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Wideband steady-state free precession for cardiac MRI

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Wideband steady-state free precession for cardiac MRI

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Content WIDEBAND STEADY-STATE FREE PRECESSION
FOR CARDIAC MRI
by
Hsu-Lei Lee
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
December 2008
Copyright 2008 Hsu-Lei Lee
Acknowledgements
In writing this thesis I received huge amount of help from many people. Among them
all I would first like to express my sincere gratitude to my advisor Professor Krishna
Nayak, who constantly inspired me with the passion for research; who supported and
cared for me, and guided me through my Ph.D. study. Four years ago I arrived at USC
being unassured and having no clue on what to expect. Now I graduate with confidence
that I’ve accomplished something worthwhile, and shall achieve more in the future. It
has been a real honor and great pleasure to work with him.
Thanks are also due to all the members of USC Magnetic Resonance Engineering
Lab, for their encouragement and company. I’ve had a wonderful time here at USC and
will certainly miss those long nights in the freezing hospital offices, where we worked
and fumbled and laughed and grumbled together. I want to thank Dr. Ajit Shankara-
narayanan from GE Applied Science Lab for his help in sequence programming and all
the valuable discussions. Also I must acknowledge all the people who volunteered (or
were forced to volunteer, in the name of science/friendship) for my experiments. Their
contribution is essential to this thesis.
I would like to thank my friends in every corner of the world who made my life full
of joy. In particular I have to thank Ivy Tseng and May-Chen Kuo, who helped me a
ii
great deal when I first came to this city of angels. We all have been long way from home,
and for years we’ve looked after each other. I truly cherish every moment we shared.
Finally my deepest gratitude goes to my parents and my little brother back home.
Their understanding and unconditional support made everything possible. My dearest
mom and dad raised me, educated me, prepared me for the world. Then when their
beloved little girl waved them goodbye, they simply smiled and sent her on her own
adventure with all the good wishes. There will never be enough words to describe how
grateful I am; I can only hope that I’ve made them proud. To them I dedicate this thesis,
along with all my love.
iii
Table of Contents
Acknowledgements ii
List of Tables vii
List of Figures viii
Abstract xv
Chapter 1 : Introduction 1
1.1 Motivation and Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 : Cardiac MRI 4
2.1 MR Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Nuclear Spins and Static Magnetic Field . . . . . . . . . . . . . . . . 4
2.1.2 Excitation Using Radio-frequency Field . . . . . . . . . . . . . . . . 6
2.1.3 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.4 Spatial Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.5 Image Signal-to-Noise Ratio . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Clinical Cardiac MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Balanced Steady-State Free Precession Imaging . . . . . . . . . . . . . . . . 12
2.3.1 SSFP Sequence Properties . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Cardiac Applications of SSFP . . . . . . . . . . . . . . . . . . . . . . 14
2.4 High-Field MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Field Strength and Signal Intensity . . . . . . . . . . . . . . . . . . . 16
2.4.2 Challenges in High-Field MRI . . . . . . . . . . . . . . . . . . . . . 17
2.5 Fundamental Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Chapter 3 : Wideband SSFP Seqeunces 21
3.1 Alternating-TR SSFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Spectral Response of Wideband SSFP . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Image Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 SNR Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5 Other Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
iv
3.5.1 Central Dip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.2 Eddy-current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter 4 : Simplified Model for Stabilizing Alternating TR SSFP Sequences 42
4.1 Initial Preparation for Steady-State Sequences . . . . . . . . . . . . . . . . . 42
4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2.1 Characterization of the Cycle Rotation . . . . . . . . . . . . . . . . . 45
4.2.2 Approach to Steady-State from Thermal Equilibrium . . . . . . . . 47
4.2.3 Transient Oscillatory Residues . . . . . . . . . . . . . . . . . . . . . 48
4.2.4 General Model for ATR SSFP Sequences . . . . . . . . . . . . . . . . 52
4.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Chapter 5 : Ventricular Function Imaging with Wideband SSFP 62
5.1 Overview of Ventricular Function MRI . . . . . . . . . . . . . . . . . . . . . 62
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.1 Sequence Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.2 Band Spacing and Temporal Resolution . . . . . . . . . . . . . . . . 66
5.2.3 Blood/myocardium Contrast . . . . . . . . . . . . . . . . . . . . . . 67
5.3 Experimental Design and Results . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3.1 In-vivo evaluation of off-resonance artifacts . . . . . . . . . . . . . 68
5.3.2 In-vivo evaluation of the achievable spatial resolution . . . . . . . 72
5.3.3 Complete LV function examinations . . . . . . . . . . . . . . . . . . 74
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Chapter 6 : Coronary Artery Imaging with Wideband SSFP 78
6.1 MR and Other Imaging Modalities . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2.1 Increased Band Spacing Using Wideband SSFP . . . . . . . . . . . . 83
6.2.2 Initial Preparation for Reducing Transient Oscillations of Wide-
band SSFP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2.3 Imaging Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2.4 SNR Efficiency of Wideband SSFP and Conventional SSFP . . . . . 87
6.2.5 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Chapter 7 : Future Work 96
References 101
v
Appendix A : Initial Preparation 108
A.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
vi
List of Tables
4.1 Measured signal oscillation magnitude during the first ten cycles of wide-
band SSFP , for three initial preparation schemes. Values are averaged over
half the passband. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Measured signal oscillation magnitude during the first ten cycles of FS-
ATR SSFP , for three initial preparation schemes. Values are averaged over
half the water band and fat band. . . . . . . . . . . . . . . . . . . . . . . . . 60
5.1 In-vivo blood-myocardium CNR for balanced SSFP and wideband SSFP
with different TR
s
/TR ratio. CNR values of wideband SSFP drops with
TR
s
/TR ratio. Balanced SSFP CNR was used as a reference in the bottom
row. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Scan parameters for in-vivo evaluation of the achievable spatial resolu-
tion. Imaging TRs were set to the minimum given the prescribed readout
matrix sizes. TR
s
in wideband SSFP was chosen so that the sequence had
a band spacing above 300 Hz for all scans. . . . . . . . . . . . . . . . . . . 72
6.1 In-vivo scan parameters. The row "Spatial Res." represents the spatial res-
olution in readout direction. The resolution in other two phase-encoding
directions are both 1.0 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 In-vivo imaging results: SNR, scan time, and SNR efficiency of 0.68
1.0 1.0 mm
3
resolution images averaged over six volunteer scans. . . . . 92
vii
List of Figures
2.1 Left: Nuclear spin; right: the magnetic dipole moment created by this
spinning charged sphere. (figure provided by Kyunghyun Sung) . . . . . 5
2.2 Left: randomly oriented magnetizations; right: magnetizations aligned
either parallel or anti-parallel to the direction of external magnetic field.
(figure provided by Kyunghyun Sung) . . . . . . . . . . . . . . . . . . . . 6
2.3 The magnetization rotates about the field direction at Larmor frequency
w
0
= g B
0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 A electromagnetic field B
1
rotating at frequencyw
0
is applied to the mag-
netization M, M will start to rotate toward the transverse plane following
the trajectory depicted in (a)-(d). (figure from Brian Hargreaves [31]) . . . 8
2.5 Relaxation of magnetizations. (a) from time t
1
to t
2
, magnetization M
relaxes from M(t
1
) to M(t
2
). Its longitudinal (M
z
) and transversal (M
xy
)
components are functions of relaxation time constants T
1
and T
2
, respec-
tively. (b) longitudinal (T
1
) relaxation, M
z
is a function of T
1
and time t;
(c) transversal (T
2
) relaxation, M
xy
is a function of T
2
and t. . . . . . . . . 9
2.6 Left: 2DFT sequence diagram; right: 2DFT k-space trajectory, which is the
time-integral of spatial encoding gradients. . . . . . . . . . . . . . . . . . . 9
2.7 SSFP sequence. All gradients are fully refocused during one TR. Grey
circles represent the position of echoes. . . . . . . . . . . . . . . . . . . . . 13
2.8 Frequency response of SSFP signal at TE = TR/2. The profile repeats itself
every
1
TR
Hz. There is ap phase increment between adjacent bands. . . . 14
2.9 Simulated SSFP frequency response of different T
1
/T
2
values. Signal in-
tensity increases as T
1
/T
2
is reduced. Myocardium: T
1
/T
2
= 1100/40 ms,
Blood: T
1
/T
2
= 1500/140 ms, Phantom (water): T
1
/T
2
= 150/30 ms. Flip
angle is 30

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
viii
2.10 Simulated SSFP frequency response of different flip angles. When a is
decreased from a high angle (70

), signal intensity starts to increase. After
reaching the flip angle that generates maximum signal intensity (which
can be calculated from Eqn. 2.12), on-resonance signal will drop as a is
lowered, and the signal around 1/TR null band starts to increase. T
1
/T
2
=
1100/40 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.11 Off-resonance induced artifacts in SSFP cardiac image. White arrow: dark
band inside left ventricle wall ; gray arrow: flow transient artifact caused
by banding inside blood pool. . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 Wideband SSFP sequence. All gradients are fully refocused during TR
and TR
s
. The echoes in TR (black circle) and TR
s
(dotted green circle)
correspond to the profiles in Figure 3.2. . . . . . . . . . . . . . . . . . . . . 23
3.2 Steady-state magnetization paths of conventional balanced SSFP (subfig-
ures a to c) and wideband SSFP (subfigures d to i) sequence. Lines in
different colors represent spins of different resonant frequencies. In bal-
anced SSFP , magnetization paths are symmetric about x, y and z axes,
while in wideband SSFP they are only symmetric about the y axis. Black
solid lines in the right column represent the spectral response of signals
in TR, and green dashed lines represent signals in TR
s
. . . . . . . . . . . . 24
3.3 Wideband SSFP signal profiles for (a) fixed TR, and (b) approximately
fixed band spacing ( fixed TR +TR
s
). Signal responses during TR(top) and
TR
s
(bottom) are shown. The horizontal axis represents precession due to
off-resonance. (a) Lower a-values increase the band spacing. (b) Lower
a-values correspond to longer TR, and therefore longer available readout
time. The bottom line of each image represents conventional SSFP , and
the band sat 2kp (integerk1) disappear. Profiles correspond to a=90

and T
2
= T
1
= TR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 Null-to-null band spacing as functions of flip angle and a (=TR
s
/TR). The
spacing converges to 2/TR(1+ a) when the flip angle is small. . . . . . . 26
3.5 Measured and simulated signal profiles from a uniform ball phantom
with an applied linear shim. Data corresponds to conventional SSFP (a)
with a=1, and wideband SSFP (b,c) with a=0.75 and (d,e) with a=0.5. The
TR was 6 ms, and flip angle was 30

in all scans. There was excellent
agreement in the location of null-bands in simulated and measured pro-
files. Compared to a, the increase in band-spacing in b and c was 11% and
34% respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
ix
3.6 Simulated wideband SSFP frequency response as functions of T
2
/T
1
. Sig-
nal intensity changes in the same direction as conventional SSFP; it in-
creases as T
2
/T
1
is reduced. Myocardium: T
2
/T
1
= 1100/40 ms, Blood:
T
2
/T
1
= 1500/140 ms, Phantom (water): T
2
/T
1
= 150/30 ms. Flip angle is
30

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.7 Image contrast as a function of T
2
/T
1
and a-values. M/M
o
is an aver-
age over 2/3 of the null-to-null spacing in the spectral profile of each se-
quence. (upper lines) Signal during TR
s
. (lower lines) Signal during TR. . 31
3.8 Simulated wideband SSFP frequency response as functions of flip angle.
When a is decreased from a high angle (70

), signal intensity starts to
increase. After reaching the flip angle that generates maximum signal
intensity (which can be calculated from Eqn. 2.12), on-resonance signal
will drop asa is lowered, and the signal around1/(TR+TR
s
) null band
starts to increase. T
1
/T
2
= 1100/40 ms in this simulation. At high flip
angles there is a ‘dip’ around on-resonance area, which will be discussed
in Section 3.5.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.9 (a) Myocardium (T
1
/T
2
= 1100/40 ms) and (b) blood (T
1
/T
2
= 1500/140 ms)
contrast as a function of flip angle a and of a The curves reflect a-values
of 1.0 (highest) to 0.1 (lowest) with an increment of 0.1. The peak signal
for each curve is marked with a ‘+’. The optimal flip angle of wideband
SSFP is comparable to that of conventional SSFP when a> 0.3. . . . . . . 33
3.10 SNR efficiency of wideband SSFP with various TR
s
/TR ratio. Myocardium
T
1
, T
2
values are used in simulation. The required band spacing is 300 Hz,
and the SNR efficiency of conventional SSFP is set to 1. . . . . . . . . . . . 35
3.11 Central dip and peak in wideband SSFP signal profiles. Black line rep-
resents the spectral response in TR with a dip around the on-resonance
area, and gray line represents the spectral response in TR
s
with a peak at
the same frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.12 Magnitudes and phases of central dips in wideband SSFP signal profile
for different T
1
/TR values. The width of the central dip broadens with
lower T
1
/TR values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.13 Central dip of blood and myocardium, with different RF flip angle ratio.
RF
1
is the flip angle in TR, and RF
2
is the flip angle in TR
s
. . . . . . . . . . 38
x
3.14 Phantom wideband SSFP image showing eddy-current induced signal
change. A linear shim was applied in horizontal direction to create off-
resonance. In the area where spins have small amount of dephasing,
steady-state signal amplitude is affected by eddy current induced resid-
ual field (arrows indicate signal loss). The residual field is a function of
spatial location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1 An alternating TR SSFP sequence. Black arrows represent RF excitation
pulses that are separated by alternating repetition times TR
1
and TR
2
, and
have phases alternate betweena anda e
i(p+j)
. . . . . . . . . . . . . . . . 44
4.2 The steady-state magnetization path of an alternating TR SSFP sequence
with (0,p) phase-cycling. A full-cycle rotation of a magnetization with
resonance offsetD f starts at M
1
. It experiences phase offset ofq
1
(=D f
p TR
1
) (M
1
! M
+
1
), RF excitation of anglea (M
+
1
! M

2
), phase
offsetq
2
(=D fp TR
2
) and becomes M
2
. Then it experiences another
phase offsetq
2
(M
2
! M
+
2
), excitationa(M
+
2
! M

1
), phase offsetq
1
and
it returns to M
1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 The relation between M
1
, M
2
,~ n
1
, and~ n
2
. (a) 2D plot in x-y plane. Dotted
line represents the magnetization path as in Fig. 4.2. (b) 2D plot in y-z
plane. f
1
is the angle between z-axis and~ n (the projection of~ n
1
and~ n
2
on
y-z plane), f
2
is the angle between~ n and both M
1
and M
2
. Vector~ n
?
is
in the y-z plane and perpendicular to~ n. (c) 3D plot with three axes being
(x,~ n,~ n
?
). f
x
is the angle between~ n and~ n
1
in(x,~ n) plane. . . . . . . . . . 46
4.4 Wideband SSFP sequence: (a) an RF flip angle increment sequence {Da
k
}
designed using Kaiser-Bessel windowing functions with optimized ratios.
(b) the actual RF ramp sequence calculated using values in (a), thata
k
=
å
k
n=1
Da
n
. (c) The absolute value of simulated oscillatory residues after
an optimized 8-step linear ramp preparation. Grey solid line represents
the true residue values obtained using matrix rotation, black dashed line
represents the result given by Eq.(4.9). (d) true residue values after 8-step
linear ramp and Kaiser-Bessel windowed ramp preparation. Black solid
line: optimized Kaiser-Bessel window (b = 3), grey dashed line: Kaiser-
Bessel window (b= 3) with b
1
= b
2
= 0.5, grey solid line: linear ramp. . . 51
xi
4.5 Fat-suppressed ATR SSFP sequence: (a) an RF flip angle increment se-
quence {Da
k
} designed using Kaiser-Bessel windowing functions with(b
1
,
b
2
) optimized for water band. (b) the actual RF ramp sequence calculated
using values in (a), that a
k
= å
k
n=1
Da
n
. (c) The absolute value of simu-
lated oscillatory residues after an optimized eight-step linear ramp prepa-
ration. Grey solid line represents the true residue values obtained using
matrix rotation, black dashed line represents the result given by Eq.(4.9).
(d) true residue values after 8-step linear ramp and Kaiser-Bessel win-
dowed ramp preparation. Black solid line: Kaiser-Bessel window (b = 3)
optimized for water band, grey dotted line: Kaiser-Bessel window (b= 3)
optimized for fat band, grey solid line: linear ramp optimized for water
band. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6 Simulated and measured transient signals of a ball phantom after dif-
ferent preparation methods. (a) wideband SSFP , grey arrows indicate
when the central dips appear. (b) FS-ATR SSFP . The experimental mea-
surements show good agreement with the simulation. Kaiser-Bessel win-
dowed ramp significantly reduced the transient signal fluctuation. . . . . 57
4.7 Alternating TR SSFP phantom images after different preparation meth-
ods. Eight-step preparation was used for all the scans. Images obtained
with Kaiser-Bessel windowed ramp show better image uniformity and re-
duced artifacts. (a) Wideband SSFP images. Ramps were optimized for
the center of passband where D f = 0. (b) FS-ATR SSFP images. Reso-
nant frequencies of the two phantoms were centered at water band (pass
band) and fat band (stop band), with a25 Hz span. Ramps optimized
for water (left column) and fat (right column) bands were both tested. . . 58
5.1 Diagram of the 17-segment model. This figure is from Ref. [9], M. D
Cerqueira, Circulation, 105(4):539–542, Jan 2002. . . . . . . . . . . . . . . . 64
5.2 the 17-segment model on a circumferential polar plot. This figure is from
Ref. [9], M. D Cerqueira, Circulation, 105(4):539–542, Jan 2002. . . . . . . . 65
5.3 Prospective ECG-gated CINE imaging. During one R-R interval, the same
segment of k-space is acquired for frame 1 to N. The next k-space segment
is acquired in the following R-R interval. This process is repeated until full
k-space data are received for all N frames. . . . . . . . . . . . . . . . . . . 66
xii
5.4 Simulations of Blood and Myocardial SNR for Conventional and Wide-
band SSFP at 3 Tesla. (a) Balanced SSFP and (b) wideband SSFP blood-
myocardium signal magnitudes. Steady-state signal as a function ofa for
the myocardium (T
1
/T
2
= 1100/40 ms) and blood (T
1
/T
2
= 1500/140
ms) at 3T are simulated for both sequences. Black dotted lines indicate
the maximum CNR of the sequences. Balanced SSFP has maximum CNR
at a = 75

, wideband SSFP has maximum CNR at a = 70

. For flip an-
gles 45

(shaded area), the sequence CNR is greater than 90% of the
maximum value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.5 Blood/myocardium CNR of wideband SSFP as a function of TR
s
/TR ratio
with 30

flip angle. CNR drops as TR
s
/TR ratio decreases. . . . . . . . . . 69
5.6 Comparison of image artifacts with different TR
s
/TR combinations. Bal-
anced and wideband SSFP end-diastole frames from short axis cine im-
ages with different TR/TR
s
. Dashed lines and background colors repre-
sent band spacing range for the images. Gray arrows indicate off-resonance
artifacts that obstruct the cardiac assessment. Each row represents a fixed
imaging TR. The first column from the left represents conventional SSFP
(TR
s
/TR = 1.0). TR
s
shortens when moving to the right, and therefore
widens the band-spacing in the frequency spectrum. . . . . . . . . . . . . 71
5.7 Comparison of conventional and wideband SSFP as in-plane spatial res-
olution is increased. Balanced and wideband SSFP end-diastole frames
from 3-chamber cine images with different spatial resolution. Flip angle
was 30

, total scan time was 12 R-R intervals. Gray arrows indicate the
artifacts in higher-resolution balanced SSFP images, which increase with
TR and can obstruct the visualization of LV walls and the valves. . . . . . 73
5.8 Sample frames from a multi-slice short axis cine scan of a healthy volun-
teer at 3 Tesla. Banding artifacts can be seen in all the slices of balanced
SSFP , while wideband SSFP provides a more homogeneous signal across
the region of interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 Respiratory navigator gating. Left: navigator tracker location. Navigator
tracker is often placed across right diaphragm or lateral LV wall. Both
location have similar gating performance, so we chose right diaphragm
for its simple to implement. Right: breathing curve and the acceptance
window. (Figures from Stuber et al. [82]) . . . . . . . . . . . . . . . . . . . 80
6.2 Wideband SSFP pulse sequence (top) and its spectral response (bottom).
Black solid line represents the spectral response of the echo in TR (black
circle), gray dotted line represents the spectral response of the echo in TRs
(gray dotted circle). The signal profiles are based on a = TR
s
/TR = 0.4, and
T
1
= T
2
TR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
xiii
6.3 Wideband SSFP oronary artery images with different magnetization prepa-
ration methods. (a) dummy-cycles, (b) scaled Kaiser-Bessel ramp. The ar-
rows indicate where the scaled Kaiser-Bessel ramp reduced artifacts and
had better signal homogeneity. . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.4 Pulse sequence for 3D coronary imaging. In each R-R interval, a pencil-
beam navigator is followed by a fat saturation sequence and a 16-cycle
Kaiser-Bessel windowed ramp preparation, with actual image acquisition
centered at mid-diastole. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.5 A 3-D reformatted left coronary artery image, revealing longer segment
of proximal LAD. Reformation was done in OsiriX. . . . . . . . . . . . . . 90
6.6 Left anterior descending coronary artery images from three representative
subjects using four different imaging sequences (see Table 1). (a,e,i) Wide-
band SSFP with 0.68 1.0 1.0 mm
3
spatial resolution. (b,f,j) Conven-
tional balanced SSFP with 0.68 1.0 1.0 mm
3
spatial resolution. (c,g,k)
Conventional balanced SSFP with 1.0 1.0 1.0 mm
3
spatial resolution.
(d,h,m) Gradient echo with 0.68 1.0 1.0 mm
3
spatial resolution. Each
image is reformatted from a 3D slab acquisition. Wideband SSFP images
provided the most uniform blood signal, and artifact free depiction of dis-
tal branches of the LAD. High resolution conventional SSFP suffers from
off-resonance banding (f, see gray arrows) and flow-transient artifacts (b,j)
that disrupt visualization of the coronary lumen. Low resolution conven-
tional SSFP does not suffer from these artifacts but is unable to capture
small distal branches (e versus a, see black arrows, and g versus e, see
white arrows). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.1 3-D navigated wideband SSFP coronary artery imaging. Sensitivity en-
coding (SENSE) was used to increase image temporal resolution. (a) no
reduction, temporal resolution = 288 ms; (b) reduction factor = 1.67, tem-
poral resolution = 173 ms; (c) resuction factor = 2, temporal resolution =
144 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
xiv
Abstract
Balanced steady-state free precession (SSFP) is an MRI pulse sequence that is widely
used for cardiac imaging, because it provides superior SNR and excellent contrast be-
tween blood and myocardium compared to the alternatives. Its primary drawback is
sensitivity to off-resonance, which is related to the reciprocal of the sequence repetition
time (TR) and results in banding artifacts.
In this thesis, I introduce a novel technique that overcomes this limitation, and apply
it to two clinically important cardiac imaging applications. The new technique, called
wideband SSFP , utilizes two alternating repetition times to establish a steady state that is
more resistant to banding artifacts, because the spacing between nulls in its frequency re-
sponse is up to twice as large as that of conventional balanced SSFP . Wideband SSFP pro-
vides an efficient scheme for acquiring SSFP cardiac images with long readouts, which
allows the high SNR of SSFP to be used for achieving higher spatial resolution. This
technique is particularly suited for higher field strengths (such as 3 Tesla).
xv
A theoretical description of wideband SSFP is provided, including its spectral re-
sponse, contrast, and SNR efficiency, with phantom experiments demonstrating excel-
lent agreement between simulation and measurement. I then describe an initial magne-
tization preparation scheme based on scaled Kaiser-Bessel windowing functions to opti-
mally stabilize the alternating-TR SSFP signal. Successful implementations of wideband
SSFP for left ventricular function imaging and high-resolution coronary artery imag-
ing in humans at 3 Tesla are then presented. In both cases, wideband SSFP provided
improved spatial resolution and reduced image artifact, while maintaining a blood-
myocardium contrast comparable to conventional balanced SSFP .
xvi
Chapter 1 :
Introduction
1.1 Motivation and Aims
Magnetic resonance Imaging (MRI) has become an effective tool for evaluating certain
aspects of heart disease in the past 20 years. It’s been routinely used for diagnosis of
cardiovascular anatomy and pathology. However, current MR techniques for some ap-
plications like high-resolution myocardial function imaging, and coronary artery imag-
ing still require major improvements in spatial resolution, speed, and contrast, to make
them clinically useful.
Balanced steady-state free precession (SSFP) MRI has gained an important role in
cardiovascular imaging due to its high signal-to-noise ratio (SNR) efficiency and unique
contrast. The primary limitation of SSFP MRI is banding artifacts that are the conse-
quence of intrinsic sensitivity to off-resonance. As MRI moves to higher field strengths
(3T), this limitation becomes more and more severe. The dominant sources of off-
resonance scale linearly with field strength, making SSFP MRI unreliable at 3T and im-
practical at 7T and beyond.
1
We have been developing a new pulse sequence, called wideband SSFP [59], which
is a first step towards overcoming this limitation. Using two alternating repetition times,
wideband SSFP creates a steady-state with an imaging passband up to twice as wide as
that of conventional SSFP . The contrast is comparable to conventional SSFP , and there
is flexibility to tradeoff band spacing for SNR efficiency, and can be used to avoid off-
resonance banding artifacts.
The overall aim of this work is to analyze wideband SSFP pulse sequence elements,
develop technical improvements that make wideband SSFP applicable to a variety of
imaging tasks, and to demonstrate cardiac imaging with high spatial resolution using
Wideband SSFP at 3T in humans.
1.2 Outline
Chapter 2: Cardiac MRI contains an overview of existing cardiac MR imaging tech-
niques. We describe the impact of newly developed sequence and hardware including
steady-state free procession method and high-field MR scanner, and discuss their limi-
tations.
Chapter 3: Wideband SSFP Sequences contains the theoretical description of wide-
band SSFP . We first explain the mechanism of wideband SSFP , and then explore its char-
acteristics such as spectral response, contrast, SNR efficiency, and transient signal be-
havior. Phantom experiments were conducted to verify the band spacing calculations.
2
We observed excellent agreement between simulated and measured results. A magne-
tization preparation scheme based on Kaiser-Bessel window function was designed to
quickly stabilize wideband SSFP signal and validated in phantom tests.
Chapter 4: Simplified Model for Stabilizing Alternating TR SSFP describe the Fourier
relation between an RF sequence and the resulted oscillating magnetization components
in alternating TR SSFP sequences. A scaled Kaiser-Bessel windowed ramp was proposed
to reduce the transient signal oscillation.
Chapter 5: Ventricular Function Imaging with Wideband SSFP focus on left ventricu-
lar (LV) function imaging. A two-dimesional cardiac gated CINE imaging sequence was
designed and applied to LV function imaging at 3T. Wideband SSFP sequence yielded
high blood-myocardium contrast which is comparable to SSFP . Off-resonance banding
artifact was suppressed in wideband SSFP given the same readout duration and spatial
resolution as conventional SSFP .
Chapter 6: Coronary Artery Imaging with Wideband SSFP The second application is
coronary artery imaging. A free-breathing navigated three-dimensional wideband SSFP
coronary artery imaging sequence was used to acquire left anterior descending coronary
artery (LAD) images. A 0.68 1.0 1.0 mm
3
spatial resolution were achieved in free-
breathing navigated imaging.
Chapter 7: Future Work briefly concludes our work up to date and goals in the future.
3
Chapter 2 :
Cardiac MRI
2.1 MR Physics
2.1.1 Nuclear Spins and Static Magnetic Field
Atoms with an odd number of protons and/or an odd number of neutrons possess a
spin angular momentum S. It’s associated magnetic dipole momentm can be viewed as
generated by a charged sphere spinning about its axis (Figure 2.1). When an external
static magnetic field (B
0
) is applied to the nuclear spins, the spins tend to align in the
direction of B
0
(Figure 2.2) and create a net magnetization, which is denoted as a vector
M (= M
x
ˆ
i+ M
y
ˆ
j+ M
z
ˆ
k).
From a quantum mechanical point of view, when an external magnetic field is ap-
plied, nuclei split into parallel (n
+
) and anti-parallel (n

) states. The population will be
a Boltzmann distribution:
n

n
+
= e
DE/kT
(2.1)
4
Magnetic
dipole mement
Spinning
charged sphere
Figure 2.1: Left: Nuclear spin; right: the magnetic dipole moment created by this spin-
ning charged sphere. (figure provided by Kyunghyun Sung)
whereDE is the energy difference between n
+
and n

states, k is Boltzmann’s constant,
and T is the absolute temperature. This small amount of difference between the two
populations is the signal source of NMR and MRI. The net equilibrium nuclear magne-
tization M
o
can be found to be proportional to magnetic field strength B
0
[61]:
M
o
=
Ng
2
¯ h
2
I
z
(I
z
+ 1)B
0
3kT
(2.2)
where N is the number of nuclear spins per unit volume, ¯ h is Dirac’s constant, I
z
is the
spin quantum number. At 37

C = 370 K, M
o
for
1
H in H
2
O is 3.25 10
3
B
0
A/m.
Another effect of the external magnetic field is that spins will precess about the field
direction at the so-called Larmor frequency w
0
= g B
0
, where g is the gyromagnetic
ratio (Figure 2.3). The most common atom to be imaged with MR is
1
H, since it’s the
most abundant compared to other candidates (
13
C,
23
Na,
31
P). At 3 Tesla, the resonant
frequency of
1
H is about 128 MHz.
5
B
0
off
B
0
B
0
on
Figure 2.2: Left: randomly oriented magnetizations; right: magnetizations aligned either
parallel or anti-parallel to the direction of external magnetic field. (figure provided by
Kyunghyun Sung)
2.1.2 Excitation Using Radio-frequency Field
When applying an transverse magnetic field B
1
at the resonant frequencyw
0
, the mag-
netization M is ‘excited’ and starts to rotate toward the transverse plane (figure 2.4). Its
movement can be described by
dM
dt
= Mg B
1
(2.3)
and the rotation frequency is w
1
= g B
1
. The precessing transverse component of the
magnetization M induce an oscillating field which can be detected using a receiving
coil.
2.1.3 Relaxation
After the excitation, the magnetization will gradually ‘relax’ and return to its equilib-
rium state. The dominant mechanism of this relaxation is the magnetic dipole-dipole
6
B
0
z
x
y
Figure 2.3: The magnetization rotates about the field direction at Larmor frequencyw
0
=
g B
0
.
interactions, and the relaxation process is relate to two time constants T
1
and T
2
(Figure
2.5).
The magnitude of the longitudinal (z) component of the magnetization as a function
of time can be written as
M
z
(t)= M
o
+(M
z
(0) M
o
) e
t/T
1
(2.4)
M
z
(0) is the z component of magnetization right after the excitation. T
1
is the spin-
lattice time constant and determines the speed of M
z
returning to equilibrium. T
1
value
is affected by the energy exchange between the nuclei and surrounding lattice. At higher
magnetic field, T
1
is increased since the required energy for this interaction is larger at
higher resonant frequency.
7
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: A electromagnetic field B
1
rotating at frequency w
0
is applied to the mag-
netization M, M will start to rotate toward the transverse plane following the trajectory
depicted in (a)-(d). (figure from Brian Hargreaves [31])
The magnitude of the transverse component of the magnetization as a function of
time can be written as
M
xy
(t)= M
xy
(0) e
t/T
2
(2.5)
M
xy
(0) is the transverse component of magnetization right after the excitation. T
2
is the
spin-spin time constant and determines the speed of M
xy
decaying. T
2
value is usually
smaller than T
1
, because it’s not only affected by the interaction between the nuclei and
surrounding lattice, but also the z-component field fluctuations.
8
M
o
M
z
M
xy
t t
M
o
exp(-t/T
2
) M
O
(1-exp(-t/T
1
))
(b) (c)
M
xy
M
z
M(t1)
M(t2)
(a)
Figure 2.5: Relaxation of magnetizations. (a) from time t
1
to t
2
, magnetization M relaxes
from M(t
1
) to M(t
2
). Its longitudinal (M
z
) and transversal (M
xy
) components are func-
tions of relaxation time constants T
1
and T
2
, respectively. (b) longitudinal (T
1
) relaxation,
M
z
is a function of T
1
and time t; (c) transversal (T
2
) relaxation, M
xy
is a function of T
2
and t.
2.1.4 Spatial Encoding
RF
Gz
Gy
Gx
kx
ky
Figure 2.6: Left: 2DFT sequence diagram; right: 2DFT k-space trajectory, which is the
time-integral of spatial encoding gradients.
In MR imaging, linear gradients are used to create linear phase and resonant fre-
quency distribution as a function of magnetization spatial location. The time-integral of
gradients represents the signal position in the spatial frequency domain (the ‘k-space’),
9
and also determines the image field-of-view (FOV) and resolution. The demodulated
signal as a function of time can be written as
s(t)=
Z
x
Z
y
m(x, y) e
i2p[k
x
(t)x+k
y
(t)y]
dx dy (2.6)
where m(x,y) is the magnetization distribution function in the image domain, and
k
x
(t)=
g
2p
Z
t
0
G
x
(t) dt
k
y
(t)=
g
2p
Z
t
0
G
y
(t) dt (2.7)
An example of two-dimensional Fourier transform (2DFT) sequence diagram and its k-
space trajectory is shown in Figure 2.6. After recording oscillating signals for the whole
k-space, Fourier transform can be applied to resolve the magnetization distribution.
2.1.5 Image Signal-to-Noise Ratio
MR image signal-to-noise ratio (SNR) is usually defined as
SNR,
signal amplitude
noise standard deviation
(2.8)
which is a function of both system parameters and imaging sequence parameters. Its
relation with imaging parameters can expressed as [51]
SNRµDV
p
T
readout
M
o
f(T
1
, T
2
) (2.9)
10
whereDV is the image volume size, T
readout
is the total readout time. f(T
1
, T
2
) represents
the signal amplitudes at readout as a sequence-dependent function. The net equilibrium
nuclear magnetization M
o
is proportional to magnetic field strength B
0
(see Eqn. 2.2),
which means image SNR varies linearly with B
0
. We can also define contrast-to-noise
ratio (CNR) which measures how distinguishable two structures of interest are, that
CNR,
signal difference
noise standard deviation
= SNR difference (2.10)
2.2 Clinical Cardiac MRI
MRI involves no ionizing radiation and is a non-invasive tool for evaluating the car-
diovascular system. It has complex and flexible contrast features, which lead to its out-
standing ability to differentiate between soft tissues. Cardiac MR is routinely used to
assess cardiac wall motion [6, 14, 50, 68, 72, 73], myocardial viability [42, 43], valvular
function, morphology of great vessels, etc. Pulse sequences that are frequently used in
cardiac MR imaging includes black-blood, bright-blood CINE, contrast-enhanced, and
phase-contrast sequences.
Cardiac imaging is one of the most challenging MR field compared to imaging other
parts of human body because of the heart’s dynamic characteristic. Blood flow, cardiac
and respiratory motion cause blurring and ghosting artifacts in the images. Adequate
gating methods for cardiac and respiratory synchronization are needed to ensure diag-
nosable image quality. It is also difficult to achieve proper shimming in a non-static
area, thus field homogeneity is degraded. Although MRI is generally considered as the
11
gold standard for cardiac function imaging, in certain applications like high-resolution
myocardial function imaging or coronary artery imaging, substantial improvements in
contrast, spatial resolution, and speed are needed.
There are two recent advances in MR technique that can improve the diagnostic
value of cardiac MRI: the development of steady-state free precession (SSFP) imaging
sequences (also known as True-FISP , FIESTA, or Balanced-FFE, [7]), and the develop-
ment and availability of 3 Tesla clinical scanners.
2.3 Balanced Steady-State Free Precession Imaging
Balanced SSFP is the latest bright-blood CMR technique, which provides excellent blood-
myocardium contrast and has become a standard procedure at 1.5T. The balanced SSFP
imaging pulse sequence consists of rapid repetition of radio frequency (RF) excitation
pulses, fully refocused gradients and acquisitions as shown in Figure 2.7. Different from
conventional gradient echo and spin echo sequences which usually have gradient de-
phasers at the end of one TR to eliminate net transverse magnetization, the total gradi-
ent area between any two consecutive excitations is zero in SSFP sequences, and there is
no spatially dependent dephasing. Every magnetization is preserved from one TR to the
next TR, thus SSFP can generate the maximum possible SNR efficiency among all MR
sequences.
This technique was originally proposed by Carr in 1958 [7], and only became prac-
tical recently [16, 33] due to the development of high-speed gradients that permit rapid
switching magnetic field with short repetition times (TR).
12
RF
Gz
Gy
Gx
TR
α
-α
α
TR
Figure 2.7: SSFP sequence. All gradients are fully refocused during one TR. Grey circles
represent the position of echoes.
2.3.1 SSFP Sequence Properties
The steady-state signal of balanced SSFP can be obtained by solving the equation
M
k+1
= A M
k
+ B (2.11)
where M
k+1
= M
k
= M
ss
are the steady-state magnetization vector, A and B are
the excitation, precession and relaxation matrix during TR, we can have the steady-state
frequency response as in Figure 2.8. It consists of repeated bands with a band spacing
1/TR Hz and there is ap phase difference between adjacent bands.
Spins with resonance frequency falls into one of these null bands will produce very
low signal (local image voids) and will experience a long and oscillatory approach to
steady-state, which can cause other substantial artifacts [32]. To reduce or avoid banding
artifacts, very short repetition times are required. At 1.5T, robust SSFP imaging with a
TR of 5 to 6 ms has been demonstrated [34, 56, 60, 76].
13
Magnitude
Phase
π
-π
0
0 1/2TR -1/2TR
Figure 2.8: Frequency response of SSFP signal at TE = TR/2. The profile repeats itself
every
1
TR
Hz. There is ap phase increment between adjacent bands.
Consider only the on-resonance spins and assume TR T
1
, T
2
, we can derive the
signal equation from eqn. 2.11 [70, 71]:
M
ss
= M
o
sina
1+ cosa+(1 cosa)T
1
/T
2
(2.12)
which is a function of T
2
/T
1
, and flip angle. The frequency responses with different
T
2
/T
1
and flip angles are shown in Figure 2.9 and 2.10.
2.3.2 Cardiac Applications of SSFP
SSFP provides unique T
2
/T
1
contrast, superior SNR, and superior image quality com-
pared to gradient echo imaging. In cardiac imaging, SSFP provides excellent blood-
myocardium contrast, as well as the ability to discriminate papillary muscles and valve
leaflets [57, 60]. SSFP exhibits fewer flow related artifacts because the high blood signal
14
Myocardium Blood Phantom
0 1/2TR -1/2TR
Figure 2.9: Simulated SSFP frequency response of different T
1
/T
2
values. Signal in-
tensity increases as T
1
/T
2
is reduced. Myocardium: T
1
/T
2
= 1100/40 ms, Blood:
T
1
/T
2
= 1500/140 ms, Phantom (water): T
1
/T
2
= 150/30 ms. Flip angle is 30

.
is intrinsic (due to high T
2
/T
1
) and is not dependent on inflow enhancement, which can
vary from TR to TR. Together with its high acquisition speed, SSFP sequence has become
a standard for cine imaging at 1.5T [8].
There are several variations of balanced SSFP sequence. An SSFP technique called
fluctuating equilibrium MRI (FEMR) uses designed RF phase schedules to create alter-
nating steady-states in consecutive TRs, so images with different contrast can be ac-
quired simultaneously [83]. This method demonstrates a way to adjust image contrast
based on T
2
and resonant frequency and provides rapid fat-water discrimination. Lin-
ear combination SSFP (LCSSFP) does multiple scans with different RF phase cycling to
acquire signals that have shifted frequency responses. Combining data from different
scans allows modification of image spectral selectivity [84]. This technique can be used
to eliminate banding artifact in static tissues or achieve fat-water separation.
15
α = 30
α = 50
α = 70
α = 10 α = 5
0 1/2TR -1/2TR
Figure 2.10: Simulated SSFP frequency response of different flip angles. When a is de-
creased from a high angle (70

), signal intensity starts to increase. After reaching the flip
angle that generates maximum signal intensity (which can be calculated from Eqn. 2.12),
on-resonance signal will drop as a is lowered, and the signal around 1/TR null band
starts to increase. T
1
/T
2
= 1100/40 ms.
2.4 High-Field MRI
The introduction and FDA approval of 3 Tesla whole-body scanning in late 2001 pro-
vided a promising new platform for clinical MRI. The major advantage of 3T platform
over 1.5T is that the doubled polarization can substantially improve image SNR.
2.4.1 Field Strength and Signal Intensity
As Eqn. 2.9 suggests, image SNR is proportional to magnetic field strength. Because M
o
is increased at 3T, we can have smaller voxel size or shorter scan time and still retain
an adequate image SNR. It has been verified in cardiac experiments that SNR is roughly
proportional to the static magnetic field strength, and 3T scanner can up-to-double im-
age SNR [1,37,67,87]. With this improved SNR we are allowed to increase image spatial
resolution and reduce scan time (by reducing NEX or using parallel imaging), that may
give us the ability to detect new in-vivo phenomenon.
16
Tissue longitudinal relaxation time T
1
also changes with magnetic field strength.
Stanisz et al. showed that there is a 43% increase in myocardium T
1
and a 34% in-
crease in blood T
1
when going from 1.5T to 3T [80]. Lengthened T
1
makes myocardium
more saturated during a scan and can increase the contrast between myocardium and
blood. It leads to better contrast range when using paramagnetic contrast agents, and
techniques with pre-saturation like myocardial tagging or inversion prep pulse like spin
labeling will also become more effective.
2.4.2 Challenges in High-Field MRI
Unfortunately, high-field platforms also come with several challenges. One problem
is the increased RF inhomogeneity [75]. With the halved RF wavelength at 3T, there
could be destructive interference inside human body. It causes RF inhomogeneity and
leads to unwanted flip angle and image contrast variation. Receiving coils need to be
re-optimized to alleviate this problem.
Another issue of high-field MR is RF heating (specific absorption rate, SAR, which is
proportional to the square of resonant frequency) [74]. Increased power deposition lim-
its the use of certain high-power sequences, requiring imaging methods to be carefully
re-designed.
One more challenge that is of particular relevance to this work, the degree of un-
desirable susceptibility-induced resonance frequency shifts also increase with magnetic
field strength [1, 37, 67]. In cardiac imaging, the off-resonance induced by heart-lung
interface will become more severe at higher field strength. Susceptibility-caused low T

2
can also lead to low image SNR.
17
As a consequence, larger frequency bandwidths, and thus shorter TRs, are needed
in SSFP imaging at high field strengths. However, since the gradient capabilities have
almost reached peripheral nerve stimulation thresholds [11, 69], further shortening of
imaging TR is difficult.
2.5 Fundamental Limits
SSFP imaging suffers from its high sensitivity to B
0
inhomogeneity, which increases with
TR. So in order to prevent banding artifact, the readout length is constrained to keep TR
short. This short readout duration effectively limits spatial resolution due to the limited
amount of gradient area that can be produced, and also prevents the use of time-efficient
readout schemes such as EPI or spirals.
Performing SSFP imaging on a high-field scanner is particularly challenging, with
susceptibility-induced off-resonance increasing with field strength. Linear combination
methods can remove banding artifact by acquiring several data sets with different spec-
tral response, but requires prolonged scan time. It is also impractical in non-static area
like the heart, where motion and flow are presented, since banding inside flow region
generates transient artifact that can heavily degrade the image, as shown in Figure 2.11.
There are several reports on optimized SSFP cardiac imaging protocol at 3T. A study
done by Schär et al. achieved 1.6 1.5 in-plane resolution with a TR of 3.8 ms [70].
Another study done by Gutberlet achieved similar resolution with a TR of 3.4 ms [28].
18
Figure 2.11: Off-resonance induced artifacts in SSFP cardiac image. White arrow: dark
band inside left ventricle wall ; gray arrow: flow transient artifact caused by banding
inside blood pool.
Increased SAR at 3T platform also can be a serious issue since SSFP is composed of
rapid repeating RF pulses. It is particularly problematic in continuous imaging such as
cine sequences. To reduce SAR at 3T, RF pulse optimization is necessary.
SSFP sequences and high-field platforms both provide substantial improvements in
SNR, but to be of real clinical benefit, the additional SNR should be used to achieve
greater spatial or temporal resolution. Robust cardiac MRI at 3T requires an imaging
bandwidth of roughly 250 to 300 Hz to cover the off-resonance across human heart, or
equivalently a TR of 3.3 to 4 ms using conventional SSFP [70]. For coronary artery appli-
cations, sub-millimeter resolution is needed to identify focal stenosis, which is difficult
to achieve with such a short repetition time. Although SNR is increased at 3T, insuffi-
cient spatial resolution will limit the accuracy of diagnosis.
19
Wideband SSFP (described in Chapter 3) is one step towards solving these problems.
It allows a flexible trade-off of SNR for increased bandwidth; for a fixed band spacing
requirement, wideband SSFP increases the possible TR and also the readout duration,
which makes higher spatial resolution possible.
2.6 Experimental Setup
All experiments in this work were performed on a Signa Excite HD 3T scanner (GE
Healthcare, Waukesha, WI). Gradient system has maximum amplitude 40 mT/m and
maximum slew rate 150 mT/m/ms. Maximum receiver bandwidth is125 kHz (4ms
sampling). Pulse sequences were developed using GE’s software development package
(Environment for Pulse programming In C, EPIC). Plethysmograph gating and vector-
cardiography (VCG) are both used for cardiac gating in human scans.
20
Chapter 3 :
Wideband SSFP Seqeunces
The balanced SSFP signal provides superior SNR and image quality compared to gra-
dient echo techniques, but is highly sensitive to resonance frequency. The usable band-
width of conventional SSFP is less than 1/TR (with signal nulls occurring every 1/TR
in resonance frequency). We introduce a new technique, which we call Wideband SSFP ,
that uses two alternating TRs with excitations that alternate in sign to establish a steady-
state with a passband up to two times wider than conventional SSFP . For a given band-
width requirement, this permits the use of a longer readout duration allowing high-
resolution imaging (which require large readout gradient areas) and time-efficient imag-
ing (with EPI or spiral readouts with oscillating gradients). In particular, this could en-
able rapid high resolution cardiac SSFP at 3T.
3.1 Alternating-TR SSFP
Recently an alternating TR (ATR) sequence has been proposed as a fat suppression tech-
nique [49]. When using two alternating repetition times TR and TR
s
(= a TR, 0< a 1),
21
the periodicity of SSFP changes from 2p to the minimum value that create integer mul-
tiple of 2p dephasing during both repetition times. The frequency response function
can be arbitrarily shifted with excitation phase scheduling. By choosing TR properly, we
can have the stopband positioned at fat resonant frequency so fat signal is suppressed
during imaging.
Wideband SSFP is one variation of ATR method that uses two alternating TRs and
a 0-p phase-cycling to widen the band spacing and relax the 1/BW TR limitation [59].
It allows a flexible trade-off of the high SNR of 3T SSFP for an increased bandwidth.
It has been shown that wideband SSFP can suppress off-resonance related artifacts in
SSFP cardiac imaging for a given spatial resolution [47]. For a specific band spacing
requirement, wideband SSFP increases the possible TR and thus the readout duration,
which results in higher achievable spatial resolution.
3.2 Spectral Response of Wideband SSFP
Figure 3.1 illustrates the wideband SSFP sequence with alternating TRs. Gradient areas
are fully refocused during both TR and TR
s
. Figure 3.2 shows the steady-state magneti-
zation path and frequency response of wideband SSFP with a = TR
s
/TR = 1.0, 0.7, and
0.4. Five isochromats representing spins with different amounts of precession during TR
(0.1p, 0.3p, 0.5p, 0.7p, and 0.9p) are depicted. In conventional SSFP (a = 1.0, Figure 3.2a-
c), a magnetization experience the same amount of precession and relaxation in both TR
intervals, resulting in a symmetric steady-state. The signal profile has equally spaced
null bands. As the precession over a TR approaches p, the steady-state magnetization
22
RF
Gz
Gy
Gx
TR TRs
α -α α
Figure 3.1: Wideband SSFP sequence. All gradients are fully refocused during TR and
TR
s
. The echoes in TR (black circle) and TR
s
(dotted green circle) correspond to the
profiles in Figure 3.2.
and signal approaches zero, generating dark bands in MR images [7, 22] at resonance
frequencies
1
2TR
, -
1
2TR
, and periodically thereafter.
The alternating TRs and RF signs in wideband SSFP swings the magnetization path
to one side (Figure 3.2d-f and g-i), permitting a greater amount of precession during
TR before signal nulling occurs. When the precession over TR is greater than p and
the net deflection (along M
x
in Figure 3.2) could still be balanced by correspondingly
smaller amounts of precession during TR
s
. Both echoes in TR and TR
s
have the same
widened passband width. The echo during TR (black circle, solid black profile) has a
wide flat passband with all depicted isochromats exhibiting nearly identical transverse
magnetization, therefore producing uniform signal. The echo during TR
s
(white circle,
dashed green profile) has higher and less-uniform signal across the passband.
23
Mx
My
My
Mz
Mx
My
My
Mz
Mx
My
My
Mz
a = 1.0
a = 0.7
a = 0.4
a b c
d e f
g h i
precession during TR
π −π
Figure 3.2: Steady-state magnetization paths of conventional balanced SSFP (subfigures
a to c) and wideband SSFP (subfigures d to i) sequence. Lines in different colors repre-
sent spins of different resonant frequencies. In balanced SSFP , magnetization paths are
symmetric about x, y and z axes, while in wideband SSFP they are only symmetric about
the y axis. Black solid lines in the right column represent the spectral response of signals
in TR, and green dashed lines represent signals in TR
s
.
Figure 3.3 shows the signal profiles from TR and TR
s
of different a-values. The
images show the ability of wideband SSFP to modify the steady-state frequency re-
sponse. For a fixed TR, by shortening TR
s
, wideband SSFP widens the band spacing (see
Fig. 3.3a) and can be used to reduce banding artifacts. For fixed TR+TR
s
(see Fig. 3.3b),
there is no significant change in band spacing when a-value varies. That means a longer
TR can be used while maintaining the passband width. This increased TR (and available
readout duration) alleviates the limitation on achievable gradient area in one TR and
enables the acquisition of higher spatial resolution and the use of time-efficient readout
schemes [35, 60, 77]. In both cases the signal intensity decreases as a-value is reduced.
24

Phase offset during TR
π −π 3π −3π
a value
1
0
a value
1
0
TR
TR s

Phase offset during (TR+TRs)/2
π −π 3π −3π
a value
1
0
a value
1
0
TR
TR s
a. b.
Figure 3.3: Wideband SSFP signal profiles for (a) fixed TR, and (b) approximately fixed
band spacing ( fixed TR +TR
s
). Signal responses during TR(top) and TR
s
(bottom) are
shown. The horizontal axis represents precession due to off-resonance. (a) Lower a-
values increase the band spacing. (b) Lower a-values correspond to longer TR, and
therefore longer available readout time. The bottom line of each image represents con-
ventional SSFP , and the band sat 2kp (integerk1) disappear. Profiles correspond to
a=90

and T
2
= T
1
= TR.
Another way to look at this band spacing widening is to view wideband SSFP as
a conventional balanced SSFP with a phase-cycling scheme dependent on magnetiza-
tion off-resonance. If a magnetization has q phase offset during TR and sinq (1
e
TR/T1
), relaxation can be neglected (assume T
1
= T
2
=¥). A wideband SSFP sequence
with TR, TR
s
and 0-p phase-cycling will has the same effect as a SSFP sequence with rep-
etition time TR’ = (TR+TR
s
)/2, and a phase-cycling 0-(p+f
2
), wheref
2
= q(1 a)/2.
From Eqn. 8 in reference [49], we have
f
2
q
stop
=
1 a
2
qq
stop
=p (3.1)
25
a
null−to−null spacing
90
75
60
45
30
0
1
TR
2
TR
2
TR(1+a)
0 1 0.4 0.2 0.6 0.8
Figure 3.4: Null-to-null band spacing as functions of flip angle and a (=TR
s
/TR). The
spacing converges to 2/TR(1+ a) when the flip angle is small.
whereq
stop
is the position of the stopband. When phase off-setq falls into the stopband,
e.g.q = q
stop
, Eqn. 3.1 becomes
1+ a
2
q
stop
= p
) q
stop
=
2
1+ a
p (3.2)
which indicates that the stopband has a resonant frequency of
q
stop
2pTR
=
1
TR(1+a)
.
Figure 3.4 shows the numerical simulation of null-to-null spacing as a function of
a. When flip angle a is reduced, the band spacing approaches the theoretical value
2
TR(1+a)
=
2
TR+TR
s
in Eqn. 3.2. The error of this approximation comes from the asym-
metric T
1
and T
2
relaxation during TR and TR
s
, and is less than 5% fora< 60

(error is
measured as
band spacing
approximated
band spacing
true
band spacing
true
).
26
The band-spacing increase was first numerically simulated in MATLAB (Mathworks,
Inc., South Natick, MA), then verified in phantom experiments. A uniform ball phantom
(T
1
/T
2
150/30 ms) was imaged with a transmit/receive birdcage head coil. Linear
shim was applied to the phantom to create a frequency gradient across the scan plane.
0.4
0.3
0
0.1
0.2
Conventional SSFP, TR = 6 ms
Wideband SSFP, TR = 6 ms, TRs = 4.5 ms
Wideband SSFP, TR = 6 ms, TRs = 3 ms
measured profile
simulated profile
a
b c
d e
TR = TRs
TR
TR TRs
TRs
Figure 3.5: Measured and simulated signal profiles from a uniform ball phantom with an
applied linear shim. Data corresponds to conventional SSFP (a) with a=1, and wideband
SSFP (b,c) with a=0.75 and (d,e) with a=0.5. The TR was 6 ms, and flip angle was 30

in
all scans. There was excellent agreement in the location of null-bands in simulated and
measured profiles. Compared to a, the increase in band-spacing in b and c was 11% and
34% respectively.
Figure 3.5 shows simulated and measured signal profiles from the phantom im-
ages. The band spacing in simulated and measured spectral responses showed excellent
agreement. The measured null-to-null spacing of wideband SSFP with a = 0.75 and a =
27
0.5 were 11% and 34% larger than conventional SSFP (a = 1.0). As expected, the signal
intensity of the long TR echo was lower than that of the short TR echo.
3.3 Image Contrast
The steady state magnetization at the imaging echo can be derived analytically from the
Bloch equations in matrix form [39]:
M
ss
= A
2
R
2
(A
1
R
1
M
ss
+ B
1
)+ B
2
(3.3)
where A
1
, A
2
, B
1
, B
2
are the precession and relaxation matrices which have a form of
A=
2
6
6
6
6
6
6
4
E
2
cosq E
2
sinq 0
E
2
sinq E
2
cosq 0
0 0 E
1
3
7
7
7
7
7
7
5
, B=
2
6
6
6
6
6
6
4
0
0
1 E
1
3
7
7
7
7
7
7
5
(3.4)
whereq is the magnetization phase off-set during TR (q =D f TR) and TR
s
(q =D f
TR
s
), E
1
and E
2
are the relaxation coefficients (e
TR/T
1
, e
TR/T
2
for TR and e
TR
s
/T
1
, e
TR
s
/T
2
for TR
s
) and R
1
, R
2
are the rotation matrices of RF excitation:
2
6
6
6
6
6
6
4
cos(a) 0 sin(a)
0 1 0
sin(a) 0 cos(a)
3
7
7
7
7
7
7
5
(3.5)
28
Solving for on-resonance spins (q = 0), the magnitude of the transverse magnetiza-
tion in the steady-state simplifies to:
jM
xy
j=
[(a+ cosa)
T
1
T
2
+(1 a cosa)]sina
sin
2
a(1
T
1
T
2
)
2
+
T
1
T
2
(
p
a+
1
p
a
)
2
(3.6)
Note that when a = 1.0 (conventional SSFP), this will reduce to Eqn. 2.12.
Whena = 90

, Eqn. 3.6 simplifies to:
jM
xy
j
aT
2
T
1
+ aT
2
=
a
T
2
T
1
1+ a
T
2
T
1
(3.7)
This suggests that wideband SSFP exhibits T
2
/T
1
-like contrast similar to that of con-
ventional balanced SSFP .
Numerical Bloch simulation can be used to determine the contrast over the relevant
range of resonance offsets. Figure 3.6 shows frequency responses of spins with different
T
2
/T
1
value.
The signal amplitudes averaged over 2/3 of the null-to-null spacing in the spectral
profile as functions of T
2
/T
1
and a-value are plotted in Figure 3.7. All sequences have
approximately the same band spacing (i.e. with TR+TR
s
fixed).
Smaller a-values generate weaker signal and contrast during TR and stronger signal
and contrast during TR
s
.
The imaging flip angle is usually chosen to maximize SNR efficiency while operating
within SAR limits. Figure 3.8 shows frequency responses with different flip angles (TR,
29
Myocardium Blood Phantom
0 1/(TR+TRs) -1/(TR+TRs)
Figure 3.6: Simulated wideband SSFP frequency response as functions of T
2
/T
1
. Signal
intensity changes in the same direction as conventional SSFP; it increases as T
2
/T
1
is
reduced. Myocardium: T
2
/T
1
= 1100/40 ms, Blood: T
2
/T
1
= 1500/140 ms, Phantom
(water): T
2
/T
1
= 150/30 ms. Flip angle is 30

.
TR
s
are fixed). The steady-state signal is a function of both a and a, and therefore the
SNR or CNR optimal flip angle will vary with a. Figure 3.9 illustrates the myocardial
(T
1
/T
2
= 1100/40 ms) and blood (T
1
/T
2
= 1500/140 ms) signal at 3T for different flip
angles and a-values. The optimal flip angle for wideband SSFP is comparable to that of
conventional SSFP when a> 0.3.
30
−2 −1.5 −1 −0.5 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
TRs/TR = 0.2
TRs/TR = 0.4
TRs/TR = 0.6
TRs/TR = 0.8
TRs/TR = 1.0
ln(T2/T1)
TR M/Mo
TR s
Figure 3.7: Image contrast as a function of T
2
/T
1
and a-values. M/M
o
is an average over
2/3 of the null-to-null spacing in the spectral profile of each sequence. (upper lines)
Signal during TR
s
. (lower lines) Signal during TR.
3.4 SNR Efficiency
When only TR is used for imaging, the SNR efficiency of wideband SSFP m
w
can be
written as [59]
m
w
=
S
1+ a
m
c
(3.8)
S is the passband signal factor of wideband SSFP over conventional SSFP (
jM
xy
j
wb
jM
xy
j
ss f p
, where
jM
xy
j
wb
andjM
xy
j
ss f p
are from Eqn. 3.6 and Eqn. 2.12, respectively), a is
TR
s
TR
, m
c
is the
SNR efficiency of conventional SSFP . Considering signal in TR, from Eqn. 3.6 we know
that the factor S is always less than one. So the SNR efficiency of wideband SSFP is
always lower than conventional SSFP .
The SNR efficiency of wideband SSFP depends heavily on whether one or both
echoes are used, and on the duration of excitation and other pulses that influence the
31
α = 30
α = 50
α = 70
α = 10 α = 5
0 -1/(TR+TRs) 1/(TR+TRs)
Figure 3.8: Simulated wideband SSFP frequency response as functions of flip angle.
When a is decreased from a high angle (70

), signal intensity starts to increase. After
reaching the flip angle that generates maximum signal intensity (which can be calculated
from Eqn. 2.12), on-resonance signal will drop as a is lowered, and the signal around
1/(TR+TR
s
) null band starts to increase. T
1
/T
2
= 1100/40 ms in this simulation. At
high flip angles there is a ‘dip’ around on-resonance area, which will be discussed in
Section 3.5.1.
available readout duration. As the a-value is reduced, the signal during TR decreases
(see Eqn. 3.7) and the signal during TR
s
increases. Here, we consider the relative SNR
efficiency of wideband SSFP in the case where TR
s
is not used for data collection.
Consider only TR is used for imaging and compare wideband SSFP with conven-
tional SSFP with the same TR, the scan-time is (1+ a) times longer in wideband SSFP ,
and the passband signal is lowered by a factor S. The resulting SNR efficiency would be:
32
0 10 20 30 40 50 60 70 80 90
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
flip angle
|Mxy| / Mo
0 10 20 30 40 50 60 70 80 90
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
|Mxy| / Mo
a b
flip angle
a = 0.1
a = 0.1
a = 1 a = 1
Figure 3.9: (a) Myocardium (T
1
/T
2
= 1100/40 ms) and (b) blood (T
1
/T
2
= 1500/140 ms)
contrast as a function of flip anglea and of a The curves reflect a-values of 1.0 (highest)
to 0.1 (lowest) with an increment of 0.1. The peak signal for each curve is marked with a
‘+’. The optimal flip angle of wideband SSFP is comparable to that of conventional SSFP
when a> 0.3.
m
w
m
c
=
S
p
1+ a
(3.9)
where m
w
and m
c
represent the SNR efficiency of wideband and conventional SSFP , re-
spectively, and m is defined as
SNR
Dv
p
T
scan
, Dv is the voxel size, and T
scan
is the total scan
time. Note that S is always less than 1, even when using the optimal flip angle for wide-
band SSFP (see Fig. 3.9). The SNR efficiency of wideband SSFP is always lower than
that of conventional SSFP when they have the same imaging TR. In static imaging sce-
narios, where multiple-NEX are needed to achieve adequate SNR, multiple-acquisition
methods like LCSSFP (see Section 2.3.2) will remain the method of choice for removing
banding artifacts [30,36,90], due to their SNR efficiency. In cases where multiple acquisi-
tion methods are not applicable, or where SNR can be traded for reduced banding (com-
mon in high-field SSFP imaging), wideband SSFP will be faster than multiple-acquisition
methods by a factor of at least 2/(1+ a).
33
When only TR is used for imaging and we want to achieve the same approximate
band spacing (i.e. TR =
2
1+a
TR
c
, where TR and TR
c
are the repetition times for wide-
band and conventional SSFP , respectively), the scan-time of wideband SSFP is two times
longer, the passband signal is lowered by a factor S, and the available readout duration
is increased by a factor x. The resulting SNR efficiency would be:
m
w
m
c
= S
r
x
2
(3.10)
where T
d
is the amount of time per TR that is not usable for data acquisition. x can be
expressed as:
x =
TR T
d
TR
c
T
d
(3.11)
when T
d
is a substantial fraction of TR
c
, the increased x will make the SNR efficiency
of wideband SSFP close to that of conventional SSFP This can be the case in high-field
imaging applications where the TR
c
is limited to a few milliseconds due to off-resonance
effects within a region of interest.
In the case of cardiac imaging at 3T, the required band spacing is about 300Hz. Using
our custom 2DFT sequence with a 1.4 ms long T
d
, the SNR efficiency can be calculated
from Eqn. 3.10 and the result is shown in Figure 3.10. In this case T
d
is smaller than
TR
c
/2, so SNR efficiency decreases with the TR
s
/TR ratio. In order to optimize SNR,
TR
s
should be chosen as close to TR as possible, while fulfilling a given bandwidth
requirement.
34
0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1
0.65
TRs/TR
SNR efficiency
0.6
0.7
Figure 3.10: SNR efficiency of wideband SSFP with various TR
s
/TR ratio. Myocardium
T
1
, T
2
values are used in simulation. The required band spacing is 300 Hz, and the SNR
efficiency of conventional SSFP is set to 1.
3.5 Other Considerations
3.5.1 Central Dip
When calculating the stopband in Eqn. 3.1, we assume that T
1
and T
2
are large and
neglected relaxation effect. This is a good approximation when phase offset q during
TR is large. If the spin is close to on-resonance (D f = 0) and the assumption sinq
(1 e
TR/T1
) doesn’t hold, T
1
and T
2
relaxation effect become more significant than
precession in the steady-state signal. The different amounts of relaxation during TR and
TR
s
create the unique dip around on-resonance in the spectral response (the black line
in Fig. 3.11). A similar effect on TR
s
echo is that a small peak appears at on-resonance
area (the gray line in Fig. 3.11).
Our empirical observations are that the size of the dip is a function of T
2
/T
1
(deeper
for lower ratios), and the width of the dip is a function of absolute T
2
/TR and T
1
/TR
35
−π −π/2 0 π/2 π
0
0.1
0.2
Phase oset during (TR+TRs)/2
|Mxy| (M0)
Figure 3.11: Central dip and peak in wideband SSFP signal profiles. Black line repre-
sents the spectral response in TR with a dip around the on-resonance area, and gray line
represents the spectral response in TR
s
with a peak at the same frequency.
(see Fig. 3.12). For the 3T cardiac study parameters used in later chapters, numerical
simulation concluded that the signal dip size is about 4% for myocardium and blood
and is not expected to have significant affect on the images. In scans with higher RF
flip angle this dip becomes more significant and may appear as a narrow signal band in
tissues exactly on-resonance, and might cause mild transient artifacts if there is flow or
motion through this region.
A simple way to compensate for the unbalanced T
1
, T
2
relaxation during TR and TR
s
is to change the amplitude of RF excitation in one of the two repetition times. As shown
in Figure 3.13, decreasing the RF pulse amplitude in TR
s
by a very small amount can re-
duce the dip/peak magnitude. The RF
2
/RF
1
ratio to accurately smooth out the spectral
response is dependent on the tissue relaxation constant. The ratio for myocardium at 3T
is 0.9975 , and 0.99925 for blood. During a cardiac scan, we choose the ratio based
on the major target tissue of the application.
36
2500
250
125
62.5
-0.16π 0.16 π
0.17
0.14
“Dip” Amplitude
0
6
o
-6
o
“Dip” Phase:
precession during TR
T1/TR
Figure 3.12: Magnitudes and phases of central dips in wideband SSFP signal profile for
different T
1
/TR values. The width of the central dip broadens with lower T
1
/TR values.
3.5.2 Eddy-current
According to Lenz’s law, when there is a varying magnetic flux intersecting a conductor,
a swirling current will be induced within the conductor. This current is called eddy-
current, which creates magnetic fields in the opposite direction of the change in applied
magnetic field. The magnitude of eddy-current is proportional to the changing rate of
magnetic flux.
In MRI, the rapidly varying gradient fields may induce eddy-current in the cryostat
of superconducting magnets, which causes distortion in the fields and artifacts in the
images. SSFP-based sequences are very sensitive to imperfect magnetic field that is not
fully refocused over TR. Any imperfection can result in disturbance to the equilibrium
state. In conventional SSFP , the primary source of eddy-current related residual fields is
37
−10 −5 0 5 10
0.108
0.114
0.12
0.126
−10 −5 0 5 10
0.054
0.055
0.056
0.057
0.058
1.0000
0.99925
0.9985
1.9975
RF2/RF1
1.0000
0.99925
0.9985
1.9975
RF2/RF1
Blood Myocardium
Figure 3.13: Central dip of blood and myocardium, with different RF flip angle ratio.
RF
1
is the flip angle in TR, and RF
2
is the flip angle in TR
s
.
the stepwise changing phase-encoding gradients. Straightforward compensation meth-
ods such as view order pairing can provide good correction and produce artifact-free
images [4, 40].
Eddy-Current in Wideband SSFP
In wideband SSFP , major eddy-current related residual fields come from readout gra-
dients that are substantially different in TR and TR
s
, which cannot be compensated by
simple view ordering. The unbalanced dephasing alters the magnetization steady-state
and changes the signal profile with respect to resonant frequency. This deviation leads
to low signal from spins with small amount off-resonance, which are particularly sensi-
tive to unbalanced dephasing (Figure 3.14). In situations that the SNR loss is substantial,
image contrast and achievable spatial resolution may be compromised. Therefore an ef-
fective eddy-current compensation method for wideband SSFP is necessary in order to
maintain a reliable image quality. There are three possible compensation methods, in the
38
Figure 3.14: Phantom wideband SSFP image showing eddy-current induced signal
change. A linear shim was applied in horizontal direction to create off-resonance. In
the area where spins have small amount of dephasing, steady-state signal amplitude is
affected by eddy current induced residual field (arrows indicate signal loss). The resid-
ual field is a function of spatial location.
future we will implement each of these and compare the results in phantom and in-vivo
experiments to determine their feasibility.
Possible Solutions
In situations that the SNR loss due to central dip or eddy-current is substantial, image
contrast and achievable spatial resolution may be compromised. Therefore an effective
compensation method is necessary in order to maintain a reliable image quality. Three
possible compensation methods are listed below:
Refocusing Method This is the method currently implemented in our cardiac appli-
cations. Wideband SSFP uses alternating RF phases for the two TR intervals, and there
is a phase difference of p between two steady-state magnetizations. Thus a phase er-
rorDq induced in imaging TR can be canceled out by producing an extra dephasing in
39
TR
s
of the same direction and an amount ofDq
TR
s
TR
. This can be done by adding an
unbalanced refocusing gradient in readout direction during TR
s
. The amplitude of the
compensating gradient can be determined based on knowledge of the residual fields
during TR induced by the readout gradient.
Through-Slice Equilibration Method Spins of positive and negative off-resonance
have opposite dephasing direction when experiencing the same induced led. Thus a
symmetric distribution of magnetization dephasing inside a voxel can balance the sig-
nal fluctuation [4]. By modifying the slice-selection gradients we can introduce a small
amount of through-slice dephasing that evens out the phase deviation, and smoothes
the frequency response.
Direct Method The induced fields can be measured by acquiring the free induction de-
cay (FID) immediately after eddy-current generating gradients and analyzing its phase
evolution. With the knowledge of residual eddy-current we can design compensating
gradients to generate opposite fields and cancel the dephasing [24]. The compensating
gradients will be placed right after the readout gradients. The compensating gradient
waveform will be function of the applied readout gradients and sequence timing, and is
likely to be system and scan-plane dependent.
3.6 Summary
Wideband SSFP can achieve a wider passband compared to conventional SSFP by gener-
ating an asymmetric steady state magnetization path. This technique reduces the effect
40
of frequency sensitivity, which is the primary limitation of SSFP . Phantom experiments
showed improved central bandwidth from Wideband SSFP . The current techniques suf-
fer from limited spatial resolution caused by insufficient SNR (GRE) or banding (SSFP),
and we expect wideband SSFP to overcome these problems in cardiac imaging. We im-
plemented wideband SSFP in two cardiac applications, and they will be described in the
next chapter.
41
Chapter 4 :
Simplified Model for Stabilizing Alternating TR SSFP
Sequences
4.1 Initial Preparation for Steady-State Sequences
In balanced steady-state free precession (SSFP) MR imaging [7], both the magnetization
and the received signal oscillates during the approach to steady state. The fluctuating
signal creates a non-smooth weighting in k-space that results in substantial image arti-
fact [17, 33]. The duration of these transient oscillations is on the order of the tissue T
1
relaxation time. It is possible to simply wait for the steady-state to be reached, how-
ever this compromises the effectiveness of magnetization preparation schemes (e.g. fat
saturation or inversion recovery) that are essential in many SSFP applications. Efficient
initial preparation schemes are critical for the broad use of SSFP sequences. Simple
methods such as a/2-TR/2 preparation [17] can quickly align the magnetization in the
direction of its steady-state, but only for a limited off-resonance range.
To achieve good transient oscillation suppression for a wider range of frequencies,
more elaborate methods were proposed. For conventional balanced SSFP , Le Roux [48]
42
used the SU
2
formalism [5, 39, 55] to develop a simplified model for transient signal
behavior, and to demonstrate a Fourier relation between RF flip angle increments and
the resulting oscillatory residues. A Kaiser-Bessel windowed ramp preparation method
was proposed to minimize oscillatory transients [48]. This approach has been widely
adopted, and is the current method-of-choice for reducing transient artifacts in con-
ventional balanced SSFP imaging. Initial preparation schemes based on the Shinnar-
Le Roux (SLR) algorithm have also been proposed [32, 65], which rely on sequences of
RF pulses that accurately generate the steady-state frequency response by magnitude-
scaling and direction-selection. In addition to its design complexity, this method is sen-
sitive to B
1
variation.
Alternating TR SSFP has been recently proposed as a way to achieve a favorable fre-
quency response compared to conventional SSFP . In the case of fat-suppressed ATR (FS-
ATR) SSFP [49], a wide stopband is achieved capable of suppressing fat in the steady-
state. In the case of wideband SSFP [59], the spacing between nulls in the frequency
response can be increased which mitigates banding artifacts for a given TR. Single-tip
preparation was previously used for alternating TR SSFP sequences [49]. Paired Kaiser-
Bessel design has been recently shown to have a performance comparable to optimum
SLR design when there is a sufficient number of preparation cycles [15].
In this work, we adapt the SU
2
formalism approach to build a mathematical model
for alternating TR SSFP signal behavior. This model provides justification for the use of
Kaiser-Bessel windowed ramps, and a method for optimizing these ramps. Optimized
43
+α α
⋅
e
i(π+ φ )
+ α
α
⋅
e
i (π+ φ )
+α
TR
1
. . . . . .
TR
2
Figure 4.1: An alternating TR SSFP sequence. Black arrows represent RF excitation
pulses that are separated by alternating repetition times TR
1
and TR
2
, and have phases
alternate betweena anda e
i(p+j)
.
initial preparation sequences for fat suppressed ATR SSFP and wideband SSFP are val-
idated in simulation and phantom studies. We also describe a preparation scheme that
can be applied to any alternating TR sequence with any RF phase cycling scheme.
4.2 Theory
In alternating TR SSFP (Figure 4.1), two repetition times TR
1
and TR
2
are used, and
the phases of RF excitation in the two TRs are 0 and (p+ j), respectively [49, 59]. A
full cycle of the steady state contains two excitations and two periods of free precession
and relaxation. Unlike conventional SSFP , the steady-state magnetization is alternating
between two positions instead of returning to the same place after each excitation.
In the following section we setj= 0 for simplicity, and later will show that the result
can be extended to arbitrary j when 0 j< p. Relaxation is neglected since its effects
on signal oscillation are not as significant as the direction of the magnetization [48].
44
α −α
θ 1 θ 1
θ 2 θ 2
M1
M2
x
y
M1
+
M1
-
M2
-
M2
+
Figure 4.2: The steady-state magnetization path of an alternating TR SSFP sequence
with(0,p) phase-cycling. A full-cycle rotation of a magnetization with resonance offset
D f starts at M
1
. It experiences phase offset of q
1
(=D fp TR
1
) (M
1
! M
+
1
), RF
excitation of anglea (M
+
1
! M

2
), phase offset q
2
(= D fp TR
2
) and becomes
M
2
. Then it experiences another phase offsetq
2
(M
2
! M
+
2
), excitationa(M
+
2
! M

1
),
phase offsetq
1
and it returns to M
1
.
4.2.1 Characterization of the Cycle Rotation
In order to determine the resulting magnetization after multiple cycles of ATR SSFP
sequence, first we need to characterize its cycle-rotation matrix. We define R
0
to be the
transition matrix for one full cycle of the alternating TR sequence. When R
0
rotates a
magnetization from its position at TR
1
/2 (M
1
) to TR
2
/2 (M
2
) and back to M
1
at the next
TR
1
/2 (M
1
= R
0
M
1
, see Figure 4.2), we find M
1
to be the steady-state magnetization,
which is identical to the axis of R
0
rotation. R
0
can be written as the product of a series
of 3 3 orthogonal rotation matrices (all representing right-hand rotations):
R
0
= R
1
R
2
=[R
z
(q
1
) R
x
(a) R
z
(q
2
)][R
z
(q
2
) R
x
(a) R
z
(q
1
)] (4.1)
45
M1
M2
x
y
n1 n2
Rθ/2 R θ/2
z
y
φ1
φ2
φ2
M1
M2
n
n ⊥
φ2
a b c
u 1
u 2
M2
n ⊥
n
x
n 1
φx
Ω/2
u 2
Figure 4.3: The relation between M
1
, M
2
,~ n
1
, and~ n
2
. (a) 2D plot in x-y plane. Dotted line
represents the magnetization path as in Fig. 4.2. (b) 2D plot in y-z plane. f
1
is the angle
between z-axis and~ n (the projection of~ n
1
and~ n
2
on y-z plane),f
2
is the angle between
~ n and both M
1
and M
2
. Vector~ n
?
is in the y-z plane and perpendicular to~ n. (c) 3D plot
with three axes being(x,~ n,~ n
?
). f
x
is the angle between~ n and~ n
1
in(x,~ n) plane.
wherea is the flip angle,q
1
(=D fp TR
1
) andq
2
(=D fp TR
2
) are the magnetiza-
tion phase offsets due to off-resonance during two half-TRs. R
1
and R
2
are the rotation
matrices for the first and second half-cycles, that M
2
= R
2
M
1
and M
1
= R
1
M
2
. By re-
writing the above matrices using SU
2
formalism (see Appendix A), we find the rotation
axis~ n
1
(= n
1x
ˆ
i+ n
1y
ˆ
j+ n
1z
ˆ
k, without normalization) and rotation angleW
1
of R
1
matrix
to be
n
1x
= sin

a
2

cos

Rq
2

n
1y
= sin

a
2

sin

Rq
2

n
1z
= cos

a
2

sin

q
2

W
1
= 2 cos
1
h
cos

a
2

cos

q
2
i
(4.2)
46
whereq = q
1
+q
2
and R = (q
1
q
2
)/(q
1
+q
2
). Similarly, R
2
has its rotation axis~ n
2
(=
n
2x
ˆ
i+ n
2y
ˆ
j+ n
2z
ˆ
k, without normalization) and rotation angleW
2
as
n
2x
= sin

a
2

cos

Rq
2

n
2y
= sin

a
2

sin

Rq
2

n
2z
= cos

a
2

sin

q
2

W
2
= 2 cos
1
h
cos

a
2

cos

q
2
i
(4.3)
We then defineWW
2
=W
1
, whereW 2 cos
1
[cos(q/2)] = q for smalla values.~ n
1
,
~ n
2
, M
1
, and M
2
are plotted in Figure 4.3. Note that~ n
1
and~ n
2
are situated in the bisector
plane of
\
M
1
M
2
and are symmetric about the y-z plane, with the norms
k~ n
1
k=k~ n
2
k=[1 cos
2
(a/2) cos
2
(q/2)]
1
2
=[1 cos
2
W]
1
2
= sinW. (4.4)
4.2.2 Approach to Steady-State from Thermal Equilibrium
Figures 4.3a and 4.3b show the projections of the vectors in x-y and y-z planes, respec-
tively, and Figure 4.3c contains the three-dimensional depiction. We define f
1
as the
zenith angle between z-axis and~ n (the projection of~ n
1
and~ n
2
on y-z plane), and f
2
as
the angle between~ n and M
1
(which is equal the angle between~ n and M
2
). The values
of f
1
and f
2
are determined by the RF flip angles of the current R
1
and R
2
rotation.
47
These two variables indicate the direction of the steady-state magnetizations, hence are
essential for the calculation of transient oscillating residues.
Figure 3 along side with the derivation in Appendix B describes the relation between
f
1
, f
2
, and RF flip angle. Starting from thermal equilibrium (when magnetizations are
aligned with z-axis), an initial varying RF sequencefa
k
g is applied. From Figure 4.3b we
find that after the k
th
excitation, when the flip angle a
k
is small, the change in f
1
value
during this half-cycle (denoted asDf
1
(k)) is proportional to the RF flip angle increment
Da
k
(= a
k
a
k1
) that
Df
1
(k)=Da
k

sin(Rq/2)
2 sin(q/2)
(4.5)
From Figure 4.3c we also findDf
2
(k) to be proportional toDa
k
:
Df
2
(k)=Da
k

cos(Rq/2)
2 cos(q/2)
(4.6)
Please see Appendix B for complete derivations of Eq. (4.5) and (4.6).
4.2.3 Transient Oscillatory Residues
We define the oscillatory residue~ # to be the magnetization component perpendicular
to its steady-state position. It lies in the (~ u
1
,~ x) plane (perpendicular to M
1
) at TR
1
/2
and in (~ u
2
,~ x) plane (perpendicular to M
2
) at TR
2
/2 (see Fig. 4.3b). After the k
th
RF
excitation, the new oscillatory residue~ #
k
can be calculated by first adding the shift in
the steady-state magnetization vector(= the origin of(~ u,~ x) plane) to~ #
k1
, then apply the
48
W rotation. The relation between the oscillatory residues in two consecutive echoes can
thus be written as
~ #
k
= e
iW
[~ #
k1
+Df
1
(k)jMj+ e
ipk
Df
2
(k)jMj] (4.7)
The e
ipk
term represents the alternating sign ofDf
2
during TR
1
and TR
2
.
Defining the phase-shifted oscillatory residue e
k
= #
k
e
iWk
and setting the magne-
tization magnitudejMj = 1, with Eq.(4.5) and (4.6), we find the oscillatory residue e
p
after p excitations (p is an even number) to be
e
p
=
1
2

sin(Rq/2)
sin(q/2)
p
å
k=1
(e
iq(k1)
Da
k
)

cos(Rq/2)
cos(q/2)
p
å
k=1
(e
i(qp)(k1)
Da
k
)

(4.8)
which shows that the oscillatory residue function is a linear combination of the Fourier
transforms of the flip angle increment sequence {Da
k
} (see Appendix C for the complete
derivation). Note that when TR
1
= TR
2
, this simplifies to balanced SSFP , and is equiv-
alent to Eq.(24) in reference [48]. The preparation sequence for a steady-state sequence
with imaging flip anglea
0
has two constraints, which area
0
= 0 anda
p
= a
0
.
A windowing function {w
k
} is then chosen as the base flip angle increment sequence
for initial preparation. We split {w
k
} into two separate series of its odd and even ele-
ments, multiply them with scalars b
1
and b
2
respectively (b
1
+ b
2
= 1 in order to meet
49
thea
p
= a
0
constraint). The new flip angle increment sequence becomes {b
m
w
k
} (m = 1
when k is even, m= 2 when k is odd), and the oscillatory residue can be re-written as
e
p
=
sin(Rq/2)
sin(q/2)
h
b
1
p/2
å
k=1
(e
iq(2k1)
w
2k
)
+ b
2
p/2
å
k=1
(e
iq(2k2)
w
2k1
)
i
+
cos(Rq/2)
cos(q/2)
h
b
1
p/2
å
k=1
(e
iq(2k1)
w
2k
)
b
2
p/2
å
k=1
(e
iq(2k2)
w
2k1
)
i
(4.9)
We can then optimize b
1
and b
2
for any resonance offset by minimizingje
p
j atq q
0
=
D fp(TR
1
+ TR
2
). From Eq.(4.9) we know thatje
p
j
qq
0
has its minimum when
je
p
j
qq
0
=

sin(Rq/2)
sin(q/2)
(b
1
+ b
2
)
+
cos(Rq/2)
cos(q/2)
(b
1
b
2
)

Ffw
2k1
g= 0
=
tan(Rq/2)
tan(q/2)
(b
1
+ b
2
)+(b
1
b
2
) (4.10)
Considering a wideband SSFP sequence (alternating TR SSFP with (0,p) phase-
cycling) [59], for the center of passbandq 0, the optimized b
1
/b
2
(1 R)/(1+ R)=
TR
2
/TR
1
. Figure 4.4a shows an optimized eight-step Kaiser-Bessel windowed flip angle
increment sequence {Da
k
}, that its elements form an alternatively scaled Kaiser-Bessel
windowing function. The actual flip angle ramp for the initial preparation is shown in
Figure 4.4b.
50
↔ ↔
α
Time →
0
1
TR2
Δ α1 Δ α2 Δ α3 Δ α8
α1 α2 α3 α8
TR1
TR2 TR1
a b
0
1
0
1
c d
-π 0 π
phase oset during (TR1+TR2)/2
-π 0 π
phase oset during (TR1+TR2)/2
→
Figure 4.4: Wideband SSFP sequence: (a) an RF flip angle increment sequence {Da
k
} de-
signed using Kaiser-Bessel windowing functions with optimized ratios. (b) the actual
RF ramp sequence calculated using values in (a), that a
k
= å
k
n=1
Da
n
. (c) The absolute
value of simulated oscillatory residues after an optimized 8-step linear ramp prepara-
tion. Grey solid line represents the true residue values obtained using matrix rotation,
black dashed line represents the result given by Eq.(4.9). (d) true residue values after
8-step linear ramp and Kaiser-Bessel windowed ramp preparation. Black solid line: op-
timized Kaiser-Bessel window (b = 3), grey dashed line: Kaiser-Bessel window (b = 3)
with b
1
= b
2
= 0.5, grey solid line: linear ramp.
Numerical simulations of different choices of window function {w
k
} and scalars (b
1
, b
2
)
were performed for a wideband SSFP sequence with p= 8 (four full-cycles). Figure 4.4c
shows the oscillatory residues after linear ramps (ramps based on a rectangular win-
dow, i.e. the flip angle increments are constant) with optimized b
1
, b
2
. The solid line
represents the true oscillatory residue values calculated using four R
0
matrix rotations,
and dotted line represents the approximated values obtained from Eq.(4.9). The approx-
imated and trueje
p
j functions are in close agreement within the passband. Fig 4.4d
shows true oscillatory residues after a linear ramp (optimized b
1
, b
2
) and Kaiser-Bessel
51
windowed [41] ramps (flip angle increments forms a Kaiser-Bessel window) with both
optimized (b
1
, b
2
) and b
1
= b
2
= 0.5. The Kaiser-Bessel window was chosen because
its shape can be flexibly modified by adjusting one control parameter b, and because it
provides a near-optimal solution [64]. The black solid line represents the Kaiser-Bessel
windowed ramp with optimized b
1
and b
2
, which shows the best oscillatory residue
attenuation among the three methods.
4.2.4 General Model for ATR SSFP Sequences
This approach can be generalized to alternating TR sequences with an RF phase-cycling
of(0,p+j), 0 j< p by writing down the new full-cycle rotation matrix R
0
0
as
R
0
0
= R
0
1
R
0
2
=[R
z
(q
1
) R
x
(a) R
z
(q
2
)]
[R
z
(q
2
) R
z
(j) R
x
(a) R
z
(j) R
z
(q
1
)]
=[R
z
(q
0
1
) R
x
(a) R
z
(q
0
2
)][R
z
(q
0
2
) R
x
(a) R
z
(q
0
1
)] (4.11)
52
which has the same form as R
0
in Eq.(4.1), withq
0
1
= q
1
j/2,q
0
2
= q
2
+j/2. Therefore
the oscillatory residue can be obtained by substituting Rq in Eq.(4.9) with (Rqj):
e
p
=
sin((Rqj)/2)
sin(q/2)
[ b
1
p/2
å
k=1
(e
iq(2k1)
w
2k
)
+b
2
p/2
å
k=1
(e
iq(2k2)
w
2k1
)]
+
cos((Rqj)/2)
cos(q/2)
[ b
1
p/2
å
k=1
(e
iq(2k1)
w
2k
)
b
2
p/2
å
k=1
(e
iq(2k2)
w
2k1
)] (4.12)
and the relation between optimized scalars b
1
and b
2
becomes

1+
tan[(Rq
0
j)/2]
tan(q
0
/2)

b
1
=

1
tan[(Rq
0
j)/2]
tan(q
0
/2)

b
2
(4.13)
For example, an FS-ATR SSFP sequence [49] with TR
2
= TR
1
/3 and(0,
3
4
p) RF phase-
cycling has center of passband (water frequency) atq
0
=p/2 (omitting the RF phase
increment to shift water toq = 0, for simplicity). Using Eq.(4.13), the optimized b
1
and
b
2
for water frequency will be
b
1
= b
2
= 0.5
We can also optimize b
1
and b
2
for the center of the stopband (fat frequency), which is at
q
0
= p/2, and obtain
b
1
= 0, b
2
= 1
53
Flip angle increments and amplitudes in the ATR SSFP preparation scheme designed
using Kaiser-Bessel window and the optimized (b
1
, b
2
) values for the water band are
shown in Figure 4.5a and b.
→
↔ ↔
α
Time →
α1 α2 α3 α8
TR2 TR1
0
1
-π 0 π
phase oset during (TR1+TR2)/2
c d
a b
-π 0 π
phase oset during (TR1+TR2)/2
0
1
0
Δ α1 Δ α2 Δ α3 Δ αp
Figure 4.5: Fat-suppressed ATR SSFP sequence: (a) an RF flip angle increment se-
quence {Da
k
} designed using Kaiser-Bessel windowing functions with(b
1
, b
2
) optimized
for water band. (b) the actual RF ramp sequence calculated using values in (a), that
a
k
= å
k
n=1
Da
n
. (c) The absolute value of simulated oscillatory residues after an opti-
mized eight-step linear ramp preparation. Grey solid line represents the true residue
values obtained using matrix rotation, black dashed line represents the result given by
Eq.(4.9). (d) true residue values after 8-step linear ramp and Kaiser-Bessel windowed
ramp preparation. Black solid line: Kaiser-Bessel window (b = 3) optimized for water
band, grey dotted line: Kaiser-Bessel window (b = 3) optimized for fat band, grey solid
line: linear ramp optimized for water band.
Numerical simulations of different {w
k
} and (b
1
, b
2
) were also performed for this se-
quence with p = 8 (four full-cycles), and the results are shown in Figure 4.5. In Fig-
ure 4.5c, solid and dotted lines represent the true oscillatory residue values after four
54
R
0
0
rotations and the approximated values from Eq.(4.12), respectively. The approxi-
mated and trueje
p
j functions are in close agreement except for frequencies around the
null bands of the ATR SSFP . Figure 4.5d shows true oscillatory residues after a linear
ramp (b
1
= b
2
= 0.5, optimized for water) and Kaiser-Bessel windowed [41] ramps
(b
1
= b
2
= 0.5, optimized for water and b
1
= 0, b
2
= 1, optimized for fat). The black
solid line represents the Kaiser-Bessel windowed ramp with b
1
and b
2
optimized for
water, which shows the best oscillatory residue attenuation within the water passband.
Grey dotted line represents Kaiser-Bessel windowed ramp with b
1
and b
2
optimized for
fat, and this sequence suppresses oscillatory residues better inside the fat-band.
4.3 Experimental Methods
Experiments were performed on a Signa Excite HD 3T scanner (GE Healthcare, Wauke-
sha, WI) with a single-channel head coil. To measure the transient signal of different
resonant frequencies, a linear shim was used to generate a frequency gradient in a uni-
form spherical ball phantom (T
1
/T
2
= 150/35). A pulse sequence was designed to wait
for thermal equilibrium, apply an eight-step initial preparation sequence, and then ac-
quire the same phase encode for 64 full-cycles. The process repeats for all the phase
encoding steps, so that a complete image can be reconstructed for each imaging TR after
starting from thermal equilibrium. Finally, we extract one line from each image to plot
the spectral profile evolution during the approach to steady-state.
Experimentally measured transient signals were compared with Bloch simulations
in MATLAB (Mathworks, Inc., South Natick, MA). Three types of initial preparation
55
were considered: dummy-cycles, linear ramp and Kaiser-Bessel ramp preparations (b
1
,
b
2
optimized for water). All preparations consisted of eight pulses (four full-cycles) and
were 28ms in length. Two alternating TR SSFP sequences were considered: wideband
SSFP and FS-ATR SSFP . The prescribed flip angle was 45

in all scans.
Phantom imaging with eight-step initial preparations and centric phase-encoding
ordering was also performed for wideband SSFP and FS-ATR SSFP sequences to observe
the artifacts caused by transient signal oscillation. Three ramp types were used: dummy
cycles, linear ramp, and Kaiser-Bessel windowed ramp. Shim gradients were applied to
create a25 Hz off-resonance span in the uniform ball phantoms. In wideband SSFP
experiments the ramps were optimized for the center of passband (D f = 0). Ramps
optimized for different frequencies were tested in FS-ATR SSFP scans. Two phantoms
were imaged with their resonant frequencies centered at water (pass band) and fat (stop
band).
4.4 Results
Figure 4.6 contains the simulated and measured transient signals from a uniform phan-
tom, as functions of number of cycles and resonant frequency. The experimental mea-
surements show good agreement with the simulation. The measured spectral profiles
are smoother compared to simulated ones because the real phantom reflects a contin-
uous intra-voxel frequency distribution, whereas the simulation is discretely sampled
in frequency. This frequency distribution also facilitates the decay of signal oscillation
in experiments compared to simulations. Grey arrows indicate the point when central
56
a b
# of cycles
Dummy
cycles
Linear
ramp
Kaiser
ramp
Phase-oset in (TR1+TR2)/2
# of cycles
Wideband SSFP ATR-SSFP
π
-π
π
-π
π
-π
π
-π
π
-π
π
-π
Simulation Measurement Simulation Measurement
1 64 1 64 1 64 1 64
Figure 4.6: Simulated and measured transient signals of a ball phantom after different
preparation methods. (a) wideband SSFP , grey arrows indicate when the central dips
appear. (b) FS-ATR SSFP . The experimental measurements show good agreement with
the simulation. Kaiser-Bessel windowed ramp significantly reduced the transient signal
fluctuation.
dips [59] become visible. The formation of a central dip in the spectral profile is related
to magnetization relaxation, and it begins to form after the sequence reaches a constant
flip angle. Hence, the two ramp-up preparation schemes result in a delayed appearance
of the dip compared to dummy-cycle preparation.
Initial preparations consisted of eight RF pulses (four full cycles), were 28 ms in
length, and consisted of either dummy cycles, linear ramp, or Kaiser-Bessel ramp opti-
mized for the center of the water band. Table 4.1 and 4.2 contains the averaged measured
57
Dummy
cycles
Linear
ramp
Kaiser
ramp
Water band Fat band
Optimized for water band Optimized for fat band
a b
Figure 4.7: Alternating TR SSFP phantom images after different preparation methods.
Eight-step preparation was used for all the scans. Images obtained with Kaiser-Bessel
windowed ramp show better image uniformity and reduced artifacts. (a) Wideband
SSFP images. Ramps were optimized for the center of passband whereD f = 0. (b) FS-
ATR SSFP images. Resonant frequencies of the two phantoms were centered at water
band (pass band) and fat band (stop band), with a25 Hz span. Ramps optimized for
water (left column) and fat (right column) bands were both tested.
magnitude of oscillation over half of the passband and stopband in the first ten imag-
ing cycles after different preparation schemes. Table values reflect the magnitude of
oscillation relative to the steady-state signal amplitude. In wideband SSFP (Table 4.1),
linear ramp reduced the oscillation from 18.7% to 4.6%, and Kaiser-Bessel ramp prepa-
ration further reduced it to 1.8% (the percentage represents the amount of oscillation
compared to steady-state magnitude). In FS-ATR SSFP (Table 4.2), linear and Kaiser-
Bessel ramps optimized for water resonant frequency reduced the amount of oscillation
in water band from 41.3% to 1.0% and 0.4%, respectively. The oscillation reduction in fat
band was from 48.6% to 9.4% (linear ramp) and 8.3% (Kaiser-Bessel ramp).
58
Figure 4.7 shows the actual images obtained after different eight-step initial prepa-
ration schemes. Images obtained with Kaiser-Bessel windowed ramp have significantly
reduced artifacts in both sequences. In FS-ATR SSFP images (Figure 4.7b), initial ramps
with different (b
1
, b
2
) scalars show slightly more uniform signal and less artifact along
the phase-encoding (vertical) direction, around the frequency bands they are optimized
for. However the visible differences are subtle.
4.5 Discussion
Simulations and phantom experiments demonstrate ATR SSFP imaging with reduced
signal oscillation using optimized Kaiser-Bessel windowed ramp preparation, compared
to dummy-cycles and linear ramp preparation. The preparation scheme can be eas-
ily modified to minimize oscillatory residue at the desired resonant frequency using
Eq.(4.12), and only a simple recalculation is needed when changing the length of prepa-
ration. This method is expected to be robust in the presence of B
+
1
variation because it
only relies on relative flip angle amplitudes.
The Fourier relation between RF amplitude increments and the amount of oscillatory
residue is based on the assumption that half of the imaging flip angle a/2 is small. As
the flip angle becomes larger, actual oscillatory residues start to deviate from Eq.(4.8).
Nevertheless, note that the small angle approximation (tan(a/2) a/2) used in Eq.(4.5)
Dummy Cycles / Linear / Kaiser-Bessel
center passband 18.7% 4.6% 1.8%
Table 4.1: Measured signal oscillation magnitude during the first ten cycles of wideband
SSFP , for three initial preparation schemes. Values are averaged over half the passband.
59
and Eq.(4.6) only has a 10% error even when the value ofa is as high as 60

. This more
than covers the flip angle range typically used in ATR SSFP imaging.
Relaxation effects are neglected in our model, due to the fact that T
1
and T
2
has little
effect on the magnetization direction during initial preparation [48]. In reality, relaxation
would result in a decreasing magnetization length which would introduce an additional
smooth transient signal weighting in k-space, which is not expected to cause substantial
deviation from this model.
In this work the coefficients b
1
and b
2
are optimized solely with respect to the center
of passband, independent of the chosen windowing function. Therefore, the ramps may
become slightly less effective as the amount of off-resonance increases. For this reason
a Kaiser-Bessel windowing function is preferred since it has peak concentration around
its pass band center and good attenuation in the side-lobes [64], thus the oscillatory
residue can remain suppressed for a wide range of frequencies. As Figure 4.7 shows,
Kaiser-Bessel windowed ramps optimized for water frequency still perform well in the
fat band, and the same for the opposite case. Further optimization using numerical
calculation over a frequency band is possible, in which case the spectral response of the
windowing function and subject off-resonance characteristic will also become factors in
the decision of b
1
and b
2
.
No Prep / Linear / Kaiser-Bessel
water band 41.3% 1.0% 0.4%
fat band 48.6% 9.4% 8.3%
Table 4.2: Measured signal oscillation magnitude during the first ten cycles of FS-ATR
SSFP , for three initial preparation schemes. Values are averaged over half the water band
and fat band.
60
4.6 Summary
We have developed a model for transient magnetization in alternating TR SSFP . Initial
preparation sequences can be designed using a two-step process: first choose a win-
dowing function (preferably a Kaiser-Bessel window), then optimize the(b
1
, b
2
) param-
eters by minimizing the oscillatory residue given in Eq. (4.12). Kaiser-Bessel windowed
ramps with scaling factors optimized for wideband SSFP and FS-ATR SSFP were tested
in phantom experiments, and the results showed signifiant reduction of transient sig-
nal oscillation in both cases. The proposed design can be applied to any combination
of repetition times and RF phase-cycling. It is easy to implement, and actively reduces
oscillatory residues during the transient approach to steady-state.
61
Chapter 5 :
Ventricular Function Imaging with Wideband SSFP
5.1 Overview of Ventricular Function MRI
Cardiovascular disease has been the leading cause of death in the Western world. There
are three types of diagnostic tests that are widely used to assess the status of the heart: 1)
anatomical and functional tests that measure the efficiency of the pumping action of the
heart muscle; 2) angiographic methods to evaluate the status of the coronary arteries; 3)
tests of myocardial perfusion and viability. The study of left ventricular (LV) function
at rest and with stress is important for the evaluation of cardiovascular diseases such as
heart failure, dyssynchrony, coronary artery disease, and infarction. Cine MR imaging
which provides a non-invasive way to assess ventricular volumes, function, and mass,
has been regarded as the most accurate and reproducible method for evaluating LV func-
tion. The cine image is a series of images corresponding to different cardiac phases that
represent a full cardiac cycle, which is often acquired in a single breath-hold to eliminate
respiratory motion.
62
In clinical practice, quantification of global left ventricular LV function usually in-
cludes measurement of end-diastolic volume (EDV), end-systolic volume (ESV), stroke
volume (SV), left-ventricular ejection fraction (LVEF), and cardiac output (CO). Also es-
sential is the assessment of regional function which includes local wall motion and wall
thickening. The assessment of both global and regional function require an accurate ex-
traction of the endocardial contour. A 17-segment model (16-segment if excluding the
apex) of the LV wall is usually used for regional analysis of LV function or myocardial
perfusion (Fig. 5.1 and 5.2, [9]). The left ventricle is divided along the long axis of the
heart equally into basal, mid-cavity, and apical parts. The basal part is divided into
basal anterior, basal anteroseptal, basal inferoseptal, basal inferior, basal inferolateral,
and basal anterolateral. Similarly the mid-cavity part is divided into mid anterior, mid
anteroseptal, mid inferoseptal, mid inferior, mid inferolateral, and mid anterolateral.
Apical segments include apical anterior, apical septal, apical inferior, and apical lateral.
The apex represents the myocardium at the tip of left ventricle where there is no cavity
present. Assessment using the above measurements can determine the level of ventric-
ular decompensation or failure, which provides the guidance for choosing the type and
aggressiveness of treatment. Such measurements are provided most conveniently by
echocardiography, or more accurately by MRI.
At 1.5T, SSFP has been used as the standard method to evaluate cardiac function due
to its high SNR and excellent contrast between blood-myocardium and myocardium-
epicardial fat, short acquisition time, which allows a better delineation of endocardial
and epicardial borders, papillary muscles, trabeculae, atrioventricular and semilunar
valves [58]. Reference values of LV function quantification have been well established
63
Figure 5.1: Diagram of the 17-segment model. This figure is from Ref. [9], M. D
Cerqueira, Circulation, 105(4):539–542, Jan 2002.
for SSFP sequences. LV images typically have in-plane resolution on the order of 1.5 to
2.0 mm, with TR on the order of 3 to 5 ms [2, 26, 27, 58]. At higher magnetic fields such
parameters will lead to off-resonance artifacts and we often need to sacrifice spatial res-
olution in exchange for an artifact-free image. Now that clinical cardiac MRI is moving
towards higher field strengths like 3T, the reliability of SSFP needs to be re-established.
By using wideband SSFP we expect to reduce banding artifacts in cardiac images
at 3T with long readouts, which will allow the high SNR of 3T SSFP to be translated
into higher spatial resolution. We implemented wideband SSFP for gated breath-hold
cardiac cine imaging at 3T. When we compared the results to conventional balanced
SSFP , wideband SSFP sequence demonstrated improved achievable spatial resolution in
single-slice cine imaging. Multi-slice cine images from eight healthy subjects showed
reduced number of artifact-affected LV myocardial segments.
64
Figure 5.2: the 17-segment model on a circumferential polar plot. This figure is from
Ref. [9], M. D Cerqueira, Circulation, 105(4):539–542, Jan 2002.
5.2 Methods
5.2.1 Sequence Structure
Figure 5.3 shows the structure of a cine imaging sequence. It is continuous with TR
and TR
s
alternating throughout the scan. When scan begins, the sequence plays only
the excitation pulses and no acquisition (dummy cycles) until the first cardiac trigger
signal arrives. The same k-space segment of each cardiac phase is acquired after the
trigger signal. The number of echoes acquired per frame per heart beat is chosen to
comply with SAR regulation and subject’s breath-hold capability, while maximizing the
temporal resolution. After all frames are acquired in the R-R interval, the sequence
switches back to dummy cycles until the next trigger occurs. This process is repeated
until complete images are collected. The typical breath-hold time for one cine scan is 10
to 20 seconds.
65
frame 1 frame 2 frame N
frame N frame N frame 1 frame 1 frame 2 frame 2
dummy
cycles
k-space
dummy
cycles
dummy
cycles
Figure 5.3: Prospective ECG-gated CINE imaging. During one R-R interval, the same
segment of k-space is acquired for frame 1 to N. The next k-space segment is acquired in
the following R-R interval. This process is repeated until full k-space data are received
for all N frames.
5.2.2 Band Spacing and Temporal Resolution
As described in earlier chapters, wideband SSFP uses two alternating repetition times
(TR and TR
s
) and alternating RF phase (0-p) to establish an oscillating steady state with
a null-to-null band spacing of approximately 2/(TR+TR
s
) [59]. We used a TR
s
/TR ratio
of 0.6 in the multi-slice LV function imaging, which gives wideband SSFP a 25% increase
in band spacing over balanced SSFP with the same imaging TR.
In this work, data were only collected during the long TR. As a result, while keep-
ing the total scan time unchanged the temporal resolution is decreased by a factor of
(1+TR
s
/TR) in wideband SSFP because of the additional short TR.
66
5.2.3 Blood/myocardium Contrast
Wideband SSFP signal magnitude on resonance can be expressed as a function of flip
angle, T
1
, T
2
, and TR
s
/TR ratio [59]:
jM
xy
j=
[(a+ cosa)
T
1
T
2
+(1 a cosa)] sina
sin
2
a(1
T
1
T
2
)
2
+
T
1
T
2
(
p
a+
1
p
a
)
2
(5.1)
where a = TR
s
/TR. As TR
s
/TR ratio is reduced, the signal intensity of TR echo
decreases.
Using Eq. 5.1, simulations of balanced SSFP and wideband SSFP blood/myocardium
signals as functions of flip angle are shown in Figure 5.4. Other parameters are the same
as in our LV function imaging protocol. The optimized flip angle in terms of contrast-
to-noise ratio (CNR) is 75

for balanced SSFP and 70

for wideband SSFP with TR
s
/TR
= 0.6. The maximum achievable CNR of wideband SSFP is 72% of balanced SSFP in
this case. However in the practice of in-vivo imaging the flip angles are often limited by
SAR, and a smaller angle has to be used. For a flip angle 30 a 90, the wideband
SSFP CNR is often around 70% of balanced SSFP .
5.3 Experimental Design and Results
In-vivo scans were performed on a Signa Excite HD 3T scanner (GE Healthcare, Wauke-
sha, WI), with gradient system maximum amplitude of 40 mT/m and maximum slew
rate of 150 mT/m/ms. A body coil was used for RF transmission and an 8-channel car-
diac phased-array coil was used for signal reception. The maximum receiver bandwidth
67
10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90
1.2
2.2
0.2
1.2
2.2
0.2
Flip Angle (˚) Flip Angle (˚)
|Mxy| (a.u.)
|Mxy| (a.u.)
a b
Myocardium
Blood
Myocardium
Blood
a = 1.0 a = 0.6
Figure 5.4: Simulations of Blood and Myocardial SNR for Conventional and Wideband
SSFP at 3 Tesla. (a) Balanced SSFP and (b) wideband SSFP blood-myocardium sig-
nal magnitudes. Steady-state signal as a function of a for the myocardium (T
1
/T
2
=
1100/40 ms) and blood (T
1
/T
2
= 1500/140 ms) at 3T are simulated for both sequences.
Black dotted lines indicate the maximum CNR of the sequences. Balanced SSFP has
maximum CNR at a = 75

, wideband SSFP has maximum CNR at a = 70

. For flip
angles 45

(shaded area), the sequence CNR is greater than 90% of the maximum
value.
was125 kHz (4ms sampling). Localized shimming was performed with the shim vol-
ume placed over left ventricle. 2D cine images were obtained with sequential k-space
segmentation. ECG gating was used and subjects were instructed to hold their breath at
exhale position during image acquisitions.
5.3.1 In-vivo evaluation of off-resonance artifacts
In one healthy subject, balanced SSFP and wideband SSFP CINE loops from a mid short-
axis scan plane were obtained with 20 different TR
s
/TR combinations. The scan param-
eters were: FOV = 30 cm, in-plane resolution = 1.2 1.2 mm
2
(256 256 acquisition
matrix), slice thickness = 8 mm, flip angle = 30

. The total scan time was 16 R-R inter-
vals.
68
0.5 0.75 1.0 0.1
1.0
TRs/TR
CNR (a.u.)
0.64
0.84
Figure 5.5: Blood/myocardium CNR of wideband SSFP as a function of TR
s
/TR ratio
with 30

flip angle. CNR drops as TR
s
/TR ratio decreases.
Figure 5.5 contains numerical simulations of blood/myocardium CNR given the
particular parameter setting of this single-slice imaging protocol and as a function of
TR
s
/TR ratio. Blood/myocardium CNR is reduced as TR
s
/TR ratio decreases. Estima-
tion of relative CNR values of the single-slice images are also in Figure 5.5. At TR
s
/TR =
0.75 and TR
s
/TR = 0.5, wideband SSFP CNR is estimated to be 84% and 64% of balanced
SSFP , respectively.
Image CNR was calculated as SNR
blood
-SNR
myocardium
. Signal intensity (SI) was mea-
sured as the average magnitude over regions of interest in the myocardium and LV blood
pool at both end-diastolic and end-systolic phases [88]. Noise was measured as the sig-
nal standard deviation outside the body.
Figure 5.6 shows LV images (end diastolic frames from CINE loops) acquired with
balanced and wideband SSFP with different TR
s
and TR values. Dotted and dashed lines
represent the contour of equivalent-band spacing. As expected, the banding-related ar-
tifacts increase with TR, and the SNR decreases with TR
s
/TR ratio. A band spacing
> 250Hz can eliminate most severe flow transient artifacts (as the gray arrows indicate),
69
which supports the literature reports that the off-resonance across human heart at 3T is
about 260Hz [62].
CNR was measured in images with TR = 3.6 ms and 4.0 ms and the results are listed
in Table 5.1. Flow artifacts in balanced SSFP with longer repetition times were substan-
tial, that signal measurement was greatly affected by these artifacts and would not rep-
resent the true contrast. The average CNR reduction in TR
s
/TR = 0.75 wideband SSFP
sequence was 88% of balanced SSFP , and was 71% for wideband SSFP with TR
s
/TR =
0.5.
TR
s
/TR ratio 1.0 0.75 0.5
CNR (TR = 3.6 ms) 51.5 43.3 36.7
CNR (TR = 4.0 ms) 59.5 54.5 42.0
Relative CNR (average) 100% 88% 71%
Table 5.1: In-vivo blood-myocardium CNR for balanced SSFP and wideband SSFP with
different TR
s
/TR ratio. CNR values of wideband SSFP drops with TR
s
/TR ratio. Bal-
anced SSFP CNR was used as a reference in the bottom row.
70
TRs/TR
TR
(ms)
3.6
4.0
4.5
5.0
5.5
6.0
1.0
0.75 0.5 0.25
min.TRs = 1.4 ms
300 Hz
250 Hz
200 Hz
Band Spacing
Figure 5.6: Comparison of image artifacts with different TR
s
/TR combinations. Bal-
anced and wideband SSFP end-diastole frames from short axis cine images with differ-
ent TR/TR
s
. Dashed lines and background colors represent band spacing range for the
images. Gray arrows indicate off-resonance artifacts that obstruct the cardiac assess-
ment. Each row represents a fixed imaging TR. The first column from the left represents
conventional SSFP (TR
s
/TR = 1.0). TR
s
shortens when moving to the right, and therefore
widens the band-spacing in the frequency spectrum.
71
5.3.2 In-vivo evaluation of the achievable spatial resolution
The ability of wideband SSFP to reduce off-resonance artifacts allows for the use of
longer imaging TR and acquisition window. It is possible to obtain a higher spatial res-
olution image compared to balanced SSFP . In-vivo evaluation of the increase in achiev-
able spatial resolution was performed on one healthy subject, where balanced SSFP and
wideband SSFP cine images with different spatial resolutions in the readout direction
were obtained at a 3-chamber scan plane. Imaging TR was set to the minimum accord-
ing to the desired readout matrix size, and the TR
s
in wideband SSFP was chosen so that
a null-to null band spacing 300Hz was achieved. The matrix size, spatial resolution,
TR, TR
s
, and band spacing of each scan are listed in Table 5.2. Other scan parameters
were: FOV = 30 cm, slice thickness = 8 mm, flip angle = 30

, with total scan time of 12
R-R intervals.
Matrix Size 192 192 256 192 320 192 384 192
In-plane Resolution(mm
2
) 1.6 1.6 1.2 1.6 0.9 1.6 0.8 1.6
TR (ms) 3.4 3.7 3.9 4.2
TR
s
(ms) - 2.9 2.7 2.4
Band Spacing of Balanced SSFP (Hz) 294 278 256 238
Band Spacing of Wideband SSFP (Hz) 303 303 303 303
Table 5.2: Scan parameters for in-vivo evaluation of the achievable spatial resolution.
Imaging TRs were set to the minimum given the prescribed readout matrix sizes. TR
s
in
wideband SSFP was chosen so that the sequence had a band spacing above 300 Hz for
all scans.
72
1.2 x 1.6 0.9 x 1.6 0.8 x 1.6
End-of-
Systole
End-of-
Diastole
Spatial
Resolution (mm
2
)
TR = 3.4 ms 3.7 ms 3.9 ms 4.2 ms
Wideband
SSFP
Wideband
SSFP
Balanced
SSFP
Balanced
SSFP
1.6 x 1.6
Figure 5.7: Comparison of conventional and wideband SSFP as in-plane spatial reso-
lution is increased. Balanced and wideband SSFP end-diastole frames from 3-chamber
cine images with different spatial resolution. Flip angle was 30

, total scan time was
12 R-R intervals. Gray arrows indicate the artifacts in higher-resolution balanced SSFP
images, which increase with TR and can obstruct the visualization of LV walls and the
valves.
73
Figure 5.7 shows wideband SSFP and conventional balanced SSFP 3-chamber images
of different spatial resolution. As the readout matrix getting larger, the required TR was
also longer. At a spatial resolution of 0.8 1.6 mm
2
, wideband SSFP still maintained
a homogeneous signal across the ROI while artifacts in balanced SSFP increased with
TR and obstructed the visualization of LV walls and the valves. Wideband SSFP images
avoided these severe artifacts. With reduction in CNR it provides a consistent image
quality when TR was increased.
5.3.3 Complete LV function examinations
Complete LV function examinations were performed on eight healthy volunteers. Six to
eight slices were prescribed to cover the subjects’ left ventricles. A 2DFT readout was
used for gated cine imaging with parameters: FOV = 32 28.8 cm, in-plane resolution
= 1.25 1.8 mm
2
(256 160 acquisition matrix), slice thickness = 8 mm, flip angle = 45

.
The total scan time was 10 R-R intervals, with temporal resolution 32 ms for balanced
SSFP and 51 ms for wideband SSFP . Simulation suggests that with these parameters the
null-to-null spacing should be 312Hz for wideband SSFP and 250Hz for SSFP .
Figure 5.8 contains samples of multi-slice short-axis image set obtained with wide-
band SSFP and conventional balanced SSFP . Both sequences showed high contrast be-
tween blood and myocardium (average blood/myocardium CNR of balanced SSFP: 40,
wideband SSFP: 32.3). For the same spatial resolution settings, wideband SSFP provided
better image quality in terms of reduced artifact and signal homogeneity.
74
Balanced
SSFP
Balanced
SSFP
Wideband
SSFP
Wideband
SSFP
End-of-Diastole End-of-Systole
Figure 5.8: Sample frames from a multi-slice short axis cine scan of a healthy volunteer at
3 Tesla. Banding artifacts can be seen in all the slices of balanced SSFP , while wideband
SSFP provides a more homogeneous signal across the region of interest.
5.4 Discussion
We observe that an imaging sequence with band spacing < 250Hz can easily suffer
from substantial off-resonance artifact across the heart at 3T, which is consistent with
the literature report that the off-resonance across human heart at 3T is about 260300
Hz [62]. To ensure the accurate depiction of myocardium contour, a band spacing
300Hz is preferred. In conventional balanced SSFP this means a TR 3.4 ms, whereas
by shortening TR
s
in wideband SSFP , the imaging TR can be extended to up to more than
4.2 ms and we have demonstrated this increased TR in-vivo. We have determined that
spatial resolution can be improved with wideband SSFP since a longer TR is allowed.
75
As shown in Figure 5.7, a sub-millimeter 3-chamber image was achieved by wideband
SSFP without introducing severe off-resonance artifact.
One important compromise is that blood/myocardium CNR drops with TR
s
/TR ra-
tio. In the single-slice scans we performed, TR
s
/TR = 0.75 provided an CNR that is
about 88% of balanced SSFP , and TR
s
/TR = 0.5 provided an CNR that is about 71% of
balanced SSFP . The amount of reduction was less than theory predicted. This under-
reduction may come from the change in blood signal at lower TR
s
/TR ratio. There are
two possible sources for this. First, the estimation was based on steady-state signal. Ven-
tricular blood is in fact a pulsative flow, and it is often in transient state during image
acquisition. Magnetizations generate fluctuating signals before they are stabilized. The
image SNR becomes a complex mixture of multiple transient states that are partial T2-
weighting, and deviate from the predicted value. This blood inflow may also contribute
to the increase in CNR when imaging TR is longer. The second is the B
1
variation in
the region of interest. In some areas the spins may not experience a 30

excitation as we
prescribed. The variance in flip angles changes the resulted signal intensity and contrast
in a non-linear fashion with respect to both flip angles and TR
s
/TR ratio.
Another considertaion is the fact that RF heating is increased in wideband SSFP se-
quences. Because of the additional TR
s
, the number of RF pulses needed to obtain a
complete cine series is doubled compared to conventional balanced SSFP . In order to
maintain SAR within the safety limits the flip angle might have to be reduced, which
can lead to suboptimal SNR or CNR. A possible solution to reduce SAR is to use vari-
able rate selective excitation (VERSE) [13] excitation pulses, which we did not attempt
in this study.
76
Multi-slice wideband SSFP images also showed reduced artifacts for a fix scan pa-
rameter set, which can provide more reliable assessment to LV function and help to
improve the diagnostic quality of cardiac function at 3T platform. A GE pre-product
sequence based on this work has been designed and tested in collaboration with Dr. Ajit
Shankaranarayanan from GE Global Applied Science Lab. Clinical study of wideband
SSFP LV function imaging is being planned at Loma Linda University, which will help to
determine the efficacy of this method and build its LV function measurement standards.
5.5 Summary
Given the same readout duration and/or spatial resolution as conventional SSFP , we
demonstrated wideband SSFP’s ability to suppress off-resonance banding artifact and
provide better image quality for cardiac function assessment. A 0.8 1.6 mm
2
in-plane
resolution was achieved in single-slice 3-chamber imaging, and a 1.25 1.8 mm
2
in-
plane resolution was achieved in multi-slice short-axis LV function imaging without ma-
jor artifact. The improved readout duration makes it possible to acquire high-resolution
images or implement time-efficient acquisition schemes [47], which can be used to shorten
the length of breath-hold or to do free-breathing real-time imaging. Our preliminary re-
sults show the feasibility and image quality improvement of implementing wideband
SSFP sequences for cardiac imaging at 3T.
77
Chapter 6 :
Coronary Artery Imaging with Wideband SSFP
Coronary artery disease is the leading cause of death in the western world, and is re-
sponsible for approximately 450,000 deaths per year in the United States [12]. For this
reason, imaging of the coronary artery lumen (particularly lumenal narrowing) is one
of the most critical applications of medical imaging. Coronary arteries have complex
geometry, and the images for diagnosis should be able to cover the main coronary ar-
teries and their major branches. The most widely used MR coronary imaging protocols
are based on segmented 2DFT gradient acquisitions with cardiac gating and respiratory
navigation, and have proved useful for the diagnosis of proximal disease and coronar-
ies with anomalous origin [44]. Reliable imaging of distal coronary segments remains
an open problem, and may become possible with improvements in signal-to-noise ratio
(SNR), contrast, and spatial resolution.
6.1 MR and Other Imaging Modalities
The current gold standard for detecting coronary artery diseases is contrast-enhanced x-
ray catheterization angiography. It provides high spatial resolution, excellent contrast,
78
and temporal information with the necessary details and physiologic data that deter-
mine the severity of specific lesions and provide a global view of the disease. It is an
invasive process, with small risk of complications.
Echocardiography visualizes the coronary arteries using the transthoracic and trans-
esophageal approaches [20, 89]. Visualization of the proximal segments of both the left
and right coronary systems has been made clinically. However, the more distal coronary
artery segments remains difficult to visualize with echocardiography.
Cardiac multislices computed tomography (MSCT) has emerged for more than five
years. MSCT is a non-invasive technique with the ability of 3D image reconstruction
and achieving sub-millimeter spatial resolution. The disadvantage of MDCT is radiation
exposure and the need to inject iodinated contrast.
Coronary artery MR angiography is also a non-invasive 3D imaging technique. It
does not require ionizing radiation exposure and can visualize coronary arteries with
only intrinsic tissue signal, or non-iodinated contrast agents. The study time of coronary
artery MRA is long (20-30 minutes) and the patient is restricted to confined space during
the whole scan.
One challenge of coronary MRA is to compensate cardiac and respiratory motion.
Cardiac gating like ECG, VCG, and PG are often used to eliminate cardiac motion. Two
methods are usually used for avoiding respiratory motion artifact: breath-hold and free-
breathing navigator gating. Breath-hold can almost eliminate artifacts caused by chest
movement, but the short span of breath-hold time restricts the spatial resolution that
fits into single scan. Navigator gating removes the need for breath-hold and allows the
79
LV navigator
Right diaphragm
navigator Acceptance window
Navigator signal
ECG trigger
Navigator
Accepted
heartbeat
Rejected
heartbeat
Figure 6.1: Respiratory navigator gating. Left: navigator tracker location. Navigator
tracker is often placed across right diaphragm or lateral LV wall. Both location have
similar gating performance, so we chose right diaphragm for its simple to implement.
Right: breathing curve and the acceptance window. (Figures from Stuber et al. [82])
acquisition of large k-space matrix, making high-resolution 3-D imaging possible. It con-
tains a pencil beam (‘tracker’) excitation positioned across right diaphragm or the lateral
LV wall (Figure 6.1). An 1-D signal is acquired after the excitation, and its correlation
coefficient with baseline signal is calculated to find out the lung-liver interface location,
so the current respiratory phase can be decided. The performance of navigator depends
on the position of the tracker, correlation coefficient threshold and acceptance window.
Another challenge is to acquire adequate contrast within the scan time. This includes
sufficient SNR, good fat suppression, sufficient SNR and blood/myocardium contrast.
Usually a spectral-selective RF pulse is applied every heart beat to saturate epicardial
fat. Gadolinium based T
1
shortening contrast agents and T
2
preparation can be used to
enhance blood signal. SSFP sequence also provides a way to substantially improve SNR
and blood/myocardium contrast.
At 1.5T, balanced steady state free precession (SSFP , also known as True-FISP , FI-
ESTA, or Balanced-FFE) imaging has been shown to provide significantly superior SNR
80
and CNR compared to gradient echo imaging [18], and may alleviate the need for con-
trast agents. High-field MRI platforms can also lead to improved SNR, which is roughly
proportional to the static magnetic field strength. In experimental coronary MR angiog-
raphy studies, patient blood SNR using gradient echo sequences at 3T has been mea-
sured to be 30% higher than at 1.5T [79], and SSFP blood SNR at 3T has been measured
to be 53% higher than at 1.5T [3].
The promise of higher SNR at 3.0T is especially appealing for coronary artery MRA.
Stuber et. al. reported the first coronary MRA study at 3T in 2002 [81]. Bi et. al. per-
formed comparison between 1.5T and 3T breath-hold SSFP coronary MRA, and ob-
served SNR and CNR increase in 3T scans. Preliminary results show that coronary artery
MRA at 3T is feasible, but major improvements are needed to get diagnostic quality im-
ages.
Balanced SSFP imaging suffers from sensitivity to B
0
inhomogeneity [7, 22, 63, 90].
Susceptibility-induced resonance frequency shifts increase linearly with magnetic field
strength and generate more off-resonance artifact, resulting in degradation of SSFP im-
age quality. This [7, 22, 63, 90] sensitivity is proportional to TR. In order to prevent off-
resonance banding artifacts in SSFP imaging, the readout length must be constrained
to maintain a short TR. Robust cardiac MRI at 3T demands an imaging bandwidth of
250 to 300 Hz to cover the range of resonance offsets across the human heart, which
requires a TR no longer than 3.3 to 4 ms using conventional SSFP [70]. For diagnostic
quality coronary artery imaging, sub-millimeter resolution is essential. The need for a
short TR limits the usable readout duration given the gradient hardware limitations on
81
commercial systems, and makes it difficult to achieve sub-millimeter resolution which
is essential for diagnostic quality coronary artery images.
Alternating TR (ATR) methods have been recently developed as a means for mod-
ifying the spectral response of SSFP . This approach can be used with specific TR com-
binations and corresponding phase cycling to achieve fat suppression [49], or with 0-p
phase cycling to widen the band spacing and relax the TR limitation [59]. The latter
approach, which we have called wideband SSFP , allows a flexible trade-off of the high
SNR of 3T SSFP for an increased band spacing. It has been shown that, compared to
conventional SSFP , wideband SSFP can suppress off-resonance related banding artifacts
in steady-state cardiac imaging for a given spatial resolution [47]. For a specific band
spacing requirement, wideband SSFP increases the possible TR and thus the available
readout duration, which improves the achievable spatial resolution.
Volume-targeted imaging cover an adequate volume per scan to visualize a major
coronary artery branch. It minimizes the scan time by accurately localizing the scan
plane. The localization process is time-consuming and operator-dependent. To avoid
this problem Weber et. al. proposed a whole-heart coronary MRA approach in the year
2003 [86]. It acquires the whole heart with a free-breathing navigated sequence. 3-D
reformatting of whole-heart data allows display of more distal and branching vessels
compared to volume-targeted scheme.
we present the design and application of a wideband SSFP technique for sub-millimeter
resolution coronary artery imaging at 3T. A three-dimensional free-breathing respiratory
navigated sequence was used with spectrally selective fat saturation. The results were
compared to conventional SSFP and GRE sequences. We demonstrate that wideband
82
SSFP provides a marked improvement in image quality. Sensitivity encoding (SENSE)
parallel acquisition was implemented in a breath-hold 3D wideband SSFP sequence to
test its ability to improve spatial resolution.
6.2 Methods
6.2.1 Increased Band Spacing Using Wideband SSFP
Wideband SSFP [59] uses two alternating repetition times (TR and TR
s
) with alternating
RF phase (0-p) to establish an oscillating steady state with two distinct echoes, as shown
in Figure 6.2. The ratio of the short and long repetition times is defined as a = TR
s
/TR,
where 0 < a <= 1. This sequence has a null-to-null band spacing of approximately
2/(TR+TR
s
), and the signal intensity decreases as a-value is reduced. In this work, only
the long TR is used for data acquisition.
a = 0.4
+α −α +α −α +α −α
TR TR
s
. . . . . .
1/(TR+TRs) -1/(TR+TRs)
time
Δƒ
Figure 6.2: Wideband SSFP pulse sequence (top) and its spectral response (bottom).
Black solid line represents the spectral response of the echo in TR (black circle), gray
dotted line represents the spectral response of the echo in TRs (gray dotted circle). The
signal profiles are based on a = TR
s
/TR = 0.4, and T
1
= T
2
TR.
83
6.2.2 Initial Preparation for Reducing Transient Oscillations of Wideband
SSFP
When starting at thermal equilibrium, the SSFP signal amplitude oscillates during the
approach to steady state. The oscillation creates non-smooth k-space weighting along
the phase-encoding direction(s), which results in image artifacts [32]. The long wait-
ing period before the signal reaches steady state degrades the effectiveness of important
magnetization preparation schemes, such as fat saturation, T
2
-preparation, and inver-
sion recovery. Thus an efficient initial preparation is critical in non-continuous scans
(e.g. gated cardiac imaging).
We derived the modified Fourier relationship between excitation flip angle incre-
ments and the resulting signal profile of alternating TR sequences using an approach
similar to Le Roux’s work on conventional SSFP [48], and designed a scaled Kaiser-
Bessel preparation scheme to efficiently reduce transient signal fluctuation in wideband
SSFP [46]. In the proposed preparation scheme, the RF amplitude increments in TR and
TRs are scaled functions of the same Kaiser-Bessel window, with scale factors of a and
1, respectively. Before the 3D coronary artery scans, we compared the performance of
the scaled Kaiser-Bessel preparation with dummy-cycle preparation in low resolution
breath-held LAD imaging.
Figure 6.3 illustrates the influence of the wideband SSFP initial preparation scheme
on final image quality. The figure contains two low-resolution LAD coronary artery im-
ages that were acquired in separate breath-holds using the same wideband SSFP imag-
ing sequence, but with two different eight-cycle initial preparation schemes (a: dummy
84
cycles and b: scaled Kaiser-Bessel ramp [46]). The image obtained with the scaled Kaiser-
Bessel ramp shows reduced artifacts and more homogeneous blood signal intensity (see
arrows). This example was shown for illustration, however a 16-cycle Kaiser-Bessel
ramp provided slightly more uniform signal in-vivo, and was used in all subsequent
studies.
a b
Figure 6.3: Wideband SSFP oronary artery images with different magnetization prepa-
ration methods. (a) dummy-cycles, (b) scaled Kaiser-Bessel ramp. The arrows indicate
where the scaled Kaiser-Bessel ramp reduced artifacts and had better signal homogene-
ity.
6.2.3 Imaging Sequence
Free-breathing coronary magnetic resonance images were acquired using a three-dimensional
respiratory navigated sequence with either a wideband SSFP , conventional SSFP or gra-
dient echo acquisition. The pulse sequence structure is shown in Figure 6.4.
The trigger delay is determined from a cine image to center the acquisition window
at a rest period, usually during mid- to end-diastole. A pencil-beam navigator over the
right hemidiaphragm was acquired prior to data acquisition in each cardiac cycle. If its
signal falls within the2.5 mm acceptance window, the signal from this R-R interval will
be collected and stored in the data matrix, otherwise all the RF amplitudes inside this
R-R interval will be set to zero and the received data discarded. A spectral-selective fat
85
F ATSAT
Initial
preparation
Imaging
Navigator
trigger delay
Figure 6.4: Pulse sequence for 3D coronary imaging. In each R-R interval, a pencil-
beam navigator is followed by a fat saturation sequence and a 16-cycle Kaiser-Bessel
windowed ramp preparation, with actual image acquisition centered at mid-diastole.
saturation pulse is then applied, followed by dephasing gradients in all three directions
to spoil the fat signal. The flip angle of this fatsat pulse is chosen to maximize fat satura-
tion performance by nulling the fat signal at the center of k-space, and is calculated from
fat T
1
, TR, TR
s
, the number of initial preparation steps and the number of k-space lines
acquired in one heart beat. A 16-cycles initial preparation RF train following a scaled
Kaiser-Bessel ramp (as described in Section 4.6) is played right after the fat saturation for
wideband and balanced SSFP sequences. Acquisition starts after the preparation stage.
The acquisition window length was determined based on the 2D CINE scout scan, and
was usually about 20% of the R-R interval. 3DFT partial k-space readout was used with
a interleaved sequential phase-encoding ordering and centric slice ordering (16-20 slices
per slab). The same process is repeated in the next heart beat. It stops when the full 3-D
volume data is acquired.
Scan parameters for the four different imaging protocols are listed in Table 6.1. The
four scans were conducted in the order they appear in the table (left to right). For each
subject, imaging TR was set to the minimum value considering the variant gradient slew
86
rate limitation in individual oblique scan planes. The TR
s
of wideband SSFP was chosen
to maintain a null-to-null band spacing greater than 300 Hz.
Sequence Wideband bSSFP #1 bSSFP #2 GRE
TR (ms) 3.9 - 4.2 3.9 - 4.2 3.4 - 3.8 5.0 - 5.8
Flip Angle 55

55

55

15

Matrix Size 384 256 384 256 256 256 384 256
Spatial Res. (mm) 0.68 0.68 1.0 0.68
Band Spacing(Hz) 300 238 256 300 -
Table 6.1: In-vivo scan parameters. The row "Spatial Res." represents the spatial reso-
lution in readout direction. The resolution in other two phase-encoding directions are
both 1.0 mm.
6.2.4 SNR Efficiency of Wideband SSFP and Conventional SSFP
The total acquisition time of wideband SSFP is (1+ a) times longer than conventional
SSFP because only one k-space line is collected per (TR+TR
s
). The length of acquisition
window in one R-R interval has to be kept within the diastolic rest period to avoid car-
diac motion artifact, hence the total number of heart beats needed to obtain the same
3D volume is also increased by a factor of (1+ a). To reduce the effect of the increased
possibility of patient movement during a prolonged scan, we use a centric slice- encode
ordering to acquire the center part of k-space at the beginning of the scan.
When only TR is used for imaging, the SNR efficiency of wideband SSFPm
w
can be
written as
m
w
=
m
c
1+ a

jM
xy
j
w
jM
xy
j
c
(6.1)
87
wherejM
xy
j
w
andjM
xy
j
c
are the pass band signal intensity of wideband SSFP and con-
ventional SSFP , respectively, andm
c
is the SNR efficiency of conventional SSFP [59].
As described in Eq.1 of reference [59],jM
xy
j
w
/jM
xy
j
c
is always less than one, hence
the SNR efficiency of wideband SSFP is always lower than that of conventional SSFP .
Numerical simulations indicate that the 0.681.01.0 mm
2
resolution wideband SSFP
coronary artery imaging sequence in this study should exhibit a theoretical blood SNR
reduction of roughly 30% and an SNR efficiency reduction of roughly 45% compared to
conventional SSFP .
After the LAD scans, regions of interest (ROIs) in the aorta (blood) and outside the
body (background air) were manually selected in the high-resolution images. Blood
SNR was defined as SNR
blood
= SI
blood
/SD
air
, where the signal intensity (SI) of aortic
blood pool and standard deviation (SD) of background noise were directly measured
from the images. SNR efficiencies were calculated by dividing SNR values by the square
root of total scan time, and were then normalized such that conventional SSFP images
have a mean SNR efÞciency of 1.0.
6.2.5 Experimental Methods
Experiments were performed on a Signa Excite HD 3T scanner (GE Healthcare, Wauke-
sha, WI). The gradient system had maximum amplitude 40 mT/m and maximum slew
rate 150 mT/m/ms. The maximum receiver bandwidth was125 kHz (4ms sampling).
The body coil was used for RF transmission and an 8-channel cardiac phased-array coil
(GE Healthcare Technologies, Waukesha, WI) was used for signal reception.
88
Subjects were in supine position with electrocardiograph (ECG) gating; a 3-plane lo-
calizer was performed at the beginning of the session to collect low-resolution spatial
information of the subject. I-Drive interactive scan control tool is used to tailor the scan
plane according to the subject coronary artery anatomy in real time. Once the scan plane
is selected, a cine image is acquired to determine the best trigger delay to minimize the
cardiac motion artifact. Localized shimming was performed to reduce the off-resonance
within the region of interest, which was centering at the coronary artery segment cur-
rently being imaged. Center frequency adjustment was done with five scout scan [19],
each having a 30 Hz excitation RF frequency increment. Before the imaging begins, a
24-step navigator pre-scan was used to collect information of subject breathing pattern
and navigator baseline information.
Six healthy volunteers were scanned after providing written informed consent, and
with an imaging protocol approved by our institutional review board. Wideband SSFP
and balanced SSFP #1 scans were performed on all subjects, and additional balanced
SSFP #2 and gradient echo scans were performed on three of the six subjects. After the
scans, on-line reconstruction was performed and a stack of 2D images was displayed
on the scanner console. 3D reformation was done off-line in an open-source medical
image processing software OsiriX. A example 3D reformation of coronary artery image
is shown in Figure 6.5. LAD of greater length is visible in the reformatted image.
89
Figure 6.5: A 3-D reformatted left coronary artery image, revealing longer segment of
proximal LAD. Reformation was done in OsiriX.
6.3 Results
Figure 6.6 contains 3D reformatted LAD coronary artery images from three representa-
tive subjects. The four columns contain data from four separate navigated acquisitions:
1) wideband SSFP with 0.681.01.0 mm
3
spatial resolution, 2) balanced SSFP #1 with
the same spatial resolution and TR as column 1, 3) balanced SSFP #2 with a band spacing
similar to column 1 and 1.01.01.0 mm
3
spatial resolution, and 4) gradient echo with
the same spatial resolution as column 1.
In all studies, wideband SSFP provided the most uniform blood signal, and artifact-
free depiction of distal branches of the LAD (see Fig 6.6a, 6.6e and 6.6i ). Balanced SSFP
suffered from substantial flow-related transient artifacts (see Figs. 6.6b and 6.6j) [52, 70]
that interfered with coronary assessment. Wideband SSFP and balanced SSFP with
shorter TR did not suffer from these artifacts, presumably due to the wider null-to-
null spacing in their spectral profile. Note that the high resolution balanced SSFP im-
age of subject 2 (Fig. 6.6f) did not suffer from any noticeable flow artifact, however
90
a b c d
e f g h
Subject #3 Subject #2 Subject #1
Wideband SSFP Balanced SSFP #1 Balanced SSFP #2 Gradient Echo
i j k m
Figure 6.6: Left anterior descending coronary artery images from three representa-
tive subjects using four different imaging sequences (see Table 1). (a,e,i) Wideband
SSFP with 0.68 1.0 1.0 mm
3
spatial resolution. (b,f,j) Conventional balanced SSFP
with 0.68 1.0 1.0 mm
3
spatial resolution. (c,g,k) Conventional balanced SSFP with
1.0 1.0 1.0 mm
3
spatial resolution. (d,h,m) Gradient echo with 0.68 1.0 1.0 mm
3
spatial resolution. Each image is reformatted from a 3D slab acquisition. Wideband
SSFP images provided the most uniform blood signal, and artifact free depiction of dis-
tal branches of the LAD. High resolution conventional SSFP suffers from off-resonance
banding (f, see gray arrows) and flow-transient artifacts (b,j) that disrupt visualization
of the coronary lumen. Low resolution conventional SSFP does not suffer from these
artifacts but is unable to capture small distal branches (e versus a, see black arrows, and
g versus e, see white arrows).
dark bands appear in the mid-LAD region, and could confound image interpretation.
Balanced SSFP with short TR was relatively artifact-free, but was not able to capture
smaller branches due to the coarser spatial resolution (see white arrows in Fig. 6.6g ver-
sus Fig. 6.6e). In subject 3, the left main coronary artery in the balanced SSFP image
was affected by the flow transient artifact (see black arrows in Fig. 6.6j). Wideband SSFP
(Fig. 4i) avoided this artifact, but also suffered from reduced SNR. As a result, the mid-
and distal-LAD were not as clearly depicted as in the balanced SSFP images. Gradient
91
echo images (Figs. 6.6d, 6.6h, 6.6m) did not suffer from off-resonance banding artifact,
however the blood SNR was substantially lower than the alternatives.
The navigator efficiency, scan-time, blood SNR, blood SNR efficiencies from the four
scans are summarized in Table 6.2. Navigator efficiencies ranged from 35.0% to 59.7%
across the six subjects. The average blood SNR (measured in the aorta) of the wideband
SSFP data was 22% lower than that of balanced SSFP data with the same spatial resolu-
tion. Considering the change in scan time, the average SNR efficiency of wideband SSFP
was 70% of the SNR efficiency of conventional balanced SSFP .
Sequence Wideband bSSFP #1 bSSFP #2 GRE
Navigator Efficiency (%) 51.9 5.1 49.0 6.3 42.6 7.6 49.9 4.4
Scan time (min.) 5.8 0.7 4.8 0.5 4.9 0.1 5.5 0.5
Aortic Blood SNR 14.8 3.2 19.1 4.7 22.2 4.8 7.3 1.1
Aortic Blood SNR Efficiency 0.70 0.15 1.0 0.23 1.2 0.3 0.36 0.04
Table 6.2: In-vivo imaging results: SNR, scan time, and SNR efficiency of 0.68 1.0
1.0 mm
3
resolution images averaged over six volunteer scans.
6.4 Discussion
We have designed, implemented, and evaluated a wideband SSFP-based method for 3D
high-resolution free-breathing coronary artery imaging. In 0.681.01.0 mm
3
balanced
SSFP scans, off-resonance banding and flow-related artifacts severely degraded the de-
piction of coronary arteries (Fig. 6.6b, 6.6f and 6.6j). Balanced SSFP with lower spatial
resolution (and shorter TR) was able to avoid these artifacts but was not able to cap-
ture small and distal branches. Wideband SSFP was able to achieve 0.681.01.0 mm
3
92
spatial resolution with no visible artifacts and the most homogeneous blood signal inten-
sity over the regions of interest. With TR/TRs = 3.9/2.4 ms, wideband SSFP had a 24%
wider null-to-null spacing in its spectral profile (317 Hz) compared to conventional
SSFP with the same TR.
The use of wideband SSFP involves a fundamental trade-off of SNR for spatial res-
olution and bandwidth. The balance between the three should be carefully evaluated
to optimize image quality and the eventual ability to detect CAD from images. This in-
cludes optimization of the TR, TRs, bandwidth, and flip angle. It is worth noting that
the reduction blood SNR in this study was less than the value predicted by Eqn. 6.1.
Numerical simulations suggest that in the steady state blood SNR should be 30% lower
when using wideband SSFP compared to balanced SSFP #1. The discrepancy could be
due to inflow, which would mean that blood SNR is better modeled as a mix of various
transient signals and partial T2-weighting. This would affect the choice of the imaging
flip angle. It is likely that to maximize blood to myocardium contrast in the SSFP-based
sequences, the flip angle should be set to the largest possible value within SAR con-
straints, since blood signal is always higher than that of myocardium and the difference
increases with flip angle.
The total scan time for wideband SSFP is expected to increase by TRs /TR compared
to balanced SSFP #1, when the length of acquisition window is kept identical and TRs
is unused. In this study, the scan time increase was expected to be 50% to 60%, but
was only 24% on average, as a result of sequence restrictions on the number of k-space
segments (which caused acquisition window length to vary during different scans), and
also variations in the navigator efficiency. As a result, the wideband SSFP approach
93
achieved a 70% SNR efficiency compared to balanced SSFP , which was higher than the
theoretical prediction of 55%.
Parallel imaging [66,78] was not used in this study, but can be easily incorporated as
a means to shorten scan time, reduce the size of the acquisition window, and/or improve
spatial coverage. It may be possible for autocalibrated parallel imaging methods [25] to
obtain low resolution coil sensitivity or k-space interpolator information during the TRs,
further reducing the required acquisition time.
It may also be possible to acquire low-resolution data (e.g. 1-D projections) from
the imaging volume during the short TR. Such data would provide direct information
about heart’s position and could be used for self-gating [45] or automated detection of
the stable diastolic window within a prolonged acquisition [23]. No additional sequence
or acquisition time would be needed to perform this procedure.
Many cardiac applications such as first pass perfusion [10] and global cardiac func-
tion imaging [29] benefit from higher field strengths, and the clinical use of cardiac MRI
has begun to migrate towards 3T. Coronary artery imaging, as part of a comprehensive
cardiac assessment, will also require a robust method to acquire high-quality artifact-
free images at 3T. This study has demonstated wideband SSFP’s ability to achieve sub-
millimeter resolution while avoiding banding artifacts that confound the use of conven-
tional balanced SSFP at 3T. This approach should also have roughly 25% higher SNR
efficiency compared to balanced SSFP at 1.5T, making it a promising candidate for non-
contrast coronary MRA at 3T.
Wideband SSFP is a flexible pulse sequence, and this represents it’s first application
to coronary artery imaging. There are several opportunities for further development that
94
include utilization of TRs for improving SNR, navigation, self-gating, or autocalibration
(for parallel imaging), and the optimization of imaging parameters. Further studies are
needed to further develop this approach and determine the imaging parameters that
will provide optimal image quality and optimal detection of CAD in clinical cohorts.
6.5 Summary
We have demonstrated a new approach to non-contrast, high-resolution coronary artery
imaging at 3T, based on wideband SSFP . Compared to conventional balanced SSFP , this
pulse sequence provided reduced sensitivity to off-resonance and permits prolonged
readout duration. This directly led to the ability to achieve sub-millimeter resolution
without the banding and flow-transient image artifacts that confound conventional bal-
anced SSFP coronary artery imaging. Wideband SSFP retained superior SNR compared
to gradient echo sequences. This work has provided an initial demonstration of the
advantages of applying wideband SSFP to coronary artery imaging (higher resolution,
reduced artifact) in healthy subjects. Further studies in patients are needed to deter-
mine imaging parameters that provide optimal image quality and optimal assessment
of coronary artery disease with this new approach.
95
Chapter 7 :
Future Work
Using Parallel Acquisition
Parallel imaging techniques [66, 78] use the sensitivity information from different re-
ceiving coils in a phased-array to replace part of the spatial information provided by
gradient-encoding. It can reduce the number of phase-encoding steps for a specific FOV
and resolution requirement. By implementing parallel acquisition in cardiac imaging
we can choose to have one of the following improvements: 1) increase the temporal res-
olution or shorten the total scan time, 2) increase the spatial resolution or expand the
FOV coverage.
Preliminary results of combining parallel acquisition with breath-hold 3-D wideband
SSFP LMCA imaging is shown in Figure 7.1. Sensitivity Encoding (SENSE) was applied
using data from all 8 receiving channels. Reduction factor = 1.67 and 2 were used. The
performance of parallel imaging depends on phased-array geometry and scan plane
orientation; in this axial slice a reduction factor of two created ghosting artifact that
96
obstruct the assessment to the region of interest. The best reduction factor has to be
found for different scan planes.
a b c
Figure 7.1: 3-D navigated wideband SSFP coronary artery imaging. Sensitivity encoding
(SENSE) was used to increase image temporal resolution. (a) no reduction, temporal res-
olution = 288 ms; (b) reduction factor = 1.67, temporal resolution = 173 ms; (c) resuction
factor = 2, temporal resolution = 144 ms.
Utilizing the Echo in TR
s
In this work we only collect the echo in TR. This results in a decreased SNR while sup-
pressing the banding artifact. From Figure 3.2 we see that the discarded echo in TR
s
has
higher signal intensity, and the level of signal increase depends on the degree of TR/TR
s
asymmetry.
Improvement of Image SNR
We will study the possibility to acquire data during TR
s
. Since TR
s
is often very short
(about 2 ms), we can only acquire a narrow portion of k-space data during that limited
time. We need to develop a method to combine this low spatial resolution, high signal
97
intensity data with the full k-space, lower signal intensity data from TR. We expect this
will provide a way to partially compensate the SNR loss when using wideband SSFP
sequence.
Auto-Calibration for Parallel Imaging
In parallel imaging the coil sensitivity information is crucial for robust reconstruction.
The most direct method to obtain this information is to acquire full data lines in the
central region of k-space. A number of auto-calibration approaches have been demon-
strated which extract real-time coil sensitivity information from under-sampled data
[38, 54].
A short TR (TR
s
) in the alternating SSFP sequences is typically added in order to
establish a favorable spectral response (e.g. avoid banding, or suppress fat). No data
is acquired during that period because its length doesn’t allow the acquisition of a full
k-space line. However it is possible to acquire a smaller k-space matrix during TR
s
which can be used for calibrating the GRAPPA reconstruction kernel, or generating a
sensitivity map for SENSE reconstruction. This signal can be acquired at the same time
as the reduced-FOV image, and eliminates the need for additional scan-time for auto-
calibration.
Self-Navigating for Cardaic Imaging
Respiratory motion is a major issue in cardiac imaging. Short breath-holds and naviga-
tor techniques [21, 53, 85] are two methods that are often used to eliminate the problem.
98
The effect of breath-holds depends on the subjects’ ability to hold their breath; and nav-
igators (usually placed at the right diaphragm) only provide an indirect assessment of
the heart’s position.
In the case of wideband SSFP , it is possible to acquire an echo during TR
s
, which
provides direct indication of current heart position in the imaging plane and can be used
for self-navigation. We can collect data from continuous wideband SSFP sequence and
retrospectively use this signal to reconstruct cine images at a desired respiratory phase.
Bandwidth Beyond 2x
The current Wideband SSFP technique uses two alternating TRs to achieve band spacing
up to two times the inverse of imaging TR. Along with the emergence of 3T and higher
field strength scanners, the need for increased bandwidth for SSFP imaging will become
more and more critical as the off-resonance grows proportionally with field strength.
Thus we propose to develop wideband sequences that can have central band widening
beyond two-fold.
Repetition times of different length can be arranged to form a sequence that permits a
desired amount of precession before there’s a signal null. A complete cycle that contains
more than two TRs will generate more than two distinct steady states with different
signal levels. We expect the SNR in the long TR to be lowered further (compared to the
two-TR Wideband SSFP sequence) in exchange of the central bandwidth. The amount of
SNR loss is a function of sequence timing. Since there is intrinsic high SNR that increases
99
with field strength, the targeted spatial resolution can stay unaffected by this SNR drop
with a carefully designed wideband sequence.
100
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107
Appendix A :
Initial Preparation
A.1
Using SU
2
formalism, R
1
(representing the rotation from M
2
to M
1
) can be re-written as
a 2 2 spinor matrix Q
1
:
Q
1
=Q
z
(q
1
) Q
x
(a) Q
z
(q
2
)
=
2
6
6
4
e
iq
1
/2
0
0 e
iq
1
/2
3
7
7
5

2
6
6
4
cos(
a
2
) i sin(
a
2
)
i sin(
a
2
) cos(
a
2
)
3
7
7
5

2
6
6
4
e
iq
2
/2
0
0 e
iq
2
/2
3
7
7
5
= cos

a
2

cos

q
2

I
i
2
6
6
4
cos(
a
2
) sin(
q
2
) sin(
a
2
) e
iRq/2
sin(
a
2
) e
iRq/2
cos(
a
2
) sin(
q
2
)
3
7
7
5
108
whereq = q
1
+q
2
and R = (q
1
q
2
)/(q
1
+q
2
). As described in Ref. [65], an SU
2
matrix
Q can have its rotation axis~ n(= n
x
ˆ
i+ n
y
ˆ
j+ n
z
ˆ
k) and rotation angleW extracted directly
from the matrix elements, that
Q= cos

W
2

I i sin

W
2

2
6
6
4
n
z
n
x
in
y
n
x
+ in
y
n
z
3
7
7
5
I is the identity matrix. Thus for matrix Q
1
we find
n
1x
= sin

a
2

cos

Rq
2

n
1y
= sin

a
2

sin

Rq
2

n
1z
= cos

a
2

sin

q
2

W
1
= 2 cos
1
h
cos

a
2

cos

q
2
i
109
The same approach can be applied to R
2
rotation to get the another 2 2 matrix Q
2
:
Q
2
=Q
z
(q
2
) Q
x
(a) Q
z
(q
1
)
=
2
6
6
4
e
iq
2
/2
0
0 e
iq
2
/2
3
7
7
5

2
6
6
4
cos(
a
2
) i sin(
a
2
)
i sin(
a
2
) cos(
a
2
)
3
7
7
5

2
6
6
4
e
iq
1
/2
0
0 e
iq
1
/2
3
7
7
5
= cos

a
2

cos

q
2

i
2
6
6
4
cos(
a
2
) sin(
q
2
) sin(
a
2
) e
iRq/2
sin(
a
2
) e
iRq/2
cos(
a
2
) sin(
q
2
)
3
7
7
5
and its rotation axis~ n
2
(= n
2x
ˆ
i+ n
2y
ˆ
j+ n
2z
ˆ
k) and rotation angleW
2
are
n
2x
= sin

a
2

cos

Rq
2

n
2y
= sin

a
2

sin

Rq
2

n
2z
= cos

a
2

sin

q
2

W
2
= 2 cos
1
h
cos

a
2

cos

q
2
i
=W
1
110
A.2
In Figure 4.3b we definef
1
as the angle between z-axis and~ n, and observe that
tanf
1
=
n
1y
n
1z
=
n
2y
n
2z
=
sin(a/2) sin(Rq/2)
cos(a/2) sin(q/2)
= tan

a
2

sin(Rq/2)
sin(q/2)
For smalla/2 values we have tan(a/2) a/2, therefore
f
1
a
sin(Rq/2)
2 sin(q/2)
Considering a sequence of excitations with RF flip angles {a
k
}, the change in f
1
value
after the k
th
excitation can be expressed as
Df
1
(k)= f
1
(k)f
1
(k 1)
=[a
k
a
k1
]
sin(Rq/2)
2 sin(q/2)
=Da
k

sin(Rq/2)
2 sin(q/2)
.
Defining f
2
as the angle between~ n and both M
1
and M
2
, and plotting M
1
, M
2
,~ n
1
and~ n
2
in 3D space (Fig.4.3c), we find
M
2
cosf
2
sinf
x
tan

W
2

= M
2
sinf
2
111
Solving forf
2
, we have
tanf
2
= sinf
x
tan

W
2

=
jn
1x
j
k~ n
1
k

sin(W/2)
cos(W/2)
=
sin(a/2)
cos(a/2)

cos(Rq/2)
cos(q/2)
= tan

a
2

cos(Rq/2)
cos(q/2)
Again we apply small-a approximation and obtain
f
2
a
cos(Rq/2)
2 cos(q/2)
Hence the change inf
2
value after the k
th
excitation is
Df
2
(k)= f
2
(k)f
2
(k 1)
=[a
k
a
k1
]
cos(Rq/2)
2 cos(q/2)
=Da
k

cos(Rq/2)
2 cos(q/2)
The above equations indicate that for spins of a certain resonant frequency, the amounts
of increment inf
1
andf
2
is proportional to the amount of RF flip angle incrementDa.
112
A.3
Multiplying e
iWk
to both side of Eq.(4.7), we obtain a phase-shifted form (e
k
) of the oscil-
latory residue that
e
k
= e
iWk
~ #
k
= e
iW(k1)
~ #
k1
+ e
iW(k1)
[Df
1
(k)+ e
ipk
Df
2
(k)]
= e
k1
+ e
iW(k1)
sin(Rq/2)
2 sin(q/2)
Da
k
e
i(Wp)(k1)
cos(Rq/2)
2 cos(q/2)
Da
k
(A.1)
Using the fact that when the sequence first starts from thermal equilibrium,#
0
= e
0
= 0
andW q, the oscillatory residue e
p
after p excitations (p is an even number) can be
calculated by summing up the last two terms in Eq.(A.1):
e
p
=
1
2

sin(Rq/2)
sin(q/2)
p
å
k=1
(e
iq(k1)
Da
k
)

cos(Rq/2)
cos(q/2)
p
å
k=1
(e
i(qp)(k1)
Da
k
)

which suggests the Fourier relation between e
p
and {Da
k
}: the first term is the Fourier
transform of {Da
k
} multiplied by a function of q; the second term is the same Fourier
transform shifted byp and multiplied by another function ofq.
113

Abstract (if available)

Abstract Balanced steady-state free precession (SSFP) is an MRI pulse sequence that is widely used for cardiac imaging, because it provides superior SNR and excellent blood-myocardium contrast compared to the alternatives. Its primary drawback is sensitivity to off-resonance, which is related to the reciprocal of the sequence repetition time (TR) and results in banding artifacts.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Lee, Hsu-Lei (author)

Core Title Wideband steady-state free precession for cardiac MRI

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 12/04/2008

Defense Date 10/08/2008

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

Tag alternating repetition times,coronary artery imaging,initial preparation,LV function,OAI-PMH Harvest,steady-state free precession,wideband SSFP

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nayak, Krishna S. (committee chair), Leahy, Richard M. (committee member), Reisler, Hannah (committee member)

Creator Email hsulee@usc.edu,hsulei.lee@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1866

Unique identifier UC1215330

Identifier etd-Lee-2399 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-131278 (legacy record id),usctheses-m1866 (legacy record id)

Legacy Identifier etd-Lee-2399.pdf

Dmrecord 131278

Document Type Dissertation

Rights Lee, Hsu-Lei

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