University of Southern California Dissertations and Theses

Radiofrequency pulse performance for myocardial ASL

(USC Thesis Other)

Radiofrequency pulse performance for myocardial ASL

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content

Radiofrequency Pulse Performance for
Myocardial ASL

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)

Vanessa Landes
December 2019

Abstract
Since its invention almost 50 years ago, Magnetic Resonance Imaging (MRI) has emerged as
an important imaging modality for obtaining high resolution anatomic images with excellent soft
tissue contrast. MRI is often clinically prescribed in static tissues, including brain or musculoskeletal
areas. Because MRI is radiation-free, it is desirable to increase clinical applications of MRI that
require frequent or routine monitoring.
Works in this dissertation were motivated by the need to improve a contrast-free myocardial
perfusion imaging (MPI) technique using MRI, called myocardial arterial spin labeling (ASL).
Myocardial ASL is a desirable MPI technique for diagnosing or monitoring patients with coronary
artery disease because it is the only MPI modality without ionizing radiation or contrast agents. This
technique is especially suited for patients with end stage renal disease, who cannot tolerate contrast
agents and require annual screening. Myocardial ASL uses blood as an endogenous contrast agent to
create a measurable signal that is proportional to myocardial perfusion. Myocardial ASL is under
development in our lab and its feasibility for detecting coronary artery disease has been
demonstrated in a single mid-short axis slice of the heart (1,2). Spatial coverage must be efficiently
increased and sensitivity to transit delay must be effectively eliminated for clinical adaption.
This thesis specifically focuses on technical improvements in radiofrequency pulse
performance for myocardial ASL to achieve these needs. First, a hardware-free, efficient RF
predistortion technique is developed to improve simultaneous multi-slice imaging for increased
spatial coverage of myocardial ASL. Second, a velocity selective pulse is designed using Fourier
Velocity encoding techniques and tailored specifically for labeling of coronary blood at 3T to remove
transit delay sensitivities of myocardial ASL. With the proposed methods, the development of
myocardial ASL approaches clinical reality.

Dedication

Dedicated to my grandparents Marie and Eugene Liberati, for devoting their lives to family.

Acknowledgements
I am truly grateful for all the people who have supported me during my time at USC. I am
fortunate to have worked in a lab with supportive mentors and coworkers, and have been able to
learn from each person. I would first like to extend my gratitude to Krishna, my PhD advisor, who
has mentored me through the years. He truly cares for his students, making sure we have the
necessary skills to achieve our career dreams. We have gained broad knowledge of technical aspects
in the MRI field, as well as the necessary communication skills for establishing meaningful
collaborations with other researchers. I have been stubborn at times about learning these skills, but
he has persisted, making sure I develop and improve. I would also like to thank Danny Wang, Eric
Wong, Cristina Zavaleta, John Wood, Kirk Shung and Justin Haldar for serving on my committees. I
appreciate the effort and time they afforded in reading my documents, attending my presentations,
and providing invaluable feedback to further my research.
I forever thankful for my myocardial ASL teammates. They truly know the joys, pains, and
requirements associated with this work.. We ran countless experiments using MRI scanners at the
hospital late at night and celebrated successful scans with tacos or pho parties. I’ll start with Ahsan
Javed first. He started the PhD program with me, endured all of the excitement and disappointments,
and has decided to continue enduring whatever I put him through as my husband. Next I would like
to thank Terrence Jao, who mentored me throughout my PhD. His work laid the foundation for my
thesis. Hung Do was always available to discuss research problems and brainstorm potential
solutions. He was the glue of our group and continues to keep us united.
My labmates at USC have helped me on this PhD journey, but I’ll only mention a few. I am grateful
for Johannes Töger, who has taught me how to design experiments as well as produce and present
figures. I would also like to thank Sajan Lingala, for teaching me how to solve optimization problems
with constraints. I thank Eamon Doyle for showing me the importance of presenting research in a
concise, effective manner and for how to be a confident professional. I appreciate Xin Miao, who has
been a great friend and career role model.
Next I would like to express my gratitude to my parents and brother Nathan. My family has been
there anytime I needed them, despite living thousands of miles away. Mom in particular has kept me
in touch with daily phone updates. Dad has helped brighten my mood by making light of whatever
situation I may have found myself in. Nathan has been able to relate to the PhD process, being in one
himself, and always offered grounding support.
Finally I’d like to thank my old and new friends, back in Rhode Island and in California. I’ve
known most of my friends in Rhode Island from middle school, and I expect we’ll stay in each other’s
hearts for the rest of our lives. These are the people who remind me of where I came from and who I
am, always supportive and encouraging. My friends in California have softened my heart. I’ve learned
from their incredible generosity, selfless love, and service to others. These are the people who
organized my wedding, visit me in my home, and check in often. These are the people who have
helped me see California as a second home.
I am forever grateful for my time at USC, both for all I have learned and for the lifestyle I have
shared.

Contents

Abstract ................................................................................................................................................................... ii
Dedication ............................................................................................................................................................. iii
Acknowledgements ........................................................................................................................................... iv
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 ................................................................................................................................ 5
2 MRI Background ......................................................................................................................................... 6
2.1 MRI Physics ............................................................................................................................................................. 8
2.1.1 Signal Polarization ......................................................................................................................................... 8
2.1.2 Sample Excitation ........................................................................................................................................... 9
2.1.3 Signal Reception .............................................................................................................................................. 9
2.1.4 Signal Localization ....................................................................................................................................... 10
2.1.5 Image Reconstruction ................................................................................................................................. 12
2.1.6 Parallel Imaging ............................................................................................................................................. 13
2.2 Basic RF Pulse Design ....................................................................................................................................... 16
2.2.1 Slice Selective Excitation ........................................................................................................................... 16
2.2.2 Small-tip approximation ............................................................................................................................ 18
2.2.3 Shinnar-Le Roux ............................................................................................................................................ 19
2.2.4 Variable Rate Selective Excitation ......................................................................................................... 21
2.3 Advanced RF pulse Design ............................................................................................................................. 24
2.3.1 Multi-band RF pulses .................................................................................................................................. 24
2.3.2 Velocity Selective RF pulses ..................................................................................................................... 26
2.3.3 Common Challenges .................................................................................................................................... 28
3 Cardiac Arterial Spin Labeling ............................................................................................................. 30
3.1 Arterial Spin Labeling (Brain first, then heart) ..................................................................................... 31
3.2 Current Implementation ................................................................................................................................. 32
3.3 Unmet needs ........................................................................................................................................................ 34
3.4 Clinical Justification .......................................................................................................................................... 35
4 Simple Method for RF pulse measurement using Gradient Reversal ..................................... 37
4.1 Introduction ......................................................................................................................................................... 37
4.2 Theory ..................................................................................................................................................................... 38
4.3 Methods .................................................................................................................................................................. 41
4.4 Results ..................................................................................................................................................................... 46
4.5 Discussion ............................................................................................................................................................. 53
4.6 Conclusion ............................................................................................................................................................. 56
5 Iterative correction of RF envelope distortion with GRATER-measured waveforms ....... 57
5.1 Introduction ......................................................................................................................................................... 57
5.2 Methods .................................................................................................................................................................. 58
5.3 Results ..................................................................................................................................................................... 61
5.4 Discussion ............................................................................................................................................................. 65
5.5 Conclusion ............................................................................................................................................................. 67
6 Improved Velocity-Selective Labeling for Myocardial ASL ........................................................ 68
6.1 Introduction ......................................................................................................................................................... 68
6.2 Methods .................................................................................................................................................................. 70
6.3 Results ..................................................................................................................................................................... 76
6.4 Discussion ............................................................................................................................................................. 82
6.5 Conclusion ............................................................................................................................................................. 84
7 Concluding Remarks ............................................................................................................................... 85
Bibliography ........................................................................................................................................................ 90

List of Publications
Journal Papers
1. VL Landes, KS Nayak. “Simple Method for RF pulse measurement using Gradient
Reversal.” Magnetic Resonance in Medicine. 79(5):2642-2651, May 2018. DOI:
10.1002/mrm.26920.

2. VL Landes, KS Nayak. “Iterative correction of RF envelope distortion with GRATER-
measured waveforms.” Magnetic Resonance in Medicine. July 2019. DOI:
10.1002/mrm.27930

3. K Jiang, CM Ferguson, JR Woollard, VL Landes, JD Krier, X Zhu, KS Nayak, and LO
Lerman. “Magnetization Transfer Imaging is Unaffected by Decreases in Renal
Perfusion in Swine.” Investigative Radiology. July 2019. DOI:
10.1097/RLI.0000000000000588

4. VL Landes, A Javed, TR Jao, Q Qin, KS Nayak, “Improved Velocity-Selective Labeling
for Myocardial ASL.” Magnetic Resonance in Medicine. 2019. In Prep.

Conference Papers
1. VL Landes, KS Nayak. “GRATER-based RF pulse predistortion improves multi-
band bSSFP imaging.” Proc. ISMRM 27
th
Scientific Sessions. Montreal. May 2019.
Power-pitch. Magna Cum Laude Merit Award.

2. VL Landes, TR Jao, A Javed, KS Nayak. “Improved Velocity-Selective Labeling
Pulses for Myocardial ASL.” Proc. ISMRM 27
th
Scientific Sessions. Montreal. May
2019.

3. VL Landes, KS Nayak. “Improved multi-band RF performance using GRATER-
based predistortion.” Proc. ISMRM 26
th
Scientific Sessions. Paris. June 2018.
Oral.

4. VL Landes, TR Jao, KS Nayak. “Practical implementation of SMS bSSFP in the
Heart.” Proc. ISMRM 26
th
Scientific Sessions. Paris. June 2018.

5. VL Landes, TR Jao, KS Nayak. “Simultaneous Multi-slice bSSFP CMR: Is it
feasible?” Proc. SCMR 21
st
Scientific Session. Barcelona. February 2018, p. 333.
6. VL Landes, KS Nayak. "Simple Method for RF Pulse measurement using Gradient
Reversal." Proc. ISMRM 25
th
Annual Meeting & Exhibition. Honolulu. April 2017,
p. 78. Oral. Magna Cum Laude Merit Award.

7. VL Landes, CM Ferguson, HP Do, JR Woollard, LO Lerman, KS Nayak.
"Comparison of Renal Blood Flow Measurements Obtained using ASL-MRI and
CT Perfusion." Proc. ISMRM 25
th
Annual Meeting & Exhibition. Honolulu. April
2017, p. 4856.

8. VL Landes, EK Doyle, PJ Prado, JC Wood, KS Nayak. "Feasibility of Non-invasive
Proton-Density Fat Fraction Evaluation using a Single-sided MR device." Proc.
ISMRM 24
th
Annual Meeting & Exhibition. Singapore. May 2016, p. 2206.

9. VL Landes, TH Kim, JP Haldar, KS Nayak. "Experimental Validation of SMS-
LORAKS." ISMRM Workshop on Simultaneous Multi-slice Imaging. 2015. Pacific
Grove. July 2015.

10. VL Landes, TR Jao, KS Nayak. "CAIPIRINHA-SSFP with improved banding artifact
performance." ISMRM Workshop on Simultaneous Multi-slice Imaging. 2015.
Pacific Grove. July 2015.

11. VL Landes, “Intro to Magnetic Resonance Imaging Using Real-Life, Hands-On
Activities,” AAAS 2015 Annual Meeting. San Jose. February 2015.
Introduction - Motivation 1
1 Introduction
1.1 Motivation
Coronary Artery Disease (CAD) is the leading cause of death in the United States, accounting
for 1/3 of all deaths in people over the age of 35 (3). CAD is caused by atherosclerosis, an
inflammatory process caused by lipid accumulation in the vessel wall which leads to vessel
narrowing. Figure 1.1 illustrates coronary atherosclerosis progression.
Myocardial perfusion imaging (MPI) is an important tool for diagnosing or monitoring
patients with CAD (4). There are a variety of available methods for perfusion Imaging. SPECT and
PET techniques are the most widely used but
expose patients to radiation. First pass MRI
perfusion offers superior spatial resolution
but requires use of contrast agents. X-ray
angiography is viewed as the gold standard
for MPI techniques because it offers direct
visualization of coronary vessels, however it
is invasive.
The limitation of these MPI
techniques is that they use contrast agents
and/or ionizing radiation. Contrast agents
are poorly tolerated in patients with end
stage kidney disease (ESRD) or chronic
kidney disease (CKD) and ionizing radiation
poses increased risks with routine
monitoring. There is an estimated 610,000
Americans with ESRD and 26 million Americans with CKD (5), and this number is projected to grow
(6). These patients have over 10 times higher cardiovascular mortality and require frequent CAD
assessment (7).

Figure 1.1: Progression of coronary artery disease. The heart
receives blood, oxygen and, nutrients through coronary arteries
(circled, left). A healthy cross section is shown (top, right). Over
time, plaque can build up and lead to CAD (middle, right). If a
blood clot forms and blood flow is blocked, a heart attack can
occur (bottom, right). Image source: mayoclinic.org.
Introduction - Motivation 2
Myocardial Arterial Spin Labeling: Preliminary Studies
An alternative MPI technique is myocardial arterial spin labeling (ASL) (8). ASL is a non-
contrast magnetic resonance imaging (MRI) technique that has no radiation and poses no
incremental risk to the patient. ASL measures tissue perfusion by subtracting ‘control’ images from
‘label’ images as shown in Figure 1.2.
A pilot study
performed by our group
showed that myocardial
ASL is compatible with
adenosine stress testing
and is capable of
detecting coronary
artery disease. Measured
ASL signal in 10 healthy
volunteers was
comparable to published
literature and increased
with stress testing (1).
Additionally, a study of
29 patients that underwent rest and stress cardiac ASL showed that areas of decreased myocardial
blood flow reserve corresponded with stenosed coronary vessels determined by coronary
angiography (9). An example is given in Figure 1.3.

Myocardial ASL: Room for
improvement
Clinical adaptation of
myocardial ASL is currently
limited by poor spatial
coverage; the current
protocol only acquires one
short-axis slice. At least 3
slices of the heart are needed
to diagnose the coronary

Figure 1.2: ASL signal acquisition involves the difference between two acquisitions. In
the first acquisition, arterial blood is labeled with a special MRI sequence. After waiting
1-2 seconds for delivery of arterial blood to the left ventricle, an image is obtained of the
myocardium plus the labeled blood. In a second acquisition, a control image is acquired
without labeled blood. The difference gives the ASL signal. Figure courtesy Eric Wong.

Figure 1.3: MPI in a patient with total left anterior descending occlusion (2).
Areas of decreased ASL signal in the myocardium (left) corresponded with
ischemic segments in angiography (right).
Introduction - Contributions 3
territory responsible for CAD and to inform treatment decisions (10). The challenge is that increased
coverage must be obtained without increasing scan time as pharmacological stress testing is limited
to 3-4 minutes.
Transit delay is one of the largest potential sources of error in quantification of perfusion
using ASL (11). Flow alternating inversion recovery (FAIR) labeling in the current protocol works
with the assumption that tagged blood will reach the myocardium after 1-2 heartbeats. Disease
processes with slow coronary flows, such as heart failure (12) or circuitous coronary collateral
vascularization (13), can exhibit prolonged transit delay (14). When transit delay becomes too long,
loss of ASL signal occurs and myocardial perfusion (MP) is underestimated (15).

1.2 Contributions
To address concerns of limited spatial coverage with myocardial ASL, we sought to
incorporate 3-band simultaneous multi-slice imaging with the current protocol to cover the basal,
mid, and apical short axis slices of the heart. We discovered a high signal intensity artifact in 3-band
SMS bSSFP imaging which prevented direction implementation of SMS bSSFP myocardial ASL. ASL
signal is only 1-4% of background tissue signal, and so only negligible artifacts can be tolerated
without confounding measurements. We determined this artifact was due to RF transmit
imperfections which caused spurious side-lobe excitation, and sought to develop an efficient RF
predistortion method without extra hardware to reduce these artifacts, using a simple method for RF
pulse measurement.
To address concerns of transit delay effects on myocardial ASL methods, we sought to refine
a previous implementation of myocardial velocity selective ASL, which produced comparable
measurements as FAIR ASL at the cost of 2.8x lower TSNR. The major innovation lied in using Fourier
Velocity Encoding techniques to develop a pulse specifically to label coronary arterial blood at 3T.

Simple method for RF pulse measurement using Gradient Reversal
We developed and evaluated a simple method for measuring the envelope of small-tip RF
excitation waveforms in MRI, without extra hardware or synchronization. The Gradient Reversal
Approach to Evaluate RF (GRATER) involves RF excitation with a constant gradient and reversal of
that gradient during signal reception to acquire the time-reversed version of an RF envelope. An
outer-volume suppression (OVS) pre-pulse was optionally used to pre-select a uniform volume.
GRATER was evaluated in phantom and in-vivo experiments. It was compared to the programmed
Introduction - Contributions 4
waveform and the traditional pick-up coil method. We determined the pick-up coil, GRATER, and
OVS+GRATER measurements matched the programmed waveforms to <2.1%, <6.1% and <2.4%
normalized root mean square error (NRMSE), respectively, for a variety of RF pulses in a uniform
phantom. For flip angles >30°, GRATER measurement error increased as predicted by Bloch
simulation. Fat-water phantom and in-vivo experiments with OVS+GRATER demonstrated <6.4%
NRMSE. In conclusion, the developed GRATER sequence measures small-tip RF envelopes without
extra hardware or synchronization in just over two times the RF duration.

Iterative correction of RF envelope distortion using GRATER-measured waveforms
We used GRATER to develop and evaluate a method for RF envelope correction without
extra hardware or synchronization. Transmitted RF waveforms are were measured through GRATER.
The measured RF waveforms were used to compute predistorted RF waveforms. This process was
repeated until a stopping criterion was met. Excitation profiles and simultaneous multi-slice (SMS)
image quality were compared before and after RF predistortion. The proposed RF predistortion
method improved the accuracy of multiband RF pulses, reducing normalized root mean squared
error (NRMSE) by more than 12-fold, and reducing spurious side-lobe excitation by more than 6-fold.
The reduction in unwanted side-lobe signal was demonstrated using SMS bSSFP imaging at 3T in
phantoms and in the heart. In conclusion, iterative GRATER-based predistortion is a practical,
hardware-free way to boost performance of short duration, low flip angle RF pulses, such as those
used in SMS bSSFP imaging. Because of its efficiency, this technique could be included as part of an
initial scan setup or for use with subsequent scans.

Improved Velocity Selective Pulses for Myocardial ASL
We developed and evaluated an improved velocity selective (VS) labeling pulse for
myocardial VS arterial spin labeling (ASL) perfusion imaging by addressing two limitations of current
pulses: 1) spurious labeling of moving myocardium and 2) low labeling efficiency. The proposed
myocardial VS ASL labeling pulse was designed using Fourier Velocity Encoding (FVE) techniques.
Specifically, the pulse utilizes bipolar velocity encoding gradients, a 9-tap velocity encoding envelope,
and double-refocusing pulses with MLEV phase cycling. The amplitudes of the 9-tap velocity
encoding envelope were optimized to minimize labeling of myocardial velocities during stable
diastole (±2-3 cm/s) and maximize labeling of coronary velocities (10-130 cm/s during rest and
stress, or 10-70 cm/s during rest). Optimization was performed over anticipated variation in b1 scale
(0.5-1) and off-resonance (±125 Hz) across the heart at 3T. Myocardial ASL experiments were
Introduction - Dissertation Organization 5
performed in 4 healthy subjects using the previously developed VS-ASL protocol by Jao et al with two
proposed VS pulses and original VS pulse. Myocardial ASL experiments were also performed using
FAIR ASL. Myocardial perfusion (MP), physiological noise (PN), and temporal SNR were evaluated
and compared. VSASL experiments show reduction in PN and increase in TSNR using the proposed
pulses compared to the original VS pulse. The proposed pulses provided MP measurements which
are comparable to FAIR-ASL.

1.3 Dissertation Organization
Chapters 2 contains background information on MRI, including basic MRI physics, basic RF
pulse design, and advanced RF pulse design. Chapter 3 gives an overview of Cardiac ASL, describing
ASL’s beginnings in the brain, current implement in the heart, and its unmet needs. Chapter 4
describes development of a fast technique to measure RF pulses without the need for additional
hardware, called the Gradient Reversal Approach to Evaluate RF (GRATER). Chapter 5 presents an
efficient, iterative correction method for RF envelope predistortion using GRATER-measured
waveforms. Chapter 6 presents improved Velocity Selective Labeling pulses for Myocardial ASL.
Finally, Chapter 7 gives concluding remarks. Chapter 4 to 5 present peer-reviewed published works
while Chapter 6 is unpublished.
MRI Background - Dissertation Organization 6
2 MRI Background
My favorite nontechnical description of
Magnetic Resonance Imaging is “a magnet, in the shape
of a donut, that takes pictures of the inside of the body”
(16). Just like an actual camera that takes pictures, the
MRI scanner records information that must be
processed before pictures can appear. This processing involves converting frequency information
into spatial information. Of course, this analogy is not complete because some MRI scanners use other
magnet configurations or measure biomarkers instead of taking pictures. However, it provides a
basic understand of what MRI does.
The way that information is obtained using an MRI scanner can be described using the key
components of the MR system and their effects on the MRI pipeline. Unless otherwise cited,
information from Section 2.1 is adapted from Nishimura’s textbook Principles of MRI (17), Justin
Haldar’s thesis (18), and Allen Elster’s Questions and Answers in MRI (19).
Key components of the MR system can be seen in Figure 2.1A and include a main magnetic
field 𝐵
"
, radio frequency field 𝐵
#
, and gradient coils 𝐺
%
,𝐺
'
,𝐺
(
. These components alter the magnetic
field over time to create a time-varying magnetic field and generate spatial frequency information
from the human body. This information is acquired with receiver coil 𝑅𝑥 and reconstructed to create
an image.
𝐵
"
causes nuclei in the body to precess at a frequency proportional to its magnitude. Ideally,
𝐵
"
is spatially homogeneous and all nuclei of a particular type will precess at the same frequency. In
reality, 𝐵
"
is not homogeneous and can be described in terms of 𝛥𝐵
"
, a spatially-dependent term for
inhomogeneity. After 𝐵
#
, oriented orthogonally to 𝐵
"
, is pulsed, ‘precession signal’ becomes oriented
in a way which can be measured. Adding Gradient fields, defined as dB/dt (change in magnetic field
over time), allows nuclei from different spatial locations to precess at different frequencies. In this
way, a variety of signals in the body can be acquired with a predictable relationship between spatial
location and frequency of precession. If enough data is collected in the spatial frequency domain, it
can be transformed into the image domain (i.e. an image is created).
For ease, 𝐵
"
is defined to point in the 𝑧 direction of the the coordinate plane while 𝐵
#
points
in 𝑥 and 𝑦. The gradients 𝐺
%
, 𝐺
'
, and 𝐺
(
point in 𝑥, 𝑦, and 𝑧, respectively (Figure 2.1A). Manipulation

MRI uses time-varying magnetic fields to
generate spatial-frequency information
from the body. This information is
reconstructed to form an image.
MRI Background - Dissertation Organization 7
of the MRI scanner’s magnetic field can be described in terms of its main components; the total
magnetic field 𝐵
/ ⃗
is described as
𝐵
/ ⃗
=2𝐵
"
+𝛥𝐵
"
+𝐺
%
𝑥+𝐺
'
𝑦+𝐺
(
𝑧4 𝑘
/ ⃗
+𝐵
#'
𝚥 ⃗+𝐵
#,%
𝚤 ⃗ [2.1]

Figure 2.1: Magnetic Resonance Imaging (MRI) main components and pipeline. A) MRI uses a large magnetic
field 𝐵
"
, radio frequency field 𝐵
#
, and gradient coils 𝐺
%
,𝐺
'
,𝐺
(
to generate spatial frequency information. This
information is acquired with receiver coils 𝑅𝑥 and transferred to a local computer for image reconstruction. B)
MRI exploits properties of nuclei with odd atomic mass, mainly hydrogen, to generate images. Each nuclei
possesses its own magnetic dipole moment 𝜇 ⃗ (green) and is randomly oriented. B) In the presence of 𝐵
"
, each
𝜇 ⃗ precessess about the magnetic field at a rate 𝜔 dependent on total field strength. After some time, each
𝜇 ⃗ together will form a nonzero bulk magnetization vector 𝑀
/ / ⃗
. C) A portion of 𝑀
/ / ⃗
can be “tipped” into the plane
transverse to 𝐵
"
, called 𝑀
%'
/ / / / / / / ⃗
, in the presence of 𝐵
#
. D) After 𝐵
#
is turned off, 𝑀
%'
/ / / / / / / ⃗
continues to precess and
return to equilibrium. As 𝑀
%'
/ / / / / / / ⃗
precesses, it generates flux in a nearby receiver coil 𝑅𝑥. This generates an
electromotive force we can measure called the free induction decay signal 𝑠(𝑡). E) The magnetic field can be
altered as a function of spatial position with gradient fields 𝐺
%
,𝐺
'
, and 𝐺
(
. This causes each spatial location 𝑟 ⃗ to
precess at different resonant frequencies, forming k-space signal 𝑠2𝑘
/ ⃗
4. E) 𝑠2𝑘
/ ⃗
4 can be reconstructed into an
image through several methods, the most common being the inverse 2D Fourier Transform I2DFT.

! # #
$%
& ' & ( )(+ ⃗)
signal
polarization
.
/
magnetic
dipole
moment
bulk
magnetization
vector
sample
excitation
.
0
signal
reception
12
signal
localization
3(+ ⃗)
image
reconstruction
I2567
transverse
magnetization
free
induction
decay signal
k-space
signal
reconstructed
image
H+
.
/
.
0
/12
3
$
3
%
3
9
!
0
!
:
!
;

#
#
$%
B) C)
D)
E) F) G)
A)
.
/
.
0
.(+ ⃗)
< = >. < + ⃗ = >.(+ ⃗)
?: .
/
,3
9
2B: .
0
,3
$%
,Rx
MRI Background - MRI Physics 8
2.1 MRI Physics
2.1.1 Signal Polarization
Each nucleus has an atomic mass. If the atomic
mass is odd, it will possess a magnetic dipole moment 𝜇 ⃗
and angular momentum 𝐽
⃗
that are nonzero. They are
related by a nuclei-specific constant 𝛾 known as the
gyromagnetic ratio:
𝜇 ⃗ =𝛾𝐽
⃗
[2.2]
In the absence of a strong magnetic field, nuclei
are randomly oriented. In MRI, the nuclei of interest are
usually hydrogen because of their abundance in the body (Figure 2.1B). In the presence of a magnetic
field 𝐵
"
, nuclei are still randomly oriented, however, there will be a torque 𝛵
/ ⃗
, such that
𝛵
/ ⃗
= 𝜇 ⃗ × 𝐵
"
=𝑑𝐽
⃗
/𝑑𝑡 [2.3]
Here, 𝑑𝐽
⃗
/𝑑𝑡 is the rate of change of angular momentum. Looking at the rate of change of 𝜇 ⃗
and generalizing to any magnetic field 𝐵
/ ⃗
,
𝑑𝜇 ⃗/𝑑𝑡 =𝛾𝑑𝐽
⃗
/𝑑𝑡 =𝛾 𝜇 ⃗ × 𝐵
/ ⃗
[2.4]
This is the equation of motion for 𝜇 ⃗ in a magnetic field, meaning that nuclei in a magnetic
field begin to precess at a rate related to the magnetic field and the gyromagnetic ratio.
Each nucleus has both energy associated with the magnetic field’s orientation and thermal
energy. Thermal energy is much larger and so 𝜇 ⃗ only has a slight tendency to point in the direction of
𝐵
"
. This situation can be compared to a group of compasses placed in a running tumble dryer. The
compasses all have the tendency to point North, however, they likely are not. This is because the
energy associated with being tossed around is much higher than the energy associated with pointing
North. If we look at the orientation of all the compasses together, we can measure their slight
preference for North (20). Similarly, each 𝜇 ⃗ together will form a nonzero bulk magnetization vector
𝑀
/ / ⃗
. I.e.,
𝑀
/ / ⃗
=∑ 𝜇
H
/ / / ⃗
I
[2.5]
The precession and orientation of 𝑀
/ / ⃗
is called sample polarization and is represented in
Figure 2.1C. Combining this with Equation 2.4 produces the simplified Bloch Equation of motion for
the bulk magnetization of spins:
𝑑𝑀
/ / ⃗
/𝑑𝑡 =𝛾 𝑀
/ / ⃗
× 𝐵
/ ⃗
[2.6]

Outside a magnetic field, nuclei are
randomly oriented. Inside a magnetic
field, nuclei are still randomly oriented
and precess about the field. Sample
polarization occurs as the sum of the
magnetic dipole moments 𝝁 / / ⃗ form a bulk
magnetization vector 𝑴
/ / / / ⃗
.
MRI Background - MRI Physics 9

2.1.2 Sample Excitation
Initially 𝑀
/ / ⃗
is pointing in the direction 𝐵
"
. Let
this purely longitudinal magnetization be called 𝑀
"
. If
a radiofrequency field or pulse 𝐵
#
(𝑡) is turned on in the
transverse plane, a transverse component of 𝑀
/ / ⃗
, 𝑀
%'
/ / / / / / / / ⃗
,
can form. The reasoning is as follows. Let 𝐵
#
(𝑡) be
played in the x-direction only. According to Equation 2.6,

LM
/ /⃗
LN
=𝛾 𝑀
/ / ⃗
× 𝐵
/ ⃗
=𝛾 ( 0 𝚤 ⃗+0 𝚥 ⃗+𝑀
"
𝑘
/ ⃗
) ×( 𝐵
#,%
(𝑡) 𝚤 ⃗ +0 𝚥⃗+𝐵
"
𝑘
/ ⃗
) [2.7]
Solving this further,

LM
PQ
LN
= −𝑖𝛾𝐺
(
𝑧𝑀
%'
+𝑖𝛾𝐵
#,%
(𝑡)𝑀
T
[2.8]

LM
U
LN
= −𝛾𝐵
#,%
(𝑡)𝑀
'
[2.9]
This shows that a nonzero 𝑀
%'
will form as 𝐵
#
(𝑡) is played over time and is illustrated in
Figure 2.1D. The magnitude of 𝑀
%'
depends on the strength and duration of 𝐵
#
(𝑡). I.e., the amount
that M is tipped into the transverse plane can be described by the ‘tip angle’ or ‘flip angle’ 𝛼 in degrees.
Letting 𝜏 be the duration of the RF pulse, they are related by
𝛼 =𝛾∫ 𝐵
#
(𝑠)𝑑𝑠
Y
"
[2.10]

2.1.3 Signal Reception
After 𝐵
#
(𝑡) is turned off, magnetization 1)
precesses about 𝐵
"
, 2) longitudinal magnetization
grows through 𝑇
#
relaxation, and 3) transverse
magnetization approaches zero through 𝑇
[
relaxation.
Precession occurs at a resonant frequency of 𝜔 =𝛾𝐵 radians/sec and is depicted in Figure
2.1E. If off-resonance is present, 𝜔 will vary with spatial position. 𝑇
#
or longitudinal relaxation
describes the way 𝑀
/ / ⃗
returns to 𝑀
"
in the longitudinal direction. It occurs at an exponential rate 𝑇
#
.
𝑇
[
or transverse relaxation describes the way the transverse component of magnetization dephases
and decays. It occurs at an exponential rate 𝑇
[
. Both 𝑇
#
and 𝑇
[
are tissue-specific. Taking these terms
into account, the complete Bloch Equation is an expansion of Equation 2.6:

LM
/ /⃗
LN
=𝛾 𝑀
/ / ⃗
× 𝐵
/ ⃗
−
M
P
\
]
𝚤 ⃗−
M
Q
\
]
𝚥 ⃗−
M
U
^M
_
\
`
𝑘
/ ⃗
[2.11]

In the presence of a radiofrequency field
𝑩
𝟏
(𝒕) , 𝑴
/ / / / ⃗
will no longer point soley in
the direction of 𝑩
𝒐
. It will form a
transverse component 𝑴
𝒙𝒚

/ / / / / / / / / ⃗
.
𝑴
𝒙𝒚

/ / / / / / / / / ⃗
generates measurable current in a
receiver coil 𝑹𝒙, called free induction
decay signal 𝒔(𝒕).
MRI Background - MRI Physics 10
T1 and T2 relaxation can be described with the following equations:
𝑀
(
=𝑀
"
(1−𝑒
kl
m
`
) [2.12]
𝑀
%'
=𝑀
"
𝑒
kl
m
]
[2.13]
The path of the magnetization vector follows a bee-hive shape as it returns to equilibrium,
with 𝑇
[
<𝑇
#
. Figure 2.2 depicts 𝑇
#
and 𝑇
[
relaxation in the rotating frame for different tissue types
at 3T (21). The rotating frame rotates with precessing nuclei.

Figure 2.2: Example of longitudinal (Mz) and transverse
(Mxy) magnetization for different tissue types at 3T after a
90º excitation pulse 𝐵
#
(𝑡) . Over time, magnetization
returns back to the z-direction, or equilibrium. This
process usually takes a few seconds, if no other RF pulses
are played.

As 𝑀
%'
/ / / / / / / / ⃗
precesses and its signal relaxes, the magnetic field is changing. According to the
Faraday-Lentz law of electromagnetism, this changing magnetic field will generate current in a
nearby receiver coil 𝑅𝑥. Without the use of gradients, signal will be at oscillating at the Larmor
frequency 𝜔 =𝛾𝐵 and decaying exponentially. 𝑇
[
∗
, the observed rate of decay, is a combination of
tissue-specific 𝑇
[
and additional signal decay from magnetic field inhomogeneity. The free induction
decay (FID) signal 𝑠(𝑡) is then described as the integral over the excited magnetization 𝑀(𝑟) of
oscillating, decaying signal:
𝑠(𝑡)= ∫ 𝑀(𝑟)
pTq
𝑒
^Ir (s)N
𝑒
^N/\
]
∗
𝑑𝑟 [2.14]
2.1.4 Signal Localization
Passing current through gradient coils 𝐺(𝑟 ⃗)
changes the magnetic field as a function of spatial
position. This causes each spatial location 𝑟 ⃗ to precess
at different resonant frequencies and is depicted in
Figure 2.1F. Frequency information is acquired with a
variety of gradient and RF combinations to form a set of
Gradients vary magnetic field strength
over space. This varies resonant
frequencies of nuclei as a function of
spatial position, creating a relationship
between spin frequency and location.
This is recorded as a set of FIDs 𝒔(𝒌
/ / ⃗
).
MRI Background - MRI Physics 11
FIDs called k-space signal 𝑠2𝑘
/ ⃗
4. The combination of RF and gradient waveforms is called a pulse
sequence.
With slice-selective excitation, a slab of thickness 𝛥𝑧 with slice center 𝑧
u
is excited. Slice-
selective excitation is achieved using a slice-select gradient of amplitude 𝐺
vv
and a band-limited RF
pulse. 𝐺
vv
is typically played as a constant gradient in the logical z-direction. The RF pulse is typically
played as a truncated, windowed sinc concurrently with 𝐺
vv
. This produces a linear relationship
between slice location and excitation frequency (Figure 2.3). Assuming a homogeneous 𝐵
"
, let the
center frequency be 𝜔
u
(𝑧
u
)=𝛾( 𝐵
"
+𝐺
vv
𝑧
"
). Then, the FID can be described according to
𝑠(𝑡)= ∫ ∫ ∫ 𝑚(𝑟)𝑒
^Ix(y
_
z{
||
(
_
)N
𝑒
^N/\
]
∗
% ' (
𝑑𝑥𝑑𝑦𝑑𝑧 [2.15]

Figure 2.3 depicts the direct relationship between slice
location and frequency during slice-selective RF excitation.
The slice or frequency profile is proportional to the Fourier
Transform of the RF pulse. For example, if a sinc-shape RF
pulse is played during RF excitation, a rectangular shaped
slice-profile will occur. Slice thickness 𝛥𝑧 has an inverse
relationship with slice-select gradient amplitude. Slice
location is based on the center frequency of the RF pulse.

Assume through slice signal variations and 𝑇
[
∗
decay are negligible and consider a basic 2DFT
pulse sequence shown in Figure 2.4. Let phase encode gradient of amplitude 𝐺
}
be played for some
time 𝑡
'
along the logical y-direction. After time 𝑡
'
, signal is acquired in the presence of a readout
gradient 𝐺
~
along the logical x-direction, and demodulated at 𝜔 =𝛾𝐵
"
. Then
𝑠2𝑡;𝑡

4= ∫ ∫ 𝑚(𝑥,𝑦)𝑒
^Ixy
_

𝑒
zIxy
_
𝑒
^Ix{

'N
Q
' %
𝑒
^Ix{

%N
𝑑𝑦𝑑𝑥 [2.16]
3 𝑠2𝑡;𝑡

4 = ∫ ∫ 𝑚(𝑥,𝑦)𝑒
^Ix{

'N
Q
' %
𝑒
^Ix{

%N
𝑑𝑦𝑑𝑥 [15
]
!
"
→ ←
&'()*+, ∼ .
/0
{2
3
(5)}
↓
↑
slice thickness Δ!
;
<
"
=
MRI Background - MRI Physics 12

Figure 2.4 shows a basic 2DFT pulse sequence. The slice
select portion of the pulse sequence occurs during 𝐵
#
(𝑡) and
the 𝐺
(
gradient with amplitude 𝐺
vv
. One phase encode line in
k-space is acquired at a time with 𝐺
'
gradient with amplitude
𝐺

. Signal readout, or acquisition, occurs in the frequency
encoding direction during the 𝐺
%
gradient with amplitude
𝐺
~
. This is repeated every 𝑇𝑅 for different values of 𝐺

to
acquire 2D k-space information (see Figure 2.5).

Now k-space variables 𝑘
%
and 𝑘
'
can be defined in units of spatial-frequency according to:
𝑘
%
≐
x
[
∫ 𝐺
%
(𝜏)𝑑𝑡 =
N
"
x
[
𝐺
~
𝑡 [2.17]
And
𝑘
'
≐
x
[
∫ 𝐺
'
(𝜏)𝑑𝑡 =
N
"
=
x
[
𝐺
}
𝑡

[2.18]
These k-space variables allow a direct relationship to form between the transverse
magnetization and the FIDs. More specifically, using 𝑘
%
and 𝑘
'
with Equation 2.15, a 2D Fourier
Transform relationship becomes apparent
𝑠2𝑡;𝑡

4=𝐹
[
{𝑚(𝑥,𝑦)}|𝑘
%
,𝑘
'
[2.19]
𝑠2𝑡;𝑡

4 is said to form one “line” in k-space. If this sequence is repeated several times with different
phase encode gradient amplitudes, different lines can be acquired. After assembling all the FIDs, a
matrix in k-space 𝑠(𝑘
/ ⃗
) can be formed.

2.1.5 Image Reconstruction
K-space signal 𝑠2𝑘
/ ⃗
4 needs to be processed, or
reconstructed to form an image 𝜌(𝑟 ⃗). The inverse 2D
Fourier Transform I2DFT is the most common method
and is adequate to reconstruct the sequence described in the previous section.
Figure 2.5 depicts the Fourier transform relationship between k-space and image space.
Often k-space samples are acquired along a grid for simple 2DFT image reconstruction. There is an
K-space data is reconstructed to form an
image, often using the inverse 2D Fourier
Transform.
MRI Background - MRI Physics 13
inverse relationship between image resolution 𝛥𝑟 ⃗ and total distance, or width in k-space 𝑊

/ / ⃗
There
is also an inverse relationship between image field-of-view 𝐹𝑂𝑉
s⃗
and resolution in k-space 𝛿𝑘
s⃗
.

Figure 2.5 depicts the Fourier transform relationship between k-space and image space in Cartesian imaging. A) K-space
samples are acquired along a grid, allowing for simple 2DFT image reconstruction. For the sequence depicted in Figure
2.4, one line across 𝑘
%
will be acquired for each 𝑇𝑅. B) The reconstructed gray object is depicted. If the field of view (FOV)
is not limited, it would be replicated indefinitely in image space. Conversely, if the FOV is too small, the imaged object would
appear aliased. Note, there is an inverse relationship between 𝐹𝑂𝑉 and resolution in k-space 𝛿𝑘
s⃗
.There is an inverse
relationship between image resolution 𝛥𝑟 ⃗ and total distance, or width in k-space 𝑊

/ / ⃗
.

Signal-to-noise ratio (SNR) is one of the fundamental measures of image quality in MRI. SNR
is defined over an image voxel or over a region of interest as
𝑆𝑁𝑅 ≐
vIq qINL
vNLsL LpINIT T TIv
[2.20]
SNR is dependent on many things, including image resolution, signal acquisition time, and
pulse sequence type. The pulse sequence determines signal amplitudes during readout, which are a
function 𝑓 of the tissue’s proton density 𝜌, 𝑇
#
, and 𝑇
[
. A general dependence may be described as
𝑆𝑁𝑅 ∝ 𝛥𝑟 ⃗𝑠𝑖𝑔𝑛𝑎𝑙 𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒𝑓(𝜌,𝑇
#
,𝑇
[
) [2.21]
2.1.6 Parallel Imaging
The body coil in an MRI scanner is capable of
both transmitting RF pulses and receiving FID signal
(black, Figure 2.1A). The body coil is often used to
transmit RF signal. Multiple coils close to the body are
often used to receive signal. This configuration allows
for each coil signal to have increased SNR because they
are closer to the body, the source of MR signal. Combining each coil signal further increases SNR.
Parallel imaging undersamples data to
reduce scan time and artifacts related to
long acquisition. Reconstruction occurs
through SENSE or GRAPPA-based
methods.
MRI Background - MRI Physics 14
Finally, each receiver coil’s unique FOV, or sensitivity, can be exploited to allow for undersampled
data and reduced scan times. Figure 2.6 gives a cartoon example of a multi-channel body coil and
each coil’s sensitivity.

Figure 2.6: While the single-channel body coil (Figure
2.1A) is most commonly used to transmit RF signal,
multiple-channel surface coils are often used to receive
FIDs. Surface coils are placed close to the source of signal
(i.e. object being imaged) and signal from each coil is
combined to increase SNR. The object being images in this
example is a smiley face and the surface coils are labeled
𝐶
#
−𝐶
¨
. Each coil has a different view, or sensitivity, based
on its geometry and distance from the signal. Example coil
images are labeled 𝐼
#
−𝐼
¨
. High to low received signal
intensity is represented with bright to dark colors,
respectively.

The process of strategically undersampling and reconstructing data based on coil sensitivity
is called Parallel Imaging (PI). PI undersamples data, acquiring a reduced number of phase encodes
to reduce scan time and artifacts related to a long acquisition. This comes at the cost of reduced SNR
and PI-specific artifacts, however data can be undersampled to cause aliasing in a way that enhances
reconstruction.
Reconstruction can occur through either 1) sensitivity encoding (SENSE) based methods in
the image domain (22) or 2) generalized autocalibrating partial parallel acquisition (GRAPPA) based
methods in the k-space domain (23). An overview of SENSE and GRAPPA techniques are given in
Figures 2.7 and 2.8, respectively. More information can be found in seminal papers(22,23).
!
"
!
#
!
$
!
%
&
%
&
$
&
#
&
"
MRI Background - MRI Physics 15

Figure 2.7: SENSE involves 4 major steps. 1) Generate coil sensitivity maps from low-resolution, full FOV images by
dividing surface coil images by the whole body coil image and filtering. 2) Acquire undersamped k-space data by
periodically skipping phase encode lines. 3) Reconstruct undersampled data to obtain partial FOV coil images. 4)
Reconstruct full FOV image by matrix inversion. The basic idea behind the matrix inversion is that aliased pixel 𝑎
I
for coil
𝑖 can be written as a linear combination of the full-FOV image at different pixel locations 𝑓
ª
multiplied by their coil
sensitivities 𝑐
I,ª
. For example, 𝑎
#
= 𝑓
#
𝑐
#,#
+f
[
𝑐
#,[
. These combinations can be formed into a matrix and inverted to find
the full FOV image 𝐹 . Letting 𝐴 and 𝜓 represent aliased coil images and the noise covariance matrix, 𝐹 =
(𝐴
®
𝜓
^#
𝐴)𝐴
®
𝜓
^#
.

Figure 2.8: In GRAPPA, partial k-space data is acquired by periodically skipping
phase encoding lines, albeit for a fully sampled center, called an autocalibration
(ACS) region (grey circles). Data from multiple lines from all coils (black circles)
are used to fit an ACS line in a single coil (black lines) and create convolution
kernels or weights 𝜅. 𝜅 are used to generate missing lines from each coil (white
circles). The Fourier transform is taken to generate coil images, which are then
combined using sum of squares.

Defining acceleration factor R as the number of fully sampled divided by the number of
acquired phase encoding lines, a √𝑅 SNR penalty is expected due to a due to R reduction in scan time.
PI is subject to additional SNR losses based on the number of aliased replicates for each point and
their associated differences in coil sensitivity. It is described by a spatially dependent g-factor. G-
factor, or “noise amplification factor”, depends on 1) number and location of surface coils, 2) coil
1)
2)
3)
4)
!
"
!
#
PE
RO
$
%
$
&
$
'
$
(
)
%
)
(
)
&
)
'
*
+
%
+
&
,
%
,
&
,
'
,
(
-
%,%
-
%,&
!
" #
$
!
%
!
&
!
'
#
$
= 0
MRI Background - Basic RF Pulse Design 16
loading, 3) imaging plane, 4) direction of phase-encoding within the scan plane, and 5) voxel location
within the imaged region. The relationship between SNR with and without PI is described as
𝑆𝑁𝑅
}±
=
²³~
´µ¶¶
√~
[2.22]
PI is especially useful for applications with a large FOV, like chest and abdominal imaging,
where high resolution is also desirable. Reconstruction quality is adequate as long as each coil has a
sufficiently unique sensitivity.
2.2 Basic RF Pulse Design
2.2.1 Slice Selective Excitation
Two steps are required to excite a slice in 2D MRI:
(1) A slice-select gradient is played in the direction
perpendicular to the desired slice. This produces a
linear variation of resonance frequencies in that
direction.

(2) An RF-pulse is played at the same time as the slice-select gradient. Its frequency components
are designed to match the range of frequencies in the desired slice.

These steps were briefly described in Section 2.1.4 Signal Localization and RF pulse design
for slice-selective excitation will be discussed now more in-depth.
When an MRI RF Engineer designs an RF pulse, they design only the RF envelope. The scanner
is equipped with hardware to easily modulate the RF pulse to 𝜔
u
during transmission, and so
modulation is not considered. RF pulse design is synonymous with RF envelope design for the rest of
this thesis.
For sake of simplicity, consider an ideal RF pulse for small flip angles as there is a direct
Fourier relationship between RF pulse shape and excitation profile. The reasons for this are
described in Section 2.2.2 Small-tip approximation. Because it’s Fourier transform is a rect, the
ideal RF pulse is then a sinc
𝐵
#
(𝑡)=𝐾𝑠𝑖𝑛𝑐(𝛥𝜔𝑡) [2.23]
𝛥𝜔 is known as the transmit bandwidth of the pulse. Transmit bandwidth should be distinguished
from receiver bandwidth. Receiver bandwidth is a function of the digitization rate of the recorded
MR signal and not related to slice selection, and will be discussed more in Section 2.2.4 Variable-
rate selective excitation.
Ideal sinc pulses require an infinite number of side lobes and are of infinite duration. To
uniformly and exclusively excite the desired 𝛥𝜔, the sinc pulse must be windowed, or modified
The ideal RF pulse excites a rectangular
slice profile and is of infinite duration.
Pulses typically limited to a few
milliseconds, requiring careful design.
MRI Background - Basic RF Pulse Design 17
through ‘apodization’, a process which involves limiting the number of side-lobes so that the total
duration is only a few milliseconds. The resulting waveform is then filtered to prevent undesirable
excitation. An example of a sinc pulse is given in Figure 2.9.

Figure 2.9: To excite tissue in the body, RF pulses are transmitted at the Larmor frequency. For example,
protons are excited with RF pulses transmitted at around 128 MHz of a couple milliseconds duration (a & b,
red). These pulses are transmitted so quickly and oscillate so rapidly that they would appear as a solid red blob
on the page (here fewer samples are shown). Modulation of RF pulses is easy and so RF engineers concentrate
on the design of the RF envelope (a & b, blue) to correctly excite desired tissue. To excite a uniform slice, sinc-
shaped RF envelopes are used, due to an approximately Fourier transform relationship between RF envelope
shape and slice profile (a & c and b & d are related through the Fourier transform). An RF pulse with an infinite
number of zero-crossings (of infinite duration) would excite an exactly rectangular profile. Instead, RF pulses
are limited in time, and more zero crossings correspond to a sharper slice profile for a given duration.

Sinc-shaped RF pulses designed with more zero-crossings have sharper (more rectangular)
slice profiles, at the cost of a longer pulse duration and longer scan times. A useful metric to describe
the sharpness of slice profiles is the time-bandwidth (TBW) product. TBW describes the number of
zero-crossings in a sinc-shaped pulse. It highlights the tradeoff between transmit bandwidth 𝐵𝑊
\%

and pulse duration 𝑇
y#
for a given slice profile
𝑇𝐵𝑊 =𝑇
y#
𝐵𝑊
\%
∝𝑝𝑟𝑜𝑓𝑖𝑙𝑒 𝑠ℎ𝑎𝑟𝑝𝑛𝑒𝑠𝑠𝑠 [2.24]
Today most RF pulses are not designed using simple waveforms, and are instead designed
using a technique in Section 2.2.3 Shinnar-Le Roux (SLR), a technique which allows for accurate
pulse design at high flip angles.
MRI Background - Basic RF Pulse Design 18

2.2.2 Small-tip approximation
Recall Section 2.1.2 Sample Excitation. Let
radiofrequency pulse 𝐵
#
(𝑡) be turned on in the x-
direction forming transverse magnetization 𝑀
%'
/ / / / / / / / ⃗
. The
Bloch equations give us Equations of motion for the
transverse and longitudinal magnetization in the
rotating frame, Equations 8 and 9, respectively. Note,
these equations are not easily solved.
However, if magnetization starts from
equilibrium, i.e. is aligned with the longitudinal direction, and 𝐵
#
(𝑡) has a small flip angle (i.e. <30°),
then the change in longitudinal magnetization is negligible. Further assuming on-resonance
excitation and ignoring relaxation,

LM
PQ
LN
= −𝑖𝛾𝐺
(
𝑧𝑀
%'
+𝑖𝛾𝐵
#,%
(𝑡)𝑀
T
[2.25]

LM
U
LN
≅ 0 [2.26]
LM
PQ
LN
then becomes a first order linear differential equation which is easily solvable in the Laplace
transform domain
𝑀
%'
(𝑡,𝑧)= 𝑖𝑀
"
𝑒
Ix{
U
(
𝑡∫ 𝑒
Ix{
U
(v
𝛾𝐵
#
(𝑠)𝑑𝑠
N
"
[2.27]
Furthermore, if a symmetric RF pulse is played after an RF pulse of duration 𝜏, there is a Fourier
transform relationship between 𝐵
#
(𝑡) and 𝑀
%'
(𝜏,𝑧).
|𝑀
%'
(𝜏,𝑧)| = 𝑀
"
𝐹½𝐵
#
¾𝑡+
Y
[
¿À|
Á^
Â
]Ã
{
U
(
[2.28]
The temporal frequency content of 𝐵
#
(𝑡) predicts what tissue will be excited, i.e. the slice
profile. This assumption holds reasonably well for larger flip angles, as depicted in Figure 2.10.

The small-tip approximation assumes
that longitudinal magnetization after an
RF pulse is approximately equal to it its
equilibrium value. This allows the Bloch
equation to be simplified such that the
transverse magnetization becomes the
Fourier Transform of the weighted k-
space trajectory.
MRI Background - Basic RF Pulse Design 19

Figure 2.10: (A) and (b) are RF pulses designed
using the small-tip approximation for a 30° and
90° RF pulse, respectively. The side-lobe ripple in
the excitation profile of the small (c) and large-tip
pulses (d) is 1 and 4 percent, respectively. Here it
can be seen that imperfections in slice profile are
small but apparent outside of the small-tip
regime.

2.2.3 Shinnar-Le Roux
The Shinnar Le-Roux (SLR) algorithm is useful
for designing slice-selective RF pulses without linear
phase or with large flip angles (24). SLR generated
pulses provide better control of RF phase properties,
allowing the designer to trade off several parameters
including frequency profile, ripple, duration, and energy
deposition. The SLR algorithm is based on the discrete
approximation to the spin domain version of the Bloch
equation. It allows the RF design problem to be mapped
into a digital filter design problem, solved using well known algorithms, and then mapped back into
an RF pulse.
RF waveforms are often generated on commercial scanners using a piece-wise constant
approximation, shown in Figure 2.11. Each RF “constant” can be thought of as rotating the
magnetization some small amount. In other words, the final magnetization rotation 𝑄 after an RF
pulse is the product of 𝑛 small rotations
𝑄 =𝑄

𝑄
^#
⋅⋅⋅𝑄
#
[2.29
The SLR algorithm is useful for designing
RF pulses at high flip angles. SLR
generated pulses allow trade-offs
between several parameters. It allows
the RF design problem to be mapped into
a digital filter design problem, solved
using well known algorithms, and then
mapped back into an RF pulse.
MRI Background - Basic RF Pulse Design 20

Figure 2.11: An RF pulse is implemented on the
scanner as a piece-wise constant approximation
to a continuous waveform. RF pulses that are not
transmitted finely enough can negatively affect
slice profile performance.

For the jth rotation, 𝑄
ª
can be described in the spin domain using 2x2 unitary matrices. This
representation allows for the RF pulse to be mapped into two complex polynomials called the
Forward SLR transform. The basic idea is that each small rotation in a piece-wise constant portion of
an RF pulse can be modeled by 1) precession under the effect of the local gradient field by an angle
–𝛾𝐺
(
𝛥𝑡 and 2) rotation about the applied RF vector by an angle –𝛾𝐵
#
𝛥𝑡. In that way 𝑄
ª
can be broken
into two matrices for precession and rotation
𝑄
ª
≅ Ç
𝐶
ª
−𝑆
ª
∗
𝑆
ª
𝐶
ª
ÈÉ
𝑧
#/[
0
0 𝑧
^#/[
Ê [2.30]
where
𝐶
ª
=cosÉ
xÎy
`,Ï
ÎÐN
[
Ê [2.31]
𝑆
ª
=𝑖𝑒
IÑy
`,Ï
sinÉ
xÎy
`,Ï
ÎÐN
[
Ê [2.32]
and
𝑧 =𝑒
Ix{
U
ÐN
[2.33]
The Cayley-Klein parameters can then be calculated at each time-step as
É
𝑎
ª
𝑏
ª
Ê=𝑧
`
]
Ç
𝐶
ª
−𝑆
ª
∗
𝑆
ª
𝐶
ª
È¾
1 0
0 𝑧
^#
¿É
𝑎
ª^#
𝑏
ª^#
Ê [2.34]
Cayley-Klein parameters at the 𝑛
NÕ
time step are (𝑛−1) order polynomials in 𝑧
^#

𝐴

(𝑧) = ∑ 𝑎
ª
𝑧
^ª ^#
ªÁ"
[2.35]
𝐵

(𝑧)= ∑ 𝑏
ª
𝑧
^ª ^#
ªÁ"
[2.36]
where
𝑧
^#
=𝑒
^Ix{
U
ÐN
[2.37]
In other words, the RF pulse 𝐵
#
(𝑡) has been mapped into two complex polynomials 𝐴

(𝑧)
and 𝐵

(𝑧) called the forward SLR transform, which reduces to the z-transform for small flip angles.
If 𝐴

(𝑧) and 𝐵

(𝑧) are given, 𝐵
#
(𝑡) can then be calculated using the inverted, or inverse SLR
MRI Background - Basic RF Pulse Design 21
transform, with the constraint that |𝐴

(𝑧)|
[
+|𝐵

(𝑧)|
[
=1 for all complex z such that |𝑧|=1. The
RF waveform is then
𝐵
#,ª
=
[
xÐN
tan
^#
Ø
y
Ï,_
Ù
Ï,_
Ø𝑒
IÑÇ^
ÚÛ
Ï,_
Ü
Ï,_
È
[2.38]
In this way RF pulse design equates to the design of two complex polynomials. 𝐵

2𝑒
Ix{%ÐN
4 is
proportional to the sine of half the tip angle at position x. 𝐵

(𝑧)is designed to approximate the ideal
slice profile. 𝐴

(𝑧) is then calculated to be consistent with 𝐵

(𝑧), subject to the additional constraint
that the resulting RF pulse have minimum energy. From there 𝐵
#
(𝑡) can be found by the inverse SLR
transform. One popular way of designing the polynomials with linear-phase finite impulse response
digital filters is through the Parks-McClellan algorithm. Figure 2.12 compares filtered, truncated sinc
pulses with those designed using the SLR algorithm.

Figure 2.12: Comparison of RF pulses and
corresponding slice profiles for 90° RF pulses using
Shinnar Le-Roux pulse design (a & c) and the small-
tip approximation (b & d). The differences between
the two RF pulses is not immediately apparent (a vs.
b). However, the Shinnar Le-Roux algorithm
produces more accurate slice profiles at high flip
angles (c). The small-tip approximation produces
profiles with extra excited side-lobes (d).

2.2.4 Variable Rate Selective Excitation
VERSE is a procedure for refabricating any
spatially selective excitation pulse to reduce its specific
absorption rate (SAR) or duration while maintaining
quality of the on-resonance slice profile (25). VERSE
works by allowing a variable trade-off of RF amplitude
for duration at each sample of the pulse. SAR reduction
of 50% is possible at the cost of a smeared off resonance
slice profile. Intuition for the VERSE algorithm follows
The VERSE algorithm is useful for
designing RF pulses with reduced SAR
and/or duration, however it is sensitive
to off-resonance. VERSE works by
allowing a variable trade-off of RF
amplitude for duration at each sample of
the pulse to create a new facsimile pulse.
MRI Background - Basic RF Pulse Design 22
from the piecewise constant implementation of an excitation pulse as well as the desire to achieve a
certain net rotation regardless of pulse shape.
During one sample 𝛥𝑡 of a piece-wise constant selective excitation pulse (introduced in
Section 2.1.3 SLR pulse design), magnetic field 𝐵 is determined by the gradient and RF fields. Net
rotation 𝜃 during 𝛥𝑡 is then
𝜃 =𝛾𝐵𝛥𝑡 [2.39]
Following Equation 39, identical net rotation can be achieved many different ways. The 𝑘
NÕ

net rotation 𝜃(𝑘) can achieved with an excitation 𝜌(𝑘)𝛥𝑡 time as long with field strength 𝐵/𝜌(𝑘), or
with an excitation
ÐN
[Þ()
long with field strength 2𝜌(𝑘)B. 𝜌(𝑘) represent a degree of freedom which is
exploited with VERSE. I.e. VERSE allows each sample to be independent and exploits the trade-off of
time and amplitude to produce a facsimile pulse with redistributed pulse area. Let the new set of
VERSE facsimile pulses be
𝑏
#
(𝑘)=𝜌(𝑘)𝐵
#
(𝑘) [2.40]
and
𝑔(𝑘)=𝜌(𝑘)𝐺 [2.41]
Consider intuitively how VERSE will affect a sinc-shaped RF pulse. This pulse is peaked at the
middle. VERSE will lower the amplitude in the middle and extending its duration, while raising the
amplitudes of the side-lobes and shortening their duration. This redistributes the pulse area to and
decreases SAR while keeping the amplitude and net rotation the same.
Now consider how VERSE will lower SAR in this new facsimile pulse, where the middle has
been slowed down and attenuated, while the side lobes have been accelerated and amplified. SAR is
the energy delivered during an RF pulse, which is proportional to the integral of squared magnitude
of the RF. For a piecewise constant variable-rate RF pulse,
𝑆𝐴𝑅 ∝ ∑ Î𝑏
#()
Î
[
𝑡(𝑘)
³
Á#
= ∑
Îy
`(à)
Î
]
N()
³
Á#
[2.42]
Facsimile pulses can be formed by minimizing SAR, minimizing duration, and by using
parametric optimization. The minimum-SAR facsimile pulse would be of constant magnitude, unless
the VERSE gradient violates the maximum gradient constraint. For a minimum-SAR gradient, a limit
for each sample would have to be set and solved for iteratively:
𝑔(𝑘)=min½𝐺
%
,
u
|y
`
()|
À [2.43]

MRI Background - Basic RF Pulse Design 23
The minimum-time facsimile pulse can be described in terms of the duration of each 𝑘
NÕ

sample
𝑡(𝑘)=𝛥𝑡max½
{
{
ãäP
,
|y
`
()|
y
ãäP
À [2.44]
The parametric optimization facsimile pulse can account for gradient slew-rate constraints.
This formulation guarantees smooth gradient waveforms while minimizing SAR. An example of
parametric SAR minimization that uses a Gaussian-shaped gradient waveform is:
𝑔(𝑘) = 𝐺
%
å1−𝛼𝑒
^¾^
æ
]
¿
]

ç [2.45]
Figure 2.13 shows experimental slice profiles for the original 180 degree pulse, minimum-SAR
pulse, minimum-time pulse, and the parametric optimized pulse. After finding VERSE facsimile pulses,
these pulses must be uniformly resampled for practical scanner implementation. In addition,
gradients may need smoothing to not exceed slew-rate limitations.

Figure 2.13: Here are the experimental slice profiles
for the original 180º pulse (a), VERSE minimum-SAR
formulation (b), VERSE minimum-time formulation
(c), and the VERSE parametric optimized formulation
(d). It can be seen that all profiles produce a
frequency profile of similar quality. Figure adapted
from Connoly et al (25).

VERSE has great potential to reduce the power of a pulse but is very sensitive to off-resonance
effects. Whereas a standard RF pulse off-resonance experiences a slice shift, the sensitivity of a VERSE
pulse to off-resonance varies with time. This is due to the varying ratio between gradient strength
and magnitude of field inhomogeneity. This can lead to a corrupted slice profile as shown in Figure
2.14.
a)
c)
b)
d)
MRI Background - Advanced RF pulse Design 24

Figure 2.14: RF excitation to VERSE is sensitive to off-resonance. While off-resonance of slice-selective
excitation causes a shift in the center of the excited slice, VERSE causes more complicated effects. This
sensitivity changes with the rate of variation in the slice-select gradient waveform. Three example gradient
waveforms are shown in (a) along with their corresponding frequency profiles at 200 Hz off resonance. It can
be seen that higher rates-of-change in the gradient correspond to higher degradation in the frequency profile.
Figure adapted from Connoly et al (25).

2.3 Advanced RF pulse Design
2.3.1 Multi-band RF pulses
Multiband (MB) RF pulses are composed of a
complex sum of single-band RF pulses with different
phase offsets (resulting in different resonant
frequencies). When used with an excitation gradient,
they excite more than one slice at the same time. When
MB pulses are used for imaging, it is called simultaneous
multi-slice (SMS) imaging. SMS imaging uses these MB
pulses together with parallel imaging to simultaneously
image multiple slices with a significant reduction in
acquisition time and little SNR penalty.
A multiband pulse 𝐵
#M
(𝑡) can be described as the multiplication of a single-band RF pulse
𝐵
#²
(𝑡) with a sum of complex exponentials 𝐷(𝑡)
𝐵
#M
(𝑡)=𝐵
#²
(𝑡)⋅𝐷(𝑡) [2.46]
Here, 𝐵
#²
(𝑡) is proportional to the inverse Fourier Transform of the slice profile 𝑀(𝜔), i.e. it
determines the slice profile,
𝐵
#²
(𝑡)∝𝐹𝑇
^#
{𝑀(𝜔)} [2.47]
a) b)
MB RF pulses are composed of a complex
sum of single-band RF pulses with
different phase offsets. In the most basic
formulation, peak 𝑩
𝟏
(𝒕) increases
linearly with MB factor. As MB factor
increases, peak amplitude and/or SAR
limitations may be exceeded unless more
advanced formulations are considered.
MRI Background - Advanced RF pulse Design 25
Often 𝐵
#²
(𝑡) is sinc or hyperbolic secant shaped. 𝐷(𝑡) is often comprised of a sum of complex
exponentials to replicate the pulse at different locations 𝑧
I
for a given gradient amplitude 𝐺
vv
, i.e. it
determines the slice position. A basic formulation is
𝐷(𝑡)= ∑ 𝑒
Ix{
||
(
Ú
N
I
[2.48]
In this formulation, peak 𝐵
#
(𝑡) increases linearly with the number of simultaneously excited
slices, or MB factor. As MB factor increases, the peak amplitude of the RF amplifier may be exceeded
and/or total pulse power may surpass SAR limitations.
Design of MB pulses can be difficult. The simplest way to lower peak RF amplitude and reduce
SAR is to increase the duration of the RF pulse while keeping time-bandwidth product and flip angle
the same to ensure the same profile. This is not ideal, especially for applications with high MB factors,
for sequences that are sensitive to off-resonance effects, or for pulses so long that non-negligible T2*
decay occurs during the pulse.
In theory, 𝐷(𝑡) can be formed with any N arbitrary waveforms at arbitrary slice positions
through complex summation, as long as each pulse is consistent with the slice select gradient.
Established methods to reduce peak RF pulse amplitude include time and phase shifting of the
overlapping pulses. Power scaling and reduction techniques include VERSE and PINS excitation
(VERSE was discussed in Section 1.2.4). These techniques limit RF power deposition by dynamically
adjusting the slice-selection gradient (26).
One elegant method of reducing peak 𝐵
#
(𝑡) is through optimized phase scheduling. This
method strategically adds phase 𝜙
I
to each component of 𝐷(𝑡) corresponding to different slice
locations 𝑧
I
using a function to minimize peak 𝐵
#
(𝑡). 𝐷(𝑡) can be expressed as
𝐷(𝑡)= ∑ 𝑒
I(x{
||
(
Ú
Nz ê
Ú
)
I
[2.49]
Optimal 𝜙
I
was found for 3 to 16 bands and was reported by Wong et al (27). Figure 2.15
illustrates multiband pulses with the basic formulation (blue) and with optimized phase scheduling
(green).

Figure 2.15: example of a 3-band pulse with equal slice
spacing, with the basic formulation (blue) and with
optimized phase scheduling (green). The real and imaginary
components of each pulse are shown in solid and dashed
lines, respectively. The basic formulation produces a real RF
pulse while the optimized phase scheduling produces a
complex RF pulse with lower peak amplitude.

MRI Background - Advanced RF pulse Design 26
2.3.2 Velocity Selective RF pulses

Flow encoding (FE) gradients encode
information about velocity, acceleration, or higher
derivatives of motion. The most common FE gradient is
a bipolar velocity-encoding gradient consisting of a pair
of gradients with equal area and opposite polarity
(Figure 2.16a). The bipolar velocity-encoding gradient
is used in arterial spin labeling techniques and in phase-
contrast angiography, in which both the speed and the
direction of flow or motion along the gradient direction can be mapped.

Figure 2.16: Bipolar velocity encoding gradient (a) and associated phase accumulation of static and moving
spins over time. (a) A bipolar velocity-encoding gradient consists of two gradient lobes of equal area and
opposite polarity. (b) The phase accumulation of spins during a bipolar gradient is plotted for two locations,
𝑥
#
and 𝑥
[
, where 𝑥
#
is closer to the gradient isocenter. Phase accumulation is linear when the gradient is on,
from 𝑡 =0 to Δ𝑡 and from 𝑡 =𝑇 to 𝑇+Δ𝑡. Spins at 𝑥
[
are farther from gradient isocenter and experience
higher phase accumulation. Static spins experience zero phase accumulation after the bipolar velocity encoding
gradient, as phase accumulation during the first lobe is unwound during the second lobe. If a spin moves from
𝑥
#
to 𝑥
[
during the time interval between the lobes, a net phase accumulation is produced (dashed line). Figure
adapted from (28).
Phase accumulation is linearly proportional to the gradient area under one of the lobes, the
temporal separation of the lobes, and the velocity along the direction of the gradient. The first
moment of velocity-encoding waveforms is derived from the moment expansion of the phase of a
spin isochromat:
𝜙(𝑡)=𝛾∫ 𝐺(𝑢)𝑥(𝑢)𝑑𝑢 =𝛾¾𝑚
"
𝑥
"
+𝑚
#
𝑣
"
+⋯+
#
!
𝑚

¾
L
ï
%
LN
ï
¿
NÁ"
+⋯¿
N
"
[2.50]
!
Δ#
Δ#
$
%
Area &
(a)
(b)
'
(
'
)
*
Static spins:
Zero phase accumulation
Moving spins (e.g. '
)
to '
(
):
Net phase accumulation
* =,&!-
t
t
Bipolar gradients produce a phase
linearly proportional to velocity. They
are used to encode flow information.
Fourier velocity-encoding methods allow
parameters analogous to pixel size and
FOV to be defined and utilized to create
precise velocity-selective profiles.
MRI Background - Advanced RF pulse Design 27
where 𝑚

is the nth gradient moment, and 𝑥
"
and 𝑣
"
are initial displacement and velocity of the spin
isochromatic, respectively, along the direction of the gradient.
Velocity-selective waveforms are typically designed to null 𝑚
"
so that it does not select
spatial locations. The first moment of the bipolar gradient waveform in Figure2.16a is:
𝑚
#
= ∫ −𝐺
"
𝑡𝑑𝑡+ ∫ 𝐺
"
𝑡𝑑𝑡 =
{
_
[
(−Δ𝑡
[
+(𝑇+Δ𝑡)
[
−𝑇
[
)=𝐺
"
Δ𝑡
\zðN
NÁ\
ðN
NÁ"
[2.51]
The total area under the bipolar waveform is 0, and so 𝑚
#
is independent of temporal origin.
Letting area A=𝐺
"
Δ𝑡 be the area of an individual gradient lobe, 𝑚
#
=𝐴𝑇. Combining these equations
and selecting only the velocity term, the phase shift 𝜙 =𝛾𝐴𝑇𝑣 is obtained (Figure 2.16). Although
the first moment equation was derived for rectangular lobe shapes, it is a general result regardless
of the shape of the bipolar waveform’s lobes.
Fourier velocity-encoding methods (29) allow for velocity profiles to be designed using
similar techniques as those used for traditional slice selection. With these methods, parameters
analogous to the pixel size and FOV for standard imaging can be defined. Because the discrete Fourier
transform is used to reconstruct velocity-encoded imaging, the basic relationship between k-space
step size Δ𝑘
p
and pixel size Δ𝑣 still applies
Δ𝑘
p
Δ𝑣 =
#
³
[2.52]
Where N is the number of total velocity-encoding sub-pulses used in the discrete Fourier
transform. Quantities such as the velocity FOV and pixel size can be obtained by replacing the
gradient area (zeroth moment) by the first moment in expressions in the phase Taylor expansion
equation.
This basic VS pulse design suffers from a shift in velocity profile as a function of off-resonance
(Figure 2.17). 180
∘
pulses can be used around bipolar gradients to minimize off-resonance effects
and concomitant phase errors (30). Both lobes of the bipolar gradients are often placed on the same
side of the 180
∘
pulse to avoid artifacts introduced by 𝐵
#
inhomogeneity.
MRI Background - Advanced RF pulse Design 28

Figure 2.17: (a) Example of a bipolar velocity-encoding waveform and (b) it’s corresponding velocity profile
as a function of off-resonance. This velocity selective RF pulse (a) consists of a series of sub-pulses flowed by
bipolar gradients. The sub-pulse envelope is proportional to the Fourier transform of the velocity profile. The
velocity profile (b) shifts with off-resonance. This off-resonance sensitivity can be reduced with additional
inversion pulses. Figure from (30).

2.3.3 Common Challenges
MRI pulse sequences depend on accurate
production of RF waveforms for precise excitation.
Common challenges in RF excitation include sensitivity
to off-resonance and b1 variation. Certain areas of the
body experience higher variation than others. For
example, draining veins around the myocardiaum and
the air-tissue interface between the heart and lung
produce large range of off-resonance across the heart.
This varies from subject to subject, and variance is around ±125 Hz. In addition, the positioning of
the heart incurs ~50% b1 variation (31). RF pulses designed for any application must consider B0
and B1 field variations across the intended target tissues.
In addition to field variations, some pulses utilize rapidly changing gradient fields. Rapidly
changing gradient fields are subject to being played imperfectly and can cause eddy currents, which
are unwanted induced electrical currents. These create additional time-varying gradients and shifts
in the main magnetic field, producing artifacts in resulting images. Velocity selective excitation, for
example, utilizes flow-encoding bipolar gradients. If a sufficient delay is not added after these bipolar
gradients, eddy currents produce undesirable artifacts (30,32).
Common challenges in RF excitation
include sensitivity to off-resonance and
b1 variations. In more advanced
applications, other effects become
apparent, such as eddy current effects in
velocity selective excitation and amplifier
distortion in multi-band RF excitation.
MRI Background - Advanced RF pulse Design 29
Another challenge in RF excitation comes from nonlinear effects due to amplifier distortion.
RF pulses with a high peak 𝐵
#
(𝑡) and rapid RF supply current changes which can push the RF power
amplifier, incurring nonlinearity and incidental phase modulation. This leads to incorrect RF
transmission and imperfect excitation, leading undesirable effects (33). For example, multiband RF
excitation can suffer from system nonlinearities because they typically have high peak 𝐵
#
(𝑡) and
rapid current oscillations (34).
Nonlinear distortion on a multiband RF pulse results in undesired higher harmonics to be
excited in the frequency domain. This equates to spuriously excited side-lobes in the slice-select
direction. These higher harmonics have the same slice spacing as the desired slices, but appear with
only a few percent of the signal of the main lobe, causing undesirable artifacts in the reconstructed
image. In other words, these side-lobes will alias into the reconstructed images. The undesired band
signal may be so small that it is hard to notice in the reconstructed images. However, this may be a
confounding factor for further analysis of multiband images, especially for quantitative applications.
The best way to visualize signal from undesired side-lobe excitation in a multiband pulse is
by acquiring a slice profile of the excited volume. From there, side-lobe energy and max side-lobe
intensity are useful metrics to determine how much unwanted signal can alias into reconstructed
slices. Side-lobe signal in a slice profile is best visualized on a logarithmic scale, as depicted in Figure
2.18.

Figure 2.18: (A) shows an example of RF envelope nonlinearity, measured using a pick-up coil (black) as
compared to a desired pulse (blue, dashed). The error between measured and desired pulses can be added to
the desired pulse to form a predistored pulse (green, dashed). The measured predistorted pulse (red) is then
closer to the desired pulse. (b) shows the frequency profile without (black) and with (predistortion), showing
that undesired excitation of higher harmonics is reduced from <4.43% to <0.87%. Figure from Zhu et al (34).
a)
b)
Cardiac Arterial Spin Labeling - Advanced RF pulse Design 30

Transmitted RF nonlinearity can be directly measured using a pick-up coil. A simple pick-up
coil can be created by taking a coaxial cable, stripping off the shielding to expose the copper core, and
forming the copper core into a loop. The pickup coil can then wound around a choke and plugged into
an oscilloscope. The modulated RF waveform can be measured with adequate sampling period. After
lowpass filtering, the RF waveform can be measured to within 2% error using the simple setup shown
in Figure 2.19. There are other methods for RF measurement, such as the Gradient Reversal
Approach to Evaluate RF (GRATER) (35). This will be discussed in subsequent chapters. A popular
metric for evaluating the accuracy of the transmitted RF envelope is simply through Normalized Root
Mean Square Error (NRMSE).

Figure 2.19: An established method for measuring RF pulses is through the use of an external pick-up coil. This
coil can be wound around a choke and transmitted RF can be sampled with an oscilloscope. The waveform must
then be demodulated, low-pass filtered, and time and phase adjusted for comparison with the desired RF
envelope.
3 Cardiac Arterial Spin Labeling
Arterial spin labeling (ASL) MRI technique for measuring tissue perfusion in an organ. It has
been demonstrated in the brain, kidney, and heart. ASL works by labeling arterial blood and imaging
the labeled blood after it has perfused the organ of interest. ASL offers several benefits and
drawbacks compared to other techniques.
ASL is a promising technique because it does not use ionizing radiation or exogenous contrast
agents. Because of this, it causes no known side effects, and so it is useful in applications where
repeated measurements of tissue perfusion are needed (e.g. for long term monitoring). For
Cardiac Arterial Spin Labeling - Arterial Spin Labeling (Brain first, then heart) 31
comparison, first-pass MRI uses gadolinium to detect brain perfusion abnormality and angiography
is an invasive, ionizing technique used to examine blood vessels.
Quantification is also a strength for ASL; allows absolute quantification of tissue blood flow
and arterial transit time with simple post-processing algorithms. Although it is still a developing
technique, reproducibility of ASL has been determined in brain and kidney MRI (36). The
reproducibility of ASL measurements are expected because the labeling pulses create a perfectly
reproducible bolus close to the imaged region.
ASL also has several disadvantages. First, perfusion signal is 1-4% of the background tissue
itself and so ASL has intrinsically low SNR. Many of ASL’s other disadvantages may be solved with
further development. Current ASL protocols require a minimum acquisition time of 3 minutes and
have limited spatial resolution. In addition, there is a variety of available techniques, and a “winner”
must be adopted to standardize the technique. The best labeling, imaging, and post-processing
techniques have been recommended for brain ASL (37), however the best solutions remain an active
area of research for cardiac ASL (38).

3.1 Arterial Spin Labeling (Brain first, then heart)
Brain ASL has developed to the point where a
consensus document has been provided to recommend
protocols for commercial platforms. Cardiac ASL,
however, is still in development. The success of brain
ASL provides both motivation and a toolbox of
techniques for cardaic ASL. Several factors make direct
application of the brain ASL consensus non-ideal and
the optimized labeling, imaging, and post-processing
methods are current areas of research for cardiac ASL (38).

1. Tissue blood flow is 2-7x higher in the myocardium compared to the brain, depending on stress
conditions, resulting in a stronger ASL signal.

2. The path that blood travels to perfuse the myocardium is more complicated than in the brain.
Perfusion signal needs to be labeled in an area without pulsatile flow and without spurious
tagging of the heart. This influences scan timing and the selection of labeling geometries.

3. The heart is also moving rapidly and blood flow is highly pulsatile. This requires labeling and
imaging methods that are synchronized to the cardiac cycle. Imaging is typically performed
Many techniques have been developed
for labeling, imaging, and post-
processing in brain ASL. A consensus has
been reached on the best available
methods in brain ASL. Cardiac ASL is still
in development and direct adaptation of
the consensus for the brain is not ideal.
Cardiac Arterial Spin Labeling - Current Implementation 32
during quiescent periods, end-systole and mid-diastole. ECG-triggered acquisition and breath
holding is most widely used. Post-processing image registration and motion tracking using a
navigator are also available in reduce motion error.
4. SNR efficiency is ~3.5x lower in the heart compared to the brain. This is mainly due to the greater
distance between receive coils and heart than in the brain. This SNR penalty increases with
subject size.

5. 𝑇
#
and 𝑇
[
are different in the heart than in the brain. This affects SNR efficiency, which is already
low in ASL, and so imaging must be optimized separately for the heart.

3.2 Current Implementation
Zun et al implemented cardiac ASL in the heart
using a pulsed ASL (PASL) labeling technique called flow
alternating inversion recovery (FAIR) and balanced
steady-state free precession (bSSFP) imaging (39).
Cardiac gating and breath-holding was used to reduce
motion between scans. 6 pairs were taken to increase
SNR of ASL signal. Quantification was based on the
model by Detre et al (40).

Compared to other available labeling techniques PASL has lower SNR and poorer labeling
efficiency because labeled spins experience 𝑇
#
decay before leaving the labeling region. PASL is used
mainly in cardiac ASL, however, because the complex geometry of the heart makes it difficult to use
a labeling pulse with a localized labeling plane. FAIR is the most commonly used PASL technique. In
FAIR, a slice selective inversion pulse is used to invert signal in the myocardium during a control
acquisition. In a following acquisition a global inversion pulse is used to invert all signal during a
tagged acquisition. The signal difference in the myocardium between control and tagged images is
proportional to myocardial blood flow this is described visually in Figure 3.1.
The current implementation of cardiac
ASL uses FAIR labeling and bSSFP
imaging. FAIR labeling acquires control
image with a myocardium-selective
inversion and a tagged image with a
global inversion. Myocardial blood flow is
then proportional to the difference
between control and tagged images.
Cardiac Arterial Spin Labeling - Current Implementation 33

Figure 3.1 FAIR labeling technique consists of a control and labeled acquisition. (A) Control acquisition
consists of a slice selective inversion pulse and imaging during the next heartbeat. After allowing time for
magnetization to return to equilibrium, a following acquisition occurs. Labeled acquisition consists a global
inversion pulse and imaging occurs during the next heart beat. (B) The signal difference in the myocardium
between control and labeled images is proportional to myocardial blood flow.

Quantification of cardiac ASL is based on a signal intensity difference method developed by
Detre, who modified the Bloch equation to include blood flow. Letting 𝑓 be perfusion, 𝜆 be a
coefficient describing water exchange between the blood and myocardium, and 𝑀

be the
magnetization from inflowing blood. Then, the longitudinal magnetization can be described as

LM
U
LN
=−
M
U
^M
_
\
`
+

ô
𝑀

−

ô
𝑀
(
[3.1]
With FAIR labeling, 𝑀

is essentially inversion recovery signal, i.e. 𝑀

=2𝑀
"
𝑒
^
mõ
m
`
, where TI
is the inversion time. Let 𝑇
#
=
#
\
`
+𝑓/𝜆 represent the apparent change in 𝑇
#
associated with
perfused signal. Assume myocardial and blood 𝑇
#
are identical and 𝑓 ≪ 𝜆. Solving Equation 3.1,
𝛥𝑀 =2𝑀
"
𝑓𝑇𝐼𝑒
^\±/\
`÷¶øøù
[3.2]
This equation allows for direction subtraction of image pairs to detect changes in myocardial
blood flow as long as heart rate variations are minimal between acquired image pairs (< 4 bpm) (41).
a)
b)
Cardiac Arterial Spin Labeling - Unmet needs 34
3.3 Unmet needs
Physiological noise, or the variance of MP from
individual control and labeled pairs, is an important
metric to consider when using ASL MP quantification. In
practice, physiological noise can be caused by very small
amounts of cardiac or respiratory motion between
scans. High physiological noise can corrupt ASL signal,
which is only 1-4% of background tissue. It is these
unresolved sources of physiological noise that limit
sensitivity of cardiac ASL. Do et al (42) found that
shortening the imaging window through parallel imaging reduced physiological noise at the cost of
expected SNR loss. Background suppression may reduce physiological noise. An example background
suppression scheme is depicted in Figure 3.2.

Figure 3.2: Background suppression (BGS) sequence consists of a saturation pulse followed by one or more
non-selective inversion pulses. They have the potential to suppress background signal without suppressing
perfusion signal. In the above example, perfusion imaging consists of 1) labeling, 2) a saturation quadruple-
inversion BGS module, and 3) imaging. Figure from Maleki et al (43).

Many heart disease patients do not show symptoms at rest. Instead, patients must undergo
“stress” testing and myocardial blood flow must be evaluated across the whole heart. Stress testing
often involves the use of pharmacologic agents such as adenosine and regadenosin, to cause
vasodilation of the blood vessels. Peak vasodilation is limited 3 minutes in the body. Current cardiac
ASL techniques measure MP in only one slice during 3 minutes of scan time. To evaluate ischemic
disease, MP must be measured in all coronary territories by using at least 3 slices. The use of
accelerated acquisition schemes like simultaneous multislice imaging or undersampled 3D
acquisition may allow for whole heart coverage without increased scan time. Recommended
coverage according to the American Heart Association (10) is shown in Figure 3.3.
The sensitivity of cardiac ASL must be
increased by reducing physiological
noise. Cardiac ASL coverage must be
increased to detect coronary artery
disease and inform treatment decisions.
Sensitivity to transit delay is one of the
largest potential sources of error in the
ASL quantification.
Cardiac Arterial Spin Labeling - Clinical Justification 35
Finally, transit delay is one of the largest potential sources of error in quantification of
perfusion using ASL (11). It is assumed that tagged blood will reach the myocardium after 1-2
heartbeats. In certain diseases this time may change. Disease processes with slow coronary flows,
such as heart failure (12) or circuitous coronary collateral vascularization (13), can exhibit prolonged
transit delay (14). When transit delay becomes too long, loss of ASL signal occurs and MBF is
underestimated (15). Transit delay insensitive labeling is desirable for myocardial ASL and can be
achieved through velocity selective labeling (11).

Figure 3.3: The American Heart Association recommends covering 16 segments in the heart in the basal, mid
and apical short axis views of the heart as well as in the apex of the long axis view.

3.4 Clinical Justification
Coronary artery disease (CAD) is responsible for 1/3 of deaths in Americans over the age of 35,
or about 500,000 deaths every year. It leads to a decreased quality of life for 13 million Americans
(44). Coronary artery disease is diagnosed through evaluation of contractile function, patency of
coronary arteries, and myocardial perfusion (MP). Myocardial perfusion imaging refers to a group of
imaging methods used to evaluate MP for detection of CAD.
MP imaging techniques include SPECT, PET, and first pass perfusion MRI. SPECT is most widely
used, with 10 million scans every year in the United States. SPECT is limited by poor spatial resolution
and ionizing radiation. PET provides higher spatial resolution and improved quantitation, however
it is not widely available, is more expensive, and provides ionizing radiation.
Cardiac MR stress perfusion is increasingly being used identify CAD (4), and several studies have
shown superiority of cardiac MR stress perfusion to both SPECT imaging (4,45–47) and contrast
Cardiac Arterial Spin Labeling - Clinical Justification 36
stress echocardiography (47), suggesting that invasive coronary angiography could have been
avoided in many patients (45,46). Cardia MR stress perfusion is limited by unresolved artifacts, inter-
observer variability, and contrast agents (48).

The current MP imaging techniques carry risks for patients due to ionizing radiation or
contrast agents. Contrast agents are not tolerated well in patients with kidney disease (7,49). There
is an estimated 610,000 Americans with end stage renal disease (ESRD) and 26 million Americans
with chronic kidney disease. ESRD prevalence is on the rise, with an annual growth rate of 3-4% in
the US (7,49). Patients with ESRD are at over 10 times higher risk of cardiovascular mortality than
patients with normal kidney function, and require annual assessment of heart disease (50). Most
patients undergo testing with either SPECT imaging or stress echocardiography. Patients with
abnormal stress findings subsequently undergo invasive coronary angiography procedures to
identify CAD. ESRD patients receive significant cumulative radiation exposure from SPECT imaging
(51,52). SPECT imaging can result in doses of 10 to 25 mSv per study, and a cumulative effective dose
of >50-100 mSv (53). Cancer and CAD are the leading causes of death in ESRD patients and radiation
from medical imaging could be an under-recognized risk factor in these patients (54). A safe,
contrast-free myocardial perfusion stress test could have a significant impact on management of
these patients.
The proposed test has the potential to be significantly cheaper than all existing myocardial
perfusion stress tests. It is expected to require 30 minutes of MRI scan time and will not require
contrast agents. The Medicare reimbursement rate for nuclear stress testing and stress MRI with
contrast is ~$1,000 per scan. Myocardial ASL-MRI stress testing could qualify as a stress MRI without
contrast material with a reimbursement of ~$300 per scan (a reduction by $100 per study over stress
echocardiography, and by $800 per study over both SPECT and gadolinium stress MRI). Facility fees
vary by hospital and geographic region, but the myocardial ASL technique could be less expensive
than gadolinium-perfusion stress Cardiac MR due to these upfront savings. Several European studies
have shown that perfusion stress CMR is cost-effective for the diagnosis of CAD when compared to
SPECT and stress echocardiography (55,56), and similar outcomes are plausible in the US.
Myocardial ASL-MRI has the potential for broader impact beyond stress testing. Early brain ASL
focused on qualitative functional mapping, much like this study is focused on perfusion reserve
mapping. Brain ASL evolved into a quantitative technique that measures several hemodynamic
parameters. Similarly, myocardial ASL can evolve to enable new tests, including but not limited to 1)
Simple Method for RF pulse measurement using Gradient Reversal - Introduction 37
characterization of microvascular disease (common in women and diabetics), 2) identification of
coronary vascular territories and collaterals, 3) identification of myocardial scar, and 4) continuous
monitoring of myocardial perfusion during stress.
In summary, many patients undergo cardiac stress testing to diagnose or monitor heart disease.
Current testing is limited in frequency due to ionizing radiation and/or risks associated with contrast
agents. The goal of the myocardial ASL project is to develop a new, safer testing option for patients
who require frequent monitoring, such as those suffering from kidney disease.
4 Simple Method for RF pulse measurement using Gradient
Reversal
4.1 Introduction
MRI pulse sequences depend on accurate production of RF waveforms for precise excitation.
Pulses with a high peak transmit radiofrequency magnetic field (B1+) and rapid fluctuations in their
RF supply current can push the RF power amplifier to its limits, causing amplifier nonlinearity and
incidental phase modulation (33,34,57). This leads to an incorrectly transmitted RF envelope and
imperfect frequency profile, which can lead to undesirable effects in several advanced MRI
applications (58). For example, distortions of multi-band RF pulse envelopes can excite additional,
unwanted side-lobes and introduce errors in the separated, desired slices (34,59). Second,
distortions of RF pulses used in Hydrogen MR spectroscopy can lead to incorrect metabolite
concentration quantification as distorted water suppression pulses saturate signal outside the
expected bandwidth (60). Third, distortions of RF pulses used in hyperpolarized Xenon lung imaging
can prevent excitation of Xenon inside vessels and tissues, and instead excite the 50-fold larger gas-
phase magnetization pool (61). Due to increasing demand for higher fields, transmit array technology,
and more complex excitation waveforms (62), accurate control of the RF field is now more necessary
than ever.
Recent work has focused on improving the linearity of RF excitation by measuring the RF
envelope to create a new waveform that corrects for expected nonlinearity. For example, Stang et al.
(63,64) utilized a Vector Iterative Predistortion (VIP) method to iteratively detect and correct errors
in RF transmit behavior in four parallel transmit channels until the detected RF converged to the
expected RF. Several groups have utilized forms of Cartesian feedback (CF), namely frequency-offset
Simple Method for RF pulse measurement using Gradient Reversal - Theory 38
CF, to linearize coil current in multi-coil transmit arrays through a negative feedback loop that
corrects for transmit amplitude and phase error (62,65–67). Recently, Zhu et. al (34) presented a
simple and elegant approach to correct for envelope distortion. This method uses an external pickup-
coil placed in the scanner bore to measure RF and processes the acquired data offline to determine
the actualized envelope in relation to the programmed envelope. This method requires less hardware
and processing and has been demonstrated using single-channel transmit in a real RF pulse. The
aforementioned methods can all minimize amplifier distortions, but at the cost of extra hardware,
synchronization, and processing to measure actualized RF waveforms.
In this paper, we present a fast and simple method to measure RF waveforms without the
need for extra hardware and synchronization. The proposed Gradient-Reversal Approach to Evaluate
RF (GRATER) involves 1) excitation in the presence of a gradient and 2) immediate signal acquisition
in the presence of an inverted gradient along the same axis. GRATER relies on the scanner’s intrinsic
hardware and software to obtain the RF envelope by filtering and demodulating the RF signal. We
demonstrate in phantoms and in-vivo the ability of GRATER to quickly and easily capture RF
waveforms and compare measurements to the “gold standard” pick-up coil (PUC) method (34).

4.2 Theory
Figure 1 shows the GRATER pulse sequence for RF measurement with an optional outer
volume suppression (OVS) pre-pulse (68). A constant gradient used during RF excitation is inverted
during signal reception to acquire a time-reversed version of the RF pulse; the rationale follows.

RF Excitation with Constant Gradient
Assuming a uniform object along the axis of an applied gradient and the small tip-angle
approximation, the transverse magnetization M(τ,r) can be described at time τ after the RF pulse is
played to select slice z. Here, M(τ,r) is proportional to the phase accumulated over the duration of
the gradient with amplitude G to select slice z (i.e., ω(G,r) =γGz), multiplied by the inverse Fourier
transform of the angular frequency ω1(s) at frequency ω(G,r) (see Equation 4.1):
𝑀(τ,r)∝ 𝑒
^Iü({ ,s)Y
∫ 𝑒
Iü({ ,s)v
𝜔
#
(𝑠)𝑑𝑠
Y
vÁ"
[4.1]
The angular frequency ω1(s) is a function of the Larmor frequency γ and the RF pulse B1(s),
i.e. ω1(s) = γ B1(s).

Simple Method for RF pulse measurement using Gradient Reversal - Theory 39
Signal Reception with Inverted Gradient
Using the small-tip approximation, GRATER signal is defined as SGR(t), where t = 0
corresponds to the beginning of the readout gradient with amplitude –𝐺. Here, SGR(t) is proportional
to the inverse Fourier transform of the Magnetization at the frequency which corresponds to phase
accrual during the readout gradient −𝜔(𝐺,𝑟)= 𝛾(−𝐺)𝑧. Phase terms ∆𝜔(𝑟) and R2
*
(r) are added to
account for off-resonance and transverse relaxation rates, respectively (see Equation 4.2):
𝑆
{~
(𝑡)∝ ∫ ∫ ∫ 𝑀(𝜏,𝑟)𝑒
^I2^r ({ ,s)4N
𝑒
^I∆r (s)N
𝑒
^~
]
∗
(s)N
( ' %
𝑑𝑧𝑑𝑦𝑑𝑧 [4.2]
Assuming the object is uniform in x and y, off-resonance is minimal (𝛥𝜔(𝑟)≈0), and R2
*
effects are
minimal (𝑅
[
∗
(𝑟)≈0), Equation 4.2 can be simplified:
𝑆
{~
(𝑡)∝ ∫ 𝑀(𝜏,𝑟)𝑒
^I2^r ({ ,s)4N
(
𝑑𝑧 [4.3]
The GRATER Signal
Inserting Equation 1 into Equation 3, terms can be grouped such that the GRATER signal is
proportional to the integral of the RF pulse with respect to s, multiplied by integrals of exponential
terms with respect to s and z. These exponential terms can be regrouped and Fourier transformed
with respect to z to obtain a time-reversed, time-shifted impulse function. Finally, the sifting property
can be applied to the integral of the product of the RF pulse and impulse function to obtain an
expression for the GRATER signal SGR(t) in terms of the RF pulse B1(t) and readout time 𝜏 (also slice-
select time):
𝑆
{~
(𝑡) ∝𝐵
#
( 𝜏 −𝑡) [4.4]
From Equation 4.4, it can be seen that 𝑆
{~
(𝑡) is proportional to a time-reversed version of
the RF pulse. Therefore, the signal 𝑆
{~
(𝑡) can be used to measure the RF waveform under the
assumptions stated above.
For in-vivo applications, we anticipate that a sufficiently large homogenous region can be
found such that an outer-volume suppression (OVS) pulse

can be used eliminate signal from
neighboring regions, allowing for a reasonable RF measurement to be made in-vivo. The OVS pulse
shown in Figure 1 is the design by Smith and Nayak (68), and includes a B1

-insensitive non-selective
tip-down followed by a cylindrical tip-up pulse. This suppresses signal outside of a cylinder with a
diameter of 5 cm. In addition, the GRATER pulse sequence is shown in Figure 1. Note that the Fourier
transform of 𝑆
{~
(𝑡) gives a slice profile measurement in the small tip angle regime. Therefore,
simultaneous multi-slice (SMS) pulses must be excited so that each slice contributes equal signal for
an accurate GRATER measurement. In addition, any spurious sidebands must be within the sample
volume to be detected by the GRATER method, as illustrated in Figure 2.

Simple Method for RF pulse measurement using Gradient Reversal - Theory 40

Figure 1: GRATER RF measurement consists of an (A) optional OVS pre-pulse and (B) GRATER with a simulated
asymmetric RF pulse B1(t). The OVS pre-pulse (14) consists of a +90° BIR-4 tipdown, a -90° spiral tipback pulse,
and a gradient spoiler. GRATER consists of B1(t) in the presence of a constant gradient followed by signal
acquisition in the presence of the same gradient, inverted. The received GRATER signal SGR(t) (red) is a time-
reversed version of B1(t) (blue). (C) OVS and a slice-selective B1(t) excite volume with a single coil. SGR(t) is then
acquired with the same coil.

Simple Method for RF pulse measurement using Gradient Reversal - Methods 41

Figure 2: Cartoon of excited slices from a 5-band SMS RF pulse in a spherical phantom. The Fourier transform
of 𝑆
{~
(𝑡) gives a slice profile measurement in the small tip angle regime. (A) If a GRATER measurement is
obtained, artifacts will result from unequal signal contribution from each band (purple). (B) If an OVS+GRATER
measurement is taken, each band will contribute equal signal but SNR will be lower. (C) If waveform distortion
is present, undesired bands can become excited (purple, hashed) and must be contained within the imaging
volume to be detected.

4.3 Methods
Experiments were performed on a GE HD23 3T scanner using the body coil. The number of
samples in the GRATER waveform was either matched to the programmed waveform or doubled by
halving the GRATER readout gradient amplitude (RGA) and extending the readout duration. This
allowed for easy comparison of measured vs. expected (programmed) waveforms. Echo times were
minimized to mitigate R2
*
effects. RF waveforms were simultaneously measured using GRATER and
an external pick-up coil, then adjusted as described in subsequent subsections.
Accuracy of GRATER was explored under near-ideal and non-ideal conditions. To explore
GRATER and OVS+GRATER under ideal conditions, experiments were performed on a variety of small
Simple Method for RF pulse measurement using Gradient Reversal - Methods 42
flip-angle pulses in a uniform sphere phantom. Accuracy of the OVS+GRATER measurements were
determined for different numbers of averages. GRATER adjustment parameters were compared for
waveforms acquired on the same day.
To explore GRATER under non-ideal conditions, GRATER was first evaluated with large flip
angles in a uniform sphere phantom and compared to Bloch simulation of GRATER waveforms.
Second, GRATER was evaluated in non-uniform imaging volumes using GRATER and OVS+GRATER
measurements in a fat-water (FW) phantom and in-vivo.
PUC measurements were considered the “gold standard” measurement method, and was
compared to the GRATER measurement method. Normalized root mean square error (NRMSE) was
calculated between programmed and measured waveforms. Raw GRATER data, raw PUC data, code to
adjust measured waveforms, and code perform Bloch simulations of GRATER measurements are available
(69), Repository: https://github.com/usc-mrel/GRATER; Release v1.2:
https://doi.org/10.5281/zenodo.831849.

GRATER Measurements
If the number of points in the measured GRATER waveform 𝑆
{~
(𝑡) was twice that of the
programmed waveform 𝑆
}ÿ
(𝑡) by halving RGA and extending the readout duration, then 𝑆
{~
(𝑡) was
first decimated with a Chebyshev Type 1 IIR filter of order 12.
Measured 𝑆
{~
(𝑡) were adjusted for a scale factor 𝐴, average relaxation rate 𝑅
[
∗
, average off-
resonance 𝛥𝑤, initial-phase angle 𝜙, and sub-sample time-shifts 𝑡
"
by solving a bounded minimum-
norm least squares (MNLS) problem. 𝑆
}ÿ
(𝑡) was used as a reference, assuming RF amplifier
distortion is not present and thus not concealed. 𝐴 captures proton density, transmit efficiency, and
receiver gain.
The GRATER waveform was modeled as a distorted, time-reversed version of the
programmed waveform:
𝑆
{~
(𝑡)≈𝐴𝑒
^~
]
∗
N
𝑒
^I(ÐrN zê)
𝑆
}ÿ
(𝜏− 𝑡−𝑡
"
) [4.5]
The adjustment parameters were estimated according to:
𝑃∈{𝐴,𝑅
[
∗
,𝛥𝜔,𝜙,𝑡
"
} [4.6]
𝑃 =min
}
$𝐹
^#
% 𝐹% 𝐴𝑒
^~
]
∗
N
𝑒
^I(ÐrN zê)
𝑆
}ÿ
(𝜏−𝑡−𝑡
"
)&𝑒
^
U
N
_
&−𝑆
{~
(𝑡)$
[
[
[4.7]
Parameters were bounded to prevent unreasonable estimates: 𝐴>0, 0.2<𝑅
[
∗
< 1000 1/𝑠,
−2𝜋600< 𝛥𝜔 <2𝜋600 𝑟𝑎𝑑/𝑠, −𝜋 <𝜙 <𝜋, and −10<𝑡
"
<10 𝜇𝑠 . Initial values were 𝐴=
max (𝑎𝑏𝑠(𝑆
{~
(𝑡))/max (𝑎𝑏𝑠2𝑆
}ÿ
(𝑡)4, 𝑅
[
∗
= 1000 1/𝑠 , and 𝑡
"
=0 𝜇𝑠 . Choosing a high
Simple Method for RF pulse measurement using Gradient Reversal - Methods 43
initial 𝑅
[
∗
prevented finding local-minimum solutions of this parameter. Because 𝛥𝜔 and 𝜙 adjusted
complex GRATER data and were more likely to produce local-minimum solutions, 10 equally-spaced
initial values were chosen for these two parameters, and parameters that gave lowest NRMSE were
kept. The GRATER waveform was adjusted as 𝑆
{~ ,Ù
(𝑡):
𝑆
{~ ,Ù
(𝑡) =𝐹
^#
% 𝐹% 1/𝐴 𝑒
~
]
∗
N
𝑒
I(ÐrN zê)
𝑆
{~
(𝑡)&𝑒

U
N
_
& [4.8]
The transmitted RF envelopes in this study were real and so the real part of the adjusted
waveform was compared with the programmed waveform and PUC measurements. Previous
approaches have noted that measurement then predistortion of the real RF pulse is a simple,
sufficient way to reduce undesired higher harmonics (2), and the ultimate intended application of
GRATER is for use with predistortion techniques.

Pick-Up Coil (PUC) Measurements
PUC measurements were demodulated and filtered similarly to the method described by Zhu
et al (34) with the following exceptions. First, the modulated RF data was bandpass filtered to allow
±5 𝑀𝐻𝑧 around the center frequency. Second, the demodulated RF data was low-pass filtered with a
cut-off frequency of 200 𝐾𝐻𝑧. Lowering the range of the bandpass filter and lowering the cutoff
frequency of the low-pass filter reduced noise without compromising the shape of the measured
waveform. Third, a bounded MNLS optimization problem was solved and corrected for amplitude,
timing, and center frequency offsets. This problem was similar to the GRATER bounded MNLS
problem, except that 𝑅
[
∗
≈0.

RF Pulse Design
Table 1 describes the parameters of the RF pulses used in each experiment. Single-band RF
pulses were generated in MATLAB using the function dzrf() from the rf_tools software package
based on (24). The sampling period was 4 μs. Then, the single-band pulse was multiplied by a sum of
complex exponentials, B(t), to create multi-band pulses. The sum followed the form

𝐵(𝑡)= ∑ 𝑒
Ir ({ ,(
Ú
)
I
[4.9]

where 𝑧
I
represents the slice location of an i-band pulse.

Simple Method for RF pulse measurement using Gradient Reversal - Methods 44
Near-Ideal Conditions
Measurements were made in a 27 cm diameter uniform sphere with several multi-band
pulses to demonstrate GRATER in near-ideal conditions. Pulse parameters: 2 ms pulses; 500 points;
TBW=2,4,6, or 8; 2-band with FA=30°, 3-bands with FA=20°, 4-bands with FA=15°, or 5-bands with
FA=12°.
To ensure each excited slice was contained within the 27 cm volume and measurable by
GRATER, and to ensure that signal-producing volume came from the linear region of the gradients to
avoid side-band amplitude weighting, pulses were designed to have slice centers within ±5 cm of the
center of the phantom. Because the different slices in the uniform sphere phantom could contribute
different signal, OVS+GRATER measurements were obtained and compared to GRATER
measurements. To account for limited SNR with a limited excited volume, multiple averages were
obtained and NRMSE was calculated for measurements using averages of 2:2:64 GRATER
measurements. The NRMSE for different averages was fitted according to % 𝑁𝑅𝑀𝑆𝐸 =𝑚/
# 𝑎𝑣𝑒𝑟𝑎𝑔𝑒𝑠+ 𝑏 where A represents the fitted error floor and B represents the rate of error decay.
To measure high-frequencies in the GRATER-measured waveforms, the amplitude of the
GRATER readout gradient was halved to effectively double the sampling period of the GRATER
waveform. Results were compared to measurements obtained with a sampling period matched to the
transmitted waveform.
To assess the consistency of MNLS-determined adjustment parameters, values were
calibrated and compared for each pulse in GRATER measurements using matched RF sampling and
transmit periods.

Non-Ideal Conditions: Large Flip Angles
GRATER measurements and Bloch Simulations of GRATER measurements were compared to
evaluate GRATER outside the small-tip regime (70). To rule out error in GRATER measurements due
to sources other than large flip angles, a uniform sphere phantom was used. A real single-band
(TBW=4) RF pulse with flip angles ranging from 5° to 90° in 5° increments was measured. This simple
pulse was used to isolate and identify the predictable errors in large flip-angle GRATER
measurements from other sources of error.
Bloch Simulations were performed using a sampling period of 4 𝜇𝑠, 𝑇
#
=2000 𝑚𝑠, 𝑇
[
=
200 𝑚𝑠, gradient amplitude 𝐺 =0.733983 𝐺/𝑐𝑚, and z-positions =30:0.1:30 𝑐𝑚. Off-resonance
was assumed to be negligible. After simulating RF excitation in the presence of a gradient, the
magnetization was calculated every 4 𝜇𝑠 for each z-position during a subsequently inverted gradient
Simple Method for RF pulse measurement using Gradient Reversal - Methods 45
to simulate the GRATER measurement. Then, the final GRATER measurement was calculated as the
1D temporal signal averaged over each z-position (i.e. the whole simulated imaging volume).
GRATER measurements and Bloch simulations of GRATER measurements were adjusted by
solving the bounded MNLS problem described above with the programmed waveform, divided by its
maximum amplitude, as reference. This scaling was done to emphasize errors in the shape of GRATER
measurement and Bloch simulation of the measurement. To test the predictability of GRATER
measurement error due to deviations from the small-tip approximation, NRMSE between GRATER
and simulations of GRATER measurements were compared.

Non-Ideal Conditions: Inhomogeneous Objects
To evaluate GRATER in inhomogeneous objects with high off-resonance, a fat-water (FW)
phantom was used to compare RF measurements using 1) GRATER, 2) OVS+GRATER, and 3) the PUC
method in regions containing 1) water only, 2) fat only, and 3) both fat and water. Measurements
were made in a 2-band, 1.28 ms, 320 point, TBW=4 RF pulse with FA=15°. GRATER measurements
were made without averaging and with matched sampling and transmit rates.
To demonstrate GRATER in an in-vivo imaging volume, the same 2-band pulse in the FW
phantom experiments was measured using 1) GRATER, 2) OVS+GRATER and 3) the PUC method in
an axial brain slice above the ventricles in two healthy volunteers (M, 27 and 30). Each subject was
screened and provided written informed consent with approval from the Institutional Review Board.

Expt.

# bands

Dur
(ms)
TBW BW
(Hz)
FA
(°)
Sl Ctr(s)
(cm)
Sl Thk
(cm)
Uniform sphere
(ideal conditions)

2 2 2:2:8 TBW/2e-3 30 ±2.5 1
3 2 2:2:8 TBW/2e-3 20 0, ±3.3 1
4 2 2:2:8 TBW/2e-3 15 ±1.25, ±3.75 1
5 2 2:2:8 TBW/2e-3 12 0, ±2.5, ±5 1
Uniform sphere
(large FA)
1 1.28 4 3125 5:5:90 0 1
FW & in-vivo 2 1.28 4 3125 15 ±2.5 1
Table 1: Summary of RF pulse parameters used in a uniform sphere, fat-water (FW) phantom, and in-vivo
experiments: number of excited bands (# bands), duration (Dur), bandwidth per band (BW), time-bandwidth
product (TBW), flip angle (FA), slice center (Sl Ctr), and slice thickness (Sl Thk).

Simple Method for RF pulse measurement using Gradient Reversal - Results 46
4.4 Results
Near-Ideal Conditions
GRATER measurements were made in a variety of pulses using the uniform sphere phantom.
NRMSE of GRATER measurements increased for higher numbers of bands and time-bandwidth
products in Figure 3A. Higher error comes from unequal signal contribution from each excited band
and is described in Figure 2. For example, the waveforms matched most closely in the 2-band, TBW
= 2 RF pulse, where GRATER vs. programmed and PUC vs. programmed waveforms had 1.1% and
0.9% NRMSE, respectively. NRMSE was highest in the 5-band, TBW = 8 RF pulse, where NRMSE
between GRATER vs. programmed and PUC vs. programmed waveforms had 6.1% and 2.1% NRMSE,
respectively. To lower NRMSE in GRATER, two strategies were shown to be helpful: 1) averaged
OVS+GRATER measurements and 2) lowering RGA and extending the readout duration to acquire
more points in the GRATER-measured waveform.
Figure 3A shows lower NRMSE with 64 averaged OVS+GRATER measurements vs. 64
averaged GRATER measurements. The biggest improvement was seen in the 5-band, TBW = 8 RF
pulse with 3.8% reduction in NRMSE from 6.1% 2.4%. Over the 16 RF pulses with parameters
described in Table 2, mean ± standard deviation of NRMSE was 4.4±1.7% NRMSE for averaged
GRATER measurements and 1.9±0.60% NRMSE for averaged OVS+GRATER measurements.
Furthermore, the clear trend of higher NRMSE for higher numbers of bands and higher TBW product
in GRATER measurements is not seen in OVS+GRATER measurements. For comparison, mean ±
standard deviation was 1.5±0.30% NRMSE with the PUC method.
Figure 3B shows improvement with lowered RGA as a function of number of averaged
OVS+GRATER measurements in the 5-band, TBW = 8 RF pulse. Over 64 averages, NRMSE decreased
from 2.4% for RGA = -G to 1.5% NRMSE for RGA = -G/2. After fitting the curves of NRMSE vs. #
averages to the equation % 𝑁𝑅𝑀𝑆𝐸 =𝑚/# 𝑎𝑣𝑒𝑟𝑎𝑔𝑒𝑠+ 𝑏 the fitted error floor b decreased from
1.9% to 0.9% NRMSE for RGA = -G and RGA=-G/2, respectively. Furthermore, the fitted rate of error
decay m increased from 3.7% to 4.2% NRMSE for RGA = -G and RGA = -G/2, respectively.

Simple Method for RF pulse measurement using Gradient Reversal - Results 47

Figure 3: NRMSE of uniform sphere experiments for SMS pulses with different numbers of bands (# bands)
and time-bandwidth (TBW) products. (A) NRMSE for 64 averaged GRATER and OVS+GRATER with RGA = -G,
the negative excitation gradient amplitude. GRATER NRMSE was higher with more slices and was reduced with
OVS to ≤2.4% (black dashed line) by up to 3.8% (red arrow). NRMSE in PUC was ≤2.1%. (B) NRMSE decreases
with averaging of OVS+GRATER in a 5 band, TBW=8 pulse for RGA=-G. It decreases more and faster for RGA=-
G/2. Data was fitted to % 𝑁𝑅𝑀𝑆𝐸 =𝑚/# 𝑎𝑣𝑒𝑟𝑎𝑔𝑒𝑠+ 𝑏 (solid lines). Fitted error floors are shown (arrows).

Figure 4 visualizes the best-measured improvement of the 5-band, TBW=8 RF pulse by
combining both strategies of 64 averages of OVS+GRATER combined with RGA=-G/2 to lower NRMSE.
GRATER measurements without OVS, PUC measurements, and the programmed waveform are
shown for comparison. Figure 4A shows that the errors in GRATER measurement are most
prominent in the high-frequency peaks and valleys of the RF lobes, due to the unequal signal
contribution for each of the 5 bands. This error is greatly reduced with OVS. The difference between
measured and the programmed waveform are also shown in Figure 4B. There is clear structure to
the difference waveform of GRATER without OVS. This structure is reduced with OVS however the
cause of the remaining structure is unresolved.
Simple Method for RF pulse measurement using Gradient Reversal - Results 48

Figure 4: GRATER using a 5-band, TBW=8 RF pulse in a uniform sphere. (A) A (black) programmed RF pulse
was measured using (black) PUC, and 64 averages with RGA = -G/2 of (blue) GRATER, and (cyan) OVS+GRATER.
The zoomed-in lobes in the GRATER waveform show error from unequally excited bands and can be seen more
clearly with the difference between waveforms in (B). Compared with programmed waveforms and PUC,
GRATER matches with <5.7% NRMSE and <1.5% with OVS+GRATER. There is structure in the difference
between programmed and OVS+GRATER measurements (arrows) and the source of this error is unresolved.

Table 2 is shows the consistency of MNLS-determined adjustment parameters determined
for each of the 16 SMS RF pulses in GRATER measurements using matched RF sampling and transmit
periods, all acquired during the same scan session. Pre-scan was run once for these experiments and
CV was low for 𝐴. The calculated 𝑅
[
∗
values were all larger than the phantom’s true 𝑅
[
of 33 1/sec.
With a good shim, 𝛥𝜔 ≈0 in all cases. 𝑡
"
was consistent to within 7.1% CV. Of the adjustment
parameters, 𝜙 varied the most from scan to scan.

Simple Method for RF pulse measurement using Gradient Reversal - Results 49
# bands, TBW

𝑨 (a.u.) 𝑹
𝟐
∗
(𝟏/𝒔) 𝚫𝝎 (rad/s) 𝝓 (rad) 𝒕
𝟎
(𝝁𝒔)
2,2 .69 100 -0.0022 -0.15 -0.62
2,4 .68 110 -0.0023 -0.15 -0.60
2,6 .68 130 -0.0027 -0.13 -0.63
2,8 .67 140 -0.0032 -0.11 -0.63
3,2 .69 86 -0.0023 -0.15 -0.72
3,4 .70 90 -0.0025 -0.14 -0.66
3,6 .69 97 -0.0031 -0.11 -0.56
3,8 .68 110 -0.0036 -0.09 -0.60
4,2 .68 110 -0.0025 -0.13 -0.63
4,4 .68 110 -0.0030 -0.11 -0.57
4,6 .67 130 -0.0032 -0.10 -0.56
4,8 .66 140 -0.0030 -0.12 -0.67
5,2 .69 100 -0.0025 -0.12 -0.66
5,4 .68 100 -0.0024 -0.14 -0.66
5,6 .68 120 -0.0029 -0.12 -0.62
5,8 .66 140 -0.0060 -0.01 -0.68
MEAN .68 110 0.0030 -0.12 -0.63
CV (%) 2.8% 16.3% 30% 28% 7.1%
Table 2: Summary of adjustment parameters for GRATER waveforms without OVS or averaging in uniform
sphere experiments in the same scan session with the same pre-scan. Parameters were solved with a bounded
MNLS problem for pulses with different numbers of bands (# bands) and time-bandwidth (TBW) products. The
bottom two rows show the mean and coefficient of variation (CV) for each parameter value. CV was low for 𝐴.
Calculated 𝑅
[
∗
values were larger than the phantom’s 𝑅
[
of 33 1/sec. With a good shim, 𝛥𝜔 ≈0 in all cases. 𝛥𝜙
varied from scan to scan. 𝑡
"
was consistent to within 7.1% CV.

Simple Method for RF pulse measurement using Gradient Reversal - Results 50
Non-Ideal Conditions: High Flip-Angles
Figure 5 shows results of high flip-angle experiments in Bloch simulations of GRATER
measurements and experimental GRATER measurements, plotted over the same range to emphasize
the shape of the GRATER measurement compared to the programmed waveform. Both plots show
the programmed RF pulse as a reference in dashed-cyan. RF pulses with flip angles ≤40° are plotted
in blue, 45-65° in green, and ≥70° in red. This demonstrates that GRATER measurement error
increases for increasing flip angles. GRATER-measured and Bloch-simulated measurements matched
to <2.4% for each flip angle pair. This implies GRATER measurement error occurred in a patterned,
predictable way.

Figure 5: (A) Experimental GRATER measurements and (B) Bloch simulations of GRATER measurements of a
single-band RF pulse in a uniform sphere phantom with flip angles in 5° increments from 5° to 90°, adjusted so
the programmed pulse, divided by its maximum amplitude, was used as reference. Measurements with a small
flip angle (5°£FA£40°) are shown in blue, in-between flip angles(45°£FA£65°) in green, and large flip angles
(70°£FA£90°) in red. NRMSE between GRATER measurements and simulations for a given flip angle was <2.4%.
Top row shows the total waveform. The boxed-off portions are shown in the bottom row, zoomed.

Simple Method for RF pulse measurement using Gradient Reversal - Results 51
Non-Ideal Conditions: Inhomogeneous Objects
Figure 6 compares RF measurements of a FW phantom using GRATER, OVS+GRATER, and
the PUC method to evaluate GRATER in inhomogeneous objects with high off-resonance. The imaging
slice is shown without OVS in Figure 6A where ‘F’ and ‘W’ represent fat and water, respectively. The
imaging slice is shown with OVS in Figure 6B to demonstrate the ability of the OVS pulse to select a
5 cm diameter region. Figure 6C shows the programmed 1.28 ms, 320 point, 2-band, and TBW=4 RF
pulse in black, the PUC method in red, and the OVS+GRATER measurement in dashed black.

Figure 6: GRATER in a fat-water phantom. The imaging slice (A) without and (B) with OVS. ‘F’ and ‘W’ in (A)
represent fat and water, respectively. (C) A (black) programmed 1.28 ms, 320 point, 2-band, and TBW=4 RF
pulse was measured using (green) PUC and (magenta) OVS+GRATER. NRMSE was <6.4% between
programmed, PUC, and OVS+GRATER measurements. OVS+GRATER is a time-reversed measurement (see
Equation 4.2); noise increases towards the end of the measurement (arrow).

Figure 7 compares RF measurements in two healthy subjects using GRATER, OVS+GRATER,
and the PUC method. Figure 7A shows an axial slice above the ventricles was excited in the brain for
GRATER measurements. Figure 7B shows an excited 5 cm cylinder in the center of the axial slice to
avoid off-resonance at the brain-skull interface. Figure 7C shows measurements of a 1.28 ms, 320
point, 2-band, and TBW=4 RF pulse against the programmed waveform. The PUC, GRATER, and
programmed waveform all matched to <3.0% difference. The PUC and OVS+GRATER waveform
matched to <4.5%.
Simple Method for RF pulse measurement using Gradient Reversal - Results 52

Figure 7: GRATER in the brain of one volunteer. The imaging slice (A) without and (B) with OVS. An imaging
slice was chosen superior to the ventricles. Measurements of a 1.28 ms, 320 point, 2-band, and TBW=4 RF pulse
using 1) the PUC method and 2) the OVS+GRATER method are plotted against the programmed waveform in
(C). PUC, GRATER, and programmed waveforms match to <3.0% NRMSE. OVS+GRATER vs. PUC had <4.5%
NRMSE.

Figure 8 summarizes NRMSE values for FW phantom and in-vivo experiments. There was
<1.5% difference in PUC vs. programmed measurements. PUC vs. GRATER measurements differed by
58% in the fat+water of the FW phantom and <12% NRMSE in all other cases. PUC vs. OVS+GRATER
measurements differed by <6.4% NRMSE in the water of the FW phantom and in the brain. While
OVS+GRATER vs. PUC had lower NRMSE than GRATER vs. PUC in the FW phantom, an OVS pre-pulse
increased NRMSE of GRATER measurements in the brain. Mean NRMSE in inhomogeneous objects of
PUC vs. programmed was 1.2±0.2%, PUC vs. GRATER was 17±25%, and PUC vs. OVS+GRATER was
5.1±1.1%.

Simple Method for RF pulse measurement using Gradient Reversal - Discussion 53

Figure 8: NRMSE of experiments in non-uniform samples: the fat-water (FW) phantom, subject 1 (S1), and
subject 2 (S2). NRMSE was calculated between the PUC method and 1) the programmed waveform, 2) the
measured GRATER waveform, and 3) the measured OVS+GRATER waveform. PUC vs. GRATER had 58%
NRSME in fat+water. OVS improved the accuracy of GRATER to 6.4%. PUC vs. programmed waveforms had
<1.5% NRMSE.

4.5 Discussion

This study has successfully demonstrated measurement in a variety of small-tip RF
waveforms to within <2.4% NRMSE using averaged OVS+GRATER measurements in uniform
volumes. It has also demonstrated that acquiring more points in the measured waveform further
lowered NRMSE. In non-uniform volumes, NRMSE <6.4% was achieved using OVS+GRATER without
averaging. A variety of methods to further improve the GRATER technique form the core of this
discussion.
NRMSE was used in this study as a generic metric to describe error between any RF
waveforms or measurements and to establish GRATER’s accuracy under different conditions. NRMSE
may not be the ideal metric for RF pulse correction and application-specific metrics could be more
useful. For example, spurious side lobe excitation may be more appropriate to evaluate SMS-RF
pulses, or stop-band suppression for spectral-editing RF pulses. Regardless of the specific metric, the
accuracy of GRATER would have to match or surpass the accuracy of the PUC method to be a
successful measurement technique and detect subtle RF amplifier nonlinearity. Therefore, it is
important to acknowledge GRATER’s successes and investigate ways to overcome current limitations.
Simple Method for RF pulse measurement using Gradient Reversal - Discussion 54
GRATER and PUC measurements matched very closely in the uniform sphere phantom for
small-flip angle pulses with two bands, such as the 2msec, 2-band, TBW=2 RF pulse. However, error
in GRATER measurements increased in RF pulses with higher numbers of bands due to the unequal
signal coming from each excited slice. These RF pulses may have also contained error that GRATER
was unable to fully capture at the current sampling period of 4 𝜇𝑠 (i.e. readout bandwidth of 125 kHz).
This limitation is best seen the 2 msec, 5-band, TBW=8 RF pulse, where GRATER error is highest on
either side of the main lobe. NRMSE was reduced by 1) using an OVS prepulse to obtain equal signal
from each slice, 2) averaging to overcome the reduced SNR in each slice due to OVS, and 3) lowering
the amplitude and extending the duration of the readout gradient to traverse excitation k-space more
slowly and acquire more points in the GRATER-measured waveform. While the error has been
reduced, the difference between the programmed and best-measured waveform still has structure.
This could be due to the need for an even faster sampling period through a further lowered and
extended readout gradient or increased receive sampling rate. This could also be explained by
imperfect OVS pulse performance.
For measurements in inhomogeneous objects, recall GRATER is a proton-density weighted
measurement. Because of this, GRATER measurements will be best in areas where the excited region
has as uniform proton density as possible. Therefore, error measurement the chosen slices could be
due to signal coming from inhomogeneous tissues, i.e. fine structures in the brain. While one OVS
pre-pulse is demonstrated in this study (14), GRATER in different situations may benefit from
selection of different size volumes. Spectral pre-pulses could also be used, such as a water saturation
pre-pulse followed by GRATER measurement in subcutaneous fat near a receive coil.
OVS+GRATER is a time-reversed measurement and was clearly emphasized in GRATER
measurements with fast signal attenuation in the fat-water phantom and is not likely to be resolved
with averaging. It could be seen that noise in the end of the measurement became more prominent.
To resolve this error, different sections of the RF pulse could be recorded in successive GRATER
measurements, then combined to produce a complete measurement. More signal remained from the
RF measurement towards the end of the OVS+GRATER measurement in the brain than in the FW
phantom. This indicates different 𝑅
[
∗
of the two volumes.
Compared to GRATER, OVS+GRATER more accurately captured RF waveforms in the FW
phantom, but not in the brain. Gains in excited volume uniformity with an OVS pre-pulse were not
enough to offset the decrease in signal-to-noise ratio caused by limiting the region of excited tissue
with an OVS pulse. While OVS+GRATER measurement averaging is a viable option, as demonstrated
in the uniform sphere experiments, adjusting the GRATER excitation and readout gradient
Simple Method for RF pulse measurement using Gradient Reversal - Discussion 55
amplitudes may further reduce NRMSE. If the amplitudes are decreased, slice-thickness and SNR
could be increased in volumes with low signal. However, this may decrease excited sample
uniformity and increase through-slice dephasing. If the amplitudes are increased, errors caused by
erroneous phase in SMS bands due to 𝐵
"
variation will be mitigated by making the excited volume
small in the z direction. In addition, potential amplitude weighting of side-bands due to non-linearity
in the selection gradient, similar to the pile-up artifacts seen in scans with non-linear frequency
position mapping, could be reduced.
The waveforms in this study were designed to establish and evaluate feasibility of the
GRATER method in phantoms and in-vivo, and were not designed to push the RF amplifier into its
non-linear regime. If one is using GRATER to correct for RF amplifier non-linearity, it is of concern
that adjustments relative to the ideal programmed waveform may conceal waveform distortions. The
consistency of adjustment parameters has been demonstrated from scan to scan, and this decreases
concern. So, GRATER recon may be made more efficient by re-using parameters from scan-to-scan.
Despite all of this, comparing or even replacing MNLS-determined adjustment parameters
with sequence-based measurements will be useful in the future. For example, simple pulse sequences
can be used to measure or correct for 𝑅
[
∗
, 𝛥𝜔, and 𝑡
"
instead of estimating them in a bounded MNLS
problem. More specifically, 𝑅
[
∗
, 𝛥𝜔 , and 𝜙 can be measured with an FID. In addition, 𝛥𝜔 can be
measured and corrected for using a 𝐵
"
mapping technique. Also, 𝑡
"
between the GRATER
measurement and PUC waveform can corrected with gradient delays. Finally, to reduce noise in
GRATER using averaging while simultaneously measuring 𝑅
[
∗
, the GRATER read-out waveform can
be repeatedly inverted and data can be acquired during each inversion to acquire multiple GRATER
measurements. These measurements will be weighted with the 𝑅
[
∗
relaxation rate. Timing errors
would likely occur with reverse polarity readouts, and so other adjustment parameters, especially
𝑡
"
, would have to be calculated for each readout.
Finally, GRATER may be useful for predistortion with large imaging volumes and small flip-
angle RF pulses, such as short SMS pulses with a high number of bands that push the RF amplifier
into its non-linear region. For large flip-angle pulses, it has been demonstrated that GRATER
measurement error and Bloch simulation of GRATER measurement error increased as the flip angle
increased from 30
T
to 90
T
and that GRATER measurement error was predictable by simulation.
While GRATER’s potential for RF measurement has been demonstrated, its applicability for use with
predistortion techniques is a topic of future work, both in small and large flip-angle RF pulses.

Simple Method for RF pulse measurement using Gradient Reversal - 56
4.6 Conclusion
In conclusion, GRATER is a promising new technique for RF envelope measurement.
Compared to the traditional pick-up coil technique, GRATER is fast, requires no hardware, and no
synchronization. GRATER measured the 2-band, TBW = 2 RF pulse accurately compared to the PUC
method under ideal conditions. Including OVS pre-pulses, averaging measurements, and acquiring
more points in the GRATER waveform were shown to increase accuracy for pulses with higher
numbers of bands and TBW. In large flip angles, GRATER measurement error occurs in a way that is
predictable by Bloch simulation. In non-uniform volumes, an OVS pre-pulse may select a uniform
region and improve GRATER measurements. GRATER may be useful in pre-scan calibration, and for
measurement and pre-compensation of RF amplifier nonlinearity.

Iterative correction of RF envelope distortion with GRATER-measured waveforms - Introduction 57
5 Iterative correction of RF envelope distortion with GRATER-
measured waveforms
5.1 Introduction
Magnetic resonance imaging (MRI) depends on accurate production of RF waveforms for
precise excitation. RF pulses with a high peak radiofrequency (RF) transmit field and rapid
fluctuations in supply current can push the RF subsystem to its limits, leading to RF transmit
imperfection (34,58). This can lead to undesirable effects in several advanced MRI applications,
including spurious side-lobe excitation in simultaneous multi-slice imaging (33,34). A precise
excitation profile is especially important for SMS balanced steady-state free precession (bSSFP)
imaging. bSSFP imaging necessitates short duration, high flip-angle (FA) RF pulses that are more
likely to incur RF transmit imperfection and produce spurious side-lobe excitation. Spuriously
excited side-lobes are often subject to low FA excitations. If this side-lobe is in the stop-band of the
bSSFP off-resonance profile, it produces high signal intensity (71). These extra excited slices can alias
into desired slices after reconstruction, producing high signal intensity artifacts with structures from
unwanted excited side-lobes.
Predistortion techniques have been developed to improve the fidelity of RF excitation by
measuring the RF envelope to create new waveforms that correct for expected nonlinearity
(34,62,63,65). These methods require extra hardware, synchronization, and processing to measure
transmitted RF waveforms. Recently, the Gradient-Reversal Approach to Evaluate RF (GRATER) was
introduced as a fast and simple way to measure RF pulses without extra hardware or synchronization
(35). GRATER involves 1) excitation in the presence of a gradient and 2) immediate signal acquisition
in the presence of an inverted gradient along the same axis. GRATER was combined with an outer-
volume suppression (OVS) pre-pulse (68) to ensure equal excited signal along the slice-select
direction and produce measurements with <2.4% error in a variety of small FA multiband pulses.
GRATER, however, had not been used to facilitate predistortion.
In this work, we present a method for iterative correction of RF imperfection with GRATER-
measured waveforms. We show that predistorted waveforms can correct for transmission
imperfection in a variety of multiband pulses. Finally, we demonstrate improved image quality with
predistorted 3-band bSSFP cardiac imaging.

Iterative correction of RF envelope distortion with GRATER-measured waveforms - Methods 58
5.2 Methods
Experiments were performed on a clinical 3T MRI Scanner (HD23, GE Healthcare, Waukesha, WI).
GRATER measurements were obtained with the body coil, centered about a
60x10x10 cm
:
rectangular phantom. Final RF waveforms were produced after 40 iterations of
GRATER-based predistortion. Forty iterations were used to experimentally demonstrate
convergence. SMS bSSFP images were acquired in phantoms and in-vivo using an 8-channel cardiac
coil.

Predistortion Technique

RF excitation was improved by correcting for expected errors in transmitted waveforms.
Figure 1 illustrates iterative GRATER-based predistortion using a flow-chart. GRATER
measurements were performed with the readout gradient amplitude set to half the negative slice-
select gradient amplitude; twice the number of RF resolution points were then acquired in the
GRATER-measured waveform. This excitation and readout pair took 3.2 ms. The raw measured data
was then processed in MATLAB in <2 seconds and a new predistorted waveform was created. The
next iteration of predistortion would then begin a total of 10 s after the previous measurement.
Iteration time was set conservatively at 10 seconds to ensure complete T1 relaxation between
measurements. GRATER measurement averaging and OVS were not used. The waveform was
corrected for off-resonance, T2
*
decay, time-shift, scaling, and initial phase angle calculated during
the first iteration. Scaling and time-shift were calculated and updated each iteration. Computation
time for an in-house MATLAB implementation was reduced to <2 seconds (compared to <7 seconds
in Ref. (35)) by setting the initial guess for initial phase angle as the difference between the mean of
the phase angle of the desired waveform and the raw GRATER data.

Iterative correction of RF envelope distortion with GRATER-measured waveforms - Methods 59

Figure 1: The proposed predistortion method consists of a series of GRATER-measurements 𝑅
I
and creation
of predistorted waveforms 𝑇
Iz#
until a certain stopping criterion is met, for example, based on a performance
threshold and/or a maximum number of iterations. Predistortion consists of 1) determining error 𝐸 between
desired waveform 𝐷 and 𝑅
I
and 2) adding a weighted version of 𝐸 to the previously transmitted waveform to
create a new predistorted waveform.

Evaluation: Predistortion Technique and Subsequent RF Performance

GRATER-based predistortion was used to measure a variety of multiband pulses with
different damping factors 𝛼 in a uniform rectangular phantom. RF pulses were tested with multi-
band (MB) factors MB=3,4,5 and slice thicknesses to spacing ratios (STR) STR=2,4. These pulses were
designed using the Shinnar-Le Roux algorithm (59) with 648 𝜇s duration, 324 point resolution,
FA=30
∘
(MB=4,5) or FA=42
∘
(MB=3), and optimized phase scheduling (27). In subsequent
experiments, GRATER-based predistortion was performed with 𝛼 =0.25 to prevent over-shooting
the solution (72).
Experiments performed without and with low-pass filtering of the predistorted waveform
to demonstrate impact of filtering to improve data quality and facilitate convergence. The low-pass
filter had a cut-off frequency of ±80 kHz. GRATER measurements before predistortion were also
examined to determine feasibility of using a scanner-specific distortion function for RF predistortion.
Quality of predistortion was assessed using root mean square error between desired and
measured waveforms, normalized with respect to the L2 norm of the desired waveform (NRMSE).
Improvement in excitation was evaluated with slice profile measurements, and the mean signal from
the largest side-lobe was reported. The slice profile was obtained by acquiring multiple GRATER
start
T
1
= D
i = 1
t
end
GRATER
transmit T
i
measure R
i
performance
E = D – R
i
stop?
no yes
predistortion
T
i+1
= T
i
+⍺E
i = i + 1
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Methods 60
measurements with 15 phase-encodes each along x and y. A 1 sec pause was used between
measurements to allow for sample relaxation. 648 waveform points were acquired in each GRATER
measurement. A long TR was used with phase encoding to ensure sample relaxation between TRs
(phantom T1 was 200 ms). The inverse Fourier transform was then taken and signal was discarded
except at the center of the phantom. In this way, a frequency profile is obtained along an area with
uniform signal.

Evaluation: SMS bSSFP Imaging

SMS bSSFP images were acquired in phantoms and in-vivo. Imaging parameters include
TR=3.2, TE=1.5, FA=42
∘
, and per-slice matrix size=96x96. Twelve seconds of dummy acquisitions
were performed before imaging to establish steady-state. An MB=3, STR=4 pulse was used before
and after predistortion to demonstrate differences in image quality. In-vivo images were obtained in
a healthy volunteer (F, 28) after screening and providing written informed consent with approval
from the Institutional Review Board.
A phantom of ABS bricks (LEGO) with a different pattern every 2 cm deep was submerged
in water and imaged to indicate aliased signal from extra excited slices. 3-band bSSFP imaging was
performed with full-gradient encoding (FGE), center-to-center slice spacing=20 mm, and slice
thickness=5 mm. Eleven slices were encoded about the 3 excited slices using kz-gradient encoding
(57). This experiment was performed with and without predistorted waveforms to demonstrate
differences in encoded side-lobe signal. The same 3-band experiment was repeated with an added z-
shim to create a spatial variation in frequency along the z-axis and illustrate low-flip angle, off-
resonant bSSFP imaging (i.e. to demonstrate the need for precise excitation with SMS bSSFP imaging).
This 3-band pulse was again evaluated in-vivo and the sequence was adjusted for center-
to-center slice spacing=24 mm and slice thickness=6 mm. 3 short axis slices of the heart were
obtained during diastole using 1) single-slice bSSFP imaging, 2) SMS bSSFP imaging with FGE and 3
encoded slices, and 3) SMS bSSFP imaging with blipped-CAIPI encoding (BCE) (57). Single-slice and
SMS images with FGE were reconstructed using a simple inverse Fourier Transform. SMS images with
BCE were reconstructed using split-slice GRAPPA (73).

Iterative correction of RF envelope distortion with GRATER-measured waveforms - Results 61
5.3 Results
The proposed iterative predistortion technique substantially improved RF transmission in all
6 multi-band pulses that were studied. NRMSE between desired and measured waveforms and side-
lobe signal were reduced after predistortion (Figure 2a). With low-pass filtering of predistorted
waveforms, NRMSE decreased most rapidly over the first 10 iterations and had standard deviation
0.0008<𝜎<0.0042 for subsequent iterations. NRMSE was reduced from <20.1% to <2.7% (Figure
2b). Mean signal from the largest spuriously excited side-lobes were <6.6% and <1.1%, before and
after predistortion, respectively (Figure 2c). The relative improvement was largest in the MB=3,
STR=2 pulse with 41.7-fold reduction in NRMSE and 12.7-fold reduction in mean signal of the largest
side-lobe. Improvement was lowest in the MB=4, STR=4 pulse 4.8-fold reduction in NRMSE and 6-
fold reduction in mean side-lobe signal. For each pulse, the largest spuriously excited side-lobe was
always next to the main lobe. Without low-pass filtering of the predistorted waveforms, NRMSE
diverged after the first 10 iterations in 5 of 6 tested pulses (Supporting Information Figure S1),
hence this filtering step was retained for all subsequent experiments. We observed no direct
mapping between desired and measured waveforms (Supporting Information Figure S2) that
would have allowed a one-step solution.

Figure 2: Multiband pulses were evaluated in pulses with multi-band (MB) factors of 3, 4, and 5 and slice
spacing to thickness ratios (STR) of 4 and 2. (A) NRMSE is shown over 40 iterations of predistortion. NRMSE
decreases over the first 10 iterations then remains within 2.7% of its final value. Before and after predistortion,
(B) NRMSE was <20.1% and <2.7%, and (C) mean side-lobe signal from the largest side-lobe was <6.7% and
<1.1%, respectively. Relative improvement (before/after ratio) is listed on the left column for each pulse.
Relative improvement ranges from 4.8 to 41.7-fold.

B C A
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Results 62

Supporting Information Figure S1: NRMSE between desired and measured waveforms for 1 to 40 iterations
of predistortion, (A) with low-pass filtering of the predistorted waveform, and (B) without low-pass filtering.
Without low-pass filtering, NRMSE steadily increases after iteration 10 in each example except for in the MB=3,
STR=4 pulse.

Supporting Information Figure S2: The real, imaginary, amplitude and phase components of desired and
measured waveforms before predistortion. We observed no direct mapping between desired and measured RF
waveforms. Estimating the gradient is a topic for future research (this has been demonstrated successfully with
gradient nonlinearity corrections (74)). Instead, this paper proposes a pulse-specific method to improve RF
performance.

A B
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Results 63
The slice profile of a MB=3, STR=4 pulse matches the desired profile after predistortion
(Figure 3). Before predistortion, spurious side-lobe signal has similar spacing and width as the main
desired lobes at z=±4, ±6, ±8, and ±10 cm. Side-lobe intensity is highest closest to the main lobes and
decreases with distance from the main lobes. After predistortion, side-lobe signal approaches the
noise floor of 0.3% for frequencies below the cutoff frequency of the predistorted waveform’s low-
pass filter. Side-lobe signal before predistortion is <0.7% for frequencies above this cutoff frequency
and is not significantly reduced after predistortion.

Figure 3: Amplitude and Phase components of MB=3 and STR=4 waveforms (A-B) are shown with their
corresponding excitation profiles (C) using 1) Bloch simulations and the desired waveform, 2) experimental
measurements and the waveform before predistortion, and 3) experimental measurements and the waveform
after predistortion. Excitation profiles are on a log scale to accentuate side-lobe behavior. NRMSE between
desired and measured waveforms is reduced from 7.4% to 0.9% with predistortion. Spurious side lobes are
reduced from <7.6% to <0.32% for frequencies between ±80kHz (the low-pass filter cutoff frequency). This
approaches the noise floor of 0.3%.

Reduction in side-lobe excitation is seen after predistortion in a LEGO phantom with 3-band
bSSFP imaging, FGE, and 12 encoded slices (Figure 4). Before predistortion, encoded image signal
about z=-4 cm was highest with mean/max=6.7%/0.74% compared to the reference image,
respectively. After predistortion, encoded signal approached the level of noise; this is apparent in
both the measured z-profile and the encoded image. In other words, no spurious side-lobe signal was
measured or encoded, indicating an improvement in RF excitation. Signal in the slice at z=4 cm
contains features from the desired reference slice at z=-2 cm, likely due to imperfections in 3D
encoding.
A B C
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Results 64

Figure 4: Phantom with 3-band bSSFP imaging, full-gradient encoding (FGE), and 11 encoded slices (z=-
10:2:10 cm) is shown next to single-band reference slices (row 1) before (rows 2) and after (row 3)
predistortion. Without windowing, 3 excited slices are comparable to the reference slices (±2 and 0 cm) and
there is no visually detectable signal in the extra encoded slices. With windowing, extra excited side-lobes are
seen with features from reference slices (red arrows). After predistortion, extra encoded signal is reduced.
Signal in the slice at z=4 cm contains features from the desired slice at 2 cm (green arrows).

Off-resonant side-lobe excitation was also reduced after predistortion (Supporting
Information Figure S3). The intensity of excited off-resonant signal was highest before
predistortion in slices at z=4 cm (mean/max signal: 33.5%/103.0% of main lobes). After
predistortion, encoded signal was reduced to mean/max signal: 4.2%/10.98%). After predistortion,
residual signal contained features from the desired slices about z=-2 cm as well as the side-lobe at
z=4 cm.

Supporting Information Figure S3: Phantom with 3-band bSSFP imaging, full-gradient encoding (FGE), 11
encoded slices, and added off-resonance is shown next to single-band reference slices (row 1) before (rows 2-
3) and after (rows 4-5) predistortion. Before predistortion, main lobe signal has different signal intensity
compared to the reference slices and off-resonant side-lobe excitation has higher signal variation than on-
resonant (see Figure 5). Side-lobe signal is reduced after predistortion (red arrows) and residual encoded
signal contains features from the desired slices (green arrows).

-10cm -8cm -6cm -4cm -2cm 0cm 2cm 4cm 6cm 8cm 10cm
REF
FGE
FGE,P
FGE,P x20
FGE x20
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Discussion 65
SMS bSSFP artifacts were reduced after predistortion in-vivo with FGE and BCE (Figure 5);
features in (left to right) basal, mid, and apical short axes slices are discernable after predistortion.
Image quality between reference and SMS bSSFP images with FGE are comparable after predistortion.
Image quality is improved in SMS bSSFP imaging with BCE after predistortion. Additional artifacts
are still present, due to the aggressive acceleration (R=3) with low channel count (8-channel cardiac
array) (75).

Figure 5: Steady-state (left) and transient (right) bSSFP images of the basal, mid and apical short-axis slices of
the heart. Single-slice reference (REF) images are shown next to SMS images with full-gradient encoding (FGE)
and blipped-CAIPI encoding (BCE) before and after predistortion (P). Artifacts due to RF transmit error are
reduced after predistortion in each SMS image with both FGE and BCE (green arrows). Additional artifacts are
still present in SMS images with BCE, due to the aggressive acceleration (R=3) with low channel count (8-
channel cardiac array).

5.4 Discussion
Iterative GRATER-based predistortion improved multiband pulse performance with >12-fold
reduction in NRMSE and >6-fold reduction in max side-lobe signal. Predistorted waveforms were
used with SMS bSSFP imaging to successfully reduce excitation artifacts. This technique could be
especially beneficial for in-vivo SMS bSSFP cardiac imaging. Cardiac muscle has a low T2/T1 ratio
compared to fat and a low relative signal intensity. When off-resonant fat is excited in a spuriously
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Discussion 66
excited side-lobe, it can alias into the myocardium, confounding image quality. This low-flip angle,
off-resonant, high-signal excitation was demonstrated with the added z-shim in lego phantom images
and in-vivo cardiac images. This technique could also be useful in situations where precise excitation
is desirable, including other SMS imaging applications, MR spectroscopy (60), and hyperpolarized
lung imaging (61).
The main advantage of using GRATER-based predistortion is that is doesn’t require any extra
hardware to measure RF envelopes. However, GRATER comes with several disadvantages, including
potential biases due to object non-uniformity, nonlinearity of the excited signal with higher flip
angles, and sensitivity to noise (35). Despite these disadvantages, these experiments demonstrated
significant improvement in RF excitation after predistortion and <2.7% NRMSE. Remaining NRMSE
could stem from inaccuracies in GRATER measurements. The GRATER technique assumes each
excited slice contributes equal signal. It is possible error was introduced into the measurements due
to unintended RF excitation outside the phantom’s volume of 60x10x10 cm
3
. If this is the case,
NRMSE can be reduced by increasing the size of the phantom used for predistortion. It is also possible
that off-resonance introduced error in GRATER measurements. In this situation, averaging
measurements and an OVS pre-pulse could reduce error.
Iterative RF predistortion using a pulse-sequence based RF measurement technique has been
previously demonstrated (76). There are two differences between the Lebsack and Wright work and
our work. First, the previous RF measurement technique uses a spin-echo (SE) pulse, while GRATER
does not. SE introduces some risk of scaling error due to imperfections in the SE pulse. In addition,
SE cannot be used with a short TR and GRATER measurements are substantially faster (10 msec).
Second, the previous iteration scheme compares desired and measured magnetization profiles. A
windowed version of the Fourier Transform of the difference between profiles was taken and scaled
by a damping factor to produce updated RF waveforms. The damping factor changed during each
iteration based on differences between magnetization profiles. This ensured stability of technique.
GRATER-based predistortion utilizes measured and desired RF waveforms directly, does not
dynamically update the damping factor, and stability has been demonstrated in this work.
Forty iterations were sufficient to demonstrate feasibility of GRATER-based predistortion.
NRMSE did not increase after 10 iterations if a low-pass filter was applied to the predistorted
waveform. With 10 seconds per iteration, predistortion of each waveform took almost 7 minutes,
which is needlessly long and not practical for the clinical setting. We expect that 10 iterations with a
repetition time on the order of 2 seconds is more than adequate, and will be practical clinically. This
time can be further shortened using a more sophisticated iteration and stopping criterion. In these
Iterative correction of RF envelope distortion with GRATER-measured waveforms - Conclusion 67
experiments, for example, choosing a stopping criterion as ∆NRMSE<0.1% between iterations, would
have allowed for a solution to be reached within 10 iterations. Other stopping criterion could be to
stop iterative predistortion when a certain NRMSE or spurious side-lobe signal level has been
reached.
The chosen update direction was simply the difference between desired and measured
waveforms in an effort to minimize NRMSE between these waveforms (77). If an approximated
derivative were available for this NRMSE function being minimized, other more sophisticated
schemes could be employed, such as gradient descent. Unfortunately, no clear relationship was
discernable between the distortion in measured RF pulses and desired pulses in this study.
Estimating the gradients is a topic for future research. The current method works with few iterations,
is fast, and is easy to implement. A gradient-based likely would not accelerate convergence compared
to the current implementation but could potentially achieve lower NRMSE.
A limitation of this study is that GRATER-based predistortion was not compared with an
alternative technique such as the pick-up coil approach (34). RF measurements made with GRATER
and the pick-up coil method proved comparable (35), however equivalence in the context of pre-
distortion remains future work.

5.5 Conclusion
This study demonstrates feasibility of iterative GRATER-based RF predistortion as part of an
initial sequence setup to improve image quality in later scans. This could be useful for a wide range
of RF pulses with high peak B1+ and rapid current oscillations that could incur nonlinearity, or with
low-cost RF amplifiers with a limited linearity range. This technique is likely to be critical for SMS
bSSFP imaging at 3 Tesla where short, high flip angle RF pulses are desirable but also likely to
produce side-lobe excitation that can alias back into the desired slices.

Improved Velocity-Selective Labeling for Myocardial ASL - Introduction 68
6 Improved Velocity-Selective Labeling for Myocardial ASL
6.1 Introduction
Myocardial arterial spin labeling (ASL) is a promising non-contrast technique for myocardial
perfusion (MP) imaging. Myocardial ASL with flow alternating inversion recovery (FAIR) labeling
produces MP measurements that are comparable to PET (1) and can detect clinically relevant
changes in perfusion under Adenosine stress conditions (2). The current protocol is limited to a
single mid short-axis slice of the heart. Evaluation of at least 3 short axis slices during rest and stress
is recommended by the American Heart Association to diagnose coronary artery disease and inform
treatment decisions (3). For multi-slice acquisitions, FAIR inversion slab thickness must be increased
to encompass the larger imaging volume. The distance between the labeled edge and imaging slice
will increase as slices are acquired farther from the aortic root. This results in increased sensitivity
to transit delay and potential underestimation of MP (4).
Velocity-selective (VS) labeling would be desirable largely due to its insensitivity to transit
delay; if a proper velocity cut-off (Vc) is chosen, the label signal comes from coronary blood flow
adjacent to myocardium, reducing transit delay effects. Jao et al recently demonstrated VS-ASL with
similar MP compared to FAIR at the cost of 2.8x lower temporal signal-to-noise ratio (TSNR). The
demonstrated VS-ASL technique suffered from two limitations: 1) spurious labeling of moving
myocardium and 2) low labeling efficiency (5). The previous pulse design used a BIR-8 module by
Guo et al (6). This pulse had off-resonance and b1 insensitivity over ±250 Hz and ±50% b1 variation,
respectively, at the cost of decreased labeling efficiency and a wide transition bandwidth between
labeled and unlabeled signal.
Fourier Transform based velocity selective (FT-VS) labeling techniques offer a plethora of
options for velocity selective pulse design. FT-VS pulse design was first documented by Rochefort et
al in 2005 and subsequent research improved upon this original concept (7). The Rochefort design
used a series of sub-pulses and bipolar gradient pairs to encode signal in the velocity domain. The
drawback of this technique is a shift in velocity profile as a function of off-resonance. Shin et al
described how refocusing pulses reduced this shift and improved off-resonance robustness (8). Qin
and Shin et al recently proposed VS pulse design with double refocused pulses and MLEV phase
cycling (9) to further improve immunity to off-resonance (10). The drawback of these techniques
are the presence of VS-stripe artifact in static tissues due to imperfect refocusing of the 0
th
gradient
moment with large b1 variation (>±20%) (11). Finally, Shin and Qin formally characterized the VS-
Improved Velocity-Selective Labeling for Myocardial ASL - Introduction 69
stripe artifact, demonstrated effective suppression through alternate application of phase-shifted VS
preparations along with k-space averaging (12). VS-stripe artifact is not compatible with myocardial
VS-ASL because it can confound ASL signal, which is only 1-4% of background tissue signal. VS phase
cycling is an option to reduce the effects of stripe-artifact in static organs; however, it is not
compatible with myocardial ASL because the heart moves between pairs of control and label
acquisitions, compromising the effectiveness of the averaging step. Although an ideal FT-VS pulse
design does not currently exist for myocardial ASL, these FT-VS design techniques can be explored
and tailored for this specific application.
Compared to the previous BIR-8 pulse (13), an ideal FT-VS pulse for myocardial ASL would achieve
1) inversion over a short duration to increase labeling efficiency, 2) refocusing pulses with MLEV
phase cycling to reduce sensitivity to off-resonance, 3) labeling of flowing blood only to maintain
compatibility with background suppression, and 4) bipolar velocity-encoding gradients to remove
the influence of VS-stripe artifact on ASL signal. In this manuscript, we utilize FT-VS pulse design
concepts to produce pulses specifically for myocardial ASL at 3T that reduce spurious labeling of
moving myocardium and improve labeling efficiency. ASL measurements and physiological noise are
compared in 1) the original implementation of VSASL (13), 2) an implementations of VSASL using
proposed pulses, and 3) FAIR-ASL (15).

Improved Velocity-Selective Labeling for Myocardial ASL - Methods 70
6.2 Methods
Phantom and in-vivo experiments were performed on a 3T whole body scanner (Signa HDxT;
General Electric Healthcare, Waukesha, WI) using an 8-channel cardiac coil receiver array.

VS pulse design
The original VS pulse (VS-Orig) used by Jao et al (13) utilized an adiabatic symmetric BIR-8
pulse design (6). This pulse was optimized for off-resonance and b1 conditions in the heart and had
the following parameters: sub-pulse duration = 2.24 ms, 𝜅 = 62.96, 𝜔
%
= 21.6, and ξ = 20.5. Bipolar
gradients were inserted between the paired refocusing pulses to avoid the striping artifact in label
acquisitions (16,17), and no gradients were used in control acquisitions, imparting T2-weighting only.
Vc is defined under assumptions of laminar flow, where the velocity distribution is uniform from 0 to
twice the mean velocity within each blood vessel. The velocity profile then becomes sinc-shaped and
velocity cutoff is defined as the first zero-crossing of the velocity profile. Vc = 10 cm/s with velocity-
encoding along the through-slice direction gave the best performance and was used in the
experiments.
The design of the proposed VS pulses (VS-Prop) is informed by physiologic velocity ranges
for myocardium and coronary blood during mid-diastole, the cardiac phase when VS labeling is
applied. During this phase, coronary blood velocities are highest and myocardial motion is lowest.
Literature suggests that myocardial through-plane velocities are up to ±3 cm/s during diastole
(18,19). Gorcsan et al reported a range of peak myocardial velocities along the endocardial walls in
healthy subjects and heart disease patients using tissue Doppler imaging (13). From early to late
diastole, the velocity range was 2.90±0.14 cm/s to 1.15±0.74 cm/s in posterior segments, and
2.36±0.69 cm/s to 1.94±0.88 cm/s in anteroseptal segments (18). Movement was less in abnormal
segments of heart disease patients; from early to late diastole, the velocity range was 1.4±7 cm/s to
0.7±0.3 cm/s in posterior segments and was 1.83±0.84 to 0.96±0.53 cm/s in anteroseptal segments.
Simpson et al reported a mean peak longitudinal velocity (motion towards the apex) of -6.5 ± 1.85
cm/s in the mid-short axis of the heart during early diastole in healthy subjects using phase-velocity
mapping, an MRI-based myocardial velocity mapping technique, but was between ±3 cm/s from mid-
diastasis to early systole (19). As previously noted by Jao et al., a VS pulse that labels low velocities
can result in inadvertent labeling of myocardium, substantially increasing physiological noise (13).
The ideal VS pulse will therefore be played during mid-diastasis and label nothing between ±3 cm/s,
while maximally labeling coronary blood.
Improved Velocity-Selective Labeling for Myocardial ASL - Methods 71
Coronary arterial velocities vary between different arteries and between different disease
states. In general, proximal coronary velocities are higher than the distal velocities, and the velocities
in the left anterior descending (LAD) artery are higher than in the left circumflex (LCX) and right
coronary artery (RCA) (20). Peak coronary velocities in healthy individuals and coronary artery
disease (CAD) patients were reported using Doppler Flow wires, and ranged from 49±20 cm/s in the
proximal LAD to 28±8 cm/s in the distal RCA (20–22). Peak coronary velocities in healthy individuals
with adenosine stress were reported from 104±28 cm/s in the proximal LAD and 67±16 cm/s in the
distal RCA (20). The coronary vasodilator reserve, the ratio of stress to rest mean velocity, was 2.3 ±
0.8 in healthy arteries and was 1.6 ± 0.7 in diseased arteries, indicating a reduced stress response in
diseased arteries (20).
In this work, velocity is encoded in the base-apex direction, resulting in potential angle effects.
This means pulses are sensitive to velocity along a single direction, and the encoding velocity is the
actual velocity multiplied by the cosine of the angle between the vessel and the direction of velocity
encoding (23). In this work, we account for up to a 60º angle. We design pulses to label spin within
a velocity range, where the lowest velocity is ½ cos(60°) of the mean minus one standard deviation
of the coronary velocity in the distal RCA. The upper velocity is the mean plus one standard deviation
of the coronary velocity in the proximal LAD. The relevant coronary arterial velocity range for
subjects at rest then becomes 10-70 cm/s along the base-apex direction. This range increases to 10-
130 cm/s when considering both rest and stress conditions.
Pulse design must also consider imaging imperfections. In cardiac MRI at 3 Tesla, the
amplitude of the transmitted RF field (b1) field varies by up to 50% across the myocardium, with a
decreasing b1 scale from the lateral to septal wall (14). There is also substantial off-resonance due
to proximity of the lungs and draining veins. The reported variation is 125±40.6 Hz across the entire
heart at 3T (14,24). This necessitates the need for a VS pulse which is robust to both b1 and off-
resonance variation. In this work, we consider the relevant b1 scale to be 0.5 to 1 and the relevant off-
resonance range to be ±125 Hz. Note that both b1 and off-resonance variation increase with B0 field
strength. This work is performed at 3T, but we would expect these constraints to be relaxed at ≤1.5T
(24) and more stringent at ≥7T (25).
The proposed VS pulse is based on designs by Shin et al and Qin et al, due to their robustness
to off-resonance and b1 variation (8,10), as well as their ability to predictably modify the velocity
profile using FT-VS encoding techniques. Nine sub-pulses are used with double-refocusing and
MLEV-16 phase cycling (9). The velocity-encoding gradients were adjusted to include only bipolar
gradient pairs between the paired refocusing pulses, which eliminates the potential for VS-stripe
Improved Velocity-Selective Labeling for Myocardial ASL - Methods 72
artifact (16,17). Control acquisitions are similar to label acquisitions, except gradients are turned off.
Velocity field of view (FOVv) was chosen to be twice the mean relevant coronary velocity range. Initial
values for the nine sub-pulse amplitudes were designed using the RF Tools toolbox (26). Specifically,
we used a linear-phase inversion design with a time-bandwidth product of 6, assuming no relaxation,
off-resonance, or b1 effects. This initial design was empirically chosen for its ability to minimize
labeling between ±3 cm/s, the range of myocardial motion during stable diastole, while maximizing
labeling between the relevant coronary range. 𝜋 phase was added to alternate sub-pulse amplitudes
to shift FOVv and invert signal in coronary velocities as opposed to static tissues. This allows for
compatibility with background suppression designed for the original VSASL scheme.
Sub-pulse amplitudes 𝒑 were optimized to maximize coronary ASL signal and minimize
labeling of myocardium over a range of parameters 𝚽=(𝑣;Δ𝑓;𝑏
#
), where velocity is represented by
𝑣 =−0.5𝐹𝑂𝑉
p
:0.5:0.5𝐹𝑂𝑉
p
cm/s, off-resonance by ∆f=-125:25:125 Hz, and B1 scale by
𝑏
#
=0.5:0.1:1.0. ASL signal 𝑆(𝚽,𝒑) is defined as the difference between Bloch simulations of
magnetization immediately after the control pulse and after the label pulse (27). Simulations
assumed no relaxation. The cost function, below, was adjusted for two separate settings of
myocardial and coronary velocities: 1) |𝑣|≤ 3cm/s and 10≤|𝑣|≤ 130 cm/s, and 2) |𝑣|≤ 2 cm/s
and 10≤|𝑣|≤ 70 cm/s, respectively. The first setting was chosen to cover the complete range of
velocities found in literature at rest and stress for subjects, while the second setting was chosen in
an effort to maximize ASL signal from coronary arterial blood in healthy subjects at rest at the cost
of relaxing the assumption for a relevant myocardial velocity range. These two terms were weighted
using parameter 𝜆. The cost function is then
𝒑=argmin
𝒑
A−mean
𝚽∈𝚽
𝒃
|𝑆(𝚽,𝒑)| +𝜆max
𝚽∈𝚽
𝒎
|𝑆(𝚽,𝒑)|E, where
𝚽
𝒃
is the set of 𝚽 that includes velocities for coronary arterial blood, and 𝚽
𝒎
is the set of 𝚽 that
includes velocities for myocardial movement during stable diastole. 𝚽 is depicted in Figure 1.
Improved Velocity-Selective Labeling for Myocardial ASL - Methods 73

Figure 6.1: Cartoon representation of Φ, which includes velocities 𝑣 over ±FOVv, off-resonance values Δ𝑓
across ±125 Hz, and RF transmit scaling 𝑏
#
from 1-0.5. Φ
G
∈Φ, where Φ
G
includes only low-velocities
𝑣

anticipated over the myocardium during stable diastole. Φ

∈Φ, where Φ

includes the range of expected
coronary arterial blood velocities 𝑣
G
. 𝑣 represents the velocity vector component encoded along the z-direction.
While this whole space is considered for optimization, later figures only show ASL signal as a function of off-
resonance for a b1=1, and ASL signal as a function of b1 scale for Δ𝑓 =0.

𝜆 allows a tradeoff between maximizing ASL signal from coronary blood flow against
suppression of spurious myocardial signal (higher values suppress spurious myocardial signal, while
lower values maximize ASL signal from coronary blood flow). 𝜆 =10.^(−3:2) were evaluated to
assess the relative importance of weighting myocardial labeling compared to coronary blood labeling.
The final 𝜆 was chosen as the highest 𝜆 where max
𝚽∈𝚽
𝒎
|𝑆(𝚽,𝒑)|<0.02 to allow a low tolerance for
potential spurious labeling of myocardium while maximizing labeling of coronary blood. Maximum
labeling of moving myocardium and mean coronary velocity labeling can be seen as a function of 𝜆 in
Figure 6.2. FT-VS pulse design source code and demo scripts are available
(https://github.com/orgs/usc-mrel/teams/cardiac-asl/velocity_demo) to facilitate FT-VS pulse
designs for other applications.

!
"
#
Δ%
Φ
'
Φ
(
Φ
(
Φ
0.5≤ "1 ≤ 1.0
Δ% ≤125 01
!
'
≤ 3 34/6 10≤ !
(
≤70 34/6 89
10≤ !
(
≤130 34/6
−;<=! ;<=!
Improved Velocity-Selective Labeling for Myocardial ASL - Methods 74

Figure 6.2: The two terms of the pulse optimization cost function, mean blood ASL signal and max myocardial
ASL signal, are shown after optimization, with myocardial signal weighted by 𝜆. ASL signal refers to Bloch
simulations of the longitudinal magnetization immediately after the control pulse minus the label pulse. The
ideal pulse will have blood ASL signal of 2, indicating perfect inversion of coronary blood, and myocardial ASL
signal of 0, indicating no potential to spuriously label moving myocardium. As expected, the curve is monotonic
with different 𝜆. As 𝜆 increases, max myocardial signal decreases, as desired, at the cost of decreased blood
signal. The final 𝜆 is chosen as the largest value which allows <2% max myocardial signal. Mean myocardial
signal is also plotted to show average labeling of myocardial signal <0.1 for 𝜆≥1.

Bloch Simulations
Bloch simulations were obtained of the longitudinal magnetization after the VS-Orig and VS-
Prop pulses using MATLAB (MathWorks, Inc., Natick, MA) over v = ±FOVv cm/s, b1 = 0.5-1, and ∆f =
±125 Hz to observe pulse performance in conditions expected in the heart at 3T, before and after
optimization of sub-pulse amplitudes. In addition, the kv-encoding location was calculated during
each velocity-encoding sub-pulse and was compared to the ∆f = 0, b1 = 1 VS profile before and after
optimization.

Silicone Phantom Experiments
Experiments were performed in a silicone oil phantom (T1/T2 = 1111/227 ms) in order to
determine the proper delay after each bipolar gradient pair and mitigate artifacts from gradient
imperfections. Silicone oil is a suitable substance for evaluating these types of artifacts due to its low
diffusion coefficient and long relaxation times (6,28). A time delay was empirically chosen by
gradually increasing the time delay and evaluating signal difference between center-out GRE images
Improved Velocity-Selective Labeling for Myocardial ASL - Methods 75
acquired immediately after the VS-Prop pulse with FOVv = 80 cm/s. This pulse was used because it
had larger gradients than the VS-Prop pulse with FOVv = 140 cm/s and was expected to incur larger
artifacts. A final delay time was chosen based on the shortest delay with minimal difference signal.

ASL experiments
Five healthy volunteers (2M/3F, age 24-30Y) were scanned in the study and all procedures
were conducted in accordance with protocols approved by Internal Review Board of the University
of Southern California. The VS-BGS scheme described by Jao et al (13) was used with the 1) VS-Orig,
2) VS-Prop (FOVv = 140 cm/s), and 3) VS-Prop (FOVv = 80 cm/s). The FAIR-ASL described by Zun et
al was also used (4). Image acquisition was performed in a single mid short-axis slice using a snapshot
2DFT balanced SSFP sequence (TR=3.2ms, TE=1.5ms, prescribed FA=50
∘
, matrix size=96x96,
FOV=18-22 cm, slice thickness=10 cm, GRAPPA (24 ACS, 60 acquired). Semi-automatic segmentation
of the myocardium was performed (29). For VS-BGS ASL experiments, the timing of the background
suppression pulse was optimized for different heart rates and took into account T2 signal loss from
the respective VS labeling pulses (13,30).
As noted by Jao et al (13) and Zun et al (4), six pairs of control and labeled images were
acquired for myocardial perfusion (MP) and physiological noise (PN) measurements. Each image pair
was acquired with breath holding (10-12 s) to prevent misregistration and to avoid spurious labeling
from respiratory motion. A 6-s delay between image acquisition allowed full recovery between
labeling and imaging. In an additional 2-s breath hold, a baseline image was acquired without labeling
to calculate coil sensitivity maps and a noise image was acquired to calculate the noise covariance
matrix. MP and PN were calculated globally across the mid-short axis slice of the heart in each ASL
experiment. VS-ASL calculations were performed as described previously (13), except that the VS-
prop signal was divided by 2 to account for an inversion of flowing spins and the T2-weighting term
was updated to reflect the duration of the VS-Prop pulses. FAIR-ASL calculations were performed as
described by Zun et al (4). A two one-sided test, or TOST test, was used to evaluate equivalence of MP
values between methods. A t-test was performed to determine whether PN was difference between
methods.

Improved Velocity-Selective Labeling for Myocardial ASL - Results 76

6.3 Results
Figure 6.3 illustrates the proposed pulse (FOVv = 140 cm/s). It has a pulse duration of 74 ms,
which includes a 0.25 ms delay after each gradient pair to reduce sensitivity to gradient
imperfections. These imperfections include eddy currents, and are scanner-specific. We found a delay
of 0.25 ms to be adequate on our system. The proposed pulse is similar to the initial guess with
modified sub-pulse amplitudes. Velocity-encoding sub pulses work together to shape the velocity
profile, and most velocity-selective inversion of spins occurs in the middle sub-pulse of highest-
amplitude.

Figure 6.3: The proposed VSI pulse is designed using Fourier Velocity Encoding techniques to reduce spurious
labeling of moving myocardium and achieve better labeling efficiency. This pulse is ~2x the duration of the
original VS pulse and larger signal loss due to relaxation. 9 20° sub-pulses (blue) achieve velocity-selective
inversion. Hard refocusing pulses (green) utilize MLEV phase cycling to reduce sensitivity to off-resonance.
Labeling of coronary velocities (as opposed to myocardium) is achieved by applying alternating 0 and 𝜋 phase
to each sub-pulse and its subsequent inversion. Bipolar velocity encoding gradients between each RF
component (red) achieve velocity encoding while removing potential for VS-stripe artifact. A 0.25 ms delay
follows each gradient pair to reduce sensitivity to eddy currents.

Figure 6.4 illustrates the reduced labeling of myocardium and improved labeling efficiency
of blood after optimization. ASL signal across myocardial velocities, reflecting potential to spuriously
label moving myocardium, varied over ±2% for 𝑣≠0 cm/s. This is especially apparent as a function
of off-resonance. After optimization, ASL signals across these velocities is substantially reduced. ASL
signal is <0.002 for |𝑣|≤2 cm/s and up to 0.02 for 2<𝑣≤3 cm/s.
Improved Velocity-Selective Labeling for Myocardial ASL - Results 77

Figure 6.4: Bloch simulations of the proposed VS pulse with FOVv =140 cm/s for coronary 10≤|𝑣|≤
130 𝑐𝑚/𝑠 (left) and for myocardial velocities |𝑣|≤3 𝑐𝑚/𝑠 before (top) and after (bottom) optimization of sub-
pulse amplitudes. Bloch simulations are shown for Δ𝑓 =0 and 𝑏1=0.5−1 as well as 𝑏1=1 and |Δ𝑓|≤
125 𝐻𝑧. The VS pulse achieves better labeling efficiency of flowing signal (green regions) after optimization,
especially for different off-resonance values. In addition, it can be seen that the VS pulse allows for less spurious
labeling of moving myocardium (purple regions) after optimization.

Figure 6.5 demonstrates the Fourier-relationship between Δ𝑓 =0, b1 = 1 velocity profile
and sub-pulse envelope. It depicts kv-encoding as a function of velocity-encoding sub-pulse
amplitude and the corresponding Δ𝑓 =0, b1 = 1 velocity profile, before and after optimization. The
overall shape of the sub-pulses is sinc-shaped to select a range of velocities before and after
optimization, and the middle sub-pulse amplitude remained. Other sub-pulse amplitudes were
adjusted with optimization to improve pulse performance. The stop-band of the velocity-selective
profile flattens to reduce labeling of myocardial velocities, and the pass-band ripples are reduced.

myocardium
-0.02
0
0.02
before
sub-pulse
optimization
after
sub-pulse
optimization
ASL signal (Δ"= 0) ASL signal (b1=1)
0.5 0.75 1.0 -125 0 125
b1 Δ"
v (cm/s)
0
-140
140
0
-140
140
v (cm/s)
ASL signal (Δ"= 0) ASL signal (b1=1)
0.5 0.75 1.0 -125 0 125
b1 Δ"
v (cm/s)
0
-3
3
0
-3
3
v (cm/s)
blood
0
1
2
Improved Velocity-Selective Labeling for Myocardial ASL - Results 78

Figure 6.5: On-resonant, b1=1 velocity profile (top) and corresponding kv-encoding (blue) for the proposed VS
pulse with FOVv=140 cm/s before (black) and after (blue) sub-pulse optimization. The kv-encoding is shaped
as a windowed sinc, which leads to a slice-like selection of velocities. After optimization, the transition band of
the velocity profile narrows, improving labeling efficiency of coronary velocities above ±10 cm/s. The velocity
profile also flattens around v=±3 cm/s, reducing the potential to spuriously label moving myocardium in stable-
diastole.

Figure 6.6 demonstrates low ASL signal bias in an oil phantom (<0.3%) due to gradient
imperfections with the proposed VS pulse and a delay 0.25 ms delay after each gradient pair. This
bias is on the order of noise. A shorter delay was found to increase ASL signal bias due to increased
sensitivity to gradient imperfections.

Figure 6.6 Baseline (B), control (C), and label (L) center-out GRE images are shown in a silicone oil phantom
in the proposed VS pulse with FOVv=80 cm/s and a delay of 0.25 ms. (a) shows the individual images, while (b)
shows the ‘ASL signal’ (L-C)/B the difference between label and control acquisitions. ASL signal is well
suppressed with mean+SD=-0.0004±0.008 and min/max values=-0.0036/-.0023. This suggests this labeling
scheme will not bias ASL signal due to artifacts associated with gradient imperfection.
!−#
$
! # $
mean±SD: -0.0004±0.0008
min/max: -0.0036/0.0023
(a)
(b)
-0.4
1.0 0.01
-0.01
Improved Velocity-Selective Labeling for Myocardial ASL - Results 79

Figure 6.7 demonstrates labeling at the level of the coronary arteries. Center-out GRE images
of the cross-section of the right coronary artery was obtained 1) immediately after a VS label
acquisition, and 2) immediately after a VS control acquisition. A clear difference is seen between
control and label coronary blood signal.

Figure 6.7: Myocardial perfusion (MP), physiological noise (PN) and temporal SNR (TSNR) across
four healthy subjects (S1-S4) using FAIR-ASL and VS-ASL with the original or proposed VS pulses.
MP measurements are comparable using proposed pulses and FAIR labeling in S2, S3, and S4. No
trend of over or underestimation was observed with the original VS pulse compared to FAIR labeling.
PN is significantly reduced in S1, S2, and S3. TSNR is higher using FAIR labeling and the proposed VS
pulses in every subject compared to the original VS pulse.

Figure 6.8 presents examples of control and label acquisitions in the VS-Orig and VS-Prop
pulse. It illustrates the expected T2-weighting in control images and labeling of blood signal in label
images. Furthermore, these images demonstrate reduced labeling of left ventricular blood pool signal
in the VS-Prop pulse compared to the VS-Orig pulse. The VS-Prop pulse is designed to label coronary
velocities; velocities in the left ventricular blood pool are often much higher.
Improved Velocity-Selective Labeling for Myocardial ASL - Results 80

Figure 6.8: Control (C), and label (L) images are obtained of a cross-section of the left coronary artery using
center-out GRE imaging immediately after proposed VS (VS-Prop) pulses or the original VS pulse (VS-Orig).
Labeling occurs during stable diastole where coronary velocities are highest and is designed to specifically label
coronary velocities to reduce transit delay effects associated with myocardial ASL. As expected, the coronary
arterial blood is inverted in label images and non-inverted in control images (red arrows).

Figure 6.9 shows MP and PN measured using 4 ASL experiments (three VS and one FAIR)
across 4 subjects. MP is within a physiologically reasonable range (1-3 ml/g/min), and PN is lower
in subjects 1 and 2 with VS-Prop compared to VS-Orig. TOST with a difference of 0.3 ml/g/min and
p=0.05 indicated MP measured with FAIR and VS-Prop (140 cm/s FOVv) were statistically equivalent.
A t-test with p=0.05 indicated FAIR and VS-Prop (140 cm/s FOVv) had lower PN compared to the
original VS pulse (2.5x).

VS-Prop
(140 cm FOVv)
VS-Prop
(80 cm FOVv)
VS-Orig
C L
Improved Velocity-Selective Labeling for Myocardial ASL - Results 81

Figure 6.9: Example control (C) and label (L) images are shown using the VS scheme developed by Jao et al and
the original (VS-Orig) or proposed VS pulse (VS-Prop). Labeling occurs during stable diastole and imaging
occurs during the following stable diastole. In between, an inversion pulse is played to suppress myocardial
signal. The images exemplify T2-weighting of control images and labeling of blood signal in label images, as
expected. The VS-Prop pulse is designed to label coronary velocities; there is less labeling of left ventricle blood
pool signal in the VS-Prop pulse compared to the VS-Orig pulse.

Figure 6.10 depicts a reduction in spurious labeling of moving myocardium in the VS-Prop
pulse compared to the VS-Orig pulse. The VS-Orig pulse shows a high MP measurement of >4
ml/g/min in the lateral wall, which is likely due to spuriously labeled myocardium. MP is more
uniform across the myocardium using the VS-Prop pulse, suggesting a reduction in spurious labeling.

Figure 6.10: Myocardial perfusion (MP) results are shown in subject 1 using the original (VS-Orig) and
proposed (VS-Prop) pulse. The Vs-Orig pulse has very high MP (>4 ml/g/min) in the lateral wall, indicating
possible spurious labeling of moving myocardium. Comparatively, VS-prop has more consistent MP across the
septal and lateral walls, indicating reduction in spurious labeling of moving myocardium.

C
L
VS-Orig
VS-Prop
(140 cm/s FOVv)
TSNR
MP
(ml/g/min)
VS-Orig
VS-Prop
(140 cm/s FOVv)
Improved Velocity-Selective Labeling for Myocardial ASL - Discussion 82

6.4 Discussion
The specially tailored VS pulse was demonstrated to reduce spurious labeling of moving
myocardium and reduce PN compared to the prior implementation of myocardial VSASL. The new
VSASL scheme also gave statistically equivalent MP compared to FAIR ASL, as expected. It is
anticipated that this VS pulse will be useful for VSASL with reduced sensitivity to transit delay.
This work demonstrates how FT-based velocity-selective RF pulses can be tailored for an
application. Low-field applications and brain applications will likely require optimization over
smaller range of off-resonance and b1 variations. It is possible that single or no inversions will be
required between velocity encoding sub-pulses. This will allow for a sufficient, shorter pulse to be
designed. Applications in other areas of the body will also change pulse design criteria. Body
applications with less motion will relax constraints on the stop-band of the designed velocity
selective pulse. This tradeoff could allow for a pulse design with higher labeling efficiency across the
desired range of velocities. Other VS applications may also benefit from consideration of relaxation
effects. The sub-pulse amplitudes of the velocity selective inversion pulses were optimized assuming
no T2 relaxation, which simplified the optimization problem. Empirically, we found that optimizing
using T2 relaxation for arterial blood, myocardium, or a combination of both with respect to their
velocities resulted in similar sub-pulse amplitudes. However, it can be desirable to consider
relaxation in other VS applications.
The proposed VS pulses can easily be modified for compatibility with steady-pulsed ASL
(SPASL) techniques. SPASL is desirable for its ability to efficiently acquire perfusion signal by driving
the tissue magnetization into a perfusion-dependent steady-state (31). A SPASL-compatible VS pulse
can be designed by adjusting the velocity-encoding sub-pulses to achieve velocity-selective
saturation instead of inversion.
A tradeoff existed between labeling efficiency and potential to spuriously label myocardium
in the two proposed VS pulses. VS-Prop (140 cm/s FOVv) was designed to label coronary velocities
at rest and stress. Bloch simulations demonstrated less spurious labeling but lower labeling efficiency.
VS-Prop (80 cm/s FOVv) was designed to label coronary velocities only at rest and Bloch simulations
demonstrated increased potential for spurious labeling for v>2 cm/s but higher labeling efficiency.
This study showed potential superiority of VS-Prop (140 cm/s FOVv) over VS-Prop (80 cm/s FOVv),
however it only considered healthy subjects at rest. A future study is needed to demonstrate
differences under stress.
Improved Velocity-Selective Labeling for Myocardial ASL - Discussion 83
Statistical testing in this study is limited by analysis across only 4 subjects. MP measurements
across methods presented in this paper were physiologically reasonable but not statistically
equivalent and statistical significance could be realized with inclusion of more datasets. PN measured
with VS-Prop (140 cm/s FOVv) VSASL and FAIR ASL was statistically lower compared to the original
VS-Orig VSASL. PN measured with VS-prop (80 cm/s FOVv) VSASL, surprisingly, was not statistically
lower. This could be due to a low number of samples, or the tradeoff between increased labeling
efficiency at the cost of potential spurious labeling of myocardium.
Labeling of coronary velocities was demonstrated with each VS pulse in this paper but did
not result in reasonable quantitative measurements of labeling efficiency. It was expected that
coronary blood flow would be inverted in the proposed VS pulses and saturated in the original VS
pulse. To confirm this expectation, the difference between coronary signal in control and label
acquisitions was taken and divided by a baseline image with no labeling. After phase-sensitive
reconstruction, it was expected that this signal would be >1, representing inversion in the proposed
pulses, and closer to 1, representing saturation in the original VS pulse. However, ratios in the
proposed VS pulses were 0.6 and 0.9 for the 140 cm/s and 80 cm/s pulses, respectively. The original
VS pulse had a ratio of 1.3. These results are not as expected. These counterintuitive results could be
due to practical limitations. For example, insufficient resolution could have caused partial voluming
to affect measurements. These results could also be due to the variance in coronary labeling efficiency
as a function of off-resonance and b1. According to Bloch simulations, the proposed VS pulses
achieved ASL signal of 1.2-1.3 averaged across the coronary velocities, where 2 represents maximum
potential ASL signal. This range of coronary velocities is expected to achieve a max ASL signal of 1.6.
This number is <2 as it accounts for relaxation during the pulse. However, ASL signal can reach ~ 0
for other velocities.
This study, like the previous study of myocardial VSASL (13), lacks experimental verification
of insensitivity to transit delay. VSASL in the brain is traditionally done with a low Vc to label blood
at the capillary level and eliminate transit delay effects (6,28). This is experimentally demonstrated
by evaluating ASL signal at several post-labeling delays, and fitting with a kinetic model. Myocardial
VSASL is performed with a higher Vc to avoid spurious labeling of myocardium. Theoretically, the
proposed VS pulses are designed to label coronary blood and reduce transit delay effects. In reality,
coronary blood flow may be labeled but the extent to which transit delay is reduced is unknown due
to a higher Vc causing blood to be labeled at higher levels of coronary vasculature depending on an
individual’s particular anatomy. Future work is needed to experimentally verify the insensitivity to
transit delay. This is complicated to perform in the heart since coronary flow is pulsatile, labeling and
Improved Velocity-Selective Labeling for Myocardial ASL - Conclusion 84
imaging must be cardiac gated, and short post-labeling delays are very difficult to acquire. Validation
could instead be performed by comparing the performance of VS labeling and FAIR labeling in multi-
slice experiments. Sensitivity to transit delay is increased with multi-slice FAIR due to the need for a
thicker inversion slab. Validation could also be performed in subjects with slow coronary flow or
substantial collaterals, although identification of such a cohort could be challenging.

6.5 Conclusion
We have demonstrated reduced physiological noise in myocardial VSASL with specially
tailored velocity-selective inversion pulse. The proposed VS pulse was designed using a Fourier
Transform based Velocity-Selective labeling pulse train and was optimized to reduce spurious
labeling of moving myocardium and maximize labeling of coronary blood velocities in the cardiac 3T
MRI environment. This technique gives comparable MP measurements as FAIR ASL, making it a
suitable candidate for multislice myocardial ASL and for myocardial ASL in patients with slow
coronary flow.

Concluding Remarks - Conclusion 85
7 Concluding Remarks
Myocardial ASL has the potential to be a radiation-free and contrast-free MPI technique, and
could especially benefit patients with advanced kidney disease, who have higher cardiovascular
mortality and require frequent monitoring and stress testing. This technique is still in the
development phase, and there are a number of limitations which must be addressed before it is ready
for clinical use. I address two limitations in this thesis. First, myocardial ASL provides inadequate
coverage, which must be increased without increasing scan time. I sought to implement simultaneous
multi-slice imaging as a solution. Second, myocardial ASL is limited by sensitivity to transit delay, and
I developed velocity selective labeling to mitigate this. Myocardial ASL is a very technically
challenging project because of the unique cardiac anatomy and physiology, and the 3T environment.
Blood that perfuses into the heart comes from the heart ~1s beforehand. Blood that perfuses into the
brain also comes from the heart, increasing transit delay. In addition, imaging is limited to stable
parts of the cardiac cycle. Finally, the 3T environment is desirable for myocardial ASL because long
T1 relaxation times and higher field strengths bolster ASL signal, which is a low SNR technique. The
3T environment also presents some tradeoffs, which include high off-resonance on the order of ±125
Hz and b1 variations of about 50% in the heart (94).

Broadening Spatial Coverage
Chapters 4 and 5 describe my work to improve SMS bSSFP imaging for myocardial ASL. A fast
RF measurement and compensation technique was developed without additional hardware. While
artifacts were reduced, I have not applied and tested SMS imaging with myocardial ASL because of
significant undersampling artifacts using our scanner’s 8-channel cardiac coil (a higher number of
channels was not available). I believe that undersampled 3-band SMS imaging with myocardial ASL
can be implemented using a cardiac coil with a higher number of channels. I also believe that 3-band
SMS imaging with myocardial ASL may be implemented with a lower reduction factor, however, the
duration of the imaging window will be limited by the stable periods of the cardiac cycle. With
cardiac imaging and our 8-channel cardiac coil, most coil signal appeared in the 4 anterior coils on
the chest. I attempted to obtain 3-band images with a reduction factor of rate 3 and noted that
artifacts were present in the reconstructed images. I confirmed that they were not due to RF
excitation errors, leading me to believe they were reconstruction artifacts from insufficient
information.
Concluding Remarks - Conclusion 86
Improved spatial coverage could be achieved in many ways. EPI, SMS-EPI or GRE could be
better than SMS bSSFP imaging and are worth investigation. I worked on SMS bSSFP imaging and
determined that low-flip angle off-resonant excitation of spuriously excited side lobes can confound
ASL signal, and reduced this artifact through a simple predistortion procedure. As shown by Javed et
al, EPI is desirable for ASL as a fast imaging techniques and allows 2 slices to be obtained in the heart
during stable systole, and 3 in stable diastole (95). SMS-EPI is another desirable option. SMS
excitation requirements will be relaxed with EPI. SMS pulses can be made much longer, reducing the
potential for RF transmit imperfection. Even if small excitation artifacts are present, EPI imaging is
unlike bSSFP imaging in that it will not suffer from high signal intensity low-flip angle off-resonant
excitation. SMS with GRE is also desirable because it will not incur this artifact, however it has lower
SNR and is not as fast as EPI (96).

Incidental Discovery: RF distortion and correction
Working on SMS bSSFP opened new questions into the nature of imperfect RF transmission.
This research depended on attending the ISMRM annual meetings and discussing this problem with
researchers at different institutions who worked on different MRI hardware. It became clear that the
spurious side-lobe artifacts were likely to be system and vendor dependent.
My first potential explanation was that rapid oscillations and high peak B1 pushed the RF
amplifier into the nonlinear range. This was also observed by Zhu et al who worked on a similar
platform (34). Nonlinear effects of RF amplifiers can show up as spurious side-lobe excitation, and so
this initial hypothesis seemed plausible. However, I experimentally determined that predistortion
performed in one scanner setting (i.e. with a certain load) would also produce accurate transmitted
RF waveforms in a variety of other loads. In other words, this side-lobe excitation was loading
independent. Finding an explanation for our side-lobes is a topic of future research. This will require
in-depth knowledge of the RF subsystem. This type of knowledge is often company-specific and
proprietary, and would require a close collaborations with an industry professional.
I have identified two other potential explanations for spurious side-lobe excitation. One is a
digital to analog conversion issue. The RF envelop is designed assuming a smooth envelope, but is
played on our scanners with 2 𝜇𝑠 sampling period. This may lead to quantization errors. Another
possible explanation is timing delay between amplitude and phase components of the transmitted
waveform. A simple Bloch simulation was performed to see whether slight timing delays could be
causing these sorts of artifacts. Different sub-sample time shifts were placed between amplitude and
Concluding Remarks - Conclusion 87
phase components of simultaneous multi-slice RF pulses. They produced spurious side-lobes of a
similar nature to the ones I experienced. Future work is needed to determine if either of these
potential explanations are the exact cause.
While I was studying SMS imaging, I learned that there are other situations where GRATER-
based predistortion could be valuable as a method to improve RF fidelity, including spectroscopy,
hyperpolarized imaging, and low-cost MRI. GRATER-based RF predistortion could be implemented
as part of a prescan procedure in patients and it could be performed in under 1 minute (each iteration
must be long enough for sample relaxation between iterations, and in my experience, about 10
iterations are sufficient) (72). An outer-volume suppression pulse could be used to select a uniform
region within the body, or a uniform phantom could be placed inside the scanner with the patient
and OVS could be used to select the phantom. Selecting a uniform region allows for accurate GRATER-
based RF measurements (35). GRATER-based RF predistortion can be useful to lower costs of
scanners. For example, a cheaper, less accurate amplifier may be used to transmit the RF pulse,
incurring RF transmit imperfections. GRATER-based RF predistortion may then improve RF
transmission. This technique may be useful in spectroscopy applications, where inaccurately
transmitted RF pulses confound measurements of metabolites (60). This technique may also be
useful in hyperpolarized imaging, where distortions of RF pulses can prevent excitation of Xenon
inside vessels and tissues, and instead excite the 50-fold larger gas-phase magnetization pool (61).

Alternative Labeling Schemes
Chapter 6 describes efforts to improve velocity selective RF pulses for myocardial ASL. The
new pulse demonstrated improved sensitivity compared to the previous pulse. However, there is
likely still room for improvement. All coronary velocities were considered equally important. It was
difficult to model exact coronary velocities, or distributions of velocities, because coronary velocities
vary between people and are also impacted by disease (84–88). This could be an interesting problem
to explore for future research. Perhaps the distribution could be modeled across several subjects to
see variations among people, however deeper insights will be available once VSASL is deployed
clinically. In addition, improvement over the previous velocity-selective myocardial ASL
implementation was only demonstrated in four healthy volunteers. Further testing should be done
to establish statistical significance.
Labeling efficiency of blood in coronary artery and in-sensitivity to transit delay were not
experimentally evaluated, because they are both difficult to measure. Cross-sectional images of the
proximal RCA were obtained immediately after a control and label VS pulse. This demonstrated
Concluding Remarks - Conclusion 88
velocity selective labeling in a single coronary artery. The extent of coronary arterial labeling across
the coronary territories has not been measured, and should be considered as a function of off-
resonance, b1 scale, and velocity. Not knowing the extent or location of labeling also removes the
possibility of making concrete statements about the extent to which sensitivity to transit delay is
reduced with velocity selective labeling. Determining the labeling efficiency and evaluating
sensitivity to transit delay remain subjects of future research. Insensitivity to transit delay could be
tested by performing ASL experiments with labeling in mid-diastole, and then imaging in the
following systole. Labeling using velocity selective pulses would be compared to FAIR and a
thickened inversion slab around the left ventricle. Imaging would be performed in the basal, mid, and
apical short axis slices of the heart. It is hypothesized that ASL signal will be highest in the basal slice
and lowest in the apical slice with FAIR labeling, indicating sensitivity to transit delay. It is
hypothesized that ASL signal will be consistent with VS labeling, indicating insensitivity to transit
delay. Another approach is to perform VSASL experiments with a variety of transit delays, and to
analyze the trend of ASL signal as a function of transit delay. This is expected to provide inconclusive
results, however, because labeling is limited to mid-diastole, where coronary flows are highest, and
imaging is usually performed in mid-diastole or systole, where the heart is most still. With these
limitations, ASL signal can only be measured with a few different transit delays before signal
relaxation, making it difficult to determine trends. Sensitivity to transit delay could also be tested in
patients with slow coronary flow, with disease states including circuitous coronary vasculature or
enlarged hearts. This will not be possible, however, until myocardial ASL is ready for clinical testing.
VSASL with Fourier Velocity Encoding could be useful in a variety of applications. Coronary
MRA is one exciting opportunity (98). With precise control over VS pulse design, profiles can be used
to excite specific velocities corresponding to specific vessels within the body. Profiles can also be
designed to avoid labeling of moving tissues. VSASL with Fourier Velocity Encoding may also be
desirable in other organs to reduce transit delay effects, such as the kidneys (99) or lungs (100).
Velocity selective pulses can also be redesigned for different tissues in the body using the
optimization framework in Chapter 6. This can be adapted for the unique tissue’s movement, target
range of velocities to label, off-resonance conditions, and b1 variations. VSASL with FVE may be
desirable and useful at low field strengths for both ASL and MRA. Shorter pulses with more velocity-
encoding sub-pulses can be designed to have improved control over the velocity profile. Pulses will
be shorter because refocusing pulses are less likely needed between velocity-encoding sub-pulses,
as there is less off-resonance and b1 variation at lower fields. A shorter pulse will also be beneficial
at low-field, where relaxation times are shorter.
Concluding Remarks - Conclusion 89
I still do not know the optimal ASL labeling technique. I believe velocity selective labeling has
the highest potential to work in a clinical setting, however a head-to-head comparison of the labeling
methods is required. The myocardial ASL labeling techniques that have been explored so are FAIR,
steady-pulsed, and velocity selective. Each of these labeling techniques have pros and cons (38). FAIR
has been shown to work well in a single-slice of the heart. However, FAIR is sensitive to transit delay,
and this limitation will need to be considered in multi-slice settings and in patients with slow
coronary flow. Steady-pulsed ASL is desirable for its potential to increase ASL signal, however it is
sensitive to heart rate variation, which is common in patients. Velocity Selective Labeling is desirable
for its insensitivity to transit delay, however the unique cardiac environment prevents labeling at the
capillary level because velocities in the capillaries are similar to velocities of the myocardium during
mid-diastole. Instead, labeling is tailored to theoretically label the coronary arteries, where velocity
is higher than moving myocardium. This theory needs to be confirmed.

Final Thoughts
I have developed and expanded upon the myocardial ASL body of knowledge with sound
scientific findings related to simultaneous multi-slice imaging and velocity selective labeling. My
work has highlighted the difficulties of obtaining precise simultaneous multi-slice bSSFP cardiac
images at 3T. It has also scrutinized the complex and various assumptions made in order to design a
pulse for myocardial velocity selective ASL. Both of these works have contributed to the scientific
body of knowledge and demonstrate incremental improvements. Myocardial ASL must ultimately
seek a repeatable, reproducible solution to achieve consistent MP maps with increased coverage and
sensitivity. I hope my contributions are beneficial for future researchers and that myocardial ASL
may one day become a clinical reality.

Bibliography - Conclusion 90
Bibliography
1. Zun Z, Wong EC, Nayak KS. Assessment of myocardial blood flow (MBF) in humans using arterial
spin labeling (ASL): feasibility and noise analysis. MRM. 2009;62:975–983.
2. Zun Z, Varadarajan P, Pai RG, Wong EC, Nayak KS. Arterial spin labeled CMR detects clinically
relevant increase in myocardial blood flow with vasodilation. JACC. 2011;4:1253–1261.
3. Go AS, Mozaffarian D, Roger VL, et al. Heart Disease and Stroke Statistics - 2014 Update. AHA.
2014.
4. Greenwood JP, Maredia N, Younger JF, et al. Cardiovascular magnetic resonance and single-
photon emission computed tomography for diagnosis of coronary heart disease (CE-MARC): A
prospective trial. Lancet. 2012;379:453–460.
5. Care FM. 2013 Atlas of CKD & ESRD. https://www.usrds.org/atlas13.aspx.
6. Fresenius Medical Care. ESRD Patients in 2012 A Global Perspective. 2012.
http://www.vision4fmc.com/files/pdf_2/ESRD_Patients_2012.pdf.
7. Di Angelantonio E, Chowdhury R, Sarwar N, Aspelund T, Danesh J, Gudnason V. Chronic kidney
disease and risk of major cardiovascular disease and non-vascular mortality: Prospective
population based cohort study. BMJ. 2010;341:768.
8. Calamante F, Thomas DL, Pell GS, Wiersma J, Turner R. Measuring Cerebral Blood Flow Using
Magnetic Resonance Imaging Techniques. JCBFM. 1999;19:701–735.
9. Zun Z, Varadarajan P, Pai RG, Wong EC, Nayak KS. Arterial spin labeled CMR detects clinically
relevant increase in myocardial blood flow with vasodilation. JACC. 2011;4:1253–61.
10. Cerqueira MD. Standardized Myocardial Segmentation and Nomenclature for Tomographic
Imaging of the Heart. Child. AHA. 2003:1448–1453.
11. Wong EC, Cronin M, Wu W-C, Inglis B, Frank LR, Liu TT. Velocity-selective arterial spin labeling.
MRM. 2006;55:1334–1341.
12. Beohar N, Erdogan AK, Lee DC, Sabbah HN, Kern MJ, Teerlink J, Bonow RO, Gheorghiade M.
Acute Heart Failure Syndromes and Coronary Perfusion. JACC. 2008;52:13–16.
13. Muehling OM, Huber A, Cyran C, Schoenberg SO, Reiser M, Steinbeck G, Nabauer M, Jerosch-
Herold M. The delay of contrast arrival in magnetic resonance first-pass perfusion imaging: A novel
non-invasive parameter detecting collateral-dependent myocardium. Heart. 2007;93:842–847.
14. Jao TR, Nayak KS. Demonstration of velocity selective myocardial arterial spin labeling
perfusion imaging in humans. MRM. 2017;81:1–7.

Bibliography - Conclusion 91
15. Qiu D, Straka M, Zun Z, Bammer R, Moseley ME, Zaharchuk G. CBF measurements using
multidelay pseudocontinuous and velocity-selective arterial spin labeling in patients with long
arterial transit delays: Comparison with xenon CT CBF. JMRI. 2012;36:110–119.
16. Dowshen S. Magnetic Resonance Imaging (MRI) For Parents.
https://kidshealth.org/en/parents/mri.html.
17. Nishimura D. Principles of Magnetic Resonance Imaging. Raleigh: Lulu; 1996;1:119–132.
18. Haldar JP. Constrained imaging: denoising and sparse sampling. Univ. Illinois 2011.
19. Elster A. Questions and Answers in MRI. mriquestions.com.
20. Hanson LG. Is quantum mechanics necessary for understanding magnetic resonance? Concepts
in MR. 2008;32:329–340.
21. Stanisz GJ, Odrobina EE, Pun J, Escaravage M, Graham SJ, Bronskill MJ, Henkelman RM. T1, T2
relaxation and magnetization transfer in tissue at 3T. MRM. 2005;54:507–512.
22. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: Sensitivity encoding for fast
MRI. MRM. 1999;42:952–962.
23. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J, Kiefer B, Haase A.
Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA). MRM. 2002;47:1202–1210.
24. Pauly J, Nishimura D, Macovski A, Roux P Le. Parameter Relations for the Shinnar-Le Roux
Selective Excitation Pulse Design Algorithm. IEEE TMI. 1991; 10:53-65.
25. Conolly S, Nishimura D, Macovski A, Glover G. Variable-rate selective excitation. JMRI.
1988;78:440–458.
26. Barth M, Breuer F, Koopmans PJ, Norris DG, Poser BA. Simultaneous multislice (SMS) imaging
techniques. MRM. 2016;75:63–81.
27. Wong E. Optimized Phase Schedules for Minimizing Peak RF Power in Simultaneous Multi-Slice
RF Excitation Pulses. Proc. 20th ISMRM, Melbourne, Aust. 2012;20:2209.
28. Bernstein M, King K, Zhou X. Handbook of MRI pulse sequences. 2004.
29. De Rochefort L, Maître X, Bittoun J, Durand E. Velocity-selective RF pulses in MRI. MRM.
2006;55:171–176.
30. Shin T, Hu BS, Nishimura DG. Off-resonance-robust velocity-selective magnetization preparation
for non-contrast-enhanced peripheral MR angiography. MRM. 2013;70:1229–1240.
31. Sung K, Nayak KS. B1+ compensation in 3T cardiac imaging using short 2DRF pulses. MRM.
2008;59:441–446.
32. Qin Q, van Zijl PCM. Velocity-selective-inversion prepared arterial spin labeling. MRM.
2016;76:1136–1148.
Bibliography - Conclusion 92
33. Chan F, Pauly J, Macovski a. Effects of RF amplifier distortion on selective excitation and their
correction by prewarping. MRM. 1992;23:224–238.
34. Zhu K, Dougherty RF, Middione MJ, Wu H, Scott G, Pauly JM, Kerr AB. RF Amplifier Nonlinearity
Correction for Multiband RF Pulses. Proc. 23rd ISMRM. 2015;23:1830.
35. Landes VL, Nayak KS. Simple method for RF pulse measurement using gradient reversal. MRM.
2017;79:2642-2651.
36. Ferré JC, Bannier E, Raoult H, Mineur G, Carsin-Nicol B, Gauvrit JY. Arterial spin labeling (ASL)
perfusion: Techniques and clinical use. DII. 2013;94:1211–1223.
37. Alsop DC, Detre JA, Golay X, et al. Recommended implementation of arterial spin-labeled
Perfusion mri for clinical applications: A consensus of the ISMRM Perfusion Study group and the
European consortium for ASL in dementia. MRM. 2015;73:102–116.
38. Kober F, Jao T, Troalen T, Nayak KS. Myocardial arterial spin labeling. JCMR. 2016;18:22.
39. Zun Z, Wong EC, Nayak KS. Assessment of myocardial blood flow (MBF) in humans using
arterial spin labeling (ASL): feasibility and noise analysis. MRM. 2009;62:975–983.
40. Detre JA, Leigh JS, Williams DS, Koretsky AP. Perfusion imaging. MRM. 1992;23:37–45.
41. Do HP, Yoon AJ, Fong MW, Saremi F, Barr ML, Nayak KS. Double-gated myocardial ASL perfusion
imaging is robust to heart rate variation. MRM. 2017;77:1975–1980.
42. Do HP, Jao TR, Nayak KS. Myocardial arterial spin labeling perfusion imaging with improved
sensitivity. JCMR. 2014;16:15.
43. Maleki N, Dai W, Alsop DC. Optimization of background suppression for arterial spin labeling
perfusion imaging. MRM PBM. 2012;25:127–133.
44. Go AS, Mozaffarian D, Roger VL, et al. Executive Summary: Heart Disease and Stroke Statistics—
2013 Update. Circulation 2013;127:143–152.
45. Schwitter J, Wacker CM, Wilke N, et al. MR-IMPACT II: Magnetic resonance imaging for
myocardial perfusion assessment in coronary artery disease trial: Perfusion-cardiac magnetic
resonance vs. single-photon emission computed tomography for the detection of coronary artery
disease: A comparative multicentre, multivendor trial. J Eur Heart. 2013;34:775–781.
46. Bruder O, Schneider S, Nothnagel D, et al. EuroCMR (European Cardiovascular Magnetic
Resonance) Registry. Results of the German Pilot Phase. JACC. 2009;54:1457–1466.
47. De Jong MC, Genders TSS, Van Geuns RJ, Moelker A, Hunink MGM. Diagnostic performance of
stress myocardial perfusion imaging for coronary artery disease: A systematic review and meta-
analysis. Eur. Radiol. 2012;22:1881–1895.

Bibliography - Conclusion 93
48. Gerber B, Raman S, Nayak K, Epstein FH, Ferreira P, Axel L, Kraitchman D. Myocardial first-pass
perfusion cardiovascular magnetic resonance: history, theory, and current state of the art. JCMR.
2008;5:1–5.
49. Go AS, Chertow GM, Fan D, McCulloch CE, Hsu CY. Chronic kidney disease and the risks of death,
cardiovascular events, and hospitalization. NEJM. 2004;351:1296–1305.
50. Care FM. ESRD Patients in 2012 A Global Perspective. USRDS. 2012.
https://www.usrds.org/2012/view/v2_12.aspx.
51. Brambilla M, De Mauri A, Leva L, Carriero A, Picano E. Cumulative radiation dose from medical
imaging in chronic adult patients. Am J Med. 2013;126:480–486.
52. Picano E, Vañó E, Rehani MM, et al. The appropriate and justified use of medical radiation in
cardiovascular imaging: A position document of the ESC Associations of Cardiovascular Imaging,
Percutaneous Cardiovascular Interventions and Electrophysiology. Eur. Heart J. 2014;35:665–672.
53. De Mauri A, Brambilla M, Chiarinotti D, Matheoud R, Carriero A, De Leo M. Estimated radiation
exposure from medical imaging in hemodialysis patients. J. Am. Soc. Nephrol. 2011;22:571–578.
54. Melamed ML, Hostetter TH. Ionizing radiation exposure: Another underrecognized risk factor
for poor health outcomes in dialysis patients. Kidney Int. 2010;78:724–725.
55. Walker S, Girardin F, McKenna C, Ball SG, Nixon J, Plein S, Greenwood JP, Sculpher M. Cost-
effectiveness of cardiovascular magnetic resonance in the diagnosis of coronary heart disease: An
economic evaluation using data from the CE-MARC study. Heart. 2013;99:873–881.
56. Thom H, West NEJ, Hughes V, Dyer M, Buxton M, Sharples LD, Jackson CH, Crean AM. Cost-
effectiveness of initial stress cardiovascular MR, stress SPECT or stress echocardiography as a gate-
keeper test, compared with upfront invasive coronary angiography in the investigation and
management of patients with stable chest pain: Mid-term outcomes from the CECaT randomised
controlled trial. BMJ Open. 2014;4:3419.
57. Setsompop K, Gagoski BA, Polimeni JR, Witzel T, Wedeen VJ, Wald LL. Blipped-controlled
aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g-factor
penalty. MRM. 2012;67:1210–1224.
58. Razavi B. RF Microelectronics. Upper Saddle River; 2013.
59. Cunningham CH, Wood ML. Method for improved multiband excitation profiles using the
Shinnar-Le Roux transform. MRM. 1999;42:577–584.
60. Kreis R. Issues of spectral quality in clinical 1H-magnetic resonance spectroscopy and a gallery
of artifacts. NMR Biomed. 2004;17:361–381.

Bibliography - Conclusion 94
61. Kaushik SS, Freeman MS, Cleveland ZI, et al. Probing the regional distribution of pulmonary gas
exchange through single-breath gas- and dissolved-phase 129Xe MR imaging. JAP. 2013;115:850–
860.
62. Zanchi MG, Stang P, Kerr A, Pauly JM, Scott GC. Frequency-offset cartesian feedback for MRI
power amplifier linearization. IEEE TMI. 2011;30:512–522.
63. Stang P, Kerr AB, Grissom W, Pauly JM, Scott GC. Vector Iterative Pre-Distortion: An Auto-
calibration Method for Transmit Arrays. Proc. 17th ISMRM. 2009;17:395.
64. Stang P, Zanchi M, Grissom W a, Kerr A, Pauly JM, Scott GC. RF Sensor Considerations for Input
Predistortion Correction of Transmit Arrays. Proc. 18th ISMRM. 2010;18:44.
65. Hoult DI, Kolansky G, Kripiakevich D, King SB. The NMR multi-transmit phased array: A
Cartesian feedback approach. JMR. 2004;171:64–70.
66. Zanchi M, Pauly J, Scott G. Frequency Offset Cartesian Feedback Control System for MRI Power
Amplifier. Proc., Proc. 17th ISMRM. 2009;17:398.
67. Stang PP, Zanchi MG, Kerr A, Pauly JM, Scott GC. Active Coil Decoupling by Impedance Synthesis
using Frequency-Offset Cartesian Feedback. Proc. 19th ISMRM. 2011;19:332.
68. Smith TB, Nayak KS. Reduced field of view MRI with rapid, B 1-robust outer volume
suppression. MRM. 2012;67:1316–1323.
69. Landes V, Nayak KS. Release v1.2. Zenodo 2017. https://doi.org/10.5281/zenodo.831849.
70. Hargreaves B. Bloch Equation Simulation. http://mrsrl.stanford.edu/~brian/bloch/
71. Hargreaves B. Fast Gradient Echo Sequences Including Balanced SSFP. JMRI. 2004;20:857–864.
72. Landes V, Nayak KS. Imrpoved multi-band RF performance using GRATER-based predistort.
Proc. 26th ISMRM. Paris; 2018;26:171.
73. Cauley SF, Polimeni JR, Bhat H, Wald LL, Setsompop K. Interslice leakage artifact reduction
technique for simultaneous multislice acquisitions. MRM. 2014;72:93–102.
74. Vannesjo SJ, Haeberlin M, Kasper L, Pavan M, Wilm BJ, Barmet C, Pruessmann KP. Gradient
system characterization by impulse response measurements with a dynamic field camera. MRM.
2013;69:583–593.
75. Reeder SB, Wintersperger BJ, Dietrich O, Lanz T, Greiser A, Reiser MF, Glazer GM, Schoenberg
SO. Practical approaches to the evaluation of signal-to-noise ratio performance with parallel
imaging: Application with cardiac imaging and a 32-channel cardiac coil. MRM. 2005;54:748–754.
76. Lebsack ET, Wright SM. Iterative RF pulse refinement for magnetic resonance imaging. IEEE
Trans. BME. 2002;49:41–48.

Bibliography - Conclusion 95
77. Scherzer O. Convergence criteria of iterative methods based on landweber iteration for solving
nonlinear problems. JMAA. 1995;194:911–933.
78. Chareonthaitawee P, Kaufmann PA, Rimoldi O, Camici PG. Heterogeneity of resting and
hyperemic myocardial blood flow in healthy humans. Cardiovasc. Res. 2001;50:151–161.
79. Guo J, Meakin JA, Jezzard P, Wong EC. An optimized design to reduce eddy current sensitivity in
velocity-selective arterial spin labeling using symmetric BIR-8 pulses. MRM. 2015;73:1085–1094.
80. Levitt M. Broadband Heteronuclear Decoupling. JMR. 1981;47:328–330.
81. Qin Q, Shin T, Schar M, Guo H, Chen H, Qiao Y. Velocity-selective magnetization-prepared non-
contrast-enhanced cerebral MR angiography at 3 Tesla: Improved immunity to B0/B1
inhomogeneity. MRM. 2016;75:1232–1241.
82. Shin T, Qin Q. Magnetic Resonance in Medicine Characterization and suppression of stripe
artifact in MR angiography. MRM. 2018;80;1997-2005.
83. Sung K, Nayak KS. Measurement and characterization of RF nonuniformity over the heart at 3T
using body coil transmission. JMRI. 2008;27:643–648.
84. Gorcsan J, Gulati VK, Mandarino WA, Katz WE. Color-coded measures of myocardial velocity
throughout the cardiac cycle by tissue Doppler imaging to quantify regional left ventricular
function. AHJ. 1996;131:1203–1213.
85. Simpson R, Keegan J, Firmin D. Efficient and reproducible high resolution spiral myocardial
phase velocity mapping of the entire cardiac cycle. JCMR. 2013;15:1–14.
86. Ofili EO, Labovitz AJ, Kern MJ. Coronary flow velocity dynamics in normal and diseased arteries.
AJC. 1993;71.
87. Pereira VFA, De Carvalho Frimm C, Rodrigues ACT, Tsutsui JM, Cúri M, Mady C, Ramires JAF.
Coronary flow velocity reserve in hypertensive patients with left ventricular systolic dysfunction.
Clin. Cardiol. 2002;25:95–102.
88. Anderson HV, Stokes MJ, Leon M, Abu-Halawa SA, Stuart Y, Kirkeeide RL. Coronary artery flow
velocity is related to lumen area and regional left ventricular mass. Circulation. 2000;102:48–54.
89. Fan Z, Sheehan J, Bi X, Liu X, Carr J, Li D. 3D noncontrast MR angiography of the distal lower
extremities using flow-sensitive dephasing (FSD)-prepared balanced SSFP. MRM. 2009;62:1523–
1532.
90. Kellman P, Herzka DA, Arai AE, Hansen MS. Influence of Off-resonance in myocardial T1-
mapping using SSFP based MOLLI method. JCMR. 2013;15:1–8.
91. Niendorf T, Sodickson DK, Krombach GA, Schulz-Menger J. Toward cardiovascular MRI at 7 T:
Clinical needs, technical solutions and research promises. Eur. Radiol. 2010;20:2806–2816.
Bibliography - Conclusion 96
92. Javed A, Jao TR, Nayak KS. Motion correction facilitates the automation of cardiac ASL perfusion
imaging. JCMR. 2015;17:51.
93. Capron T, Troalen T, Robert B, Jacquier A, Bernard M, Kober F. Myocardial perfusion assessment
in humans using steady-pulsed arterial spin labeling. MRM. 2015;74:990–998.
94. Sung K, Nayak KS. Design and use of tailored hard-pulse trains for uniformed saturation of
myocardium at 3 Tesla. MRM. 2008;60:997–1002.
95. A Javed, TR Jao KN. Velocity Sensitivity of Inner-Volume Cardiac Echo Planar Imaging. Proc. 26
th

ISMRM. 2018; 26:4240.
96. Jao T, Nayak K. Analysis of physiological noise in quantitative cardiac magnetic resonance. PLoS
One. 2019;14.
97. Kober F, Bernard M, Troalen T, Capron T. Cardiovascular Magnetic Resonance of Myocardial
Structure, Function, and Perfusion in Mouse and Rat Models. Curr. Cardiovasc. Imaging Rep.
2012;5:109–115.
98. Sakuma H, Ichikawa Y, Chino S, Hirano T, Makino K, Takeda K. Detection of Coronary Artery
Stenosis With Whole-Heart Coronary Magnetic Resonance Angiography. JACC. 2006;48:1946–1950.
99. Martirosian P, Klose U, Mader I, Schick F. FAIR True-FISP Perfusion Imaging of the Kidneys.
MRM. 2004;51:353–361.
100. Mai VM, Berr SS. MR perfusion imaging of pulmonary parenchyma using pulsed arterial spin
labeling techniques: FAIRER and FAIR. JMRI. 1999;9:483–487.

Abstract (if available)

Abstract Since its invention almost 50 years ago, Magnetic Resonance Imaging (MRI) has emerged as an important imaging modality for obtaining high resolution anatomic images with excellent soft tissue contrast. MRI is often clinically prescribed in static tissues, including brain or musculoskeletal areas. Because MRI is radiation-free, it is desirable to increase clinical applications of MRI that require frequent or routine monitoring. ❧ Works in this dissertation were motivated by the need to improve a contrast-free myocardial perfusion imaging (MPI) technique using MRI, called myocardial arterial spin labeling (ASL). Myocardial ASL is a desirable MPI technique for diagnosing or monitoring patients with coronary artery disease because it is the only MPI modality without ionizing radiation or contrast agents. This technique is especially suited for patients with end stage renal disease, who cannot tolerate contrast agents and require annual screening. Myocardial ASL uses blood as an endogenous contrast agent to create a measurable signal that is proportional to myocardial perfusion. Myocardial ASL is under development in our lab and its feasibility for detecting coronary artery disease has been demonstrated in a single mid-short axis slice of the heart (1,2). Spatial coverage must be efficiently increased and sensitivity to transit delay must be effectively eliminated for clinical adaption. ❧ This thesis specifically focuses on technical improvements in radiofrequency pulse performance for myocardial ASL to achieve these needs. First, a hardware-free, efficient RF predistortion technique is developed to improve simultaneous multi-slice imaging for increased spatial coverage of myocardial ASL. Second, a velocity selective pulse is designed using Fourier Velocity encoding techniques and tailored specifically for labeling of coronary blood at 3T to remove transit delay sensitivities of myocardial ASL. With the proposed methods, the development of myocardial ASL approaches clinical reality.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

Improving the sensitivity and spatial coverage of cardiac arterial spin labeling for assessment of coronary artery disease

PDF

Assessment of myocardial blood flow in humans using arterial spin labeled MRI

PDF

Improved myocardial arterial spin labeled perfusion imaging

PDF

Improving sensitivity and spatial coverage of myocardial arterial spin labeling

PDF

Mapping water exchange rate across the blood-brain barrier

PDF

Measurement of human brain perfusion with arterial spin labeling magnetic resonance imaging at ultra-high field

PDF

Improving arterial spin labeling in clinical application with deep learning

PDF

Characterization of lenticulostriate arteries using high-resolution black blood MRI as an early imaging biomarker for vascular cognitive impairment and dementia

PDF

Improved brain dynamic contrast enhanced MRI using model-based reconstruction

PDF

New methods for carotid MRI

PDF

Quantitative MRI for oxygenation imaging in cerebrovascular diseases

PDF

Estimating liver iron non-invasively with high-field MRI

PDF

Seeing sleep: real-time MRI methods for the evaluation of sleep apnea

PDF

Susceptibility-weighted MRI for the evaluation of brain oxygenation and brain iron in sickle cell disease

PDF

Pattern detection in medical imaging: pathology specific imaging contrast, features, and statistical models

PDF

Technology for improved 3D dynamic MRI

PDF

Contributions to structural and functional retinal imaging via Fourier domain optical coherence tomography

PDF

On the electrophysiology of multielectrode recordings of the basal ganglia and thalamus to improve DBS therapy for children with secondary dystonia

Asset Metadata

Creator Landes, Vanessa Lee (author)

Core Title Radiofrequency pulse performance for myocardial ASL

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 12/16/2019

Defense Date 10/16/2019

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

Tag arterial spin labeling,Fourier velocity encoding pulse design,MRI,MRI pulse sequence design,myocardial arterial spin labeling,OAI-PMH Harvest,RF predistortion,signal and image processing,velocity selective pulse design

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nayak, Krishna (committee chair), Wang, Danny (committee member), Zavaleta, Christine (committee member)

Creator Email vanessa.landes@live.com,vanessallandes@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-254600

Unique identifier UC11673336

Identifier etd-LandesVane-8062.pdf (filename),usctheses-c89-254600 (legacy record id)

Legacy Identifier etd-LandesVane-8062.pdf

Dmrecord 254600

Document Type Dissertation

Rights Landes, Vanessa Lee

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