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Improving sensitivity and spatial coverage of myocardial arterial spin labeling

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Improving sensitivity and spatial coverage of myocardial arterial spin labeling

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Improving Sensitivity and Spatial
Coverage of Myocardial Arterial Spin
Labeling

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)

Terrence Jao
August 2017

Abstract ii

Abstract
Magnetic resonance imaging (MRI) is a medical imaging technique invented by Paul
Lauterbur in 1971 that uses the principles of nuclear magnetic resonance to generate images. Widely
touted as the most important medical invention in the last 50 years, MRI has transformed the medical
landscape by providing high resolution anatomic images with excellent soft tissue contrast. MRI is
important for identifying neuropathology, assessing cardiovascular function, evaluating spinal and
joint disease, and diagnosing and staging cancer both pre-and-post-operatively. The power of MRI
lies in its ability to generate novel contrast mechanisms, which has expanded the scope of MRI
beyond anatomic imaging into quantitative imaging of an array of both physical and physiological
processes, including diffusion, spectroscopy, blood flow, and perfusion.
In this dissertation, I focus specifically on perfusion imaging of the heart. Many techniques
asides from MRI are also sensitive to perfusion, such as SPECT, PET, CT, and ultrasound. We believe
MRI has the potential to supersede these various modalities because it can offer high spatial
resolution without ionizing radiation and can even avoid injected contrast agents through a novel
technique called arterial spin labeling. The benefits of using ASL MRI are two-fold. One, ASL can be
used repeatedly in patients for long-term evaluation of perfusion defects, which may be useful to
assess disease progression. Two, ASL is contrast free and can be tolerated in a large population of
patients with renal disease. This population is more susceptible to coronary artery disease than the
general population and have the most to gain from a clinically viable cardiac ASL protocol.
Therefore, the focus of this work is to take the necessary steps to make ASL clinically viable.
In its current implementation, ASL has poor sensitivity and limited spatial coverage. Poor sensitivity
is unavoidable because without contrast agents, the perfusion signal in ASL is low, on the order of 1-
2% of the background signal from the heart itself. This makes maximizing the sensitivity of the ASL
signal all the more important. Our first step was to determine how imaging parameters influence the
sensitivity of not only ASL, but quantitative cardiac MRI in general. The metric we used to quantify
sensitivity was the variability of cardiac images over time, or in technical terms, the temporal signal
to noise ratio. If certain imaging parameters lead to large fluctuations in the cardiac images, there
would be no hope of unmasking a small 1-2% ASL signal change. Through this study, I made the
important finding that there is a fundamental limit towards minimizing these fluctuations, at which
point further increases in the raw signal strength become unnecessary.
With suitable imaging parameters at hand, I turned my attention towards the ASL pulse
sequence itself. Traditionally, ASL labels arterial blood using a magnetization preparation upstream
Abstract iii

of the tissue of interest and images after a post labeling delay to allow the labeled blood to enter the
tissue. The amount of time it takes the labeled blood to reach the imaged tissue, called the transit
delay, is a critical determinant of the sensitivity of the ASL signal because labeled blood decays over
time. In an extreme example, if the labeled blood signal has completely decayed before its arrival,
ASL would have zero sensitivity. To counteract transit delay, I opted to use velocity selective labeling,
which labels arterial blood based on its velocity as opposed to its spatial position. In theory, blood
within small arterioles within the imaging slice can be labeled to eliminate transit delay completely.
In practice, blood further upstream the arterial tree is typically targeted to minimize the transit time.
The choice of velocity selective parameters determines how far upstream and in which direction
labeling occurs in the arterial tree. These parameters were systematically varied and resulting
perfusion estimate were compared with those obtained from the standard spatially selective FAIR
ASL. Through this study, I found suitable velocity selective parameters and demonstrated the
feasibility of VSASL.
Lastly, I sought to increase spatial coverage of ASL. Simple sequential multi-slice imaging is
not possible due to the limited scan times (~ 3 min) required for ASL under pharmacologically
induced stress. 3D imaging may have superior slice coverage, but has long scan times and is
unnecessary; three axial slices of the heart is sufficient for clinical evaluation. Instead, I chose
simultaneous multi-slice imaging because of its fast imaging time. In SMS imaging, multiple slices are
simultaneously excited and shifted with respect to each other to ease their reconstruction. While still
preliminary, I demonstrated that two slices can be simultaneously excited and reconstructed to
obtain perfusion similar with single slice cardiac ASL.

Dedicated to my wife, Susan Zhang, for her unwavering and loving support

Acknowledgements v

Acknowledgements
I would like to thank the many people who have helped me over the past six years to complete
this dissertation. I am in their debt.
First and foremost, I would like to express my gratitude and deepest respect for my advisor,
Professor Krishna Nayak. He fostered a lab culture that was conducive to creativity and always
encouraged me to pursue my own ideas, no matter how nutty or far-fetched. He was not only a
mentor in science and engineering, but also a role model for my professional development.
I am also grateful to Professor Justin Haldar for serving on my dissertation committee. Justin has
always been enthusiastic to help me with my work and taught one of the most memorable classes I
had taken at USC. His guidance enriched my learning experience at USC immensely.
I would also like to thank Dr. Meng Law, who served on my dissertation committee. He provided
invaluable feedback and helped me take a step back to look at the broader clinical impact of my work.
I also would like to thank him for his guidance and mentorship during my shadowing experience with
him at Keck Hospital for over two years.
I am also indebted to Dr. John Wood for serving on my dissertation committee. He is always able
to pinpoint the scientific nuances and find connections in disparate fields. He provided engaging
discussion and helped me take a deep look at my work from a variety of perspectives.
I would also like to express my gratitude to Professor Eric Wong, a renowned expert in arterial
spin labeling, for serving on my dissertation committee. I thank him for making countless trips from
San Diego to meet with me at USC to impart wisdom and guidance. Whenever I faced difficulties or
challenges, I could always count on his expertise to help set me in the right direction.
I have also been fortunate to be a part of the Magnetic Resonance Engineering Lab. MREL not
only provided an engaging environment for learning, but also an atmosphere of camaraderie. I would
like to thank all current and past lab members for their continued support. They have been invaluable
team members, especially when they are subjects, willing or unwilling, of my countless hours of
experiments. I would like to especially thank Hung Do, the partner in crime I have worked alongside
with during my entire tenure at USC, Ahsan Javed, for his insightful discussions and creative ideas,
and Yi Guo, for his invaluable friendship through thick and thin.
Finally, I would like to thank my parents for encouraging me to pursue my dreams and career.
Contents vi

Contents

Abstract ..................................................................................................................................................................... ii
Acknowledgements ............................................................................................................................................... v
Contents ................................................................................................................................................................... vi
List of Publications ............................................................................................................................................... ix
Journal Papers .................................................................................................................................................................... ix
Conference Papers ............................................................................................................................................................ ix
1 Introduction ................................................................................................................................................... 1
1.1 Motivation ............................................................................................................................................................... 1
1.2 Contributions ......................................................................................................................................................... 3
1.3 Dissertation Organization ................................................................................................................................. 4
2 Background .................................................................................................................................................... 5
2.1 Pathophysiology of Coronary Artery Disease........................................................................................... 5
2.1.1 Normal Artery Wall.................................................................................................................................... 5
2.1.2 Atherosclerosis ............................................................................................................................................ 6
2.2 MRI Physics ............................................................................................................................................................. 7
2.2.1 Components of MRI - B0, B1, and Gradient Fields ........................................................................ 7
2.2.2 Relaxation ...................................................................................................................................................... 9
2.2.3 Bloch Equation ........................................................................................................................................... 10
2.2.4 RF Excitation with Bloch Formulation ............................................................................................. 11
2.2.5 MRI Signal Equation and Fourier Interpretation ........................................................................ 12
2.3 Adiabatic Pulses .................................................................................................................................................. 13
2.4 Signal to Noise Ratio in MRI ........................................................................................................................... 14
2.4.1 B 0 Dependence ........................................................................................................................................... 15
2.4.2 Acquisition Time ....................................................................................................................................... 15
Contents vii

2.4.3 Spatial Resolution ..................................................................................................................................... 16
2.5 Velocity Encoding ............................................................................................................................................... 16
2.6 Simultaneous Multi-Slice Imaging ............................................................................................................... 19
2.6.1 RF phase cycled CAIPIRINHA .............................................................................................................. 19
2.6.2 Blipped CAIPI ............................................................................................................................................. 21
2.6.3 Reconstruction of SMS images ............................................................................................................ 22
2.7 Arterial Spin Labeling ....................................................................................................................................... 24
2.7.1 Overview of arterial spin labeling ..................................................................................................... 24
2.7.2 ASL Pulse Sequences ............................................................................................................................... 25
2.7.3 Arterial Spin Labeling Signal Equation ............................................................................................ 28
2.7.4 Challenges and Limitations .................................................................................................................. 30
3 Temporal Signal-to-Noise Ratio in Quantitative CMR .................................................................. 32
3.1 Introduction ......................................................................................................................................................... 32
3.2 Methods .................................................................................................................................................................. 33
3.2.1 Noise Analysis ............................................................................................................................................ 33
3.2.2 Experimental Methods ........................................................................................................................... 34
3.2.3 Image Reconstruction and Data Analysis ....................................................................................... 35
3.3 Results..................................................................................................................................................................... 36
3.4 Discussion ............................................................................................................................................................. 39
3.5 Conclusion ............................................................................................................................................................. 42
3.6 Appendix ................................................................................................................................................................ 42
4 Velocity Selective Arterial Spin Labeling.......................................................................................... 44
4.1 Introduction ......................................................................................................................................................... 44
4.2 Methods .................................................................................................................................................................. 45
4.2.1 Velocity Selective Pulse .......................................................................................................................... 45
4.2.2 VSASL Acquisition .................................................................................................................................... 46
4.2.3 Data Analysis .............................................................................................................................................. 48
Contents viii

4.3 Results..................................................................................................................................................................... 49
4.3.1 Validation of VS Labeling in RCA ........................................................................................................ 49
4.3.2 Sensitivity to Velocity Cutoff ................................................................................................................ 50
4.3.3 Sensitivity to Encoding Direction ...................................................................................................... 52
4.4 Discussion ............................................................................................................................................................. 53
4.5 Conclusion ............................................................................................................................................................. 54
4.6 Appendix ................................................................................................................................................................ 55
5 Simultaneous Multi-Slice Arterial Spin Labeling ........................................................................... 56
5.1 Introduction ......................................................................................................................................................... 56
5.2 Methods .................................................................................................................................................................. 57
5.2.1 Blipped-CAIPI bSSFP ............................................................................................................................... 57
5.2.2 Imaging ......................................................................................................................................................... 57
5.2.3 SNR Analysis ............................................................................................................................................... 58
5.3 Results..................................................................................................................................................................... 58
5.4 Discussion ............................................................................................................................................................. 60
5.5 Conclusion ............................................................................................................................................................. 61
6 Conclusions ................................................................................................................................................. 62
Bibliography ......................................................................................................................................................... 64

List of Publications ix

List of Publications
Journal Papers
1. Jao T, Nayak K. Demonstration of Velocity Selective Myocardial Arterial Spin Labeling
Perfusion Imaging in Humans. MRM 2017; In Prep.

2. Jao T, Nayak K. Maximizing Temporal Signal-to-Noise Ratio in Quantitative CMR. JMRI
2017; In Prep.

3. Miao X, Lingala SG, Guo Y, Jao T, Usman M, Prieto C, Nayak KS. Accelerated cardiac
cine MRI using locally low rank and finite difference constraints. Magnetic Resonance
Imaging 2016;34:707–714. doi: 10.1016/j.mri.2016.03.007.

4. Kober F, Jao T, Troalen T, Nayak KS. Myocardial arterial spin labeling. Journal of
Cardiovascular Magnetic Resonance 2016;18:22. doi: 10.1186/s12968-016-0235-4.

5. Do H, Jao T, Nayak KS. Myocardial arterial spin labeling perfusion imaging with
improved sensitivity. Journal of Cardiovascular Magnetic Resonance 2014;16:15. doi:
10.1186/1532-429X-16-15.

Conference Papers
1. Jao T, Nayak K. Simultaneous Multi-slice Cardiac ASL. Proc. ISMRM 25th Scientific
Sessions, Honolulu, April 2017, p1888.

2. Jao T, Nayak K. The Physiological Noise Contribution to Temporal Signal-to-Noise
Increases with Decreasing Resolution and Acceleration in Quantitative CMR. In: Proc.
ISMRM 24th Scientific Sessions. Singapore, Singapore; 2016.

3. Jao T, Nayak K. Demonstration of Velocity Selective Myocardial Arterial Spin
Labeling. In: Proc. ISMRM 24th Scientific Sessions. Singapore, Singapore; 2016.

4. Jao T, Nayak K. Demonstration of Velocity Selective Myocardial Arterial Spin Labeling
Perfusion CMR. In: SCMR 19th Scientific Sessions. Los Angeles, USA; 2016.

5. Jao T, Do H, Nayak K. Myocardial ASL-CMR Perfusion Imaging with Improved
Sensitivity using GRAPPA. In: SCMR 19th Scientific Sessions. ; 2016.

6. Do Hung, Ramanan V, Jao T, Wright G, Nayak K, Ghugre N. Non-contrast Myocardial
Perfusion Assessment in Porcine Acute Myocardial Infarction using Arterial Spin
Labeled CMR. In: SCMR 19th Scientific Sessions. Los Angeles; 2016.
List of Publications x

7. Landes V, Jao T, Nayak K. CAIPIRINHA-SSFP with improved banding artifact
performance. In: Pacific Grove; 2015.

8. Miao X, Lingala SG, Guo Y, Jao T, Nayak K. Accelerated Cardiac Cine Using Locally Low
Rank and Total Variation Constraints. In: Proc. ISMRM 23rd Scientific Sessions.
Toronto, Canada; 2015.

9. Do H, Javed A, Jao T, Kim HW, Garg P, Yoon AJ, Nayak K. Arterial Spin Labeling CMR
Perfusion Imaging is Capable of Continuously Monitoring Myocardial Blood Flow
during Stress. In: Proc. SCMR 18th Scientific Sessions. Nice, France; 2015.

10. Javed A, Jao T, Nayak KS. Motion correction facilitates the automation of cardiac ASL
perfusion imaging. In: Journal of Cardiovascular Magnetic Resonance. Vol. 17. ; 2015.
p. P51. doi: 10.1186/1532-429X-17-S1-P51.

11. Jao T, Do H, Nayak K. Temporal SNR of Myocardial ASL does not Increase with
Improved Spatial Consistency of Background Suppression. In: BMES Annual Meeting.
San Antonio, USA; 2014. p. 599.

12. Do H, Jao T, Nayak K. Myocardial ASL with Improved Sensitivity to MBF Using Parallel
Imaging. In: Proc. ISMRM 22nd Scientific Sessions. Milan, Italy; 2014.

13. Jao T, Do H, Nayak K. In Vivo Performance of Myocardial Background Suppression.
In: ISMRM 21st Scientific Session. Salt Lake City; 2013. p. 4525.

14. Jao T, Zun Z, Varadarajan P, Ramdas P, Nayak K. Myocardial ASL Data Filtering for
Improved Detection of CAD. In: ISMRM 20th Scientific Sessions. Melbourne, Australia;
2012. p. 3892.

15. Jao T, Zun Z, Varadarajan P, Pai R, Nayak K. Mapping of myocardial ASL perfusion and
perfusion reserve data. In: ISMRM 19th Scientific Sessions. Montreal, Canada; 2011.
p. 1339.

16. Zun Z, Jao T, Smith N, Varadarajan P, Pai RG, Wong EC, Nayak KS. Myocardial ASL
perfusion reserve test detects ischemic segments in initial cohort of 10 patients with
angiographic CAD. J Cardiovasc Magn Reson 2011;13:P110. doi: 10.1186/1532-429X-
13-S1-P110.
Introduction - Motivation 1

1 Introduction
1.1 Motivation
Coronary heart disease (CHD) is one of the leading causes of death and disability in the United
States, accounting for approximately one third of all deaths in individuals over the age of 35 (1–3).
Chest pain, myocardial infarction, heart failure, and other clinical manifestations of CHD are a result
of narrowing or occlusion of the coronary arteries, which reduces blood flow to the heart. Cardiac
stress testing in an important tool for evaluating patients with known or suspected CHD and is
usually performed using the cost-effective exercise treadmill ECG. Exercise ECG is sufficient for the
majority of patients with subtle perfusion deficits when used as a screening tool, but is unsuitable for
a large population of patients with more advanced disease that are intolerant of exercise and require
more detailed clinical information, such as local ischemia and myocardial viability (4). The gold
standard for diagnosing CHD is through direct visualization of the epicardial vessels with X-ray
angiography. However, X-ray angiography is an unattractive first-line diagnostic tool because of its
cost, invasiveness, and inability to assess the microcirculation and is reserved for only the most high-
risk of patients. The alternative is to use myocardial perfusion imaging, which can non-invasively
assess and localize CHD by comparing blood flow between rest and stress (4). Clinicians have an
abundance of imaging options to choose from to measure myocardial perfusion, each with their
unique advantages and disadvantages. Stress echocardiography detects aberrations in regional wall
motion as a surrogate for perfusion defects, but has lower sensitivity (4). Radionuclide perfusion
imaging, which include single positron emission computed tomography (SPECT) and positron
emission tomography (PET), are more sensitive, but exposes patients to radiation through injected
tracers (4). First-pass cardiac magnetic resonance (CMR) utilize the principles of nuclear magnetic
resonance (NMR) to form images and emits no radiation, but require injected gadolinium contrast
agents that have been linked to nephrogenic systemic fibrosis (NSF) in patients with renal failure (5).
These methods to evaluate CHD are limited by either low sensitivity (EKG, stress echo) or exposure
to injected tracers (SPECT, PET, MRI) and contrast, which are poorly tolerated in a large subset of
patients with comorbid kidney disease. Nevertheless, patients with kidney disease, especially those
with chronic kidney disease (CKD), and end stage renal disease (ESRD), would benefit the most from
cardiac perfusion evaluation. Both reduced glomerular filtration rate (GFR) and proteinuria in CKD
Introduction - Motivation 2

patients increase the risk of CHD. Yet these patients avoid routine coronary evaluation due to their
increased risk of contrast-induced nephropathy and NSF. Poorly managed CKD invariably progresses
to ESRD. There are approximately 615,000 patients with ESRD in the United States with an annual
growth rate of 3-4% (6). Almost half of all deaths in patients with ESRD are cardiovascular related,
of which 20% can be attributed to CHD (7). The hazard ratio for cardiovascular mortality increases
with kidney disease severity. When GFR < 60 ml/min/1.73m
2
in CKD, the hazard ratio is 1.11 and
increases to 3.08 when GFR < 15 ml/min/1.73m
2
in ESRD (8). Put simply, patients with ESRD are
over three times more likely to die from cardiovascular disease than the general population. Kidney
transplantation is the only curative treatment for ESRD and transplant candidates require yearly
cardiovascular assessment to determine preoperative cardiovascular risk. This assessment is usually
performed using dobutamine stress echocardiography, despite its lower sensitivity. We believe that
there is room for a new perfusion imaging technique that is both sensitive and contrast free to better
serve the CKD population. Arterial spin labeling (ASL) of the heart is that promising alternative.
ASL is a contrast free MRI technique that uses patients’ own blood as an endogenous tracer.
The technique works by magnetically labeling arterial blood and imaging the labeled blood after it
has perfused the organ of interest. Work on applying ASL in the heart was pioneered concurrently by
Poncelet (9) and Wacker (10). Poncelet performed ASL in pigs and observed that under
pharmacologic stress when perfusion is high, ASL showed moderate correlation with microspheres,
the gold standard for perfusion measurement. Wacker demonstrated feasibility of ASL in humans
and showed reduced perfusion reserve, the ratio of stress and rest perfusion, in patients with CAD.
Zun et. al. later successfully developed myocardial ASL at a single mid-short axis slice of the heart
that could detect clinically relevant changes in MBF in patients with or suspected of having CAD
(11,12). He introduced an experimental model for physiological noise based on ASL signal variations
among repetitions. Wang et. al. varied the time between labeling and imaging to estimate the transit
time of blood in addition to perfusion (13). Most recently, Keith et. al. was able to compare ASL
measurements from multiple slices of the heart using look-locker FAIR(14). These groups have
demonstrated the feasibility of cardiac ASL and its usefulness for diagnosing CAD, but have also
exposed several technical hurdles that must be overcome for widespread clinical adoption. First,
perfusion measurement in ASL is noisy because the detected blood signal is dwarfed by the
background myocardial signal. Even though the heart is one of the most highly perfused organs of
the body, the signal advantage is lost due to cardiac and respiratory motion, called physiological noise,
which corrupts the ASL measurement. Second, Wang et. al. (13) observed that perfusion is
underestimated without simultaneous measurement of the blood transit time. However, estimating
Introduction - Contributions 3

the transit time is impractical because the ASL protocol would have to be repeated for multiple
labeling delays, prohibitively increasing the scan time. Third, acquiring ASL under pharmacologic
stress limits the scan time to a few minutes for patient comfort and safety making it difficult to obtain
full heart coverage. In this thesis, we try address all these limitations by developing an accelerated
multi-slice cardiac ASL sequence that addresses underestimation from blood transit delay.

1.2 Contributions
PN and TSNR quantification in CMR
We borrowed the work of Triantafyllou et. al. (15) that analyzed physiological noise in brain
functional MRI and applied it for cardiac ASL. Through this analysis framework, we experimentally
determined the effect imaging parameters, including spatial resolution and parallel imaging
reduction factor had on physiological noise and temporal SNR (TSNR). Using these findings, we
determined a set of imaging parameters that balanced resolution and acceleration with high TSNR
for ASL. While the results of this work are specific to the MRI apparatus and receiver coil, it is simple
to reproduce and need only be performed once. The results of this work are applicable not only to
ASL, but also to other quantitative CMR techniques including T 1, T 2, ECV mapping, BOLD, and first
pass perfusion imaging.

VSASL and Transit Delay
To address the concern of blood transit delay and the underestimation of myocardial
perfusion, we implemented a velocity selective ASL (VSASL) sequence that labels blood based on its
flow velocity rather than spatial position. By targeting coronary flows, blood can be labeled adjacent
to myocardium, theoretically eliminating transit delay. We demonstrated initial feasibility of the
pulse sequence. Pulse performance was validated in simulation, phantom, and in-vivo, VSASL was
performed under various velocity cutoffs and velocity directions to experimentally determine the
impact of these parameters on myocardial blood flow (MBF) and physiological noise. We also
compared VSASL with the most widely used spatial labeling technique in heart called FAIR. Lastly,
we outline the advantages and disadvantages of using velocity labeling for ASL.

SMS ASL
ASL require repeated measurements for accurate perfusion quantification, which increases
scan time. Reducing the image acquisition window, while important for reducing physiological noise
Introduction - Dissertation Organization 4

as described by Do. et. al (16), does not speed up ASL scan time, which is limited by T 1 recovery of
blood. Images can be accelerated using parallel imaging and acquired sequentially. The order in
which slices are acquired impact the ASL estimate differently. Labeled blood is altered by imaging RF
pulses as it traverses down the vascular tree with a base to apex acquisition order. Acquisition from
apex to the base avoids RF contamination, but make apical slices more susceptible to transit delay
effects. We chose to increased spatial coverage by using simultaneous multi-slice acquisitions of the
heart to avoid these issues. SMS FAIR was performed using two simultaneously excited slices and
was found to have comparable MBF with their respective single slice counterparts.

1.3 Dissertation Organization
Chapters 2 reviews MRI background material used in later chapters. The topics include
fundamentals of MRI physics, tissue relaxation, the Bloch equation, velocity encoding, simultaneous
multi-slice imaging, and arterial spin labeling. Chapter 3 describes the work to measure TSNR and
physiological noise for cardiac images and provides details on image noise analysis and
reconstruction in SNR units. Chapter 4 presents the feasibility study of using VSASL to in the heart.
Chapter 5 summarizes the application of SMS imaging for FAIR ASL. Chapter 3 to 4 present peer-
reviewed published works while chapter 5 is unpublished.
Background - Pathophysiology of Coronary Artery Disease 5

2 Background
This chapter begins by introducing the pathophysiology of coronary artery disease.
Afterwards, it delves into various concepts in MRI that will help in understanding material presented
in later chapters. Section 2.2 begins with an overview on MRI physics to describe the generation of
the MRI signal and image formation. Relaxation is also introduced in this section to explain the
mechanism behind image contrast and ASL labeling. Section 2.3 introduces a special class of RF
pulses called adiabatic pulses. These pulses are relatively insensitive to the size and makeup of the
imaging object, allowing for consistent ASL labeling. Section 2.4 delves into noise considerations in
MRI, which play a role in the signal stability and sensitivity of ASL. Section 2.5 describes how velocity
is encoding in MRI to help in understanding velocity selective ASL. Section 2.6 gives a general
overview of simultaneous multi-slice imaging because of its potential to achieve full heart coverage.
Lastly, an overview of ASL as well as the current state of the art is reviewed in section 2.7 to motivate
the work in the following chapters.
2.1 Pathophysiology of Coronary Artery Disease
Ischemic heart disease is caused by a mismatch between myocardial oxygen demand and
supply. The vast majority of ischemic heart disease is a result of atherosclerosis within the coronary
arteries, which narrows the vessel lumen and reduces blood flow to the heart. Left untreated,
ischemic heart disease can manifest clinically as angina pectoris, an uncomfortable pain within the
chest, and myocardial infarction, an area of necrotic myocardium caused by a prolonged loss of blood
usually from a complete blockage of a coronary artery.
2.1.1 Normal Artery Wall
The normal arterial wall is composed of three layers, the intima (inner), media (middle), and
adventitia (outer) (17). The intima consists of a single layer of endothelial cells and serves as a barrier
between blood within the lumen and the subintima(17). Endothelial cells also produce an abundance
of molecules to prevent blood from clotting including heparin sulfate and nitric oxide (NO). The
intima plays an important role in vessel resistance, by secreting vasodilators (nitric oxide and
prostacyclin) or vasoconstrictors (endothelin) that alter the contractility of smooth muscles in the
underlying media. Finally, the intima also serves an anti-inflammatory role by preventing white
blood cells from attaching when healthy. In response to injury, endothelial cells produce surface
Background - Pathophysiology of Coronary Artery Disease 6

adhesion molecules which anchor white blood cells and secrete chemokines that attract them to the
site of injury.
The media is composed of smooth muscle cells and is separated from the intima through a
thick layer of extracellular matrix made of elastin, collagen and other molecules that provide
structural stability and elasticity (17). In larger vessels such as the aorta, the extracellular matrix is
more prominent to provide elasticity under high pressure while in smaller arterioles, smooth
muscles cells are more prominent to alter vessel resistance. Smooth muscle cells serve a contractile
role mentioned previously to alter vessel resistance and a synthetic role to produce molecules of the
extracellular matrix as well as inflammatory mediators.
The outer layer or adventitia of an artery is composed of nerves, lymph, and in large vessels
such as the aorta, more blood vessels (vasa vasorum) to provide nutrients to cells within the vessels
(17).
2.1.2 Atherosclerosis
Figure 2-1 Progression of atherosclerosis. A. Normal artery wall has three layers, the intima, media, and
adventitia. The intima is made of endothelial cells that form a tight barrier and regulates contractility of smooth
muscles in the media. The media contains smooth muscle that controls vessel resistance and secretes extracellular
matrix molecules. The adventitia contains nerves, lymphatics, and blood vessels to supply nutrients to the artery.
A. In the first step of atherosclerosis, a fatty streak forms because of endothelial dysfunction. The endothelial
barrier is disrupted and LDL along with other lipids are deposited into the subintima. Leukocytes are recruited to
clear the lesion. B. As the plaque forms, smooth muscles cells are recruited into the subintima to form extracellular
matrix fibrous cap surrounding the lipid core. Leukocytes in the core phagocytose the lipid and become foams cells
and are unable to leave the lesion. C. When the fibrous cap is too thin, the plaque ruptures into the vessel lumen
and initiates a clotting cascade which forms the thrombus, completely occluding the artery.
Background - MRI Physics 7

The pathogenesis of atherosclerosis usually begins with deposition of fat on the vessel wall.
These fatty streaks are visible on gross inspection, but do not narrow the vessel wall or impede blood
flow and exist in the coronary arteries in most people by age 20 (17). The primary event in the
development of atherosclerosis is endothelial dysfunction. Endothelial dysfunction can arise from
either physical or chemical stress. In areas with greater turbulent flows, especially at a bifurcation of
the artery, atherosclerosis is common. In contrast, in straight sections of arteries, laminar flows
produce less stress on the endothelium and promote secretion of anticoagulants and anti-
inflammatory substances. When vessel walls are exposed to chemical stress from high circulating
lipids, smoking, and diabetes, they produce highly reactive oxygen species that promote
inflammation (17). Inflammation weakens the barrier of the intima and promotes white blood cell
recruitment
Low density lipoproteins are one of the first molecules that deposit in the subintima in a
permeable and dysfunctional endothelial wall (17). When LDL becomes trapped in the subintima,
they undergo proinflammatory chemical changes and recruit white blood cells into the vessel walls.
Certain white blood cells begin to phagocytose the lipoproteins in an attempt to clear the lesion, but
are unable to leave the site. Accumulation of lipid engorged white blood cells, called foam cells, in the
atherosclerotic lesion recruits smooth muscles from the media to proliferate in the subintima to
deposit extraceullar matrix molecules around the forming lesion. Over the course of many years, the
resulting atherosclerotic plaque contains a lipid core surrounded by a fibrous cap that narrows the
vessel. When stenosis of the vessel exceeds 70%, symptoms of coronary artery disease begin to
emerge, including angina, shortness of breath under mild exertion, and fatigue. Ultimately, it is the
thickness of the fibrous cap that determines the risk of an acute myocardial infarction or heart attack.
Stable plaques with a thick cap are resistant to rupture while a thin fibrous cap has a high risk of
rupture. A ruptured plaque forms a thrombus that completely blocks the coronary artery and leads
to myocardial infarction.

2.2 MRI Physics
2.2.1 Components of MRI - B0, B1, and Gradient Fields
Magnetic resonance imaging (MRI) uses the principles of nuclear magnetic resonance (NMR)
to generate images. Atoms and isotopes with odd number of protons and neutrons experience a non-
zero magnetic moment and can be probed using NMR. In MRI, the most common atom that is imaged
is hydrogen because of its abundance in water and tissues, but other atoms like sodium and carbon-
Background - MRI Physics 8

13 can also be used. MRI utilizes the interactions of these types of atoms to three magnetic fields, an
external main field 𝐵 0
, a radiofrequency field 𝐵 1
, and a linear gradient field 𝐺 . In the absence of an
external field, atoms are oriented randomly and their individual magnetic moments cancel. When
subjected to an external magnetic field, they align themselves with the direction of the field, called
the longitudinal direction, to generate a net magnetic moment. They also resonate or precess at a
frequency determined by their unique gyromagnetic ratio and field strength (18).
𝜔 0
= 𝛾 𝐵 0
(2-1)
where 𝜔 0
is the larmor frequency and 𝛾 is the gyromagnetic ratio unique to each atom. These atoms
can absorb and emit radiofrequency energy transmitted at their larmor frequency. B 1 is applied
perpendicular to the main field on the transverse plane and excites the atoms out of their equilibrium
state. When B 1 is turned off, the atoms recover to thermal equilibrium and release radiofrequency
energy that can be captured by a RF receiver. Through Faraday’s law of induction, the precessing
magnetization from the atomic nuclei generates flux which induce an electromotive force in the RF
receiver called the free induction decay (FID).
The FID signal generated by the external main field and radiofrequency field come from all
atoms within the imaging sample. To localize these signals, linear gradient fields, G, are applied in the
longitudinal direction to vary the magnetic field linearly in space, thereby encoding spatial position
with precession frequency (18). Linear gradient fields that modify the longitudinal magnetization in
all three spatial directions can thus be used to fully localize the signals in space to generate images.

Background - MRI Physics 9

Figure 2-2 Components of a MRI scanner (19). The main field polarizes the spins, the RF field excites the spins,
and the gradient field localizes the spins.
2.2.2 Relaxation
After B 1 excitation, the longitudinal and transverse component independently recover to the
equilibrium magnetization state through T 1 recovery and T 2 decay. T 1 or spin-lattice relaxation is the
mechanism in which longitudinal magnetization along the direction of the external magnetic field 𝐵 0

reaches thermodynamic equilibrium(18). Physically, atomic nuclei within a molecular structure are
randomly vibrating and rotating. Nuclei in high energy states, excited by the RF field, distribute their
energy to their surrounding lower energy nuclei, most commonly through dipole-dipole interactions.
This energy exchange must occur in the transverse component at the larmor frequency. In nuclei that
are highly mobile such as free water, rotations are not restricted and only a small fraction of energy
exchange occur at the larmor frequency. Hence recovery is slow and T 1 is large . In molecules where
water is bound and restricted, a greater fraction of nuclei interacts near the larmor frequency and
have lower T 1. As field strength increases, the fraction of nuclei that can interact at the larmor
frequency decreases, which increases T 1. Therefore, for most tissue types at field strengths used for
MRI, T 1 increases with higher field strength.
T 2 or spin-spin relaxation is the mechanism in which transverse magnetization decays
towards equilibrium. Excited nuclei are exposed to local magnetic field inhomogeneity at the micro
or nano scale. This leads to a broadening of the resonant frequency, which in aggregate causes
incoherence and dephasing. Local magnetic inhomogeneity is caused by dipole interactions in their
longitudinal components. This interaction occurs at frequencies much lower than the larmor
frequency. Therefore, molecules that have restricted motion, such as those in solids, will experience
greater local field inhomogeneity and have short T 2. The independence of spin-spin relaxation from
the larmor frequency also makes it independent of field strength.
T 1 and T 2 relaxation forms the basis of image contrast in MRI. Different tissues have different
T 1 and T 2 values, which are shown in Figure 2-3. Adjusting the different parameters of the MRI
imaging sequence creates images with different degrees of T 1 or T 2 weighting.
Background - MRI Physics 10

Figure 2-3 A T1 values and B T2 values for fat, blood, heart and liver. The larger the T1 the slower the recovery,
the larger the T2, the slower the decay.

2.2.3 Bloch Equation
The Bloch equation is a phenomenological equation that describes the effects of magnetic
precession and relaxation. It is stated as follows (18):
𝑑 𝑴 𝑑𝑡
= 𝑴 ×𝛾 𝑩 −
𝑀 𝑥 𝒊 + 𝑀 𝑦 𝒋 𝑇 2
−
(𝑀 𝑧 − 𝑀 0
)𝒌 𝑇 1
(2-2)
Where 𝑴 is the nuclear magnetization vector, 𝛾 is the gyromagnetic constant, 𝑀 0
is the
magnetization at thermal equilibrium, and 𝑩 is the applied magnetic field vector with 𝐵 0
and G
contributing to the z-component (longitudinal) and 𝐵 1
contributing to the x and y components
(transverse). i, j, and k are unit vectors in the x, y, and z directions respectively. The cross product
describes precession while the subsequent terms describe T 2 and T 1 relaxation. The Bloch equation
can be written in matrix form (18):
𝑑 𝑴 𝑑𝑡
=
[

−
1
𝑇 2
𝛾 𝐵 0
0
−𝛾 𝐵 0
−
1
𝑇 2
0
0 0 −
1
𝑇 1

]

𝑴 +
[

0
0
𝑀 0
𝑇 1

]

(2-3)
The solution of this equation is as follows:
Background - MRI Physics 11

𝑴 (𝑡 )= [
𝑒 −𝑡 /𝑇 2
0 0
0 𝑒 −𝑡 /𝑇 2
0
0 0 𝑒 −𝑡 /𝑇 1
] 𝑹 𝒛 (𝜔 0
𝑡 )𝑴 (0)+ [
0
0
𝑀 0
(1− 𝑒 −𝑡 /𝑇 1
)
] (2-4)
where
𝑹 𝒛 (𝜔 0
𝑡 )= [−
cos(𝜔 0
𝑡 ) sin(𝜔 0
𝑡 ) 0
sin(𝜔 0
𝑡 ) cos(𝜔 0
𝑡 ) 0
0 0 1
]
The rotation, R z, describes rotation about the z-axis due to free precession while the matrix and
vector containing exponential decay terms describe relaxation.

2.2.4 RF Excitation with Bloch Formulation
Spins polarized by the main field must be tipped into the transverse plane for the RF receiver
coil to detect a FID signal for image generation. This is performed by the 𝐵 1
field, which can be written
as follows: (18)
𝐵 1
(𝑡 )= 𝐴 (𝑡 )𝑒 −𝑖𝜔𝑡 (2-5)

where 𝐴 (𝑡 ) is the amplitude modulating function and 𝜔 is the carrier frequency. RF excitation can be
more readily understood through a transformation into a rotating reference frame because spins are
constantly precessing due to the main field 𝐵 0
. The relationship between the static (lab) and rotating
frame can be written as: (18)
𝑴 = 𝑹 𝒛 (𝜔 0
𝑡 )𝑴 𝒓𝒐𝒕 𝑩 = 𝑹 𝒛 (𝜔 0
𝑡 )𝑩 𝒓𝒐𝒕 (2-6)
Ignoring relaxation due to the short duration of typical RF excitation pulses, the Bloch equation can
be expressed as: (18)

𝑑 𝑴 𝒓𝒐𝒕 𝑑𝑡
= 𝑴 𝒓𝒐𝒕 ×𝛾 𝑩 𝒆𝒇𝒇 𝑩 𝒆𝒇𝒇 = 𝑩 𝒓𝒐𝒕 +
𝝎 𝒓𝒐𝒕 𝛾 ; 𝝎 𝒓𝒐𝒕 = [
0
0
−𝜔 ]
(2-7)

In the rotating frame, the Bloch equation takes on the same form it had in the static lab frame with
the exception that the magnetic field 𝑩 is now replaced by the effective field 𝑩 𝒆𝒇𝒇
. In the rotating
frame, spins precess about the effective field, which is made of a transverse and longitudinal
component.
Background - MRI Physics 12

𝑩 𝒆𝒇𝒇
= 𝐴 (𝑡 )𝒊 +
1
𝛾 (𝜔 0
− 𝜔 (𝑡 ))𝒌 (2-8)
In the presence of RF excitation, the transverse component is given by the amplitude of the RF pulse,
𝐴 (𝑡 ) , and the longitudinal component is determined by the RF frequency, 1/𝛾 [𝜔 0
− 𝜔 (𝑡 )]. When RF
is transmitted on-resonance, 𝜔 = 𝜔 0
, and the effective field lies completely in the transverse plane.
After excitation the amount of magnetization that ends up in the transverse plane is dependent on
the amplitude and duration of 𝐵 1
(𝑡 ) and can be expressed as a solution to the Bloch equation (18).
𝑴 𝒓𝒐𝒕 (𝒕 )= 𝑹 𝒙 (∫ 𝛾𝐴 (𝑠 )𝑑𝑠
𝑡 0
)𝑴 𝒓𝒐𝒕 (𝟎 ) (2-9)
The amount of rotation caused by RF excitation is called the flip angle 𝜃 . For a RF pulse of duration 𝑇 ,
the flip angle can be expressed as (18)
𝜃 = ∫ 𝛾𝐵
1
(𝑡 )𝑑𝑡
𝑇 0
(2-10)
In the slice-selective case, a gradient modifies the precession frequency in the spatial
dimension.
𝑩 𝒆𝒇𝒇
= 𝐴 (𝑡 )𝒊 +
1
𝛾 (𝜔 0
+ 𝛾𝐺
𝑧 𝑧 − 𝜔 (𝑡 ))𝒌 (2-11)
The effective field will have a larger longitudinal component the further from isocenter a spin is (18).
When 𝐵 𝑒𝑓𝑓 is dominated by the longitudinal component, the amount of magnetization that gets
tipped into the transverse plane is small. This is the basis for slice-selective excitation; spins near
isocenter are excited while spins far away are not.

2.2.5 MRI Signal Equation and Fourier Interpretation
In the case of 2D slice-selective imaging the MRI signal equation can be expressed as follows
𝑠 (𝑡 )= ∫ ∫𝑚 (𝑥 ,𝑦 )𝑒 −2𝜋𝑖 [𝑘 𝑥 (𝑡 )𝑥 +𝑘 𝑦 (𝑡 )𝑦 ]
𝑑𝑥𝑑𝑦 𝑦 𝑥 (2-12)

where
𝑘 𝑥 (𝑡 )=
𝛾 2𝜋 ∫ 𝐺 𝑥 (𝜏 )𝑑𝜏
𝑡 0
𝑘 𝑦 (𝑡 )=
𝛾 2𝜋 ∫ 𝐺 𝑦 (𝜏 )𝑑𝜏
𝑡 0
(2-13)
The equation relates the acquired FID, 𝑠 (𝑡 ) , with the image, 𝑚 (𝑥 ,𝑦 ) (18). It is important to note that
the signal equation is in fact the Fourier transform of the image, 𝑠 (𝑡 )= 𝑀 (𝑘 𝑥 ,𝑘 𝑦 ) and that the
acquired data in 𝑘 𝑥 and 𝑘 𝑦 space are in spatial frequency units of cm
-1
. The acquisition space is
Background - Adiabatic Pulses 13

therefore called k-space and can be reconstructed into an image with an inverse Fourier transform.
In practice, images are not sampled infinitely, but on a finite grid. The following equation reflects how
k-space, 𝑆 , is sampled to generate a 𝑁 ×𝑁 image (18).
𝑚 (𝑥 ,𝑦 )= ∑ ∑ 𝑆 (𝑙 Δ𝑘 𝑥 ,𝑚 Δ𝑘 𝑦 )𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 𝑦 +𝑙 Δ𝑘 𝑥 𝑥 )
𝑁 2
−1
𝑚 =−
𝑁 2
𝑁 2
−1
𝑙 =−
𝑁 2
(2-14)

2.3 Adiabatic Pulses
RF transmission over the imaging volume is ideally uniform. In practice, a homogenous B 1
field is difficult to achieve with RF coils, especially when the object is large. In a conventional pulse,
the amount of transverse magnetization is proportional to 𝑠𝑖𝑛𝜃 , where 𝜃 is the flip angle, and will
vary with 𝐵 1
. Adiabatic pulses are a special class of pulses that can perform uniformly even in the
presence of an inhomogeneous 𝐵 1
field. A typical adiabatic pulse has a time-varying amplitude and
time-varying frequency as follows (20)
𝐵 1
(𝑡 )= 𝐴 (𝑡 )𝑒 −𝑖 𝜔 𝑟𝑓
(𝑡 )𝑡 (2-15)
Like any RF pulse, spins precess about the effective field. The effective field has a transverse and
longitudinal component given by 𝐵 𝑥 and 𝐵 𝑧 respectively. The magnitude and phase of the effective
field can be written as follows (20)
|𝐵 ⃑

𝑒𝑓𝑓 | = (𝐵 𝑥 (𝑡 )+ 𝐵 𝑦 (𝑡 ))
1/2
(2-16)

𝜓 = arctan(
𝐵 𝑥 (𝑡 )
𝐵 𝑧 (𝑡 )
) (2-17)
The principle behind adiabatic pulses is that the direction of the effective field is slowly
changed to allow spins to effectively track it. Formally, this is known as the adiabatic passage
principle, which states that the magnetization vector of a spin system precesses about 𝐵 𝑒𝑓𝑓 provided
that the direction of 𝐵 𝑒𝑓𝑓 does not vary much during one rotation. Mathematically, it can be
expressed as follows (20)
|
𝑑𝜓
𝑑𝑡
| ≪ 𝛾 |𝐵 ⃑

𝑒𝑓𝑓 | (2-18)
𝜂 =
𝛾 |𝐵 ⃑

𝑒𝑓𝑓 |
|
𝑑𝜓
𝑑𝑡
|
(2-19)

This first expression is known as the adiabatic condition, which requires the change in phase to be
much smaller the magnitude of the effective field. In practice, it is common to define an adiabatic
Background - Signal to Noise Ratio in MRI 14

factor, 𝜂 , as the ratio of the left and right hands side of the adiabatic condition. The adiabatic condition
is met when 𝜂 is sufficiently larger than unity. Generally, to fulfill the adiabatic condition, the
amplitude function, 𝐴 (𝑡 ) , starts out small and increases during the duration of the pulse while the
frequency function, 𝜔 𝑟𝑓
(𝑡 ) , starts out high and then decreases to 0, on resonance at the end of the
pulse.

Figure 2-4 Hyperbolic Secant Adiabatic Pulse. A. Magnitude B. Phase C. Slice-select Gradient.
In ASL, adiabatic pulses are most commonly used as labeling pulses to tag arterial blood.
Figure 2-4 shows an example of a hyperbolic secant adiabatic pulse used to perform slice-selective
inversion. It is critical to attain consistent performance for the label, regardless of 𝐵 1
, which can vary
by up to 53% in a 2D mid-short axis slice of the heart (21). The most commonly used adiabatic pulses
for labeling are the hyperbolic secant for slice-selective inversion and the BIR-4 for non-selective
saturation.

2.4 Signal to Noise Ratio in MRI
The signal to noise ratio (SNR) in MRI is defined as the signal amplitude (A) divided by the
noise standard deviation (𝜎 ) (18).
𝑆𝑁𝑅 ≜
𝐴 𝜎 (2-20)
It is determined largely by 3 factors, (1) B 0 field strength, (2) acquisition time, and (3) spatial
resolution.
Background - Signal to Noise Ratio in MRI 15

2.4.1 B 0 Dependence
The signal amplitude in MRI is proportional to the square of the main B 0 field (18). Noise power from
the within the receiver coil is proportional to the square root of the main field, while noise power
from the body is also proportional the square of the main field. This leads to the following
dependence
𝑆𝑁𝑅 ∝
𝐵 0
2
√𝛼 𝐵 0
1/2
+ 𝛽 𝐵 0
2

(2-21)

Where 𝛼 and 𝛽 are constants that determine the relative contribution of coil and body noise. Both
noise sources are characterized as being additive, Gaussian, and white. Coil noise is thought to arise
from resistance within the receiver coil while body noise is thought to arise from inductive coupling
between the coil and the body. In most clinical MRI scanners, the body is the dominant source of noise,
𝛼 approaches 0 and 𝛽 approaches 1 and
𝑆𝑁𝑅 ∝
𝐵 0
2
√𝐵 0
2
= 𝐵 0
(2-22)

Therefore, for most clinical applications, SNR is proportional to the field strength.
2.4.2 Acquisition Time
Acquisition time can be increased by performing more signal averaging and increasing the
readout time (18). Going back to the original definition of SNR that has been averaged 𝑁 𝑎𝑣𝑔
number
of times
𝑆𝑁𝑅 =
𝑁 𝑎𝑣𝑔
𝐴 √𝑁 𝑎𝑣𝑔
𝜎 2
=
√
𝑁 𝑎𝑣𝑔
𝐴 𝜎 (2-23)

SNR has increased by the square root of the number of averages,
√
𝑁 𝑎𝑣𝑔
because the signal level
increased by 𝑁 𝑎𝑣𝑔
while the noise standard deviation only increased by
√
𝑁 𝑎𝑣𝑔
. The noise variance is
additive because the samples are assumed to be independent. In parallel imaging, the samples are no
longer independent and noise becomes spatially varying.
In the case where the readout time is increased 2-fold, to maintain the same field of view, the
sampling rate and gradient amplitude must be halved. This has the effect of halving the anti-aliasing
bandwidth filter. The noise variance is proportional to the filter bandwidth (Δ𝑓 ) and sampling rate
(1/Δ𝑡 )
𝜎 ∝ Δ𝑓 =
1
Δ𝑡 (2-24)
Background - Velocity Encoding 16

Therefore,
𝑆𝑁𝑅 =
𝐴 √
𝜎 2
2
=
√2𝐴 𝜎 (2-25)

Doubling the readout time increased the SNR by √2. SNR is proportional to the square root of the
readout duration (18).
𝑆𝑁𝑅 ∝ √𝑟𝑒𝑎𝑑𝑜𝑢𝑡 𝑡𝑖𝑚𝑒
To summarize, SNR is proportional to the square root of both the number of averages and readout
time. This can be generalized that SNR is proportional to the square root of the total scan time, given
that the spatial resolution does not change (18).
𝑆𝑁𝑅 ∝ √𝑡𝑜𝑡𝑎𝑙 𝑠𝑐𝑎𝑛 𝑡𝑖𝑚𝑒

2.4.3 Spatial Resolution
SNR is directly proportional to the voxel size. Given a voxel with dimensions of Δ𝑥 , Δ𝑦 , and Δ𝑧 (18)
𝑆𝑁𝑅 ∝ Δ𝑥 ×Δ𝑦 ×Δ𝑧
An important consideration is that SNR is directly proportional to the voxel size while it is
proportional to the square root of the number of averages. Therefore, it is typically better to directly
acquire a lower resolution image than acquiring a higher resolution image followed by averaging.
2.5 Velocity Encoding
Flow encoding (FE) in MRI is performed using gradients that encode information about
coherent motion into the phase of the MR signal. Velocity, acceleration, as well as higher orders of
motion can all be encoded by modifying the FE gradient. Velocity encoding uses bipolar gradients,
which are composed of two concatenated gradient lobes of opposite polarity (20). Static spins will
experience no net phase because there is no net gradient area, but moving spins that travels in the
direction of the gradient will experience accumulated phase based on its velocity. To better illustrate
the mechanism behind phase accumulation, let a moving spin travel away from isocenter. Static spins
closer to isocenter accumulate phase more slowly than those further away. Any accumulated phase
from the first gradient lobe is reversed by the second. A moving spin will accumulate increasing phase
the further from isocenter it is, therefore accumulated phase from the first gradient lobe will never
be exactly unwound by the second lobe. A mathematical description reveals that the relationship
between phase accumulation and velocity is linear. The position of a spin can be written using a
Taylor series expansion (20):
Background - Velocity Encoding 17

𝑥 (𝑡 )= 𝑥 0
+ 𝑣 0
𝑡 +
1
2
𝑎 0
𝑡 2
+ ⋯ (2-26)
𝑥 0
,𝑣 0
,𝑎 0
are the initial position, velocity, and acceleration respectively. The accumulated phase from
a gradient 𝐺 (𝑡 ) is
𝜙 (𝑡 )= 𝛾 ∫ 𝐺 (𝑢 )𝑥 (𝑢 )𝑑𝑢
𝑡 0
(2-27)
and can be written in terms of a moment expansion
𝜙 (𝑡 )= 𝛾 𝑚 0
(𝑡 )𝑥 0
+ 𝛾𝑚
1
(𝑡 )𝑣 0
+ 𝛾𝑚
2
(𝑡 )𝑎 0
+ ⋯ (2-28)
𝑚 𝑛 (𝑡 )= ∫ 𝐺 (𝑢 )𝑢 𝑛 𝑑𝑢
𝑡 0
(2-29)
For a moving spin at constant velocity 𝑣 0

𝜙 (𝑡 )= 𝛾𝑚
1
(𝑡 )𝑣 0
(2-30)
Let’s assume a bipolar gradient of 𝐺 0
amplitude with rectangular lobes of width Δ𝑡 starting at 𝑡 = 0
and 𝑡 = 𝑇 respectively. The first moment can be calculated (20):
𝑚 1
(𝑡 )= ∫ −𝐺 0
𝑢𝑑𝑢 Δ𝑡 0
+ ∫ 𝐺 0
𝑢𝑑𝑢 T+Δ𝑡 𝑇
𝑚 1
(𝑡 )= −
1
2
𝐺 0
Δ𝑡 2
+
1
2
𝐺 0
(T+ Δ𝑡 )
2
−
1
2
𝐺 0
T
2
= 𝐺 0
Δ𝑡𝑇 = 𝐴 𝑇
here 𝐴 is the area of each individual gradient lobe. The accumulated phase is clearly linear
𝜙 (𝑡 )= 𝛾𝐴𝑇𝑣 (2-31)
The result can be generalized into any arbitrary gradient waveform by decomposing the waveform
into a sum of rectangles of infinitely small widths.
Velocity encoding can also be used as a preparation pulse. In the most basic implementation,
the velocity encoding waveform is sandwiched between two 90
0
pulses (20). The first RF pulse tips
the magnetization into the transverse plane, the bipolar gradients encode velocity information, and
the second RF pulse tips the encoded magnetization into the longitudinal axis. A spoiler is performed
afterwards to dephase any residual transverse magnetization. The addition of refocusing pulses
between the tip down and tip back RF pulses are common to reduce the effect of off-resonance. In
certain applications, adiabatic RF pulses are used to counter B 1

inhomogeneity.

Background - Velocity Encoding 18

Figure 2-5 Velocity encoding under assumptions of laminar flow. A. Velocity is uniformly distributed between 0
and twice the mean velocity 𝑣 0
. B. The resultant velocity profile is sinc shaped with its first zero crossing defined
at 𝑉 𝐶 = 𝜋 /2𝛽 .
By encoding velocity into the phase of the MR signal, the velocity profile becomes periodic
and produces a modulation of 𝑀 𝑧 given by 𝑀 𝑧 = 𝑀 0
cos (βv) where 𝛽 = 𝛾𝐴𝑇 and 𝐴 is the area of the
individual gradient lobe, 𝑇 is the separation between leading edges of the gradient lobes, and 𝑣 is
velocity (20). Figure 2-5 shows the velocity distribution under conditions of laminar flow, which is
uniform from 0 to twice the mean velocity, 𝑣 0
. Under this assumption, the velocity profile becomes
sinc shaped and is given by 𝑀 𝑧 = 𝑀 0
sinc(2𝛽𝑣 ) (22). The first zero crossing of the sinc is defined as
the cutoff velocity 𝑉 𝑐 = 𝜋 /2𝛽 . The derivation is as follows:
In the transverse plane, the signal equation governing velocity distribution is a Fourier
relationship where instead of sampling in spatial frequency k space, the signal can be sampled in
velocity frequency 𝑘 𝑣 space. Movement along k-space is determined by the zeroth

moment of the
gradients while movement along 𝑘 𝑣 space is determined by the first moment.
𝑀 𝑥𝑦
(𝑘 𝑣 )= ∫𝑚 (𝑣 )𝑒 −2𝜋 𝑘 𝑣 𝑣 𝑑𝑣
𝑣 (2-32)

𝑘 𝑣 =
𝛾 2𝜋 𝑚 1
(𝑡 )=
𝛾 2𝜋 𝐴𝑇 =
𝛽 2𝜋 (2-33)
Under the laminar flow assumption, 𝑚 (𝑣 ) is uniformly distributed between 0 and 𝑣 0
and is described
by a rect function
𝑚 (𝑣 )=
𝑀 0
2𝑣 0
⨅(
𝑣 − 𝑣 0
2𝑣 0
) (2-34)
Using the Fourier relationship for a rect and the shifting property, the resulting velocity profile in the
transverse plane becomes
𝑀 𝑥𝑦
(𝑘 𝑣 )= 𝑀 0
sin(2𝜋 𝑣 0
𝑘 𝑣 )
2𝜋 𝑣 0
𝑘 𝑣 𝑒 −𝑗 2𝜋 𝑣 𝑜 𝑘 𝑣 (2-35)
Background - Simultaneous Multi-Slice Imaging 19

In the velocity selective preparation, a second 90
0
RF pulse tips the transverse magnetization along
the x-axis into the longitudinal axis, which is achieved by taking the real part of the transverse
magnetization.
𝑀 𝑧 = 𝑅𝑒 {𝑀 𝑥𝑦
(𝑘 𝑣 )} = 𝑀 0
sin(2𝜋 𝑣 0
𝑘 𝑣 )
2𝜋 𝑣 0
𝑘 𝑣 cos(2𝜋 𝑣 0
𝑘 𝑣 )= 𝑀 0
sin(4𝜋 𝑣 0
𝑘 𝑣 )
4𝜋 𝑣 0
𝑘 𝑣 = 𝑀 0
sinc(4𝜋 𝑣 𝑜 𝑘 𝑣 )
Substituting the definition of 𝑘 𝑣 yields
𝑀 𝑧 = 𝑀 0
𝑠𝑖𝑛𝑐 (2𝛽 𝑣 𝑜 ) (2-36)
2.6 Simultaneous Multi-Slice Imaging
Simultaneous multi-slice (SMS) imaging has its roots from parallel imaging, a class of imaging
methods that accelerate data acquisition by acquiring fewer samples and reconstructing the missing
data by exploiting redundancies and differing sensitivity of multiple receiver coils. In SMS imaging,
the same principle is used to separate simultaneously excited, superimposed slices. Simultaneously
excited slices are generated by summing N single band pulses modulated with differing phase to shift
their position in space. Let 𝑏 1
(𝑡 ) be a single band RF pulse and 𝑏 𝑆𝑀𝑆 (𝑡 ) be a SMS pulse. The SMS pulse
is given by
𝑏 𝑆𝑀𝑆 (𝑡 )= ∑𝑏 1
(𝑡 )𝑒 2𝜋𝑖 (𝛾 𝐺 𝑧 𝑧 𝑗 𝑡 )
𝑁 𝑗 =1
(2-37)
Where 𝐺 𝑧 is typically a gradient of constant amplitude for linear traversal of excitation k-space. The
difficulty of SMS imaging lies in separating superimposed slices because they share similar coil
sensitivity. Breuer et. al. (23) popularized SMS imaging by shifting individual slices with respect to
one another by modulating the phase of each slice. This has the effect of diversifying coil sensitivity
among slices, easing their reconstruction.

2.6.1 RF phase cycled CAIPIRINHA
Two techniques have been popularized for modulating the phase of the slices. In its original
implementation by Breuer et. al (23), RF phase cycling was used to modify the phase patterns for
each slice to create inter-slice image shifts. This had the effect of generating varying amounts of linear
phase in the phase encoding direction for different slices. A one-dimensional image can be used to
illustrate the concept. A basic single slice acquisition can be written as follows
Background - Simultaneous Multi-Slice Imaging 20

𝜌 (𝑦 )= ∑ 𝑆 (𝑚 Δ𝑘 𝑦 )×𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 𝑦 )
𝑀 2
−1
𝑚 =−
𝑀 2
(2-38)
Where 𝜌 (𝑦 ) is an image and S is its Fourier transform, which is uniformly sampled at M points with
a spacing of Δ𝑘 𝑦 = 1/𝐹 𝑂 𝑉 𝑦 . SMS images are formed from the superposition of individual slices and
can be written as
𝜌 (𝑥 ,𝑦 )= ∑𝜌 𝑗 (𝑥 ,𝑦 )
𝑁 𝑗 = ∑ ∑ 𝑆 𝑗 (𝑚 Δ𝑘 𝑦 )×𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 𝑦 )
𝑀 2
−1
𝑚 =−
𝑀 2
𝑁 𝑗 (2-39)
In this formulation, the slices are superimposed and are difficult to reconstruct. To create inter-slice
image shifts, each slice, j, is multiplied by a unique phase Φ
j
(𝑚 )= 𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 Δ𝑦 𝑗 )
, which denotes the
phase of the m
th
RF pulse. According to the Fourier shift theorem, slice j is shifted by Δ𝑦 𝑗 as follows
𝜌 𝐶𝐴𝐼𝑃𝐼 (𝑥 ,𝑦 )= ∑𝜌 𝑗 (𝑥 ,𝑦 + Δ𝑦 𝑗 )
𝑁 𝑗 = ∑ ∑ 𝑆 𝑗 (𝑚 Δ𝑘 𝑦 )𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 Δ𝑦 𝑗 )
×𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 𝑦 )
𝑀 2
−1
𝑚 =−
𝑀 2
𝑁 𝑗 (2-40)
Figure 2-6 shows an example using 2 slices with a shift of the second slice by Δ𝑦 = 𝐹𝑂𝑉 /2. This is
achieved by multiplying the second slice with a phase of Φ
2
(𝑚 )= 𝑒 𝜋𝑖𝑚 and is expressed as
𝜌 1
(𝑦 )+ 𝜌 2
(𝑦 + Δ𝑦 )= ∑ (𝑆 1
(𝑚 Δ𝑘 𝑦 )+ 𝑆 2
(𝑚 Δ𝑘 𝑦 )𝑒 𝜋𝑖𝑚 )𝑒 2𝜋𝑖 (𝑚 Δ𝑘 𝑦 𝑦 )
𝑀 2
−1
𝑚 =−
𝑀 2

In general, the amount of shift can be generated arbitrarily for each slice. Typically, maximum slice
separation is desired, which requires a FOV/N image shift. In this case,
Φ
j
(𝑚 )= 2𝜋 iΔ𝑘 𝑦 (𝑚 − 1)(𝑗 − 1)/𝑁 (2-41)

.
Background - Simultaneous Multi-Slice Imaging 21

Figure 2-6 RF phase cycling is achieved by alternatively applying two RF pulses that simultaneously excite both
S1 and S2. RF1 imparts no phase on the two slices while RF2 imparts 𝜋 phase to the S2. This has the effect of creating
linear phase in ky for S2, shifting it by FOV/2. Shifting the slices with respect to each other shifts the coil sensitivity,
easing reconstruction.
2.6.2 Blipped CAIPI
One of the limitations of Breuer’s method is it requires multiple RF pulses with varying phase
cycles. In echo-planar imaging, multiple phase encoding lines are acquired after each RF excitation.
To be compatible with RF phase cycling, the number of EPI excitations or “shots” must be an integer
multiple of the number of phase cycles, which itself is dependent on the number of simultaneously
excited slices. For large number of slices, this takes away the speed advantage of EPI imaging; single-
shot imaging also becomes impossible. Setsompop et. al. (24) overcame this limitation by using the
slice gradient to introduce slice dependent linear phase. This is implemented by applying an
additional blip gradient in the slice direction along with conventional PE blip gradients. The amount
of shift is determined by the distance of the slice from isocenter and the area of the blips. To achieve
a FOV/N image shift,
𝛾 𝐴 𝑏𝑙𝑖𝑝 𝑧 𝑔𝑎𝑝 = 2𝜋 /𝑁 (2-42)

Where 𝐴 𝑏𝑙𝑖𝑝 = ∫𝐺 𝑏𝑙𝑖𝑝 𝑑𝑡 is the area of the blip gradient and 𝑧 𝑔𝑎𝑝 is the distance between adjacent
slices. Each blip imparts a 2𝜋 /𝑁 phase increment per phase encode line, leading to a FOV/N slice shift.
Additional details of the blipped CAIPI scheme are presented in Figure 2-7. They include a re-winder
gradient every N
th
PE line to reverse the accumulated phases of the previous N-1 blips and restart the
phase cycle. An additional pre-winder gradient at the very start of the blipped CAIPI scheme serves
to center the accumulated phase from blips about 0. Blipped CAIPI can be adapted to non-EPI readout
Background - Simultaneous Multi-Slice Imaging 22

schemes. In this formulation blip gradients are replaced by PE gradients in the slice direction with
their step size equal to the gradient blips, Δ𝑘 𝑧 = 𝐺 𝑏𝑙𝑖𝑝 .

Figure 2-7 Blipped CAIPI A. Diagram of two slices simultaneously encoded using blipped caipi. B. A plot of the
amount of linear phase through the slice shows that the slice edges accrue a different amount of phase than the
slice center. C. Each blip imparts a 2𝜋 /𝑁 phase increment for a 𝐹𝑂𝑉 /𝑁 field of view shift. A pre-winder (green) is
used to center the phase accrued at the slice edges around zero so all ky lines experience the same signal
attenuation. D. Adapting the Blip CAIPI scheme for non-EPI readout replaces blip gradients with Gz phase encodes
(red, and blue) where the step size is equal to the gradient blip, 𝛥 𝑘 𝑧 = 𝐺 𝑏𝑙𝑖𝑝 .

2.6.3 Reconstruction of SMS images
Reconstruction of SMS images can be performed using techniques borrowed from parallel
imaging (23). SENSE reconstruction (25) uses differences in coil sensitivity to unwrap aliased pixels
in the image domain. A two-slice example is formulated as follows:
[
𝐼 1
𝐼 2
] = [
𝐶 11
𝐶 12
𝐶 21
𝐶 22
][
𝜌 1
𝜌 2
]
𝐼
= 𝐶 ̂
𝜌 (2-43)
Background - Simultaneous Multi-Slice Imaging 23

where 𝐼
contains aliased pixels from two receiver coils, 𝐶 ̂
is a matrix of coil sensitivities, and 𝜌 is the
desired image to be reconstructed. This system can be solved because 𝐶 ̂
is invertible and is described
as having sufficient coil sensitivity. In the SMS case, a spatial shift is included in the equation
[
𝐼 1
(𝑥 ,𝑦 )
𝐼 2
(𝑥 ,𝑦 )
] = [
𝐶 11
(𝑥 ,𝑦 ) 𝐶 12
(𝑥 ,𝑦 + Δ𝑦 )
𝐶 21
(𝑥 ,𝑦 ) 𝐶 22
(𝑥 ,𝑦 + Δ𝑦 )
][
𝜌 1
(𝑥 ,𝑦 )
𝜌 2
(𝑥 ,𝑦 + Δ𝑦 )
] (2-44)
The spatial shift allows 𝐶 ̂
to become invertible and the individual slices can be separated. Using
SENSE, coil sensitivity maps for each slice must be acquired beforehand.

Figure 2-8 Slice-GRAPPA Reconstruction. A. Slice GRAPPA weights are calculated from fully sampled reference
data, Ref1 and Ref2. The reference data are summed and multiplied by their corresponding phase cycling pattern
to simulate an acquired dataset, called RefSMS. Kernel weights are calculated in a similar way as GRAPPA, with the
source points taken from RefSMS and the target data from Ref1 and Ref2. Weights are found as the Stg multiplied by
the pseudo-inverse of Ssrc𝑤 = 𝑆 𝑡𝑔
pinv(𝑆 𝑠𝑟𝑐 ) . B. SMS images are reconstructed by synthesizing separate k-space for
Background - Arterial Spin Labeling 24

each slice, S1 and S2 from applying the kernel weights w1 and w2 to the acquired data SSMS. In this example, the
acquired data has a different contrast from the reference data but was still reconstructed.
The other most commonly used parallel imaging technique is GRAPPA (26), where fully
sampled low frequency k-space lines are acquired to calculate a kernel that is used to fill in the
missing lines in k-space. Unlike SENSE, GRAPPA is not directly applicable in SMS and a variation of
the technique called slice-GRAPPA was developed by Setsompop et. al and summarized in Figure 2-8
(24). In slice-GRAPPA, A GRAPPA like kernel for each slice is fit from separately acquired
conventional single slices images. The reconstruction kernel with N k elements is slid through source
data that is generated by taking the sum of phase cycled individual fully sampled data to match the
acquisition scheme. For all 𝑁 𝑝 kernel repetitions, a source matrix 𝑺 𝒔𝒓𝒄 (𝑁 𝑐 𝑁 𝑘 ×𝑁 𝑟𝑒𝑝 ) and target
matrix, 𝑺 𝒕𝒈
(𝑁 𝑠𝑙𝑖𝑐𝑒 ×𝑁 𝑐 ×𝑁 𝑟𝑒𝑝 ) are assembled, where the target matrix consists of data from the
individual slices themselves. The kernel, 𝒘 (𝑁 𝑠𝑙𝑖𝑐𝑒 ×𝑁 𝑐 ×𝑁 𝑐 𝑁 𝑘 ) is found through a pseudo-inverse
procedure
𝒘 = 𝑺 𝒕𝒈
𝑺 𝒔𝒓𝒄 +
(2-45)

These GRAPPA like kernels are then applied to the acquired superimposed SMS data to
synthesize entirely new k-space data for each coil of each slice. The reconstruction algorithm can be
written as
𝑆 𝑧 ,𝑗 (𝑘 𝑥 ,𝑘 𝑦 )= ∑ ∑ ∑ 𝑤 𝑧 ,𝑗 ,𝑙 𝑏 𝑥 ,𝑏 𝑦 𝑆 𝑙 ,𝑆𝑀𝑆 ×(𝑘 𝑥 − 𝑏 𝑥 Δ𝑘 𝑥 ,𝑘 𝑦 − 𝑏 𝑦 Δ𝑘 𝑦 )
𝐵 𝑦 𝑏 𝑦 =−𝐵 𝑦 𝐵 𝑥 𝑏 𝑥 =−𝐵 𝑥 𝐿 𝑙 =1
(2-46)
𝑆 𝑧 ,𝑗 is the k-space data from slice z and coil j. 𝑤 𝑧 ,𝑗 ,𝑙 𝑏 𝑥 ,𝑏 𝑦 is the weight coefficient taken from the kernel
matrix 𝒘 at position (𝑏 𝑥 ,𝑏 𝑦 ) of the 𝑙 𝑡 ℎ
coil that is applied to the acquired SMS data, 𝑆 𝑙 ,𝑆𝑀𝑆 to generate
data at slice z and coil j. As opposed to traditional GRAPPA which fill in missing k-space lines, slice-
GRAPPA generates an entirely new set of k-space data for each slice from the collapsed SMS data.

2.7 Arterial Spin Labeling
2.7.1 Overview of arterial spin labeling
Perfusion is the delivery of blood to the capillary bed to provide tissue with oxygen and other
nutrients. It is an important clinical indicator to determine whether organs receive sufficient blood
flow and is useful for the diagnosis of a variety of diseases, including stroke, renal insufficiency, and
coronary artery disease. Perfusion is traditionally measured by administering a contrast agent that
Background - Arterial Spin Labeling 25

is detected using various imaging methods, including PET, SPECT, CT, and MRI. Arterial spin labeling
(ASL) is a unique MRI perfusion imaging technique that magnetically labels arterial blood as a source
of endogenous contrast. Therefore, ASL does not require injection of any exogenous contrast (27)
and uses no ionizing radiation, making it completely non-invasive with no incremental risk to
patients after repeated use.
Perfusion sensitivity in ASL is achieved by generating two image types called the “control”
and “labeled” image. The two image types have equal sensitivity to static tissue but varying sensitivity
to in-flowing blood. Arterial blood is labeled upstream of the tissue of interest using radiofrequency
pulses that are usually designed to invert or saturate the magnetic spins. Images are acquired after a
time delay (TD) to allow the labeled blood to perfuse the tissue of interest. Subtraction of the control
and labeled images produces a difference image that is proportional to in-flowing blood.

2.7.2 ASL Pulse Sequences
ASL imaging techniques can be broadly divided into three categories, Pulsed ASL (PASL),
continuous ASL (CASL), and velocity selective ASL (VSASL) and are summarized in Figure 2-9. PASL
techniques label a large bolus of blood using a short RF pulse on the order of milliseconds while CASL
techniques continuously apply RF for a few seconds to label all blood that passes through a labeling
plane. Theoretical and experimental studies have demonstrated that PASL has lower SNR and poorer
labeling efficiency than CASL. This is because in PASL, labeled spins experience T 1 decay before
leaving the labeling region, which is avoided in CASL(28). However, CASL has further technical
considerations though, as it suffers from greater magnetization transfer (MT) effects and requires a
stable labeling plane. In contrast to both PASL and CASL, VSASL labels based on velocity rather than
spatial location. Blood is labeled by saturating or inverting spins above a velocity cutoff, 𝑉 𝑐 . In
principle VSASL can generate labels adjacent to tissue by choosing a low 𝑉 𝑐 to eliminate transit delay
effects. However, VSASL has reduced labeling efficiency from T 2 decay that occur during the duration
of the pulse.
Background - Arterial Spin Labeling 26

Figure 2-9 A In PASL, a short RF pulse (milliseconds) is used to label a bolus of blood upstream the tissue of
interest. The time it takes the bolus to traverse the vasculature into the imaging plane is the transit time. B In
CASL, RF is continuously applied (seconds) at a labeling plane that labels all blood flowing through it. C In VSASL,
blood is labeled regardless of its spatial position and can in theory have no transit time. D The simulated ASL signal
for the different techniques is plotted over time with MBF = 1 ml/g/min, transit time = 0.5s, bolus width of 2s, and
saturation labeling.
PASL techniques have been used exclusively in the heart despite having lower signal than
CASL. This is largely due to the complex geometry found in the heart; there are few arteries that feed
the heart that are not themselves also within the heart. Potential labeling candidates include the
pulmonary veins and the ascending aorta for CASL. The pulmonary veins are difficult to localize and
may require sophisticated 2D pulses to avoid spurious labeling of the heart. Pulsatile flow in the aorta
may prevent the flow driven adiabatic condition from being satisfied. Due to the difficulty in finding
Background - Arterial Spin Labeling 27

a suitable labeling plane, CASL has largely been ignored. Instead, the most common labeling scheme
for cardiac ASL has been flow alternating inversion recovery (FAIR) and is shown in Figure 2-10 A.
In FAIR, a slice selective inversion pulse that encompasses the imaging slice is used for control images
and a global non-selective inversion is used for labeled images. Therefore, in-flow is positive in
control while in-flow is inverted in labeled images. Subtraction of the images yield twice the inflow,
after correcting for T 1 recovery.
Recently, steady pulsed ASL (spASL) was developed by Capron et. al. (29) to increase the ASL
signal. Labeling and imaging occur every heart beat to drive the perfusion signal into a flow
dependent steady state. This technique uses either EPISTAR or PICORE labeling of the aorta, which
are shown in Figure 2-10 BC. Both EPISTAR and PICORE are PASL techniques. In EPISTAR, the label
is performed using a slice selective inversion or saturation proximal to the imaging slice, while in
control acquisitions, the pulses are performed distally. The symmetric placement of the slice selective
pulses about the imaging slice is used to balance magnetization transfer effects. In PICORE, the label
is identical to EPISTAR. Control acquisitions use an off-resonance pulse at the same frequency offset
to the imaging slice as the label without gradients. By doing so, PICORE can reduce magnetization
transfer effects by one half when compared to EPISTAR.

Background - Arterial Spin Labeling 28

Figure 2-10 Diagrams for various PASL techniques. The labeling pulse is shown in red, the control pulse is shown
in green, and the imaging slice is shown in blue. A In FAIR, a non-selective inversion is used for labeling and a slice-
selective inversion is used for control. The symmetry of the acquisition imparts minimal MT effect. B In EPISTAR,
labeling is performed at the aortic root and the control pulse is placed equidistantly from the central imaging slice.
Only the central slice is MT balanced. C In PICORE, the labeling pulse is placed similarly with EPISTAR. The control
pulse is applied at the same frequency offset used for the labeling pulse without slice-selective gradients. This
halves the MT effect.

2.7.3 Arterial Spin Labeling Signal Equation
Quantification of FAIR ASL falls into two main categories that either use a signal intensity
difference method or a dual T1 approach. The intensity method is derived from Detre’s (30)
modification of the Bloch equation to include the effect of flow:

𝑑 𝑀 𝑧 (𝑡 )
𝑑𝑡
=
𝑀 0
− 𝑀 𝑧 (𝑡 )
𝑇 1
+
𝑓 𝜆 𝑀 𝑎 −
𝑓 𝜆 𝑀 𝑧 (2-47)
𝑀 0
is the equilibrium magnetization, 𝑓 is perfusion, 𝜆 is the partition coefficient of water between
blood and myocardium, and 𝑀 𝑎 is the magnetization received from inflowing blood. The input
function for inversion recovery is 𝑀 𝑎 = 2𝑀 0
𝑒 −𝑇𝐼 /𝑇 1
where 𝑇𝐼 is the inversion time. Eq 2-47 can be
integrated to yield
𝛥𝑀 = 2𝑀 0
𝑓 (
𝑒 −𝑇𝐼 /𝑇 1𝑎𝑝𝑝 − 𝑒 −𝑇𝐼 /𝑇 1𝑏𝑙𝑜𝑜𝑑 1/𝑇 1𝑏𝑙𝑜𝑜𝑑 − 1/𝑇 1𝑎𝑝𝑝 ) (2-48)
𝑇 1𝑎𝑝𝑝 = 1/𝑇 1
+ 𝑓 /𝜆 .
In the heart, myocardial and blood T 1 are nearly identical. By assuming 𝑇𝐼 𝑓 ≪ 𝜆 quantification can
be simplified to
Δ𝑀 = 2𝑀 0
𝑓𝑇𝐼 𝑒 −𝑇𝐼 /𝑇 1𝑏𝑙𝑜𝑜𝑑 (2-49)
Two variations of the difference method have emerged. In its original implementation, both
the labeling pulse and the image acquisition were gated to the same cardiac phase in consecutive
heartbeats. While this ensured that labeling and image acquisition excited the same volume of heart,
it also introduced a changing labeling time (TI) from heart rate variation that prevents direct
subtraction of global and slice-selective image pairs. Instead, myocardial data along with two
additional images at a short and long TI were fit to a three parameter inversion recovery model to
Background - Arterial Spin Labeling 29

generate a global and a slice-selective inversion recovery curve (9). The signal difference was
subsequently extrapolated at the average labeling time.
Zun et al. (11) and Wang et al. (13) used a simplified version of the difference method that
kept the TI constant between pairs of control and slice-selective images (11). The pulse sequence
they used is shown in Figure 2-11. While this allows for direct subtraction of image pairs, it is more
susceptible to quantification errors when heart rate variations are ≥ 4 bpm between image pairs (31).
Wang et al. (13) found that non-rigid motion correction was able to mitigate quantification error and
improve reliability.

Figure 2-11: ECG-gated FAIR Pulse Sequence Diagram with single inversion time readout mainly (but not
exclusively) used in the human heart. Labeling and imaging are placed in the same cardiac phase to ensure the
same volume of myocardium is excited. Imaging is preceded by a fat saturation and an initial preparation
consisting of a catalyzation ramp to reduce transient oscillations.

The dual T1 approach can also be derived from Detre et. al. (30) using the modified Bloch
equation that incorporates flow, Eq 2-47. Quantification was elaborated by Bauer et. al. (32) for an
inversion recovery sequence in an isolated perfused cardioplegic rat heart.. In this approach, T 1 maps
Background - Arterial Spin Labeling 30

of the heart are generated for both the non-selective control and slice-selective labeled image series.
Flow is calculated from the maps through the following equation:
𝑓 =
𝜆 𝑇 1𝑏𝑙𝑜𝑜𝑑 (
𝑇 1𝑛𝑠
𝑇 1𝑠𝑠
− 1) (2-50)
Wacker et al. (10) used a saturation recovery FLASH sequence at nine different saturation
delays for T1 quantification. They reported overestimated perfusion values, potentially related to the
fact that the labeling saturation was done in varying cardiac phases. Northrup et al. (33) used a look-
locker inversion recovery sequence to ensure that labeling and imaging occurred in the same cardiac
phase. However, the authors noted that in a study by Zhou et. al (34), dual T1 quantification can either
underestimate or overestimate FAIR perfusion in the presence of transit delay while the difference
approach can only underestimate perfusion.

2.7.4 Challenges and Limitations
Under physiological blood flow conditions of 0.5 ml/g/min to 4 ml/g/min in the heart, signal
from in-flowing blood is only 1% to 8% of that from static tissue (27). Therefore, ASL is intrinsically
signal limited by both the physiology of perfusion as well as the T 1 decay of arterial blood itself, which
is between 1-2 sec. To overcome low signal, a typical ASL acquisition requires several averages with
large voxel sizes, leading to long scan times. Having low sensitivity to perfusion also makes ASL
particularly susceptible to imperfection in subtraction of the control and labeled series; a subtraction
error in static tissue of only 1% could potentially be the same order of magnitude as the perfusion
signal itself. Imperfect subtraction arises from misregistration between control and labeled images,
typically due to respiratory or cardiac motion in the heart. These sources of errors are termed
physiological noise, 𝜎 𝑝 , as opposed to error that arise from the interactions between the MR imaging
apparatus and the imaged object, which is called thermal noise, 𝜎 𝑡 . These two sources of noise are
modeled as additive independent processes such that the total noise, 𝜎 , in a MR image is 𝜎 =
√𝜎 𝑡 2
+ 𝜎 𝑝 2
. In cardiac ASL, physiological noise is the dominant source of noise and have been found
to be 2-3 times larger than thermal noise (11).
Due to the high physiological noise, ASL control and labeled image pairs must be acquired
multiple times and averaged, which increases total scan time. For a single slice, six pairs of images
take 2-3 minutes to acquire. Pharmacologically induced stress using adenosine requires continuous
infusion due to its short half-life (< 10 sec) and is typically only performed for 3-4 minutes at a time
Background - Arterial Spin Labeling 31

due to concerns for patient comfort and safety. This limits spatial coverage of stress ASL to a single
slice.
Another source of error in ASL is the transit delay of blood to the imaging slice. Ideally, labeled
blood will instantly perfuse the tissue of interest by placing the label directly adjacent to the imaging
slice to eliminate T 1 decay of blood. In practice, a gap is required between the labeling and imaging
slice to prevent imperfections of the slice profile from altering the imaging slice. Even if a perfect slice
profile were achieved, in a multi-slice or 3D acquisition, transit time will still vary along the imaging
slab. There are also physiological conditions of slow flow and are prevalent in the setting of coronary
artery stenosis in coronary heart disease (CHD).

Temporal Signal-to-Noise Ratio in Quantitative CMR - Introduction 32

3 Temporal Signal-to-Noise Ratio in Quantitative CMR
3.1 Introduction
Recent advances in cardiovascular magnetic resonance (CMR) imaging techniques have
enabled clinically feasible quantitative mapping of magnetic relaxation properties and perfusion of
the heart (35). T1 and ECV mapping can assess diffuse myocardial fibrosis and infiltration (36–38)
and can measure extracellular volume when acquired with contrast (39,40). Inflammation and
edema in the heart can be detected with T2 mapping (41) while T2* is sensitive to iron induced field
inhomogeneity in hemochromatosis (42) and hemorrhage (43). Quantitative myocardial perfusion
imaging performed using either first-pass CMR (44), arterial spin labeling (ASL) (12), or blood
oxygen level dependent (BOLD) (45) has been shown to detect regions of ischemia to evaluate
coronary artery disease severity. These quantitative maps are all formed by imaging the myocardium
multiple times with different magnetization preparations to vary the sensitivity of each image to the
parameter of interest. These preparations produce changes in the signal intensity of the acquired
images, which are fit to models of the underlying physiology or relaxation parameter to generate a
quantitative map.
Unexpected signal changes that are not from the designed preparations will cause errors in
the parameter estimates. These errors arise from thermal noise as well as physiological fluctuations
from cardiac, respiratory, and hemodynamic motion. Thermal noise is well understood and is
modeled as an independent additive bivariate Gaussian process. It can be easily measured from
noise-only data (acquired without RF excitation) or from a manually-selected noise-only region
within an image. In contrast, the physiological noise distribution is largely unknown and cannot be
directly measured. Physiological noise contributes to the temporal standard deviation of an image
series, and can become a dominant contributor to measurement variability. In quantitative imaging,
temporal signal-to-noise ratio (TSNR) is measured as the mean signal intensity within an ROI divided
by its temporal standard deviation.
Triantafyllou et. al. (15) demonstrated that in the brain image acquisition parameters,
including spatial resolution, parallel imaging acceleration factor, and flip angle, altered the TSNR.
They were also able to experimentally confirm that physiological noise increases proportionally with
the signal strength (46). This is problematic because a simple increase of signal strength through
higher field or denser receiver arrays may not translate to improvements in TSNR if physiological
noise is dominant. In this case, efforts should be made to increase spatial resolution or speed
Temporal Signal-to-Noise Ratio in Quantitative CMR - Methods 33

acquisition through parallel imaging. Northrup et. al. (33) observed this phenomenon in ASL CMR,
which exhibited similar TSNR at 1.5T and 3.0T, despite the SNR advantage at 3.0T. Do et al. (16) used
parallel imaging to speed up the acquisition of ASL CMR and observed an increase in TSNR despite a
decrease in SNR.
In this study, we measure the SNR and TSNR of cardiac mid short-axis image series under
different spatial resolutions and parallel imaging acceleration factors and assess the ratio between
physiological and thermal noise. We study snapshot bSSFP and GRE acquisitions because they are
the most commonly used acquisition schemes for CMR T 1, T 2, and ECV mapping and for perfusion
imaging. While the results of this work are specific to our MRI apparatus, receiver coil, and pulse
sequence, it is simple to reproduce and need only be performed once. To the best of our knowledge,
this is the first study that experimentally examines how the choice of imaging parameters affects
TSNR and PN for quantitative CMR.

3.2 Methods
3.2.1 Noise Analysis
Our analysis of physiological noise and TSNR follows the work of Triantafyllou et. al. (15) for
multi-channel coil arrays in fMRI image series in the brain. The total noise, 𝜎 in a CMR image series
is modeled as the independent sum of thermal noise, 𝜎 𝑡 and physiological noise, 𝜎 𝑝 .
𝜎 = √𝜎 𝑡 2
+ 𝜎 𝑝 2
(3-1)
Physiological noise is described by the Krüger and Glover model (KG) (46) to scale proportionally by
a constant, 𝜆 , with the MR signal level, 𝑆 , such that 𝜎 𝑝 = 𝜆𝑆 . According to this model for noise, TSNR
can be derived from image SNR as follows:
𝑇𝑆𝑁𝑅 =
𝑆 𝜎 =
𝑆𝑁𝑅 √(1+ (𝜆 ∙ 𝑆𝑁𝑅 )
2
)
(3-2)

In practice, 𝜆 is unknown and TSNR is directly measured by dividing the mean signal intensity by its
temporal standard deviation. However, an important result of this model is that TSNR reaches an
asymptotic limit of 1/𝜆 when SNR becomes large. This implies that attempts to increase TSNR by
increasing SNR will fail if SNR is already high.
From measurements of SNR and TSNR, the ratio of physiological noise to thermal noise can
be measured as follows:
Temporal Signal-to-Noise Ratio in Quantitative CMR - Methods 34

𝜎 𝑝 𝜎 𝑡 =
√
(
𝑆𝑁𝑅 𝑇𝑆𝑁𝑅 )
2
− 1 (3-3)

This noise ratio determines whether an image series is thermal noise or physiological noise dominant.
When images are thermal noise dominant, improvements in TSNR can be achieved by increasing the
signal, through higher field strength of denser surface coils. However, when images are physiological
noise dominant, improvements in SNR have negligible impact on TSNR. Instead, SNR can be traded
for other gains, such as in spatial resolution or parallel imaging acceleration factor up until the
physiological noise is comparable to thermal noise.
3.2.2 Experimental Methods
Images were acquired on a 3T GE Signa Excite HD with an 8-channel cardiac receiver array
in 4 healthy volunteers. Images were acquired using snapshot bSSFP and GRE. All images were
acquired during mid-diastole at a single mid short-axis slice. For each unique set of acquisition
parameters, twenty images were acquired. Images were acquired with a 1 second breath hold with a
3 second wait between acquisitions to allow the magnetization to fully recover. A cardiac
cinema/video [CINE] scout scan was acquired in each subject to determine the exact timing of mid-
diastole relative to the ECG R-wave. Noise only images without RF were also acquired to calculate the
thermal noise and coil noise covariance matrix in each subject.
In each subject, data were acquired at various matrix sizes (192×96, 192×128, 192×192)
and accelerated (1, 1.33, 1.6, 2) by GRAPPA (26) and partial Fourier imaging. Other imaging
parameters were fixed throughout the experiment, which include TR/TE of 3.6/1.8 ms, FA of 50
0
/5
0

for SSFP and GRE respectively, BW of ±125 kHz, and slice thickness of 10 mm. Differences in the size
of the volunteers led to different choices of FOV and image resolution. Specific imaging parameters
are summarized in Table 3-1, and inter-subject variations in the FOV and image resolutions are
summarized in Table 3-2.

Reconstructed
Matrix
Acquired Matrix Partial Fourier Acceleration Imaging Window
(ms)
192 x 96 192 × 96 1 1 336
192 × 72 6/8 1.33 252
192 × 60 1 1.6 210
192 × 48 6/8 2 168
192 x 128 192 × 128 1 1 448
Temporal Signal-to-Noise Ratio in Quantitative CMR - Methods 35

192 × 96 6/8 1.33 336
192 × 76 1 1.6 266
192 × 60 6/8 2 210
192 x 192 192 × 192 1 1 672
192 × 144 6/8 1.33 504
192 × 108 1 1.6 378
192 × 84 6/8 2 294
Table 3-1 Acquisition parameters used for acquiring cardiac image series at various resolutions and acceleration
factors
Subject FOV (mm
2
) Resolution (mm)
1 320 1.67 × (3.33, 2.50, 1.67)
2 360 1.88 × (3.75, 2.81, 1.88)
3 360 1.88 × (3.75, 2.81, 1.88)
4 320 1.67 × (3.33, 2.50, 1.67)
Table 3-2 Variations in FOV and image resolution in the different subjects. Resolution is reported for matrix sizes
of 192 x (96, 128, 192).

3.2.3 Image Reconstruction and Data Analysis
Image were reconstructed offline using software written in Matlab (Mathworks Inc. Natick,
MA, USA). Partial Fourier image reconstruction was carried out using homodyne reconstruction
with a linear ramp weighting while GRAPPA reconstruction was performed using custom written
software. Images were coil combined using an optimal B1 weighted combination and aligned with
non-rigid motion correction using advanced normalization tools (ANTs) (47).
SNR maps were calculated for each image using the “pseudo-replica” method described by
Robson et al. For each image, correctly scaled and correlated synthetic noise is added to acquired k-
space data before reconstruction. This is repeated multiple times, each with a different instantiation
of synthetic noise, to generate an image stack. Under the assumption that the reconstruction
process acts independently on the signal and the noise, SNR can be calculated as the ratio of the
image reconstructed without noise addition to the standard deviation of the image stack. In
contrast, TSNR was measured from the “actual multiple replicas” that were acquired. It is calculated
as the mean intensity of a pixel or ROI of the left ventricular myocardium divided by the temporal
standard deviation. SNR and TSNR were used to calculate the noise ratio from Eq 3-3 . The
Temporal Signal-to-Noise Ratio in Quantitative CMR - Results 36

relationship between TSNR and SNR was also fit to the KG model of Eq 2 using a non-linear least
squares algorithm provided by Matlab to find the physiological noise scaling parameter, 𝜆 .
3.3 Results
Figure 3-1 shows a representative SNR, TSNR, and noise ratio map from a volunteer with an
acceleration factor of 1 using a 192×192 matrix. SNR is always greater than or equal to TSNR. The
noise ratio map is low in areas with little movement such as the musculature in the back and highest
in areas with large fluctuations in signal intensity, such as blood vessels.

Figure 3-1: A representative SNR, TSNR, and PN/TN map at an image matrix size of 192x192, R= 1, Resolution =
1.67x1.67mm
2
. The SNR, TSNR, and PN/TN ratio within the left ventricular myocardium ROI was 51.3± 9.8,
30.5±10.2, and 1.48 ± 0.70 respectively. The noise ratio map is lowest in areas with little movement, such as the
muscles of the back and highest in areas with large fluctuations in signal intensity such as blood vessels. In a static
phantom and stable imaging environment, TSNR = SNR. In vivo, TSNR ≤ SNR due to additional sources of PN. The
PN/TN ratio determines whether PN or TN is the dominant source of noise. When PN is dominant (PN/TN >> 1),
SNR gains will not improve TSNR.

Figure 3-2A shows TSNR as a function of SNR in the left ventricular myocardium. Each point
represents an average across subjects while the error bars represent the standard deviation within
the ROI averaged across subjects. Red solid points represent SSFP acquisitions while blue outlined
points represent GRE acquisitions. The points were fit to equation 2, shown as the solid black line,
with a physiological noise scale factor, 𝜆 , of 0.0235. The lower and upper 95% confidence interval of
𝜆 was 0.0221 and 0.0249 and are plotted with their corresponding dotted black lines. The vertical
dashed red line corresponds to the SNR in which the noise ratio is unity and has a value of 42.5 (1/𝜆 ).
Temporal Signal-to-Noise Ratio in Quantitative CMR - Results 37

The noise ratio is less than unity when left of the line, and greater than unity when right of the line.
The horizontal dashed red line corresponds to the asymptotic value for TSNR which also has a value
of 42.5 (1/𝜆 ).
The data were also analyzed within the lateral and septal walls, which are shown in Figure 3-2C
and Figure 3-2D respectively. Septal and lateral segments are defined by the AHA 17-segment model
(48) and are shown in Figure 3-2B. SNR and TSNR variation within the lateral wall is higher than in
the septum using SSFP imaging as indicated by the error bars. The standard deviation for SNR and
TSNR measurements are 12.88 and 11.75 respectively within the lateral wall and are 7.67 and 9.26
respectively within the septum. 𝜆 is higher within the lateral walls with a value of 0.0244 with lower
and upper 95% confidence interval of 0.0230 and 0.0258 while 𝜆 is lower in the septum with a value
of 0.206 with confidence interval of 0.0192 and 0.0220. This leads to an asymptotic value for TSNR
of 41.0 and 48.5 for the lateral wall and septum respectively.
Figure 3-3 contains plots of average SNR, TSNR, and PN/TN within the left ventricular
myocardium ROI as a function of the image matrix size and acceleration factor. SNR consistently
decreased as the image resolution (matrix size) and acceleration factor (R) increased for both GRE
and SSFP imaging. In GRE imaging, TSNR decreased as the image resolution and acceleration factor
increased. The noise ratio was consistently lower than unity, represented by the dashed red line, for
all matrix sizes and acceleration factors. In contrast, TSNR only slightly decreased as the matrix size
increased in SSFP imaging, but remained constant when acceleration factor increased. The noise ratio
in SSFP imaging was consistently above unity and only decreased to approach unity at the largest
matrix size and acceleration factor.
Temporal Signal-to-Noise Ratio in Quantitative CMR - Results 38

Figure 3-2: TSNR vs. SNR A) globally and within C) septal and D) lateral segments. Septal and lateral segments
are defined in B). Each point represents an average over different subjects while the error bars represent the
standard deviation within the ROI averaged over different subjects. SSFP acquisitions are shown in solid red while
GRE acquisitions are shown in outlined blue. The solid black line represents the fit to the KG model along with the
lower and upper 95% confidence interval shown in dotted black. The dashed black line indicates the line of unity.
Vertical and horizontal dashed red lines represent when the noise ratio is equal to one and the asymptotic limit of
TSNR respectively. Both occur at 1/𝜆 . TSNR and SNR is well parameterized by the KG model in the heart. At low
SNR, TSNR varies linearly with SNR while at high SNR, TSNR approaches an asymptotic limit. Measurements
within the lateral wall have greater variability than within the septum. Variations of SNR and TSNR within the
lateral wall were 1.61 and 1.24 times greater than variations within the septum respectively. The lateral wall also
has more physiological noise (𝜆 = 0.0244) and hence lower asymptotic TSNR than the septum (𝜆 = 0.0206) .

Temporal Signal-to-Noise Ratio in Quantitative CMR - Discussion 39

Figure 3-3: Comparison of SNR, TSNR, and the noise ratio (𝜎 𝑝 /𝜎 𝑡 ) at various image matrix sizes and acceleration
factors in A) GRE and B) SSFP. SNR decreases with increasing resolution and acceleration factors. In GRE, TSNR
follows a similar relationship with the imaging parameters while in SSFP TSNR remains relatively constant. This
causes the noise ratio to remain < 1 for all imaging settings in GRE. In SSFP the noise ratio remains ≥1 at low
acceleration factors and approaches 1 only at higher accelerations and larger matrix sizes.

3.4 Discussion
In this work, we investigated how changes in spatial resolution and parallel imaging
acceleration factor affects SNR, TSNR, and the noise ratio for quantitative CMR using snapshot GRE
and SSFP imaging. We found that when spatial resolution is made coarser and acceleration factor is
Temporal Signal-to-Noise Ratio in Quantitative CMR - Discussion 40

reduced, SNR consistently increases while TSNR faces diminishing returns. In particular, we
observed that TSNR varies linearly with SNR using GRE imaging (SNR < 20) and approaches an
asymptotic limit using SSFP imaging (SNR > 40). This makes the noise ratio (𝜎 𝑝 /𝜎 𝑡 ) thermal noise
dominant (<1) for GRE and physiological noise dominant (>1) for SSFP in all but the largest of matrix
sizes and acceleration factors (192× 192, R=2). These results are predicted by the KG model;
physiological noise scales with signal strength and above a certain threshold, further improvements
in SNR do not necessarily translate to improvements in TSNR.
The relationship between SNR and TSNR, as descried by the KG model, can be categorized
into three regimes - the linear, transition, and asymptotic regime. The linear regime is defined as the
range of SNR where the noise ratio is less than unity while the asymptotic regime is defined as the
range of SNR where TSNR is greater than 95% of its asymptotic value. The transition regime lies
between the two. Imaging should never be performed in the linear regime because TSNR can always
be improved by increasing SNR. Similarly, imaging should never be performed in the asymptotic
regime because SNR can be sacrificed with little to no loss in TSNR for improvements in spatial
resolution or acquisition speed. Therefore, all quantitative CMR protocols should be performed in the
transition regime. In applications that are less sensitive to physiological noise, such as in T 1, T 2, and
ECV mapping, TSNR can be traded for improvements in spatial resolution or acquisition speed at the
boundary with the linear regime. Alternatively, in applications that are sensitive to physiological
noise, such as in BOLD or ASL, TSNR needs to be maximized and image acquisition parameters should
be adjusted to approach the asymptotic regime.
Previous studies have only investigated the relationship between SNR and TSNR for
functional MRI of the brain (15,46). In those studies, reported values for the physiological noise
scaling parameter, 𝜆 , (0.009) are significantly lower than values we report for the heart (0.0235).
This is likely due to cardiac and respiratory motion found in the heart that are absent in the brain.
We also reported regional variations in SNR and TSNR and found that 𝜆 is 1.18 times larger in the
lateral wall (0.0244) than in the septum (0.0206). We suspect that this is due to greater off-resonance
sensitivity and motion found in the lateral wall.
Recently, Triantafyllou et. al. proposed a new model that captures coil to coil noise
correlations from physiological fluctuations by splitting the noise covariance matrix into a thermal
and physiological component (49). When the physiological covariance matrix scales with the signal
level, the model reduces to the KG model. However, if there are correlations of physiological noise
sources that are not signal level dependent, an additional parameter, 𝛼 , is used to generalize the
model such that
Temporal Signal-to-Noise Ratio in Quantitative CMR - Discussion 41

𝑇𝑆𝑁𝑅 =
𝑆𝑁𝑅 √1+ 𝛼 + (𝜆 ∙ 𝑆𝑁𝑅 )
2
(3-4)

We compared the fit using the KG model with this new generalized physiological noise covariance
(PNC) model using the F test, which yielded a F statistic of 1.15 and no statistically significant
difference between the two fits (p = 0.296), even though the PNC model has less residual error. We
suspect that this is due to the fewer number of coil elements used in this study (8 compared with 12
and 32 channels used by Triantafyllou et. al.). Future analysis with a denser receiver array will be
necessary to determine the validity of the PNC model for quantitative CMR.
One concern about the results of this study is the precision of the TSNR estimate, which is
dependent on the accuracy of the noise standard deviation. The noise standard deviation is
determined by the number of images acquired and pixels within the ROI. Using a Monte Carlo
simulation for 20 images with 150 pixels within the left ventricular myocardium, 50 pixels for
regional analysis, and individual pixel-wise analysis, the relative error of the TSNR measurement was
1.6%, 2.1%, and 12.97% respectively. This is below the inter-subject variation for SNR and TSNR and
does not alter the conclusions of the study. Another concern in our analysis is the existence of
physiological noise within an imaging window, which may be more pronounced in longer acquisition
windows (e.g. 672 ms for a 192×192 matrix size without acceleration). TSNR can only be measured
between images and all noise within an image is assumed to come from thermal noise. Therefore,
SNR may be underestimated and the SNR-TSNR curve may be shifted to the right. Rapid acquisition
schemes such as EPI or spiral imaging may be evaluated to observe the degree of this bias. We
hypothesize that these acquisition schemes, with their shorter imaging window, may even lie on a
completely different SNR-TSNR curve with a lower 𝜆 and higher asymptotic TSNR.
Another natural follow-up to this study would be to investigate whether the relationship
between SNR, TSNR, and the noise ratio changes in systolic imaging, during exercise or
pharmacologic stress, or with different cardiac pathologies. For instance, arrhythmia and stress may
cause more cardiac motion during imaging and decrease TSNR while heart failure and post-acute
myocardial infarct scar may reduce cardiac motion and increase TSNR. These studies may be difficult
to perform in humans, but could potentially be examined in a large animal model, where respiration
can be controlled and many images can be acquired. The drawback is that animals are typically
anesthetized and may have a different stress response than humans. Nevertheless, it would be
insightful to determine whether image acquisitions parameters can be optimized for cardiac phase,
stress, or pathology.

Temporal Signal-to-Noise Ratio in Quantitative CMR - Appendix 42

3.5 Conclusion
In this work, we demonstrated that SNR and TSNR in quantitative CMR is well parametrized
by the KG model and varies with different image acquisition parameters, including image resolution
and acceleration factor. We have also defined regimes where quantitative CMR should be performed.
In applications that are less sensitive to physiological noise, such as those used in T1, T2, and ECV
mapping, sequence parameters should be adjusted such that the noise ratio is close to unity (finer
resolution, higher acceleration). In applications that are sensitive to physiological noise, such as those
used in ASL and BOLD, sequence parameters should be adjusted until the TSNR approaches the
asymptotic regime (coarser resolution, lower acceleration). Future work needs to be done to
characterize these different regimes for systolic imaging, stress imaging, and in different cardiac
pathologies.

3.6 Appendix
An alternate method for calculating SNR is through direct computation on a per-pixel basis.
This method is useful when a noise-only pre-scan is acquired to accurately estimate the noise
statistics and noise covariance. It has the advantage of having a lower computation time than
Monte-Carlo based methods, which require reconstruction of the image multiple times. However,
direct SNR calculation is challenging in reconstructions that imparts spatial filtering or
interpolation because the local noise statistics vary and must be characterized and compensated.
This is especially challenging to perform for partial Fourier homodyne reconstruction, where the
noise statistics of phase estimation is not well characterized. For completeness, we describe the
details of direct computation of SNR in images without partial Fourier reconstruction below.
The SNR of a coil combined image is dependent on how the coils are combined. When using
optimal 𝐵 1
coil combination, the resultant SNR can be written as follows (50):
𝑆𝑁𝑅 =
|𝑝 𝑇 𝛹 −1
𝑠 ∗
|
√𝑠 𝑇 𝛹 −1
𝑠 ∗
(5)
where 𝑝 is the complex image vector, Ψ is the coil noise covariance matrix, and 𝑠 is the complex coil
sensitivity. Eq 5 by itself does not produce SNR in absolute units. Four additional correction
factors described by Kellman and McVeigh (51) must be applied. First, thermal noise is not flat
across the acquired bandwidth and must be scaled by an equivalent noise bandwidth, 𝑏 𝑛𝑜𝑖𝑠𝑒 . The
equivalent noise bandwidth of a filter is defined as the bandwidth of a rectangular filter that
produces the same output noise power when its input noise is white. It is measured from noise-only
Temporal Signal-to-Noise Ratio in Quantitative CMR - Appendix 43

data as the ratio of the mean-squared power of the noise spectrum to its maximum value at the
center of the spectrum. The correction is applied by dividing Ψ by b noise. A second correction factor
accounts for noise averaging during the Fourier Transform by normalizing the coil covariance Ψ by
the number of acquired samples, 𝑁 𝑎𝑐𝑞
. The third correction factor is a simple scaling of √2 because
noise is complex with independent, identically distributed real and imaginary parts. Lastly, a
correction needs to be made for the spatially varying noise amplification from parallel imaging by
the coil geometry factor (g-factor), 𝑔 . After accounting for the correction factors, the final SNR
becomes:
𝑆𝑁𝑅 =
√2𝑏 𝑛 𝑜 𝑖𝑠𝑒 𝑔 √
𝑁 𝑎𝑐𝑞 |𝑝 𝑇 Ψ
−1
𝑠 ∗
|
√𝑠 𝑇 Ψ
−1
𝑠 ∗
(6)
Velocity Selective Arterial Spin Labeling - Introduction 44

4 Velocity Selective Arterial Spin Labeling
4.1 Introduction
Arterial spin labeled (ASL) cardiac magnetic resonance (CMR) is a promising non-contrast
technique for mapping myocardial blood flow (MBF). Other modalities such as single-photon
emission computed tomography (SPECT), positron emission tomography (PET), or first-pass
perfusion CMR rely on intravenous contrast agents and/or are unsuitable for patients with poor renal
clearance or who require frequent evaluations. ASL avoids these drawbacks by using magnetic
preparations to label the blood itself as a source of endogenous contrast. Blood upstream of the tissue
of interest is labeled with a radiofrequency (RF) pulse and allowed to perfuse the tissue before
imaging. In the heart, flow-sensitive alternating inversion recovery (FAIR) has been the most
commonly used labeling scheme, whereby a slab-selective inversion containing the imaging slice is
used for control preparations and a non-selective inversion is used for labeled preparations (1–3).
For single-slice acquisitions, FAIR has been demonstrated to obtain measurements of MBF
that are comparable to those found using PET (4) and could detect clinically relevant changes in
perfusion under vasodilation (5). However, in a multi-slice acquisition scheme, the FAIR inversion
slab thickness must be increased to encompass the larger imaging volume. Zun et al. found
substantial underestimation of MBF at a mid-short axis slice by 68% when the FAIR inversion slab
was increased from 3 to 12 cm (3). We hypothesize that FAIR is incompatible with multi-slice
acquisitions because the thick inversion slab, which increases the spatial gap between the labeled
edge and the imaging slices, leading to longer arterial transit times (ATT) and underestimation of
MBF (3). Similarly, disease processes with slow coronary flows, such as heart failure (6,7), or
circuitous coronary collateral vascularization also exhibit prolonged ATT. Muehling et al. (8) found
that the ATT due to collateral circulation (1.7 sec) was significantly longer than antegradely perfused
vessels (0.9 sec) and vessels in healthy subjects (0.8 sec). When ATT becomes much longer than the
post-labeling delay, marked loss of ASL signal occurs and MBF is underestimated (9).
Velocity selective ASL (VSASL) was developed in the brain to mitigate ASL signal loss caused
by slow flow and long ATT (10). Blood is labeled based on its velocity by saturating spins above a
velocity cutoff, termed. V_C. In principle VSASL can generate labels adjacent to tissue by choosing a
low V_C to eliminate transit delay effects. In practice, choosing a high V_C along with a short inflow
delay, TI, has the potential to generate large intravascular signals that could confound ASL
measurements (11). In subtractive magnetic resonance angiography (MRA), this is seen as an
Velocity Selective Arterial Spin Labeling - Methods 45

advantage and VS pulses have recently been used to great effect in visualizing vasculature in both
abdomen (12) and brain (13). By designating flowing spins within the passband of the VS pulse and
static tissue in the saturation band, flowing blood within the vasculature will produce signal,
regardless of spatial location. In ASL, V C, TI, as well as the velocity encoding direction must be
considered more carefully to avoid intravascular signal. In brain, V C is typically set to 2 cm/s to match
mean velocity within the small feeding arterioles while optimal TI was determined to be the T1 of
blood, which is roughly 1664 ms (11). Due to the tortuous path by which small arterioles travel,
Wong et. al. (10) found that encoding direction did not have a noticeable impact on perfusion
measurements.
The choice of V_C. TI, and encoding direction must be reevaluated in the heart due to the
unique challenge of cardiac motion. Myocardium can move as fast as 2 cm/s (14,15) during stable
diastole. Therefore, targeting blood within the small arterioles that flow at speeds similar to
myocardial movement may cause spurious labeling of the heart. A larger V_C must be used, which
would label blood in the coronary tree. However, coronary blood flow is pulsatile and changes
throughout the cardiac cycle; it is highest during diastole (>15-40 cm/s) and lowest during systole
(~ 0 cm/s). Coronary velocity also varies depending on disease states. Anderson et. al. (16) found
that peak coronary velocity was inversely proportional to the lumen area to reginal left ventricular
mass ratio (A/M ratio); stenotic vessels had faster peak velocities. However, under hyperemia, this
trend was reversed, possibly due to coronary steal. In the setting of hypertension, mean coronary
velocity can reach upwards of 51 cm/s, but when presented alongside left ventricular dysfunction,
coronary velocities were similar to those in healthy vessels (~30 cm/s) (17). An additional challenge
for VSASL in the heart is the larger range of off resonance and B1 variation found in the chest cavity
compared to brain. This places further design constraints on the VS pulse, which would have to be
redesigned using Bloch simulation.
In this work, we describe a practical implementation of cardiac VSASL and demonstrate its
ability to measure myocardial perfusion, in comparison to FAIR ASL. In humans, we experimentally
determine the sensitivity of cardiac VSASL to selection of V_C and encoding direction.
4.2 Methods
4.2.1 Velocity Selective Pulse
An adiabatic symmetric BIR-8 pulse described by Guo et. al. (52) was used for VS labeling.
BIR8 pulses have been demonstrated to have lower eddy current sensitivity than other velocity
selective preparations such as double refocused hyperbolic secant (DRHS) or BIR4 pulses (53). Bloch
Velocity Selective Arterial Spin Labeling - Methods 46

simulation was used to simulate and optimize pulse parameters for a peak 𝐵 1
of at least 0.08 G and
off-resonance range of ±250 Hz, which is consistent with what can be reasonably expected in the
heart at 3T (21,54). RF sub-pulses were 2.24. ms each with the following parameters as described by
Meakin et al. (53), 𝜅 = 62.96, 𝜔 max
=21.6, and 𝜁 =20.5. Single gradient lobes between RF sub pulses
were replaced with bipolar gradients to avoid striping artifacts from occurring over myocardium, as
described by Fan et al. (55). An additional delay of 0.5 ms after each bipolar gradient module was
used to further reduce eddy current sensitivity. Bipolar gradients were designed to saturate spins
above a designated velocity cutoff, 𝑉 𝑐 , for labeled acquisitions and were turned off during control
acquisitions to impart similar T 2 weighting only. 𝑉 𝐶 is given by 𝑉 𝑐 = 𝜋 /(2𝛾 𝑀 1
), where 𝛾 is the
gyromagnetic ratio and 𝑀 1
is the first moment of the BIR8 gradient waveform with 𝑀 1
= 𝑔 (2𝑇 2
+
6𝑅𝑇 + 4𝑅 2
) , where g is the gradient amplitude, T is the duration of the plateau of an individual
gradient lobe, and R is the ramp duration, which we set to 0.5 ms. The choice of pulse parameters
was the result of significant experimental fine tuning in a spherical phantom. The settings described
above are the results that produced the most consistent labeling with the fewest artifacts and
shortest pulse duration.
Pulse performance was validated within the lumen of the right coronary artery (RCA) in two
healthy volunteers. VS labeling with both the control (gradients off) and labeled (gradients on)
settings was performed immediately before imaging using centric view ordered GRE (FA = 5
0
, TR =
3.2, 64×64 matrix). An additional image without the VS preparation pulse was also acquired to
measure saturation efficiency of blood within the coronary lumen.

4.2.2 VSASL Acquisition
Cardiac VSASL was performed at a single mid-short axis slice illustrated in Fig 1, using cardiac
gated velocity selective (VS) labeling and bSSFP imaging. VS labeling was performed during mid-
diastole, as determined from a cinema/video [CINE] scout scan, when coronary blood velocity is high
(>15-40 cm/s) (56) and myocardial velocity is low (< 2 cm/s) (57,58) to increase labeling efficiency
and avoid spurious myocardial labeling. Imaging was performed during mid-diastole in the
subsequent RR such that MBF estimates reflect the time-average perfusion rate of pulsatile blood
flow over the course of one heartbeat. Background suppression using a single non-selective
hyperbolic secant inversion pulse placed between labeling and imaging was designed to null
myocardial T1s between roughly 1250 ms and 1450 ms. The timing of the background suppression
pulse was optimized for different heart rates and took into account T 2 signal loss from the VS labeling
pulse (59). Image acquisition parameters were: TR/TE of 3.2/1.5ms, prescribed flip angle of 50,
Velocity Selective Arterial Spin Labeling - Methods 47

acquired matrix size of 96×96, GRAPPA (24 ACS, 60 acquired). FAIR ASL was performed using a
similar pulse sequence without background suppression and utilized a 3-cm slice-selective and a
non-selective hyperbolic secant inversion pulse for control and labeled acquisitions respectively.
Six pairs of control and labeled images were acquired for MBF quantification. Each image pair
was acquired under a single breath hold (10-12 sec) to prevent spatial image misregistration and to
avoid spurious VS labeling from respiratory motion. A 6 second time delay was placed between image
acquisition to allow full recovery of the VS label. Control and labeled image acquisition order was
alternated after each pair to avoid bias from the acquired order. A baseline image and a noise image
were also acquired in an additional 2 second breath hold to calculate coil sensitivity maps and noise
co-variance matrix.
All images were acquired on a 3T GE Signa Excite HD using an 8-channel cardiac receiver
array. Ten healthy volunteers were recruited for this study (1F/9M age 23-30). In 5 healthy
volunteers, VSASL was performed with four different 𝑉 𝑐 of 10, 20, 30, and 40 cm/s in the longitudinal
(z) encoding direction. In 1 volunteer VSASL was performed at 𝑉 𝐶 of 5 cm/s and 15 cm/s. In 4 healthy
volunteers, VSASL was performed using the radial (X, Y) and longitudinal (Z) encoding directions at
𝑉 𝐶 of 10 cm/s. Cardiac ASL using FAIR was acquired in each subject for comparison. The imaging
protocol was approved by our institutional review board, and all subjects provided written informed
consent.
Velocity Selective Arterial Spin Labeling - Methods 48

Figure 4-1. VSASL Pulse Sequence. A: The BIR8 pulse used for VS labeling. B: The timing Diagram of VSASL is to
scale for a heart rate of 60 bpm. VS-labeling (orange) was performed during diastasis, when myocardial velocities
are low and coronary flows are high. Imaging (blue) occurs 1 RR interval later. A single NS inversion (red) is placed
between labeling and imaging for background suppression of Myocardial T1 of 1250-1450 ms.
4.2.3 Data Analysis
Images were reconstructed using GRAPPA and coil combined using optimal 𝐵 1
coil
combination (51). The left ventricular (LV) myocardium was manually segmented in a single control
and labeled image pair and the resultant masks were propagated through their respective image
series using automatic motion correction (60) . LV myocardium was divided into 6 segments in
accordance with the AHA 17-segment standard (48) through a spatial averaging algorithm (61) to
Velocity Selective Arterial Spin Labeling - Results 49

increase SNR for MBF estimation. MBF quantification was derived from Buxton’s general kinetic
model (62) at a single 𝑇𝐼 and was calculated using the following equation:
𝑀𝐵𝐹 =
𝐿 − 𝐶 𝛼 ⋅ 𝐵 ⋅ 𝑇𝐼 𝑒 −
𝑇 𝑉𝑆
𝑇 2𝑏𝑙𝑜𝑜𝑑 ⋅ 𝑒 −
𝑇𝐼
𝑇 1𝑏𝑙𝑜𝑜𝑑 (4-1)

𝐶 , 𝐿 , and 𝐵 refer to the myocardial signal intensity within the control, labeled, and baseline image. 𝛼
is the efficiency of the background suppression inversion pulse while 𝑇𝐼 is the time between labeling
and imaging, which is fixed according to the heart rate. An additional exponential term reflects 𝑇 2

signal loss from the VS pulse with duration 𝑇 𝑉𝑆
in the transverse plane. With 𝑇 𝑉𝑆
of 25.5 ms and a
𝑇 2𝑏𝑙𝑜𝑜𝑑 of 186 ms, this corresponds to a 13% signal loss. Physiological noise (PN) was calculated in
the same way as Zun et. al. (11) with the following equation:
𝑃𝑁 = √
𝜎 𝑜𝑑𝑑 2
+ 𝜎 𝑒𝑣𝑒𝑛 2
2𝑁 𝑝𝑎𝑖𝑟 (4-2)
𝜎 𝑜𝑑𝑑 2
and 𝜎 𝑒𝑣𝑒𝑛 2
correspond to variance of MBF in odd and even breath holds. Temporal SNR (TSNR)
is a metric for signal stability and was calculated as the ratio of MBF to PN.
𝑇𝑆𝑁𝑅 =
𝑀𝐵𝐹
𝑃𝑁
(4-3)
4.3 Results
4.3.1 Validation of VS Labeling in RCA
Figure 4-2 shows the performance of the VS BIR8 pulse within the RCA in two healthy volunteers. In
the control setting (left image), coronary blood within the RCA was preserved while in the labeled setting (right
image), blood within the RCA was saturated. Saturation efficiency within the coronary lumen was measured at
89.7% and 74.6% for each volunteer respectively.

Figure 4-2. Demonstration of VS labeling within the RCA of two healthy volunteers. Red arrows indicate location
of RCA. Control acquisitions have gradients turned off, labeled acquisitions have gradients turned on. 𝑉 𝐶 was set
Velocity Selective Arterial Spin Labeling - Results 50

at 10 cm/s. Saturation efficiency within the coronary lumen was 89.7% and 74.6% for volunteers 1 and 2
respectively.
4.3.2 Sensitivity to Velocity Cutoff
Figure 4-3 contains MBF (left) and TSNR (right) for FAIR and VSASL at cutoffs of 10, 20, 30,
and 40 cm/s for septal, lateral, and all segments averaged across 5 subjects. Septal and lateral
segments are defined in the illustration of the heart; septal segments correspond to anteroseptal and
posteroseptal segments of the AHA 17-segment model (48). while lateral segments correspond to the
anterolateral and posterolateral segments. Global MBF for VSASL (1.21± 0.46 ml/g/min) at 𝑉 𝐶 of 10
cm/s was similar to MBF for FAIR (1.12± 0.26 ml/g/min), but had lower TSNR of 4.87 ± 1.58 and
13.62± 5.25 respectively. These measurements of MBF were similar to those found using PET,
which were 0.95±0.28 ml/g/min (63) and 0.985±0.230 ml/g/min (64), as well as those found in
first-pass perfusion CMR at 3T of 1.02±0.22 ml/g/min (65). A two one-sided test (TOST) (66) at a
difference of 0.3 ml/g/min showed that MBF was statistically equivalent with a p-value of 0.046 while
a paired t-test showed that TSNR was statistically different with a p-value of 0.005. As 𝑉 𝐶 increased,
both estimated MBF and TSNR decreased. MBF and TSNR were consistently lower in lateral segments
compared with septal segments. A paired t-test showed statistical difference with p values of 0.019
and 0.008 respectively. Figure 4-4 shows representative MBF maps for a single volunteer using FAIR
and VSASL at 𝑉 𝐶 of 5 cm/s and 15 cm/s. MBF of septal segments were 1.09, 1.70, and 1.62 ml/g/min
while MBF for lateral segments were 1.12, 5.64, and 1.34 ml/g/min for FAIR and VSASL at 𝑉 𝐶 of 5
cm/s and 15 cm/s respectively.

Velocity Selective Arterial Spin Labeling - Results 51

Figure 4-3 VSASL sensitivity to 𝑉 𝐶 A: The location of septal (blue) and lateral (red) segments used in regional
analysis follows the AHA 17-segment model for the mid short axis slice. B: MBF and TSNR measured globally
(yellow) decreases when 𝑉 𝐶 increases due to poor labeling efficiency. VSASL at 𝑉 𝐶 of 10 cm/s has statistically
equivalent MBF as FAIR using the TOST procedure at a difference of .3 ml/g/min (p=0.046). TSNR in VSASL at all
cutoffs was consistently lower than in FAIR (p≤0.005). C: MBF and TSNR in the septum. D: MBF and TSNR in the
lateral wall. We suspect that off-resonance in the lateral wall causes greater degradation of pulse performance.
Velocity Selective Arterial Spin Labeling - Results 52

This lead to greater underestimation of MBF and lower TSNR in lateral segments when compared to the septum
(p=0.019 and p=0.008 respectively).

Figure 4-4 Representative MBF map in a single volunteer. A: The FAIR MBF map is displayed over the control
image. FAIR has spatially homogenous MBF. B: The VSASL MBF map at 𝑉 𝐶 of 15 cm is comparable to the MBF map
in FAIR. Contrast of the VSASL control image is inverted because of the single inversion recovery background
suppression preparation. C: The VSASL MBF map at 𝑉 𝐶 of 15 cm/s is not homogenous and overestimates MBF in
the lateral wall, indicated by the red arrow. MBF of the lateral wall was 1.12, 1.34, and 5.64 for FAIR and VSASL
at 𝑉 𝐶 of 15 cm/s and 5 cm/s respectively. We suspect that at 𝑉 𝐶 of 5 cm/s, overestimation of MBF in the lateral
wall is due to spurious labeling of moving myocardium. Units are in ml/g/min.

4.3.3 Sensitivity to Encoding Direction
Figure 4-5 shows MBF (left) and TSNR (right) for FAIR and VSASL at the apical-basal (Z) and anterior-
posterior (X), and lateral-septal(Y) encoding directions averaged across 4 subjects. X and Y encoding directions
are defined in the illustration of the heart in Figure 4-5A. Lateral-septal Y severely underestimated MBF
(0.39 ± 0.28 ml/g/min) and had the lowest TSNR (1.26± 1.03) when compared to FAIR ASL, which had a
MBF of 1.27± 0.19ml/g/min and TSNR of 10.26± 4.17. Anterior-posterior X underestimated MBF (0.91±
0.20 ml/g/min) to a lesser extent while apical-basal Z slightly overestimated MBF (1.68 ± 1.04 ml/g/min).
TSNR was roughly equal between X (4.17± 2.32) and Z (3.97 ± 0.56), but X had more inter-subject variability.
Septal and lateral segments were not found to have statistically different MBF and TSNR.X had more inter-
subject variability. Septal and lateral segments were not found to have statistically different MBF and
TSNR.
Velocity Selective Arterial Spin Labeling - Discussion 53

Figure 4-5 VSASL sensitivity to the anterior-posterior (X), lateral-septal (Y), and apical-basal (Z) encoding
directions. A: Diagram of different encoding directions. B: MBF and TSNR as a function of encoding direction
globally averaged across subjects. The radial Y direction severely underestimated MBF and had the lowest TSNR.
Performance of X was similar to Z, possibly due to labeling of the left circumflex in X. Detailed analysis of individual
segments did not reveal significant differences.

4.4 Discussion
This study demonstrates the feasibility of myocardial VSASL with background suppression in
9 healthy volunteers. VSASL was able to yield a measurable signal difference within human
myocardium and obtain MBF estimates similar to those reported in FAIR ASL (12,14,33,67–69).
This study also investigated how the choice of 𝑉 𝐶 and encoding direction affected the VSASL
signal globally as well as in septal and lateral segments individually. When 𝑉 𝐶 increased, labeling
efficiency and VSASL signal decreased, which lead to an underestimation of MBF. If the labeling
efficiency were measured, MBF quantification could potentially be corrected. In practice, labeling
efficiency would be difficult to measure due to the challenge of high resolution imaging of the
coronary lumen, which would need to be measured over the entire length of the coronary tree. In
addition, at low 𝑉 𝐶 (≤5 cm/s), VSASL overestimated MBF. We hypothesize that this is due to spurious
labeling of myocardium that was not resolved with background suppression. There was also a
statistical difference between MBF and TSNR found in septal and lateral segments with changing 𝑉 𝐶 .
Lateral segments consistently underestimated MBF and had lower TSNR than septal segments at
𝑉 𝐶 >10 cm/s. This could be due to poorer labeling efficiency of the left circumflex artery that supplies
the region. In contrast, at low 𝑉 𝐶 ≤ 5 cm/s, lateral segments overestimated MBF. We suspect that this
is due to spurious labeling of myocardium due to movement of the lateral wall (58).
As opposed to VSASL in brain (22), we found that myocardial VSASL was sensitive to
encoding direction. MBF and TSNR had the lowest inter-subject variation in the longitudinal Z
direction. Surprisingly, anterior-posterior (X) and lateral-septal (Y) directions performed very
Velocity Selective Arterial Spin Labeling - Conclusion 54

differently; X achieved similar MBF and TSNR as Z while Y severely underestimated MBF. This may
be due to the coronary geometry, with no major vessels running in the lateral to septal direction
while the circumflex runs in the anterior to posterior direction. Nevertheless, we would still
recommend performing VSASL in the apical-basal Z direction due to its lower inter-subject variation
as well as the ease of scan prescription. Although not studied, it is feasible to play multiple VS modules
with different labeling directions to improve direction sensitivity with the tradeoff of decreased
labeling efficiency from 𝑇 2
of blood.
VSASL had the highest TSNR when performed using a 𝑉 𝐶 of 10 cm/s in the longitudinal
direction. However, it was still 2.8 times lower than the TSNR of FAIR. This is due to 50% signal loss
from using a saturation pulse as opposed to inversion, as well as 13% signal loss from 𝑇 2
weighting
during the VS preparation. Despite having lower TSNR, the main draw of VSASL is its insensitivity to
transit delay. This study was unable to highlight this advantage because transit delay is only 400ms
(69) in healthy volunteers, which has a negligible impact on MBF estimation. A natural follow up to
this study would be to perform VSASL in patients with coronary artery disease with collateral
circulation (70,71) or in an animal model with slow coronary flow (72).
One drawback of VSASL is its sensitivity to the timing of the label to avoid spurious tagging
of moving myocardium. Rapid variations in heart rate could cause mistriggering and spurious
labeling of moving myocardium. A possible solution would be to use an alternate VS pulse with a
sharper velocity profile. The velocity profile of the BIR8 preparation is sinusoidal, which becomes
sinc shaped under the assumption of laminar flow (22). A sharper rectangular velocity profile could
be achieved using Shinar le-Roux (SLR) and the excitation k-space formalism by Shin et al (73,74).
Moreover, the SLR pulse can be designed to achieve inversion rather than saturation to increase the
VSASL signal. However, SLR pulses are not adiabatic and would have to be redesigned and tested to
tolerate off-resonance and 𝐵 1
variation found in the heart.

4.5 Conclusion
We have demonstrated the feasibility of using a velocity selective pulse for ASL of the heart
and have measured the performance of VSASL under a range of velocity cutoffs and encoding
directions. At the best performing setting using a 𝑉 𝐶 of 10 cm/s in the longitudinal direction, we found
VSASL had 2.8 times lower TSNR than FAIR. We anticipate that TSNR can be improved by using a
velocity selective inversion pulse with less sensitivity to myocardial motion. Opportunities exist to
Velocity Selective Arterial Spin Labeling - Appendix 55

conduct experiments that highlight the transit delay insensitivity of myocardial VSASL in patients or
in an animal model.

4.6 Appendix
Subject FAIR VC=5 VC=10 VC=15 VC=20
1 1.37 ± 0.14 (9.96) 1.15 ± 0.4 (2.88) 0.94 ± 0.2 (4.65) 1.01 ± 0.31 (3.23)

2 1.41 ± 0.07 (18.84) 1.97 ± 0.27 (7.2) 0.37 ± 0.18 (2.07) 0.37 ± 0.27 (1.35)

3 1.12 ± 0.06 (18.95) 0.75 ± 0.14 (5.22) 1.08 ± 0.2 (5.49) 0.4 ± 0.14 (2.81) 0.28 ± 0.16 (1.72)
4 0.67 ± 0.12 (5.43)

1.58 ± 0.63 (2.5) 0.76 ± 0.75 (1.02) -0.61± 0.39 (-1.55)
5 1.03 ± 0.07 (14.9) 0.99 ± 0.24 (4.16) 0.2 ± 0.05 (4.11) 0.79 ± 0.2 (3.96) 0.1 ± 0.09 (1.1)
Mean 1.12 ± 0.09 (13.62) 1.21 ± 0.26 (4.87) 0.83 ± 0.25 (3.76) 0.67 ± 0.33 (2.47) -0.08 ± 0.22 (0.43)
Table 4-1 VSASL sensitivity to velocity cutoff for individual subjects. MBF, PN, and TSNR are shown in MBF ± PN
(TSNR) format. MBF and PN are in units of ml/g/min. VSASL settings that achieved the highest TSNR are bolded.
At 𝑉 𝐶 of 10 or 20 cm/s, TSNR was optimal for all subjects. However, TSNR was 2.8 times lower in VSASL compared
to FAIR on average. This is due to signal loss from using a saturation as opposed to inversion along with additional
T2 losses from the VS pulse.
Table 4-2 VSASL sensitivity to velocity encoding direction for individual subjects. MBF, PN, and TSNR are shown
in MBF ± PN (TSNR) format. MBF and PN are in units of ml/g/min. VSASL settings that achieved the highest TSNR
are bolded. TSNR was optimal in the longitudinal Z and radial X direction in all subjects. * = rejected from
equivalency test (TOST) between FAIR and VSASL because PN > 50% MBF from FAIR.

Subject FAIR Longitudinal (Z) Radial (Y) Radial (X)
1 1.18 ± 0.23 (5.19) 1.21 ± 0.33 (3.62) 0 ± 0.3 (0.00) 0.96 ± 0.24 (3.99)
2 1.42 ± 0.12 (12.03) 1.28 ± 0.27 (4.67) 0.6 ± 0.24 (2.53) 1.08 ± 0.21 (5.05)
3 1.03 ± 0.07 (14.9) 0.99 ± 0.24 (4.16) 0.37 ± 0.33 (1.13) 0.97 ± 0.15 (6.58)
4 1.43 ± 0.16 (8.91) 3.22 ± 0.94 (3.45) 0.59 ± 0.43 (1.36) 0.62 ± 0.58 (1.08)
Mean 1.27 ± 0.14 (10.26) 1.68 ± 0.45 (3.98) 0.39 ± 0.32 (1.26) 0.91 ± 0.3 (4.18)
Simultaneous Multi-Slice Arterial Spin Labeling - Introduction 56

5 Simultaneous Multi-Slice Arterial Spin Labeling
5.1 Introduction
Cardiac arterial spin labeling (ASL) is a promising technique for measuring myocardial blood
flow (MBF) that does not require the use of ionizing radiation or contrast agents. Instead, ASL uses
arterial blood itself as a tracer by altering its magnetization state, typically through either saturation
or inversion. Labeled arterial blood is subsequently imaged when it enters the tissue of interest. The
most popular ASL labeling scheme used in the heart has been flow-alternating inversion recovery
(FAIR), which has been shown to detect clinically relevant changes in myocardial perfusion under
vasodilator stress (12). However, due to the limited duration of pharmacologically induced peak
stress with adenosine (~ 3 min), cardiac ASL has been restricted to single slice coverage, which is
insufficient for clinical evaluation.
Many strategies exist to increase spatial coverage for cardiac imaging. The most practical
approach is to acquire different slices sequentially using either snapshot GRE or SSFP during one
portion of the cardiac cycle. This restricts the amount of time available for imaging (~300 ms in
diastasis for heart rate 60 bpm) and the only realistic option is to spread the acquisition across
multiple heartbeats. In ASL, this is disadvantageous because the perfusion signal decays with the T 1
of blood and slices acquired at a later heartbeat will suffer from greater T 1 loss. A 3D acquisition
would circumvent this limitation because the entire imaging volume is excited together and all slices
will share the same perfusion weighting. This comes at the expense of a longer acquisition time to
acquire data in a third dimension. 3D first pass perfusion (FPP) CMR has embraced a whole slew of
techniques to reduce acquisition times to achieve high temporal resolution (of 1RR or 2RR) for
accurate sampling of the time-intensity curve of the injected gadolinium contrast (75). These
techniques rely on sub-Nyquist sampling that take advantage of spatiotemporal redundancies of
their dynamic datasets. These redundancies emerge from cardiac images with only gradual contrast
changes over time under optimal breath-holding and proper cardiac gating. In its most basic form
(UNFOLD), the data is transformed in a spatial and temporal frequency space (x-f space) and aliasing
from undersampling can be removed through a simple temporal filter (76). More advanced
techniques such as k-t BLAST and k-t SENSE (77) use fully sampled low resolution training data to
allow separation of multiple overlapping signals in the acquired data with even higher degrees of
undersampling. Unfortunately, these techniques are difficult to apply in ASL because the contrast
changes from labeled arterial blood is only on the order of 1-2% of the background myocardial signal.
Simultaneous Multi-Slice Arterial Spin Labeling - Methods 57

Fast, non-cartesian sampling trajectories such as echo-planar imaging (EPI) (78) or spiral (79) may
be more effective for ASL, but face distortion and off-resonance artifacts in the high susceptibility
environment of cardiac imaging (80).
Instead, we have opted for simultaneous multi-slice (SMS) imaging, which can increase slice
coverage without increasing scan time. In SMS imaging, multiple slices are simultaneously excited
using a multi-band RF pulse and individual slices are shifted with respect to one another in a
technique called CAIPIRNHA to achieve better coil sensitivity. Parallel imaging techniques based on
SENSE or slice-GRAPPA can subsequently be used to separate the superimposed slices. In its original
implementation, interslice image shifts were achieved using RF phase cycling. However, this leads to
an unfavorable tradeoff between the effective off-resonance profile and multiband acceleration
factor for bSSFP imaging (81,82) that can lead to severe banding artifacts. Banding artifact reduction
can be achieved by acquiring additional phase cycles, but comes at the cost of increasing scan time
(83). Alternatively, another strategy called blipped CAIPI uses gradients to achieve interslice shifts
without changing the off-resonance behavior and is therefore more suitable for bSSFP imaging (24).
In this work, we test the feasibility of using blipped CAIPI SSFP for cardiac FAIR ASL.

5.2 Methods
5.2.1 Blipped-CAIPI bSSFP
A FOV/n interslice image shift was achieved by cycling through n G z phase encoding gradients
in the slice direction that were applied simultaneously with conventional G y phase encodes. The
difference in gradient area between adjacent G z phase encodes is calculated as ∆𝐴 = 2𝜋 /(𝛾𝑛 𝑧 𝑔𝑎𝑝 ) ,
where 𝑧 𝑔𝑎𝑝 is the slice separation and n is the desired FOV/n interslice shift. Phase encodes were
acquired using an interleaved view order that grouped G z phase encodes together to reduce the
number of k-space jumps to minimize eddy current artifacts. Images were reconstructed using split-
slice GRAPPA(84) to minimize interslice leakage with a kernel size of 5×5 and coil combined using
optimal B 1 coil combination(50). Sensitivity maps were estimated from fully sampled reference
images.

5.2.2 Imaging
All images were acquired on a 3T GE scanner (Signa Excite HD) with an 8-channel cardiac coil.
In four healthy volunteers (age 29 ± 2.6 years, 3M/1F), two short axis cardiac images were acquired
Simultaneous Multi-Slice Arterial Spin Labeling - Results 58

during mid-diastole at a multiband factor of 2 (FOV/2 shift) and a 2.5 cm slice gap with TR/TE =
3.8/1.6 ms, FA = 30
0
, matrix size = 128x128, and partial Fourier factor = 6/8. FAIR ASL was
performed using a selective inversion slab of 7 cm, symmetrically spaced about the two acquired
slices for control acquisitions and a non-selective inversion for labeled acquisitions. Imaging
occurred during stable diastole one heartbeat after labeling under breath-holding. The
corresponding single slice FAIR references were acquired using the same slice locations and labeling
pulse for comparison. MBF, physiological noise (PN), and temporal SNR (TSNR = MBF/PN) were
calculated within a ROI corresponding to the left ventricle, as described by Zun et. al (11).

5.2.3 SNR Analysis
SNR and g-factor maps were calculated on the acquired baseline (no ASL contrast) images. G-
factor maps were estimated using the pseudo-replica approach(85). In a single volunteer with a
stable heart rate and consistent breath-holds, SS and SMS control and labeled images were compared
and the nRMSE was calculated.

5.3 Results
Figure 5-1 contains representative SMS images from a single volunteer with corresponding SNR and
g-factor maps. The average g-factor loss within the myocardium was 1.08 ± 0.08. G-factor losses of up to 1.31
were observed in the lateral wall. SS, SMS, as well as the difference between SS and SMS are shown in Figure
5-2 for a single volunteer in both control and labeled ASL acquisitions. The normalized root mean squared error
(nRMSE) for the basal slices was 0.024 and 0.047 for labeled and control images respectively; in mid-short axis
slices, nRMSE was 0.046 and 0.066 for labeled and control images respectively. nRMSE of the left-ventricular ROI
increased to .119 and .161 in basal slices and increased to .141 and .117 in mid-short axis slices for labeled and
control images respectively. As shown in Table 5-1, MBF estimates from SMS FAIR were 1.65 ± 0.69 ml/g/min,
0.67 ± 0.30 ml/g/min for the basal and mid short axis slices, respectively. This was comparable to single slice
FAIR with 1.06 ± 0.30 ml/g/min, 1.04±0.23 ml/g/min respectively. Figure 5-3 contains a representative MBF
and TSNR map. We observed lower TSNR in SMS as well as single slice FAIR of 3.17 and 5.08 respectively for the
Simultaneous Multi-Slice Arterial Spin Labeling - Results 59

mid-short axis slice, compared to previous studies (11). We attribute this to the longer imaging window and a
thickened inversion slab.

Figure 5-1 Reconstructed SMS slices are shown along with the corresponding SNR and g factor maps in a single
subject. Average g-factor was 1.08±0.08 and ranges from .92 to 1.31 within the left ventricular myocardium.
Higher g-factor losses are seen in the lateral wall and posterior segments.

Figure 5-2 Reconstructed SS and SMS FAIR A Labeled and B Control images in a subject with a steady heart rate
and consistent breath-holding. nRMSE values of the difference images are shown in white. nRMSE is higher in
control images and in the mid-short axis slice.
0
0. 5
1
1. 5
2
0
0. 5
1
1. 5
2
0
20
40
60
80
100
0
20
40
60
80
100
Basal Apical
Reference SMS SNR g-factor
Basal Mid
SS SMS Diff
Labeled
A
SS SMS Diff
Control
B
0.024
0.046 0.066
0.047
Simultaneous Multi-Slice Arterial Spin Labeling - Discussion 60

Figure 5-3. A Representative MBF and B TSNR maps from a single volunteer using SMS and single slice FAIR ASL
at the basal (top row) and mid-short axis (bottom row) slices. Green arrows indicate overestimation of MBF while
red arrow indicate underestimation.
Global (n=4) Segmental (n=24)
Basal Mid Basal Mid
SMS (MBF/PN/TSNR) 1.65/0.69/4.73 0.67/0.30/3.17 1.64/0.76/3.15 0.67/0.39/2.52
SS (MBF/PN/TSNR) 1.06/0.30/4.74 1.04/0.23/5.08 1.10/0.43/4.54 1.03/0.30/4.64

Table 5-1 Myocardial blood flow (MBF), physiological noise (PN), and temporal SNR (TSNR) reported in SMS and
single slice (SS) FAIR ASL. SMS ASL has lower TSNR and higher physiological noise than SS ASL due to g-factor
losses. MBF and PN are reported in units of ml/g/min.
5.4 Discussion
We have demonstrated that blipped CAIPI bSSFP can be used for SMS imaging of the heart
and is compatible with FAIR ASL. When compared with single slice reference images, we found that
the SMS reconstructed images only had a modest decrease in SNR, which we attribute to the relatively
low average g-factor of 1.08±0.08 within the left-ventricular myocardium. We observed greater g-
factor losses within the lateral wall of up to 1.31, which we hypothesize is due to the low number of
MBF (ml/g/min)
0.00 0.80 1.60 2.40 3.20 4.00
Temporal SNR
1.00 1.80 2.60 3.40 4.20 5.00
SMS SS
Basal Mid
Basal Mid
SMS SS
A B
Simultaneous Multi-Slice Arterial Spin Labeling - Conclusion 61

coil elements and the lack of coil diversity in the slice direction. In the septum, we observed g-factors
of less than 1, which implies a reduction of noise. This is due to de-noising effect of Tikhonov
regularization in split-slice GRAPPA reconstruction.
Comparing SS and SMS ASL images is difficult due to changes in image contrast from heart
rate variation and changes in the position of the heart due to imperfect breath-holds. However, we
were able to compare SS and SMS control and labeled images directly in a single volunteer with a
steady heart rate and consistent breath-holds. We found that the difference images had low nRMSE
that were less than 0.066, suggesting that split-slice GRAPPA can reconstruct ASL images of varying
contrasts that differ from the baseline contrast of fully sampled reference images.
In this study, we found decreased TSNR of SS FAIR ASL of 5.08 in the mid-short axis slice
when compared to previous studies (11,16). This is due to the increased slice-thickness of the FAIR
inversion slab which introduces greater physiological noise. A comparison of single slice and SMS
FAIR ASL reveals that SMS ASL consistently overestimated MBF in the basal slice and underestimated
MBF within the mid-axial slice, despite the low reconstruction error demonstrated by the low nRMSE.
However, when restricting the ROI to within the left ventricle, nRMSE increased to a maximum of
0.161, which explains the bias found in the ASL measurement. While the exact cause of this bias has
not been thoroughly investigated, we believe it may be due to eddy currents from the blip gradients,
phase accrual through the slice thickness of blipped-CAIPI acquisitions, or excited extraneous side
bands in the slice direction from RF amplifier distortion. Eddy currents can be minimized through
sequence optimization by reducing the slew rate and adding gradient delays at the cost of increased
TR. The phase accrual of blipped CAIPI acquisitions can be minimized by using a larger slice
separation and thinner slice thickness. Finally, RF distortion can be minimized by using a lower flip
angle and longer RF duration to prevent rapid oscillations of the RF envelope, both at the cost of
increased TR.

5.5 Conclusion
We demonstrate the feasibility of using blipped CAIPI bSSFP imaging for cardiac ASL using FAIR.
Compared to single-slice FAIR, the proposed method can acquire two slices simultaneously, but produce biased
estimates of MBF. Possible causes of this bias include eddy currents, phase accrual across the slice, and side bands
from RF distortion and needs to be investigated. Extension to more than two slices remains future work and will
likely require the use of higher density receiver arrays (>8 elements) that provide diversity in the slice direction.
Conclusions - Conclusion 62

6 Conclusions
A reliable cardiac ASL protocol that is clinically viable for assessing coronary artery disease
has been an elusive goal for the past decade. While we have looked at many novel and sophisticated
ASL techniques in the brain for inspiration, many of those ideas fall flat when translated into the heart
due to the many unique challenges of cardiac imaging. I have mentioned many of these in previous
chapters, but briefly, they include limited imaging time due to the cardiac cycle, breath-holding, and
short half-life of pharmacologic stress agents, significant cardiac and respiratory motion, difficult
geometry for labeling, and transit delays found in diseased hearts. These challenges significantly
reduce the sensitivity of ASL in the heart; the CASL technique that produces the highest ASL signal is
not feasible due to the cardiac geometry and the limited imaging time prevents cardiac ASL protocols
from acquiring many image pairs (over 40) typically used in brain ASL.
Despite these difficulties, in this dissertation, I have presented different strategies that
improve the sensitivity and spatial coverage of cardiac arterial spin labeling. I examined how imaging
parameters, including matrix size and parallel imaging acceleration factor affected SNR and TSNR of
cardiac images. We now have a theoretical basis and experimental procedure that justifies the
imaging parameters used by Do et. al (10). In his work, he used parallel imaging to shorten the
acquisition window at the cost of lowering raw SNR. We now know that his imaging parameters were
in the asymptotic limit of TSNR and that sacrificing SNR for improvements in acquisition speed was
a correct design choice.
Most cardiac ASL protocols use FAIR labeling, which becomes sensitive to transit delay when
the inversion slab is thickened to accommodate multiple imaging slices. My contribution in
developing cardiac VSASL is an attractive alternative labeling scheme for eventual multi-slice or 3D
cardiac ASL protocols because of its insensitivity to transit delay. I have designed one such protocol
using simultaneous multi-slice imaging, which has the benefit of a short acquisition duration.
The contributions I have made are drawn from preliminary studies in small samples of
healthy volunteers and must be validated in the controlled setting of animal studies and reproduced
in large patient studies. I have mentioned several possible improvements to the proposed methods.
In brief, the relationship between SNR and TSNR should be characterized in EPI sequences, which
have a much shorter acquisition time and may have a higher asymptotic limit for TSNR. VSASL must
eventually be validated in pigs in a slow coronary flow model to confirm insensitivity to transit delay
and tested in patients with heart failure and/or heavy coronary collateralization. SMS imaging still
Conclusions - Conclusion 63

faces technical hurdles, and thorough examination of phase accumulation through the slice and side-
band aliasing must be performed.
The history of cardiac ASL is nearly two decades long, with the first attempt by Poncelet in
1999. We have made significant progress since then, but a clinically robust protocol still remains out
of reach. Our cardiac ASL community is small, but we have the opportunity to make a real impact on
many patients with kidney disease who need cardiac perfusion evaluation, but cannot tolerate
existing contrast based perfusion methods. While this dissertation only makes a small step towards
improving cardiac ASL, I am hopeful that others will build upon and improve this work to make our
shared goal of improving patient care a reality.
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Abstract (if available)

Abstract Magnetic resonance imaging (MRI) is a medical imaging technique invented by Paul Lauterbur in 1971 that uses the principles of nuclear magnetic resonance to generate images. Widely touted as the most important medical invention in the last 50 years, MRI has transformed the medical landscape by providing high resolution anatomic images with excellent soft tissue contrast. MRI is important for identifying neuropathology, assessing cardiovascular function, evaluating spinal and joint disease, and diagnosing and staging cancer both pre-and-post-operatively. The power of MRI lies in its ability to generate novel contrast mechanisms, which has expanded the scope of MRI beyond anatomic imaging into quantitative imaging of an array of both physical and physiological processes, including diffusion, spectroscopy, blood flow, and perfusion. ❧ In this dissertation, I focus specifically on perfusion imaging of the heart. Many techniques asides from MRI are also sensitive to perfusion, such as SPECT, PET, CT, and ultrasound. We believe MRI has the potential to supersede these various modalities because it can offer high spatial resolution without ionizing radiation and can even avoid injected contrast agents through a novel technique called arterial spin labeling. The benefits of using ASL MRI are two-fold. One, ASL can be used repeatedly in patients for long-term evaluation of perfusion defects, which may be useful to assess disease progression. Two, ASL is contrast free and can be tolerated in a large population of patients with renal disease. This population is more susceptible to coronary artery disease than the general population and have the most to gain from a clinically viable cardiac ASL protocol. ❧ Therefore, the focus of this work is to take the necessary steps to make ASL clinically viable. In its current implementation, ASL has poor sensitivity and limited spatial coverage. Poor sensitivity is unavoidable because without contrast agents, the perfusion signal in ASL is low, on the order of 12% of the background signal from the heart itself. This makes maximizing the sensitivity of the ASL signal all the more important. Our first step was to determine how imaging parameters influence the sensitivity of not only ASL, but quantitative cardiac MRI in general. The metric we used to quantify sensitivity was the variability of cardiac images over time, or in technical terms, the temporal signal to noise ratio. If certain imaging parameters lead to large fluctuations in the cardiac images, there would be no hope of unmasking a small 1-2% ASL signal change. Through this study, I made the important finding that there is a fundamental limit towards minimizing these fluctuations, at which point further increases in the raw signal strength become unnecessary. ❧ With suitable imaging parameters at hand, I turned my attention towards the ASL pulse sequence itself. Traditionally, ASL labels arterial blood using a magnetization preparation upstream of the tissue of interest and images after a post labeling delay to allow the labeled blood to enter the tissue. The amount of time it takes the labeled blood to reach the imaged tissue, called the transit delay, is a critical determinant of the sensitivity of the ASL signal because labeled blood decays over time. In an extreme example, if the labeled blood signal has completely decayed before its arrival, ASL would have zero sensitivity. To counteract transit delay, I opted to use velocity selective labeling, which labels arterial blood based on its velocity as opposed to its spatial position. In theory, blood within small arterioles within the imaging slice can be labeled to eliminate transit delay completely. In practice, blood further upstream the arterial tree is typically targeted to minimize the transit time. The choice of velocity selective parameters determines how far upstream and in which direction labeling occurs in the arterial tree. These parameters were systematically varied and resulting perfusion estimate were compared with those obtained from the standard spatially selective FAIR ASL. Through this study, I found suitable velocity selective parameters and demonstrated the feasibility of VSASL. ❧ Lastly, I sought to increase spatial coverage of ASL. Simple sequential multi-slice imaging is not possible due to the limited scan times (~ 3 min) required for ASL under pharmacologically induced stress. 3D imaging may have superior slice coverage, but has long scan times and is unnecessary

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Asset Metadata

Creator Jao, Terrence Richard (author)

Core Title Improving sensitivity and spatial coverage of myocardial arterial spin labeling

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 07/24/2017

Defense Date 08/01/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag arterial spin labeling,coronary artery disease,magnetic resonance imaging,OAI-PMH Harvest,perfusion

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nayak, Krishna (committee chair), Haldar, Justin (committee member), Law, Meng (committee member), Wong, Eric (committee member), Wood, John (committee member)

Creator Email tjao@usc.edu,tjtiger86@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-416837

Unique identifier UC11214548

Identifier etd-JaoTerrenc-5639.pdf (filename),usctheses-c40-416837 (legacy record id)

Legacy Identifier etd-JaoTerrenc-5639.pdf

Dmrecord 416837

Document Type Dissertation

Format application/pdf (imt)

Rights Jao, Terrence Richard

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA