RAPID DIXON ACQUISITIONS FOR WATER / LIPID SEPARATION IN MRI
by
Christopher Alan Flask
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Dissertation Adviser: Dr. Jeffrey L. Duerk
Department of Biomedical Engineering
CASE WESTERN RESERVE UNIVERSITY
January 14, 2005
CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the dissertation of
Christopher Alan Flask
______________________________________________________
candidate for the Ph.D. degree *.
Jeffrey L. Duerk
(signed)_______________________________________________
(chair of the committee)
Robert Kirsch
________________________________________________
David Wilson
________________________________________________
Robert Brown
________________________________________________
Jonathan Lewin
________________________________________________
________________________________________________
Oct 25, 2004
(date) _______________________
*We also certify that written approval has been obtained for any
proprietary material contained therein.
I grant to Case Western Reserve University the right to use this work, irrespective of any
copyright, for the University’s own purposes without cost to the University or to its
students, agents and employees. I further agree that the University may reproduce and
provide single copies of the work, in any format other than in or from microforms, to the
public for the cost of reproduction.
To Vaishali:
Through the best times and the worst times, you are and will always be, the greatest love
of my life. Thank you for everything.
To Leena:
You are the daughter I have forever dreamed of. I can only hope to give you the love,
patience, and understanding that you have given to me.
To Baby
May the joy you bring match the happiness you have brought us already. Stay
warm for the winter while you can.
Table of Contents
Table of Contents
1
List of Tables
5
List of Figures
6
Acknowledgements
8
List of Abbreviations
9
Abstract
11
Chapter 1: Introduction
13
1.1 MRI Pulse Sequences
13
1.2 K-Space Sampling
15
1.3 Pulse Sequence Optimization
17
1.4 Parallel Imaging
19
1.5 Fat Suppression in MRI
20
1.6 Overview of Dissertation
24
1.6.1 Keyhole Dixon Acquisition
24
1.6.2
Radial 1-Point Dixon
24
1.6.3
Rectilinear 1-Point Dixon
25
1.6.4
Time-optimal 2-Point Dixon Acquisitions
26
1.6.5
Subjective Image Ratings
26
1.6.6
Future Work
26
Chapter 2: Keyhole Dixon
27
27
2.1 Background
1
2.2 Materials and Methods
28
2.2.1
Keyhole Dixon Acquisition of Fat/Water Phantoms
28
2.2.2
Perceptual Difference Model and Human Observer Studies
30
2.2.3
Clinical Image Evaluation with the PDM
33
34
2.3 Results
2.3.1
Keyhole Dixon Phantom Results
34
2.3.2
Perceptual Difference Model and Human Observer Studies
35
2.3.3
Phantom and Clinical Image Evaluation with the PDM
37
42
2.4 Discussion
Chapter 3: Radial 1-Point Dixon
47
3.1 Background
47
3.2 Materials and Methods
49
3.2.1
Sequence Development
49
3.2.2
Phantom and Clinical Images
49
3.2.3 Radial Point Spread Function Analysis
50
51
3.3 Results
3.3.1
Phantom and Clinical Images
51
3.3.2
Point Spread Functions (PSFs)
53
3.4 Discussion
55
Chapter 4: Rectilinear 1-Point Dixon (LEENA)
60
4.1 Background
60
4.2 Materials and Methods
62
4.2.1
Conventional FISP Sequence and Coil Sensitivity Maps
2
62
4.2.2
Rectilinear 1PD Trajectory - LEENA
63
4.2.3 LEENA Image Reconstruction
64
4.2.4
65
Off-Resonance Correction (ORC)
4.2.5 Phantom and Volunteer LEENA Images and CNR Analysis
66
4.3 Results
66
4.4 Discussion
71
Chapter 5: Time-Optimal 2PD Pulse Sequences
75
5.1 Background
75
5.2 Materials and Methods
76
5.2.1
Genetic Algorithm
76
5.2.2
2-Point Dixon True FISP Pulse Sequence
77
5.2.3
Imaging Applications
80
5.3 Results
80
5.3.1
2-Point Dixon True FISP Optimization
80
5.3.2
Pareto-Optimal 2-Point Dixon Images
83
84
5.4 Discussion
Chapter 6: Subjective Rating Comparison of LEENA and 2PD Images
89
6.1 Background
89
6.2 Materials and Methods
90
6.2.1
Experimental Design
90
6.2.2
Human rating Procedures
93
6.2.3
Statistical Analysis of Ratings
96
6.3 Results
97
3
6.3.1
Rating Data Normalization
97
6.3.2
Fat Suppression Rating Statistical Analysis
99
6.3.3
Resolution Rating Statistical Analysis
101
6.4 Discussion
102
107
Chapter 7: Radial 1-Point Dixon
7.1 Summary
107
7.1.1 Specific Aim #1: Keyhole Dixon
108
7.1.2 Specific Aim #2: Radial 1PD
109
7.1.3 Specific Aim #3: Rectilinear 1PD (LEENA)
110
7.1.4
111
Specific Aim #4: Time-Optimal 2PD Acquisitions
7.2 Preclinical Research – Metabolic Syndrome
112
7.3 High Field MRI – Single Shot Acquisitions
115
7.4 Dixon Flow Suppression
117
7.5 Conclusions
119
Appendix A
120
Appendix B
122
Bibliography
124
4
List of Tables
Table 2.1:
PDM Optimization Results of Keyhole Dixon Images
Table 7.1
Summary of rapid fat suppression techniques
5
List of Figures
Figure 1.1: Gradient echo pulse sequence diagram
Figure 1.2: K-space trajectories
Figure 2.1: Keyhole Dixon trajectory
Figure 2.2: Phantom images from Keyhole Dixon trajectory
Figure 2.3: PDM analysis of Keyhole Dixon images
Figure 2.4: PDM curves for phantom and clinical Keyhole Dixon images
Figure 2.5: Phantom Keyhole Dixon images
Figure 2.6: Axial knee Keyhole Dixon images
Figure 2.7: Axial optic nerve Keyhole Dixon images
Figure 2.8: Axial abdominal Keyhole Dixon images
Figure 3.1: Schematic of Radial Dixon trajectories
Figure 3.2: Phantom radial 1PD and 2PD images
Figure 3.3: Orbit and abdominal radial 1PD and 2PD images
Figure 3.4: Radial Point-Spread-Functions (PSFs) for 1PD and 2PD trajectories
Figure 4.1: Schematic of SENSE algorithm
Figure 4.2: Coil sensitivity map images
Figure 4.3: Radial and rectilinear 1PD trajectories
Figure 4.4: LEENA phantom images
Figure 4.5: CNR measurements of LEENA acquisition
Figure 4.6: Abdominal LEENA and 2PD images
Figure 4.7: Schematic of combined LEENA/SMASH algorithms
Figure 5.1: Schematic of single-echo and dual-echo True FISP pulse sequences
6
Figure 5.2: Timing parameters for gradient lobes used in genetic algorithm
Figure 5.3: Pareto-optimal curves for dual-echo True FISP pulse sequence
Figure 5.4: Example optimized dual-echo pulse sequences
Figure 5.5: Axial abdominal images from single-echo and dual-echo sequences
Figure 5.6: Axial optic nerve images from single-echo- and dual-echo sequences
Figure 6.1: Experimental design for fat suppression ratings
Figure 6.2: Experimental design for resolution ratings
Figure 6.3: Example fat suppression rating slide
Figure 6.4: Example resolution rating slide
Figure 6.5: Qualitative and quantitative rating scales
Figure 6.6: Plot of raw ratings scores
Figure 6.7: Plot of normalized rating scores
Figure 6.8: Plot of mean fat suppression rating as a function of acquisition method
Figure 6.9: Plot of mean resolution rating as a function of acquisition method
Figure 7.1: Lipid distribution extracted from MRI images of a mouse model of
metabolic syndrome
7
Acknowledgements
I would like to thank our entire MRI research group for their gracious support over the
past 5 years. It is their willingness to share their valuable insight that has made my PhD
research such an outstanding experience. I would also like to extend a personal thanks to
Jeff Duerk for completely supporting Vaishali, me, and Leena in our adoption process.
8
List of Abbreviations
1D
one dimensional
2D
two dimensional
3D
three dimensional
4D
four dimensional
1PD
1-Point Dixon
2PD
2-Point Dixon
ADC
analog to digital converter
BW
bandwidth or bandwidth/pixel
c1PD
Cartesian 1-Point Dixon
c2PD
Cartesian 2-Point Dixon
CNR
contrast to noise ratio
CT
computed tomography
DCE
Dynamic Contrast Enhancement
DFT
discrete Fourier transform
DSCQS
double stimulus continuous quality scale
EPI
echo planar imaging
FA
flip angle
FFT
fast Fourier transform
FISP
fast imaging with steady-state free precession
FLASH
fast low-angle shot
FOV
field of view
FT
Fourier transform
9
GA
genetic algorithm
iMRI
interventional magnetic resonance imaging
MR
magnetic resonance
MRI
magnetic resonance imaging
NSGA
non-dominated sorting genetic algorithm
PNS
peripheral nerve stimulation
r1PD
Radial 1-Point Dixon
r2PD
Radial 2-Point Dixon
RF
radio frequency
ROI
region of interest
SAFE
stimulation approximation by filtering and evaluation
SAR
specific absorption rate
SNR
signal to noise ratio
SPIDER
steady-state projection imaging with dynamic echo-train readout
T1
longitudinal relaxation time
T2
transverse relaxation time
T2*
transverse relaxation time for gradient echo acquisitions
TE
echo time
TR
repetition time
10
Rapid Dixon Acquisitions for Water / Lipid Separation in MRI
by
Chris A. Flask
Abstract
The main limitation of current lipid/water suppression techniques in MRI is that
these methods significantly increase the overall acquisition time of the particular
sequence. For example, the multi-point Dixon methods utilize multiple acquisitions at
different echo times to algebraically calculate separate fat and water images. Extended
acquisition times result in an undesirable increase in respiratory and cardiac motion
artifacts.
Rapid acquisitions also reduce the duration of and potential errors in
interventional MRI procedures thereby reducing the overall risk to the patient. In this
work, rapid acquisition and image reconstruction techniques were developed to improve
the temporal resolution of the conventional 2-Point Dixon (2PD) method for lipid / water
separation.
A Keyhole Dixon acquisition was developed by combining a full K-space
acquisition with a partial (i.e., keyhole) K-space acquisition. The number of acquired
views for the centrally-symmetric keyhole acquisitions was optimized with a perceptual
difference model (PDM) to sufficiently oversample the central region of K-space. The
11
Keyhole Dixon technique resulted in a 25-38% reduction in the overall acquisition time
relative to the 2PD acquisition for phantom and volunteer imaging studies with
perceptual change in image quality.
Radial and rectilinear 1-Point Dixon (1PD) acquisitions were developed by
applying the Dixon echo time variation between even and odd K-space lines. The
oversampling of the central region of K-space inherent in radial acquisitions produced fat
and water images from a single acquisition.
For the rectilinear 1PD acquisition, a
SENSE-like parallel imaging technique was used to separate the on-resonance water
signal from the off-resonance lipid signal. Both 1PD acquisitions resulted in a 50%
reduction in the 2PD acquisition time with comparable spatial resolution.
A genetic algorithm (GA) was used to create time-optimal 2-Point Dixon pulse
sequences. The GA produced a Pareto-optimal series of pulse sequences at varying fieldof-view (FOV) and readout bandwidth with the combined constraints of both gradient
hardware and a vendor-specific peripheral nerve stimulation (PNS) model. The genetic
optimization resulted in a 10-15% reduction in acquisition time in comparison to a
standard dual-echo pulse sequence and a ~50% reduction in comparison to a single-echo
2PD acquisition.
12
Chapter 1
Introduction
MRI is one of the most important medical imaging modalities with modern
scanners available in virtually all hospitals and some satellite clinics. MRI scanners were
created by combining the physical chemistry principles of Nuclear Magnetic Resonance
(2) with the spatial encoding capabilities provided by magnetic field gradient coils (3).
The molecular-level principles underlying the creation, manipulation, and detection of the
MRI signal creates a modality with inherent sensitivity to many physical parameters
including magnetic relaxivity, susceptibility, motion, flow, chemical shift, magnetization
transfer, and other physical quantities (2,4). This breadth of sensitivities is a key feature
in the utility of MRI for a wide variety of clinical and research imaging applications.
1.1 MRI Pulse Sequences
With such a wide range of sensitivities, it is necessary to maximize the sensitivity
of a particular acquisition to the parameter(s) of interest while minimizing the sensitivity
to other potentially confounding parameters.
Failure to do so could result in an
inaccurate diagnosis or an unacceptable increase in the level of image artifacts. This
control of the MRI acquisition sensitivity is obtained through an acquisition design
algorithm known as a pulse sequence (Fig. 1.1). The objective of the pulse sequence is to
control the evolution of the magnetization that is generated by the static magnetic field
(B0) and controls three main functions of the scanner: a radiofrequency (RF) excitation
pulse, linear magnetic field gradients, and signal detection. The temporal arrangement of
the various pulse sequence components results in the desired contrast in the acquired
signal.
13
TR
TE
Radio Frequency
Excitation Pulse
Linear Gradient Field (Gx)
Linear Gradient Field (Gy)
ADC
Fig. 1.1: Generalized pulse sequence diagram showing a gradient-recalled echo
(GRE) sequence which illustrates the three main components of all MRI pulse
sequences: RF excitation pulse, linear magnetic field gradients, and the signal
detection switch (ADC). Also shown are the relevant timing parameters: the
repetition time (TR) and echo time (TE).
The RF excitation pulse results in a set of “excited” spins. All or a portion of
these spins collectively form a macroscopic transverse magnetization perpendicular to B0.
The transverse magnetization oscillates, or precesses in the main magnetic field at a
frequency (ω0) proportional to the product of the main magnetic field (B0) and the
gyromagnetic ratio (γ) of the nucleus of interest (Eq. 1.1).
ω0 = γ B0
(1.1)
This time-varying magnetic field generates the MRI signal as a voltage in induced in a
receiver coil placed near the source of the transverse magnetization.
The three
orthogonal and independent magnetic field gradients superimpose an additional magnetic
field on B0 that varies linearly in the direction of the gradient. These gradients provide
14
the spatial encoding required which mathematically assigns the transverse magnetization
to individual voxels in the final image. The final part of a pulse sequence is an analog-todigital (ADC) switch that instructs the receiver chain to begin acquiring the MRI signal.
1.2 K-Space Sampling
The MRI signal produced by the pulse sequence is sampled and demodulated by
the MR receiver chain.
This raw, complex MRI data is a sampling of the spatial-
frequency domain of the acquired image known as K-space (Fig. 1.2).
(b)
(a)
(c)
ky
ky
ky
kx
kx
kx
Fig. 1.2: K-space sampling trajectories. (a) Conventional rectilinear (Cartesian), (b)
radial, and (c) spiral acquisitions. Note the increased sampling of the radial and spiral
trajectories near the center of K-space.
The low spatial frequencies (center of K-space) contain information about the image that
is slowly varying from voxel-to-voxel in the image, including basic contrast. On the
other hand, high spatial frequencies (edges of K-space) contain information about edges
and other fine structures in the image. In a conventional rectilinear acquisition, K-space
15
is sampled one line at a time in a rectilinear fashion (Fig. 1.2a). An Inverse Fourier
Transform (IFT) is then applied to the k-space data transform the complex data set to
image space. Movement in k-space is performed with the magnetic field gradients
applied during the pulse sequence, and the sampling path is called the k-space trajectory.
The relationship between the k-space position and the gradient waveform is given in
Equation 1.2.
t r
r
k (t ) = γ ∫ G (t )dt
(1.2)
0
The rectilinear sampling pattern described above is the most common trajectory.
Other notable trajectories include radial (Fig. 1.2b), and spiral trajectories (Fig. 1.2c).
These trajectories offer different advantages that make each better suited to particular
imaging applications. Rectilinear trajectories offer a simple implementation and image
reconstruction process as described above since the data are already aligned to a grid-like
pattern. However, rectilinear sampling is also sensitive to flow and motion artifacts.
Radial trajectories have been shown to be less sensitive to motion than rectilinear
acquisitions (2,5,6), and spiral trajectories are relatively insensitive to motion and flow
artifacts because of their gradient moments (7). One drawback is that these trajectories
require a more complex image reconstruction process since the data are not sampled
along a Cartesian grid. Fortunately, many efforts have been put into developing fast
image reconstruction algorithms for non-rectilinear trajectories (8,9).
One interesting feature of spiral, radial, and rosette trajectories is that the low
spatial frequencies of k-space are sampled multiple times (oversampling). This results in
an effective averaging of the data acquired at the k-space center. This can have negative
consequences such as blurring artifacts if patient motion occurs between sampling
16
periods. However, this feature can also be advantageous if used to cancel signal from
off-resonance signal components such as lipids (10). Oversampling of the low spatial
frequencies normally does not occur in rectilinear sampling. In this case, the k-space
lines near ky=0 must be resampled in order to achieve the same averaging effect (11).
Other major differences between rectilinear and non-Cartesian sampling
trajectories are properties associated with undersampling.
Violation of the Nyquist
criterion shown in Equation 3 below results in aliasing artifacts which are manifest
depending on the sampling trajectory.
∆k ≤ 1/L
(1.3)
where ∆k is the maximum difference between adjacent data points in K-space and L is
the size of the object in the image. For rectilinear sampling, the aliased portion of the
image is folded back onto other portions of the image, oftentimes rendering the image
unusable. For radial and spiral acquisitions, the aliasing artifacts are more diffuse and
take the form of streak and spiral blurring artifacts, respectively (12). Because of this
feature, acceptable images with limited aliasing artifacts can still be obtained from
undersampled non-Cartesian trajectories potentiating further reductions in acquisition
time (6).
1.3 Pulse Sequence Optimization
Current pulse sequence design techniques rely on the skill and expertise of the
developer and a few simple heuristic rules derived from the collective years of
experience.
The majority of pulse sequence optimization routines were developed
primarily to maximize desired contrast or the signal-to-noise ratio (SNR) of a particular
acquisition (13-16). Other sequence optimization studies were focused on selecting the
17
best time for beginning the acquisition following bolus administration of an exogenous
contrast agent (17-19).
For many MRI applications, one of the primary concerns is the temporal
resolution of the imaging sequence. For diagnostic imaging applications, acquisition
speed is important in order to reduce respiratory and cardiac motion artifacts (20-23).
Faster imaging sequences improve interventional procedures by allowing real-time
monitoring and positioning of surgical devices (24,25). Optimization of the timing of a
particular sequence normally involves minimization of RF excitation and magnetic field
gradient durations that result in a reduced sequence repetition time.
For modern scanners equipped with rapid steady-state and EPI pulse sequences,
the acquisition speed is no longer limited by the gradient and RF excitation hardware.
The acquisition speed of the majority of fast acquisitions is now limited by peripheral
nerve stimulation (PNS) and Specific Absorbed Radiation (SAR) limits instituted by the
US Food and Drug Administration (26-28).
These safety limits are enforced by
analytical safety models active on all clinically-approved MRI scanners and can prohibit
the implementation of pulse sequences with rapid gradient switching and/or excessive RF
power deposition. In general, these analytical safety models are manufacturer-specific
and can involve numerous parameters and calculations and are dependent on the
orientation of the imaging slice (29). With this degree of complexity, developing a timeoptimal pulse sequence can become extremely difficult and normally involves an
extensive trial-and-error effort.
18
1.4 Parallel Imaging
Parallel imaging is a unique approach to dramatically reducing acquisition time in
MRI; these methods circumvent the limitations provided by conventional gradient and
RF hardware as well as the PNS and SAR safety systems. Parallel imaging relies on
known spatial sensitivity patterns of phased array coils to reconstruct images with
reduced k-space lines (30-38).
SiMultaneous Acquisition of Spatial Harmonics
(SMASH) and SENSitivity Encoding (SENSE) are the two primary parallel imaging
techniques in MRI. SMASH imaging is a K-space parallel imaging method where the
coil sensitivity profiles are combined into spatial harmonics that allows multiple lines of
K-space to be acquired during each readout period . SENSE was developed to “unalias”
images acquired with reduced FOVs (increased ∆k) using measured coil sensitivity
profiles (39,40). SMASH and SENSE have both been implemented with rectilinear
trajectories for a wide variety of clinical applications (41-44).
For non-Cartesian
trajectories, however, the SENSE algorithm is more completely developed (45). The
main disadvantage of parallel imaging techniques is a decrease in SNR due to the reduced
number of encoding lines as well as noise amplification caused by the parallel imaging
calculations.
A number of variations of the SENSE and SMASH techniques have been
developed over the past 4-6 years (35,46-49). These methods improve upon the basic
SENSE and SMASH techniques by reducing artifacts for a given reduction factor. One
of these methods developed by Kellman and McVeigh (47) uses the SENSE approach
with full FOV imaging to correct for ghosting artifacts in Echo-Planar Imaging (EPI).
19
This technique focuses on the correction of ghosting artifacts from off-resonance spins
and assumes that motion and flow have been compensated for during the acquisition.
Off-resonance spins precess at a frequency different from that of the main
magnetic field (ωo). This frequency difference is established by spatial inhomogeneities
in the magnetic field as well as local material properties such as chemical shift and
magnetic susceptibility.
The ability of the Kellman and McVeigh technique to
appropriately deal with off-resonance in EPI sequences makes it a possible tool for
improving image quality in rapid, multi-echo acquisitions.
1.5 Lipid / Water Separation in MRI
The capability to produce images with either the lipid or water signal suppressed
is an important component on all modern MRI scanner systems. Suppression of either
the lipid or water signal increases the conspicuity of a wide variety of anatomic and
pathologic structures that would otherwise be obscured (50-52). The need for selective
suppression / off-resonance correction (ORC) is especially critical in rapid imaging
applications.
Effective tissue suppression leads to decreased blurring (improved
resolution) in spiral acquisitions (53,54) and decreased ghosting artifact in both echoplanar imaging (EPI) and multi-echo rectilinear acquisitions .
Several lipid / water suppression techniques are based on the use of specialized
radio-frequency (RF) excitation pulses.
The first of these types of methods is the
inversion recovery pulse sequence (55,56). An initial 180° excitation pulse inverts the
longitudinal magnetization of both fat and water spins from the +z axis to the –z axis. At
this point, the longitudinal magnetizations relax back towards their equilibrium levels.
However, adipose tissues have faster relaxation rates (shorter T1) than water-based tissue
20
structures (57). As a result, the fat longitudinal magnetization reaches the null-point
(zero longitudinal magnetization) while the water longitudinal magnetization has partially
relaxed but is still aligned along the –z axis.
Application of a slice-selective RF
excitation pulse at this inversion time (TI) results in nutation of only the water spins.
Alternatively, the inversion time can be selected to null the water spins resulting in a fatonly image.
Inversion recovery sequences rely solely on the T1 differences between fat and
water and are therefore insensitive to field inhomogeneities. However, the inversion
pulse is typically applied prior to each excitation and requires a 100-200ms inter-pulse
delay to allow the fat magnetization to reach the null-point. This results in a large
increase in the overall acquisition time. These methods also suffer from a decreased SNR
since the magnitude of the water magnetization has decreased as it has partially relaxed
towards the null-point as well.
Another major difference in the magnetic properties of fat and water spins is their
resonant frequency. Because the water protons are relatively electron-poor (de-shielded)
as compared to fat protons due to the high electronegativity of oxygen atoms, water
proton spins experience a higher main magnetic field than fat proton spins and therefore
precess at a higher frequency (3.5ppm = 220Hz at 1.5T).
Chemical shift selective
excitation pulses (58,59) are designed with a limited bandwidth (longer duration, 10ms @
1.5T) to selectively excite either fat or water spins. Binomial excitation schema also
utilize the frequency difference between fat and water spins for fat suppression / water
excitation (60,61). Here, a series of short, non-selective, rectangular pulses are applied
with specific tip angles and interpulse spacing resulting in a net water excitation / fat
21
suppression. Spatial-spectral excitation pulses (SPSP) replace the non-selective pulses of
binomial excitations with slice-selective excitation pulses to provide spatial selectivity as
well as spectral selectivity (60-63). The only major difference between binomial and
SPSP excitation schema is the RF pulse envelope for the individual pulses and
application of slice-select gradients. Binomial / SPSP pulses typically employ 3-4 pulses
with a significant inter-pulse delay (2.2ms at 1.5T) which will also extend the acquisition
time similar to the CHESS pulse. These frequency selective excitation pulses are much
shorter than the inversion times in the inversion recovery method, but can still
significantly extend the TR for short TR pulse sequences (i.e, True FISP, TR=3-5ms). In
general, longer pulses achieve better spectral selectivity but with an equal increase in
acquisition time. These methods are typically sensitive to field inhomogeneities, and
longer pulses result in additional signal loss because of T2* relaxation.
Another lipid / water suppression technique that makes use of the spectral
difference between fat and water spins are the multi-point Dixon techniques (64-66).
Here, multiple acquisitions of k-space are repeated with different echo times.
The
simplest Dixon technique, 2-Point Dixon (2PD), acquires two complete k-space data sets
where the fat magnetization in the second acquisition is 180° out-of-phase relative to the
first acquisition at the respective echo times (65). If magnetic field inhomogeneities are
negligible, separate and distinct water and fat images are obtained by simple addition or
subtraction of the complex raw data sets prior to image reconstruction.
When field inhomogeneities become larger, the original 2PD method fails and fat
suppression and water excitation in the water image is non-uniform. This is the case for
many clinical applications where global shimming algorithms cannot completely
22
compensate for local field variations. Higher order Dixon methods such as 3PD or 4PD
were developed to correct for these field inhomogeneities (and also susceptibility artifacts
(66)), but these methods require additional acquisition time relative to 2PD.
More
recently, image reconstruction algorithms have been developed to correct for field
inhomogeneities from only two full acquisitions (64). While this method is faster than
3PD or 4PD, two full acquisitions are still required resulting in a doubling of the
acquisition time relative to a typical acquisition with both fat and water signal.
Additional fat / water separation techniques are being developed that generate
water and fat images from a single steady-state progression (67-70). These methods
incorporate RF modulation techniques (i.e., phase and/or tip angle modulation) to achieve
fat suppression in steady-state free precession (SSFP) sequences. These techniques offer
opportunities for dynamic imaging applications where multiple contrasts are required for
comparison. However, these multiple contrasts still extend the overall imaging time as
multiple, interleaved TR’s are needed to establish and maintain the desired steady-state
conditions.
The main limitation of the aforementioned suppression / separation techniques is
an increase in the overall acquisition time. Most of these methods rely on specialized
excitations to provide the desired image contrast. These methods are typically sensitive
to field inhomogeneities and restrict the timing of the excitation pulses to obtain the
tissue selectivity. The multi-point Dixon methods do not require a spectrally-selective
excitation which results in fewer SAR constraints. In addition, algorithms have been
developed to correct for off-resonance artifacts in the Dixon acquisitions (54,71-74).
These advantages increase the utility of the Dixon techniques on high-field systems
23
where SAR limitations and susceptibility artifacts are more problematic (75). The main
limitation of the Dixon methods is the requirement for multiple acquisitions which can
lead to motion artifacts in certain imaging applications.
1.6 Overview of Dissertation
This study will focus on expanding the usefulness of the Dixon methods for use in
rapid imaging applications. This work was initiated with four specific aims in mind. The
organization of the remainder of the dissertation roughly parallels this structure.
1.6.1 Keyhole Dixon Acquisition
Chapter 2 describes a modified rectilinear 2-Point Dixon acquisition where one of
the two acquisitions is truncated. The truncated, or keyhole, acquisition samples only the
central K-space lines while the other acquisition samples the full set of k-space lines as in
a conventional acquisition.
Sampling only a small number of k-space lines (small
keyhole width) improves the acquisition speed but results in poor suppression and
increased truncation artifacts (Gibbs’ ringing, (76)). Larger keyholes provide improved
image quality at the expense of increased acquisition time.
Image analysis and
optimization of the number of lines in the keyhole acquisition with the assistance of a
perceptual difference model (PDM) reveals an opportunity to reduce the acquisition time
of the 2-Point Dixon acquisition with minimal effect on overall image quality.
1.6.2 Radial 1-Point Dixon (1PD)
Chapter 3 details the development of a single radial acquisition where the echo
time (TE) of successive K-space projections is alternated between the two echo times
used in a typical 2-Point Dixon acquisition. The oversampling at the central K-space
region inherent in radial trajectories produces the desired water / lipid contrast. This
24
efficient trajectory halves the acquisition time for a given image resolution since the same
lines of k-space do not have to be resampled as in a typical 2-Point Dixon acquisition
(65).
1.6.3 Rectilinear 1-Point Dixon
Chapter 4 covers the adaptation of the radial trajectory described in chapter 2 to a
rectilinear trajectory. The lack of oversampling at the center K-space in rectilinear
trajectories eliminates the fat suppression contrast provided by the radial 1PD trajectory
described in chapter 3. Instead of fat suppression, echo-shifting between alternating
rectilinear K-space lines results in ghosting artifacts common in multi-echo acquisitions
such as non-interleaved segmented EPI.
The ghosting artifact is caused by phase
variation as a function of K-space line caused by off-resonance spins (fat).
An effective method for correcting echo-shifting related ghosting artifacts was
described by Kellman and McVeigh (47). Their method was used to eliminate the
ghosting artifact and restore the off-resonance ghosts to their proper location in the
corrected image. This method uses a SENSE-like algorithm to transform images with
ghosting artifacts from multiple receiver coils to mathematically determine the ghosted
and unghosted portions of a combined image.
In this study, the ghost correction
algorithm was modified and expanded to produce separate water (fat-suppressed) and fat
(water-suppressed) images. Like the radial 1PD trajectory, this new acquisition reduces
the acquisition time of the 2-Point Dixon acquisition by 50%. Use of the rectilinear 1PD
trajectory also offers the advantage of higher SNR/time and no gridding algorithm as
compared to the radial 1PD acquisition.
25
1.6.4 Time-optimal 2-Point Dixon Acquisitions
Chapter 5 describes a method to produce time-optimal pulse sequences taking the
PNS and/or SAR safety limits into account. PNS stimulation limits frequently limit the
gradient slew rates and amplitudes for rapid acquisitions such as True-FISP (Fast
Imaging with Steady-state free Precession) pulse sequences. A multi-objective genetic
algorithm (MOGA) was employed to create sets of pareto-optimal 2PD pulse sequence
designs that do not violate the stimulation limits. Optimized rectilinear 2PD True FISP
sequences were designed and implemented on a Siemens Sonata 1.5T scanner. These
novel trajectories utilize unique gradient waveforms to reduce the overall acquisition
times without a tedious and exhaustive pulse sequence design approach.
1.6.5 Subjective Image Ratings
The images obtained in Chapter 5 were quantitatively evaluated for spatial
resolution, artifacts, SNR, and overall image utility. A series of expert image raters were
instructed to quantitatively compare the optimized rectilinear 1PD and rectilinear 2PD
phantom and volunteer images. The image ratings were then evaluated with a statistical
procedures similar to the methodology reported by the Radiocommunications Sector of
the International Telecommunications Union (ITU-R, (1)).
1.6.6 Future Work
A summary of this work is presented in Chapter 7, along with some speculations
on the future importance of this work and the directions that may prove most fruitful for
further investigations.
26
Chapter 2
Development of Keyhole 2-Point Dixon Acquisition
2.1 Background
As described in the introduction (Chapter 1), the conventional 2-Point Dixon
acquisition consists of two separate but similar acquisitions (65). Typically, only the
echo time is shifted between the acquisitions generating a relative phase difference for
off-resonance spins. The TE shift is achieved with a compensatory time-shift of the
readout, or frequency encoding, gradient pulses. However, the TE shift has no effect on
the k-space (kx, ky, kz) trajectory sampled during the acquisition.
This repetitive
sampling of k-space is temporally inefficient and suggests opportunities for
improvement.
In many interventional MRI applications, specific imaging slices are repetitively
acquired in order to visualize a minimally-invasive, surgical procedure such as stent
placement, tumor ablation, or biopsy. In these cases, the rapid, repetitive sampling of the
same k-space data is useful to track the incremental progress during the procedure. With
limited changes in successive images, small changes are expected for the k-space data as
well. Therefore, instead of resampling the entire k-space trajectory, a variety of viewsharing techniques were developed to decrease the number of acquired lines (views) for
successive acquisitions (77-79).
During an MRI-guided biopsy, for example, the
advancement of the biopsy needle can be accurately tracked by acquiring only a
centrically-symmetric portion (keyhole) of k-space (80,81). A complete k-space data set
is obtained by combining the newly acquired keyhole lines of k-space with the nonkeyhole lines from a previously-acquired reference acquisition. In this way, the images
27
are acquired more rapidly with an acceptable increase in edge blurring or other artifact
during the dynamic acquisition.
In this study, we sought to determine if the total acquisition time of the 2-Point
Dixon technique could be improved through the use of a variant of the keyhole
acquisition technique (82-86).
Specifically, we sought to determine if the total
acquisition time for the 2-Point Dixon method could be reduced by combining a keyhole
acquisition for one data set with a full acquisition for the second data set. Here, the
keyhole acquisitions always resample a centrically-symmetric portion of k-space sampled
in the full acquisition in order reproduce the desired fat suppression contrast from a
reduced-view acquisition. A perceptual difference model (PDM) was incorporated to
perform a differential comparison between the Keyhole Dixon and 2-Point Dixon images
(87,88).
2.2 Materials and Methods
2.2.1 Keyhole Dixon Acquisition of Water and Fat Phantoms
A typical FLASH (Fast Low Angle SHot) sequence was implemented on a 1.5T
Siemens Sonata scanner (Siemens Medical Solutions, Erlangen Germany) to obtain the
two K-space data sets of a typical 2-Point Dixon acquisition (TE = 6.6/8.8ms, matrix
size=192x256, TR=20ms, BW=250Hz/pixel, symmetric readout) for a phantom
consisting of water (saline) and fat (baby oil) containers. The two containers occupied a
field of view of approximately 18cm. The phantom was placed near isocenter of the
magnet. The sequence parameters (BW, slew rates, etc) were established to prevent the
gradient stimulation from being exceeded.
28
A series of 96 keyhole Dixon images was generated by combining centrally
symmetric portions (2,4,6...192 k-space lines) of the keyhole data set (TE=8.8ms) with
the complete data set (TE=6.6ms) in an algorithm similar to that described by Coombs et
al. (Fig. 2.1). The same image reconstruction method was implemented for each of the
keyhole images as well as the full 2-Point Dixon images (192-line keyhole). This
reconstruction technique (outlined below) was incorporated in order to limit the effects of
B0 inhomogeneities in the Keyhole Dixon and 2-Point Dixon images (89).
ky
ky
kx
Typical Acquisition
(TE1)
kx
Figure 2.1: Representation of
the K-space sampling used in
the Keyhole Dixon technique.
The shaded regions represent
the portions of K-space
sampled during the acquisitions
at two different echo times.
Note the unsampled (unshaded)
regions of K-space in the
Keyhole Acquisition
(TE2)
After zero-padding the keyhole K-space data set to 192 lines to match the
resolution of the two acquisitions, a 2D-Inverse Fourier Transform (2D-IFT) was applied
to transform the data to complex image space. The phase difference between the two
image sets (Φpd) was then calculated from Equation 2.1,
Φpd = Arg [ ( Iip • Iop*)2]
(2.1)
where Iip is the in-phase image data and Iop* is the complex conjugate of the out-of-phase
image data. A field inhomogeneity phase map (Φi) was then calculated by applying a 3x3
median filter to reduce noise in Φpd at tissue boundaries, unwrapping the phase with a
29
region-growing algorithm, and finally dividing the phase by 2. The separate water and
fat images for both the full 2-point Dixon and Keyhole Dixon methods were then
calculated from Equations 2.2a and 2.2b, respectively.
Water Image = Iop + exp(-i • Φi) • Iip
(2.2a)
Fat Image = Iop - exp(-i • Φi) • Iip
(2.2b)
2.2.2 Perceptual Difference Model (PDM) and Human Observer Studies
Each keyhole image was compared to the corresponding 2-Point Dixon image
using a PDM in order to determine the minimum number of k-space lines in the keyhole
acquisition required to generate a fat-suppressed image perceptually equivalent to the 2Point Dixon image. The PDM models the functional anatomy of the human visual
system. The PDM provides an objective means to quantify image quality that more
accurately reflects human perception than either contrast-to-noise ratio or mean-squarederror measurements.
PDM’s have a long and successful track record in image
processing, specifically image compression (90-92), and a number of medical imaging
and psychophysics related tasks, such as tumor detection (93,94), microcalcification
detection (95), and image display quality evaluation (96,97).
The model used here contains human visual system processing similar to the
Image Difference Model developed by Daly (98,99) and is designed to mimic the
functional anatomy of the visual pathway.
Grayscale non-linearity of the retina
(100,101), contrast sensitivity function (102), spatial frequency channels found in the
visual cortex (103), and a measure of the contrast and visual detection (104,105) are
among the components of the human visual system that are modeled by the PDM. For
this study, a version of the PDM was used that has been previously described and
30
validated in rapid MR imaging applications (87). These previous studies confirmed the
validity of using the PDM model for keyhole imaging techniques by comparing PDM
output with subjective human observer quality ratings for image degradations such as
blur and noise.
In this study, the PDM is provided with two images as inputs: a 2-Point Dixon
image and a Keyhole Dixon image. The output of the model is a two-dimensional PDM
error map representing the likelihood that a human observer will perceive a difference
between the two images at each pixel location. The mean PDM error in the region of
visual interest in the PDM error map is calculated to give a scalar PDM error score.
Three PDM / human observer experiments were performed using the water and
fat phantom Keyhole Dixon images. The first experiment, similar to previous work by
Salem et. al. (87) and Martens and Meesters (106), confirmed the correlation between
PDM scoring and human observer ratings of image difference. Three observers were each
shown a two-panel display containing a 2-Point Dixon phantom image and a Keyhole
Dixon phantom images randomly selected from the set of 96. The observers were asked
to give an image quality score (0-100, 100 = best) to the Keyhole Dixon image, using the
2-Point Dixon image as a reference with an assigned score of 80. The observers were
instructed that the 2-Point Dixon reference image would remain in view (left panel) and
that the Keyhole Dixon images (right panel) would be changed following each rating.
Ratings were obtained for each of the 96 Keyhole Dixon images. These image ratings
were subtracted from the assigned 2-Point Dixon score of 80 to quantify the perceived
differences between the 2-Point Dixon and Keyhole Dixon images. An error of 0
corresponded to no difference and a score of 80 corresponded to maximal degradation of
31
the Keyhole Dixon image. The raters were instructed to rate the Keyhole Dixon images
better than the 2-Point Dixon image (image rating > 80) if appropriate. In each of two
repeated experiments, the observers provided human observer scores for each of the 96
keyhole Dixon phantom images. The error scores were normalized to eliminate interobserver differences, and then averaged. The PDM was also used to analyze the same
image pairs and provide an overall PDM error score. PDM error scores were plotted
versus human observer error ratings, and linear regression was used to relate the PDM
and human error results.
The second experiment established a PDM error threshold below which human
observers perceive no difference between two images. In this experiment, three observers
were asked to classify each of the 96 Keyhole Dixon images as being either visually
equivalent or visually different from the 2-Point Dixon image. Again, observers were
presented with a two-panel display with the 2-Point Dixon image on the left and a
randomly selected Keyhole Dixon image on the right. In each experiment, all of the 96
Keyhole Dixon phantom images were presented and evaluated with respect to the
corresponding 2-Point Dixon image. Data were processed by calculating the percent of
observer responses for which the images were classified as being the same as a function
of the keyhole size. The data set was fit to the sigmoidal model shown below (Eq. 2.3)
using nonlinear least squares regression.
P = 1 / (1 + exp[-A*(x-B)])
(2.3)
In this equation, P is the probability of the Keyhole Dixon image being classified as the
same as the 2-Point Dixon image, A and B are model parameters, and x is the number of
lines acquired in the particular Keyhole Dixon image. The PDM error threshold for
32
equivalence was set as the PDM error score for the Keyhole Dixon image closest to
having a 50% probability of being classified as the same as the 2-Point Dixon image.
A third experiment focused on local PDM scores within the phantom. A regionof-interest (ROI) analysis was performed to generate individual PDM error scores for the
water and fat components of the phantoms. These were compared to the global PDM
error. All three PDM error scores (i.e., fat, water and global) were plotted as a function
of the number of K-space lines in the keyhole acquisition to determine the minimum
keyhole width (fewest k-space lines, fastest acquisition) needed to obtain perceptual
equivalence with the 2-Point Dixon image. Results also provide information about the
relative contributions of the water and fat phantoms to the global error and the minimum
keyhole width for perceptual equivalence.
2.2.3 Clinical Image Evaluation with the PDM
Clinical Keyhole Dixon images from three different anatomical locations (knee,
orbit, and abdomen) were also analyzed with the PDM for relevant comparison with the
phantom experiments described above. The FLASH sequence parameters were modified
slightly from those used in phantom trials (e.g., TR=100ms, Four averages of each
acquisition) to obtain clinically acceptable images at each location. The Keyhole Dixon
and 2-Point Dixon images were analyzed with the PDM as described above to determine
the amount of time-savings possible with undetectable differences in image quality using
the Keyhole Dixon fat suppression technique.
Each of the 96 Keyhole Dixon images was compared to the 2-Point Dixon image,
and a PDM analysis was performed as follows. PDM error scores were calculated in a
manually selected region of interest (ROI) encompassing the relevant clinical structures
33
for each application. PDM error scores were plotted as a function of the number of Kspace lines in the keyhole acquisition. The PDM threshold, as determined from the
previous phantom experiments, was applied to the data showing the possible time-savings
with the proposed technique in clinically-relevant imaging applications.
2.3 Results
2.3.1 Keyhole Dixon Acquisition of Water and Fat Phantoms
A subset of Keyhole Dixon phantom images and the reference 2-Point Dixon
phantom image are shown in Figure 2.2. The visual quality of the phantom keyhole
images improved with increasing keyhole width as the blurring and edge enhancement of
the fat phantom diminished.
Small keyhole widths (2-10 k-space lines) produced
excessive blurring of the fat phantom (Fig. 2.2a). The level of blurring decreased rapidly
as the keyhole width was increased, but edge enhancement/Gibbs artifacts remained on
the edges of the fat phantom perpendicular to the keyhole (Fig. 2.2b).
The water
phantom displayed a ringing artifact that also diminished as the keyhole width was
increased. All of these artifacts appeared to be eliminated with a keyhole width greater
than approximately 96/192 lines (50% keyhole, Fig. 2.2c) resulting in an image visibly
similar to the 2-Point Dixon image (Fig. 2.2d).
34
Water
Phantom
a
d
Fat
Phantom
b
c
Figure 2.2: Conventional FLASH
(a) and Keyhole Dixon images of
saline and baby oil phantoms. (b)
2/192 keyhole lines, (c) 32/192
keyhole lines, (d) 96 keyhole line (e)
reference 2-Point Dixon (192/192
keyhole lines). The image quality
increases monotonically as the
number of lines in the keyhole
acquisition increases.
e
2.3.2 Perceptual Difference Model (PDM) and Human Observer Studies
The PDM error scores obtained for the phantom Keyhole Dixon images in the
human observer studies displayed a good linear correlation with the human observer
visual ratings (R2 = 0.9083, Fig. 2.3a). For the visual threshold experiment, the nonlinear
least squares regression to fit the sigmoidal model resulted in a threshold keyhole width
of 96/192 K-space lines. This phantom Keyhole Dixon image corresponded to a PDM
score of 1.5 and was closest to having a 50% probability of being classified as the same
as the full 2-Point Dixon image based on the qualitative human observer ratings. A PDM
score of 1.5 was set as the PDM error threshold for perceptual equivalence in all the
clinical imaging experiments.
35
6
Water
5
R2 = 0.9083
3.5
PDM Model Error
PDM Model Error
4.5
2.5
1.5
Fat
Global
4
3
2
1
0.5
0
0
a
20
40
60
80
b
Human Observer Error Scores
0
40
80
120
160
200
Number of Keyhole Lines
Figure 2.3: Results of PDM Analysis on Keyhole Dixon phantom images. (a) Plot of
PDM error vs. Human Observer error ratings for 96 Keyhole Dixon images
demonstrating relationshipof the PDM to the human system. (b) Plot of PDM error
score as a function of the number of K-space lines in the keyhole acquisition for the
entire (global) phantom image as well as ROI’s encompassing the individual fat and
Plots of PDM error as a function of keyhole width showed that global phantom
image error decreases monotonically towards zero with increasing keyhole width as
expected (Fig. 2.3b). Note that a zero PDM error infers that the Keyhole Dixon image is
identical to that of the 2-Point Dixon image. The error from the global PDM analysis
(solid line) shows an initial sudden drop in PDM error followed by a steady decline in
PDM error as the keyhole width increased. In the ROI analyses, the errors associated
with the fat phantom were slightly smaller but still mirrored the global error results; they
were also somewhat smoother (small dashed line). The PDM errors associated with the
water phantom (dotted line) were smaller than the fat phantom errors especially for small
keyhole widths where the global errors were dominated by artifacts associated with the
fat phantom. Representative ROIs for the fat and water phantom are shown in Figure 2.5
below.
36
2.3.3 Phantom and Clinical Image Evaluation with the PDM
Reconstruction and analysis of the three clinical applications for keyhole Dixon
images resulted in minimum keyhole widths of 44-88 views, resulting in a 27-38%
reduction in total scan time (Table 2.1) with perceptual equivalence to the corresponding
2-Point Dixon image. The minimum keyhole widths for all three clinical applications
were smaller than the phantom threshold keyhole width. The PDM error curves for the
phantom and clinical images are shown in Figure 2.4. The Keyhole Dixon images
corresponding to three points along each PDM error curve were selected for
reconstruction and are shown in Figures 2.5, 2.6, 2.7, and 2.8, respectively. The 2-Point
Dixon image is also shown in each image set with the corresponding PDM ROI outlined
with a white dashed line. Keyhole Dixon images provided at four points along PDM
curves demonstrated that significant artifacts as compared to the 2-Point Dixon image are
observed for subthreshold keyhole widths (PDM scores > 1.5) while minimal artifacts are
observed for images with keyhole widths greater than the threshold for equivalence.
37
6
7
(a)
PDM Model Error
PDM Model Error
(a)
4
(b)
2
(c)
0
0
a
150
50
100
Number of Keyhole Lines
(d)
5
3
(b)
1
6
(b)
(c)
0
0
c
PDM Model Error
PDM Model Error
3
100
4
(b)
2
(c)
0
0
d
200
(a)
(d)
150
200
50
100
Number of Keyhole Lines
150
Number of Keyhole Lines
b
(a)
1
50
0
200
4
2
(d)
(c)
(d)
150
200
50
100
Number of Keyhole Lines
Figure 2.4: PDM Curves for phantom and clinical Keyhole Dixon images. Selected
Keyhole Dixon images representing points along each PDM curve are shown in
Figures 2.5, 2.6, 2.7, 2.8 respectively.
38
Table 2.1
PDM Optimization Results of Keyhole Dixon Images
Image Type
Threshold
Keyhole Width
% Reduction in
Acquisition time
Phantom
96/192
25%
Knee
88/192
27%
Orbit
44/192
38%
Kidney
50/192
37%
a
a
d
b
c
e
Figure 2.5: Conventional FLASH (a) and Keyhole Dixon images of saline and baby
oil phantoms. Keyhole Dixon images of fat and water phantoms with (b) 2, (c) 80, and
(d) 100 lines are shown in comparison to the full 2-point Dixon image (e). These
images correspond to points a-d on the PDM curve shown in Figure 2.4a.
39
a
b
c
d
Figure 2.6: Reconstructed keyhole Dixon images of a volunteer's knee with (a) 40,
(b) 70, and (c) 100 lines corresponding to PDM error scores of 5, 2, 1, respectively,
are shown in comparison to the full 2-point Dixon image (d). These images
correspond to points a-d on the PDM curve shown in Figure 2.4b.
40
a
b
c
d
Figure 2.7: Reconstructed keyhole Dixon images of a volunteer's orbit with
(a) 2, (b) 20, and (c) 50 lines corresponding to PDM error scores of 3.7, 1.7,
and 1.3, respectively are shown in comparison to the full 2-point Dixon image
(d). These images correspond to points a-d on the PDM curve shown in Figure
2.4c.
41
a
b
c
d
Figure 2.8: Reconstructed keyhole Dixon images of a volunteer's abdomen with (a) 2,
(b) 30, and (c) 70 lines corresponding to PDM error scores of 5.8, 1.9, and 1.2,
respectively are shown in comparison to the full 2-point Dixon image (d). These images
correspond to points a-d on the PDM curve shown in Figure 2.4d.
2.4 Discussion
In this study, a series of Keyhole Dixon images was generated by adjusting the
number of k-space lines acquired in one of the acquisitions of the 2-Point Dixon method.
A perceptual difference model of the human visual system was then used to measure the
difference that a human (e.g., radiologist) would perceive between the 2-Point Dixon
image and the faster Keyhole Dixon images (both with off-resonance correction). The
PDM was used to quantify the effectiveness of the Keyhole Dixon method by
42
determining the level of visually-detectable increases in artifacts relative to the 2-Point
Dixon image. The main advantage of the Keyhole Dixon method is that a 25-38%
reduction in the scan time of the 2-Point Dixon method can be obtained with no
perceived change in image quality and no additional RF energy deposition. A significant
reduction in acquisition time makes the Dixon techniques better suited for dynamic
imaging application, especially on high field MRI systems where SAR may limit the use
of spectrally selective RF excitation pulses.
The FLASH sequence used in this study was designed mainly to generate the
required 2-Point Dixon gradient-recalled echo (GRE) data sets with relatively short
acquisition times (4-20 sec). Because the sequence was designed primarily for short
acquisition time, less consideration was placed on SNR, resolution, field-of-view (FOV),
or contrast in the clinical images. The PDM thresholds may be affected by the image
contrast, SNR, etc., which can be altered through changes in pulse sequence parameters.
Other GRE pulse sequences (ex., True FISP), may offer significant advantages for
specific dynamic imaging applications and are adaptable to the Keyhole Dixon technique.
However, these other sequences were not considered during this study.
The keyhole acquisition strategy and reconstruction technique has previously
been shown to affect the quality of the keyhole images (107-110). Reconstruction of a
centrically symmetric keyhole data suffers from truncation and magnitude mismatch
artifacts that have been observed in this study for sub-threshold keyhole widths. It is
anticipated that applying more advanced keyhole techniques such as CURE, generalized
series reconstruction, or other hybrid techniques to the Keyhole Dixon method could
43
reduce the level of these artifacts and allow the threshold keyhole width to be further
reduced.
The PDM’s ability to accurately track image error as determined by a human
observer made it an excellent method for the objective assessment of image quality. The
objective assessment of a fat suppression technique is a difficult task. Common measures
of MRI image quality such as SNR or contrast-to-noise ratio (CNR) fail to account for
the spatial variations found by an actual human observer viewing the images. While a
high SNR or CNR is a general measure of image quality, it is difficult to define a
particular lower bound for SNR or CNR that corresponds to "adequate" fat suppression.
In addition, CNR is limited to basic measurements of signal amplitude for two tissues in
ROI's with uniform signal amplitude that do not account for other image features such as
edge enhancement, blurring, and ringing artifacts. The PDM, however, can detect and
quantify the differential artifacts in two images.
Selecting specific ROI’s for PDM analysis assisted in measuring the quality of the
keyhole images. The ROI's selected for the clinical images improved the sensitivity of
the PDM analysis by excluding both regions of the anatomy that were of little clinical
interest and background regions where only noise variations are observed. For the knee
images (Fig. 2.6), the ROI was selected to eliminate a large background signal where no
significant keyhole artifacts were visually detected. For the orbital images (Fig. 2.7),
much of the volunteer's head anatomy was eliminated by selecting a small ROI including
the optic nerves, extra-ocular muscles and globes. The ROI in the kidney images (Fig.
2.8) was selected to minimize the affects of respiratory motion in subcutaneous fat.
44
The threshold keyhole widths for the clinical images were smaller than that
required for the phantom images. One possible cause for this difference is that truncation
artifacts are easily visualized in phantoms with large uniform signal regions.
Alternatively, the reduction in threshold may be related to the sensitivity of the PDM to
artifacts either included in or excluded from the particular ROI. Regardless, the PDM
results show that the threshold keyhole width among the three clinical applications is
fairly consistent (27-38%, Table 2.1). In general, the PDM error approaches the PDM
threshold slowly, suggesting that there is only a small change in image error on either
side of the limit. Therefore, the PDM threshold is not necessarily a hard limit, but allows
some flexibility in determining an appropriate keyhole width for a particular imaging
application. However, the results shown here indicate that a nominal keyhole width of
40% of the second acquisition (30% timesavings overall) should provide a useful
compromise between speed and image quality for most clinical applications.
One limitation of the Keyhole Dixon method is that more than one acquisition of
portions of K-space are required to obtain fat (or water) suppression. At common field
strengths (ex. 1.5T), binomial and CHESS excitation provide suppression from a single
acquisition with a small increase in acquisition time (111,112). However, these water
excitation methods are limited to shimming techniques in order compensate for the
effects of field inhomogeneities. In addition, these specialized excitation pulses typically
increase the TR by ~5ms. For rapid steady-state acquisitions, a 5ms increase in TR can
more than double the overall acquisition time.
Another limitation of the Keyhole Dixon technique is that the number of acquired
views is significantly reduced resulting in a decrease in SNR/CNR of the final suppressed
45
images relative to the full 2-Point Dixon image. The PDM/human observer results shown
here indicated that the differences in SNR/CNR had little impact on the perceived quality
of the images. The same results may not be obtained for extremely low SNR/CNR
applications where further decreases in SNR/CNR are unacceptable.
In conclusion, the well-known keyhole acquisition strategy was extended to
improve the temporal resolution of the conventional Dixon methods.
Phantom and
clinical imaging results show that the acquisition time of one acquisition of the 2-Point
Dixon method can be reduced 25-38% with no perceptual difference in image quality.
The reduction in acquisition time improves the temporal resolution obtainable with the
Dixon techniques making them more useful for rapid imaging applications. B0
inhomogeneity correction was implemented on both the keyhole and full 2-Point Dixon
image sets and provided uniform fat / water separation for both the phantom and clinical
imaging applications. A perceptual difference model (PDM) was useful for quantifying
the difference between the Keyhole Dixon images and the reference 2-Point Dixon
images. The PDM improves on traditional methods for image comparison (e.g., CNR) by
including all perceivable artifacts including blurring and edge enhancement in the error
analysis.
46
Chapter 3
Development of Radial 1-Point Dixon Acquisition (r1PD)
3.1 Background
The Keyhole Dixon method described in Chapter 2 demonstrates the
inefficiencies of the repetitive K-space trajectories in the Dixon techniques. Specifically,
the Keyhole Dixon techniques demonstrate that fat / water contrast can still be achieved
by resampling only the low spatial frequencies (center) of K-space. As a result, the time
required to resample the high spatial frequencies (edges) of K-space in the conventional
2-Point Dixon technique is largely wasted time for the acquisition. The Keyhole Dixon
technique utilized these principles to reduce the 2-Point Dixon acquisition time by ~2540% depending on the imaging application. Chapters 3 and 4 extend these principles to
other K-space trajectories to reduce the acquisition time even further and to develop
techniques where the temporal resolution of the Dixon suppression techniques are less
dependent on the specific imaging application.
The Dixon techniques typically are implemented with a repetitive rectilinear
trajectory as described in Chapters 1 and 2. However, various non-Cartesian trajectories
offer significant advantages over rectilinear trajectories in terms of temporal resolution,
motion compensation, and aliasing properties.
One major advantage of the Dixon
methods is that practically any K-space trajectory can be adapted to these lipid / water
separation methods (53,54). All that is required is to resample K-space at different echo
times. An example of a radial 2-Point Dixon trajectory is shown in Figure 3.1a. This
trajectory offers the potential for motion compensation and other advantageous properties
of a radial acquisition (6,113). However, the radial 2-Point Dixon acquisition still suffers
47
from the relative sampling inefficiencies of the 2-Point Dixon method.
TE2
TE1
a
TE1
TE2
b
Figure 3.1: Schematics
of (a) radial 2-Point Dixon
(r2PD) and (b) radial 1Point
Dixon
(r1PD)
trajectories.
Different
echo times (TE1 and TE2)
are represented with solid
and
dashed
lines
respectively.
To improve the temporal efficiency of the 2-Point Dixon acquisition, we can take
advantage of the oversampling of the low spatial frequencies of K-space inherent in all
radial acquisitions. For a single radial acquisition, we can adjust the echo time for each
K-space projection to obtain phase variation in the fat magnetization.
This results in
nulling of the fat signal while the water signal is acquired as normal for a radial
acquisition.
This technique provides Dixon-like fat / water contrast from a single
acquisition resulting in a 50% reduction in acquisition time over the 2-Point Dixon
acquisition.
In this chapter, a new radial K-space trajectory was developed with
alternating echo times between even and odd K-space projections (Fig. 3.1b). This
48
trajectory provides a more efficient K-space sampling strategy than a conventional radial
2-Point Dixon (r2PD) acquisition. The effects of this Radial 1-Point Dixon (r1PD)
acquisition are described in detail.
3.2 Materials and Methods
3.2.1 Sequence Development
A radial 1-Point Dixon (r1PD) pulse sequence was developed from a radial True
FISP (Fast Imaging with Steady-State Free Precession, refs) sequence by applying
different TE’s between even and odd lines in radial K-space (α=70°, TR=8ms,
TE=3.1/5.3ms, BW=390Hz/pixel, 256 samples/projection, TH=3mm, Fig. 3.1b). The
sequence was implemented on a 1.5T Siemens Sonata MR scanner. The TE's were
selected to obtain 180° phase variation in the fat magnetization between the two echo
times (TE1 and TE2). A radial 2-Point Dixon sequence (r2PD) was also developed from
the same True FISP sequence for comparison (Fig. 3.1a). As in a conventional rectilinear
2PD acquisition, each projection in the r2PD trajectory was acquired twice along the
same K-space trajectory, one at each TE.
3.2.2 Phantom and Clinical Images
Phantom and clinical images were acquired with the r1PD and r2PD sequences.
The reconstructed images were visually inspected to compare the resolution of waterbased image components and the level of streak and blurring artifacts resulting from
azimuthal undersampling.
The contrast-to-noise ratio (CNR) was measured in the
phantom r1PD and r2PD images to quantify the level of fat suppression. The formula
used to determine the CNR is shown in Equation 3.1,
CNR =
(S
water
σ
49
− S fat )
back
[3.1]
where Swater and Sfat are the mean signal amplitudes of the water and fat phantoms,
respectively, and σback is the standard deviation of a background region of interest.
All images were reconstructed online with a fast, table-based griddingreconstruction algorithm with a 3x3 Kaiser-Bessel window (114). A measured trajectory
was used in the development of the gridding table to limit the amount of artifacts related
to gradient nonlinearities and gradient delays (115). For this initial investigation, offresonance correction to limit the effects of field inhomogeneities was not incorporated
into the reconstruction process of the r1PD or r2PD images. A 3D shimming algorithm
was applied prior to sequence implementation. The two r2PD rawdata sets (TE1 and TE2
in Fig. 3.1a) were summed prior to image reconstruction to produce the fat-suppressed
images while the single r1PD rawdata set was reconstructed as described above.
3.2.3 Radial Point-Spread Function Analysis
To better quantify the effects of azimuthal undersampling, point-spread functions
(PSFs) were also measured for the r1PD and r2PD sequences. As shown by Lauzon and
Rutt (116), more complete K-space coverage results in less streak artifact and also an
increased diameter of the primary ring-lobe in the PSF. As discussed above, the r1PD
sequence should provide a more temporally-efficient K-space coverage for the onresonance spins. Therefore, with half the total number of acquired projections, the PSF
from the r1PD sequence should theoretically provide a primary ring-lobe with the same
diameter as the r2PD sequence (compare Figures 3.1a and 3.1b).
To generate on-resonance (fat-suppressed) PSFs, a 3ml syringe (8mm ID) was
filled with saline and positioned with its long axis aligned with the main magnetic field.
It was placed near isocenter in the magnet to act as an approximation to a point signal
50
source for axially acquired images. The sequences were all executed with a 300mm FOV
/ TH=2mm for adequate visualization of the PSFs. The reconstructed images of the
saline syringe were considered an approximation to the actual K-space sampling PSFs.
Off-resonance PSFs were reconstructed by replacing the saline syringe with a syringe
filled with baby oil and repeating the above experiments.
The r1PD PSFs were
reconstructed as a single data set while the r2PD PSFs were generated by first summing
the two individual raw data sets prior to reconstruction.
3.3 Results
3.3.1 Phantom and Clinical Images
Phantom images from the r2PD and r1PD sequences are shown in Figure 3.2
(FOV = 400mm). The resolution of the water phantom in the 128-view r1PD image (Fig.
3.2a) is better than in the r2PD image with the same total number of acquired views (Fig.
3.2b). The resolution of the water phantoms in the 128-view r1PD image and 256-view
r2PD (Fig. 3.2c) are visibly equivalent. However, the 128-view r1PD image has an
increased level of artifact. The CNR measurements produced values of 101, 111, and
190 for the three phantom images in Figure 3.2, respectively. The small difference in
CNR between the two 128-line acquisitions (Fig. 3.2a,b) is primarily due to the increased
artifact level in the r1PD acquisition.
The large difference in CNR in the r2PD
acquisitions (Fig. 3.2b.c) is due to the difference in the number of acquired views as well
as aliasing artifacts from azimuthal undersampling.
51
b
a
Fat
Phantom
c
Water
Phantom
Fat
Phantom
d
Figure 3.2: Saline (water) and baby oil (fat) phantom images generated from r1PD (a)
and r2PD (b,c) sequences with (a,b) 128 and (c) 256 projections. The resolution of the
water phantom in the 128-view r1PD image is improved relative to the 128-view r2PD
image and approximately equal to the resolution in the 256-view r2PD image. A
conventional true FISP image is shown in (d) for comparison.
Clinical images of a healthy volunteer's orbit and abdomen are shown in Figure
3.3 below. For the clinical, 128-view r1PD images (Figs. 3.3a,d), the resolution of the
water-based tissue structures is improved and the level of streak artifact is decreased
substantially relative to the clinical r2PD images with the same total number of views
(Fig. 3.3b,e). When compared with the r2PD images with 256 views (Fig. 3.3c,f), the
resolutions are again essentially equivalent. As in the phantom images, the 128-view
r1PD image has a decreased signal-to-noise ratio (SNR) and an increased level of artifact.
52
a
b
c
d
e
f
Figure 3.3: Orbit (a,b,c) and abdomimal (d,e,f) images from a healthy volunteer
generated from the (a,d) 128-view r1PD, (b,e) 128-view r2PD, and (c,f) 256-view r2PD.
As in the phantom images, the resolution of the water structures (i.e., orbits, optic nerve,
vessels, kidneys) in the 128-view r1PD image is improved relative to the 128-view r2PD
image and approximately equal to the resolution in the 256-view r2PD image.
3.3.2 Point-Spread Functions (PSF)
The on-resonance PSFs from the r2PD and r1PD sequences are shown in Figure
3.4 for both 128 (Fig. 3.4a,b) and 256 projections (Fig. 3.4d,e).
As expected, the
diameter of the primary ring-lobe in the on-resonance r1PD PSF is twice that of the onresonance r2PD PSF with the same total number of acquired views. In addition, the 128view r1PD PSF indicates the same effective water resolution as the 256-view r2PD PSF.
As expected, these results demonstrate that the r1PD sequence provided more efficient kspace coverage as compared to the r2PD sequence for unsuppressed, on-resonance water
spins.
53
a
b
c
d
e
f
Figure 3.4: PSFs from r2PD (a,d) and r1PD (b,c,e,f) sequences with either 128 (a,b,c)
or 256 (d,e,f) total acquired projections. The r2PD sequence produced a water PSF (d)
similar to the r1PD water PSF (b) with half the number of acquired views. Therefore,
the r1PD sequence provides the same effective water resolution in half the acquisition
time. (c,f) The fat PSFs resulted in a primary ring-lobe diameter half that of r1PD
water PSF with the same number of views. Therefore, fat and other off-resonance spins
will be undersampled in the r1PD images with half the number of acquired projections.
The off-resonance PSFs generated from the r1PD sequence with 128 and 256
projections are shown in Figures 3.4c and 3.4f, respectively. The off-resonance PSFs
have primary ring-lobe diameters that are equivalent to the on-resonance r2PD PSFs and
smaller than the on-resonance r1pd PSFs. Therefore, the spatial resolution / view
improvement observed for on-resonance species in the r1PD sequence is lost for offresonance species. The off-resonance PSFs from the r2PD sequence were equivalent to
their on-resonance analogues (not shown).
54
3.4 Discussion
In this study, a new radial 1-Point Dixon (r1PD) acquisition was developed that
provides separate water and fat images through selective echo time variation between
consecutive projections.
This r1PD sequence provided effective lipid (or water)
suppression with improved k-space coverage resulting in reduced artifacts in the
reconstructed images as compared to the r2PD sequence for equal scan times. The
artifact reduction was confirmed through phantom and clinical images as well as pointspread functions. The reduction in artifacts suggests an opportunity to improve the
temporal resolution of the r2PD method by reducing the total number of views required
to obtain the same effective resolution of the unsuppressed species. The main advantage
of improving the temporal resolution of the Dixon methods is to provide a fast and
efficient method for selective suppression without the SAR constraints and/or acquisition
time increases of CHESS pulses and inversion recovery sequences.
The True FISP sequence used in this study was designed mainly to obtain the
radial gradient-echo data sets with relatively short acquisition times (1-10 sec). The True
FISP pulse sequence offers significant contrast and SNR / time advantages over the
FLASH pulse sequence used in the Keyhole Dixon development.
The measured
trajectory used in the gridding reconstruction corrected for gradient imperfections in the
acquired trajectory and has been shown to significantly reduce artifacts in the
reconstructed image as compared to the theoretical, designed trajectory (117). With these
artifacts removed, the images were easily compared to determine the impact of the r1PD
sequence on the level and distribution of blurring and streak artifacts with respect to the
Dixon trajectory.
55
The CNR measurements demonstrate an interesting effect of CNR as a function of
the number of acquired views. Based on the number of acquired views alone, the CNR
for the r2PD trajectories would theoretically be expected to increase by ~41% as the
number of views was increased from 128 to 256. However, the CNR actually increased
from 110 to 190 (~73%). The larger-than-expected increase in CNR is most likely due to
increased aliasing artifacts in the 128-view r2PD as the Nyquist criterion is violated at
shorter distances from the center of K-space. Aliasing artifacts from radial trajectories
are typically more enhanced near the edges of the image. Therefore, measuring the noise
based on background noise levels may lead artificially low CNR measurements near the
center of the image where the streak artifacts are less, but typically not measured. An
alternative method would have been to measure the image noise within the water
phantom to limit the effects of aliasing artifacts. Another option would have been to use
a smaller phantom and sample the noise level in the background regions inside of the
streak artifacts. However, there is no guarantee that the effect of these artifacts would be
removed from the analysis as the aliasing artifacts are present in varying degrees
throughout the FOV. These results further demonstrate the limitations of CNR as a tool
to measure image quality. A possible solution to separating these effects would be to
selectively “tune” the parameters of the PDM model to ignore the aliasing artifacts in the
image comparisons.
The on-resonance PSFs confirmed the effects of improved K-space sampling on
azimuthal undersampling. For on-resonance/unsuppressed spins (i.e., water spins in a
water reconstruction or fat spins in a fat reconstruction), the r1PD trajectory samples kspace with ∆kθ(r) exactly half of that from the r2PD trajectory.
56
For the off-
resonance/suppressed spins (i.e., fat spins in a water reconstruction or water spins in a fat
reconstruction), the variation in echo time results in a repeating 0°/180° phase variation
along any circular path through K-space.
This could be viewed as an additional
azimuthal undersampling resulting in effectively the same trajectory as the r2PD method
with the same number of acquired views.
A similar effect would be expected from the SPIDER sequence described by
Larson et. al.(118). The SPIDER sequence results in inherent fat suppression from the
TE variation between projections, but now the fat phase varies slower at approximately
0°/90°/180°/270° along a circular path through K-space.
While the on-resonance
SPIDER PSF would be expected to be equivalent to the on-resonance r1PD PSF, the
SPIDER off-resonance PSF would be expected to have a primary ring-lobe diameter onehalf that of the r1PD PSFs with the same number of views. These results demonstrate
that the selection of echo times is important in minimizing the level of radial aliasing
artifacts associated with the off-resonance spins. Further, this suggests that the fat phase
variation produced in the r1PD sequence is optimal relative to the SPIDER acquisitions
with the same number of acquired projections.
The radial 1-Point Dixon concept can be adapted to any other trajectory that
provides multiple passes through the K-space center. Multishot spiral, rosette, and other
trajectories can be designed with gradient waveforms to allow phase variation in either
fat or water magnetization between passes through the center of K-space (119). As in the
radial case, a balance must be found between the total acquisition time and the level of
aliasing artifacts. These other trajectories may offer advantages over a radial acquisition
57
for specific applications in terms of acquisition time, contrast, SNR, and level/type of
artifacts.
Radial sequences are less efficient than conventional rectilinear acquisitions in
sampling K-space because they oversample the low spatial frequencies.
However,
undersampled radial acquisitions result in streak artifacts in the reconstructed image. In
comparison, the aliasing artifacts obtained from a sparsely sampled Cartesian acquisition
results in fold-over artifacts. Therefore, novel radial trajectories such as r1PD may prove
more useful for dynamic or real-time imaging applications such as cardiac imaging where
undersampled acquisitions limit the effects of motion artifacts (120,121).
Though not discussed in detail up to this point, the r1PD trajectory is capable of
producing both a water image and a fat (water-suppressed) image from a single
acquisition. The water images are produced as described above. The fat images can be
obtained by first multiplying either the even or the odd projections (not both) by –1 prior
to gridding. This multiplication results in a net 180° phase increment to the water
magnetization and a 0° phase increment in the fat magnetization between the two echo
times. Water suppressed images could also be obtained by shifting the on-resonance
frequency of the scan to the precession frequency of fat spins.
The advantage of
acquiring both water and fat images in a single acquisition is to use the combined
information to generate a phase map for the image. This phase map represents the phase
variation generated by inhomogeneity in the main magnetic field. This information can
be used develop an off-resonance correction with benefits as described below.
One important limitation of this acquisition is the effect of off-resonance spins on
artifacts. As shown by the PSFs and the clinical images, the r1PD sequence with half the
58
number of views relative to the r2PD sequence results in degraded resolution for offresonance tissue structures. Off-resonance species include fat spins and water spins that
are off-resonance due to field inhomogeneities. Therefore, the level of aliasing artifact
due to radial undersampling is dependent on the spatial homogeneity of the magnetic
field as well as the fat content within the object to be imaged. Incorporation of an
algorithm to correct for field inhomogeneities through adaptations of existing offresonance correction algorithms (122) or through improved shimming algorithms would
reduce the effects of field inhomogeneities on resolution degradation and improve the
uniformity of fat suppression. Additional algorithms could be developed to correct for
aliasing artifacts caused by the radial undersampling of the high spatial frequencies of fat
spins.
In conclusion, a new radial 1-Point Dixon (r1PD) sequence was developed with
alternating echo times between even and odd K-space projections. The TE variation
resulted in inherent fat suppression in the reconstructed images as the fat signals were
nulled at low spatial frequencies. The radial 1PD trajectory provides for the first time a
1-Point Dixon acquisition with the same total number of acquired views as a CHESS or
other spectrally-selective excitation fat suppression method. Further, the echo shifting
required for this fat suppression requires a relatively small increase in TR as compared to
CHESS pulses (2.2ms vs. 10ms). As a result, the r1PD acquisition provides improved
temporal resolution over the radial 2-Point Dixon and other fat suppression techniques
while maintaining the effective spatial resolution of on-resonance structures.
59
Chapter 4
Lipid Elimination with an Echo-Shifting N/2-Ghost Acquisition (LEENA)
4.1 Background
The radial 1PD trajectory described in Chapter 3 provides a temporally efficient
means to generate separate fat and water images in a single acquisition in less time than is
required for sequences with spectrally-selective excitations. One major limitation of this
technique is the increase in streak artifacts determined to be caused by relative
undersampling of off-resonance spins (123). In the discussion section of Chapter 3 (Sect.
3.4), it was speculated that the off-resonance aliasing artifacts could be reduced by offresonance correction algorithms or by improved shimming algorithms. Unfortunately,
these methods cannot completely correct for the off-resonance aliasing inherent in the
radial 1PD trajectory.
Parallel imaging techniques were developed primarily to significantly reduce the
acquisition time of pulse sequences by using the additional degrees of freedom obtained
by
using
multiple
coils
(30,31,33,36,37,39,46,47,124).
(ex.
phased-array
coil
set)
for
the
acquisition
These techniques unalias images from rectilinear
acquisitions and reduce aliasing artifacts (i.e., radial streaking, spiral blurring) in images
from non-Cartesian acquisitions. The net effect is to allow the number of acquired views
to be reduced resulting in the desired rapid acquisition. Sensitivity Encoding, or SENSE,
is one of the two fundamental methods of parallel imaging in MRI (39). Raw data are
first acquired with a reduced FOV acquisition (Fig. 4.1a). Reconstruction of the images
from the acquired K-space data results in individual aliased images from each coil as
shown in Figure 4.1b.
SENSE then uses apriori knowledge of the complex coil
60
sensitivity maps to calculate the final unaliased, full-FOV image (Fig. 4.1c).
(a)
(b)
ky
(c)
Coil1
Coil2
kx
Coil3
Coil4
Fig. 4.1:
Parallel imaging outline.
(a) Schematic of K-space sampling for
undersampled, reduced FOV acquisition with solid lines representing acquired views and
dashed lines representing omitted views. (b) Raw aliased images from multiple coils
obtained from undersampled rectilinear trajectory, (c) Unaliased image produced from
SENSE algorithm. (Pruessmann et. al., MRM 1999; 42:952-962)
In this chapter, the rapid 1-Point Dixon trajectory is combined with a parallel
imaging technique similar to SENSE to extend the application of parallel imaging to fat
suppression.
For this initial study, the pulse sequence and unaliasing algorithm is
developed and demonstrated for a rectilinear 1-Point Dixon trajectory (Lipid Elimination
with an Echo-shifting N/2-ghost Acquisition - LEENA) described in detail below. Like
the radial 1PD acquisition, the rectilinear 1PD trajectory and image reconstruction
algorithm provides separate fat and water images from a single acquisition. The LEENA
technique allows a 1-Point Dixon trajectory to be developed for rectilinear trajectories
where, unlike radial trajectories, oversampling of the center of K-space is not typically
performed.
61
4.2 Materials and Methods
4.2.1 Conventional FISP Sequence and Coil Sensitivity Maps
A rapid, FISP (Fast Imaging with Steady-State Free Precession) sequence was
implemented on a 1.5T Siemens Sonata scanner (Siemens Medical Solutions, Erlangen
Germany) to obtain the coil sensitivity maps required for the parallel imaging
reconstruction (TR/TE = 12ms/4.8ms, FOV = 300, Matrix = 256 x 256, FA = 70°, BW =
390 Hz/pixel, NSA = 12).
The FISP sequence was developed from a True FISP
acquisition by removing the prephase lobe of the slice-select gradient after the ADC to
minimize the effects of banding artifacts on the coil sensitivity maps (125,126).
The coil sensitivity maps were calculated from the individual coil images (with no
fat suppression) generated by the FISP sequence. Sample results are shown in Figure 4.2
for an acquired phantom image set. The coil images (Fig. 4.2b) were first thresholded to
reduce background noise then divided by the sum-of-squares image (Fig. 4.2a) to reduce
the effects of pulse sequence contrast on the coil sensitivity maps (39). The normalized
images were then median filtered to reduce the noise amplified in the normalization
procedure. The result is the unshifted coil sensitivity map shown for a phantom image in
Fig. 4.2c). Shifted or N/2-ghost sensitivity maps were also required for the LEENA
unaliasing procedure and were generated by reordering the image data to produce an N/2
shift (Fig. 4.2d). The shifted and unshifted coil sensitivity maps were generated for each
of the coils utilized in the FISP acquisition (i.e., 3 coils).
62
Fat
Phantom
Water
Phantom
a
b
c
d
Fig. 4.2: Demonstration of coil sensitivity map calculations for a phantom image
generated from a conventional FISP acquisition. (a) Sum-of-squares image generated
from the 3-coil combination. (b) Initial coil image (Coil 3). (c) Unshifted coil
sensitivity map for coil3. (d) N/2-shifted coil sensitivity map for coil 3. Note the lack
of fat suppression in the raw images as well as the sensitivity maps.
4.2.2 Rectilinear 1-Point Dixon Trajectory - LEENA
The FISP sequence described above was modified to traverse the LEENA
trajectory shown in Figure 4.3b (TR/TE1/TE2 = 12ms/4.6ms/7.0ms, FOV = 300, Matrix
= 256 x 256, FA = 70°, BW = 390 Hz/pixel). Like the radial 1PD trajectory (Fig. 4.3a),
the LEENA trajectory utilizes 2.2ms echo shifts between successive lines in K-space
(Fig. 4.3b). The TE variation was selected to allow the fat magnetization to precess 180°
between adjacent k-space lines and results in an N/2-ghost for off-resonance (fat) spins
63
typical of non-interleaved, multi-shot EPI and other multi-echo acquisitions (47). This
trajectory differs from the conventional, multi-point Dixon methods where the echoshifting is applied for multiple acquisitions of the same K-space lines. For this study,
only one echo was acquired in each TR. The repetition time was kept constant among the
odd and even lines of K-space to maintain the steady-state magnetization profiles for the
coherent steady-state acquisition.
TE2
TE1
ky
ky
kx
kx
a
b
Fig. 4.3: Schematics of K-space trajectories for (a) radial 1PD and (b) LEENA
(rectilinear 1PD) acquisitions. Note the intentional TE difference (2.2ms at 1.5T)
between successive lines of K-space
4.2.3 LEENA Image Reconstruction
The raw data from each coil in the LEENA acquisition was transformed to image
space with a 2D-IFT. As described in the PAGE method developed by Kellman and
McVeigh (47), the unghosted water image and the ghosted fat image are calculated from
Equation 4.1 below.
64
fg(x,y) = [ S(x,y)H Rn-1 S(x,y) ]-1 S(x,y)H Rn-1 G(x,y)
(4.1)
where S is the sensitivity matrix obtained from the combination of shifted and unshifted
coil sensitivity maps described in Sect. 4.2.1 above, G is the matrix of ghosted images
from the individual coils, and Rn is the noise covariance matrix assumed to be identity for
this initial study. The superscript
H
represents the transpose of the complex conjugate,
and the matrix in brackets is inverted by a least-squares, pseudo-inverse operation. The
images (fg) resulting from Equation 4.1 represent the 0th (water image) and 1st ghosts (fat
image), respectively. The unaliasing algorithm was implemented on a pixel-by-pixel
basis to generate separate water and fat images with the same resolution as the aliased
LEENA image.
The main difference between the SENSE algorithm and the LEENA method in
Equation 4.1 lies in the definition of the coil sensitivity matrix, S(x,y). For the LEENA
algorithm, the 2D coil sensitivity matrix has dimensions of Number of coils (Nc) x
number of ghosts (Ng). Note that for this study the number of ghosts is set to 2 (0th and
1st ghosts). In contrast, the coil sensitivity matrix is a Nc x 1 vector in the conventional
SENSE algorithm.
4.2.4 Off-Resonance Correction (ORC)
An off-resonance correction (ORC) algorithm was also developed and applied to
the water and fat images (fg) to limit the effects of field inhomogeneities. First, the
complex images, fg, were algebraically combined to produce complex “Water+Fat”
(IW+F) and “Water-Fat” (IW-F) image data sets. A differential phase map (Φi) was
generated from these images as described in Chapter 2, and the final, corrected water and
fat images were calculated from Equations 4.2a and 4.2b, respectively.
65
Corrected Water Image = IW-F + exp(-i • Φi) • IW+F
(4.2a)
Corrected Fat Image = IW-F - exp(-i • Φi) • IW+F
(4.2b)
Also as described in Chapter 2, a phase unwrapping algorithm based on a region-growing
algorithm was utilized to correct for large field inhomogeneities that would otherwise
result in erroneous assignment of water and fat signals.
4.2.5 Phantom and Volunteer LEENA Images and CNR Analysis
Phantom and volunteer abdominal images were obtained with the LEENA
technique for comparison with the conventional FISP pulse sequence (FOV=350mm,
matrix=128x256) were acquired with a body phase-array coil and a single coil from the
spine coil array on the Siemens Sonata 1.5T scanner (Nc = 3). Similar 2-Point Dixon
images were also acquired for the volunteer abdominal images for comparison. The
contrast-to-noise ratio of the phantom images was determined at various stages of the
LEENA process according to Equation 4.2 below.
CNR = (µwater - µfat) / σwater
(4.2)
where µwater , µfat are the mean amplitudes of the water and fat phantoms in the image and
σwater is the standard deviation in the water phantom. The variation in the water phantom
was used for these calculations to limit the effects of thresholding and filtering on the
noise level in the images.
4.3 Results
Phantom LEENA images are shown in Figure 4.4 in comparison to the
conventional FISP images. The majority of the fat phantom was shifted to the edges of
the FOV in the aliased LEENA acquisitions (Fig. 4.4b). A slight N/2-ghost of the water
phantom was also produced in the aliased LEENA image because of field
66
inhomogeneities. Similarly, a small portion of the fat phantom signal remains unghosted
(on-resonance) because of field inhomogeneities as well as local deshielding of hydrogen
nuclei in compounds found in baby oil. Unaliasing the image in 4.3b with Equation 4.1
above resulted in the unaliased water (Fig. 4.3c) and fat (not shown) images.
Implementation of the off-resonance correction algorithm resulted in a visible decrease in
the misassignment of fat and water in the respective images.
a
b
c
d
Fig. 4.4: LEENA phantom images. (a) conventional FISP image with no fat
suppression. (b) Initial LEENA image with off-resonance N/2-ghost. Unaliased
LEENA images are shown (c) before and (d) after off-resonance correction to correct
Contrast-to-noise measurements of the phantom images in Fig. 4.4 are shown in
Figure 4.5. As expected, the CNR’s of the LEENA images are substantially larger than
67
the conventional FISP image with no fat suppression. More importantly, the unaliasing
algorithm has no measureable effect on the CNR as observed in the aliased and unaliased
LEENA images. Note that this observation is limited to cases where the aliasing causes
no real overlap in the image. Limited benefit in CNR (98% vs 100%) was observed in
this case for off-resonance correction because of the high quality shimming possible in
phantom images.
CNR (Normalized to LEENA - ORC)
120
100
80
60
40
20
0
FISP
Aliased LEENA
LEENA
LEENA - ORC
Fig. 4.5: Measured contrast-to-noise ratios for conventional FISP and LEENA
images normalized to the LEENA image with off-resonance correction
(LEENA-ORC).
68
Volunteer abdominal images are shown in Figure 4.6. The fat suppression in the
abdominal off-resonance corrected LEENA and 2PD images (4.6b vs. 4.6d) was visibly
equivalent and markedly better than the conventional FISP image (4.6e) as well as the
uncorrected images (4.6a and 4.6c). The aliased LEENA image (Fig. 4.6f) demonstrated
the foldover of the subcutaneous fat back into the unghosted water image. The unaliasing
algorithm removed the alaising energy with no apparent defect in the final water image
(Fig. 4.6b). The resolution in the LEENA and 2PD images was visibly equivalent as
predicted from the LEENA trajectory as well as the radial 1PD results in Chapter 3. A
more quantitative comparison of the LEENA and 2PD acquisitions is presented in
Chapter 6.
69
a
b
c
d
e
f
Fig. 4.6: Axial abdominal images of a healthy volunteer. (a,b) LEENA images
before and after off-resonance correction. (c,d) 2-Point Dixon images with the same
number of acquired views with and without off-resonance correction. (e) conventional
FISP image. (f) The raw LEENA image is included to demonstrate the lack of aliasing
artifact in the unaliased images.
70
4.4 Discussion
The LEENA algorithm is a rectilinear 1-Point Dixon method similar to the radial
1PD acquisition described in Chapter 3. The LEENA procedure halves the acquisition
time of the 2-Point Dixon acquisition with no decrease in image resolution. Coupled
with an off-resonance correction algorithm, the LEENA method provides separate,
uniform fat and water images from a single acquisition. The LEENA algorithm was
primarily designed to reduce aliasing artifacts from off-resonance spins in rectilinear
multi-echo trajectories.
However, adaptations of non-Cartesian parallel imaging
reconstructions could be developed for similar results in radial and multi-shot spiral
acquisitions.
The sensitivity maps calculated for this study were derived from the combination
of body array coils and a spine array coil (Nc = 3). Increasing the number the coils in the
reconstruction would improve the SNR properties of both the ghost separation calculation
as well as the raw ghosted images in the individual coils (39). The SNR properties of the
coils could also be improved by creating coil sets designed to minimize the noise increase
associated with parallel imaging reconstructions.
However, a balance must be
maintained for depth-of-field sensitivity of the coil arrays, especially for through-body
imaging applications such as the abdominal images shown here.
The LEENA unaliasing procedure provides a new fat suppression technique by
using a special case of the PAGE algorithm developed by Kellman and McVeigh (47).
The LEENA trajectory produces ghosting artifacts in a known distribution similar to EPI
acquisitions where echo-shifting in the phase encode direction results as multiple lines of
K-space are acquired in a single TR. In the LEENA acquisition, the echo shifts are
71
maintained at 2.2ms (at 1.5T) to maximize the portion of fat signal in the N/2 ghost. This
allows the ghost separation calculation (Equation 4.1) to produce separate fat and water
images. Applying any other echo shift would result in decreased fat suppression contrast
as a greater portion of the fat signal would remain in the 0th ghost image. However, this
effect had no negative impact in the Kellman and McVeigh manuscript as their goal was
merely to replace the off-resonance signal correctly within the unghosted image.
Direct application of the LEENA method as described here is limited to a
reduction factor of 2 relative to the 2-Point Dixon method. The use of other echo shift
variation schema only results in more complex ghosting patterns. Fortunately, higher
order order reduction factors (R>2) can be obtained by coupling the LEENA acquisition
with other conventional parallel imaging techniques. An example LEENA SMASH
algorithm is shown in Figure 4.7. In this example, a reduction factor of four relative to
the 2-Point Dixon acquisition would be obtained.
Acquired Data
SMASH Data
Combined Data
Fig. 4.7: Schematic of potential combination of LEENA and SMASH algorithms. Kspace lines acquired at TE1 and TE2 are represented with solid and dashed lines,
respectively. Sparsely sampled data are acquired as normal in a parallel imaging
application. Gaps in K-space data are filled in by SMASH estimation to produce the
LEENA K-space data set shown in Figure 4.2b. LEENA unaliasing would then result in
separate fat and water images with 1/4th the acquired views as the 2-Point Dixon method.
72
The LEENA and 2PD images in this paper were acquired with the same total
number of acquired views (NSALEENA = 12, NSA2PD = 6) to better understand the effects
of the LEENA trajectory and unaliasing algorithm on image resolution, fat suppression,
and aliasing artifacts. These results would likely be duplicated for imaging applications
that are not SNR-limited. It is expected that a significant decrease in image quality
would be obtained for the LEENA acquisition in SNR-limited imaging applications.
Fortunately, the number of these applications should decrease in the future as the industry
moves towards higher field strength.
The abdominal images here demonstrate the importance of off-resonance
correction algorithms in all Dixon-like fat suppression techniques. This is the main
advantage of the Dixon methods in comparison to CHESS, SPSP, and binomial fat
suppression techniques. A significant advantage of the LEENA algorithm is that the
ORC algorithm requires only the final, combined phase image to be unwrapped. In
comparison, the 2PD images required that the individual coil images be unwrapped prior
to combination. This has the potential to create phase discontinuities in the combined
image which could result in the incorrect assignment of water and fat signals in the final
off-resonance-corrected 2PD image.
The main disadvantage of LEENA technique is a decrease in SNR (relative to
2PD) from both a reduced number of acquired views as well as the SENSE-like
reconstruction. As in all parallel imaging applications, the noise level increases as a
function of the reduction factor, R (39). For the LEENA method, the SNR is primarily a
function of the number of ghosts, Ng (47).
73
The 2.2ms echo shift described here
minimizes the SNR loss as only the N/2 ghost is utilized (Ng).
Additional ghosts
obtained through other echo variation schemes would require higher order ghost
separation calculations. However, higher order ghosting acquisitions (Ng >2) could be
advantageous for high SNR imaging applications where echo shifts and TR must be
minimized. In addition, the echo shifts are directly reduced at higher field strengths as
the absolute frequency difference between fat and water increases. Therefore, imaging
on high-field systems offers the opportunity for even faster
The SNR could also be
improved by utilizing a variety of SENSE regularization methods (37,127).
Another limitation of the LEENA method is the added acquisition time required
for the coil sensitivity maps reduces the real acquisition rate of the LEENA technique.
To overcome this limitation, the LEENA technique could be coupled with other parallel
imaging strategies as shown in Figure 4.7. Alternatively, a GRAPPA-based LEENA
method could be developed which could significantly reduce the number of views
required to calculate the unaliased fat and water images (30).
In conclusion, the LEENA technique provides a new method from obtaining
separate fat and water images in a single rectilinear acquisition. The LEENA method
produces images with equal resolution in comparison to the conventional 2-Point Dixon
acquisition in half the acquisition time. An off-resonance correction algorithm was also
developed to produce images with uniform fat / water separation throughout the FOV.
This technique can also be used in combination with other parallel imaging strategies to
obtain higher-order reduction factors for very high-speed imaging applications.
74
Chapter 5
Development of Time-Optimal 2-Point Dixon Pulse Sequences
5.1 Background
Previous chapters have focused on improving the temporal resolution of the 2Point Dixon method by reducing the total number of acquired K-space lines. In this
chapter, we focus on reducing the acquisition time by minimizing the repetition time
(TR) of the pulse sequence. Rapid steady-state pulse sequences (ex. True FISP) require
high performance gradient systems to achieve short repetition times ≤ 5ms (125). These
gradient systems are now standard on modern MRI scanners providing ~40mT/m
gradient amplitudes and ~200 mT/m/ms slew rates. However, rapid gradient switching
can lead to peripheral nerve stimulation (PNS) (128,129). As a result, the acquisition
speed of steady-state pulse sequences is frequently limited by gradient stimulation effects
rather than gradient hardware.
Because of the inherent complexity of the empirical stimulation models on MR
scanners, few, if any, optimization studies have incorporated a PNS model into pulse
sequence design (130,131). Therefore, reducing the TR of a particular pulse sequence
requires a tedious, iterative process involving adjustment of gradient lobe parameters
until the PNS limits are approached but generally avoided.
Automating the pulse
sequence optimization process requires a model capable of searching through many pulse
sequence parameters with multiple objectives in a timely fashion.
Genetic Algorithms
(GAs) are a class of optimization techniques that are capable of finding global minima in
the face of highly non-linear or otherwise ill-behaved objective and constraint functions
(132).
They use a biological metaphor where model parameters are encoded in a
75
numerical “gene”.
Genetic alternatives then compete according to one or more
predefined objectives to selectively retain the positive attributes that will be passed on to
future generations. The population of possible alternatives thus evolves to an optimal set
after multiple iterations, or generations.
In this study, a multi-objective GA incorporating the PNS model was used to
optimize a 2-Point Dixon True FISP pulse sequence. The acquisition speeds, contrast,
and SNR properties of True FISP acquisitions makes this pulse sequence suitable for
many rapid imaging applications where motion artifacts and long breath holds make
imaging problematic.
Image quality, resolution, and acquisition speed are three
important considerations in most applications. This work sought to improve all three by
simultaneously attempting to minimize the repetition time (TR), field of view (FOV), and
the bandwidth/pixel (BW) of a two-echo 2-Point Dixon acquisition. Because FOV, TR,
and BW are conflicting objectives, a set of pulse sequences was generated with each
sequence representing the lowest possible TR for a given BW and FOV.
5.2 Materials and Methods
5.2.1 Genetic Algorithm
The GA utilized in this work was the non-dominated sorting genetic algorithm
(NSGA-II) first proposed by Deb for general work in optimization and later used by Dale
for work specifically looking at MRI pulse sequence design (132-134). The NSGA-II
provides faster convergence and more evenly distributed results than many other
GA’s(132). The NSGA-II is capable of simultaneously optimizing multiple objectives in
the presence of ill-behaved objective or constraint functions. Here, the population size
was set to 50 and the optimization was run for 500 generations resulting in a total of
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approximately 25,000 sequences evaluated.
The initial population was randomly
generated with the aforementioned constraints imposed.
Genetic selection and reproduction operations were performed on the parent
sequences for each generation.
Parent sequences were ranked and selected for
reproduction using a binary tournament selection procedure (135). Here, two sequences
were selected at random for competition. The more fit of the two was then used in the
simulated reproduction operations. For this study, fitness was based on crowding (i.e.,
coverage of Pareto-optimal space) and overall optimality (TR, FOV, BW).
The
combination of these selection pressures was designed to push the population of
sequences towards a set of the most rapid sequences spanning the range of BW
(minimum possible to 1000Hz) and FOV (200mm to 300mm).
Two child sequences
were produced from each pair of parent solutions using simulated binary crossover (135)
(i.e., genetic recombination). This was followed by a mutation function which effectively
applied an average of one mutation per child (135).
5.2.2 2-Point Dixon True FISP Pulse Sequence
A dual-echo, 2-Point Dixon True FISP pulse sequence was chosen as the template
for the GA optimization in this study (Fig. 5.1b). The dual-echo True FISP sequence has
nine gradient lobes. The BW was held constant for the two echoes, and a 2.2ms delay
was maintained between the two Dixon echoes for fat /water separation (65).
77
b
a
RF
Slice
Read
Phase
ADC
Figure 5.1. Schematic representations of both (a) conventional True FISP and (b) 2Point Dixon True FISP pulse sequences. Note the two separate ADC windows in the 2Point Dixon acquisition where the same line of K-space is acquired at different echo
times as required for the Dixon techniques.
All gradient lobes were designed as trapezoidal gradient pulses.
Nonlinear
gradient waveform ramps could be included in the GA, but were not considered for this
study (133,134). Each trapezoidal gradient lobe was specified using 4 timing parameters:
Delay, Ramp Up Time, Flat Top Time, and Ramp Down Time (Fig. 5.2). The NSGA-II
accepted discrete parameters; therefore, the individual timing parameters were
constrained to integer multiples of the hardware gradient raster time (10 µs). The FOV
was included as an additional parameter, resulting in a total of 36 parameters for the dualecho optimization. The constant sequence values used during the optimization were a
fixed matrix (256 x 256), slice orientation (axial), slice thickness (3 mm), and BW-time
product of the RF pulse (1.6). Note, once the gradient timing parameters are established
by the Genetic Algorithm, the amplitude of each gradient lobe can be uniquely
determined from the FOV, slice thickness, RF pulse, and/or Readout BW and is therefore
78
not a free parameter. All timing parameters were greater than or equal to zero and the
FOV was constrained to between 200 mm and 300 mm in 50mm increments. The timing
of the phase encode gradients were held constant for each view of a particular pulse
sequence.
Previous gradient
Figure 5.2: Trapezoidal gradient
lobe design timing parameters. Each
gradient lobe can be completely
described by the four indicated timing
parameters. Once the timing is fixed,
the gradient amplitude is determined
by other known sequence parameters
such as FOV, RF pulse envelope, etc.
Ramp Down
Flat Top
Ramp Up
Delay
The 2PD True FISP sequence was implemented on a Siemens Sonata 1.5T
scanner. Therefore the slew rate was constrained to be less than 200 mT/m/ms and the
gradient magnitude on each axis was constrained to be less than 40 mT/m. The sequence
was also constrained to avoid reaching the PNS limits as determined by the SAFE model
(Stimulation Approximation by Filtering and Evaluation) (29). The model uses multiple
low-pass digital filters to approximate the generation of action potentials within the nerve
cells and the spread of the signal via synapses. The SAFE model accepts the x,y,z
gradient waveforms as input and returns a single stimulation waveform where values
greater than 1.0 indicate that PNS limitations would be violated. A PNS violation on the
Siemens Sonata scanner prevents the implementation of the pulse sequence.
79
5.2.3 Imaging Applications
Images of a volunteer’s abdomen (FOV = 300 mm) and optic nerve (FOV =
200mm) were obtained for selected Pareto-optimal 2PD True FISP pulse sequences
designed by the genetic algorithm. The Pareto-optimal 2PD True FISP sequences were
selected from the Pareto-optimal sets for comparison with a conventional True FISP
sequence provided with the Siemens Sonata 1.5T scanner. The images from the dualecho sequences were reconstructed offline incorporating an off-resonance correction
algorithm similar to that used in Chapters 2 and 4 to obtain uniform fat / water separation
(136).
The conventional True FISP sequence was a rapid, single-echo acquisition
without fat suppression contrast. The single-echo images were reconstructed online with
a 2D-IFT. Rather than a genetic algorithm, the conventional True FISP sequence uses a
heuristic binary search algorithm to minimize the TR for a given FOV/BW combination.
Aside from the second readout gradient and TR, the sequence parameters of the Paretooptimal sequence were equivalent to the conventional True FISP sequence.
5.3 Results
5.3.1 2-Point Dixon True FISP Optimization
For three-objective optimizations, the Pareto-optimal set is typically a curved
surface in the 3D objective space. Recall that Pareto-optimal for this work means that
each sequence represents the shortest TR possible (without causing stimulation) at a
given combination of BW and FOV. The Pareto-optimal surfaces for the Dual-echo, 2Point Dixon True FISP optimization are represented in Figure 5.3 by plotting BW as a
function of TR for several different FOVs. Note that all curves were obtained from a
single GA optimization. The optimization exhibited a “diminishing returns” type of
80
behavior where successive improvements in one objective came at progressively greater
sacrifices in another objective. This was observed in the Pareto-optimal curves where
smaller FOVs required extended acquisition times. In addition, shorter repetition times
generally required an increase in BW (lower SNR) for a given FOV. Note also the
relatively hard floor on the BW (> 450 Hz/pixel) as the optimization was constrained to a
TE difference of 2.2ms.
Readout BW (Hz/pixel)
900
FOV mm
300
250
200
800
700
600
500
5.5
6
6.5
7
7.5
8
TR (ms)
Figure 5.3: Pareto-optimal Curves for Dual-Echo 2-Point Dixon True FISP
pulse sequence. Each point represents an individual Pareto-optimal pulse
sequence plotted with the three objectives: BW/FOV/TR. Note the relative
trade-offs between shorter TR (better temporal resolution) and larger FOVs
(degraded spatial resolution), as well as higher readout BW (lower SNR).
Selected 200mm and 300mm Pareto-optimal pulse sequences are shown in Figure
5.4. Each plot displays the three gradient axes as well as the stimulation waveform
generated by the SAFE model. Note the details of the gradient waveforms and their
relative impact on the stimulation waveforms. Note that the lower stimulation levels
81
between the readout gradient lobes would allow the LEENA sequence to be derived from
these Pareto-optimal 2PD True FISP templates by inserting a phase encoding gradient
lobe between the two ADCs. These results are presented and discussed in Chapter 6.
a
Gphase
Gread
Gslice
(mT/m) (mT/m) (mT/m)
20
-20
20
-20
20
-20
1
0
Stim
Stim
Gphase
Gread
Gslice
(mT/m) (mT/m) (mT/m)
b
1
2
5
3 4
time (ms)
6
20
-20
20
-20
20
-20
1
0
1
2
3
4
time (ms)
5
6
Figure 5.4: Selected Pareto-optimal 2-Point Dixon True FISP pulse sequences. (a)
FOV = 200 mm, TR = 6.8 ms, BW = 560 Hz, max stim = 92%, (b) FOV = 300 mm,
TR = 6.1 ms, BW = 560 Hz, max stim = 97%. Because of computational errors in the
SAFE model and the exponential increases in PNS during gradient ramping, a pulse
sequence with a maximum PNS value >90% was considered to be stimulation-limited.
The PNS stimulation constraints were encountered across the entire Paretooptimal population, regardless of FOV, TR, and BW. For the pulse sequences shown in
Figure 5.4, the stimulation first approached the FDA limit during the ramping of the slice
select gradient. The maximum slew-rate (200 mT/m/ms) was utilized for both the largest
and smallest FOV sequences across all TRs, while the gradient amplitude limit (40
mT/m) was reached for the shorter TR sequences across all FOVs.
These results
demonstrate that PNS and gradient hardware simultaneously place significant limitations
on pulse sequence design.
82
5.3.2 Pareto-Optimal 2-Point Dixon Images
Fat-suppressed True FISP images of a volunteer’s abdomen (FOV = 300 mm)
were obtained for the optimized 2PD pulse sequence described above and are in
comparison to a conventional True FISP acquisition in Figure 5.5.
Conventional True FISP
TR=4.7 ms
Pareto-optimal 2-Point Dixon True FISP
TR=6.1 ms
a
b
Figure 5.5: Axial abdominal images acquired with FOV = 300 mm and BW = 560 Hz
for both (a) conventional single-echo and (b) Pareto-optimal Dual-Echo True FISP
pulse sequences. The dual-echo sequence has uniform fat suppression of both visceral
and subcutaneous fat.
The Pareto-optimal 200mm True FISP sequence was used to obtain images of a
volunteer’s head/optic nerve (FOV = 200 mm) as shown in Figure 5.6. Multiple signal
averages (NSA = 5) were obtained to improve the image quality.
83
Conventional True FISP
TR=4.7 ms
a
Pareto-optimal 2-Point Dixon True FISP
TR=6.8 ms
b
Figure 5.6: Axial head images acquired with FOV = 200 mm and BW = 560 Hz
for both (a) conventional single-echo and (b) Pareto-optimal Dual-Echo True FISP
pulse sequences.
The Pareto-optimal dual-echo image provides uniform fat suppression for both
peritoneal and subcutaneous fat, while the conventional single-echo sequence results in a
bright fat contrast as expected for True FISP acquisitions.
The noise level in the
optimized sequence is also reduced because of the repeated acquisition of the same Kspace lines.
5.4 Discussion
The GA provided multiple, Pareto-optimal True FISP sequences that would have
been very difficult to design by conventional means. Typical pulse sequence design
involves an iterative process where the gradient pulse timing and shapes are varied until
the TR is at an acceptable level without violating the stimulation limits. Even when this
process is successful, small changes in sequence parameters during imaging applications
84
often lead to PNS violations. Prior to this optimization work, PNS violations caused by
small parameter changes were particularly problematic during the development of the
dual-echo sequences. The Pareto-optimal solution sets provided by the GA overcome
this limitation and allow the sequence to remain time-optimal for a variety of specified
imaging conditions.
The NSGA-II converged to a reasonably well-defined Pareto-optimal set within
500 generations for the dual-echo 2-Point Dixon True-FISP pulse sequences. The greater
smoothness of the large-FOV curves suggests that these optimizations may have
converged more completely than the small FOV regions. This is further substantiated by
the observation that, during the optimization, the sequence populations tended to have a
higher proportion of large FOV individuals. This may be a direct result of using a
random initial population, because random small-FOV individuals are more likely to be
severely penalized for violating hardware and PNS constraints.
An alternative to using a random initial population would be to design an initial
population based on product pulse sequences. The GA could also have been designed to
generate separate 200mm, 250mm, and 300mm Pareto-optimal sets independently to
remove the ranking process among FOVs.
Another potential method to improve
convergence would be to use a hybrid GA where a genetic optimization and a heuristic
“hill climbing” optimization routine are used together (137). Such algorithms would
have faster and more complete convergence properties than pure GA’s, while being more
able to escape from local minima than pure heuristic optimization routines.
The constraint activity has important implications for hardware design. All of the
Pareto-optimal pulse sequences were stimulation limited (Stim > 90%). This implies that
85
improvements in hardware would only allow increases in acquisition speed if they were
coupled with mechanisms to maintain or reduce stimulation levels.
Without such
mechanisms, sequence designers will only be able to make improvements by sliding
along the PNS constraint surface, and thus sequence-design methods like the one
presented here will become more important.
Perhaps one of the most important advantages of a multi-objective GA is that it is
possible to sample the entire Pareto-optimal set in a single run. This allows for a more
complete understanding of the inherent trade-offs amongst the various objectives. The
alternative is usually to do a single-objective optimization by assigning weighting
coefficients to the various objectives.
Such weighting coefficients are notoriously
difficult to obtain with any degree of confidence and are generally different for each
application. Instead, by using the multi-objective approach, the optimization can be
performed once and the results may be used for any application without repeating the
optimization.
This is important because the 500 generations used here required
approximately 12 hours of computation time (mostly for evaluating the SAFE model).
Therefore, it is not necessary to repeat the optimization on-line during the selection of
sequence parameters, as would be required with weighting methods.
The time-optimal dual-echo sequences described here combine the short-TR /
high SNR capabilities inherent in True FISP acquisitions with the uniform fat suppression
of the Dixon techniques. Incorporating the dual-echo framework into the pulse sequence
extends the TR relative to the conventional True FISP acquisition (4.7ms to 6.1ms or
6.8ms). However, this increase is much less than would be required for a spectrally
selective excitation pulse (∆TR ~ 10ms).
86
The images shown in this study demonstrate a select few of the Pareto-optimal
dual-echo True FISP pulse sequences. Because the Pareto-optimal set was generated
from a single optimization, a table of Pareto-optimal pulse sequences could be generated.
Then, a specific sequence could be selected from the table for a particular imaging
application.
The simplest selection procedure involves plotting the trade-off curve for
two objectives while fixing the remaining objectives and selecting the best trade-off for a
particular application. This procedure can be repeated for other pairs of objectives until
the best sequence is obtained. However, it becomes progressively more cumbersome
with increased numbers of objectives. In such cases, a suitable alternative is to use a
clustering algorithm to select a small number of representative sequences (135). The best
one for the application is selected and the corresponding cluster is repeatedly sub-divided
into a similar number of sub-clusters until the single best sequence is obtained.
One main limitation of using MOGA’s for pulse sequence optimization is the
need to run the algorithm for any sequence variation. Any change in trajectory, RF pulse
design, or any other pulse sequence design parameter held constant for this study would
require additional modeling to establish new Pareto-optimal curve sets. However, rapid
imaging sequences are normally designed for specific imaging applications. In addition,
like FOV in this study, other imaging parameters can be included as objectives in the
optimization process.
Another limitation of this work is the implementation details of the SAFE model.
While the results from the SAFE model used in this study are typically within 5% of the
actual Siemens Sonata SAFE model, the results are not exact. Therefore, the SAFE
model used in the GA was designed to be slightly more conservative than the actual
87
Siemens SAFE model to avoid generating sequences that would violate the PNS limits on
the scanner. As a result, some sequence designs may violate the PNS constraint in the
GA model, but not on the Sonata scanner. Therefore, implementation of the exact
Siemens SAFE model in the GA optimization could improve upon the results presented
here.
In conclusion, the NSGA-II genetic algorithm was able to successfully converge
and generate time-optimal, dual-echo 2-Point Dixon True FISP pulse sequences for
combinations of BW and FOV without requiring selection of weighting coefficients. The
multi-objective GA was able to converge despite the complex, non-linear nature of the
SAFE model in a complex dual-echo acquisition. This technique solved some of the real
challenges encountered when developing novel, high-speed pulse sequences.
88
Chapter 6
Subjective Rating Comparison of LEENA and 2-Point Dixon Images
6.1 Background
In Chapter 2, we described the methodology for obtaining objective quantitative
image quality comparisons of the Keyhole Dixon images using a perceptual difference
model (PDM) (138,139).
While these models show tremendous promise for image
ratings under certain experimental conditions, they do have inherent limitations. The
main constraint inherent in any difference operation is the requirement for no motion.
Two images equal in all respects other than a spatial displacement within the field of
view will be identified as markedly different by a simple difference model.
This
limitation is particularly important for image comparisons where respiratory and/or
cardiac motion cannot be completely controlled. For example, substantial respiratory
motion (rigid-body and non-rigid body) is observed from breathhold-to-breathhold as the
degree of inhalation / exhalation varies.
In this study, subjective human image ratings of phantom and volunteer images
were obtained to compare the fat suppression and resolution obtained from the LEENA
and 2PD trajectories. Subjective human ratings require substantial training and effort to
establish reliable ratings even among “expert” raters. However, human ratings are less
sensitive to small differences in image repositioning that may occur between acquisitions
because of involuntary patient motion. The human ratings in this study were obtained in
a rigorous manner similar to that established by the International Telecommunications
Union – Radiocommunications Sector (ITU-R) for evaluating the signal quality of
television images.
89
6.2 Materials and Methods
6.2.1 Experimental Design
Multiple phantom and volunteer abdominal images were obtained from the
LEENA and 2PD acquisitions to compare the acquisitions for both fat suppression and
resolution. Experimental matrix designs are shown for the fat suppression and resolution
comparisons in Figures 6.1 and 6.2 respectively. Phantom and abdominal images were
obtained from both LEENA and 2PD trajectories using several different steady-state
acquisitions: a single-echo FISP acquisition (TR/TE1/TE2 = 12ms/4.8ms/7.0ms, chapter
4), a Pareto-optimal True FISP (TR/TE1/TE2 = 6.1ms/1.9ms/4.1ms, chapter 5), and a
Pareto-optimal FISP acquisition derived from the above True FISP sequence by
eliminating the final rephase lobe of the slice select gradient. The True FISP acquisition
was not utilized in the phantom images to limit the effects of banding artifacts on the fat
suppression and resolution ratings.
The total number of acquired views was kept constant for these images to
minimize the effects of noise on the resolution and fat suppression ratings. The read
bandwidth of the unoptimized FISP acquisition was maintained at 390Hz/pixel while the
optimized sequences used a BW of 560 Hz/pixel. All other parameters in the acquisition
were kept constant (i.e., tip angle = 70º, FOV = 300mm) to maintain the contrast and
SNR properties of the acquisitions. All images were reconstructed according to the
methods previously described in Chapters 2, 4.
90
Image
Sequences
ORC
Phantom
FISP
OptFISP
Yes
No
Abdomen
FISP
OptFISP
OptTRUFI
Yes
No
Figure 6.1: Experimental design for fat suppression ratings. The phantom and volunteer
images are compared for optimized and unoptimized steady-state acquisitions both with
and without off-resonance correction. Conventional FISP?TRUFI images without fat
suppression were included for reference.
For the fat suppression ratings, images were compared before and after offresonance correction to determine the significance of the fat suppression techniques in
relation to ORC. A final image was created from a conventional FISP acquisition
(TR/TE = 12ms/4.8ms) with no fat suppression to calculate the coil sensitivity maps for
the LEENA acquisition and to provide a “poor” reference image fir the fat suppression
ratings.
91
Image
Sequences
Resolution
Phantom
FISP
OptFISP
256 x 256
128 x 128
Abdomen
FISP
OptFISP
OptTRUFI
256 x 256
128 x 128
64 x 64
Figure 6.2: Experimental design for resolution ratings. The phantom and volunteer
images were compared for optimized and unoptimized steady-state acquisitions at two
resolution settings. A third low resolution 2PD image was used included for
reference. All images were reconstructed with off-resonance correction.
Only off-resonance-corrected images were used for the resolution ratings. The
highest resolution LEENA and 2PD images (256 x 256) were reconstructed at 128 x 128
resolution to compare the resolution ratings of the two techniques at two different
resolutions. A 2PD image was also reconstructed at 64 x 64 resolution to provide a
“poor” resolution reference.
92
6.2.2 Human Rating Procedures
Seven expert raters from MRI and Radiology were enlisted to provide fat
suppression and resolution ratings of the LEENA and 2PD images. The images for the
experiments were imported into Powerpoint for presentation.
The raters were shown 14 slides. Each slide contained five images to be rated for
either fat suppression or resolution as instructed at the top of slide. The first four slides
were a training set to allow the raters to acquire some experience in the rating process
prior to performing the measured ratings (1). The images on slides 5-9 were rated on fat
suppression while the images on slides 10-14 were rated on resolution. Example fat
suppression and resolution rating slides are shown in Figures 6.3 and 6.4 respectively.
Fat Suppression Ratings
Fat
Image #1
Water
LEENA
ORC 2PD
Water
Fat
Image #2
Fat
Fat
WaterFISP
Water
2PD
Image #3
Image #4
Fat
Image #5
Water
ORC LEENA
7
Figure 6.3: Example fat suppression rating slide shown to all raters. Raters
were instructed to rate each of the images according to the level/uniformity of
suppression of the fat phantom in each image. Note the unsuppressed fat in
image #3.
93
Resolution Ratings
Image #1
ORC stdfisp
2PD 64
ORC stdfisp
2PD 256
Image #3
ORC stdfisp
2PD 128
ORC stdfisp
LEENA 256
Image #5
Image #2
Image #4
ORC STDfisp
LEENA128
14
Figure 6.4: Example resolution rating slide shown to all raters. Raters were instructed
to rate each of the images according to the detail clarity and pixelation of the kidney
edges and renal vessels..
Hardcopy image rating sheets were provided to each rater. Each of the 14 rating
sheets corresponded to a specific slide of images and provided 5 separate image ratings
scales. An example scale is shown in Figure 6.5a (1). The raters were asked to rate all
five images on each slide in comparison to one another according to the fat suppression
and resolution rating criteria. The images on one page were not to be rated in comparison
to images on another page. The order of the images on each slide was randomized to
limit the systematic bias in the image ratings.
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(b)
(a)
Excellent
100
Good
75
Fair
50
Poor
25
0
Bad
Figure 6.5: (a) qualitative rating scale used for all image ratings. Recommended scale
for DSCQS method described in ITU-R image analysis rating methodology (1). (b)
Quantitative scale used to convert the quantitative ratings in (a) to a 0-100 scale for
statistical analysis.
For the fat suppression ratings, four of the images consisted of LEENA and 2PD
images with and without off-resonance correction. The fifth image was a conventional
FISP image without fat suppression.
A single fat suppression slide was prepared for
each of the five sequences shown in Figure 6.1 (2 x phantom, 3 x abdomen). The raters
were instructed to rate the images according to the relative signal level of fat visible in
each image. For the phantom images, the raters were instructed to focus on the fat
phantom. For the abdominal images, the raters were asked to evaluate the level of both
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subcutaneous and internal fat visible in the images. More visible fat corresponded to a
worse rating on the scale shown in Figure 6.5a.
For the resolution ratings, four of the five images consisted of LEENA and 2PD
images (all with off-resonance correction) at 256 x 256 and 128 x 128 resolution. A fifth
image was the 64 x 64 2PD image. A single resolution slide was prepared for each of the
five sequences shown in Figure 6.2 (2 x phantom, 3 x abdomen). The raters were
instructed to rate the images according to detail clarity and pixelation in each image. For
the phantom images, the raters were instructed to focus on the pixelation and any
potential ringing artifacts in the water phantom. For the abdominal images, the raters
were asked to rate the images according to the pixelation and detail clarity of the edges of
the kidneys and the renal vessels. More pixelation and less detail clarity corresponded to
a worse rating on the scale shown in Figure 6.5a.
6.2.3 Statistical Analysis of Ratings
The qualitative ratings from each rater were converted to quantitative ratings with
by overlaying the quantitative scale (Fig. 6.5b) on the qualitative rating scales. The
quantitative ratings from all raters were compiled for an initial normalization procedure
to limit the effects of outliers and minimize the rater-to-rater error in the final analyses.
For each specific image (resolution and fat suppression) the ratings from each rater were
plotted as a function of the mean rating for each of the image ratings. A linear regression
was performed for each individual’s ratings and the slope of each regression was
determined.
The ratings from each rater were normalized to a slope of one by
multiplying the individual’s ratings by 1/slope.
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A univariate analysis of variance comparison was then performed on the
normalized rating data to determine the effects of the image target (phantom, abdomen)
and acquisition method (LEENA vs 2PD) as the independent factors (140). The analysis
was facilitated with SPSS for Windows Version 12.0.1 (LEAD Technologies Inc.). PostHoc Tukey HSD and Fisher’s LSD analyses were performed on the acquisition method to
determine the effects of the different levels of the acquisition (ex., 64 vs 128 vs 256
resolution) on the image ratings.
These two tests were selected to determine the
sensitivity of the results to a more conservative (Tukey) or less conservative (Fisher)
estimate of the difference in means.
6.3 Results
6.3.1 Rating Data Normalization
Before performing the complete statistical analyses, the data for each rater was
normalized to the mean ratings as described above. The raw, untransformed data are
shown in Figure 6.6. The individual rating scores varied approximately linearly as a
function of the mean rating score with a mean R-squared of 0.90. However, the slopes of
the regression lines vs. mean varied from 0.83 to 1.21 for the seven raters. The adjusted
data produced by dividing the individual’s ratings by the regression slope are shown in
Figure 6.7. The resulting slopes of the regression of the transformed ratings vs. the
adjusted mean scores varied between 0.997 and 1.003. Note that the adjusted data were
not constrained to between and including 0 and 100. An intercept adjustment was not
used in the transformation because all but one rater yielded a rating of zero for at least
one image in the rating experiments. Frequency plots of the rating variances for the raw
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and normalized image ratings (not shown) revealed that the normalized data produced
results with fewer outliers and an overall tighter distribution.
Individual's Ratings
120
100
Rater 1
80
Rater 2
Rater 3
60
Rater 4
40
Rater 5
Rater 6
20
Rater 7
0
0
20
40
60
80
100
Mean Rating
Figure 6.6: Plot of raw individual rating scores against the mean rating for each
image. Individual rating scores show reasonable linear correlation with the mean
ratings, but each rater displays a slightly different slope.
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120
Individual's Ratings
100
Rater 1
Rater 2
80
Rater 3
Rater 4
60
Rater 5
40
Rater 6
Rater 7
20
0
0
20
40
60
80
100
Mean Rating
Figure 6.7: Plot of transformed individual rating scores against the mean rating
for each image. Ratings were adjusted to a regression slope of 1.0 to normalize
ratings and limit the error from rater-to-rater variability.
6.3.2 Fat Suppression Rating Statistical Analysis
A linear model of the fat suppression ratings was developed with the imaging
target (phantom and abdomen) and acquisition method as the main factors. The mean
rater score for each image was entered into the model for analysis. The results were
based on 25 mean fat suppression ratings (15 abdomen, 10 phantom). The complete
tabular results are shown in Appendix A. The overall model accounted for 93% of the
variance in the data (adj. R2) and was statistically significant (F = 35.7, df = 9, p < 0.001).
As expected, the effect of acquisition method was statistically significant (F = 73.1, df =
4, p < 0.001) across the 5 levels (Conventional FISP, LEENA, 2PD, LEENA with ORC,
and 2PD with ORC). The effect of the imaging target was not statistically significant (F
= 3.0, df = 1, p > 0.10). However, a significant interaction was found between the
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imaging target and the acquisition method (F = 3.6, df = 4, p < 0.031) indicating that the
strong effect of the acquisition method was slightly different among abdominal and
phantom images.
The Post-Hoc Tukey HSD analysis determined the significance of the difference
in means among all levels of the acquisition method (Fig. 6.8).
Expectedly, the
conventional FISP images without fat suppression were consistently rated worse (Mean =
3.6) than any of the fat suppressed images. The off-resonance-corrected images (LEENA
and 2PD) were statistically better than the images before ORC confirming the importance
of an effective ORC method in fat suppression. The LEENA (Mean = 48.7) and 2PD
(Mean = 50.6) images before ORC were not statistically different. The LEENA and 2PD
images after ORC were not statistically different using Tukey’s HSD test (p > 0.18) but
were statistically different under the Fisher LSD test (p < 0.018).
Mean Rating
100
75
50
25
0
FISP
LEENA
2PD
LEENAORC
2PDORC
Figure 6.8: Mean fat suppression ratings for different acquisition methods.
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6.3.3 Resolution Rating Statistical Analysis
A similar linear model was developed and analyzed for the resolution ratings.
The only difference in the resolution model was the different levels of the acquisition
method. Here, the five levels were 2PD and LEENA images at 256 x 256 resolution,
2PD and LEENA images at 128 x 128 resolution, and a 2PD image at 64 x 64 resolution.
The complete tabular results are shown in Appendix B.
The overall model was
statistically significant (F = 135, df = 9, p < 0.001) accounted for 98% of the variation in
the data (Adj. R2). Mean resolution ratings for the different acquisition levels is shown
Figure 6.9. For the resolution ratings, the acquisition method (F = 283, df = 4, p < 0.001)
and imaging target (F = 5.6, df = 1, p < 0.033) were determined to be significant main
effects.
The main effect detected for the imaging target was small relative to the
acquisition method. In this case, there was no significant interaction between acquisition
type and imaging target.
Mean Rating
100
75
50
25
0
2PDORC
64
LEENAORC
128
2PDORC
128
LEENAORC
256
2PDORC
256
Figure 6.9: Mean resolution ratings for different acquisition methods.
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The Post-Hoc Tukey HSD and Fisher’s LSD analysis for determining the 95%
confidence intervals of the difference in the means generated consistent results for the
resolution ratings. All of the 64 x 64, 128 x 128, and 256 x 256 images were statistically
different from each other. Most importantly, The LEENA images were not significantly
different from the 2PD images at either 128 x 128 or 256 x 256 resolution in both the
Fisher and Tukey tests.
6.4 Discussion
The resolution ratings confirm the capabilities of the LEENA acquisition to
provide comparable resolution (equal K-space coverage) images in half the number of
acquired views compared to the 2-Point Dixon acquisition. The fat suppression ratings
demonstrate a possibly significant decrease in the overall fat suppression obtained from
the LEENA method. However, it should be noted that the difference in fat suppression is
due in part to the extensive image processing required in the LEENA image
reconstruction process.
Therefore, improvements in the LEENA acquisition and
reconstruction process could further reduce the difference in fat suppression / image
quality between the LEENA and 2PD acquisition techniques.
The pulse sequences implemented for this analysis were selected mainly for their
short acquisition times. The image similarity across all three acquisitions provided a
means to acquire multiple images from a single volunteer. As mentioned above, the True
FISP sequences were not used for the phantom images because of the tendency to create
banding artifacts that are generally more noticeable in phantom images.
Banding
artifacts can be removed on a case-by-case with accurate shimming. However, the FISP
sequence was selected instead to provide a more reliable approach.
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A relatively high readout bandwidth (>500 Hz / pixel) was selected for these
acquisitions to constrain the off-resonance shift to less than 1 pixel for the dual-echo
acquisitions. Lower bandwidth settings would result in improved SNR, but would also
generate edge artifacts as fat structures would be display significant read direction shifts.
This shift could be particularly problematic for the dual-echo acquisitions because the
read direction shift is effectively doubled because of the positive and negative readout
gradients. Therefore, the readout bandwidth was kept constant among the LEENA and 2Point Dixon acquisitions to make sure that the off-resonance shift would not bias the
subjective image ratings.
The image rating process developed for this study has several advantages. First,
the individual’s ratings spanned the entire range of possible ratings. Part of the reason for
this result is the fact that good, medium, and poor quality images were compared on each
slide in the rating display. This allowed the rater to accurately compare the images over
the whole range of results. In addition, the raters developed experience in the rating
process during the training phase. This training was valuable for some raters who had
little or no experience in evaluating fat-suppressed images.
The use of multiple pulse sequence acquisitions from a single volunteer also
provided some intrinsic benefits to the ratings analysis. First, the similar pulse sequences
allowed the data to be collapsed for the difference-in-means comparisons.
One
alternative would have been to scan multiple volunteers with a single acquisition.
However, additional volunteer images could increase the error in the ratings as the raters
could be skewed by the variation in image content rather than the acquisition technique.
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The methods described here provide a direct side-by-side comparison of the acquisition
methods in an in-vivo imaging study.
Normalization of the ratings to match the slope of the regression lines vs. the
mean ratings resulted in a more homogeneous data set across all raters. Limiting the
rater-to-rater variability was essential to obtaining an accurate model of the variation in
the data set. Without this transformation, minor effects such as the imaging target effect
in the resolution ratings may have been obscured by the inter-rater variability.
In
addition, the trend of the difference between the fat suppression ratings for LEENA and
2PD acquisitions would have been completely obscured by the rating error.
Analysis of the rating data using the univariate ANOVA and subsequent post-hoc
tests proved to be a useful and efficient means to compare the LEENA and 2PD
acquisitions. The results confirm a strong dependence of fat suppression and resolution
on the acquisition method. This result was expected as the FISP acquisition without fat
suppression and the 64 x 64 2PD acquisition were analyzed as specific levels in the main
effects analysis.
The off-resonance corrected images demonstrated a consistent improvement over
the uncorrected images for both abdominal and phantom images. The unsuppressed fat in
the uncorrected images tended to be brightest at the edges of the FOV, but the internal, or
visceral, fat signal was not completely suppressed in the abdominal images.
The
development of advanced shimming algorithms like those used on MRI/MRS scanners
could alleviate the need for ORC for general fat suppression acquisitions. Even for these
systems, however, ORC could improve the spectral resolution obtained from CSI and
other spectroscopic acquisitions.
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The main limitation of this study is that the differences in the images from the
optimized and unoptimized pulse sequences were assumed to be negligible.
This
assumption appears validated by the striking similarity between the optimized and
unoptimized volunteer and phantom images. However, this limitation results in the
inability to determine the effects of the optimization process on the fat suppression in the
images. An alternative approach would have been to acquire optimized and unoptimized
images for multiple volunteers. Unfortunately, this approach could result in additional
rating error if raters are influenced by the image content.
The primary limitation of the results is determining the actual significance of the
difference between the fat suppression ratings of the corrected LEENA and 2PD
acquisitions. From the shift in mean ratings as well as the post hoc analyses, it is clear
that a trend has been established between the two acquisition methods. An opportunity
for improvement in the LEENA acquisition involves determining the causes for this
trend. One possibility is that the noise cancellation and edge artifacts inherent in SENSE
reconstructions resulted in decreased fat suppression ratings (39). The equivalent fat
suppression of the uncorrected LEENA and 2PD images supports this possibility. Future
improvements in the LEENA method could resolve these confounding effects. For
example, development of a GRAPPA-like version of the LEENA acquisition could
eliminate some of these artifacts as well as reduce the overall acquisition time of the
LEENA technique by greatly reducing the number of extra views required for the parallel
imaging reconstruction (30).
In conclusion, the human visual ratings performed here demonstrate the similarity
of the LEENA and 2PD acquisitions for both fat suppression and resolution. Analysis of
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the resolution ratings confirms the theoretical benefits of the LEENA trajectory in
obtaining twice the resolution / time as the 2PD acquisition. Prior to off-resonance
correction, the benefits in resolution were obtained with no corresponding decrease in the
level of fat suppression in volunteer and phantom images.
When off-resonance
correction was employed, fat suppression improved for the LEENA and 2PD
acquisitions, but the overall fat suppression trended toward superior performance by the
2PD method.
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Chapter 7
Summary and Future Applications
7.1 Summary
The work presented and discussed in previous chapters results in a significant
improvement in the temporal efficiency of the multi-point Dixon acquisitions. The
collective results from these developments are shown in Table 7.1.
Method
% Reduction in
Acquisition Time
Theoretical
% Reduction in SNR
Keyhole Dixon
25-38%
13-21%
Radial 1-Point Dixon
50%
29%
Rectilinear 1PD (LEENA)
50%
29%
Dual-Echo 2-Point Dixon
~50%
0%
Dual-Echo LEENA
~75%
29%
Table 7.1: Summary of new rapid fat/water imaging techniques described in
this thesis. The reduction in acquisition times / SNR are calculated in relation to
the conventional 2-Point Dixon acquisition.
The theoretical decreases in SNR tabulated above for the Keyhole Dixon, Radial
1PD, and LEENA methods are calculated from the reduction in the number of acquired
views as described by Equation 7.1 below. For example, a 50% reduction in the number
of acquired views (i.e., LEENA) would decrease the SNR by a factor of ◊2 (29%
reduction in SNR relative to 2PD).
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Relative SNR =
N acq / N 2 PD
7.1
where Nacq and N2PD are the number of acquired views for the acquisition technique of
interest and the conventional 2-Point Dixon technique, respectively. The new fat/water
separation methods developed in this body of work result in additional image artifacts
that may or may not be accurately reflected in either SNR or CNR measurements. The
impact of these methods on the level of artifacts and SNR / CNR are discussed in more
detail below.
7.1.1 Specific Aim #1: Keyhole Dixon
The Keyhole Dixon method produced images of perceptually equivalent image
quality (as measured by the PDM and subjective human visual ratings) as compared to
the conventional 2-Point Dixon technique with a timesavings of 25-38% for phantom and
volunteer imaging applications (138). The Keyhole Dixon trajectory was designed with
one full K-space acquisition and a centrally-symmetric, partial K-space acquisition to
provide oversampling at low K-space frequencies.
This technique demonstrated
convincingly the inefficiency inherent in repetitively sampling the high spatial
frequencies of K-space typical of a conventional 2-Point Dixon acquisition.
The 25-38% reduction in the number of acquired views achieved by the Keyhole
Dixon method resulted in a modest 13-21% decrease in the image SNR. However, the
PDM error measurements obtained for the Keyhole Dixon images reflected both the
decrease in SNR as well as the increase in truncation / lipid edge enhancement generated
by the Keyhole Dixon trajectory.
Therefore, the optimal keyhole size would be
substantially reduced if the level of artifact could be minimized by either image
processing or via an improved keyhole acquisition strategy.
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7.1.2 Specific Aim #2: Radial 1PD
A radial 1PD trajectory was developed that alternates the echo times between
successive K-space projections. The echo shifting resulted in phase variation of the fat
magnetization resulting in a net nulling of the fat signal at low K-space frequencies. The
short delay for this echo-shifting at 1.5T (2.2ms) had minimal effect on the water signal.
As a result, the radial 1PD trajectory provided fat suppression at equivalent resolution
(radial PSFs) of on-resonance tissues in comparison to a radial 2PD acquisition with half
the number of acquired views. These results were demonstrated with radial point-spread
functions as well as phantom and volunteer images (123).
The Radial 1PD acquisition resulted in a 50% reduction in acquisition time (29%
reduction in SNR) relative to a radial 2PD acquisition.
In theory, the radial 1PD
acquisition would be expected to produce a 29% reduction in SNR / CNR just because of
the reduction in the number of acquired views. In practice, however, the radial 1PD
acquisition resulted in a 48% decrease in CNR in comparison the radial 2PD acquisition
(Chapter 3). This discrepancy was caused by the increased level of aliasing artifacts
produced from azimuthal undersampling of off-resonance spins.
The off-resonance artifacts can be reduced by incorporating a robust offresonance correction algorithm to ensure uniform fat suppression and to reduce the level
of radial streak artifacts. Another potential method to reduce the intensity of the streak
artifacts would be to incorporate additional echo times into the trajectory. The result
would be to distribute the aliasing energy more evenly throughout the image. The only
way to remove the aliasing energy would be to use a parallel imaging strategy using
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either a segmented GRAPPA approach or an iterative parallel imaging reconstruction
technique (30).
7.1.3 Specific Aim #3: Rectilinear 1PD (LEENA)
The rectilinear 1PD or LEENA acquisition utilizes echo shifting between even
and odd lines of K-space similar to the radial 1PD acquisition in Specific Aim #2. The
LEENA method uses parallel image reconstruction techniques rather than oversampling
of the low K-space frequencies to obtain separate fat and water images. As demonstrated
by subjective image ratings (Chapter 6), the LEENA method obtains a higher resolution /
time in comparison to the rectilinear 2PD with a more efficient K-space coverage.
Further development of sensitivity regularization methods, more robust phase
unwrapping algorithms, and the utilization of improved parallel imaging coil sets would
improve the overall SNR and reduce the level of artifacts in the LEENA images.
The LEENA technique results in a 50% reduction in acquisition time as the total
number of acquired views is halved.
As for the Radial 1PD acquisition, the SNR
decreases in the LEENA acquisition go beyond the theoretical values predicted by
Equation 7.1.
The LEENA technique creates an additional decrease in SNR to
reconstruct the unaliased images (Chapter 4).
This effect can vary greatly and is
dependent on the number of coils, the reduction factor, and the image processing methods
used in the unaliasing algorithm (39). In fact, the level of image processing (ex. low-pass
filtering, thresholding, etc) involved in the LEENA algorithm produced images with a
greater SNR than the conventional 2PD acquisition. Therefore, a more comprehensive
measure of image quality such as the PDM or human visual ratings should be used to
compare images generated from parallel imaging methods.
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The main disadvantage of the LEENA acquisition and other image-based parallel
imaging techniques is the requirement for measurement of coil sensitivities (30,39). The
additional acquisition time required to obtain even a low resolution image to estimate coil
sensitivities is significant. Based on the results in Chapter 2, the acquisition time could
more efficiently be used to obtain a Keyhole Dixon acquisition instead. This limitation
can be partially overcome by developing a SMASH-like version of the LEENA technique
which would only require a small number of acquired views (~4) to correctly reconstruct
the unaliased fat and water images.
7.1.4 Specific Aim #4: Time-Optimal 2PD Acquisitions
Optimized dual-echo rectilinear True FISP 2PD acquisitions were developed
using a multi-objective genetic algorithm (Chapter 5). LEENA pulse sequences were
developed from these models by adding a small phase encoding gradient between the two
readout gradients. The LEENA and 2PD sequences were used to acquire both FISP
and/or True FISP images of both volunteer and phantom images. The images were
subjectively compared in Chapter 6. The genetic algorithm generated sets of timeoptimal (minimum TR) dual-echo pulse sequences with FOV (200mm, 300mm) and the
readout BW (Hz/pixel) as the other two Pareto-optimal objectives. The images generated
no additional artifacts as compared to sub-optimal FISP images (Chapter 4 vs. Chapter 5)
in a reduced acquisition time. Further reductions in the overall acquisition time can be
obtained by adding more than two echoes. However, more echoes would require the use
of additional coils for the parallel image reconstruction for the LEENA acquisition.
The dual-echo acquisitions should produce no fundamental change in SNR
relative to the single-echo LEENA and 2PD acquisitions as the number of acquired views
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and the parallel imaging reduction factor have not changed.
However, multi-echo
acquisitions result in additional chemical shift artifacts manifest as either ghosts or
distortions. In these experiments, the off-resonance correction algorithms reduced the
level of artifacts to the point that no differences were perceived among the single-echo
and multi-echo images.
The main disadvantage of the GA-based optimization is in implementing the
Pareto-optimal sequences on a routine basis. Slight changes to FOV, resolution, phase
oversampling, slice orientation, or many other parameters either makes the sequence suboptimal, or worse, impossible to implement. Even with a successful implementation, the
improvements in acquisition speed will be modest in comparison to existing protocol
optimization algorithms. However, the method does provide a means to explore novel
trajectories and pulse sequences in order to optimize the acquisitions for specific imaging
applications.
7.2 Preclinical Research – Metabolic Syndrome
As described in the Introduction (Chapter 1), the primary benefit of reducing the
acquisition time of MR pulse sequences is to reduce the level of cardiac and respiratory
motion artifacts. This is particularly problematic for preclinical research on rodents
where the high metabolic rates of mice and rats requires shorter respiratory and cardiac
cycles (21,141,142). In addition, voluntary breathholds are not a possibility in animal
imaging research. Therefore, the rapid fat suppression techniques developed here may be
particularly useful for a variety of preclinical MR imaging applications such as breast
cancer imaging or lung imaging. The following paragraphs describe another possible
application for preclinical imaging research where fat suppression can be directly
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beneficial for phenotyping the effects of intentional genetic variations on metabolic
syndrome.
Figure 7.1: Segmentation and quantification of lipid level and distribution in A/J
and B6 mice. The B6 mice were fed a high glucose diet and display enhanced lipid
levels (subcutaneous and visceral) consistent with metabolic syndrome. Rapid fat
suppression techniques offer opportunities for high throughput phenotyping of
genetic variants with MRI.
Metabolic Syndrome is characterized by enhanced lipid accumulation, insulin
resistance, and development of cardiovascular disease (143-145). Initial studies have
demonstrated the capability to quantify the regional fat distribution of normal (A/J) and
fat-laden B6 mice with MRI (146-150). Sagittal water-suppressed T1-weighted spin echo
images images of the two mouse lines are shown in Figure 7.1. Individual axial images
(not shown) were segmented with a region-growing algorithm to calculate the
subcutaneous and visceral fat distributions.
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The resultant profiles demonstrate the
differences in lipid level and distribution in these two mouse strains.
While these
conventional spectral-suppression methods have proven effective in separating visceral
and subcutaneous fat, the spatial and spectral resolution of these acquisitions was
insufficient to distinguish between specific fat pads. The improved resolution / time of
the 1PD acquisitions described here provides an opportunity to generate separate and
uniform fat and water images from a short (< 1 sec) high SNR acquisition. Decreased
blurring would allow the boundary of fat pads and other organs to be more clearly
delineated providing a means for a more detailed analysis of lipid distribution.
In addition to the improved spatial resolution, the 1PD acquisitions could also be
modified to generate a more complete spectral analysis of the lipid components
(149,150).
On high-field systems designed specifically for small animal imaging
research (>7T), the absolute frequency differences become large enough so that higherorder Dixon acquisitions (ex. 3PD) could be developed to distinguish between various
lipid molecules (ex. triglycerides). The Dixon equations described in Chapters 2 and 4
could be expanded to solve for 3 or more species with different chemical shifts. This
method would only require an additional echo for each additional species. As a result,
the Dixon techniques could be used as a fast, low-spectral resolution, high-spatial
resolution chemical shift imaging (CSI) technique.
The LEENA technique could also be adapted for this high-spatial resolution CSI
method by using more than 2 echo times in the 1PD acquisition. In the LEENA method,
the number of ghosts will increase directly with the number of echo times. TE variation
schema could be designed to optimally separate the various species into known ghosting
patterns like the N/2 ghosts used in the lipid/water separation. The LEENA unaliasing
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algorithm could then be easily expanded to calculate the necessary ghost images.
Depending on the species of interest, the resultant ghost images would be either a single
tissue component or a known algebraic combinations of multiple components. The only
requirement for this method is an increase in the unaliasing reduction factor, and the
minimum number of coils, to separate the individual ghost images. The use of higherorder parallel imaging coil sets makes this a viable alternative for further application of
this technique.
The advantage of these methods would be the possibility of generating 3D
(whole-body) maps of lipid component distribution. This kind of imaging data may
provide a more useful quantification of genetic variation as the effects in the liver (or
other organs of interest) can be directly mapped by this technique rather sampled at
specific, potentially heterogeneous, voxels by conventional spectroscopic methods.
7.3 High Field MRI – Single-Shot Acquisitions
As discussed many times throughout this work, the images generated by modern
MRI scanners are no longer limited by SNR. The progression to higher field strengths in
combination with modern receiver chains, shim coils, and pulse sequences has allowed
MR acquisition times to be significantly reduced by simply reducing he number of views
acquired in the acquisition (30,32,39,124). As a result, as described in Chapter 5, the
acquisition speed in many imaging applications is now limited by both PNS and SAR
rather than scanner hardware (151,152).
The GA-based sequence optimization
techniques provide only an incremental improvement in acquisition speed over protocol
optimization methods currently available on clinical MR scanners. The LEENA and
radial 1PD trajectories make a significantly larger step forward by halving the total
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number of K-space views required to obtain both fat and water images of equal resolution
in a single or two-echo pulse sequence. The LEENA and radial 1PD pulse sequences
provide especially significant improvements over CHESS, SPSP, and binomial
acquisitions at high field strengths where SAR limitations will be particularly
problematic (54,58,59,61-63). Even with these advances, typical steady-state, rectilinear,
fat suppression acquisitions will still require ~1 second for acquisitions with reasonable
resolution (~100um).
One method to drastically reduce the acquisition time needed for a given
acquisition is the use of single-shot acquisitions such as single-shot spiral, single-shot
radial, and rectilinear EPI. To this point, these sequences have been limited by artifacts
from off-resonance spins as well as signal decay during the readout period
(54,62,71,72,153,154).
Parallel imaging techniques can reduce off-resonance and
relaxation artifacts by reducing the readout duration of the single-shot sequence with no
loss in resolution. For example, a LEENA acquisition at 1.5T with a total reduction
factor of 4 (2 x 1PD + 2 x SMASH) would reduce the number of echoes in a rectilinear
EPI-2PD acquisition by a factor of four. This LEENA-EPI acquisition with 64 acquired
views (64 x 2.2ms = 140ms) would be able produce fat and water images of equal
resolution as a 256-view 2PD acquisition which would require ~500ms.
The acquisition speed of single-shot acquisitions is further improved on high field
systems (i.e., 4T and above) because the Dixon echo shifts are inversely proportional to
the field strength.
At 4T, an echo shift of only 825us is required for Dixon fat
suppression (2200us *1.5T/4.0T). Therefore, the same 64-view LEENA-EPI acquisition
would only require ~50ms at 4T. Higher order parallel imaging constructs are currently
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being implemented with arrays with as many as 32 individual coils (155). Therefore, the
50ms acquisitions described above could be reduced much further down to ~10ms. As a
result, real-time MR imaging may be a real possibility. A similar argument can be made
for radial EPI acquisitions provided that effective parallel image reconstruction
techniques continue to be developed for non-Cartesian trajectories (36,45).
Single-shot acquisitions would also provide the potential for high speed 4D
acquisitions such as diffusion tensor imaging, BOLD imaging, and MR spectroscopy
(156-161). A single-shot version of the 1PD techniques in particular would provide a
means to obtain rapid in-vivo snapshots of the composition of various tissues. For
oncologic applications such as breast cancer where bright lipid signal obscures the tumor
cells, the spectroscopic analysis of the tumor region can lead to a more complete
characterization of the tumor physiology (162-164). These high-speed acquisitions could
eventually lead to the identification and characterization of small metastases in lung and
liver tissue where motion artifacts are especially problematic.
7.4 Dixon Flow Suppression
The True FISP and FISP images reported in this study demonstrate the bright
blood signal caused by rapid through-plane flow and the long T2 relaxation time of blood
spins.
This bright blood signal limits the use of MRI as a tool to characterize
cardiovascular plaques because the vessel walls are obscured by the bright lumen signal
(165,166). New methods are being developed using novel SSFP pulse sequences (167).
However, these methods still suffer from incomplete suppression of the lumen signal as a
result of blood pulsatility and in-plane flow. This problem can be overcome by adapting
117
the phase-based fat suppression techniques that were developed in this study to rapidly
and uniformly suppress the signal from flowing spins.
Bipolar gradients have been used to generate phase-contrast (PC) images for MR
angiography (MRA) for many years (168,169). In these applications, the phase (Φ) of a
moving spin is intentionally modified by application of bipolar gradients according to
Equation 7.1 below.
Φ = γ G•v (τ + τrt) (τ + 2τrt)
7.1
Where G, τ, τrt are the amplitude, flat top time, and ramp times of the bipolar gradient
lobes. The “•” refers to the dot product between the velocity and gradient vectors.
The direct relationship between velocity and phase can be used to convert the
Dixon equations for fat and water to static and flowing spins as shown in Equation 7.2.
(S + Fexp(iΦv))exp(iΦRF)exp(iΦi)
7.2
where S and F are the magnitude of the static and flowing spins, respectively. As in the
Dixon fat suppression equations, ΦRF and Φi represent the spatial phase variation due to
RF and field inhomogeneities. The velocity dependent phase, Φv, is dependent the
velocity of the flowing spins as well as the amplitude of the bipolar gradient as described
by Equation 7.1. Solving Equation 7.2 will result in the desired flow suppressed (S) and
angiographic (F) images. Instead of echo time variation, the amplitude of the bipolar
gradient would be varied here to acquire the multiple data points needed to solve Eq. 7.2.
There are several difficulties in calculating the flow-suppressed image. First, the
velocity-dependent phase in also time-dependent because of the pulsatility of the blood.
Therefore, it would be important to make sure that the multiple data points are acquired
in close chronologic proximity. Another difficulty in solving Eq. 7.2 is the fact that flow
118
is a vector quantity dependent on the direction of the bipolar gradients. Therefore, more
than 2 data points may be required to calculate the flow-suppressed image. The singleshot acquisitions described in section 7.3 may provide a viable solution for both of these
difficulties since multiple K-space data sets could be obtained in under 100ms.
7.5 Conclusions
As described above and in previous chapters, the temporal improvements in the
Dixon methods developed in this study have general utility for a wide variety of clinical
and preclinical imaging applications.
The main advantage of these techniques
collectively is to demonstrate the effectiveness of these rapid Dixon techniques in steadystate pulse sequences where CHESS pulses and spatial-spectral excitations significantly
extend the overall acquisition time and can increase the deposition of RF energy. The
Dixon methods are no longer limited to a minimum of 2 full acquisitions as conventional
wisdom dictates. Breaking that barrier provides the opportunity for a wide variety of
research opportunities in the future.
119
Appendix A
Fat Suppression Rating Analysis
Between-Subjects Factors
N
method
target
2PD
2PDORC
FISP
LEENA
LEENAORC
Ab
Phantom
5
5
5
5
5
15
10
Tests of Between-Subjects Effects
Dependent Variable: rating
Type III Sum
of Squares
22247.719a
69570.574
20218.732
204.254
993.194
1037.385
94192.286
23285.103
Source
Corrected Model
Intercept
method
target
method * target
Error
Total
Corrected Total
df
9
1
4
1
4
15
25
24
Mean Square
2471.969
69570.574
5054.683
204.254
248.298
69.159
F
35.743
1005.952
73.088
2.953
3.590
Sig.
.000
.000
.000
.106
.030
a. R Squared = .955 (Adjusted R Squared = .929)
rating
Tukey HSDa,b
method
FISP
LEENA
2PD
LEENAORC
2PDORC
Sig.
N
5
5
5
5
5
1
3.5920
Means for groups in homogeneous subsets are displayed.
Based on Type III Sum of Squares
The error term is Mean Square(Error) = 69.159.
a. Uses Harmonic Mean Sample Size = 5.000.
120
3
48.7468
50.5648
1.000
b. Alpha = .05.
Subset
2
.997
74.6561
88.7243
.106
Post-Hoc Tests
Multiple Comparisons
Dependent Variable: rating
Tukey HSD
(I) method
2PD
2PDORC
FISP
LEENA
LEENAORC
LSD
2PD
2PDORC
FISP
LEENA
LEENAORC
(J) method
2PDORC
FISP
LEENA
LEENAORC
2PD
FISP
LEENA
LEENAORC
2PD
2PDORC
LEENA
LEENAORC
2PD
2PDORC
FISP
LEENAORC
2PD
2PDORC
FISP
LEENA
2PDORC
FISP
LEENA
LEENAORC
2PD
FISP
LEENA
LEENAORC
2PD
2PDORC
LEENA
LEENAORC
2PD
2PDORC
FISP
LEENAORC
2PD
2PDORC
FISP
LEENA
Mean
Difference
Std. Error
(I-J)
-38.1595*
5.25962
46.9728*
5.25962
1.8180
5.25962
-24.0913*
5.25962
38.1595*
5.25962
85.1323*
5.25962
39.9776*
5.25962
14.0682
5.25962
-46.9728*
5.25962
-85.1323*
5.25962
-45.1547*
5.25962
-71.0641*
5.25962
-1.8180
5.25962
-39.9776*
5.25962
45.1547*
5.25962
-25.9094*
5.25962
24.0913*
5.25962
-14.0682
5.25962
71.0641*
5.25962
25.9094*
5.25962
-38.1595*
5.25962
46.9728*
5.25962
1.8180
5.25962
-24.0913*
5.25962
38.1595*
5.25962
85.1323*
5.25962
39.9776*
5.25962
14.0682*
5.25962
-46.9728*
5.25962
-85.1323*
5.25962
-45.1547*
5.25962
-71.0641*
5.25962
-1.8180
5.25962
-39.9776*
5.25962
45.1547*
5.25962
-25.9094*
5.25962
24.0913*
5.25962
-14.0682*
5.25962
71.0641*
5.25962
25.9094*
5.25962
Based on observed means.
*. The mean difference is significant at the .05 level.
121
Sig.
.000
.000
.997
.003
.000
.000
.000
.106
.000
.000
.000
.000
.997
.000
.000
.001
.003
.106
.000
.001
.000
.000
.734
.000
.000
.000
.000
.017
.000
.000
.000
.000
.734
.000
.000
.000
.000
.017
.000
.000
95% Confidence Interval
Lower Bound Upper Bound
-54.4008
-21.9182
30.7315
63.2141
-14.4233
18.0593
-40.3327
-7.8500
21.9182
54.4008
68.8910
101.3736
23.7363
56.2189
-2.1731
30.3095
-63.2141
-30.7315
-101.3736
-68.8910
-61.3960
-28.9134
-87.3054
-54.8228
-18.0593
14.4233
-56.2189
-23.7363
28.9134
61.3960
-42.1507
-9.6681
7.8500
40.3327
-30.3095
2.1731
54.8228
87.3054
9.6681
42.1507
-49.3701
-26.9489
35.7622
58.1834
-9.3926
13.0286
-35.3020
-12.8807
26.9489
49.3701
73.9217
96.3429
28.7669
51.1882
2.8576
25.2788
-58.1834
-35.7622
-96.3429
-73.9217
-56.3654
-33.9441
-82.2747
-59.8535
-13.0286
9.3926
-51.1882
-28.7669
33.9441
56.3654
-37.1200
-14.6988
12.8807
35.3020
-25.2788
-2.8576
59.8535
82.2747
14.6988
37.1200
Appendix B
Resolution Rating Analysis
Between-Subjects Factors
N
target
method
Ab
Phantom
2PDORC128
2PDORC256
2PDORC64
LEENAORC128
LEENAORC256
15
10
5
5
5
5
5
Tests of Between-Subjects Effects
Dependent Variable: rating
Source
Corrected Model
Intercept
target
method
target * method
Error
Total
Corrected Total
Type III Sum
of Squares
18408.150a
67574.822
83.948
17090.292
96.318
226.553
90021.040
18634.704
df
Mean Square
2045.350
67574.822
83.948
4272.573
24.080
15.104
9
1
1
4
4
15
25
24
F
135.422
4474.102
5.558
282.885
1.594
Sig.
.000
.000
.032
.000
.227
Subset
2
3
a. R Squared = .988 (Adjusted R Squared = .981)
rating
Tukey HSDa,b
method
2PDORC64
LEENAORC128
2PDORC128
LEENAORC256
2PDORC256
Sig.
N
5
5
5
5
5
1
8.6233
47.6659
47.9204
1.000
Means for groups in homogeneous subsets are displayed.
Based on Type III Sum of Squares
The error term is Mean Square(Error) = 15.104.
a. Uses Harmonic Mean Sample Size = 5.000.
b. Alpha = .05.
122
1.000
81.3345
81.6381
1.000
Post-Hoc Tests
Multiple Comparisons
Dependent Variable: rating
Tukey HSD
(I) method
2PDORC128
2PDORC256
2PDORC64
LEENAORC128
LEENAORC256
LSD
2PDORC128
2PDORC256
2PDORC64
LEENAORC128
LEENAORC256
(J) method
2PDORC256
2PDORC64
LEENAORC128
LEENAORC256
2PDORC128
2PDORC64
LEENAORC128
LEENAORC256
2PDORC128
2PDORC256
LEENAORC128
LEENAORC256
2PDORC128
2PDORC256
2PDORC64
LEENAORC256
2PDORC128
2PDORC256
2PDORC64
LEENAORC128
2PDORC256
2PDORC64
LEENAORC128
LEENAORC256
2PDORC128
2PDORC64
LEENAORC128
LEENAORC256
2PDORC128
2PDORC256
LEENAORC128
LEENAORC256
2PDORC128
2PDORC256
2PDORC64
LEENAORC256
2PDORC128
2PDORC256
2PDORC64
LEENAORC128
Mean
Difference
(I-J)
-33.7177*
39.2971*
.2544
-33.4141*
33.7177*
73.0148*
33.9721*
.3036
-39.2971*
-73.0148*
-39.0427*
-72.7112*
-.2544
-33.9721*
39.0427*
-33.6685*
33.4141*
-.3036
72.7112*
33.6685*
-33.7177*
39.2971*
.2544
-33.4141*
33.7177*
73.0148*
33.9721*
.3036
-39.2971*
-73.0148*
-39.0427*
-72.7112*
-.2544
-33.9721*
39.0427*
-33.6685*
33.4141*
-.3036
72.7112*
33.6685*
Based on observed means.
*. The mean difference is significant at the .05 level.
123
Std. Error
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
2.45793
Sig.
.000
.000
1.000
.000
.000
.000
.000
1.000
.000
.000
.000
.000
1.000
.000
.000
.000
.000
1.000
.000
.000
.000
.000
.919
.000
.000
.000
.000
.903
.000
.000
.000
.000
.919
.000
.000
.000
.000
.903
.000
.000
95% Confidence Interval
Lower Bound Upper Bound
-41.3076
-26.1278
31.7072
46.8870
-7.3355
7.8444
-41.0040
-25.8242
26.1278
41.3076
65.4249
80.6047
26.3822
41.5620
-7.2863
7.8935
-46.8870
-31.7072
-80.6047
-65.4249
-46.6326
-31.4528
-80.3011
-65.1213
-7.8444
7.3355
-41.5620
-26.3822
31.4528
46.6326
-41.2584
-26.0786
25.8242
41.0040
-7.8935
7.2863
65.1213
80.3011
26.0786
41.2584
-38.9566
-28.4787
34.0581
44.5361
-4.9845
5.4934
-38.6530
-28.1751
28.4787
38.9566
67.7758
78.2538
28.7332
39.2111
-4.9353
5.5426
-44.5361
-34.0581
-78.2538
-67.7758
-44.2816
-33.8037
-77.9501
-67.4722
-5.4934
4.9845
-39.2111
-28.7332
33.8037
44.2816
-38.9075
-28.4296
28.1751
38.6530
-5.5426
4.9353
67.4722
77.9501
28.4296
38.9075
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