University of Southern California Dissertations and Theses

Radio-frequency non-uniformity in cardiac magnetic resonance imaging

(USC Thesis Other)

Radio-frequency non-uniformity in cardiac magnetic resonance imaging

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content RADIO-FREQUENCY NON-UNIFORMITY
IN CARDIAC MAGNETIC RESONANCE IMAGING
by
Kyunghyun Sung
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2008
Copyright 2008 Kyunghyun Sung
Dedication
To my wife Heidi Heehyun
ii
Acknowledgements
First of all, I would like to express my deep gratitude to my advisor Krishna Nayak.
Throughout all the time of research and writing of this thesis, Krishna was always there
with patience, encouragement, and sense of humor. He was a remarkable teacher, a great
mentor, and sometimes a good friend. I was so lucky to meet him through the MRI class
(EE591) in 2004, and I have appreciated all the interesting discussions with him since
then.
I want to extend my appreciation to the members of my qualifying exam committee
and Ph.D. dissertation committee who have made the completion of this thesis: Dr.
Alexander Sawchuk, Dr. Richard Leahy, Dr. Surya Prakash, Dr. Antonio Ortega, and
Dr. Stephan Haas. I also thank to all EE and SIPI sta members for their enormous
administrative assistance: Diane Demetras, Gloria Halfacre, Talyia Veal, Mary Francis,
and Alan Weber.
The Magnetic Resonance Engineering Laboratory (MREL) was a unique place to
research, and I am very proud of being heavily involved in many initial setups with
Krishna. I have enjoyed spending time at MREL, and will miss all the MREL members.
I specially thank to Jon Nielsen for all his initiatives, and much advice on many issues
for my research. I also appreciate Houchun (Harry) Hu for sharing many thoughts on
iii
dierent problems and answering numerous technical questions in many aspects. I have
been really fortunate to work with Harry and Jon, and I am deeply indebted to them for
their great mentorship.
Joao Carvalho, Hsu-Lei Lee, and I joined the MREL almost at the same time, and
we have spent so much time together in EEB 412. With many useful (sometimes not
useful) discussions, I really appreciate the opportunity to meet Joao and Lei, as labmates
and friends. In addition, I acknowledge other "current" MREL members for useful dis-
cussions and collaborations: Taehoon Shin, Yoon-Chul Kim, Zungho (Wesley) Zun, and
Mahendra Makhijani. I also thank the "new generation" of MREL students for their
great enthusiasm: Samir Sharma and Travis Smith, as well as former members of MREL:
Chia Liu, Barry Venek and Zihong Fan.
I have remarkably benetted from great collaborations with several clinical and tech-
nical researchers: Gerald Pohost, Sam Valencerina, Hee-won Kim, Chuck Cunningham,
and Brian Hargreaves.
I gratefully acknowledge the nancial support from the Korea Science and Engineering
Foundation (KOSEF) scholarship during my Master's degree, and the grant supports from
the National Institute of Health (NIH) and American Heart Association (AHA) during
my Ph.D. program.
Aside from many colleagues at MREL, I have been fortunate to meet many wonder-
ful people at USC. They have made my ve years at USC an enjoyable and satisfying
experience. Particularly, I would like to show my thanks to USC Good Shepherd (GS)
(especially, to Jina Lee, Samuel Kim and Hae-Bum Yoon for their great leadership), and
iv
the engineering outreach program (especially, to Tara Chklovski). I appreciate all of other
close friends who have kept me going.
As a nal point, I wish to express my gratitude to my family for their support and
guidance. Mom and Dad were always encouraging and supporting me with unlimited
love. My older sister, Jeeyoung, has set always a great example, and I am very proud
of her at all times. Most of all, I would like to give my special thanks to my wife Hee-
hyun (Heidi) for her love and support. Her patient love enabled me to complete this work.
Kyunghyun Sung
University of Southern California
August 2008
v
Table of Contents
Dedication ii
Acknowledgements iii
List Of Tables ix
List Of Figures x
Abstract xvi
Chapter 1: Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2: MRI Background 6
2.1 Basic Principles of MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Main Field B
0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Radio-frequency (RF) Field B
1
. . . . . . . . . . . . . . . . . . . . 10
2.1.3 Linear Gradient Fields G . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.4 Bloch Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 RF Pulse Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Small-tip Excitation Pulse . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Adiabatic Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 High Field Cardiac MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 RF Non-uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Increased O-resonance (Susceptibility) . . . . . . . . . . . . . . . 22
2.3.3 Tissue Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 3: B
+
1
Non-uniformity Measurement 25
3.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Double Angle Method (DAM) . . . . . . . . . . . . . . . . . . . . . 26
3.1.2 Saturated Double Angle Method (SDAM) . . . . . . . . . . . . . . 27
3.1.3 Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
vi
3.2 Optimized SDAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Cardiac SDAM Pulse Sequence . . . . . . . . . . . . . . . . . . . . 31
3.2.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Chapter 4: B
+
1
Compensation for 2D Imaging 45
4.1 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 2DRF Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.2 Tailored 2DRF Pulse Design Based on Measurement . . . . . . . . 50
4.3 Phantom Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 In-vivo Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter 5: B
+
1
-insensitive Saturation Pulses 64
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.1 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.2 Measurement of B
0
and B
+
1
Variation . . . . . . . . . . . . . . . . 67
5.2.3 Optimization of Pulse Trains . . . . . . . . . . . . . . . . . . . . . 68
5.2.4 In-vivo Pulse Performance . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3.1 Measurements of B
0
and B
+
1
Variation . . . . . . . . . . . . . . . . 70
5.3.2 Simulated Pulse Performance . . . . . . . . . . . . . . . . . . . . . 71
5.3.3 In-vivo Pulse Performance . . . . . . . . . . . . . . . . . . . . . . . 75
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Chapter 6: Myocardial Signal Behavior during Balanced SSFP Imaging 81
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2.1 Simplied Balanced SSFP Signal Model . . . . . . . . . . . . . . . 84
6.2.2 Modied Balanced SSFP Signal Models . . . . . . . . . . . . . . . 85
6.2.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
vii
Chapter 7: Summary and Recommendations 101
7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.1.1 B
+
1
Inhomogeneity Measurements . . . . . . . . . . . . . . . . . . . 103
7.1.2 B
+
1
Compensation using 2DRF pulses . . . . . . . . . . . . . . . . 103
7.1.3 B
+
1
-insensitive Tailored Pulse Designs . . . . . . . . . . . . . . . . 104
7.1.4 Signal Behavior during Balanced SSFP Imaging . . . . . . . . . . 105
References 106
Appendix A: Small Tip-Angle Selective Excitation 113
A.1 Small-tip Slice Selective Excitation . . . . . . . . . . . . . . . . . . . . . . 113
A.2 Multidimensional Selective Excitation . . . . . . . . . . . . . . . . . . . . 115
Appendix B: Amplitude/Frequency Modulation Functions for BIR-4 118
Appendix C: Steady-state Signal Equation 120
viii
List Of Tables
2.1 Relation between the physical parameters and the static eld strength.
r
is the relative permittivity. . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 Repeatability and prole analysis data in the mid-short axis slices from all
ten subjects.
a
A represents the average standard deviation of the measured

ip angle (in degrees) over the LV ROI, and is an indicator of overall
repeatability.
b
B represents the relative approximation error between the
true (2D) pattern and the unidirectional (1D) approximation along the
primary in-plane axis of variation.
c

max
and
min
are the maximum and
minimum measured
ip angle over the LV ROI.
d
Variation is calculated
as (
max
-
min
)/
max
in percentage. . . . . . . . . . . . . . . . . . . . . 40
3.2 Repeatability and prole analysis data over the 3D LV volumes from all
ten subjects.
a
3D volume parameters include all six to ten slices in the
analysis.
b
A represents the average standard deviation of the measured

ip angle (in degrees) over the LV ROI, and is an indicator of overall
repeatability.
c
B represents the relative approximation error between the
true (2D) pattern and the unidirectional (1D) approximation along the
primary in-plane axis of variation.
d

max
and
min
are the maximum and
minimum measured
ip angle over the LV ROI.
e
Variation is calculated
as (
max
-
min
)/
max
in percentage. . . . . . . . . . . . . . . . . . . . . 41
4.1 Overview of dierent B1 shimming methods. . . . . . . . . . . . . . . . . 46
5.1 Prescribed
ip angles, maxjM
z
/M
0
j, and relative RF power for optimized
tailored pulse trains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 In-vivo performance of myocardial saturation pulses at 3 Tesla. . . . . . . 76
6.1 Computed relative saturation factors (SF) for dierent TR/ combinations
and the corresponding SF for each TR. SF was dened as SF
;min
-
SF
;max
and MT measurements were made for the upper triangular region.

The repeatability was tested with ve measurements. . . . . . . . . . . . 90
ix
List Of Figures
2.1 A spinning charged hydrogen nucleus producing a magnetic dipole moment. 7
2.2 When there is no external magnetic eld, spins are oriented randomly. The
net magnetization is zero. In the presence of a B
0
eld, spins align either
parallel or anti-parallel. The net magnetization becomes non-zero and the
ratio of parallel to anti-parallel follows the Boltzmann distribution. . . . . 8
2.3 In the presence of B
0
, a proton not only rotates about its own axis but also
precesses about the axis of B
0
. The frequency of precession is described
by the Larmor equation and is proportional to B
0
. . . . . . . . . . . . . . 9
2.4 B
1
radio frequency eld tuned to Larmor frequency and applied in trans-
verse plane excites the magnetization vector (gure provided by Brian
Hargreaves [27]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 B
1
induces rotation of magnetization toward transverse plane (gure pro-
vided by Brian Hargreaves [27]). . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Relaxation of magnetic spins. From a perturbed position, spins relax both
(a) longitudinally based on T
1
and (b) in the transverse plane based on T
2
. 12
2.7 Three types of linear gradient elds cause B
z
to vary linearly with position
(a) in the transverse plane and (b) along the longitudinal direction. . . . . 13
2.8 The Fourier Transform relationship between (left) the slice selective RF
pulse B
1
(t) and (right) the corresponding slice prole. . . . . . . . . . . . 16
2.9 An example for a 2DRF pulse design: (left) the 2-dimensional excitation
prole, and (right) the corresponding B
1
(t), G
x
(t), and G
z
(t). A
y-back
(the RF pulse is only transmitted during positive gradient lobes) echo-
planar trajectory is used in this example. . . . . . . . . . . . . . . . . . . 17
2.10 RF non-uniformity and susceptibility artifacts in 3T cardiac imaging. . . . 21
x
3.1 Pulse sequence diagrams for (a) DAM and (c) SDAM, and (b and d) their
corresponding M
z
/M
0
curves. The typical TR for 3T cardiac imaging is
more than 6 seconds to ensure full relaxation (i.e. f(T
1
;;TR) = 1) while
much smaller T
SR
can be utilized in SDAM (e.g. T
SR
= 500 ms). Note
that M
z
after the saturation pulse is zero, and both f(T
1
;;T
SR
) and
f(T
1
; 2;T
SR
) become identical (i.e. f(T
1
;;T
SR
) =f(T
1
; 2;T
SR
)6= 1). . 28
3.2 The eect of image noise on
ip angle measurement using double-angle
methods. The mean and standard deviation of estimated
ip angle (b )
as a function of true
ip angle () is plotted for two dierent values of
SNR
intrinsic
. The chart on the right re
ects the approximate noise statis-
tics of the in-vivo data presented in this thesis, which had a measured
SNR
intrinsic
of 70 to 120. Note that
b
becomes relatively small when
is larger than 30

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Cardiac SDAM pulse sequence. Full images are acquired with a prescribed
2 and prescribed
ip angle. (a) Acquisitions are cardiac gated in a
single breath-hold to prevent motion artifacts, and consist of a magneti-
zation reset, delay (T
SR
), fat saturation, and multislice acquisition. (b)
The RESET module consists of an 8 ms BIR-4 saturation pulse followed
by a dephaser. (c) The FATSAT preparation consists of a fat-selective
saturation followed by a dephaser. (d) The IMAGING module consists of
a slice-selective excitation, a short spiral readout (5.9 ms), and a dephaser.
Note that the IMAGING excitation is slice selective, while the RESET and
FATSAT excitations are not spatially-selective. . . . . . . . . . . . . . . . 33
3.4 Cardiac
ip angle maps from one representative volunteer at 3 Tesla. All
seven short-axis slices were acquired in a single 16 R-R breath-hold. Magni-
tude images are provided for anatomical reference. Note that the variation
appears strong and primarily unidirectional. . . . . . . . . . . . . . . . . . 36
3.5 Illustration of repeatability analysis. Pixel-by-pixel (a) mean (gray-scale
20

- 70

) and (b) standard deviation (0

- 10

) of the measured
ip angle
map in a short axis slice (slice #3 in subject #1). The metricA is computed
by averaging
b
(x;y) over the ROI (white circle). . . . . . . . . . . . . . 37
3.6 Illustration of prole analysis. (a) The approximation error, B(), as a
function of in-plane angle , dened in degrees clockwise from the vertical
axis. (b) Flip angle variationb (x;y) in a circular ROI can be approximated
by (c) a 1D function b (r) along the primary in-plane axis (dotted line).
The primary in-plane axis angle is 108

and the approximation error is
1.2% in this example (slice #3 in subject #1). . . . . . . . . . . . . . . . 38
xi
3.7 Mid-short axis B
+
1
maps in all ten subjects (eight healthy volunteers: 1-
8 and two cardiac patients: 9 and 10). Magnitude images are included
for anatomical reference. Within each ROI (white circle), the primary in-
plane axis of variation is indicated (dotted line). The
ip angle variation
in mid-short-axis slices was found to be 23 - 53%. . . . . . . . . . . . . . . 39
4.1 Proposed 2DRF excitation for B
+
1
compensation: (a) excitation pulse and
(b) excitation k-space trajectory. The subpulse duration is 0.5 ms, and
overall duration is 3 ms including all gradients. A
y-back echo-planar
design is used where RF is only transmitted during positive gradient lobes
of G
z
. Note that points a, b, and c indicate the same point on time on
both (a) and (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Measurement-based tailored 2DRF pulse design procedure. Data from one
slice in a cardiac study is shown for illustration. In this example, the
computed control parameters were: the primary in-plane axis = 86

,
max
= 90

, k
r
= 0.065, and = 80

. . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Measured (a and b) and simulated (c and d) excitation proles of the pro-
posed 2DRF pulse. The cross-section plots (e and f) along the r-direction
show an excellent agreement between experiment (solid line) and simu-
lation (dotted line). The measured slice thickness was 22% larger than
simulation. As expected, o-resonance results in a prole shift along the
r-axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Illustration of 2DRF excitation prole control using the design parameters:
(a)~ r, the radial axis of variation, (b) k
r
, the frequency of variation, and
(c) , prole shifting. After the primary in-plane axis is determined from
the measured B
+
1
prole, the parameters (k
r
,, and
max
) are chosen by
non-linear least squares estimation. Note that higher k
r
value was used
in (a) and (c), containing multiple null points. . . . . . . . . . . . . . . . . 54
4.5 Phantom validation using 2DRF pulses. The
ip angle varied from left (low

ip angle) to right (high
ip angle) using a conventional slice-selective RF
pulse. The proposed 2DRF was used to correct unidirectional
ip angle
variation over the ROI (white dotted circle). Magnitude images and
ip
angle distributions are shown (a and b) along with the corresponding
ip
angle histograms (c and d). The
ip angle SD/mean within the ROI was
improved from 10.4% (53:9

5:6

) to 4.9% (59:3

2:9

) using the proposed
2DRF approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
xii
4.6 Cardiac B
+
1
inhomogeneity compensation in a healthy volunteer at 3T.
Magnitude images and
ip angle distributions are shown (a and b) along
with the corresponding
ip angle histograms (c and d). Magnitude images
are shown for anatomical landmarks. The value of SD/mean within the LV
(white circle) was improved from 7.0% (58:3

4:1

) to 1.8% (51:2

0:9

)
using the proposed 2DRF pulse. . . . . . . . . . . . . . . . . . . . . . . . 57
4.7 Whole heart B
+
1
inhomogeneity compensation in a healthy volunteer at 3T.
Mean and SD plots (a and b) are compared for conventional excitation and
the proposed compensating 2DRF excitation for six short-axis slices. The
gray dotted line indicates the intended
ip angle (100%). The SD/mean
values (c) were computed for slice-selective and 2DRF (expected in simu-
lation and measured). Note that the expected (gray bars) and measured
(white bars) values show an excellent agreement except in the basal slice. 58
4.8 ROI-based B
+
1
inhomogeneity compensation in the head of a healthy vol-
unteer at 3T. The B
+
1
prole was parabolic in shape and two symmetric
ROIs (A and B) were selected. Using the proposed 2DRF approach, the

ip angle SD/mean was improved from 6.5% to 1.9% when focusing on
ROI A, and from 7.1% to 1.9% when focusing on ROI B. . . . . . . . . . 60
5.1 Schematic of a conventional SR-FGRE/SSFP pulse sequence used in rst-
pass MRI. Either 2-3 slices are acquired each heartbeat, or 4-6 slices are
acquired in an interleaved fashion every two heartbeats. The amount of
T
1
contrast is primarily determined by the type of preparation pulse and
the available T
1
recovery time (T
SR
). . . . . . . . . . . . . . . . . . . . . 66
5.2 Measured B
0
and B
+
1
inhomogeneity over the LV at 3 Tesla: (a) B
0
and
B
+
1
maps from a single slice for one subject, and (b) the combined 2D
histogram from all slices for all eight subjects. The extent of the B
0
-
B
+
1
ROI (red rectangle) was based on the extent of the B
0
-B
+
1
clusters
(red oval) computed using Gaussian mixture models for each slice in each
subject. The ROI contains 99.7% of all scattered pixels. . . . . . . . . . . 70
5.3 Behavior of residual M
z
and the corresponding RF energy as a function of
n. (a) MaxjM
z
/M
0
j, (b) MeanjM
z
/M
0
j, (c) SD of M
z
/M
0
, and (d) relative
RF energy were simulated for the BIR-4 pulse (dotted line), conventional
pulse train (gray line), and tailored pulse train (black line). The tailored
pulse train when n 3 shows superior saturation performance than the
BIR-4 and pulse train while maintaining lower relative RF energy than the
BIR-4 pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
xiii
5.4 Saturation pulse sequence diagrams for (a) the BIR-4, (b) conventional
pulse train and (c) tailored pulse train (n=3), and corresponding simu-
latedjM
z
/M
0
j proles (d-f). The B
0
-B
+
1
ROI is indicated by the red box.
The simulation prole for the tailored pulse train (f) shows reduced peak
jM
z
/M
0
j within the ROI. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.5 Representative normalized SR images with (a) the BIR-4, (b) conventional
pulse train, and (c) tailored pulse train in three cardiac views. The pro-
posed saturation pulse demonstrates superior saturation performance over
the LV and RV than the BIR-4 and pulse train. . . . . . . . . . . . . . . . 74
5.6 Optimization of BIR-4 amplitude and frequency modulation function pa-
rameters andtan(). Simulations of (a) mean(jM
z
/M
0
j) over the ROI as
a function of and tan(), and (b) relative RF power which is a function
of only. The red dot (relative RF power = 0.80) indicates the pulse used
in this study, and the green dot (relative RF power = 0.86) indicates the
pulse with the lowest residual magnetization. . . . . . . . . . . . . . . . . 77
5.7 The saturation eectiveness as a function of T
1
relaxation times. (a) Max
jM
z
/M
0
j, (b) MeanjM
z
/M
0
j, and (c) SD M
z
/M
0
were simulated for the
BIR-4 pulse (dotted line), pulse train (gray line), and tailored pulse train
(black line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.1 An introductory example of 2D balanced SSFP signal behavior. A sub-
stantial deviation between simulated (red solid line) and measured (blue
) signal has been observed. The simulated result suggests 22

as an opti-
mal
ip angle while the measured signal intensity shows 45

as an optimal

ip angle to produce the maximum myocardial signal. . . . . . . . . . . . 83
6.2 The illustration of the high TB (TB = 16; gray) and the low TB (TB
= 2; black) RF pulses: (a) RF pulses, (b)
ip angle proles, and (c)
their corresponding
ip angle histograms. The ideal slice prole with the
nominal
ip angle of 20

(dotted line) was shown in (b). . . . . . . . . . . 86
6.3 Phantom validation of the steady-state signal models: (a) representative
magnitude phantom images overlapped with a circular ROI, and (b) The
simplied signal model (dotted line - M
ss
), the modied signal model con-
sidering a non-ideal slice prole (solid line - M
ss;A
), and the measured
signal intensity over the ROI () as a function of the prescribed
ip angle. 92
xiv
6.4 The representative in-vivo B
0
and B
+
1
measurements. (a and b) The B
0
and B
+
1
eld inhomogeneities over the myocardium were overlapped with
the cardiac magnitude images. (c) The relative resonant oset W (f)
over the ROI (septal myocardium) and (d) the histogram of relative B
+
1
inhomogeneity over the ROI. The relative B
+
1
variation over the ROI was
averaged to be 0.67 in this subject. . . . . . . . . . . . . . . . . . . . . . . 93
6.5 In-vivo evaluation of the steady-state signal models in 3T cardiac imaging:
(a) selective cardiac cine images with dierent prescribed
ip angles, and
(b) the simplied signal model (dotted line - M
ss
), the proposed signal
model (solid line - M
ss;A+B+C
), and the measured myocardial signals over
the ROI () as a function of the prescribed
ip angle. . . . . . . . . . . . 94
6.6 The relative errors (mean standard deviation) with all possible steady-
state signal models for all ve subjects. The simplied steady-state model
(M
ss
) showed 28.2 4.3% of the relative error, and the signal model in-
cluding all three factors (M
ss;A+B+C
) reduced the relative error to 4.2
2.1%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.7 Cardiac images with dierent RF elongation scales with the TR of 5.6 ms.
Five repeated measurements with separate breath-holds were performed on
= 1 and 6. The myocardium signal intensity over the ROI was increased
by 9.8% using a six-fold elongated RF pulse ( = 6) and MTR(SF =
35) was measured to be 8.9%. . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.8 MTR values over the ROI as a function of the TR=SF combinations
when the actual
ip angle is (a) 31.4

and (b) 25.2

. The prescribed
ip
angle was 45

. The combination of 4.4/(41) and 5.2/(37) produced the
maximum MTR of (a) 15.2% and (b) 12.3%, respectively. The maximum
MTR was 15.6 2.9% over all four subjects. . . . . . . . . . . . . . . . . 97
C.1 Basic steady-state free precession sequence: A string of pulses separated
by a TR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
xv
Abstract
Cardiovascular magnetic resonance imaging (MRI) is now routinely used for evaluating
cardiac function, and myocardial viability. Due to its unique
exibility, MRI has the
potential to assess many other aspects of heart disease in the same examination, including
the evaluation of coronary arteries, functions of the heart valves, and perfusion of heart
muscle. However, the development of cardiac MRI is, in many ways, limited by signal-
to-noise ratio (SNR).
Compared to 1.5 Tesla, 3 Tesla MRI systems are able to achieve higher signal-to-
noise ratio due to increased polarization, which allows for improvements in spatial and/or
temporal resolution. Cardiac MRI at 3T, however, is signicantly dierent from imaging
at 1.5T because of a variety of artifacts that result from inhomogeneities of the static
magnetic eld (B
0
) and radio-frequency (RF) transmit eld (B
+
1
).
In this thesis, I present new methods to measure and mitigate one of these eects,
B
+
1
inhomogeneity. First, I present a variation of the saturated double-angle method for
measuring B
+
1
non-uniformity across the heart. Measured B
+
1
proles are then analyzed
to determine the amount of variation and dominant patterns of variation across the left
ventricle.
xvi
Secondly, I present tailored 2DRF excitation pulse designs that compensate for in-
plane B
+
1
non-uniformity in 2D imaging. Excitation pulse proles are designed to ap-
proximate the reciprocal of the measured B
+
1
variation where the variation over the left
ventricle was approximated as unidirectional.
Thirdly, I present a novel saturation pulse design that improves the performance
of saturation. The B
0
and B
+
1
variation across the left ventricle has been previously
measured and a train of weighted hard pulses is optimally chosen to saturate proton
spins over the expected region in B
0
-B
+
1
space.
Finally, I present a method to accurately predict the myocardial signal during bal-
anced steady-state free precession (SSFP) imaging. I included the eects of non-ideal
slice prole, o-resonance, and B
+
1
eld variation in a model that accurately predicts
myocardial signal behavior.
xvii
Chapter 1
Introduction
Magnetic Resonance Imaging (MRI) has been called 'the most important development in
medical diagnosis since the discovery of the x-ray 100 years ago' [29]. Compared to other
imaging modalities such as X-ray or ultrasound, MRI has the unique ability to acquire
several dierent types of soft tissue image contrast as well as
ow, spectral, and other
diagnostic information.
The phenomenon of nuclear magnetic resonance (NMR) was rst discovered indepen-
dently by Bloch [7] and Purcell [59] in 1945. For many years, development in NMR led to
the widespread use of NMR spectroscopy as a tool for identifying chemical compositions
based on dierences in atomic resonant frequencies. In 1973, Paul Lauterbur proposed
a method for constructing an image from spatially encoded NMR signals [43], which
spawned the eld of MRI.
MRI has evolved into a premier medical imaging modality for imaging soft tissue,
particularly in stationary body areas. Improved hardware, novel pulse sequences, and
new contrast mechanisms have further improved MRI and much of research today is
geared toward enabling new clinical applications.
1
1.1 Motivation
In the United States, cardiovascular disease is the leading cause of death among adults.
Among dierent imaging modalities such as echocardiography, X-ray angiography, and
single photon emission computed tomography (SPECT), MRI plays an important role
for high-resolution imaging of cardiac morphology, cardiac function, and identication of
myocardial scarring. In addition, MRI expands its role in the diagnosis and assessment
of patients with ischemic heart disease, by virtue of myocardial perfusion imaging and
coronary artery imaging.
The introduction and Food and Drug Administration (FDA) approval of 3 Tesla
whole body MRI platform in late 2001 provided a promising new platform for cardiac
imaging [18]. Compared to 1.5 Tesla MRI systems, 3 Tesla MRI can double image signal-
to-noise ratio (SNR) and the increased SNR can be used to improve spatial resolution or
shorten scan times. Despite many preliminary studies [47,50,73,90], signicant challenges
with regard to static (B
0
) and radio frequency (RF) eld (B
+
1
) homogeneities have limited
major progresses and clinical uses of cardiac imaging at 3T.
1.2 Outline
The thesis consists of four parts, all relating to the handling of B
+
1
inhomogeneity in 3T
cardiac MRI: (1) Rapid mapping of the B
+
1
eld, (2) Accurate slice selection using 2DRF
excitation pulses, (3) Accurate saturation using tailored pulse trains, and (4) Prediction
of myocardial signal in balanced steady-state free precession (SSFP) imaging. The outline
of the thesis is as follows:
2
Chapter 2: MRI Background
This chapter contains a basic overview of MR imaging concepts, with emphasis on the re-
lationship between the higher static magnetic eld and imaging parameters. Two types of
RF pulse designs (small-tip excitation and adiabatic RF pulses) are also brie
y explained.
Chapter 3: B
+
1
Non-uniformity Measurement
Knowledge of the B
+
1
eld is necessary for the calibration of pulse sequences, image-
based quantication, and SNR optimization. This chapter describes a novel, rapid, and
volumetric method for measuring B
+
1
non-uniformity across the heart. The B
+
1
non-
uniformity over the LV with body-coil transmission is on the order of 32 - 63%, and
a predominantly unidirectional pattern was observed in short-axis slices. The standard
deviation of multiple
ip angle measurements was less than 1.4

over the LV in all subjects,
indicating excellent repeatability of the proposed measurement method.
Chapter 4: B
+
1
Compensation in Slice Selective Excitation
This chapter describes a method to compensate B
+
1
non-uniformity using 2DRF pulses.
Based on the results from Chapter 3, excitation pulse proles are designed to approxi-
mate the reciprocal of the measured B
+
1
variation where the variation over the LV was
approximated as unidirectional. A simple 2DRF pulse design utilizing three subpulses
was used, such that proles could be quickly and easily adapted to dierent regions of
interest. Compared to conventional slice-selective excitation, the average
ip angle vari-
ation over the LV was reduced with p < 0.001 and the average reduction was 41% in
cardiac studies at 3 Tesla
3
Chapter 5: B
+
1
-insensitive Saturation Pulses
Complete and uniform saturation of the myocardium is essential for myocardial perfusion
imaging using the rst-pass of an exogenous contrast agent. At 3 Tesla, inhomogeneities
of both B
0
and B
+
1
elds have led to the use of adiabatic B
1
-insensitive rotation type-4
(BIR-4) pulses, which in practice are constrained by RF heating. This chapter describes
the design of trains of weighted hard pulses that are optimized for the measured variation
of B
0
and B
1
elds in the myocardium. These pulses are simple to design, and require
substantially lower RF power when compared to BIR-4 pulses. In volunteers at 3T, we
demonstrate that the proposed saturation pulse with three sub-pulses results in lower
peak and lower average residual longitudinal magnetization over the heart, compared to
8 ms BIR-4 pulses and conventional hard-pulse trains (p < 0.05).
Chapter 6: Myocardial Signal Behavior during Balanced SSFP Imaging
Balanced SSFP imaging has an established role in the cardiac magnetic resonance as-
sessment of ventricular function and wall motion. However, the measured in-vivo image
appearance does not always agree with simple theoretical predictions. More accurate sig-
nal predictions would enable optimization of imaging parameters such as the prescribed

ip angle and repetition time in order to maximize SNR and/or contrast-to-noise ratio
(CNR). This chapter describes the eects of non-ideal slice prole, o-resonance, B
+
1
variation, and magnetization transfer eects, to identify a model that accurately predicts
myocardial signal behavior during balanced SSFP imaging, over the range of imaging pa-
rameters routinely used at 3T. The conventional steady-steady signal formula showed the
4
relative error to be 28.2% suggesting a substantial dierence from the actual myocardium
signal, and the modied model reduced the relative error to 4.2%.
Chapter 7: Summary and Recommendations
The contributions presented in this thesis are summarized with recommendations for
future works.
5
Chapter 2
MRI Background
This chapter contains an introduction to radio frequency (RF) non-uniformity in high-
eld MRI. It starts with a brief outline for the basic principles and physics in MR which
can also be found in many popular textbooks [4,25,44,46,49]. A motivation of the higher
magnetic eld strength in MRI is outlined along with a discussion of some technical
challenges in 3T cardiac imaging.
2.1 Basic Principles of MRI
Atoms with an odd number of protons and/or neutrons (e.g.
1
H,
31
P,
23
Na and
13
C)
exhibit a nuclear spin angular momentum, represented by vectors. Qualitatively, these
nucleons are all spinning about their own axes and the spinning charged sphere, often
referred as spin, creates a magnetic dipole moment (shown in Figure 2.1). Without any
external magnetic eld, the spins are distributed randomly. If we add up all the spins,
the magnetic moments cancel each other and the net magnetization is zero.
1
H (proton) are dealt with in MR imaging because hydrogen protons are the most
abundant in the body (approximately 60% of the body is composed of water) and are the
6
Magnetic
dipole mement
Spinning
charged sphere
Figure 2.1: A spinning charged hydrogen nucleus producing a magnetic dipole moment.
most sensitive (gives rise to the largest signal) [49]. Therefore, unless noted otherwise,
the remainder of this thesis will assume
1
H imaging.
The nature of MR imaging is based on the interaction of spins including polarization,
precession, and relaxation. These spin behaviors are used to form images with three types
of magnetic elds: a) main eld B
0
, b) radio frequency eld B
1
, c) linear gradient elds
G.
2.1.1 Main Field B
0
In the presence of an external magnetic eld B
0
, two interesting phenomena occur to spins:
polarization and precession. First, spins tend to align either parallel or antiparallel to
the direction of B
0
, but more are parallel than antiparallel. This produces a non-zero
net magnetization, commonly called polarization or alignment (Figure 2.2). Second,
spins precess about the axis of the B
0
eld, called resonance (Figure 2.3). The resonant
frequency is known as the Larmor frequency.
7
B
0
off
B
0
B
0
on
Figure 2.2: When there is no external magnetic eld, spins are oriented randomly. The
net magnetization is zero. In the presence of a B
0
eld, spins align either parallel or anti-
parallel. The net magnetization becomes non-zero and the ratio of parallel to anti-parallel
follows the Boltzmann distribution.
A hydrogen proton has two energy states, denoted as -1/2 and +1/2. With the
B
0
eld, protons are aligned either parallel (n
+
, low energy state) or anti-parallel (n

,
high energy state) to the magnetic eld (shown in Figure 2.2). Macroscopically, the
uneven distribution of parallel and anti-parallel spins induces a net magnetization along
the z-direction or the longitudinal direction. The ratio of parallel to antiparallel spins
determines the strength of the longitudinal magnetization and is given by the Boltzmann
distribution,
n
+
n

=exp(
E
kT
) (2.1)
where k is the Boltzmann constant and T is the absolute temperature. The energy
dierence between parallel and anti-parallel E is linearly related to the strength of the
B
0
eld. The ratio of parallel to anti-parallel spins is roughly 6-7 parts per million at 1.5
Tesla, and therefore all imaging is based on a weak polarization.
8
B
0
z
x
y
Figure 2.3: In the presence of B
0
, a proton not only rotates about its own axis but also
precesses about the axis of B
0
. The frequency of precession is described by the Larmor
equation and is proportional to B
0
.
Second phenomenon is precession (Figure 2.3). The protons precess about the axis
of the external magnetic eld while spins continue to rotate about their own axis. Each
proton spins much faster about its own axis than it precesses around the axis of the
external magnetic eld. The frequency of precession is described by the Larmor equation,
!
0
=
B
0
: (2.2)
The resonance frequency, called Larmor frequency !
0
, is proportional to the main mag-
netic eld strength. Note that if we increase the static magnetic eld B
0
, both the
longitudinal magnetization and the resonant frequency will be increased.
Typically, the static eld strength of clinical systems ranges from 0.2 to 3 Tesla and a
strong homogeneous constant magnetic eld is highly desirable, especially in higher eld
9
x’
M
B
1
z
y’
(a) (b)
(c) (d)
x’
B
1
M
z
y’
x’
z
M
B
1
y’
x’
B
1
M
z
y’
Figure 2.4: B
1
radio frequency eld tuned to Larmor frequency and applied in transverse
plane excites the magnetization vector (gure provided by Brian Hargreaves [27]).
strength. When the magnetic eld is inhomogeneous, often called o-resonance, a myriad
of eects are introduced from image distortion to blurring and replication artifacts.
2.1.2 Radio-frequency (RF) Field B
1
The only detectable signal in MRI is an oscillating component in the transverse (x-y)
plane. The precession of magnetization in the transverse plane induces an oscillating
voltage which can be detected by a receive coil. The magnetization vector M
0
has no
10
x’
M
0
B
1
z
y’
x
M
0
B
1
z
y
(a) (b)
Figure 2.5: B
1
induces rotation of magnetization toward transverse plane (gure provided
by Brian Hargreaves [27]).
component along the x or y axis and therefore an additional magnetic eld is necessary
to perturb magnetic spins out of their equilibrium state.
The purpose of the RF pulse is to generate a readable signal by
ipping the longitudi-
nal magnetization. The RF pulse is tuned to the resonant frequency !
0
and transmitted
into the transverse plane, perpendicular to the magnetization vector. Eectively, B
1
, a
weak magnetic eld generated by the RF pulse, applies a torque which rotates the mag-
netization vectors. Figure 2.4 shows the process in which the longitudinal magnetization
is
ipped toward the transverse plane. Note that the strength of the RF pulse B
1
and its
duration determine the
ip angle (the fraction angle of a single precession).
The excitation process can also be viewed in a rotating frame where the coordinate
system rotates at the Larmor frequency (!
0
) about the z-axis. Compared to the still
coordinate frame or the laboratory frame (Figure 2.5a), the magnetization tips from the
longitudinal axis smoothly to the transverse plane in the lab frame (Figure 2.5b).
11
M
0
M
z
M
xy
t t
M
0
exp(-t/T
2
) M
0
(1-exp(-t/T
1
))
(a) (b)
Figure 2.6: Relaxation of magnetic spins. From a perturbed position, spins relax both
(a) longitudinally based on T
1
and (b) in the transverse plane based on T
2
.
After perturbed from equilibrium alignment by the RF pulse, the magnetization re-
turns to its equilibrium position based on two time constant (T
1
and T
2
). The longi-
tudinal relaxation rate T
1
species the relaxation rate along the z direction while the
transverse relaxation rate T
2
species the relaxation rate in the x-y plane. Both relax-
ation rates vary in dierent tissues and play an important role in determining the signal
intensity and contrast of the resulting image. The longitudinal magnetization due to T
1
relaxation and the transverse magnetization due to T
2
relaxation are shown in Figure 2.6.
2.1.3 Linear Gradient Fields G
In the presence of B
0
, all spins possess the same resonance frequency!
0
and the RF pulse
is also tuned to one value !
0
. Because the excitation RF coil encompasses the entire
region of interest, it is not possible to excite a selected portion of the volume without
any spatial partiality of the resonant frequency. In addition, the received signal has no
12
(a) (b)
z
z
x,y x,y
Figure 2.7: Three types of linear gradient elds cause B
z
to vary linearly with position
(a) in the transverse plane and (b) along the longitudinal direction.
spatial information and can not be distinguished the signals generated from dierent
spatial location.
Three types of gradient coils (slice select, frequency encoding, and phase encoding)
are employed for the purpose of spatial discrimination (shown in Figure 2.7). In addition
to B
0
, linear gradient magnetic elds produce a variation of the longitudinal component
of the magnetic eld with position,
B
z
=jB
0
j +Gr (2.3)
where G is the gradient vector, and r is a position vector with respect to a central origin.
The variation of longitudinal eld strength results in a corresponding linear variation
13
of resonant frequency with position. This resonant frequency dierence resolves spatial
position in reconstructed images.
2.1.4 Bloch Equation
The behavior of the magnetization vector M is characterized by the Bloch equation:
dM
dt
= (M
B)
M
x
^ x +M
y
^ y
T
2

(M
z
M
0
)^ z
T
1
; (2.4)
where ^ x, ^ y, and ^ z are unit vectors in the x, y, and z directions respectively, M
0
is the equi-
librium magnetization arising from the main eld B
0
, and B represents the net magnetic
eld vector. Note that the equation expresses all the main spin behaviors: polarization
(M
0
^ z), precession (
dM
dt
=M
B
0
^ z), and relaxation (with T
1
and T
2
)
2.2 RF Pulse Design
The general approach to excitation involves the application of a RF magnetic eld in
the transverse plane, as discussed inx 2.1.2. RF pulses can be divided into excitation,
refocusing, and inversion pulses based on their eect on the magnetization. In each
operation, many dierent RF pulse design schemes can be considered and we discuss two
main types of RF pulses with dierent magnetization tipping mechanisms in the following
section.
14
2.2.1 Small-tip Excitation Pulse
Slice Selective Excitation:
Ignoring relaxation and o-resonance, the Bloch equation (Eq. 2.4) for slice-selective
excitation in the rotating frame can be expressed as
0
B
B
B
B
B
B
@
_
M
x
_
M
y
_
M
z
1
C
C
C
C
C
C
A
=
0
B
B
B
B
B
B
@
0 G
z
z 0
G
z
z 0 B
1
(t)
0 B
1
(t) 0
1
C
C
C
C
C
C
A
0
B
B
B
B
B
B
@
M
x
M
y
M
z
1
C
C
C
C
C
C
A
: (2.5)
With the initial state (0,0,M
0
), the small-tip approximation assumes that M
z
is approxi-
mately equal to its equilibrium value M
0
(constant),
M
z
M
o
and
dM
z
dt
0: (2.6)
Under this assumption, Eq. 2.5 can be simplied and solved as the Fourier Transform
(FT) relation between B
1
(t) and M
xy
(z) (see Appendix A.1 for further details),
M
xy
(z) =i
M
0
Z
T
0
B
1
(t)e
izk(t)
dt: (2.7)
where k(t) is dened as k(t) =
R
T
t
G
z
(s)ds [4, 49, 57]. k(t) is a spatial frequency
variable given by the integral of the remaining gradient area. Therefore, the slice prole
(M
xy
(z)) is the FT of the applied RF energy along a k-space trajectory k(t) determined
by the gradient waveform G
z
(s).
15
RF pulse Slice Profile
- M
x
- M
y
FT
time z
Figure 2.8: The Fourier Transform relationship between (left) the slice selective RF pulse
B
1
(t) and (right) the corresponding slice prole.
An example is shown in Figure 2.8 where the RF pulse (left) has been chosen such
that its frequency spectrum excites a certain slice region along z (right). A Hamming
windowed sinc waveform was used in this example. A useful concept for slice selection
is the time-bandwidth (TB) product, which is duration of the RF pulse multiplied by
width of the pass-band. RF pulses with the same TB have the same shape of the slice
prole, even if they have dierent RF pulse durations. Typically, the TB represents the
number of zero crossings of the RF waveform, and the example in Figure 2.8 has a TB of 8.
Multidimensional Excitation:
The principle of the Fourier-domain relationship can be extended to higher-dimensional
selectivity by applying gradients G
r
(t) in several spatial directions r during the RF
pulse [57]. Then, the transverse magnetization M
xy
is proportional to,
M
xy
(x;y)/FT (W (k)S(k)) (2.8)
16
2D excitation 2DRF pulse
RF
G
y
G
z
z
y
Figure 2.9: An example for a 2DRF pulse design: (left) the 2-dimensional excitation
prole, and (right) the corresponding B
1
(t), G
x
(t), and G
z
(t). A
y-back (the RF pulse
is only transmitted during positive gradient lobes) echo-planar trajectory is used in this
example.
where W (k) is a spatial frequency weighting function and S(k) is a a spatial frequency
sampling function [53,57]. See Appendix A.2 for more details. It denes the relationship
between the RF pulse shape and the multidimensional excitation prole, which signi-
cantly facilitates the actual RF pulse design.
At the pulse sequence level, there exist several ways to generate the W (k)S(k). Typi-
cally, the transmit k-space is covered in a
y-back scheme (RF is only transmitted during
positive gradient lobes) [19, 94]. This approach is highly robust against gradient imper-
fections since most of them aect k-space transverse of equal directions in nearly the
same way. Conversely, the forward-backward (non-
yback) design where RF power is
applied during both positive and negative gradient lobes is more time-ecient but is also
more prone to eddy-current and o-resonance eects [53]. An example for 2-dimensional
excitation using a
y-back echo-planar RF pulse trajectory is shown in Figure 2.9.
17
2.2.2 Adiabatic Pulse
Adiabatic Half-Passage (AHP) and Full-Passage (AFP) Pulses:
The RF pulse excites a certain band of spectral frequencies, and its carrier frequency
is applied at the center of the spectral region of interest. The conventional RF pulses
typically keep the carrier frequency constant, and the B
1
eld strength determines the

ip angle :
=
Z
T
0
B
1
(t)dt; (2.9)
where T is the RF pulse duration. Here, the non-uniform B
1
eld directly relates
ip
angle variation since the
ip angle is proportional to the B
1
amplitude.
An alternative RF tipping approach is to change the carrier frequency with time.
These frequency-swept pulses, known as adiabatic pulses, are a special class of the RF
pulses, and have amplitude and frequency modulation functions to sweep the eective B
1
eld from one side of resonance to the other side. The adiabatic pulses do not follow the
conventional relationship, as described in Eq. 2.9. Instead, the magnetization follows a
sweep diagram, determined by the amplitude/frequency modulation functions, and the
net rotation of magnetization is produced by the nal orientation of the eective B
1
eld. The spins will experience the uniform
ip angle as long as the amplitude of the
B
1
modulation envelope exceeds a threshold, often called a adiabatic condition. These
adiabatic approaches are highly insensitive to B
1
eld inhomogeneity because the
ip
angle is not proportional to the B
1
eld amplitude [4,22,23,86].
Adiabatic pulses which rotate longitudinal magnetization to the transverse plane are
called adiabatic half-passage (AHP) pulses (90

excitation), and to the -z axis are called
18
adiabatic full-passage (AFP) pulses (180

inversion) [3,68,86].
Composite Adiabatic Pulses (BIR-4):
The classical adiabatic passage pulses (AHP/AFP) are insensitive to B
1
eld inhomogene-
ity only when certain conditions of the sweep diagram meet. The net
ip angle should a
multiple of 90

because the nal orientation of the eective B
1
eld only remains the same
when it is on the transverse plane (90

) or along -z axis (180

). Secondly, o-resonance
can cause a shift in the sweep diagram, and the net rotation is aected by the frequency
response prole. To ensure a sucient B
0
bandwidth, the adiabatic pulses typically re-
quire long pulse duration and high RF power. In addition, the magnetization not along
with the longitudinal axis is not aected by these types of pulses, making adiabatic pulses
hard to use in a plane rotation, which is important in spin-echo sequences.
The plane rotation of any desired
ip angle can be achieved by the class of composite
adiabatic pulses, known as B
1
independent rotation (BIR) pulses. Unlike the previous
composite adiabatic pulses (BIR-1 and BIR-2), the modulation functions for the BIR-4
pulse are symmetric with respect to the center of the pulse. The symmetry of these
modulation functions re
ects the symmetric B
0
bandwidth (o-resonance performance).
The BIR-4 pulse is composed of four adiabatic half-passage pulses, and provides both
arbitrary choice of rotation angle and immunity to B
0
and B
1
inhomogeneities [70]. The
details of the amplitude and frequency modulation functions are in Appendix B. Although
the BIR-4 pulse is robust for o-resonance, it still requires long pulse duration and high
RF power and the both limitations are even worse than the conventional adiabatic passage
pulses.
19
Physical Parameters Relationship
Signal-to-noise ratio SNR/B
0
Susceptibility f/B
0
Chemical shift f
cs
/B
0
Specic Absorbtion Rate (SAR) SAR/B
2
0
RF wavelength () / 1=(B
0
p

r
)
Table 2.1: Relation between the physical parameters and the static eld strength.
r
is
the relative permittivity.
2.3 High Field Cardiac MRI
As discussed in the previous section (x 2.1.1), a stronger static eld results in both greater
polarization and higher resonant frequency of nuclear spins. The greater polarization
directly benets the image signal-to-noise ratio (SNR) while the higher resonant frequency
causes some drawbacks due to increased o-resonance. In addition, tissue relaxation time
varies with eld strength and contrast between dierent types of tissue may be increased
by the higher eld strength. Table 2.1 contains a summary of relationship between several
physical parameters and the eld strength.
The predominant eld strength for clinical cardiovascular MRI is 1.5 Tesla. The
emergence with FDA approval of the 3 Tesla imaging platform in late 2001 has opened
up a wide range of possibilities for improving cardiac MRI. Compared to 1.5T, 3T MRI
can double the SNR as well as may increase the tissue contrast. The improved SNR can
be used to shorten the acquisition time, to improve spatial resolution at a xed scan time,
or a combination of both.
20
s u r f a c e c oi l
S u s c e p t i b i l i t y A r ti f a c t R F P e n e t r a t i o n A r t i f a c t a: b:
Figure 2.10: RF non-uniformity and susceptibility artifacts in 3T cardiac imaging.
The number of installed 3T scanners continues to grow, largely motivated by com-
pelling image quality in neurological, musculoskeletal, and angiographic applications.
However, major improvements in 3T cardiac MRI have not been shown yet and the
progress has been slower due to the technical challenges: a) RF non-uniformity, b) in-
creased o-resonance or susceptibility, and c) RF heating.
2.3.1 RF Non-uniformity
The B
1
eld consists of two dierent parts: the RF transmit eld (B
+
1
) and the reception
eld (B

1
). In particular, inhomogeneous B
+
1
produces non-uniform
ip angles, causing
spatially dependent tissue contrast and signal intensity. Unlike other intensity variation,
the contrast variation due to RF non-uniformity is problematic since it is hard to correct
in post-processing, and it can hurt the diagnostic power and hamper the quantitative
21
imaging. Figure 2.10a shows one cardiac example that contains both B
+
1
and B

1
inho-
mogeneity artifacts [47].
B
+
1
non-uniformity is in
uenced by several factors including the distance from the
RF transmit coil, conductivity, tissue dielectric constant, and factors related to the body
size and RF wavelength. In 3T cardiac imaging, the RF wavelength is comparable to the
chest size and wave propagation eects result in more severe and diverse patterns of RF
non-uniformity [11,24,69,81,90].
2.3.2 Increased O-resonance (Susceptibility)
Magnetic susceptibility is the degree of magnetization of a material in response to an
external magnetic eld. When two dierent tissues are next to each other, dierent
magnetic susceptibilities cause local distortions in the magnetic eld and the distortions
scale roughly linearly with the eld strength (shown in Table 2.1).
Figure 2.10b shows an example of susceptibility artifacts [47]. An coronary artery
image is obscured by local susceptibility artifact (black arrow). Near air-tissue interfaces
and certain tissue-tissue interfaces induce resonant frequency shifts in cardiac imaging
and a myriad of eects are introduced to MR acquisitions. This results in artifacts in the
MR image, mostly a loss of signal (T
2
*), but also a distortion of the image.
2.3.3 Tissue Heating
The RF transmit eld has associated electromagnetic waves encompassing two compo-
nents: an electric component and a magnetic component. The magnetic component is
only of interest while the unavoidable electric component causes tissue heating. The
22
heating is measured by the Specic Absorption Rate (SAR), and increases quadratically
with eld strength, as described in Table 2.1. The FDA limits patient heating to 4 W/kg
averaged over the whole body for any 15 minute period; 3 W/kg averaged over the head
for any 10 minute period; or 8 W/kg in any gram of tissue in the extremities for any
period of 5 minutes.
With the quasi-static approximation, the SAR can be expressed as
SAR =!
2
0
jB
1
j
2
r
2
=; (2.10)
where is the density of tissue, and is the conductivity of tissue. B
1
is the RF pulse
amplitude and!
0
is the Larmor frequency. The coil diameter or patient size is specied by
r. The safety limits are typically not considered restrictive at 1.5T, but often prohibitive
at 3T and therefore careful consideration of RF pulse design is required.
2.4 Experimental Setup
For this thesis, all experiments were performed on two identical GE Signa 3.0 T EXCITE
systems (General Electric Healthcare, Waukesha, WI) each with gradients capable of
40 mT/m amplitude and 150 T/m/s slew rate, and a receiver supporting 4 s sampling
( 125 kHz). Quadrature birdcage body coils (60cm diameter and 32 rungs) were used for
RF transmission and an 8-channel cardiac phased array coil was used for signal reception.
Parallel imaging was not used. The transmit gain was calibrated using the vendor-
supplied pre-scan process and the localized center frequency was adjusted over a 3D
region of interest.
23
The institutional review boards of the University of Southern California approved the
imaging protocols. Subjects were screened for magnetic resonance imaging risk factors
and provided informed consent in accordance with institutional policy.
24
Chapter 3
B
+
1
Non-uniformity Measurement
Knowledge of B
+
1
non-uniformity is crucial for pulse sequence calibration, image-based
quantitation, SNR and contrast-to-noise (CNR) optimization, and the design of new pulse
sequences. Estimated variations of 30 - 50% in the B
+
1
eld over the heart at 3 Tesla
have been reported in the literature [11,24,69]. However, the complete analysis of in-vivo
B
+
1
variations in the chest has been limited by the lack of time-ecient methods for B
+
1
mapping where the technique is required to be fast (single breath-hold) and volumetric
(whole heart coverage) .
3.1 Related Works
In the presence of B
+
1
non-uniformity, the measured actual
ip angle (x;y) can be
expressed as:
(x;y) =
nom
b
1
(x;y) (3.1)
where
nom
is the nominal
ip angle (operator prescribed value in the MRI scanner) and
b
1
(x;y) is the spatially varying relative RF amplitude. Among several existing methods
25
for B
+
1
mapping in static body regions [1,11,24,32,36,71,83,88], one of the most simplest
and the most straightforward methods to measure (x;y) is the double angle method
(DAM) [35,36,71,72], and the following describes the conventional DAM and its variation.
3.1.1 Double Angle Method (DAM)
The magnitude image (I
nom
(x;y)) with the prescribed
ip angle
nom
of a gradient echo
(GRE) sequence can be expressed as:
I
nom
(x;y) =(x;y)sin((x;y))f(T
1
(x;y);(x;y);TR)S(x;y)e
TE=T

2
(3.2)
where is a system constant, (x;y) is the spin density, S(x;y) is the receive coil sensi-
tivity, and TE is the echo-time. (x;y) is the spatial distribution of the actual
ip angle,
andf(T
1
(x;y);(x;y);TR) is the T
1
relaxation factor with the preceding
ip angle and
repetition time (TR). If we acquire images with identical scan parameters except
nom
,
only and f(T
1
;;TR) will be altered and other signal-aecting parameters ((x;y),
rho(x;y), S(x;y), and e
TE=T

2
) will remain the same.
With Eq. 3.2, the ratio of magnitude images with two dierent
ip angles,
nom
and
2
nom
, can be written as:
I
2nom
(x;y)
I
nom
(x;y)
=
sin(2(x;y))f(T
1
(x;y); 2(x;y);TR)
sin((x;y))f(T
1
(x;y);(x;y);TR)
: (3.3)
Note that other image non-uniformities are completely canceled out, but there still
remains an unwanted T
1
relaxation factor f(T
1
;=2;TR). This limits the further
26
simplication of the remaining trigonometric functions, and it is not trivial to remove
f(T
1
;=2;TR) because f(T
1
;=2;TR) requires =2 as a priori knowledge.
The simplest way to eliminatef(T
1
;=2;TR) is to accommodate a long TR, known
as a double angle method (DAM). With a long TR (TR 5T
1
), the longitudinal magne-
tization (M
z
) before each RF pulse can be fully recovered, and both T
1
relaxation factors
become identical (i.e. f(T
1
;;TR) =f(T
1
; 2;TR) = 1). As long as this condition holds,
Eq. 3.3 can be simply reduced to:
I
2nom
(x;y)
I
nom
(x;y)
=
2 sin((x;y)) cos((x;y))
sin((x;y))
= 2 cos((x;y)): (3.4)
The actual
ip angle (x;y) can then be easily computed by:
(x;y) =arccos(
I
2nom
(x;y)
2I
nom
(x;y)
): (3.5)
The B
+
1
mapping using DAM has been validated to be adequate and accurate in
static regions, and well explored in many studies [35,36,71,72]. However, a long imaging
time still limits its applicability to dynamic body regions, and is considered to be a
main drawback. For example, the typical TR constraint to ensure full relaxation for 3T
cardiac B
+
1
mapping is more than 6 seconds (TR > 51200 ms), and the total scan time
is required to be at least more than 6 minutes.
3.1.2 Saturated Double Angle Method (SDAM)
Cunningham et al. recently proposed the saturated double angle method (SDAM), which
permits rapid B
+
1
mapping with TR much shorter than T
1
[11]. Figure 3.1 illustrates
27
b:
α° 2α°
D
A
Q
D
A
Q
°
TR
a:
α° 2α°
S
A
T
D
A
Q
D
A
Q
°
T
SR
c:
d:
M
z
/M
0
ƒ(T
1
,α,TR)
ƒ(T
1
,α,T
SR
)
M
z
/M
0
S
A
T
Figure 3.1: Pulse sequence diagrams for (a) DAM and (c) SDAM, and (b and d) their
corresponding M
z
/M
0
curves. The typical TR for 3T cardiac imaging is more than
6 seconds to ensure full relaxation (i.e. f(T
1
;;TR) = 1) while much smaller T
SR
can
be utilized in SDAM (e.g. T
SR
= 500 ms). Note that M
z
after the saturation pulse is
zero, and both f(T
1
;;T
SR
) and f(T
1
; 2;T
SR
) become identical (i.e. f(T
1
;;T
SR
) =
f(T
1
; 2;T
SR
)6= 1).
the dierence between conventional DAM and SDAM. The method includes a saturation
(SAT) pulse after each data acquisition (DAQ) with the goal of putting the spin popu-
lation in the same state regardless of excitation
ip angles for the preceding acquisition.
Since the saturation pulse at the end of each data acquisition resets the longitudinal
magnetization to a known state (i.e. f(T
1
;;TR) =f(T
1
; 2;TR)6= 1), the B
+
1
eld can
be still derived from the ratio of signal magnitudes using Eq. 3.5. SDAM with TR < T
1
was successfully validated against DAM with TR 5T
1
in phantoms and static body
28
regions. The feasibility of rapid cardiac B
+
1
mapping was shown but the methodology
was susceptible to irregular heart-rates and B
0
and B
+
1
variation.
3.1.3 Noise Analysis
Considering noise, both base images (I
2nom
and I
nom
) using SDAM can be rewritten
as:
I
nom
(x;y) =jI
nom
(x;y) +n(x;y)j: (3.6)
Image noise, n(x;y), is modeled as additive I.I.D. bi-variate Gaussian with zero mean
and variance
2
n
[49].
Provided that the saturation of magnetization destroys M
z
uniformly, we can decom-
pose the estimate ofb (x;y) into true
ip angle (x;y) and noise n

(x;y).
b (x;y) =(x;y) +n

(x;y) (3.7)
where n

(x;y) is noise in the
ip angle map derived from eqn [3.6] and can be analyzed
using second order statistics: E(b (x;y)) = (x;y) +E(n

(x;y)) and VAR(b (x;y)) =
VAR(n

(x;y)). Both E(b (x;y)) and VAR(b (x;y)) are dependent on the true
ip angle
(x;y) and the SNR
intrinsic
(x;y) where we dene SNR
intrinsic
as
SNR
intrinsic
=
f(T
1
;T
SR
)

n
(3.8)
This provides a convenient measure for the reliability of the
ip angle measurements.
TheE(b ) and
b
are plotted as a function of true
ip angle for two values ofSNR
intrinsic
29
0 20 40 60 80
20
40
60
80
100
SNR
intrinsic
= 20
True flip-angles (degree)
0 20 40 60 80 100
20
40
60
80
100
SNR
intrinsic
= 100
True flip-angles (degree)
Estimated flip-angles (degree)
± σ
α
E(α)
± σ
α
E(α)
Figure 3.2: The eect of image noise on
ip angle measurement using double-angle meth-
ods. The mean and standard deviation of estimated
ip angle (b ) as a function of true

ip angle () is plotted for two dierent values of SNR
intrinsic
. The chart on the right
re
ects the approximate noise statistics of the in-vivo data presented in this thesis, which
had a measured SNR
intrinsic
of 70 to 120. Note that
b
becomes relatively small when
is larger than 30

.
in Figure 3.2. It is clear that double-angle methods are most reliable when the true
ip
angle, (x;y), is close to 90

. For the cardiac studies, intrinsic SNR was roughly 70-120,
indicating that error in the
ip angle maps is quite small as long as the measured
ip
angle is larger than 30

. Note that the intrinsic SNR is large in B
+
1
mapping applications
because of the relatively coarse spatial resolution.
3.2 Optimized SDAM
We implemented a variation of SDAM for B
+
1
measurement across the entire heart in a
single breath-hold by considering the B
0
and B
1
sensitivity of saturation pulses, possible
variations in heart rate, and possible cross-talk between slices in a multi-slice acquisition.
In addition, we measured and analyzed whole-heart B
+
1
proles from 10 subjects using
30
two 3T MRI scanners with body-coil transmission. Repeatability testing was performed
to determine practical utility of the measurement methodology for pre-scan calibration.
Prole analysis was performed to determine patterns of variation that may be exploited
during B
+
1
shimming.
3.2.1 Cardiac SDAM Pulse Sequence
Successful multi-slice cardiac B
+
1
measurement at 3T using SDAM requires: (a) robust
magnetization saturation in the presence of the B
0
and B
+
1
inhomogeneity, (b) identical
saturation recovery time (T
SR
) even during irregular R-R intervals, and (c) minimization
of cross-talk between adjacent slices in an interleaved multi-slice acquisition.
To address the rst issue, we examined the eectiveness of various saturation pulses.
The performance of saturation pulses as a function of B
0
and B
+
1
inhomogeneity was
investigated [11], and we selected an adiabatic composite pulse (BIR-4) [70] to support
a B
0
bandwidth of 130 Hz, typical for 3T cardiac imaging [50]. Although the BIR-4
pulse (8 ms) has longer pulse duration and higher RF power than conventional pulses, its
eects are minimal in this work because the pulse is applied only once per R-R interval
and its duration is relatively small compared to the total image acquisition time (80 ms).
The second issue deals with variations in the R-R interval. When the saturation pulse
is timed at the end of data acquisition [11], even a small change in heart rate produces
variation in T
SR
, causing an error in the true
ip angle calculation. In this work, we
timed the saturation pulse with a prospective triggering signal to make T
SR
independent
of heart rate, producing more robust B
+
1
mapping.
31
The third issue deals with multi-slice acquisitions, for which B
+
1
measurements may
be aected by
ow-induced cross-talk between slices. If TR for each slice is too long or
an inter-slice gap is too small, cross-talk can occur because the through plane
ow can
reach to the next slice to be imaged. The maximum through plane
ow (V
max
) without
cross-talk can be derived from the inter-slice gap (SG) and TR,
V
max

SG
TR
(3.9)
We implemented a short multi-slice acquisition and enforced a minimum gap of 15 mm.
For TR of 11 ms, this gap completely avoids cross-talk for through plane velocities in the
left ventricle (LV) up to 1.36 m/s.
The pulse sequence, shown in Fig. 3.3, consists of three modules. The RESET module
is timed with the gating signal, and consists of a BIR-4 saturation pulse (8 ms) followed
by a gradient spoiler. The FATSAT module consists of a fat-selective excitation (8 ms)
followed by a gradient spoiler. The IMAGING module consists of a slice selective exci-
tation, 5.9 ms spiral readout, and gradient spoiler. T
SR
begins at the end of the RESET
module. T
SR
for slice #1 was set to 300 - 400 ms for plethysmograph gating and 500 -
600 ms for electrocardiogram (ECG) gating, depending on the heart rate.
32
RF
Gz
Gx
Gy
IMAGING module:
2αº tip T
SR
FATSAT module:
RF
Gz
|RF|
Gz
RESET module: b:
c:
d:
a:
F
A
T
S
A
T
R
E
S
E
T
1 2 6 1 2 6 1 2 6
RF
� �
� �
F
A
T
S
A
T
F
A
T
S
A
T
αº tip 2αº tip
R
E
S
E
T
R
E
S
E
T
TR
Figure 3.3: Cardiac SDAM pulse sequence. Full images are acquired with a prescribed
2 and prescribed
ip angle. (a) Acquisitions are cardiac gated in a single breath-
hold to prevent motion artifacts, and consist of a magnetization reset, delay (T
SR
), fat
saturation, and multislice acquisition. (b) The RESET module consists of an 8 ms BIR-
4 saturation pulse followed by a dephaser. (c) The FATSAT preparation consists of a
fat-selective saturation followed by a dephaser. (d) The IMAGING module consists of a
slice-selective excitation, a short spiral readout (5.9 ms), and a dephaser. Note that the
IMAGING excitation is slice selective, while the RESET and FATSAT excitations are
not spatially-selective.
33
3.2.2 Data Analysis
Circular regions of interest (ROIs) covering left ventricular myocardium and blood pool
were manually dened based on magnitude images. Based onb (x;y), the percentage of

ip angle variation was dened as
Variation =
b
max
b
min
b
max
100 % (3.10)
Repeatability test
We used the standard deviation (SD) across measurements on the same subject and
under the same conditions (imaging parameters and scan plane). The repeatability test
determined an upper bound of measurement repeatability and indicated the usefulness
of the technique for pre-scan calibration.
Factors that likely contributed to the variation in measurements were n

(x;y) and
inconsistent breath-hold positions. Pixel-by-pixel mean E(b (x;y)) and SD
b
(x;y) of
the
ip angle maps based on the 5 - 10 measurements were computed to provide the
repeatability. The pixel based
b
(x;y) was then averaged over the ROI to produce a
single number
A =E(
b
(x;y)) ; x;y2ROI (3.11)
as an indicator of overall repeatability.
Prole analysis
After observing that the in-plane
ip angle variations were primarily unidirectional
over the LV, we attempted to model the measured
ip angle prole, b (x;y), with a
34
one-dimensional approximation in each short-axis slice. We computed minimum mean
squared error (MMSE) 1D approximations,b (r), at all angles with a 1 degree increment,
and dened the primary in-plane axis as the one that minimized the approximation error,
B:
B =E(
jb (x;y)b (r)j
jb (x;y)j
) 100 % ; x;y2ROI (3.12)
3.3 Experimental Setup
The acquisition parameters were: 2.6 ms sinc RF pulse, TE = 2 ms, TR = 11 ms, FOV
= 30 cm, 2.2 mm in-plane resolution, and 5 mm slice thickness. Only the rst 1.9 ms
of each spiral readout was used during reconstruction by applying an appropriate sized
Hamming window to the raw k-space data. This increased the base image SNR while
reducing the in-plane spatial resolution to 5 mm.
Cardiac B
+
1
measurements were acquired in 8 healthy volunteers and 2 cardiac patients
(8 males and 2 females, ages 24-71, weights 55-86 kg, resting heart rates 49-81 bpm). Scan
plane localization was performed using the GE I-drive real-time system. In each volunteer,
6 to 10 parallel short axis slices were prescribed spanning the LV from base to apex. The
basal slice was denoted as #1 and the apical slice was denoted as #6 - 10. Whole heart
B
+
1
mapping was achieved in single breath-holds of 16 R-R intervals. Acquisitions were
cardiac gated using either plethysmograph (5 subjects) [31] or ECG (5 subjects) signals,
with imaging occurring in mid-diastole.
Ten repeated measurements were obtained in the healthy volunteers and ve repeated
measurements were obtained in cardiac patients in separate breath-holds with the same
35
Base
Apex 40°
50°
60°
Figure 3.4: Cardiac
ip angle maps from one representative volunteer at 3 Tesla. All seven
short-axis slices were acquired in a single 16 R-R breath-hold. Magnitude images are
provided for anatomical reference. Note that the variation appears strong and primarily
unidirectional.
scan plane prescription. Subjects were instructed to perform each breath-hold in a com-
fortable exhaled position. The subjects had no prior training for consistent breath-hold
positioning. Measurements containing at least one missed trigger were excluded from the
data analysis, resulting in 8 - 10 useful scans for the normal volunteers and 5 useful scans
for the patients.
3.4 Results
Representative
ip angle maps for all seven short-axis slices in one healthy volunteer are
shown in Figure 3.4. For a nominal
ip angle of 60

, the observed
ip angles across the
LV myocardium ranged from 32

to 64

. The percentage variations within 2D short-axis
36
σ
α
(x,y)
E(α(x,y))
a: b:
Figure 3.5: Illustration of repeatability analysis. Pixel-by-pixel (a) mean (gray-scale 20

- 70

) and (b) standard deviation (0

- 10

) of the measured
ip angle map in a short
axis slice (slice #3 in subject #1). The metric A is computed by averaging
b
(x;y) over
the ROI (white circle).
slices ranged from 29% to 48% in this volunteer. One can qualitatively observe that the

ip angle variation appears to be signicant, smooth, and primarily along one in-plane
axis.
Figure 3.5 illustrates the measurement repeatability testing. The pixel-by-pixel mean
E(b (x;y)) is assumed to be close to true
ip angle prole(x;y), and
b
(x;y) depicts the
variation among measurements. The pixel-by-pixel SD within the ROI was less than 1.0

in 90% of pixels (0

is black, 10

is white). High pixel SD values exist at the epicardial
border and the edge of the chest wall due to inconsistencies in breath-hold position.
The average SD metric, A, was less than 1.4

in all subjects, which suggests that the
measurement methodology produces highly repeatable results.
Figure 3.6 illustrates the prole analysis used to determine the dominant direction
of variation. The vertical line was selected from the magnitude image and the in-plane
angle () was dened as a clockwise angle from the vertical line to an axis of variation
in degrees. The approximation error as a function of has one clear minima, which
37
40
60
40
60
b: c:
α(x,y)
α(x’)
B(θ)
0
º
θ(
º
) 180
º
a:
α(x’)
θ
Figure 3.6: Illustration of prole analysis. (a) The approximation error, B(), as a
function of in-plane angle , dened in degrees clockwise from the vertical axis. (b) Flip
angle variationb (x;y) in a circular ROI can be approximated by (c) a 1D functionb (r)
along the primary in-plane axis (dotted line). The primary in-plane axis angle is 108

and the approximation error is 1.2% in this example (slice #3 in subject #1).
38
1: 2: 3: 4: 5:
6: 9:
30
40
50
60
47 % 41 % 45 % 47 % 23 %
10:
30
40
50
60
7: 8:
25 % 42 % 48 % 36 % 53 %
Figure 3.7: Mid-short axis B
+
1
maps in all ten subjects (eight healthy volunteers: 1-8 and
two cardiac patients: 9 and 10). Magnitude images are included for anatomical reference.
Within each ROI (white circle), the primary in-plane axis of variation is indicated (dotted
line). The
ip angle variation in mid-short-axis slices was found to be 23 - 53%.
indicates a unique primary axis of variation. The approximation errors between the true
(2D) prole and "best" unidirectional (1D) approximation were 3.1% in all subjects,
and were 1.5% in eight of the subjects. The observed proles were consistent for both
3T scanners.
Figure 3.7 contains mid-short axis
ip angle maps and illustrates the region-of-interest
analysis for all ten subjects. Magnitude images (background) are shown for anatomical
reference. The amount of
ip angle variation over the 3D LV volume for the ten subjects
ranges from 31% - 66% while the
ip angle variation over the LV in 2D mid-short-axis
slices ranges from 23% - 53%. Flip angle maps from all subjects exhibit unidirectional
variation along one primary in-plane axis.
Table 3.1 and 3.2 contains the statistical parameters for all subjects. Subjects 9 and
10 were cardiac patients. The average heart rate for the cardiac patients was 74 bpm
39
mid short-axis 2D slice
A
a
B
b

min

max
c
Variation
d
Subject 1 0.6

1.2 % 34

- 64

47.1 %
Subject 2 0.6

1.2 % 36

- 62

41.3 %
Subject 3 0.6

0.8 % 37

- 67

44.9 %
Subject 4 1.4

1.9 % 31

- 58

47.0 %
Subject 5 0.4

1.0 % 48

- 63

23.0 %
Subject 6 1.0

1.2 % 44

- 59

25.2 %
Subject 7 0.8

1.4 % 30

- 57

48.0 %
Subject 8 0.9

1.5 % 38

- 65

41.6 %
Subject 9 0.5

1.5 % 42

- 66

36.0 %
Subject 10 1.4

3.1 % 27

- 58

52.5 %
Table 3.1: Repeatability and prole analysis data in the mid-short axis slices from all
ten subjects.
a
A represents the average standard deviation of the measured
ip angle (in de-
grees) over the LV ROI, and is an indicator of overall repeatability.
b
B represents the relative approximation error between the true (2D) pattern and the
unidirectional (1D) approximation along the primary in-plane axis of variation.
c

max
and
min
are the maximum and minimum measured
ip angle over the LV ROI.
d
Variation is calculated as (
max
-
min
)/
max
in percentage.
40
3D volume
a
A
b
B
c

min

max
d
Variation
e
Subject 1 0.8

1.1 % 32

- 64

50.2 %
Subject 2 0.6

1.5 % 34

- 64

46.0 %
Subject 3 0.9

1.1 % 34

- 67

49.4 %
Subject 4 1.4

2.1 % 26

- 59

55.6 %
Subject 5 0.5

1.1 % 45

- 66

31.3 %
Subject 6 1.0

1.2 % 42

- 61

31.2 %
Subject 7 0.8

1.4 % 28

- 58

52.2 %
Subject 8 1.1

1.4 % 34

- 67

49.0 %
Subject 9 0.6

1.2 % 42

- 66

36.0 %
Subject 10 1.3

3.0 % 20

- 60

65.7 %
Table 3.2: Repeatability and prole analysis data over the 3D LV volumes from all ten
subjects.
a
3D volume parameters include all six to ten slices in the analysis.
b
A represents the average standard deviation of the measured
ip angle (in degrees) over
the LV ROI, and is an indicator of overall repeatability.
c
B represents the relative approximation error between the true (2D) pattern and the
unidirectional (1D) approximation along the primary in-plane axis of variation.
d

max
and
min
are the maximum and minimum measured
ip angle over the LV ROI.
e
Variation is calculated as (
max
-
min
)/
max
in percentage.
41
and the average heart rate for the healthy subjects was 65 bpm. Subjects 7 and 8 were
scanned in a dierent scanner than the other subjects.
3.5 Discussion
The observed unidirectional trend at 3T may be used to compensate in-plane B
+
1
inho-
mogeneity using tailored radiofrequency (TRF) pulses [61, 74, 80, 82]. The presence of
unidirectional in-plane B
+
1
variation greatly simplies the design of compensating pulses,
and enables the design of exceptionally short pulses [74, 80, 82]. Further reductions in
the duration of compensating pulses can be accomplished using parallel RF transmis-
sion [38,93].
The IMAGING module can incorporate spin-echo schemes or alternate k-space seg-
mentations such as echo planar imaging (EPI). Spin-echo approaches are able to refocus
T

2
related inhomogeneities and may provide better noise behavior at lower
ip angles [88]
but are dicult to combine with interleaved multi-slice imaging. Although spiral read-
outs were chosen due to their eciency and short echo time to reduce T

2
eects, EPI
readouts may also be used.
The cardiac B
+
1
measurement may have an important clinical role during pre-scan
calibration at 3 Tesla. Kim et al. [40] demonstrated that B
+
1
inhomogeneity can result
in regional contrast variations across the heart. Uniform saturation may potentially
be achieved if cardiac B
+
1
measurements are used to guide the choice of B
1
amplitude.
Knowledge of the B
+
1
eld may also improve the calibration of time-intensity curves in
rst-pass myocardial perfusion imaging along with several existing methods to correct
42
intensity variations [33,60]. Finally, an ideal
ip angle in balanced SSFP imaging is often
pre-calculated to achieve the highest contrast between tissues [62] and this contrast can
be further optimized with B
+
1
mapping.
O-resonance eects during excitation and readout can be considered separately. O-
resonance during slice-selective excitation creates a small distortion in the excited slice
prole but the distortion is independent of the RF amplitude. O-resonance during
spiral acquisitions can cause image blurring when the amount of phase accrual during a
readout is greater than =2 [52]. The truncated 1.9 ms spiral readout has a bandwidth
of 132 Hz within which the phase accrual is less than =2. Re-design of the BIR-4
saturation and data acquisition scheme may be needed for cardiac B
+
1
mapping in the
presence of extreme o-resonance, caused by inadequate shimming, sternal wires or metal
clips from prior surgery, or imaging at > 3 Tesla.
The measurement variations found here can be considered upper bounds on the true
variation of the measurement methodology. Further improvements in repeatability may
be achieved by 3D image registration and wavelet-based de-noising [14] which could sup-
press contributions from breath-hold inconsistency and the additive noise term. The
dierence in overall quality may be subtle due to the low image resolution in this work.
During acquisition, we used a spatial resolution of 2.2 mm with 8-interleaved 5.9 ms
spiral readouts, and during data analysis we windowed k-space data which reduced the
eective resolution to 5 mm. In future studies, the same spatial resolution can be achieved
with shorter 1.9 ms readouts and 8 interleaves, or with 5.9 ms readouts and just 3 inter-
leaves. The low resolution condition may assist to either shorten the breath-hold duration
43
(by a factor of 3) or increase the number of slices with the cross-talk free through plane
velocities up to 2.14 m/s.
The trigonometric double angle formula (Eq. 3.5) has a limited measurable bound.
The arccosine function contains only a positive signal ratio, and therefore the derived
value ranges from 0

to 90

. The calculation assumes a linear relationship between
ip
angles and B
+
1
elds and the deviation from the relationship must be taken into account
for larger
ip angles (> 70

) [71]. In addition, the repeatability may become worse for
smaller
ip angles (< 20

in this work). These limitations should be carefully considered
when severe transmitted B
+
1
variation is expected.
3.6 Summary
Knowledge of the B
+
1
eld is necessary for the calibration of pulse sequences, image-based
quantitation, and signal-to-noise and contrast-to-noise optimization. In this section, a
variation of the saturated double-angle method for cardiac B
+
1
mapping was described.
We have (a) veried that the proposed cardiac SDAM pulse sequence produced repro-
ducible cardiac B
+
1
maps (SD 1.4

) over the entire heart in a single breath-hold of 16
heartbeats, (b) shown the
ip angle variation at 3T to be approximately 32 - 63% over
the 3D LV, and approximately 23 - 48% within 2D short-axis slices, and (c) established
that the variation is primarily along one in-plane axis in short-axis slices with a residual
variation of 3% in all subjects.
44
Chapter 4
B
+
1
Compensation for 2D Imaging
Inhomogeneous RF transmission (B
+
1
) produces non-uniform
ip angles, causing spa-
tially dependent tissue contrast and signal intensity. This is a critical source of error
when quantifying NMR parameters from image data. B
+
1
non-uniformity is in
uenced
by several factors including the distance from the RF transmit coil, conductivity, tissue
dielectric constant, and factors related to the body size and RF wavelength. Methods
for reducing B
+
1
inhomogeneity are highly desirable in high eld imaging [23, 24, 47, 87]
and imaging with surface coil transmission [12]. In high-eld cardiac imaging (3T), B
+
1
inhomogeneity on the order of 30 - 50% across the imaging volume has been predicted
and observed [11,24,69,81,83,90].
4.1 Related works
Table 4.1 summarizes the dierent types of B
+
1
compensation methods in slice selective
excitation. First way to reduce
ip angle variation is using a coil array for RF transmis-
sion, called basic shimming [87]. Conventional slice selective RF pulses are transmitted
45
Single transmit channel Multiple transmit channels
Slice selective
RF pulses
Basic shimming
2D/3D RF pulses
Single channel
tailored shimming
Multichannel
tailored shimming
Table 4.1: Overview of dierent B1 shimming methods.
with dierent weights in dierent coils. Each weight (amplitude and phase) is designed
to minimize the RF non-uniformity.
Second method is single transmit channel RF shimming using 2D or 3D tailored RF
excitation pulses [12,13,61]. Homogeneous tissue excitation can be achieved by tailoring
the excitation with a spatial prole that is approximately equal to the reciprocal of the
B
+
1
variation. The physical B
+
1
inhomogeneity is still present, but uniform excitation can
be achieved.
The last method is a combination of the rst and second methods using multichannel
RF transmission, often called as parallel transmission [38, 93]. The multichannel RF
pulses can be accelerated by shortening their trajectory in the excitation k-space.
Since the multi-channel based techniques require additional hardware systems to sup-
port multiple transmit RF coils, we conne the B
+
1
compensation method to the single
channel tailored shimming in this section, and several methods using the tailored RF
pulses have been proposed for neurologic applications [13,61]. Diechmann et al. [13] de-
scribed an RF excitation pulse that performs rapid 2D compensation and was eective for
structural 3D brain imaging. Small tip-angle 3D tailored RF pulses designed by Saekho
46
et al. [61] included slice selection and were also promising in neuro imaging. Both pulse
designs, however, are limited to a small family of variation patterns and not fully based
on B
+
1
measurement.
4.2 Methods
In 3T cardiac imaging, the patterns of B
+
1
variation across the heart are dierent from
the typical patterns in brain imaging. More severe and diverse patterns of variation
are expected because the chest is of comparable dimension to the RF wavelength at
3T [11, 24, 69, 81, 83, 90]. Tailored RF pulse designs based on actual measurements are
needed for robust B
+
1
compensation. Until recently, this approach has been limited by 1)
the lack of time-ecient and volumetric methods for B
+
1
mapping, and 2) long duration
of appropriate tailored RF pulses. The SDAM [11] was recently demonstrated as a rapid
and appropriate method for B
+
1
mapping in the chest at 3T [81,83]. Performed in a single
breath-hold, this method can provide accurate and repeatable in-vivo B
+
1
measurement
covering the whole heart in a single breath-hold [81,83]. The most recent study involving
ten subjects and two scanners found the pattern of
ip angle variation to be largely
unidirectional across the heart when using a single-channel conventional body-coil for RF
transmission [81,83]. This suggests the possibility of a one-dimensional B
+
1
compensation
scheme using short 2DRF pulses, which is simpler and potentially more robust than 3D
tailored RF schemes.
We introduce a short tailored 2DRF pulse for compensating for B
+
1
non-uniformity
in single transmit channel slice-selective cardiac imaging. The pulse utilizes a
y-back
47
echo-planar trajectory in excitation k-space, enabling a measurement-based adjustment
of excitation proles to compensate in-plane B
+
1
variations. The unidirectional B
+
1
com-
pensation method was demonstrated and evaluated in phantoms, and in in-vivo cardiac
imaging at 3 Tesla.
4.2.1 2DRF Pulse
For small-tip excitation, 2DRF pulses can be designed and analyzed with the excitation
k-space framework developed by Pauly et al. [57]. Ignoring relaxation and o-resonance,
the transverse magnetization M
xy
is proportional to the Fourier Transform (FT) of the
product of a spatial frequency weighting functionW (k) and a spatial frequency sampling
function S(k) [53,57].
The 2D echo-planar excitation k-space trajectory is suitable in this work because the
design considerations for slice selection and B
+
1
compensation are independent and sepa-
rable [4,19].The pulse design involves two stages: the design of subpulses (fast direction,
k
z
) and the design of subpulse weighting (slow direction,k
r
). The subpulse design is based
on the desired slice prole, and the r-axis can be any in-plane radial axis, as determined
by the 1D approximation [81,83].
For the r-axis, the excitation pulse prole
b
f(r) can be written as
b
f(r)/FT (W (k
r
)S(k
r
)): (4.1)
48
Time (ms)
0 1 2 3
k
r
k
z
∆k
r
a
a b
b
c
c
Excitation pulse Excitation k-space a: b:
|RF|
RF phase
G
r
G
z
Figure 4.1: Proposed 2DRF excitation for B
+
1
compensation: (a) excitation pulse and
(b) excitation k-space trajectory. The subpulse duration is 0.5 ms, and overall duration
is 3 ms including all gradients. A
y-back echo-planar design is used where RF is only
transmitted during positive gradient lobes of G
z
. Note that points a, b, and c indicate
the same point on time on both (a) and (b).
Assuming the sampling density k
r
is uniform and the number of subpulses is odd
(2N+1), W (k
r
)S(k
r
) may be expressed as
W (k
r
)S(k
r
) =
N
X
n=N
A
n
(k
r
nk
r
)e
inkr
; (4.2)
where(k
r
) is the Kronecker delta function.
b
f(r) is the FT of the series of delta functions
with subpulse weighting A
n
and phase
n
. Standard methods for nite impulse response
(FIR) lter design provide an excellent way to obtain an appropriate
b
f(r).
Figure 4.1 shows the proposed RF pulse and the corresponding excitation k-space
trajectory. G
r
represents a combination of the logical G
x
and G
y
gradients. The RF
subpulse duration is 0.5 ms while the overall pulse duration including refocusing gradient
lobe is 3 ms, suciently fast for cardiac imaging.
49
The individual subpulse shape was designed using the Shinnar-LeRoux (SLR) algo-
rithm [58]. Subpulse duration was minimized by taking full advantage of the gradients
(40 mT/m amplitude and 150 T/m/s slew rate) and RF capabilities (peak B
1
= 16T).
A time-bandwidth product (TB) of 2 was used for slice selection (5 mm slice thickness).
The variable-rate selective excitation (VERSE) technique was applied to compensate for
the fact that RF is transmitted during gradient ramps [9].
For the in-plane
ip angle variation, we set the number of subpulses as three to
make the total pulse duration as short as possible and used a 1-2-1 binomial weighting
(A
1
= 1;A
0
= 2;A
1
= 1) in all studies. We also used a phase increment (
1
=
;
0
= 0;
1
=). With these conditions,
b
f(r) becomes simply a raised cosine:
b
f(r) =

max
2
(1 + cos(k
r
r +)): (4.3)
where
max
is the peak
ip angle value in
b
f(r).
4.2.2 Tailored 2DRF Pulse Design Based on Measurement
Figure 4.2 illustrates the tailored 2DRF pulse design procedure based on B
+
1
measurement.
The
ip angle variation
measured
(x;y) is rst measured using SDAM [11,81,83] and can
be expressed as
(x;y) =
nom
b
1
(x;y) (4.4)
where
nom
is the nominal
ip angle entered in the scanner and b
1
(x;y) is the spatially
varying relative RF amplitude.
50
Perform
B1+ measurement
Identify and compute
1D Approximation
Compute
Desired Excitation
Least Squares
Curve Fitting
α
measured
(r)
α
measured
(x,y)
86°
α
max
= 90°, ∆k
r
= 0.065, Θ = 80°
f(r)
40°
60°
80°
40°
60°
f(r)
^
40°
60°
80°
LV
Figure 4.2: Measurement-based tailored 2DRF pulse design procedure. Data from one
slice in a cardiac study is shown for illustration. In this example, the computed control
parameters were: the primary in-plane axis = 86

,
max
= 90

, k
r
= 0.065, and =
80

.
51
Circular ROIs covering left ventricular myocardium and blood pool are then manually
selected based on magnitude images. A one-dimensional approximation
measured
(r) is
computed by minimizing mean square error (MMSE) along the primary in-plane axis
(dotted line in Figure 4.2). MMSE 1D approximations are computed at all angles with
a 1

increment, and the primary in-plane axis, r, is dened such that it minimizes the
approximation error.
The desired excitation pulse prole f(r) is then simply dened as the reciprocal of

measured
(r) to cancel out the RF transmit variation.
f(r) =
target
=b
1
(r) (4.5)
where
target
is the intended
ip angle after B
+
1
compensation.
To produce a practical approximation,
b
f(r), and identify design parameters:
max
,
k
r
, and, the non-linear curve-tting problem is solved in the least-squares sense (Op-
timization Toolbox, MATLAB 7.0), minimizing:
min
max;kr;
1
2
X
rn2ROI
(f(r
n
)
b
f(r
n
))
2
: (4.6)
Note that
max
had a upper bound of 90

and was allowed to range from=2 to
=2. The r-axis,
max
, k
r
, and were calculated separately for each slice in multislice
studies.
52
-6.5 0 6.5
2
0
-2
2
0
-2
2
0
-2
2
0
-2
a:
b:
c: d:
On-Resonance Off-Resonance (-440 Hz)
Experiment Simulation
-6.5 0 6.5
r
z
r
z
r
z
r
z
1D plot
e: f:
Figure 4.3: Measured (a and b) and simulated (c and d) excitation proles of the proposed
2DRF pulse. The cross-section plots (e and f) along the r-direction show an excellent
agreement between experiment (solid line) and simulation (dotted line). The measured
slice thickness was 22% larger than simulation. As expected, o-resonance results in a
prole shift along the r-axis.
4.3 Phantom Experiments
In the phantom study, a single-channel birdcage transmit/receive head coil was used.
A 28 cm diameter ball phantom was positioned halfway out at the end of the coil to
articially produce B
+
1
non-uniformity. Imaging was performed with a 2DFT gradient-
echo (GRE) acquisition, 30 cm FOV, 256256 matrix size, and 5 mm slice thickness.
During reconstruction, a Gaussian lter was applied to smooth the base images.
Figure 4.3 contains a comparison between measured and simulated excitation proles
with and without o-resonance (-440 Hz). The excitation pulse prole
b
f(r) was measured
using a ball phantom with a spin-echo pulse sequence and computed with numerical Bloch
53
a:
b:
c:
Figure 4.4: Illustration of 2DRF excitation prole control using the design parameters:
(a) ~ r, the radial axis of variation, (b) k
r
, the frequency of variation, and (c) , prole
shifting. After the primary in-plane axis is determined from the measured B
+
1
prole, the
parameters (k
r
, , and
max
) are chosen by non-linear least squares estimation. Note
that higher k
r
value was used in (a) and (c), containing multiple null points.
simulation. The slice thickness (full-width at half maximum) of measured proles was
22% thicker and, as expected, o-resonance caused a shift along the r-axis.
Figure 4.4 illustrates measured changes in the excitation pulse prole when modifying
the three control parameters. Any axis of variation can be formed by using both the
logical G
x
and G
y
gradients (Fig 4.4a). k
r
changes the period of
b
f(r) (Fig 4.4b). The
phase increment for each RF subpulse shifts
b
f(r) along the r-axis (Fig 4.4c).
54
To evaluate the proposed approach, we used two sets of excitation pulses: a slice-
selective RF pulse and the proposed 2DRF pulse. The slice-selective RF pulse was made
by removing the G
r
gradient from the 2DRF pulse and therefore had the same pulse
duration. The 2DRF pulse has an amplitude 1.8 times higher than that of the reference
slice-selective pulse and a 3.24 times increase in SAR. Two magnitude base images (I

1
and I
2
1
) were acquired [71] to measure the
ip angle variation. Because I
2
1
has a
nominal
ip angle of 2
1
, the proposed RF pulse needed to be able to accommodate a
maximum
ip angle of 180

and therefore was redesigned with twice the pulse duration
(6 ms). In each dataset, the mean and standard deviation (SD) of
ip angle over the ROI
was measured. The value of the SD/mean (%) was used as metric, independent of the
transmit gain, to quantify the amount of the
ip angle variation.
30˚
50˚
70˚
Slice-selective Proposed 2DRF
Flip-angle map Flip-angle map
(SD/mean) = 10.4% (SD/mean) = 4.9%
Magnitude Magnitude
a: b:
40° 50° 60° 40° 50° 60°
c: d:
Figure 4.5: Phantom validation using 2DRF pulses. The
ip angle varied from left (low

ip angle) to right (high
ip angle) using a conventional slice-selective RF pulse. The
proposed 2DRF was used to correct unidirectional
ip angle variation over the ROI (white
dotted circle). Magnitude images and
ip angle distributions are shown (a and b) along
with the corresponding
ip angle histograms (c and d). The
ip angle SD/mean within
the ROI was improved from 10.4% (53:9

5:6

) to 4.9% (59:3

2:9

) using the proposed
2DRF approach.
55
Figure 4.5 contains the results of 2DRF B
+
1
compensation in a phantom. An articial

ip angle variation, from left to right, was generated by placing the ball phantom halfway
out at the end of the transmit-receive head coil. A circular ROI was manually selected
to cover a region with B
+
1
variation. Both
nom
and
target
were set to 60

. The
ip
angle experienced within the ROI was 53:9

5:6

(mean SD) using the slice-selective
RF pulse and was 59:3

2:9

using the proposed 2DRF pulse. The value of SD/mean
was reduced from 10:4% to 4:9%. The expected SD/mean predicted by simulation, and
considered as a lower bound of this methodology, was 3:8% (60:7

2:3

).
4.4 In-vivo Experiments
In-vivo testing was performed in ve healthy volunteers (4 males and 1 female, weights
55-88 kg). The body coil was used for RF transmission and an 8-channel phased array
cardiac coil was used for signal reception. Scan plane localization was performed using
the GE I-drive real-time system. In each volunteer, 4-6 parallel short axis slices were
prescribed spanning the LV from base to apex. The basal slice was denoted as #1 and the
apical slice was denoted as #6. A multi-slice spiral imaging acquisition was used within
a single breath-hold of 16 R-R intervals (FOV = 30 cm). Acquisitions were cardiac gated
using either plethysmograph (4 subjects) [31] or ECG signals (1 subject), with imaging
occurring in mid-diastole. During reconstruction, a Hamming window was applied to k-
space data to increase the base image SNR while reducing the in-plane spatial resolution
to 5 mm. Statistical comparison of the SD/mean was performed using ANOVA and a
p-value of less than 0.05 was considered statistically signicant.
56
30˚
50˚
70˚
Flip-angle map Flip-angle map
a: b:
40˚ 50˚ 60˚ 40˚ 50˚ 60˚
(SD/mean) = 7.0% (SD/mean) = 1.8%
c: d:
Slice-selective Proposed 2DRF
Figure 4.6: Cardiac B
+
1
inhomogeneity compensation in a healthy volunteer at 3T. Magni-
tude images and
ip angle distributions are shown (a and b) along with the corresponding

ip angle histograms (c and d). Magnitude images are shown for anatomical landmarks.
The value of SD/mean within the LV (white circle) was improved from 7.0% (58:3

4:1

)
to 1.8% (51:2

0:9

) using the proposed 2DRF pulse.
Figure 4.6 contains one of the most successful results of 2DRF B
+
1
compensation in
cardiac imaging at 3T. Magnitude images provide anatomical landmarks, and the circular
ROIs covered the LV in all short-axis scan planes. We set
nom
to 60

and
target
to 50

.
In this mid-short-axis slice, the primary in-plane axis was 89

. In this slice, the
ip angle
experienced within the ROI was 58

4:1

(mean SD) using the slice-selective RF pulse
and was 51

0:9

using the proposed 2DRF pulse. The value of SD/mean was reduced
from 7.0% to 1.8%. Considering all ve slices in this subject, the
ip angle SD/mean
was signicantly reduced with p = 0.0126 (4.4% - 8.4% using conventional excitation and
1.8% - 5.5% using the proposed 2DRF pulse).
Figure 4.7 illustrates the improvement in all six slices in another subject at 3T. The
mean and SD
ip angle plots (Fig 4.7a,b) in all six slices show the improved
ip angle
57
1 2 3 4 5 6 1 2 3 4 5 6
60
80
100
1 2 3 4 5 6
2
4
6
8
10
Slice-selective
2DRF (expected)
2DRF (measured)
Slice Number
SD/Mean X 100 (%)
Slice-selective Proposed 2DRF a: b:
c:
(base) (apex)
Intended FA (%)
Figure 4.7: Whole heart B
+
1
inhomogeneity compensation in a healthy volunteer at 3T.
Mean and SD plots (a and b) are compared for conventional excitation and the proposed
compensating 2DRF excitation for six short-axis slices. The gray dotted line indicates
the intended
ip angle (100%). The SD/mean values (c) were computed for slice-selective
and 2DRF (expected in simulation and measured). Note that the expected (gray bars)
and measured (white bars) values show an excellent agreement except in the basal slice.
uniformity and accuracy of the mean
ip angle over the LV. The vertical axis indicates the
percentage of the intended
ip angle (
nom
= 60

for slice-selective RF and
target
= 50

for 2DRF). Fig 4.7c shows a bar graph containing the values of SD/mean for the slice-
selective RF pulse and the proposed 2DRF pulse (expected and measured). 9.0% - 10.8%

ip angle variation was reduced to 5.0% - 7.1%. Considering all slices in all ve subjects,
the SD/mean was signicantly smaller with p < 0.001 and the average reduction was
41%. Note that the measured values (white bars) are similar to the expected values in
58
simulation (gray bars) except in the basal slice (slice #1). We suspect that o-resonance
in the basal slice may have contributed to this deviation.
The proposed method is based on unidirectional B
+
1
variation, which may apply to
other body areas, especially when focusing on an ROI. Figure 4.8 contains an example of
ROI-based B
+
1
compensation in head imaging at 3T. An axial scan plane was prescribed
and two symmetric ROIs containing white matter were manually selected. For ROI A,
the value of SD/mean was reduced from 6.5% (55

3:6

) to 1.9% (62

1:2

) using the
proposed 2DRF approach. For ROI B, the value of SD/mean was reduced from 7.1%
(55

3:9

) to 1.9% (59

1:1

) using the proposed 2DRF approach.
4.5 Discussion
We have demonstrated that short tailored 2DRF pulses are a practical option for B
+
1
inhomogeneity compensation in slice-selective cardiac imaging at 3T. 2DRF pulses were
designed to excite spins with a pulse prole that is approximately the reciprocal of the
measured variation. However, when the transmitted B
+
1
is close to zero due to destructive
interference, the proposed pulse design can not recover the excitation because the pulse
prole needs to have an innity value.
This approach can be applied to a wide variety of applications. Kim et al. [40]
demonstrated that non-uniform saturation due to B
+
1
inhomogeneity leads to regional
contrast variations in rst-pass myocardial perfusion imaging and suggested adiabatic
composite (BIR-4) pulses [70] as a solution.BIR-4 pulses work well but their use is limited
by SAR, especially at 3T or higher eld strength. Similar to the proposed 2DRF pulse,
59
tailored 1D saturation pulses can be designed to saturate uniformly over LV with a much
lower RF power. This may be useful in the applications where SAR is a critical constraint
such as rst-pass perfusion imaging with more than 5 slices per heart-beat.
The proposed method is based on unidirectional B
+
1
variation, which may apply to
other body areas, especially when focusing on an ROI. Figure 4.8 contains an example of
30˚
50˚
70˚
30˚
50˚
70˚
ROI A: 6.5%
ROI A: 1.9%
Magnitude
a:
c:
ROI B: 7.1%
ROI B: 1.9%
40° 50° 60°
40° 50° 60°
40° 50° 60°
40° 50° 60°
ROI A ROI B
ROI B ROI A
Flip-angle
b:
d:
Slice-selective
Proposed 2DRF
Figure 4.8: ROI-based B
+
1
inhomogeneity compensation in the head of a healthy volunteer
at 3T. The B
+
1
prole was parabolic in shape and two symmetric ROIs (A and B) were
selected. Using the proposed 2DRF approach, the
ip angle SD/mean was improved from
6.5% to 1.9% when focusing on ROI A, and from 7.1% to 1.9% when focusing on ROI B.
60
ROI-based B
+
1
compensation in head imaging at 3T. An axial scan plane was prescribed
and two symmetric ROIs containing white matter were manually selected. For ROI A,
the value of SD/mean was reduced from 6.5% (55

3:6

) to 1.9% (62

1:2

) using the
proposed 2DRF approach. For ROI B, the value of SD/mean was reduced from 7.1%
(55

3:9

) to 1.9% (59

1:1

) using the proposed 2DRF approach.
O-resonance during 2DRF
y-back echo-planar excitation creates a linear phase
along k
r
, and results in a shift in
b
f(r) along the r-axis (see Fig 4.3). This can be
modeled as spatially varying phase increment (x;y) in addition to . (x;y) can
have a range of46:8

based on the typical o-resonance range (130 Hz) over the LV at
3T [50]. Although not problematic in our studies, this may be an issue when using longer
subpulses. Localized center frequency and ROI-based shimming are highly desirable in
this case [62]. High-order shimming would decrease the o-resonance range to90 Hz
over the LV at 3T [50], and may be helpful in improving the accuracy of B
+
1
compensation.
The calculation of the control parameters is based on a B
+
1
prole that is measured
in a separate breath-hold. Respiratory motion may create dierences in slice position.
This small image mis-registration may not aect the overall quality due to the low spatial
resolution (5 mm), unless B
+
1
patterns vary with breath-hold position. The investigation
of the intrinsic B
+
1
variation between exhale and inhale positions would be helpful to
understand how much this may or may not in
uence the performance of measurement-
based B
+
1
compensation.
Our initial RF pulse design conned the number of subpulses to three and used a
1-2-1 subpulse weighting for simplicity and to minimize pulse duration. The number
of subpulses could be increased, and the subpulse weighting could be free parameters
61
to add more degrees of freedom to the in-plane prole variation
b
f(r), and potentially
yield more accurate compensation. Any portion of the spectral response of the subpulse
weights (conceptually an FIR lter) can be used to nd the optimal prole. As such, the
subpulse weights would then become additional control parameters.
The original design for the proposed 2DRF pulse (shown in Fig 4.1) has duration of
3 ms and can accommodate a maximum
ip angle of 60

. Although we redesigned the RF
pulse (6 ms) to support a maximum
ip angle of 180

for validation(used in Fig 4.5-4.7),
the original design is more useful in practice. The 3 ms pulse (used in Fig 4.3-4.4) can
compensate up to the intended
ip angle of 40

. In addition, the original design has
shorter RF subpulse duration (0.5 ms), and therefore the 3 ms pulse will bemore resilient
to o-resonance artifacts than the 6 ms pulse.
4.6 Summary
Short tailored 2DRF excitation pulses can be used to substantially reduce
ip angle varia-
tion in cardiac imaging at 3 Tesla. Excitation pulse proles were designed to approximate
the reciprocal of the measured
ip angle variation where the variation over the LV was
approximated as unidirectional. A simple 2DRF pulse design utilizing three subpulses
was used, such that proles could be quickly and easily adapted to dierent regions of
interest by adjusting a few control parameters (primary in-plane axis,
max
,, and k
r
).
Results are presented from phantom and in-vivo cardiac imaging. Compared to conven-
tional slice-selective excitation, the average
ip angle variation over the LV (measured as
the standard deviation divided by the mean
ip angle) was reduced with p < 0.001 and
62
the average reduction was 41% in cardiac studies at 3 Tesla. This type of reduction in
ip
angle variation is particularly important in high eld imaging and quantitative imaging.
63
Chapter 5
B
+
1
-insensitive Saturation Pulses
First-pass MR myocardial perfusion imaging (MPI) is an established technique for the
assessment of ischemic heart disease [2,45,67]. Saturation recovery preparation is widely
used in order to produce T
1
-weighted images rapidly and with multiple slice coverage.
Qualitative and quantitative MPI both rely on complete and uniform saturation of my-
ocardium, and the performance of saturation pulses is sensitive to variations in the B
0
and
B
+
1
elds. Recent studies have compared the eectiveness of dierent saturation pulses,
and shown that the rectangular RF pulse train [54] and the adiabatic BIR-4 pulse [70]
exhibit superior saturation eectiveness than the conventional 90

rectangular hard pulse
in 1.5T and 3T cardiac imaging [39{42]. However, the conventional RF pulse train is more
susceptible to B
+
1
inhomogeneity than the BIR-4 pulse. Conversely, the BIR-4 pulse has
a higher SAR. These costs inherently limit their application at 3T where low RF power
deposition and immunity to B
0
and B
+
1
eld inhomogeneities are highly desirable.
64
5.1 Motivation
First-pass MRI using paramagnetic contrast agents is the most promising emerging tech-
nique for myocardial perfusion imaging because of its ability to clearly depict the trans-
mural distribution of perfusion defects. It is a non-invasive technique that can poten-
tially characterize the complete gamut of perfusion patterns including sub-endocardial
defects and balanced ischemia. Compared to single photon emission computed tomogra-
phy (SPECT), rst-pass MRI does not involve ionizing radiation, and is able to generate
results in under an hour.
Successful rst-pass MRI requires: a) high temporal resolution, b) high spatial resolu-
tion, c) volumetric coverage (multi-slice), and d) strong and spatially-uniform T
1
contrast
between enhanced (short-T
1
) and non-enhanced (long-T
1
) myocardium. The standard
MR pulse sequence is saturation recovery (SR) followed by fast gradient-echo (FGRE)
or balanced SSFP acquisitions (see Fig 5.1). Saturation recovery is used (rather than
inversion recovery) because the resulting image contrast remains stable even when the
heart rate varies [2].
The T
1
contrast in rst-pass MRI relies on uniform saturation of myocardial spins.
Kim et al. [40] demonstrated that non-uniform saturation due to B
+
1
inhomogeneity leads
to regional contrast variations and substantive errors in rst-pass myocardial perfusion
imaging. Based on the preliminary studies (described in Chapter 3), tailored saturation
pulses can be designed to saturate myocardial spins uniformly, while keeping a low RF
power. This would reduce the contrast variation, and may improve the interpretation of
time-intensity curve and the quantitation of regional perfusion parameters.
65
P
R
E
P
T
SR
1 2 3 4 5 6 1
image acquisition
FGRE or SSFP
Figure 5.1: Schematic of a conventional SR-FGRE/SSFP pulse sequence used in rst-
pass MRI. Either 2-3 slices are acquired each heartbeat, or 4-6 slices are acquired in
an interleaved fashion every two heartbeats. The amount of T
1
contrast is primarily
determined by the type of preparation pulse and the available T
1
recovery time (T
SR
).
5.2 Method
We hypothesize that tailored pulse train designs, based on estimated B
0
and B
+
1
proles
that were measured a priori over the heart, can overcome both SAR and B
+
1
inhomogene-
ity constraints. Compared to the conventional 90

pulse train, the tailored pulse train
consists of hard pulses with unequal weighting. The tailored pulse train design is consid-
ered to improve the immunity to B
+
1
variation [55] while maintaining low RF power. The
performance of the proposed tailored pulse train is tested using simulations and in-vivo
experiments at 3 Tesla.
5.2.1 Experimental Methods
A body coil was used for RF transmission and an 8-channel phased array cardiac coil
was used for signal reception. Parallel imaging was not used. In all studies, the transmit
gain was calibrated using a standard pre-scan and the center frequency was adjusted over
66
a 3D region of interest containing the LV. Synchronization with the cardiac cycle was
achieved with prospective triggering based on an ECG signal.
5.2.2 Measurement of B
0
and B
+
1
Variation
B
0
and B
+
1
maps were measured in eight healthy subjects (1 female and 7 male, age = 29
4.7 years, height = 177 5.8 cm, and weight = 70 7.1 kg) with 6 - 8 parallel short-axis
slices (6 subjects) and 1 short-axis slice (2 subjects). Cardiac B
0
maps were obtained in a
single breath-hold using cardiac-gated gradient echo sequences at two echo-times (TEs).
Signal from fat was reduced using a fat saturation pre-pulse. Imaging parameters: FOV
= 30 cm, in-plane resolution = 2.6 mm, TE = 1.6 ms and 3.6 ms ( 250Hz frequency
range), TR = 12.8 ms,
ip angle = 30

, and slice thickness = 5 mm.
Cardiac B
+
1
maps were acquired in a single breath-hold using the cardiac gated sat-
urated double angle method (SDAM), as previously described [11, 71, 83]. The transmit
gain was calibrated for each individual subject. The B
+
1
scale was computed as the mea-
sured
ip angle divided by the prescribed
ip angle. Imaging parameters: FOV = 30 cm,
in-plane resolution = 5 mm, TE = 2 ms, TR = 7.2 ms, prescribed
ip angle = 60

and
120

, and slice thickness = 5 mm.
The LV myocardium was manually segmented in each image, and a composite 2D
histogram was produced in B
0
-B
+
1
space. A ROI was dened that contains B
0
and B
+
1
values representative of nearly all myocardial pixels from all subjects and all imaging
slices. This ROI was used for subsequent tailored pulse train optimization.
67
5.2.3 Optimization of Pulse Trains
Weighted hard pulse trains (
1
;:::;
n
) of length n were designed to minimize the maxi-
mum residual longitudinal magnetization (M
z
) over the B
0
-B
+
1
ROI. An exhaustive search
based on numerical Bloch simulations was performed with the following cost function:
C = max
ROI
j
M
z
M
0
j: (5.1)
Each
i
ranged from 70

to 240

in steps of 1

for n 3, and 5

for otherwise (4 n
6). Minimum and maximum
i
constraints were determined by 90

divided by the
minimum and maximum B
+
1
scale of the ROI. The peak B
+
1
amplitude was xed as
0.115G, a typical value of body-coil transmission in commercial scanners when imaging
medium to large sized humans. We ignored T
1
relaxation between RF sub-pulses, and
assumed the residual transverse magnetization was completely removed by the crusher
gradients. Therefore, the sub-pulses in a set (
1
;:::;
n
) had no specic order, reducing
the computation time.
5.2.4 In-vivo Pulse Performance
In-vivo tests of the proposed method were performed in four healthy volunteers (1 female
and 3 male, age = 31 2.1 years, height = 173 5.3 cm, and weight = 67 8.1 kg) with
three cardiac views (axial, short-axis, and four-chamber). The tailored pulse train with
n = 3 was compared with an 8 ms BIR-4 pulse with tanh/tan (amplitude/frequency)
modulation functions ( = 5 andtan() = 80) [70], and conventional pulse train using a
68
saturation-no-recovery (SR) experiment, as previously described [40,41]. Identical trans-
mit gain and shim values were maintained during the comparison. A 2DFT fast gradient
echo (FGRE) acquisition with a center-out k-space trajectory was used with 10

ip an-
gle. Proton-density (PD) weighted images with 3

ip angle were also acquired in the
same breath-hold for normalization. The pulse sequence was cardiac-gated and there was
one heartbeat between SR and PD acquisition to allow full recovery of magnetization,
resulting in a single breath-hold of ve heartbeats (two for SR images, one for recovery,
and two for PD images). Each saturation pulse (BIR-4, pulse train, and tailored pulse
train) was employed in the FGRE pulse sequence, and acquired in a separate breath-hold.
Imaging parameters were: FOV = 30 cm, TE = 1.2 ms, TR = 3.4 ms, acquisition matrix
= 64 64, in-plane resolution = 4.7 mm, slice thickness = 5 mm, image acquisition time
= 109 ms, and bandwidth =125 kHz.
For image analysis, the SR images were normalized by the PD images (SR/PD) to
remove the eect of receive coil sensitivity and other system imperfections, and then
multiplied by sin3

/sin10

to compensate for the excitation angle dierence. The resulting
images re
ectjM
z
/M
0
j and have a range from 0 (complete saturation) to 1 (no saturation).
LV and right ventricle (RV) were manually dened based on the PD images. We computed
the maximum and averagejM
z
/M
0
j over the LV and LV + RV, and reported mean
SD. All image analysis and numerical simulation were performed in MATLAB 7.0 (The
Mathworks, Inc., Natick, MA).
69
0.2
0.6
1
−50
0
50
B0 map
B1 map
a:
−200 −100 0 100 200
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (Hz)
B1 scale
b:
−200 −100 0 100 200
0.6
0.8
1
1.2
1.4
Frequency (Hz)
B1 scale
B1 map
B1 scale
Frequency (Hz)
number of pixels (log scale)
Figure 5.2: Measured B
0
and B
+
1
inhomogeneity over the LV at 3 Tesla: (a) B
0
and B
+
1
maps from a single slice for one subject, and (b) the combined 2D histogram from all
slices for all eight subjects. The extent of the B
0
-B
+
1
ROI (red rectangle) was based on
the extent of the B
0
-B
+
1
clusters (red oval) computed using Gaussian mixture models for
each slice in each subject. The ROI contains 99.7% of all scattered pixels.
5.3 Results
5.3.1 Measurements of B
0
and B
+
1
Variation
Figure 5.2a (top) illustrates the measured B
0
and B
+
1
maps from a mid short-axis slice
in one representative volunteer. A Gaussian mixture model (GMM) was initially applied
to cluster a region by using the expectation maximization algorithm to estimate the
order and parameters of the GMM [16]. The 2D histogram of a given B
0
-B
+
1
set and its
clustered region (red line) are shown in Figure 1a (bottom). We then chose a rectangular
B
0
-B
+
1
ROI to represent the expected B
0
-B
+
1
variation based on the GMM clustered
regions, and minimum and maximum B
0
-B
+
1
values. Figure 5.2b shows the 2D histogram
of all eight subjects and its corresponding rectangular ROI. The ROI overestimates the
inhomogeneities of B
0
-B
+
1
elds to consider all possible cases, and contains 99.7% of all
70
n Optimal Weighting maxjM
z
/M
0
j Relative RF power
1 114

0.737 1.3
2 116

231

0.268 3.9
3 96

228

141

0.087 5.2
4 120

90

180

230

0.043 6.9
5 90

110

145

205

235

0.016 8.7
6 90

170

130

105

220

240

0.007 10.6
Table 5.1: Prescribed
ip angles, maxjM
z
/M
0
j, and relative RF power for optimized
tailored pulse trains.
scattered data points. The ROI spans resonance osets of -144 Hz to +144 Hz which is
in good agreement with the range reported in the literature [51], and a B
+
1
scaling range
of 0.38 to 1.2, which contains the range obtained in a previous study (0.45 - 1.12) [83].
5.3.2 Simulated Pulse Performance
The pulse train weighting was optimized to produce the minimum cost according to
Eq. 5.1. Table 5.1 contains the optimal
ip angles for n = 1 through 6, and the corre-
sponding maxjM
z
/M
0
j and relative RF energies. The relative RF energy was calculated
as the RF energy of a pulse train divided by the RF energy of a single 90

hard pulse
(duration 0.5 ms). Figure 5.3 plots the residual M
z
/M
0
and the RF energy as a function
of n in simulation. The maximum values ofjM
z
/M
0
j within the ROI for the tailored pulse
train were compared with those for the BIR-4 and pulse train. Since the rectangular ROI
overestimates the actual behavior of B
0
-B
+
1
inhomogeneity for each subject, we also com-
puted the averagejM
z
/M
0
j value and the standard deviation (SD) of M
z
/M
0
over the
71
Number of pulse (n) Number of pulse (n)
a: b:
0
0.2
0.4
0.6
0.8
1
Max |M
z
/M
0
|
0
0.1
0.2
0.3
0.4
0.5
Mean |M
z
/M
0
|
1 2 3 4 5 6
0
0.1
0.2
0.3
0.4
0.5
SD (M
z
/M
0
)
1 2 3 4 5 6
0
5
10
15
20
25
Relative RF Energy
c: d:
BIR-4
Pulse Train
Tailored Train
BIR-4
Pulse Train
Tailored Train
Figure 5.3: Behavior of residual M
z
and the corresponding RF energy as a function of
n. (a) MaxjM
z
/M
0
j, (b) MeanjM
z
/M
0
j, (c) SD of M
z
/M
0
, and (d) relative RF energy
were simulated for the BIR-4 pulse (dotted line), conventional pulse train (gray line),
and tailored pulse train (black line). The tailored pulse train when n 3 shows superior
saturation performance than the BIR-4 and pulse train while maintaining lower relative
RF energy than the BIR-4 pulse.
ROI. The tailored pulse train designs show superior saturation performance compared to
the conventional pulse train, with only a small increment in the relative RF energy.
When n = 3 , the behavior of the residual M
z
/M
0
(maximumjM
z
/M
0
j, meanjM
z
/M
0
j,
and SD M
z
/M
0
) for the tailored pulse train indicates better saturation performance
compared to the BIR-4 pulse, while maintaining lower relative RF energy. Figure 5.4 a-c
shows pulse sequence diagrams for the three dierent saturation pulses considered in this
study. The tailored pulse train (n = 3) has 7.7 ms pulse duration (Fig. 5.4c). The optimal
72
0.2
0.4
0.6
0.8
1
frequency
0 200
frequency
0 200
frequency
−200 0 200
1.5
1
0.5
0
−200 −200
BIR-4 Pulse train Tailored pulse train
B1 scale
d: f: e:
RF
G
z
RF
G
x
G
y
G
z
RF
G
x
G
y
G
z
90° 90° 90°
a: c: b:
141° 96° 228°
Figure 5.4: Saturation pulse sequence diagrams for (a) the BIR-4, (b) conventional pulse
train and (c) tailored pulse train (n=3), and corresponding simulatedjM
z
/M
0
j proles
(d-f). The B
0
-B
+
1
ROI is indicated by the red box. The simulation prole for the tailored
pulse train (f) shows reduced peakjM
z
/M
0
j within the ROI.
pulse weighting was 96

, 228

, and 141

(0.548, 1.296, and 0.804 ms, respectively), and the
order was chosen among all the six possible combinations by including T
1
relaxation (T
1
= 1115 ms) in the cost function. The spoiler gradients (1 ms) and crusher gradients (3 ms
- 2 ms - 2 ms) were cycled to avoid stimulated echoes, as previously described [41,42,54].
The tailored pulse train produced 4.2 times lower relative RF energy than the BIR-4
pulse, and 1.7 times higher relative RF energy than the pulse train.
Figure 5.4 d-f show the saturation proles as a function of o-resonance (horizontal
axis) and B
+
1
scale (vertical axis) using numerical Bloch simulation for the three saturation
pulses. The ROI used for optimization is shown in red. The prole for the BIR-4 pulse
(Fig. 5.4d) shows excellent saturation for most of the B
+
1
range, but its B
0
bandwidth
becomes less than110 Hz as the B
+
1
scale falls below 0.43. This can be problematic when
73
both the B
0
and B
+
1
elds are severely distorted. The conventional pulse train (Fig. 5.4e)
shows superb B
0
variation insensitivity due to its eective bandwidth of1000 Hz, but
the peak Mz/Mo becomes larger than 0.1 when the B
+
1
scale is smaller than 0.7. This
explains the weaker B
+
1
immunity of the pulse train as previously discussed. The tailored
pulse train with the optimal weighting (Fig. 5.4f), however, improved the saturation
performance, and produced excellent saturation eectiveness over the entire ROI.
Axial Short-axis 4-Chamber
0
0.1
0.2
0.3
0.4
0.5
BIR-4 Pulse Train Tailored
Pulse Train
a: b: c:
Figure 5.5: Representative normalized SR images with (a) the BIR-4, (b) conventional
pulse train, and (c) tailored pulse train in three cardiac views. The proposed saturation
pulse demonstrates superior saturation performance over the LV and RV than the BIR-4
and pulse train.
74
5.3.3 In-vivo Pulse Performance
Figure 5.5 shows representative normalized SR images with the dierent saturation pulses
in three cardiac views. Cardiac cine images (left column) are displayed to provide an
anatomical reference. Table 5.2 summarizes the saturation eectiveness for the dierent
saturation pulses. Both the BIR-4 and tailored pulse show comparable saturation per-
formance over the LV while the conventional pulse train becomes less eective in septal
myocardium. The peak and average residualjM
z
/M
0
j over the LV for the tailored pulse
train were smaller than those for the BIR-4 and conventional pulse train, but only the
peak value was signicantly dierent (p < 0.05). The residualjM
z
/M
0
j within the LV
+ RV behaves dierently, and the BIR-4 pulse demonstrates inferior performance com-
pared to the tailored pulse train. The peak and average residualjM
z
/M
0
j over the LV
+ RV for the tailored pulse train were signicantly smaller than those for the BIR-4 and
conventional pulse train (p< 0.05). Note that the measured values are in
uenced by low
SNR and T
1
recovery during the acquisition, and therefore cannot represent the absolute
saturation eectiveness.
5.4 Discussion
The proposed modication of RF pulse trains was implemented to increase immunity to
B
0
and B
+
1
variation. We demonstrated the train of tailored hard RF pulses to have
superior saturation eectiveness in simulation and in-vivo, with the cost of 1.7 times
higher RF power than the conventional 90

pulse train. Compared to the BIR-4 pulse,
the tailored pulse showed superior saturation over the heart while requiring 4.2 times less
75
LV LV and RV
maxjM
z
/M
0
j meanjM
z
/M
0
j maxjM
z
/M
0
j meanjM
z
/M
0
j
BIR-4
0.280.066 0.110.022 0.570.259 0.140.046
Conventional
Pulse Train
0.320.133 0.120.055 0.810.335 0.210.093
Tailored
Pulse Train
0.220.062 0.090.017 0.260.086 0.0970.019
Table 5.2: In-vivo performance of myocardial saturation pulses at 3 Tesla.
RF power. This alleviates the SAR-constraints and should enable more frequent use of
saturation pulses or more extensive coverage of the myocardium in 3T MPI (e.g. more
slices per heartbeat).
We conned the total number of subpulses to three in this validation study because
three subpulses were the minimum number that was predicted to produce saturation per-
formance superior to both the conventional pulse train and BIR-4. Tailored pulse trains
with more than three subpulses may improve the saturation performance (maxjM
z
/M
0
j
and meanjM
z
/M
0
j) with a small increment in RF power and pulse duration, as shown
in Table 5.1. It should be noted that BIR-4 pulses can also be optimized based on B
0
-
B
+
1
maps, for example, when choosing amplitude and frequency modulation functions.
Figure 5.6 shows the meanjM
z
/M
0
j as a function of and tan() with a xed RF pulse
duration (8 ms). This simulation suggests that an optimized BIR-4 pulse can reduce
average residual M
z
by 4.3% while increasing RF power by 8.3%.
76
0.2
0.4
0.6
0.8
1
β
100
200
300
400
0.1
0.2
0.3
0.4
0.5
5 10 15 20
relative RF power
tan(κ)
Mean|M
z
/M
0
|
a:
b:
Figure 5.6: Optimization of BIR-4 amplitude and frequency modulation function param-
eters and tan(). Simulations of (a) mean(jM
z
/M
0
j) over the ROI as a function of
andtan(), and (b) relative RF power which is a function of only. The red dot (relative
RF power = 0.80) indicates the pulse used in this study, and the green dot (relative RF
power = 0.86) indicates the pulse with the lowest residual magnetization.
Paramagnetic contrast agents during the rst-pass, and stents, sternal wire and other
metal implants can potentially create additional B
0
inhomogeneity due to increased sus-
ceptibility eects [15, 17], widening the B
0
-B
+
1
ROI. The tailored pulse train consists of
RF pulses with dierent bandwidths, and has an eective B
0
bandwidth of390 Hz.
Therefore, the additional o-resonance caused by the contrast agents is not expected to
degrade the saturation performance of the tailored pulse. However, the saturation perfor-
mance of the BIR-4 pulse, due to its limited bandwidth, can be impacted. The eective
bandwidth in the tailored pulse train can be increased by either lowering the maximum

i
constraint in the cost function or increasing the peak B
1
amplitude in the pulse design.
77
a:
0
0.2
0.4
0.6
0.8
T1(ms)
Max |M
z
/M
0
|
0 500 1000 1500 2000
b:
0 500 1000 1500 2000
0
0.05
0.1
0.15
0.2
T1(ms)
BIR-4
Pulse Train
Tailored Train
Mean |M
z
/M
0
|
c:
0
0.05
0.1
0.15
0.2
T1(ms)
SD (M
z
/M
0
)
0 500 1000 1500 2000
Figure 5.7: The saturation eectiveness as a function of T
1
relaxation times. (a) Max
jM
z
/M
0
j, (b) MeanjM
z
/M
0
j, and (c) SD M
z
/M
0
were simulated for the BIR-4 pulse
(dotted line), pulse train (gray line), and tailored pulse train (black line).
First-pass contrast agents also cause a reduction in T
1
relaxation time, and longitu-
dinal recovery during saturation may aect pulse performance. Figure 5.7 contains the
results of a numerical simulation of the residualjMz/M0j within the ROI with dierent
T
1
relaxation times (50 ms - 2000 ms). The BIR-4 pulse showed the least T
1
-dependency
with less than 2% variation for all cases (maximumjM
z
/M
0
j, meanjM
z
/M
0
j, and SD
M
z
/M
0
), but the tailored pulse train also maintained comparable saturation performance
78
in the short T
1
regime. Based on the robustness to o-resonance and T
1
-dependency,
we would expect the proposed saturation pulse to maintain its performance under the
conditions of dynamic contrast-enhanced MRI.
The B
+
1
scale range in the ROI (0.38 - 1.2) overestimates the actual B
+
1
behavior
of each subject because the individual B
+
1
distribution never spans the entire B
+
1
scale
range. This can be partially attributed to errors in the transmit gain calibration, and
specically, the fact that transmit gain is typically calibrated based on a signal from
an entire slice or prescribed volume. Similar to localized shimming and localized center
frequency adjustment, the localized calibration of the transmit gain specically to the
heart would be desirable to produce more accurate and tighter expected B
+
1
scale range.
The proposed pulse designs can also be applied to other areas of the body such as the
abdomen. Tailored pulse trains should be optimized with respect to the B
0
-B
+
1
ROI of
each application, which in the abdomen could include fat.
5.5 Summary
Complete and uniform saturation of myocardium is essential for quantitative myocardial
perfusion imaging using the rst-pass of a contrast agent. At 3 Tesla, inhomogeneities of
both B
0
and B
+
1
elds have led to the use of adiabatic BIR-4 pulses, which in practice
are constrained by RF heating. We have described and experimentally validated the
use of tailored pulse trains that optimally saturate myocardium at 3 Tesla, based on
measurements of typical B
0
and B
+
1
eld variation. Weighted hard pulse trains are simple
to design, require substantially lower RF power compared to BIR-4 pulses, and show
79
higher B
+
1
insensitivity compared to conventional hard pulse trains. Furthermore, the
proposed saturation pulse demonstrated lower peak and average residual M
z
/M
0
over
the heart at 3 Tesla, compared to a standard 8-ms BIR-4 pulse and a conventional hard-
pulse train (p < 0.05). Tailored pulse trains may therefore have an important benecial
role in quantitative rst-pass myocardial perfusion imaging at 3 Tesla.
80
Chapter 6
Myocardial Signal Behavior during Balanced SSFP Imaging
Fully balanced steady-state free precession (SSFP) (equivalently known as TrueFISP, FI-
ESTA, or Balanced-FFE) consists of a rapidly repeating sequence of excitations and
acquisitions [8, 26, 56]. With the ability to achieve high SNR eciency and unique
blood/myocardium contrast, balanced SSFP has emerged as a powerful technique for
cardiovascular applications. It is routinely used on clinical 1.5T platforms, and has also
gained increased importance on 3T systems where balanced SSFP also shows promising
results in various cardiac applications [34,64,65].
6.1 Introduction
High image SNR or CNR is important for enhancing diagnostic power, improving image-
based analysis, and generating more accurate signal intensity-based quantication. In
order to maximize the SNR or CNR of balanced SSFP pulse sequences, a major consider-
ation is to adjust imaging parameters such as the excitation angle and the corresponding
TR within SAR limits. One systemic approach is to estimate the optimal
ip angle so
that optimal balanced SSFP performance can be achieved accordingly. The optimal
ip
81
angle value is typically derived from the signal evolution behavior during balanced SSFP
imaging.
The theoretical characteristics of steady-state signals has been well explored over the
past years [34,64,65]. Unlike the spoiled gradient echo sequence, balanced SSFP has non-
zero steady-state transverse magnetization before each excitation pulse, which is a non-
trivial function of multiple parameters, and can be described by matrix formulas [20,28].
One unique feature of balanced SSFP is that the signal intensity is aected by phase
shifts due to o-resonance within a single TR, which cause an unwanted signal loss as a
function of resonant osets. The shape of the spectral response depends on T
1
, T
2
and

ip angle, and a spatial region that suers from the signal loss is commonly known as a
dark band.
Measured balanced SSFP signals, unfortunately, do not always agree with previously
reported models [10,66], which make the sequence optimization less eective. Figure 6.1
presents an introductory example of the deviation between simulated and measured signal
behavior during balanced SSFP imaging. Many practical factors related to
ip angle and
spectral variation can make the ideal steady-state formulas less accurate, and contribute
to the apparent deviations between measured and predicted signals. In addition, recent
studies have shown that magnetization transfer (MT) can also be responsible for the low
apparent signal of certain tissues [5]. These factors need to be considered to accurately
describe the signal behavior and ensure the reliability of balanced SSFP cardiac studies.
To the best of our knowledge, however, little has been reported on the quantitative
comparison between the myocardial signal behavior in theory and the corresponding im-
age appearances in measurements. In this work, we rst examine multiple practical factors
82
10° 20° 30° 40° 50° 60° 70° 80° 90°
0.2
0.4
0.6
0.8
1
Myocardial SI (a.u.)
Prescribed flip angle
Simulation
Measurement
Figure 6.1: An introductory example of 2D balanced SSFP signal behavior. A substan-
tial deviation between simulated (red solid line) and measured (blue) signal has been
observed. The simulated result suggests 22

as an optimal
ip angle while the measured
signal intensity shows 45

as an optimal
ip angle to produce the maximum myocardial
signal.
that can contribute to the balanced SSFP signal such as a non-ideal slice prole [10], static
magnetic eld (B
0
) inhomogeneity [51], RF transmit eld (B
+
1
) inhomogeneity [24,83] and
MT eects [5]. Introducing the above factors into the signal prediction process, we then
establish an amended model that accurately predicts myocardial signal behavior in 2D
balanced SSFP by quantitatively comparing with the measured myocardial signal.
83
6.2 Method
6.2.1 Simplied Balanced SSFP Signal Model
The steady-state magnetization for balanced SSFP imaging sequences can be analyti-
cally expressed in the form of a simple propagation approach (see Appendix C for more
details) [20, 28]. On-resonance, the steady-state transverse magnetization (M
ss
) is often
written as:
M
ss
(
n
) =
(1E
1
)
p
E
2
1 (E
1
E
2
)cos
n
E
1
E
2
sin
n
(6.1)
where E
1;2
= e
TR=T
1;2
(15). For short TR (TR T
1;2
), E
1;2
can be approximated to
(1TR=T
1;2
), and the steady-state formula can be further reduced to:
M
ss
(
n
) =
sin
n
(T
1
=T
2
+ 1)cos
n
(T
1
=T
2
1)
: (6.2)
This equation indicates that the myocardial signal in a cardiac scan is solely controlled
by
ip angle
n
, and the signal can be maximized when the
ip angle is

n;optimium
=
T
1
T
2
T
1
+T
2
: (6.3)
However, during most in-vivo studies the true signal behavior can substantially de-
viate from Eq. 6.2, resulting in inaccurate estimation of
n;optimum
. This suggests the
steady-state model (Eq. 6.2) is over-simplied and needs to be corrected. Based on our
clinical experience, we believe that deviations to Eq. 6.2 can occur in the presence of
non-ideal slice prole, o-resonance (B
0
inhomogeneity), spatially varying
ip angle (B
+
1
84
inhomogeneity), and MT. In the following sections, we separately analyze the eects of
each of these four factors on the steady-state balanced SSFP signal.
6.2.2 Modied Balanced SSFP Signal Models
A. Slice Prole
Short TR is always desirable to avoid banding artifacts in balanced SSFP, and this TR
constraint limits the choice of excitation RF pulses. Common selections in 2D balanced
SSFP include low time-bandwidth (TB) product (e.g. 1.5 or 2) windowed SINCs and
Gaussian shapes. These RF pulses sacrice the sharp transition between in- and out-
of-slice selections for shorter excitation length, producing a smooth slice prole. This
smooth transition directly in
uences
ip angle distribution
n
(z) along the slice selective
direction.
The Bloch equation for a given RF pulse can be used to express a longitudinal mag-
netization slice prole M
z
(
n
;z), and the corresponding
n
(z) can be described as,

n
(z) =arccos(M
z
(
n
;z)=M
0
) (6.4)
where M
0
is the initial longitudinal magnetization. Figure 6.2 compares the
ip angle
distributions with high and low TB SINC RF pulses. The high TB RF pulse (TB = 16)
produces a large portion of constant
n
with the sharp transition (i.e. well-approximated
to rectangular) whereas the low TB RF pulse (TB = 2) creates a smooth
ip angle
distribution rather than
n
. Considering
n
(z) as a function of z location rather than a
85
α(z)
TB=16 TB=2
b1(t)
Time (ms)
Slice location (cm)
0 0.5 1 1.5 2
−0.1
0
0.1
−1 −0.5 0 0.5 1
0
10
20
30
0 10 20 30
0
20
40
b1(G) flip angle (°)
flip angle (°)
num of pixels
(a.u.)
a:
b:
c:
Figure 6.2: The illustration of the high TB (TB = 16; gray) and the low TB (TB = 2;
black) RF pulses: (a) RF pulses, (b)
ip angle proles, and (c) their corresponding
ip
angle histograms. The ideal slice prole with the nominal
ip angle of 20

(dotted line)
was shown in (b).
constant value can improve the accuracy of the theoretical prediction. The contribution
of
n
(z) in M
ss
signal across the imaging slice can be described as
M
ss;A
(
n
) =
Z
M
ss
(
n
(z))dz: (6.5)
86
B. B
0
inhomogeneity
There exists increased o-resonance variation across the myocardium, mostly due to mag-
netic susceptibility eects. M
ss
(
n
) behaves dierently at various resonant frequencies
and has a frequency response M
ss
(
n
; f). O-resonance (B
0
) mapping provides the
information of resonant frequencies (f), and allows the estimation of M
ss
(
n
; f). A
small ROI contains multiple resonant osets, and M
ss
(
n
) over the ROI consists of spec-
trally weighted signals where the spectrally weighted signals can be computed by the
multiplication of M
ss
(
n
; f) and relative resonant frequency oset W (f). Therefore,
the modied myocardial signal model including B
0
inhomogeneity describes the sum of
the spectrally weighted signal, and can be expressed as,
M
ss;B
(
n
(z)) =
Z
M
ss
(
n
(z); f)W (f)df: (6.6)
C. B
+
1
inhomogeneity
B
+
1
inhomogeneity can cause discrepancy between the prescribed and actual
ip angles,
resulting in severe disagreement in the expected and measured signals. The relative B
+
1
variation, denoted by the parameter b1, was computed as the measured
ip-angle divided
by the prescribed
ip-angle based on the cardiac B
+
1
mapping [11,83]. We estimated the
actual
ip angle
n;actual
in the ROI for each prescribed
ip angle value in balanced SSFP
by

n;actual
=
n
b1 (6.7)
87
We assumed that the B
+
1
inhomogeneity distribution within a small ROI is negligibly
small and independent of the prescribed
ip angle, and therefore b1 was considered as a
constant value. Considering B
+
1
inhomogeneity, the Eq. 6.2 can be rewritten as
M
ss;C
(
n
) =M
ss
(
n;actual
): (6.8)
Magnetization Transfer Eects
The saturation of the macromolecular spins can be transferred to the liquid spins, called
MT, when the spin state of the macromolecular protons in
uences the spin state of the
liquid protons through exchange processes [30,91,92]. Recent studies suggested that MT
can in
uence balanced SSFP signals when short TRs and large
ip angles saturate a large
amount of macromolecular spins [5,6]. This can cause a reduction in overall myocardial
signal, which can be an additional factor to the inaccuracy of the signal prediction.
An elongated RF pulse has a dierent RF pulse energy and bandwidth compared to
the original short pulse with the same
ip angle. This change in RF length only alters
the degree of the macromolecular spin saturation, and therefore any signal changes will
represent the MT eect. An RF pulse elongated by a factor of is expected to decrease
its saturation factor (SF) by
2
. This SF can be even smaller when increasing TR, but it
may induce unwanted signal variation due to B
0
inhomogeneity, as previously discussed.
Therefore, we only evaluated the RF pulse elongation factor with the xed TR in
this work, and dened the MT ratio (MTR) to quantify the possible range of the MT
eects [6],
MTR(SF ) =
SI
;max
SI
;min
SI
;max
100(%): (6.9)
88
SF is a relative dierence between the maximum and minimum SFs, and SI
;max=min
is the myocardial signal intensity over the ROI with the maximum/minimum for a
given TR. It is important to note that SI
;max
was considered to be a unperturbed signal,
whereas SI
;min
is assumed to be a MT weighted signal.
6.2.3 Experimental Setup
A body coil was used for RF transmission and an 8-channel phased array cardiac coil
was used for signal reception. Parallel imaging was not used. In all studies, the transmit
gain was calibrated using a standard pre-scan and the center frequency was adjusted over
a 3D region of interest containing the LV. Synchronization with the cardiac cycle was
achieved with prospective triggering based on an ECG signal.
Both the B
0
and B
+
1
maps [11, 83] were obtained before acquiring cardiac SSFP se-
quence, and used in the myocardial signal models. Spiral readouts were used in both B
0
and B
+
1
mapping, and two separate breath-holds were required for them. Signal from fat
were reduced using a fat saturation pre-pulse. Imaging parameters (B
0
mapping): FOV
= 30 cm, in-plane resolution = 2.6 mm, TE = 1.6 ms and 3.6 ms ( 250 Hz frequency
range), TR = 12.8 ms,
ip angle = 30

, and slice thickness = 5 mm. Imaging parameters
(B
+
1
mapping): FOV = 30 cm, in-plane resolution = 5 mm, TE = 2 ms, TR = 7.2 ms,
prescribed
ip angle = 60

and 120

, and slice thickness = 5 mm.
Cardiac SSFP cine loops were acquired using a product 2D FIESTA sequence with
prescribed
ip angles from 10

to 90

in steps of 5

. We xed the TR and RF pulse
duration, and adjusted the RF pulse amplitude to change the prescribed
ip angles.
Imaging parameters: FOV = 30 cm, matrix = 224 224, slice thickness = 5 mm, cardiac
89
TR
3.6 ms 4.0 ms 4.4 ms 4.8 ms 5.2 ms 5.6 ms
Scale 1 56.0

50.4 45.8 42.0 38.8 36.0

Scale 2 12.6 11.5 10.5 9.7 9.0
Scale 3 5.1 4.7 4.3 4.0
Scale 4 2.6 2.4 2.3
Scale 5 1.6 1.4
Scale 6 1.0

SF 0 38 41 39 37 35
Table 6.1: Computed relative saturation factors (SF) for dierent TR/ combinations
and the corresponding SF for each TR. SF was dened as SF
;min
- SF
;max
and MT
measurements were made for the upper triangular region.

The repeatability was tested with ve measurements.
phases = 10, views per segment = 20, and TR = 5.0 ms (4 subjects) and 5.9ms (1 subject).
RF pulse parameters: duration = 1.28 ms and TB = 2.
For MT experiments, dierent RF elongation eects were measured with six dierent
TRs (ranged from 3.6 to 5.6 ms) in separate four healthy volunteers. For each TR, we
started with = 1, and increased until the timing limitation was reached. Accordingly,
only = 1 was used for the shortest TR (3.6ms), and = 1 to 6 were used for the
longest TR (5.6ms). Table 6.1 shows the relative SF for TR/ combinations and the
corresponding SFs. MT measurements were made for the upper triangular region of
Table 6.1. Repeatability was tested for of 1 and 6 with 5 measurements acquired in
separate breath-holds. Imaging parameters: FOV = 30 cm, acquisition matrix = 128
90
128, views per segment = 16, and heartbeats = 8. RF pulse parameters: duration =
0.488 ms, TB = 2, prescribed
ip angle = 45

, and slice thickness = 5 mm.
6.2.4 Data Analysis
Images from mid-diastole were selected for analysis, and we manually dened ROIs con-
taining septal myocardium. Numerical simulations assumed myocardial relaxation times
of T
1
= 1115 ms and T
2
= 41 ms [51]. All seven combinations that either considered or
excluded each factor (A, B, and C) and the simplied signal model (ignoring all three)
were evaluated using a relative error metric dened as:
Relative Error =
1
9
9
X
n=1
jSI
measured
(
n
)SI
expected
(
n
)j
jSI
measured
(
n
)
: (6.10)
The expected signal intensity (SI
expected
) was adjusted to have the same minimum and
maximum range of SI
measured
, and then both SI
measured
and SI
expected
were normalized
by the maximum SI
measured
. Image analysis and Bloch simulation were performed in
MATLAB 7.0 (The Mathworks, Inc., Natick, MA).
6.3 Results
The steady-state signal as a function of the prescribed
ip angle (10

- 90

) was rst
measured in a uniform ball phantom (T
1
=T
2
= 200/30 ms) in conjunction with B
0
and
B
+
1
mapping. In this phantom validation, as shown in Figure 6.3,we only evaluated the
non-ideal slice prole (M
ss;A
) because the resonant oset within the ROI was close to
0 Hz and the relative B
+
1
scale was close to 1 (b1 = 0.97). Fig 6.3a shows the selected
91
Prescribed flip angle
Signal Intensity (a.u.)
20° 40° 60° 80°
0
0.5
1

M
ss
M
ss,A
Measured
b:
10° 30° 50° 70° 90°
ROI ROI ROI ROI ROI
a:
Figure 6.3: Phantom validation of the steady-state signal models: (a) representative
magnitude phantom images overlapped with a circular ROI, and (b) The simplied signal
model (dotted line - M
ss
), the modied signal model considering a non-ideal slice prole
(solid line - M
ss;A
), and the measured signal intensity over the ROI () as a function of
the prescribed
ip angle.
magnitude images with the dierent prescribed
ip angles overlapped with a circular ROI.
The signal intensity curves as a function of the prescribed
ip angle (Fig 6.3b) illustrate
the reduced discrepancy between measured and expected signals with the modied signal
model including the non-ideal slice prole (Eq. 6.5).The relative errors were 10.9% and
4.0% using M
ss
and M
ss;A
, respectively.
Figure 6.4 shows the inhomogeneities of B
0
and B
+
1
elds over the myocardium. The
representative B
0
and B
+
1
maps are overlapped with the balanced SSFP image. The
histogram of the relative resonant frequency o-set W (f), and the relative B
+
1
scale
92
B
0
measurement B
1
+
measurement
−50
0
50
0.2
0.6
1
0 0.2 0.4 0.6 0.8 1
B1 scale
num of pixels (a.u.)
−50 0 50
Off-resonance (Hz)
num of pixels (a.u.)
a:
c:
b:
d:
W(∆ƒ) b1
↓
Figure 6.4: The representative in-vivo B
0
and B
+
1
measurements. (a and b) The B
0
and
B
+
1
eld inhomogeneities over the myocardium were overlapped with the cardiac magni-
tude images. (c) The relative resonant oset W (f) over the ROI (septal myocardium)
and (d) the histogram of relative B
+
1
inhomogeneity over the ROI. The relative B
+
1
vari-
ation over the ROI was averaged to be 0.67 in this subject.
(b1) within the ROI were shown in Fig 6.4 c and d. In this subject, the resonant oset
ranged from 0 Hz to 25.0 Hz, and b1 was 0.67 where the values were used in the modied
signal models, Eq. 6.6 and Eq. 6.8, respectively.
Figure 6.5 illustrates the representative in-vivo validation result. Representative mag-
nitude images (shown in Fig 6.5a) are overlapped with the manually selected ROI. The
simplied signal model showed a great deviation from the measured values while the
modied signal model including all practical factors (slice proles, o-resonance, and B
+
1
93
20° 80° 60° 40°
Prescribed flip angle
Myocardial SI (a.u.)
20° 40° 60° 80°
0
0.5
1

b:
M
ss
M
ss,A+B+C
Measured
Figure 6.5: In-vivo evaluation of the steady-state signal models in 3T cardiac imaging: (a)
selective cardiac cine images with dierent prescribed
ip angles, and (b) the simplied
signal model (dotted line - M
ss
), the proposed signal model (solid line - M
ss;A+B+C
), and
the measured myocardial signals over the ROI () as a function of the prescribed
ip
angle.
inhomogeneity) were in good agreement with measured values (Fig 6.5b). In this subject,
the relative error was 33.3% using M
ss
, and 2.3% using M
ss;A+B+C
.
Figure 6.6 contains the mean and standard deviations of the relative error averaged
over all ve subjects. All the possible combinations and the simplied signal model were
94
0
10
20
30
40
50
Relative Error (%)
M
ss
M
ss,A
M
ss,A+C
M
ss,A+B+C
Signal Prediction Models
M
ss,B
M
ss,C
M
ss,B+C
M
ss,A+B
A. Slice profile
B. B
0
inhomogeneity
C. B
1
+
inhomogeneity
Figure 6.6: The relative errors (mean standard deviation) with all possible steady-state
signal models for all ve subjects. The simplied steady-state model (M
ss
) showed 28.2
4.3% of the relative error, and the signal model including all three factors (M
ss;A+B+C
)
reduced the relative error to 4.2 2.1%.
evaluated because each factor independently contributes the signal deviation. The mini-
mal relative error was 4.2 2.1% when considering all the practical factors (M
ss;A+B+C
)
while M
ss;A
and M
ss;A+C
showed comparable superior performance (7.1 3.6% and 5.5
2.5%, respectively), compared to 28.2 4.3% using M
ss
.
Figure 6.7 shows representative cardiac images as a function of the pulse elongation
scale () for a constant TR of 5.6 ms. The dierent elongated RF pulses ( = 1 to 6)
with the xed TR and the same
ip angle were illustrated in Fig 6.7a. Magnitude cardiac
images are overlapped with the manually selected ROI (shown in Fig 6.7b) and the cor-
responding myocardial signal intensity (SI) was plotted in Fig 6.7c. No major myocardial
signal variation was observed, and the myocardial SI showed a subtle increment with the
large values of (i.e. less saturation on macromolecular spins). The MTR(SF =35)
was computed to be 8.9% in this subject.
95
1 2 3 4 5 6
1 2 3 4 5 6
2.2
2.4
2.6
2.8
Myocaridal SI (a.u.)
β
2.34±0.07
2.57±0.12
β a:
b:
c:
Figure 6.7: Cardiac images with dierent RF elongation scales with the TR of 5.6 ms.
Five repeated measurements with separate breath-holds were performed on = 1 and
6. The myocardium signal intensity over the ROI was increased by 9.8% using a six-fold
elongated RF pulse ( = 6) and MTR(SF = 35) was measured to be 8.9%.
Figure 6.8 shows the MTR values as a function of TR with two dierent subjects. The
combination of 4.4ms/(SF = 41) produced the maximum MTR of 15.2% for rst subject
(Fig 6.8a) when the actual
ip angle was 31.4

. On the other hand, the combination of
5.2ms/(SF = 37) produced the maximum MTR of 12.3% for second subject (Fig 6.8b)
when the actual
ip angle was 25.2

. The prescribed
ip angle was 45

in all cases. The
maximum MTR for each subject ranged from 12% to 19% (15.6 2.9%) across all four
subjects.
96
0
5
10
15
3.6
(0)
MTR (%)
Flip angle = 31.4° Flip angle = 25.2°
4
(38)
4.4
(41)
4.8
(39)
5.2
(37)
5.6
(35)
Fixed TR
(∆SF)
3.6
(0)
4
(38)
4.4
(41)
4.8
(39)
5.2
(37)
5.6
(35)
Fixed TR
(∆SF)
a: b:
8.7±4.8
11.1±3.3
Figure 6.8: MTR values over the ROI as a function of the TR=SF combinations when
the actual
ip angle is (a) 31.4

and (b) 25.2

. The prescribed
ip angle was 45

. The
combination of 4.4/(41) and 5.2/(37) produced the maximum MTR of (a) 15.2% and (b)
12.3%, respectively. The maximum MTR was 15.6 2.9% over all four subjects.
6.4 Discussion
The study quantitatively compared the simplied steady-state formula (Eq. 6.2) with
the measured myocardial signal as a function of the prescribed
ip angle. The relative
error was measured to be 28.2 4.3%, which indicates substantial deviation from the
actual measurements. The modied signal model including all three practical factors
(M
ss;A+B+C
) reduced the relative error to 4.2 2.1%. Among all other combinations,
M
ss;A
and M
ss;A+C
also showed comparable results, 7.1 3.6% and 5.5 2.5%, respec-
tively, compared to M
ss;A+B+C
. It is important to note that a non-ideal slice prole is
not dependent on the subject whereas the B
0
and B
+
1
mapping requires the additional
subject-based calibration.
We evaluated the modied steady-state models on a 3T system, which possibly con-
tains more B
0
and B
+
1
eld inhomogeneities compared to 1.5T. The slice prole for a
97
given RF pulse is expected to be independent of static eld strengths while the B
0
and
B
+
1
eld inhomogeneities and MT eects depend on the eld strength. Although the rela-
tive contribution to the modied signal models will vary due to the dierence in absolute
values in dierent static eld strengths, we believe the similar accuracy would hold for
1.5T balanced SSFP cardiac imaging.
The non-ideal slice proles due to short RF pulses are mostly responsive to 2D bal-
anced SSFP imaging. 3D balanced SSFP imaging typically accommodates sharp slab
proles and chooses only the region containing a relatively constant slab selection. There-
fore, the non-ideal slab prole can be less prominent and create only the minor signal
deviation as a function of the distance to the slice center. The B
0
and B
+
1
eld inhomo-
geneities, however, will still remain as important factors for the modied signal models
for both 2D and 3D balanced SSFP.
Our observation suggested the MTR of 15.6 2.9% in 3T balanced SSFP cardiac
imaging. This is relatively small compared to the 30 - 50% reported in brain tissue [5,6],
but may be benecial in the detection of infarcts and in
ammation [89]. Possible sources
of this discrepancy were low actual
ip angles due to B
+
1
inhomogeneity (25

- 41

;
prescribed
ip angle = 45

), low steady-state myocardial signal, and the limited TR
range (3 - 5 ms) to avoid the banding artifacts, which collectively contributed to the
smaller range of MTR.
The MTR dependency on
ip angle has been previously investigated for white matter
(WM) and gray matter (GM), and only limited variation (< 5%) has been observed
within 60

10

(50

10

) for WM (GM) [6]. We expect the modied signal models
and its corresponding optimum
ip angle estimation would not be much aected by MT
98
because the observed MTR for myocardium was relatively small, and the MTR
ip angle
dependency was subtle near the optimum
ip angle (40

- 60

). As a result, we excluded
the MT eect in the modied signal models.
Only the steady-state signal intensity for myocardium has been evaluated in this
study. The signal intensity for LV blood is always enhanced when the prescribed
ip
angle increased, indicating the blood does not reach the steady-state. The signal model
can also be modied to accurately describe the transient signal behavior based on the
previous theoretical frameworks in transient state [21, 28, 34, 63, 65] and the addressed
practical considerations (A, B, and C). The full assessment of both transient and steady-
state signal behavior in balanced SSFP will be appreciated in many applications where
the tissues of interest exhibit both the transient and steady-state behavior.
The excitation angle plays a critical role in achieving the maximum SNR and/or CNR
in many applications. The myocardial signal in the LV function study can be directly
guided by the estimation of the optimum
ip angle. The other possible applications of
balanced SSFP pulse sequences include the rst-pass myocardial perfusion imaging, ar-
terial spin labeling (ASL) imaging, blood oxygenation level-dependent (BOLD) imaging,
and T
2
-weighted edema imaging.
6.5 Summary
We have demonstrated a modied model for the balanced SSFP signal that takes into
account the eects of non-ideal slice proles, o-resonance, B
+
1
inhomogeneity, and MT.
99
The proposed model predicted myocardial signals that accurately matched the exper-
imental observations, and will be benecial to SNR and CNR optimization in clinical
protocols.
100
Chapter 7
Summary and Recommendations
Cardiac MRI is making considerable advances toward being a "one-stop shop" for heart
disease assessment, largely because of continued improvements in MRI hardware and
software. The use of higher eld strength, such as 3 Tesla, allows for improvements in
spatial and temporal resolution. Cardiac MRI at 3 Tesla, however, is noticeably dierent
from imaging at 1.5 Tesla because of a variety of artifacts related to susceptibility eects
and augmentation of B
+
1
inhomogeneity.
The work presented in this thesis concentrated on methods to mitigate B
+
1
inhomo-
geneity artifacts in 3 Tesla cardiac MRI. The key contributions of this thesis include:
The development of a practical and time-ecient method for measuring
B
+
1
variation over the heart. We veried that the proposed method produces
reproducible B
+
1
maps over the entire heart within a single breath-hold [75,81,83].
This method is an extension of previously established B
+
1
mapping techniques in
static tissue (DAM [35,36,71,72] and SDAM [11]).
The development and validation of a strategy for compensating B
+
1
in-
homogeneity eects in slice selective imaging. We designed 2DRF pulses
101
to compensate B
+
1
inhomogeneity over the heart, and the proposed RF pulse has
been validated theoretically and experimentally. The initial comparison between
the conventional slice selective and the proposed RF pulses showed a promising
improvement for achieving uniform
ip angles over the heart [74,80,82].
The design and implementation of a novel saturation pulse design to
improve the saturation eectiveness over the heart. A tailored pulse train
consisting of hard pulses with unequal weighting has been designed and validated
for complete saturation of myocardium based on estimated B
0
and B
+
1
maps. This
improved saturation eectiveness provides an accurate T
1
-weighted signal, and is
essential for quantitative myocardial rst-pass perfusion imaging [79,85].
The establishment of a method that predicts myocardial signal behavior
during balanced SSFP imaging. We have examined multiple practical factors
in 3T cardiac MRI, and quantitatively validated that the amended model is well
matched with the experimental observations. This will be benecial to SNR and
CNR optimization in clinical cardiac protocols using balanced SSFP [76{78,84].
7.1 Future Work
This sections summarizes some possible future directions to make 3T cardiac MRI more
practical and feasible in cardiac applications. The following list contains more specic
possibilities for future works.
102
7.1.1 B
+
1
Inhomogeneity Measurements
B
+
1
mapping may become a useful clinical protocol as a pre-scan calibration procedure
for many applications.
The SDAM single breath-hold acquisition is currently being incorporated into the
3T cardiac MR protocol at our institution. We expect to compile a library of B
+
1
maps from more than 100 cardiac patients for further analysis. A large number
of patients will determine more generalized B
+
1
distribution over the heart at 3T.
Redesign of the saturation pulse and data acquisition scheme for patient scans may
be needed when additional B
0
inhomogeneity, caused by inadequate shimming,
sternal wires or metal clips from prior surgery, is present in cardiac patients.
The proposed B
+
1
mapping can also be applied to other body areas such as the
abdomen. Abdominal imaging at 3T typically suers from local signal drop-os
due to B
+
1
inhomogeneity. Abdominal B
+
1
mapping also requires breath-holds, a
large eld-of-view (40 cm), and additional considerations of signicant fat signals.
The possible range of B
0
inhomogeneity over the entire abdomen at 3T should be
newly dened.
7.1.2 B
+
1
Compensation using 2DRF pulses
The initial 2DRF pulse design conned the total number of subpulses to three for sim-
plicity, and we have validated the proposed method using body coil transmission.
The proposed method is based on unidirectional B
+
1
variation over the heart, and
this ROI-based B
+
1
compensation is applied to other body regions, focusing on a
103
small region only. Appropriate clinical applications need to be investigated for
future works.
More
exible choices of the in-plane
ip angle prole at the expense of pulse du-
ration will reduce the subject dependent limitation and be more useful in many
applications. The number of subpulses can be increased (more than three) or de-
creased (two), and the subpulse weighting can be an additional free parameter for
more
exible B
+
1
compensation. Any portion of the spectral response of the subpulse
weights (conceptually an FIR lter) can be used to nd the optimal prole. Further
reduction in RF pulse duration can be made using parallel RF transmission [38,93],
reducing T
2
or T
2
* artifacts.
7.1.3 B
+
1
-insensitive Tailored Pulse Designs
This work has shown that the tailored pulse train based on B
0
and B
+
1
maps can improve
the saturation performance. This optimization approach can be extended to many other
contrast preparation pulses such as inversion and T
2
-preparation pulses.
Tailored pulse trains with more than three subpulses can be tested for more complete
saturation performance. This will result in a small increment in RF power and pulse
duration.
The possibility of unwanted stimulated echoes should be considered when more
extensive coverage of the myocardium is used in myocardial perfusion imaging.
104
The BIR-4 pulses can be tailored based on B
0
and B
+
1
maps. Modulation function
parameters and its pulse duration can be selected to improve the saturation per-
formance. For imaging sequences where the SAR limitation is less restrictive, the
tailored BIR-4 pulses and tailored pulse trains can be quantitatively compared to
choose the best saturation pulse.
Adiabatic inversion pulses can also be tailored. New amplitude/frequency modu-
lation functions, tted to the B
0
and B
+
1
space, can be designed and evaluated in
many applications. T
2
-preparation pulses employing adiabatic inversion pulses [48]
can benet from tailored adiabatic inversion pulses.
7.1.4 Signal Behavior during Balanced SSFP Imaging
Accurate estimation of an optimum
ip angle is important for sequence optimization in
clinical protocols. Several improvements can be considered for many applications using
balanced SSFP.
The modied signal model has been studied and evaluated in 2D balanced SSFP
imaging at 3T. The evaluation of 3D balanced SSFP and/or at dierent B
0
eld
strength (e.g. 1.5 Tesla) can also be performed to identify the accurate signal model.
The proposed signal model can be modied to describe transient signal behavior.
Theoretical characteristics of transient response has been well explored, and can
easily be incorporated with the addressed practical considerations to improve its
accuracy. The full assessment of both transient and steady-state signal behavior
will be useful in many applications.
105
References
[1] S. Akoka, F. Franconi, F. Seguin, and A. Le Pape. Radiofrequency map of an NMR
coil by imaging. Magn. Reson. Imaging, 11:437{441, 1993.
[2] D. J. Atkinson, D. Burstein, and R. R. Edelman. First-pass cardiac perfusion: eval-
uation with ultrafast MR imaging. Radiology, 174(3):757{762, 1990.
[3] J. Baum, R. Tycko, and A. Pines. Broadband and adiabatic inversion of a two-level
system by phase-modulated pulses. Phys. Rev. A, 32(6):3435{3447, Dec 1985.
[4] M. A. Bernstein, K. F. King, and X. J. Zhou. Handbook of MRI Pulse Sequences.
Academic, 2004.
[5] O. Bieri and K. Scheer. On the origin of apparent low tissue signals in balanced
SSFP. Magn. Reson. Med., 56(5):1067{1074, 2006.
[6] O. Bieri and K. Scheer. Optimized balanced steady-state free precession magneti-
zation transfer imaging. Magn. Reson. Med., 58(3):511{518, 2007.
[7] F. Bloch, W. W. Hansen, and M. E. Packard. Nuclear induction. Phys. Rev., 69:127,
1946.
[8] H. Y. Carr. Steady-state free precession in nuclear magnetic resonance. Phys. Rev.,
112(5):1693{1701, 1958.
[9] S. Conolly, D. G. Nishimura, A. Macovski, and G. Glover. Variable-rate selective
excitation. J. Magn. Reson., 78(3):440{458, 1988.
[10] B. F. Coolen, E. Heijman, K. Nicolay, and G. J. Strijkers. On the use of steady-state
equations to estimate signal intensities in 2D TrueFISP imaging. In Proc., ISMRM,
16th Annual Meeting, page 833, Toronto, 2008.
[11] C. H. Cunningham, J. M. Pauly, and K. S. Nayak. SDAM: Saturated double angle
method for rapid B1+ mapping. Magn. Reson. Med., 55:1326{1333, 2006.
[12] R. Deichmann. Optimized RF excitation for anatomical brain imaging of the occip-
ital lobe using the 3D MDEFT sequence and a surface transmit coil. Magn. Reson.
Med., 53:1212{1216, 2005.
[13] R. Deichmann, C. D. Good, and R. Turner. RF inhomogeneity compensation in
structural brain imaging. Magn. Reson. Med., 47:398{402, 2002.
106
[14] D. L. Donoho and I. M. Johnstone. Adapting to unknown smoothness via wavelet
shrinkage. J. Amer. Stat. Assn., 90:1200{1224, 1995.
[15] R. R. Edelman, P. Storey, E. Dunkle, W. Li, A. Carrillo, A. Vu, and T. J. Car-
roll. Gadolinium-enhanced o-resonance contrast angiography. Magn. Reson. Med.,
57(3):475{484, 2007.
[16] B. S. Everitt and D. J. Hand. Finite mixture distributions. Chapman and Hall New
York, 1981.
[17] P. Ferreira, P. Gatehouse, D. Firmin, C. Bucciarelli-Ducci, and R. Wage. Investigat-
ing myocardial eld distortions during rst pass of a gadolinium based contrast agent
in perfusion studies. In Proc., ISMRM, 16th Annual Meeting, page 46, Toronto, 2008.
[18] J. R. Forder, K. S. Nayak, and G. M. Pohost. Cardiac imaging at 3T: new pulse
sequences and strategies for cardiac imaging and spectroscopy must be developed.
Diagnostic Imaging, 24(13):65{73, 2002.
[19] J. O. Fredrickson, C. H. Meyer, and N. J. Pelc. Flow eects of spectral spatial
excitation. In Proc., ISMRM, 5th Annual Meeting, page 113, Vancouver, 1997.
[20] R. Freeman and HDW. Hill. Phase and intensity anomalies in fourier transform
NMR. J. Magn. Reson., 4:366{383, 1971.
[21] C. Ganter. O-resonance eects in the transient response of SSFP sequences. Magn.
Reson. Med., 52(2):368{375, 2004.
[22] M. Garwood and L. DelaBarre. The return of the frequency sweep: Designing adi-
abatic pulses for contemporary NMR. J. Magn. Reson. Imaging, 153(2):155{177,
2001.
[23] M. Garwood and Y. Ke. Symmetric pulses to induce arbitrary
ip angles with com-
pensation for RF inhomogeneity and resonance osets. J. Magn. Reson., 94(3):511{
525, 1991.
[24] R. L. Greenman, J. E. Shirosky, R. V. Mulkern, and N. M. Rofsky. Double inversion
black-blood fast spin-echo imaging of the human heart: A comparison between 1.5T
and 3.0T. J. Magn. Reson. Imaging, 17:648{655, 2003.
[25] E. M. Haacke, R. W. Brown, M. R. Thompson, and R. Venkatesan. Magnetic Res-
onance Imaging: Physical Principles and Sequence Design. John Wiley and Sons,
1999.
[26] E. M. Haacke, P. A. Wielopolski, J. A. Tkach, and M. T. Modic. Steady-state free
precession imaging in the presence of motion: application for improved visualization
of the cerebrospinal
uid. Radiology, 175(2):545{552, 1990.
[27] B. A. Hargreaves. Spin Manipulation Methods for Ecient Magnetic Resonance
Imaging. PhD thesis, Stanford University, 2001.
107
[28] B. A. Hargreaves, S. S. Vasanawala, J. M. Pauly, and D. G. Nishimura. Character-
ization and reduction of the transient response in steady-state MR imaging. Magn.
Reson. Med., 46(1):149{158, 2001.
[29] R. Hashemi, W. G. Bradley, and L. Christopher. MRI: The Basics. Lippincott
Williams and Wilkins, 2003.
[30] R. M. Henkelman, G. J. Stanisz, and S. J. Graham. Magnetization transfer in MRI:
a review. NMR Biomed, 14(2):57{64, 2001.
[31] D.E. Hokanson, D.S. Sumner, and D.E. Strandness. An electrically calibrated
plethysmograph for direct measurement of limb blood
ow. IEEE Trans Biomed
Eng, pages 25{29, 1975.
[32] J. P. Hornak and J. Szumowski. Magnetic eld mapping. Magn. Reson. Med.,
6:158{163, 1988.
[33] L. Y. Hsu, K. L. Rhoads, J. E. Holly, P. Kellman, A. H. Aletras, and A. E. Arai.
Quantitative myocardial perfusion analysis with a dual-bolus contrast-enhanced rst-
pass MRI technique in humans. J. Magn. Reson. Imaging, 23:315{322, 2006.
[34] T-Y. Huang, I-J. Huang, C-Y. Chen, K. Scheer, H-W. Chung, and H-C. Cheng.
Are TrueFISP images T2/T1-weighted? Magn. Reson. Med., 48(4):684{688, 2002.
[35] E. K. Insko and L. Bolinger. B
1
mapping. In Proc., SMRM, 11th Annual Meeting,
page 4302, Berlin, 1992.
[36] E. K. Insko and L. Bolinger. Mapping of the radiofrequency eld. J. Magn. Reson.
A, 103:82{85, 1993.
[37] H. Jung, K. Sung, K. S. Nayak, E. Y. Kim, and J. C. Ye. k-t FOCUSS: a general
compressed sensing framework for high resolution dynamic MRI. Magn. Reson. Med.
in press.
[38] U. Katscher, P. Bornert, C. Leussler, and J. S. van den Brink. Transmit SENSE.
Magn. Reson. Med., 49:144{150, 2003.
[39] P. Kellman and A. E. Arai. Imaging sequences for rst pass perfusion {a review. J.
Cardiovasc. Magn. Reson., 9(3):525{537, 2007.
[40] D. Kim, A. Cernicanu, and L. Axel. B0 and B1-insensitive uniform T1-weighting
for quantitative, rst-pass myocardial perfusion magnetic resonance imaging. Magn.
Reson. Med., 54(6):1423{1429, 2005.
[41] D. Kim, O. Gonen, N. Oesingmann, and L. Axel. Comparison of the eectiveness of
saturation pulses in the heart at 3T. Magn. Reson. Med., 59(1):209{215, 2008.
[42] A. Kino, S. Zuehlsdor, P. Weale, N. Leloudas, X. Liu, R. Jerecic, and J. C. Carr.
Comparison of dierent eld insensitive saturation pulses for 3T cardiac rst pass
perfusion. In Proc., ISMRM, 15th Annual Meeting, page 2532, Berlin, 2007.
108
[43] P. C. Lauterbur. Image formation by induced local interactions: Examples employing
nuclear magnetic resonance. Nature, 242:190, 1973.
[44] Z-P. Liang and P. C. Lauterbur. Principles of Magnetic Resonance Imaging: A
Signal Processing Perspective. IEEE Press Series in Biomedical Engineering, 1999.
[45] M. T. McNamara, C. B. Higgins, R. L. Ehman, D. Revel, R. Sievers, and R. C.
Brasch. Acute myocardial ischemia: magnetic resonance contrast enhancement with
gadolinium-DTPA. Radiology, 153(1):157{163, 1984.
[46] P. G. Morris. Nuclear Magnetic Resonance Imaging in Medicine and Biology. Oxford
University Press, 1986.
[47] K. S. Nayak, C. H. Cunningham, J. M. Santos, and J. M. Pauly. Real-time cardiac
MRI at 3 Tesla. Magn. Reson. Med., 51(4):655{660, 2004.
[48] R. Nezafat, M. Stuber, R. Ouwerkerk, A. M. Gharib, M. Y. Desai, and R. I. Pet-
tigrew. B1-insensitive T2 preparation for improved coronary magnetic resonance
angiography at 3 T. Magn. Reson. Med., 55(4):858{864, 2006.
[49] D. G. Nishimura. Principles of magnetic resonance imaging. Stanford University
EE369B Course Notes, 1996.
[50] R. Noeske, F. Seifert, K. H. Rhein, and H. Rinneberg. Human cardiac imaging at
3 T using phased array coils. Magn. Reson. Med., 44(6):978{982, 2000.
[51] R. Noeske, F. Seifert, K. H. Rhein, and H. Rinneberg. Human cardiac imaging at 3
T using phased array coils. Magn. Reson. Med., 44(6):978{982, 2000.
[52] D. C. Noll, J. M. Pauly, C. H. Meyer, D. G. Nishimura, and A. Macovski. Deblurring
for non-2d Fourier transform magnetic resonance imaging. Magn. Reson. Med.,
25:319{333, 1992.
[53] M. Oelhafen, K. P. Pruessmann, S. Kozerke, and P. Boesiger. Calibration of echo-
planar 2D-selective RF excitation pulses. Magn. Reson. Med., 52(5):1136{1145,
2004.
[54] N. Oesingmann, Q. Zhang, and O. Simonetti. Improved saturation rf pulse design for
myocardial rst-pass perfusion at 3T. J. Cardiovasc. Magn. Reson., 6(1):373{374,
2004.
[55] R. J. Ogg, P. B. Kingsley, and J. S. Taylor. WET, a T1- and b1-insensitive water-
suppression method for in vivo localized 1H NMR spectroscopy. J Magn Reson B,
104(1):1{10, 1994.
[56] A. Oppelt, R. Graumann, H. Barfuss, H. Fischer, W. Hartl, and W. Schajor. FISP?
a new fast MRI sequence. Electromedica, 54(1):15{18, 1986.
[57] J. M. Pauly, D. G. Nishimura, and A. Macovski. A k-space analysis of small tip
excitation. J. Magn. Reson., 81:43{56, 1989.
109
[58] J. M. Pauly, P. Le Roux, D. G. Nishimura, and A. Macovski. Parameter relations
for the Shinnar-Le Roux selective excitation pulse design algorithm. IEEE Trans.
Med. Imaging, 10(1):53{65, 1991.
[59] E. M. Purcell, H. C. Torrey, and R. V. Pound. Resonance absorption by nuclear
magnetic moments in a solid. Phys. Rev., 69:37, 1946.
[60] C. Ruan, S. Yang, K. Cusi, F. Gao, and G. D. Clarke. Correction of myocardial
perfusion reserve data from rst-pass MR imaging at 3.0 Tesla with parallel imaging.
In Proc., ISMRM, 14th Annual Meeting, page 1167, Seattle, 2006.
[61] S. Saekho, F. E. Boada, D. C. Noll, and V. A. Stenger. Small tip angle three-
dimensional tailored radiofrequency slab-select pulse for reduced B1 inhomogeneity
at 3 T. Magn. Reson. Med., 53(2):479{484, 2005.
[62] M. Schar, S. Kozerke, S. E. Fischer, and P. Boesiger. Cardiac SSFP imaging at 3
Tesla. Magn. Reson. Med., 51(4):799{806, 2004.
[63] K. Scheer. On the transient phase of balanced SSFP sequences. Magn. Reson.
Med., 49(4):781{783, 2003.
[64] K. Scheer and S. Lehnhardt. Principles and applications of balanced SSFP tech-
niques. European Radiology, 13(11):2409{2418, 2003.
[65] P. Schmitt, M. A. Griswold, V. Gulani, A. Haase, M. Flentje, and P. M. Jakob.
A simple geometrical description of the TrueFISP ideal transient and steady-state
signal. Magn. Reson. Med., 55(1):177{186, 2006.
[66] P. Schmitt, M. A. Griswold, P. M. Jakob, M. Kotas, V. Gulani, M. Flentje, and
A. Haase. Inversion recovery TrueFISP: quantication of T
1
, T
2
, and spin density.
Magn. Reson. Med., 51(4):661{667, 2004.
[67] J. Schwitter, C. M. Wacker, A. C. van Rossum, M. Lombardi, N. Al-Saadi,
H. Ahlstrom, T. Dill, Henrik B. W. Larsson, S. D. Flamm, M. Marquardt, and L. Jo-
hansson. MR-IMPACT: comparison of perfusion-cardiac magnetic resonance with
single-photon emission computed tomography for the detection of coronary artery
disease in a multicentre, multivendor, randomized trial. Eur Heart J, 29(4):480{489,
2008.
[68] M. S. Silver, R. I. Joseph, and D. I. Hoult. Selective spin inversion in nuclear
magnetic resonance and coherent optics through exact solution of the bloch-riccati
equation. Phys. Rev. A, 31:2753{2755, 1985.
[69] R. W. Singerman, T. J. Denison, H. Wen, and R. S. Balaban. Simulation of B
1
eld distribution and intrinsic signal-to-noise in cardiac MRI as a function of static
magnetic eld. J. Magn. Reson., 125:72{83, 1997.
[70] R. S. Staewen, A. J. Johnson, B. D. Ross, T. Parrish, H. Merkle, and M. Garwood.
3-D FLASH imaging using a single surface coil and a new adiabatic pulse, BIR-4.
Invest. Radiol., 25(5):559{567, May 1990.
110
[71] R. Stollberger and P. Wach. Imaging of the active B
1
eld in Vivo. Magn. Reson.
Med., 35(2):246{251, 1996.
[72] R. Stollberger, P. Wach, G. McKinnon, E. Justich, and F. Ebner. Rf-eld mapping
in vivo. In Proc., SMRM, 7th Annual Meeting, page 106, San Francisco, 1988.
[73] M. Stuber, R. M. Botnar, S. E. Fischer, R. Lamerichs, J. Smink, P. Harvey, and
W. J. Manning. Preliminary report on in vivo coronary MRA at 3 Tesla in humans.
Magn. Reson. Med., 48:425{429, 2002.
[74] K. Sung, C. H. Cunningham, and K. S. Nayak. Validation of B1+ non-uniformity
correction in the chest at 3T using TIP-COMP. In Proc., ISMRM, 14th Annual
Meeting, page 597, Seattle, 2006.
[75] K. Sung, E. K. Doyle, S. Valencerina, and K. S. Nayak. B1+ non-uniformity in
3T CMR: Patient study. In Proc., SCRM, 11th Annual Meeting, page 1091, Los
Angeles, 2008.
[76] K. Sung, Y-C. Kim, G. M. Pohost, and K. S. Nayak. Experiment and simulation-
based optimization of blood-myocardium CNR in cardiac SSFP imaging. In Proc.,
ISMRM, 14th Annual Meeting, page 3595, Seattle, 2006.
[77] K. Sung, H-L. Lee, H. H. Hu, and K. S. Nayak. Myocardial signal behavior during
balanced SSFP imaging. Magn. Reson. Med. submitted.
[78] K. Sung, H-L. Lee, H. H. Hu, and K. S. Nayak. Magnetization transfer eects in
cardiac balanced SSFP imaging at 3T. In Proc., ISMRM, 16th Annual Meeting,
page 1401, Toronto, 2008.
[79] K. Sung and K. S. Nayak. The design and use of tailored hard-pulse trains for
uniform saturation of myocardium at 3 Tesla. Magn. Reson. Med. in press.
[80] K. Sung and K. S. Nayak. B1+ non-uniformity correction using 2D RF pulse design.
In Proc., ISMRM, 13th Annual Meeting, page 18, Miami, 2005.
[81] K. Sung and K. S. Nayak. RF non-uniformity over the whole heart at 3T. In Proc.,
ISMRM, 15th Annual Meeting, page 355, Berlin, 2007.
[82] K. Sung and K. S. Nayak. B
+
1
compensation in 3T cardiac imaging using short
2DRF pulses. Magn. Reson. Med., 2008.
[83] K. Sung and K. S. Nayak. Measurement and characterization of RF nonunifor-
mity over the heart at 3T using body coil transmission. J. Magn. Reson. Imaging,
27(3):643{648, 2008.
[84] K. Sung and K. S. Nayak. Myocardial signal behaviors of balanced SSFP imaging
at 3T. In Proc., SCRM, 11th Annual Meeting, page 150, Los Angeles, 2008.
[85] K. Sung and K. S. Nayak. SAR-constraint saturation pulse design based on B0 and
B1 maps. In Proc., ISMRM, 16th Annual Meeting, page 228, Toronto, 2008.
111
[86] A. Tannus and M. Garwood. Adiabatic pulses. NMR in Biomedicine, 10(8):423{434,
1997.
[87] J.T. Vaughan, G. Adriany, C.J. Snyder, J. Tian, T. Thiel, L. Bolinger, H. Liu,
L. DelaBarre, and K. Ugurbil. Ecient high-frequency body coil for high-eld MRI.
Magn. Reson. Med., 52(4):851{859, 2004.
[88] J. Wang, M. Qiu, Q. X. Yang, M. B. Smith, and R. T. Constable. Measurement
and correction of transmitter and receiver induced nonuniformities in vivo. Magn.
Reson. Med., 53(2):408{417, 2005.
[89] O. Weber, K. Scheer, and O. Bieri. Magnetization transfer in cardiac TrueFISP
imaging. In Proc., ISMRM, 15th Annual Meeting, page 2518, Berlin, 2007.
[90] H. Wen, T. J. Denison, R. W. Singerman, and R. S. Balaban. The intrinsic signal-to-
noise ratio in human cardiac imaging at 1.5, 3, and 4 T. J. Magn. Reson., 125:65{71,
1997.
[91] S. D. Wol and R. S. Balaban. Magnetization transfer contrast (MTC) and tissue
water proton relaxation in vivo. Magn. Reson. Med., 10(1):135 { 144, 1989.
[92] S. D. Wol and R. S. Balaban. Magnetization transfer imaging: practical aspects
and clinical applications. Radiology, 192:593{599, 1994.
[93] Y. Zhu. Parallel excitation with an array of transmit coils. Magn. Reson. Med.,
51:775{784, 2004.
[94] Y. Zur. Design of improved spectral-spatial pulses for routine clinical use. Magn.
Reson. Med., 43(3):410{420, 2000.
112
Appendix A
Small Tip-Angle Selective Excitation
A.1 Small-tip Slice Selective Excitation
Providing that the small tip-angle approximation (M
z
M
0
= constant) is satised,
Eq 2.5 can be expanded into three scalar equations:
dM
x
dt
=
G
z
zM
y
;
dM
y
dt
=
G
z
zM
x
+
B
1
(t)M
z
; (A.1)
dM
z
dt
= 0:
By dening a complex notation for the transverse magnetization:
M
xy
=M
x
+iM
y
; (A.2)
113
the rst two equations in Eq A.1 can be written as:
dM
xy
dt
=i
G
z
zM
xy
+i
B
1
(t)M
0
(A.3)
which also can be rewritten as
dM
xy
dt
+i
G
z
zM
xy
=i
B
1
(t)M
0
: (A.4)
If we multiply an intergrading factor (e
i
Gzzt
), the left side can be expressed as,
dM
xy
dt
e
i
Gzzt
+i
G
z
ze
i
Gzzt
M
xy
: (A.5)
The above can be rewritten by using a fact that
d[AB]
dt
=
dA
dt
B +A
dB
dt
:
d[M
xy
(t)e
i
Gzzt
]
dt
=
dM
xy
dt
e
i
Gzzt
+i
G
z
ze
i
Gzzt
M
xy
: (A.6)
Multiplying by (e
i
Gzzt
) for both sides in Eq A.4:
d[M
xy
(t)e
i
Gzzt
]
dt
=iB
1
(t)M
0
e
i
Gzzt
(A.7)
then, integrating with an initial condition (M
xy
(0) = 0) gives,
M
xy
(t;z) =e
i
Gzzt

Z
t
0
i
B
1
(s)M
0
e
i
Gzzs
ds: (A.8)
114
The nal transverse magnetization (M
xy
(z)) at time T,
M
xy
(z) =i
M
0
Z
T
0
B
1
(t)e
iz
R
T
t
Gzds
dt (A.9)
where
R
T
t
G
z
ds can also be expressed as k(t).
A.2 Multidimensional Selective Excitation
In multiple dimensions, the transverse magnetization M
xy
with a non-constant gradient
G
r
(t) at any spatial position r can be expressed as:
M
xy
(r) =i
M
0
Z
T
0
B
1
(t)e
irk(t)
dt (A.10)
where k(t) =
R
T
t
G
r
(s)ds. k(t) is a spatial frequency variable. We can write the
exponential factor as an integral of a three-dimensional delta function,
e
irk(t)
=
Z
k
3
(k(t)k)e
ixk
dk (A.11)
and then Eq A.10 can be rewritten as,
M
xy
=i
M
0
Z
T
0
B
1
(t) [
Z
k
3
(k(t)k)e
ixk
dk]dt: (A.12)
Interchanging the order of integration,
M
xy
=i
M
0
Z
k
[
Z
T
0
B
1
(t)
3
(k(t)k)dt]e
ixk
dk: (A.13)
115
The inner integral over time is the three dimensional path, and can be depicted by p(k):
M
xy
=i
M
0
Z
k
p(k)e
ixk
dk (A.14)
where p(k) is dened to be
R
T
0
B
1
(t)
3
(k(t)k)dt. p(k) shows the weighting of k-space
by the RF excitation B
1
(t). For a non-constant gradient, the k-space velocity should be
normalized to make the weighting explicit, and we multiply the delta function by the the
derivative of its argument,
p(k) =
Z
T
0
B
1
(t)
j
G
r
(t)j

3
(k(t)k)j
G
r
(t)jdt: (A.15)
For the case that the k-space trajectory does not cross itself, we can dene a weighting
function:
W (k(t)) =
B
1
(t)
j
G
r
(t)j
(A.16)
The path p(k) factors into two terms, the spatial weighting function W(k) and a para-
metric description of the unit weight trajectory
S(k) =
Z
T
0
3
((k(t))k)j
G
r
(t)jdt (A.17)
S(k) may be thought of as a sampling structure. It determines both the area and the
density of the k-space representation. The expression for the transverse magnetization
given in Eq. A.10 may be rewritten as,
M
xy
(r) =FT (p(k)) =FT (W (k)S(k)): (A.18)
116
Hence, the transverse magnetization is the FT of the applied RF energy (W(k)) along a
k-space trajectory determined by the gradient waveform (S(k)).
117
Appendix B
Amplitude/Frequency Modulation Functions for BIR-4
The amplitude (f
b
(t))and frequency (f
!
(t))modulation functions used to dene the indi-
vidual segments of BIR-4 are
segment 1:
f
b
(t) =tanh[(1)]; (0< < 1)
f
!
(t) =
tan[]
tan[]
segment 2:
f
b
(t) =tanh[( 1)]; (1< < 2)
f
!
(t) =
tan[( 1)]
tan[]
segment 3:
f
b
(t) =tanh[(3)]; (2< < 3)
f
!
(t) =
tan[( 2)]
tan[]
118
segment 4:
f
b
(t) =tanh[( 3)]; (3< < 4)
f
!
(t) =
tan[( 3)]
tan[]
where and tan are the modulation function parameters.
119
Appendix C
Steady-state Signal Equation
A simple propagation approach can be used to derive the steady-state magnetization for
balanced SSFP imaging sequences, shown in Figure C.1. During a repetition time, each
spin experiences excitation (by pulse), precession (by o-resonance f), and relaxation
(by T
1
and T
2
). Each operation can be separated and described by a matrix notation.
Firstly, rotation about x-axis of an
ip angle can be expressed as:
R
x
() =
0
B
B
B
B
B
B
@
1 0 0
0 cos sin
0 sin cos
1
C
C
C
C
C
C
A
: (C.1)
Similarly, free precession over a period t has a precession angle ( = 2ft) about the
z-axis, and corresponds to a multiplication by the rotation matrix:
P (t) =
0
B
B
B
B
B
B
@
cos(2ft) sin(2ft) 0
sin(2ft) cos(2ft) 0
0 0 1
1
C
C
C
C
C
C
A
: (C.2)
120
TE
TR
M
a
M
b
M
c
M
d
α α α
Figure C.1: Basic steady-state free precession sequence: A string of pulses separated
by a TR.
Finally, T
1
and T
2
relaxation over a time period of t can be described by:
C(t) =
0
B
B
B
B
B
B
@
e
t=T
2
0 0
0 e
t=T
2
0
0 0 e
t=T
1
1
C
C
C
C
C
C
A
; (C.3)
and an addition of the vector:
D(t) = (IC(t))
0
B
B
B
B
B
B
@
0
0
m
0
1
C
C
C
C
C
C
A
: (C.4)
Based on these matrix operations, the magnetization for each point b, c, and c in
Figure C.1 is related by:
M
b
=P (TRTE)C(TRTE)M
a
+D(TRTE)
121
M
c
=R
x
()M
b
(C.5)
M
d
=P (TE)C(TE)M
c
+D(TE)
In steady-state, M
a
is equal to M
d
and both can be replaced by the steady-state magne-
tization M
ss
:
M
ss
=P (TE)C(TE)R
x
()(P (TRTE)C(TRTE)M
ss
+D(TRTE)) +D(TE): (C.6)
Simplifying the above equation:
M
ss
=AM
ss
+B (C.7)
where
A =P (TE)C(TE)R
x
()P (TRTE)C(TRTE)
B =P (TE)C(TE)R
x
()D(TRTE) +D(TE): (C.8)
Then, Eq. C.7 is easily solved for M
ss
:
M
ss
= (IA)
1
B (C.9)
where I is the 33 identity matrix. The derivation of A and B is relatively simple for
most sequences.
122

Abstract (if available)

Abstract Cardiovascular magnetic resonance imaging (MRI) is now routinely used for evaluating cardiac function, and myocardial viability. Due to its unique exibility, MRI has the potential to assess many other aspects of heart disease in the same examination, including the evaluation of coronary arteries, functions of the heart valves, and perfusion of heart muscle. However, the development of cardiac MRI is, in many ways, limited by signal-to-noise ratio (SNR).

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

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

PDF

Dynamic cardiovascular magnetic resonance imaging for improved assessment of ischemic heart disease

PDF

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

PDF

Wideband steady-state free precession for cardiac MRI

PDF

Improving sensitivity and spatial coverage of myocardial arterial spin labeling

PDF

Velocity-encoded magnetic resonance imaging: acquisition, reconstruction and applications

PDF

Improved myocardial arterial spin labeled perfusion imaging

PDF

Dynamic functional magnetic resonance imaging to localize activated neurons

PDF

Fast upper airway MRI of speech

PDF

Estimating liver iron non-invasively with high-field MRI

PDF

Shift-invariant autoregressive reconstruction for MRI

PDF

Correction, coregistration and connectivity analysis of multi-contrast brain MRI

PDF

Quantitative MRI for oxygenation imaging in cerebrovascular diseases

PDF

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

PDF

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

PDF

Pediatric magnetic resonance image processing: applications to posterior fossa cancer and normal development

Asset Metadata

Creator Sung, Kyunghyun (author)

Core Title Radio-frequency non-uniformity in cardiac magnetic resonance imaging

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 07/30/2008

Defense Date 06/18/2008

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

Tag B1 inhomogeneity,cardiac imaging,high field imaging,magnetic resonance imaging,OAI-PMH Harvest

Language English

Advisor Nayak, Krishna S. (committee chair), Leahy, Richard M. (committee member), Prakash, Surya (committee member), Sawchuk, Alexander A. (committee member)

Creator Email kyunghsu@sipi.usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1456

Unique identifier UC182833

Identifier etd-Sung-20080730 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-90505 (legacy record id),usctheses-m1456 (legacy record id)

Legacy Identifier etd-Sung-20080730.pdf

Dmrecord 90505

Document Type Dissertation

Rights Sung, Kyunghyun

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu