2

t∑ .

2.4 Methods

2.4.1 Heart Rate Models

In this study, a matter of minutes was considered an acceptable search time, which restricted the

heart rate models to one- and two-parameter searches based on available computer hardware.

The one-parameter model assumed a constant heart rate throughout the scan with the single

parameter specifying this constant, unknown heart rate. In addition, two two-parameter models

were considered—each motivated by different assumptions and a priori information. First, the

knowledge that the fetal heart rate typically contains less short-term variation than that of an

adult motivated a linear model where the heart rate is specified by a constant baseline and a

“drift” term (i.e. slope). Second, the knowledge that the majority of the dynamic information is

contained in the centre of k-space motivated a model where the two degrees of freedom were

chosen to maximize the flexibility during the middle of the scan when these data are acquired.

This model is piecewise-constant with a discontinuity in the middle of the scan, and the heart rate

in each half of the scan is specified by an independent, constant value.

2.4.2 MR Data

All clinical measurements were acquired with informed written consent and approval from the

hospital research ethics board, and were consistent with the guidelines for fetal MR imaging at

our institution. Patients were directed to MR if the prior fetal echocardiography was difficult or

inconclusive, as in patients with oligohydramnios or severe obesity. Patients who were referred

for fetal MR for extracardiac reasons were also studied with consent and hospital IRB approval.

The data were acquired on a 1.5T Avanto Syngo system (SIEMENS, Erlangen, Germany), using

an abdominal multi-channel surface coil. A conventional gradient echo phase-contrast sequence

was used with flip angle = 30°, TE/TR = 2.9/6.6 ms, and VENC = 150 cm/s. The positive and

25

negative velocity encodes were acquired alternately, doubling the time for each measurement to

13.15 ms. A voxel size of 1.25×1.25×5 mm3 was required due to the small size of fetal

structures, and a relatively large field of view of 32×48 cm2 was used to prevent excessive

wrapping of the maternal abdomen. To simplify off-line reconstruction, parallel imaging was not

used. Instead, every 4 lines of k-space were segmented to accelerate the scan, giving an effective

temporal resolution of 52.6 ms. Ten repetitions were acquired regardless of the fetal heart rate,

resulting in the continuous acquisition of each segment for 526 ms. Although this is slightly

shorter than the upper bound provided in the literature (545 ms), estimates of fetal heart rates

with cardiotocography prior to each MR examination suggest that it was sufficiently long in all

cases. In addition, the number of repetitions can be adjusted to accommodate lower heart rates,

if necessary. The scan time was 34 s, requiring that the acquisition be free-breathing. Data were

retrospectively reconstructed offline (MATLAB, The Mathworks Inc, Natick, MA, USA) and

reconstructed images were analyzed with clinical flow quantification software (QFlow®, Medis,

Leiden, Netherlands). Multicoil data were combined using quadrature magnitude weighting (72)

and phase images were corrected for background phase offsets (73). Linear interpolation was

used to generate intermediate cardiac phases through view-sharing (74,75), resulting in 30

cardiac phases.

2.4.3 Simulation

A phase-contrast acquisition of pulsatile flow through a vessel was numerically simulated to

study the effects of HRV on the reconstruction algorithm. The simulated matrix size, spatial and

temporal resolutions, and view ordering were all equal to their respective clinical parameters and

the vessel diameter, signal-to-noise ratio (SNR), and parabolic flow profile were based on direct

fetal measurements. An arterial flow pattern was simulated as

where , , and ,

and T is the cardiac period. The final calculated flow pattern was compared to the known input

flow to determine the quality of the reconstruction. The start of the cardiac cycle cannot be

determined by this technique, so the temporal offset between the two curves was fit as a free

parameter and agreement was quantified by the reduced χ2 residual.

A fetal heart rate simulation was constructed to test the effects of heart rate variability on the

reconstruction process. The observation that fetal heart rate traces are well described by

26

Brownian motion (57) motivated the simulation used in this work. The heart rate was simulated

as a bounded random walk superimposed on a constant baseline:

€

RRn+1 = RRn +N Δ⋅ RR0 − RRn( ) , σ2[ ] (2)

where N is a normally distributed random variable, RR0 is the baseline heart rate, σ is the

standard deviation of the beat-to-beat step size in milliseconds, and

€

Δ ∈ 0,1[ ] is the strength of

the bias bounding the walk around the baseline value. Values of Δ = 0.1 and σ = 7 ms were found

to give HRV that was quantitatively representative of typical fetal HRV, as measured by a

number of HRV indices (60,76). The reconstruction process was tested over a range of HRV

values, with 1000 random simulated heart rate traces at each value.

2.4.4 Phantom

A phantom experiment was completed to test the effects of misgating and to validate the heart

rate search algorithm and image metric. The phantom consisted of a computer-controlled

servomotor (FlexDriveII, Baldor Motors and Drives, Fort Smith, AR, USA) and gear pump

(Shertech AK Series AMBV1A, Hypro Corporation, New Brighton, MN, USA) connected to a

tube with 10 mm inner-diameter. The programmable nature of the pump allowed for the

combination of physiologically realistic flow patterns with the convenience of a relatively

constant, known pump frequency. The setup also permitted electrical triggering of the MR

scanner to the pump cycle to provide gated PC-MRI measurements for reference. The pump was

cycled at the maximum achievable frequency of 80 bpm. The diameter was larger than that of

typical fetal vessels; however, the spatial resolution was reduced to 2x2 mm to compensate. This

resulted in an equivalent number of voxels per vessel, albeit with a higher SNR than would be

expected in a fetal measurement.

2.4.5 Volunteer Experiment

Due to the difficulty associated with validating fetal PC-MRI flow measurements and the

absence of heart rate variability in the in vitro model, a validation experiment was carried out

using the carotid arteries in adult volunteers. This provided a good model of the fetal great

arteries with a more straightforward validation. The carotid arteries were chosen because they

provide similar vessel diameters and flow patterns to what would be expected in the great vessels

27

in a fetus. Exercising on an MR compatible cycling apparatus achieved heart rates comparable

to that of a fetus (120-150 bpm), as well as an appreciable degree of HRV. The carotid arteries

were imaged at the same resolution as the fetal vessels, providing approximately the same

number of voxels per diameter and a similar SNR.

There are several factors that make adult carotid arteries well suited for the validation of flow

curves. First, orthogonal slice prescriptions through the neck are easy to achieve, eliminating

effects due to poor slice prescriptions. Second, there are two carotid arteries in each image, as

well as two vertebral arteries and two jugular veins. This provides a wealth of data for validation

as well as the possibility of internal comparisons in the data. Third, adult volunteers are less

prone to random movement than fetal subjects and the carotid arteries do not move appreciably

with respiration, eliminating the confounding effects of motion. Finally, and most importantly,

measurements in adults made it possible to acquire an ECG signal in synchrony with the PC-

MRI measurements. Each data set could then be reconstructed with ECG gating and MOG,

allowing the comparison of the measured and modeled heart rate traces as well as the ECG gated

and MOG flow measurements.

2.5 Results

2.5.1 Heart Rate Models

Search times varied depending on the number of coils activated during the scan, the number of

function evaluations required by the search function, the number of parameters used in the

model, and the computer hardware; however, in general, a one-parameter search could be

completed in approximately 1 minute, and a two-parameter search could be completed in 4-5

minutes on a conventional desktop computer with non-optimized coding. The reconstruction

quality, as measured by the flow-fit residual, for the different heart rate models averaged over

1000 simulation runs are shown in Table 1. It is apparent that the addition of the second

parameter provides a significant improvement over the constant heart rate model and that the

piecewise-constant model provides better results than the linear model. For this reason, the

piecewise-constant model was used for optimization of the volunteer and fetal data. Due to the

relative stability of the pump frequency in the phantom, the one-parameter model was sufficient

to provide an accurate reconstruction.

28

Table 1: Results of 1000 simulated reconstructions testing the ability of the three heart-rate models to account for variability in the simulated heart rate traces. The simulated traces were generated using Eq. 2, with σ = 7, Δ = 0.1, and a baseline heart rate of 150 bpm. The same 1000 simulated measurements were reconstructed using each heart rate model. The residual is the mean reduced χ2 residual between the measured and known flow patterns.

Model Residual (×103) Constant 12.00 ± 0.04 Linear 7.24 ± 0.02

Piecewise-constant 6.65 ± 0.02

2.5.2 Phantom Experiment

Results from the flow phantom experiment are shown in Figure 3. These results demonstrate the

characteristic effects of misgating as well as the sensitivity of the metric to these effects. Figure

3a and Figure 3c depict images and flow patterns corresponding to reconstructions at a range of

assumed pump frequencies. The effects of misgating are apparent in both the images and the

flow patterns. The misgated images contain severe smearing in the phase-encode direction and

the flow patterns have reduced pulsatility, even when the reconstruction frequency was incorrect

by only a few cycles per minute. On the other hand, the optimized images are sharp and artifact

free, and the flow extracted from the optimized images is almost indistinguishable from the gated

reference flow. The time-entropy values plotted in Figure 3b show excellent discrimination

between correct and incorrect reconstructions, with a pronounced minimum at the correct

frequency.

29

0102030405060708090100

0 0.2 0.4 0.6 0.8 1

Flow

(ml/

s)

Cardiac Phase

GatedABCDE

A B C D E

2

2.5

3

3.5

4

-10 -5 0 5 10

Tim

e-en

trop

y

Frequency Offset (bpm)

a

b

c

Figure 3: Results from an experiment with a pulsatile flow phantom. (a) Images of the tube reconstructed at a range of hypothetical pump frequencies using the one-parameter heart rate model. The frequency at which the images were reconstructed is given on the axis below, where the axis values denote the difference between the supposed pump frequency used in the reconstruction and the true frequency. (b) The time-entropy values corresponding to the images in (a). (c) Flow patterns extracted from the image series indicated with the corresponding letters, as well as the flow pattern extracted from the ECG gated images.

2.5.3 Volunteer Measurements

Results from the volunteer carotid artery experiment are depicted in Figure 4. The heart rate

trace in Figure 4a shows a large degree of HRV during the scan, both in terms of random

fluctuations and a cyclic oscillation due to respiration. The model reflects the “mean” or

consensus of this trace; however, it fails to account for much of this variation. Regardless, there

is good agreement between the ECG gated and MOG images shown in Figure 4b and Figure 4c,

respectively, as well as the ECG gated and MOG flow patterns shown in Figure 4d.

30

Finally, Figure 4e presents the time-entropy values as a function of reconstruction heart rate

(using the one-parameter model for display purposes), evaluated on four different neighborhoods

of the images. The 11×11 voxel window was placed on the left and right carotid arteries and the

left and right jugular veins. It is apparent that despite differences in waveform shapes and vessel

sizes, all four regions are able to identify an optimal reconstruction heart rate. Furthermore, the

metric minima all occur at the same heart rate, which is consistent with the known mean heart

rate measured with ECG.

-5

0

5

10

15

20

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(ml/

s)

Cardiac Phase

RC Gated

RC MOG

a

b

d

120

125

130

135

140

0 10 20 30

Hea

rt R

ate

(bpm

)

Time (s)

ECGHR Model

c

2.4

2.6

2.8

3

3.2

3.4

3.6

110 120 130 140 150

Tim

e-en

trop

y

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LCRCLJRJ

e

Figure 4: Results from an experiment using the carotid arteries in adult volunteers. (a) Comparison of the optimized heart rate model and the true heart rate trace, as measured by ECG. The two-parameter model was used, and the two model parameters converged to nearly identical values. (b) and (c) show a single frame from the ECG gated and MOG image series, respectively. The magnitude images are shown on the left and the masked phase images are shown on the right. (d) Right carotid artery flow patterns extracted from the images shown in (b) and (c). The left carotid artery flow patterns were indistinguishable and were not included for clarity. (e) Metric values corresponding to four one-parameter heart rate searches in the left carotid artery (LC), right carotid artery (RC), left jugular vein (LJ), and right jugular vein (RJ).

31

2.5.4 Fetal Measurements

The results from a single fetal case with normal cardiac function are shown in Figure 5 and Table

2. The MR exam involved several measurements, each of which was optimized independently.

The full set of optimized heart rates indicates that the fetal heart rate varied between 138-175

bpm over the course of the exam. The MOG optimization and images for one representative

measurement are shown in Figure 5a and Figure 5b. The two-parameter metric optimization

shows a pronounced minimum and the images corresponding to this minimum depict a clear

view of the fetal pulmonary artery with little image artifact. Figure 5c shows three repeated

measurements of the pulmonary artery made at different times during the scan. They show good

agreement with each other and are consistent with the expected waveform shape shown in the

inset, which was taken from a normal fetal pulmonary artery Doppler trace from another subject

at the same gestational age. Additionally, the mean flow values of 287, 275, and 281 ml/min/kg,

and pulsatility indices of 3.87, 3.76, and 3.82 suggest that the measurements are reproducible.

Table 2 presents the mean flow rates and fractional distributions compiled from the full set of

measurements, as well as estimates of these values derived from the literature. Flow volumes

were divided by fetal weight, following the convention in the literature. The fractional

distribution of flow shows good agreement with previous measurements in most vessels, and the

mean flow values are within the expected range. Differences between individual values may

reflect natural variation, random error, or inaccuracies in the literature values.

The data can also be tested for internal consistency based on the conservation of blood volumes.

The flow in the main pulmonary artery is distributed between the lungs and the ductus arteriosus,

and indeed, two times the flow in the right pulmonary artery plus the flow in the ductus

arteriosus gives 295 ml/min/kg, which is in good agreement with the flow in the main pulmonary

artery (281 ml/min/kg). Also, the flow in the descending aorta is given by the sum of the flows

in the ascending aorta and the ductus arteriosus, minus the flow to the head and arms that returns

to the heart via the superior vena cava. This combination gives a value of 224 ml/min/kg, which

agrees with the measured flow in the descending aorta (217 ml/min/kg).

32

a

b

c -10

0

10

20

30

40

50

60

70

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(ml/

s)

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Hea

rt R

ate

2 (b

pm)

120 130 140 150 160 170120

130

140

150

160

170

2.4

2.6

2.8

3

3.2

Figure 5: Results from a 37 week fetal case with normal cardiac anatomy and function. (a) The metric value as a function of the model parameters for one representative measurement. (b) The magnitude and phase images corresponding to the optimum in (a), with the fetal pulmonary artery indicated by the arrow. (c) Three repeated measurements of the flow in the pulmonary artery. The inset shows the expected shape of the flow pattern in the pulmonary artery in a late-gestation fetus as measured by Doppler ultrasound.

33

Table 2: Measured mean flow values and fractional distributions corresponding to the 37 week fetal case shown in Figure 5, as well as reference values derived from the literature (5,7,9,25-28). Literature values are based on measurements with Doppler ultrasound and experiments involving the injection of radionuclide-labelled microspheres.

Flow (ml/min/kg) Distribution (% Combined Ventricular Output)

Vessel Measured Reference Measured Reference Combined Ventricular Output 481 400 – 553 100 100

Pulmonary Artery 281 248 – 302 58 55 – 60 Ascending Aorta 200 174 – 202 42 40 – 45 Descending Aorta 217 171 45 38 Ductus Arteriosus 165 135 – 196 34 30 – 46

Right Pulmonary Artery 65 23 – 113 13 5.5 – 12.5 Superior Vena Cava 141 83 – 165 29 23 – 37

Umbilical Vein 153 112 – 128 32 26 – 32

2.5.5 Simulation

The results of a randomly selected simulation are shown in Figure 6. The heart rate trace in

Figure 6a shows a significant amount of HRV, most of which is not accounted for in the heart

rate model. Despite this, the extracted and reference flow patterns shown in Figure 6b show good

agreement. Both the mean flow and pulsatility index are preserved to within 3% or their true

values.

Figure 7 shows the effects of increasing HRV on the flow pattern accuracy through Monte Carlo

simulation. Each bar reflects the mean and standard deviation of 1000 simulation runs with

simulated heart rate traces. For each execution, the data were optimized with the piecewise-

constant heart rate model and the mean flow and pulsatility index were extracted from the

measured flow. In general, as HRV increases, the measured flow pattern becomes less accurate;

however, over the range of expected fetal HRV the mean flow and pulsatility index are preserved

to within approximately 5 and 10 percent of their true values, respectively.

34

a

b

140

145

150

155

160

165

0 10 20 30H

eart

Rat

e (b

pm)

Time (s)

Simulated TraceOptimized Model

-5

0

5

10

15

20

0 0.2 0.4 0.6 0.8 1

Flow

(ml/

s)

Cardiac Phase

True FlowReconstructed Flow

Figure 6: Results of a simulation with σ = 7, Δ = 0.1, and a baseline heart rate of 150 bpm. (a) The simulated heart rate trace generated by Eq. 2 using the aforementioned parameters, as well as the optimized piecewise-constant heart rate model. (b) Comparison of the reference and calculated flow patterns.

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Flow

Par

amet

er

Heart Rate Variability ( )

PulsatilityMean Flow

Figure 7: Results of a Monte Carlo simulation testing the effects of HRV on the quality of MOG reconstruction. Each data point represents the mean and standard deviation of 1000 simulations with random HRV, determined by Δ = 0.1 and σ as shown. The mean and pulsatility are normalized against the correct values. The two-sided arrow denotes the typical range of fetal HRV based on reports in the literature (55,76).

35

2.6 Discussion

2.6.1 Validation

Collectively, the phantom, volunteer, and simulation experiments presented in this study provide

a strong validation of the MOG technique. The phantom experiment demonstrates the

effectiveness of the proposed metric in detecting the expected effects of misgating, and its ability

to accurately identify correctly gated images. The volunteer data provided in vivo application in

a representative model, and the simultaneous acquisition of an ECG signal permitted a direct

validation of both the optimized heart rate model and the measured flow pattern against accepted

techniques (30). Finally, numerical simulations showed that MOG can accurately optimize data

in the presence of realistic fetal HRV.

2.6.2 Fetal Application

The fetal measurements provided proof-of-principle application in the target population. The

fetal data reflect preliminary experience with a small number of cases, but the results are

encouraging. Validation of fetal data is difficult because a gold-standard technique is

unavailable for flow volume measurements in utero; however, these early results were

reproducible, in agreement with previous estimates, and internally consistent. It should be noted

that the preliminary fetal data set presented in this work is but one of several. MOG has been

attempted in 12 cases to date and the piecewise-constant heart rate model has provided an

acceptable reconstruction for all image series with accurate slice prescriptions.

2.6.3 Limitations

MOG

The primary limitation of MOG lies in its inability to fully correct data acquired with wildly

varying heart rates. This is evident in the Monte Carlo simulation where an obvious bias is

introduced in both the mean flow and pulsatility in the presence of high HRV. The gradual loss

in pulsatility reflects the temporal blurring that results from the inevitable scrambling of data in

the presence of high HRV. The overestimation of the mean value of a pulsatile waveform is a

well-characterized effect (43,77) that results from weighted temporal averaging due to inflow

effects in the signal magnitude. While these effects are undesirable, the results of the simulation

36

suggest that they are small in practice, and future research may further reduce this problem, as

will be discussed in the next chapter.

The second limitation of MOG is the inability to confirm the validity of the optimized

measurements. Although many of the experiments in this study included a means of validation,

no good alternative is available for fetal measurements. While the results of this study suggest

that MOG is capable of optimizing fetal data with typical levels of HRV, it is conceivable that a

particular measurement may contain sufficiently large HRV that even the optimized

reconstruction is not necessarily an accurate representation of reality. As MOG continues to be

validated in the fetal population, repeated measurements can be used to test reproducibility.

General fetal cardiac MRI limitations

Although MOG may be effective in mitigating problems associated with a lack of cardiac gating

in the fetus, there exist a wide variety of challenges associated with fetal cardiac MRI in general.

These include partial-volume effects in PC-MRI flow measurements, inaccurate slice

prescriptions, bulk fetal movement, and maternal breathing. There are a number of

improvements that may be made to address these issues in the future, which will be discussed in

the next chapter.

2.7 Conclusion

In summary, this study has demonstrated the feasibility of MOG through successful application

in a flow phantom, adult volunteers, and in utero. In addition, simulation results confirmed that

MOG is expected to perform well in the presence of HRV typical of the fetal population.

Although many other challenges remain in fetal cardiac MRI, this technique allows for

reconstruction of nontriggered phase-contrast images acquired with conventional pulse

sequences, facilitating fetal cardiac flow measurements with existing protocols and hardware.

The next chapter will discuss potential solutions to some of the issues identified in both the

methodology and results in this work. Additionally, it will include suggestions for further

avenues of research and potential extensions of the MOG technique.

37

Chapter 3 Future Work

3.1 Introduction

The previous chapter presented the theory, implementation, and validation of a new technique

for reconstructing PC-MRI data acquired without a gating signal. This chapter outlines potential

improvements to the reconstruction process, further investigation that would improve the

soundness of the conclusions, and future directions for research into the extension, adaptation,

and application of this technique.

3.2 Improvements

Although a large effort was made to optimize the scan protocol and MOG process, there is

certainly room for improvement. The previous chapter identified several limitations of MOG

and fetal MR in general, including the long scan time, the relatively low spatial resolution, the

difficulty associated with accurately prescribing image slices, and the bias introduced to flow

measurement in the presence of large HRV. These limitations may be addressed with the

improvements to the acquisition and reconstruction outlined below.

The long scan time precluded breath-holding, which introduced motion artifact due to maternal

respiration. Additionally, the long scan time increased the likelihood of bulk fetal motion,

physiologic changes, and HRV during the scan. The temporal resolution was near the minimum

allowable value, precluding the use of an increased number of views-per-segment to accelerate

the scan, although the data were not SNR limited so acceleration by some other means may be

possible. Spatial (78,79), temporal (80), or spatio-temporal undersampling (81) are all promising

options for accelerating the scan. In addition to reducing motion artifact, shorter scan times

would also decrease the amount of HRV that occurs during a scan, allowing the heart rate to be

better described by a simple model.

Second, increased spatial resolution may be beneficial for fetal flow measurements. It has been

shown that spatial resolution of at least 3 voxels per diameter is necessary for reliable flow

measurements (31,32), which is typically achievable in the fetal great vessels with the voxel size

38

used in this study; however, this is the lower bound on the acceptable resolution. While spatial

resolution cannot be increased without sacrificing scan time and SNR, automated lumen

segmentation (31) or model based approaches (82,83) may be used to increase the accuracy of

PC-MRI flow measurements in small vessels.

The presence of fetal movement between the acquisition of localizers and the PC-MRI series

often results in incorrect slice prescriptions. While, it will always depend on the experience of

the radiologist to prescribe slices accurately and identify slices that are erroneous, improvements

to the imaging protocol can also help. Minimizing scan times, prematurely terminating multi-

slice scans after the relevant anatomy has been identified, and continuously reacquiring

localizers may all help reduce this problem by ensuring that the localizer images reflect the

current position of the fetus.

The final issue that will need to be addressed is the bias in the mean flow and pulsatility that is

due to the inability of the heart rate model to fully account for the fetal HRV. This can be

overcome by adding complexity to the heart rate model used in the MOG reconstruction to better

accommodate fetal HRV. This will necessarily increase search times, but improved hardware for

computation and better code optimization may accelerate the reconstruction to the point where

higher order models are feasible.

3.3 Further Investigation

In addition to the experiments presented in the previous chapter, MOG may be further validated

with additional experiments and improvements on existing experiments. These include further

simulations with an improved simulation of the fetal heart rate, an experiment combining a gold

standard validation technique with physiological fetal HRV, a comparison against other

potentially applicable techniques, and evaluation of the technique in a larger population. These

suggestions for further validation are discussed below.

The heart rate simulation used in this work was chosen because fetal HRV is fractal in nature and

was adjusted to be quantitatively similar to true fetal HRV. It is true, however, that not all

fractals are alike, and that fetal HRV is not perfectly described by Brownian motion. A

generalized form of Brownian motion called fractional Brownian motion may provide a more

39

representative model by allowing the fractal dimension to be exactly matched to the literature.

The simulations could then be rerun with this new heart rate simulation, although the effects are

likely to be minimal.

The experiment with an adult volunteer provided excellent validation through the simultaneous

measurement of an ECG signal; however, it was limited by the fact that there are important

differences between adult and fetal HRV. An ideal experiment would involve acquiring images

in a fetal animal model, with a direct, invasive measurement of the cardiac cycle to combine a

gold standard validation with more representative fetal HRV. The gating would be acquired in

parallel with the regular oversampled acquisition, just as it was in the adult volunteer experiment,

permitting comparison between the optimized heart rate model and the measured heart rate, as

well as the MOG and traditionally gated images. Recently, Yamamura et al. (84) published

preliminary work involving PC-MRI in fetal lambs where cardiac gating was accomplished with

catheter measurements in the fetal carotid artery, suggesting that such an experiment is possible.

In addition to the validation of MOG against gold standard techniques in research settings, it

must also be directly compared against alternative techniques in the target population.

Specifically, MOG and self-gating should be applied back-to-back in several fetal cases and

compared in terms of their reconstruction qualities. In fact, some implementations of self-gating

involve sampling strategies that are consistent with MOG, allowing a single dataset to be

reconstructed with both techniques for a direct comparison.

Finally, the most important addition is the validation of MOG in a broader population. Due to

patient availability, only a limited number of fetal scans have been completed to date. Large

patient numbers could provide tests of reproducibility and reliability, further strengthening the

validation. Additionally, application in known cases of congenital heart disease could provide

measurements demonstrating the ability of PC-MRI to differentiate between healthy and

diseased states, demonstrating the utility of time-resolved PC-MRI measurements for the

assessment of the fetal heart.

40

3.4 Extensions

The most obvious extension of this technique would be its application to anatomical image

series, expanding the role of fetal MR to the assessment of cardiac anatomy and wall motion.

Although the artifacts resulting from misgated anatomical images are less severe than those in

PC-MR images, they do exist and have been well-characterized (85). The extension of this

technique to different types of images would simply involve an investigation of alternative image

metrics to identify one that is appropriate for that particular type of data. Furthermore, time-

entropy has been shown to be sufficient for MOG of PC-MRI images, but additional research in

image metrics may yield more effective metrics for this application as well.

3.5 Final Remarks

In conclusion, I have demonstrated that MOG provides an effective and reliable method of

reconstructing fetal PC-MRI data acquired without a gating signal. In all validation experiments,

MOG was able to produce measurements that were consistent with reference values, suggesting

that MOG is both reliable and accurate. While there are still several limitations that must be

addressed, the implementation of the recommendations in this chapter may resolve, or at least

reduce, many of these. More widespread application in the fetal population is still necessary;

however, MOG appears to provide an effective tool, enabling time-resolved PC-MRI flow

measurements in utero. It is my hope that the simplicity and efficacy of this technique will

promote its adoption in the lab and the clinic, contributing to a better understanding of human

fetal circulation and improved patient management in the years to come.

41

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Copyright Acknowledgements 1 Congenital Diseases of the Heart: Clinical-Physiological Considerations, 3rd Ed. Copyright © 2009 Abraham Rudolph; Reprinted with permission of John Wiley & Sons, Inc.

2 Metric Optimized Gating for Fetal Cardiac MRI, doi: 10.1002/mrm.22542. Copyright © 2010 Wiley-Liss, Inc.; Reprinted with permission of John Wiley & Sons, Inc.